CHARACTERIZATION OF SEMICONDUCTORS BY Title ELECTRON …

121
RIGHT: URL: CITATION: AUTHOR(S): ISSUE DATE: TITLE: CHARACTERIZATION OF SEMICONDUCTORS BY ELECTRON BEAM INDUCED CURRENT( Dissertation_全文 ) Fuyuki, Takashi Fuyuki, Takashi. CHARACTERIZATION OF SEMICONDUCTORS BY ELECTRON BEAM INDUCED CURRENT. 京都大学, 1981, 工学博士 1981-05-23 https://doi.org/10.14989/doctor.k2585

Transcript of CHARACTERIZATION OF SEMICONDUCTORS BY Title ELECTRON …

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RIGHT

URL

CITATION

AUTHOR(S)

ISSUE DATE

TITLE

CHARACTERIZATION OFSEMICONDUCTORS BY ELECTRONBEAM INDUCED CURRENT(Dissertation_全文 )

Fuyuki Takashi

Fuyuki Takashi CHARACTERIZATION OF SEMICONDUCTORS BY ELECTRON BEAMINDUCED CURRENT 京都大学 1981 工学博士

1981-05-23

httpsdoiorg1014989doctork2585

いvl}丿

CHARACTERIZATIONOFSEMICONDUCTORS

BY

ELECTRONBEAMINDUCEDCURRENT

BY

TAKASHIFUYUKI

JANUARY1981

DEPARTMENTOFELECTRONICS

KYOTOUNIVERSITY

KYOTOJAPAN

犬CHARACTERIZATIONOFSEMICONDUCTORS

IBY

ELECTRONBEAMINDUCEDCURRENT

BY

TAKASHIFUYUKI

JANUARY1981

DOC

1981

電気系

DEPARTMENTOFELECTRONICS

KYOTOUNIVERSITY

KYOTOJAPAN

1 一 心

ABSTRACT

-Theelectronbeaminducedcurrent(EBIC)wasanalyzed

quantitativelyconsideringthethree-dimensionalgeneration

distributionbyanelectronbeamThesolutionsofthesteady-

stateortime-dependentdiffusionequationsassumingapoint

sourcecanbeappliedtothecaseofthefinitegeneration

distributionbythedividingmethodTheEBICwasfoundtobe

affectedverymuchbythegenerationdistニributiontheextentof

whichwascomparablewiththeminoritycarrierdiffusionlength

InthelinescanmethodthedependenceofEBIConthescanning

distancerepresentsmainlythelateralextentofthegeneration

distributionThethree-dimensionalgenerationdistributionvas

clarifiedcombiningthenormalIncidenceandthelinescanmethods

ofEBICTheImprovedmethodtomeasurethediffusionlength

andthesurfacerecombinationvelocitywassuggested

Theminoritycarrierdistributionisinfluencedverymuch

bythesampledimensionswhentheyareequaltoorsmallerthan

thediffusionlengthTheEBICwasanalyzedbyasimplemethod

usinganimagesource-and-sinkdistributionTheEBICwasfound

tobedependentonthesurfacerecombinationvelocityand

thesampledimensionsratherthanthediffusionlength

Thelifetimeandthediffusionconstantofminority

carrierscouldbedetermineddefinitelywithoutanyrestriction

ofmodulationfrequencybythephaseshifttechniqueusingEBIC

Theimprovedmethodtomeasurethediffusionlength

wasappliedtotheheattreatmenteffectinSiThediffusion

lengthwasfoundtobedecreasedverymuchaftertheheat

treatmentat1000degCforonlyafewminutes

-1-

Thephysicalpropertiessuchasthediffusionlengthin

thesmallselectedareascouldbecharacterizedbyEBIC

consideringthethree-dinensionalgenerationdistributionbyan

electronbeamandthesampledimensionsExperimentalresults

inSiandGaAsshowedgoodagreementwiththetheoryandthe

generationdistributionsinSiandGaAswererevealedWitニh

experiments

一旦-

hellipJVi_--Wrsquordquo>>-trsquomjrsquordquordquo^>-≫^

f1

ACKNOWLEDGEMENTS

Theauthorwishestoexi】resshisdeepgratitudetoformer

jブProfessorTetsuroTanakaforhiscontinuingguidanceandワバandrrsquoI

helliphellipノ1encouragementTheauthorwishestoexpresshis9万ざlltや1appreciation

toAssociateProfessorHiroyukiMatsuna万万mlforhispreciousguidance

andhelpfuladvicethroughouttニhepresentstudyTheauthor

acknowledgesProfessorAkiraKawabataforhisgenialguidanceand

encouragementTheauthorisgがIattilltoProfessorToshinoriTakagi

forhisstimulatingdiscussionsandusefulcriticismsonthemanuscript

TheauthorwouldalsoliketothankProfessorAkioSasakifora

criticalreadingofthemanuscriptandvaluablecomments

MuchattentionisduetoDrJuniiSaraieDrShigehiro

NishinoandDrAkiraSuzukifortheircontinuousencouragement

andstimulativediscussions

TheauthorthanksothermembersofSemiconductorLaboratory

fortheirconsiderableassistanceandexperimentalfacilities

一斑-

CONTENTS

ABSTRACT

ACKNOWLEDGEMENTS

L工STOFSYMBOLS

INTRODUCTION

References

i一m

VL

lVO

INFLUENCEOFMINORITYCARRIERGENERATIONDISTR工BUTION13

0NELECTRONBEAMINDUCEDCURRENTINTHENORMALINCIDENCE

METHOD

2-1

2-2

2-3

Introduction

Determinationofdiffusionlengthandelectron-

holepaircreationenergy

ExperimentalresultsinGaAs

2-4Summary

References

13

15

VOON

CMCM

30

DETERMINATIONOFDIFFUSIONLENGTHSURFACERECOMBINATION31

VELOCITYANDELECTRON-HOLEPAIRCREAT工ONENERGYBYTHE

LINESCANMETHOD

3-1Introduction31

3-2Surfacerecombinationeffectconsideringpoint33

source

3-3Analysisofelectronbeaminducedcurrenttaking37

tニhree-dimensionalgenerationdistributioninto

account

3-4ExperimentalresultsinSi

3-5Summary

References

一分-

`j7

44

48

】V

V江

ⅧI

ANALYSISOFTHREE-DIMENSIONALGENERATIONDISTRIBUTION50

BYTHECOMBINATIONOFTHENORMALINCIDENCEANDTHE

L工NESCANMETHODS

4-1Introduction

4-2 Influenceofthree-dimensionalgeneration

distributiononelectronbeaminducedcurrent

02

inin

4-3Three-dimensionalgenerationdistributioninGaAs57

4-4Summary

References

12

vOVD

ANALYSISOFELECTRONBEAMINDUCEDCURRENTCONSIDERING64

SAMPLEDIMENSIONS

5-1Introduction

5-2

5-3

Determinationofdiffusionlengthandsurface

recombinationvelocity

ApplicationtoSi

5-4Summary

References

Appendix

DETERMINATIONOFLIFETIMEANDDIFFUSIONCONSTANT

BYPHASESHIFTTECHNIQUE

6-1Introduction

6-2Relationbetweenlifetimeandphaseshift

6-3ExperimentalresultsinSi

6-4Summary

References

HEATTREATMENTEFFECTONDIFFUSIONLENGTHINS1

7-1Introduction

7-2Experimentalresultsanddiscussions

References

CONCLUS工ONS

References

LISTOFPUBLICATIONS

4vO

CVD

73

78

9VO>

77

81

lro

88

CNJVO

qNas

7O

O^(J

99

102

104

105

108

109

-V-

LISTOFSYMBOLS

Cl

cBC

ggpgBELOS嚢

cdDDeEfgGIIIIIlj一jJ

J大

correctionfactorwithwhichthethree-dimensionalsolutions

oftheヽgradientofphaseshiftcanbeexpressedbytheone-

dimensionalapproximations

exponentofGaussiandistribution

positionofgenerationsourcefromthesurfacealongthedepth

diffusionconstantofminoritycarriers

(equivdgL)normalizedgenerationdepth

chargeofanelectronz

electron-holepaircreationenergybyanelectronbeam

modulationfrequencyofprimaryelectronbeam

generationrateofactualpointsource

variablepartofgenerationsource

thewholegenerationstrengthinthegenerationregion

Imaginaryunit

primaryelectronbeamcurrent

measuredelectronbeaminducedcurrent

currentwhichflowsthroughtheloadresistance

backwardsaturationcurrent

shortcircuitcurrent

electronbeaminducedcurrent

variablepartofcomplexelectronbeaminducedcurrent

(≒n)normalizedelectronbeaminducedcurrentitbecomes

unitywhenallthegeneratedcarrierscontributeto

electニronbeaminducedcurrent

normalizedelectronbeaminducedcurrentconsideringthe

Influenceofohmiccontact

一吐-

誉~Lay

L大eff

p卵`μrRRCReRmSStTuva

correctionfactorfortheincidentbeamenergyconsidering

theenergylossduetobackscatteredelectrons

thermalvoltagersquo259mVatroomtemperature

second-modifiedfirst-orderBesselfunction

diffusionlengthofminoritycarriers

diffusionlengthestimateddirectlyfromtheslopeof

electronbeaminducedcurrentvsscanningdistancecurve

diffusionlengthestimateddirectlyfromtheslopeof

electronbeaminducedcurrentvsscanningdistancecurve

consideringtheinfluenceofohmiccontact

(ΞLJ百石iT)complexeffectivediffusionlength

distニributionofminoritニycarrierdensity

distributionofminoritycarrierdensityconsideringthe

influenceofohmiccontニact

variablepartofthedistributionofminoritycarrier

densitycomplexvariable

distancebetweenthecenteroftニhegenerationregionand

eachdividedsegment

radiusofgenerationregion

centerofgenerationregion

extraporatedelectronrange

loadresistance

maximumelectronrange

surfacerecombinationvelocity

(ΞS(Lて))surfacerecombinationvelocityparameter

time

variableforintegrat10n

para万7rdquo万eterforGaussiandistribution

acceleratingvoltageofprimaryelectronbeam

一吐-

rdquod

wm

Xxx

χy

ZZ

np

Pau

^GaAs

SpてφΦω

distancebetweenthepotentialbarrierandtheohmiccontact

depletionlayerwidth

metalthicknessofSchottkydiode

Cartesianco-ordinateofscanningdistance

(ΞxL)

distancebetweenthepotentialbarrierandthegeneration

pointalongthescanningdirection

(ΞL)

Cartesianco-ordinateonthescanningsurfacenormalto

thescanningdirection

Cartesianco-ordinatealongthedepth

peakoftheGaussiandistribution<

(=J)collectionefficiency

collectionefficiencyofthevariablepartニofthegeneration

source

resistivityofsemiconductors

massdensityofAu゜189gcm^

massdensityofGaAs゜53gcm^

massdensityofSi=23gcm^

minoritycarrierlifetime

phaseshiftbetweentheelectronbeaminducedcurrentand

tニhemodulatedgenerationsource

diameterofprimaryelectronbeam

angularfrequencyofmodulatedprimaryelectronbeam

-VnL-

IINTRODUCT工ON

Theremarkableprogressinthesolidstatedevicesisowing

totheadvancementinthecharacterizationtechniqueofthedevice

materialsWhenthedeviceshavingnewfunctionsaredevelopedthe

detailknowledgeofthephysicalpropertiesofthesemiconducting

material(bandgaplifetimeandmobilityofcarriersetc)mustbe

neededInparticularthosepropertiesmustbecharacterizedafter

theactualmanufacturingprocessbecausetheoriginalpropertiesmay

beaffectニedbythevariousprocessconditions

Inrecentyearstocharacterizeverysmalldevices(ie

LSI゛sorlaserdiodes)therehasbeenagrowinginteresttousea

finelyfocusedelectronbeamThetwodimensionalInformationofthe

materialpropertiescanbeobtainednon-destructivelywithhigh

spatialresolutionfromtheelectronbeamInteractionwithsamples

[121Surfacemorphologycanbeobservedwithgreatニdepthoffocus

byascanningelectronmicroscope(SEM)Crystaldefectsinthin

samplesaredetectedusingascanningelectrontransmission

microscope(STEM)[34]AscanningAugerelectronmicroscope(SAM)

[5]hasbecomeaveryusefultooltoanalyzethesurfaceandthe

interfaceregion

Themethodusinganelectronbeaminducedcurrent(EBIC)[6-10]

1saveryconvenienttechniquetodeterminethefundamentalparameters

(egthediffusionlengththelifetimeandthesurfacerecombination

velocityofminoritycarriers)whichcontroltheelectricalperfor-

manceofthedevicesTheelectron-holepairsgeneratedbyanelectron

beamareseperatedbytheinternalfieldInp-njunctionsorSchottky

barriersandthecurrent1SInducedIntheexternalcircuitThe

EBICdependsverymuchondiffusionandrecombinationofminority

carriersInsemiconductorsandthediffusionlengthetccanbe

-1-

Fig1-1

type

type

Primaryelectrbe≪m

^^trrttDepletionlayer

Electron-hotep弗i「6gerwrationregion

Primaryelectronbeam

rArrScanningdirection

(A)

(B)

Principalconfigurationstomeasurethe

electronbeaminducedcurrent(EBIC)

(A)normalincidencemethod

(B)linescanmethod

-2-

く二rArr|t夕

EBICく二rArr

-一一--

p-typentype

aver`

1ミミ二l∽rsquoebic

determinedfromtheanalysisofEBICInadditiontothetwodlmen-

sionalinformationofthediffusionlengthandthelifetimetheir

variationsalongthedeptニhcanbeobtainedforvariousgeneration

depthsbychangingtheacceleratingvoltageofanelectronbeam

TheprincipalconfigurationstomeasureEBICarethersquonormal

incidencemethodrsquoandthersquolinescanmethodrsquo(seeFig1-1)Inthe

normalincidencemethodtheelectronbeam1Sincidentnormaltothe

barrierplaneandisscannedonthesurfaceparalleltothatplane

ThedislocationsanddefectsinSiwereobservedinp-njunctionsand

Schottkybarrierdiodes[11-28]Inrecentyearselectricalactivity

ofoxidationinducedstackingfaults(OSF゛s)anditsrelationwith

deviceperformanceshavebeenstudied[29-35]Thenormalincidence

methodisalsousedforthefailureanalysisoftニheMOSdevices[36-

39]Usingthelinescanmethodthediffusionlengthandthesurface

recombinatニionvelocitycanbedeterminedfromthedependenceofEBIC

onthescanningdistancewhentheelectronbeamisscannedacrossthe

barrierTherehavebeenmanytheoretical[AO-46]andexperimental

[47-69]reportstomeasurethediffusionlengthandthesurface

recombinationvelocityinlight-emittingdiodes(LEDrsquos)andlaser

diodes

InalmostalltheworkssofarEB工Chasbeenanalyzedonly

qualitatively0rsemi-quantitativelyThediffusionlengthandthe

surfacerecombinationvelocityhavebeendeterminedunderrather

specialconditionsasmentionedbelowforthesimpletheoretical

calculationInthenormalincidencemethodtheyconsideredonly

theone-dimensionalgenerationdistributionalongthedepth[70-75]

undertheconfigurationthatthelateralextentofthegeneration

volumewasverysmallcomparedwithsampleareasInthelinescan

methodthegenerationvolumewasassumedtobeapoint[53546061]

undertheconditionthatthegenerationvolumewassufficiently

-3-

smallerthanthediffusionlengthandthesampledimensionsBut

intheactualcasethegenerationvolumehasafinitethree-

dimensionalextentreLatedtotheacceleratingvoltage[76-78]

Thelatestmicroelectronicdevices(ieLSIrsquosandthelaserdiodes

etc)havethesamedimensionsasthegenerationvolumeandS0

theanalysesconsideringtニhepointsourceortheone-dimensional

generationdistributニionareinaccuratetodeterminethediffusion

lengthandthesurfacerecombinationvelocityThenewmethodfor

thequantitativeanalysisofEBICmustbedevelopedtakingthethree-

dimensionalgenerationdistributionandtheinfluencesofthesample

dimensionsintoaccount[7980]

InthepresentstudyEBICisanalyzedquantitativelyby

solvingthesteady-stateortime-dependenttニhree-dimensionaldiffusion

equationsTheinfluenceofthefinitegenerationvolumeonEBICis

discussedwhentheextentofthegenerationvolumecannotbeignored

andimprovedmetニhodsaresuggestedtomeasurethephysicalproperties

(diffusionlengthlifetimeandsurfacerecombinationvelocityof

minoritycarrierselectron-holepaircreationenergybyanelectron

beametc)inthesmallselectニedareas

InChapternvariousmodelsforthegeneratニiondistribution

alongthedepth[7781-83]arecomparedwitheachotherandtニhe

influenceofthegenerationdistributiononthedeterminationofthe

diffusionlengthbythenormalincidencemethodisdiscussed

ChapterⅡIshowstheinfluenceofthegenerationvolumeon

EB工Cinthelinescanmethodtakingtニhesurfacerecombinationeffect

intoaccountAnimprovedmethodforthedeterminationofthe

diffusionlengthandthesurfacerecombinationvelocityisdescribed

-4-

InChapterVthree-dimensionalgenerationdistribution

isclarifiedbymeasuringEBICusingboththenormalincidenceand

thelinescanmethodsinthesamesamplewhichyieldsthe

quantitativeanalysisofEB工C

ChaptervdescribestheInfluenceofthesampledimensions

onEBICInthelinescanmethodEBICisInvestigatedbyextending

themirrorimagemethodlsquo[41-43]whenthediffusionlengthisof

theorderofthesampledimensions

InChapterWthephaseshifttechniqueinthemeasurement

ofEBIC[84-86]isdescribedTherelationbetweenthelifetime

andthephaseshiftisclarifiedbysolvingthethree-dimensional

time-dependentdiffusionequationThelifetimeandtニhediffusion

constantofminoritycarrierscanbedeterminedcombiningthe

phaseshifttechniquewiththeconventionallinescanmethod

Chaptervnshowstheheattreatmenteffectonthediffusion

lengthinSi

FinallyconclusionsandsuggestionsforfurtherInvestigation

aresummarizedinChaptervnr

ExperimentalresultsinSiandGaAsareshovmineverychapter

Themethoddiscussedinthesechapterscanbeappliedeasilyto

anysemiconductormaterialsbyconsideringthephysicalproperties

inherentinthematerials

-5-

References

[1

[21

[3]

4]

5]

6]

[7]

[8]

[9]

[10]

VEJohnson十Sm119151p763

0CWellsSEM1972p375

pMrdquoPetroffDVLangJLStrudelandRALogan

SEM71978pp325-332

CELymanSEM1978pp529-536

NCMcDonaldSEM1971p89

DBHoltrdquoQuantitativeScanningElectronMicroscopyrdquo

(DBHolteta1edsAcademicPress974)pp213-286

DBWittryrdquoMicroprobeAnalysisrdquo(CAAndersoned

JohnWileySonsNewYork1973)pp123-187

CJVarkerrdquoNondestructiveEvaluationofSemiconductor

MaterialsandDevicesrdquo(edJayNZemelNATOADVANCED

STUDYINST工TUTESSERIESSERIESBPhysicsvol46

PLENUMPRESS1979)pp515-580

HJLeamyLCKimerlingandSDFerris

SEM1978pp717-725

ThebibliographyonEBICislistedinthefollowing

K0LeedySolidStateTechnologyFeb1977pp45-48

--

-- - -

rdquo-

rdquo- - 言

争心- -

SEM19xxrdquoScanningElectronMicroscopyrdquoProceedingofAnnualConference

before1977(IITResearchInstituteChicago)

after1978(SEMIncAMFOrsquoHare)

-6-

[11]JJLanderHSchrelberJrTMBuckandJRMathews

ApplPhysLett旦206-207(1963)

[12]WCzajaandGHWheatleyJApplPhys亜

2782-2783(1964)

[13] WCzajaandJRPatelJApplPhys11476-1482

(L965)

[14]NFBNeveandPRThorntonSolid-stateElectron

旦900-901(1966)

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

IGDaviesKAHughesDVSulwayandPRThornton

Solid-stateElectron9275-279(1966)-

WCzajaJApplPhysyi918-919(1966)

DVSulwayPRThorntonandMJTurner

Soli-StateElectron11567-568C1968)-

AJRKockSDFerrisLCKimerlingandHJLeamy

ApplPhysLett27313-315(1975)

DBHoltandROgdenSolid-stateElectron1937-40(1976)-

HJLeamyLCKimerlingandSDFerris

SEM1976pp529-538

TKatoTMatsukawaandRShlmizu

ApplPhysLett26415-416(1975)

RBMarcusMRobinsonTTShengSEHaszkoand

SPMurarkaJElectrochemSOC124425-430(1977)

LCKimerlingHJLeamyandJRPatel

ApplPhysLett30217-219(1977)

DEIoannouandSMDavidson

physstatsol(a)丘旦K1-K4(1978)

-7-

[25]

[26]

HBlumtrittRGlelchmannJHeydenderichandH

Johansenphysstatsol(a)55611-620(1979)

HMennigerHRaidtandRGleichmann

physstat-sol(a)5旦173-180(1980)

[27]pAshburnandCJBullSolid-stateElectron

Tl_105-110(1979)

[28] pAshburnCJBullandJRABeale

JApplPhys503472-3477(1979)

[29]KVRaviCJVarkerandCEVolk

JElectrochemSoc120533-541(1973)-

[30]

【31】

[32]

[33]

[34]

[35]

[36]

[37]

[38]

[39]

[40]

CJVarkerandKVRaviJApplPhys45272-287(1974)

SKawadoYHayafujiandTAdachi

JpnJApplPhys14407-408(1975)

TESeidelSEHaszkoandDMMaher

JApplPhys485038-5042(1977)

AMurgaiJYChiandHCGatos

JElectrochemSoc1271182-1186(1980)-

SKawadqJpnJApplPhys191591-1602(1980)

JMDishmanSEHaszkoRBMarcusSPMurarka

andTTShengJApplPhys502689-2696(1979)

JLGatesand0KGriffith

ApplPhysLett27kZ-45(1975)

JFKatalanoSEM71976pp521-528

PRoltmanandWRBottomsSEM1977pp731-738

CLWilsonSolid-stateElectron23345-356(1980)-

WHHackettJrJApplPhys431649-1654(1972)

-8-

[41]

[42]

[431

[44]

[45]

【46】

[47]

[48]

[49]

[50]

FBerzandHKKuikenSolid-stateElectron

19437-445(1976)

CvanOpdorpPhilipsResKept32^192-249(1977)

0vonRoosSolid-stateElectron互lsquo1063-1067(1978)

0vonRoosSolid-StateElectron211069-1077(1978)

0vonRoosSolid-stateElectron22113-114and773-778-

(1979)

WvanRoosbroeckJApplPhys旦D380-391(1955)

DBWittryandDFKyserJApplPhysj11387-1389

(1965)

HHiguchiandHTamura

JpnJApplPhys4^

316-317(1965)

YuPDemidovRPGurovaYuMKushnirAIFrltner

andDVFetisovSovPhys-Semicond1030-1035(1968)

KMaedaAKasamiMToyamaandNWakamatsu

JpnJApplPhys旦65-75(1969)

[51]ZhIAlferovVMAndreevVIKorolrsquokovand

vIStreminSovPhys-Semicond41113-1116(1971)

[52]

[53]

[54]

[551

CJHwangSEHaszkoandAABergh

JApplPhys425117-5119(1971)

WHHackettJrRHSaulRWDiχonandGWKammlott

JApplPhys432857-2868(1972)

WZimmermannphysstatsol(a)^2671-678(1972)

MAvenJZDevineRBBolonandGWLudwlg

JApplPhys434136-4142(1972)

-9-

[56]

[57]

[58]

[59]

【60】

[61]

[62]

[63]

[64]

[65]

[66]

GLidgardSolid-stateElectron15159-164(1972)

DBHoltBDChaseandMCenslive

physstatsol(a)20459-467(1973)-

DBHoltandBDChasephysstatsol(a)2(

135-144(1973)

CvanOpdorpRCPetersandMKlerk

ApplPhysLett24125-126(1974)

LJBalkEKubalekandEMenzel

IEEETransED-22707^712(1975)-

LJastrzebskiJLagowskiandHCGatos

ApplPhysLett11_537-539(1975)

LJBalkEKubalekandEMenzelSEM71975pp447-455

JJOakesIGGreenfieldandDLPartaln

JApplPhys丘旦2548-2555(1977)

MLanirAHBVanderwyckandCCWang

JApplPhys496182-6184(1978)

DLPartainAGMilnesandLFVassamlllet

JElectrochemSoc1261584-1588(1979)-

NTohgeTMinamiandMTanaka

JpnJApplPhys172155-2156(1978)

【67】DLPartainAGMilnesandLFVassamillet

JElectronicMaterials旦493-499(1979)

[68]

[69]

DEIoannouandSMDavidson

JPhysDApplPhys昆1339-1344(1979)

ShengSLiWLWangPWLaiandRTOwen

JElectronicMaterials旦335-354(1980)

-10-

[70]

【71】

[72]

[73]

[74]

JFBresseSEM119111pp105-112

JFBresseSEM1977pp683-693

CJWuandDBWittryJApplPhyspound92827-2836(1978)

GEPossinSEM1979pp245-256

GEPossinandCGKirkpatrlck

JApplPhys旦4033-4041(1979)

[75]GEPossinandCGKirkpatrick

JVacSciTechnol161917-1920(1979)-

[76]

[77]

[78]

[79]

[80]

VonAEGruenZNaturforsch12aHeft289-95(1957)-

KKanayaandSOkayama

JPhysDApplPhys5A3-58(1972)

RShimizuYKataokaTIkutaTKoshikawaand

HHashimotoJPhysDApplPhys旦101-114(1976)

GVSpivakGVSaparinandLFKomolova

SEM1977pp191-199

CDonolatoandHKlann

-JApplPhys511624-1633(1980)

[81]DBWittryandDFKyser

JApplPhys2旦375-382(1967)

[82]

[83]

[84]

[85]

[86]

TEEverhartandPHHoff

JApplPhys425837-5846(1971)

VVMakarovSovPhys-Semicond旦in-llk(1975)

JDKannnandHBerntSolid-stateELectronヌ1957-964(1978)-

JDKammrdquoSemiconductorSilicon1977rdquo(JElectrochemical

Society)pp491-501

0vonRoosJApplPhys503738-3742(1979)

-n-

-L2-

2-1

INFLUENCEOFM工NORITYCARRIERGENERATIONDISTRIBUTION

ONELECTRONBEAMINDUCEDCURRENTINTHENOR^IALINCIDENCE

METHOD

Introduction

Accuratedeterminationofminoritycarrierdiffusionlength

LisveryimportanttocharacterizesemiconductorsOneofthe

convenientmethodstomeasureLIstheuseofelectronbeam

inducedcurrent(EBIC)Theelectron-holepairsgeneratedbyan

electronbeamareseperatedbyapotentialbarrier(egp-n

junctionorSchottkybarrier)andthecurrentisInducedinthe

externalcircuitThevalueofLcanbedeterminedfromthe

dependenceofEBIConthelengthzbetweenthepotentialbarrier

andthegenerationpointInthenormalIncidencemethodzis

variedbychangingtheacceleratingvoltagevaofanelectronbeam

andthesmallvalueofLoftheorderofumcanbedetermined

ThevalueofLintニhesmallregionisobtainedusingafocused

beamgeneratedbyascanningelectronmicroscope(SEM)lsquo

Czaja[1]measuredLinp-ndiodesofSiandGaPHe

assumedthegenerationdistributionasacombinationoftwo

exponentialfunctionsBresse[2]andWu[3]measuredLandthe

electron-holepaircreationenergyE^^inSiandGaAsTheyused

Schottkydiodesbecausetheelectronbeamenteredthroughthemetal

contactandthesurfacerecombinationeffectcouldbeneglected

IntheiranalysesBresseusedthesemi-sphericalgeneration

distrlbutionproposedbyKanayaeta1[4]andWuassumedGaussian

distリbutlonPossineta1[5]analyzedEBICindetailtakingthe

influencesofthesurfacerecombinationandtheinternalfield

-13-

Metal

Depletio

layer

Primaryelectronbeam

Numberofgeneratedcarriers

Fig2-1Schematicviewofexperimentalconditions

jusingSchottkydiodesMetalthicknessis

wanddepletionlayerwidthiswright-handillustぷふこsthedぶdosefunctionRandR

-givethemaxiraum

andextraporaiedmelectrSnolinerangerespectively

-14-

0generatedcarrier

に_---___1

我_______Iuarrヽ

y重ダ

1ごpermil

andestimatedthedepthdistributionoflifetimeinion-implantedSi

TheylsquousedthepolynomialfunctionderivedbyEverhart[6]forthe

generationdistribution

工ntheanalysisofEBICtheminoritycarriergeneration

distributionplaysanimportantroletodeterminetheaccurate

valueofLandEHoweverthedistributionmodelsusedinthepc

analysesaredifferentwitheachotherasmentionedaboveIntニhis

chapterwecomparevariousmodelsforthegenerationdistribution

inGaAsandSiWecalculateEBICandclarifytheinfluenceofthe

generationdistributiononthedeterminationofLandEpc

Experimentalresultsarealsopresented

2-2 Determinationofdiffusionlengthandelectron-holepair

creationenergy

ASchottkybarrierdiodeisusedinordertoneglectthe

influenceofthesurfacerecombinationTheelectronbeamis

irradiatednormallytothebarrierplanethroughthemetalas

shownInFig2-1Thethicknessofthemetalandthedepletion

layerareputaswmandwd゛respectivelyTheminoritycarrier

generationdistributionalongthedepth(Socalledthedepthdose

function)isIllustratedalso1nFig2-1TheEBICiscalculated

basedonthefollowingassumptions1)Theminoritycarriers

generatedinthemetal(regionI)cannotcontributetoEBIC

2)Theelectron-holepairsgeneratedinthedepletionlayer(

regionlsquoTL)areseperatedquicklybythefieldofthedepletion

layerandwhollycontributetoEBIC3)Theminoritycarriers

generatedinthebulk(regionⅡI)partlycontributetoEBICie

theminoritycarrierswhichreachtotheedgeofthedepletion

-15-

mDiwi)iunMd

SMtjjesp≫)ejAU≫6|o』ψsEコz

Normalizedgenerationdepth^rsquoRm

Fig2-2

Generationdistribution

inGaAsTheMakarov゛SWittryrsquos

andKanayarsquosmodelsareexpressed

bytニhesolidbrokenanddotted

linesrespectivelyThegener-

atlondepthisnormalizedby

themaximumelectronrangeR

ThetotalgenerationrateiSm

normaLlzedtobeunity

-16-

2 0

1 05

(Efi)≪MJO^M

d6ue」

CO』oa3

rdquorsquo5102050Acceleratingvoltageva(kv)

Fig2-3

ElectronrangesinrsquoGaAsforvariousmodelsThesolidbrokendottedanddashedanddottedlinesaretheresultsusingMakarovrsquosWitニtryrsquosKanayarsquosandEverhartrsquosmodels

respectively

rdquoゝゝGaAs

χ

`Makarov20χ

----Wittry

χhelliphelliphellipKanaya

11S

15

゛S≒

rsquoχ≒

χrsquo

10trsquolsquo

卜卜゜χ゛

卜ゝrsquo

05χrsquo゛rsquoゝ

ゝrsquoゝ1

ゝゝrsquoゝゝ

ゝゝ

00

50

GaAso々

タグrsquo

Makarov

15-rsquo一一Wittry

ノKanaya

12

---Everhart

13yelr(2゛十`゛dinFig2-1)bydiffusioncanflowintothemetal

bythefieldofthedepletionlayer

Therehavebeenmanytheoretical147]andexperimental

[68-11】worksonthegenerationdistributionKanayaand

Okayama[4]proposedasemi-sphericalgenerationdistribution

usingthemodifieddiffusionmodel0fArchard[7]Wittryeta1

assumedGaussiandistributionandappliedtoGaAs[89]

EverhartandHoffl6]derivedapolynomialfunctionfromtheir

experimentsIntheA1olineSi02olineSisystemdegMakarov[10]showedthat

thegenerationdistributioncouldbeexpressedasGaussianlike

(exp(-((z-z)u)2))andthep8゛゜eters2manduvariedaccording

totheatomicnumberandthedensityofthematerialInorderto

comparethesedistributionsnormalizeddepthdosefunctionwas

introducedGruen[11]showedthattheshapeofthedepthdose

curveispracticallyinvariantifthepenetrationdepthis

normalizedbytheelectronrange

ThedepthdosefunctioninGaAsnormalizedbythemaximum

electronrangeRm(atwhichnoelectronentersintothematerial

seeFig2-1)areshowninFig2-2bythesolidbrokenanddotted

linesusingthefollowingequationsforthemodelsofMakarov

WittryandKanayarespectively

2RmolineOdeg138

g(z)=exp(-(rarr元でi

g(z)=exp(-(

2Rmoline

Odeg125

-035

)2)

)2)

(Makarov)(2-1)

(Wittry)(2-2)

g(z)゜(RmolineOdeg242Rtri)2oline(2olineOrsquo242Rm)2(K゛3y8)゛(2lsquo3)

-17-

こrsquo

Aouepj^^auoiiDaii〇D

Fig2-4

10203040

Acceleratingvoltage

5060

Va(kV)

CollectニionefficiencynvsVacurves

GaAsSchottkydiodeThevaluesofLare505μmfromuppert0lowergroupofcurves

for

2and

respectivelyTheresultsusingtheMakarovrsquosWittry゛SandKanayarsquosmodelsareexpressedbythesolidbrokenanddottedlinesrespectivelyThevaluesofwandWare10nmand015ymrespectively^hedashedanddottedlineisinthecaseofw=50nmw=015umandL=2umusingtheWittryrsquosmode1

-18-

GaAs一一Makarov

--rdquo-Wittry

10Wf^=10nmhelliphelliphelliphellipKanayaL(pm)

rsquo≒゜ニ1こii4degこ7T`ヽヽヽ5

05万でヽこミア斗辿こTTZご

50nふyミ゛1helliphelliphelliphellip4゛`゛ζ゛ζ

Orsquo1capparacapcap

か4

5060

ThereareobviousdifferencesbetweenthesethreemodelsThe

MakarovrsquosandWittryrsquosmodelshavethelargesurfaceconcentration

butthepeakvalueatzRm゛Odeg13oftheMakarovrsquosmodelissmaller

thanthatoftheWittryrsquosmodelTheKanaya゛smodelhasmoreevenly

spreadeddistributionthantheothertwomodelsThisisbecause

theelectron-holepairconcentrationisassumedtobeuniformin

thesemi-sphereintheKanayarsquosmodelwhichisasimplefirst-

orderapproximationforthegenerationdistributionButinthe

actualcasetheelectron-holepairsareconcentratedaroundthe

centerofthesemi-sphereOnemustusetheimprovedelectron-hole

pairconcentrationmodelInsteadoftheuniformoneinorderto

expressthegenerationdistributionprecisely

InthecalculationofEBICtheabsolutevalueofRmustm

beneededSomereportedvaluesbyMakarovWittryandKanayaare

shownbythesolidbrokenanddottedlinesrespectively

inFig2-3forGaAsThedashedanddottedlineisderivedby

Everhart[6]anddiscussedlaterTherangesoftheWittryrsquosand

Kanayarsquosmodelsarealmostagreewitheachotherbutthatofthe

Makarovrsquosmodelisabout70ZofthoseoftheWittryrsquosandKanayarsquos

models

ThecalculatedEBICinGaAs(iethecollectionefficiency

nwhichbecomesunitywhenallthegeneratedcarrierscontribute

toEBIC)bythesamemethoddescribedinref[3]isshownIn

Fig2-4Thesolidbrokenanddottedlinesareforthemodelsof

MakarovWittryandKanayarespectivelyThevalueoftheacceler-

atlngvoltageva1Schangedfrom5t060kVThevalueofLIs50

20and05ymfromuppert0lowergroupofthecurvesrespectively

ThevaluesofWmandwdaretakenastypicalvaluesof10nmand

015ymrespectivelyTheelectronrange1SInverselyproportional

tothedensityofthematerialThemetalthicknessiscorrected

-19-

takingthedifferenceofthedensitiesbetweenthemetalandthe

bulksemiconductorinorderthatthesamplehasuniformdensityfrom

thesurfacetothebulkforasimpletheoreticalcalculationWhen

goldistakenastheSchottkycontactwmustbemultipliedby

pAupGaAS(゜3`゜6rsquopAudeg189andpGaASdeg5゛3

1cll3)

゛OIlecanestimateL

mainlyfromthegradientofthecurvebecausethegradientdecreases

monotonouslywithincreasingLupt05umTheestimatedvaluesof

LbyMakarovrsquosandWittry゛Smodelsarealmostequalbecausethe

gradientsofthecurvesagreewitheachotherforthesameLvalue

ThevalueofLlargerthan5μmcannotbedetermineddefinitely

becauseEBIChardlychangeswithvevenifLbecomeslargeThea

maximumvalueofLthatcanbedetermineddefinitelyincreasesas

thehighestvalueofvaincreasesbutanotherproblems(idegedeg

damagesofthesamplebyhighenergyelectronsetc)mayoccur

Theelectron-holepaircreatニionenergyEcanbeobtainedfrom

theabsolutevalueofEBICbytherelationndeg^C^EBIC^^B^

(IEBICmeasuredEBICIBprimarybeamcurrentkcorrectionfactニor

fortheenergylossduetobackscattニeredelectrons)[3]

TheabsolutevaluesoftニheMakarovrsquosmodelareabout10へj20Z

largerthanthoseoftheWittry゛smodelAndsothevalueofEpC

obtainedbytheformeris10へj20Zlargerthanthatbythelatter

ThegradientニSandtheabsolutevaluesofthecurvesoftheKanayarsquos

modelarequitedifferentfromthosebytwoothermodelsThe

reasonofthedifferenceisowingtotheassumptionoftheuniform

concentrationoftheelectron-holepairsinthesemi-sphereas

discussedbeforeTheKanayarsquosmodelisafirst-orderapproximation

forthegenerationdistributionandisnotsuitableforthe

accuratedeterminationofLandEThevalueofwdoesnotaffectpc(I

EBICsomuchfromtheresultsoftニhecalculation工fWbecomesm

largetheabsolutevalueofEBICat10wvaisdecreasedverymuch

-20-

butthegradientofthecurveintheregionofhighVadoesnot

changeasshowninFig2-4(thedashedanddottedlineisinthe

caseofwmdeg50nm゛wdrsquoOrsquo15pmandL=2ymusingtheWittry゛Smode1)

ThereforeLcanbedeterminedinanycaseofwm゛asfaraswm1S

sufficientlysmallinorderthattheelectronbeamcanenterinto

thebulkregion

ThenormalizeddepthdosefunctionsInSiexpressedbythe

followingequationsareshowninFig2-5bythesolidbroken

dottedanddashedanddottedlinesforthemodelsofMakarov

WittryKanayaandEverhartrespectively

zR-0261

g(z)=exp(-(-jyヲー-7)2)(Makarov)(2-4)

zR-0156

g(z)=exp(-(―q2L_一一

g(z)゜(RmolineOrsquo336Rm)2

g(z)=06+6212Re

(Wittry) (2-5)

(゛0336R)^(Kanay゛1)(2oline6)

oline12deg40(2Re)2+5lsquo69(zR

(Everhart)e)3

(2-7)

Makarovshowedthattheparameterszmlsquoanduhadvoltagedependencesl

andthetypicalvaluesatvadeg30kVaretakenItshouldbenoted

thatthedepthdosefunctionoftheEverhartrsquosmodelisnormalized

bytheextraporatedrangeRe(seeFiglsquo2-1)whichisdetermined

byextraporatingthestraightlineportionofthecurve

-21-

Fig2-5

11

u)6ua))iunjed

sjdiJieopdiejdud6lo」4sEコz

Normalizedgenerationdepth^rsquoRm

GenerationdistributionsinSiTheMakarov゛s

Witニビry゛sKanayarsquosandEverhart゛Smodelsare

expressedbythesolidbrokendottedanddashedanddottedlinesrespectivelyThegener-

atlondepthisnormalizedbythemaximumelectron

rangeRTheextraporatedrangesR゛SoftheMakarovrsquosWittryrsquosandEverhartrsquosmodelsare

takentobeagreedwitheachotherThetotニal

generatニionrateisnormalizedtobeunity

-22-

KUkarov

--一一-Wittry2deg

二ぷ芯t

15へ

゜¥レ臨べhellip

hellip

10rsquoS゛lsquoNhellip

helliphellip

05

hellip

helliphellip

1helliphellip

hellip

005

工nordertocomparetheEverhartrsquosmodelwithothersthe

extraporatedrangefortheGaussiandistributionisdeduced

(seefootnote)十andtheextraporatedrangesoftheMakarovrsquoS

WittryrsquosandEverhart゛Smodelsaretakentobeagreedwitheach

otherThepeakvaluesofthegenerationdistributionsofthe

MakarovrsquosWlttryrsquosandEverhartrsquosmodelsarealmostequalbut

thevalueofzRmatthepeakfortheWittryrsquosmodelisabout

015andsmallerthanthoseoftheothertwomodelsCzR=025)゜

ThegenerationdistributionoftheWittryrsquosmodelcomesnearerto

thesurfacethanthoseoftheMakarovrsquosandEverhartrsquosmodelsIt

isbecausetheWittryrsquosmodelisderivedInthecaseofGaAsand

ontheotherhandtheMakarovrsquosandEverhart゛Smodelsareconcerned

inthecaseofSiThedensityofG゛1AS(pGaAS゛5deg3gcm^)islarger

thanthatofS1(pSirsquo2deg3gcm^)andsotheWittry゛Smodelshows

themoresurfaceconcentrationthantheothersTheKanayarsquosmodel

isquitニedifferentwiththeotherthreemodelsowingtothesame

reasonasdiscussedinGaAs

- -

-- - - - -

- - - -

Gaussiandistribution(e゛p(oline((2oline2m)11)2))

showsthealmostlineardecreasearoundthepoint

ofinflection(zdegu゛Σ十zm)lsquoTheextraporatedrange

Re(1゛ersquothepointwithwhichthestraightline

atthepointofinflectioncrossesthezaxis)

becomes2u十zfromtheresultsofcalculationm

(seeFig2-5)゜TheextraporatedrangeRebecomes

078Rand062RfortheMakarovrsquosandWittryrsquosmm

modelrespectively

-23-

Fig2-6

0 102030

Acceleratin9

4050

voltage

60

va(kv)

CollectionefficiencynvsVacurvesforSiSchottkydiodeThevaluesofLare1052andlymfromuppert0lowergroupofcurvesrespectivelyTheresultsusingtheMakarovrsquosWittryrsquosKanayarsquosandEverhartrsquosmodelsareexpressedbythesolidbrokendottedanddashedanddottedlinesrespectivelyThevaluesofWandware10nmand05ymrespectivelymd

-24-

MakarovSi---rdquoWittry

Kanaya

----Everhart

ジhttpwwwL(pm)卜

)渫回ブモジミ穫

WmニlOnmrdquoミ4helliphellipで``rsquoヽ4゜

゛ゝ1rsquohelliphelliphellip

゛rsquoN

u1C

larrl

0E

501

Figure2-6showsthecollectionefficiencyinSiusing

thefourdifferentmodelsofMakarovWittryKanayaandEverhart

bythesolidbrokendottedanddashedanddottedlines

respectivelyThevalueofLIs1005020and10umfrom

uppert0lowergroupofcurvesrespectivelyThevaluesofW

andrdquodaretakenastypicalvaluesof10nmand05]imrespectively

Thevalueofwmismultipliedby821nthecalculationowingto

thedifferenceofdensitiesbetweenAuandS1

asdiscussedbeforeThevalueofLlargerthan10μmcannotbe

determinedaccuratelybecauseEBIChardlychangesevenifLvaries

ThegradientofthecurveoftheEverhartrsquosmodel1Sslightly

steeperthanthoseoftheMakarovrsquosandWittry゛smodelswhich

almostagreewitheachotニherAndsotheestimatedvalueofLby

theEverhartrsquosmodelbecomeslargerthanthatbytheMakarovrsquosor

Wittry゛smodelforthesamer)vSdegvaCurve(egL=lutnbythe

Everhartrsquosmodelbecomes07umiftheMakarov゛Smodel1Sused)

ThegradientofthecurveoftheKanayarsquosmodelisalmostequal

tothatニoftheEverhartrsquosmddelbuttheabsolutevalueofthe

formeris30Zsmallerthanthatofthelatterforthesamevalue

ofLThereforetheestimatedLbyKanayarsquosmodelalmostagree

withthatbytheEverhartrsquosmodelbutthevalueofE

pCuSing

theformeris30Zsmallerthanthatusingthelatter

Asmentionedbeforetheelectronrangeisinversely

proportionaltothedensityoftニhematerialTheelectronrange

derivedbyEverhartinSicanbeappliedtoGaAsconsideringthe

differenceofthedensitiesbetweenSiandGaAsThecalculated

valuesareplottedbythedashedanddottedlineinFig2-3

TherangesoftheMakarov゛SandWittry゛Smodelsarelargerthan

thatoftheEverhart゛smodelOneofthereasonsforthe

disagreementisthedifferentdefinitionsoftheelectronrange

-25-

ieMakarovandWittryusedthemaximumrangeRbutEverhart

usedtheextraporatedrangeRelsquoInordertニocomparethesevalues

theextraporatedrangesfortheMakarovrsquosandWittryrsquosmodels

inGaAsarededuced(seefootnoteinpage23)andbecome075Rm

andOlsquo62Rm゛respectivelylsquoForexampleinthecaseofvadeg30kv゛

thevaluesofRforMakarovrsquosandWittryrsquosmodelsare34andm

48ymandthenthevaluesofRebecome26and30ym

respectivelylsquoThevalueofReintheEverhartrsquosmodel(29umat

vadeg30kV)isslightlylargerthanthatoftheMakarovrsquosmodel

butagreeswiththatoftheWittryrsquosmodel

2-3 ExperimentalresultsinGaAs

AconventionalSEMwasusedfortheprimaryelectronbeam

whichwasmodulatedat3kHzwithachoppingcoilinsertedinto

thebeampathTheinducedcurrentwasmeasuredfromthevoltage

dropacrosstheloadresistancewhichwasconnectedtotheSchottky

barrierwithanohmiccontactThesignalwasdetectedbyalock-in

amplifierThebeamcurrentwasmeasuredbyaFaradaycageThe

beamwassomewhataefocussed(Φ|=10umφbeamdiameter)inorder

toavoidhighinjectionTheinducedcurrentwasnotchangedeven

ifthebeamwasirradiatedatthesamepointforanhour

TheSchottkybarrierwasrsquomadeonn-typeGaAs(Sndoped

ndeg62times1016cmoline3)byevaporatingAuofabout10nmthickina

vacuumofabout10oline7TorrTheohmiccontactwasobtainedby

evaporatingAu-Geandalloyingat400degCfor2mlnThecarrier

densityandthedepletionlayerwidthweredeterminedbyG-V

measurements

-26-

(Hiunqj≫)

U一SU

BeamcurrentIb(A)

Fig2-7

MeasuredEBICinGaAs(Sn-

dopedn=62)(1016cmoline3)Schottky

diodeatVa=10and50kVThe

beamcurrentwaschangedinthe

rangeof2)(10oline11≦I≦5)(10oline9A

-B-Theopenandsolidcirclesare

theexperimentalresultsforvadeg

10and50kVrespectivelyand

thegradientsofthesolidlines

areunity

Tab2-1

(s≫UコqjB)Aouapu

く1)

uoiioaiion

AcceleratingvoltageVa(kV)

Fig2-8

Curvefittingsoftheexperi-

mentalresultstothetheoretical

collectionefficienciesinGaAs

SchottkydiodeThesolidbroken

anddottedlinesaretheresultニS

usingtheMakarovrsquosWittry゛Sand

Kanayarsquosmodelsrespectively

Vaischangedfrom5t050kVwith

thefixedvalueofl゛10oline1oA

w=10nmandwmd

L(unj)Ec(ev)

Makarov

Wittry

Kanaya

03

03

05

48

41

41

二〇15um

ご洸竺詐比飛ぱ器ぶごぷ詣ぷ

-27-

000

5Gなfimf4ilvalu

0v≪>iakv

50

100

10

lylrsquo16rsquo1(i

acuteン゛tGaAs(Sndoed)

5n=62

lope

1二痙7

5Kanayao

21020304050

ThevalueofEBICatv=10and50kVareshownbythesolida

linesinFig2-7whenthebeamcurrentIBischangedintherange

of2)(10oline11≦I≦5)(10oline9AIftheminoritycarrier-B-

concentrationexceedsthethermalequilibriumconcentrationof

majoritycarriers(iehighinjection)theminoritycarrier

lifetimeisprolonged[12]ThereforeEBICbecomestoincrease

superlinearlywiththenumberofgeneratedcarriersie

withIBforafixedvalueofvarsquoInthisexperiment゛EBIC

increaseslinearlywithIBatbothvals゛WhichShoWsthe10w

injectionTheexperimentalresultsareshownbycirclesin

Fig2-8whenvischangedintherangeof5くVく50kVata=adeg

thefixedvalueofIBdeg10oline10A゛Theoreticalcollectionefficiencies

usingtheMakarovrsquosWitニtryrsquosandKanayarsquosmodelsareshownbythe

solidbrokenanddottedlinesrespectivelyinFig2-8The

valuesofLandEpcdeterminedbyfittingtheexperimentaldata

totニhetheoreticalcurvesaretabulatedinTab2-1forthethree

differentmodelsofMakarovWittryandKanayaThecollection

efficiencybytheMakarovrsquosmodelshowedfairlygoodagreement

withtheexperimentalresultsbutthatusingtheWittryrsquosmodel

isslightlylargerthantheexperimentalvaluesinthe10Wva

l`egioll(va≦10kV)Thediscrepancyinthelowvaregionbecomes

largeiftheKanaya゛SmodelisusedInthecaseofWittryrsquosand

Kanaya゛Smodelspoundheexperimentaldatawerefittedintherange

ofhighva(va≧15kv)TheestimatedvaluesofLis03urnby

usingboththeMakarovrsquosandtheWittryrsquosmodelsbutthatusing

theKanayarsquosmodelis05ymandabouttwiceoftheresultby

theMakarovrsquosandWittryrsquosmodelsThevaluesofEdeterminedpc

bytheMakarovrsquosWittryrsquosandKanaya゛Smodelsare4841and41

eVrespectivelyBythenormalincidencemetニhodofEBICWuand

Wittry[3]andKobayashieta1[L3]determinedEas468and457

eVrespectivelywhicharealmostequaltotheresultusingthe

Makarovrsquosmodelbutareabout10Zlargerthanthevalueobtained

bytheWittryrsquosandKanayarsquosmodels

-28-

2-4 Summary

ThevaluesofLandEcanbedeterminedfromthe

PC

ceofEBIConvbythenormalincidencemethodThe-

dependenceofEBIConVabythenormalincidencemethodThe

minoritycarriergenerationdistributionplaysanImportantrole

intheanalysisofEBICVariousgenerationdistributionmodels

arecomparedwitheachotherunitingthedifferentdefinitionsof

theelectronrange(Iemaximumrangeandextraporatedrange)

InGaAsGaussiandistributionsproposedbyMakarovand

Wittryhavelargesurfaceconcentrationsandthepeaksofthe

distributionsexistatabout0130fthemaximumelectronrange

Kanaya゛Smodelhasevenlyspreadeddistributionowingtothe

assumptionoftheuniformconcentrationofthegeneratedelectron-

holepairsThevalueofLlargerthan5μmcannotbedetermined

definitelybecauseEBIChardlychangesevenifLvariesThe

estimatedLbytheMakarovrsquosmodelalmostagreeswiththatblsquoythe

WittryrsquosmodelbutEdeterminedbytheformeris10へj20ZrdquoPC

largerthanthatbythelatter

InSithepeaksofthegenerationcistributionbecome

deeperthanthoseinGaAsbecausethedensityofS11Sabouthalf

ofthatofGaAsThelargestvalueofLthatcanbedetermined

definitelybecomestwiceofthatofGaAsbecausetheelectronrange

inSiisabouttwiceofthatinGaAsTheestimatedLbythe

MakarovrsquosorWittryrsquosmodelisabout30Zsmallerthanthatbythe

Everhartrsquosmodel

IntheexperimentsinGaAstheestimatedLbytheMakarovrsquos

modelagreedwiththatbytheWittryrsquosmodelbuttheestimated

Epcbytheformerwas48eVandabout17Zlargerthanthatbythe

latter

-29-

References

[1]

[2]

[5]

WCzajaJApplPhys374236(1966)

JFBresserdquoScanningElectronMicroscopy71972partlrdquo

(iiTRiChicago111)p105

CJWuandDBWittryJApplPhys丘旦2827(1978)

KKanayaandSOkayamaJPhysDApplPhys

543(1972)-

口EPosslnandCGKirkpatrickJApplPhys

5^4033(1979)

[6]TEEverhartandPHHoffJApplPhys

425837(1971)

[10]

[11]

[12]

[13]

GDArchardJApplPhys竪91505(1961)

DBWittryandDFKyserJApplPhys28375(1967)

TSRao-SahibandDBWittryJApplPhys

403745(1969)

VVMakarovSovPhysSemicond旦722(1975)

jVonAEGruenZNaturforsch12aHeft289(1957)-

JCornuRSittigandWZimmermannISolid-stateElectron

TKobayashiTSugitニaMKoyamaandSTakayanagi

IEEETransNuclSciNS-19324(1972)-

-30-

3-1

DETERMINATIONOFDIFFUSIONLENGTHSURFACERECOMBINATION

VELOCITYANDELECTRON-HOLEPAIRCREATIONENERGYBYTHE

LINESCANMETHOD

Introduction

Anelectronbeaminducedcurrent(EBIC)methodisa

convenienttechniquetomeasuretheminoritycarrierdiffusion

lengtニhLandthesurfacerecombinationvelocitysinsemi-

conductingmaterialsInthelinescanmethodLandScanbe

determinedfromthedependenceofEBIConthescanningdistance

whentheelectronbeamisscannedacrossthebarrierBerzand

Kuiken[1]gaveadetailedtheoryforthedeterminationofLand

sandOpdorp[2]investigatedexperimentallytheinfluenceof

surfacerecombinationonEBICJastrzebskieta1[31measured

Landsfordifferentgenerationdepthsbyvaryingtheaccelera-

tingvoltageofanelectronbeam

Inthosestudiesthegenerationsourcewasassumedto

beapointbutinpracticetheregionexcitedbytheelectron

beamhasafinitevolumeChiandGatos[4]determinedthe

junctiondepthbyanEBICtechniqueassumingafinitegeneration

volumeCzaja[5]andBresse[6]measuredthephysicalparameters

suchasLandtheelectron-holepaircreationenergyEpC゛when

theelectronbeamwasdirectednormaltothebarrierplane

Sheaeta1[7]investigatedtheresolutionlimitsoftheEBIC

linescanmethodtheyobtainedaone-dimensionallateraldose

functionandappliedittothemeasurementofLintheCuxSCdS

systemHowevertheydidnotdiscusstheeffectofsurface

recombinationonEBICSincethesurfacerecombination1S

stronglyconnectedwiththedepthofgenerationathree-

-31-

Fig3-1

Schematicviewof

anddefinitionsofthe

-32-

experimentalconditionscoordinatesystems

Electronbeam

Surfacecross-sectic

O゛9χ

Schottky哨Rbarrier

dimensionalgenerationdistributionmustbetakenforthedetailed

analysisofEBIC[81

Inthischapterfirstlywediscussthesurfacerecombi-

nationeffectonEBICassumingapointsourceandthendescribe

theinfluenceofthegenerationvolumeonEBICinthelinescan

methodtakingaccountofsurfacerecombinationWehavestudied

EB工Ctheoreticallyforthefinitevolumesourcewhichisdependent

ontheacceleratingvoltageandshowanimprovedmethodfor

thedeterminationofphysicalparametersofsemiconducting

materialsbasedonexperimentalresultsobtainedinSi

3-2 Surfacerecombinationeffectconsideringpointsource

ForsimpletheoreticalconsiderationwetakeaSchottky

diodeAsshowninFig3-1theSchottkybarrier1Sinthey-z

planeTheelectronbeamisincidentperpendiculartothesample

surfaceandthescanningdirectionisalongtheχ-axiswhichis

normaltothebarrierplane

Thegenerationsourceisconsideredtobeapointata

distancexgfromthebarrierandatadepthdfromthesurface

correspondingtotheacceleratingvoltagevarsquoThepositionis

XS

ぐi g゛ O゛dg)Thesteadystateexcessminoritycarrierdistribution

obtainedfromthefollowingdiffusionequation

pDnabla2pdeg - -

g6(x-゜cg゛yrsquo2olinedg)rsquo (3-1)

whereDisthediffusionconstantて1sthelifetimeandgisthe

generationrateofelectron-holepairsWhen

thesampledimensionsareassumedtobesufficientlylarge

-33-

3ta3

Normalizedscanningdistancex

(a)

Fig3-2

Fig3-3

U』

Normalizedscanningdistancex

(b)

3193

p≫Zl≫E』oz

Normalizrdscanningdistanceχ

(c)

PrimeNormalizedEBICvsnormalizedscanningdistanceχcurvesfordifferentvaluesofthesurfacerecombination

velocityparameter(seetext)SNormalizedgenerationdepthDis0001and10in(a)(b)and(c)

respectively

Oino

tou

iSu一uojsn}|ipMzireujjoZ

SurfacerecombinationvelocityparameterS

EstimateddiffusionlengthL大directlyfromthe

slopesofthecurvesbetweenthepointsatχ=2and3

Svariesfromoneto50

-34-

Dg=10

Dg=QO

151050

112345

Og<ao

161

S>0

21

Idrsquo

S5

10^

550

1必12345

135

sc^-at

SO⑤

バ宍

1012345

112345

SPg≪10

161

162S=0

SI

1(i3

1(541235

comparedwiththediffusionlengththeboundaryconditionsare

並Sz

χ=0

z=O゛

spl

z=0

=0

χ=+(x)

=0

(atthesurface) (3-2a)

(attheSchottkybarrier)(3-2b)

(3-2c)

Oncethedistributionp1SknowntheEBICcanbefound

asfollows

トeリンint]キレ

o4バ2rsquo(3-3)

whereeisthechargeofanelectronThevalueofjwascalculated

二二二二二二二エフエム2こ二言

J=

-eg

丁T

4oo

int

Dg

馴D戸

exp(-S(T-

S(司7)-

dT} (3-4)

wherexL゛DgdegdgLrsquoS=s(Lて)andTIsthevariablefor

integrationThefunctiony可7)1sthesecond-modified

first-orderBesselfunctionTheEBICisnormalizedtobeunity

whenallthegeneratedcarrierscontributetoEBIC

-35-

177FΞ-一一permil

(ぷ71

y))二1supe≧rsquo

四F

InFigs3-2(a)(b)and(c)thelogarithmofJis

plottedvsX(ΞxL)basedoneq(3-4)overtherangeofO≦X≦5一一

forS=へj50ThevalueofDgis0001and10in(a)(b)

and(c)respectivelyForS=0theintegralineq(3-4)leads

toJ=exp(-X)whichyieldsstraightlinesasshown

inFig3-20ntheotherhandallcurvesforS>Odeviate

fromthestraightlineThesurfacerecombinationgivesmuch

effectontheexcesscarrierdistributionasthegenerationdepth

becomessha110WerWhenDgis00and01thevaluesoflogJ

decreasesuperlinearlyovertheinterval0fO≦χ≦2and--

almostニlinearlyovertherangeofx≧2WhenDis10the一琴

surfacerecombinationhasaslightinfluenceandthevaluesof

logJdecreasealmostlinearlyovertheinterval0fO≦X≦5__

HowevertheslopesshowsubstantialdeviationfromunityThe

estimatedvaluesofdiffusionlengthdirectlyfromtheslopes

ofthecurvesinthelinearlydecreasingregion2≦X≦3are--

putasL火andplottedagainstSinFig3-3forDgdeg00and10

工nordinarysemiconductorsSvariesfromlt050Overthis

rangeL大Isabout80t090ZoftニherealvalueL

WhenweevaluatetheaccuratevaluesofLandSwemust

fittheexperimenpoundaldatatothetheoreticalcurvesoverthe

wholerangeofO≦X≦5WecanestimateSbyfitting--

particularlyovertheIntervalofO≦X≦2becausetheeffect--

ofthesurfacerecombinationappearsremarkablyinthisInterval

-36-

3-3 Analysisofelectronbeaminducedcurrenttakingthree-

dimensionalgenerationdistributionintoaccount

Insect3-2theminoritycarrierdistributionisassumedto

beapointButinpracticethegenerationdistributionhasa

finitevolumeinconnectionwithvThegenerationdistributiona

mustbetakenintoaccountwhentheextentofthegeneration

distributioncannotbeignoredcomparedwithL

Electronpenetratニionintosolidmaterialshasbeenstudied

bymanyauthorsTheminoritycarriergenerationdistribution

alongthedepthwasdiscussedindetailinChapterHWittry

andKyser[9]assumedthedepthdosefunctiontobeaGaussian

distributionandobtainedgoodagreementwithexperiments

EverhartandHoff[10]assumedapolynomialfunctiontoexplain

theirexperimentalresultsintheAl-SiO2-SisystemdegInthose

studiesonlythedistributionalongthezaxiswasdiscussedso

thedistributionalongthexaxiswasnotconsideredSheaeta1

[7]definedthelateraldosefunctionalongthexaxisfrom

VonGrlinrsquos[11]databutdidnotdiscusstheinfluenceofsurface

recombinationindetailSincetheinfluenceofsurfacerecombi-

nationonEBICdependsonthedepthfromthesurfacewemust

takethedistributionofgeneratedminoritycarriersinthe

x゛zplaneWeusethemodifieddiffusionmodelofKanayaand

Okayama[12]Themodel1Sverysimplebutissufficientfor

thefirst-orderapproximationtニothethree-dimensional

generationdistributionAccordingtothemodeltheelectrons

penetratestraightintothematerialtothemaximumenergy

dissipationdepthandthenscatterequallyinalldirections

makingelectron-holepairsTheshapeofthegenerationregion

becomesaspherepartofwhichisabovethesurface

-37-

Fig3-4

Tab3-1

11-

Schematicviewofelectronpenetrationisthemaximumenergydissipationdepth

a(W)

00000

1CMCO<rm

d(ym)

rdquo047

149

291

in<yi

vDVO

4VO

R(um)

100

295

13

74

20

Valuesofthecenterdgofthegeneration

volumeandtheradiusRinSiforseveralvalues

ofacceleratingvoltagevarsquo

-38-

IElectronbeam

O335

S`」「fdegce

uarrで0559j

10゛」

helliphelliphelliphelliphellip

Thecenterdgofthesphere(iethemaximumenergydissipation

depth)andtheradiusRaredependentontheacceleratingvoltage

va゛b゛lttheratiodgRisassumedtobeaconstantasshownin

Fig3-4evenWhenvaisvariedThevaluesofdgandRinSi

forseveralvaluesofvaaregiveninTab3-1calculatedwith

theaidoftheequationsofKanayaandOkayama[121

Wedividethesemi-sphereintomanysegmentsoflength

lessthanLandrepresenteachsegmentbyonepointsource

Thedensityoftheelectron-holepairsisassumedtobeuniform

withinthespheretosimplifytheanalysisThenthegeneration

strengthgofeachpointsourceisgivenbytニhefollowing

relation

Σg=G(3-5)

whereGisthewholegenerationstニrengthandΣexpressesthe

totalsummationwithinthesemi-sphereundertニhesamplesurface

TheEBICforthefinitevolumesourceisderivedby

summimgupthesolutionoftニhediffusionequationforeachpoint

sourcewhichisexpressedbyeq(3-4)Whenthedistance

betweenthebarrierandtheIrradiatedpointxbecomessmallerg

thanRsomeofthepointsourcesareforcedoutofthediode

andcannotcontributetoEBICThustheEBICdecreasesnearthe

barrierplaneWecallthisphenomenonanedgeeffectTosimplfy

thecalculationweassumethattheEBICcontributedbythe

forced-outsourcesiszeroThisedgeeffectmustbetakeninto

accountwhenthegenerationvolumeislargeincomparisonwith

thediffusionlengthWeshowanexampleforL=8ymandS=20

Whenvais10kVtheradiusRissmallcomparedwithLand

thegenerationsourcecanbeassumedasapointThelogarithm

-39-

Fig3-5

Qコー

山11

pdznpoi」oz

1020

Scanningdistanceχ

NormalizedEBICversusscanningdistanceχ

forthefinitevolumesourceThediffusionlengthLis8lsquoUmandthesurfacerecombinationvelocityparameterS(seetext)is20TheacceleratingvoltageVais50タ30and10kVfromuppertolowersolidcurverespectivelyThedottedcurveisthepointsourcesolutionforVa=50kVandtニhedashedlineisthegradientthereciprocal0fwhichgivesL=8um

-40-

1020304050(p『

゛X5入L=8μm

゛χS=20

2rsquoχyχ

゜χ

ldquoゝ5rdquo-Re-くiprocalsk)

rsquox9vesL=8|jm

rdquoゝ

2rsquo゜χ`Va=50KV

2rsquoχ

lsquoχ

lsquoゝ

5degχ

rsquoχ

rsquoχ2χ

30≒3rsquo

11diPointsourcelsquo

5solutionfor

va=50KV10

1020304050(μΓΥ

ofEBICJisplottedwithafullcurveasafunctionofthe

scanningdistancexinFig3-5logJdecreasessuperlinearlyover

theinterval0≦X≦2L(ie16uminthiscase)anddecreases--

almostlinearlyovertherangex≧2LTheslopeintherange-

O≦x≦2LisInfluencedverymuchbysurfacerecombination一一

〇necanestimateSbyfittingtheexperimentaldatatothe

theoreticalcurveinthisrangedegWhenva1S300r50kVthe

radiusRbecomesofthesameorderasLandthegeneration

volumecannotbeassumedasapointThenwedividethesemi-

sphereintomanysegmentsoflym^Thecalculatedvaluesof

EBICusingthefinitevolumesourcemethodareshowninFig3-5

ThelogJvsXcurvesshowamaximumnearthebarrierplane(

Xdeg4and7μmatvadeg30and50kVrespectively)andlogJdecreases

almostlinearlybeyondthesemaximumpointsThemaximumvalue

ofJbecomessmallasvincreasesThesurfacerecombinationadoesnotaffecttheshapeofthecurvesandsoLcanbedetermined

mainlyfromtheslopeofthelinearregionofthesecurves

independentlyofsThereciprocalslopeofthislinearportion

gives7ymwhichis87Zoftherealdiffusionlength

ThevalueofEpc゛rsquobywhichanelectron-holepairis

createdcanbedeterminedfromtheabsolutevalueofEBIC[13]

ThevalueofJinthecaseofS=501sabout70Zofthatinthe

caseofSdeg1whenvais50kv゛andsowemakelargeerrorsinthe

determinationofEifwedonotconsiderthesurfacerecomblna-pc

tioneffect

Thepointsourcesolutionatva゛50kVisshowninFig3-5

bythedottedlinewhenthegenerationoccursatthemaximum

energydissipationdepth(ie67ymfromTab3-1)

Theslopeofthepointsourcesolutionovertherangex≧2LIs-

almostequaltothatofthevolumesourcesolutionbutthe

normalizedEBICis60Zofthatofthevolumesourcesolution

-41-

Fig3ldquo6

Chopping

こ011

Scanningcoil

Schematicdiagramoftheexperimentalset-up

-42-

コ4[Osc

lsquo~|-

|コt

||IElectronbeamReference

||

Sample

RL`Lock-inampχ-yrecorder

3-4 ExperimentalresultsinS1

Aschematicdiagramoftheexperimentalset-upisshown

inFig3-6Theacceleratingvoltage1Svariedfrom10t050kV

TheprimaryelectronbeamcurrentismeasuredbyaFaradaycage

andabout2times10oline10ATheinducedcurrentwasmeasuredfromthe

voltagedropacrosstheloadresistanceILdegThecurrentニIL

whichflowsthroughtheresistanceisexpressedasfollows

hdeg^sc-I{exp[(ekT)ILRL]-1} (3-6)

whereloisthebackwardsaturationcurrentand^scisthe

short-circuitcurrentwhichistherealEBICInordertoneglect

thesecondtermofeq(3-6)theEBICwasmeasuredinthefollowing

condition

h゛kTe (3-7)

InthepresentexperimenttheEB工Cwasmeasuredatroomtempera-

tureandso゛hhwaskeptlessthanlmvdeg

Theelectronbeamwaschoppedat3kHzwithachopping

coilinsertedintothebeampathSignalsassmallas1μVcould

bemeasuredwithagoodsignaltonoiseratiousingalock-in

amplifier

Thesamplesweren-typeSiwithresistivitypof10

and01ΩCm0hmiccontactsweremadebyevaporatingantimony-

dopedgoldontothesampleandalloyingat400degCfor2mln

Schottkycontactsweremadebyevaporatinggoldinavacuumas10W

as10oline7TorrThesamplewasinsertedintoavacuumchamberfor

EBICmeasurementimmediatelyafteritwascleavedandmeasured

-43-

3IS3

paziicuijoz

1020304050(pm)

Scanningdistancex

Fig3-7

Experimentalresultsfor

sampleA(p=lf2cin)whereL=

8μmandS=20Fullcurves

arethetheoreticalrsquoones

11(il

>P≪4<N1≪CM<Pq

1 1

3193paziipujjoZ

1164

50

Scanning

100

distance

Fig3-8

150

X(μm)

200

ExperimentalresultsforsampleB

(p=01f2cin)whereL=80urnandS=50

Fullcurvesarethetheoreticalones

Valueswithouttheinfluenceofan

ohmiccontニactareshownbydotted

curves

-44-

124(m)

5XExperimentalvaluesX---Va=50KV

2NNo30

1X一--10KV4

5しL=8pm

2χ

2χ

5χ

-Theoretical

5curve

41

50100150200

Experimentalvalues

--4=50Kv

lo―30KV

hellip-10KV

-ゝゝI゛゛゜゛ペヘヘ

helliphelliphelliphellipyhelliphelliphelliphellip

Theoreticalcurvehelliphelliphelliphellip9lsquorsquolsquo゜

Ldeg80μΓTlぶ

S=50

inavacuumas10was1times10oline8TorrTheresidualgasesonthe

cleavedsurfacewerecleanedbyargonionsputteringtoavoid

contaminationofthesurfacebyanirradiatニedelectronbeam

TheexperimentalresultsofsampleA(p=10ncm)are

showninFig3-7forva=1030and50kVrespectivelyEach

fullcurveisthetheoreticaloneforthecaseofL=8umandS=20

工fthediffusionconstantD1Stakenas16cm2Solinelthelifetime

てis4times10oline2μSandthesurfacerecombinationvelocitysis

4times105cmsolinelSurfacerecombinationhasagreatereffectasthe

generationdepthbecomesshallowerthatisVbecomeslower

AndsothevaluesofSandLcanbeestimatedmainlyfromthe

curvesforthelowestニandthehighestva(idege103゛d50kV

inthisexperiment)respectivelyTheexperimentalresultsfor

eachacceleratingvoltageagreeverywellwiththetheory

Theexperimentalcurvesforvadeg1030and50kVhaveamaximum

atxdeg02and4ymrespectivelyandeachmaximumvaluebecomes

smallerasvincreasesasdescribedinthetheoryHowevera

themaximumvalueandthepositionwheretheEBICshowsapeak

deviateslightlyfromthetheoryinthecasesofvadeg30and50kVdeg

Thisdiscrepancymaybeattributedtotheassumptionofuniform

densityofgenerationTheactualdistributionmaybelocalized

atthecenterofthegenerationvolume[9]andmoredetailed

treatmentforthegenerationshapeandthegenerationdensity

Isneeded

Inthecaseofthelocalizeddistributionofgeneration

wecanapplythesamemethodasdiscussedinsect3-3Ifthe

constantgischangedintoanappropriatevariablewhichexpresses

thelocalizeddistributionbetterresultswillbeobtained

HowevertheassumptionoftheunifoinndensityIssufficientfor

thequalitativeanalysisoftheInfluenceofthegenerationvolume

onEBIC

-45-

TheexperimentalresultsofsampleB(p=01ficm)are

indicatedinFig3-8inthesamewayassampleAThevalues

ofLandSare80ymand509respectivelyIfDis16cm2solinel

てis4ysandsis1)(105cmSoline11nthiscaseLisgreaterthan

thegenerationvolumeevenwhenvadeg50kVandthevolumesource

effectappearslessclearlythaninsampleAThediscrepancy

witニhintheinterval0<xく15urnisduetothesamereasonas

thatdiscussedInthecaseofsampleATheslopesofthecurves

overtherange15≦x≦100μmarelesssteepasvbecomes--a

higherbecausetheinfluenceofsurfacerecombinationdecreases

Theinfluenceofohmiccontactappearsovertherangex≧120μm-

sincethediffusionlengthisabouthalfofthesamplethickness

of200μmTheoreticalvaluescalculatedusingthemirror

imagemethod[14]discussedinChaptervareshownbyfull

curvesinFig3-8Valueswitニhoutニtheinfluenceofanohmic

contactarealsoshownbydottedcurves

Thescanningsurfacewasnotaffectedbyanelectronbeam

oftheorderof2times10oline10Abecausethesameresultwasobtained

forshallowexcitation(vadeg10kV)afterthesamplewasirradiated

for1hatV=10へ一50kVa

ThedepletionlayerwidthisnotbroughtIntoconsidera-

tionbecauseofitsnarrownesscomparedwiththescanningdistance

Theelectronbeamdiameterofabout50nminthisexperiment

1Snottakenintoaccountsinceitisverysmallincomparison

withthegenerationregionevenifvais10kvdeg

工fthebeamcurrentiskeptconstantthegeneration

densitydecreaseswithincreasingVbecausethegeneration

volumeincreasessuperlinearlywithvarsquo゜Whenthebeamcurrentis

2times10oline10Aandvais10kVtheexcessminoritycarrierdensity

-46-

atthegenerationpointisabout5times1014Cmoline3(themaximum

generationdensityinthisexperiment)followingthediscuss10n

inref[1]whichissmallerthanthemajoritycarrierdensity

1nthesamplesThereforethevalueofLismeasuredatthe

lowinjectlonlevel

3-5 Summary

Thegenerationvolumeofminoritycarriershasa

considerableeffectontheEBIClinescanprofilesespecially

whenItisequaltoorlargerthanthediffusionlengthWe

investigatedthedependenceofEBIConxforgeneralsurface

recombinationvelocityinthecaseofthefinitevolumesource

Whenvaislowandthegenerationdepthisshallow

surfacerecombinationhasalargeeffectonEBICWhenvaishigh

andthegeneratニiondepthisaslargeasthediffusionlengththe

generationregioncann0longerbeassumedasapointandthe

finitevolumesourceshouldbeusedintheanalysisThetheo-

reticalcalculationshowsthatsurfacerecombinationhasonlya

slighteffectontheshapeoflogJvsXcurvesbutaffectsthe

absolutevalueofJTheaccuratevaluesofLsandEshouldbepc

estimatedbyfittingtheexperimentaldatatothetheoretical

curvesforallacceleratingvoltagesExperimentalresultsinthe

measurementofLandSonS1Schottkydiodesshowedgoodagreement

withthetheoryatboth10Wandhighvadeg

TheexperimentalresultthatEBIChasamaximumnear

thebarrierplanewasexplainedqualitativelyusingthesimple

model0fthefinitevolumesourceItcouldnotbeexplainedby

thepointsourcesolutionFurtherinvestigationofthisedge

effectwillclarifythegenerationdistributionbyanelectronbeam

-47-

References

[1]

2]

31

[41

[7]

[8]

[9]

[10]

FBerzandHKKuikenSolid-stateElectron

437(1976)

19

CvanOpdorpPhilipsResRep_32192(1977)

LJastrzebskiJLagowskiandHCGatos

ApplPhysLett27537(1975)

JApplPhys481730(1977)

JYChiandHCGatosIEEETransElectronDev

ED-241366(1977)

WCzajaJApplPhys2Z^236(1966)

JFBresserdquoScanningElectronMicroscopy1972

Partlrdquo[SEM]nc工ITRIChicago)pp105-112

SpSheaLDPartニainandpJWarterrdquoScanning

ElectronMicroscopy1978Vol1rdquo(SEMIncAMFOrsquoHare)

pp435-444

GVSpivakGVSaparinandLFKomolova

rdquoScanningElectronMicroscopy1977rdquo(SEMInc

IITRIChicago)pp191-199

DBWittryandDFKyserJApplPhysj廻375

(1967)

TEEverhartandpHHoffJApplPhys

(1971)

-48-

42

-5837

[n] AEvonGriinZNaturforsch12a89(1957)

【12】KKanayaandSOkayamaJPhysDApplPhys

543(1972)

[13]CJWuandDBWlttryJApplPhys492827

(1978)

[1410vonROOSSolid-stateElectron111063(1978)

-49-

4-1

ANALYSISOFTHREE-DIMENSIONALGENERATIONDISTRIBUTION

BYTHECOMBINATIONOFTHENORMALINCIDENCEANDTHE

LINESCANMETHODS

Introduction

TheminoritycarrierdiffusionlengthLandthesurface

recombinationvelocityScanbedeterminedbyanEBICtechnique

withboththenormalincidenceandtニhelinescanmethodsusing

SEMasdiscussedinChapters皿andHITheminoritycarrier

generationdistributニionbyanelectronbeamplaysanimportant

roleintheanalysisofEBICWhenthedimensionofthegeneration

regioniscomparablewithorlargertニhanLthegenerationregion

cannotbeassumedasapointandthegenerationdistribution

mustbetakenintoaccount

Thegenerationdistributionbyanelectronbeamhasbeen

investigatedbyseveralauthorstheoretically[1]andexperimental-

1y[2-51Asregardstheone-dimensionaldistributionaGaussian

[2-3]orpolynomial[4]functionwasassumedforthedepthdose

functionandthecombinationofexponentialdecayfunctions[51

wasusedforthelateraldosefunctionInChapter工皿the

influenceofthethree-dimensionalgenerationdistributionon

EBICinthelinescanmethodswasstudiedassumingasimple

distribution(semisphere)withuniformminoritycarrierdensity

Ineachoftheseexperimentsonlyonemethodタeitherlinescan

ornomalincidencewastakenTheelectronpenetrationdepth

andthegenerationdistributiondifferedfromeachother

-50-

Schottky

barrier

Fig4-1

2P

Surfacecrosssection

「egion

Oneofthedividedsegments

Schematicviewofexperimentalconditionsandthedefinitionofthecoordinatesystem

-51-

Electronbeam

hottkySurfacecrossse

arrierOGene芯ion

Re゛region

Oneofthe

々dividedsegi

InthischapterwemeasuredEBICbyboththelinescan

andthenormalincidencemethodsinthesamesampleandclarified

thegenerationdistributionTheinfluenceofthethree-dimensional

generationdistributiononEBICisdiscussedassumingthatthe

electron-holepairsarelocalizedatニthecenterofthegeneration

regionTheexperimentニalresultsforGaAsSchottkydiodesare

alsoshown

4-2 Influenceofthree-dimensionalgenerationdistribution

onelectronbeaminducedcurrent

WeusedaSchottkydiodesinceitcanbeappliedforboth

thelinescanandthenormalincidencemethodsInthelinescan

methodtheEBICiscalculatedtakingtニhegenerationdistニrlbution

intoaccountbyasimilarmethoddiscussedinChapterⅡ工The

generationregionisdividedintomanysegmentsthesizeofwhich

issmallerthanLandeachsegmentisrepresentedbyonepoint

sourceTheEBICforthefinitevolumesourceisderivedby

summingupthesolutionofthediffusionequationforeachpoint

sourcersquo

Thedistributionisassumedtobesphericallysymmetric

asisshowninFig4-1Theelectron-holerdquopairsgeneratedbyan

electronbeanareconsideredtobelocalizedatthecenterRCof

thegenerationregionThegenerationstrengthgalonganyradius

vectorfromRc1Sassumedtobegivenby

gdeg^exp[-C(r2R2)] (4-1)

whereRisthedistancebetweenRandthemaximumelectronrange

CRm゛andristhedistancebetweenRCandeachdividedsegment

(seeFig4-1)

-52-

TheexponentCrelatestothedistributiondensityThedensity

becomesuniformasdiscussedinChapterl[EwhenC1Szeroand

theelectron-holepairslocalizenearRcwhenCbecomeslarge

Thedistributionisassumedinorderthatthedepthdosefunction

maybecomeGaussianasisreportedinthereferences[23]

ThevalueofLshouldbesmallinorderthatitcanbe

measuredbyboththelinescanandthenormalIncidencemethods

ThereforewetakeGaAsasanexampleInthelinescanmethodwe

calculatetheEBICintensity(whichiscalledthecollection

efficiencynandisnormalizedtobeunitywhenallthegenerated

carrierscontributetoEBIC)forseveralvaluesofCandR

The゛ilueofRmisgiven[2]by

町゜001A8Vノ゛フurn

cR

m゛

(4-2)

wherevaistheacceleratingvoltニageinkVThevaluesofCand

RRareassumedtobeconstantevenifvisvariedWhenvisCm

10and30kVaa

Rm

becomesOdeg74and4deg8ymrespectニivelyWetake

thetypicalvalueofLas1μminordertoexaminetheinfluence

ofthegenerationdistributiononEBICbecausethevalueofRm

issmallerthanLatva゛10kVbutlargerthanLatvadeg30kvrsquo

SincethesurfacerecombinationvelocitySofGaAsisoftheorder

of105-106cmSoline1[6-9]wetakevaluesofland50asthe

surfacerecombinationvelocityparameterSdefinedbySΞS(Lて)

(TisthelifetimeoforderofnS)

TheresultsofthecalculationareshowninFig4-2The

fullcurvesandthebrokencurvesareforCdeg8rsquo2゛RcRm゛Olsquo13and

C=54RR゜013respectivelyThesevaluesofCandRじmolinersquoCrsquom

thetypicalvaluesobtainedbythenormalincidencemethodin

GaAs[23]Thepointsourcesolutions(whichareobtainedby

assumingthatallthegenerationoccursatRc

-53-

are

)arealsoshownby

g`

A3U413Ud

COP≫no3

Fig4-2

ScanningdistanceX(pm)

j一次゜ごゴ野謡ごごご二ににごS

ご諧驚お謡謡S回読で昌翼麗

二竃Jeぎ驚謡じ雲Cにニごまふ(

ごごぶ謡1ば昌permilお穴混戮ずpermil

ぶぶごご1ここなSttedcdeges゛ecm

-54-

helliphellipl

]]1A

Ee

ビゲヤ

12

ss50

helliphelliphellipyJミ4sdeg50

dottedcurvesAtVa゛10kVthesizeofthedividedsegmentis

takenas005umwhichissmallerthanLsothateachdivided

segmentcanberepresentedbyonepointsourceIntheregion

05≦x≦15ymthelogarithmofEBICdecreasessuperlinearly--

anditdecreasesalmostlinearlyovertherangeofx≧15um-

ThetendencyappearsmoreapparentasSbecomeslargeThechange

oftheexponentCmakeslittledifferencetotheprofilesofthe

curvesTheabsolutevalueofnovertherangeofx≧05umis-

almostequaltothepointsourcesolutionwhenS1S1butbecomes

twicethatwhenSis50Thepeaksnearthebarrierareduetothe

edgeeffectasdescribedinChapterl工゛Atvadeg30kVthesizeof

thedividedsegmentistakenas02ymforthesamereasonas

Wit二hvadeg10kVThecurvesarequitedifferentfromthepointsource

solutionbothatS=1andS=50becausethedimensionsofthe

generationregionarelargeincomparisonwithLandthepoint

sourceassumptionisn0longervalidinthiscaseTheprofiles

ofthecurvesreflectthegeneratニiondistributionasoneseesthat

theprofilechangesifCvalsquotiesfrom54t082WhenSisvaried

fromlto50theprofiledoesnotchangeatthesameCvaluebutニ

ndecreasesbyabout30ZofthatofS=lItshouldbenotedthat

thesurfacerecombinationhasaninfluenceontheabsolutevalue

ofEBICevenifthevalueofRm(4deg8pm8tvadeg30kV)ismuch

greaterthanLThereforewecanevaluateLmainlyfromthe

slopeofthelinearregionat10Wvaconsideringthesurface

recombinationeffectandestimatethegenerationdistribution

fromtheprofilesofthecurvesinthecaseofhighva゛

-55-

Fig4-3

pasube

coipai

-O

Maximumelectronraり9eRm(μm)

AcceleratingvoltageVa(kv)

Experimentニalresultsofthenormalincidence

methodforthesampleA(SndopedGaAsn=62times1016

cm^L=03)Jm)andthesampleB(TedopedGaAs

ndeg80times1016cmoline3Ldeg07μm)Experimentalvaluesare

shownbycirclesThefullandbrokencurvesare

theoreticalcurvesforC=82RR=013andC=54

RcRmdeg013respectivelywdeg10cnmmandwddegOdeg151Jmdeg

-56-

12410oline

GaAsn(c「7i」

5A訟ばn

2ゝゝゝ

ゝゝ

ゝゝゝ

ゝゝゝrsquoL(pm)

1゛゛`ヽBO7J

yWヽ

5oline`olinersquo54013A03

≒旨

2φ

(52Schottkか

デ1テシフ)卜

1020304050

Theelectron-holepaircreationenergyEisobtained

fromthefollowingequation[101

n=ErdquordquoEBIC

pcIBvak(4-3)

whereIBisthebeamcurrentandkisthecorrectionfactorfor

theback-scatteredelectronsAsdescribedpreviouslythevalueof

nisinfluencedbySevenwhenVishighandsowemusttakeolinea`lsquorsquoolineolineolineolineolineolineolineolineolineolineoline

thesurfacerecombinationeffectintoaccountwhenweevaluateE

pc

4-3 Three-dimensionalgenerationdistributニioninGaAs

Thesameapparatusandthelock-intechniquewereused

asdescribedinsect3-4TheSchottkybarrierwasmadeonn-typeGaAs

wafersbyevaporatingAuofabout10nmthickinavacuumofabout

10rsquo7TorrTheohmiccontactwasobtainedbyevaporatingAu-Geand

alloyingat400degCfor2minThecarrierdensitynofeachsample

wasdeterminedbyc-vmeasurements

Theexperimentalresultsofthenormalincidencemethod

forthesampleA(Sndopedn=62times1016cmoline3)andthesampleB

(Tedopedn=80times1016cmoline3)areshowninFig4-3byfulland

opencirclesrespectivelyThevalueofvawaSvariedbetween5

and50kVTheEBICintensityincreasedlinearlywithIBwithin

therangeof1times10oline11≦IB≦-1times10oline9Awhenvawasfixed

whichsatisfiedthelowinjectionlevelconditionThecollection

efficiencynwascalculatedbythesamemethodreportedinref[10]

bychangi昭RcRmfrom01t0025andCfrom30to90

respectivelyThebestfitcurveswiththeexperimentalresults

wereobtainedInthecaseofL=03and07umforsamplesAandB

respectivelywhenRcRm゛O゛13andC=82wereusedThevaluesof

-57-

II

A3ua<3UduqjDaiion

ScanningdistanceX((jm)

Fig4-4

Experimentalresultsofthe

linescanmethodforthesampleA

[SndopedGaAsn=62times]016cmoline3)

Thefullandbrokencurvesare

ー い゛I

゛゛

ldquooU 5

Scanningdistancex(μm)

Fig4-5

ExperimentalresultニSofthe

linescanmetニhodforthesampleB

(TedopedGaAsn=80times1016cmoline3)

Thefullandbrokenlinesare

theoreticalcurvesforC=82RRtheoreticalcurvesforC=82R

=013andC=54RR=013cdeg=013andC=54RR=013c

respectivelyLdeg03cμmS゛20respectivelyLdeg07ymSdeg20

-58-

ぎ忌

五゛

olinelo

jV

ズごy

23

times1

GaAだj

j73C4Electron

L=07μmEbeam

2Sdeg20χ

1rsquo`

゛x

ya(W

2゛Va=30W

2_JE201

4一一―54013

5≒

脅χ

21`f

ゝ≒

ゝへ

5χ

147

RCRmandCagrees`゛iththerepoidegtedvalues[2]゜Thefulland

brokencurvesinthefigurearetheoreticalcurvesforC=82

RcRmdegOdeg13andC゛5deg4゛RcRmdegOlsquo13respectニivelylsquoThediscrepancy

betweenthetheoreticalcurvesandtheexperimentalvaluesat

10WvacanbeexplainedinthefollowingwaydegThegeneration

regionbecomesshallownearthesurfaceatlowVandtheEBIC

ismainlycontributedbytheseperatedelectron-holepairsin

thespace-chargeregionjustunderthesurfaceInthetheoretical

calculationitisassumedthatthere1Snorecombinationinthe

space-chargeregionButニinactualfactthecarriersrecomblne

throughthevarioustrapswhichreducestheEBIC

Theexperimentalresultsofthelinescanmethodforthe

samplesAandBareshownbycirclesinFigs4-4and4-5

respectivelyThetheoreticalcurvesareexpressedbythefull

(Cdeg82RcRmdeg013)andthebroken(C=54rsquoRcRmdegOdeg13)curves111

bothfiguresTheEBICintensityincreasedlinearlywithIBwitニhin

therange1times10oline11くrsquoIく1times10oline9Awhenvwasfixedat100r=B=a

30kVwhichsatisfiedthe10wInjectionlevelconditionasinthe

normalincidencemethodThetheoreticalcurvescalculatedusing

thesameparameterdeterminedbythenormalincidencemethodshow

goodagreementwiththeexperimentニalresultsatbothvadeg10and30

kVWhenwetakeintoaccountthattheexperimentalresultsat

vadeg30kVreflectthegenerationdistributiontheassumedgeneration

distributionbyeq(4-1)withC=5Aへ82andRcRmdegOdeg131s

consideredtobeappropriateforthethree-dimensionalgeneration

distributioninGaAs

Thevalueofkchangesfrom078to075whenvvariesa

from5t050kV[10]Whenwetaketheappropriatevalueofkfor

themeaSuredva゛Epccanbedeterminedbyeq(4-3)Thevaluesof

-59-

Normalincidence Line scan

V(kv)a

E(eV)GaAsCSndoped)pc

GaAs(Tedoped)

5-50

41

39

14

3 9

30

Tab4-1 Valuesoftheelectron-holepaircreationenergyEinGaAsdeterminedbytニhenormalincidenceandlinepc

scanmethods

-60-

Eobtainedbythenormalincidenceandthelinescanmethodsarepc

39Oi41eVand38へj44eVrespectivelyastabulatedin

Tab4-1BythenormalIncidencemethodWuandWittry[10]

determinedEpCas468eVwhichwasabout15Zlargerthanour

resultsOnereasonforthediscrepancy1Sthedifferenceofthe

generationdistributionsThemodifiedGaussiandistributionused

bythemslightlydifferedfromtheGaussiandistributionusedin

ouranalysisAnotニherreason1Stheaccuracyofmetalthickness

WeestimatethethicknessfromtheweightofthechargedAuwhich

1SevaporatedtomaketheSchottkybarrierThereforetニheobtained

valuemaybedifferentfromtherealthicknessInthelinescan

methodEBICbecomesinsensitivetothemetaltニhicknessandthe

trapsinthespace-chargeregionbutisinfluencedbysurface

recombinationasdiscussedbeforeAlferoveta1[11]andWittニry

andKyser[12]reportedEpcas32へj44eVand46eVrespectニive-

lyfromthepeakvalueofEBICwhentheelectronbeamcrossedthe

p-njunctionOurresultsof38へj44eVareinthemiddlerange

oft二heirvaluesIntheiranalysestheydidnottakethesurface

recombinationeffectintoaccountandsoourresultsareconsidered

tobemorereliablethantheirs

4-4 Summary

Thethree-dimensionalgenerationdistributionbyan

electronbeaminGaAswasinvestigatedbymeasuringEBICwitha

combinationofnormalincidenceandlinescanmethods

TheprofileoftheEBICcurvesinthelinescanmetニhod

expressesthegenerationdistributionwhenvaishighandthe

dimensionofthegenerationregionislargerthanLThesurface

-61-

recombinationdoesnotaffecttheprofileofEBICbutlowersthe

collectionefficiencyTheaccuratevalueoftheelectron-hole

paircreationenergymustbedeterminedbytakingthesurface

recombinationeffectintoaccount

TheexperimentalresultsinGaAsSchotニtkydiodeswith

differentdiffusionlengthsshowedthatthecenterofthe

generationregion(iethemaximumenergydissipationdepth)

waslocatedatthepointof0130fthemaximumelectronrange

andtheradialdistributionfromthecenterwasshowntobe

Gaussianwithaneχponentof54へ-82Theelectron-holepair

creationenergyinGaAswasdeterminedas38rsquoV44eV

References

[1]

[2]

[5]

[6]

KKanayaandSOkayamaJPhysDApplPhys

543(1972)

DBWittryandDFKyserJApplPhys旦旦375

(L967)

VVMakarovSovPhys-Semicond旦722(1975)

TEEverhartandpHHoffJApplPhysを

5837(1971)

SpSheaLDPartainandpJWarterrdquoScanning

ElectronMicroscopy71978V011uml(SEMIncAMFOrsquoHare)

pp435-444

LJastrzebskiHCGatosandJLagowski

JApplPhys481730(1977)

-62-

[7]

[81

[9]

[10]

[11]

[12]

LJastrzebskiJLagowskiandHCGatos

ApplPhysLettri537(1975)

MEttenbergHKresselandSLGilbert

JApplPhys44827(1973)

CAHoffmanKJarasiunasHJGerritsenand

AVNurmikkoApplPhysLett22536(1978)

CJWuandDBWlttryJApp1PhySpoundrsquo2827

(1978)

ZhIAlferovVMAndreevVIKorolrsquokovand

vIStreminSovPhys-Semlcond41113(1971)-

DBWittryandDFKyserJApplPhys

361387(1965)

-63-

5-1

ANALYSISOFELECTRONBEAMINDUCEDCURRENTCONSIDERING

SAMPLEDIMENSIONS

Introduction

Anelectronbeaminducedcurrent(EBIC)methodusing

ascanningelectronmicroscope(SEM)isaconvenienttechniqueto

measuretニheminoritycarrierdiffusionlengthLandthesurface

recombinationvelocitySinsemiconductorsTherehavebeenmany

theoreticalandexperimentalstudiesonthelinescanmethodof

EBICInChaptersI工andytheEBICwasanalyzedquantitatively

takingthethree-dimensionalgenerationdistributionintoaccount

bythedividingmethodandtheimprovedmethodtocharacterize

Landswassuggestedχihenthesampledimensionsarelessthan

oneortwodiffusionlengthstheminoritycarrierdistribution

isaffectedverymuchbysampledimensionsRoos[1]analyzed

EBICtheoreticallyinthecaseofthinlayersHecalculated

thedependenceofEBIConthescanningdistancexintherange

ofxL≪1inthesampleswithwL=land05(wlayerthickness)j

andshowedthatLcouldnotbedetermineddefinitelyfromthe

slopeofthelogarithmofEBICvsXcurve

InthischaptertoanalyzeEBICconsideringthesample

dimensionsgwediscussasimplemethodusinganimagesource-and-

sinkdistributionWeshowthedependenceofEBIConxoverafull

scanrangewhenthelengthbetweenapotニentialbarrierandan

ohmiccontactisequaltoandsmallerthanthediffusionlength

andmentionsomeimportantニpointstobenoticedinthedetermination

ofLandsTheexperimentalresultsinSiSchottkydiodesarealso

shown

-64-

Fig5-1

ySご

uarrj

Schottkybarrier

uarr

Ohmiccontact

Schematicviewofexperimentalconditionsanddefinitionofthecoordinatesystem

-65-

Electronbeam

-J-

レじ2「lingtrack_^一分

りhelliphelliphellipljc1お迄゛

IL

5-2 Determinationofdiffusionlengthandsurfacerecombination

velocity

ForsimpletheoreticalconsiderationwetakeaSchottky

barrierdiodeAsshowninFig5-1theSchottkybarrierisin

they-zplaneandtheelectronbeamisincidentニperpendicularto

thesamplesurface(χ-yplane)Thescanningdirectionisalong

theX-axiswhichisnormaltothebarrierplaneThegeneration

sourceisconsideredtobeapointニandislocatedat(゛grsquo

Thesteadystニateexcessminoritycarrierdistributionpis

obtainedfromthefollowingdiffusionequation

Dnabla2pdeg二T

-g6(x-xyz-d)rsquo

O゛dg)

(5-1)

whereDisthediffusionconstantンTisthelifetimeandgisthe

generationratニeofelectron-holepairs

工fthethicknesswbetweenthepotentialbarrierandthe

ohmiccontactismuchgreatニerthanLandtheotherboundariesin

theyandzdirectionsarebothmuchfurtherawayfromthe

generationsourceEBICiscalculatedunderthefollowingboundary

conditionsasdiscussedinsect3-2

3p-9z

χ=0

x=-H≫

Z=0

Z=0

=0(attheSchottkybarrier)

=0

wheresIsthesurfacerecombinationvelocity

-66-

(5-2a)

(5-2b)

(5-2c)

(5-4)d帽

wherexgrsquoLrsquoDgdegdLSdegs(Lて)andTisthevariablefor

-67-

integrationThevalueofJ(x)isnormalizedtobeunitywhena11

thegeneratedcarrierscontributetoEBICThefunctionK(ぺ7)

isthesecond-modifiedfirst-orderBesselfunction

FortheanalysisofEBICconsideringsampledimensions

wetakethefundamentalcasethatthediffusionlength1S

comparablewithorlargerthanthethicknessw(seeFig5-1)

OncethedistributionpisknownEBICcanbefoundasfollows

十(゛十(゜3p

j=eDintint-

0 -003χ

dydz

χ=0

(5-3)

whereeisthechargeofanelectronBerzeta1【2】solvedthe

diffusionequation(5-1)undertheboundaryconditions(5-2a)

(5-2b)and(5-2c)bythemirrorimagemethodInadditiontothe

reaLsourceatxg゛animagesinkwasintroducedatthesymmetric

position-XwithrespecttotheSchottkybarrier(seeFig5-2)

Whenthematerialextendstoχ=plusmndegdegthesolutionofeq(5-l)is

givenbypμ](゛゜土)゛WhentheSchottkybarrierisintroduced

theminoritycarrierdistribution1Sexpressedasp[x]十p[oline゛g]

inordertosatisfytheboundarycondition(5-2bplχ=OdegO)rsquo

andjisobtainedasfollows

J()゜

-eg-

-π

DgK(ぶ77F)

リinto

うと縦卜-dT

-H≫

十intexp(-S(T-D))

Dg

g ぜ)ケ

Thenonemustusethefollowingboundaryconditioninsteadof

(5-2c)

Ix=wdegO(attheohmiccontact) (5-2crsquo)

ThesolutionQfeq(5-1)undertheboundaryconditions(5-2a)

(5-2b)and(5-2crsquo)canbeobtainedbyextendingthemirrorimage

methodproposedbyBerz[2]andOpdorp[3]Inadditiontothereal

sourceatXafamilyofvirtuaLimagesourcesandsinksare

introducedatthesymmetricpositionswithrespecttothebarrier

andtheohmiccontact(seeFig5-2)Openandsolidcircles

representthesourcesandsinksrespectivelyThereforethe

sourcesareatX2w十Kg4W十xg゛゜rsquo゜lsquoand-(2w-x)-(4w-x)rdquoldquo゛

andthesinksareat-X-(2w十X)-(4w十X)and2゛゛olinersquo4゛olinersquo

respectivelyWhenthematerialextendstox=士≪>thesolution

ofeq(5-l)isgivenbyp【゛】(゛゜土゛grsquo士(2゛`7oline゛g)rsquo土(2W十)rdquorsquo゜rsquo)

(seeFig5-2)Iftニheinfluenceofohmiccontactニmustbetaken

intoaccounttheminoritycarrierdistributionisexpressedusing

thefollowinginfiniteseriesinordertosatisfytheboundary

conditions(5oline2brsquoplx=OdegO)811d(5oline2c≒Plx=wdegO)rsquo

p゛[゛g]゜jp[≒ 十p[oline

十p[2゛oline]十p[-(2W-X)

+p[2w十゛g]十p[-(2w十)

十一一一一一一-一一

9 (5-5)

Theinducedcurrentsbypairsofsourcesandsinksie

p[゛g]andp[oline゜cg]rsquop[2゛olineへ]andpr-(2w-x)]rsquop[2゛十]andp[-(2v゛十)]rsquo

areexpressedbyJ(x)-J(2v゛oline゜cg)J(2w十)゛rsquo゛゜゛rsquo

respectivelywiththeaidofeq(5-4)ThenthetotalEBICis

expressedintheinfiniteseriesasfollows

-68-

Fig5-2

Source

helliphelliphellipSink

Concentration

Sdηitky

barrier

Ohmic

contact

Schematicviewofexcessminoritycarrierconcentrationpatternforeachsourceandsinkwhicharerepresentedbytheopenandsolidcircles-respectively

-69-

pr2wχ9]

plE【2w->り》】1

1rdquoMI

-E唇-

゜(2WdegO`92Wi

ミplE)rsquo゛p[2w-xg]

pl-《2w+x)】)゜91

s哺

(n

L1)

paziipEJoz

1 2 3

Normalizedscanningdistancex

0 5

M)DUd|UOISコ|}Ppazneaijoz

12 5 X)2050

Fig5-3

DependenceofEBIConthe

normalizedscanningdistanceχ(equivxL)

fullandbrokencurvesarefortニhecaseswithandwithouttheinflu-

enceofohmiccontニactrespectivelyThenormalizedsamplewidthwLis

1020and30andthenormalized

generationdepthDgisOdeg0Thevaluesofthesurfacerecombination

velocityparameterS(seetext)

areland10forupperandlower

groupofcurvesIrespectively

Fig5-4

Estimateddiffusionlength

fromthereciprocalgradientof

thecurveatthecenteroftニhe

scanningdistanceinthecaseof

DgdegOlsquoOandwLdeg1lsquoOSvaries

fromlt050L大andL訟are

forthecaseswithoutandwith

theinfluenceofohmiccontact

respectively

SurfacerecombinationvelKitypmmeterS

-70-

Dgdeg00

そー=10

L゛で

ヽ1慟1

111

25=1rsquo1

1`11

【flll

11

51s

degilOII

211`4

111

(flll゛

芒゜11゛|`

51S`|

11゛1

|ぎ=21`ヽ

||rsquo゜3|

(y

J(Xg)=J(x)-J(2v゛oline゛g

olineJ(匈゛≒

)十J(2wトxg

)十J(4wヽ4-xg

----

II

(5-6)

ThevalueofJ大convergestoacertainvalueandcanbecalculated

byacomputerincasesofanyvaluesofwLandS

InFig5-3thelogarithmofJisplottedbysolidlines

asafunctionofx(=xL)whetvwL1S1020and30and

Dgis00Thedashedlinesareforthecasewithouttheinfluence

ofohmiccontactTheupperandlowercurvesareforS=1and10

respectivelyThevaluesoflogJ大decreasesuperlinearlywithin

onediffusionlengthawayfromthebarrierThereforeonemakes

considerableerrorsifoneestimatesthevalueofLfromthe

reciprocalgradientofthecurveatarbitraryXInordertoshow

anextremeexampleweconsiderthecaseofw7Ldeg1゛08叫DgdegO`Odeg

Thereciprocalgradientofthecurveinthelinearregionat

xdeg05withoutandwiththeinfluenceofohmiccontactareputas

L大andLrespectivelyThevaluesofLandL幼thuSobtained

areplottedasafunctionofSinFig5-4WhenSisunityL

1Sabout68ZofLandL政isabout44ZofLThevaluesofL大

andL政reducetoonlyaboutonethirdofLwhenSis50

Themethodoftheanalysisforapointsourcementioned

abovecanbeeasilyappliedtothefinitegenerationdistribution

bythedividingmethoddiscussedinChaptersI工andHEspecially

inthecasesoflight-emittingdiodes(LEDrsquos)andlaserdiodes

(LDrsquos)usingGaAsandGaPthedimensionofthegenerationregion

istheorderofymforva゛20へrsquo30kVandiscomparablewiththe

thicknessoftheepitaxiallayersThereforethedividingmethod

becomesaneffectivemeanstomeasureLandSintheepitaxial

layers

-71-

Fig5-5

Q‐rsquoQ]

loline

11(52

ち5

0 50Scanningdistancex

100

(pm)

jDependenceofEBIConthescanningdistancexforn-SiSchottkydiodesThelengthWbetweenthe

barrierandtheohmiccontactis100Umthe

acceleratingvoltageVais50kVandLis20へj200lim

SolidandbrokenlinesareforSdeg104and105cmsec

respectニivelytakingthegenerationdistributioninto

accountThediffusionconstantDofholesis125

cm^sec

-72-

n-SiVa=50kVw00μm

5aD=iZ5cm2ss(cms)

1-helliphellip104

2゛l`4-----helliphellip105

`L(μm)

1へ`a-2001

≒yyhelliphelliphellip100i

5゛゛ぐ丈i

へ゛`恥i

`ヽ

`lsquolブjl

ゝゝjφ1

0h白contactム

2rsquo

5-3 ApplicationtoS1

ThediffusionlengthintheSibulkmaterialusedfor

solarcellsorLS工゛S1Scomparablewiththedimensionsofeach

elementAndsotheminoritycarrierdistributionisaffected

verymuchbyelementdimensionsTheSchottkydiodewastakenfor

afundamentalmodeltorevealtheinfluenceofsampledimensions

CalculatedEBICrsquosbythedividingmethodinthecaseof

n-Siforwdeg100umandva゛50kvareshowninFig5-5Thediffusion

constantDofholesistakenasatypicalvalueof125cm^sec

Solidanddashedlinesareforsdeg101゛and105cmsecrespectively

andLis20010050and20umforthecurvesfromupperto

lowerineachgroupThegenerationsourceisassumedtobeasemi-

sphereThenumberofthegeneratedelectron-holepairsatany

pointinthesemi-sphereisproportionaltoexp(-40(rR)2)

(rthedistancebetweenthepointandthecenterdRthe

radiusofthesemi-sphere)Thegenerationdistribution1Sassumed

inorderthatthedepthdosefunctionalongthez-axlsagreeswith

thatproposedbyEverhart[4]andthevaluesofdgandRare

5ymand11ymrespectively゛forvadeg50kvrsquo

AsshowninFig5-5theabsolutevalueofEB工Cincreases

withdecreasingSforthesameLvalueThecurvesconvergetoa

certaincurveforboths=10rsquoand105cmsecwhenLbecomesgreater

thanwForconveniencethelogJvsχcurvesaredividedinto

threepartsi

range(30≦X-

く一一

eA)nearthebarrier(0≦x≦30ym)B)middle--

70ym)andC)neartheohmiccontact(70≦x≦100--

μm)IntheregionA)peaksappearatxdeg6ymowingtotheedge

effectdescribedinsect3-3and10gヽJdecreasessuperlinearlybecause

ofthesurfacerecombinationeffectIntheregionC)logj大decreases

-73-

Fig5-6

゜1(il

四a3

U」

-01

Ddziieujjoz

゛D=1Z5cm2s巡付

1 03

orini=-

にuarrヤuarr

uarrにヤ

Ohmiccontactづ50100

Scanningdistancex(μm)

JDependenceofEBIConthescanningdistancex

forn-SiwhenLismuchgreaterthanWThesolid

linesareresultsbythethree-dimensionalsolutions

forsdeg1035times1031045)(104and105cmsec

respectivelyThedashedlineisEBICbyone-

dimensionalapproximationV=50kVw=100ymand

L=1000Uma

-74-

゛ぐpermil

゛`xズit

darrレ

rapidlybecausetheohmiccontactisacarriersinkInthemiddle

rangeB)logJ大decreasesalmostlinearlyThereciprocalgradient

ofthecurveincreasesasLbecomeslargeintherangeofL≦100pm-

Thegradientsofthecurvesarenotsoaffectedbysurface

recombinationIfvisloweredt010kVthesurfacerecombinationa

affectsEB工Cmuchmorethanforvadeg50kVbecausethegeneration

depthbecomesshallowerInfactthegradientsofthecurvesin

regionA)aresteeperthanthoseforv=50kVforthesameLvaluesa

ThereforeinthecaseofL≦100ymLandscanbedetermined-

mainlyfromtheslopesofthelinearlydecreasingregionforhigh

va(50kVinthiswork)andthesuperlinearlydecreasingregionnear

theSchottkybarrierfor10Wva(10kVinthiswork)respectively

takingtheinfluenceofohmiccontactintoaccountButinthe

caseofL≧100ymthevalueofLcannotbedetニermineddefinitely-

becausetheslopeofthecurveinthelinearlydecreasingregion

doesnotchangeevenifLvaries

WhenLbecomesmuchlargerthanwthecurvesofEBICvsX

convergetoacertaincurveCalculatedEBICrsquosinthecaseofn-Si

forva゛50kVwdeg100ymandLdeg1000ymareshownbysolidlines

1nFig5-6forsdeg1035times1031045times104and105cmsec

respectivelyThegenerationsource1Sassumedtobeapointatthe

depthdThedashedlineisasolutionofone-dimensionalg

approximation(seeappenditimes1nthischapter)Theabsolutevalueof

EBICbecomeslargerwithdecreasingSandthecurveforS40cmsec

approachestothesolutionofone-dimensionalapproximationItcan

beexplainedasfollowsInthecaseofs=Ocmsecthereisno

carrierrecombinationatthesurfaceHencethematerialcanbe

consideredtoextendtoz=_oobyintroducinganimagesourceat

(x0-d)EBICisobtainedbyintegratingdpdxinthey-zplane

atx=0AndsotheEBICbythepointsourceat(x

-75-

grsquoO゛plusmnd)using

JOoline1

Ig3paziieuijoz

Fig5-7

(a)

UI「rrsquo

a3

U」

rsquo一lsquo51 0

pdziieujjoz

Scanningdistance

(b)

X(pm)

ExperimentalresultsinSiSchottkydiodesfor

w゛200μmand83μminfigures(a)and(b)respectively

Vais1030and50kVSolidanddottニedlinesare

theoreticalresultsforL=80UmandS=50withand

withouttheinfluenceofohmiccontニactrespectively

-76-

inlsquoSiL=80μm

こ沼o

rsquoバ町「i「でなl`Jes

l悶

2卜Ohmiccontact今|

トj

rsquohelliphelliphelliphelliphellipi

15

≒|

2helliphellip1

0Scanningdistancex150(pm)00

へn-SiL=80μm

5゜`S=50

deg゜w=83um

degムExperimentalvalues2deg`4≒Vi=50kV

I゛lsquorsquo4≒oVadeg30kV

≒゜rdquoVa≪10kV

丿4

lrsquo

2lsquoo1

rsquo゜i

2degi

2Ohmiccontactrarr

050100

thethree-dimensionaldiffusionequationbecomesidenticaltothat

derivedbyone-dimensionaldiffusionequationconsideringthe

planarsourceatxrsquoxginthey-zplane[5]Howeverinpractice

SihasafinitevalueofSandsothethree-dimensionalsolution

mustbeneededinthecaseofL>wThevalueofscanbedeter-

minedfromtheabsolutevalueofEBICfollowingthediscussionof

sect4-2usingtheelectron-holepaircreationenergyE^^byan

electronbeam

TheexperimentalresultsinSiSchottkydiodeswith

w=200umand83μmmadefromonewaferareshowninFigs5-7(a)

and5-7(b)respectivelySamplepreparationsandmeasurement

procedureshavebeenalreadyshowninsect3-4Theresultsofthe

theoreticalcalculationusingL=80vimandS=50forthreedifferent

va゛s(10rsquo30and50kV)areshownbysolidlinesinbothfigures

Theresultsofthetheoreticalcalculationwithouttheinfluence

ofohmiccontactareshownbydottedlinesinFig5-7

Inthecaseofw=200ymthesamplewidthisthreetニimeslargerthan

Landsotheslopeofthelinearregion(50≦x≦120um)isnot--

verychangedbytheinfluenceofohmiccontactInthecaseof

Wdeg83umthecurvesarequitedifferentfromthoseforw=200ym

andthereciprocalgradientofthecurvesinthemiddlerange

(25≦x≦55ym)givesL=20ymwhichisaquarterofthereal--

diffusionlengthBothinFigs5-7(a)and(b)theoretical

calculationsshowgoodagreementwiththeexperimentalresuLts

whichshowsthatthemethoddiscussedinsect5-21Saneffective

meanstニoanalyzetheeffectofsampledimensions

-77-

5-4 Summary

Theminoritycarrierdistributionisaffectedverymuch

bythelengthwbetweenapotentialbarrierandanohmiccontact

ifWisequaltoorshorterthanthediffusionlengthLThe

dependenceofEBICJ大onthescanningdistancexwasinvestigated

byextendingthemirrorimagemethod

InthecaseofwL≧1logJ゛decreasesalmostlinearly-

inthemiddlerangeofthescanningdistancebuttheestimated

diffusionlengthfromthecurvesismuchshorterthanthereal

diffusionlength(eg30t044ZinthecaseofL=w)The

valuesofLandScanbedeterminedmainlyfromtheslopesof

thecurvesforhighand10Wva゛reSpectively゛takingtheinfluence

ofohmiccontニactintoaccount

工nthecaseofwLく1theslopeofthelinearly

decreasingregionoflogJvsXcurvesdoesnotchangeevenif

LvariesThedependenceofEBIConχconvergestoacertaincurve

ThevalueofLcannotbedetermineddefinitelybutthevalueofS

canbeobtニainedfromtheabsolutevalueofEBIC

TheexperimentalresultsinSiSchottkydiodesagreed

fairlywellwiththetheorywhichshowedthattheextendedmirror

imagemethodwaseffectiveinanalyzingEBICconsideringthesample

dimensions

-78-

References

[1]

[2]

[5]

OldwigvonRoosSolid-stateElectron

(1978)

211063

FBerzandHKKuikenSolid-stateElectron19

(1976)

437

CvanOpdorpPhilipsResRep32192(1977)

TEEverhartandPHHoffJApplPhys丘5837

(1971)

WHHackettJrJApplPhys

Appendix0nedegdimensionalapproximation

431649(1972)-

IfthediffusionlengthLisinfinitelylongminority

carriersdonotrecomblneuntiltheyflowintothebarrierorthe

ohmiccontactThereforethediffusioncurrentdoesnotvary

spatiallyTheminoritycarrierdistributionpcanbeexpressed

asalinearfunctionofχ1nthecaseofone-dimensional

approximation工fthepointsourceg1Slocatedatdegcgrsquop(゜c)is

putasfollows

p(x)=ax十b(a>00≦゛≦)rsquo

p(x)゜c゛十d(c<0X≦゛≦゛)゜

(5-Al)

(5-A2)

Thefactorsabcanddcanbedeterminedfromthefollowing

conditions

-79-

p(O)=0

p(w)=0

卵石

-卜-卵匹 ゜g

(5-A3)

(5-A4)

(5-A5)

(5-A6)

Theeq(5-A5)showsthecontinuityconditionatxdegxg゛andtheeq

(5-A6)givesthatallthegeneratedcarriersflowintothe

Schottニkybarrierandtheohmiccontactニwithoutrecombinationin

materialsThesolutionp(x)becomesasfoLlows

p(x)=

p(x)=

(1-ミj1)x(O≦x

--^(w-x)(Kg

NormalizedEBICJisexpressedby

J大=

-egeD

dp

-dxχ=0

=1-

こ)

3Wく

一一

Xく一一

(5-A7)

(5-A8)

X』

-80-

(5-A9)

6-1

DETERMINATIONOFLIFETIMEANDDIFFUSIONCONSTANT

BYPHASESHIFTTECHNIQUE

Introduction

Accuratedeterminationoflifetimeてofminoritycarriers

1Sveryimportantincharactニerizingsemiconductingmaterials

Thevalueofてcanbemeasureddirectlyfromthetransientresponse

aftertheinjectionofminoritycarriersTheradiativerecombina-

tionlifetimewasmeasuredinGaPandGaAsfromthedecayofphoto-

luminescence[1]cathodoluminescence[2]orelectroluminescence[3]

Thephotoconductancedecaymethod[4]Isthemostcommonlyused

techniquetomeasurelifetimeincludingradiatニiveandnon-

radiativeprocessesInthesemethodsmeasurementofTinsmall

areaoftheorderofym^isverydifficultbecausethesample

surfacemustberelativelywideinordertoobtainasufficient

signalThespatialvariationofてcouldbedeterminedfromthe

decayoftheelectronbeaminducedcurrent(EBIC)usinga

scanningelectronmicroscope(SEM)[5-8]Thevalueofてismuch

influencedbysurfacerecombinationsincelightoranelectron

beamforexcitationentersthroughthesurface

Thevalueofてcanbeobtainedfromthediffusionlength

LusingtherelationL=j5マThevalueofLcanbedeterminedbythe

spectralresponsemethodusingsolarcells[910rbythesurface

photovoltaicmethod[1011nbothmethodstheaccurateabsorption

coefficientmustbeneededtodeterminethevalueofL

AsdiscussedinChapters皿rsquov^VtheEBICmethodusingSEMisa

veryconvenienttechniquetomeasureLinsmallareaoftheorder

-81-

ofym^andtherehavebeenmanytheoretical【11-14】and

experimental[15-16]worksuptodateInthemetニhodhowever

thediffusionconstantDmustbegiveninordertoobtainT

Whentheintensityofexcitationforelectron-holepair

generationisrdquomodulatedthephaseofluminescenceorinducedcurrent

isshiftedfromthatoftheexcitationsourcebecauseofthe

recombinationofinjectedminoritycarriersinamaterialThe

valueofてcanbedeterminedfromtheamountofthephaseshift

Hwang[17]obtainedTinGaAsfromthephaseshiftofphoto-

luminescenceInthemethodtニhephaseshiftisinfluencedbythe

surfacerecombinationvelocityandtheabsorptioncoefficient

whichaffectminoritycarrierdistributionverymuchReichleta1

measuredでinSi[18-20]andGaAs[21]usingthephaseshiftin

photニ0-inducedcurrentMunakata[22]andOthmer[23]measuredて

bythephaseshiftofEBICinGeandSirespectivelyTheyused

tニhesolutionoftheone-dimensionaLdiffusionequationwithout

anyconsiderationofthesurfacerecombinationeffect

Ifsuchaphaseshiftmethodiscombinedwiththe

conventニionallinescanmethodofEBIC(iemeasurementofLusing

DCelectronbeam)thelifetimeandthediffusionconstantof

minoritycarriersinsmallareacanbedeterminedsimultaneously

Kammeta1[241determinedてandDinSiTheymadeaSchottky

barrierwithasilverpaintonSisurfacesandmeasuredEB工Cby

scanningtheelectronbeamonthesurfaceparalleltothebarrier

InthatmethodsurfacepreparationhasmucheffectonT[25]

andtheconfigurationusedbythemisnotconvenientwhenone

measuresてandDinmaterialswithsmallLTheanalysisisvery

complicatedandRoospointedouterrorsintheiranalysis[26]

andsuggestedasimpleconfiguration[271

-82-

Inthischapterwetaketheconfigurationthatthe

electronbeamscansonthesurfaceperpendiculartothebarrier

planeWiththisconfigurationtニhetime-dependentdiffusion

equationcanbesimplyreducedtothesteady-statediffusion

equationandthecomplicationintheanalysisthatRoosindicated

[26]canbeexcludedThisphaseshiftmethodcanbeappliedto

materialswithsmallLWesolvethethree-dimensionaltime-

dependentdiffusionequationtakingthesurfacerecombination

effectintoaccountandclarifytherelationofTandthephase

shifttheoreticallyWeshowthatthree-dimensionalsolutions

canbeexpressedbyone-dimensionalsolutionswithempirical

correctionfactorsandthatてandDcanbedeterminedwitニhout

anyrestrictionformodulationfrequencyExperimentalresults

inSiarealsoshown

6-2 Relationbetweenlifetimeandphaseshift

WetakeaSchottkydiodeasshowninFig6-1for

simpletheoreticalcalculationWeassumeapointgeneration

sourcewhichhastime-variabLepartgelωt(ω゜2TTfωangular

frequencyfmodulationfrequency)at(x゛0d)Whenthetldegeoline

variablepartofthenumberofminoritycarriers1Sputas

恥eiωt(isacomplexvariable)psatisfiestheconventional

steady-statediffusionequationbyintroducingthecompleχ

effectivediffusionlengthL゛eff(ΞL゛1171瓦JTL=ぷF)゜If

thetime-variablepartofEBICIsputasj`゛e(J゛1Scomplex-

EBIC)icanbeexpressedasfollowsbythemirrorImagemethod

asdiscussedinsect3-2

-83-

Fig6-1

ylご

uarrj

Schottkybarrier

uarr

Ohmiccontact

Schematicviewofeχperimentalconditionsand

definitionoftheco-ordinatesystem

-84-

Electronbeam

SOlyScanningtrack_xj

ズニに匹二oline-一一゛

lsquo9surface

lL-__--ang__helliphellip_

|`1

丑昌之

9gπLaf ―K

gdof

(ノダr7olineT

)酉ff

L大effl゛ぶ弓+T『

+0O

(-1(じ(lg)

)X[

jiご]ご

)ことりsube

dgDIL火eff

xlてこi7

dT

J(6-1)

whereeisthechargeofanelectronsisthesurfacerecombination

velocityandTisthevariableforintegratニionThefunctionK^

1sthesecond-modifiedfirst-orderBesselfunctionwithcomplex

variablesTheabsolutevalueofEBICnandthephaseshiftφ

fromthesourcearegivenasfollows

TI=

|」と

eg

φ=tan-1

Im一J

Rej゛

(6-2)

(6-3)

whereReandImstandforrealandimaginarypartsrespectively

Thevalueofnisnormalizedtobeunitywhenallthevariable

-partgcontributetothevariablepartofEB工CSincej火isa

functionofてthevalueofφbecomesafunctionofてThevalues

ofnandφcanbecalculatednumericallyWeassumeapointsource

forsimplecalculationbutthemethodmentionedabovecanbeeasily

appliedtothefinitegenerationdistributionbythedividing

methoddescribedinChapters工江andy

-85-

Fig6-2

Fig6-3

U2

Cχ310-rsquo

山5

ト2

10lsquo3

velocitysis

35225N

(Eu

一))

j^

9st^d

10

Jo}CIで噌」

ひpF

ぐりぐ

ごヽこ

W゛`みノー-

うて`゜ldegw-rsquo゜rsquordquorsquoPrime゛ご

゜二

゛゜〆ノ〆゛`゜

゜゛〆ノ

(MJD≪p)j

UMS

asEMd

ofEBICvsscanning

thealmostlinear

0 50 100 150

ScanningdistanceX(pm)

Normalizedintensityandphaseshift

distancexcurvesTheconcavecurvesand

linesarefortheIntensity(leftaxis)andthephaseshift

(rightaxis)respectivelyThesolidbrokenanddottedlines

areforf=10100and500kHz(ieωT=031314and157)

respectivelyLifetimeTistakenas5μSThediffusion

constantDis30_cm2Secandthesurfacerecombination

105CmSeC

S=105CmS

D=30ori^s

Lifetimeで(sec)

DependenceofgradientofphaseshiftdφdxonTD=30cmsecandrsquos=105cmsec

-86-

rsquoD=30crrfis

ωで=5f

5ヽ2MHz

ヽ1MHz

2`500kHz

1`

100kHz

``50kHz

`ヽ`10khtt

pwww

kHz

`ωで=01

1(jrsquo

825

1(i

725

1(jrsquo

6251(irsquo

525

10lsquo4

Mm2s)lsquo1-123lsquoj「rsquoQ心Hz」t

=10cms-10a3i

i=30kV-一一一一1003K

helliphelliphelliphelliphellip500157

Thevaluesofnandφwerecalculatedasafunction

ofscanningdistanceχforp-SiasanexampleTheresultsare

showninFig6-2whenてisputasatypicalvalueof5μs

Inthefiguretheconcavecurvesandthealmostlinearlines

areforn-χandφ-xrelationsrespectivelyThesolid

brokenanddottedlinesareforf=10100and500kHz(ie

ωT=031314and157)respectivelyThediffusionconstant

Disputas30cm^secThesurfacerecombinationvelocitysIs

takenas105cmsecsincetheordinarysurfacerecombination

velocitニyofSiis103へj105cmsecTheacceleratingvoltage

Isputas30kVThepointsourceisassumedtobelocatedat

themaximumenergydissipationdepthofabout3μmunderthe

surfacebasedonKanayarsquosmodel[28]forelectron-holepair

generationdistributニIon

Inthecaseofωてく01tニhedependenceofnonX

agreeswiththat-measuredbyaconventionallinescanmethod

usingDCelectronbeamThevalueofLcanbedeterminedfrom

theslopeofthen-χcurvestakingthesurfacerecombination-

effectintoaccountasdiscussedinChaptermThevalueof

L大effalmoStequaltoLandSOφbecomesnearlyzero

Inthecaseofωて≧01φincreasesalmostlinearly-

withxovertherangeofx≧Landthegradientdφdxbecomes-

largewithIncreasingfasshownInFig6-2Thegradient

dφdxisfoundtoIncreaseasてbecomeslargeforthesamefvalue

andnottochangeevenifSvariesfrom10^t0105cmsecfrom

thecalculationforvariousparametersFigure6-3showsthe

dependenceofdφdχonTwhenfisvariedfrom5kHzto2MHz

ThevaluesofDandsare30cm^secand105cmsecrespectively

ForeachvalueoffdφdxincreasesmonotonouslywithTwithin

therangeof01≦ωて≦5andapproachestoacertainvalue--

asymptoticallyovertherangeofωて≧5-

-87-

「ujopp」)

調uiusas^qdj〇}c心石司」

Fig6-4

Lifetimeて (sec)

10

Expressionofthedependenceofdφdxonてusingtheapproximatedsolutionsoftheone-

dimensionaldiffusioneuationinthecaseofD=30cm^secandf=10sectHzSolidlineisa

three-dimensionalsolutionLines(A)and(B)

aretheapproximatedone-dimensionalsolutionsand(Arsquo)and(Brsquo)aretheasymntotesforthethree-dimensionalsolutionThecorrectionfactorCforthethree-dimensionalsolutionis087

-88-

2(8)登ニ4F

helliphellipj(Å

(A)

D(EI)-(jじ硲ゴどこ二こhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip

2helliphelliphelliphelliphelliphelliphelliphellip(畿f3゛(c緊八(醤y3

d≫_Kii「」(A)石rsquo7『

5Ddeg30cm2sfdeg105Hz

c=087

Ursquo725J625_-52542

Ifwetakethesolutionsoftheone-dimensionaldiffusion

equationdφdxisgivenasfollows[241

O「

dφ

dx

助こ

Lω

2D

一 一 S

irfr

一万

(ωて≪1)

(ωT≫1)

(6-4)

(6-5)

Followingthethree-dimensionalsolution(eqs(6-l)(6-2)and

(6-3))asshowninFig6-3ydφdxincreasesproportionallyt07

intherangeofωてく05andreachestoacertainvalueoverthe

rangeofωて>5whichcanbeeχplainedqualitativelybyeqS

(6-4)and(6-5)respectivelyThedφdxvsTcurvesinFig6-3

canberepresentedbyonefunctionwiththecombinationofthe

approximatedsolutionsoftheone-dimensionaldiffusionequation

(eqs(6-4)and(6-5))Weshowanexampleinthecaseoff=105Hz

andD=30cm^secinFig6-4Thesolidlineisthethree-

dimensionalsolutionfromFig6-3andthedottedlines(A)and

(B)expresseqs(6-4)and(6-5)respectivelyThebrokenlines

(Arsquo)and(B゛)showtheasymptoticsolutionsofthethree-

dimensionalsolutionintherangesofωて<05andωて>5The

absolutevaluesof(A)and(Brsquo)becomeabout87Zofthoseof

(A)and(B)basedontheresultsofcalculationAsshownin

Fig6-4thethree-dimensionalsolutionisgivenbyacombination

ofthelines(Arsquo)and(Brsquo)andIsexpressedasfollows

-89-

「―」)畠一

uiMSaseudpazneaijoz

Fig6-5

rsquo0

ω^t「

NormalizedphaseshiftニLdφdxvSωてcurves

Solidlineisathree-dimensionalsolution

expressedbytheapproximatedone-dimensional

solutionswithempiricalcorrectionfactors

Brokenlineistheone-dimensionalsolution

-90-

2One-dimensionalノrsquosolution゛`4xrsquo

10バ

5acuteThree-dimensional

ぶacutesolution

2acute

(yl

言二分ヽ同r〔2μ(ldquoμ

゛1)rsquo1

5primeacute

cべ1251251cap25

dφ

dx

)=(c

TTfr TTf)ldquo゛十(c

yでワ

)rsquo゛

-91-

十1}3

(6-6)

(6-フ)

函rsquo

wherenisapositiveintegerWecalculatedeq(6-6)Inthe

casesofn=1へj5anddeterminednas31norderthatthe

solidcurveinFig6-4canbewellrepresentedbyeq(6-6)

Thevalueofc1Sthecorrectionfactorforthethree-dimensional

solutionandcisabout087asmentニionedabove

Fromeq(6-6)wecanderivethefollowingrelation

usingtheconventionaldiffusionlengthL

_

=pound石{2Σ(則2万

ThetermLdφdxisconsideredtobethenormalizedphaseshift

whichistheamountofthephaseshiftwhentheelectronbeam

scansoveronediffusionlengthItshouldbenotedthatLdφdx

isafunctニionofonlyωでFigure6-5showsthedependenceof

LdφdxonωてbythesolidlineIfthevaluesofLanddφdxare-

knownてcanbedeterminedfromthecurveforanymodulation

frequencyandDisalsoobtainedbytherelationofL=iF

Themodulationfrequencyfcanbechosenfreelyandthe

restrictionsofωΥ<050Γωて>5fortheapproximatIonneednot

tobetakenintoaccount

ThephaseshiftderivedbyMcKelvey[29]usingtheone-

dimensionaldiffusionequationisshownbythedashedlinein

Fig6-5Theestimatedvalueofωてbytheone-dimensional

solutionisabout76へ87Zofthatbythethree-dimensional

solutionforeveryvalueofLdφdxInthecaseoftheone-

dimensionalsolutionLisdetermineddirectlyfromthegradient

ofthelinearlydecreasingregionofEBICcurveandisabout

60へj80Zoftherealvaluefromtheresultsofthedetailanalysis

takingthesurfacerecombinationeffectintoaccount[14]

ThereforethevalueofωΥderivedbytheone-dimensionalsolution

isonly30へJ丁0Zoftherealvaluebecauseωてdecreases

proportionallytOLandL2intheregionsofLdφdxく03and

Ldφdx>2respectivelyOnemustusethethree-dimensional

solutioninordertodeterminetheaccuratevalueofて

6-3 ExperimentalresultsinSi

AconventionalSEMwasusedfortheprimaryelectron

beamwhichwasmodulatedat1rsquoj50kHzwiththedutyof05by

achoppingcoilinsertedintothebeampathThebeamcurrentwas

as10was10oline10AThemaximumminoritycarrierdensityinthis

experimentwasconsideredtobeabout3times1014Cmoline3andthe10w

injectionconditionwassatisfiedTheinducedcurrentwas

measuredbythevoltagedropacrosstheloadresistancewhich

wasconnectedtotheSchottkybarrierwithanohmiccontactThe

signalhadarectangularwaveformowingtothechoppedprimary

electronbeamandsothefundamentalfrequencycomponentinthe

Fourierseriesofthesignalwasdetectedbyanauto-phaselock-

inamplifierTheEBICnandthephaseshiftφfromthesource

wererecordedsimultaneously

ThediffusionlengthLisdeterminedinthecaseof

ωて<01takingthesurfacerecombinationeffectintoaccount

Thedependenceofnonxagreeswiththatニmeasuredbyaconventional

linescanmethodusingDCelectronbeamasdiscussedinsect6-2

-92-

Whenvaislowgivingtheshallowgenerationdepthsurface

recombinationhasalargeeffectonEBICWhenvaishigh

givingthedeepgenerationdepththesurfacerecombinationeffect

1SreducedTheaccuratevalueofLcouldbedeterminedbyfitting

experimentaldatatotheoreticalcurvesforboth10wandhighva゛S

(10and50kVrespectivelyInthiswork)asshownInsect3-3

Thevalueofdφdxisobtainedatanappropriate

modulationfrequencywhichsatisfiesωて>01AthighVthe

surfacerecombinationeffectIsreducedandsowechosetニhe

highestva(30kVinthiswork)asfarastheelectronbeamcould

bechoppedOncethevaluesofLanddφdxareknownthevalues

ofてandDcanbedeterminedfromthecurveinFig6-5

Sampleswerep-andn-typeSiwithtニheresistivitypof

10and01f2cmrespectivelyOhmiccontactsweremadeby

evaporatinggallium-dopedgoldandantimony-dopedgoldontothe

p-andn-typesamplesrespectivelySchottkycontactsweremade

byevaporatingaluminiumandgoldontothep-andn-typesamples

respectivelyinavacuumas10was10oline7TorrThesampleswere

insertedintoavacuumchamberforEBICmeasurementimmediately

aftertheywerecleaved

ThediffusionlengthLinp-typeSiwasdeterminedas

130μmfromthen-xcurvesinthecaseofωてく01The

experimentalresultsofthephaseshiftmethodareshownIn

Fig6-6bysolidlinesforf=5102030and50kHzrespectively

ThephaseshiftIncreaseswithxalmostlinearlyasdescribedin

sect6-2ThevaluesofてweredeterminedusingFig6-5as9595

8886and83ysfromthegradientsofthelinesinFig6-6

for5102030and50kHzrespectivelyTheobtainedvaluesof

てshowlittledifferencewitheachotherinanymeasurement

-93-

11

es^Md

Fig6-6

P-Si(r=10ncm)f=

20

1 0一

----n-Si(r=Q1ftcm)

Va=30kV

圭T

rdquo

------ニr二ご二二耳一一3

50100

Scanningdistance

150

Experimental

methodinp-(p=10

200

(μm)

resultsofthephaseshift

Ωcm)andn-type(p=01ncm)Si

-94-

rdquoolinersquordquooline`rsquolsquorsquoolinerdquordquoolinersquo50kHz

Vadeg30kVZ

10deg

30

FJ゛

一一20

〆がノrdquo〆〆〆

メノrdquo

〆〆〆〆〆ノ10

---rdquordquo|-sニニニldquo-notこ9

conditionfromωて=03(atf=5kHz)to30(atf=50kHz)

Itprovedthatthemodulationfrequencycouldbechosenfreelyas

mentionedinsect6-2Ifwetaketheaveragedvalueofて(ie

で89ys)thediffusionconstantDofelectronswasdeterminedas

19cra^secwhichalmostagreedwiththereportedvalue[301The

slightdeviationfromthestraightlineforf=50kHzmaycomefrom

unstablenessofthechoppedbeambecausethechoppingcoilused

inourexperimentwasnotdesignedforhighfrequencymodulation

above50kHz

Thediffusionlengthinn-SiwasobtainedasL=80ymand

thephaseshiftsareshowninFig6-6bybrokenlinesforf=3

10920and50kHzrespectivelyThedeterminedvaluesofてfrom

thegradientsofthelineswere889292and105usfor

fdeg3s1020and50kHzrespectivelyThevaluesofTalmost

equalwitheachotherasinthecaseofp-SiIfwetakethe

averagedvalueofT(ieで=94ps)tニhediffusionconstantD

ofholesbecomes7cm^secwhichalsoagreeswithtニhereported

value[301

Thegenerationdistributionisconsideredtobeasemi-

spheretheradiusofwhichisabout6ymatニvadeg30kVusingthe

Kanayarsquosmodel[28]Thedimensionsofgenerationdistribution

aresufficientlysmallincomparisonwiththediffusionlengthof

thesamplesThereforethepointsourceassumptioninthe

analysisisreasonable

-95-

6-4 Summary

Whentheintensitymodulatedelectronbeamisusedthe

phaseofinducedcurrent(EBIC)isshiftedfromthatofexcitation

sourcebecauseoftherecombinationinmaterialsWesolvedthe

three-dimensionaltime-dependentdiffusionequationtakingthe

surfacerecombinationeffectintoaccountandclarifiedthe

relationofてandthephaseshiftφtheoretically

Inthecaseofωて≧01φincreasesalmostlinearlywith-

Xovertherangeofx≧LThegradientdφdxbecomesafunction-

ofTandisnotaffectedbysurfacerecombinationTherelation

ofdφdxonてwasfoundtobeexpressedusingtheapproximated

solutionsoftheone-dimensionaldiffusionequatニionwithtニhe

empiricalcorrectionfactorsThenormalizedphaseshiftLdφdx

becomesafunctionofonlyωてIfthevaluesofLanddφdxare

knownてandDaredeterminedwiththeaidofLdφdxvsU3てcurve

withoutanyrestrictionformodulationfrequencyTheestimated

valueofてbytheone-dimensionalsolutionswithoutニthecorrection

factorsisonly30へノ70Zoftherealvaluederivedbythethree-

dimensionalsolution

Experimentalresultsinp-andn-typeSiSchottkydiodes

showedgoodagreementwiththetheoryandtheminoritycarrier

diffusionconstantsofelectronsandholesweredeterminedas

19and7cm^secrespectively

-96-

References

[11

[2]

[31

[4]

5]

6]

[10]

[11]

[12]

[13]

[14]

[15]

PDDapkusWHHackettJr0GLorimorandRZ

BachrachJApplPhys^54920(1974)

MBoulouandDBoisJApplPhysj旦4713(1977)

MEttenbergHKresselandSLGilbertJAppLPhys

44827(1973)

SWangrdquoSolid-stateElectronicsrdquo(McGraw一HillInc

1966)p300

WZimmermannphysstatsol(a)12671(1972)

DRHunterDHPaχmanMBurgessandGRBooker

rdquoScanningElectronMicroscopySystemsandApplications

1973rdquo(工nstPhysLondon)pp208-213

HKKuikenSolid-stateElectron19447(1976)-

AJakubowiczSolid-stateElectron22635(1980)

HTWeaverandRDNasbySolid-stateElectron

22687(1979)-

DLLileandNMDavisSolid-stateElectron

18699(1975)-

WvanRoosbroeckJApplPhys2plusmn380(1955)

WHHackettJr=JApplPhyspound1649(1972)

FBerzandHKKuikenSolid-stateElectron

19437(1976)

CvanOpdorpPhilipsResRept22192(1977)

DBWittryandDFKyserJApplPhys261387

(1965)

-97-

[16] CvanOpdorpRCPetersandMKlerkApplPhysLett

2h_125(1974)

[17]CJHwangJApplPhys4^4408(1971)

[18]

[19]

HReichlandHBerntSolid-stateElectron

18453(1975)

GSchwabHBerntandHReichlSolid-stateElectron

2091(1977)

[201JMiillerHBerntandHReichlSolid-stateElectron

21999(1978)

[211

[22]

JMiillerHReichlandHBerntSolid-stateElectron

22257(1979)

CMunakataandTEEverhartJpnJApplPhys

11913(1972)-

[23]SOthmerrdquoScanningElectronMicroscopy1978Vol1uml

(SEMIncOrsquoHare111)p727

[24] JDKaiiraiandHBerntSolid-stateElectron

21957(1978)-

【25】JDKammrdquoSemiconductorSilicon1977uml(The

ElectrochemicalSociety工nc)p491

[26] 0vonRoosSolid-stateElectron23177(1980)

[27]0vonRoosJApplPhys1^3738(1979)

[28]KKanayaandSOkayamaJPhysDApplPhys

543(1972)

[29]JpMckelveyrdquoSolidStateandSemiconductorPhysicsrdquo

(HarperandRowNewYork1966)pp439-440

[30]HFWolfrdquoSiliconSemiconductorDatardquo(Pergamon

PresslnC1969)

-98-

ⅥI

7-1

HEATTREATMENTEFFECTONDIFFUSIONLENGTHINS1

Introduction

Therehavebeenmanystudies[1]onthepropertiesofthe

processinducedfaults(PIFrsquos)Thedegradationoftheelectrical

performanceofthedeviceshasmuchconnectionwiththesegregated

impuritiesatPIFrsquosorthedecoratedfaultsofeachPIFRecently

thefaultproducedespeciallybytheoxidationathightemperatures

(IesocalledoxidationInducedstackingfault(OSF))has

receivedconsiderableattention[2-5]becausetheoxidationisa

fundamentalprocessinmakingLS工rsquosorcharge-coupleddevices(

CCDrsquos)Ravieta1[67]showedthattheelectricallyactive

OSF゛sincreasedtheleakagecurrentinprsquonjunctionsKimerllng[8]

determinedtheenergylevelofthefaultsfromtheelectron

beaminducedcurrent(EBIC)measurementsatvarioustemperatures

Generallythefaultsbecomerecombinationcentersanddecrease

thelifetimeandthediffusionlengthofminoritycarriers

Shimizu[9]showedthatthelifetimecouldbecontrolledpreferably

bytheintrinsicgetteringusingOSFrsquosRozgonyi[10]and

Tanikawa[11]reportedthattherelaxationtimeofMOScapacitors

decreasedasthedensityofOSFincreasedButtherehavebeen

alittlestudyonthequantitativeinformationofthedecreaseof

thediffusionlengthaftertheoxidationprocessathightemperatures

Inthischapterwemeasuredthechangesofthediffusion

lengthbyEBICmethodaftertheheattreatmentsathightemperature

andshowedthattheheattreatmentforafewminutescouldaffectthe

diffusionlengthatthesurfaceregionTheobservationofsurface

faultsbychemicaletchingwerealsoshown

-99-

(―)

<j)6udI

ColコこI()

Fig7-1

Heattreatmenttimet(min)

Diffusionlengthaftertheheattreatments

forvarioustimelengthsrangingfromlt0120minutesat1000degCOpenandsolidcirclesare

forthecasesindry02andArrespectivelyOriginaldiffusionlengthbeforeannealingis80pm

-100-

5ohellipumlindryO2

uml゜umlinArat1000degC

ol

12510251002

- W ゝ

rsquo _ l - ~ ヽ jS j - -

磨 卜

Fig7-2

(a)

(c)

rarr100Mm

ぶミ

卜`

r-^

rsquo

1Is

≪バ

rdquorsquo‐゛t

rsquo

grバ4≪

rsquo1

Surfacefaultsrevealedby

usingSirtletchantSamples(a)

wereannealedindryoat1000

and120minutesrespectively

-101-

い゛フバrdquo

゛para

`i

(b)

(d)

permilご}

->嗜

-゛

rsquo

III

`ヽご

いい

一J

t七

~貿で

rsquo

゛`1

鴫ヽ

rsquoq

-≪

ゝく

chemicaletching

(b)(c)and(d)

Cfor0830

一 一

- 一 一 -一 一

7-2

Experimentalresultsanddiscussions

Samplesaren-tニypeSigrownbyczmethodTheoriginal

resistivitybeforeannealingisaboutニ01ΩcmTheheattニreatment

wasdoneat1000degCintheflowofdry02andArrespectivelydeg

ThenthesampleswererinsedinHFforlmintoremovetheoxidized

layerandgoldwasevaporatedinordertomakeaSchottkybarrier

forEBICmeasurementsTheproceduresofthedeterminatニionofthe

diffusionlengthhavealreadybeendiscussedinChaptersmandでIV

Figure7-1showsthediffusionlengthaftertheheat

treatmentThetimetoftheheattreatmentwaschangedfromlto

120minutesTheopenandsolidcirclesareforthecaseIndryO2

andArrespectivelyTheoriginalvalueofdiffusionlengthis

80μmThediffusionlengthdecreasedtoabout7μmrapidlyas

tincreasedt05minandbecamealmostconstantovertherange

oft>5mlnThediffusionlengthdecreasedslightlymorerapidly

in02tニhaninArThelifetimechangedfrom5μsto003usif

thediffusionconstantofminoritycarrierswastakenasatypical

valueof125cmsecThesurfacefaultsofthesamplesannealed

indry02areSho゛linFigsdeg7-2(a)(b)(c)and(d)forlsquot゛

0830and120minrespectivelyThesampleswereetニchedby

SirtletchantforthesametimeThenumberoffaultsdidnotニ

increaseuntilt=8minbutbecameverylargeattdeg120min

ThesameresultwasobtainedforthesamplesannealedinAr

Itshouldbenotedthatthenumberoffaultsdidnotニchangedinthe

rangeofO≦t≦8minbutthediffusionlengthdecreasedrapidly--

inthesamerangeThelengthsbetweenthefaultsareverylarge

incomparisonwiththediffusionlengthinthesamplesannealed

for1くtく8minandsothediffusionlengthisconsidered

nottoberestrictedbytheaverageintervalbetweenthefaults

whenthefaultsareconsideredtobethecarriersink

-102-

TheuniformEBICwasobtainedwhentheelectニronbeamwasscanned

onthesurfacethroughtheSchottkybarrtersandthedarkpoints

correspondingtothefaultswerenotobserved

Therapiddecreaseofthediffusionlengthwasconsidered

tobecausedbytheformatonofnucleioffaultsattheearly

stageoftheheattreatmentTheverysmallnucleicanbecomethe

recombinationcenterseveniftheycannotberevealedbychemical

etchingIftheheattreatmenttimeissufficientlylongthe

nucleibecomelargeandcanberevealedbyetchingAsshownin

Fig7-2(d)thelengthbetweenthefaultsafterlongtimeheat

treatmentisthesameorderofthediffusionlengthTheformation

ofnucleiwasnotaffectedverymuchbytheoxidationbecausethe

decreaseofthediffusionlengthwasalsoobservedintheheat

treatmentinArAsisknowngenerallytheczgrownSIcontains

oversaturatedoxygenandtheformationofnucleiisrelatedtニO

theoxygenprecipitation[12]Thediffusionlengthdecreasedless

rapidlyinArthaninO2degOnereasonofthisphenomenonisconsidered

tobetheformationofSiOAnotherreasonistheoutdiffusion

ofoxygenbecauseoxygencanoutdiffusemorerapidlyinArthan

inO2degFurtherinvestigationmustbeneededfortheclarification

ofthenucleiformation

Inconclusionthediffusionlengthatthesurfaceregion

inSidecreasedtoabout10Zoftheoriginalvalueafterthevery

shortheattreatmentat1000degCforafewminutesNevertheless

thesurfacefaultsrevealedbychemicaletchingdidnotchange

Thenucleioffaultswereconsideredtobeformedattheearly

stageofheattreatmentandtheybecameminoritycarrier

recombinationcentersThedecreaseofthediffusionlengthwasnot

soaffectedbytheambientgases(ieoxygenorinertone)Much

attentionmustbepayedintheheattreatmentprocessathigh

temperatureevenifthetimeIsveryshort

-103-

i J I

References

[1]

21

31

71

81

[91

[10]

[n]

[12]

HFoilNGoreleandB0KolbesetirdquoSemiconductor

Silicon1977rdquo(JElectrochemicalSocietyInc

Prircetion1977)pp565-574

DJDThomasphysstatso1旦2261(1963)

CMMelliar-SmithrdquoCrystalcefectsinsiliconintegratニed

circuits-TheircauseandeffectrdquoinrdquoTreatieson

MaterialScienceandTechnologyrdquovol11(AcademicPress

NewYork1977)

KVRaviandCJVarkerJApplPhys45263(1974)

SMHuJApplPhys513666(1980)

KVRaviCJVarkerandCEVolk

JElectrochemSoc120533(1973)-

CJVarkerandKVRaviJApplPhys亘272(1974)

LCKlmerlingHJLeamyandJRPatel

ApplPhysLett30217(1977)

HShimizuAYoshinakaandYSuglta

JpnJApplPhys17767(1978)

GARozgonyiandRAKushner

JElectrochemSoc123570(1976)-

KTanikawaYItoandHSei

ApplPhysLett28285(1976)

JRPatelrdquoSemiconductorSilicon1977rdquo(The

ElectrochemicalSocietyIncPrinceton1977)

pp521-545

-104-

ⅧI CONCLUSIONS

InthepresentstudyEBICwasanalyzedquantitativelyby

solvingthesteady-stateortime-dependentthree-dimensional

diffusionequationsTheinfluenceofthefinitegenerationvolume

onEBICwasdiscussedandanImprovedmethodtocharacterize

thephysicalpropertiesinthesmallselectedareasofsemiconduc-

torswassuggestedTheobtニainedresultswereasfollows

InChapterHtheshortdiffusionlengthoftheorderof

ymcouldbedeterminedbythenormalincidencemethodofEBIC

Variousmodelsforgenerationdistributionusedintheanalysis

yieldedtheambiguityforthedeterminationofthediffusionlength

andtheelectron-holepaircreationenergybyanelectronbeam

Detailedinformationonthegenerationdistributionmustbe

necessarytoanalyzeEBICaccurately

InChaptニermthegenerationvolumeofminoritycarriers

hadrsquoaconsiderableeffectonEBICinthelinescanmethod

especiallywhenthedimensionsofthegenerationvolumewasequal

toorlargerthanthediffusionlengthWhentheaccelerating

voltagewaslowandsothegenerationdepthwasshallow

surfacerecombinationhadalargeeffectonEBICWhereaswhen

theacceleratingvoltagewashighandsothegenerationdepth

wasaslargeasthediffusionlengthsurfacerecombinationhad

aslighteffectonEBICTheaccuratevaluesofphysicalparameters

suchasthediffusionlengthshouldbedeterminedbyfittingthe

experimentaldatatothetニheoreticalcurvesforalltheaccelerating

voltagesTheexistenceofamaximuminEBICnearthebarriercould

beexplainedbythersquoedgeeffectrsquoattributedtothefinite

generationvolume

-105-

InChapter】5inthelinescanmethodthedependence

ofEBIConthescanningdistancerepresentedmainlythelateral

extentofthegenerationdistributionwhentheacceleratingvoltage

washighandwhenthedimensionsofthegeneratニionregionwere

largerthanthediffusionlengthThethree-dimensionalgeneration

distributionbasedupontheexperimentalresultsforthenormal

incidencecouldexplaintheexperimentalresultsofthelinescan

methodInGaAsthecenterofthegeneratニionregionwaslocated

atthepointof0130fthemaximumelectronrangeandthe

radialdistributionfromthecentニerwasshowntobeGaussianwith

anexponentニof54Q82Thevaluesof38へj44eVfortheelectron-

holepaircreationenergybyanelectronbeamwasobtainedtaking

thesurfacerecombinationeffectintニoaccount

InChapterVinthelinescanmethodtheminoritycarrier

distributionwasaffectedverymuchbyanohmiccontactwhenthe

lengthwbetweenthepotentialbarrierandtheohmiccontactwas

lessthanoneortwodiffusionlengthsTheslopeofthecurveof

EBICvsscanningdistancedidnotchangeevenwhentニhediffusion

lengthvariedandthediffusionlengthcouldnotbedetermined

definitelyfromtheslopeofthecurveTheabsolutevalueof

EBICwasdependentonthesurfacerecombinatニionvelocityand

thelengthW

InChapterⅥ[thephaseshiftbetweenthemodulated

electronbeamandEBICwasclarifiedbysolvingthethree-

dimensionaltime-dependentdiffusionequationTherelation

betweenthephaseshiftandthelifetimewasfoundtobeexpressed

usingtheapproximatedsolutionsoftheone-dimensionaldiffusion

equationwithempiricalcorrectionfactorsThelifetimeandthe

diffusionconstantofminoritycarrierscouldbedetermined

definitelywithoutanyrestrictionformodulationfrequency

-106-

InChapterVIIthediffusionlengthinthesurfaceregion

ofSiwasfoundtobedecreasedverymuchafterheattreatment

at1000degCforonlyafewminutesneverthelesssurfacefaults

revealedbychemicaletchingwerenotincreasedThenuclei

ofthefaultsmightbeformedattheearlystageofheattreatment

ThisinvestigationprovedthatEBICcouldbeanalyzed

quantitativelyinthesmallselectedareaconsideringthethree-

dimensionalgenerationdistributionbyanelectronbeamBut

thereexistsomepointstobestudiedfurtherasfollows

FirstbyEBICmethodthetotニalrecombinationlifetimeincluding

bothradiativeandnon-radiativeprocessescanbemeasuredBut

onecannotobservetheradiativerecombinatニionlifetimealone

whichIstheimportantparametニertocharacterizethellght-emittニing

diodesorlaserdiodes[1]Deeperunderstandingcanbeacquired

byinvestigatingtheluminescenceemitニtedbyrecombinationof

generatedelectron-holepairs(iecathodoluminescence)[23]

SecondlyEBICtechniquecannotrevealtheenergylevelsand

densitiesofimpuritiesandtrapsaccuratelywhichaffectthe

electricalpropertiesofmaterialsverymuchTherehavebeena

fewreports[4]todeterminetheenergylevelsoffaultsinSi

fromEBICmeasurementsatvarioustemperaturesButthe

experimentalaccuracyofEBICtニechnlqueisinferiortothat

ofthephotoluminescence[5]orthecapacitance[67]methods

Thirdly万thedoseofhighenergyelectronbeldquo万171万causesdamagesin

samplesSeveralinvestigationshaveshownthedecreaseoftニhe

tニhresholdvoltageinMOSdevices[8]andtheincreaseofthe

interfacestatedensitybetweentheoxideandthesemiconductors[9]

-107-

Improvementsofmeasurementtechniques(ieuseofthe10W

energyprimaryelectronbeam万orlthedecreaseoftニhetotal

amountofdose)wirsquollbenecessary

Electricalpropertiesofsemiconductorscanbecharacterized

collectivelybyEBICjointlywiththeothertechniqueswhich

complementtheweakpointsinEBICmethod

REFERENCES

[1]

[21

[5]

[6]

[7]

[8]

[9]

PDDapkusWHHackettJr0GLorimorandRZ

BachrachJApplPhys45

4920(1974)

DBHoltandBDChasephysstatS01(a)旦旦

135(1973)

MBoulouandDBoisJApplPhys 484713(1977)

LCKimerlingHJLeamyandJRPatel

ApplPhysLett30217(1977)

HBarryBebbandEWWilliamsrdquoSemiconductorsand

Semimetalsrdquo(edRKWillardsonandACBeer

AcademicPress1972)vol8pp182-392

SMSzerdquoPhysicsofSemiconductorDevicesrdquo(JohnWiley

SonsInc1969)

DVLangJApplPhys453023(1974)

WJKeeryK0LeedyandKFGallowayrdquoScanning

ElectronMicroscopy1976rdquo[IITR]Chicago)pp507-514

RHezelSolid-stateElectron11^

735(1979)

-108-

4i

rsquoII

LISTOFPUBLICAT工ONS

[1]

[21

[3]

[4]

[5]

[6]

Papers

Theinfluenceofthegenerationvolumeofminoritycarriers

onEBICrdquo

TFuyukiHMatsunamiandTTanaka

JPhysDApplPhys131093-1100(1980)

rdquoAnalysisofEB工CconsideringthegeneratニIondistribution

ofminoritycarriersrdquo

TFuyukiHMatsunamiandTTanaka

JPhysDApplPhys131503-1510(1980)

rdquoDeterminationoflifetimeanddiffusionconstantof

minoritycarriersbyaphaseshifttechniqueusing

electronbeaminducedcurrentrdquo

TFuyukiandHMatsunami

JApplPhys旦(1981)

rdquoAnalysisofelectronbeaminducedcurrentconsidering

sampledimensions一一-Measurementofdiffusionlength

andsurfacerecombinationvelocity-rdquo

TFuyukiandHMatsunami

JpnJApplPhys20(1981)No4

rdquoInfluenceofminoritycarriergenerationdistributionon

electronbeaminducedcurrentinthenormalincidencemethodrdquo

TFuyukiandHMatsunami

(tobepublished)

rdquoHeattreatmenteffectondiffusionlengthinSirdquo

TFuyukiandHMatsunami

(tobepublished)

-109-

[1]

[21

[3]

PublicationsintheInstituteofElectronicsandCommunication

EngineersofJapan

(inJapanese)

rdquoMeasurementofminoritycarrierdiffusionlengthby

EBICmethodrdquo

TFuyukiHMatsunamiandTTanaka

ReptTechSSD78-102(Feb1979)

rdquoCharacterizationofdiffusionlengthandlifetimebyEBICrdquo

TFuyukiandHMatsunami

ReptTechSSD79-103(Feb1980)

rdquoMeasurementoflifetimeanddiffusionconstantofminority

carriersbyphaseshifttechniqueinEBICrdquo

TFuyukiandHMatsunami

TransSectionJ63-C832-837(1980)

-110-

  • page1
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  • page119
  • page120
Page 2: CHARACTERIZATION OF SEMICONDUCTORS BY Title ELECTRON …

いvl}丿

CHARACTERIZATIONOFSEMICONDUCTORS

BY

ELECTRONBEAMINDUCEDCURRENT

BY

TAKASHIFUYUKI

JANUARY1981

DEPARTMENTOFELECTRONICS

KYOTOUNIVERSITY

KYOTOJAPAN

犬CHARACTERIZATIONOFSEMICONDUCTORS

IBY

ELECTRONBEAMINDUCEDCURRENT

BY

TAKASHIFUYUKI

JANUARY1981

DOC

1981

電気系

DEPARTMENTOFELECTRONICS

KYOTOUNIVERSITY

KYOTOJAPAN

1 一 心

ABSTRACT

-Theelectronbeaminducedcurrent(EBIC)wasanalyzed

quantitativelyconsideringthethree-dimensionalgeneration

distributionbyanelectronbeamThesolutionsofthesteady-

stateortime-dependentdiffusionequationsassumingapoint

sourcecanbeappliedtothecaseofthefinitegeneration

distributionbythedividingmethodTheEBICwasfoundtobe

affectedverymuchbythegenerationdistニributiontheextentof

whichwascomparablewiththeminoritycarrierdiffusionlength

InthelinescanmethodthedependenceofEBIConthescanning

distancerepresentsmainlythelateralextentofthegeneration

distributionThethree-dimensionalgenerationdistributionvas

clarifiedcombiningthenormalIncidenceandthelinescanmethods

ofEBICTheImprovedmethodtomeasurethediffusionlength

andthesurfacerecombinationvelocitywassuggested

Theminoritycarrierdistributionisinfluencedverymuch

bythesampledimensionswhentheyareequaltoorsmallerthan

thediffusionlengthTheEBICwasanalyzedbyasimplemethod

usinganimagesource-and-sinkdistributionTheEBICwasfound

tobedependentonthesurfacerecombinationvelocityand

thesampledimensionsratherthanthediffusionlength

Thelifetimeandthediffusionconstantofminority

carrierscouldbedetermineddefinitelywithoutanyrestriction

ofmodulationfrequencybythephaseshifttechniqueusingEBIC

Theimprovedmethodtomeasurethediffusionlength

wasappliedtotheheattreatmenteffectinSiThediffusion

lengthwasfoundtobedecreasedverymuchaftertheheat

treatmentat1000degCforonlyafewminutes

-1-

Thephysicalpropertiessuchasthediffusionlengthin

thesmallselectedareascouldbecharacterizedbyEBIC

consideringthethree-dinensionalgenerationdistributionbyan

electronbeamandthesampledimensionsExperimentalresults

inSiandGaAsshowedgoodagreementwiththetheoryandthe

generationdistributionsinSiandGaAswererevealedWitニh

experiments

一旦-

hellipJVi_--Wrsquordquo>>-trsquomjrsquordquordquo^>-≫^

f1

ACKNOWLEDGEMENTS

Theauthorwishestoexi】resshisdeepgratitudetoformer

jブProfessorTetsuroTanakaforhiscontinuingguidanceandワバandrrsquoI

helliphellipノ1encouragementTheauthorwishestoexpresshis9万ざlltや1appreciation

toAssociateProfessorHiroyukiMatsuna万万mlforhispreciousguidance

andhelpfuladvicethroughouttニhepresentstudyTheauthor

acknowledgesProfessorAkiraKawabataforhisgenialguidanceand

encouragementTheauthorisgがIattilltoProfessorToshinoriTakagi

forhisstimulatingdiscussionsandusefulcriticismsonthemanuscript

TheauthorwouldalsoliketothankProfessorAkioSasakifora

criticalreadingofthemanuscriptandvaluablecomments

MuchattentionisduetoDrJuniiSaraieDrShigehiro

NishinoandDrAkiraSuzukifortheircontinuousencouragement

andstimulativediscussions

TheauthorthanksothermembersofSemiconductorLaboratory

fortheirconsiderableassistanceandexperimentalfacilities

一斑-

CONTENTS

ABSTRACT

ACKNOWLEDGEMENTS

L工STOFSYMBOLS

INTRODUCTION

References

i一m

VL

lVO

INFLUENCEOFMINORITYCARRIERGENERATIONDISTR工BUTION13

0NELECTRONBEAMINDUCEDCURRENTINTHENORMALINCIDENCE

METHOD

2-1

2-2

2-3

Introduction

Determinationofdiffusionlengthandelectron-

holepaircreationenergy

ExperimentalresultsinGaAs

2-4Summary

References

13

15

VOON

CMCM

30

DETERMINATIONOFDIFFUSIONLENGTHSURFACERECOMBINATION31

VELOCITYANDELECTRON-HOLEPAIRCREAT工ONENERGYBYTHE

LINESCANMETHOD

3-1Introduction31

3-2Surfacerecombinationeffectconsideringpoint33

source

3-3Analysisofelectronbeaminducedcurrenttaking37

tニhree-dimensionalgenerationdistributioninto

account

3-4ExperimentalresultsinSi

3-5Summary

References

一分-

`j7

44

48

】V

V江

ⅧI

ANALYSISOFTHREE-DIMENSIONALGENERATIONDISTRIBUTION50

BYTHECOMBINATIONOFTHENORMALINCIDENCEANDTHE

L工NESCANMETHODS

4-1Introduction

4-2 Influenceofthree-dimensionalgeneration

distributiononelectronbeaminducedcurrent

02

inin

4-3Three-dimensionalgenerationdistributioninGaAs57

4-4Summary

References

12

vOVD

ANALYSISOFELECTRONBEAMINDUCEDCURRENTCONSIDERING64

SAMPLEDIMENSIONS

5-1Introduction

5-2

5-3

Determinationofdiffusionlengthandsurface

recombinationvelocity

ApplicationtoSi

5-4Summary

References

Appendix

DETERMINATIONOFLIFETIMEANDDIFFUSIONCONSTANT

BYPHASESHIFTTECHNIQUE

6-1Introduction

6-2Relationbetweenlifetimeandphaseshift

6-3ExperimentalresultsinSi

6-4Summary

References

HEATTREATMENTEFFECTONDIFFUSIONLENGTHINS1

7-1Introduction

7-2Experimentalresultsanddiscussions

References

CONCLUS工ONS

References

LISTOFPUBLICATIONS

4vO

CVD

73

78

9VO>

77

81

lro

88

CNJVO

qNas

7O

O^(J

99

102

104

105

108

109

-V-

LISTOFSYMBOLS

Cl

cBC

ggpgBELOS嚢

cdDDeEfgGIIIIIlj一jJ

J大

correctionfactorwithwhichthethree-dimensionalsolutions

oftheヽgradientofphaseshiftcanbeexpressedbytheone-

dimensionalapproximations

exponentofGaussiandistribution

positionofgenerationsourcefromthesurfacealongthedepth

diffusionconstantofminoritycarriers

(equivdgL)normalizedgenerationdepth

chargeofanelectronz

electron-holepaircreationenergybyanelectronbeam

modulationfrequencyofprimaryelectronbeam

generationrateofactualpointsource

variablepartofgenerationsource

thewholegenerationstrengthinthegenerationregion

Imaginaryunit

primaryelectronbeamcurrent

measuredelectronbeaminducedcurrent

currentwhichflowsthroughtheloadresistance

backwardsaturationcurrent

shortcircuitcurrent

electronbeaminducedcurrent

variablepartofcomplexelectronbeaminducedcurrent

(≒n)normalizedelectronbeaminducedcurrentitbecomes

unitywhenallthegeneratedcarrierscontributeto

electニronbeaminducedcurrent

normalizedelectronbeaminducedcurrentconsideringthe

Influenceofohmiccontact

一吐-

誉~Lay

L大eff

p卵`μrRRCReRmSStTuva

correctionfactorfortheincidentbeamenergyconsidering

theenergylossduetobackscatteredelectrons

thermalvoltagersquo259mVatroomtemperature

second-modifiedfirst-orderBesselfunction

diffusionlengthofminoritycarriers

diffusionlengthestimateddirectlyfromtheslopeof

electronbeaminducedcurrentvsscanningdistancecurve

diffusionlengthestimateddirectlyfromtheslopeof

electronbeaminducedcurrentvsscanningdistancecurve

consideringtheinfluenceofohmiccontact

(ΞLJ百石iT)complexeffectivediffusionlength

distニributionofminoritニycarrierdensity

distributionofminoritycarrierdensityconsideringthe

influenceofohmiccontニact

variablepartofthedistributionofminoritycarrier

densitycomplexvariable

distancebetweenthecenteroftニhegenerationregionand

eachdividedsegment

radiusofgenerationregion

centerofgenerationregion

extraporatedelectronrange

loadresistance

maximumelectronrange

surfacerecombinationvelocity

(ΞS(Lて))surfacerecombinationvelocityparameter

time

variableforintegrat10n

para万7rdquo万eterforGaussiandistribution

acceleratingvoltageofprimaryelectronbeam

一吐-

rdquod

wm

Xxx

χy

ZZ

np

Pau

^GaAs

SpてφΦω

distancebetweenthepotentialbarrierandtheohmiccontact

depletionlayerwidth

metalthicknessofSchottkydiode

Cartesianco-ordinateofscanningdistance

(ΞxL)

distancebetweenthepotentialbarrierandthegeneration

pointalongthescanningdirection

(ΞL)

Cartesianco-ordinateonthescanningsurfacenormalto

thescanningdirection

Cartesianco-ordinatealongthedepth

peakoftheGaussiandistribution<

(=J)collectionefficiency

collectionefficiencyofthevariablepartニofthegeneration

source

resistivityofsemiconductors

massdensityofAu゜189gcm^

massdensityofGaAs゜53gcm^

massdensityofSi=23gcm^

minoritycarrierlifetime

phaseshiftbetweentheelectronbeaminducedcurrentand

tニhemodulatedgenerationsource

diameterofprimaryelectronbeam

angularfrequencyofmodulatedprimaryelectronbeam

-VnL-

IINTRODUCT工ON

Theremarkableprogressinthesolidstatedevicesisowing

totheadvancementinthecharacterizationtechniqueofthedevice

materialsWhenthedeviceshavingnewfunctionsaredevelopedthe

detailknowledgeofthephysicalpropertiesofthesemiconducting

material(bandgaplifetimeandmobilityofcarriersetc)mustbe

neededInparticularthosepropertiesmustbecharacterizedafter

theactualmanufacturingprocessbecausetheoriginalpropertiesmay

beaffectニedbythevariousprocessconditions

Inrecentyearstocharacterizeverysmalldevices(ie

LSI゛sorlaserdiodes)therehasbeenagrowinginteresttousea

finelyfocusedelectronbeamThetwodimensionalInformationofthe

materialpropertiescanbeobtainednon-destructivelywithhigh

spatialresolutionfromtheelectronbeamInteractionwithsamples

[121Surfacemorphologycanbeobservedwithgreatニdepthoffocus

byascanningelectronmicroscope(SEM)Crystaldefectsinthin

samplesaredetectedusingascanningelectrontransmission

microscope(STEM)[34]AscanningAugerelectronmicroscope(SAM)

[5]hasbecomeaveryusefultooltoanalyzethesurfaceandthe

interfaceregion

Themethodusinganelectronbeaminducedcurrent(EBIC)[6-10]

1saveryconvenienttechniquetodeterminethefundamentalparameters

(egthediffusionlengththelifetimeandthesurfacerecombination

velocityofminoritycarriers)whichcontroltheelectricalperfor-

manceofthedevicesTheelectron-holepairsgeneratedbyanelectron

beamareseperatedbytheinternalfieldInp-njunctionsorSchottky

barriersandthecurrent1SInducedIntheexternalcircuitThe

EBICdependsverymuchondiffusionandrecombinationofminority

carriersInsemiconductorsandthediffusionlengthetccanbe

-1-

Fig1-1

type

type

Primaryelectrbe≪m

^^trrttDepletionlayer

Electron-hotep弗i「6gerwrationregion

Primaryelectronbeam

rArrScanningdirection

(A)

(B)

Principalconfigurationstomeasurethe

electronbeaminducedcurrent(EBIC)

(A)normalincidencemethod

(B)linescanmethod

-2-

く二rArr|t夕

EBICく二rArr

-一一--

p-typentype

aver`

1ミミ二l∽rsquoebic

determinedfromtheanalysisofEBICInadditiontothetwodlmen-

sionalinformationofthediffusionlengthandthelifetimetheir

variationsalongthedeptニhcanbeobtainedforvariousgeneration

depthsbychangingtheacceleratingvoltageofanelectronbeam

TheprincipalconfigurationstomeasureEBICarethersquonormal

incidencemethodrsquoandthersquolinescanmethodrsquo(seeFig1-1)Inthe

normalincidencemethodtheelectronbeam1Sincidentnormaltothe

barrierplaneandisscannedonthesurfaceparalleltothatplane

ThedislocationsanddefectsinSiwereobservedinp-njunctionsand

Schottkybarrierdiodes[11-28]Inrecentyearselectricalactivity

ofoxidationinducedstackingfaults(OSF゛s)anditsrelationwith

deviceperformanceshavebeenstudied[29-35]Thenormalincidence

methodisalsousedforthefailureanalysisoftニheMOSdevices[36-

39]Usingthelinescanmethodthediffusionlengthandthesurface

recombinatニionvelocitycanbedeterminedfromthedependenceofEBIC

onthescanningdistancewhentheelectronbeamisscannedacrossthe

barrierTherehavebeenmanytheoretical[AO-46]andexperimental

[47-69]reportstomeasurethediffusionlengthandthesurface

recombinationvelocityinlight-emittingdiodes(LEDrsquos)andlaser

diodes

InalmostalltheworkssofarEB工Chasbeenanalyzedonly

qualitatively0rsemi-quantitativelyThediffusionlengthandthe

surfacerecombinationvelocityhavebeendeterminedunderrather

specialconditionsasmentionedbelowforthesimpletheoretical

calculationInthenormalincidencemethodtheyconsideredonly

theone-dimensionalgenerationdistributionalongthedepth[70-75]

undertheconfigurationthatthelateralextentofthegeneration

volumewasverysmallcomparedwithsampleareasInthelinescan

methodthegenerationvolumewasassumedtobeapoint[53546061]

undertheconditionthatthegenerationvolumewassufficiently

-3-

smallerthanthediffusionlengthandthesampledimensionsBut

intheactualcasethegenerationvolumehasafinitethree-

dimensionalextentreLatedtotheacceleratingvoltage[76-78]

Thelatestmicroelectronicdevices(ieLSIrsquosandthelaserdiodes

etc)havethesamedimensionsasthegenerationvolumeandS0

theanalysesconsideringtニhepointsourceortheone-dimensional

generationdistributニionareinaccuratetodeterminethediffusion

lengthandthesurfacerecombinationvelocityThenewmethodfor

thequantitativeanalysisofEBICmustbedevelopedtakingthethree-

dimensionalgenerationdistributionandtheinfluencesofthesample

dimensionsintoaccount[7980]

InthepresentstudyEBICisanalyzedquantitativelyby

solvingthesteady-stateortime-dependenttニhree-dimensionaldiffusion

equationsTheinfluenceofthefinitegenerationvolumeonEBICis

discussedwhentheextentofthegenerationvolumecannotbeignored

andimprovedmetニhodsaresuggestedtomeasurethephysicalproperties

(diffusionlengthlifetimeandsurfacerecombinationvelocityof

minoritycarrierselectron-holepaircreationenergybyanelectron

beametc)inthesmallselectニedareas

InChapternvariousmodelsforthegeneratニiondistribution

alongthedepth[7781-83]arecomparedwitheachotherandtニhe

influenceofthegenerationdistributiononthedeterminationofthe

diffusionlengthbythenormalincidencemethodisdiscussed

ChapterⅡIshowstheinfluenceofthegenerationvolumeon

EB工Cinthelinescanmethodtakingtニhesurfacerecombinationeffect

intoaccountAnimprovedmethodforthedeterminationofthe

diffusionlengthandthesurfacerecombinationvelocityisdescribed

-4-

InChapterVthree-dimensionalgenerationdistribution

isclarifiedbymeasuringEBICusingboththenormalincidenceand

thelinescanmethodsinthesamesamplewhichyieldsthe

quantitativeanalysisofEB工C

ChaptervdescribestheInfluenceofthesampledimensions

onEBICInthelinescanmethodEBICisInvestigatedbyextending

themirrorimagemethodlsquo[41-43]whenthediffusionlengthisof

theorderofthesampledimensions

InChapterWthephaseshifttechniqueinthemeasurement

ofEBIC[84-86]isdescribedTherelationbetweenthelifetime

andthephaseshiftisclarifiedbysolvingthethree-dimensional

time-dependentdiffusionequationThelifetimeandtニhediffusion

constantofminoritycarrierscanbedeterminedcombiningthe

phaseshifttechniquewiththeconventionallinescanmethod

Chaptervnshowstheheattreatmenteffectonthediffusion

lengthinSi

FinallyconclusionsandsuggestionsforfurtherInvestigation

aresummarizedinChaptervnr

ExperimentalresultsinSiandGaAsareshovmineverychapter

Themethoddiscussedinthesechapterscanbeappliedeasilyto

anysemiconductormaterialsbyconsideringthephysicalproperties

inherentinthematerials

-5-

References

[1

[21

[3]

4]

5]

6]

[7]

[8]

[9]

[10]

VEJohnson十Sm119151p763

0CWellsSEM1972p375

pMrdquoPetroffDVLangJLStrudelandRALogan

SEM71978pp325-332

CELymanSEM1978pp529-536

NCMcDonaldSEM1971p89

DBHoltrdquoQuantitativeScanningElectronMicroscopyrdquo

(DBHolteta1edsAcademicPress974)pp213-286

DBWittryrdquoMicroprobeAnalysisrdquo(CAAndersoned

JohnWileySonsNewYork1973)pp123-187

CJVarkerrdquoNondestructiveEvaluationofSemiconductor

MaterialsandDevicesrdquo(edJayNZemelNATOADVANCED

STUDYINST工TUTESSERIESSERIESBPhysicsvol46

PLENUMPRESS1979)pp515-580

HJLeamyLCKimerlingandSDFerris

SEM1978pp717-725

ThebibliographyonEBICislistedinthefollowing

K0LeedySolidStateTechnologyFeb1977pp45-48

--

-- - -

rdquo-

rdquo- - 言

争心- -

SEM19xxrdquoScanningElectronMicroscopyrdquoProceedingofAnnualConference

before1977(IITResearchInstituteChicago)

after1978(SEMIncAMFOrsquoHare)

-6-

[11]JJLanderHSchrelberJrTMBuckandJRMathews

ApplPhysLett旦206-207(1963)

[12]WCzajaandGHWheatleyJApplPhys亜

2782-2783(1964)

[13] WCzajaandJRPatelJApplPhys11476-1482

(L965)

[14]NFBNeveandPRThorntonSolid-stateElectron

旦900-901(1966)

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

IGDaviesKAHughesDVSulwayandPRThornton

Solid-stateElectron9275-279(1966)-

WCzajaJApplPhysyi918-919(1966)

DVSulwayPRThorntonandMJTurner

Soli-StateElectron11567-568C1968)-

AJRKockSDFerrisLCKimerlingandHJLeamy

ApplPhysLett27313-315(1975)

DBHoltandROgdenSolid-stateElectron1937-40(1976)-

HJLeamyLCKimerlingandSDFerris

SEM1976pp529-538

TKatoTMatsukawaandRShlmizu

ApplPhysLett26415-416(1975)

RBMarcusMRobinsonTTShengSEHaszkoand

SPMurarkaJElectrochemSOC124425-430(1977)

LCKimerlingHJLeamyandJRPatel

ApplPhysLett30217-219(1977)

DEIoannouandSMDavidson

physstatsol(a)丘旦K1-K4(1978)

-7-

[25]

[26]

HBlumtrittRGlelchmannJHeydenderichandH

Johansenphysstatsol(a)55611-620(1979)

HMennigerHRaidtandRGleichmann

physstat-sol(a)5旦173-180(1980)

[27]pAshburnandCJBullSolid-stateElectron

Tl_105-110(1979)

[28] pAshburnCJBullandJRABeale

JApplPhys503472-3477(1979)

[29]KVRaviCJVarkerandCEVolk

JElectrochemSoc120533-541(1973)-

[30]

【31】

[32]

[33]

[34]

[35]

[36]

[37]

[38]

[39]

[40]

CJVarkerandKVRaviJApplPhys45272-287(1974)

SKawadoYHayafujiandTAdachi

JpnJApplPhys14407-408(1975)

TESeidelSEHaszkoandDMMaher

JApplPhys485038-5042(1977)

AMurgaiJYChiandHCGatos

JElectrochemSoc1271182-1186(1980)-

SKawadqJpnJApplPhys191591-1602(1980)

JMDishmanSEHaszkoRBMarcusSPMurarka

andTTShengJApplPhys502689-2696(1979)

JLGatesand0KGriffith

ApplPhysLett27kZ-45(1975)

JFKatalanoSEM71976pp521-528

PRoltmanandWRBottomsSEM1977pp731-738

CLWilsonSolid-stateElectron23345-356(1980)-

WHHackettJrJApplPhys431649-1654(1972)

-8-

[41]

[42]

[431

[44]

[45]

【46】

[47]

[48]

[49]

[50]

FBerzandHKKuikenSolid-stateElectron

19437-445(1976)

CvanOpdorpPhilipsResKept32^192-249(1977)

0vonRoosSolid-stateElectron互lsquo1063-1067(1978)

0vonRoosSolid-StateElectron211069-1077(1978)

0vonRoosSolid-stateElectron22113-114and773-778-

(1979)

WvanRoosbroeckJApplPhys旦D380-391(1955)

DBWittryandDFKyserJApplPhysj11387-1389

(1965)

HHiguchiandHTamura

JpnJApplPhys4^

316-317(1965)

YuPDemidovRPGurovaYuMKushnirAIFrltner

andDVFetisovSovPhys-Semicond1030-1035(1968)

KMaedaAKasamiMToyamaandNWakamatsu

JpnJApplPhys旦65-75(1969)

[51]ZhIAlferovVMAndreevVIKorolrsquokovand

vIStreminSovPhys-Semicond41113-1116(1971)

[52]

[53]

[54]

[551

CJHwangSEHaszkoandAABergh

JApplPhys425117-5119(1971)

WHHackettJrRHSaulRWDiχonandGWKammlott

JApplPhys432857-2868(1972)

WZimmermannphysstatsol(a)^2671-678(1972)

MAvenJZDevineRBBolonandGWLudwlg

JApplPhys434136-4142(1972)

-9-

[56]

[57]

[58]

[59]

【60】

[61]

[62]

[63]

[64]

[65]

[66]

GLidgardSolid-stateElectron15159-164(1972)

DBHoltBDChaseandMCenslive

physstatsol(a)20459-467(1973)-

DBHoltandBDChasephysstatsol(a)2(

135-144(1973)

CvanOpdorpRCPetersandMKlerk

ApplPhysLett24125-126(1974)

LJBalkEKubalekandEMenzel

IEEETransED-22707^712(1975)-

LJastrzebskiJLagowskiandHCGatos

ApplPhysLett11_537-539(1975)

LJBalkEKubalekandEMenzelSEM71975pp447-455

JJOakesIGGreenfieldandDLPartaln

JApplPhys丘旦2548-2555(1977)

MLanirAHBVanderwyckandCCWang

JApplPhys496182-6184(1978)

DLPartainAGMilnesandLFVassamlllet

JElectrochemSoc1261584-1588(1979)-

NTohgeTMinamiandMTanaka

JpnJApplPhys172155-2156(1978)

【67】DLPartainAGMilnesandLFVassamillet

JElectronicMaterials旦493-499(1979)

[68]

[69]

DEIoannouandSMDavidson

JPhysDApplPhys昆1339-1344(1979)

ShengSLiWLWangPWLaiandRTOwen

JElectronicMaterials旦335-354(1980)

-10-

[70]

【71】

[72]

[73]

[74]

JFBresseSEM119111pp105-112

JFBresseSEM1977pp683-693

CJWuandDBWittryJApplPhyspound92827-2836(1978)

GEPossinSEM1979pp245-256

GEPossinandCGKirkpatrlck

JApplPhys旦4033-4041(1979)

[75]GEPossinandCGKirkpatrick

JVacSciTechnol161917-1920(1979)-

[76]

[77]

[78]

[79]

[80]

VonAEGruenZNaturforsch12aHeft289-95(1957)-

KKanayaandSOkayama

JPhysDApplPhys5A3-58(1972)

RShimizuYKataokaTIkutaTKoshikawaand

HHashimotoJPhysDApplPhys旦101-114(1976)

GVSpivakGVSaparinandLFKomolova

SEM1977pp191-199

CDonolatoandHKlann

-JApplPhys511624-1633(1980)

[81]DBWittryandDFKyser

JApplPhys2旦375-382(1967)

[82]

[83]

[84]

[85]

[86]

TEEverhartandPHHoff

JApplPhys425837-5846(1971)

VVMakarovSovPhys-Semicond旦in-llk(1975)

JDKannnandHBerntSolid-stateELectronヌ1957-964(1978)-

JDKammrdquoSemiconductorSilicon1977rdquo(JElectrochemical

Society)pp491-501

0vonRoosJApplPhys503738-3742(1979)

-n-

-L2-

2-1

INFLUENCEOFM工NORITYCARRIERGENERATIONDISTRIBUTION

ONELECTRONBEAMINDUCEDCURRENTINTHENOR^IALINCIDENCE

METHOD

Introduction

Accuratedeterminationofminoritycarrierdiffusionlength

LisveryimportanttocharacterizesemiconductorsOneofthe

convenientmethodstomeasureLIstheuseofelectronbeam

inducedcurrent(EBIC)Theelectron-holepairsgeneratedbyan

electronbeamareseperatedbyapotentialbarrier(egp-n

junctionorSchottkybarrier)andthecurrentisInducedinthe

externalcircuitThevalueofLcanbedeterminedfromthe

dependenceofEBIConthelengthzbetweenthepotentialbarrier

andthegenerationpointInthenormalIncidencemethodzis

variedbychangingtheacceleratingvoltagevaofanelectronbeam

andthesmallvalueofLoftheorderofumcanbedetermined

ThevalueofLintニhesmallregionisobtainedusingafocused

beamgeneratedbyascanningelectronmicroscope(SEM)lsquo

Czaja[1]measuredLinp-ndiodesofSiandGaPHe

assumedthegenerationdistributionasacombinationoftwo

exponentialfunctionsBresse[2]andWu[3]measuredLandthe

electron-holepaircreationenergyE^^inSiandGaAsTheyused

Schottkydiodesbecausetheelectronbeamenteredthroughthemetal

contactandthesurfacerecombinationeffectcouldbeneglected

IntheiranalysesBresseusedthesemi-sphericalgeneration

distrlbutionproposedbyKanayaeta1[4]andWuassumedGaussian

distリbutlonPossineta1[5]analyzedEBICindetailtakingthe

influencesofthesurfacerecombinationandtheinternalfield

-13-

Metal

Depletio

layer

Primaryelectronbeam

Numberofgeneratedcarriers

Fig2-1Schematicviewofexperimentalconditions

jusingSchottkydiodesMetalthicknessis

wanddepletionlayerwidthiswright-handillustぷふこsthedぶdosefunctionRandR

-givethemaxiraum

andextraporaiedmelectrSnolinerangerespectively

-14-

0generatedcarrier

に_---___1

我_______Iuarrヽ

y重ダ

1ごpermil

andestimatedthedepthdistributionoflifetimeinion-implantedSi

TheylsquousedthepolynomialfunctionderivedbyEverhart[6]forthe

generationdistribution

工ntheanalysisofEBICtheminoritycarriergeneration

distributionplaysanimportantroletodeterminetheaccurate

valueofLandEHoweverthedistributionmodelsusedinthepc

analysesaredifferentwitheachotherasmentionedaboveIntニhis

chapterwecomparevariousmodelsforthegenerationdistribution

inGaAsandSiWecalculateEBICandclarifytheinfluenceofthe

generationdistributiononthedeterminationofLandEpc

Experimentalresultsarealsopresented

2-2 Determinationofdiffusionlengthandelectron-holepair

creationenergy

ASchottkybarrierdiodeisusedinordertoneglectthe

influenceofthesurfacerecombinationTheelectronbeamis

irradiatednormallytothebarrierplanethroughthemetalas

shownInFig2-1Thethicknessofthemetalandthedepletion

layerareputaswmandwd゛respectivelyTheminoritycarrier

generationdistributionalongthedepth(Socalledthedepthdose

function)isIllustratedalso1nFig2-1TheEBICiscalculated

basedonthefollowingassumptions1)Theminoritycarriers

generatedinthemetal(regionI)cannotcontributetoEBIC

2)Theelectron-holepairsgeneratedinthedepletionlayer(

regionlsquoTL)areseperatedquicklybythefieldofthedepletion

layerandwhollycontributetoEBIC3)Theminoritycarriers

generatedinthebulk(regionⅡI)partlycontributetoEBICie

theminoritycarrierswhichreachtotheedgeofthedepletion

-15-

mDiwi)iunMd

SMtjjesp≫)ejAU≫6|o』ψsEコz

Normalizedgenerationdepth^rsquoRm

Fig2-2

Generationdistribution

inGaAsTheMakarov゛SWittryrsquos

andKanayarsquosmodelsareexpressed

bytニhesolidbrokenanddotted

linesrespectivelyThegener-

atlondepthisnormalizedby

themaximumelectronrangeR

ThetotalgenerationrateiSm

normaLlzedtobeunity

-16-

2 0

1 05

(Efi)≪MJO^M

d6ue」

CO』oa3

rdquorsquo5102050Acceleratingvoltageva(kv)

Fig2-3

ElectronrangesinrsquoGaAsforvariousmodelsThesolidbrokendottedanddashedanddottedlinesaretheresultsusingMakarovrsquosWitニtryrsquosKanayarsquosandEverhartrsquosmodels

respectively

rdquoゝゝGaAs

χ

`Makarov20χ

----Wittry

χhelliphelliphellipKanaya

11S

15

゛S≒

rsquoχ≒

χrsquo

10trsquolsquo

卜卜゜χ゛

卜ゝrsquo

05χrsquo゛rsquoゝ

ゝrsquoゝ1

ゝゝrsquoゝゝ

ゝゝ

00

50

GaAso々

タグrsquo

Makarov

15-rsquo一一Wittry

ノKanaya

12

---Everhart

13yelr(2゛十`゛dinFig2-1)bydiffusioncanflowintothemetal

bythefieldofthedepletionlayer

Therehavebeenmanytheoretical147]andexperimental

[68-11】worksonthegenerationdistributionKanayaand

Okayama[4]proposedasemi-sphericalgenerationdistribution

usingthemodifieddiffusionmodel0fArchard[7]Wittryeta1

assumedGaussiandistributionandappliedtoGaAs[89]

EverhartandHoffl6]derivedapolynomialfunctionfromtheir

experimentsIntheA1olineSi02olineSisystemdegMakarov[10]showedthat

thegenerationdistributioncouldbeexpressedasGaussianlike

(exp(-((z-z)u)2))andthep8゛゜eters2manduvariedaccording

totheatomicnumberandthedensityofthematerialInorderto

comparethesedistributionsnormalizeddepthdosefunctionwas

introducedGruen[11]showedthattheshapeofthedepthdose

curveispracticallyinvariantifthepenetrationdepthis

normalizedbytheelectronrange

ThedepthdosefunctioninGaAsnormalizedbythemaximum

electronrangeRm(atwhichnoelectronentersintothematerial

seeFig2-1)areshowninFig2-2bythesolidbrokenanddotted

linesusingthefollowingequationsforthemodelsofMakarov

WittryandKanayarespectively

2RmolineOdeg138

g(z)=exp(-(rarr元でi

g(z)=exp(-(

2Rmoline

Odeg125

-035

)2)

)2)

(Makarov)(2-1)

(Wittry)(2-2)

g(z)゜(RmolineOdeg242Rtri)2oline(2olineOrsquo242Rm)2(K゛3y8)゛(2lsquo3)

-17-

こrsquo

Aouepj^^auoiiDaii〇D

Fig2-4

10203040

Acceleratingvoltage

5060

Va(kV)

CollectニionefficiencynvsVacurves

GaAsSchottkydiodeThevaluesofLare505μmfromuppert0lowergroupofcurves

for

2and

respectivelyTheresultsusingtheMakarovrsquosWittry゛SandKanayarsquosmodelsareexpressedbythesolidbrokenanddottedlinesrespectivelyThevaluesofwandWare10nmand015ymrespectively^hedashedanddottedlineisinthecaseofw=50nmw=015umandL=2umusingtheWittryrsquosmode1

-18-

GaAs一一Makarov

--rdquo-Wittry

10Wf^=10nmhelliphelliphelliphellipKanayaL(pm)

rsquo≒゜ニ1こii4degこ7T`ヽヽヽ5

05万でヽこミア斗辿こTTZご

50nふyミ゛1helliphelliphelliphellip4゛`゛ζ゛ζ

Orsquo1capparacapcap

か4

5060

ThereareobviousdifferencesbetweenthesethreemodelsThe

MakarovrsquosandWittryrsquosmodelshavethelargesurfaceconcentration

butthepeakvalueatzRm゛Odeg13oftheMakarovrsquosmodelissmaller

thanthatoftheWittryrsquosmodelTheKanaya゛smodelhasmoreevenly

spreadeddistributionthantheothertwomodelsThisisbecause

theelectron-holepairconcentrationisassumedtobeuniformin

thesemi-sphereintheKanayarsquosmodelwhichisasimplefirst-

orderapproximationforthegenerationdistributionButinthe

actualcasetheelectron-holepairsareconcentratedaroundthe

centerofthesemi-sphereOnemustusetheimprovedelectron-hole

pairconcentrationmodelInsteadoftheuniformoneinorderto

expressthegenerationdistributionprecisely

InthecalculationofEBICtheabsolutevalueofRmustm

beneededSomereportedvaluesbyMakarovWittryandKanayaare

shownbythesolidbrokenanddottedlinesrespectively

inFig2-3forGaAsThedashedanddottedlineisderivedby

Everhart[6]anddiscussedlaterTherangesoftheWittryrsquosand

Kanayarsquosmodelsarealmostagreewitheachotherbutthatofthe

Makarovrsquosmodelisabout70ZofthoseoftheWittryrsquosandKanayarsquos

models

ThecalculatedEBICinGaAs(iethecollectionefficiency

nwhichbecomesunitywhenallthegeneratedcarrierscontribute

toEBIC)bythesamemethoddescribedinref[3]isshownIn

Fig2-4Thesolidbrokenanddottedlinesareforthemodelsof

MakarovWittryandKanayarespectivelyThevalueoftheacceler-

atlngvoltageva1Schangedfrom5t060kVThevalueofLIs50

20and05ymfromuppert0lowergroupofthecurvesrespectively

ThevaluesofWmandwdaretakenastypicalvaluesof10nmand

015ymrespectivelyTheelectronrange1SInverselyproportional

tothedensityofthematerialThemetalthicknessiscorrected

-19-

takingthedifferenceofthedensitiesbetweenthemetalandthe

bulksemiconductorinorderthatthesamplehasuniformdensityfrom

thesurfacetothebulkforasimpletheoreticalcalculationWhen

goldistakenastheSchottkycontactwmustbemultipliedby

pAupGaAS(゜3`゜6rsquopAudeg189andpGaASdeg5゛3

1cll3)

゛OIlecanestimateL

mainlyfromthegradientofthecurvebecausethegradientdecreases

monotonouslywithincreasingLupt05umTheestimatedvaluesof

LbyMakarovrsquosandWittry゛Smodelsarealmostequalbecausethe

gradientsofthecurvesagreewitheachotherforthesameLvalue

ThevalueofLlargerthan5μmcannotbedetermineddefinitely

becauseEBIChardlychangeswithvevenifLbecomeslargeThea

maximumvalueofLthatcanbedetermineddefinitelyincreasesas

thehighestvalueofvaincreasesbutanotherproblems(idegedeg

damagesofthesamplebyhighenergyelectronsetc)mayoccur

Theelectron-holepaircreatニionenergyEcanbeobtainedfrom

theabsolutevalueofEBICbytherelationndeg^C^EBIC^^B^

(IEBICmeasuredEBICIBprimarybeamcurrentkcorrectionfactニor

fortheenergylossduetobackscattニeredelectrons)[3]

TheabsolutevaluesoftニheMakarovrsquosmodelareabout10へj20Z

largerthanthoseoftheWittry゛smodelAndsothevalueofEpC

obtainedbytheformeris10へj20Zlargerthanthatbythelatter

ThegradientニSandtheabsolutevaluesofthecurvesoftheKanayarsquos

modelarequitedifferentfromthosebytwoothermodelsThe

reasonofthedifferenceisowingtotheassumptionoftheuniform

concentrationoftheelectron-holepairsinthesemi-sphereas

discussedbeforeTheKanayarsquosmodelisafirst-orderapproximation

forthegenerationdistributionandisnotsuitableforthe

accuratedeterminationofLandEThevalueofwdoesnotaffectpc(I

EBICsomuchfromtheresultsoftニhecalculation工fWbecomesm

largetheabsolutevalueofEBICat10wvaisdecreasedverymuch

-20-

butthegradientofthecurveintheregionofhighVadoesnot

changeasshowninFig2-4(thedashedanddottedlineisinthe

caseofwmdeg50nm゛wdrsquoOrsquo15pmandL=2ymusingtheWittry゛Smode1)

ThereforeLcanbedeterminedinanycaseofwm゛asfaraswm1S

sufficientlysmallinorderthattheelectronbeamcanenterinto

thebulkregion

ThenormalizeddepthdosefunctionsInSiexpressedbythe

followingequationsareshowninFig2-5bythesolidbroken

dottedanddashedanddottedlinesforthemodelsofMakarov

WittryKanayaandEverhartrespectively

zR-0261

g(z)=exp(-(-jyヲー-7)2)(Makarov)(2-4)

zR-0156

g(z)=exp(-(―q2L_一一

g(z)゜(RmolineOrsquo336Rm)2

g(z)=06+6212Re

(Wittry) (2-5)

(゛0336R)^(Kanay゛1)(2oline6)

oline12deg40(2Re)2+5lsquo69(zR

(Everhart)e)3

(2-7)

Makarovshowedthattheparameterszmlsquoanduhadvoltagedependencesl

andthetypicalvaluesatvadeg30kVaretakenItshouldbenoted

thatthedepthdosefunctionoftheEverhartrsquosmodelisnormalized

bytheextraporatedrangeRe(seeFiglsquo2-1)whichisdetermined

byextraporatingthestraightlineportionofthecurve

-21-

Fig2-5

11

u)6ua))iunjed

sjdiJieopdiejdud6lo」4sEコz

Normalizedgenerationdepth^rsquoRm

GenerationdistributionsinSiTheMakarov゛s

Witニビry゛sKanayarsquosandEverhart゛Smodelsare

expressedbythesolidbrokendottedanddashedanddottedlinesrespectivelyThegener-

atlondepthisnormalizedbythemaximumelectron

rangeRTheextraporatedrangesR゛SoftheMakarovrsquosWittryrsquosandEverhartrsquosmodelsare

takentobeagreedwitheachotherThetotニal

generatニionrateisnormalizedtobeunity

-22-

KUkarov

--一一-Wittry2deg

二ぷ芯t

15へ

゜¥レ臨べhellip

hellip

10rsquoS゛lsquoNhellip

helliphellip

05

hellip

helliphellip

1helliphellip

hellip

005

工nordertocomparetheEverhartrsquosmodelwithothersthe

extraporatedrangefortheGaussiandistributionisdeduced

(seefootnote)十andtheextraporatedrangesoftheMakarovrsquoS

WittryrsquosandEverhart゛Smodelsaretakentobeagreedwitheach

otherThepeakvaluesofthegenerationdistributionsofthe

MakarovrsquosWlttryrsquosandEverhartrsquosmodelsarealmostequalbut

thevalueofzRmatthepeakfortheWittryrsquosmodelisabout

015andsmallerthanthoseoftheothertwomodelsCzR=025)゜

ThegenerationdistributionoftheWittryrsquosmodelcomesnearerto

thesurfacethanthoseoftheMakarovrsquosandEverhartrsquosmodelsIt

isbecausetheWittryrsquosmodelisderivedInthecaseofGaAsand

ontheotherhandtheMakarovrsquosandEverhart゛Smodelsareconcerned

inthecaseofSiThedensityofG゛1AS(pGaAS゛5deg3gcm^)islarger

thanthatofS1(pSirsquo2deg3gcm^)andsotheWittry゛Smodelshows

themoresurfaceconcentrationthantheothersTheKanayarsquosmodel

isquitニedifferentwiththeotherthreemodelsowingtothesame

reasonasdiscussedinGaAs

- -

-- - - - -

- - - -

Gaussiandistribution(e゛p(oline((2oline2m)11)2))

showsthealmostlineardecreasearoundthepoint

ofinflection(zdegu゛Σ十zm)lsquoTheextraporatedrange

Re(1゛ersquothepointwithwhichthestraightline

atthepointofinflectioncrossesthezaxis)

becomes2u十zfromtheresultsofcalculationm

(seeFig2-5)゜TheextraporatedrangeRebecomes

078Rand062RfortheMakarovrsquosandWittryrsquosmm

modelrespectively

-23-

Fig2-6

0 102030

Acceleratin9

4050

voltage

60

va(kv)

CollectionefficiencynvsVacurvesforSiSchottkydiodeThevaluesofLare1052andlymfromuppert0lowergroupofcurvesrespectivelyTheresultsusingtheMakarovrsquosWittryrsquosKanayarsquosandEverhartrsquosmodelsareexpressedbythesolidbrokendottedanddashedanddottedlinesrespectivelyThevaluesofWandware10nmand05ymrespectivelymd

-24-

MakarovSi---rdquoWittry

Kanaya

----Everhart

ジhttpwwwL(pm)卜

)渫回ブモジミ穫

WmニlOnmrdquoミ4helliphellipで``rsquoヽ4゜

゛ゝ1rsquohelliphelliphellip

゛rsquoN

u1C

larrl

0E

501

Figure2-6showsthecollectionefficiencyinSiusing

thefourdifferentmodelsofMakarovWittryKanayaandEverhart

bythesolidbrokendottedanddashedanddottedlines

respectivelyThevalueofLIs1005020and10umfrom

uppert0lowergroupofcurvesrespectivelyThevaluesofW

andrdquodaretakenastypicalvaluesof10nmand05]imrespectively

Thevalueofwmismultipliedby821nthecalculationowingto

thedifferenceofdensitiesbetweenAuandS1

asdiscussedbeforeThevalueofLlargerthan10μmcannotbe

determinedaccuratelybecauseEBIChardlychangesevenifLvaries

ThegradientofthecurveoftheEverhartrsquosmodel1Sslightly

steeperthanthoseoftheMakarovrsquosandWittry゛smodelswhich

almostagreewitheachotニherAndsotheestimatedvalueofLby

theEverhartrsquosmodelbecomeslargerthanthatbytheMakarovrsquosor

Wittry゛smodelforthesamer)vSdegvaCurve(egL=lutnbythe

Everhartrsquosmodelbecomes07umiftheMakarov゛Smodel1Sused)

ThegradientofthecurveoftheKanayarsquosmodelisalmostequal

tothatニoftheEverhartrsquosmddelbuttheabsolutevalueofthe

formeris30Zsmallerthanthatofthelatterforthesamevalue

ofLThereforetheestimatedLbyKanayarsquosmodelalmostagree

withthatbytheEverhartrsquosmodelbutthevalueofE

pCuSing

theformeris30Zsmallerthanthatusingthelatter

Asmentionedbeforetheelectronrangeisinversely

proportionaltothedensityoftニhematerialTheelectronrange

derivedbyEverhartinSicanbeappliedtoGaAsconsideringthe

differenceofthedensitiesbetweenSiandGaAsThecalculated

valuesareplottedbythedashedanddottedlineinFig2-3

TherangesoftheMakarov゛SandWittry゛Smodelsarelargerthan

thatoftheEverhart゛smodelOneofthereasonsforthe

disagreementisthedifferentdefinitionsoftheelectronrange

-25-

ieMakarovandWittryusedthemaximumrangeRbutEverhart

usedtheextraporatedrangeRelsquoInordertニocomparethesevalues

theextraporatedrangesfortheMakarovrsquosandWittryrsquosmodels

inGaAsarededuced(seefootnoteinpage23)andbecome075Rm

andOlsquo62Rm゛respectivelylsquoForexampleinthecaseofvadeg30kv゛

thevaluesofRforMakarovrsquosandWittryrsquosmodelsare34andm

48ymandthenthevaluesofRebecome26and30ym

respectivelylsquoThevalueofReintheEverhartrsquosmodel(29umat

vadeg30kV)isslightlylargerthanthatoftheMakarovrsquosmodel

butagreeswiththatoftheWittryrsquosmodel

2-3 ExperimentalresultsinGaAs

AconventionalSEMwasusedfortheprimaryelectronbeam

whichwasmodulatedat3kHzwithachoppingcoilinsertedinto

thebeampathTheinducedcurrentwasmeasuredfromthevoltage

dropacrosstheloadresistancewhichwasconnectedtotheSchottky

barrierwithanohmiccontactThesignalwasdetectedbyalock-in

amplifierThebeamcurrentwasmeasuredbyaFaradaycageThe

beamwassomewhataefocussed(Φ|=10umφbeamdiameter)inorder

toavoidhighinjectionTheinducedcurrentwasnotchangedeven

ifthebeamwasirradiatedatthesamepointforanhour

TheSchottkybarrierwasrsquomadeonn-typeGaAs(Sndoped

ndeg62times1016cmoline3)byevaporatingAuofabout10nmthickina

vacuumofabout10oline7TorrTheohmiccontactwasobtainedby

evaporatingAu-Geandalloyingat400degCfor2mlnThecarrier

densityandthedepletionlayerwidthweredeterminedbyG-V

measurements

-26-

(Hiunqj≫)

U一SU

BeamcurrentIb(A)

Fig2-7

MeasuredEBICinGaAs(Sn-

dopedn=62)(1016cmoline3)Schottky

diodeatVa=10and50kVThe

beamcurrentwaschangedinthe

rangeof2)(10oline11≦I≦5)(10oline9A

-B-Theopenandsolidcirclesare

theexperimentalresultsforvadeg

10and50kVrespectivelyand

thegradientsofthesolidlines

areunity

Tab2-1

(s≫UコqjB)Aouapu

く1)

uoiioaiion

AcceleratingvoltageVa(kV)

Fig2-8

Curvefittingsoftheexperi-

mentalresultstothetheoretical

collectionefficienciesinGaAs

SchottkydiodeThesolidbroken

anddottedlinesaretheresultニS

usingtheMakarovrsquosWittry゛Sand

Kanayarsquosmodelsrespectively

Vaischangedfrom5t050kVwith

thefixedvalueofl゛10oline1oA

w=10nmandwmd

L(unj)Ec(ev)

Makarov

Wittry

Kanaya

03

03

05

48

41

41

二〇15um

ご洸竺詐比飛ぱ器ぶごぷ詣ぷ

-27-

000

5Gなfimf4ilvalu

0v≪>iakv

50

100

10

lylrsquo16rsquo1(i

acuteン゛tGaAs(Sndoed)

5n=62

lope

1二痙7

5Kanayao

21020304050

ThevalueofEBICatv=10and50kVareshownbythesolida

linesinFig2-7whenthebeamcurrentIBischangedintherange

of2)(10oline11≦I≦5)(10oline9AIftheminoritycarrier-B-

concentrationexceedsthethermalequilibriumconcentrationof

majoritycarriers(iehighinjection)theminoritycarrier

lifetimeisprolonged[12]ThereforeEBICbecomestoincrease

superlinearlywiththenumberofgeneratedcarriersie

withIBforafixedvalueofvarsquoInthisexperiment゛EBIC

increaseslinearlywithIBatbothvals゛WhichShoWsthe10w

injectionTheexperimentalresultsareshownbycirclesin

Fig2-8whenvischangedintherangeof5くVく50kVata=adeg

thefixedvalueofIBdeg10oline10A゛Theoreticalcollectionefficiencies

usingtheMakarovrsquosWitニtryrsquosandKanayarsquosmodelsareshownbythe

solidbrokenanddottedlinesrespectivelyinFig2-8The

valuesofLandEpcdeterminedbyfittingtheexperimentaldata

totニhetheoreticalcurvesaretabulatedinTab2-1forthethree

differentmodelsofMakarovWittryandKanayaThecollection

efficiencybytheMakarovrsquosmodelshowedfairlygoodagreement

withtheexperimentalresultsbutthatusingtheWittryrsquosmodel

isslightlylargerthantheexperimentalvaluesinthe10Wva

l`egioll(va≦10kV)Thediscrepancyinthelowvaregionbecomes

largeiftheKanaya゛SmodelisusedInthecaseofWittryrsquosand

Kanaya゛Smodelspoundheexperimentaldatawerefittedintherange

ofhighva(va≧15kv)TheestimatedvaluesofLis03urnby

usingboththeMakarovrsquosandtheWittryrsquosmodelsbutthatusing

theKanayarsquosmodelis05ymandabouttwiceoftheresultby

theMakarovrsquosandWittryrsquosmodelsThevaluesofEdeterminedpc

bytheMakarovrsquosWittryrsquosandKanaya゛Smodelsare4841and41

eVrespectivelyBythenormalincidencemetニhodofEBICWuand

Wittry[3]andKobayashieta1[L3]determinedEas468and457

eVrespectivelywhicharealmostequaltotheresultusingthe

Makarovrsquosmodelbutareabout10Zlargerthanthevalueobtained

bytheWittryrsquosandKanayarsquosmodels

-28-

2-4 Summary

ThevaluesofLandEcanbedeterminedfromthe

PC

ceofEBIConvbythenormalincidencemethodThe-

dependenceofEBIConVabythenormalincidencemethodThe

minoritycarriergenerationdistributionplaysanImportantrole

intheanalysisofEBICVariousgenerationdistributionmodels

arecomparedwitheachotherunitingthedifferentdefinitionsof

theelectronrange(Iemaximumrangeandextraporatedrange)

InGaAsGaussiandistributionsproposedbyMakarovand

Wittryhavelargesurfaceconcentrationsandthepeaksofthe

distributionsexistatabout0130fthemaximumelectronrange

Kanaya゛Smodelhasevenlyspreadeddistributionowingtothe

assumptionoftheuniformconcentrationofthegeneratedelectron-

holepairsThevalueofLlargerthan5μmcannotbedetermined

definitelybecauseEBIChardlychangesevenifLvariesThe

estimatedLbytheMakarovrsquosmodelalmostagreeswiththatblsquoythe

WittryrsquosmodelbutEdeterminedbytheformeris10へj20ZrdquoPC

largerthanthatbythelatter

InSithepeaksofthegenerationcistributionbecome

deeperthanthoseinGaAsbecausethedensityofS11Sabouthalf

ofthatofGaAsThelargestvalueofLthatcanbedetermined

definitelybecomestwiceofthatofGaAsbecausetheelectronrange

inSiisabouttwiceofthatinGaAsTheestimatedLbythe

MakarovrsquosorWittryrsquosmodelisabout30Zsmallerthanthatbythe

Everhartrsquosmodel

IntheexperimentsinGaAstheestimatedLbytheMakarovrsquos

modelagreedwiththatbytheWittryrsquosmodelbuttheestimated

Epcbytheformerwas48eVandabout17Zlargerthanthatbythe

latter

-29-

References

[1]

[2]

[5]

WCzajaJApplPhys374236(1966)

JFBresserdquoScanningElectronMicroscopy71972partlrdquo

(iiTRiChicago111)p105

CJWuandDBWittryJApplPhys丘旦2827(1978)

KKanayaandSOkayamaJPhysDApplPhys

543(1972)-

口EPosslnandCGKirkpatrickJApplPhys

5^4033(1979)

[6]TEEverhartandPHHoffJApplPhys

425837(1971)

[10]

[11]

[12]

[13]

GDArchardJApplPhys竪91505(1961)

DBWittryandDFKyserJApplPhys28375(1967)

TSRao-SahibandDBWittryJApplPhys

403745(1969)

VVMakarovSovPhysSemicond旦722(1975)

jVonAEGruenZNaturforsch12aHeft289(1957)-

JCornuRSittigandWZimmermannISolid-stateElectron

TKobayashiTSugitニaMKoyamaandSTakayanagi

IEEETransNuclSciNS-19324(1972)-

-30-

3-1

DETERMINATIONOFDIFFUSIONLENGTHSURFACERECOMBINATION

VELOCITYANDELECTRON-HOLEPAIRCREATIONENERGYBYTHE

LINESCANMETHOD

Introduction

Anelectronbeaminducedcurrent(EBIC)methodisa

convenienttechniquetomeasuretheminoritycarrierdiffusion

lengtニhLandthesurfacerecombinationvelocitysinsemi-

conductingmaterialsInthelinescanmethodLandScanbe

determinedfromthedependenceofEBIConthescanningdistance

whentheelectronbeamisscannedacrossthebarrierBerzand

Kuiken[1]gaveadetailedtheoryforthedeterminationofLand

sandOpdorp[2]investigatedexperimentallytheinfluenceof

surfacerecombinationonEBICJastrzebskieta1[31measured

Landsfordifferentgenerationdepthsbyvaryingtheaccelera-

tingvoltageofanelectronbeam

Inthosestudiesthegenerationsourcewasassumedto

beapointbutinpracticetheregionexcitedbytheelectron

beamhasafinitevolumeChiandGatos[4]determinedthe

junctiondepthbyanEBICtechniqueassumingafinitegeneration

volumeCzaja[5]andBresse[6]measuredthephysicalparameters

suchasLandtheelectron-holepaircreationenergyEpC゛when

theelectronbeamwasdirectednormaltothebarrierplane

Sheaeta1[7]investigatedtheresolutionlimitsoftheEBIC

linescanmethodtheyobtainedaone-dimensionallateraldose

functionandappliedittothemeasurementofLintheCuxSCdS

systemHowevertheydidnotdiscusstheeffectofsurface

recombinationonEBICSincethesurfacerecombination1S

stronglyconnectedwiththedepthofgenerationathree-

-31-

Fig3-1

Schematicviewof

anddefinitionsofthe

-32-

experimentalconditionscoordinatesystems

Electronbeam

Surfacecross-sectic

O゛9χ

Schottky哨Rbarrier

dimensionalgenerationdistributionmustbetakenforthedetailed

analysisofEBIC[81

Inthischapterfirstlywediscussthesurfacerecombi-

nationeffectonEBICassumingapointsourceandthendescribe

theinfluenceofthegenerationvolumeonEBICinthelinescan

methodtakingaccountofsurfacerecombinationWehavestudied

EB工Ctheoreticallyforthefinitevolumesourcewhichisdependent

ontheacceleratingvoltageandshowanimprovedmethodfor

thedeterminationofphysicalparametersofsemiconducting

materialsbasedonexperimentalresultsobtainedinSi

3-2 Surfacerecombinationeffectconsideringpointsource

ForsimpletheoreticalconsiderationwetakeaSchottky

diodeAsshowninFig3-1theSchottkybarrier1Sinthey-z

planeTheelectronbeamisincidentperpendiculartothesample

surfaceandthescanningdirectionisalongtheχ-axiswhichis

normaltothebarrierplane

Thegenerationsourceisconsideredtobeapointata

distancexgfromthebarrierandatadepthdfromthesurface

correspondingtotheacceleratingvoltagevarsquoThepositionis

XS

ぐi g゛ O゛dg)Thesteadystateexcessminoritycarrierdistribution

obtainedfromthefollowingdiffusionequation

pDnabla2pdeg - -

g6(x-゜cg゛yrsquo2olinedg)rsquo (3-1)

whereDisthediffusionconstantて1sthelifetimeandgisthe

generationrateofelectron-holepairsWhen

thesampledimensionsareassumedtobesufficientlylarge

-33-

3ta3

Normalizedscanningdistancex

(a)

Fig3-2

Fig3-3

U』

Normalizedscanningdistancex

(b)

3193

p≫Zl≫E』oz

Normalizrdscanningdistanceχ

(c)

PrimeNormalizedEBICvsnormalizedscanningdistanceχcurvesfordifferentvaluesofthesurfacerecombination

velocityparameter(seetext)SNormalizedgenerationdepthDis0001and10in(a)(b)and(c)

respectively

Oino

tou

iSu一uojsn}|ipMzireujjoZ

SurfacerecombinationvelocityparameterS

EstimateddiffusionlengthL大directlyfromthe

slopesofthecurvesbetweenthepointsatχ=2and3

Svariesfromoneto50

-34-

Dg=10

Dg=QO

151050

112345

Og<ao

161

S>0

21

Idrsquo

S5

10^

550

1必12345

135

sc^-at

SO⑤

バ宍

1012345

112345

SPg≪10

161

162S=0

SI

1(i3

1(541235

comparedwiththediffusionlengththeboundaryconditionsare

並Sz

χ=0

z=O゛

spl

z=0

=0

χ=+(x)

=0

(atthesurface) (3-2a)

(attheSchottkybarrier)(3-2b)

(3-2c)

Oncethedistributionp1SknowntheEBICcanbefound

asfollows

トeリンint]キレ

o4バ2rsquo(3-3)

whereeisthechargeofanelectronThevalueofjwascalculated

二二二二二二二エフエム2こ二言

J=

-eg

丁T

4oo

int

Dg

馴D戸

exp(-S(T-

S(司7)-

dT} (3-4)

wherexL゛DgdegdgLrsquoS=s(Lて)andTIsthevariablefor

integrationThefunctiony可7)1sthesecond-modified

first-orderBesselfunctionTheEBICisnormalizedtobeunity

whenallthegeneratedcarrierscontributetoEBIC

-35-

177FΞ-一一permil

(ぷ71

y))二1supe≧rsquo

四F

InFigs3-2(a)(b)and(c)thelogarithmofJis

plottedvsX(ΞxL)basedoneq(3-4)overtherangeofO≦X≦5一一

forS=へj50ThevalueofDgis0001and10in(a)(b)

and(c)respectivelyForS=0theintegralineq(3-4)leads

toJ=exp(-X)whichyieldsstraightlinesasshown

inFig3-20ntheotherhandallcurvesforS>Odeviate

fromthestraightlineThesurfacerecombinationgivesmuch

effectontheexcesscarrierdistributionasthegenerationdepth

becomessha110WerWhenDgis00and01thevaluesoflogJ

decreasesuperlinearlyovertheinterval0fO≦χ≦2and--

almostニlinearlyovertherangeofx≧2WhenDis10the一琴

surfacerecombinationhasaslightinfluenceandthevaluesof

logJdecreasealmostlinearlyovertheinterval0fO≦X≦5__

HowevertheslopesshowsubstantialdeviationfromunityThe

estimatedvaluesofdiffusionlengthdirectlyfromtheslopes

ofthecurvesinthelinearlydecreasingregion2≦X≦3are--

putasL火andplottedagainstSinFig3-3forDgdeg00and10

工nordinarysemiconductorsSvariesfromlt050Overthis

rangeL大Isabout80t090ZoftニherealvalueL

WhenweevaluatetheaccuratevaluesofLandSwemust

fittheexperimenpoundaldatatothetheoreticalcurvesoverthe

wholerangeofO≦X≦5WecanestimateSbyfitting--

particularlyovertheIntervalofO≦X≦2becausetheeffect--

ofthesurfacerecombinationappearsremarkablyinthisInterval

-36-

3-3 Analysisofelectronbeaminducedcurrenttakingthree-

dimensionalgenerationdistributionintoaccount

Insect3-2theminoritycarrierdistributionisassumedto

beapointButinpracticethegenerationdistributionhasa

finitevolumeinconnectionwithvThegenerationdistributiona

mustbetakenintoaccountwhentheextentofthegeneration

distributioncannotbeignoredcomparedwithL

Electronpenetratニionintosolidmaterialshasbeenstudied

bymanyauthorsTheminoritycarriergenerationdistribution

alongthedepthwasdiscussedindetailinChapterHWittry

andKyser[9]assumedthedepthdosefunctiontobeaGaussian

distributionandobtainedgoodagreementwithexperiments

EverhartandHoff[10]assumedapolynomialfunctiontoexplain

theirexperimentalresultsintheAl-SiO2-SisystemdegInthose

studiesonlythedistributionalongthezaxiswasdiscussedso

thedistributionalongthexaxiswasnotconsideredSheaeta1

[7]definedthelateraldosefunctionalongthexaxisfrom

VonGrlinrsquos[11]databutdidnotdiscusstheinfluenceofsurface

recombinationindetailSincetheinfluenceofsurfacerecombi-

nationonEBICdependsonthedepthfromthesurfacewemust

takethedistributionofgeneratedminoritycarriersinthe

x゛zplaneWeusethemodifieddiffusionmodelofKanayaand

Okayama[12]Themodel1Sverysimplebutissufficientfor

thefirst-orderapproximationtニothethree-dimensional

generationdistributionAccordingtothemodeltheelectrons

penetratestraightintothematerialtothemaximumenergy

dissipationdepthandthenscatterequallyinalldirections

makingelectron-holepairsTheshapeofthegenerationregion

becomesaspherepartofwhichisabovethesurface

-37-

Fig3-4

Tab3-1

11-

Schematicviewofelectronpenetrationisthemaximumenergydissipationdepth

a(W)

00000

1CMCO<rm

d(ym)

rdquo047

149

291

in<yi

vDVO

4VO

R(um)

100

295

13

74

20

Valuesofthecenterdgofthegeneration

volumeandtheradiusRinSiforseveralvalues

ofacceleratingvoltagevarsquo

-38-

IElectronbeam

O335

S`」「fdegce

uarrで0559j

10゛」

helliphelliphelliphelliphellip

Thecenterdgofthesphere(iethemaximumenergydissipation

depth)andtheradiusRaredependentontheacceleratingvoltage

va゛b゛lttheratiodgRisassumedtobeaconstantasshownin

Fig3-4evenWhenvaisvariedThevaluesofdgandRinSi

forseveralvaluesofvaaregiveninTab3-1calculatedwith

theaidoftheequationsofKanayaandOkayama[121

Wedividethesemi-sphereintomanysegmentsoflength

lessthanLandrepresenteachsegmentbyonepointsource

Thedensityoftheelectron-holepairsisassumedtobeuniform

withinthespheretosimplifytheanalysisThenthegeneration

strengthgofeachpointsourceisgivenbytニhefollowing

relation

Σg=G(3-5)

whereGisthewholegenerationstニrengthandΣexpressesthe

totalsummationwithinthesemi-sphereundertニhesamplesurface

TheEBICforthefinitevolumesourceisderivedby

summimgupthesolutionoftニhediffusionequationforeachpoint

sourcewhichisexpressedbyeq(3-4)Whenthedistance

betweenthebarrierandtheIrradiatedpointxbecomessmallerg

thanRsomeofthepointsourcesareforcedoutofthediode

andcannotcontributetoEBICThustheEBICdecreasesnearthe

barrierplaneWecallthisphenomenonanedgeeffectTosimplfy

thecalculationweassumethattheEBICcontributedbythe

forced-outsourcesiszeroThisedgeeffectmustbetakeninto

accountwhenthegenerationvolumeislargeincomparisonwith

thediffusionlengthWeshowanexampleforL=8ymandS=20

Whenvais10kVtheradiusRissmallcomparedwithLand

thegenerationsourcecanbeassumedasapointThelogarithm

-39-

Fig3-5

Qコー

山11

pdznpoi」oz

1020

Scanningdistanceχ

NormalizedEBICversusscanningdistanceχ

forthefinitevolumesourceThediffusionlengthLis8lsquoUmandthesurfacerecombinationvelocityparameterS(seetext)is20TheacceleratingvoltageVais50タ30and10kVfromuppertolowersolidcurverespectivelyThedottedcurveisthepointsourcesolutionforVa=50kVandtニhedashedlineisthegradientthereciprocal0fwhichgivesL=8um

-40-

1020304050(p『

゛X5入L=8μm

゛χS=20

2rsquoχyχ

゜χ

ldquoゝ5rdquo-Re-くiprocalsk)

rsquox9vesL=8|jm

rdquoゝ

2rsquo゜χ`Va=50KV

2rsquoχ

lsquoχ

lsquoゝ

5degχ

rsquoχ

rsquoχ2χ

30≒3rsquo

11diPointsourcelsquo

5solutionfor

va=50KV10

1020304050(μΓΥ

ofEBICJisplottedwithafullcurveasafunctionofthe

scanningdistancexinFig3-5logJdecreasessuperlinearlyover

theinterval0≦X≦2L(ie16uminthiscase)anddecreases--

almostlinearlyovertherangex≧2LTheslopeintherange-

O≦x≦2LisInfluencedverymuchbysurfacerecombination一一

〇necanestimateSbyfittingtheexperimentaldatatothe

theoreticalcurveinthisrangedegWhenva1S300r50kVthe

radiusRbecomesofthesameorderasLandthegeneration

volumecannotbeassumedasapointThenwedividethesemi-

sphereintomanysegmentsoflym^Thecalculatedvaluesof

EBICusingthefinitevolumesourcemethodareshowninFig3-5

ThelogJvsXcurvesshowamaximumnearthebarrierplane(

Xdeg4and7μmatvadeg30and50kVrespectively)andlogJdecreases

almostlinearlybeyondthesemaximumpointsThemaximumvalue

ofJbecomessmallasvincreasesThesurfacerecombinationadoesnotaffecttheshapeofthecurvesandsoLcanbedetermined

mainlyfromtheslopeofthelinearregionofthesecurves

independentlyofsThereciprocalslopeofthislinearportion

gives7ymwhichis87Zoftherealdiffusionlength

ThevalueofEpc゛rsquobywhichanelectron-holepairis

createdcanbedeterminedfromtheabsolutevalueofEBIC[13]

ThevalueofJinthecaseofS=501sabout70Zofthatinthe

caseofSdeg1whenvais50kv゛andsowemakelargeerrorsinthe

determinationofEifwedonotconsiderthesurfacerecomblna-pc

tioneffect

Thepointsourcesolutionatva゛50kVisshowninFig3-5

bythedottedlinewhenthegenerationoccursatthemaximum

energydissipationdepth(ie67ymfromTab3-1)

Theslopeofthepointsourcesolutionovertherangex≧2LIs-

almostequaltothatofthevolumesourcesolutionbutthe

normalizedEBICis60Zofthatofthevolumesourcesolution

-41-

Fig3ldquo6

Chopping

こ011

Scanningcoil

Schematicdiagramoftheexperimentalset-up

-42-

コ4[Osc

lsquo~|-

|コt

||IElectronbeamReference

||

Sample

RL`Lock-inampχ-yrecorder

3-4 ExperimentalresultsinS1

Aschematicdiagramoftheexperimentalset-upisshown

inFig3-6Theacceleratingvoltage1Svariedfrom10t050kV

TheprimaryelectronbeamcurrentismeasuredbyaFaradaycage

andabout2times10oline10ATheinducedcurrentwasmeasuredfromthe

voltagedropacrosstheloadresistanceILdegThecurrentニIL

whichflowsthroughtheresistanceisexpressedasfollows

hdeg^sc-I{exp[(ekT)ILRL]-1} (3-6)

whereloisthebackwardsaturationcurrentand^scisthe

short-circuitcurrentwhichistherealEBICInordertoneglect

thesecondtermofeq(3-6)theEBICwasmeasuredinthefollowing

condition

h゛kTe (3-7)

InthepresentexperimenttheEB工Cwasmeasuredatroomtempera-

tureandso゛hhwaskeptlessthanlmvdeg

Theelectronbeamwaschoppedat3kHzwithachopping

coilinsertedintothebeampathSignalsassmallas1μVcould

bemeasuredwithagoodsignaltonoiseratiousingalock-in

amplifier

Thesamplesweren-typeSiwithresistivitypof10

and01ΩCm0hmiccontactsweremadebyevaporatingantimony-

dopedgoldontothesampleandalloyingat400degCfor2mln

Schottkycontactsweremadebyevaporatinggoldinavacuumas10W

as10oline7TorrThesamplewasinsertedintoavacuumchamberfor

EBICmeasurementimmediatelyafteritwascleavedandmeasured

-43-

3IS3

paziicuijoz

1020304050(pm)

Scanningdistancex

Fig3-7

Experimentalresultsfor

sampleA(p=lf2cin)whereL=

8μmandS=20Fullcurves

arethetheoreticalrsquoones

11(il

>P≪4<N1≪CM<Pq

1 1

3193paziipujjoZ

1164

50

Scanning

100

distance

Fig3-8

150

X(μm)

200

ExperimentalresultsforsampleB

(p=01f2cin)whereL=80urnandS=50

Fullcurvesarethetheoreticalones

Valueswithouttheinfluenceofan

ohmiccontニactareshownbydotted

curves

-44-

124(m)

5XExperimentalvaluesX---Va=50KV

2NNo30

1X一--10KV4

5しL=8pm

2χ

2χ

5χ

-Theoretical

5curve

41

50100150200

Experimentalvalues

--4=50Kv

lo―30KV

hellip-10KV

-ゝゝI゛゛゜゛ペヘヘ

helliphelliphelliphellipyhelliphelliphelliphellip

Theoreticalcurvehelliphelliphelliphellip9lsquorsquolsquo゜

Ldeg80μΓTlぶ

S=50

inavacuumas10was1times10oline8TorrTheresidualgasesonthe

cleavedsurfacewerecleanedbyargonionsputteringtoavoid

contaminationofthesurfacebyanirradiatニedelectronbeam

TheexperimentalresultsofsampleA(p=10ncm)are

showninFig3-7forva=1030and50kVrespectivelyEach

fullcurveisthetheoreticaloneforthecaseofL=8umandS=20

工fthediffusionconstantD1Stakenas16cm2Solinelthelifetime

てis4times10oline2μSandthesurfacerecombinationvelocitysis

4times105cmsolinelSurfacerecombinationhasagreatereffectasthe

generationdepthbecomesshallowerthatisVbecomeslower

AndsothevaluesofSandLcanbeestimatedmainlyfromthe

curvesforthelowestニandthehighestva(idege103゛d50kV

inthisexperiment)respectivelyTheexperimentalresultsfor

eachacceleratingvoltageagreeverywellwiththetheory

Theexperimentalcurvesforvadeg1030and50kVhaveamaximum

atxdeg02and4ymrespectivelyandeachmaximumvaluebecomes

smallerasvincreasesasdescribedinthetheoryHowevera

themaximumvalueandthepositionwheretheEBICshowsapeak

deviateslightlyfromthetheoryinthecasesofvadeg30and50kVdeg

Thisdiscrepancymaybeattributedtotheassumptionofuniform

densityofgenerationTheactualdistributionmaybelocalized

atthecenterofthegenerationvolume[9]andmoredetailed

treatmentforthegenerationshapeandthegenerationdensity

Isneeded

Inthecaseofthelocalizeddistributionofgeneration

wecanapplythesamemethodasdiscussedinsect3-3Ifthe

constantgischangedintoanappropriatevariablewhichexpresses

thelocalizeddistributionbetterresultswillbeobtained

HowevertheassumptionoftheunifoinndensityIssufficientfor

thequalitativeanalysisoftheInfluenceofthegenerationvolume

onEBIC

-45-

TheexperimentalresultsofsampleB(p=01ficm)are

indicatedinFig3-8inthesamewayassampleAThevalues

ofLandSare80ymand509respectivelyIfDis16cm2solinel

てis4ysandsis1)(105cmSoline11nthiscaseLisgreaterthan

thegenerationvolumeevenwhenvadeg50kVandthevolumesource

effectappearslessclearlythaninsampleAThediscrepancy

witニhintheinterval0<xく15urnisduetothesamereasonas

thatdiscussedInthecaseofsampleATheslopesofthecurves

overtherange15≦x≦100μmarelesssteepasvbecomes--a

higherbecausetheinfluenceofsurfacerecombinationdecreases

Theinfluenceofohmiccontactappearsovertherangex≧120μm-

sincethediffusionlengthisabouthalfofthesamplethickness

of200μmTheoreticalvaluescalculatedusingthemirror

imagemethod[14]discussedinChaptervareshownbyfull

curvesinFig3-8Valueswitニhoutニtheinfluenceofanohmic

contactarealsoshownbydottedcurves

Thescanningsurfacewasnotaffectedbyanelectronbeam

oftheorderof2times10oline10Abecausethesameresultwasobtained

forshallowexcitation(vadeg10kV)afterthesamplewasirradiated

for1hatV=10へ一50kVa

ThedepletionlayerwidthisnotbroughtIntoconsidera-

tionbecauseofitsnarrownesscomparedwiththescanningdistance

Theelectronbeamdiameterofabout50nminthisexperiment

1Snottakenintoaccountsinceitisverysmallincomparison

withthegenerationregionevenifvais10kvdeg

工fthebeamcurrentiskeptconstantthegeneration

densitydecreaseswithincreasingVbecausethegeneration

volumeincreasessuperlinearlywithvarsquo゜Whenthebeamcurrentis

2times10oline10Aandvais10kVtheexcessminoritycarrierdensity

-46-

atthegenerationpointisabout5times1014Cmoline3(themaximum

generationdensityinthisexperiment)followingthediscuss10n

inref[1]whichissmallerthanthemajoritycarrierdensity

1nthesamplesThereforethevalueofLismeasuredatthe

lowinjectlonlevel

3-5 Summary

Thegenerationvolumeofminoritycarriershasa

considerableeffectontheEBIClinescanprofilesespecially

whenItisequaltoorlargerthanthediffusionlengthWe

investigatedthedependenceofEBIConxforgeneralsurface

recombinationvelocityinthecaseofthefinitevolumesource

Whenvaislowandthegenerationdepthisshallow

surfacerecombinationhasalargeeffectonEBICWhenvaishigh

andthegeneratニiondepthisaslargeasthediffusionlengththe

generationregioncann0longerbeassumedasapointandthe

finitevolumesourceshouldbeusedintheanalysisThetheo-

reticalcalculationshowsthatsurfacerecombinationhasonlya

slighteffectontheshapeoflogJvsXcurvesbutaffectsthe

absolutevalueofJTheaccuratevaluesofLsandEshouldbepc

estimatedbyfittingtheexperimentaldatatothetheoretical

curvesforallacceleratingvoltagesExperimentalresultsinthe

measurementofLandSonS1Schottkydiodesshowedgoodagreement

withthetheoryatboth10Wandhighvadeg

TheexperimentalresultthatEBIChasamaximumnear

thebarrierplanewasexplainedqualitativelyusingthesimple

model0fthefinitevolumesourceItcouldnotbeexplainedby

thepointsourcesolutionFurtherinvestigationofthisedge

effectwillclarifythegenerationdistributionbyanelectronbeam

-47-

References

[1]

2]

31

[41

[7]

[8]

[9]

[10]

FBerzandHKKuikenSolid-stateElectron

437(1976)

19

CvanOpdorpPhilipsResRep_32192(1977)

LJastrzebskiJLagowskiandHCGatos

ApplPhysLett27537(1975)

JApplPhys481730(1977)

JYChiandHCGatosIEEETransElectronDev

ED-241366(1977)

WCzajaJApplPhys2Z^236(1966)

JFBresserdquoScanningElectronMicroscopy1972

Partlrdquo[SEM]nc工ITRIChicago)pp105-112

SpSheaLDPartニainandpJWarterrdquoScanning

ElectronMicroscopy1978Vol1rdquo(SEMIncAMFOrsquoHare)

pp435-444

GVSpivakGVSaparinandLFKomolova

rdquoScanningElectronMicroscopy1977rdquo(SEMInc

IITRIChicago)pp191-199

DBWittryandDFKyserJApplPhysj廻375

(1967)

TEEverhartandpHHoffJApplPhys

(1971)

-48-

42

-5837

[n] AEvonGriinZNaturforsch12a89(1957)

【12】KKanayaandSOkayamaJPhysDApplPhys

543(1972)

[13]CJWuandDBWlttryJApplPhys492827

(1978)

[1410vonROOSSolid-stateElectron111063(1978)

-49-

4-1

ANALYSISOFTHREE-DIMENSIONALGENERATIONDISTRIBUTION

BYTHECOMBINATIONOFTHENORMALINCIDENCEANDTHE

LINESCANMETHODS

Introduction

TheminoritycarrierdiffusionlengthLandthesurface

recombinationvelocityScanbedeterminedbyanEBICtechnique

withboththenormalincidenceandtニhelinescanmethodsusing

SEMasdiscussedinChapters皿andHITheminoritycarrier

generationdistributニionbyanelectronbeamplaysanimportant

roleintheanalysisofEBICWhenthedimensionofthegeneration

regioniscomparablewithorlargertニhanLthegenerationregion

cannotbeassumedasapointandthegenerationdistribution

mustbetakenintoaccount

Thegenerationdistributionbyanelectronbeamhasbeen

investigatedbyseveralauthorstheoretically[1]andexperimental-

1y[2-51Asregardstheone-dimensionaldistributionaGaussian

[2-3]orpolynomial[4]functionwasassumedforthedepthdose

functionandthecombinationofexponentialdecayfunctions[51

wasusedforthelateraldosefunctionInChapter工皿the

influenceofthethree-dimensionalgenerationdistributionon

EBICinthelinescanmethodswasstudiedassumingasimple

distribution(semisphere)withuniformminoritycarrierdensity

Ineachoftheseexperimentsonlyonemethodタeitherlinescan

ornomalincidencewastakenTheelectronpenetrationdepth

andthegenerationdistributiondifferedfromeachother

-50-

Schottky

barrier

Fig4-1

2P

Surfacecrosssection

「egion

Oneofthedividedsegments

Schematicviewofexperimentalconditionsandthedefinitionofthecoordinatesystem

-51-

Electronbeam

hottkySurfacecrossse

arrierOGene芯ion

Re゛region

Oneofthe

々dividedsegi

InthischapterwemeasuredEBICbyboththelinescan

andthenormalincidencemethodsinthesamesampleandclarified

thegenerationdistributionTheinfluenceofthethree-dimensional

generationdistributiononEBICisdiscussedassumingthatthe

electron-holepairsarelocalizedatニthecenterofthegeneration

regionTheexperimentニalresultsforGaAsSchottkydiodesare

alsoshown

4-2 Influenceofthree-dimensionalgenerationdistribution

onelectronbeaminducedcurrent

WeusedaSchottkydiodesinceitcanbeappliedforboth

thelinescanandthenormalincidencemethodsInthelinescan

methodtheEBICiscalculatedtakingtニhegenerationdistニrlbution

intoaccountbyasimilarmethoddiscussedinChapterⅡ工The

generationregionisdividedintomanysegmentsthesizeofwhich

issmallerthanLandeachsegmentisrepresentedbyonepoint

sourceTheEBICforthefinitevolumesourceisderivedby

summingupthesolutionofthediffusionequationforeachpoint

sourcersquo

Thedistributionisassumedtobesphericallysymmetric

asisshowninFig4-1Theelectron-holerdquopairsgeneratedbyan

electronbeanareconsideredtobelocalizedatthecenterRCof

thegenerationregionThegenerationstrengthgalonganyradius

vectorfromRc1Sassumedtobegivenby

gdeg^exp[-C(r2R2)] (4-1)

whereRisthedistancebetweenRandthemaximumelectronrange

CRm゛andristhedistancebetweenRCandeachdividedsegment

(seeFig4-1)

-52-

TheexponentCrelatestothedistributiondensityThedensity

becomesuniformasdiscussedinChapterl[EwhenC1Szeroand

theelectron-holepairslocalizenearRcwhenCbecomeslarge

Thedistributionisassumedinorderthatthedepthdosefunction

maybecomeGaussianasisreportedinthereferences[23]

ThevalueofLshouldbesmallinorderthatitcanbe

measuredbyboththelinescanandthenormalIncidencemethods

ThereforewetakeGaAsasanexampleInthelinescanmethodwe

calculatetheEBICintensity(whichiscalledthecollection

efficiencynandisnormalizedtobeunitywhenallthegenerated

carrierscontributetoEBIC)forseveralvaluesofCandR

The゛ilueofRmisgiven[2]by

町゜001A8Vノ゛フurn

cR

m゛

(4-2)

wherevaistheacceleratingvoltニageinkVThevaluesofCand

RRareassumedtobeconstantevenifvisvariedWhenvisCm

10and30kVaa

Rm

becomesOdeg74and4deg8ymrespectニivelyWetake

thetypicalvalueofLas1μminordertoexaminetheinfluence

ofthegenerationdistributiononEBICbecausethevalueofRm

issmallerthanLatva゛10kVbutlargerthanLatvadeg30kvrsquo

SincethesurfacerecombinationvelocitySofGaAsisoftheorder

of105-106cmSoline1[6-9]wetakevaluesofland50asthe

surfacerecombinationvelocityparameterSdefinedbySΞS(Lて)

(TisthelifetimeoforderofnS)

TheresultsofthecalculationareshowninFig4-2The

fullcurvesandthebrokencurvesareforCdeg8rsquo2゛RcRm゛Olsquo13and

C=54RR゜013respectivelyThesevaluesofCandRじmolinersquoCrsquom

thetypicalvaluesobtainedbythenormalincidencemethodin

GaAs[23]Thepointsourcesolutions(whichareobtainedby

assumingthatallthegenerationoccursatRc

-53-

are

)arealsoshownby

g`

A3U413Ud

COP≫no3

Fig4-2

ScanningdistanceX(pm)

j一次゜ごゴ野謡ごごご二ににごS

ご諧驚お謡謡S回読で昌翼麗

二竃Jeぎ驚謡じ雲Cにニごまふ(

ごごぶ謡1ば昌permilお穴混戮ずpermil

ぶぶごご1ここなSttedcdeges゛ecm

-54-

helliphellipl

]]1A

Ee

ビゲヤ

12

ss50

helliphelliphellipyJミ4sdeg50

dottedcurvesAtVa゛10kVthesizeofthedividedsegmentis

takenas005umwhichissmallerthanLsothateachdivided

segmentcanberepresentedbyonepointsourceIntheregion

05≦x≦15ymthelogarithmofEBICdecreasessuperlinearly--

anditdecreasesalmostlinearlyovertherangeofx≧15um-

ThetendencyappearsmoreapparentasSbecomeslargeThechange

oftheexponentCmakeslittledifferencetotheprofilesofthe

curvesTheabsolutevalueofnovertherangeofx≧05umis-

almostequaltothepointsourcesolutionwhenS1S1butbecomes

twicethatwhenSis50Thepeaksnearthebarrierareduetothe

edgeeffectasdescribedinChapterl工゛Atvadeg30kVthesizeof

thedividedsegmentistakenas02ymforthesamereasonas

Wit二hvadeg10kVThecurvesarequitedifferentfromthepointsource

solutionbothatS=1andS=50becausethedimensionsofthe

generationregionarelargeincomparisonwithLandthepoint

sourceassumptionisn0longervalidinthiscaseTheprofiles

ofthecurvesreflectthegeneratニiondistributionasoneseesthat

theprofilechangesifCvalsquotiesfrom54t082WhenSisvaried

fromlto50theprofiledoesnotchangeatthesameCvaluebutニ

ndecreasesbyabout30ZofthatofS=lItshouldbenotedthat

thesurfacerecombinationhasaninfluenceontheabsolutevalue

ofEBICevenifthevalueofRm(4deg8pm8tvadeg30kV)ismuch

greaterthanLThereforewecanevaluateLmainlyfromthe

slopeofthelinearregionat10Wvaconsideringthesurface

recombinationeffectandestimatethegenerationdistribution

fromtheprofilesofthecurvesinthecaseofhighva゛

-55-

Fig4-3

pasube

coipai

-O

Maximumelectronraり9eRm(μm)

AcceleratingvoltageVa(kv)

Experimentニalresultsofthenormalincidence

methodforthesampleA(SndopedGaAsn=62times1016

cm^L=03)Jm)andthesampleB(TedopedGaAs

ndeg80times1016cmoline3Ldeg07μm)Experimentalvaluesare

shownbycirclesThefullandbrokencurvesare

theoreticalcurvesforC=82RR=013andC=54

RcRmdeg013respectivelywdeg10cnmmandwddegOdeg151Jmdeg

-56-

12410oline

GaAsn(c「7i」

5A訟ばn

2ゝゝゝ

ゝゝ

ゝゝゝ

ゝゝゝrsquoL(pm)

1゛゛`ヽBO7J

yWヽ

5oline`olinersquo54013A03

≒旨

2φ

(52Schottkか

デ1テシフ)卜

1020304050

Theelectron-holepaircreationenergyEisobtained

fromthefollowingequation[101

n=ErdquordquoEBIC

pcIBvak(4-3)

whereIBisthebeamcurrentandkisthecorrectionfactorfor

theback-scatteredelectronsAsdescribedpreviouslythevalueof

nisinfluencedbySevenwhenVishighandsowemusttakeolinea`lsquorsquoolineolineolineolineolineolineolineolineolineolineoline

thesurfacerecombinationeffectintoaccountwhenweevaluateE

pc

4-3 Three-dimensionalgenerationdistributニioninGaAs

Thesameapparatusandthelock-intechniquewereused

asdescribedinsect3-4TheSchottkybarrierwasmadeonn-typeGaAs

wafersbyevaporatingAuofabout10nmthickinavacuumofabout

10rsquo7TorrTheohmiccontactwasobtainedbyevaporatingAu-Geand

alloyingat400degCfor2minThecarrierdensitynofeachsample

wasdeterminedbyc-vmeasurements

Theexperimentalresultsofthenormalincidencemethod

forthesampleA(Sndopedn=62times1016cmoline3)andthesampleB

(Tedopedn=80times1016cmoline3)areshowninFig4-3byfulland

opencirclesrespectivelyThevalueofvawaSvariedbetween5

and50kVTheEBICintensityincreasedlinearlywithIBwithin

therangeof1times10oline11≦IB≦-1times10oline9Awhenvawasfixed

whichsatisfiedthelowinjectionlevelconditionThecollection

efficiencynwascalculatedbythesamemethodreportedinref[10]

bychangi昭RcRmfrom01t0025andCfrom30to90

respectivelyThebestfitcurveswiththeexperimentalresults

wereobtainedInthecaseofL=03and07umforsamplesAandB

respectivelywhenRcRm゛O゛13andC=82wereusedThevaluesof

-57-

II

A3ua<3UduqjDaiion

ScanningdistanceX((jm)

Fig4-4

Experimentalresultsofthe

linescanmethodforthesampleA

[SndopedGaAsn=62times]016cmoline3)

Thefullandbrokencurvesare

ー い゛I

゛゛

ldquooU 5

Scanningdistancex(μm)

Fig4-5

ExperimentalresultニSofthe

linescanmetニhodforthesampleB

(TedopedGaAsn=80times1016cmoline3)

Thefullandbrokenlinesare

theoreticalcurvesforC=82RRtheoreticalcurvesforC=82R

=013andC=54RR=013cdeg=013andC=54RR=013c

respectivelyLdeg03cμmS゛20respectivelyLdeg07ymSdeg20

-58-

ぎ忌

五゛

olinelo

jV

ズごy

23

times1

GaAだj

j73C4Electron

L=07μmEbeam

2Sdeg20χ

1rsquo`

゛x

ya(W

2゛Va=30W

2_JE201

4一一―54013

5≒

脅χ

21`f

ゝ≒

ゝへ

5χ

147

RCRmandCagrees`゛iththerepoidegtedvalues[2]゜Thefulland

brokencurvesinthefigurearetheoreticalcurvesforC=82

RcRmdegOdeg13andC゛5deg4゛RcRmdegOlsquo13respectニivelylsquoThediscrepancy

betweenthetheoreticalcurvesandtheexperimentalvaluesat

10WvacanbeexplainedinthefollowingwaydegThegeneration

regionbecomesshallownearthesurfaceatlowVandtheEBIC

ismainlycontributedbytheseperatedelectron-holepairsin

thespace-chargeregionjustunderthesurfaceInthetheoretical

calculationitisassumedthatthere1Snorecombinationinthe

space-chargeregionButニinactualfactthecarriersrecomblne

throughthevarioustrapswhichreducestheEBIC

Theexperimentalresultsofthelinescanmethodforthe

samplesAandBareshownbycirclesinFigs4-4and4-5

respectivelyThetheoreticalcurvesareexpressedbythefull

(Cdeg82RcRmdeg013)andthebroken(C=54rsquoRcRmdegOdeg13)curves111

bothfiguresTheEBICintensityincreasedlinearlywithIBwitニhin

therange1times10oline11くrsquoIく1times10oline9Awhenvwasfixedat100r=B=a

30kVwhichsatisfiedthe10wInjectionlevelconditionasinthe

normalincidencemethodThetheoreticalcurvescalculatedusing

thesameparameterdeterminedbythenormalincidencemethodshow

goodagreementwiththeexperimentニalresultsatbothvadeg10and30

kVWhenwetakeintoaccountthattheexperimentalresultsat

vadeg30kVreflectthegenerationdistributiontheassumedgeneration

distributionbyeq(4-1)withC=5Aへ82andRcRmdegOdeg131s

consideredtobeappropriateforthethree-dimensionalgeneration

distributioninGaAs

Thevalueofkchangesfrom078to075whenvvariesa

from5t050kV[10]Whenwetaketheappropriatevalueofkfor

themeaSuredva゛Epccanbedeterminedbyeq(4-3)Thevaluesof

-59-

Normalincidence Line scan

V(kv)a

E(eV)GaAsCSndoped)pc

GaAs(Tedoped)

5-50

41

39

14

3 9

30

Tab4-1 Valuesoftheelectron-holepaircreationenergyEinGaAsdeterminedbytニhenormalincidenceandlinepc

scanmethods

-60-

Eobtainedbythenormalincidenceandthelinescanmethodsarepc

39Oi41eVand38へj44eVrespectivelyastabulatedin

Tab4-1BythenormalIncidencemethodWuandWittry[10]

determinedEpCas468eVwhichwasabout15Zlargerthanour

resultsOnereasonforthediscrepancy1Sthedifferenceofthe

generationdistributionsThemodifiedGaussiandistributionused

bythemslightlydifferedfromtheGaussiandistributionusedin

ouranalysisAnotニherreason1Stheaccuracyofmetalthickness

WeestimatethethicknessfromtheweightofthechargedAuwhich

1SevaporatedtomaketheSchottkybarrierThereforetニheobtained

valuemaybedifferentfromtherealthicknessInthelinescan

methodEBICbecomesinsensitivetothemetaltニhicknessandthe

trapsinthespace-chargeregionbutisinfluencedbysurface

recombinationasdiscussedbeforeAlferoveta1[11]andWittニry

andKyser[12]reportedEpcas32へj44eVand46eVrespectニive-

lyfromthepeakvalueofEBICwhentheelectronbeamcrossedthe

p-njunctionOurresultsof38へj44eVareinthemiddlerange

oft二heirvaluesIntheiranalysestheydidnottakethesurface

recombinationeffectintoaccountandsoourresultsareconsidered

tobemorereliablethantheirs

4-4 Summary

Thethree-dimensionalgenerationdistributionbyan

electronbeaminGaAswasinvestigatedbymeasuringEBICwitha

combinationofnormalincidenceandlinescanmethods

TheprofileoftheEBICcurvesinthelinescanmetニhod

expressesthegenerationdistributionwhenvaishighandthe

dimensionofthegenerationregionislargerthanLThesurface

-61-

recombinationdoesnotaffecttheprofileofEBICbutlowersthe

collectionefficiencyTheaccuratevalueoftheelectron-hole

paircreationenergymustbedeterminedbytakingthesurface

recombinationeffectintoaccount

TheexperimentalresultsinGaAsSchotニtkydiodeswith

differentdiffusionlengthsshowedthatthecenterofthe

generationregion(iethemaximumenergydissipationdepth)

waslocatedatthepointof0130fthemaximumelectronrange

andtheradialdistributionfromthecenterwasshowntobe

Gaussianwithaneχponentof54へ-82Theelectron-holepair

creationenergyinGaAswasdeterminedas38rsquoV44eV

References

[1]

[2]

[5]

[6]

KKanayaandSOkayamaJPhysDApplPhys

543(1972)

DBWittryandDFKyserJApplPhys旦旦375

(L967)

VVMakarovSovPhys-Semicond旦722(1975)

TEEverhartandpHHoffJApplPhysを

5837(1971)

SpSheaLDPartainandpJWarterrdquoScanning

ElectronMicroscopy71978V011uml(SEMIncAMFOrsquoHare)

pp435-444

LJastrzebskiHCGatosandJLagowski

JApplPhys481730(1977)

-62-

[7]

[81

[9]

[10]

[11]

[12]

LJastrzebskiJLagowskiandHCGatos

ApplPhysLettri537(1975)

MEttenbergHKresselandSLGilbert

JApplPhys44827(1973)

CAHoffmanKJarasiunasHJGerritsenand

AVNurmikkoApplPhysLett22536(1978)

CJWuandDBWlttryJApp1PhySpoundrsquo2827

(1978)

ZhIAlferovVMAndreevVIKorolrsquokovand

vIStreminSovPhys-Semlcond41113(1971)-

DBWittryandDFKyserJApplPhys

361387(1965)

-63-

5-1

ANALYSISOFELECTRONBEAMINDUCEDCURRENTCONSIDERING

SAMPLEDIMENSIONS

Introduction

Anelectronbeaminducedcurrent(EBIC)methodusing

ascanningelectronmicroscope(SEM)isaconvenienttechniqueto

measuretニheminoritycarrierdiffusionlengthLandthesurface

recombinationvelocitySinsemiconductorsTherehavebeenmany

theoreticalandexperimentalstudiesonthelinescanmethodof

EBICInChaptersI工andytheEBICwasanalyzedquantitatively

takingthethree-dimensionalgenerationdistributionintoaccount

bythedividingmethodandtheimprovedmethodtocharacterize

Landswassuggestedχihenthesampledimensionsarelessthan

oneortwodiffusionlengthstheminoritycarrierdistribution

isaffectedverymuchbysampledimensionsRoos[1]analyzed

EBICtheoreticallyinthecaseofthinlayersHecalculated

thedependenceofEBIConthescanningdistancexintherange

ofxL≪1inthesampleswithwL=land05(wlayerthickness)j

andshowedthatLcouldnotbedetermineddefinitelyfromthe

slopeofthelogarithmofEBICvsXcurve

InthischaptertoanalyzeEBICconsideringthesample

dimensionsgwediscussasimplemethodusinganimagesource-and-

sinkdistributionWeshowthedependenceofEBIConxoverafull

scanrangewhenthelengthbetweenapotニentialbarrierandan

ohmiccontactisequaltoandsmallerthanthediffusionlength

andmentionsomeimportantニpointstobenoticedinthedetermination

ofLandsTheexperimentalresultsinSiSchottkydiodesarealso

shown

-64-

Fig5-1

ySご

uarrj

Schottkybarrier

uarr

Ohmiccontact

Schematicviewofexperimentalconditionsanddefinitionofthecoordinatesystem

-65-

Electronbeam

-J-

レじ2「lingtrack_^一分

りhelliphelliphellipljc1お迄゛

IL

5-2 Determinationofdiffusionlengthandsurfacerecombination

velocity

ForsimpletheoreticalconsiderationwetakeaSchottky

barrierdiodeAsshowninFig5-1theSchottkybarrierisin

they-zplaneandtheelectronbeamisincidentニperpendicularto

thesamplesurface(χ-yplane)Thescanningdirectionisalong

theX-axiswhichisnormaltothebarrierplaneThegeneration

sourceisconsideredtobeapointニandislocatedat(゛grsquo

Thesteadystニateexcessminoritycarrierdistributionpis

obtainedfromthefollowingdiffusionequation

Dnabla2pdeg二T

-g6(x-xyz-d)rsquo

O゛dg)

(5-1)

whereDisthediffusionconstantンTisthelifetimeandgisthe

generationratニeofelectron-holepairs

工fthethicknesswbetweenthepotentialbarrierandthe

ohmiccontactismuchgreatニerthanLandtheotherboundariesin

theyandzdirectionsarebothmuchfurtherawayfromthe

generationsourceEBICiscalculatedunderthefollowingboundary

conditionsasdiscussedinsect3-2

3p-9z

χ=0

x=-H≫

Z=0

Z=0

=0(attheSchottkybarrier)

=0

wheresIsthesurfacerecombinationvelocity

-66-

(5-2a)

(5-2b)

(5-2c)

(5-4)d帽

wherexgrsquoLrsquoDgdegdLSdegs(Lて)andTisthevariablefor

-67-

integrationThevalueofJ(x)isnormalizedtobeunitywhena11

thegeneratedcarrierscontributetoEBICThefunctionK(ぺ7)

isthesecond-modifiedfirst-orderBesselfunction

FortheanalysisofEBICconsideringsampledimensions

wetakethefundamentalcasethatthediffusionlength1S

comparablewithorlargerthanthethicknessw(seeFig5-1)

OncethedistributionpisknownEBICcanbefoundasfollows

十(゛十(゜3p

j=eDintint-

0 -003χ

dydz

χ=0

(5-3)

whereeisthechargeofanelectronBerzeta1【2】solvedthe

diffusionequation(5-1)undertheboundaryconditions(5-2a)

(5-2b)and(5-2c)bythemirrorimagemethodInadditiontothe

reaLsourceatxg゛animagesinkwasintroducedatthesymmetric

position-XwithrespecttotheSchottkybarrier(seeFig5-2)

Whenthematerialextendstoχ=plusmndegdegthesolutionofeq(5-l)is

givenbypμ](゛゜土)゛WhentheSchottkybarrierisintroduced

theminoritycarrierdistribution1Sexpressedasp[x]十p[oline゛g]

inordertosatisfytheboundarycondition(5-2bplχ=OdegO)rsquo

andjisobtainedasfollows

J()゜

-eg-

-π

DgK(ぶ77F)

リinto

うと縦卜-dT

-H≫

十intexp(-S(T-D))

Dg

g ぜ)ケ

Thenonemustusethefollowingboundaryconditioninsteadof

(5-2c)

Ix=wdegO(attheohmiccontact) (5-2crsquo)

ThesolutionQfeq(5-1)undertheboundaryconditions(5-2a)

(5-2b)and(5-2crsquo)canbeobtainedbyextendingthemirrorimage

methodproposedbyBerz[2]andOpdorp[3]Inadditiontothereal

sourceatXafamilyofvirtuaLimagesourcesandsinksare

introducedatthesymmetricpositionswithrespecttothebarrier

andtheohmiccontact(seeFig5-2)Openandsolidcircles

representthesourcesandsinksrespectivelyThereforethe

sourcesareatX2w十Kg4W十xg゛゜rsquo゜lsquoand-(2w-x)-(4w-x)rdquoldquo゛

andthesinksareat-X-(2w十X)-(4w十X)and2゛゛olinersquo4゛olinersquo

respectivelyWhenthematerialextendstox=士≪>thesolution

ofeq(5-l)isgivenbyp【゛】(゛゜土゛grsquo士(2゛`7oline゛g)rsquo土(2W十)rdquorsquo゜rsquo)

(seeFig5-2)Iftニheinfluenceofohmiccontactニmustbetaken

intoaccounttheminoritycarrierdistributionisexpressedusing

thefollowinginfiniteseriesinordertosatisfytheboundary

conditions(5oline2brsquoplx=OdegO)811d(5oline2c≒Plx=wdegO)rsquo

p゛[゛g]゜jp[≒ 十p[oline

十p[2゛oline]十p[-(2W-X)

+p[2w十゛g]十p[-(2w十)

十一一一一一一-一一

9 (5-5)

Theinducedcurrentsbypairsofsourcesandsinksie

p[゛g]andp[oline゜cg]rsquop[2゛olineへ]andpr-(2w-x)]rsquop[2゛十]andp[-(2v゛十)]rsquo

areexpressedbyJ(x)-J(2v゛oline゜cg)J(2w十)゛rsquo゛゜゛rsquo

respectivelywiththeaidofeq(5-4)ThenthetotalEBICis

expressedintheinfiniteseriesasfollows

-68-

Fig5-2

Source

helliphelliphellipSink

Concentration

Sdηitky

barrier

Ohmic

contact

Schematicviewofexcessminoritycarrierconcentrationpatternforeachsourceandsinkwhicharerepresentedbytheopenandsolidcircles-respectively

-69-

pr2wχ9]

plE【2w->り》】1

1rdquoMI

-E唇-

゜(2WdegO`92Wi

ミplE)rsquo゛p[2w-xg]

pl-《2w+x)】)゜91

s哺

(n

L1)

paziipEJoz

1 2 3

Normalizedscanningdistancex

0 5

M)DUd|UOISコ|}Ppazneaijoz

12 5 X)2050

Fig5-3

DependenceofEBIConthe

normalizedscanningdistanceχ(equivxL)

fullandbrokencurvesarefortニhecaseswithandwithouttheinflu-

enceofohmiccontニactrespectivelyThenormalizedsamplewidthwLis

1020and30andthenormalized

generationdepthDgisOdeg0Thevaluesofthesurfacerecombination

velocityparameterS(seetext)

areland10forupperandlower

groupofcurvesIrespectively

Fig5-4

Estimateddiffusionlength

fromthereciprocalgradientof

thecurveatthecenteroftニhe

scanningdistanceinthecaseof

DgdegOlsquoOandwLdeg1lsquoOSvaries

fromlt050L大andL訟are

forthecaseswithoutandwith

theinfluenceofohmiccontact

respectively

SurfacerecombinationvelKitypmmeterS

-70-

Dgdeg00

そー=10

L゛で

ヽ1慟1

111

25=1rsquo1

1`11

【flll

11

51s

degilOII

211`4

111

(flll゛

芒゜11゛|`

51S`|

11゛1

|ぎ=21`ヽ

||rsquo゜3|

(y

J(Xg)=J(x)-J(2v゛oline゛g

olineJ(匈゛≒

)十J(2wトxg

)十J(4wヽ4-xg

----

II

(5-6)

ThevalueofJ大convergestoacertainvalueandcanbecalculated

byacomputerincasesofanyvaluesofwLandS

InFig5-3thelogarithmofJisplottedbysolidlines

asafunctionofx(=xL)whetvwL1S1020and30and

Dgis00Thedashedlinesareforthecasewithouttheinfluence

ofohmiccontactTheupperandlowercurvesareforS=1and10

respectivelyThevaluesoflogJ大decreasesuperlinearlywithin

onediffusionlengthawayfromthebarrierThereforeonemakes

considerableerrorsifoneestimatesthevalueofLfromthe

reciprocalgradientofthecurveatarbitraryXInordertoshow

anextremeexampleweconsiderthecaseofw7Ldeg1゛08叫DgdegO`Odeg

Thereciprocalgradientofthecurveinthelinearregionat

xdeg05withoutandwiththeinfluenceofohmiccontactareputas

L大andLrespectivelyThevaluesofLandL幼thuSobtained

areplottedasafunctionofSinFig5-4WhenSisunityL

1Sabout68ZofLandL政isabout44ZofLThevaluesofL大

andL政reducetoonlyaboutonethirdofLwhenSis50

Themethodoftheanalysisforapointsourcementioned

abovecanbeeasilyappliedtothefinitegenerationdistribution

bythedividingmethoddiscussedinChaptersI工andHEspecially

inthecasesoflight-emittingdiodes(LEDrsquos)andlaserdiodes

(LDrsquos)usingGaAsandGaPthedimensionofthegenerationregion

istheorderofymforva゛20へrsquo30kVandiscomparablewiththe

thicknessoftheepitaxiallayersThereforethedividingmethod

becomesaneffectivemeanstomeasureLandSintheepitaxial

layers

-71-

Fig5-5

Q‐rsquoQ]

loline

11(52

ち5

0 50Scanningdistancex

100

(pm)

jDependenceofEBIConthescanningdistancexforn-SiSchottkydiodesThelengthWbetweenthe

barrierandtheohmiccontactis100Umthe

acceleratingvoltageVais50kVandLis20へj200lim

SolidandbrokenlinesareforSdeg104and105cmsec

respectニivelytakingthegenerationdistributioninto

accountThediffusionconstantDofholesis125

cm^sec

-72-

n-SiVa=50kVw00μm

5aD=iZ5cm2ss(cms)

1-helliphellip104

2゛l`4-----helliphellip105

`L(μm)

1へ`a-2001

≒yyhelliphelliphellip100i

5゛゛ぐ丈i

へ゛`恥i

`ヽ

`lsquolブjl

ゝゝjφ1

0h白contactム

2rsquo

5-3 ApplicationtoS1

ThediffusionlengthintheSibulkmaterialusedfor

solarcellsorLS工゛S1Scomparablewiththedimensionsofeach

elementAndsotheminoritycarrierdistributionisaffected

verymuchbyelementdimensionsTheSchottkydiodewastakenfor

afundamentalmodeltorevealtheinfluenceofsampledimensions

CalculatedEBICrsquosbythedividingmethodinthecaseof

n-Siforwdeg100umandva゛50kvareshowninFig5-5Thediffusion

constantDofholesistakenasatypicalvalueof125cm^sec

Solidanddashedlinesareforsdeg101゛and105cmsecrespectively

andLis20010050and20umforthecurvesfromupperto

lowerineachgroupThegenerationsourceisassumedtobeasemi-

sphereThenumberofthegeneratedelectron-holepairsatany

pointinthesemi-sphereisproportionaltoexp(-40(rR)2)

(rthedistancebetweenthepointandthecenterdRthe

radiusofthesemi-sphere)Thegenerationdistribution1Sassumed

inorderthatthedepthdosefunctionalongthez-axlsagreeswith

thatproposedbyEverhart[4]andthevaluesofdgandRare

5ymand11ymrespectively゛forvadeg50kvrsquo

AsshowninFig5-5theabsolutevalueofEB工Cincreases

withdecreasingSforthesameLvalueThecurvesconvergetoa

certaincurveforboths=10rsquoand105cmsecwhenLbecomesgreater

thanwForconveniencethelogJvsχcurvesaredividedinto

threepartsi

range(30≦X-

く一一

eA)nearthebarrier(0≦x≦30ym)B)middle--

70ym)andC)neartheohmiccontact(70≦x≦100--

μm)IntheregionA)peaksappearatxdeg6ymowingtotheedge

effectdescribedinsect3-3and10gヽJdecreasessuperlinearlybecause

ofthesurfacerecombinationeffectIntheregionC)logj大decreases

-73-

Fig5-6

゜1(il

四a3

U」

-01

Ddziieujjoz

゛D=1Z5cm2s巡付

1 03

orini=-

にuarrヤuarr

uarrにヤ

Ohmiccontactづ50100

Scanningdistancex(μm)

JDependenceofEBIConthescanningdistancex

forn-SiwhenLismuchgreaterthanWThesolid

linesareresultsbythethree-dimensionalsolutions

forsdeg1035times1031045)(104and105cmsec

respectivelyThedashedlineisEBICbyone-

dimensionalapproximationV=50kVw=100ymand

L=1000Uma

-74-

゛ぐpermil

゛`xズit

darrレ

rapidlybecausetheohmiccontactisacarriersinkInthemiddle

rangeB)logJ大decreasesalmostlinearlyThereciprocalgradient

ofthecurveincreasesasLbecomeslargeintherangeofL≦100pm-

Thegradientsofthecurvesarenotsoaffectedbysurface

recombinationIfvisloweredt010kVthesurfacerecombinationa

affectsEB工Cmuchmorethanforvadeg50kVbecausethegeneration

depthbecomesshallowerInfactthegradientsofthecurvesin

regionA)aresteeperthanthoseforv=50kVforthesameLvaluesa

ThereforeinthecaseofL≦100ymLandscanbedetermined-

mainlyfromtheslopesofthelinearlydecreasingregionforhigh

va(50kVinthiswork)andthesuperlinearlydecreasingregionnear

theSchottkybarrierfor10Wva(10kVinthiswork)respectively

takingtheinfluenceofohmiccontactintoaccountButinthe

caseofL≧100ymthevalueofLcannotbedetニermineddefinitely-

becausetheslopeofthecurveinthelinearlydecreasingregion

doesnotchangeevenifLvaries

WhenLbecomesmuchlargerthanwthecurvesofEBICvsX

convergetoacertaincurveCalculatedEBICrsquosinthecaseofn-Si

forva゛50kVwdeg100ymandLdeg1000ymareshownbysolidlines

1nFig5-6forsdeg1035times1031045times104and105cmsec

respectivelyThegenerationsource1Sassumedtobeapointatthe

depthdThedashedlineisasolutionofone-dimensionalg

approximation(seeappenditimes1nthischapter)Theabsolutevalueof

EBICbecomeslargerwithdecreasingSandthecurveforS40cmsec

approachestothesolutionofone-dimensionalapproximationItcan

beexplainedasfollowsInthecaseofs=Ocmsecthereisno

carrierrecombinationatthesurfaceHencethematerialcanbe

consideredtoextendtoz=_oobyintroducinganimagesourceat

(x0-d)EBICisobtainedbyintegratingdpdxinthey-zplane

atx=0AndsotheEBICbythepointsourceat(x

-75-

grsquoO゛plusmnd)using

JOoline1

Ig3paziieuijoz

Fig5-7

(a)

UI「rrsquo

a3

U」

rsquo一lsquo51 0

pdziieujjoz

Scanningdistance

(b)

X(pm)

ExperimentalresultsinSiSchottkydiodesfor

w゛200μmand83μminfigures(a)and(b)respectively

Vais1030and50kVSolidanddottニedlinesare

theoreticalresultsforL=80UmandS=50withand

withouttheinfluenceofohmiccontニactrespectively

-76-

inlsquoSiL=80μm

こ沼o

rsquoバ町「i「でなl`Jes

l悶

2卜Ohmiccontact今|

トj

rsquohelliphelliphelliphelliphellipi

15

≒|

2helliphellip1

0Scanningdistancex150(pm)00

へn-SiL=80μm

5゜`S=50

deg゜w=83um

degムExperimentalvalues2deg`4≒Vi=50kV

I゛lsquorsquo4≒oVadeg30kV

≒゜rdquoVa≪10kV

丿4

lrsquo

2lsquoo1

rsquo゜i

2degi

2Ohmiccontactrarr

050100

thethree-dimensionaldiffusionequationbecomesidenticaltothat

derivedbyone-dimensionaldiffusionequationconsideringthe

planarsourceatxrsquoxginthey-zplane[5]Howeverinpractice

SihasafinitevalueofSandsothethree-dimensionalsolution

mustbeneededinthecaseofL>wThevalueofscanbedeter-

minedfromtheabsolutevalueofEBICfollowingthediscussionof

sect4-2usingtheelectron-holepaircreationenergyE^^byan

electronbeam

TheexperimentalresultsinSiSchottkydiodeswith

w=200umand83μmmadefromonewaferareshowninFigs5-7(a)

and5-7(b)respectivelySamplepreparationsandmeasurement

procedureshavebeenalreadyshowninsect3-4Theresultsofthe

theoreticalcalculationusingL=80vimandS=50forthreedifferent

va゛s(10rsquo30and50kV)areshownbysolidlinesinbothfigures

Theresultsofthetheoreticalcalculationwithouttheinfluence

ofohmiccontactareshownbydottedlinesinFig5-7

Inthecaseofw=200ymthesamplewidthisthreetニimeslargerthan

Landsotheslopeofthelinearregion(50≦x≦120um)isnot--

verychangedbytheinfluenceofohmiccontactInthecaseof

Wdeg83umthecurvesarequitedifferentfromthoseforw=200ym

andthereciprocalgradientofthecurvesinthemiddlerange

(25≦x≦55ym)givesL=20ymwhichisaquarterofthereal--

diffusionlengthBothinFigs5-7(a)and(b)theoretical

calculationsshowgoodagreementwiththeexperimentalresuLts

whichshowsthatthemethoddiscussedinsect5-21Saneffective

meanstニoanalyzetheeffectofsampledimensions

-77-

5-4 Summary

Theminoritycarrierdistributionisaffectedverymuch

bythelengthwbetweenapotentialbarrierandanohmiccontact

ifWisequaltoorshorterthanthediffusionlengthLThe

dependenceofEBICJ大onthescanningdistancexwasinvestigated

byextendingthemirrorimagemethod

InthecaseofwL≧1logJ゛decreasesalmostlinearly-

inthemiddlerangeofthescanningdistancebuttheestimated

diffusionlengthfromthecurvesismuchshorterthanthereal

diffusionlength(eg30t044ZinthecaseofL=w)The

valuesofLandScanbedeterminedmainlyfromtheslopesof

thecurvesforhighand10Wva゛reSpectively゛takingtheinfluence

ofohmiccontニactintoaccount

工nthecaseofwLく1theslopeofthelinearly

decreasingregionoflogJvsXcurvesdoesnotchangeevenif

LvariesThedependenceofEBIConχconvergestoacertaincurve

ThevalueofLcannotbedetermineddefinitelybutthevalueofS

canbeobtニainedfromtheabsolutevalueofEBIC

TheexperimentalresultsinSiSchottkydiodesagreed

fairlywellwiththetheorywhichshowedthattheextendedmirror

imagemethodwaseffectiveinanalyzingEBICconsideringthesample

dimensions

-78-

References

[1]

[2]

[5]

OldwigvonRoosSolid-stateElectron

(1978)

211063

FBerzandHKKuikenSolid-stateElectron19

(1976)

437

CvanOpdorpPhilipsResRep32192(1977)

TEEverhartandPHHoffJApplPhys丘5837

(1971)

WHHackettJrJApplPhys

Appendix0nedegdimensionalapproximation

431649(1972)-

IfthediffusionlengthLisinfinitelylongminority

carriersdonotrecomblneuntiltheyflowintothebarrierorthe

ohmiccontactThereforethediffusioncurrentdoesnotvary

spatiallyTheminoritycarrierdistributionpcanbeexpressed

asalinearfunctionofχ1nthecaseofone-dimensional

approximation工fthepointsourceg1Slocatedatdegcgrsquop(゜c)is

putasfollows

p(x)=ax十b(a>00≦゛≦)rsquo

p(x)゜c゛十d(c<0X≦゛≦゛)゜

(5-Al)

(5-A2)

Thefactorsabcanddcanbedeterminedfromthefollowing

conditions

-79-

p(O)=0

p(w)=0

卵石

-卜-卵匹 ゜g

(5-A3)

(5-A4)

(5-A5)

(5-A6)

Theeq(5-A5)showsthecontinuityconditionatxdegxg゛andtheeq

(5-A6)givesthatallthegeneratedcarriersflowintothe

Schottニkybarrierandtheohmiccontactニwithoutrecombinationin

materialsThesolutionp(x)becomesasfoLlows

p(x)=

p(x)=

(1-ミj1)x(O≦x

--^(w-x)(Kg

NormalizedEBICJisexpressedby

J大=

-egeD

dp

-dxχ=0

=1-

こ)

3Wく

一一

Xく一一

(5-A7)

(5-A8)

X』

-80-

(5-A9)

6-1

DETERMINATIONOFLIFETIMEANDDIFFUSIONCONSTANT

BYPHASESHIFTTECHNIQUE

Introduction

Accuratedeterminationoflifetimeてofminoritycarriers

1Sveryimportantincharactニerizingsemiconductingmaterials

Thevalueofてcanbemeasureddirectlyfromthetransientresponse

aftertheinjectionofminoritycarriersTheradiativerecombina-

tionlifetimewasmeasuredinGaPandGaAsfromthedecayofphoto-

luminescence[1]cathodoluminescence[2]orelectroluminescence[3]

Thephotoconductancedecaymethod[4]Isthemostcommonlyused

techniquetomeasurelifetimeincludingradiatニiveandnon-

radiativeprocessesInthesemethodsmeasurementofTinsmall

areaoftheorderofym^isverydifficultbecausethesample

surfacemustberelativelywideinordertoobtainasufficient

signalThespatialvariationofてcouldbedeterminedfromthe

decayoftheelectronbeaminducedcurrent(EBIC)usinga

scanningelectronmicroscope(SEM)[5-8]Thevalueofてismuch

influencedbysurfacerecombinationsincelightoranelectron

beamforexcitationentersthroughthesurface

Thevalueofてcanbeobtainedfromthediffusionlength

LusingtherelationL=j5マThevalueofLcanbedeterminedbythe

spectralresponsemethodusingsolarcells[910rbythesurface

photovoltaicmethod[1011nbothmethodstheaccurateabsorption

coefficientmustbeneededtodeterminethevalueofL

AsdiscussedinChapters皿rsquov^VtheEBICmethodusingSEMisa

veryconvenienttechniquetomeasureLinsmallareaoftheorder

-81-

ofym^andtherehavebeenmanytheoretical【11-14】and

experimental[15-16]worksuptodateInthemetニhodhowever

thediffusionconstantDmustbegiveninordertoobtainT

Whentheintensityofexcitationforelectron-holepair

generationisrdquomodulatedthephaseofluminescenceorinducedcurrent

isshiftedfromthatoftheexcitationsourcebecauseofthe

recombinationofinjectedminoritycarriersinamaterialThe

valueofてcanbedeterminedfromtheamountofthephaseshift

Hwang[17]obtainedTinGaAsfromthephaseshiftofphoto-

luminescenceInthemethodtニhephaseshiftisinfluencedbythe

surfacerecombinationvelocityandtheabsorptioncoefficient

whichaffectminoritycarrierdistributionverymuchReichleta1

measuredでinSi[18-20]andGaAs[21]usingthephaseshiftin

photニ0-inducedcurrentMunakata[22]andOthmer[23]measuredて

bythephaseshiftofEBICinGeandSirespectivelyTheyused

tニhesolutionoftheone-dimensionaLdiffusionequationwithout

anyconsiderationofthesurfacerecombinationeffect

Ifsuchaphaseshiftmethodiscombinedwiththe

conventニionallinescanmethodofEBIC(iemeasurementofLusing

DCelectronbeam)thelifetimeandthediffusionconstantof

minoritycarriersinsmallareacanbedeterminedsimultaneously

Kammeta1[241determinedてandDinSiTheymadeaSchottky

barrierwithasilverpaintonSisurfacesandmeasuredEB工Cby

scanningtheelectronbeamonthesurfaceparalleltothebarrier

InthatmethodsurfacepreparationhasmucheffectonT[25]

andtheconfigurationusedbythemisnotconvenientwhenone

measuresてandDinmaterialswithsmallLTheanalysisisvery

complicatedandRoospointedouterrorsintheiranalysis[26]

andsuggestedasimpleconfiguration[271

-82-

Inthischapterwetaketheconfigurationthatthe

electronbeamscansonthesurfaceperpendiculartothebarrier

planeWiththisconfigurationtニhetime-dependentdiffusion

equationcanbesimplyreducedtothesteady-statediffusion

equationandthecomplicationintheanalysisthatRoosindicated

[26]canbeexcludedThisphaseshiftmethodcanbeappliedto

materialswithsmallLWesolvethethree-dimensionaltime-

dependentdiffusionequationtakingthesurfacerecombination

effectintoaccountandclarifytherelationofTandthephase

shifttheoreticallyWeshowthatthree-dimensionalsolutions

canbeexpressedbyone-dimensionalsolutionswithempirical

correctionfactorsandthatてandDcanbedeterminedwitニhout

anyrestrictionformodulationfrequencyExperimentalresults

inSiarealsoshown

6-2 Relationbetweenlifetimeandphaseshift

WetakeaSchottkydiodeasshowninFig6-1for

simpletheoreticalcalculationWeassumeapointgeneration

sourcewhichhastime-variabLepartgelωt(ω゜2TTfωangular

frequencyfmodulationfrequency)at(x゛0d)Whenthetldegeoline

variablepartofthenumberofminoritycarriers1Sputas

恥eiωt(isacomplexvariable)psatisfiestheconventional

steady-statediffusionequationbyintroducingthecompleχ

effectivediffusionlengthL゛eff(ΞL゛1171瓦JTL=ぷF)゜If

thetime-variablepartofEBICIsputasj`゛e(J゛1Scomplex-

EBIC)icanbeexpressedasfollowsbythemirrorImagemethod

asdiscussedinsect3-2

-83-

Fig6-1

ylご

uarrj

Schottkybarrier

uarr

Ohmiccontact

Schematicviewofeχperimentalconditionsand

definitionoftheco-ordinatesystem

-84-

Electronbeam

SOlyScanningtrack_xj

ズニに匹二oline-一一゛

lsquo9surface

lL-__--ang__helliphellip_

|`1

丑昌之

9gπLaf ―K

gdof

(ノダr7olineT

)酉ff

L大effl゛ぶ弓+T『

+0O

(-1(じ(lg)

)X[

jiご]ご

)ことりsube

dgDIL火eff

xlてこi7

dT

J(6-1)

whereeisthechargeofanelectronsisthesurfacerecombination

velocityandTisthevariableforintegratニionThefunctionK^

1sthesecond-modifiedfirst-orderBesselfunctionwithcomplex

variablesTheabsolutevalueofEBICnandthephaseshiftφ

fromthesourcearegivenasfollows

TI=

|」と

eg

φ=tan-1

Im一J

Rej゛

(6-2)

(6-3)

whereReandImstandforrealandimaginarypartsrespectively

Thevalueofnisnormalizedtobeunitywhenallthevariable

-partgcontributetothevariablepartofEB工CSincej火isa

functionofてthevalueofφbecomesafunctionofてThevalues

ofnandφcanbecalculatednumericallyWeassumeapointsource

forsimplecalculationbutthemethodmentionedabovecanbeeasily

appliedtothefinitegenerationdistributionbythedividing

methoddescribedinChapters工江andy

-85-

Fig6-2

Fig6-3

U2

Cχ310-rsquo

山5

ト2

10lsquo3

velocitysis

35225N

(Eu

一))

j^

9st^d

10

Jo}CIで噌」

ひpF

ぐりぐ

ごヽこ

W゛`みノー-

うて`゜ldegw-rsquo゜rsquordquorsquoPrime゛ご

゜二

゛゜〆ノ〆゛`゜

゜゛〆ノ

(MJD≪p)j

UMS

asEMd

ofEBICvsscanning

thealmostlinear

0 50 100 150

ScanningdistanceX(pm)

Normalizedintensityandphaseshift

distancexcurvesTheconcavecurvesand

linesarefortheIntensity(leftaxis)andthephaseshift

(rightaxis)respectivelyThesolidbrokenanddottedlines

areforf=10100and500kHz(ieωT=031314and157)

respectivelyLifetimeTistakenas5μSThediffusion

constantDis30_cm2Secandthesurfacerecombination

105CmSeC

S=105CmS

D=30ori^s

Lifetimeで(sec)

DependenceofgradientofphaseshiftdφdxonTD=30cmsecandrsquos=105cmsec

-86-

rsquoD=30crrfis

ωで=5f

5ヽ2MHz

ヽ1MHz

2`500kHz

1`

100kHz

``50kHz

`ヽ`10khtt

pwww

kHz

`ωで=01

1(jrsquo

825

1(i

725

1(jrsquo

6251(irsquo

525

10lsquo4

Mm2s)lsquo1-123lsquoj「rsquoQ心Hz」t

=10cms-10a3i

i=30kV-一一一一1003K

helliphelliphelliphelliphellip500157

Thevaluesofnandφwerecalculatedasafunction

ofscanningdistanceχforp-SiasanexampleTheresultsare

showninFig6-2whenてisputasatypicalvalueof5μs

Inthefiguretheconcavecurvesandthealmostlinearlines

areforn-χandφ-xrelationsrespectivelyThesolid

brokenanddottedlinesareforf=10100and500kHz(ie

ωT=031314and157)respectivelyThediffusionconstant

Disputas30cm^secThesurfacerecombinationvelocitysIs

takenas105cmsecsincetheordinarysurfacerecombination

velocitニyofSiis103へj105cmsecTheacceleratingvoltage

Isputas30kVThepointsourceisassumedtobelocatedat

themaximumenergydissipationdepthofabout3μmunderthe

surfacebasedonKanayarsquosmodel[28]forelectron-holepair

generationdistributニIon

Inthecaseofωてく01tニhedependenceofnonX

agreeswiththat-measuredbyaconventionallinescanmethod

usingDCelectronbeamThevalueofLcanbedeterminedfrom

theslopeofthen-χcurvestakingthesurfacerecombination-

effectintoaccountasdiscussedinChaptermThevalueof

L大effalmoStequaltoLandSOφbecomesnearlyzero

Inthecaseofωて≧01φincreasesalmostlinearly-

withxovertherangeofx≧Landthegradientdφdxbecomes-

largewithIncreasingfasshownInFig6-2Thegradient

dφdxisfoundtoIncreaseasてbecomeslargeforthesamefvalue

andnottochangeevenifSvariesfrom10^t0105cmsecfrom

thecalculationforvariousparametersFigure6-3showsthe

dependenceofdφdχonTwhenfisvariedfrom5kHzto2MHz

ThevaluesofDandsare30cm^secand105cmsecrespectively

ForeachvalueoffdφdxincreasesmonotonouslywithTwithin

therangeof01≦ωて≦5andapproachestoacertainvalue--

asymptoticallyovertherangeofωて≧5-

-87-

「ujopp」)

調uiusas^qdj〇}c心石司」

Fig6-4

Lifetimeて (sec)

10

Expressionofthedependenceofdφdxonてusingtheapproximatedsolutionsoftheone-

dimensionaldiffusioneuationinthecaseofD=30cm^secandf=10sectHzSolidlineisa

three-dimensionalsolutionLines(A)and(B)

aretheapproximatedone-dimensionalsolutionsand(Arsquo)and(Brsquo)aretheasymntotesforthethree-dimensionalsolutionThecorrectionfactorCforthethree-dimensionalsolutionis087

-88-

2(8)登ニ4F

helliphellipj(Å

(A)

D(EI)-(jじ硲ゴどこ二こhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip

2helliphelliphelliphelliphelliphelliphelliphellip(畿f3゛(c緊八(醤y3

d≫_Kii「」(A)石rsquo7『

5Ddeg30cm2sfdeg105Hz

c=087

Ursquo725J625_-52542

Ifwetakethesolutionsoftheone-dimensionaldiffusion

equationdφdxisgivenasfollows[241

O「

dφ

dx

助こ

Lω

2D

一 一 S

irfr

一万

(ωて≪1)

(ωT≫1)

(6-4)

(6-5)

Followingthethree-dimensionalsolution(eqs(6-l)(6-2)and

(6-3))asshowninFig6-3ydφdxincreasesproportionallyt07

intherangeofωてく05andreachestoacertainvalueoverthe

rangeofωて>5whichcanbeeχplainedqualitativelybyeqS

(6-4)and(6-5)respectivelyThedφdxvsTcurvesinFig6-3

canberepresentedbyonefunctionwiththecombinationofthe

approximatedsolutionsoftheone-dimensionaldiffusionequation

(eqs(6-4)and(6-5))Weshowanexampleinthecaseoff=105Hz

andD=30cm^secinFig6-4Thesolidlineisthethree-

dimensionalsolutionfromFig6-3andthedottedlines(A)and

(B)expresseqs(6-4)and(6-5)respectivelyThebrokenlines

(Arsquo)and(B゛)showtheasymptoticsolutionsofthethree-

dimensionalsolutionintherangesofωて<05andωて>5The

absolutevaluesof(A)and(Brsquo)becomeabout87Zofthoseof

(A)and(B)basedontheresultsofcalculationAsshownin

Fig6-4thethree-dimensionalsolutionisgivenbyacombination

ofthelines(Arsquo)and(Brsquo)andIsexpressedasfollows

-89-

「―」)畠一

uiMSaseudpazneaijoz

Fig6-5

rsquo0

ω^t「

NormalizedphaseshiftニLdφdxvSωてcurves

Solidlineisathree-dimensionalsolution

expressedbytheapproximatedone-dimensional

solutionswithempiricalcorrectionfactors

Brokenlineistheone-dimensionalsolution

-90-

2One-dimensionalノrsquosolution゛`4xrsquo

10バ

5acuteThree-dimensional

ぶacutesolution

2acute

(yl

言二分ヽ同r〔2μ(ldquoμ

゛1)rsquo1

5primeacute

cべ1251251cap25

dφ

dx

)=(c

TTfr TTf)ldquo゛十(c

yでワ

)rsquo゛

-91-

十1}3

(6-6)

(6-フ)

函rsquo

wherenisapositiveintegerWecalculatedeq(6-6)Inthe

casesofn=1へj5anddeterminednas31norderthatthe

solidcurveinFig6-4canbewellrepresentedbyeq(6-6)

Thevalueofc1Sthecorrectionfactorforthethree-dimensional

solutionandcisabout087asmentニionedabove

Fromeq(6-6)wecanderivethefollowingrelation

usingtheconventionaldiffusionlengthL

_

=pound石{2Σ(則2万

ThetermLdφdxisconsideredtobethenormalizedphaseshift

whichistheamountofthephaseshiftwhentheelectronbeam

scansoveronediffusionlengthItshouldbenotedthatLdφdx

isafunctニionofonlyωでFigure6-5showsthedependenceof

LdφdxonωてbythesolidlineIfthevaluesofLanddφdxare-

knownてcanbedeterminedfromthecurveforanymodulation

frequencyandDisalsoobtainedbytherelationofL=iF

Themodulationfrequencyfcanbechosenfreelyandthe

restrictionsofωΥ<050Γωて>5fortheapproximatIonneednot

tobetakenintoaccount

ThephaseshiftderivedbyMcKelvey[29]usingtheone-

dimensionaldiffusionequationisshownbythedashedlinein

Fig6-5Theestimatedvalueofωてbytheone-dimensional

solutionisabout76へ87Zofthatbythethree-dimensional

solutionforeveryvalueofLdφdxInthecaseoftheone-

dimensionalsolutionLisdetermineddirectlyfromthegradient

ofthelinearlydecreasingregionofEBICcurveandisabout

60へj80Zoftherealvaluefromtheresultsofthedetailanalysis

takingthesurfacerecombinationeffectintoaccount[14]

ThereforethevalueofωΥderivedbytheone-dimensionalsolution

isonly30へJ丁0Zoftherealvaluebecauseωてdecreases

proportionallytOLandL2intheregionsofLdφdxく03and

Ldφdx>2respectivelyOnemustusethethree-dimensional

solutioninordertodeterminetheaccuratevalueofて

6-3 ExperimentalresultsinSi

AconventionalSEMwasusedfortheprimaryelectron

beamwhichwasmodulatedat1rsquoj50kHzwiththedutyof05by

achoppingcoilinsertedintothebeampathThebeamcurrentwas

as10was10oline10AThemaximumminoritycarrierdensityinthis

experimentwasconsideredtobeabout3times1014Cmoline3andthe10w

injectionconditionwassatisfiedTheinducedcurrentwas

measuredbythevoltagedropacrosstheloadresistancewhich

wasconnectedtotheSchottkybarrierwithanohmiccontactThe

signalhadarectangularwaveformowingtothechoppedprimary

electronbeamandsothefundamentalfrequencycomponentinthe

Fourierseriesofthesignalwasdetectedbyanauto-phaselock-

inamplifierTheEBICnandthephaseshiftφfromthesource

wererecordedsimultaneously

ThediffusionlengthLisdeterminedinthecaseof

ωて<01takingthesurfacerecombinationeffectintoaccount

Thedependenceofnonxagreeswiththatニmeasuredbyaconventional

linescanmethodusingDCelectronbeamasdiscussedinsect6-2

-92-

Whenvaislowgivingtheshallowgenerationdepthsurface

recombinationhasalargeeffectonEBICWhenvaishigh

givingthedeepgenerationdepththesurfacerecombinationeffect

1SreducedTheaccuratevalueofLcouldbedeterminedbyfitting

experimentaldatatotheoreticalcurvesforboth10wandhighva゛S

(10and50kVrespectivelyInthiswork)asshownInsect3-3

Thevalueofdφdxisobtainedatanappropriate

modulationfrequencywhichsatisfiesωて>01AthighVthe

surfacerecombinationeffectIsreducedandsowechosetニhe

highestva(30kVinthiswork)asfarastheelectronbeamcould

bechoppedOncethevaluesofLanddφdxareknownthevalues

ofてandDcanbedeterminedfromthecurveinFig6-5

Sampleswerep-andn-typeSiwithtニheresistivitypof

10and01f2cmrespectivelyOhmiccontactsweremadeby

evaporatinggallium-dopedgoldandantimony-dopedgoldontothe

p-andn-typesamplesrespectivelySchottkycontactsweremade

byevaporatingaluminiumandgoldontothep-andn-typesamples

respectivelyinavacuumas10was10oline7TorrThesampleswere

insertedintoavacuumchamberforEBICmeasurementimmediately

aftertheywerecleaved

ThediffusionlengthLinp-typeSiwasdeterminedas

130μmfromthen-xcurvesinthecaseofωてく01The

experimentalresultsofthephaseshiftmethodareshownIn

Fig6-6bysolidlinesforf=5102030and50kHzrespectively

ThephaseshiftIncreaseswithxalmostlinearlyasdescribedin

sect6-2ThevaluesofてweredeterminedusingFig6-5as9595

8886and83ysfromthegradientsofthelinesinFig6-6

for5102030and50kHzrespectivelyTheobtainedvaluesof

てshowlittledifferencewitheachotherinanymeasurement

-93-

11

es^Md

Fig6-6

P-Si(r=10ncm)f=

20

1 0一

----n-Si(r=Q1ftcm)

Va=30kV

圭T

rdquo

------ニr二ご二二耳一一3

50100

Scanningdistance

150

Experimental

methodinp-(p=10

200

(μm)

resultsofthephaseshift

Ωcm)andn-type(p=01ncm)Si

-94-

rdquoolinersquordquooline`rsquolsquorsquoolinerdquordquoolinersquo50kHz

Vadeg30kVZ

10deg

30

FJ゛

一一20

〆がノrdquo〆〆〆

メノrdquo

〆〆〆〆〆ノ10

---rdquordquo|-sニニニldquo-notこ9

conditionfromωて=03(atf=5kHz)to30(atf=50kHz)

Itprovedthatthemodulationfrequencycouldbechosenfreelyas

mentionedinsect6-2Ifwetaketheaveragedvalueofて(ie

で89ys)thediffusionconstantDofelectronswasdeterminedas

19cra^secwhichalmostagreedwiththereportedvalue[301The

slightdeviationfromthestraightlineforf=50kHzmaycomefrom

unstablenessofthechoppedbeambecausethechoppingcoilused

inourexperimentwasnotdesignedforhighfrequencymodulation

above50kHz

Thediffusionlengthinn-SiwasobtainedasL=80ymand

thephaseshiftsareshowninFig6-6bybrokenlinesforf=3

10920and50kHzrespectivelyThedeterminedvaluesofてfrom

thegradientsofthelineswere889292and105usfor

fdeg3s1020and50kHzrespectivelyThevaluesofTalmost

equalwitheachotherasinthecaseofp-SiIfwetakethe

averagedvalueofT(ieで=94ps)tニhediffusionconstantD

ofholesbecomes7cm^secwhichalsoagreeswithtニhereported

value[301

Thegenerationdistributionisconsideredtobeasemi-

spheretheradiusofwhichisabout6ymatニvadeg30kVusingthe

Kanayarsquosmodel[28]Thedimensionsofgenerationdistribution

aresufficientlysmallincomparisonwiththediffusionlengthof

thesamplesThereforethepointsourceassumptioninthe

analysisisreasonable

-95-

6-4 Summary

Whentheintensitymodulatedelectronbeamisusedthe

phaseofinducedcurrent(EBIC)isshiftedfromthatofexcitation

sourcebecauseoftherecombinationinmaterialsWesolvedthe

three-dimensionaltime-dependentdiffusionequationtakingthe

surfacerecombinationeffectintoaccountandclarifiedthe

relationofてandthephaseshiftφtheoretically

Inthecaseofωて≧01φincreasesalmostlinearlywith-

Xovertherangeofx≧LThegradientdφdxbecomesafunction-

ofTandisnotaffectedbysurfacerecombinationTherelation

ofdφdxonてwasfoundtobeexpressedusingtheapproximated

solutionsoftheone-dimensionaldiffusionequatニionwithtニhe

empiricalcorrectionfactorsThenormalizedphaseshiftLdφdx

becomesafunctionofonlyωてIfthevaluesofLanddφdxare

knownてandDaredeterminedwiththeaidofLdφdxvsU3てcurve

withoutanyrestrictionformodulationfrequencyTheestimated

valueofてbytheone-dimensionalsolutionswithoutニthecorrection

factorsisonly30へノ70Zoftherealvaluederivedbythethree-

dimensionalsolution

Experimentalresultsinp-andn-typeSiSchottkydiodes

showedgoodagreementwiththetheoryandtheminoritycarrier

diffusionconstantsofelectronsandholesweredeterminedas

19and7cm^secrespectively

-96-

References

[11

[2]

[31

[4]

5]

6]

[10]

[11]

[12]

[13]

[14]

[15]

PDDapkusWHHackettJr0GLorimorandRZ

BachrachJApplPhys^54920(1974)

MBoulouandDBoisJApplPhysj旦4713(1977)

MEttenbergHKresselandSLGilbertJAppLPhys

44827(1973)

SWangrdquoSolid-stateElectronicsrdquo(McGraw一HillInc

1966)p300

WZimmermannphysstatsol(a)12671(1972)

DRHunterDHPaχmanMBurgessandGRBooker

rdquoScanningElectronMicroscopySystemsandApplications

1973rdquo(工nstPhysLondon)pp208-213

HKKuikenSolid-stateElectron19447(1976)-

AJakubowiczSolid-stateElectron22635(1980)

HTWeaverandRDNasbySolid-stateElectron

22687(1979)-

DLLileandNMDavisSolid-stateElectron

18699(1975)-

WvanRoosbroeckJApplPhys2plusmn380(1955)

WHHackettJr=JApplPhyspound1649(1972)

FBerzandHKKuikenSolid-stateElectron

19437(1976)

CvanOpdorpPhilipsResRept22192(1977)

DBWittryandDFKyserJApplPhys261387

(1965)

-97-

[16] CvanOpdorpRCPetersandMKlerkApplPhysLett

2h_125(1974)

[17]CJHwangJApplPhys4^4408(1971)

[18]

[19]

HReichlandHBerntSolid-stateElectron

18453(1975)

GSchwabHBerntandHReichlSolid-stateElectron

2091(1977)

[201JMiillerHBerntandHReichlSolid-stateElectron

21999(1978)

[211

[22]

JMiillerHReichlandHBerntSolid-stateElectron

22257(1979)

CMunakataandTEEverhartJpnJApplPhys

11913(1972)-

[23]SOthmerrdquoScanningElectronMicroscopy1978Vol1uml

(SEMIncOrsquoHare111)p727

[24] JDKaiiraiandHBerntSolid-stateElectron

21957(1978)-

【25】JDKammrdquoSemiconductorSilicon1977uml(The

ElectrochemicalSociety工nc)p491

[26] 0vonRoosSolid-stateElectron23177(1980)

[27]0vonRoosJApplPhys1^3738(1979)

[28]KKanayaandSOkayamaJPhysDApplPhys

543(1972)

[29]JpMckelveyrdquoSolidStateandSemiconductorPhysicsrdquo

(HarperandRowNewYork1966)pp439-440

[30]HFWolfrdquoSiliconSemiconductorDatardquo(Pergamon

PresslnC1969)

-98-

ⅥI

7-1

HEATTREATMENTEFFECTONDIFFUSIONLENGTHINS1

Introduction

Therehavebeenmanystudies[1]onthepropertiesofthe

processinducedfaults(PIFrsquos)Thedegradationoftheelectrical

performanceofthedeviceshasmuchconnectionwiththesegregated

impuritiesatPIFrsquosorthedecoratedfaultsofeachPIFRecently

thefaultproducedespeciallybytheoxidationathightemperatures

(IesocalledoxidationInducedstackingfault(OSF))has

receivedconsiderableattention[2-5]becausetheoxidationisa

fundamentalprocessinmakingLS工rsquosorcharge-coupleddevices(

CCDrsquos)Ravieta1[67]showedthattheelectricallyactive

OSF゛sincreasedtheleakagecurrentinprsquonjunctionsKimerllng[8]

determinedtheenergylevelofthefaultsfromtheelectron

beaminducedcurrent(EBIC)measurementsatvarioustemperatures

Generallythefaultsbecomerecombinationcentersanddecrease

thelifetimeandthediffusionlengthofminoritycarriers

Shimizu[9]showedthatthelifetimecouldbecontrolledpreferably

bytheintrinsicgetteringusingOSFrsquosRozgonyi[10]and

Tanikawa[11]reportedthattherelaxationtimeofMOScapacitors

decreasedasthedensityofOSFincreasedButtherehavebeen

alittlestudyonthequantitativeinformationofthedecreaseof

thediffusionlengthaftertheoxidationprocessathightemperatures

Inthischapterwemeasuredthechangesofthediffusion

lengthbyEBICmethodaftertheheattreatmentsathightemperature

andshowedthattheheattreatmentforafewminutescouldaffectthe

diffusionlengthatthesurfaceregionTheobservationofsurface

faultsbychemicaletchingwerealsoshown

-99-

(―)

<j)6udI

ColコこI()

Fig7-1

Heattreatmenttimet(min)

Diffusionlengthaftertheheattreatments

forvarioustimelengthsrangingfromlt0120minutesat1000degCOpenandsolidcirclesare

forthecasesindry02andArrespectivelyOriginaldiffusionlengthbeforeannealingis80pm

-100-

5ohellipumlindryO2

uml゜umlinArat1000degC

ol

12510251002

- W ゝ

rsquo _ l - ~ ヽ jS j - -

磨 卜

Fig7-2

(a)

(c)

rarr100Mm

ぶミ

卜`

r-^

rsquo

1Is

≪バ

rdquorsquo‐゛t

rsquo

grバ4≪

rsquo1

Surfacefaultsrevealedby

usingSirtletchantSamples(a)

wereannealedindryoat1000

and120minutesrespectively

-101-

い゛フバrdquo

゛para

`i

(b)

(d)

permilご}

->嗜

-゛

rsquo

III

`ヽご

いい

一J

t七

~貿で

rsquo

゛`1

鴫ヽ

rsquoq

-≪

ゝく

chemicaletching

(b)(c)and(d)

Cfor0830

一 一

- 一 一 -一 一

7-2

Experimentalresultsanddiscussions

Samplesaren-tニypeSigrownbyczmethodTheoriginal

resistivitybeforeannealingisaboutニ01ΩcmTheheattニreatment

wasdoneat1000degCintheflowofdry02andArrespectivelydeg

ThenthesampleswererinsedinHFforlmintoremovetheoxidized

layerandgoldwasevaporatedinordertomakeaSchottkybarrier

forEBICmeasurementsTheproceduresofthedeterminatニionofthe

diffusionlengthhavealreadybeendiscussedinChaptersmandでIV

Figure7-1showsthediffusionlengthaftertheheat

treatmentThetimetoftheheattreatmentwaschangedfromlto

120minutesTheopenandsolidcirclesareforthecaseIndryO2

andArrespectivelyTheoriginalvalueofdiffusionlengthis

80μmThediffusionlengthdecreasedtoabout7μmrapidlyas

tincreasedt05minandbecamealmostconstantovertherange

oft>5mlnThediffusionlengthdecreasedslightlymorerapidly

in02tニhaninArThelifetimechangedfrom5μsto003usif

thediffusionconstantofminoritycarrierswastakenasatypical

valueof125cmsecThesurfacefaultsofthesamplesannealed

indry02areSho゛linFigsdeg7-2(a)(b)(c)and(d)forlsquot゛

0830and120minrespectivelyThesampleswereetニchedby

SirtletchantforthesametimeThenumberoffaultsdidnotニ

increaseuntilt=8minbutbecameverylargeattdeg120min

ThesameresultwasobtainedforthesamplesannealedinAr

Itshouldbenotedthatthenumberoffaultsdidnotニchangedinthe

rangeofO≦t≦8minbutthediffusionlengthdecreasedrapidly--

inthesamerangeThelengthsbetweenthefaultsareverylarge

incomparisonwiththediffusionlengthinthesamplesannealed

for1くtく8minandsothediffusionlengthisconsidered

nottoberestrictedbytheaverageintervalbetweenthefaults

whenthefaultsareconsideredtobethecarriersink

-102-

TheuniformEBICwasobtainedwhentheelectニronbeamwasscanned

onthesurfacethroughtheSchottkybarrtersandthedarkpoints

correspondingtothefaultswerenotobserved

Therapiddecreaseofthediffusionlengthwasconsidered

tobecausedbytheformatonofnucleioffaultsattheearly

stageoftheheattreatmentTheverysmallnucleicanbecomethe

recombinationcenterseveniftheycannotberevealedbychemical

etchingIftheheattreatmenttimeissufficientlylongthe

nucleibecomelargeandcanberevealedbyetchingAsshownin

Fig7-2(d)thelengthbetweenthefaultsafterlongtimeheat

treatmentisthesameorderofthediffusionlengthTheformation

ofnucleiwasnotaffectedverymuchbytheoxidationbecausethe

decreaseofthediffusionlengthwasalsoobservedintheheat

treatmentinArAsisknowngenerallytheczgrownSIcontains

oversaturatedoxygenandtheformationofnucleiisrelatedtニO

theoxygenprecipitation[12]Thediffusionlengthdecreasedless

rapidlyinArthaninO2degOnereasonofthisphenomenonisconsidered

tobetheformationofSiOAnotherreasonistheoutdiffusion

ofoxygenbecauseoxygencanoutdiffusemorerapidlyinArthan

inO2degFurtherinvestigationmustbeneededfortheclarification

ofthenucleiformation

Inconclusionthediffusionlengthatthesurfaceregion

inSidecreasedtoabout10Zoftheoriginalvalueafterthevery

shortheattreatmentat1000degCforafewminutesNevertheless

thesurfacefaultsrevealedbychemicaletchingdidnotchange

Thenucleioffaultswereconsideredtobeformedattheearly

stageofheattreatmentandtheybecameminoritycarrier

recombinationcentersThedecreaseofthediffusionlengthwasnot

soaffectedbytheambientgases(ieoxygenorinertone)Much

attentionmustbepayedintheheattreatmentprocessathigh

temperatureevenifthetimeIsveryshort

-103-

i J I

References

[1]

21

31

71

81

[91

[10]

[n]

[12]

HFoilNGoreleandB0KolbesetirdquoSemiconductor

Silicon1977rdquo(JElectrochemicalSocietyInc

Prircetion1977)pp565-574

DJDThomasphysstatso1旦2261(1963)

CMMelliar-SmithrdquoCrystalcefectsinsiliconintegratニed

circuits-TheircauseandeffectrdquoinrdquoTreatieson

MaterialScienceandTechnologyrdquovol11(AcademicPress

NewYork1977)

KVRaviandCJVarkerJApplPhys45263(1974)

SMHuJApplPhys513666(1980)

KVRaviCJVarkerandCEVolk

JElectrochemSoc120533(1973)-

CJVarkerandKVRaviJApplPhys亘272(1974)

LCKlmerlingHJLeamyandJRPatel

ApplPhysLett30217(1977)

HShimizuAYoshinakaandYSuglta

JpnJApplPhys17767(1978)

GARozgonyiandRAKushner

JElectrochemSoc123570(1976)-

KTanikawaYItoandHSei

ApplPhysLett28285(1976)

JRPatelrdquoSemiconductorSilicon1977rdquo(The

ElectrochemicalSocietyIncPrinceton1977)

pp521-545

-104-

ⅧI CONCLUSIONS

InthepresentstudyEBICwasanalyzedquantitativelyby

solvingthesteady-stateortime-dependentthree-dimensional

diffusionequationsTheinfluenceofthefinitegenerationvolume

onEBICwasdiscussedandanImprovedmethodtocharacterize

thephysicalpropertiesinthesmallselectedareasofsemiconduc-

torswassuggestedTheobtニainedresultswereasfollows

InChapterHtheshortdiffusionlengthoftheorderof

ymcouldbedeterminedbythenormalincidencemethodofEBIC

Variousmodelsforgenerationdistributionusedintheanalysis

yieldedtheambiguityforthedeterminationofthediffusionlength

andtheelectron-holepaircreationenergybyanelectronbeam

Detailedinformationonthegenerationdistributionmustbe

necessarytoanalyzeEBICaccurately

InChaptニermthegenerationvolumeofminoritycarriers

hadrsquoaconsiderableeffectonEBICinthelinescanmethod

especiallywhenthedimensionsofthegenerationvolumewasequal

toorlargerthanthediffusionlengthWhentheaccelerating

voltagewaslowandsothegenerationdepthwasshallow

surfacerecombinationhadalargeeffectonEBICWhereaswhen

theacceleratingvoltagewashighandsothegenerationdepth

wasaslargeasthediffusionlengthsurfacerecombinationhad

aslighteffectonEBICTheaccuratevaluesofphysicalparameters

suchasthediffusionlengthshouldbedeterminedbyfittingthe

experimentaldatatothetニheoreticalcurvesforalltheaccelerating

voltagesTheexistenceofamaximuminEBICnearthebarriercould

beexplainedbythersquoedgeeffectrsquoattributedtothefinite

generationvolume

-105-

InChapter】5inthelinescanmethodthedependence

ofEBIConthescanningdistancerepresentedmainlythelateral

extentofthegenerationdistributionwhentheacceleratingvoltage

washighandwhenthedimensionsofthegeneratニionregionwere

largerthanthediffusionlengthThethree-dimensionalgeneration

distributionbasedupontheexperimentalresultsforthenormal

incidencecouldexplaintheexperimentalresultsofthelinescan

methodInGaAsthecenterofthegeneratニionregionwaslocated

atthepointof0130fthemaximumelectronrangeandthe

radialdistributionfromthecentニerwasshowntobeGaussianwith

anexponentニof54Q82Thevaluesof38へj44eVfortheelectron-

holepaircreationenergybyanelectronbeamwasobtainedtaking

thesurfacerecombinationeffectintニoaccount

InChapterVinthelinescanmethodtheminoritycarrier

distributionwasaffectedverymuchbyanohmiccontactwhenthe

lengthwbetweenthepotentialbarrierandtheohmiccontactwas

lessthanoneortwodiffusionlengthsTheslopeofthecurveof

EBICvsscanningdistancedidnotchangeevenwhentニhediffusion

lengthvariedandthediffusionlengthcouldnotbedetermined

definitelyfromtheslopeofthecurveTheabsolutevalueof

EBICwasdependentonthesurfacerecombinatニionvelocityand

thelengthW

InChapterⅥ[thephaseshiftbetweenthemodulated

electronbeamandEBICwasclarifiedbysolvingthethree-

dimensionaltime-dependentdiffusionequationTherelation

betweenthephaseshiftandthelifetimewasfoundtobeexpressed

usingtheapproximatedsolutionsoftheone-dimensionaldiffusion

equationwithempiricalcorrectionfactorsThelifetimeandthe

diffusionconstantofminoritycarrierscouldbedetermined

definitelywithoutanyrestrictionformodulationfrequency

-106-

InChapterVIIthediffusionlengthinthesurfaceregion

ofSiwasfoundtobedecreasedverymuchafterheattreatment

at1000degCforonlyafewminutesneverthelesssurfacefaults

revealedbychemicaletchingwerenotincreasedThenuclei

ofthefaultsmightbeformedattheearlystageofheattreatment

ThisinvestigationprovedthatEBICcouldbeanalyzed

quantitativelyinthesmallselectedareaconsideringthethree-

dimensionalgenerationdistributionbyanelectronbeamBut

thereexistsomepointstobestudiedfurtherasfollows

FirstbyEBICmethodthetotニalrecombinationlifetimeincluding

bothradiativeandnon-radiativeprocessescanbemeasuredBut

onecannotobservetheradiativerecombinatニionlifetimealone

whichIstheimportantparametニertocharacterizethellght-emittニing

diodesorlaserdiodes[1]Deeperunderstandingcanbeacquired

byinvestigatingtheluminescenceemitニtedbyrecombinationof

generatedelectron-holepairs(iecathodoluminescence)[23]

SecondlyEBICtechniquecannotrevealtheenergylevelsand

densitiesofimpuritiesandtrapsaccuratelywhichaffectthe

electricalpropertiesofmaterialsverymuchTherehavebeena

fewreports[4]todeterminetheenergylevelsoffaultsinSi

fromEBICmeasurementsatvarioustemperaturesButthe

experimentalaccuracyofEBICtニechnlqueisinferiortothat

ofthephotoluminescence[5]orthecapacitance[67]methods

Thirdly万thedoseofhighenergyelectronbeldquo万171万causesdamagesin

samplesSeveralinvestigationshaveshownthedecreaseoftニhe

tニhresholdvoltageinMOSdevices[8]andtheincreaseofthe

interfacestatedensitybetweentheoxideandthesemiconductors[9]

-107-

Improvementsofmeasurementtechniques(ieuseofthe10W

energyprimaryelectronbeam万orlthedecreaseoftニhetotal

amountofdose)wirsquollbenecessary

Electricalpropertiesofsemiconductorscanbecharacterized

collectivelybyEBICjointlywiththeothertechniqueswhich

complementtheweakpointsinEBICmethod

REFERENCES

[1]

[21

[5]

[6]

[7]

[8]

[9]

PDDapkusWHHackettJr0GLorimorandRZ

BachrachJApplPhys45

4920(1974)

DBHoltandBDChasephysstatS01(a)旦旦

135(1973)

MBoulouandDBoisJApplPhys 484713(1977)

LCKimerlingHJLeamyandJRPatel

ApplPhysLett30217(1977)

HBarryBebbandEWWilliamsrdquoSemiconductorsand

Semimetalsrdquo(edRKWillardsonandACBeer

AcademicPress1972)vol8pp182-392

SMSzerdquoPhysicsofSemiconductorDevicesrdquo(JohnWiley

SonsInc1969)

DVLangJApplPhys453023(1974)

WJKeeryK0LeedyandKFGallowayrdquoScanning

ElectronMicroscopy1976rdquo[IITR]Chicago)pp507-514

RHezelSolid-stateElectron11^

735(1979)

-108-

4i

rsquoII

LISTOFPUBLICAT工ONS

[1]

[21

[3]

[4]

[5]

[6]

Papers

Theinfluenceofthegenerationvolumeofminoritycarriers

onEBICrdquo

TFuyukiHMatsunamiandTTanaka

JPhysDApplPhys131093-1100(1980)

rdquoAnalysisofEB工CconsideringthegeneratニIondistribution

ofminoritycarriersrdquo

TFuyukiHMatsunamiandTTanaka

JPhysDApplPhys131503-1510(1980)

rdquoDeterminationoflifetimeanddiffusionconstantof

minoritycarriersbyaphaseshifttechniqueusing

electronbeaminducedcurrentrdquo

TFuyukiandHMatsunami

JApplPhys旦(1981)

rdquoAnalysisofelectronbeaminducedcurrentconsidering

sampledimensions一一-Measurementofdiffusionlength

andsurfacerecombinationvelocity-rdquo

TFuyukiandHMatsunami

JpnJApplPhys20(1981)No4

rdquoInfluenceofminoritycarriergenerationdistributionon

electronbeaminducedcurrentinthenormalincidencemethodrdquo

TFuyukiandHMatsunami

(tobepublished)

rdquoHeattreatmenteffectondiffusionlengthinSirdquo

TFuyukiandHMatsunami

(tobepublished)

-109-

[1]

[21

[3]

PublicationsintheInstituteofElectronicsandCommunication

EngineersofJapan

(inJapanese)

rdquoMeasurementofminoritycarrierdiffusionlengthby

EBICmethodrdquo

TFuyukiHMatsunamiandTTanaka

ReptTechSSD78-102(Feb1979)

rdquoCharacterizationofdiffusionlengthandlifetimebyEBICrdquo

TFuyukiandHMatsunami

ReptTechSSD79-103(Feb1980)

rdquoMeasurementoflifetimeanddiffusionconstantofminority

carriersbyphaseshifttechniqueinEBICrdquo

TFuyukiandHMatsunami

TransSectionJ63-C832-837(1980)

-110-

  • page1
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Page 3: CHARACTERIZATION OF SEMICONDUCTORS BY Title ELECTRON …

犬CHARACTERIZATIONOFSEMICONDUCTORS

IBY

ELECTRONBEAMINDUCEDCURRENT

BY

TAKASHIFUYUKI

JANUARY1981

DOC

1981

電気系

DEPARTMENTOFELECTRONICS

KYOTOUNIVERSITY

KYOTOJAPAN

1 一 心

ABSTRACT

-Theelectronbeaminducedcurrent(EBIC)wasanalyzed

quantitativelyconsideringthethree-dimensionalgeneration

distributionbyanelectronbeamThesolutionsofthesteady-

stateortime-dependentdiffusionequationsassumingapoint

sourcecanbeappliedtothecaseofthefinitegeneration

distributionbythedividingmethodTheEBICwasfoundtobe

affectedverymuchbythegenerationdistニributiontheextentof

whichwascomparablewiththeminoritycarrierdiffusionlength

InthelinescanmethodthedependenceofEBIConthescanning

distancerepresentsmainlythelateralextentofthegeneration

distributionThethree-dimensionalgenerationdistributionvas

clarifiedcombiningthenormalIncidenceandthelinescanmethods

ofEBICTheImprovedmethodtomeasurethediffusionlength

andthesurfacerecombinationvelocitywassuggested

Theminoritycarrierdistributionisinfluencedverymuch

bythesampledimensionswhentheyareequaltoorsmallerthan

thediffusionlengthTheEBICwasanalyzedbyasimplemethod

usinganimagesource-and-sinkdistributionTheEBICwasfound

tobedependentonthesurfacerecombinationvelocityand

thesampledimensionsratherthanthediffusionlength

Thelifetimeandthediffusionconstantofminority

carrierscouldbedetermineddefinitelywithoutanyrestriction

ofmodulationfrequencybythephaseshifttechniqueusingEBIC

Theimprovedmethodtomeasurethediffusionlength

wasappliedtotheheattreatmenteffectinSiThediffusion

lengthwasfoundtobedecreasedverymuchaftertheheat

treatmentat1000degCforonlyafewminutes

-1-

Thephysicalpropertiessuchasthediffusionlengthin

thesmallselectedareascouldbecharacterizedbyEBIC

consideringthethree-dinensionalgenerationdistributionbyan

electronbeamandthesampledimensionsExperimentalresults

inSiandGaAsshowedgoodagreementwiththetheoryandthe

generationdistributionsinSiandGaAswererevealedWitニh

experiments

一旦-

hellipJVi_--Wrsquordquo>>-trsquomjrsquordquordquo^>-≫^

f1

ACKNOWLEDGEMENTS

Theauthorwishestoexi】resshisdeepgratitudetoformer

jブProfessorTetsuroTanakaforhiscontinuingguidanceandワバandrrsquoI

helliphellipノ1encouragementTheauthorwishestoexpresshis9万ざlltや1appreciation

toAssociateProfessorHiroyukiMatsuna万万mlforhispreciousguidance

andhelpfuladvicethroughouttニhepresentstudyTheauthor

acknowledgesProfessorAkiraKawabataforhisgenialguidanceand

encouragementTheauthorisgがIattilltoProfessorToshinoriTakagi

forhisstimulatingdiscussionsandusefulcriticismsonthemanuscript

TheauthorwouldalsoliketothankProfessorAkioSasakifora

criticalreadingofthemanuscriptandvaluablecomments

MuchattentionisduetoDrJuniiSaraieDrShigehiro

NishinoandDrAkiraSuzukifortheircontinuousencouragement

andstimulativediscussions

TheauthorthanksothermembersofSemiconductorLaboratory

fortheirconsiderableassistanceandexperimentalfacilities

一斑-

CONTENTS

ABSTRACT

ACKNOWLEDGEMENTS

L工STOFSYMBOLS

INTRODUCTION

References

i一m

VL

lVO

INFLUENCEOFMINORITYCARRIERGENERATIONDISTR工BUTION13

0NELECTRONBEAMINDUCEDCURRENTINTHENORMALINCIDENCE

METHOD

2-1

2-2

2-3

Introduction

Determinationofdiffusionlengthandelectron-

holepaircreationenergy

ExperimentalresultsinGaAs

2-4Summary

References

13

15

VOON

CMCM

30

DETERMINATIONOFDIFFUSIONLENGTHSURFACERECOMBINATION31

VELOCITYANDELECTRON-HOLEPAIRCREAT工ONENERGYBYTHE

LINESCANMETHOD

3-1Introduction31

3-2Surfacerecombinationeffectconsideringpoint33

source

3-3Analysisofelectronbeaminducedcurrenttaking37

tニhree-dimensionalgenerationdistributioninto

account

3-4ExperimentalresultsinSi

3-5Summary

References

一分-

`j7

44

48

】V

V江

ⅧI

ANALYSISOFTHREE-DIMENSIONALGENERATIONDISTRIBUTION50

BYTHECOMBINATIONOFTHENORMALINCIDENCEANDTHE

L工NESCANMETHODS

4-1Introduction

4-2 Influenceofthree-dimensionalgeneration

distributiononelectronbeaminducedcurrent

02

inin

4-3Three-dimensionalgenerationdistributioninGaAs57

4-4Summary

References

12

vOVD

ANALYSISOFELECTRONBEAMINDUCEDCURRENTCONSIDERING64

SAMPLEDIMENSIONS

5-1Introduction

5-2

5-3

Determinationofdiffusionlengthandsurface

recombinationvelocity

ApplicationtoSi

5-4Summary

References

Appendix

DETERMINATIONOFLIFETIMEANDDIFFUSIONCONSTANT

BYPHASESHIFTTECHNIQUE

6-1Introduction

6-2Relationbetweenlifetimeandphaseshift

6-3ExperimentalresultsinSi

6-4Summary

References

HEATTREATMENTEFFECTONDIFFUSIONLENGTHINS1

7-1Introduction

7-2Experimentalresultsanddiscussions

References

CONCLUS工ONS

References

LISTOFPUBLICATIONS

4vO

CVD

73

78

9VO>

77

81

lro

88

CNJVO

qNas

7O

O^(J

99

102

104

105

108

109

-V-

LISTOFSYMBOLS

Cl

cBC

ggpgBELOS嚢

cdDDeEfgGIIIIIlj一jJ

J大

correctionfactorwithwhichthethree-dimensionalsolutions

oftheヽgradientofphaseshiftcanbeexpressedbytheone-

dimensionalapproximations

exponentofGaussiandistribution

positionofgenerationsourcefromthesurfacealongthedepth

diffusionconstantofminoritycarriers

(equivdgL)normalizedgenerationdepth

chargeofanelectronz

electron-holepaircreationenergybyanelectronbeam

modulationfrequencyofprimaryelectronbeam

generationrateofactualpointsource

variablepartofgenerationsource

thewholegenerationstrengthinthegenerationregion

Imaginaryunit

primaryelectronbeamcurrent

measuredelectronbeaminducedcurrent

currentwhichflowsthroughtheloadresistance

backwardsaturationcurrent

shortcircuitcurrent

electronbeaminducedcurrent

variablepartofcomplexelectronbeaminducedcurrent

(≒n)normalizedelectronbeaminducedcurrentitbecomes

unitywhenallthegeneratedcarrierscontributeto

electニronbeaminducedcurrent

normalizedelectronbeaminducedcurrentconsideringthe

Influenceofohmiccontact

一吐-

誉~Lay

L大eff

p卵`μrRRCReRmSStTuva

correctionfactorfortheincidentbeamenergyconsidering

theenergylossduetobackscatteredelectrons

thermalvoltagersquo259mVatroomtemperature

second-modifiedfirst-orderBesselfunction

diffusionlengthofminoritycarriers

diffusionlengthestimateddirectlyfromtheslopeof

electronbeaminducedcurrentvsscanningdistancecurve

diffusionlengthestimateddirectlyfromtheslopeof

electronbeaminducedcurrentvsscanningdistancecurve

consideringtheinfluenceofohmiccontact

(ΞLJ百石iT)complexeffectivediffusionlength

distニributionofminoritニycarrierdensity

distributionofminoritycarrierdensityconsideringthe

influenceofohmiccontニact

variablepartofthedistributionofminoritycarrier

densitycomplexvariable

distancebetweenthecenteroftニhegenerationregionand

eachdividedsegment

radiusofgenerationregion

centerofgenerationregion

extraporatedelectronrange

loadresistance

maximumelectronrange

surfacerecombinationvelocity

(ΞS(Lて))surfacerecombinationvelocityparameter

time

variableforintegrat10n

para万7rdquo万eterforGaussiandistribution

acceleratingvoltageofprimaryelectronbeam

一吐-

rdquod

wm

Xxx

χy

ZZ

np

Pau

^GaAs

SpてφΦω

distancebetweenthepotentialbarrierandtheohmiccontact

depletionlayerwidth

metalthicknessofSchottkydiode

Cartesianco-ordinateofscanningdistance

(ΞxL)

distancebetweenthepotentialbarrierandthegeneration

pointalongthescanningdirection

(ΞL)

Cartesianco-ordinateonthescanningsurfacenormalto

thescanningdirection

Cartesianco-ordinatealongthedepth

peakoftheGaussiandistribution<

(=J)collectionefficiency

collectionefficiencyofthevariablepartニofthegeneration

source

resistivityofsemiconductors

massdensityofAu゜189gcm^

massdensityofGaAs゜53gcm^

massdensityofSi=23gcm^

minoritycarrierlifetime

phaseshiftbetweentheelectronbeaminducedcurrentand

tニhemodulatedgenerationsource

diameterofprimaryelectronbeam

angularfrequencyofmodulatedprimaryelectronbeam

-VnL-

IINTRODUCT工ON

Theremarkableprogressinthesolidstatedevicesisowing

totheadvancementinthecharacterizationtechniqueofthedevice

materialsWhenthedeviceshavingnewfunctionsaredevelopedthe

detailknowledgeofthephysicalpropertiesofthesemiconducting

material(bandgaplifetimeandmobilityofcarriersetc)mustbe

neededInparticularthosepropertiesmustbecharacterizedafter

theactualmanufacturingprocessbecausetheoriginalpropertiesmay

beaffectニedbythevariousprocessconditions

Inrecentyearstocharacterizeverysmalldevices(ie

LSI゛sorlaserdiodes)therehasbeenagrowinginteresttousea

finelyfocusedelectronbeamThetwodimensionalInformationofthe

materialpropertiescanbeobtainednon-destructivelywithhigh

spatialresolutionfromtheelectronbeamInteractionwithsamples

[121Surfacemorphologycanbeobservedwithgreatニdepthoffocus

byascanningelectronmicroscope(SEM)Crystaldefectsinthin

samplesaredetectedusingascanningelectrontransmission

microscope(STEM)[34]AscanningAugerelectronmicroscope(SAM)

[5]hasbecomeaveryusefultooltoanalyzethesurfaceandthe

interfaceregion

Themethodusinganelectronbeaminducedcurrent(EBIC)[6-10]

1saveryconvenienttechniquetodeterminethefundamentalparameters

(egthediffusionlengththelifetimeandthesurfacerecombination

velocityofminoritycarriers)whichcontroltheelectricalperfor-

manceofthedevicesTheelectron-holepairsgeneratedbyanelectron

beamareseperatedbytheinternalfieldInp-njunctionsorSchottky

barriersandthecurrent1SInducedIntheexternalcircuitThe

EBICdependsverymuchondiffusionandrecombinationofminority

carriersInsemiconductorsandthediffusionlengthetccanbe

-1-

Fig1-1

type

type

Primaryelectrbe≪m

^^trrttDepletionlayer

Electron-hotep弗i「6gerwrationregion

Primaryelectronbeam

rArrScanningdirection

(A)

(B)

Principalconfigurationstomeasurethe

electronbeaminducedcurrent(EBIC)

(A)normalincidencemethod

(B)linescanmethod

-2-

く二rArr|t夕

EBICく二rArr

-一一--

p-typentype

aver`

1ミミ二l∽rsquoebic

determinedfromtheanalysisofEBICInadditiontothetwodlmen-

sionalinformationofthediffusionlengthandthelifetimetheir

variationsalongthedeptニhcanbeobtainedforvariousgeneration

depthsbychangingtheacceleratingvoltageofanelectronbeam

TheprincipalconfigurationstomeasureEBICarethersquonormal

incidencemethodrsquoandthersquolinescanmethodrsquo(seeFig1-1)Inthe

normalincidencemethodtheelectronbeam1Sincidentnormaltothe

barrierplaneandisscannedonthesurfaceparalleltothatplane

ThedislocationsanddefectsinSiwereobservedinp-njunctionsand

Schottkybarrierdiodes[11-28]Inrecentyearselectricalactivity

ofoxidationinducedstackingfaults(OSF゛s)anditsrelationwith

deviceperformanceshavebeenstudied[29-35]Thenormalincidence

methodisalsousedforthefailureanalysisoftニheMOSdevices[36-

39]Usingthelinescanmethodthediffusionlengthandthesurface

recombinatニionvelocitycanbedeterminedfromthedependenceofEBIC

onthescanningdistancewhentheelectronbeamisscannedacrossthe

barrierTherehavebeenmanytheoretical[AO-46]andexperimental

[47-69]reportstomeasurethediffusionlengthandthesurface

recombinationvelocityinlight-emittingdiodes(LEDrsquos)andlaser

diodes

InalmostalltheworkssofarEB工Chasbeenanalyzedonly

qualitatively0rsemi-quantitativelyThediffusionlengthandthe

surfacerecombinationvelocityhavebeendeterminedunderrather

specialconditionsasmentionedbelowforthesimpletheoretical

calculationInthenormalincidencemethodtheyconsideredonly

theone-dimensionalgenerationdistributionalongthedepth[70-75]

undertheconfigurationthatthelateralextentofthegeneration

volumewasverysmallcomparedwithsampleareasInthelinescan

methodthegenerationvolumewasassumedtobeapoint[53546061]

undertheconditionthatthegenerationvolumewassufficiently

-3-

smallerthanthediffusionlengthandthesampledimensionsBut

intheactualcasethegenerationvolumehasafinitethree-

dimensionalextentreLatedtotheacceleratingvoltage[76-78]

Thelatestmicroelectronicdevices(ieLSIrsquosandthelaserdiodes

etc)havethesamedimensionsasthegenerationvolumeandS0

theanalysesconsideringtニhepointsourceortheone-dimensional

generationdistributニionareinaccuratetodeterminethediffusion

lengthandthesurfacerecombinationvelocityThenewmethodfor

thequantitativeanalysisofEBICmustbedevelopedtakingthethree-

dimensionalgenerationdistributionandtheinfluencesofthesample

dimensionsintoaccount[7980]

InthepresentstudyEBICisanalyzedquantitativelyby

solvingthesteady-stateortime-dependenttニhree-dimensionaldiffusion

equationsTheinfluenceofthefinitegenerationvolumeonEBICis

discussedwhentheextentofthegenerationvolumecannotbeignored

andimprovedmetニhodsaresuggestedtomeasurethephysicalproperties

(diffusionlengthlifetimeandsurfacerecombinationvelocityof

minoritycarrierselectron-holepaircreationenergybyanelectron

beametc)inthesmallselectニedareas

InChapternvariousmodelsforthegeneratニiondistribution

alongthedepth[7781-83]arecomparedwitheachotherandtニhe

influenceofthegenerationdistributiononthedeterminationofthe

diffusionlengthbythenormalincidencemethodisdiscussed

ChapterⅡIshowstheinfluenceofthegenerationvolumeon

EB工Cinthelinescanmethodtakingtニhesurfacerecombinationeffect

intoaccountAnimprovedmethodforthedeterminationofthe

diffusionlengthandthesurfacerecombinationvelocityisdescribed

-4-

InChapterVthree-dimensionalgenerationdistribution

isclarifiedbymeasuringEBICusingboththenormalincidenceand

thelinescanmethodsinthesamesamplewhichyieldsthe

quantitativeanalysisofEB工C

ChaptervdescribestheInfluenceofthesampledimensions

onEBICInthelinescanmethodEBICisInvestigatedbyextending

themirrorimagemethodlsquo[41-43]whenthediffusionlengthisof

theorderofthesampledimensions

InChapterWthephaseshifttechniqueinthemeasurement

ofEBIC[84-86]isdescribedTherelationbetweenthelifetime

andthephaseshiftisclarifiedbysolvingthethree-dimensional

time-dependentdiffusionequationThelifetimeandtニhediffusion

constantofminoritycarrierscanbedeterminedcombiningthe

phaseshifttechniquewiththeconventionallinescanmethod

Chaptervnshowstheheattreatmenteffectonthediffusion

lengthinSi

FinallyconclusionsandsuggestionsforfurtherInvestigation

aresummarizedinChaptervnr

ExperimentalresultsinSiandGaAsareshovmineverychapter

Themethoddiscussedinthesechapterscanbeappliedeasilyto

anysemiconductormaterialsbyconsideringthephysicalproperties

inherentinthematerials

-5-

References

[1

[21

[3]

4]

5]

6]

[7]

[8]

[9]

[10]

VEJohnson十Sm119151p763

0CWellsSEM1972p375

pMrdquoPetroffDVLangJLStrudelandRALogan

SEM71978pp325-332

CELymanSEM1978pp529-536

NCMcDonaldSEM1971p89

DBHoltrdquoQuantitativeScanningElectronMicroscopyrdquo

(DBHolteta1edsAcademicPress974)pp213-286

DBWittryrdquoMicroprobeAnalysisrdquo(CAAndersoned

JohnWileySonsNewYork1973)pp123-187

CJVarkerrdquoNondestructiveEvaluationofSemiconductor

MaterialsandDevicesrdquo(edJayNZemelNATOADVANCED

STUDYINST工TUTESSERIESSERIESBPhysicsvol46

PLENUMPRESS1979)pp515-580

HJLeamyLCKimerlingandSDFerris

SEM1978pp717-725

ThebibliographyonEBICislistedinthefollowing

K0LeedySolidStateTechnologyFeb1977pp45-48

--

-- - -

rdquo-

rdquo- - 言

争心- -

SEM19xxrdquoScanningElectronMicroscopyrdquoProceedingofAnnualConference

before1977(IITResearchInstituteChicago)

after1978(SEMIncAMFOrsquoHare)

-6-

[11]JJLanderHSchrelberJrTMBuckandJRMathews

ApplPhysLett旦206-207(1963)

[12]WCzajaandGHWheatleyJApplPhys亜

2782-2783(1964)

[13] WCzajaandJRPatelJApplPhys11476-1482

(L965)

[14]NFBNeveandPRThorntonSolid-stateElectron

旦900-901(1966)

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

IGDaviesKAHughesDVSulwayandPRThornton

Solid-stateElectron9275-279(1966)-

WCzajaJApplPhysyi918-919(1966)

DVSulwayPRThorntonandMJTurner

Soli-StateElectron11567-568C1968)-

AJRKockSDFerrisLCKimerlingandHJLeamy

ApplPhysLett27313-315(1975)

DBHoltandROgdenSolid-stateElectron1937-40(1976)-

HJLeamyLCKimerlingandSDFerris

SEM1976pp529-538

TKatoTMatsukawaandRShlmizu

ApplPhysLett26415-416(1975)

RBMarcusMRobinsonTTShengSEHaszkoand

SPMurarkaJElectrochemSOC124425-430(1977)

LCKimerlingHJLeamyandJRPatel

ApplPhysLett30217-219(1977)

DEIoannouandSMDavidson

physstatsol(a)丘旦K1-K4(1978)

-7-

[25]

[26]

HBlumtrittRGlelchmannJHeydenderichandH

Johansenphysstatsol(a)55611-620(1979)

HMennigerHRaidtandRGleichmann

physstat-sol(a)5旦173-180(1980)

[27]pAshburnandCJBullSolid-stateElectron

Tl_105-110(1979)

[28] pAshburnCJBullandJRABeale

JApplPhys503472-3477(1979)

[29]KVRaviCJVarkerandCEVolk

JElectrochemSoc120533-541(1973)-

[30]

【31】

[32]

[33]

[34]

[35]

[36]

[37]

[38]

[39]

[40]

CJVarkerandKVRaviJApplPhys45272-287(1974)

SKawadoYHayafujiandTAdachi

JpnJApplPhys14407-408(1975)

TESeidelSEHaszkoandDMMaher

JApplPhys485038-5042(1977)

AMurgaiJYChiandHCGatos

JElectrochemSoc1271182-1186(1980)-

SKawadqJpnJApplPhys191591-1602(1980)

JMDishmanSEHaszkoRBMarcusSPMurarka

andTTShengJApplPhys502689-2696(1979)

JLGatesand0KGriffith

ApplPhysLett27kZ-45(1975)

JFKatalanoSEM71976pp521-528

PRoltmanandWRBottomsSEM1977pp731-738

CLWilsonSolid-stateElectron23345-356(1980)-

WHHackettJrJApplPhys431649-1654(1972)

-8-

[41]

[42]

[431

[44]

[45]

【46】

[47]

[48]

[49]

[50]

FBerzandHKKuikenSolid-stateElectron

19437-445(1976)

CvanOpdorpPhilipsResKept32^192-249(1977)

0vonRoosSolid-stateElectron互lsquo1063-1067(1978)

0vonRoosSolid-StateElectron211069-1077(1978)

0vonRoosSolid-stateElectron22113-114and773-778-

(1979)

WvanRoosbroeckJApplPhys旦D380-391(1955)

DBWittryandDFKyserJApplPhysj11387-1389

(1965)

HHiguchiandHTamura

JpnJApplPhys4^

316-317(1965)

YuPDemidovRPGurovaYuMKushnirAIFrltner

andDVFetisovSovPhys-Semicond1030-1035(1968)

KMaedaAKasamiMToyamaandNWakamatsu

JpnJApplPhys旦65-75(1969)

[51]ZhIAlferovVMAndreevVIKorolrsquokovand

vIStreminSovPhys-Semicond41113-1116(1971)

[52]

[53]

[54]

[551

CJHwangSEHaszkoandAABergh

JApplPhys425117-5119(1971)

WHHackettJrRHSaulRWDiχonandGWKammlott

JApplPhys432857-2868(1972)

WZimmermannphysstatsol(a)^2671-678(1972)

MAvenJZDevineRBBolonandGWLudwlg

JApplPhys434136-4142(1972)

-9-

[56]

[57]

[58]

[59]

【60】

[61]

[62]

[63]

[64]

[65]

[66]

GLidgardSolid-stateElectron15159-164(1972)

DBHoltBDChaseandMCenslive

physstatsol(a)20459-467(1973)-

DBHoltandBDChasephysstatsol(a)2(

135-144(1973)

CvanOpdorpRCPetersandMKlerk

ApplPhysLett24125-126(1974)

LJBalkEKubalekandEMenzel

IEEETransED-22707^712(1975)-

LJastrzebskiJLagowskiandHCGatos

ApplPhysLett11_537-539(1975)

LJBalkEKubalekandEMenzelSEM71975pp447-455

JJOakesIGGreenfieldandDLPartaln

JApplPhys丘旦2548-2555(1977)

MLanirAHBVanderwyckandCCWang

JApplPhys496182-6184(1978)

DLPartainAGMilnesandLFVassamlllet

JElectrochemSoc1261584-1588(1979)-

NTohgeTMinamiandMTanaka

JpnJApplPhys172155-2156(1978)

【67】DLPartainAGMilnesandLFVassamillet

JElectronicMaterials旦493-499(1979)

[68]

[69]

DEIoannouandSMDavidson

JPhysDApplPhys昆1339-1344(1979)

ShengSLiWLWangPWLaiandRTOwen

JElectronicMaterials旦335-354(1980)

-10-

[70]

【71】

[72]

[73]

[74]

JFBresseSEM119111pp105-112

JFBresseSEM1977pp683-693

CJWuandDBWittryJApplPhyspound92827-2836(1978)

GEPossinSEM1979pp245-256

GEPossinandCGKirkpatrlck

JApplPhys旦4033-4041(1979)

[75]GEPossinandCGKirkpatrick

JVacSciTechnol161917-1920(1979)-

[76]

[77]

[78]

[79]

[80]

VonAEGruenZNaturforsch12aHeft289-95(1957)-

KKanayaandSOkayama

JPhysDApplPhys5A3-58(1972)

RShimizuYKataokaTIkutaTKoshikawaand

HHashimotoJPhysDApplPhys旦101-114(1976)

GVSpivakGVSaparinandLFKomolova

SEM1977pp191-199

CDonolatoandHKlann

-JApplPhys511624-1633(1980)

[81]DBWittryandDFKyser

JApplPhys2旦375-382(1967)

[82]

[83]

[84]

[85]

[86]

TEEverhartandPHHoff

JApplPhys425837-5846(1971)

VVMakarovSovPhys-Semicond旦in-llk(1975)

JDKannnandHBerntSolid-stateELectronヌ1957-964(1978)-

JDKammrdquoSemiconductorSilicon1977rdquo(JElectrochemical

Society)pp491-501

0vonRoosJApplPhys503738-3742(1979)

-n-

-L2-

2-1

INFLUENCEOFM工NORITYCARRIERGENERATIONDISTRIBUTION

ONELECTRONBEAMINDUCEDCURRENTINTHENOR^IALINCIDENCE

METHOD

Introduction

Accuratedeterminationofminoritycarrierdiffusionlength

LisveryimportanttocharacterizesemiconductorsOneofthe

convenientmethodstomeasureLIstheuseofelectronbeam

inducedcurrent(EBIC)Theelectron-holepairsgeneratedbyan

electronbeamareseperatedbyapotentialbarrier(egp-n

junctionorSchottkybarrier)andthecurrentisInducedinthe

externalcircuitThevalueofLcanbedeterminedfromthe

dependenceofEBIConthelengthzbetweenthepotentialbarrier

andthegenerationpointInthenormalIncidencemethodzis

variedbychangingtheacceleratingvoltagevaofanelectronbeam

andthesmallvalueofLoftheorderofumcanbedetermined

ThevalueofLintニhesmallregionisobtainedusingafocused

beamgeneratedbyascanningelectronmicroscope(SEM)lsquo

Czaja[1]measuredLinp-ndiodesofSiandGaPHe

assumedthegenerationdistributionasacombinationoftwo

exponentialfunctionsBresse[2]andWu[3]measuredLandthe

electron-holepaircreationenergyE^^inSiandGaAsTheyused

Schottkydiodesbecausetheelectronbeamenteredthroughthemetal

contactandthesurfacerecombinationeffectcouldbeneglected

IntheiranalysesBresseusedthesemi-sphericalgeneration

distrlbutionproposedbyKanayaeta1[4]andWuassumedGaussian

distリbutlonPossineta1[5]analyzedEBICindetailtakingthe

influencesofthesurfacerecombinationandtheinternalfield

-13-

Metal

Depletio

layer

Primaryelectronbeam

Numberofgeneratedcarriers

Fig2-1Schematicviewofexperimentalconditions

jusingSchottkydiodesMetalthicknessis

wanddepletionlayerwidthiswright-handillustぷふこsthedぶdosefunctionRandR

-givethemaxiraum

andextraporaiedmelectrSnolinerangerespectively

-14-

0generatedcarrier

に_---___1

我_______Iuarrヽ

y重ダ

1ごpermil

andestimatedthedepthdistributionoflifetimeinion-implantedSi

TheylsquousedthepolynomialfunctionderivedbyEverhart[6]forthe

generationdistribution

工ntheanalysisofEBICtheminoritycarriergeneration

distributionplaysanimportantroletodeterminetheaccurate

valueofLandEHoweverthedistributionmodelsusedinthepc

analysesaredifferentwitheachotherasmentionedaboveIntニhis

chapterwecomparevariousmodelsforthegenerationdistribution

inGaAsandSiWecalculateEBICandclarifytheinfluenceofthe

generationdistributiononthedeterminationofLandEpc

Experimentalresultsarealsopresented

2-2 Determinationofdiffusionlengthandelectron-holepair

creationenergy

ASchottkybarrierdiodeisusedinordertoneglectthe

influenceofthesurfacerecombinationTheelectronbeamis

irradiatednormallytothebarrierplanethroughthemetalas

shownInFig2-1Thethicknessofthemetalandthedepletion

layerareputaswmandwd゛respectivelyTheminoritycarrier

generationdistributionalongthedepth(Socalledthedepthdose

function)isIllustratedalso1nFig2-1TheEBICiscalculated

basedonthefollowingassumptions1)Theminoritycarriers

generatedinthemetal(regionI)cannotcontributetoEBIC

2)Theelectron-holepairsgeneratedinthedepletionlayer(

regionlsquoTL)areseperatedquicklybythefieldofthedepletion

layerandwhollycontributetoEBIC3)Theminoritycarriers

generatedinthebulk(regionⅡI)partlycontributetoEBICie

theminoritycarrierswhichreachtotheedgeofthedepletion

-15-

mDiwi)iunMd

SMtjjesp≫)ejAU≫6|o』ψsEコz

Normalizedgenerationdepth^rsquoRm

Fig2-2

Generationdistribution

inGaAsTheMakarov゛SWittryrsquos

andKanayarsquosmodelsareexpressed

bytニhesolidbrokenanddotted

linesrespectivelyThegener-

atlondepthisnormalizedby

themaximumelectronrangeR

ThetotalgenerationrateiSm

normaLlzedtobeunity

-16-

2 0

1 05

(Efi)≪MJO^M

d6ue」

CO』oa3

rdquorsquo5102050Acceleratingvoltageva(kv)

Fig2-3

ElectronrangesinrsquoGaAsforvariousmodelsThesolidbrokendottedanddashedanddottedlinesaretheresultsusingMakarovrsquosWitニtryrsquosKanayarsquosandEverhartrsquosmodels

respectively

rdquoゝゝGaAs

χ

`Makarov20χ

----Wittry

χhelliphelliphellipKanaya

11S

15

゛S≒

rsquoχ≒

χrsquo

10trsquolsquo

卜卜゜χ゛

卜ゝrsquo

05χrsquo゛rsquoゝ

ゝrsquoゝ1

ゝゝrsquoゝゝ

ゝゝ

00

50

GaAso々

タグrsquo

Makarov

15-rsquo一一Wittry

ノKanaya

12

---Everhart

13yelr(2゛十`゛dinFig2-1)bydiffusioncanflowintothemetal

bythefieldofthedepletionlayer

Therehavebeenmanytheoretical147]andexperimental

[68-11】worksonthegenerationdistributionKanayaand

Okayama[4]proposedasemi-sphericalgenerationdistribution

usingthemodifieddiffusionmodel0fArchard[7]Wittryeta1

assumedGaussiandistributionandappliedtoGaAs[89]

EverhartandHoffl6]derivedapolynomialfunctionfromtheir

experimentsIntheA1olineSi02olineSisystemdegMakarov[10]showedthat

thegenerationdistributioncouldbeexpressedasGaussianlike

(exp(-((z-z)u)2))andthep8゛゜eters2manduvariedaccording

totheatomicnumberandthedensityofthematerialInorderto

comparethesedistributionsnormalizeddepthdosefunctionwas

introducedGruen[11]showedthattheshapeofthedepthdose

curveispracticallyinvariantifthepenetrationdepthis

normalizedbytheelectronrange

ThedepthdosefunctioninGaAsnormalizedbythemaximum

electronrangeRm(atwhichnoelectronentersintothematerial

seeFig2-1)areshowninFig2-2bythesolidbrokenanddotted

linesusingthefollowingequationsforthemodelsofMakarov

WittryandKanayarespectively

2RmolineOdeg138

g(z)=exp(-(rarr元でi

g(z)=exp(-(

2Rmoline

Odeg125

-035

)2)

)2)

(Makarov)(2-1)

(Wittry)(2-2)

g(z)゜(RmolineOdeg242Rtri)2oline(2olineOrsquo242Rm)2(K゛3y8)゛(2lsquo3)

-17-

こrsquo

Aouepj^^auoiiDaii〇D

Fig2-4

10203040

Acceleratingvoltage

5060

Va(kV)

CollectニionefficiencynvsVacurves

GaAsSchottkydiodeThevaluesofLare505μmfromuppert0lowergroupofcurves

for

2and

respectivelyTheresultsusingtheMakarovrsquosWittry゛SandKanayarsquosmodelsareexpressedbythesolidbrokenanddottedlinesrespectivelyThevaluesofwandWare10nmand015ymrespectively^hedashedanddottedlineisinthecaseofw=50nmw=015umandL=2umusingtheWittryrsquosmode1

-18-

GaAs一一Makarov

--rdquo-Wittry

10Wf^=10nmhelliphelliphelliphellipKanayaL(pm)

rsquo≒゜ニ1こii4degこ7T`ヽヽヽ5

05万でヽこミア斗辿こTTZご

50nふyミ゛1helliphelliphelliphellip4゛`゛ζ゛ζ

Orsquo1capparacapcap

か4

5060

ThereareobviousdifferencesbetweenthesethreemodelsThe

MakarovrsquosandWittryrsquosmodelshavethelargesurfaceconcentration

butthepeakvalueatzRm゛Odeg13oftheMakarovrsquosmodelissmaller

thanthatoftheWittryrsquosmodelTheKanaya゛smodelhasmoreevenly

spreadeddistributionthantheothertwomodelsThisisbecause

theelectron-holepairconcentrationisassumedtobeuniformin

thesemi-sphereintheKanayarsquosmodelwhichisasimplefirst-

orderapproximationforthegenerationdistributionButinthe

actualcasetheelectron-holepairsareconcentratedaroundthe

centerofthesemi-sphereOnemustusetheimprovedelectron-hole

pairconcentrationmodelInsteadoftheuniformoneinorderto

expressthegenerationdistributionprecisely

InthecalculationofEBICtheabsolutevalueofRmustm

beneededSomereportedvaluesbyMakarovWittryandKanayaare

shownbythesolidbrokenanddottedlinesrespectively

inFig2-3forGaAsThedashedanddottedlineisderivedby

Everhart[6]anddiscussedlaterTherangesoftheWittryrsquosand

Kanayarsquosmodelsarealmostagreewitheachotherbutthatofthe

Makarovrsquosmodelisabout70ZofthoseoftheWittryrsquosandKanayarsquos

models

ThecalculatedEBICinGaAs(iethecollectionefficiency

nwhichbecomesunitywhenallthegeneratedcarrierscontribute

toEBIC)bythesamemethoddescribedinref[3]isshownIn

Fig2-4Thesolidbrokenanddottedlinesareforthemodelsof

MakarovWittryandKanayarespectivelyThevalueoftheacceler-

atlngvoltageva1Schangedfrom5t060kVThevalueofLIs50

20and05ymfromuppert0lowergroupofthecurvesrespectively

ThevaluesofWmandwdaretakenastypicalvaluesof10nmand

015ymrespectivelyTheelectronrange1SInverselyproportional

tothedensityofthematerialThemetalthicknessiscorrected

-19-

takingthedifferenceofthedensitiesbetweenthemetalandthe

bulksemiconductorinorderthatthesamplehasuniformdensityfrom

thesurfacetothebulkforasimpletheoreticalcalculationWhen

goldistakenastheSchottkycontactwmustbemultipliedby

pAupGaAS(゜3`゜6rsquopAudeg189andpGaASdeg5゛3

1cll3)

゛OIlecanestimateL

mainlyfromthegradientofthecurvebecausethegradientdecreases

monotonouslywithincreasingLupt05umTheestimatedvaluesof

LbyMakarovrsquosandWittry゛Smodelsarealmostequalbecausethe

gradientsofthecurvesagreewitheachotherforthesameLvalue

ThevalueofLlargerthan5μmcannotbedetermineddefinitely

becauseEBIChardlychangeswithvevenifLbecomeslargeThea

maximumvalueofLthatcanbedetermineddefinitelyincreasesas

thehighestvalueofvaincreasesbutanotherproblems(idegedeg

damagesofthesamplebyhighenergyelectronsetc)mayoccur

Theelectron-holepaircreatニionenergyEcanbeobtainedfrom

theabsolutevalueofEBICbytherelationndeg^C^EBIC^^B^

(IEBICmeasuredEBICIBprimarybeamcurrentkcorrectionfactニor

fortheenergylossduetobackscattニeredelectrons)[3]

TheabsolutevaluesoftニheMakarovrsquosmodelareabout10へj20Z

largerthanthoseoftheWittry゛smodelAndsothevalueofEpC

obtainedbytheformeris10へj20Zlargerthanthatbythelatter

ThegradientニSandtheabsolutevaluesofthecurvesoftheKanayarsquos

modelarequitedifferentfromthosebytwoothermodelsThe

reasonofthedifferenceisowingtotheassumptionoftheuniform

concentrationoftheelectron-holepairsinthesemi-sphereas

discussedbeforeTheKanayarsquosmodelisafirst-orderapproximation

forthegenerationdistributionandisnotsuitableforthe

accuratedeterminationofLandEThevalueofwdoesnotaffectpc(I

EBICsomuchfromtheresultsoftニhecalculation工fWbecomesm

largetheabsolutevalueofEBICat10wvaisdecreasedverymuch

-20-

butthegradientofthecurveintheregionofhighVadoesnot

changeasshowninFig2-4(thedashedanddottedlineisinthe

caseofwmdeg50nm゛wdrsquoOrsquo15pmandL=2ymusingtheWittry゛Smode1)

ThereforeLcanbedeterminedinanycaseofwm゛asfaraswm1S

sufficientlysmallinorderthattheelectronbeamcanenterinto

thebulkregion

ThenormalizeddepthdosefunctionsInSiexpressedbythe

followingequationsareshowninFig2-5bythesolidbroken

dottedanddashedanddottedlinesforthemodelsofMakarov

WittryKanayaandEverhartrespectively

zR-0261

g(z)=exp(-(-jyヲー-7)2)(Makarov)(2-4)

zR-0156

g(z)=exp(-(―q2L_一一

g(z)゜(RmolineOrsquo336Rm)2

g(z)=06+6212Re

(Wittry) (2-5)

(゛0336R)^(Kanay゛1)(2oline6)

oline12deg40(2Re)2+5lsquo69(zR

(Everhart)e)3

(2-7)

Makarovshowedthattheparameterszmlsquoanduhadvoltagedependencesl

andthetypicalvaluesatvadeg30kVaretakenItshouldbenoted

thatthedepthdosefunctionoftheEverhartrsquosmodelisnormalized

bytheextraporatedrangeRe(seeFiglsquo2-1)whichisdetermined

byextraporatingthestraightlineportionofthecurve

-21-

Fig2-5

11

u)6ua))iunjed

sjdiJieopdiejdud6lo」4sEコz

Normalizedgenerationdepth^rsquoRm

GenerationdistributionsinSiTheMakarov゛s

Witニビry゛sKanayarsquosandEverhart゛Smodelsare

expressedbythesolidbrokendottedanddashedanddottedlinesrespectivelyThegener-

atlondepthisnormalizedbythemaximumelectron

rangeRTheextraporatedrangesR゛SoftheMakarovrsquosWittryrsquosandEverhartrsquosmodelsare

takentobeagreedwitheachotherThetotニal

generatニionrateisnormalizedtobeunity

-22-

KUkarov

--一一-Wittry2deg

二ぷ芯t

15へ

゜¥レ臨べhellip

hellip

10rsquoS゛lsquoNhellip

helliphellip

05

hellip

helliphellip

1helliphellip

hellip

005

工nordertocomparetheEverhartrsquosmodelwithothersthe

extraporatedrangefortheGaussiandistributionisdeduced

(seefootnote)十andtheextraporatedrangesoftheMakarovrsquoS

WittryrsquosandEverhart゛Smodelsaretakentobeagreedwitheach

otherThepeakvaluesofthegenerationdistributionsofthe

MakarovrsquosWlttryrsquosandEverhartrsquosmodelsarealmostequalbut

thevalueofzRmatthepeakfortheWittryrsquosmodelisabout

015andsmallerthanthoseoftheothertwomodelsCzR=025)゜

ThegenerationdistributionoftheWittryrsquosmodelcomesnearerto

thesurfacethanthoseoftheMakarovrsquosandEverhartrsquosmodelsIt

isbecausetheWittryrsquosmodelisderivedInthecaseofGaAsand

ontheotherhandtheMakarovrsquosandEverhart゛Smodelsareconcerned

inthecaseofSiThedensityofG゛1AS(pGaAS゛5deg3gcm^)islarger

thanthatofS1(pSirsquo2deg3gcm^)andsotheWittry゛Smodelshows

themoresurfaceconcentrationthantheothersTheKanayarsquosmodel

isquitニedifferentwiththeotherthreemodelsowingtothesame

reasonasdiscussedinGaAs

- -

-- - - - -

- - - -

Gaussiandistribution(e゛p(oline((2oline2m)11)2))

showsthealmostlineardecreasearoundthepoint

ofinflection(zdegu゛Σ十zm)lsquoTheextraporatedrange

Re(1゛ersquothepointwithwhichthestraightline

atthepointofinflectioncrossesthezaxis)

becomes2u十zfromtheresultsofcalculationm

(seeFig2-5)゜TheextraporatedrangeRebecomes

078Rand062RfortheMakarovrsquosandWittryrsquosmm

modelrespectively

-23-

Fig2-6

0 102030

Acceleratin9

4050

voltage

60

va(kv)

CollectionefficiencynvsVacurvesforSiSchottkydiodeThevaluesofLare1052andlymfromuppert0lowergroupofcurvesrespectivelyTheresultsusingtheMakarovrsquosWittryrsquosKanayarsquosandEverhartrsquosmodelsareexpressedbythesolidbrokendottedanddashedanddottedlinesrespectivelyThevaluesofWandware10nmand05ymrespectivelymd

-24-

MakarovSi---rdquoWittry

Kanaya

----Everhart

ジhttpwwwL(pm)卜

)渫回ブモジミ穫

WmニlOnmrdquoミ4helliphellipで``rsquoヽ4゜

゛ゝ1rsquohelliphelliphellip

゛rsquoN

u1C

larrl

0E

501

Figure2-6showsthecollectionefficiencyinSiusing

thefourdifferentmodelsofMakarovWittryKanayaandEverhart

bythesolidbrokendottedanddashedanddottedlines

respectivelyThevalueofLIs1005020and10umfrom

uppert0lowergroupofcurvesrespectivelyThevaluesofW

andrdquodaretakenastypicalvaluesof10nmand05]imrespectively

Thevalueofwmismultipliedby821nthecalculationowingto

thedifferenceofdensitiesbetweenAuandS1

asdiscussedbeforeThevalueofLlargerthan10μmcannotbe

determinedaccuratelybecauseEBIChardlychangesevenifLvaries

ThegradientofthecurveoftheEverhartrsquosmodel1Sslightly

steeperthanthoseoftheMakarovrsquosandWittry゛smodelswhich

almostagreewitheachotニherAndsotheestimatedvalueofLby

theEverhartrsquosmodelbecomeslargerthanthatbytheMakarovrsquosor

Wittry゛smodelforthesamer)vSdegvaCurve(egL=lutnbythe

Everhartrsquosmodelbecomes07umiftheMakarov゛Smodel1Sused)

ThegradientofthecurveoftheKanayarsquosmodelisalmostequal

tothatニoftheEverhartrsquosmddelbuttheabsolutevalueofthe

formeris30Zsmallerthanthatofthelatterforthesamevalue

ofLThereforetheestimatedLbyKanayarsquosmodelalmostagree

withthatbytheEverhartrsquosmodelbutthevalueofE

pCuSing

theformeris30Zsmallerthanthatusingthelatter

Asmentionedbeforetheelectronrangeisinversely

proportionaltothedensityoftニhematerialTheelectronrange

derivedbyEverhartinSicanbeappliedtoGaAsconsideringthe

differenceofthedensitiesbetweenSiandGaAsThecalculated

valuesareplottedbythedashedanddottedlineinFig2-3

TherangesoftheMakarov゛SandWittry゛Smodelsarelargerthan

thatoftheEverhart゛smodelOneofthereasonsforthe

disagreementisthedifferentdefinitionsoftheelectronrange

-25-

ieMakarovandWittryusedthemaximumrangeRbutEverhart

usedtheextraporatedrangeRelsquoInordertニocomparethesevalues

theextraporatedrangesfortheMakarovrsquosandWittryrsquosmodels

inGaAsarededuced(seefootnoteinpage23)andbecome075Rm

andOlsquo62Rm゛respectivelylsquoForexampleinthecaseofvadeg30kv゛

thevaluesofRforMakarovrsquosandWittryrsquosmodelsare34andm

48ymandthenthevaluesofRebecome26and30ym

respectivelylsquoThevalueofReintheEverhartrsquosmodel(29umat

vadeg30kV)isslightlylargerthanthatoftheMakarovrsquosmodel

butagreeswiththatoftheWittryrsquosmodel

2-3 ExperimentalresultsinGaAs

AconventionalSEMwasusedfortheprimaryelectronbeam

whichwasmodulatedat3kHzwithachoppingcoilinsertedinto

thebeampathTheinducedcurrentwasmeasuredfromthevoltage

dropacrosstheloadresistancewhichwasconnectedtotheSchottky

barrierwithanohmiccontactThesignalwasdetectedbyalock-in

amplifierThebeamcurrentwasmeasuredbyaFaradaycageThe

beamwassomewhataefocussed(Φ|=10umφbeamdiameter)inorder

toavoidhighinjectionTheinducedcurrentwasnotchangedeven

ifthebeamwasirradiatedatthesamepointforanhour

TheSchottkybarrierwasrsquomadeonn-typeGaAs(Sndoped

ndeg62times1016cmoline3)byevaporatingAuofabout10nmthickina

vacuumofabout10oline7TorrTheohmiccontactwasobtainedby

evaporatingAu-Geandalloyingat400degCfor2mlnThecarrier

densityandthedepletionlayerwidthweredeterminedbyG-V

measurements

-26-

(Hiunqj≫)

U一SU

BeamcurrentIb(A)

Fig2-7

MeasuredEBICinGaAs(Sn-

dopedn=62)(1016cmoline3)Schottky

diodeatVa=10and50kVThe

beamcurrentwaschangedinthe

rangeof2)(10oline11≦I≦5)(10oline9A

-B-Theopenandsolidcirclesare

theexperimentalresultsforvadeg

10and50kVrespectivelyand

thegradientsofthesolidlines

areunity

Tab2-1

(s≫UコqjB)Aouapu

く1)

uoiioaiion

AcceleratingvoltageVa(kV)

Fig2-8

Curvefittingsoftheexperi-

mentalresultstothetheoretical

collectionefficienciesinGaAs

SchottkydiodeThesolidbroken

anddottedlinesaretheresultニS

usingtheMakarovrsquosWittry゛Sand

Kanayarsquosmodelsrespectively

Vaischangedfrom5t050kVwith

thefixedvalueofl゛10oline1oA

w=10nmandwmd

L(unj)Ec(ev)

Makarov

Wittry

Kanaya

03

03

05

48

41

41

二〇15um

ご洸竺詐比飛ぱ器ぶごぷ詣ぷ

-27-

000

5Gなfimf4ilvalu

0v≪>iakv

50

100

10

lylrsquo16rsquo1(i

acuteン゛tGaAs(Sndoed)

5n=62

lope

1二痙7

5Kanayao

21020304050

ThevalueofEBICatv=10and50kVareshownbythesolida

linesinFig2-7whenthebeamcurrentIBischangedintherange

of2)(10oline11≦I≦5)(10oline9AIftheminoritycarrier-B-

concentrationexceedsthethermalequilibriumconcentrationof

majoritycarriers(iehighinjection)theminoritycarrier

lifetimeisprolonged[12]ThereforeEBICbecomestoincrease

superlinearlywiththenumberofgeneratedcarriersie

withIBforafixedvalueofvarsquoInthisexperiment゛EBIC

increaseslinearlywithIBatbothvals゛WhichShoWsthe10w

injectionTheexperimentalresultsareshownbycirclesin

Fig2-8whenvischangedintherangeof5くVく50kVata=adeg

thefixedvalueofIBdeg10oline10A゛Theoreticalcollectionefficiencies

usingtheMakarovrsquosWitニtryrsquosandKanayarsquosmodelsareshownbythe

solidbrokenanddottedlinesrespectivelyinFig2-8The

valuesofLandEpcdeterminedbyfittingtheexperimentaldata

totニhetheoreticalcurvesaretabulatedinTab2-1forthethree

differentmodelsofMakarovWittryandKanayaThecollection

efficiencybytheMakarovrsquosmodelshowedfairlygoodagreement

withtheexperimentalresultsbutthatusingtheWittryrsquosmodel

isslightlylargerthantheexperimentalvaluesinthe10Wva

l`egioll(va≦10kV)Thediscrepancyinthelowvaregionbecomes

largeiftheKanaya゛SmodelisusedInthecaseofWittryrsquosand

Kanaya゛Smodelspoundheexperimentaldatawerefittedintherange

ofhighva(va≧15kv)TheestimatedvaluesofLis03urnby

usingboththeMakarovrsquosandtheWittryrsquosmodelsbutthatusing

theKanayarsquosmodelis05ymandabouttwiceoftheresultby

theMakarovrsquosandWittryrsquosmodelsThevaluesofEdeterminedpc

bytheMakarovrsquosWittryrsquosandKanaya゛Smodelsare4841and41

eVrespectivelyBythenormalincidencemetニhodofEBICWuand

Wittry[3]andKobayashieta1[L3]determinedEas468and457

eVrespectivelywhicharealmostequaltotheresultusingthe

Makarovrsquosmodelbutareabout10Zlargerthanthevalueobtained

bytheWittryrsquosandKanayarsquosmodels

-28-

2-4 Summary

ThevaluesofLandEcanbedeterminedfromthe

PC

ceofEBIConvbythenormalincidencemethodThe-

dependenceofEBIConVabythenormalincidencemethodThe

minoritycarriergenerationdistributionplaysanImportantrole

intheanalysisofEBICVariousgenerationdistributionmodels

arecomparedwitheachotherunitingthedifferentdefinitionsof

theelectronrange(Iemaximumrangeandextraporatedrange)

InGaAsGaussiandistributionsproposedbyMakarovand

Wittryhavelargesurfaceconcentrationsandthepeaksofthe

distributionsexistatabout0130fthemaximumelectronrange

Kanaya゛Smodelhasevenlyspreadeddistributionowingtothe

assumptionoftheuniformconcentrationofthegeneratedelectron-

holepairsThevalueofLlargerthan5μmcannotbedetermined

definitelybecauseEBIChardlychangesevenifLvariesThe

estimatedLbytheMakarovrsquosmodelalmostagreeswiththatblsquoythe

WittryrsquosmodelbutEdeterminedbytheformeris10へj20ZrdquoPC

largerthanthatbythelatter

InSithepeaksofthegenerationcistributionbecome

deeperthanthoseinGaAsbecausethedensityofS11Sabouthalf

ofthatofGaAsThelargestvalueofLthatcanbedetermined

definitelybecomestwiceofthatofGaAsbecausetheelectronrange

inSiisabouttwiceofthatinGaAsTheestimatedLbythe

MakarovrsquosorWittryrsquosmodelisabout30Zsmallerthanthatbythe

Everhartrsquosmodel

IntheexperimentsinGaAstheestimatedLbytheMakarovrsquos

modelagreedwiththatbytheWittryrsquosmodelbuttheestimated

Epcbytheformerwas48eVandabout17Zlargerthanthatbythe

latter

-29-

References

[1]

[2]

[5]

WCzajaJApplPhys374236(1966)

JFBresserdquoScanningElectronMicroscopy71972partlrdquo

(iiTRiChicago111)p105

CJWuandDBWittryJApplPhys丘旦2827(1978)

KKanayaandSOkayamaJPhysDApplPhys

543(1972)-

口EPosslnandCGKirkpatrickJApplPhys

5^4033(1979)

[6]TEEverhartandPHHoffJApplPhys

425837(1971)

[10]

[11]

[12]

[13]

GDArchardJApplPhys竪91505(1961)

DBWittryandDFKyserJApplPhys28375(1967)

TSRao-SahibandDBWittryJApplPhys

403745(1969)

VVMakarovSovPhysSemicond旦722(1975)

jVonAEGruenZNaturforsch12aHeft289(1957)-

JCornuRSittigandWZimmermannISolid-stateElectron

TKobayashiTSugitニaMKoyamaandSTakayanagi

IEEETransNuclSciNS-19324(1972)-

-30-

3-1

DETERMINATIONOFDIFFUSIONLENGTHSURFACERECOMBINATION

VELOCITYANDELECTRON-HOLEPAIRCREATIONENERGYBYTHE

LINESCANMETHOD

Introduction

Anelectronbeaminducedcurrent(EBIC)methodisa

convenienttechniquetomeasuretheminoritycarrierdiffusion

lengtニhLandthesurfacerecombinationvelocitysinsemi-

conductingmaterialsInthelinescanmethodLandScanbe

determinedfromthedependenceofEBIConthescanningdistance

whentheelectronbeamisscannedacrossthebarrierBerzand

Kuiken[1]gaveadetailedtheoryforthedeterminationofLand

sandOpdorp[2]investigatedexperimentallytheinfluenceof

surfacerecombinationonEBICJastrzebskieta1[31measured

Landsfordifferentgenerationdepthsbyvaryingtheaccelera-

tingvoltageofanelectronbeam

Inthosestudiesthegenerationsourcewasassumedto

beapointbutinpracticetheregionexcitedbytheelectron

beamhasafinitevolumeChiandGatos[4]determinedthe

junctiondepthbyanEBICtechniqueassumingafinitegeneration

volumeCzaja[5]andBresse[6]measuredthephysicalparameters

suchasLandtheelectron-holepaircreationenergyEpC゛when

theelectronbeamwasdirectednormaltothebarrierplane

Sheaeta1[7]investigatedtheresolutionlimitsoftheEBIC

linescanmethodtheyobtainedaone-dimensionallateraldose

functionandappliedittothemeasurementofLintheCuxSCdS

systemHowevertheydidnotdiscusstheeffectofsurface

recombinationonEBICSincethesurfacerecombination1S

stronglyconnectedwiththedepthofgenerationathree-

-31-

Fig3-1

Schematicviewof

anddefinitionsofthe

-32-

experimentalconditionscoordinatesystems

Electronbeam

Surfacecross-sectic

O゛9χ

Schottky哨Rbarrier

dimensionalgenerationdistributionmustbetakenforthedetailed

analysisofEBIC[81

Inthischapterfirstlywediscussthesurfacerecombi-

nationeffectonEBICassumingapointsourceandthendescribe

theinfluenceofthegenerationvolumeonEBICinthelinescan

methodtakingaccountofsurfacerecombinationWehavestudied

EB工Ctheoreticallyforthefinitevolumesourcewhichisdependent

ontheacceleratingvoltageandshowanimprovedmethodfor

thedeterminationofphysicalparametersofsemiconducting

materialsbasedonexperimentalresultsobtainedinSi

3-2 Surfacerecombinationeffectconsideringpointsource

ForsimpletheoreticalconsiderationwetakeaSchottky

diodeAsshowninFig3-1theSchottkybarrier1Sinthey-z

planeTheelectronbeamisincidentperpendiculartothesample

surfaceandthescanningdirectionisalongtheχ-axiswhichis

normaltothebarrierplane

Thegenerationsourceisconsideredtobeapointata

distancexgfromthebarrierandatadepthdfromthesurface

correspondingtotheacceleratingvoltagevarsquoThepositionis

XS

ぐi g゛ O゛dg)Thesteadystateexcessminoritycarrierdistribution

obtainedfromthefollowingdiffusionequation

pDnabla2pdeg - -

g6(x-゜cg゛yrsquo2olinedg)rsquo (3-1)

whereDisthediffusionconstantて1sthelifetimeandgisthe

generationrateofelectron-holepairsWhen

thesampledimensionsareassumedtobesufficientlylarge

-33-

3ta3

Normalizedscanningdistancex

(a)

Fig3-2

Fig3-3

U』

Normalizedscanningdistancex

(b)

3193

p≫Zl≫E』oz

Normalizrdscanningdistanceχ

(c)

PrimeNormalizedEBICvsnormalizedscanningdistanceχcurvesfordifferentvaluesofthesurfacerecombination

velocityparameter(seetext)SNormalizedgenerationdepthDis0001and10in(a)(b)and(c)

respectively

Oino

tou

iSu一uojsn}|ipMzireujjoZ

SurfacerecombinationvelocityparameterS

EstimateddiffusionlengthL大directlyfromthe

slopesofthecurvesbetweenthepointsatχ=2and3

Svariesfromoneto50

-34-

Dg=10

Dg=QO

151050

112345

Og<ao

161

S>0

21

Idrsquo

S5

10^

550

1必12345

135

sc^-at

SO⑤

バ宍

1012345

112345

SPg≪10

161

162S=0

SI

1(i3

1(541235

comparedwiththediffusionlengththeboundaryconditionsare

並Sz

χ=0

z=O゛

spl

z=0

=0

χ=+(x)

=0

(atthesurface) (3-2a)

(attheSchottkybarrier)(3-2b)

(3-2c)

Oncethedistributionp1SknowntheEBICcanbefound

asfollows

トeリンint]キレ

o4バ2rsquo(3-3)

whereeisthechargeofanelectronThevalueofjwascalculated

二二二二二二二エフエム2こ二言

J=

-eg

丁T

4oo

int

Dg

馴D戸

exp(-S(T-

S(司7)-

dT} (3-4)

wherexL゛DgdegdgLrsquoS=s(Lて)andTIsthevariablefor

integrationThefunctiony可7)1sthesecond-modified

first-orderBesselfunctionTheEBICisnormalizedtobeunity

whenallthegeneratedcarrierscontributetoEBIC

-35-

177FΞ-一一permil

(ぷ71

y))二1supe≧rsquo

四F

InFigs3-2(a)(b)and(c)thelogarithmofJis

plottedvsX(ΞxL)basedoneq(3-4)overtherangeofO≦X≦5一一

forS=へj50ThevalueofDgis0001and10in(a)(b)

and(c)respectivelyForS=0theintegralineq(3-4)leads

toJ=exp(-X)whichyieldsstraightlinesasshown

inFig3-20ntheotherhandallcurvesforS>Odeviate

fromthestraightlineThesurfacerecombinationgivesmuch

effectontheexcesscarrierdistributionasthegenerationdepth

becomessha110WerWhenDgis00and01thevaluesoflogJ

decreasesuperlinearlyovertheinterval0fO≦χ≦2and--

almostニlinearlyovertherangeofx≧2WhenDis10the一琴

surfacerecombinationhasaslightinfluenceandthevaluesof

logJdecreasealmostlinearlyovertheinterval0fO≦X≦5__

HowevertheslopesshowsubstantialdeviationfromunityThe

estimatedvaluesofdiffusionlengthdirectlyfromtheslopes

ofthecurvesinthelinearlydecreasingregion2≦X≦3are--

putasL火andplottedagainstSinFig3-3forDgdeg00and10

工nordinarysemiconductorsSvariesfromlt050Overthis

rangeL大Isabout80t090ZoftニherealvalueL

WhenweevaluatetheaccuratevaluesofLandSwemust

fittheexperimenpoundaldatatothetheoreticalcurvesoverthe

wholerangeofO≦X≦5WecanestimateSbyfitting--

particularlyovertheIntervalofO≦X≦2becausetheeffect--

ofthesurfacerecombinationappearsremarkablyinthisInterval

-36-

3-3 Analysisofelectronbeaminducedcurrenttakingthree-

dimensionalgenerationdistributionintoaccount

Insect3-2theminoritycarrierdistributionisassumedto

beapointButinpracticethegenerationdistributionhasa

finitevolumeinconnectionwithvThegenerationdistributiona

mustbetakenintoaccountwhentheextentofthegeneration

distributioncannotbeignoredcomparedwithL

Electronpenetratニionintosolidmaterialshasbeenstudied

bymanyauthorsTheminoritycarriergenerationdistribution

alongthedepthwasdiscussedindetailinChapterHWittry

andKyser[9]assumedthedepthdosefunctiontobeaGaussian

distributionandobtainedgoodagreementwithexperiments

EverhartandHoff[10]assumedapolynomialfunctiontoexplain

theirexperimentalresultsintheAl-SiO2-SisystemdegInthose

studiesonlythedistributionalongthezaxiswasdiscussedso

thedistributionalongthexaxiswasnotconsideredSheaeta1

[7]definedthelateraldosefunctionalongthexaxisfrom

VonGrlinrsquos[11]databutdidnotdiscusstheinfluenceofsurface

recombinationindetailSincetheinfluenceofsurfacerecombi-

nationonEBICdependsonthedepthfromthesurfacewemust

takethedistributionofgeneratedminoritycarriersinthe

x゛zplaneWeusethemodifieddiffusionmodelofKanayaand

Okayama[12]Themodel1Sverysimplebutissufficientfor

thefirst-orderapproximationtニothethree-dimensional

generationdistributionAccordingtothemodeltheelectrons

penetratestraightintothematerialtothemaximumenergy

dissipationdepthandthenscatterequallyinalldirections

makingelectron-holepairsTheshapeofthegenerationregion

becomesaspherepartofwhichisabovethesurface

-37-

Fig3-4

Tab3-1

11-

Schematicviewofelectronpenetrationisthemaximumenergydissipationdepth

a(W)

00000

1CMCO<rm

d(ym)

rdquo047

149

291

in<yi

vDVO

4VO

R(um)

100

295

13

74

20

Valuesofthecenterdgofthegeneration

volumeandtheradiusRinSiforseveralvalues

ofacceleratingvoltagevarsquo

-38-

IElectronbeam

O335

S`」「fdegce

uarrで0559j

10゛」

helliphelliphelliphelliphellip

Thecenterdgofthesphere(iethemaximumenergydissipation

depth)andtheradiusRaredependentontheacceleratingvoltage

va゛b゛lttheratiodgRisassumedtobeaconstantasshownin

Fig3-4evenWhenvaisvariedThevaluesofdgandRinSi

forseveralvaluesofvaaregiveninTab3-1calculatedwith

theaidoftheequationsofKanayaandOkayama[121

Wedividethesemi-sphereintomanysegmentsoflength

lessthanLandrepresenteachsegmentbyonepointsource

Thedensityoftheelectron-holepairsisassumedtobeuniform

withinthespheretosimplifytheanalysisThenthegeneration

strengthgofeachpointsourceisgivenbytニhefollowing

relation

Σg=G(3-5)

whereGisthewholegenerationstニrengthandΣexpressesthe

totalsummationwithinthesemi-sphereundertニhesamplesurface

TheEBICforthefinitevolumesourceisderivedby

summimgupthesolutionoftニhediffusionequationforeachpoint

sourcewhichisexpressedbyeq(3-4)Whenthedistance

betweenthebarrierandtheIrradiatedpointxbecomessmallerg

thanRsomeofthepointsourcesareforcedoutofthediode

andcannotcontributetoEBICThustheEBICdecreasesnearthe

barrierplaneWecallthisphenomenonanedgeeffectTosimplfy

thecalculationweassumethattheEBICcontributedbythe

forced-outsourcesiszeroThisedgeeffectmustbetakeninto

accountwhenthegenerationvolumeislargeincomparisonwith

thediffusionlengthWeshowanexampleforL=8ymandS=20

Whenvais10kVtheradiusRissmallcomparedwithLand

thegenerationsourcecanbeassumedasapointThelogarithm

-39-

Fig3-5

Qコー

山11

pdznpoi」oz

1020

Scanningdistanceχ

NormalizedEBICversusscanningdistanceχ

forthefinitevolumesourceThediffusionlengthLis8lsquoUmandthesurfacerecombinationvelocityparameterS(seetext)is20TheacceleratingvoltageVais50タ30and10kVfromuppertolowersolidcurverespectivelyThedottedcurveisthepointsourcesolutionforVa=50kVandtニhedashedlineisthegradientthereciprocal0fwhichgivesL=8um

-40-

1020304050(p『

゛X5入L=8μm

゛χS=20

2rsquoχyχ

゜χ

ldquoゝ5rdquo-Re-くiprocalsk)

rsquox9vesL=8|jm

rdquoゝ

2rsquo゜χ`Va=50KV

2rsquoχ

lsquoχ

lsquoゝ

5degχ

rsquoχ

rsquoχ2χ

30≒3rsquo

11diPointsourcelsquo

5solutionfor

va=50KV10

1020304050(μΓΥ

ofEBICJisplottedwithafullcurveasafunctionofthe

scanningdistancexinFig3-5logJdecreasessuperlinearlyover

theinterval0≦X≦2L(ie16uminthiscase)anddecreases--

almostlinearlyovertherangex≧2LTheslopeintherange-

O≦x≦2LisInfluencedverymuchbysurfacerecombination一一

〇necanestimateSbyfittingtheexperimentaldatatothe

theoreticalcurveinthisrangedegWhenva1S300r50kVthe

radiusRbecomesofthesameorderasLandthegeneration

volumecannotbeassumedasapointThenwedividethesemi-

sphereintomanysegmentsoflym^Thecalculatedvaluesof

EBICusingthefinitevolumesourcemethodareshowninFig3-5

ThelogJvsXcurvesshowamaximumnearthebarrierplane(

Xdeg4and7μmatvadeg30and50kVrespectively)andlogJdecreases

almostlinearlybeyondthesemaximumpointsThemaximumvalue

ofJbecomessmallasvincreasesThesurfacerecombinationadoesnotaffecttheshapeofthecurvesandsoLcanbedetermined

mainlyfromtheslopeofthelinearregionofthesecurves

independentlyofsThereciprocalslopeofthislinearportion

gives7ymwhichis87Zoftherealdiffusionlength

ThevalueofEpc゛rsquobywhichanelectron-holepairis

createdcanbedeterminedfromtheabsolutevalueofEBIC[13]

ThevalueofJinthecaseofS=501sabout70Zofthatinthe

caseofSdeg1whenvais50kv゛andsowemakelargeerrorsinthe

determinationofEifwedonotconsiderthesurfacerecomblna-pc

tioneffect

Thepointsourcesolutionatva゛50kVisshowninFig3-5

bythedottedlinewhenthegenerationoccursatthemaximum

energydissipationdepth(ie67ymfromTab3-1)

Theslopeofthepointsourcesolutionovertherangex≧2LIs-

almostequaltothatofthevolumesourcesolutionbutthe

normalizedEBICis60Zofthatofthevolumesourcesolution

-41-

Fig3ldquo6

Chopping

こ011

Scanningcoil

Schematicdiagramoftheexperimentalset-up

-42-

コ4[Osc

lsquo~|-

|コt

||IElectronbeamReference

||

Sample

RL`Lock-inampχ-yrecorder

3-4 ExperimentalresultsinS1

Aschematicdiagramoftheexperimentalset-upisshown

inFig3-6Theacceleratingvoltage1Svariedfrom10t050kV

TheprimaryelectronbeamcurrentismeasuredbyaFaradaycage

andabout2times10oline10ATheinducedcurrentwasmeasuredfromthe

voltagedropacrosstheloadresistanceILdegThecurrentニIL

whichflowsthroughtheresistanceisexpressedasfollows

hdeg^sc-I{exp[(ekT)ILRL]-1} (3-6)

whereloisthebackwardsaturationcurrentand^scisthe

short-circuitcurrentwhichistherealEBICInordertoneglect

thesecondtermofeq(3-6)theEBICwasmeasuredinthefollowing

condition

h゛kTe (3-7)

InthepresentexperimenttheEB工Cwasmeasuredatroomtempera-

tureandso゛hhwaskeptlessthanlmvdeg

Theelectronbeamwaschoppedat3kHzwithachopping

coilinsertedintothebeampathSignalsassmallas1μVcould

bemeasuredwithagoodsignaltonoiseratiousingalock-in

amplifier

Thesamplesweren-typeSiwithresistivitypof10

and01ΩCm0hmiccontactsweremadebyevaporatingantimony-

dopedgoldontothesampleandalloyingat400degCfor2mln

Schottkycontactsweremadebyevaporatinggoldinavacuumas10W

as10oline7TorrThesamplewasinsertedintoavacuumchamberfor

EBICmeasurementimmediatelyafteritwascleavedandmeasured

-43-

3IS3

paziicuijoz

1020304050(pm)

Scanningdistancex

Fig3-7

Experimentalresultsfor

sampleA(p=lf2cin)whereL=

8μmandS=20Fullcurves

arethetheoreticalrsquoones

11(il

>P≪4<N1≪CM<Pq

1 1

3193paziipujjoZ

1164

50

Scanning

100

distance

Fig3-8

150

X(μm)

200

ExperimentalresultsforsampleB

(p=01f2cin)whereL=80urnandS=50

Fullcurvesarethetheoreticalones

Valueswithouttheinfluenceofan

ohmiccontニactareshownbydotted

curves

-44-

124(m)

5XExperimentalvaluesX---Va=50KV

2NNo30

1X一--10KV4

5しL=8pm

2χ

2χ

5χ

-Theoretical

5curve

41

50100150200

Experimentalvalues

--4=50Kv

lo―30KV

hellip-10KV

-ゝゝI゛゛゜゛ペヘヘ

helliphelliphelliphellipyhelliphelliphelliphellip

Theoreticalcurvehelliphelliphelliphellip9lsquorsquolsquo゜

Ldeg80μΓTlぶ

S=50

inavacuumas10was1times10oline8TorrTheresidualgasesonthe

cleavedsurfacewerecleanedbyargonionsputteringtoavoid

contaminationofthesurfacebyanirradiatニedelectronbeam

TheexperimentalresultsofsampleA(p=10ncm)are

showninFig3-7forva=1030and50kVrespectivelyEach

fullcurveisthetheoreticaloneforthecaseofL=8umandS=20

工fthediffusionconstantD1Stakenas16cm2Solinelthelifetime

てis4times10oline2μSandthesurfacerecombinationvelocitysis

4times105cmsolinelSurfacerecombinationhasagreatereffectasthe

generationdepthbecomesshallowerthatisVbecomeslower

AndsothevaluesofSandLcanbeestimatedmainlyfromthe

curvesforthelowestニandthehighestva(idege103゛d50kV

inthisexperiment)respectivelyTheexperimentalresultsfor

eachacceleratingvoltageagreeverywellwiththetheory

Theexperimentalcurvesforvadeg1030and50kVhaveamaximum

atxdeg02and4ymrespectivelyandeachmaximumvaluebecomes

smallerasvincreasesasdescribedinthetheoryHowevera

themaximumvalueandthepositionwheretheEBICshowsapeak

deviateslightlyfromthetheoryinthecasesofvadeg30and50kVdeg

Thisdiscrepancymaybeattributedtotheassumptionofuniform

densityofgenerationTheactualdistributionmaybelocalized

atthecenterofthegenerationvolume[9]andmoredetailed

treatmentforthegenerationshapeandthegenerationdensity

Isneeded

Inthecaseofthelocalizeddistributionofgeneration

wecanapplythesamemethodasdiscussedinsect3-3Ifthe

constantgischangedintoanappropriatevariablewhichexpresses

thelocalizeddistributionbetterresultswillbeobtained

HowevertheassumptionoftheunifoinndensityIssufficientfor

thequalitativeanalysisoftheInfluenceofthegenerationvolume

onEBIC

-45-

TheexperimentalresultsofsampleB(p=01ficm)are

indicatedinFig3-8inthesamewayassampleAThevalues

ofLandSare80ymand509respectivelyIfDis16cm2solinel

てis4ysandsis1)(105cmSoline11nthiscaseLisgreaterthan

thegenerationvolumeevenwhenvadeg50kVandthevolumesource

effectappearslessclearlythaninsampleAThediscrepancy

witニhintheinterval0<xく15urnisduetothesamereasonas

thatdiscussedInthecaseofsampleATheslopesofthecurves

overtherange15≦x≦100μmarelesssteepasvbecomes--a

higherbecausetheinfluenceofsurfacerecombinationdecreases

Theinfluenceofohmiccontactappearsovertherangex≧120μm-

sincethediffusionlengthisabouthalfofthesamplethickness

of200μmTheoreticalvaluescalculatedusingthemirror

imagemethod[14]discussedinChaptervareshownbyfull

curvesinFig3-8Valueswitニhoutニtheinfluenceofanohmic

contactarealsoshownbydottedcurves

Thescanningsurfacewasnotaffectedbyanelectronbeam

oftheorderof2times10oline10Abecausethesameresultwasobtained

forshallowexcitation(vadeg10kV)afterthesamplewasirradiated

for1hatV=10へ一50kVa

ThedepletionlayerwidthisnotbroughtIntoconsidera-

tionbecauseofitsnarrownesscomparedwiththescanningdistance

Theelectronbeamdiameterofabout50nminthisexperiment

1Snottakenintoaccountsinceitisverysmallincomparison

withthegenerationregionevenifvais10kvdeg

工fthebeamcurrentiskeptconstantthegeneration

densitydecreaseswithincreasingVbecausethegeneration

volumeincreasessuperlinearlywithvarsquo゜Whenthebeamcurrentis

2times10oline10Aandvais10kVtheexcessminoritycarrierdensity

-46-

atthegenerationpointisabout5times1014Cmoline3(themaximum

generationdensityinthisexperiment)followingthediscuss10n

inref[1]whichissmallerthanthemajoritycarrierdensity

1nthesamplesThereforethevalueofLismeasuredatthe

lowinjectlonlevel

3-5 Summary

Thegenerationvolumeofminoritycarriershasa

considerableeffectontheEBIClinescanprofilesespecially

whenItisequaltoorlargerthanthediffusionlengthWe

investigatedthedependenceofEBIConxforgeneralsurface

recombinationvelocityinthecaseofthefinitevolumesource

Whenvaislowandthegenerationdepthisshallow

surfacerecombinationhasalargeeffectonEBICWhenvaishigh

andthegeneratニiondepthisaslargeasthediffusionlengththe

generationregioncann0longerbeassumedasapointandthe

finitevolumesourceshouldbeusedintheanalysisThetheo-

reticalcalculationshowsthatsurfacerecombinationhasonlya

slighteffectontheshapeoflogJvsXcurvesbutaffectsthe

absolutevalueofJTheaccuratevaluesofLsandEshouldbepc

estimatedbyfittingtheexperimentaldatatothetheoretical

curvesforallacceleratingvoltagesExperimentalresultsinthe

measurementofLandSonS1Schottkydiodesshowedgoodagreement

withthetheoryatboth10Wandhighvadeg

TheexperimentalresultthatEBIChasamaximumnear

thebarrierplanewasexplainedqualitativelyusingthesimple

model0fthefinitevolumesourceItcouldnotbeexplainedby

thepointsourcesolutionFurtherinvestigationofthisedge

effectwillclarifythegenerationdistributionbyanelectronbeam

-47-

References

[1]

2]

31

[41

[7]

[8]

[9]

[10]

FBerzandHKKuikenSolid-stateElectron

437(1976)

19

CvanOpdorpPhilipsResRep_32192(1977)

LJastrzebskiJLagowskiandHCGatos

ApplPhysLett27537(1975)

JApplPhys481730(1977)

JYChiandHCGatosIEEETransElectronDev

ED-241366(1977)

WCzajaJApplPhys2Z^236(1966)

JFBresserdquoScanningElectronMicroscopy1972

Partlrdquo[SEM]nc工ITRIChicago)pp105-112

SpSheaLDPartニainandpJWarterrdquoScanning

ElectronMicroscopy1978Vol1rdquo(SEMIncAMFOrsquoHare)

pp435-444

GVSpivakGVSaparinandLFKomolova

rdquoScanningElectronMicroscopy1977rdquo(SEMInc

IITRIChicago)pp191-199

DBWittryandDFKyserJApplPhysj廻375

(1967)

TEEverhartandpHHoffJApplPhys

(1971)

-48-

42

-5837

[n] AEvonGriinZNaturforsch12a89(1957)

【12】KKanayaandSOkayamaJPhysDApplPhys

543(1972)

[13]CJWuandDBWlttryJApplPhys492827

(1978)

[1410vonROOSSolid-stateElectron111063(1978)

-49-

4-1

ANALYSISOFTHREE-DIMENSIONALGENERATIONDISTRIBUTION

BYTHECOMBINATIONOFTHENORMALINCIDENCEANDTHE

LINESCANMETHODS

Introduction

TheminoritycarrierdiffusionlengthLandthesurface

recombinationvelocityScanbedeterminedbyanEBICtechnique

withboththenormalincidenceandtニhelinescanmethodsusing

SEMasdiscussedinChapters皿andHITheminoritycarrier

generationdistributニionbyanelectronbeamplaysanimportant

roleintheanalysisofEBICWhenthedimensionofthegeneration

regioniscomparablewithorlargertニhanLthegenerationregion

cannotbeassumedasapointandthegenerationdistribution

mustbetakenintoaccount

Thegenerationdistributionbyanelectronbeamhasbeen

investigatedbyseveralauthorstheoretically[1]andexperimental-

1y[2-51Asregardstheone-dimensionaldistributionaGaussian

[2-3]orpolynomial[4]functionwasassumedforthedepthdose

functionandthecombinationofexponentialdecayfunctions[51

wasusedforthelateraldosefunctionInChapter工皿the

influenceofthethree-dimensionalgenerationdistributionon

EBICinthelinescanmethodswasstudiedassumingasimple

distribution(semisphere)withuniformminoritycarrierdensity

Ineachoftheseexperimentsonlyonemethodタeitherlinescan

ornomalincidencewastakenTheelectronpenetrationdepth

andthegenerationdistributiondifferedfromeachother

-50-

Schottky

barrier

Fig4-1

2P

Surfacecrosssection

「egion

Oneofthedividedsegments

Schematicviewofexperimentalconditionsandthedefinitionofthecoordinatesystem

-51-

Electronbeam

hottkySurfacecrossse

arrierOGene芯ion

Re゛region

Oneofthe

々dividedsegi

InthischapterwemeasuredEBICbyboththelinescan

andthenormalincidencemethodsinthesamesampleandclarified

thegenerationdistributionTheinfluenceofthethree-dimensional

generationdistributiononEBICisdiscussedassumingthatthe

electron-holepairsarelocalizedatニthecenterofthegeneration

regionTheexperimentニalresultsforGaAsSchottkydiodesare

alsoshown

4-2 Influenceofthree-dimensionalgenerationdistribution

onelectronbeaminducedcurrent

WeusedaSchottkydiodesinceitcanbeappliedforboth

thelinescanandthenormalincidencemethodsInthelinescan

methodtheEBICiscalculatedtakingtニhegenerationdistニrlbution

intoaccountbyasimilarmethoddiscussedinChapterⅡ工The

generationregionisdividedintomanysegmentsthesizeofwhich

issmallerthanLandeachsegmentisrepresentedbyonepoint

sourceTheEBICforthefinitevolumesourceisderivedby

summingupthesolutionofthediffusionequationforeachpoint

sourcersquo

Thedistributionisassumedtobesphericallysymmetric

asisshowninFig4-1Theelectron-holerdquopairsgeneratedbyan

electronbeanareconsideredtobelocalizedatthecenterRCof

thegenerationregionThegenerationstrengthgalonganyradius

vectorfromRc1Sassumedtobegivenby

gdeg^exp[-C(r2R2)] (4-1)

whereRisthedistancebetweenRandthemaximumelectronrange

CRm゛andristhedistancebetweenRCandeachdividedsegment

(seeFig4-1)

-52-

TheexponentCrelatestothedistributiondensityThedensity

becomesuniformasdiscussedinChapterl[EwhenC1Szeroand

theelectron-holepairslocalizenearRcwhenCbecomeslarge

Thedistributionisassumedinorderthatthedepthdosefunction

maybecomeGaussianasisreportedinthereferences[23]

ThevalueofLshouldbesmallinorderthatitcanbe

measuredbyboththelinescanandthenormalIncidencemethods

ThereforewetakeGaAsasanexampleInthelinescanmethodwe

calculatetheEBICintensity(whichiscalledthecollection

efficiencynandisnormalizedtobeunitywhenallthegenerated

carrierscontributetoEBIC)forseveralvaluesofCandR

The゛ilueofRmisgiven[2]by

町゜001A8Vノ゛フurn

cR

m゛

(4-2)

wherevaistheacceleratingvoltニageinkVThevaluesofCand

RRareassumedtobeconstantevenifvisvariedWhenvisCm

10and30kVaa

Rm

becomesOdeg74and4deg8ymrespectニivelyWetake

thetypicalvalueofLas1μminordertoexaminetheinfluence

ofthegenerationdistributiononEBICbecausethevalueofRm

issmallerthanLatva゛10kVbutlargerthanLatvadeg30kvrsquo

SincethesurfacerecombinationvelocitySofGaAsisoftheorder

of105-106cmSoline1[6-9]wetakevaluesofland50asthe

surfacerecombinationvelocityparameterSdefinedbySΞS(Lて)

(TisthelifetimeoforderofnS)

TheresultsofthecalculationareshowninFig4-2The

fullcurvesandthebrokencurvesareforCdeg8rsquo2゛RcRm゛Olsquo13and

C=54RR゜013respectivelyThesevaluesofCandRじmolinersquoCrsquom

thetypicalvaluesobtainedbythenormalincidencemethodin

GaAs[23]Thepointsourcesolutions(whichareobtainedby

assumingthatallthegenerationoccursatRc

-53-

are

)arealsoshownby

g`

A3U413Ud

COP≫no3

Fig4-2

ScanningdistanceX(pm)

j一次゜ごゴ野謡ごごご二ににごS

ご諧驚お謡謡S回読で昌翼麗

二竃Jeぎ驚謡じ雲Cにニごまふ(

ごごぶ謡1ば昌permilお穴混戮ずpermil

ぶぶごご1ここなSttedcdeges゛ecm

-54-

helliphellipl

]]1A

Ee

ビゲヤ

12

ss50

helliphelliphellipyJミ4sdeg50

dottedcurvesAtVa゛10kVthesizeofthedividedsegmentis

takenas005umwhichissmallerthanLsothateachdivided

segmentcanberepresentedbyonepointsourceIntheregion

05≦x≦15ymthelogarithmofEBICdecreasessuperlinearly--

anditdecreasesalmostlinearlyovertherangeofx≧15um-

ThetendencyappearsmoreapparentasSbecomeslargeThechange

oftheexponentCmakeslittledifferencetotheprofilesofthe

curvesTheabsolutevalueofnovertherangeofx≧05umis-

almostequaltothepointsourcesolutionwhenS1S1butbecomes

twicethatwhenSis50Thepeaksnearthebarrierareduetothe

edgeeffectasdescribedinChapterl工゛Atvadeg30kVthesizeof

thedividedsegmentistakenas02ymforthesamereasonas

Wit二hvadeg10kVThecurvesarequitedifferentfromthepointsource

solutionbothatS=1andS=50becausethedimensionsofthe

generationregionarelargeincomparisonwithLandthepoint

sourceassumptionisn0longervalidinthiscaseTheprofiles

ofthecurvesreflectthegeneratニiondistributionasoneseesthat

theprofilechangesifCvalsquotiesfrom54t082WhenSisvaried

fromlto50theprofiledoesnotchangeatthesameCvaluebutニ

ndecreasesbyabout30ZofthatofS=lItshouldbenotedthat

thesurfacerecombinationhasaninfluenceontheabsolutevalue

ofEBICevenifthevalueofRm(4deg8pm8tvadeg30kV)ismuch

greaterthanLThereforewecanevaluateLmainlyfromthe

slopeofthelinearregionat10Wvaconsideringthesurface

recombinationeffectandestimatethegenerationdistribution

fromtheprofilesofthecurvesinthecaseofhighva゛

-55-

Fig4-3

pasube

coipai

-O

Maximumelectronraり9eRm(μm)

AcceleratingvoltageVa(kv)

Experimentニalresultsofthenormalincidence

methodforthesampleA(SndopedGaAsn=62times1016

cm^L=03)Jm)andthesampleB(TedopedGaAs

ndeg80times1016cmoline3Ldeg07μm)Experimentalvaluesare

shownbycirclesThefullandbrokencurvesare

theoreticalcurvesforC=82RR=013andC=54

RcRmdeg013respectivelywdeg10cnmmandwddegOdeg151Jmdeg

-56-

12410oline

GaAsn(c「7i」

5A訟ばn

2ゝゝゝ

ゝゝ

ゝゝゝ

ゝゝゝrsquoL(pm)

1゛゛`ヽBO7J

yWヽ

5oline`olinersquo54013A03

≒旨

2φ

(52Schottkか

デ1テシフ)卜

1020304050

Theelectron-holepaircreationenergyEisobtained

fromthefollowingequation[101

n=ErdquordquoEBIC

pcIBvak(4-3)

whereIBisthebeamcurrentandkisthecorrectionfactorfor

theback-scatteredelectronsAsdescribedpreviouslythevalueof

nisinfluencedbySevenwhenVishighandsowemusttakeolinea`lsquorsquoolineolineolineolineolineolineolineolineolineolineoline

thesurfacerecombinationeffectintoaccountwhenweevaluateE

pc

4-3 Three-dimensionalgenerationdistributニioninGaAs

Thesameapparatusandthelock-intechniquewereused

asdescribedinsect3-4TheSchottkybarrierwasmadeonn-typeGaAs

wafersbyevaporatingAuofabout10nmthickinavacuumofabout

10rsquo7TorrTheohmiccontactwasobtainedbyevaporatingAu-Geand

alloyingat400degCfor2minThecarrierdensitynofeachsample

wasdeterminedbyc-vmeasurements

Theexperimentalresultsofthenormalincidencemethod

forthesampleA(Sndopedn=62times1016cmoline3)andthesampleB

(Tedopedn=80times1016cmoline3)areshowninFig4-3byfulland

opencirclesrespectivelyThevalueofvawaSvariedbetween5

and50kVTheEBICintensityincreasedlinearlywithIBwithin

therangeof1times10oline11≦IB≦-1times10oline9Awhenvawasfixed

whichsatisfiedthelowinjectionlevelconditionThecollection

efficiencynwascalculatedbythesamemethodreportedinref[10]

bychangi昭RcRmfrom01t0025andCfrom30to90

respectivelyThebestfitcurveswiththeexperimentalresults

wereobtainedInthecaseofL=03and07umforsamplesAandB

respectivelywhenRcRm゛O゛13andC=82wereusedThevaluesof

-57-

II

A3ua<3UduqjDaiion

ScanningdistanceX((jm)

Fig4-4

Experimentalresultsofthe

linescanmethodforthesampleA

[SndopedGaAsn=62times]016cmoline3)

Thefullandbrokencurvesare

ー い゛I

゛゛

ldquooU 5

Scanningdistancex(μm)

Fig4-5

ExperimentalresultニSofthe

linescanmetニhodforthesampleB

(TedopedGaAsn=80times1016cmoline3)

Thefullandbrokenlinesare

theoreticalcurvesforC=82RRtheoreticalcurvesforC=82R

=013andC=54RR=013cdeg=013andC=54RR=013c

respectivelyLdeg03cμmS゛20respectivelyLdeg07ymSdeg20

-58-

ぎ忌

五゛

olinelo

jV

ズごy

23

times1

GaAだj

j73C4Electron

L=07μmEbeam

2Sdeg20χ

1rsquo`

゛x

ya(W

2゛Va=30W

2_JE201

4一一―54013

5≒

脅χ

21`f

ゝ≒

ゝへ

5χ

147

RCRmandCagrees`゛iththerepoidegtedvalues[2]゜Thefulland

brokencurvesinthefigurearetheoreticalcurvesforC=82

RcRmdegOdeg13andC゛5deg4゛RcRmdegOlsquo13respectニivelylsquoThediscrepancy

betweenthetheoreticalcurvesandtheexperimentalvaluesat

10WvacanbeexplainedinthefollowingwaydegThegeneration

regionbecomesshallownearthesurfaceatlowVandtheEBIC

ismainlycontributedbytheseperatedelectron-holepairsin

thespace-chargeregionjustunderthesurfaceInthetheoretical

calculationitisassumedthatthere1Snorecombinationinthe

space-chargeregionButニinactualfactthecarriersrecomblne

throughthevarioustrapswhichreducestheEBIC

Theexperimentalresultsofthelinescanmethodforthe

samplesAandBareshownbycirclesinFigs4-4and4-5

respectivelyThetheoreticalcurvesareexpressedbythefull

(Cdeg82RcRmdeg013)andthebroken(C=54rsquoRcRmdegOdeg13)curves111

bothfiguresTheEBICintensityincreasedlinearlywithIBwitニhin

therange1times10oline11くrsquoIく1times10oline9Awhenvwasfixedat100r=B=a

30kVwhichsatisfiedthe10wInjectionlevelconditionasinthe

normalincidencemethodThetheoreticalcurvescalculatedusing

thesameparameterdeterminedbythenormalincidencemethodshow

goodagreementwiththeexperimentニalresultsatbothvadeg10and30

kVWhenwetakeintoaccountthattheexperimentalresultsat

vadeg30kVreflectthegenerationdistributiontheassumedgeneration

distributionbyeq(4-1)withC=5Aへ82andRcRmdegOdeg131s

consideredtobeappropriateforthethree-dimensionalgeneration

distributioninGaAs

Thevalueofkchangesfrom078to075whenvvariesa

from5t050kV[10]Whenwetaketheappropriatevalueofkfor

themeaSuredva゛Epccanbedeterminedbyeq(4-3)Thevaluesof

-59-

Normalincidence Line scan

V(kv)a

E(eV)GaAsCSndoped)pc

GaAs(Tedoped)

5-50

41

39

14

3 9

30

Tab4-1 Valuesoftheelectron-holepaircreationenergyEinGaAsdeterminedbytニhenormalincidenceandlinepc

scanmethods

-60-

Eobtainedbythenormalincidenceandthelinescanmethodsarepc

39Oi41eVand38へj44eVrespectivelyastabulatedin

Tab4-1BythenormalIncidencemethodWuandWittry[10]

determinedEpCas468eVwhichwasabout15Zlargerthanour

resultsOnereasonforthediscrepancy1Sthedifferenceofthe

generationdistributionsThemodifiedGaussiandistributionused

bythemslightlydifferedfromtheGaussiandistributionusedin

ouranalysisAnotニherreason1Stheaccuracyofmetalthickness

WeestimatethethicknessfromtheweightofthechargedAuwhich

1SevaporatedtomaketheSchottkybarrierThereforetニheobtained

valuemaybedifferentfromtherealthicknessInthelinescan

methodEBICbecomesinsensitivetothemetaltニhicknessandthe

trapsinthespace-chargeregionbutisinfluencedbysurface

recombinationasdiscussedbeforeAlferoveta1[11]andWittニry

andKyser[12]reportedEpcas32へj44eVand46eVrespectニive-

lyfromthepeakvalueofEBICwhentheelectronbeamcrossedthe

p-njunctionOurresultsof38へj44eVareinthemiddlerange

oft二heirvaluesIntheiranalysestheydidnottakethesurface

recombinationeffectintoaccountandsoourresultsareconsidered

tobemorereliablethantheirs

4-4 Summary

Thethree-dimensionalgenerationdistributionbyan

electronbeaminGaAswasinvestigatedbymeasuringEBICwitha

combinationofnormalincidenceandlinescanmethods

TheprofileoftheEBICcurvesinthelinescanmetニhod

expressesthegenerationdistributionwhenvaishighandthe

dimensionofthegenerationregionislargerthanLThesurface

-61-

recombinationdoesnotaffecttheprofileofEBICbutlowersthe

collectionefficiencyTheaccuratevalueoftheelectron-hole

paircreationenergymustbedeterminedbytakingthesurface

recombinationeffectintoaccount

TheexperimentalresultsinGaAsSchotニtkydiodeswith

differentdiffusionlengthsshowedthatthecenterofthe

generationregion(iethemaximumenergydissipationdepth)

waslocatedatthepointof0130fthemaximumelectronrange

andtheradialdistributionfromthecenterwasshowntobe

Gaussianwithaneχponentof54へ-82Theelectron-holepair

creationenergyinGaAswasdeterminedas38rsquoV44eV

References

[1]

[2]

[5]

[6]

KKanayaandSOkayamaJPhysDApplPhys

543(1972)

DBWittryandDFKyserJApplPhys旦旦375

(L967)

VVMakarovSovPhys-Semicond旦722(1975)

TEEverhartandpHHoffJApplPhysを

5837(1971)

SpSheaLDPartainandpJWarterrdquoScanning

ElectronMicroscopy71978V011uml(SEMIncAMFOrsquoHare)

pp435-444

LJastrzebskiHCGatosandJLagowski

JApplPhys481730(1977)

-62-

[7]

[81

[9]

[10]

[11]

[12]

LJastrzebskiJLagowskiandHCGatos

ApplPhysLettri537(1975)

MEttenbergHKresselandSLGilbert

JApplPhys44827(1973)

CAHoffmanKJarasiunasHJGerritsenand

AVNurmikkoApplPhysLett22536(1978)

CJWuandDBWlttryJApp1PhySpoundrsquo2827

(1978)

ZhIAlferovVMAndreevVIKorolrsquokovand

vIStreminSovPhys-Semlcond41113(1971)-

DBWittryandDFKyserJApplPhys

361387(1965)

-63-

5-1

ANALYSISOFELECTRONBEAMINDUCEDCURRENTCONSIDERING

SAMPLEDIMENSIONS

Introduction

Anelectronbeaminducedcurrent(EBIC)methodusing

ascanningelectronmicroscope(SEM)isaconvenienttechniqueto

measuretニheminoritycarrierdiffusionlengthLandthesurface

recombinationvelocitySinsemiconductorsTherehavebeenmany

theoreticalandexperimentalstudiesonthelinescanmethodof

EBICInChaptersI工andytheEBICwasanalyzedquantitatively

takingthethree-dimensionalgenerationdistributionintoaccount

bythedividingmethodandtheimprovedmethodtocharacterize

Landswassuggestedχihenthesampledimensionsarelessthan

oneortwodiffusionlengthstheminoritycarrierdistribution

isaffectedverymuchbysampledimensionsRoos[1]analyzed

EBICtheoreticallyinthecaseofthinlayersHecalculated

thedependenceofEBIConthescanningdistancexintherange

ofxL≪1inthesampleswithwL=land05(wlayerthickness)j

andshowedthatLcouldnotbedetermineddefinitelyfromthe

slopeofthelogarithmofEBICvsXcurve

InthischaptertoanalyzeEBICconsideringthesample

dimensionsgwediscussasimplemethodusinganimagesource-and-

sinkdistributionWeshowthedependenceofEBIConxoverafull

scanrangewhenthelengthbetweenapotニentialbarrierandan

ohmiccontactisequaltoandsmallerthanthediffusionlength

andmentionsomeimportantニpointstobenoticedinthedetermination

ofLandsTheexperimentalresultsinSiSchottkydiodesarealso

shown

-64-

Fig5-1

ySご

uarrj

Schottkybarrier

uarr

Ohmiccontact

Schematicviewofexperimentalconditionsanddefinitionofthecoordinatesystem

-65-

Electronbeam

-J-

レじ2「lingtrack_^一分

りhelliphelliphellipljc1お迄゛

IL

5-2 Determinationofdiffusionlengthandsurfacerecombination

velocity

ForsimpletheoreticalconsiderationwetakeaSchottky

barrierdiodeAsshowninFig5-1theSchottkybarrierisin

they-zplaneandtheelectronbeamisincidentニperpendicularto

thesamplesurface(χ-yplane)Thescanningdirectionisalong

theX-axiswhichisnormaltothebarrierplaneThegeneration

sourceisconsideredtobeapointニandislocatedat(゛grsquo

Thesteadystニateexcessminoritycarrierdistributionpis

obtainedfromthefollowingdiffusionequation

Dnabla2pdeg二T

-g6(x-xyz-d)rsquo

O゛dg)

(5-1)

whereDisthediffusionconstantンTisthelifetimeandgisthe

generationratニeofelectron-holepairs

工fthethicknesswbetweenthepotentialbarrierandthe

ohmiccontactismuchgreatニerthanLandtheotherboundariesin

theyandzdirectionsarebothmuchfurtherawayfromthe

generationsourceEBICiscalculatedunderthefollowingboundary

conditionsasdiscussedinsect3-2

3p-9z

χ=0

x=-H≫

Z=0

Z=0

=0(attheSchottkybarrier)

=0

wheresIsthesurfacerecombinationvelocity

-66-

(5-2a)

(5-2b)

(5-2c)

(5-4)d帽

wherexgrsquoLrsquoDgdegdLSdegs(Lて)andTisthevariablefor

-67-

integrationThevalueofJ(x)isnormalizedtobeunitywhena11

thegeneratedcarrierscontributetoEBICThefunctionK(ぺ7)

isthesecond-modifiedfirst-orderBesselfunction

FortheanalysisofEBICconsideringsampledimensions

wetakethefundamentalcasethatthediffusionlength1S

comparablewithorlargerthanthethicknessw(seeFig5-1)

OncethedistributionpisknownEBICcanbefoundasfollows

十(゛十(゜3p

j=eDintint-

0 -003χ

dydz

χ=0

(5-3)

whereeisthechargeofanelectronBerzeta1【2】solvedthe

diffusionequation(5-1)undertheboundaryconditions(5-2a)

(5-2b)and(5-2c)bythemirrorimagemethodInadditiontothe

reaLsourceatxg゛animagesinkwasintroducedatthesymmetric

position-XwithrespecttotheSchottkybarrier(seeFig5-2)

Whenthematerialextendstoχ=plusmndegdegthesolutionofeq(5-l)is

givenbypμ](゛゜土)゛WhentheSchottkybarrierisintroduced

theminoritycarrierdistribution1Sexpressedasp[x]十p[oline゛g]

inordertosatisfytheboundarycondition(5-2bplχ=OdegO)rsquo

andjisobtainedasfollows

J()゜

-eg-

-π

DgK(ぶ77F)

リinto

うと縦卜-dT

-H≫

十intexp(-S(T-D))

Dg

g ぜ)ケ

Thenonemustusethefollowingboundaryconditioninsteadof

(5-2c)

Ix=wdegO(attheohmiccontact) (5-2crsquo)

ThesolutionQfeq(5-1)undertheboundaryconditions(5-2a)

(5-2b)and(5-2crsquo)canbeobtainedbyextendingthemirrorimage

methodproposedbyBerz[2]andOpdorp[3]Inadditiontothereal

sourceatXafamilyofvirtuaLimagesourcesandsinksare

introducedatthesymmetricpositionswithrespecttothebarrier

andtheohmiccontact(seeFig5-2)Openandsolidcircles

representthesourcesandsinksrespectivelyThereforethe

sourcesareatX2w十Kg4W十xg゛゜rsquo゜lsquoand-(2w-x)-(4w-x)rdquoldquo゛

andthesinksareat-X-(2w十X)-(4w十X)and2゛゛olinersquo4゛olinersquo

respectivelyWhenthematerialextendstox=士≪>thesolution

ofeq(5-l)isgivenbyp【゛】(゛゜土゛grsquo士(2゛`7oline゛g)rsquo土(2W十)rdquorsquo゜rsquo)

(seeFig5-2)Iftニheinfluenceofohmiccontactニmustbetaken

intoaccounttheminoritycarrierdistributionisexpressedusing

thefollowinginfiniteseriesinordertosatisfytheboundary

conditions(5oline2brsquoplx=OdegO)811d(5oline2c≒Plx=wdegO)rsquo

p゛[゛g]゜jp[≒ 十p[oline

十p[2゛oline]十p[-(2W-X)

+p[2w十゛g]十p[-(2w十)

十一一一一一一-一一

9 (5-5)

Theinducedcurrentsbypairsofsourcesandsinksie

p[゛g]andp[oline゜cg]rsquop[2゛olineへ]andpr-(2w-x)]rsquop[2゛十]andp[-(2v゛十)]rsquo

areexpressedbyJ(x)-J(2v゛oline゜cg)J(2w十)゛rsquo゛゜゛rsquo

respectivelywiththeaidofeq(5-4)ThenthetotalEBICis

expressedintheinfiniteseriesasfollows

-68-

Fig5-2

Source

helliphelliphellipSink

Concentration

Sdηitky

barrier

Ohmic

contact

Schematicviewofexcessminoritycarrierconcentrationpatternforeachsourceandsinkwhicharerepresentedbytheopenandsolidcircles-respectively

-69-

pr2wχ9]

plE【2w->り》】1

1rdquoMI

-E唇-

゜(2WdegO`92Wi

ミplE)rsquo゛p[2w-xg]

pl-《2w+x)】)゜91

s哺

(n

L1)

paziipEJoz

1 2 3

Normalizedscanningdistancex

0 5

M)DUd|UOISコ|}Ppazneaijoz

12 5 X)2050

Fig5-3

DependenceofEBIConthe

normalizedscanningdistanceχ(equivxL)

fullandbrokencurvesarefortニhecaseswithandwithouttheinflu-

enceofohmiccontニactrespectivelyThenormalizedsamplewidthwLis

1020and30andthenormalized

generationdepthDgisOdeg0Thevaluesofthesurfacerecombination

velocityparameterS(seetext)

areland10forupperandlower

groupofcurvesIrespectively

Fig5-4

Estimateddiffusionlength

fromthereciprocalgradientof

thecurveatthecenteroftニhe

scanningdistanceinthecaseof

DgdegOlsquoOandwLdeg1lsquoOSvaries

fromlt050L大andL訟are

forthecaseswithoutandwith

theinfluenceofohmiccontact

respectively

SurfacerecombinationvelKitypmmeterS

-70-

Dgdeg00

そー=10

L゛で

ヽ1慟1

111

25=1rsquo1

1`11

【flll

11

51s

degilOII

211`4

111

(flll゛

芒゜11゛|`

51S`|

11゛1

|ぎ=21`ヽ

||rsquo゜3|

(y

J(Xg)=J(x)-J(2v゛oline゛g

olineJ(匈゛≒

)十J(2wトxg

)十J(4wヽ4-xg

----

II

(5-6)

ThevalueofJ大convergestoacertainvalueandcanbecalculated

byacomputerincasesofanyvaluesofwLandS

InFig5-3thelogarithmofJisplottedbysolidlines

asafunctionofx(=xL)whetvwL1S1020and30and

Dgis00Thedashedlinesareforthecasewithouttheinfluence

ofohmiccontactTheupperandlowercurvesareforS=1and10

respectivelyThevaluesoflogJ大decreasesuperlinearlywithin

onediffusionlengthawayfromthebarrierThereforeonemakes

considerableerrorsifoneestimatesthevalueofLfromthe

reciprocalgradientofthecurveatarbitraryXInordertoshow

anextremeexampleweconsiderthecaseofw7Ldeg1゛08叫DgdegO`Odeg

Thereciprocalgradientofthecurveinthelinearregionat

xdeg05withoutandwiththeinfluenceofohmiccontactareputas

L大andLrespectivelyThevaluesofLandL幼thuSobtained

areplottedasafunctionofSinFig5-4WhenSisunityL

1Sabout68ZofLandL政isabout44ZofLThevaluesofL大

andL政reducetoonlyaboutonethirdofLwhenSis50

Themethodoftheanalysisforapointsourcementioned

abovecanbeeasilyappliedtothefinitegenerationdistribution

bythedividingmethoddiscussedinChaptersI工andHEspecially

inthecasesoflight-emittingdiodes(LEDrsquos)andlaserdiodes

(LDrsquos)usingGaAsandGaPthedimensionofthegenerationregion

istheorderofymforva゛20へrsquo30kVandiscomparablewiththe

thicknessoftheepitaxiallayersThereforethedividingmethod

becomesaneffectivemeanstomeasureLandSintheepitaxial

layers

-71-

Fig5-5

Q‐rsquoQ]

loline

11(52

ち5

0 50Scanningdistancex

100

(pm)

jDependenceofEBIConthescanningdistancexforn-SiSchottkydiodesThelengthWbetweenthe

barrierandtheohmiccontactis100Umthe

acceleratingvoltageVais50kVandLis20へj200lim

SolidandbrokenlinesareforSdeg104and105cmsec

respectニivelytakingthegenerationdistributioninto

accountThediffusionconstantDofholesis125

cm^sec

-72-

n-SiVa=50kVw00μm

5aD=iZ5cm2ss(cms)

1-helliphellip104

2゛l`4-----helliphellip105

`L(μm)

1へ`a-2001

≒yyhelliphelliphellip100i

5゛゛ぐ丈i

へ゛`恥i

`ヽ

`lsquolブjl

ゝゝjφ1

0h白contactム

2rsquo

5-3 ApplicationtoS1

ThediffusionlengthintheSibulkmaterialusedfor

solarcellsorLS工゛S1Scomparablewiththedimensionsofeach

elementAndsotheminoritycarrierdistributionisaffected

verymuchbyelementdimensionsTheSchottkydiodewastakenfor

afundamentalmodeltorevealtheinfluenceofsampledimensions

CalculatedEBICrsquosbythedividingmethodinthecaseof

n-Siforwdeg100umandva゛50kvareshowninFig5-5Thediffusion

constantDofholesistakenasatypicalvalueof125cm^sec

Solidanddashedlinesareforsdeg101゛and105cmsecrespectively

andLis20010050and20umforthecurvesfromupperto

lowerineachgroupThegenerationsourceisassumedtobeasemi-

sphereThenumberofthegeneratedelectron-holepairsatany

pointinthesemi-sphereisproportionaltoexp(-40(rR)2)

(rthedistancebetweenthepointandthecenterdRthe

radiusofthesemi-sphere)Thegenerationdistribution1Sassumed

inorderthatthedepthdosefunctionalongthez-axlsagreeswith

thatproposedbyEverhart[4]andthevaluesofdgandRare

5ymand11ymrespectively゛forvadeg50kvrsquo

AsshowninFig5-5theabsolutevalueofEB工Cincreases

withdecreasingSforthesameLvalueThecurvesconvergetoa

certaincurveforboths=10rsquoand105cmsecwhenLbecomesgreater

thanwForconveniencethelogJvsχcurvesaredividedinto

threepartsi

range(30≦X-

く一一

eA)nearthebarrier(0≦x≦30ym)B)middle--

70ym)andC)neartheohmiccontact(70≦x≦100--

μm)IntheregionA)peaksappearatxdeg6ymowingtotheedge

effectdescribedinsect3-3and10gヽJdecreasessuperlinearlybecause

ofthesurfacerecombinationeffectIntheregionC)logj大decreases

-73-

Fig5-6

゜1(il

四a3

U」

-01

Ddziieujjoz

゛D=1Z5cm2s巡付

1 03

orini=-

にuarrヤuarr

uarrにヤ

Ohmiccontactづ50100

Scanningdistancex(μm)

JDependenceofEBIConthescanningdistancex

forn-SiwhenLismuchgreaterthanWThesolid

linesareresultsbythethree-dimensionalsolutions

forsdeg1035times1031045)(104and105cmsec

respectivelyThedashedlineisEBICbyone-

dimensionalapproximationV=50kVw=100ymand

L=1000Uma

-74-

゛ぐpermil

゛`xズit

darrレ

rapidlybecausetheohmiccontactisacarriersinkInthemiddle

rangeB)logJ大decreasesalmostlinearlyThereciprocalgradient

ofthecurveincreasesasLbecomeslargeintherangeofL≦100pm-

Thegradientsofthecurvesarenotsoaffectedbysurface

recombinationIfvisloweredt010kVthesurfacerecombinationa

affectsEB工Cmuchmorethanforvadeg50kVbecausethegeneration

depthbecomesshallowerInfactthegradientsofthecurvesin

regionA)aresteeperthanthoseforv=50kVforthesameLvaluesa

ThereforeinthecaseofL≦100ymLandscanbedetermined-

mainlyfromtheslopesofthelinearlydecreasingregionforhigh

va(50kVinthiswork)andthesuperlinearlydecreasingregionnear

theSchottkybarrierfor10Wva(10kVinthiswork)respectively

takingtheinfluenceofohmiccontactintoaccountButinthe

caseofL≧100ymthevalueofLcannotbedetニermineddefinitely-

becausetheslopeofthecurveinthelinearlydecreasingregion

doesnotchangeevenifLvaries

WhenLbecomesmuchlargerthanwthecurvesofEBICvsX

convergetoacertaincurveCalculatedEBICrsquosinthecaseofn-Si

forva゛50kVwdeg100ymandLdeg1000ymareshownbysolidlines

1nFig5-6forsdeg1035times1031045times104and105cmsec

respectivelyThegenerationsource1Sassumedtobeapointatthe

depthdThedashedlineisasolutionofone-dimensionalg

approximation(seeappenditimes1nthischapter)Theabsolutevalueof

EBICbecomeslargerwithdecreasingSandthecurveforS40cmsec

approachestothesolutionofone-dimensionalapproximationItcan

beexplainedasfollowsInthecaseofs=Ocmsecthereisno

carrierrecombinationatthesurfaceHencethematerialcanbe

consideredtoextendtoz=_oobyintroducinganimagesourceat

(x0-d)EBICisobtainedbyintegratingdpdxinthey-zplane

atx=0AndsotheEBICbythepointsourceat(x

-75-

grsquoO゛plusmnd)using

JOoline1

Ig3paziieuijoz

Fig5-7

(a)

UI「rrsquo

a3

U」

rsquo一lsquo51 0

pdziieujjoz

Scanningdistance

(b)

X(pm)

ExperimentalresultsinSiSchottkydiodesfor

w゛200μmand83μminfigures(a)and(b)respectively

Vais1030and50kVSolidanddottニedlinesare

theoreticalresultsforL=80UmandS=50withand

withouttheinfluenceofohmiccontニactrespectively

-76-

inlsquoSiL=80μm

こ沼o

rsquoバ町「i「でなl`Jes

l悶

2卜Ohmiccontact今|

トj

rsquohelliphelliphelliphelliphellipi

15

≒|

2helliphellip1

0Scanningdistancex150(pm)00

へn-SiL=80μm

5゜`S=50

deg゜w=83um

degムExperimentalvalues2deg`4≒Vi=50kV

I゛lsquorsquo4≒oVadeg30kV

≒゜rdquoVa≪10kV

丿4

lrsquo

2lsquoo1

rsquo゜i

2degi

2Ohmiccontactrarr

050100

thethree-dimensionaldiffusionequationbecomesidenticaltothat

derivedbyone-dimensionaldiffusionequationconsideringthe

planarsourceatxrsquoxginthey-zplane[5]Howeverinpractice

SihasafinitevalueofSandsothethree-dimensionalsolution

mustbeneededinthecaseofL>wThevalueofscanbedeter-

minedfromtheabsolutevalueofEBICfollowingthediscussionof

sect4-2usingtheelectron-holepaircreationenergyE^^byan

electronbeam

TheexperimentalresultsinSiSchottkydiodeswith

w=200umand83μmmadefromonewaferareshowninFigs5-7(a)

and5-7(b)respectivelySamplepreparationsandmeasurement

procedureshavebeenalreadyshowninsect3-4Theresultsofthe

theoreticalcalculationusingL=80vimandS=50forthreedifferent

va゛s(10rsquo30and50kV)areshownbysolidlinesinbothfigures

Theresultsofthetheoreticalcalculationwithouttheinfluence

ofohmiccontactareshownbydottedlinesinFig5-7

Inthecaseofw=200ymthesamplewidthisthreetニimeslargerthan

Landsotheslopeofthelinearregion(50≦x≦120um)isnot--

verychangedbytheinfluenceofohmiccontactInthecaseof

Wdeg83umthecurvesarequitedifferentfromthoseforw=200ym

andthereciprocalgradientofthecurvesinthemiddlerange

(25≦x≦55ym)givesL=20ymwhichisaquarterofthereal--

diffusionlengthBothinFigs5-7(a)and(b)theoretical

calculationsshowgoodagreementwiththeexperimentalresuLts

whichshowsthatthemethoddiscussedinsect5-21Saneffective

meanstニoanalyzetheeffectofsampledimensions

-77-

5-4 Summary

Theminoritycarrierdistributionisaffectedverymuch

bythelengthwbetweenapotentialbarrierandanohmiccontact

ifWisequaltoorshorterthanthediffusionlengthLThe

dependenceofEBICJ大onthescanningdistancexwasinvestigated

byextendingthemirrorimagemethod

InthecaseofwL≧1logJ゛decreasesalmostlinearly-

inthemiddlerangeofthescanningdistancebuttheestimated

diffusionlengthfromthecurvesismuchshorterthanthereal

diffusionlength(eg30t044ZinthecaseofL=w)The

valuesofLandScanbedeterminedmainlyfromtheslopesof

thecurvesforhighand10Wva゛reSpectively゛takingtheinfluence

ofohmiccontニactintoaccount

工nthecaseofwLく1theslopeofthelinearly

decreasingregionoflogJvsXcurvesdoesnotchangeevenif

LvariesThedependenceofEBIConχconvergestoacertaincurve

ThevalueofLcannotbedetermineddefinitelybutthevalueofS

canbeobtニainedfromtheabsolutevalueofEBIC

TheexperimentalresultsinSiSchottkydiodesagreed

fairlywellwiththetheorywhichshowedthattheextendedmirror

imagemethodwaseffectiveinanalyzingEBICconsideringthesample

dimensions

-78-

References

[1]

[2]

[5]

OldwigvonRoosSolid-stateElectron

(1978)

211063

FBerzandHKKuikenSolid-stateElectron19

(1976)

437

CvanOpdorpPhilipsResRep32192(1977)

TEEverhartandPHHoffJApplPhys丘5837

(1971)

WHHackettJrJApplPhys

Appendix0nedegdimensionalapproximation

431649(1972)-

IfthediffusionlengthLisinfinitelylongminority

carriersdonotrecomblneuntiltheyflowintothebarrierorthe

ohmiccontactThereforethediffusioncurrentdoesnotvary

spatiallyTheminoritycarrierdistributionpcanbeexpressed

asalinearfunctionofχ1nthecaseofone-dimensional

approximation工fthepointsourceg1Slocatedatdegcgrsquop(゜c)is

putasfollows

p(x)=ax十b(a>00≦゛≦)rsquo

p(x)゜c゛十d(c<0X≦゛≦゛)゜

(5-Al)

(5-A2)

Thefactorsabcanddcanbedeterminedfromthefollowing

conditions

-79-

p(O)=0

p(w)=0

卵石

-卜-卵匹 ゜g

(5-A3)

(5-A4)

(5-A5)

(5-A6)

Theeq(5-A5)showsthecontinuityconditionatxdegxg゛andtheeq

(5-A6)givesthatallthegeneratedcarriersflowintothe

Schottニkybarrierandtheohmiccontactニwithoutrecombinationin

materialsThesolutionp(x)becomesasfoLlows

p(x)=

p(x)=

(1-ミj1)x(O≦x

--^(w-x)(Kg

NormalizedEBICJisexpressedby

J大=

-egeD

dp

-dxχ=0

=1-

こ)

3Wく

一一

Xく一一

(5-A7)

(5-A8)

X』

-80-

(5-A9)

6-1

DETERMINATIONOFLIFETIMEANDDIFFUSIONCONSTANT

BYPHASESHIFTTECHNIQUE

Introduction

Accuratedeterminationoflifetimeてofminoritycarriers

1Sveryimportantincharactニerizingsemiconductingmaterials

Thevalueofてcanbemeasureddirectlyfromthetransientresponse

aftertheinjectionofminoritycarriersTheradiativerecombina-

tionlifetimewasmeasuredinGaPandGaAsfromthedecayofphoto-

luminescence[1]cathodoluminescence[2]orelectroluminescence[3]

Thephotoconductancedecaymethod[4]Isthemostcommonlyused

techniquetomeasurelifetimeincludingradiatニiveandnon-

radiativeprocessesInthesemethodsmeasurementofTinsmall

areaoftheorderofym^isverydifficultbecausethesample

surfacemustberelativelywideinordertoobtainasufficient

signalThespatialvariationofてcouldbedeterminedfromthe

decayoftheelectronbeaminducedcurrent(EBIC)usinga

scanningelectronmicroscope(SEM)[5-8]Thevalueofてismuch

influencedbysurfacerecombinationsincelightoranelectron

beamforexcitationentersthroughthesurface

Thevalueofてcanbeobtainedfromthediffusionlength

LusingtherelationL=j5マThevalueofLcanbedeterminedbythe

spectralresponsemethodusingsolarcells[910rbythesurface

photovoltaicmethod[1011nbothmethodstheaccurateabsorption

coefficientmustbeneededtodeterminethevalueofL

AsdiscussedinChapters皿rsquov^VtheEBICmethodusingSEMisa

veryconvenienttechniquetomeasureLinsmallareaoftheorder

-81-

ofym^andtherehavebeenmanytheoretical【11-14】and

experimental[15-16]worksuptodateInthemetニhodhowever

thediffusionconstantDmustbegiveninordertoobtainT

Whentheintensityofexcitationforelectron-holepair

generationisrdquomodulatedthephaseofluminescenceorinducedcurrent

isshiftedfromthatoftheexcitationsourcebecauseofthe

recombinationofinjectedminoritycarriersinamaterialThe

valueofてcanbedeterminedfromtheamountofthephaseshift

Hwang[17]obtainedTinGaAsfromthephaseshiftofphoto-

luminescenceInthemethodtニhephaseshiftisinfluencedbythe

surfacerecombinationvelocityandtheabsorptioncoefficient

whichaffectminoritycarrierdistributionverymuchReichleta1

measuredでinSi[18-20]andGaAs[21]usingthephaseshiftin

photニ0-inducedcurrentMunakata[22]andOthmer[23]measuredて

bythephaseshiftofEBICinGeandSirespectivelyTheyused

tニhesolutionoftheone-dimensionaLdiffusionequationwithout

anyconsiderationofthesurfacerecombinationeffect

Ifsuchaphaseshiftmethodiscombinedwiththe

conventニionallinescanmethodofEBIC(iemeasurementofLusing

DCelectronbeam)thelifetimeandthediffusionconstantof

minoritycarriersinsmallareacanbedeterminedsimultaneously

Kammeta1[241determinedてandDinSiTheymadeaSchottky

barrierwithasilverpaintonSisurfacesandmeasuredEB工Cby

scanningtheelectronbeamonthesurfaceparalleltothebarrier

InthatmethodsurfacepreparationhasmucheffectonT[25]

andtheconfigurationusedbythemisnotconvenientwhenone

measuresてandDinmaterialswithsmallLTheanalysisisvery

complicatedandRoospointedouterrorsintheiranalysis[26]

andsuggestedasimpleconfiguration[271

-82-

Inthischapterwetaketheconfigurationthatthe

electronbeamscansonthesurfaceperpendiculartothebarrier

planeWiththisconfigurationtニhetime-dependentdiffusion

equationcanbesimplyreducedtothesteady-statediffusion

equationandthecomplicationintheanalysisthatRoosindicated

[26]canbeexcludedThisphaseshiftmethodcanbeappliedto

materialswithsmallLWesolvethethree-dimensionaltime-

dependentdiffusionequationtakingthesurfacerecombination

effectintoaccountandclarifytherelationofTandthephase

shifttheoreticallyWeshowthatthree-dimensionalsolutions

canbeexpressedbyone-dimensionalsolutionswithempirical

correctionfactorsandthatてandDcanbedeterminedwitニhout

anyrestrictionformodulationfrequencyExperimentalresults

inSiarealsoshown

6-2 Relationbetweenlifetimeandphaseshift

WetakeaSchottkydiodeasshowninFig6-1for

simpletheoreticalcalculationWeassumeapointgeneration

sourcewhichhastime-variabLepartgelωt(ω゜2TTfωangular

frequencyfmodulationfrequency)at(x゛0d)Whenthetldegeoline

variablepartofthenumberofminoritycarriers1Sputas

恥eiωt(isacomplexvariable)psatisfiestheconventional

steady-statediffusionequationbyintroducingthecompleχ

effectivediffusionlengthL゛eff(ΞL゛1171瓦JTL=ぷF)゜If

thetime-variablepartofEBICIsputasj`゛e(J゛1Scomplex-

EBIC)icanbeexpressedasfollowsbythemirrorImagemethod

asdiscussedinsect3-2

-83-

Fig6-1

ylご

uarrj

Schottkybarrier

uarr

Ohmiccontact

Schematicviewofeχperimentalconditionsand

definitionoftheco-ordinatesystem

-84-

Electronbeam

SOlyScanningtrack_xj

ズニに匹二oline-一一゛

lsquo9surface

lL-__--ang__helliphellip_

|`1

丑昌之

9gπLaf ―K

gdof

(ノダr7olineT

)酉ff

L大effl゛ぶ弓+T『

+0O

(-1(じ(lg)

)X[

jiご]ご

)ことりsube

dgDIL火eff

xlてこi7

dT

J(6-1)

whereeisthechargeofanelectronsisthesurfacerecombination

velocityandTisthevariableforintegratニionThefunctionK^

1sthesecond-modifiedfirst-orderBesselfunctionwithcomplex

variablesTheabsolutevalueofEBICnandthephaseshiftφ

fromthesourcearegivenasfollows

TI=

|」と

eg

φ=tan-1

Im一J

Rej゛

(6-2)

(6-3)

whereReandImstandforrealandimaginarypartsrespectively

Thevalueofnisnormalizedtobeunitywhenallthevariable

-partgcontributetothevariablepartofEB工CSincej火isa

functionofてthevalueofφbecomesafunctionofてThevalues

ofnandφcanbecalculatednumericallyWeassumeapointsource

forsimplecalculationbutthemethodmentionedabovecanbeeasily

appliedtothefinitegenerationdistributionbythedividing

methoddescribedinChapters工江andy

-85-

Fig6-2

Fig6-3

U2

Cχ310-rsquo

山5

ト2

10lsquo3

velocitysis

35225N

(Eu

一))

j^

9st^d

10

Jo}CIで噌」

ひpF

ぐりぐ

ごヽこ

W゛`みノー-

うて`゜ldegw-rsquo゜rsquordquorsquoPrime゛ご

゜二

゛゜〆ノ〆゛`゜

゜゛〆ノ

(MJD≪p)j

UMS

asEMd

ofEBICvsscanning

thealmostlinear

0 50 100 150

ScanningdistanceX(pm)

Normalizedintensityandphaseshift

distancexcurvesTheconcavecurvesand

linesarefortheIntensity(leftaxis)andthephaseshift

(rightaxis)respectivelyThesolidbrokenanddottedlines

areforf=10100and500kHz(ieωT=031314and157)

respectivelyLifetimeTistakenas5μSThediffusion

constantDis30_cm2Secandthesurfacerecombination

105CmSeC

S=105CmS

D=30ori^s

Lifetimeで(sec)

DependenceofgradientofphaseshiftdφdxonTD=30cmsecandrsquos=105cmsec

-86-

rsquoD=30crrfis

ωで=5f

5ヽ2MHz

ヽ1MHz

2`500kHz

1`

100kHz

``50kHz

`ヽ`10khtt

pwww

kHz

`ωで=01

1(jrsquo

825

1(i

725

1(jrsquo

6251(irsquo

525

10lsquo4

Mm2s)lsquo1-123lsquoj「rsquoQ心Hz」t

=10cms-10a3i

i=30kV-一一一一1003K

helliphelliphelliphelliphellip500157

Thevaluesofnandφwerecalculatedasafunction

ofscanningdistanceχforp-SiasanexampleTheresultsare

showninFig6-2whenてisputasatypicalvalueof5μs

Inthefiguretheconcavecurvesandthealmostlinearlines

areforn-χandφ-xrelationsrespectivelyThesolid

brokenanddottedlinesareforf=10100and500kHz(ie

ωT=031314and157)respectivelyThediffusionconstant

Disputas30cm^secThesurfacerecombinationvelocitysIs

takenas105cmsecsincetheordinarysurfacerecombination

velocitニyofSiis103へj105cmsecTheacceleratingvoltage

Isputas30kVThepointsourceisassumedtobelocatedat

themaximumenergydissipationdepthofabout3μmunderthe

surfacebasedonKanayarsquosmodel[28]forelectron-holepair

generationdistributニIon

Inthecaseofωてく01tニhedependenceofnonX

agreeswiththat-measuredbyaconventionallinescanmethod

usingDCelectronbeamThevalueofLcanbedeterminedfrom

theslopeofthen-χcurvestakingthesurfacerecombination-

effectintoaccountasdiscussedinChaptermThevalueof

L大effalmoStequaltoLandSOφbecomesnearlyzero

Inthecaseofωて≧01φincreasesalmostlinearly-

withxovertherangeofx≧Landthegradientdφdxbecomes-

largewithIncreasingfasshownInFig6-2Thegradient

dφdxisfoundtoIncreaseasてbecomeslargeforthesamefvalue

andnottochangeevenifSvariesfrom10^t0105cmsecfrom

thecalculationforvariousparametersFigure6-3showsthe

dependenceofdφdχonTwhenfisvariedfrom5kHzto2MHz

ThevaluesofDandsare30cm^secand105cmsecrespectively

ForeachvalueoffdφdxincreasesmonotonouslywithTwithin

therangeof01≦ωて≦5andapproachestoacertainvalue--

asymptoticallyovertherangeofωて≧5-

-87-

「ujopp」)

調uiusas^qdj〇}c心石司」

Fig6-4

Lifetimeて (sec)

10

Expressionofthedependenceofdφdxonてusingtheapproximatedsolutionsoftheone-

dimensionaldiffusioneuationinthecaseofD=30cm^secandf=10sectHzSolidlineisa

three-dimensionalsolutionLines(A)and(B)

aretheapproximatedone-dimensionalsolutionsand(Arsquo)and(Brsquo)aretheasymntotesforthethree-dimensionalsolutionThecorrectionfactorCforthethree-dimensionalsolutionis087

-88-

2(8)登ニ4F

helliphellipj(Å

(A)

D(EI)-(jじ硲ゴどこ二こhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip

2helliphelliphelliphelliphelliphelliphelliphellip(畿f3゛(c緊八(醤y3

d≫_Kii「」(A)石rsquo7『

5Ddeg30cm2sfdeg105Hz

c=087

Ursquo725J625_-52542

Ifwetakethesolutionsoftheone-dimensionaldiffusion

equationdφdxisgivenasfollows[241

O「

dφ

dx

助こ

Lω

2D

一 一 S

irfr

一万

(ωて≪1)

(ωT≫1)

(6-4)

(6-5)

Followingthethree-dimensionalsolution(eqs(6-l)(6-2)and

(6-3))asshowninFig6-3ydφdxincreasesproportionallyt07

intherangeofωてく05andreachestoacertainvalueoverthe

rangeofωて>5whichcanbeeχplainedqualitativelybyeqS

(6-4)and(6-5)respectivelyThedφdxvsTcurvesinFig6-3

canberepresentedbyonefunctionwiththecombinationofthe

approximatedsolutionsoftheone-dimensionaldiffusionequation

(eqs(6-4)and(6-5))Weshowanexampleinthecaseoff=105Hz

andD=30cm^secinFig6-4Thesolidlineisthethree-

dimensionalsolutionfromFig6-3andthedottedlines(A)and

(B)expresseqs(6-4)and(6-5)respectivelyThebrokenlines

(Arsquo)and(B゛)showtheasymptoticsolutionsofthethree-

dimensionalsolutionintherangesofωて<05andωて>5The

absolutevaluesof(A)and(Brsquo)becomeabout87Zofthoseof

(A)and(B)basedontheresultsofcalculationAsshownin

Fig6-4thethree-dimensionalsolutionisgivenbyacombination

ofthelines(Arsquo)and(Brsquo)andIsexpressedasfollows

-89-

「―」)畠一

uiMSaseudpazneaijoz

Fig6-5

rsquo0

ω^t「

NormalizedphaseshiftニLdφdxvSωてcurves

Solidlineisathree-dimensionalsolution

expressedbytheapproximatedone-dimensional

solutionswithempiricalcorrectionfactors

Brokenlineistheone-dimensionalsolution

-90-

2One-dimensionalノrsquosolution゛`4xrsquo

10バ

5acuteThree-dimensional

ぶacutesolution

2acute

(yl

言二分ヽ同r〔2μ(ldquoμ

゛1)rsquo1

5primeacute

cべ1251251cap25

dφ

dx

)=(c

TTfr TTf)ldquo゛十(c

yでワ

)rsquo゛

-91-

十1}3

(6-6)

(6-フ)

函rsquo

wherenisapositiveintegerWecalculatedeq(6-6)Inthe

casesofn=1へj5anddeterminednas31norderthatthe

solidcurveinFig6-4canbewellrepresentedbyeq(6-6)

Thevalueofc1Sthecorrectionfactorforthethree-dimensional

solutionandcisabout087asmentニionedabove

Fromeq(6-6)wecanderivethefollowingrelation

usingtheconventionaldiffusionlengthL

_

=pound石{2Σ(則2万

ThetermLdφdxisconsideredtobethenormalizedphaseshift

whichistheamountofthephaseshiftwhentheelectronbeam

scansoveronediffusionlengthItshouldbenotedthatLdφdx

isafunctニionofonlyωでFigure6-5showsthedependenceof

LdφdxonωてbythesolidlineIfthevaluesofLanddφdxare-

knownてcanbedeterminedfromthecurveforanymodulation

frequencyandDisalsoobtainedbytherelationofL=iF

Themodulationfrequencyfcanbechosenfreelyandthe

restrictionsofωΥ<050Γωて>5fortheapproximatIonneednot

tobetakenintoaccount

ThephaseshiftderivedbyMcKelvey[29]usingtheone-

dimensionaldiffusionequationisshownbythedashedlinein

Fig6-5Theestimatedvalueofωてbytheone-dimensional

solutionisabout76へ87Zofthatbythethree-dimensional

solutionforeveryvalueofLdφdxInthecaseoftheone-

dimensionalsolutionLisdetermineddirectlyfromthegradient

ofthelinearlydecreasingregionofEBICcurveandisabout

60へj80Zoftherealvaluefromtheresultsofthedetailanalysis

takingthesurfacerecombinationeffectintoaccount[14]

ThereforethevalueofωΥderivedbytheone-dimensionalsolution

isonly30へJ丁0Zoftherealvaluebecauseωてdecreases

proportionallytOLandL2intheregionsofLdφdxく03and

Ldφdx>2respectivelyOnemustusethethree-dimensional

solutioninordertodeterminetheaccuratevalueofて

6-3 ExperimentalresultsinSi

AconventionalSEMwasusedfortheprimaryelectron

beamwhichwasmodulatedat1rsquoj50kHzwiththedutyof05by

achoppingcoilinsertedintothebeampathThebeamcurrentwas

as10was10oline10AThemaximumminoritycarrierdensityinthis

experimentwasconsideredtobeabout3times1014Cmoline3andthe10w

injectionconditionwassatisfiedTheinducedcurrentwas

measuredbythevoltagedropacrosstheloadresistancewhich

wasconnectedtotheSchottkybarrierwithanohmiccontactThe

signalhadarectangularwaveformowingtothechoppedprimary

electronbeamandsothefundamentalfrequencycomponentinthe

Fourierseriesofthesignalwasdetectedbyanauto-phaselock-

inamplifierTheEBICnandthephaseshiftφfromthesource

wererecordedsimultaneously

ThediffusionlengthLisdeterminedinthecaseof

ωて<01takingthesurfacerecombinationeffectintoaccount

Thedependenceofnonxagreeswiththatニmeasuredbyaconventional

linescanmethodusingDCelectronbeamasdiscussedinsect6-2

-92-

Whenvaislowgivingtheshallowgenerationdepthsurface

recombinationhasalargeeffectonEBICWhenvaishigh

givingthedeepgenerationdepththesurfacerecombinationeffect

1SreducedTheaccuratevalueofLcouldbedeterminedbyfitting

experimentaldatatotheoreticalcurvesforboth10wandhighva゛S

(10and50kVrespectivelyInthiswork)asshownInsect3-3

Thevalueofdφdxisobtainedatanappropriate

modulationfrequencywhichsatisfiesωて>01AthighVthe

surfacerecombinationeffectIsreducedandsowechosetニhe

highestva(30kVinthiswork)asfarastheelectronbeamcould

bechoppedOncethevaluesofLanddφdxareknownthevalues

ofてandDcanbedeterminedfromthecurveinFig6-5

Sampleswerep-andn-typeSiwithtニheresistivitypof

10and01f2cmrespectivelyOhmiccontactsweremadeby

evaporatinggallium-dopedgoldandantimony-dopedgoldontothe

p-andn-typesamplesrespectivelySchottkycontactsweremade

byevaporatingaluminiumandgoldontothep-andn-typesamples

respectivelyinavacuumas10was10oline7TorrThesampleswere

insertedintoavacuumchamberforEBICmeasurementimmediately

aftertheywerecleaved

ThediffusionlengthLinp-typeSiwasdeterminedas

130μmfromthen-xcurvesinthecaseofωてく01The

experimentalresultsofthephaseshiftmethodareshownIn

Fig6-6bysolidlinesforf=5102030and50kHzrespectively

ThephaseshiftIncreaseswithxalmostlinearlyasdescribedin

sect6-2ThevaluesofてweredeterminedusingFig6-5as9595

8886and83ysfromthegradientsofthelinesinFig6-6

for5102030and50kHzrespectivelyTheobtainedvaluesof

てshowlittledifferencewitheachotherinanymeasurement

-93-

11

es^Md

Fig6-6

P-Si(r=10ncm)f=

20

1 0一

----n-Si(r=Q1ftcm)

Va=30kV

圭T

rdquo

------ニr二ご二二耳一一3

50100

Scanningdistance

150

Experimental

methodinp-(p=10

200

(μm)

resultsofthephaseshift

Ωcm)andn-type(p=01ncm)Si

-94-

rdquoolinersquordquooline`rsquolsquorsquoolinerdquordquoolinersquo50kHz

Vadeg30kVZ

10deg

30

FJ゛

一一20

〆がノrdquo〆〆〆

メノrdquo

〆〆〆〆〆ノ10

---rdquordquo|-sニニニldquo-notこ9

conditionfromωて=03(atf=5kHz)to30(atf=50kHz)

Itprovedthatthemodulationfrequencycouldbechosenfreelyas

mentionedinsect6-2Ifwetaketheaveragedvalueofて(ie

で89ys)thediffusionconstantDofelectronswasdeterminedas

19cra^secwhichalmostagreedwiththereportedvalue[301The

slightdeviationfromthestraightlineforf=50kHzmaycomefrom

unstablenessofthechoppedbeambecausethechoppingcoilused

inourexperimentwasnotdesignedforhighfrequencymodulation

above50kHz

Thediffusionlengthinn-SiwasobtainedasL=80ymand

thephaseshiftsareshowninFig6-6bybrokenlinesforf=3

10920and50kHzrespectivelyThedeterminedvaluesofてfrom

thegradientsofthelineswere889292and105usfor

fdeg3s1020and50kHzrespectivelyThevaluesofTalmost

equalwitheachotherasinthecaseofp-SiIfwetakethe

averagedvalueofT(ieで=94ps)tニhediffusionconstantD

ofholesbecomes7cm^secwhichalsoagreeswithtニhereported

value[301

Thegenerationdistributionisconsideredtobeasemi-

spheretheradiusofwhichisabout6ymatニvadeg30kVusingthe

Kanayarsquosmodel[28]Thedimensionsofgenerationdistribution

aresufficientlysmallincomparisonwiththediffusionlengthof

thesamplesThereforethepointsourceassumptioninthe

analysisisreasonable

-95-

6-4 Summary

Whentheintensitymodulatedelectronbeamisusedthe

phaseofinducedcurrent(EBIC)isshiftedfromthatofexcitation

sourcebecauseoftherecombinationinmaterialsWesolvedthe

three-dimensionaltime-dependentdiffusionequationtakingthe

surfacerecombinationeffectintoaccountandclarifiedthe

relationofてandthephaseshiftφtheoretically

Inthecaseofωて≧01φincreasesalmostlinearlywith-

Xovertherangeofx≧LThegradientdφdxbecomesafunction-

ofTandisnotaffectedbysurfacerecombinationTherelation

ofdφdxonてwasfoundtobeexpressedusingtheapproximated

solutionsoftheone-dimensionaldiffusionequatニionwithtニhe

empiricalcorrectionfactorsThenormalizedphaseshiftLdφdx

becomesafunctionofonlyωてIfthevaluesofLanddφdxare

knownてandDaredeterminedwiththeaidofLdφdxvsU3てcurve

withoutanyrestrictionformodulationfrequencyTheestimated

valueofてbytheone-dimensionalsolutionswithoutニthecorrection

factorsisonly30へノ70Zoftherealvaluederivedbythethree-

dimensionalsolution

Experimentalresultsinp-andn-typeSiSchottkydiodes

showedgoodagreementwiththetheoryandtheminoritycarrier

diffusionconstantsofelectronsandholesweredeterminedas

19and7cm^secrespectively

-96-

References

[11

[2]

[31

[4]

5]

6]

[10]

[11]

[12]

[13]

[14]

[15]

PDDapkusWHHackettJr0GLorimorandRZ

BachrachJApplPhys^54920(1974)

MBoulouandDBoisJApplPhysj旦4713(1977)

MEttenbergHKresselandSLGilbertJAppLPhys

44827(1973)

SWangrdquoSolid-stateElectronicsrdquo(McGraw一HillInc

1966)p300

WZimmermannphysstatsol(a)12671(1972)

DRHunterDHPaχmanMBurgessandGRBooker

rdquoScanningElectronMicroscopySystemsandApplications

1973rdquo(工nstPhysLondon)pp208-213

HKKuikenSolid-stateElectron19447(1976)-

AJakubowiczSolid-stateElectron22635(1980)

HTWeaverandRDNasbySolid-stateElectron

22687(1979)-

DLLileandNMDavisSolid-stateElectron

18699(1975)-

WvanRoosbroeckJApplPhys2plusmn380(1955)

WHHackettJr=JApplPhyspound1649(1972)

FBerzandHKKuikenSolid-stateElectron

19437(1976)

CvanOpdorpPhilipsResRept22192(1977)

DBWittryandDFKyserJApplPhys261387

(1965)

-97-

[16] CvanOpdorpRCPetersandMKlerkApplPhysLett

2h_125(1974)

[17]CJHwangJApplPhys4^4408(1971)

[18]

[19]

HReichlandHBerntSolid-stateElectron

18453(1975)

GSchwabHBerntandHReichlSolid-stateElectron

2091(1977)

[201JMiillerHBerntandHReichlSolid-stateElectron

21999(1978)

[211

[22]

JMiillerHReichlandHBerntSolid-stateElectron

22257(1979)

CMunakataandTEEverhartJpnJApplPhys

11913(1972)-

[23]SOthmerrdquoScanningElectronMicroscopy1978Vol1uml

(SEMIncOrsquoHare111)p727

[24] JDKaiiraiandHBerntSolid-stateElectron

21957(1978)-

【25】JDKammrdquoSemiconductorSilicon1977uml(The

ElectrochemicalSociety工nc)p491

[26] 0vonRoosSolid-stateElectron23177(1980)

[27]0vonRoosJApplPhys1^3738(1979)

[28]KKanayaandSOkayamaJPhysDApplPhys

543(1972)

[29]JpMckelveyrdquoSolidStateandSemiconductorPhysicsrdquo

(HarperandRowNewYork1966)pp439-440

[30]HFWolfrdquoSiliconSemiconductorDatardquo(Pergamon

PresslnC1969)

-98-

ⅥI

7-1

HEATTREATMENTEFFECTONDIFFUSIONLENGTHINS1

Introduction

Therehavebeenmanystudies[1]onthepropertiesofthe

processinducedfaults(PIFrsquos)Thedegradationoftheelectrical

performanceofthedeviceshasmuchconnectionwiththesegregated

impuritiesatPIFrsquosorthedecoratedfaultsofeachPIFRecently

thefaultproducedespeciallybytheoxidationathightemperatures

(IesocalledoxidationInducedstackingfault(OSF))has

receivedconsiderableattention[2-5]becausetheoxidationisa

fundamentalprocessinmakingLS工rsquosorcharge-coupleddevices(

CCDrsquos)Ravieta1[67]showedthattheelectricallyactive

OSF゛sincreasedtheleakagecurrentinprsquonjunctionsKimerllng[8]

determinedtheenergylevelofthefaultsfromtheelectron

beaminducedcurrent(EBIC)measurementsatvarioustemperatures

Generallythefaultsbecomerecombinationcentersanddecrease

thelifetimeandthediffusionlengthofminoritycarriers

Shimizu[9]showedthatthelifetimecouldbecontrolledpreferably

bytheintrinsicgetteringusingOSFrsquosRozgonyi[10]and

Tanikawa[11]reportedthattherelaxationtimeofMOScapacitors

decreasedasthedensityofOSFincreasedButtherehavebeen

alittlestudyonthequantitativeinformationofthedecreaseof

thediffusionlengthaftertheoxidationprocessathightemperatures

Inthischapterwemeasuredthechangesofthediffusion

lengthbyEBICmethodaftertheheattreatmentsathightemperature

andshowedthattheheattreatmentforafewminutescouldaffectthe

diffusionlengthatthesurfaceregionTheobservationofsurface

faultsbychemicaletchingwerealsoshown

-99-

(―)

<j)6udI

ColコこI()

Fig7-1

Heattreatmenttimet(min)

Diffusionlengthaftertheheattreatments

forvarioustimelengthsrangingfromlt0120minutesat1000degCOpenandsolidcirclesare

forthecasesindry02andArrespectivelyOriginaldiffusionlengthbeforeannealingis80pm

-100-

5ohellipumlindryO2

uml゜umlinArat1000degC

ol

12510251002

- W ゝ

rsquo _ l - ~ ヽ jS j - -

磨 卜

Fig7-2

(a)

(c)

rarr100Mm

ぶミ

卜`

r-^

rsquo

1Is

≪バ

rdquorsquo‐゛t

rsquo

grバ4≪

rsquo1

Surfacefaultsrevealedby

usingSirtletchantSamples(a)

wereannealedindryoat1000

and120minutesrespectively

-101-

い゛フバrdquo

゛para

`i

(b)

(d)

permilご}

->嗜

-゛

rsquo

III

`ヽご

いい

一J

t七

~貿で

rsquo

゛`1

鴫ヽ

rsquoq

-≪

ゝく

chemicaletching

(b)(c)and(d)

Cfor0830

一 一

- 一 一 -一 一

7-2

Experimentalresultsanddiscussions

Samplesaren-tニypeSigrownbyczmethodTheoriginal

resistivitybeforeannealingisaboutニ01ΩcmTheheattニreatment

wasdoneat1000degCintheflowofdry02andArrespectivelydeg

ThenthesampleswererinsedinHFforlmintoremovetheoxidized

layerandgoldwasevaporatedinordertomakeaSchottkybarrier

forEBICmeasurementsTheproceduresofthedeterminatニionofthe

diffusionlengthhavealreadybeendiscussedinChaptersmandでIV

Figure7-1showsthediffusionlengthaftertheheat

treatmentThetimetoftheheattreatmentwaschangedfromlto

120minutesTheopenandsolidcirclesareforthecaseIndryO2

andArrespectivelyTheoriginalvalueofdiffusionlengthis

80μmThediffusionlengthdecreasedtoabout7μmrapidlyas

tincreasedt05minandbecamealmostconstantovertherange

oft>5mlnThediffusionlengthdecreasedslightlymorerapidly

in02tニhaninArThelifetimechangedfrom5μsto003usif

thediffusionconstantofminoritycarrierswastakenasatypical

valueof125cmsecThesurfacefaultsofthesamplesannealed

indry02areSho゛linFigsdeg7-2(a)(b)(c)and(d)forlsquot゛

0830and120minrespectivelyThesampleswereetニchedby

SirtletchantforthesametimeThenumberoffaultsdidnotニ

increaseuntilt=8minbutbecameverylargeattdeg120min

ThesameresultwasobtainedforthesamplesannealedinAr

Itshouldbenotedthatthenumberoffaultsdidnotニchangedinthe

rangeofO≦t≦8minbutthediffusionlengthdecreasedrapidly--

inthesamerangeThelengthsbetweenthefaultsareverylarge

incomparisonwiththediffusionlengthinthesamplesannealed

for1くtく8minandsothediffusionlengthisconsidered

nottoberestrictedbytheaverageintervalbetweenthefaults

whenthefaultsareconsideredtobethecarriersink

-102-

TheuniformEBICwasobtainedwhentheelectニronbeamwasscanned

onthesurfacethroughtheSchottkybarrtersandthedarkpoints

correspondingtothefaultswerenotobserved

Therapiddecreaseofthediffusionlengthwasconsidered

tobecausedbytheformatonofnucleioffaultsattheearly

stageoftheheattreatmentTheverysmallnucleicanbecomethe

recombinationcenterseveniftheycannotberevealedbychemical

etchingIftheheattreatmenttimeissufficientlylongthe

nucleibecomelargeandcanberevealedbyetchingAsshownin

Fig7-2(d)thelengthbetweenthefaultsafterlongtimeheat

treatmentisthesameorderofthediffusionlengthTheformation

ofnucleiwasnotaffectedverymuchbytheoxidationbecausethe

decreaseofthediffusionlengthwasalsoobservedintheheat

treatmentinArAsisknowngenerallytheczgrownSIcontains

oversaturatedoxygenandtheformationofnucleiisrelatedtニO

theoxygenprecipitation[12]Thediffusionlengthdecreasedless

rapidlyinArthaninO2degOnereasonofthisphenomenonisconsidered

tobetheformationofSiOAnotherreasonistheoutdiffusion

ofoxygenbecauseoxygencanoutdiffusemorerapidlyinArthan

inO2degFurtherinvestigationmustbeneededfortheclarification

ofthenucleiformation

Inconclusionthediffusionlengthatthesurfaceregion

inSidecreasedtoabout10Zoftheoriginalvalueafterthevery

shortheattreatmentat1000degCforafewminutesNevertheless

thesurfacefaultsrevealedbychemicaletchingdidnotchange

Thenucleioffaultswereconsideredtobeformedattheearly

stageofheattreatmentandtheybecameminoritycarrier

recombinationcentersThedecreaseofthediffusionlengthwasnot

soaffectedbytheambientgases(ieoxygenorinertone)Much

attentionmustbepayedintheheattreatmentprocessathigh

temperatureevenifthetimeIsveryshort

-103-

i J I

References

[1]

21

31

71

81

[91

[10]

[n]

[12]

HFoilNGoreleandB0KolbesetirdquoSemiconductor

Silicon1977rdquo(JElectrochemicalSocietyInc

Prircetion1977)pp565-574

DJDThomasphysstatso1旦2261(1963)

CMMelliar-SmithrdquoCrystalcefectsinsiliconintegratニed

circuits-TheircauseandeffectrdquoinrdquoTreatieson

MaterialScienceandTechnologyrdquovol11(AcademicPress

NewYork1977)

KVRaviandCJVarkerJApplPhys45263(1974)

SMHuJApplPhys513666(1980)

KVRaviCJVarkerandCEVolk

JElectrochemSoc120533(1973)-

CJVarkerandKVRaviJApplPhys亘272(1974)

LCKlmerlingHJLeamyandJRPatel

ApplPhysLett30217(1977)

HShimizuAYoshinakaandYSuglta

JpnJApplPhys17767(1978)

GARozgonyiandRAKushner

JElectrochemSoc123570(1976)-

KTanikawaYItoandHSei

ApplPhysLett28285(1976)

JRPatelrdquoSemiconductorSilicon1977rdquo(The

ElectrochemicalSocietyIncPrinceton1977)

pp521-545

-104-

ⅧI CONCLUSIONS

InthepresentstudyEBICwasanalyzedquantitativelyby

solvingthesteady-stateortime-dependentthree-dimensional

diffusionequationsTheinfluenceofthefinitegenerationvolume

onEBICwasdiscussedandanImprovedmethodtocharacterize

thephysicalpropertiesinthesmallselectedareasofsemiconduc-

torswassuggestedTheobtニainedresultswereasfollows

InChapterHtheshortdiffusionlengthoftheorderof

ymcouldbedeterminedbythenormalincidencemethodofEBIC

Variousmodelsforgenerationdistributionusedintheanalysis

yieldedtheambiguityforthedeterminationofthediffusionlength

andtheelectron-holepaircreationenergybyanelectronbeam

Detailedinformationonthegenerationdistributionmustbe

necessarytoanalyzeEBICaccurately

InChaptニermthegenerationvolumeofminoritycarriers

hadrsquoaconsiderableeffectonEBICinthelinescanmethod

especiallywhenthedimensionsofthegenerationvolumewasequal

toorlargerthanthediffusionlengthWhentheaccelerating

voltagewaslowandsothegenerationdepthwasshallow

surfacerecombinationhadalargeeffectonEBICWhereaswhen

theacceleratingvoltagewashighandsothegenerationdepth

wasaslargeasthediffusionlengthsurfacerecombinationhad

aslighteffectonEBICTheaccuratevaluesofphysicalparameters

suchasthediffusionlengthshouldbedeterminedbyfittingthe

experimentaldatatothetニheoreticalcurvesforalltheaccelerating

voltagesTheexistenceofamaximuminEBICnearthebarriercould

beexplainedbythersquoedgeeffectrsquoattributedtothefinite

generationvolume

-105-

InChapter】5inthelinescanmethodthedependence

ofEBIConthescanningdistancerepresentedmainlythelateral

extentofthegenerationdistributionwhentheacceleratingvoltage

washighandwhenthedimensionsofthegeneratニionregionwere

largerthanthediffusionlengthThethree-dimensionalgeneration

distributionbasedupontheexperimentalresultsforthenormal

incidencecouldexplaintheexperimentalresultsofthelinescan

methodInGaAsthecenterofthegeneratニionregionwaslocated

atthepointof0130fthemaximumelectronrangeandthe

radialdistributionfromthecentニerwasshowntobeGaussianwith

anexponentニof54Q82Thevaluesof38へj44eVfortheelectron-

holepaircreationenergybyanelectronbeamwasobtainedtaking

thesurfacerecombinationeffectintニoaccount

InChapterVinthelinescanmethodtheminoritycarrier

distributionwasaffectedverymuchbyanohmiccontactwhenthe

lengthwbetweenthepotentialbarrierandtheohmiccontactwas

lessthanoneortwodiffusionlengthsTheslopeofthecurveof

EBICvsscanningdistancedidnotchangeevenwhentニhediffusion

lengthvariedandthediffusionlengthcouldnotbedetermined

definitelyfromtheslopeofthecurveTheabsolutevalueof

EBICwasdependentonthesurfacerecombinatニionvelocityand

thelengthW

InChapterⅥ[thephaseshiftbetweenthemodulated

electronbeamandEBICwasclarifiedbysolvingthethree-

dimensionaltime-dependentdiffusionequationTherelation

betweenthephaseshiftandthelifetimewasfoundtobeexpressed

usingtheapproximatedsolutionsoftheone-dimensionaldiffusion

equationwithempiricalcorrectionfactorsThelifetimeandthe

diffusionconstantofminoritycarrierscouldbedetermined

definitelywithoutanyrestrictionformodulationfrequency

-106-

InChapterVIIthediffusionlengthinthesurfaceregion

ofSiwasfoundtobedecreasedverymuchafterheattreatment

at1000degCforonlyafewminutesneverthelesssurfacefaults

revealedbychemicaletchingwerenotincreasedThenuclei

ofthefaultsmightbeformedattheearlystageofheattreatment

ThisinvestigationprovedthatEBICcouldbeanalyzed

quantitativelyinthesmallselectedareaconsideringthethree-

dimensionalgenerationdistributionbyanelectronbeamBut

thereexistsomepointstobestudiedfurtherasfollows

FirstbyEBICmethodthetotニalrecombinationlifetimeincluding

bothradiativeandnon-radiativeprocessescanbemeasuredBut

onecannotobservetheradiativerecombinatニionlifetimealone

whichIstheimportantparametニertocharacterizethellght-emittニing

diodesorlaserdiodes[1]Deeperunderstandingcanbeacquired

byinvestigatingtheluminescenceemitニtedbyrecombinationof

generatedelectron-holepairs(iecathodoluminescence)[23]

SecondlyEBICtechniquecannotrevealtheenergylevelsand

densitiesofimpuritiesandtrapsaccuratelywhichaffectthe

electricalpropertiesofmaterialsverymuchTherehavebeena

fewreports[4]todeterminetheenergylevelsoffaultsinSi

fromEBICmeasurementsatvarioustemperaturesButthe

experimentalaccuracyofEBICtニechnlqueisinferiortothat

ofthephotoluminescence[5]orthecapacitance[67]methods

Thirdly万thedoseofhighenergyelectronbeldquo万171万causesdamagesin

samplesSeveralinvestigationshaveshownthedecreaseoftニhe

tニhresholdvoltageinMOSdevices[8]andtheincreaseofthe

interfacestatedensitybetweentheoxideandthesemiconductors[9]

-107-

Improvementsofmeasurementtechniques(ieuseofthe10W

energyprimaryelectronbeam万orlthedecreaseoftニhetotal

amountofdose)wirsquollbenecessary

Electricalpropertiesofsemiconductorscanbecharacterized

collectivelybyEBICjointlywiththeothertechniqueswhich

complementtheweakpointsinEBICmethod

REFERENCES

[1]

[21

[5]

[6]

[7]

[8]

[9]

PDDapkusWHHackettJr0GLorimorandRZ

BachrachJApplPhys45

4920(1974)

DBHoltandBDChasephysstatS01(a)旦旦

135(1973)

MBoulouandDBoisJApplPhys 484713(1977)

LCKimerlingHJLeamyandJRPatel

ApplPhysLett30217(1977)

HBarryBebbandEWWilliamsrdquoSemiconductorsand

Semimetalsrdquo(edRKWillardsonandACBeer

AcademicPress1972)vol8pp182-392

SMSzerdquoPhysicsofSemiconductorDevicesrdquo(JohnWiley

SonsInc1969)

DVLangJApplPhys453023(1974)

WJKeeryK0LeedyandKFGallowayrdquoScanning

ElectronMicroscopy1976rdquo[IITR]Chicago)pp507-514

RHezelSolid-stateElectron11^

735(1979)

-108-

4i

rsquoII

LISTOFPUBLICAT工ONS

[1]

[21

[3]

[4]

[5]

[6]

Papers

Theinfluenceofthegenerationvolumeofminoritycarriers

onEBICrdquo

TFuyukiHMatsunamiandTTanaka

JPhysDApplPhys131093-1100(1980)

rdquoAnalysisofEB工CconsideringthegeneratニIondistribution

ofminoritycarriersrdquo

TFuyukiHMatsunamiandTTanaka

JPhysDApplPhys131503-1510(1980)

rdquoDeterminationoflifetimeanddiffusionconstantof

minoritycarriersbyaphaseshifttechniqueusing

electronbeaminducedcurrentrdquo

TFuyukiandHMatsunami

JApplPhys旦(1981)

rdquoAnalysisofelectronbeaminducedcurrentconsidering

sampledimensions一一-Measurementofdiffusionlength

andsurfacerecombinationvelocity-rdquo

TFuyukiandHMatsunami

JpnJApplPhys20(1981)No4

rdquoInfluenceofminoritycarriergenerationdistributionon

electronbeaminducedcurrentinthenormalincidencemethodrdquo

TFuyukiandHMatsunami

(tobepublished)

rdquoHeattreatmenteffectondiffusionlengthinSirdquo

TFuyukiandHMatsunami

(tobepublished)

-109-

[1]

[21

[3]

PublicationsintheInstituteofElectronicsandCommunication

EngineersofJapan

(inJapanese)

rdquoMeasurementofminoritycarrierdiffusionlengthby

EBICmethodrdquo

TFuyukiHMatsunamiandTTanaka

ReptTechSSD78-102(Feb1979)

rdquoCharacterizationofdiffusionlengthandlifetimebyEBICrdquo

TFuyukiandHMatsunami

ReptTechSSD79-103(Feb1980)

rdquoMeasurementoflifetimeanddiffusionconstantofminority

carriersbyphaseshifttechniqueinEBICrdquo

TFuyukiandHMatsunami

TransSectionJ63-C832-837(1980)

-110-

  • page1
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  • page69
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  • page71
  • page72
  • page73
  • page74
  • page75
  • page76
  • page77
  • page78
  • page79
  • page80
  • page81
  • page82
  • page83
  • page84
  • page85
  • page86
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  • page88
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  • page91
  • page92
  • page93
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  • page95
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  • page99
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  • page118
  • page119
  • page120
Page 4: CHARACTERIZATION OF SEMICONDUCTORS BY Title ELECTRON …

1 一 心

ABSTRACT

-Theelectronbeaminducedcurrent(EBIC)wasanalyzed

quantitativelyconsideringthethree-dimensionalgeneration

distributionbyanelectronbeamThesolutionsofthesteady-

stateortime-dependentdiffusionequationsassumingapoint

sourcecanbeappliedtothecaseofthefinitegeneration

distributionbythedividingmethodTheEBICwasfoundtobe

affectedverymuchbythegenerationdistニributiontheextentof

whichwascomparablewiththeminoritycarrierdiffusionlength

InthelinescanmethodthedependenceofEBIConthescanning

distancerepresentsmainlythelateralextentofthegeneration

distributionThethree-dimensionalgenerationdistributionvas

clarifiedcombiningthenormalIncidenceandthelinescanmethods

ofEBICTheImprovedmethodtomeasurethediffusionlength

andthesurfacerecombinationvelocitywassuggested

Theminoritycarrierdistributionisinfluencedverymuch

bythesampledimensionswhentheyareequaltoorsmallerthan

thediffusionlengthTheEBICwasanalyzedbyasimplemethod

usinganimagesource-and-sinkdistributionTheEBICwasfound

tobedependentonthesurfacerecombinationvelocityand

thesampledimensionsratherthanthediffusionlength

Thelifetimeandthediffusionconstantofminority

carrierscouldbedetermineddefinitelywithoutanyrestriction

ofmodulationfrequencybythephaseshifttechniqueusingEBIC

Theimprovedmethodtomeasurethediffusionlength

wasappliedtotheheattreatmenteffectinSiThediffusion

lengthwasfoundtobedecreasedverymuchaftertheheat

treatmentat1000degCforonlyafewminutes

-1-

Thephysicalpropertiessuchasthediffusionlengthin

thesmallselectedareascouldbecharacterizedbyEBIC

consideringthethree-dinensionalgenerationdistributionbyan

electronbeamandthesampledimensionsExperimentalresults

inSiandGaAsshowedgoodagreementwiththetheoryandthe

generationdistributionsinSiandGaAswererevealedWitニh

experiments

一旦-

hellipJVi_--Wrsquordquo>>-trsquomjrsquordquordquo^>-≫^

f1

ACKNOWLEDGEMENTS

Theauthorwishestoexi】resshisdeepgratitudetoformer

jブProfessorTetsuroTanakaforhiscontinuingguidanceandワバandrrsquoI

helliphellipノ1encouragementTheauthorwishestoexpresshis9万ざlltや1appreciation

toAssociateProfessorHiroyukiMatsuna万万mlforhispreciousguidance

andhelpfuladvicethroughouttニhepresentstudyTheauthor

acknowledgesProfessorAkiraKawabataforhisgenialguidanceand

encouragementTheauthorisgがIattilltoProfessorToshinoriTakagi

forhisstimulatingdiscussionsandusefulcriticismsonthemanuscript

TheauthorwouldalsoliketothankProfessorAkioSasakifora

criticalreadingofthemanuscriptandvaluablecomments

MuchattentionisduetoDrJuniiSaraieDrShigehiro

NishinoandDrAkiraSuzukifortheircontinuousencouragement

andstimulativediscussions

TheauthorthanksothermembersofSemiconductorLaboratory

fortheirconsiderableassistanceandexperimentalfacilities

一斑-

CONTENTS

ABSTRACT

ACKNOWLEDGEMENTS

L工STOFSYMBOLS

INTRODUCTION

References

i一m

VL

lVO

INFLUENCEOFMINORITYCARRIERGENERATIONDISTR工BUTION13

0NELECTRONBEAMINDUCEDCURRENTINTHENORMALINCIDENCE

METHOD

2-1

2-2

2-3

Introduction

Determinationofdiffusionlengthandelectron-

holepaircreationenergy

ExperimentalresultsinGaAs

2-4Summary

References

13

15

VOON

CMCM

30

DETERMINATIONOFDIFFUSIONLENGTHSURFACERECOMBINATION31

VELOCITYANDELECTRON-HOLEPAIRCREAT工ONENERGYBYTHE

LINESCANMETHOD

3-1Introduction31

3-2Surfacerecombinationeffectconsideringpoint33

source

3-3Analysisofelectronbeaminducedcurrenttaking37

tニhree-dimensionalgenerationdistributioninto

account

3-4ExperimentalresultsinSi

3-5Summary

References

一分-

`j7

44

48

】V

V江

ⅧI

ANALYSISOFTHREE-DIMENSIONALGENERATIONDISTRIBUTION50

BYTHECOMBINATIONOFTHENORMALINCIDENCEANDTHE

L工NESCANMETHODS

4-1Introduction

4-2 Influenceofthree-dimensionalgeneration

distributiononelectronbeaminducedcurrent

02

inin

4-3Three-dimensionalgenerationdistributioninGaAs57

4-4Summary

References

12

vOVD

ANALYSISOFELECTRONBEAMINDUCEDCURRENTCONSIDERING64

SAMPLEDIMENSIONS

5-1Introduction

5-2

5-3

Determinationofdiffusionlengthandsurface

recombinationvelocity

ApplicationtoSi

5-4Summary

References

Appendix

DETERMINATIONOFLIFETIMEANDDIFFUSIONCONSTANT

BYPHASESHIFTTECHNIQUE

6-1Introduction

6-2Relationbetweenlifetimeandphaseshift

6-3ExperimentalresultsinSi

6-4Summary

References

HEATTREATMENTEFFECTONDIFFUSIONLENGTHINS1

7-1Introduction

7-2Experimentalresultsanddiscussions

References

CONCLUS工ONS

References

LISTOFPUBLICATIONS

4vO

CVD

73

78

9VO>

77

81

lro

88

CNJVO

qNas

7O

O^(J

99

102

104

105

108

109

-V-

LISTOFSYMBOLS

Cl

cBC

ggpgBELOS嚢

cdDDeEfgGIIIIIlj一jJ

J大

correctionfactorwithwhichthethree-dimensionalsolutions

oftheヽgradientofphaseshiftcanbeexpressedbytheone-

dimensionalapproximations

exponentofGaussiandistribution

positionofgenerationsourcefromthesurfacealongthedepth

diffusionconstantofminoritycarriers

(equivdgL)normalizedgenerationdepth

chargeofanelectronz

electron-holepaircreationenergybyanelectronbeam

modulationfrequencyofprimaryelectronbeam

generationrateofactualpointsource

variablepartofgenerationsource

thewholegenerationstrengthinthegenerationregion

Imaginaryunit

primaryelectronbeamcurrent

measuredelectronbeaminducedcurrent

currentwhichflowsthroughtheloadresistance

backwardsaturationcurrent

shortcircuitcurrent

electronbeaminducedcurrent

variablepartofcomplexelectronbeaminducedcurrent

(≒n)normalizedelectronbeaminducedcurrentitbecomes

unitywhenallthegeneratedcarrierscontributeto

electニronbeaminducedcurrent

normalizedelectronbeaminducedcurrentconsideringthe

Influenceofohmiccontact

一吐-

誉~Lay

L大eff

p卵`μrRRCReRmSStTuva

correctionfactorfortheincidentbeamenergyconsidering

theenergylossduetobackscatteredelectrons

thermalvoltagersquo259mVatroomtemperature

second-modifiedfirst-orderBesselfunction

diffusionlengthofminoritycarriers

diffusionlengthestimateddirectlyfromtheslopeof

electronbeaminducedcurrentvsscanningdistancecurve

diffusionlengthestimateddirectlyfromtheslopeof

electronbeaminducedcurrentvsscanningdistancecurve

consideringtheinfluenceofohmiccontact

(ΞLJ百石iT)complexeffectivediffusionlength

distニributionofminoritニycarrierdensity

distributionofminoritycarrierdensityconsideringthe

influenceofohmiccontニact

variablepartofthedistributionofminoritycarrier

densitycomplexvariable

distancebetweenthecenteroftニhegenerationregionand

eachdividedsegment

radiusofgenerationregion

centerofgenerationregion

extraporatedelectronrange

loadresistance

maximumelectronrange

surfacerecombinationvelocity

(ΞS(Lて))surfacerecombinationvelocityparameter

time

variableforintegrat10n

para万7rdquo万eterforGaussiandistribution

acceleratingvoltageofprimaryelectronbeam

一吐-

rdquod

wm

Xxx

χy

ZZ

np

Pau

^GaAs

SpてφΦω

distancebetweenthepotentialbarrierandtheohmiccontact

depletionlayerwidth

metalthicknessofSchottkydiode

Cartesianco-ordinateofscanningdistance

(ΞxL)

distancebetweenthepotentialbarrierandthegeneration

pointalongthescanningdirection

(ΞL)

Cartesianco-ordinateonthescanningsurfacenormalto

thescanningdirection

Cartesianco-ordinatealongthedepth

peakoftheGaussiandistribution<

(=J)collectionefficiency

collectionefficiencyofthevariablepartニofthegeneration

source

resistivityofsemiconductors

massdensityofAu゜189gcm^

massdensityofGaAs゜53gcm^

massdensityofSi=23gcm^

minoritycarrierlifetime

phaseshiftbetweentheelectronbeaminducedcurrentand

tニhemodulatedgenerationsource

diameterofprimaryelectronbeam

angularfrequencyofmodulatedprimaryelectronbeam

-VnL-

IINTRODUCT工ON

Theremarkableprogressinthesolidstatedevicesisowing

totheadvancementinthecharacterizationtechniqueofthedevice

materialsWhenthedeviceshavingnewfunctionsaredevelopedthe

detailknowledgeofthephysicalpropertiesofthesemiconducting

material(bandgaplifetimeandmobilityofcarriersetc)mustbe

neededInparticularthosepropertiesmustbecharacterizedafter

theactualmanufacturingprocessbecausetheoriginalpropertiesmay

beaffectニedbythevariousprocessconditions

Inrecentyearstocharacterizeverysmalldevices(ie

LSI゛sorlaserdiodes)therehasbeenagrowinginteresttousea

finelyfocusedelectronbeamThetwodimensionalInformationofthe

materialpropertiescanbeobtainednon-destructivelywithhigh

spatialresolutionfromtheelectronbeamInteractionwithsamples

[121Surfacemorphologycanbeobservedwithgreatニdepthoffocus

byascanningelectronmicroscope(SEM)Crystaldefectsinthin

samplesaredetectedusingascanningelectrontransmission

microscope(STEM)[34]AscanningAugerelectronmicroscope(SAM)

[5]hasbecomeaveryusefultooltoanalyzethesurfaceandthe

interfaceregion

Themethodusinganelectronbeaminducedcurrent(EBIC)[6-10]

1saveryconvenienttechniquetodeterminethefundamentalparameters

(egthediffusionlengththelifetimeandthesurfacerecombination

velocityofminoritycarriers)whichcontroltheelectricalperfor-

manceofthedevicesTheelectron-holepairsgeneratedbyanelectron

beamareseperatedbytheinternalfieldInp-njunctionsorSchottky

barriersandthecurrent1SInducedIntheexternalcircuitThe

EBICdependsverymuchondiffusionandrecombinationofminority

carriersInsemiconductorsandthediffusionlengthetccanbe

-1-

Fig1-1

type

type

Primaryelectrbe≪m

^^trrttDepletionlayer

Electron-hotep弗i「6gerwrationregion

Primaryelectronbeam

rArrScanningdirection

(A)

(B)

Principalconfigurationstomeasurethe

electronbeaminducedcurrent(EBIC)

(A)normalincidencemethod

(B)linescanmethod

-2-

く二rArr|t夕

EBICく二rArr

-一一--

p-typentype

aver`

1ミミ二l∽rsquoebic

determinedfromtheanalysisofEBICInadditiontothetwodlmen-

sionalinformationofthediffusionlengthandthelifetimetheir

variationsalongthedeptニhcanbeobtainedforvariousgeneration

depthsbychangingtheacceleratingvoltageofanelectronbeam

TheprincipalconfigurationstomeasureEBICarethersquonormal

incidencemethodrsquoandthersquolinescanmethodrsquo(seeFig1-1)Inthe

normalincidencemethodtheelectronbeam1Sincidentnormaltothe

barrierplaneandisscannedonthesurfaceparalleltothatplane

ThedislocationsanddefectsinSiwereobservedinp-njunctionsand

Schottkybarrierdiodes[11-28]Inrecentyearselectricalactivity

ofoxidationinducedstackingfaults(OSF゛s)anditsrelationwith

deviceperformanceshavebeenstudied[29-35]Thenormalincidence

methodisalsousedforthefailureanalysisoftニheMOSdevices[36-

39]Usingthelinescanmethodthediffusionlengthandthesurface

recombinatニionvelocitycanbedeterminedfromthedependenceofEBIC

onthescanningdistancewhentheelectronbeamisscannedacrossthe

barrierTherehavebeenmanytheoretical[AO-46]andexperimental

[47-69]reportstomeasurethediffusionlengthandthesurface

recombinationvelocityinlight-emittingdiodes(LEDrsquos)andlaser

diodes

InalmostalltheworkssofarEB工Chasbeenanalyzedonly

qualitatively0rsemi-quantitativelyThediffusionlengthandthe

surfacerecombinationvelocityhavebeendeterminedunderrather

specialconditionsasmentionedbelowforthesimpletheoretical

calculationInthenormalincidencemethodtheyconsideredonly

theone-dimensionalgenerationdistributionalongthedepth[70-75]

undertheconfigurationthatthelateralextentofthegeneration

volumewasverysmallcomparedwithsampleareasInthelinescan

methodthegenerationvolumewasassumedtobeapoint[53546061]

undertheconditionthatthegenerationvolumewassufficiently

-3-

smallerthanthediffusionlengthandthesampledimensionsBut

intheactualcasethegenerationvolumehasafinitethree-

dimensionalextentreLatedtotheacceleratingvoltage[76-78]

Thelatestmicroelectronicdevices(ieLSIrsquosandthelaserdiodes

etc)havethesamedimensionsasthegenerationvolumeandS0

theanalysesconsideringtニhepointsourceortheone-dimensional

generationdistributニionareinaccuratetodeterminethediffusion

lengthandthesurfacerecombinationvelocityThenewmethodfor

thequantitativeanalysisofEBICmustbedevelopedtakingthethree-

dimensionalgenerationdistributionandtheinfluencesofthesample

dimensionsintoaccount[7980]

InthepresentstudyEBICisanalyzedquantitativelyby

solvingthesteady-stateortime-dependenttニhree-dimensionaldiffusion

equationsTheinfluenceofthefinitegenerationvolumeonEBICis

discussedwhentheextentofthegenerationvolumecannotbeignored

andimprovedmetニhodsaresuggestedtomeasurethephysicalproperties

(diffusionlengthlifetimeandsurfacerecombinationvelocityof

minoritycarrierselectron-holepaircreationenergybyanelectron

beametc)inthesmallselectニedareas

InChapternvariousmodelsforthegeneratニiondistribution

alongthedepth[7781-83]arecomparedwitheachotherandtニhe

influenceofthegenerationdistributiononthedeterminationofthe

diffusionlengthbythenormalincidencemethodisdiscussed

ChapterⅡIshowstheinfluenceofthegenerationvolumeon

EB工Cinthelinescanmethodtakingtニhesurfacerecombinationeffect

intoaccountAnimprovedmethodforthedeterminationofthe

diffusionlengthandthesurfacerecombinationvelocityisdescribed

-4-

InChapterVthree-dimensionalgenerationdistribution

isclarifiedbymeasuringEBICusingboththenormalincidenceand

thelinescanmethodsinthesamesamplewhichyieldsthe

quantitativeanalysisofEB工C

ChaptervdescribestheInfluenceofthesampledimensions

onEBICInthelinescanmethodEBICisInvestigatedbyextending

themirrorimagemethodlsquo[41-43]whenthediffusionlengthisof

theorderofthesampledimensions

InChapterWthephaseshifttechniqueinthemeasurement

ofEBIC[84-86]isdescribedTherelationbetweenthelifetime

andthephaseshiftisclarifiedbysolvingthethree-dimensional

time-dependentdiffusionequationThelifetimeandtニhediffusion

constantofminoritycarrierscanbedeterminedcombiningthe

phaseshifttechniquewiththeconventionallinescanmethod

Chaptervnshowstheheattreatmenteffectonthediffusion

lengthinSi

FinallyconclusionsandsuggestionsforfurtherInvestigation

aresummarizedinChaptervnr

ExperimentalresultsinSiandGaAsareshovmineverychapter

Themethoddiscussedinthesechapterscanbeappliedeasilyto

anysemiconductormaterialsbyconsideringthephysicalproperties

inherentinthematerials

-5-

References

[1

[21

[3]

4]

5]

6]

[7]

[8]

[9]

[10]

VEJohnson十Sm119151p763

0CWellsSEM1972p375

pMrdquoPetroffDVLangJLStrudelandRALogan

SEM71978pp325-332

CELymanSEM1978pp529-536

NCMcDonaldSEM1971p89

DBHoltrdquoQuantitativeScanningElectronMicroscopyrdquo

(DBHolteta1edsAcademicPress974)pp213-286

DBWittryrdquoMicroprobeAnalysisrdquo(CAAndersoned

JohnWileySonsNewYork1973)pp123-187

CJVarkerrdquoNondestructiveEvaluationofSemiconductor

MaterialsandDevicesrdquo(edJayNZemelNATOADVANCED

STUDYINST工TUTESSERIESSERIESBPhysicsvol46

PLENUMPRESS1979)pp515-580

HJLeamyLCKimerlingandSDFerris

SEM1978pp717-725

ThebibliographyonEBICislistedinthefollowing

K0LeedySolidStateTechnologyFeb1977pp45-48

--

-- - -

rdquo-

rdquo- - 言

争心- -

SEM19xxrdquoScanningElectronMicroscopyrdquoProceedingofAnnualConference

before1977(IITResearchInstituteChicago)

after1978(SEMIncAMFOrsquoHare)

-6-

[11]JJLanderHSchrelberJrTMBuckandJRMathews

ApplPhysLett旦206-207(1963)

[12]WCzajaandGHWheatleyJApplPhys亜

2782-2783(1964)

[13] WCzajaandJRPatelJApplPhys11476-1482

(L965)

[14]NFBNeveandPRThorntonSolid-stateElectron

旦900-901(1966)

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

IGDaviesKAHughesDVSulwayandPRThornton

Solid-stateElectron9275-279(1966)-

WCzajaJApplPhysyi918-919(1966)

DVSulwayPRThorntonandMJTurner

Soli-StateElectron11567-568C1968)-

AJRKockSDFerrisLCKimerlingandHJLeamy

ApplPhysLett27313-315(1975)

DBHoltandROgdenSolid-stateElectron1937-40(1976)-

HJLeamyLCKimerlingandSDFerris

SEM1976pp529-538

TKatoTMatsukawaandRShlmizu

ApplPhysLett26415-416(1975)

RBMarcusMRobinsonTTShengSEHaszkoand

SPMurarkaJElectrochemSOC124425-430(1977)

LCKimerlingHJLeamyandJRPatel

ApplPhysLett30217-219(1977)

DEIoannouandSMDavidson

physstatsol(a)丘旦K1-K4(1978)

-7-

[25]

[26]

HBlumtrittRGlelchmannJHeydenderichandH

Johansenphysstatsol(a)55611-620(1979)

HMennigerHRaidtandRGleichmann

physstat-sol(a)5旦173-180(1980)

[27]pAshburnandCJBullSolid-stateElectron

Tl_105-110(1979)

[28] pAshburnCJBullandJRABeale

JApplPhys503472-3477(1979)

[29]KVRaviCJVarkerandCEVolk

JElectrochemSoc120533-541(1973)-

[30]

【31】

[32]

[33]

[34]

[35]

[36]

[37]

[38]

[39]

[40]

CJVarkerandKVRaviJApplPhys45272-287(1974)

SKawadoYHayafujiandTAdachi

JpnJApplPhys14407-408(1975)

TESeidelSEHaszkoandDMMaher

JApplPhys485038-5042(1977)

AMurgaiJYChiandHCGatos

JElectrochemSoc1271182-1186(1980)-

SKawadqJpnJApplPhys191591-1602(1980)

JMDishmanSEHaszkoRBMarcusSPMurarka

andTTShengJApplPhys502689-2696(1979)

JLGatesand0KGriffith

ApplPhysLett27kZ-45(1975)

JFKatalanoSEM71976pp521-528

PRoltmanandWRBottomsSEM1977pp731-738

CLWilsonSolid-stateElectron23345-356(1980)-

WHHackettJrJApplPhys431649-1654(1972)

-8-

[41]

[42]

[431

[44]

[45]

【46】

[47]

[48]

[49]

[50]

FBerzandHKKuikenSolid-stateElectron

19437-445(1976)

CvanOpdorpPhilipsResKept32^192-249(1977)

0vonRoosSolid-stateElectron互lsquo1063-1067(1978)

0vonRoosSolid-StateElectron211069-1077(1978)

0vonRoosSolid-stateElectron22113-114and773-778-

(1979)

WvanRoosbroeckJApplPhys旦D380-391(1955)

DBWittryandDFKyserJApplPhysj11387-1389

(1965)

HHiguchiandHTamura

JpnJApplPhys4^

316-317(1965)

YuPDemidovRPGurovaYuMKushnirAIFrltner

andDVFetisovSovPhys-Semicond1030-1035(1968)

KMaedaAKasamiMToyamaandNWakamatsu

JpnJApplPhys旦65-75(1969)

[51]ZhIAlferovVMAndreevVIKorolrsquokovand

vIStreminSovPhys-Semicond41113-1116(1971)

[52]

[53]

[54]

[551

CJHwangSEHaszkoandAABergh

JApplPhys425117-5119(1971)

WHHackettJrRHSaulRWDiχonandGWKammlott

JApplPhys432857-2868(1972)

WZimmermannphysstatsol(a)^2671-678(1972)

MAvenJZDevineRBBolonandGWLudwlg

JApplPhys434136-4142(1972)

-9-

[56]

[57]

[58]

[59]

【60】

[61]

[62]

[63]

[64]

[65]

[66]

GLidgardSolid-stateElectron15159-164(1972)

DBHoltBDChaseandMCenslive

physstatsol(a)20459-467(1973)-

DBHoltandBDChasephysstatsol(a)2(

135-144(1973)

CvanOpdorpRCPetersandMKlerk

ApplPhysLett24125-126(1974)

LJBalkEKubalekandEMenzel

IEEETransED-22707^712(1975)-

LJastrzebskiJLagowskiandHCGatos

ApplPhysLett11_537-539(1975)

LJBalkEKubalekandEMenzelSEM71975pp447-455

JJOakesIGGreenfieldandDLPartaln

JApplPhys丘旦2548-2555(1977)

MLanirAHBVanderwyckandCCWang

JApplPhys496182-6184(1978)

DLPartainAGMilnesandLFVassamlllet

JElectrochemSoc1261584-1588(1979)-

NTohgeTMinamiandMTanaka

JpnJApplPhys172155-2156(1978)

【67】DLPartainAGMilnesandLFVassamillet

JElectronicMaterials旦493-499(1979)

[68]

[69]

DEIoannouandSMDavidson

JPhysDApplPhys昆1339-1344(1979)

ShengSLiWLWangPWLaiandRTOwen

JElectronicMaterials旦335-354(1980)

-10-

[70]

【71】

[72]

[73]

[74]

JFBresseSEM119111pp105-112

JFBresseSEM1977pp683-693

CJWuandDBWittryJApplPhyspound92827-2836(1978)

GEPossinSEM1979pp245-256

GEPossinandCGKirkpatrlck

JApplPhys旦4033-4041(1979)

[75]GEPossinandCGKirkpatrick

JVacSciTechnol161917-1920(1979)-

[76]

[77]

[78]

[79]

[80]

VonAEGruenZNaturforsch12aHeft289-95(1957)-

KKanayaandSOkayama

JPhysDApplPhys5A3-58(1972)

RShimizuYKataokaTIkutaTKoshikawaand

HHashimotoJPhysDApplPhys旦101-114(1976)

GVSpivakGVSaparinandLFKomolova

SEM1977pp191-199

CDonolatoandHKlann

-JApplPhys511624-1633(1980)

[81]DBWittryandDFKyser

JApplPhys2旦375-382(1967)

[82]

[83]

[84]

[85]

[86]

TEEverhartandPHHoff

JApplPhys425837-5846(1971)

VVMakarovSovPhys-Semicond旦in-llk(1975)

JDKannnandHBerntSolid-stateELectronヌ1957-964(1978)-

JDKammrdquoSemiconductorSilicon1977rdquo(JElectrochemical

Society)pp491-501

0vonRoosJApplPhys503738-3742(1979)

-n-

-L2-

2-1

INFLUENCEOFM工NORITYCARRIERGENERATIONDISTRIBUTION

ONELECTRONBEAMINDUCEDCURRENTINTHENOR^IALINCIDENCE

METHOD

Introduction

Accuratedeterminationofminoritycarrierdiffusionlength

LisveryimportanttocharacterizesemiconductorsOneofthe

convenientmethodstomeasureLIstheuseofelectronbeam

inducedcurrent(EBIC)Theelectron-holepairsgeneratedbyan

electronbeamareseperatedbyapotentialbarrier(egp-n

junctionorSchottkybarrier)andthecurrentisInducedinthe

externalcircuitThevalueofLcanbedeterminedfromthe

dependenceofEBIConthelengthzbetweenthepotentialbarrier

andthegenerationpointInthenormalIncidencemethodzis

variedbychangingtheacceleratingvoltagevaofanelectronbeam

andthesmallvalueofLoftheorderofumcanbedetermined

ThevalueofLintニhesmallregionisobtainedusingafocused

beamgeneratedbyascanningelectronmicroscope(SEM)lsquo

Czaja[1]measuredLinp-ndiodesofSiandGaPHe

assumedthegenerationdistributionasacombinationoftwo

exponentialfunctionsBresse[2]andWu[3]measuredLandthe

electron-holepaircreationenergyE^^inSiandGaAsTheyused

Schottkydiodesbecausetheelectronbeamenteredthroughthemetal

contactandthesurfacerecombinationeffectcouldbeneglected

IntheiranalysesBresseusedthesemi-sphericalgeneration

distrlbutionproposedbyKanayaeta1[4]andWuassumedGaussian

distリbutlonPossineta1[5]analyzedEBICindetailtakingthe

influencesofthesurfacerecombinationandtheinternalfield

-13-

Metal

Depletio

layer

Primaryelectronbeam

Numberofgeneratedcarriers

Fig2-1Schematicviewofexperimentalconditions

jusingSchottkydiodesMetalthicknessis

wanddepletionlayerwidthiswright-handillustぷふこsthedぶdosefunctionRandR

-givethemaxiraum

andextraporaiedmelectrSnolinerangerespectively

-14-

0generatedcarrier

に_---___1

我_______Iuarrヽ

y重ダ

1ごpermil

andestimatedthedepthdistributionoflifetimeinion-implantedSi

TheylsquousedthepolynomialfunctionderivedbyEverhart[6]forthe

generationdistribution

工ntheanalysisofEBICtheminoritycarriergeneration

distributionplaysanimportantroletodeterminetheaccurate

valueofLandEHoweverthedistributionmodelsusedinthepc

analysesaredifferentwitheachotherasmentionedaboveIntニhis

chapterwecomparevariousmodelsforthegenerationdistribution

inGaAsandSiWecalculateEBICandclarifytheinfluenceofthe

generationdistributiononthedeterminationofLandEpc

Experimentalresultsarealsopresented

2-2 Determinationofdiffusionlengthandelectron-holepair

creationenergy

ASchottkybarrierdiodeisusedinordertoneglectthe

influenceofthesurfacerecombinationTheelectronbeamis

irradiatednormallytothebarrierplanethroughthemetalas

shownInFig2-1Thethicknessofthemetalandthedepletion

layerareputaswmandwd゛respectivelyTheminoritycarrier

generationdistributionalongthedepth(Socalledthedepthdose

function)isIllustratedalso1nFig2-1TheEBICiscalculated

basedonthefollowingassumptions1)Theminoritycarriers

generatedinthemetal(regionI)cannotcontributetoEBIC

2)Theelectron-holepairsgeneratedinthedepletionlayer(

regionlsquoTL)areseperatedquicklybythefieldofthedepletion

layerandwhollycontributetoEBIC3)Theminoritycarriers

generatedinthebulk(regionⅡI)partlycontributetoEBICie

theminoritycarrierswhichreachtotheedgeofthedepletion

-15-

mDiwi)iunMd

SMtjjesp≫)ejAU≫6|o』ψsEコz

Normalizedgenerationdepth^rsquoRm

Fig2-2

Generationdistribution

inGaAsTheMakarov゛SWittryrsquos

andKanayarsquosmodelsareexpressed

bytニhesolidbrokenanddotted

linesrespectivelyThegener-

atlondepthisnormalizedby

themaximumelectronrangeR

ThetotalgenerationrateiSm

normaLlzedtobeunity

-16-

2 0

1 05

(Efi)≪MJO^M

d6ue」

CO』oa3

rdquorsquo5102050Acceleratingvoltageva(kv)

Fig2-3

ElectronrangesinrsquoGaAsforvariousmodelsThesolidbrokendottedanddashedanddottedlinesaretheresultsusingMakarovrsquosWitニtryrsquosKanayarsquosandEverhartrsquosmodels

respectively

rdquoゝゝGaAs

χ

`Makarov20χ

----Wittry

χhelliphelliphellipKanaya

11S

15

゛S≒

rsquoχ≒

χrsquo

10trsquolsquo

卜卜゜χ゛

卜ゝrsquo

05χrsquo゛rsquoゝ

ゝrsquoゝ1

ゝゝrsquoゝゝ

ゝゝ

00

50

GaAso々

タグrsquo

Makarov

15-rsquo一一Wittry

ノKanaya

12

---Everhart

13yelr(2゛十`゛dinFig2-1)bydiffusioncanflowintothemetal

bythefieldofthedepletionlayer

Therehavebeenmanytheoretical147]andexperimental

[68-11】worksonthegenerationdistributionKanayaand

Okayama[4]proposedasemi-sphericalgenerationdistribution

usingthemodifieddiffusionmodel0fArchard[7]Wittryeta1

assumedGaussiandistributionandappliedtoGaAs[89]

EverhartandHoffl6]derivedapolynomialfunctionfromtheir

experimentsIntheA1olineSi02olineSisystemdegMakarov[10]showedthat

thegenerationdistributioncouldbeexpressedasGaussianlike

(exp(-((z-z)u)2))andthep8゛゜eters2manduvariedaccording

totheatomicnumberandthedensityofthematerialInorderto

comparethesedistributionsnormalizeddepthdosefunctionwas

introducedGruen[11]showedthattheshapeofthedepthdose

curveispracticallyinvariantifthepenetrationdepthis

normalizedbytheelectronrange

ThedepthdosefunctioninGaAsnormalizedbythemaximum

electronrangeRm(atwhichnoelectronentersintothematerial

seeFig2-1)areshowninFig2-2bythesolidbrokenanddotted

linesusingthefollowingequationsforthemodelsofMakarov

WittryandKanayarespectively

2RmolineOdeg138

g(z)=exp(-(rarr元でi

g(z)=exp(-(

2Rmoline

Odeg125

-035

)2)

)2)

(Makarov)(2-1)

(Wittry)(2-2)

g(z)゜(RmolineOdeg242Rtri)2oline(2olineOrsquo242Rm)2(K゛3y8)゛(2lsquo3)

-17-

こrsquo

Aouepj^^auoiiDaii〇D

Fig2-4

10203040

Acceleratingvoltage

5060

Va(kV)

CollectニionefficiencynvsVacurves

GaAsSchottkydiodeThevaluesofLare505μmfromuppert0lowergroupofcurves

for

2and

respectivelyTheresultsusingtheMakarovrsquosWittry゛SandKanayarsquosmodelsareexpressedbythesolidbrokenanddottedlinesrespectivelyThevaluesofwandWare10nmand015ymrespectively^hedashedanddottedlineisinthecaseofw=50nmw=015umandL=2umusingtheWittryrsquosmode1

-18-

GaAs一一Makarov

--rdquo-Wittry

10Wf^=10nmhelliphelliphelliphellipKanayaL(pm)

rsquo≒゜ニ1こii4degこ7T`ヽヽヽ5

05万でヽこミア斗辿こTTZご

50nふyミ゛1helliphelliphelliphellip4゛`゛ζ゛ζ

Orsquo1capparacapcap

か4

5060

ThereareobviousdifferencesbetweenthesethreemodelsThe

MakarovrsquosandWittryrsquosmodelshavethelargesurfaceconcentration

butthepeakvalueatzRm゛Odeg13oftheMakarovrsquosmodelissmaller

thanthatoftheWittryrsquosmodelTheKanaya゛smodelhasmoreevenly

spreadeddistributionthantheothertwomodelsThisisbecause

theelectron-holepairconcentrationisassumedtobeuniformin

thesemi-sphereintheKanayarsquosmodelwhichisasimplefirst-

orderapproximationforthegenerationdistributionButinthe

actualcasetheelectron-holepairsareconcentratedaroundthe

centerofthesemi-sphereOnemustusetheimprovedelectron-hole

pairconcentrationmodelInsteadoftheuniformoneinorderto

expressthegenerationdistributionprecisely

InthecalculationofEBICtheabsolutevalueofRmustm

beneededSomereportedvaluesbyMakarovWittryandKanayaare

shownbythesolidbrokenanddottedlinesrespectively

inFig2-3forGaAsThedashedanddottedlineisderivedby

Everhart[6]anddiscussedlaterTherangesoftheWittryrsquosand

Kanayarsquosmodelsarealmostagreewitheachotherbutthatofthe

Makarovrsquosmodelisabout70ZofthoseoftheWittryrsquosandKanayarsquos

models

ThecalculatedEBICinGaAs(iethecollectionefficiency

nwhichbecomesunitywhenallthegeneratedcarrierscontribute

toEBIC)bythesamemethoddescribedinref[3]isshownIn

Fig2-4Thesolidbrokenanddottedlinesareforthemodelsof

MakarovWittryandKanayarespectivelyThevalueoftheacceler-

atlngvoltageva1Schangedfrom5t060kVThevalueofLIs50

20and05ymfromuppert0lowergroupofthecurvesrespectively

ThevaluesofWmandwdaretakenastypicalvaluesof10nmand

015ymrespectivelyTheelectronrange1SInverselyproportional

tothedensityofthematerialThemetalthicknessiscorrected

-19-

takingthedifferenceofthedensitiesbetweenthemetalandthe

bulksemiconductorinorderthatthesamplehasuniformdensityfrom

thesurfacetothebulkforasimpletheoreticalcalculationWhen

goldistakenastheSchottkycontactwmustbemultipliedby

pAupGaAS(゜3`゜6rsquopAudeg189andpGaASdeg5゛3

1cll3)

゛OIlecanestimateL

mainlyfromthegradientofthecurvebecausethegradientdecreases

monotonouslywithincreasingLupt05umTheestimatedvaluesof

LbyMakarovrsquosandWittry゛Smodelsarealmostequalbecausethe

gradientsofthecurvesagreewitheachotherforthesameLvalue

ThevalueofLlargerthan5μmcannotbedetermineddefinitely

becauseEBIChardlychangeswithvevenifLbecomeslargeThea

maximumvalueofLthatcanbedetermineddefinitelyincreasesas

thehighestvalueofvaincreasesbutanotherproblems(idegedeg

damagesofthesamplebyhighenergyelectronsetc)mayoccur

Theelectron-holepaircreatニionenergyEcanbeobtainedfrom

theabsolutevalueofEBICbytherelationndeg^C^EBIC^^B^

(IEBICmeasuredEBICIBprimarybeamcurrentkcorrectionfactニor

fortheenergylossduetobackscattニeredelectrons)[3]

TheabsolutevaluesoftニheMakarovrsquosmodelareabout10へj20Z

largerthanthoseoftheWittry゛smodelAndsothevalueofEpC

obtainedbytheformeris10へj20Zlargerthanthatbythelatter

ThegradientニSandtheabsolutevaluesofthecurvesoftheKanayarsquos

modelarequitedifferentfromthosebytwoothermodelsThe

reasonofthedifferenceisowingtotheassumptionoftheuniform

concentrationoftheelectron-holepairsinthesemi-sphereas

discussedbeforeTheKanayarsquosmodelisafirst-orderapproximation

forthegenerationdistributionandisnotsuitableforthe

accuratedeterminationofLandEThevalueofwdoesnotaffectpc(I

EBICsomuchfromtheresultsoftニhecalculation工fWbecomesm

largetheabsolutevalueofEBICat10wvaisdecreasedverymuch

-20-

butthegradientofthecurveintheregionofhighVadoesnot

changeasshowninFig2-4(thedashedanddottedlineisinthe

caseofwmdeg50nm゛wdrsquoOrsquo15pmandL=2ymusingtheWittry゛Smode1)

ThereforeLcanbedeterminedinanycaseofwm゛asfaraswm1S

sufficientlysmallinorderthattheelectronbeamcanenterinto

thebulkregion

ThenormalizeddepthdosefunctionsInSiexpressedbythe

followingequationsareshowninFig2-5bythesolidbroken

dottedanddashedanddottedlinesforthemodelsofMakarov

WittryKanayaandEverhartrespectively

zR-0261

g(z)=exp(-(-jyヲー-7)2)(Makarov)(2-4)

zR-0156

g(z)=exp(-(―q2L_一一

g(z)゜(RmolineOrsquo336Rm)2

g(z)=06+6212Re

(Wittry) (2-5)

(゛0336R)^(Kanay゛1)(2oline6)

oline12deg40(2Re)2+5lsquo69(zR

(Everhart)e)3

(2-7)

Makarovshowedthattheparameterszmlsquoanduhadvoltagedependencesl

andthetypicalvaluesatvadeg30kVaretakenItshouldbenoted

thatthedepthdosefunctionoftheEverhartrsquosmodelisnormalized

bytheextraporatedrangeRe(seeFiglsquo2-1)whichisdetermined

byextraporatingthestraightlineportionofthecurve

-21-

Fig2-5

11

u)6ua))iunjed

sjdiJieopdiejdud6lo」4sEコz

Normalizedgenerationdepth^rsquoRm

GenerationdistributionsinSiTheMakarov゛s

Witニビry゛sKanayarsquosandEverhart゛Smodelsare

expressedbythesolidbrokendottedanddashedanddottedlinesrespectivelyThegener-

atlondepthisnormalizedbythemaximumelectron

rangeRTheextraporatedrangesR゛SoftheMakarovrsquosWittryrsquosandEverhartrsquosmodelsare

takentobeagreedwitheachotherThetotニal

generatニionrateisnormalizedtobeunity

-22-

KUkarov

--一一-Wittry2deg

二ぷ芯t

15へ

゜¥レ臨べhellip

hellip

10rsquoS゛lsquoNhellip

helliphellip

05

hellip

helliphellip

1helliphellip

hellip

005

工nordertocomparetheEverhartrsquosmodelwithothersthe

extraporatedrangefortheGaussiandistributionisdeduced

(seefootnote)十andtheextraporatedrangesoftheMakarovrsquoS

WittryrsquosandEverhart゛Smodelsaretakentobeagreedwitheach

otherThepeakvaluesofthegenerationdistributionsofthe

MakarovrsquosWlttryrsquosandEverhartrsquosmodelsarealmostequalbut

thevalueofzRmatthepeakfortheWittryrsquosmodelisabout

015andsmallerthanthoseoftheothertwomodelsCzR=025)゜

ThegenerationdistributionoftheWittryrsquosmodelcomesnearerto

thesurfacethanthoseoftheMakarovrsquosandEverhartrsquosmodelsIt

isbecausetheWittryrsquosmodelisderivedInthecaseofGaAsand

ontheotherhandtheMakarovrsquosandEverhart゛Smodelsareconcerned

inthecaseofSiThedensityofG゛1AS(pGaAS゛5deg3gcm^)islarger

thanthatofS1(pSirsquo2deg3gcm^)andsotheWittry゛Smodelshows

themoresurfaceconcentrationthantheothersTheKanayarsquosmodel

isquitニedifferentwiththeotherthreemodelsowingtothesame

reasonasdiscussedinGaAs

- -

-- - - - -

- - - -

Gaussiandistribution(e゛p(oline((2oline2m)11)2))

showsthealmostlineardecreasearoundthepoint

ofinflection(zdegu゛Σ十zm)lsquoTheextraporatedrange

Re(1゛ersquothepointwithwhichthestraightline

atthepointofinflectioncrossesthezaxis)

becomes2u十zfromtheresultsofcalculationm

(seeFig2-5)゜TheextraporatedrangeRebecomes

078Rand062RfortheMakarovrsquosandWittryrsquosmm

modelrespectively

-23-

Fig2-6

0 102030

Acceleratin9

4050

voltage

60

va(kv)

CollectionefficiencynvsVacurvesforSiSchottkydiodeThevaluesofLare1052andlymfromuppert0lowergroupofcurvesrespectivelyTheresultsusingtheMakarovrsquosWittryrsquosKanayarsquosandEverhartrsquosmodelsareexpressedbythesolidbrokendottedanddashedanddottedlinesrespectivelyThevaluesofWandware10nmand05ymrespectivelymd

-24-

MakarovSi---rdquoWittry

Kanaya

----Everhart

ジhttpwwwL(pm)卜

)渫回ブモジミ穫

WmニlOnmrdquoミ4helliphellipで``rsquoヽ4゜

゛ゝ1rsquohelliphelliphellip

゛rsquoN

u1C

larrl

0E

501

Figure2-6showsthecollectionefficiencyinSiusing

thefourdifferentmodelsofMakarovWittryKanayaandEverhart

bythesolidbrokendottedanddashedanddottedlines

respectivelyThevalueofLIs1005020and10umfrom

uppert0lowergroupofcurvesrespectivelyThevaluesofW

andrdquodaretakenastypicalvaluesof10nmand05]imrespectively

Thevalueofwmismultipliedby821nthecalculationowingto

thedifferenceofdensitiesbetweenAuandS1

asdiscussedbeforeThevalueofLlargerthan10μmcannotbe

determinedaccuratelybecauseEBIChardlychangesevenifLvaries

ThegradientofthecurveoftheEverhartrsquosmodel1Sslightly

steeperthanthoseoftheMakarovrsquosandWittry゛smodelswhich

almostagreewitheachotニherAndsotheestimatedvalueofLby

theEverhartrsquosmodelbecomeslargerthanthatbytheMakarovrsquosor

Wittry゛smodelforthesamer)vSdegvaCurve(egL=lutnbythe

Everhartrsquosmodelbecomes07umiftheMakarov゛Smodel1Sused)

ThegradientofthecurveoftheKanayarsquosmodelisalmostequal

tothatニoftheEverhartrsquosmddelbuttheabsolutevalueofthe

formeris30Zsmallerthanthatofthelatterforthesamevalue

ofLThereforetheestimatedLbyKanayarsquosmodelalmostagree

withthatbytheEverhartrsquosmodelbutthevalueofE

pCuSing

theformeris30Zsmallerthanthatusingthelatter

Asmentionedbeforetheelectronrangeisinversely

proportionaltothedensityoftニhematerialTheelectronrange

derivedbyEverhartinSicanbeappliedtoGaAsconsideringthe

differenceofthedensitiesbetweenSiandGaAsThecalculated

valuesareplottedbythedashedanddottedlineinFig2-3

TherangesoftheMakarov゛SandWittry゛Smodelsarelargerthan

thatoftheEverhart゛smodelOneofthereasonsforthe

disagreementisthedifferentdefinitionsoftheelectronrange

-25-

ieMakarovandWittryusedthemaximumrangeRbutEverhart

usedtheextraporatedrangeRelsquoInordertニocomparethesevalues

theextraporatedrangesfortheMakarovrsquosandWittryrsquosmodels

inGaAsarededuced(seefootnoteinpage23)andbecome075Rm

andOlsquo62Rm゛respectivelylsquoForexampleinthecaseofvadeg30kv゛

thevaluesofRforMakarovrsquosandWittryrsquosmodelsare34andm

48ymandthenthevaluesofRebecome26and30ym

respectivelylsquoThevalueofReintheEverhartrsquosmodel(29umat

vadeg30kV)isslightlylargerthanthatoftheMakarovrsquosmodel

butagreeswiththatoftheWittryrsquosmodel

2-3 ExperimentalresultsinGaAs

AconventionalSEMwasusedfortheprimaryelectronbeam

whichwasmodulatedat3kHzwithachoppingcoilinsertedinto

thebeampathTheinducedcurrentwasmeasuredfromthevoltage

dropacrosstheloadresistancewhichwasconnectedtotheSchottky

barrierwithanohmiccontactThesignalwasdetectedbyalock-in

amplifierThebeamcurrentwasmeasuredbyaFaradaycageThe

beamwassomewhataefocussed(Φ|=10umφbeamdiameter)inorder

toavoidhighinjectionTheinducedcurrentwasnotchangedeven

ifthebeamwasirradiatedatthesamepointforanhour

TheSchottkybarrierwasrsquomadeonn-typeGaAs(Sndoped

ndeg62times1016cmoline3)byevaporatingAuofabout10nmthickina

vacuumofabout10oline7TorrTheohmiccontactwasobtainedby

evaporatingAu-Geandalloyingat400degCfor2mlnThecarrier

densityandthedepletionlayerwidthweredeterminedbyG-V

measurements

-26-

(Hiunqj≫)

U一SU

BeamcurrentIb(A)

Fig2-7

MeasuredEBICinGaAs(Sn-

dopedn=62)(1016cmoline3)Schottky

diodeatVa=10and50kVThe

beamcurrentwaschangedinthe

rangeof2)(10oline11≦I≦5)(10oline9A

-B-Theopenandsolidcirclesare

theexperimentalresultsforvadeg

10and50kVrespectivelyand

thegradientsofthesolidlines

areunity

Tab2-1

(s≫UコqjB)Aouapu

く1)

uoiioaiion

AcceleratingvoltageVa(kV)

Fig2-8

Curvefittingsoftheexperi-

mentalresultstothetheoretical

collectionefficienciesinGaAs

SchottkydiodeThesolidbroken

anddottedlinesaretheresultニS

usingtheMakarovrsquosWittry゛Sand

Kanayarsquosmodelsrespectively

Vaischangedfrom5t050kVwith

thefixedvalueofl゛10oline1oA

w=10nmandwmd

L(unj)Ec(ev)

Makarov

Wittry

Kanaya

03

03

05

48

41

41

二〇15um

ご洸竺詐比飛ぱ器ぶごぷ詣ぷ

-27-

000

5Gなfimf4ilvalu

0v≪>iakv

50

100

10

lylrsquo16rsquo1(i

acuteン゛tGaAs(Sndoed)

5n=62

lope

1二痙7

5Kanayao

21020304050

ThevalueofEBICatv=10and50kVareshownbythesolida

linesinFig2-7whenthebeamcurrentIBischangedintherange

of2)(10oline11≦I≦5)(10oline9AIftheminoritycarrier-B-

concentrationexceedsthethermalequilibriumconcentrationof

majoritycarriers(iehighinjection)theminoritycarrier

lifetimeisprolonged[12]ThereforeEBICbecomestoincrease

superlinearlywiththenumberofgeneratedcarriersie

withIBforafixedvalueofvarsquoInthisexperiment゛EBIC

increaseslinearlywithIBatbothvals゛WhichShoWsthe10w

injectionTheexperimentalresultsareshownbycirclesin

Fig2-8whenvischangedintherangeof5くVく50kVata=adeg

thefixedvalueofIBdeg10oline10A゛Theoreticalcollectionefficiencies

usingtheMakarovrsquosWitニtryrsquosandKanayarsquosmodelsareshownbythe

solidbrokenanddottedlinesrespectivelyinFig2-8The

valuesofLandEpcdeterminedbyfittingtheexperimentaldata

totニhetheoreticalcurvesaretabulatedinTab2-1forthethree

differentmodelsofMakarovWittryandKanayaThecollection

efficiencybytheMakarovrsquosmodelshowedfairlygoodagreement

withtheexperimentalresultsbutthatusingtheWittryrsquosmodel

isslightlylargerthantheexperimentalvaluesinthe10Wva

l`egioll(va≦10kV)Thediscrepancyinthelowvaregionbecomes

largeiftheKanaya゛SmodelisusedInthecaseofWittryrsquosand

Kanaya゛Smodelspoundheexperimentaldatawerefittedintherange

ofhighva(va≧15kv)TheestimatedvaluesofLis03urnby

usingboththeMakarovrsquosandtheWittryrsquosmodelsbutthatusing

theKanayarsquosmodelis05ymandabouttwiceoftheresultby

theMakarovrsquosandWittryrsquosmodelsThevaluesofEdeterminedpc

bytheMakarovrsquosWittryrsquosandKanaya゛Smodelsare4841and41

eVrespectivelyBythenormalincidencemetニhodofEBICWuand

Wittry[3]andKobayashieta1[L3]determinedEas468and457

eVrespectivelywhicharealmostequaltotheresultusingthe

Makarovrsquosmodelbutareabout10Zlargerthanthevalueobtained

bytheWittryrsquosandKanayarsquosmodels

-28-

2-4 Summary

ThevaluesofLandEcanbedeterminedfromthe

PC

ceofEBIConvbythenormalincidencemethodThe-

dependenceofEBIConVabythenormalincidencemethodThe

minoritycarriergenerationdistributionplaysanImportantrole

intheanalysisofEBICVariousgenerationdistributionmodels

arecomparedwitheachotherunitingthedifferentdefinitionsof

theelectronrange(Iemaximumrangeandextraporatedrange)

InGaAsGaussiandistributionsproposedbyMakarovand

Wittryhavelargesurfaceconcentrationsandthepeaksofthe

distributionsexistatabout0130fthemaximumelectronrange

Kanaya゛Smodelhasevenlyspreadeddistributionowingtothe

assumptionoftheuniformconcentrationofthegeneratedelectron-

holepairsThevalueofLlargerthan5μmcannotbedetermined

definitelybecauseEBIChardlychangesevenifLvariesThe

estimatedLbytheMakarovrsquosmodelalmostagreeswiththatblsquoythe

WittryrsquosmodelbutEdeterminedbytheformeris10へj20ZrdquoPC

largerthanthatbythelatter

InSithepeaksofthegenerationcistributionbecome

deeperthanthoseinGaAsbecausethedensityofS11Sabouthalf

ofthatofGaAsThelargestvalueofLthatcanbedetermined

definitelybecomestwiceofthatofGaAsbecausetheelectronrange

inSiisabouttwiceofthatinGaAsTheestimatedLbythe

MakarovrsquosorWittryrsquosmodelisabout30Zsmallerthanthatbythe

Everhartrsquosmodel

IntheexperimentsinGaAstheestimatedLbytheMakarovrsquos

modelagreedwiththatbytheWittryrsquosmodelbuttheestimated

Epcbytheformerwas48eVandabout17Zlargerthanthatbythe

latter

-29-

References

[1]

[2]

[5]

WCzajaJApplPhys374236(1966)

JFBresserdquoScanningElectronMicroscopy71972partlrdquo

(iiTRiChicago111)p105

CJWuandDBWittryJApplPhys丘旦2827(1978)

KKanayaandSOkayamaJPhysDApplPhys

543(1972)-

口EPosslnandCGKirkpatrickJApplPhys

5^4033(1979)

[6]TEEverhartandPHHoffJApplPhys

425837(1971)

[10]

[11]

[12]

[13]

GDArchardJApplPhys竪91505(1961)

DBWittryandDFKyserJApplPhys28375(1967)

TSRao-SahibandDBWittryJApplPhys

403745(1969)

VVMakarovSovPhysSemicond旦722(1975)

jVonAEGruenZNaturforsch12aHeft289(1957)-

JCornuRSittigandWZimmermannISolid-stateElectron

TKobayashiTSugitニaMKoyamaandSTakayanagi

IEEETransNuclSciNS-19324(1972)-

-30-

3-1

DETERMINATIONOFDIFFUSIONLENGTHSURFACERECOMBINATION

VELOCITYANDELECTRON-HOLEPAIRCREATIONENERGYBYTHE

LINESCANMETHOD

Introduction

Anelectronbeaminducedcurrent(EBIC)methodisa

convenienttechniquetomeasuretheminoritycarrierdiffusion

lengtニhLandthesurfacerecombinationvelocitysinsemi-

conductingmaterialsInthelinescanmethodLandScanbe

determinedfromthedependenceofEBIConthescanningdistance

whentheelectronbeamisscannedacrossthebarrierBerzand

Kuiken[1]gaveadetailedtheoryforthedeterminationofLand

sandOpdorp[2]investigatedexperimentallytheinfluenceof

surfacerecombinationonEBICJastrzebskieta1[31measured

Landsfordifferentgenerationdepthsbyvaryingtheaccelera-

tingvoltageofanelectronbeam

Inthosestudiesthegenerationsourcewasassumedto

beapointbutinpracticetheregionexcitedbytheelectron

beamhasafinitevolumeChiandGatos[4]determinedthe

junctiondepthbyanEBICtechniqueassumingafinitegeneration

volumeCzaja[5]andBresse[6]measuredthephysicalparameters

suchasLandtheelectron-holepaircreationenergyEpC゛when

theelectronbeamwasdirectednormaltothebarrierplane

Sheaeta1[7]investigatedtheresolutionlimitsoftheEBIC

linescanmethodtheyobtainedaone-dimensionallateraldose

functionandappliedittothemeasurementofLintheCuxSCdS

systemHowevertheydidnotdiscusstheeffectofsurface

recombinationonEBICSincethesurfacerecombination1S

stronglyconnectedwiththedepthofgenerationathree-

-31-

Fig3-1

Schematicviewof

anddefinitionsofthe

-32-

experimentalconditionscoordinatesystems

Electronbeam

Surfacecross-sectic

O゛9χ

Schottky哨Rbarrier

dimensionalgenerationdistributionmustbetakenforthedetailed

analysisofEBIC[81

Inthischapterfirstlywediscussthesurfacerecombi-

nationeffectonEBICassumingapointsourceandthendescribe

theinfluenceofthegenerationvolumeonEBICinthelinescan

methodtakingaccountofsurfacerecombinationWehavestudied

EB工Ctheoreticallyforthefinitevolumesourcewhichisdependent

ontheacceleratingvoltageandshowanimprovedmethodfor

thedeterminationofphysicalparametersofsemiconducting

materialsbasedonexperimentalresultsobtainedinSi

3-2 Surfacerecombinationeffectconsideringpointsource

ForsimpletheoreticalconsiderationwetakeaSchottky

diodeAsshowninFig3-1theSchottkybarrier1Sinthey-z

planeTheelectronbeamisincidentperpendiculartothesample

surfaceandthescanningdirectionisalongtheχ-axiswhichis

normaltothebarrierplane

Thegenerationsourceisconsideredtobeapointata

distancexgfromthebarrierandatadepthdfromthesurface

correspondingtotheacceleratingvoltagevarsquoThepositionis

XS

ぐi g゛ O゛dg)Thesteadystateexcessminoritycarrierdistribution

obtainedfromthefollowingdiffusionequation

pDnabla2pdeg - -

g6(x-゜cg゛yrsquo2olinedg)rsquo (3-1)

whereDisthediffusionconstantて1sthelifetimeandgisthe

generationrateofelectron-holepairsWhen

thesampledimensionsareassumedtobesufficientlylarge

-33-

3ta3

Normalizedscanningdistancex

(a)

Fig3-2

Fig3-3

U』

Normalizedscanningdistancex

(b)

3193

p≫Zl≫E』oz

Normalizrdscanningdistanceχ

(c)

PrimeNormalizedEBICvsnormalizedscanningdistanceχcurvesfordifferentvaluesofthesurfacerecombination

velocityparameter(seetext)SNormalizedgenerationdepthDis0001and10in(a)(b)and(c)

respectively

Oino

tou

iSu一uojsn}|ipMzireujjoZ

SurfacerecombinationvelocityparameterS

EstimateddiffusionlengthL大directlyfromthe

slopesofthecurvesbetweenthepointsatχ=2and3

Svariesfromoneto50

-34-

Dg=10

Dg=QO

151050

112345

Og<ao

161

S>0

21

Idrsquo

S5

10^

550

1必12345

135

sc^-at

SO⑤

バ宍

1012345

112345

SPg≪10

161

162S=0

SI

1(i3

1(541235

comparedwiththediffusionlengththeboundaryconditionsare

並Sz

χ=0

z=O゛

spl

z=0

=0

χ=+(x)

=0

(atthesurface) (3-2a)

(attheSchottkybarrier)(3-2b)

(3-2c)

Oncethedistributionp1SknowntheEBICcanbefound

asfollows

トeリンint]キレ

o4バ2rsquo(3-3)

whereeisthechargeofanelectronThevalueofjwascalculated

二二二二二二二エフエム2こ二言

J=

-eg

丁T

4oo

int

Dg

馴D戸

exp(-S(T-

S(司7)-

dT} (3-4)

wherexL゛DgdegdgLrsquoS=s(Lて)andTIsthevariablefor

integrationThefunctiony可7)1sthesecond-modified

first-orderBesselfunctionTheEBICisnormalizedtobeunity

whenallthegeneratedcarrierscontributetoEBIC

-35-

177FΞ-一一permil

(ぷ71

y))二1supe≧rsquo

四F

InFigs3-2(a)(b)and(c)thelogarithmofJis

plottedvsX(ΞxL)basedoneq(3-4)overtherangeofO≦X≦5一一

forS=へj50ThevalueofDgis0001and10in(a)(b)

and(c)respectivelyForS=0theintegralineq(3-4)leads

toJ=exp(-X)whichyieldsstraightlinesasshown

inFig3-20ntheotherhandallcurvesforS>Odeviate

fromthestraightlineThesurfacerecombinationgivesmuch

effectontheexcesscarrierdistributionasthegenerationdepth

becomessha110WerWhenDgis00and01thevaluesoflogJ

decreasesuperlinearlyovertheinterval0fO≦χ≦2and--

almostニlinearlyovertherangeofx≧2WhenDis10the一琴

surfacerecombinationhasaslightinfluenceandthevaluesof

logJdecreasealmostlinearlyovertheinterval0fO≦X≦5__

HowevertheslopesshowsubstantialdeviationfromunityThe

estimatedvaluesofdiffusionlengthdirectlyfromtheslopes

ofthecurvesinthelinearlydecreasingregion2≦X≦3are--

putasL火andplottedagainstSinFig3-3forDgdeg00and10

工nordinarysemiconductorsSvariesfromlt050Overthis

rangeL大Isabout80t090ZoftニherealvalueL

WhenweevaluatetheaccuratevaluesofLandSwemust

fittheexperimenpoundaldatatothetheoreticalcurvesoverthe

wholerangeofO≦X≦5WecanestimateSbyfitting--

particularlyovertheIntervalofO≦X≦2becausetheeffect--

ofthesurfacerecombinationappearsremarkablyinthisInterval

-36-

3-3 Analysisofelectronbeaminducedcurrenttakingthree-

dimensionalgenerationdistributionintoaccount

Insect3-2theminoritycarrierdistributionisassumedto

beapointButinpracticethegenerationdistributionhasa

finitevolumeinconnectionwithvThegenerationdistributiona

mustbetakenintoaccountwhentheextentofthegeneration

distributioncannotbeignoredcomparedwithL

Electronpenetratニionintosolidmaterialshasbeenstudied

bymanyauthorsTheminoritycarriergenerationdistribution

alongthedepthwasdiscussedindetailinChapterHWittry

andKyser[9]assumedthedepthdosefunctiontobeaGaussian

distributionandobtainedgoodagreementwithexperiments

EverhartandHoff[10]assumedapolynomialfunctiontoexplain

theirexperimentalresultsintheAl-SiO2-SisystemdegInthose

studiesonlythedistributionalongthezaxiswasdiscussedso

thedistributionalongthexaxiswasnotconsideredSheaeta1

[7]definedthelateraldosefunctionalongthexaxisfrom

VonGrlinrsquos[11]databutdidnotdiscusstheinfluenceofsurface

recombinationindetailSincetheinfluenceofsurfacerecombi-

nationonEBICdependsonthedepthfromthesurfacewemust

takethedistributionofgeneratedminoritycarriersinthe

x゛zplaneWeusethemodifieddiffusionmodelofKanayaand

Okayama[12]Themodel1Sverysimplebutissufficientfor

thefirst-orderapproximationtニothethree-dimensional

generationdistributionAccordingtothemodeltheelectrons

penetratestraightintothematerialtothemaximumenergy

dissipationdepthandthenscatterequallyinalldirections

makingelectron-holepairsTheshapeofthegenerationregion

becomesaspherepartofwhichisabovethesurface

-37-

Fig3-4

Tab3-1

11-

Schematicviewofelectronpenetrationisthemaximumenergydissipationdepth

a(W)

00000

1CMCO<rm

d(ym)

rdquo047

149

291

in<yi

vDVO

4VO

R(um)

100

295

13

74

20

Valuesofthecenterdgofthegeneration

volumeandtheradiusRinSiforseveralvalues

ofacceleratingvoltagevarsquo

-38-

IElectronbeam

O335

S`」「fdegce

uarrで0559j

10゛」

helliphelliphelliphelliphellip

Thecenterdgofthesphere(iethemaximumenergydissipation

depth)andtheradiusRaredependentontheacceleratingvoltage

va゛b゛lttheratiodgRisassumedtobeaconstantasshownin

Fig3-4evenWhenvaisvariedThevaluesofdgandRinSi

forseveralvaluesofvaaregiveninTab3-1calculatedwith

theaidoftheequationsofKanayaandOkayama[121

Wedividethesemi-sphereintomanysegmentsoflength

lessthanLandrepresenteachsegmentbyonepointsource

Thedensityoftheelectron-holepairsisassumedtobeuniform

withinthespheretosimplifytheanalysisThenthegeneration

strengthgofeachpointsourceisgivenbytニhefollowing

relation

Σg=G(3-5)

whereGisthewholegenerationstニrengthandΣexpressesthe

totalsummationwithinthesemi-sphereundertニhesamplesurface

TheEBICforthefinitevolumesourceisderivedby

summimgupthesolutionoftニhediffusionequationforeachpoint

sourcewhichisexpressedbyeq(3-4)Whenthedistance

betweenthebarrierandtheIrradiatedpointxbecomessmallerg

thanRsomeofthepointsourcesareforcedoutofthediode

andcannotcontributetoEBICThustheEBICdecreasesnearthe

barrierplaneWecallthisphenomenonanedgeeffectTosimplfy

thecalculationweassumethattheEBICcontributedbythe

forced-outsourcesiszeroThisedgeeffectmustbetakeninto

accountwhenthegenerationvolumeislargeincomparisonwith

thediffusionlengthWeshowanexampleforL=8ymandS=20

Whenvais10kVtheradiusRissmallcomparedwithLand

thegenerationsourcecanbeassumedasapointThelogarithm

-39-

Fig3-5

Qコー

山11

pdznpoi」oz

1020

Scanningdistanceχ

NormalizedEBICversusscanningdistanceχ

forthefinitevolumesourceThediffusionlengthLis8lsquoUmandthesurfacerecombinationvelocityparameterS(seetext)is20TheacceleratingvoltageVais50タ30and10kVfromuppertolowersolidcurverespectivelyThedottedcurveisthepointsourcesolutionforVa=50kVandtニhedashedlineisthegradientthereciprocal0fwhichgivesL=8um

-40-

1020304050(p『

゛X5入L=8μm

゛χS=20

2rsquoχyχ

゜χ

ldquoゝ5rdquo-Re-くiprocalsk)

rsquox9vesL=8|jm

rdquoゝ

2rsquo゜χ`Va=50KV

2rsquoχ

lsquoχ

lsquoゝ

5degχ

rsquoχ

rsquoχ2χ

30≒3rsquo

11diPointsourcelsquo

5solutionfor

va=50KV10

1020304050(μΓΥ

ofEBICJisplottedwithafullcurveasafunctionofthe

scanningdistancexinFig3-5logJdecreasessuperlinearlyover

theinterval0≦X≦2L(ie16uminthiscase)anddecreases--

almostlinearlyovertherangex≧2LTheslopeintherange-

O≦x≦2LisInfluencedverymuchbysurfacerecombination一一

〇necanestimateSbyfittingtheexperimentaldatatothe

theoreticalcurveinthisrangedegWhenva1S300r50kVthe

radiusRbecomesofthesameorderasLandthegeneration

volumecannotbeassumedasapointThenwedividethesemi-

sphereintomanysegmentsoflym^Thecalculatedvaluesof

EBICusingthefinitevolumesourcemethodareshowninFig3-5

ThelogJvsXcurvesshowamaximumnearthebarrierplane(

Xdeg4and7μmatvadeg30and50kVrespectively)andlogJdecreases

almostlinearlybeyondthesemaximumpointsThemaximumvalue

ofJbecomessmallasvincreasesThesurfacerecombinationadoesnotaffecttheshapeofthecurvesandsoLcanbedetermined

mainlyfromtheslopeofthelinearregionofthesecurves

independentlyofsThereciprocalslopeofthislinearportion

gives7ymwhichis87Zoftherealdiffusionlength

ThevalueofEpc゛rsquobywhichanelectron-holepairis

createdcanbedeterminedfromtheabsolutevalueofEBIC[13]

ThevalueofJinthecaseofS=501sabout70Zofthatinthe

caseofSdeg1whenvais50kv゛andsowemakelargeerrorsinthe

determinationofEifwedonotconsiderthesurfacerecomblna-pc

tioneffect

Thepointsourcesolutionatva゛50kVisshowninFig3-5

bythedottedlinewhenthegenerationoccursatthemaximum

energydissipationdepth(ie67ymfromTab3-1)

Theslopeofthepointsourcesolutionovertherangex≧2LIs-

almostequaltothatofthevolumesourcesolutionbutthe

normalizedEBICis60Zofthatofthevolumesourcesolution

-41-

Fig3ldquo6

Chopping

こ011

Scanningcoil

Schematicdiagramoftheexperimentalset-up

-42-

コ4[Osc

lsquo~|-

|コt

||IElectronbeamReference

||

Sample

RL`Lock-inampχ-yrecorder

3-4 ExperimentalresultsinS1

Aschematicdiagramoftheexperimentalset-upisshown

inFig3-6Theacceleratingvoltage1Svariedfrom10t050kV

TheprimaryelectronbeamcurrentismeasuredbyaFaradaycage

andabout2times10oline10ATheinducedcurrentwasmeasuredfromthe

voltagedropacrosstheloadresistanceILdegThecurrentニIL

whichflowsthroughtheresistanceisexpressedasfollows

hdeg^sc-I{exp[(ekT)ILRL]-1} (3-6)

whereloisthebackwardsaturationcurrentand^scisthe

short-circuitcurrentwhichistherealEBICInordertoneglect

thesecondtermofeq(3-6)theEBICwasmeasuredinthefollowing

condition

h゛kTe (3-7)

InthepresentexperimenttheEB工Cwasmeasuredatroomtempera-

tureandso゛hhwaskeptlessthanlmvdeg

Theelectronbeamwaschoppedat3kHzwithachopping

coilinsertedintothebeampathSignalsassmallas1μVcould

bemeasuredwithagoodsignaltonoiseratiousingalock-in

amplifier

Thesamplesweren-typeSiwithresistivitypof10

and01ΩCm0hmiccontactsweremadebyevaporatingantimony-

dopedgoldontothesampleandalloyingat400degCfor2mln

Schottkycontactsweremadebyevaporatinggoldinavacuumas10W

as10oline7TorrThesamplewasinsertedintoavacuumchamberfor

EBICmeasurementimmediatelyafteritwascleavedandmeasured

-43-

3IS3

paziicuijoz

1020304050(pm)

Scanningdistancex

Fig3-7

Experimentalresultsfor

sampleA(p=lf2cin)whereL=

8μmandS=20Fullcurves

arethetheoreticalrsquoones

11(il

>P≪4<N1≪CM<Pq

1 1

3193paziipujjoZ

1164

50

Scanning

100

distance

Fig3-8

150

X(μm)

200

ExperimentalresultsforsampleB

(p=01f2cin)whereL=80urnandS=50

Fullcurvesarethetheoreticalones

Valueswithouttheinfluenceofan

ohmiccontニactareshownbydotted

curves

-44-

124(m)

5XExperimentalvaluesX---Va=50KV

2NNo30

1X一--10KV4

5しL=8pm

2χ

2χ

5χ

-Theoretical

5curve

41

50100150200

Experimentalvalues

--4=50Kv

lo―30KV

hellip-10KV

-ゝゝI゛゛゜゛ペヘヘ

helliphelliphelliphellipyhelliphelliphelliphellip

Theoreticalcurvehelliphelliphelliphellip9lsquorsquolsquo゜

Ldeg80μΓTlぶ

S=50

inavacuumas10was1times10oline8TorrTheresidualgasesonthe

cleavedsurfacewerecleanedbyargonionsputteringtoavoid

contaminationofthesurfacebyanirradiatニedelectronbeam

TheexperimentalresultsofsampleA(p=10ncm)are

showninFig3-7forva=1030and50kVrespectivelyEach

fullcurveisthetheoreticaloneforthecaseofL=8umandS=20

工fthediffusionconstantD1Stakenas16cm2Solinelthelifetime

てis4times10oline2μSandthesurfacerecombinationvelocitysis

4times105cmsolinelSurfacerecombinationhasagreatereffectasthe

generationdepthbecomesshallowerthatisVbecomeslower

AndsothevaluesofSandLcanbeestimatedmainlyfromthe

curvesforthelowestニandthehighestva(idege103゛d50kV

inthisexperiment)respectivelyTheexperimentalresultsfor

eachacceleratingvoltageagreeverywellwiththetheory

Theexperimentalcurvesforvadeg1030and50kVhaveamaximum

atxdeg02and4ymrespectivelyandeachmaximumvaluebecomes

smallerasvincreasesasdescribedinthetheoryHowevera

themaximumvalueandthepositionwheretheEBICshowsapeak

deviateslightlyfromthetheoryinthecasesofvadeg30and50kVdeg

Thisdiscrepancymaybeattributedtotheassumptionofuniform

densityofgenerationTheactualdistributionmaybelocalized

atthecenterofthegenerationvolume[9]andmoredetailed

treatmentforthegenerationshapeandthegenerationdensity

Isneeded

Inthecaseofthelocalizeddistributionofgeneration

wecanapplythesamemethodasdiscussedinsect3-3Ifthe

constantgischangedintoanappropriatevariablewhichexpresses

thelocalizeddistributionbetterresultswillbeobtained

HowevertheassumptionoftheunifoinndensityIssufficientfor

thequalitativeanalysisoftheInfluenceofthegenerationvolume

onEBIC

-45-

TheexperimentalresultsofsampleB(p=01ficm)are

indicatedinFig3-8inthesamewayassampleAThevalues

ofLandSare80ymand509respectivelyIfDis16cm2solinel

てis4ysandsis1)(105cmSoline11nthiscaseLisgreaterthan

thegenerationvolumeevenwhenvadeg50kVandthevolumesource

effectappearslessclearlythaninsampleAThediscrepancy

witニhintheinterval0<xく15urnisduetothesamereasonas

thatdiscussedInthecaseofsampleATheslopesofthecurves

overtherange15≦x≦100μmarelesssteepasvbecomes--a

higherbecausetheinfluenceofsurfacerecombinationdecreases

Theinfluenceofohmiccontactappearsovertherangex≧120μm-

sincethediffusionlengthisabouthalfofthesamplethickness

of200μmTheoreticalvaluescalculatedusingthemirror

imagemethod[14]discussedinChaptervareshownbyfull

curvesinFig3-8Valueswitニhoutニtheinfluenceofanohmic

contactarealsoshownbydottedcurves

Thescanningsurfacewasnotaffectedbyanelectronbeam

oftheorderof2times10oline10Abecausethesameresultwasobtained

forshallowexcitation(vadeg10kV)afterthesamplewasirradiated

for1hatV=10へ一50kVa

ThedepletionlayerwidthisnotbroughtIntoconsidera-

tionbecauseofitsnarrownesscomparedwiththescanningdistance

Theelectronbeamdiameterofabout50nminthisexperiment

1Snottakenintoaccountsinceitisverysmallincomparison

withthegenerationregionevenifvais10kvdeg

工fthebeamcurrentiskeptconstantthegeneration

densitydecreaseswithincreasingVbecausethegeneration

volumeincreasessuperlinearlywithvarsquo゜Whenthebeamcurrentis

2times10oline10Aandvais10kVtheexcessminoritycarrierdensity

-46-

atthegenerationpointisabout5times1014Cmoline3(themaximum

generationdensityinthisexperiment)followingthediscuss10n

inref[1]whichissmallerthanthemajoritycarrierdensity

1nthesamplesThereforethevalueofLismeasuredatthe

lowinjectlonlevel

3-5 Summary

Thegenerationvolumeofminoritycarriershasa

considerableeffectontheEBIClinescanprofilesespecially

whenItisequaltoorlargerthanthediffusionlengthWe

investigatedthedependenceofEBIConxforgeneralsurface

recombinationvelocityinthecaseofthefinitevolumesource

Whenvaislowandthegenerationdepthisshallow

surfacerecombinationhasalargeeffectonEBICWhenvaishigh

andthegeneratニiondepthisaslargeasthediffusionlengththe

generationregioncann0longerbeassumedasapointandthe

finitevolumesourceshouldbeusedintheanalysisThetheo-

reticalcalculationshowsthatsurfacerecombinationhasonlya

slighteffectontheshapeoflogJvsXcurvesbutaffectsthe

absolutevalueofJTheaccuratevaluesofLsandEshouldbepc

estimatedbyfittingtheexperimentaldatatothetheoretical

curvesforallacceleratingvoltagesExperimentalresultsinthe

measurementofLandSonS1Schottkydiodesshowedgoodagreement

withthetheoryatboth10Wandhighvadeg

TheexperimentalresultthatEBIChasamaximumnear

thebarrierplanewasexplainedqualitativelyusingthesimple

model0fthefinitevolumesourceItcouldnotbeexplainedby

thepointsourcesolutionFurtherinvestigationofthisedge

effectwillclarifythegenerationdistributionbyanelectronbeam

-47-

References

[1]

2]

31

[41

[7]

[8]

[9]

[10]

FBerzandHKKuikenSolid-stateElectron

437(1976)

19

CvanOpdorpPhilipsResRep_32192(1977)

LJastrzebskiJLagowskiandHCGatos

ApplPhysLett27537(1975)

JApplPhys481730(1977)

JYChiandHCGatosIEEETransElectronDev

ED-241366(1977)

WCzajaJApplPhys2Z^236(1966)

JFBresserdquoScanningElectronMicroscopy1972

Partlrdquo[SEM]nc工ITRIChicago)pp105-112

SpSheaLDPartニainandpJWarterrdquoScanning

ElectronMicroscopy1978Vol1rdquo(SEMIncAMFOrsquoHare)

pp435-444

GVSpivakGVSaparinandLFKomolova

rdquoScanningElectronMicroscopy1977rdquo(SEMInc

IITRIChicago)pp191-199

DBWittryandDFKyserJApplPhysj廻375

(1967)

TEEverhartandpHHoffJApplPhys

(1971)

-48-

42

-5837

[n] AEvonGriinZNaturforsch12a89(1957)

【12】KKanayaandSOkayamaJPhysDApplPhys

543(1972)

[13]CJWuandDBWlttryJApplPhys492827

(1978)

[1410vonROOSSolid-stateElectron111063(1978)

-49-

4-1

ANALYSISOFTHREE-DIMENSIONALGENERATIONDISTRIBUTION

BYTHECOMBINATIONOFTHENORMALINCIDENCEANDTHE

LINESCANMETHODS

Introduction

TheminoritycarrierdiffusionlengthLandthesurface

recombinationvelocityScanbedeterminedbyanEBICtechnique

withboththenormalincidenceandtニhelinescanmethodsusing

SEMasdiscussedinChapters皿andHITheminoritycarrier

generationdistributニionbyanelectronbeamplaysanimportant

roleintheanalysisofEBICWhenthedimensionofthegeneration

regioniscomparablewithorlargertニhanLthegenerationregion

cannotbeassumedasapointandthegenerationdistribution

mustbetakenintoaccount

Thegenerationdistributionbyanelectronbeamhasbeen

investigatedbyseveralauthorstheoretically[1]andexperimental-

1y[2-51Asregardstheone-dimensionaldistributionaGaussian

[2-3]orpolynomial[4]functionwasassumedforthedepthdose

functionandthecombinationofexponentialdecayfunctions[51

wasusedforthelateraldosefunctionInChapter工皿the

influenceofthethree-dimensionalgenerationdistributionon

EBICinthelinescanmethodswasstudiedassumingasimple

distribution(semisphere)withuniformminoritycarrierdensity

Ineachoftheseexperimentsonlyonemethodタeitherlinescan

ornomalincidencewastakenTheelectronpenetrationdepth

andthegenerationdistributiondifferedfromeachother

-50-

Schottky

barrier

Fig4-1

2P

Surfacecrosssection

「egion

Oneofthedividedsegments

Schematicviewofexperimentalconditionsandthedefinitionofthecoordinatesystem

-51-

Electronbeam

hottkySurfacecrossse

arrierOGene芯ion

Re゛region

Oneofthe

々dividedsegi

InthischapterwemeasuredEBICbyboththelinescan

andthenormalincidencemethodsinthesamesampleandclarified

thegenerationdistributionTheinfluenceofthethree-dimensional

generationdistributiononEBICisdiscussedassumingthatthe

electron-holepairsarelocalizedatニthecenterofthegeneration

regionTheexperimentニalresultsforGaAsSchottkydiodesare

alsoshown

4-2 Influenceofthree-dimensionalgenerationdistribution

onelectronbeaminducedcurrent

WeusedaSchottkydiodesinceitcanbeappliedforboth

thelinescanandthenormalincidencemethodsInthelinescan

methodtheEBICiscalculatedtakingtニhegenerationdistニrlbution

intoaccountbyasimilarmethoddiscussedinChapterⅡ工The

generationregionisdividedintomanysegmentsthesizeofwhich

issmallerthanLandeachsegmentisrepresentedbyonepoint

sourceTheEBICforthefinitevolumesourceisderivedby

summingupthesolutionofthediffusionequationforeachpoint

sourcersquo

Thedistributionisassumedtobesphericallysymmetric

asisshowninFig4-1Theelectron-holerdquopairsgeneratedbyan

electronbeanareconsideredtobelocalizedatthecenterRCof

thegenerationregionThegenerationstrengthgalonganyradius

vectorfromRc1Sassumedtobegivenby

gdeg^exp[-C(r2R2)] (4-1)

whereRisthedistancebetweenRandthemaximumelectronrange

CRm゛andristhedistancebetweenRCandeachdividedsegment

(seeFig4-1)

-52-

TheexponentCrelatestothedistributiondensityThedensity

becomesuniformasdiscussedinChapterl[EwhenC1Szeroand

theelectron-holepairslocalizenearRcwhenCbecomeslarge

Thedistributionisassumedinorderthatthedepthdosefunction

maybecomeGaussianasisreportedinthereferences[23]

ThevalueofLshouldbesmallinorderthatitcanbe

measuredbyboththelinescanandthenormalIncidencemethods

ThereforewetakeGaAsasanexampleInthelinescanmethodwe

calculatetheEBICintensity(whichiscalledthecollection

efficiencynandisnormalizedtobeunitywhenallthegenerated

carrierscontributetoEBIC)forseveralvaluesofCandR

The゛ilueofRmisgiven[2]by

町゜001A8Vノ゛フurn

cR

m゛

(4-2)

wherevaistheacceleratingvoltニageinkVThevaluesofCand

RRareassumedtobeconstantevenifvisvariedWhenvisCm

10and30kVaa

Rm

becomesOdeg74and4deg8ymrespectニivelyWetake

thetypicalvalueofLas1μminordertoexaminetheinfluence

ofthegenerationdistributiononEBICbecausethevalueofRm

issmallerthanLatva゛10kVbutlargerthanLatvadeg30kvrsquo

SincethesurfacerecombinationvelocitySofGaAsisoftheorder

of105-106cmSoline1[6-9]wetakevaluesofland50asthe

surfacerecombinationvelocityparameterSdefinedbySΞS(Lて)

(TisthelifetimeoforderofnS)

TheresultsofthecalculationareshowninFig4-2The

fullcurvesandthebrokencurvesareforCdeg8rsquo2゛RcRm゛Olsquo13and

C=54RR゜013respectivelyThesevaluesofCandRじmolinersquoCrsquom

thetypicalvaluesobtainedbythenormalincidencemethodin

GaAs[23]Thepointsourcesolutions(whichareobtainedby

assumingthatallthegenerationoccursatRc

-53-

are

)arealsoshownby

g`

A3U413Ud

COP≫no3

Fig4-2

ScanningdistanceX(pm)

j一次゜ごゴ野謡ごごご二ににごS

ご諧驚お謡謡S回読で昌翼麗

二竃Jeぎ驚謡じ雲Cにニごまふ(

ごごぶ謡1ば昌permilお穴混戮ずpermil

ぶぶごご1ここなSttedcdeges゛ecm

-54-

helliphellipl

]]1A

Ee

ビゲヤ

12

ss50

helliphelliphellipyJミ4sdeg50

dottedcurvesAtVa゛10kVthesizeofthedividedsegmentis

takenas005umwhichissmallerthanLsothateachdivided

segmentcanberepresentedbyonepointsourceIntheregion

05≦x≦15ymthelogarithmofEBICdecreasessuperlinearly--

anditdecreasesalmostlinearlyovertherangeofx≧15um-

ThetendencyappearsmoreapparentasSbecomeslargeThechange

oftheexponentCmakeslittledifferencetotheprofilesofthe

curvesTheabsolutevalueofnovertherangeofx≧05umis-

almostequaltothepointsourcesolutionwhenS1S1butbecomes

twicethatwhenSis50Thepeaksnearthebarrierareduetothe

edgeeffectasdescribedinChapterl工゛Atvadeg30kVthesizeof

thedividedsegmentistakenas02ymforthesamereasonas

Wit二hvadeg10kVThecurvesarequitedifferentfromthepointsource

solutionbothatS=1andS=50becausethedimensionsofthe

generationregionarelargeincomparisonwithLandthepoint

sourceassumptionisn0longervalidinthiscaseTheprofiles

ofthecurvesreflectthegeneratニiondistributionasoneseesthat

theprofilechangesifCvalsquotiesfrom54t082WhenSisvaried

fromlto50theprofiledoesnotchangeatthesameCvaluebutニ

ndecreasesbyabout30ZofthatofS=lItshouldbenotedthat

thesurfacerecombinationhasaninfluenceontheabsolutevalue

ofEBICevenifthevalueofRm(4deg8pm8tvadeg30kV)ismuch

greaterthanLThereforewecanevaluateLmainlyfromthe

slopeofthelinearregionat10Wvaconsideringthesurface

recombinationeffectandestimatethegenerationdistribution

fromtheprofilesofthecurvesinthecaseofhighva゛

-55-

Fig4-3

pasube

coipai

-O

Maximumelectronraり9eRm(μm)

AcceleratingvoltageVa(kv)

Experimentニalresultsofthenormalincidence

methodforthesampleA(SndopedGaAsn=62times1016

cm^L=03)Jm)andthesampleB(TedopedGaAs

ndeg80times1016cmoline3Ldeg07μm)Experimentalvaluesare

shownbycirclesThefullandbrokencurvesare

theoreticalcurvesforC=82RR=013andC=54

RcRmdeg013respectivelywdeg10cnmmandwddegOdeg151Jmdeg

-56-

12410oline

GaAsn(c「7i」

5A訟ばn

2ゝゝゝ

ゝゝ

ゝゝゝ

ゝゝゝrsquoL(pm)

1゛゛`ヽBO7J

yWヽ

5oline`olinersquo54013A03

≒旨

2φ

(52Schottkか

デ1テシフ)卜

1020304050

Theelectron-holepaircreationenergyEisobtained

fromthefollowingequation[101

n=ErdquordquoEBIC

pcIBvak(4-3)

whereIBisthebeamcurrentandkisthecorrectionfactorfor

theback-scatteredelectronsAsdescribedpreviouslythevalueof

nisinfluencedbySevenwhenVishighandsowemusttakeolinea`lsquorsquoolineolineolineolineolineolineolineolineolineolineoline

thesurfacerecombinationeffectintoaccountwhenweevaluateE

pc

4-3 Three-dimensionalgenerationdistributニioninGaAs

Thesameapparatusandthelock-intechniquewereused

asdescribedinsect3-4TheSchottkybarrierwasmadeonn-typeGaAs

wafersbyevaporatingAuofabout10nmthickinavacuumofabout

10rsquo7TorrTheohmiccontactwasobtainedbyevaporatingAu-Geand

alloyingat400degCfor2minThecarrierdensitynofeachsample

wasdeterminedbyc-vmeasurements

Theexperimentalresultsofthenormalincidencemethod

forthesampleA(Sndopedn=62times1016cmoline3)andthesampleB

(Tedopedn=80times1016cmoline3)areshowninFig4-3byfulland

opencirclesrespectivelyThevalueofvawaSvariedbetween5

and50kVTheEBICintensityincreasedlinearlywithIBwithin

therangeof1times10oline11≦IB≦-1times10oline9Awhenvawasfixed

whichsatisfiedthelowinjectionlevelconditionThecollection

efficiencynwascalculatedbythesamemethodreportedinref[10]

bychangi昭RcRmfrom01t0025andCfrom30to90

respectivelyThebestfitcurveswiththeexperimentalresults

wereobtainedInthecaseofL=03and07umforsamplesAandB

respectivelywhenRcRm゛O゛13andC=82wereusedThevaluesof

-57-

II

A3ua<3UduqjDaiion

ScanningdistanceX((jm)

Fig4-4

Experimentalresultsofthe

linescanmethodforthesampleA

[SndopedGaAsn=62times]016cmoline3)

Thefullandbrokencurvesare

ー い゛I

゛゛

ldquooU 5

Scanningdistancex(μm)

Fig4-5

ExperimentalresultニSofthe

linescanmetニhodforthesampleB

(TedopedGaAsn=80times1016cmoline3)

Thefullandbrokenlinesare

theoreticalcurvesforC=82RRtheoreticalcurvesforC=82R

=013andC=54RR=013cdeg=013andC=54RR=013c

respectivelyLdeg03cμmS゛20respectivelyLdeg07ymSdeg20

-58-

ぎ忌

五゛

olinelo

jV

ズごy

23

times1

GaAだj

j73C4Electron

L=07μmEbeam

2Sdeg20χ

1rsquo`

゛x

ya(W

2゛Va=30W

2_JE201

4一一―54013

5≒

脅χ

21`f

ゝ≒

ゝへ

5χ

147

RCRmandCagrees`゛iththerepoidegtedvalues[2]゜Thefulland

brokencurvesinthefigurearetheoreticalcurvesforC=82

RcRmdegOdeg13andC゛5deg4゛RcRmdegOlsquo13respectニivelylsquoThediscrepancy

betweenthetheoreticalcurvesandtheexperimentalvaluesat

10WvacanbeexplainedinthefollowingwaydegThegeneration

regionbecomesshallownearthesurfaceatlowVandtheEBIC

ismainlycontributedbytheseperatedelectron-holepairsin

thespace-chargeregionjustunderthesurfaceInthetheoretical

calculationitisassumedthatthere1Snorecombinationinthe

space-chargeregionButニinactualfactthecarriersrecomblne

throughthevarioustrapswhichreducestheEBIC

Theexperimentalresultsofthelinescanmethodforthe

samplesAandBareshownbycirclesinFigs4-4and4-5

respectivelyThetheoreticalcurvesareexpressedbythefull

(Cdeg82RcRmdeg013)andthebroken(C=54rsquoRcRmdegOdeg13)curves111

bothfiguresTheEBICintensityincreasedlinearlywithIBwitニhin

therange1times10oline11くrsquoIく1times10oline9Awhenvwasfixedat100r=B=a

30kVwhichsatisfiedthe10wInjectionlevelconditionasinthe

normalincidencemethodThetheoreticalcurvescalculatedusing

thesameparameterdeterminedbythenormalincidencemethodshow

goodagreementwiththeexperimentニalresultsatbothvadeg10and30

kVWhenwetakeintoaccountthattheexperimentalresultsat

vadeg30kVreflectthegenerationdistributiontheassumedgeneration

distributionbyeq(4-1)withC=5Aへ82andRcRmdegOdeg131s

consideredtobeappropriateforthethree-dimensionalgeneration

distributioninGaAs

Thevalueofkchangesfrom078to075whenvvariesa

from5t050kV[10]Whenwetaketheappropriatevalueofkfor

themeaSuredva゛Epccanbedeterminedbyeq(4-3)Thevaluesof

-59-

Normalincidence Line scan

V(kv)a

E(eV)GaAsCSndoped)pc

GaAs(Tedoped)

5-50

41

39

14

3 9

30

Tab4-1 Valuesoftheelectron-holepaircreationenergyEinGaAsdeterminedbytニhenormalincidenceandlinepc

scanmethods

-60-

Eobtainedbythenormalincidenceandthelinescanmethodsarepc

39Oi41eVand38へj44eVrespectivelyastabulatedin

Tab4-1BythenormalIncidencemethodWuandWittry[10]

determinedEpCas468eVwhichwasabout15Zlargerthanour

resultsOnereasonforthediscrepancy1Sthedifferenceofthe

generationdistributionsThemodifiedGaussiandistributionused

bythemslightlydifferedfromtheGaussiandistributionusedin

ouranalysisAnotニherreason1Stheaccuracyofmetalthickness

WeestimatethethicknessfromtheweightofthechargedAuwhich

1SevaporatedtomaketheSchottkybarrierThereforetニheobtained

valuemaybedifferentfromtherealthicknessInthelinescan

methodEBICbecomesinsensitivetothemetaltニhicknessandthe

trapsinthespace-chargeregionbutisinfluencedbysurface

recombinationasdiscussedbeforeAlferoveta1[11]andWittニry

andKyser[12]reportedEpcas32へj44eVand46eVrespectニive-

lyfromthepeakvalueofEBICwhentheelectronbeamcrossedthe

p-njunctionOurresultsof38へj44eVareinthemiddlerange

oft二heirvaluesIntheiranalysestheydidnottakethesurface

recombinationeffectintoaccountandsoourresultsareconsidered

tobemorereliablethantheirs

4-4 Summary

Thethree-dimensionalgenerationdistributionbyan

electronbeaminGaAswasinvestigatedbymeasuringEBICwitha

combinationofnormalincidenceandlinescanmethods

TheprofileoftheEBICcurvesinthelinescanmetニhod

expressesthegenerationdistributionwhenvaishighandthe

dimensionofthegenerationregionislargerthanLThesurface

-61-

recombinationdoesnotaffecttheprofileofEBICbutlowersthe

collectionefficiencyTheaccuratevalueoftheelectron-hole

paircreationenergymustbedeterminedbytakingthesurface

recombinationeffectintoaccount

TheexperimentalresultsinGaAsSchotニtkydiodeswith

differentdiffusionlengthsshowedthatthecenterofthe

generationregion(iethemaximumenergydissipationdepth)

waslocatedatthepointof0130fthemaximumelectronrange

andtheradialdistributionfromthecenterwasshowntobe

Gaussianwithaneχponentof54へ-82Theelectron-holepair

creationenergyinGaAswasdeterminedas38rsquoV44eV

References

[1]

[2]

[5]

[6]

KKanayaandSOkayamaJPhysDApplPhys

543(1972)

DBWittryandDFKyserJApplPhys旦旦375

(L967)

VVMakarovSovPhys-Semicond旦722(1975)

TEEverhartandpHHoffJApplPhysを

5837(1971)

SpSheaLDPartainandpJWarterrdquoScanning

ElectronMicroscopy71978V011uml(SEMIncAMFOrsquoHare)

pp435-444

LJastrzebskiHCGatosandJLagowski

JApplPhys481730(1977)

-62-

[7]

[81

[9]

[10]

[11]

[12]

LJastrzebskiJLagowskiandHCGatos

ApplPhysLettri537(1975)

MEttenbergHKresselandSLGilbert

JApplPhys44827(1973)

CAHoffmanKJarasiunasHJGerritsenand

AVNurmikkoApplPhysLett22536(1978)

CJWuandDBWlttryJApp1PhySpoundrsquo2827

(1978)

ZhIAlferovVMAndreevVIKorolrsquokovand

vIStreminSovPhys-Semlcond41113(1971)-

DBWittryandDFKyserJApplPhys

361387(1965)

-63-

5-1

ANALYSISOFELECTRONBEAMINDUCEDCURRENTCONSIDERING

SAMPLEDIMENSIONS

Introduction

Anelectronbeaminducedcurrent(EBIC)methodusing

ascanningelectronmicroscope(SEM)isaconvenienttechniqueto

measuretニheminoritycarrierdiffusionlengthLandthesurface

recombinationvelocitySinsemiconductorsTherehavebeenmany

theoreticalandexperimentalstudiesonthelinescanmethodof

EBICInChaptersI工andytheEBICwasanalyzedquantitatively

takingthethree-dimensionalgenerationdistributionintoaccount

bythedividingmethodandtheimprovedmethodtocharacterize

Landswassuggestedχihenthesampledimensionsarelessthan

oneortwodiffusionlengthstheminoritycarrierdistribution

isaffectedverymuchbysampledimensionsRoos[1]analyzed

EBICtheoreticallyinthecaseofthinlayersHecalculated

thedependenceofEBIConthescanningdistancexintherange

ofxL≪1inthesampleswithwL=land05(wlayerthickness)j

andshowedthatLcouldnotbedetermineddefinitelyfromthe

slopeofthelogarithmofEBICvsXcurve

InthischaptertoanalyzeEBICconsideringthesample

dimensionsgwediscussasimplemethodusinganimagesource-and-

sinkdistributionWeshowthedependenceofEBIConxoverafull

scanrangewhenthelengthbetweenapotニentialbarrierandan

ohmiccontactisequaltoandsmallerthanthediffusionlength

andmentionsomeimportantニpointstobenoticedinthedetermination

ofLandsTheexperimentalresultsinSiSchottkydiodesarealso

shown

-64-

Fig5-1

ySご

uarrj

Schottkybarrier

uarr

Ohmiccontact

Schematicviewofexperimentalconditionsanddefinitionofthecoordinatesystem

-65-

Electronbeam

-J-

レじ2「lingtrack_^一分

りhelliphelliphellipljc1お迄゛

IL

5-2 Determinationofdiffusionlengthandsurfacerecombination

velocity

ForsimpletheoreticalconsiderationwetakeaSchottky

barrierdiodeAsshowninFig5-1theSchottkybarrierisin

they-zplaneandtheelectronbeamisincidentニperpendicularto

thesamplesurface(χ-yplane)Thescanningdirectionisalong

theX-axiswhichisnormaltothebarrierplaneThegeneration

sourceisconsideredtobeapointニandislocatedat(゛grsquo

Thesteadystニateexcessminoritycarrierdistributionpis

obtainedfromthefollowingdiffusionequation

Dnabla2pdeg二T

-g6(x-xyz-d)rsquo

O゛dg)

(5-1)

whereDisthediffusionconstantンTisthelifetimeandgisthe

generationratニeofelectron-holepairs

工fthethicknesswbetweenthepotentialbarrierandthe

ohmiccontactismuchgreatニerthanLandtheotherboundariesin

theyandzdirectionsarebothmuchfurtherawayfromthe

generationsourceEBICiscalculatedunderthefollowingboundary

conditionsasdiscussedinsect3-2

3p-9z

χ=0

x=-H≫

Z=0

Z=0

=0(attheSchottkybarrier)

=0

wheresIsthesurfacerecombinationvelocity

-66-

(5-2a)

(5-2b)

(5-2c)

(5-4)d帽

wherexgrsquoLrsquoDgdegdLSdegs(Lて)andTisthevariablefor

-67-

integrationThevalueofJ(x)isnormalizedtobeunitywhena11

thegeneratedcarrierscontributetoEBICThefunctionK(ぺ7)

isthesecond-modifiedfirst-orderBesselfunction

FortheanalysisofEBICconsideringsampledimensions

wetakethefundamentalcasethatthediffusionlength1S

comparablewithorlargerthanthethicknessw(seeFig5-1)

OncethedistributionpisknownEBICcanbefoundasfollows

十(゛十(゜3p

j=eDintint-

0 -003χ

dydz

χ=0

(5-3)

whereeisthechargeofanelectronBerzeta1【2】solvedthe

diffusionequation(5-1)undertheboundaryconditions(5-2a)

(5-2b)and(5-2c)bythemirrorimagemethodInadditiontothe

reaLsourceatxg゛animagesinkwasintroducedatthesymmetric

position-XwithrespecttotheSchottkybarrier(seeFig5-2)

Whenthematerialextendstoχ=plusmndegdegthesolutionofeq(5-l)is

givenbypμ](゛゜土)゛WhentheSchottkybarrierisintroduced

theminoritycarrierdistribution1Sexpressedasp[x]十p[oline゛g]

inordertosatisfytheboundarycondition(5-2bplχ=OdegO)rsquo

andjisobtainedasfollows

J()゜

-eg-

-π

DgK(ぶ77F)

リinto

うと縦卜-dT

-H≫

十intexp(-S(T-D))

Dg

g ぜ)ケ

Thenonemustusethefollowingboundaryconditioninsteadof

(5-2c)

Ix=wdegO(attheohmiccontact) (5-2crsquo)

ThesolutionQfeq(5-1)undertheboundaryconditions(5-2a)

(5-2b)and(5-2crsquo)canbeobtainedbyextendingthemirrorimage

methodproposedbyBerz[2]andOpdorp[3]Inadditiontothereal

sourceatXafamilyofvirtuaLimagesourcesandsinksare

introducedatthesymmetricpositionswithrespecttothebarrier

andtheohmiccontact(seeFig5-2)Openandsolidcircles

representthesourcesandsinksrespectivelyThereforethe

sourcesareatX2w十Kg4W十xg゛゜rsquo゜lsquoand-(2w-x)-(4w-x)rdquoldquo゛

andthesinksareat-X-(2w十X)-(4w十X)and2゛゛olinersquo4゛olinersquo

respectivelyWhenthematerialextendstox=士≪>thesolution

ofeq(5-l)isgivenbyp【゛】(゛゜土゛grsquo士(2゛`7oline゛g)rsquo土(2W十)rdquorsquo゜rsquo)

(seeFig5-2)Iftニheinfluenceofohmiccontactニmustbetaken

intoaccounttheminoritycarrierdistributionisexpressedusing

thefollowinginfiniteseriesinordertosatisfytheboundary

conditions(5oline2brsquoplx=OdegO)811d(5oline2c≒Plx=wdegO)rsquo

p゛[゛g]゜jp[≒ 十p[oline

十p[2゛oline]十p[-(2W-X)

+p[2w十゛g]十p[-(2w十)

十一一一一一一-一一

9 (5-5)

Theinducedcurrentsbypairsofsourcesandsinksie

p[゛g]andp[oline゜cg]rsquop[2゛olineへ]andpr-(2w-x)]rsquop[2゛十]andp[-(2v゛十)]rsquo

areexpressedbyJ(x)-J(2v゛oline゜cg)J(2w十)゛rsquo゛゜゛rsquo

respectivelywiththeaidofeq(5-4)ThenthetotalEBICis

expressedintheinfiniteseriesasfollows

-68-

Fig5-2

Source

helliphelliphellipSink

Concentration

Sdηitky

barrier

Ohmic

contact

Schematicviewofexcessminoritycarrierconcentrationpatternforeachsourceandsinkwhicharerepresentedbytheopenandsolidcircles-respectively

-69-

pr2wχ9]

plE【2w->り》】1

1rdquoMI

-E唇-

゜(2WdegO`92Wi

ミplE)rsquo゛p[2w-xg]

pl-《2w+x)】)゜91

s哺

(n

L1)

paziipEJoz

1 2 3

Normalizedscanningdistancex

0 5

M)DUd|UOISコ|}Ppazneaijoz

12 5 X)2050

Fig5-3

DependenceofEBIConthe

normalizedscanningdistanceχ(equivxL)

fullandbrokencurvesarefortニhecaseswithandwithouttheinflu-

enceofohmiccontニactrespectivelyThenormalizedsamplewidthwLis

1020and30andthenormalized

generationdepthDgisOdeg0Thevaluesofthesurfacerecombination

velocityparameterS(seetext)

areland10forupperandlower

groupofcurvesIrespectively

Fig5-4

Estimateddiffusionlength

fromthereciprocalgradientof

thecurveatthecenteroftニhe

scanningdistanceinthecaseof

DgdegOlsquoOandwLdeg1lsquoOSvaries

fromlt050L大andL訟are

forthecaseswithoutandwith

theinfluenceofohmiccontact

respectively

SurfacerecombinationvelKitypmmeterS

-70-

Dgdeg00

そー=10

L゛で

ヽ1慟1

111

25=1rsquo1

1`11

【flll

11

51s

degilOII

211`4

111

(flll゛

芒゜11゛|`

51S`|

11゛1

|ぎ=21`ヽ

||rsquo゜3|

(y

J(Xg)=J(x)-J(2v゛oline゛g

olineJ(匈゛≒

)十J(2wトxg

)十J(4wヽ4-xg

----

II

(5-6)

ThevalueofJ大convergestoacertainvalueandcanbecalculated

byacomputerincasesofanyvaluesofwLandS

InFig5-3thelogarithmofJisplottedbysolidlines

asafunctionofx(=xL)whetvwL1S1020and30and

Dgis00Thedashedlinesareforthecasewithouttheinfluence

ofohmiccontactTheupperandlowercurvesareforS=1and10

respectivelyThevaluesoflogJ大decreasesuperlinearlywithin

onediffusionlengthawayfromthebarrierThereforeonemakes

considerableerrorsifoneestimatesthevalueofLfromthe

reciprocalgradientofthecurveatarbitraryXInordertoshow

anextremeexampleweconsiderthecaseofw7Ldeg1゛08叫DgdegO`Odeg

Thereciprocalgradientofthecurveinthelinearregionat

xdeg05withoutandwiththeinfluenceofohmiccontactareputas

L大andLrespectivelyThevaluesofLandL幼thuSobtained

areplottedasafunctionofSinFig5-4WhenSisunityL

1Sabout68ZofLandL政isabout44ZofLThevaluesofL大

andL政reducetoonlyaboutonethirdofLwhenSis50

Themethodoftheanalysisforapointsourcementioned

abovecanbeeasilyappliedtothefinitegenerationdistribution

bythedividingmethoddiscussedinChaptersI工andHEspecially

inthecasesoflight-emittingdiodes(LEDrsquos)andlaserdiodes

(LDrsquos)usingGaAsandGaPthedimensionofthegenerationregion

istheorderofymforva゛20へrsquo30kVandiscomparablewiththe

thicknessoftheepitaxiallayersThereforethedividingmethod

becomesaneffectivemeanstomeasureLandSintheepitaxial

layers

-71-

Fig5-5

Q‐rsquoQ]

loline

11(52

ち5

0 50Scanningdistancex

100

(pm)

jDependenceofEBIConthescanningdistancexforn-SiSchottkydiodesThelengthWbetweenthe

barrierandtheohmiccontactis100Umthe

acceleratingvoltageVais50kVandLis20へj200lim

SolidandbrokenlinesareforSdeg104and105cmsec

respectニivelytakingthegenerationdistributioninto

accountThediffusionconstantDofholesis125

cm^sec

-72-

n-SiVa=50kVw00μm

5aD=iZ5cm2ss(cms)

1-helliphellip104

2゛l`4-----helliphellip105

`L(μm)

1へ`a-2001

≒yyhelliphelliphellip100i

5゛゛ぐ丈i

へ゛`恥i

`ヽ

`lsquolブjl

ゝゝjφ1

0h白contactム

2rsquo

5-3 ApplicationtoS1

ThediffusionlengthintheSibulkmaterialusedfor

solarcellsorLS工゛S1Scomparablewiththedimensionsofeach

elementAndsotheminoritycarrierdistributionisaffected

verymuchbyelementdimensionsTheSchottkydiodewastakenfor

afundamentalmodeltorevealtheinfluenceofsampledimensions

CalculatedEBICrsquosbythedividingmethodinthecaseof

n-Siforwdeg100umandva゛50kvareshowninFig5-5Thediffusion

constantDofholesistakenasatypicalvalueof125cm^sec

Solidanddashedlinesareforsdeg101゛and105cmsecrespectively

andLis20010050and20umforthecurvesfromupperto

lowerineachgroupThegenerationsourceisassumedtobeasemi-

sphereThenumberofthegeneratedelectron-holepairsatany

pointinthesemi-sphereisproportionaltoexp(-40(rR)2)

(rthedistancebetweenthepointandthecenterdRthe

radiusofthesemi-sphere)Thegenerationdistribution1Sassumed

inorderthatthedepthdosefunctionalongthez-axlsagreeswith

thatproposedbyEverhart[4]andthevaluesofdgandRare

5ymand11ymrespectively゛forvadeg50kvrsquo

AsshowninFig5-5theabsolutevalueofEB工Cincreases

withdecreasingSforthesameLvalueThecurvesconvergetoa

certaincurveforboths=10rsquoand105cmsecwhenLbecomesgreater

thanwForconveniencethelogJvsχcurvesaredividedinto

threepartsi

range(30≦X-

く一一

eA)nearthebarrier(0≦x≦30ym)B)middle--

70ym)andC)neartheohmiccontact(70≦x≦100--

μm)IntheregionA)peaksappearatxdeg6ymowingtotheedge

effectdescribedinsect3-3and10gヽJdecreasessuperlinearlybecause

ofthesurfacerecombinationeffectIntheregionC)logj大decreases

-73-

Fig5-6

゜1(il

四a3

U」

-01

Ddziieujjoz

゛D=1Z5cm2s巡付

1 03

orini=-

にuarrヤuarr

uarrにヤ

Ohmiccontactづ50100

Scanningdistancex(μm)

JDependenceofEBIConthescanningdistancex

forn-SiwhenLismuchgreaterthanWThesolid

linesareresultsbythethree-dimensionalsolutions

forsdeg1035times1031045)(104and105cmsec

respectivelyThedashedlineisEBICbyone-

dimensionalapproximationV=50kVw=100ymand

L=1000Uma

-74-

゛ぐpermil

゛`xズit

darrレ

rapidlybecausetheohmiccontactisacarriersinkInthemiddle

rangeB)logJ大decreasesalmostlinearlyThereciprocalgradient

ofthecurveincreasesasLbecomeslargeintherangeofL≦100pm-

Thegradientsofthecurvesarenotsoaffectedbysurface

recombinationIfvisloweredt010kVthesurfacerecombinationa

affectsEB工Cmuchmorethanforvadeg50kVbecausethegeneration

depthbecomesshallowerInfactthegradientsofthecurvesin

regionA)aresteeperthanthoseforv=50kVforthesameLvaluesa

ThereforeinthecaseofL≦100ymLandscanbedetermined-

mainlyfromtheslopesofthelinearlydecreasingregionforhigh

va(50kVinthiswork)andthesuperlinearlydecreasingregionnear

theSchottkybarrierfor10Wva(10kVinthiswork)respectively

takingtheinfluenceofohmiccontactintoaccountButinthe

caseofL≧100ymthevalueofLcannotbedetニermineddefinitely-

becausetheslopeofthecurveinthelinearlydecreasingregion

doesnotchangeevenifLvaries

WhenLbecomesmuchlargerthanwthecurvesofEBICvsX

convergetoacertaincurveCalculatedEBICrsquosinthecaseofn-Si

forva゛50kVwdeg100ymandLdeg1000ymareshownbysolidlines

1nFig5-6forsdeg1035times1031045times104and105cmsec

respectivelyThegenerationsource1Sassumedtobeapointatthe

depthdThedashedlineisasolutionofone-dimensionalg

approximation(seeappenditimes1nthischapter)Theabsolutevalueof

EBICbecomeslargerwithdecreasingSandthecurveforS40cmsec

approachestothesolutionofone-dimensionalapproximationItcan

beexplainedasfollowsInthecaseofs=Ocmsecthereisno

carrierrecombinationatthesurfaceHencethematerialcanbe

consideredtoextendtoz=_oobyintroducinganimagesourceat

(x0-d)EBICisobtainedbyintegratingdpdxinthey-zplane

atx=0AndsotheEBICbythepointsourceat(x

-75-

grsquoO゛plusmnd)using

JOoline1

Ig3paziieuijoz

Fig5-7

(a)

UI「rrsquo

a3

U」

rsquo一lsquo51 0

pdziieujjoz

Scanningdistance

(b)

X(pm)

ExperimentalresultsinSiSchottkydiodesfor

w゛200μmand83μminfigures(a)and(b)respectively

Vais1030and50kVSolidanddottニedlinesare

theoreticalresultsforL=80UmandS=50withand

withouttheinfluenceofohmiccontニactrespectively

-76-

inlsquoSiL=80μm

こ沼o

rsquoバ町「i「でなl`Jes

l悶

2卜Ohmiccontact今|

トj

rsquohelliphelliphelliphelliphellipi

15

≒|

2helliphellip1

0Scanningdistancex150(pm)00

へn-SiL=80μm

5゜`S=50

deg゜w=83um

degムExperimentalvalues2deg`4≒Vi=50kV

I゛lsquorsquo4≒oVadeg30kV

≒゜rdquoVa≪10kV

丿4

lrsquo

2lsquoo1

rsquo゜i

2degi

2Ohmiccontactrarr

050100

thethree-dimensionaldiffusionequationbecomesidenticaltothat

derivedbyone-dimensionaldiffusionequationconsideringthe

planarsourceatxrsquoxginthey-zplane[5]Howeverinpractice

SihasafinitevalueofSandsothethree-dimensionalsolution

mustbeneededinthecaseofL>wThevalueofscanbedeter-

minedfromtheabsolutevalueofEBICfollowingthediscussionof

sect4-2usingtheelectron-holepaircreationenergyE^^byan

electronbeam

TheexperimentalresultsinSiSchottkydiodeswith

w=200umand83μmmadefromonewaferareshowninFigs5-7(a)

and5-7(b)respectivelySamplepreparationsandmeasurement

procedureshavebeenalreadyshowninsect3-4Theresultsofthe

theoreticalcalculationusingL=80vimandS=50forthreedifferent

va゛s(10rsquo30and50kV)areshownbysolidlinesinbothfigures

Theresultsofthetheoreticalcalculationwithouttheinfluence

ofohmiccontactareshownbydottedlinesinFig5-7

Inthecaseofw=200ymthesamplewidthisthreetニimeslargerthan

Landsotheslopeofthelinearregion(50≦x≦120um)isnot--

verychangedbytheinfluenceofohmiccontactInthecaseof

Wdeg83umthecurvesarequitedifferentfromthoseforw=200ym

andthereciprocalgradientofthecurvesinthemiddlerange

(25≦x≦55ym)givesL=20ymwhichisaquarterofthereal--

diffusionlengthBothinFigs5-7(a)and(b)theoretical

calculationsshowgoodagreementwiththeexperimentalresuLts

whichshowsthatthemethoddiscussedinsect5-21Saneffective

meanstニoanalyzetheeffectofsampledimensions

-77-

5-4 Summary

Theminoritycarrierdistributionisaffectedverymuch

bythelengthwbetweenapotentialbarrierandanohmiccontact

ifWisequaltoorshorterthanthediffusionlengthLThe

dependenceofEBICJ大onthescanningdistancexwasinvestigated

byextendingthemirrorimagemethod

InthecaseofwL≧1logJ゛decreasesalmostlinearly-

inthemiddlerangeofthescanningdistancebuttheestimated

diffusionlengthfromthecurvesismuchshorterthanthereal

diffusionlength(eg30t044ZinthecaseofL=w)The

valuesofLandScanbedeterminedmainlyfromtheslopesof

thecurvesforhighand10Wva゛reSpectively゛takingtheinfluence

ofohmiccontニactintoaccount

工nthecaseofwLく1theslopeofthelinearly

decreasingregionoflogJvsXcurvesdoesnotchangeevenif

LvariesThedependenceofEBIConχconvergestoacertaincurve

ThevalueofLcannotbedetermineddefinitelybutthevalueofS

canbeobtニainedfromtheabsolutevalueofEBIC

TheexperimentalresultsinSiSchottkydiodesagreed

fairlywellwiththetheorywhichshowedthattheextendedmirror

imagemethodwaseffectiveinanalyzingEBICconsideringthesample

dimensions

-78-

References

[1]

[2]

[5]

OldwigvonRoosSolid-stateElectron

(1978)

211063

FBerzandHKKuikenSolid-stateElectron19

(1976)

437

CvanOpdorpPhilipsResRep32192(1977)

TEEverhartandPHHoffJApplPhys丘5837

(1971)

WHHackettJrJApplPhys

Appendix0nedegdimensionalapproximation

431649(1972)-

IfthediffusionlengthLisinfinitelylongminority

carriersdonotrecomblneuntiltheyflowintothebarrierorthe

ohmiccontactThereforethediffusioncurrentdoesnotvary

spatiallyTheminoritycarrierdistributionpcanbeexpressed

asalinearfunctionofχ1nthecaseofone-dimensional

approximation工fthepointsourceg1Slocatedatdegcgrsquop(゜c)is

putasfollows

p(x)=ax十b(a>00≦゛≦)rsquo

p(x)゜c゛十d(c<0X≦゛≦゛)゜

(5-Al)

(5-A2)

Thefactorsabcanddcanbedeterminedfromthefollowing

conditions

-79-

p(O)=0

p(w)=0

卵石

-卜-卵匹 ゜g

(5-A3)

(5-A4)

(5-A5)

(5-A6)

Theeq(5-A5)showsthecontinuityconditionatxdegxg゛andtheeq

(5-A6)givesthatallthegeneratedcarriersflowintothe

Schottニkybarrierandtheohmiccontactニwithoutrecombinationin

materialsThesolutionp(x)becomesasfoLlows

p(x)=

p(x)=

(1-ミj1)x(O≦x

--^(w-x)(Kg

NormalizedEBICJisexpressedby

J大=

-egeD

dp

-dxχ=0

=1-

こ)

3Wく

一一

Xく一一

(5-A7)

(5-A8)

X』

-80-

(5-A9)

6-1

DETERMINATIONOFLIFETIMEANDDIFFUSIONCONSTANT

BYPHASESHIFTTECHNIQUE

Introduction

Accuratedeterminationoflifetimeてofminoritycarriers

1Sveryimportantincharactニerizingsemiconductingmaterials

Thevalueofてcanbemeasureddirectlyfromthetransientresponse

aftertheinjectionofminoritycarriersTheradiativerecombina-

tionlifetimewasmeasuredinGaPandGaAsfromthedecayofphoto-

luminescence[1]cathodoluminescence[2]orelectroluminescence[3]

Thephotoconductancedecaymethod[4]Isthemostcommonlyused

techniquetomeasurelifetimeincludingradiatニiveandnon-

radiativeprocessesInthesemethodsmeasurementofTinsmall

areaoftheorderofym^isverydifficultbecausethesample

surfacemustberelativelywideinordertoobtainasufficient

signalThespatialvariationofてcouldbedeterminedfromthe

decayoftheelectronbeaminducedcurrent(EBIC)usinga

scanningelectronmicroscope(SEM)[5-8]Thevalueofてismuch

influencedbysurfacerecombinationsincelightoranelectron

beamforexcitationentersthroughthesurface

Thevalueofてcanbeobtainedfromthediffusionlength

LusingtherelationL=j5マThevalueofLcanbedeterminedbythe

spectralresponsemethodusingsolarcells[910rbythesurface

photovoltaicmethod[1011nbothmethodstheaccurateabsorption

coefficientmustbeneededtodeterminethevalueofL

AsdiscussedinChapters皿rsquov^VtheEBICmethodusingSEMisa

veryconvenienttechniquetomeasureLinsmallareaoftheorder

-81-

ofym^andtherehavebeenmanytheoretical【11-14】and

experimental[15-16]worksuptodateInthemetニhodhowever

thediffusionconstantDmustbegiveninordertoobtainT

Whentheintensityofexcitationforelectron-holepair

generationisrdquomodulatedthephaseofluminescenceorinducedcurrent

isshiftedfromthatoftheexcitationsourcebecauseofthe

recombinationofinjectedminoritycarriersinamaterialThe

valueofてcanbedeterminedfromtheamountofthephaseshift

Hwang[17]obtainedTinGaAsfromthephaseshiftofphoto-

luminescenceInthemethodtニhephaseshiftisinfluencedbythe

surfacerecombinationvelocityandtheabsorptioncoefficient

whichaffectminoritycarrierdistributionverymuchReichleta1

measuredでinSi[18-20]andGaAs[21]usingthephaseshiftin

photニ0-inducedcurrentMunakata[22]andOthmer[23]measuredて

bythephaseshiftofEBICinGeandSirespectivelyTheyused

tニhesolutionoftheone-dimensionaLdiffusionequationwithout

anyconsiderationofthesurfacerecombinationeffect

Ifsuchaphaseshiftmethodiscombinedwiththe

conventニionallinescanmethodofEBIC(iemeasurementofLusing

DCelectronbeam)thelifetimeandthediffusionconstantof

minoritycarriersinsmallareacanbedeterminedsimultaneously

Kammeta1[241determinedてandDinSiTheymadeaSchottky

barrierwithasilverpaintonSisurfacesandmeasuredEB工Cby

scanningtheelectronbeamonthesurfaceparalleltothebarrier

InthatmethodsurfacepreparationhasmucheffectonT[25]

andtheconfigurationusedbythemisnotconvenientwhenone

measuresてandDinmaterialswithsmallLTheanalysisisvery

complicatedandRoospointedouterrorsintheiranalysis[26]

andsuggestedasimpleconfiguration[271

-82-

Inthischapterwetaketheconfigurationthatthe

electronbeamscansonthesurfaceperpendiculartothebarrier

planeWiththisconfigurationtニhetime-dependentdiffusion

equationcanbesimplyreducedtothesteady-statediffusion

equationandthecomplicationintheanalysisthatRoosindicated

[26]canbeexcludedThisphaseshiftmethodcanbeappliedto

materialswithsmallLWesolvethethree-dimensionaltime-

dependentdiffusionequationtakingthesurfacerecombination

effectintoaccountandclarifytherelationofTandthephase

shifttheoreticallyWeshowthatthree-dimensionalsolutions

canbeexpressedbyone-dimensionalsolutionswithempirical

correctionfactorsandthatてandDcanbedeterminedwitニhout

anyrestrictionformodulationfrequencyExperimentalresults

inSiarealsoshown

6-2 Relationbetweenlifetimeandphaseshift

WetakeaSchottkydiodeasshowninFig6-1for

simpletheoreticalcalculationWeassumeapointgeneration

sourcewhichhastime-variabLepartgelωt(ω゜2TTfωangular

frequencyfmodulationfrequency)at(x゛0d)Whenthetldegeoline

variablepartofthenumberofminoritycarriers1Sputas

恥eiωt(isacomplexvariable)psatisfiestheconventional

steady-statediffusionequationbyintroducingthecompleχ

effectivediffusionlengthL゛eff(ΞL゛1171瓦JTL=ぷF)゜If

thetime-variablepartofEBICIsputasj`゛e(J゛1Scomplex-

EBIC)icanbeexpressedasfollowsbythemirrorImagemethod

asdiscussedinsect3-2

-83-

Fig6-1

ylご

uarrj

Schottkybarrier

uarr

Ohmiccontact

Schematicviewofeχperimentalconditionsand

definitionoftheco-ordinatesystem

-84-

Electronbeam

SOlyScanningtrack_xj

ズニに匹二oline-一一゛

lsquo9surface

lL-__--ang__helliphellip_

|`1

丑昌之

9gπLaf ―K

gdof

(ノダr7olineT

)酉ff

L大effl゛ぶ弓+T『

+0O

(-1(じ(lg)

)X[

jiご]ご

)ことりsube

dgDIL火eff

xlてこi7

dT

J(6-1)

whereeisthechargeofanelectronsisthesurfacerecombination

velocityandTisthevariableforintegratニionThefunctionK^

1sthesecond-modifiedfirst-orderBesselfunctionwithcomplex

variablesTheabsolutevalueofEBICnandthephaseshiftφ

fromthesourcearegivenasfollows

TI=

|」と

eg

φ=tan-1

Im一J

Rej゛

(6-2)

(6-3)

whereReandImstandforrealandimaginarypartsrespectively

Thevalueofnisnormalizedtobeunitywhenallthevariable

-partgcontributetothevariablepartofEB工CSincej火isa

functionofてthevalueofφbecomesafunctionofてThevalues

ofnandφcanbecalculatednumericallyWeassumeapointsource

forsimplecalculationbutthemethodmentionedabovecanbeeasily

appliedtothefinitegenerationdistributionbythedividing

methoddescribedinChapters工江andy

-85-

Fig6-2

Fig6-3

U2

Cχ310-rsquo

山5

ト2

10lsquo3

velocitysis

35225N

(Eu

一))

j^

9st^d

10

Jo}CIで噌」

ひpF

ぐりぐ

ごヽこ

W゛`みノー-

うて`゜ldegw-rsquo゜rsquordquorsquoPrime゛ご

゜二

゛゜〆ノ〆゛`゜

゜゛〆ノ

(MJD≪p)j

UMS

asEMd

ofEBICvsscanning

thealmostlinear

0 50 100 150

ScanningdistanceX(pm)

Normalizedintensityandphaseshift

distancexcurvesTheconcavecurvesand

linesarefortheIntensity(leftaxis)andthephaseshift

(rightaxis)respectivelyThesolidbrokenanddottedlines

areforf=10100and500kHz(ieωT=031314and157)

respectivelyLifetimeTistakenas5μSThediffusion

constantDis30_cm2Secandthesurfacerecombination

105CmSeC

S=105CmS

D=30ori^s

Lifetimeで(sec)

DependenceofgradientofphaseshiftdφdxonTD=30cmsecandrsquos=105cmsec

-86-

rsquoD=30crrfis

ωで=5f

5ヽ2MHz

ヽ1MHz

2`500kHz

1`

100kHz

``50kHz

`ヽ`10khtt

pwww

kHz

`ωで=01

1(jrsquo

825

1(i

725

1(jrsquo

6251(irsquo

525

10lsquo4

Mm2s)lsquo1-123lsquoj「rsquoQ心Hz」t

=10cms-10a3i

i=30kV-一一一一1003K

helliphelliphelliphelliphellip500157

Thevaluesofnandφwerecalculatedasafunction

ofscanningdistanceχforp-SiasanexampleTheresultsare

showninFig6-2whenてisputasatypicalvalueof5μs

Inthefiguretheconcavecurvesandthealmostlinearlines

areforn-χandφ-xrelationsrespectivelyThesolid

brokenanddottedlinesareforf=10100and500kHz(ie

ωT=031314and157)respectivelyThediffusionconstant

Disputas30cm^secThesurfacerecombinationvelocitysIs

takenas105cmsecsincetheordinarysurfacerecombination

velocitニyofSiis103へj105cmsecTheacceleratingvoltage

Isputas30kVThepointsourceisassumedtobelocatedat

themaximumenergydissipationdepthofabout3μmunderthe

surfacebasedonKanayarsquosmodel[28]forelectron-holepair

generationdistributニIon

Inthecaseofωてく01tニhedependenceofnonX

agreeswiththat-measuredbyaconventionallinescanmethod

usingDCelectronbeamThevalueofLcanbedeterminedfrom

theslopeofthen-χcurvestakingthesurfacerecombination-

effectintoaccountasdiscussedinChaptermThevalueof

L大effalmoStequaltoLandSOφbecomesnearlyzero

Inthecaseofωて≧01φincreasesalmostlinearly-

withxovertherangeofx≧Landthegradientdφdxbecomes-

largewithIncreasingfasshownInFig6-2Thegradient

dφdxisfoundtoIncreaseasてbecomeslargeforthesamefvalue

andnottochangeevenifSvariesfrom10^t0105cmsecfrom

thecalculationforvariousparametersFigure6-3showsthe

dependenceofdφdχonTwhenfisvariedfrom5kHzto2MHz

ThevaluesofDandsare30cm^secand105cmsecrespectively

ForeachvalueoffdφdxincreasesmonotonouslywithTwithin

therangeof01≦ωて≦5andapproachestoacertainvalue--

asymptoticallyovertherangeofωて≧5-

-87-

「ujopp」)

調uiusas^qdj〇}c心石司」

Fig6-4

Lifetimeて (sec)

10

Expressionofthedependenceofdφdxonてusingtheapproximatedsolutionsoftheone-

dimensionaldiffusioneuationinthecaseofD=30cm^secandf=10sectHzSolidlineisa

three-dimensionalsolutionLines(A)and(B)

aretheapproximatedone-dimensionalsolutionsand(Arsquo)and(Brsquo)aretheasymntotesforthethree-dimensionalsolutionThecorrectionfactorCforthethree-dimensionalsolutionis087

-88-

2(8)登ニ4F

helliphellipj(Å

(A)

D(EI)-(jじ硲ゴどこ二こhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip

2helliphelliphelliphelliphelliphelliphelliphellip(畿f3゛(c緊八(醤y3

d≫_Kii「」(A)石rsquo7『

5Ddeg30cm2sfdeg105Hz

c=087

Ursquo725J625_-52542

Ifwetakethesolutionsoftheone-dimensionaldiffusion

equationdφdxisgivenasfollows[241

O「

dφ

dx

助こ

Lω

2D

一 一 S

irfr

一万

(ωて≪1)

(ωT≫1)

(6-4)

(6-5)

Followingthethree-dimensionalsolution(eqs(6-l)(6-2)and

(6-3))asshowninFig6-3ydφdxincreasesproportionallyt07

intherangeofωてく05andreachestoacertainvalueoverthe

rangeofωて>5whichcanbeeχplainedqualitativelybyeqS

(6-4)and(6-5)respectivelyThedφdxvsTcurvesinFig6-3

canberepresentedbyonefunctionwiththecombinationofthe

approximatedsolutionsoftheone-dimensionaldiffusionequation

(eqs(6-4)and(6-5))Weshowanexampleinthecaseoff=105Hz

andD=30cm^secinFig6-4Thesolidlineisthethree-

dimensionalsolutionfromFig6-3andthedottedlines(A)and

(B)expresseqs(6-4)and(6-5)respectivelyThebrokenlines

(Arsquo)and(B゛)showtheasymptoticsolutionsofthethree-

dimensionalsolutionintherangesofωて<05andωて>5The

absolutevaluesof(A)and(Brsquo)becomeabout87Zofthoseof

(A)and(B)basedontheresultsofcalculationAsshownin

Fig6-4thethree-dimensionalsolutionisgivenbyacombination

ofthelines(Arsquo)and(Brsquo)andIsexpressedasfollows

-89-

「―」)畠一

uiMSaseudpazneaijoz

Fig6-5

rsquo0

ω^t「

NormalizedphaseshiftニLdφdxvSωてcurves

Solidlineisathree-dimensionalsolution

expressedbytheapproximatedone-dimensional

solutionswithempiricalcorrectionfactors

Brokenlineistheone-dimensionalsolution

-90-

2One-dimensionalノrsquosolution゛`4xrsquo

10バ

5acuteThree-dimensional

ぶacutesolution

2acute

(yl

言二分ヽ同r〔2μ(ldquoμ

゛1)rsquo1

5primeacute

cべ1251251cap25

dφ

dx

)=(c

TTfr TTf)ldquo゛十(c

yでワ

)rsquo゛

-91-

十1}3

(6-6)

(6-フ)

函rsquo

wherenisapositiveintegerWecalculatedeq(6-6)Inthe

casesofn=1へj5anddeterminednas31norderthatthe

solidcurveinFig6-4canbewellrepresentedbyeq(6-6)

Thevalueofc1Sthecorrectionfactorforthethree-dimensional

solutionandcisabout087asmentニionedabove

Fromeq(6-6)wecanderivethefollowingrelation

usingtheconventionaldiffusionlengthL

_

=pound石{2Σ(則2万

ThetermLdφdxisconsideredtobethenormalizedphaseshift

whichistheamountofthephaseshiftwhentheelectronbeam

scansoveronediffusionlengthItshouldbenotedthatLdφdx

isafunctニionofonlyωでFigure6-5showsthedependenceof

LdφdxonωてbythesolidlineIfthevaluesofLanddφdxare-

knownてcanbedeterminedfromthecurveforanymodulation

frequencyandDisalsoobtainedbytherelationofL=iF

Themodulationfrequencyfcanbechosenfreelyandthe

restrictionsofωΥ<050Γωて>5fortheapproximatIonneednot

tobetakenintoaccount

ThephaseshiftderivedbyMcKelvey[29]usingtheone-

dimensionaldiffusionequationisshownbythedashedlinein

Fig6-5Theestimatedvalueofωてbytheone-dimensional

solutionisabout76へ87Zofthatbythethree-dimensional

solutionforeveryvalueofLdφdxInthecaseoftheone-

dimensionalsolutionLisdetermineddirectlyfromthegradient

ofthelinearlydecreasingregionofEBICcurveandisabout

60へj80Zoftherealvaluefromtheresultsofthedetailanalysis

takingthesurfacerecombinationeffectintoaccount[14]

ThereforethevalueofωΥderivedbytheone-dimensionalsolution

isonly30へJ丁0Zoftherealvaluebecauseωてdecreases

proportionallytOLandL2intheregionsofLdφdxく03and

Ldφdx>2respectivelyOnemustusethethree-dimensional

solutioninordertodeterminetheaccuratevalueofて

6-3 ExperimentalresultsinSi

AconventionalSEMwasusedfortheprimaryelectron

beamwhichwasmodulatedat1rsquoj50kHzwiththedutyof05by

achoppingcoilinsertedintothebeampathThebeamcurrentwas

as10was10oline10AThemaximumminoritycarrierdensityinthis

experimentwasconsideredtobeabout3times1014Cmoline3andthe10w

injectionconditionwassatisfiedTheinducedcurrentwas

measuredbythevoltagedropacrosstheloadresistancewhich

wasconnectedtotheSchottkybarrierwithanohmiccontactThe

signalhadarectangularwaveformowingtothechoppedprimary

electronbeamandsothefundamentalfrequencycomponentinthe

Fourierseriesofthesignalwasdetectedbyanauto-phaselock-

inamplifierTheEBICnandthephaseshiftφfromthesource

wererecordedsimultaneously

ThediffusionlengthLisdeterminedinthecaseof

ωて<01takingthesurfacerecombinationeffectintoaccount

Thedependenceofnonxagreeswiththatニmeasuredbyaconventional

linescanmethodusingDCelectronbeamasdiscussedinsect6-2

-92-

Whenvaislowgivingtheshallowgenerationdepthsurface

recombinationhasalargeeffectonEBICWhenvaishigh

givingthedeepgenerationdepththesurfacerecombinationeffect

1SreducedTheaccuratevalueofLcouldbedeterminedbyfitting

experimentaldatatotheoreticalcurvesforboth10wandhighva゛S

(10and50kVrespectivelyInthiswork)asshownInsect3-3

Thevalueofdφdxisobtainedatanappropriate

modulationfrequencywhichsatisfiesωて>01AthighVthe

surfacerecombinationeffectIsreducedandsowechosetニhe

highestva(30kVinthiswork)asfarastheelectronbeamcould

bechoppedOncethevaluesofLanddφdxareknownthevalues

ofてandDcanbedeterminedfromthecurveinFig6-5

Sampleswerep-andn-typeSiwithtニheresistivitypof

10and01f2cmrespectivelyOhmiccontactsweremadeby

evaporatinggallium-dopedgoldandantimony-dopedgoldontothe

p-andn-typesamplesrespectivelySchottkycontactsweremade

byevaporatingaluminiumandgoldontothep-andn-typesamples

respectivelyinavacuumas10was10oline7TorrThesampleswere

insertedintoavacuumchamberforEBICmeasurementimmediately

aftertheywerecleaved

ThediffusionlengthLinp-typeSiwasdeterminedas

130μmfromthen-xcurvesinthecaseofωてく01The

experimentalresultsofthephaseshiftmethodareshownIn

Fig6-6bysolidlinesforf=5102030and50kHzrespectively

ThephaseshiftIncreaseswithxalmostlinearlyasdescribedin

sect6-2ThevaluesofてweredeterminedusingFig6-5as9595

8886and83ysfromthegradientsofthelinesinFig6-6

for5102030and50kHzrespectivelyTheobtainedvaluesof

てshowlittledifferencewitheachotherinanymeasurement

-93-

11

es^Md

Fig6-6

P-Si(r=10ncm)f=

20

1 0一

----n-Si(r=Q1ftcm)

Va=30kV

圭T

rdquo

------ニr二ご二二耳一一3

50100

Scanningdistance

150

Experimental

methodinp-(p=10

200

(μm)

resultsofthephaseshift

Ωcm)andn-type(p=01ncm)Si

-94-

rdquoolinersquordquooline`rsquolsquorsquoolinerdquordquoolinersquo50kHz

Vadeg30kVZ

10deg

30

FJ゛

一一20

〆がノrdquo〆〆〆

メノrdquo

〆〆〆〆〆ノ10

---rdquordquo|-sニニニldquo-notこ9

conditionfromωて=03(atf=5kHz)to30(atf=50kHz)

Itprovedthatthemodulationfrequencycouldbechosenfreelyas

mentionedinsect6-2Ifwetaketheaveragedvalueofて(ie

で89ys)thediffusionconstantDofelectronswasdeterminedas

19cra^secwhichalmostagreedwiththereportedvalue[301The

slightdeviationfromthestraightlineforf=50kHzmaycomefrom

unstablenessofthechoppedbeambecausethechoppingcoilused

inourexperimentwasnotdesignedforhighfrequencymodulation

above50kHz

Thediffusionlengthinn-SiwasobtainedasL=80ymand

thephaseshiftsareshowninFig6-6bybrokenlinesforf=3

10920and50kHzrespectivelyThedeterminedvaluesofてfrom

thegradientsofthelineswere889292and105usfor

fdeg3s1020and50kHzrespectivelyThevaluesofTalmost

equalwitheachotherasinthecaseofp-SiIfwetakethe

averagedvalueofT(ieで=94ps)tニhediffusionconstantD

ofholesbecomes7cm^secwhichalsoagreeswithtニhereported

value[301

Thegenerationdistributionisconsideredtobeasemi-

spheretheradiusofwhichisabout6ymatニvadeg30kVusingthe

Kanayarsquosmodel[28]Thedimensionsofgenerationdistribution

aresufficientlysmallincomparisonwiththediffusionlengthof

thesamplesThereforethepointsourceassumptioninthe

analysisisreasonable

-95-

6-4 Summary

Whentheintensitymodulatedelectronbeamisusedthe

phaseofinducedcurrent(EBIC)isshiftedfromthatofexcitation

sourcebecauseoftherecombinationinmaterialsWesolvedthe

three-dimensionaltime-dependentdiffusionequationtakingthe

surfacerecombinationeffectintoaccountandclarifiedthe

relationofてandthephaseshiftφtheoretically

Inthecaseofωて≧01φincreasesalmostlinearlywith-

Xovertherangeofx≧LThegradientdφdxbecomesafunction-

ofTandisnotaffectedbysurfacerecombinationTherelation

ofdφdxonてwasfoundtobeexpressedusingtheapproximated

solutionsoftheone-dimensionaldiffusionequatニionwithtニhe

empiricalcorrectionfactorsThenormalizedphaseshiftLdφdx

becomesafunctionofonlyωてIfthevaluesofLanddφdxare

knownてandDaredeterminedwiththeaidofLdφdxvsU3てcurve

withoutanyrestrictionformodulationfrequencyTheestimated

valueofてbytheone-dimensionalsolutionswithoutニthecorrection

factorsisonly30へノ70Zoftherealvaluederivedbythethree-

dimensionalsolution

Experimentalresultsinp-andn-typeSiSchottkydiodes

showedgoodagreementwiththetheoryandtheminoritycarrier

diffusionconstantsofelectronsandholesweredeterminedas

19and7cm^secrespectively

-96-

References

[11

[2]

[31

[4]

5]

6]

[10]

[11]

[12]

[13]

[14]

[15]

PDDapkusWHHackettJr0GLorimorandRZ

BachrachJApplPhys^54920(1974)

MBoulouandDBoisJApplPhysj旦4713(1977)

MEttenbergHKresselandSLGilbertJAppLPhys

44827(1973)

SWangrdquoSolid-stateElectronicsrdquo(McGraw一HillInc

1966)p300

WZimmermannphysstatsol(a)12671(1972)

DRHunterDHPaχmanMBurgessandGRBooker

rdquoScanningElectronMicroscopySystemsandApplications

1973rdquo(工nstPhysLondon)pp208-213

HKKuikenSolid-stateElectron19447(1976)-

AJakubowiczSolid-stateElectron22635(1980)

HTWeaverandRDNasbySolid-stateElectron

22687(1979)-

DLLileandNMDavisSolid-stateElectron

18699(1975)-

WvanRoosbroeckJApplPhys2plusmn380(1955)

WHHackettJr=JApplPhyspound1649(1972)

FBerzandHKKuikenSolid-stateElectron

19437(1976)

CvanOpdorpPhilipsResRept22192(1977)

DBWittryandDFKyserJApplPhys261387

(1965)

-97-

[16] CvanOpdorpRCPetersandMKlerkApplPhysLett

2h_125(1974)

[17]CJHwangJApplPhys4^4408(1971)

[18]

[19]

HReichlandHBerntSolid-stateElectron

18453(1975)

GSchwabHBerntandHReichlSolid-stateElectron

2091(1977)

[201JMiillerHBerntandHReichlSolid-stateElectron

21999(1978)

[211

[22]

JMiillerHReichlandHBerntSolid-stateElectron

22257(1979)

CMunakataandTEEverhartJpnJApplPhys

11913(1972)-

[23]SOthmerrdquoScanningElectronMicroscopy1978Vol1uml

(SEMIncOrsquoHare111)p727

[24] JDKaiiraiandHBerntSolid-stateElectron

21957(1978)-

【25】JDKammrdquoSemiconductorSilicon1977uml(The

ElectrochemicalSociety工nc)p491

[26] 0vonRoosSolid-stateElectron23177(1980)

[27]0vonRoosJApplPhys1^3738(1979)

[28]KKanayaandSOkayamaJPhysDApplPhys

543(1972)

[29]JpMckelveyrdquoSolidStateandSemiconductorPhysicsrdquo

(HarperandRowNewYork1966)pp439-440

[30]HFWolfrdquoSiliconSemiconductorDatardquo(Pergamon

PresslnC1969)

-98-

ⅥI

7-1

HEATTREATMENTEFFECTONDIFFUSIONLENGTHINS1

Introduction

Therehavebeenmanystudies[1]onthepropertiesofthe

processinducedfaults(PIFrsquos)Thedegradationoftheelectrical

performanceofthedeviceshasmuchconnectionwiththesegregated

impuritiesatPIFrsquosorthedecoratedfaultsofeachPIFRecently

thefaultproducedespeciallybytheoxidationathightemperatures

(IesocalledoxidationInducedstackingfault(OSF))has

receivedconsiderableattention[2-5]becausetheoxidationisa

fundamentalprocessinmakingLS工rsquosorcharge-coupleddevices(

CCDrsquos)Ravieta1[67]showedthattheelectricallyactive

OSF゛sincreasedtheleakagecurrentinprsquonjunctionsKimerllng[8]

determinedtheenergylevelofthefaultsfromtheelectron

beaminducedcurrent(EBIC)measurementsatvarioustemperatures

Generallythefaultsbecomerecombinationcentersanddecrease

thelifetimeandthediffusionlengthofminoritycarriers

Shimizu[9]showedthatthelifetimecouldbecontrolledpreferably

bytheintrinsicgetteringusingOSFrsquosRozgonyi[10]and

Tanikawa[11]reportedthattherelaxationtimeofMOScapacitors

decreasedasthedensityofOSFincreasedButtherehavebeen

alittlestudyonthequantitativeinformationofthedecreaseof

thediffusionlengthaftertheoxidationprocessathightemperatures

Inthischapterwemeasuredthechangesofthediffusion

lengthbyEBICmethodaftertheheattreatmentsathightemperature

andshowedthattheheattreatmentforafewminutescouldaffectthe

diffusionlengthatthesurfaceregionTheobservationofsurface

faultsbychemicaletchingwerealsoshown

-99-

(―)

<j)6udI

ColコこI()

Fig7-1

Heattreatmenttimet(min)

Diffusionlengthaftertheheattreatments

forvarioustimelengthsrangingfromlt0120minutesat1000degCOpenandsolidcirclesare

forthecasesindry02andArrespectivelyOriginaldiffusionlengthbeforeannealingis80pm

-100-

5ohellipumlindryO2

uml゜umlinArat1000degC

ol

12510251002

- W ゝ

rsquo _ l - ~ ヽ jS j - -

磨 卜

Fig7-2

(a)

(c)

rarr100Mm

ぶミ

卜`

r-^

rsquo

1Is

≪バ

rdquorsquo‐゛t

rsquo

grバ4≪

rsquo1

Surfacefaultsrevealedby

usingSirtletchantSamples(a)

wereannealedindryoat1000

and120minutesrespectively

-101-

い゛フバrdquo

゛para

`i

(b)

(d)

permilご}

->嗜

-゛

rsquo

III

`ヽご

いい

一J

t七

~貿で

rsquo

゛`1

鴫ヽ

rsquoq

-≪

ゝく

chemicaletching

(b)(c)and(d)

Cfor0830

一 一

- 一 一 -一 一

7-2

Experimentalresultsanddiscussions

Samplesaren-tニypeSigrownbyczmethodTheoriginal

resistivitybeforeannealingisaboutニ01ΩcmTheheattニreatment

wasdoneat1000degCintheflowofdry02andArrespectivelydeg

ThenthesampleswererinsedinHFforlmintoremovetheoxidized

layerandgoldwasevaporatedinordertomakeaSchottkybarrier

forEBICmeasurementsTheproceduresofthedeterminatニionofthe

diffusionlengthhavealreadybeendiscussedinChaptersmandでIV

Figure7-1showsthediffusionlengthaftertheheat

treatmentThetimetoftheheattreatmentwaschangedfromlto

120minutesTheopenandsolidcirclesareforthecaseIndryO2

andArrespectivelyTheoriginalvalueofdiffusionlengthis

80μmThediffusionlengthdecreasedtoabout7μmrapidlyas

tincreasedt05minandbecamealmostconstantovertherange

oft>5mlnThediffusionlengthdecreasedslightlymorerapidly

in02tニhaninArThelifetimechangedfrom5μsto003usif

thediffusionconstantofminoritycarrierswastakenasatypical

valueof125cmsecThesurfacefaultsofthesamplesannealed

indry02areSho゛linFigsdeg7-2(a)(b)(c)and(d)forlsquot゛

0830and120minrespectivelyThesampleswereetニchedby

SirtletchantforthesametimeThenumberoffaultsdidnotニ

increaseuntilt=8minbutbecameverylargeattdeg120min

ThesameresultwasobtainedforthesamplesannealedinAr

Itshouldbenotedthatthenumberoffaultsdidnotニchangedinthe

rangeofO≦t≦8minbutthediffusionlengthdecreasedrapidly--

inthesamerangeThelengthsbetweenthefaultsareverylarge

incomparisonwiththediffusionlengthinthesamplesannealed

for1くtく8minandsothediffusionlengthisconsidered

nottoberestrictedbytheaverageintervalbetweenthefaults

whenthefaultsareconsideredtobethecarriersink

-102-

TheuniformEBICwasobtainedwhentheelectニronbeamwasscanned

onthesurfacethroughtheSchottkybarrtersandthedarkpoints

correspondingtothefaultswerenotobserved

Therapiddecreaseofthediffusionlengthwasconsidered

tobecausedbytheformatonofnucleioffaultsattheearly

stageoftheheattreatmentTheverysmallnucleicanbecomethe

recombinationcenterseveniftheycannotberevealedbychemical

etchingIftheheattreatmenttimeissufficientlylongthe

nucleibecomelargeandcanberevealedbyetchingAsshownin

Fig7-2(d)thelengthbetweenthefaultsafterlongtimeheat

treatmentisthesameorderofthediffusionlengthTheformation

ofnucleiwasnotaffectedverymuchbytheoxidationbecausethe

decreaseofthediffusionlengthwasalsoobservedintheheat

treatmentinArAsisknowngenerallytheczgrownSIcontains

oversaturatedoxygenandtheformationofnucleiisrelatedtニO

theoxygenprecipitation[12]Thediffusionlengthdecreasedless

rapidlyinArthaninO2degOnereasonofthisphenomenonisconsidered

tobetheformationofSiOAnotherreasonistheoutdiffusion

ofoxygenbecauseoxygencanoutdiffusemorerapidlyinArthan

inO2degFurtherinvestigationmustbeneededfortheclarification

ofthenucleiformation

Inconclusionthediffusionlengthatthesurfaceregion

inSidecreasedtoabout10Zoftheoriginalvalueafterthevery

shortheattreatmentat1000degCforafewminutesNevertheless

thesurfacefaultsrevealedbychemicaletchingdidnotchange

Thenucleioffaultswereconsideredtobeformedattheearly

stageofheattreatmentandtheybecameminoritycarrier

recombinationcentersThedecreaseofthediffusionlengthwasnot

soaffectedbytheambientgases(ieoxygenorinertone)Much

attentionmustbepayedintheheattreatmentprocessathigh

temperatureevenifthetimeIsveryshort

-103-

i J I

References

[1]

21

31

71

81

[91

[10]

[n]

[12]

HFoilNGoreleandB0KolbesetirdquoSemiconductor

Silicon1977rdquo(JElectrochemicalSocietyInc

Prircetion1977)pp565-574

DJDThomasphysstatso1旦2261(1963)

CMMelliar-SmithrdquoCrystalcefectsinsiliconintegratニed

circuits-TheircauseandeffectrdquoinrdquoTreatieson

MaterialScienceandTechnologyrdquovol11(AcademicPress

NewYork1977)

KVRaviandCJVarkerJApplPhys45263(1974)

SMHuJApplPhys513666(1980)

KVRaviCJVarkerandCEVolk

JElectrochemSoc120533(1973)-

CJVarkerandKVRaviJApplPhys亘272(1974)

LCKlmerlingHJLeamyandJRPatel

ApplPhysLett30217(1977)

HShimizuAYoshinakaandYSuglta

JpnJApplPhys17767(1978)

GARozgonyiandRAKushner

JElectrochemSoc123570(1976)-

KTanikawaYItoandHSei

ApplPhysLett28285(1976)

JRPatelrdquoSemiconductorSilicon1977rdquo(The

ElectrochemicalSocietyIncPrinceton1977)

pp521-545

-104-

ⅧI CONCLUSIONS

InthepresentstudyEBICwasanalyzedquantitativelyby

solvingthesteady-stateortime-dependentthree-dimensional

diffusionequationsTheinfluenceofthefinitegenerationvolume

onEBICwasdiscussedandanImprovedmethodtocharacterize

thephysicalpropertiesinthesmallselectedareasofsemiconduc-

torswassuggestedTheobtニainedresultswereasfollows

InChapterHtheshortdiffusionlengthoftheorderof

ymcouldbedeterminedbythenormalincidencemethodofEBIC

Variousmodelsforgenerationdistributionusedintheanalysis

yieldedtheambiguityforthedeterminationofthediffusionlength

andtheelectron-holepaircreationenergybyanelectronbeam

Detailedinformationonthegenerationdistributionmustbe

necessarytoanalyzeEBICaccurately

InChaptニermthegenerationvolumeofminoritycarriers

hadrsquoaconsiderableeffectonEBICinthelinescanmethod

especiallywhenthedimensionsofthegenerationvolumewasequal

toorlargerthanthediffusionlengthWhentheaccelerating

voltagewaslowandsothegenerationdepthwasshallow

surfacerecombinationhadalargeeffectonEBICWhereaswhen

theacceleratingvoltagewashighandsothegenerationdepth

wasaslargeasthediffusionlengthsurfacerecombinationhad

aslighteffectonEBICTheaccuratevaluesofphysicalparameters

suchasthediffusionlengthshouldbedeterminedbyfittingthe

experimentaldatatothetニheoreticalcurvesforalltheaccelerating

voltagesTheexistenceofamaximuminEBICnearthebarriercould

beexplainedbythersquoedgeeffectrsquoattributedtothefinite

generationvolume

-105-

InChapter】5inthelinescanmethodthedependence

ofEBIConthescanningdistancerepresentedmainlythelateral

extentofthegenerationdistributionwhentheacceleratingvoltage

washighandwhenthedimensionsofthegeneratニionregionwere

largerthanthediffusionlengthThethree-dimensionalgeneration

distributionbasedupontheexperimentalresultsforthenormal

incidencecouldexplaintheexperimentalresultsofthelinescan

methodInGaAsthecenterofthegeneratニionregionwaslocated

atthepointof0130fthemaximumelectronrangeandthe

radialdistributionfromthecentニerwasshowntobeGaussianwith

anexponentニof54Q82Thevaluesof38へj44eVfortheelectron-

holepaircreationenergybyanelectronbeamwasobtainedtaking

thesurfacerecombinationeffectintニoaccount

InChapterVinthelinescanmethodtheminoritycarrier

distributionwasaffectedverymuchbyanohmiccontactwhenthe

lengthwbetweenthepotentialbarrierandtheohmiccontactwas

lessthanoneortwodiffusionlengthsTheslopeofthecurveof

EBICvsscanningdistancedidnotchangeevenwhentニhediffusion

lengthvariedandthediffusionlengthcouldnotbedetermined

definitelyfromtheslopeofthecurveTheabsolutevalueof

EBICwasdependentonthesurfacerecombinatニionvelocityand

thelengthW

InChapterⅥ[thephaseshiftbetweenthemodulated

electronbeamandEBICwasclarifiedbysolvingthethree-

dimensionaltime-dependentdiffusionequationTherelation

betweenthephaseshiftandthelifetimewasfoundtobeexpressed

usingtheapproximatedsolutionsoftheone-dimensionaldiffusion

equationwithempiricalcorrectionfactorsThelifetimeandthe

diffusionconstantofminoritycarrierscouldbedetermined

definitelywithoutanyrestrictionformodulationfrequency

-106-

InChapterVIIthediffusionlengthinthesurfaceregion

ofSiwasfoundtobedecreasedverymuchafterheattreatment

at1000degCforonlyafewminutesneverthelesssurfacefaults

revealedbychemicaletchingwerenotincreasedThenuclei

ofthefaultsmightbeformedattheearlystageofheattreatment

ThisinvestigationprovedthatEBICcouldbeanalyzed

quantitativelyinthesmallselectedareaconsideringthethree-

dimensionalgenerationdistributionbyanelectronbeamBut

thereexistsomepointstobestudiedfurtherasfollows

FirstbyEBICmethodthetotニalrecombinationlifetimeincluding

bothradiativeandnon-radiativeprocessescanbemeasuredBut

onecannotobservetheradiativerecombinatニionlifetimealone

whichIstheimportantparametニertocharacterizethellght-emittニing

diodesorlaserdiodes[1]Deeperunderstandingcanbeacquired

byinvestigatingtheluminescenceemitニtedbyrecombinationof

generatedelectron-holepairs(iecathodoluminescence)[23]

SecondlyEBICtechniquecannotrevealtheenergylevelsand

densitiesofimpuritiesandtrapsaccuratelywhichaffectthe

electricalpropertiesofmaterialsverymuchTherehavebeena

fewreports[4]todeterminetheenergylevelsoffaultsinSi

fromEBICmeasurementsatvarioustemperaturesButthe

experimentalaccuracyofEBICtニechnlqueisinferiortothat

ofthephotoluminescence[5]orthecapacitance[67]methods

Thirdly万thedoseofhighenergyelectronbeldquo万171万causesdamagesin

samplesSeveralinvestigationshaveshownthedecreaseoftニhe

tニhresholdvoltageinMOSdevices[8]andtheincreaseofthe

interfacestatedensitybetweentheoxideandthesemiconductors[9]

-107-

Improvementsofmeasurementtechniques(ieuseofthe10W

energyprimaryelectronbeam万orlthedecreaseoftニhetotal

amountofdose)wirsquollbenecessary

Electricalpropertiesofsemiconductorscanbecharacterized

collectivelybyEBICjointlywiththeothertechniqueswhich

complementtheweakpointsinEBICmethod

REFERENCES

[1]

[21

[5]

[6]

[7]

[8]

[9]

PDDapkusWHHackettJr0GLorimorandRZ

BachrachJApplPhys45

4920(1974)

DBHoltandBDChasephysstatS01(a)旦旦

135(1973)

MBoulouandDBoisJApplPhys 484713(1977)

LCKimerlingHJLeamyandJRPatel

ApplPhysLett30217(1977)

HBarryBebbandEWWilliamsrdquoSemiconductorsand

Semimetalsrdquo(edRKWillardsonandACBeer

AcademicPress1972)vol8pp182-392

SMSzerdquoPhysicsofSemiconductorDevicesrdquo(JohnWiley

SonsInc1969)

DVLangJApplPhys453023(1974)

WJKeeryK0LeedyandKFGallowayrdquoScanning

ElectronMicroscopy1976rdquo[IITR]Chicago)pp507-514

RHezelSolid-stateElectron11^

735(1979)

-108-

4i

rsquoII

LISTOFPUBLICAT工ONS

[1]

[21

[3]

[4]

[5]

[6]

Papers

Theinfluenceofthegenerationvolumeofminoritycarriers

onEBICrdquo

TFuyukiHMatsunamiandTTanaka

JPhysDApplPhys131093-1100(1980)

rdquoAnalysisofEB工CconsideringthegeneratニIondistribution

ofminoritycarriersrdquo

TFuyukiHMatsunamiandTTanaka

JPhysDApplPhys131503-1510(1980)

rdquoDeterminationoflifetimeanddiffusionconstantof

minoritycarriersbyaphaseshifttechniqueusing

electronbeaminducedcurrentrdquo

TFuyukiandHMatsunami

JApplPhys旦(1981)

rdquoAnalysisofelectronbeaminducedcurrentconsidering

sampledimensions一一-Measurementofdiffusionlength

andsurfacerecombinationvelocity-rdquo

TFuyukiandHMatsunami

JpnJApplPhys20(1981)No4

rdquoInfluenceofminoritycarriergenerationdistributionon

electronbeaminducedcurrentinthenormalincidencemethodrdquo

TFuyukiandHMatsunami

(tobepublished)

rdquoHeattreatmenteffectondiffusionlengthinSirdquo

TFuyukiandHMatsunami

(tobepublished)

-109-

[1]

[21

[3]

PublicationsintheInstituteofElectronicsandCommunication

EngineersofJapan

(inJapanese)

rdquoMeasurementofminoritycarrierdiffusionlengthby

EBICmethodrdquo

TFuyukiHMatsunamiandTTanaka

ReptTechSSD78-102(Feb1979)

rdquoCharacterizationofdiffusionlengthandlifetimebyEBICrdquo

TFuyukiandHMatsunami

ReptTechSSD79-103(Feb1980)

rdquoMeasurementoflifetimeanddiffusionconstantofminority

carriersbyphaseshifttechniqueinEBICrdquo

TFuyukiandHMatsunami

TransSectionJ63-C832-837(1980)

-110-

  • page1
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  • page71
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  • page73
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  • page75
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  • page117
  • page118
  • page119
  • page120
Page 5: CHARACTERIZATION OF SEMICONDUCTORS BY Title ELECTRON …

Thephysicalpropertiessuchasthediffusionlengthin

thesmallselectedareascouldbecharacterizedbyEBIC

consideringthethree-dinensionalgenerationdistributionbyan

electronbeamandthesampledimensionsExperimentalresults

inSiandGaAsshowedgoodagreementwiththetheoryandthe

generationdistributionsinSiandGaAswererevealedWitニh

experiments

一旦-

hellipJVi_--Wrsquordquo>>-trsquomjrsquordquordquo^>-≫^

f1

ACKNOWLEDGEMENTS

Theauthorwishestoexi】resshisdeepgratitudetoformer

jブProfessorTetsuroTanakaforhiscontinuingguidanceandワバandrrsquoI

helliphellipノ1encouragementTheauthorwishestoexpresshis9万ざlltや1appreciation

toAssociateProfessorHiroyukiMatsuna万万mlforhispreciousguidance

andhelpfuladvicethroughouttニhepresentstudyTheauthor

acknowledgesProfessorAkiraKawabataforhisgenialguidanceand

encouragementTheauthorisgがIattilltoProfessorToshinoriTakagi

forhisstimulatingdiscussionsandusefulcriticismsonthemanuscript

TheauthorwouldalsoliketothankProfessorAkioSasakifora

criticalreadingofthemanuscriptandvaluablecomments

MuchattentionisduetoDrJuniiSaraieDrShigehiro

NishinoandDrAkiraSuzukifortheircontinuousencouragement

andstimulativediscussions

TheauthorthanksothermembersofSemiconductorLaboratory

fortheirconsiderableassistanceandexperimentalfacilities

一斑-

CONTENTS

ABSTRACT

ACKNOWLEDGEMENTS

L工STOFSYMBOLS

INTRODUCTION

References

i一m

VL

lVO

INFLUENCEOFMINORITYCARRIERGENERATIONDISTR工BUTION13

0NELECTRONBEAMINDUCEDCURRENTINTHENORMALINCIDENCE

METHOD

2-1

2-2

2-3

Introduction

Determinationofdiffusionlengthandelectron-

holepaircreationenergy

ExperimentalresultsinGaAs

2-4Summary

References

13

15

VOON

CMCM

30

DETERMINATIONOFDIFFUSIONLENGTHSURFACERECOMBINATION31

VELOCITYANDELECTRON-HOLEPAIRCREAT工ONENERGYBYTHE

LINESCANMETHOD

3-1Introduction31

3-2Surfacerecombinationeffectconsideringpoint33

source

3-3Analysisofelectronbeaminducedcurrenttaking37

tニhree-dimensionalgenerationdistributioninto

account

3-4ExperimentalresultsinSi

3-5Summary

References

一分-

`j7

44

48

】V

V江

ⅧI

ANALYSISOFTHREE-DIMENSIONALGENERATIONDISTRIBUTION50

BYTHECOMBINATIONOFTHENORMALINCIDENCEANDTHE

L工NESCANMETHODS

4-1Introduction

4-2 Influenceofthree-dimensionalgeneration

distributiononelectronbeaminducedcurrent

02

inin

4-3Three-dimensionalgenerationdistributioninGaAs57

4-4Summary

References

12

vOVD

ANALYSISOFELECTRONBEAMINDUCEDCURRENTCONSIDERING64

SAMPLEDIMENSIONS

5-1Introduction

5-2

5-3

Determinationofdiffusionlengthandsurface

recombinationvelocity

ApplicationtoSi

5-4Summary

References

Appendix

DETERMINATIONOFLIFETIMEANDDIFFUSIONCONSTANT

BYPHASESHIFTTECHNIQUE

6-1Introduction

6-2Relationbetweenlifetimeandphaseshift

6-3ExperimentalresultsinSi

6-4Summary

References

HEATTREATMENTEFFECTONDIFFUSIONLENGTHINS1

7-1Introduction

7-2Experimentalresultsanddiscussions

References

CONCLUS工ONS

References

LISTOFPUBLICATIONS

4vO

CVD

73

78

9VO>

77

81

lro

88

CNJVO

qNas

7O

O^(J

99

102

104

105

108

109

-V-

LISTOFSYMBOLS

Cl

cBC

ggpgBELOS嚢

cdDDeEfgGIIIIIlj一jJ

J大

correctionfactorwithwhichthethree-dimensionalsolutions

oftheヽgradientofphaseshiftcanbeexpressedbytheone-

dimensionalapproximations

exponentofGaussiandistribution

positionofgenerationsourcefromthesurfacealongthedepth

diffusionconstantofminoritycarriers

(equivdgL)normalizedgenerationdepth

chargeofanelectronz

electron-holepaircreationenergybyanelectronbeam

modulationfrequencyofprimaryelectronbeam

generationrateofactualpointsource

variablepartofgenerationsource

thewholegenerationstrengthinthegenerationregion

Imaginaryunit

primaryelectronbeamcurrent

measuredelectronbeaminducedcurrent

currentwhichflowsthroughtheloadresistance

backwardsaturationcurrent

shortcircuitcurrent

electronbeaminducedcurrent

variablepartofcomplexelectronbeaminducedcurrent

(≒n)normalizedelectronbeaminducedcurrentitbecomes

unitywhenallthegeneratedcarrierscontributeto

electニronbeaminducedcurrent

normalizedelectronbeaminducedcurrentconsideringthe

Influenceofohmiccontact

一吐-

誉~Lay

L大eff

p卵`μrRRCReRmSStTuva

correctionfactorfortheincidentbeamenergyconsidering

theenergylossduetobackscatteredelectrons

thermalvoltagersquo259mVatroomtemperature

second-modifiedfirst-orderBesselfunction

diffusionlengthofminoritycarriers

diffusionlengthestimateddirectlyfromtheslopeof

electronbeaminducedcurrentvsscanningdistancecurve

diffusionlengthestimateddirectlyfromtheslopeof

electronbeaminducedcurrentvsscanningdistancecurve

consideringtheinfluenceofohmiccontact

(ΞLJ百石iT)complexeffectivediffusionlength

distニributionofminoritニycarrierdensity

distributionofminoritycarrierdensityconsideringthe

influenceofohmiccontニact

variablepartofthedistributionofminoritycarrier

densitycomplexvariable

distancebetweenthecenteroftニhegenerationregionand

eachdividedsegment

radiusofgenerationregion

centerofgenerationregion

extraporatedelectronrange

loadresistance

maximumelectronrange

surfacerecombinationvelocity

(ΞS(Lて))surfacerecombinationvelocityparameter

time

variableforintegrat10n

para万7rdquo万eterforGaussiandistribution

acceleratingvoltageofprimaryelectronbeam

一吐-

rdquod

wm

Xxx

χy

ZZ

np

Pau

^GaAs

SpてφΦω

distancebetweenthepotentialbarrierandtheohmiccontact

depletionlayerwidth

metalthicknessofSchottkydiode

Cartesianco-ordinateofscanningdistance

(ΞxL)

distancebetweenthepotentialbarrierandthegeneration

pointalongthescanningdirection

(ΞL)

Cartesianco-ordinateonthescanningsurfacenormalto

thescanningdirection

Cartesianco-ordinatealongthedepth

peakoftheGaussiandistribution<

(=J)collectionefficiency

collectionefficiencyofthevariablepartニofthegeneration

source

resistivityofsemiconductors

massdensityofAu゜189gcm^

massdensityofGaAs゜53gcm^

massdensityofSi=23gcm^

minoritycarrierlifetime

phaseshiftbetweentheelectronbeaminducedcurrentand

tニhemodulatedgenerationsource

diameterofprimaryelectronbeam

angularfrequencyofmodulatedprimaryelectronbeam

-VnL-

IINTRODUCT工ON

Theremarkableprogressinthesolidstatedevicesisowing

totheadvancementinthecharacterizationtechniqueofthedevice

materialsWhenthedeviceshavingnewfunctionsaredevelopedthe

detailknowledgeofthephysicalpropertiesofthesemiconducting

material(bandgaplifetimeandmobilityofcarriersetc)mustbe

neededInparticularthosepropertiesmustbecharacterizedafter

theactualmanufacturingprocessbecausetheoriginalpropertiesmay

beaffectニedbythevariousprocessconditions

Inrecentyearstocharacterizeverysmalldevices(ie

LSI゛sorlaserdiodes)therehasbeenagrowinginteresttousea

finelyfocusedelectronbeamThetwodimensionalInformationofthe

materialpropertiescanbeobtainednon-destructivelywithhigh

spatialresolutionfromtheelectronbeamInteractionwithsamples

[121Surfacemorphologycanbeobservedwithgreatニdepthoffocus

byascanningelectronmicroscope(SEM)Crystaldefectsinthin

samplesaredetectedusingascanningelectrontransmission

microscope(STEM)[34]AscanningAugerelectronmicroscope(SAM)

[5]hasbecomeaveryusefultooltoanalyzethesurfaceandthe

interfaceregion

Themethodusinganelectronbeaminducedcurrent(EBIC)[6-10]

1saveryconvenienttechniquetodeterminethefundamentalparameters

(egthediffusionlengththelifetimeandthesurfacerecombination

velocityofminoritycarriers)whichcontroltheelectricalperfor-

manceofthedevicesTheelectron-holepairsgeneratedbyanelectron

beamareseperatedbytheinternalfieldInp-njunctionsorSchottky

barriersandthecurrent1SInducedIntheexternalcircuitThe

EBICdependsverymuchondiffusionandrecombinationofminority

carriersInsemiconductorsandthediffusionlengthetccanbe

-1-

Fig1-1

type

type

Primaryelectrbe≪m

^^trrttDepletionlayer

Electron-hotep弗i「6gerwrationregion

Primaryelectronbeam

rArrScanningdirection

(A)

(B)

Principalconfigurationstomeasurethe

electronbeaminducedcurrent(EBIC)

(A)normalincidencemethod

(B)linescanmethod

-2-

く二rArr|t夕

EBICく二rArr

-一一--

p-typentype

aver`

1ミミ二l∽rsquoebic

determinedfromtheanalysisofEBICInadditiontothetwodlmen-

sionalinformationofthediffusionlengthandthelifetimetheir

variationsalongthedeptニhcanbeobtainedforvariousgeneration

depthsbychangingtheacceleratingvoltageofanelectronbeam

TheprincipalconfigurationstomeasureEBICarethersquonormal

incidencemethodrsquoandthersquolinescanmethodrsquo(seeFig1-1)Inthe

normalincidencemethodtheelectronbeam1Sincidentnormaltothe

barrierplaneandisscannedonthesurfaceparalleltothatplane

ThedislocationsanddefectsinSiwereobservedinp-njunctionsand

Schottkybarrierdiodes[11-28]Inrecentyearselectricalactivity

ofoxidationinducedstackingfaults(OSF゛s)anditsrelationwith

deviceperformanceshavebeenstudied[29-35]Thenormalincidence

methodisalsousedforthefailureanalysisoftニheMOSdevices[36-

39]Usingthelinescanmethodthediffusionlengthandthesurface

recombinatニionvelocitycanbedeterminedfromthedependenceofEBIC

onthescanningdistancewhentheelectronbeamisscannedacrossthe

barrierTherehavebeenmanytheoretical[AO-46]andexperimental

[47-69]reportstomeasurethediffusionlengthandthesurface

recombinationvelocityinlight-emittingdiodes(LEDrsquos)andlaser

diodes

InalmostalltheworkssofarEB工Chasbeenanalyzedonly

qualitatively0rsemi-quantitativelyThediffusionlengthandthe

surfacerecombinationvelocityhavebeendeterminedunderrather

specialconditionsasmentionedbelowforthesimpletheoretical

calculationInthenormalincidencemethodtheyconsideredonly

theone-dimensionalgenerationdistributionalongthedepth[70-75]

undertheconfigurationthatthelateralextentofthegeneration

volumewasverysmallcomparedwithsampleareasInthelinescan

methodthegenerationvolumewasassumedtobeapoint[53546061]

undertheconditionthatthegenerationvolumewassufficiently

-3-

smallerthanthediffusionlengthandthesampledimensionsBut

intheactualcasethegenerationvolumehasafinitethree-

dimensionalextentreLatedtotheacceleratingvoltage[76-78]

Thelatestmicroelectronicdevices(ieLSIrsquosandthelaserdiodes

etc)havethesamedimensionsasthegenerationvolumeandS0

theanalysesconsideringtニhepointsourceortheone-dimensional

generationdistributニionareinaccuratetodeterminethediffusion

lengthandthesurfacerecombinationvelocityThenewmethodfor

thequantitativeanalysisofEBICmustbedevelopedtakingthethree-

dimensionalgenerationdistributionandtheinfluencesofthesample

dimensionsintoaccount[7980]

InthepresentstudyEBICisanalyzedquantitativelyby

solvingthesteady-stateortime-dependenttニhree-dimensionaldiffusion

equationsTheinfluenceofthefinitegenerationvolumeonEBICis

discussedwhentheextentofthegenerationvolumecannotbeignored

andimprovedmetニhodsaresuggestedtomeasurethephysicalproperties

(diffusionlengthlifetimeandsurfacerecombinationvelocityof

minoritycarrierselectron-holepaircreationenergybyanelectron

beametc)inthesmallselectニedareas

InChapternvariousmodelsforthegeneratニiondistribution

alongthedepth[7781-83]arecomparedwitheachotherandtニhe

influenceofthegenerationdistributiononthedeterminationofthe

diffusionlengthbythenormalincidencemethodisdiscussed

ChapterⅡIshowstheinfluenceofthegenerationvolumeon

EB工Cinthelinescanmethodtakingtニhesurfacerecombinationeffect

intoaccountAnimprovedmethodforthedeterminationofthe

diffusionlengthandthesurfacerecombinationvelocityisdescribed

-4-

InChapterVthree-dimensionalgenerationdistribution

isclarifiedbymeasuringEBICusingboththenormalincidenceand

thelinescanmethodsinthesamesamplewhichyieldsthe

quantitativeanalysisofEB工C

ChaptervdescribestheInfluenceofthesampledimensions

onEBICInthelinescanmethodEBICisInvestigatedbyextending

themirrorimagemethodlsquo[41-43]whenthediffusionlengthisof

theorderofthesampledimensions

InChapterWthephaseshifttechniqueinthemeasurement

ofEBIC[84-86]isdescribedTherelationbetweenthelifetime

andthephaseshiftisclarifiedbysolvingthethree-dimensional

time-dependentdiffusionequationThelifetimeandtニhediffusion

constantofminoritycarrierscanbedeterminedcombiningthe

phaseshifttechniquewiththeconventionallinescanmethod

Chaptervnshowstheheattreatmenteffectonthediffusion

lengthinSi

FinallyconclusionsandsuggestionsforfurtherInvestigation

aresummarizedinChaptervnr

ExperimentalresultsinSiandGaAsareshovmineverychapter

Themethoddiscussedinthesechapterscanbeappliedeasilyto

anysemiconductormaterialsbyconsideringthephysicalproperties

inherentinthematerials

-5-

References

[1

[21

[3]

4]

5]

6]

[7]

[8]

[9]

[10]

VEJohnson十Sm119151p763

0CWellsSEM1972p375

pMrdquoPetroffDVLangJLStrudelandRALogan

SEM71978pp325-332

CELymanSEM1978pp529-536

NCMcDonaldSEM1971p89

DBHoltrdquoQuantitativeScanningElectronMicroscopyrdquo

(DBHolteta1edsAcademicPress974)pp213-286

DBWittryrdquoMicroprobeAnalysisrdquo(CAAndersoned

JohnWileySonsNewYork1973)pp123-187

CJVarkerrdquoNondestructiveEvaluationofSemiconductor

MaterialsandDevicesrdquo(edJayNZemelNATOADVANCED

STUDYINST工TUTESSERIESSERIESBPhysicsvol46

PLENUMPRESS1979)pp515-580

HJLeamyLCKimerlingandSDFerris

SEM1978pp717-725

ThebibliographyonEBICislistedinthefollowing

K0LeedySolidStateTechnologyFeb1977pp45-48

--

-- - -

rdquo-

rdquo- - 言

争心- -

SEM19xxrdquoScanningElectronMicroscopyrdquoProceedingofAnnualConference

before1977(IITResearchInstituteChicago)

after1978(SEMIncAMFOrsquoHare)

-6-

[11]JJLanderHSchrelberJrTMBuckandJRMathews

ApplPhysLett旦206-207(1963)

[12]WCzajaandGHWheatleyJApplPhys亜

2782-2783(1964)

[13] WCzajaandJRPatelJApplPhys11476-1482

(L965)

[14]NFBNeveandPRThorntonSolid-stateElectron

旦900-901(1966)

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

IGDaviesKAHughesDVSulwayandPRThornton

Solid-stateElectron9275-279(1966)-

WCzajaJApplPhysyi918-919(1966)

DVSulwayPRThorntonandMJTurner

Soli-StateElectron11567-568C1968)-

AJRKockSDFerrisLCKimerlingandHJLeamy

ApplPhysLett27313-315(1975)

DBHoltandROgdenSolid-stateElectron1937-40(1976)-

HJLeamyLCKimerlingandSDFerris

SEM1976pp529-538

TKatoTMatsukawaandRShlmizu

ApplPhysLett26415-416(1975)

RBMarcusMRobinsonTTShengSEHaszkoand

SPMurarkaJElectrochemSOC124425-430(1977)

LCKimerlingHJLeamyandJRPatel

ApplPhysLett30217-219(1977)

DEIoannouandSMDavidson

physstatsol(a)丘旦K1-K4(1978)

-7-

[25]

[26]

HBlumtrittRGlelchmannJHeydenderichandH

Johansenphysstatsol(a)55611-620(1979)

HMennigerHRaidtandRGleichmann

physstat-sol(a)5旦173-180(1980)

[27]pAshburnandCJBullSolid-stateElectron

Tl_105-110(1979)

[28] pAshburnCJBullandJRABeale

JApplPhys503472-3477(1979)

[29]KVRaviCJVarkerandCEVolk

JElectrochemSoc120533-541(1973)-

[30]

【31】

[32]

[33]

[34]

[35]

[36]

[37]

[38]

[39]

[40]

CJVarkerandKVRaviJApplPhys45272-287(1974)

SKawadoYHayafujiandTAdachi

JpnJApplPhys14407-408(1975)

TESeidelSEHaszkoandDMMaher

JApplPhys485038-5042(1977)

AMurgaiJYChiandHCGatos

JElectrochemSoc1271182-1186(1980)-

SKawadqJpnJApplPhys191591-1602(1980)

JMDishmanSEHaszkoRBMarcusSPMurarka

andTTShengJApplPhys502689-2696(1979)

JLGatesand0KGriffith

ApplPhysLett27kZ-45(1975)

JFKatalanoSEM71976pp521-528

PRoltmanandWRBottomsSEM1977pp731-738

CLWilsonSolid-stateElectron23345-356(1980)-

WHHackettJrJApplPhys431649-1654(1972)

-8-

[41]

[42]

[431

[44]

[45]

【46】

[47]

[48]

[49]

[50]

FBerzandHKKuikenSolid-stateElectron

19437-445(1976)

CvanOpdorpPhilipsResKept32^192-249(1977)

0vonRoosSolid-stateElectron互lsquo1063-1067(1978)

0vonRoosSolid-StateElectron211069-1077(1978)

0vonRoosSolid-stateElectron22113-114and773-778-

(1979)

WvanRoosbroeckJApplPhys旦D380-391(1955)

DBWittryandDFKyserJApplPhysj11387-1389

(1965)

HHiguchiandHTamura

JpnJApplPhys4^

316-317(1965)

YuPDemidovRPGurovaYuMKushnirAIFrltner

andDVFetisovSovPhys-Semicond1030-1035(1968)

KMaedaAKasamiMToyamaandNWakamatsu

JpnJApplPhys旦65-75(1969)

[51]ZhIAlferovVMAndreevVIKorolrsquokovand

vIStreminSovPhys-Semicond41113-1116(1971)

[52]

[53]

[54]

[551

CJHwangSEHaszkoandAABergh

JApplPhys425117-5119(1971)

WHHackettJrRHSaulRWDiχonandGWKammlott

JApplPhys432857-2868(1972)

WZimmermannphysstatsol(a)^2671-678(1972)

MAvenJZDevineRBBolonandGWLudwlg

JApplPhys434136-4142(1972)

-9-

[56]

[57]

[58]

[59]

【60】

[61]

[62]

[63]

[64]

[65]

[66]

GLidgardSolid-stateElectron15159-164(1972)

DBHoltBDChaseandMCenslive

physstatsol(a)20459-467(1973)-

DBHoltandBDChasephysstatsol(a)2(

135-144(1973)

CvanOpdorpRCPetersandMKlerk

ApplPhysLett24125-126(1974)

LJBalkEKubalekandEMenzel

IEEETransED-22707^712(1975)-

LJastrzebskiJLagowskiandHCGatos

ApplPhysLett11_537-539(1975)

LJBalkEKubalekandEMenzelSEM71975pp447-455

JJOakesIGGreenfieldandDLPartaln

JApplPhys丘旦2548-2555(1977)

MLanirAHBVanderwyckandCCWang

JApplPhys496182-6184(1978)

DLPartainAGMilnesandLFVassamlllet

JElectrochemSoc1261584-1588(1979)-

NTohgeTMinamiandMTanaka

JpnJApplPhys172155-2156(1978)

【67】DLPartainAGMilnesandLFVassamillet

JElectronicMaterials旦493-499(1979)

[68]

[69]

DEIoannouandSMDavidson

JPhysDApplPhys昆1339-1344(1979)

ShengSLiWLWangPWLaiandRTOwen

JElectronicMaterials旦335-354(1980)

-10-

[70]

【71】

[72]

[73]

[74]

JFBresseSEM119111pp105-112

JFBresseSEM1977pp683-693

CJWuandDBWittryJApplPhyspound92827-2836(1978)

GEPossinSEM1979pp245-256

GEPossinandCGKirkpatrlck

JApplPhys旦4033-4041(1979)

[75]GEPossinandCGKirkpatrick

JVacSciTechnol161917-1920(1979)-

[76]

[77]

[78]

[79]

[80]

VonAEGruenZNaturforsch12aHeft289-95(1957)-

KKanayaandSOkayama

JPhysDApplPhys5A3-58(1972)

RShimizuYKataokaTIkutaTKoshikawaand

HHashimotoJPhysDApplPhys旦101-114(1976)

GVSpivakGVSaparinandLFKomolova

SEM1977pp191-199

CDonolatoandHKlann

-JApplPhys511624-1633(1980)

[81]DBWittryandDFKyser

JApplPhys2旦375-382(1967)

[82]

[83]

[84]

[85]

[86]

TEEverhartandPHHoff

JApplPhys425837-5846(1971)

VVMakarovSovPhys-Semicond旦in-llk(1975)

JDKannnandHBerntSolid-stateELectronヌ1957-964(1978)-

JDKammrdquoSemiconductorSilicon1977rdquo(JElectrochemical

Society)pp491-501

0vonRoosJApplPhys503738-3742(1979)

-n-

-L2-

2-1

INFLUENCEOFM工NORITYCARRIERGENERATIONDISTRIBUTION

ONELECTRONBEAMINDUCEDCURRENTINTHENOR^IALINCIDENCE

METHOD

Introduction

Accuratedeterminationofminoritycarrierdiffusionlength

LisveryimportanttocharacterizesemiconductorsOneofthe

convenientmethodstomeasureLIstheuseofelectronbeam

inducedcurrent(EBIC)Theelectron-holepairsgeneratedbyan

electronbeamareseperatedbyapotentialbarrier(egp-n

junctionorSchottkybarrier)andthecurrentisInducedinthe

externalcircuitThevalueofLcanbedeterminedfromthe

dependenceofEBIConthelengthzbetweenthepotentialbarrier

andthegenerationpointInthenormalIncidencemethodzis

variedbychangingtheacceleratingvoltagevaofanelectronbeam

andthesmallvalueofLoftheorderofumcanbedetermined

ThevalueofLintニhesmallregionisobtainedusingafocused

beamgeneratedbyascanningelectronmicroscope(SEM)lsquo

Czaja[1]measuredLinp-ndiodesofSiandGaPHe

assumedthegenerationdistributionasacombinationoftwo

exponentialfunctionsBresse[2]andWu[3]measuredLandthe

electron-holepaircreationenergyE^^inSiandGaAsTheyused

Schottkydiodesbecausetheelectronbeamenteredthroughthemetal

contactandthesurfacerecombinationeffectcouldbeneglected

IntheiranalysesBresseusedthesemi-sphericalgeneration

distrlbutionproposedbyKanayaeta1[4]andWuassumedGaussian

distリbutlonPossineta1[5]analyzedEBICindetailtakingthe

influencesofthesurfacerecombinationandtheinternalfield

-13-

Metal

Depletio

layer

Primaryelectronbeam

Numberofgeneratedcarriers

Fig2-1Schematicviewofexperimentalconditions

jusingSchottkydiodesMetalthicknessis

wanddepletionlayerwidthiswright-handillustぷふこsthedぶdosefunctionRandR

-givethemaxiraum

andextraporaiedmelectrSnolinerangerespectively

-14-

0generatedcarrier

に_---___1

我_______Iuarrヽ

y重ダ

1ごpermil

andestimatedthedepthdistributionoflifetimeinion-implantedSi

TheylsquousedthepolynomialfunctionderivedbyEverhart[6]forthe

generationdistribution

工ntheanalysisofEBICtheminoritycarriergeneration

distributionplaysanimportantroletodeterminetheaccurate

valueofLandEHoweverthedistributionmodelsusedinthepc

analysesaredifferentwitheachotherasmentionedaboveIntニhis

chapterwecomparevariousmodelsforthegenerationdistribution

inGaAsandSiWecalculateEBICandclarifytheinfluenceofthe

generationdistributiononthedeterminationofLandEpc

Experimentalresultsarealsopresented

2-2 Determinationofdiffusionlengthandelectron-holepair

creationenergy

ASchottkybarrierdiodeisusedinordertoneglectthe

influenceofthesurfacerecombinationTheelectronbeamis

irradiatednormallytothebarrierplanethroughthemetalas

shownInFig2-1Thethicknessofthemetalandthedepletion

layerareputaswmandwd゛respectivelyTheminoritycarrier

generationdistributionalongthedepth(Socalledthedepthdose

function)isIllustratedalso1nFig2-1TheEBICiscalculated

basedonthefollowingassumptions1)Theminoritycarriers

generatedinthemetal(regionI)cannotcontributetoEBIC

2)Theelectron-holepairsgeneratedinthedepletionlayer(

regionlsquoTL)areseperatedquicklybythefieldofthedepletion

layerandwhollycontributetoEBIC3)Theminoritycarriers

generatedinthebulk(regionⅡI)partlycontributetoEBICie

theminoritycarrierswhichreachtotheedgeofthedepletion

-15-

mDiwi)iunMd

SMtjjesp≫)ejAU≫6|o』ψsEコz

Normalizedgenerationdepth^rsquoRm

Fig2-2

Generationdistribution

inGaAsTheMakarov゛SWittryrsquos

andKanayarsquosmodelsareexpressed

bytニhesolidbrokenanddotted

linesrespectivelyThegener-

atlondepthisnormalizedby

themaximumelectronrangeR

ThetotalgenerationrateiSm

normaLlzedtobeunity

-16-

2 0

1 05

(Efi)≪MJO^M

d6ue」

CO』oa3

rdquorsquo5102050Acceleratingvoltageva(kv)

Fig2-3

ElectronrangesinrsquoGaAsforvariousmodelsThesolidbrokendottedanddashedanddottedlinesaretheresultsusingMakarovrsquosWitニtryrsquosKanayarsquosandEverhartrsquosmodels

respectively

rdquoゝゝGaAs

χ

`Makarov20χ

----Wittry

χhelliphelliphellipKanaya

11S

15

゛S≒

rsquoχ≒

χrsquo

10trsquolsquo

卜卜゜χ゛

卜ゝrsquo

05χrsquo゛rsquoゝ

ゝrsquoゝ1

ゝゝrsquoゝゝ

ゝゝ

00

50

GaAso々

タグrsquo

Makarov

15-rsquo一一Wittry

ノKanaya

12

---Everhart

13yelr(2゛十`゛dinFig2-1)bydiffusioncanflowintothemetal

bythefieldofthedepletionlayer

Therehavebeenmanytheoretical147]andexperimental

[68-11】worksonthegenerationdistributionKanayaand

Okayama[4]proposedasemi-sphericalgenerationdistribution

usingthemodifieddiffusionmodel0fArchard[7]Wittryeta1

assumedGaussiandistributionandappliedtoGaAs[89]

EverhartandHoffl6]derivedapolynomialfunctionfromtheir

experimentsIntheA1olineSi02olineSisystemdegMakarov[10]showedthat

thegenerationdistributioncouldbeexpressedasGaussianlike

(exp(-((z-z)u)2))andthep8゛゜eters2manduvariedaccording

totheatomicnumberandthedensityofthematerialInorderto

comparethesedistributionsnormalizeddepthdosefunctionwas

introducedGruen[11]showedthattheshapeofthedepthdose

curveispracticallyinvariantifthepenetrationdepthis

normalizedbytheelectronrange

ThedepthdosefunctioninGaAsnormalizedbythemaximum

electronrangeRm(atwhichnoelectronentersintothematerial

seeFig2-1)areshowninFig2-2bythesolidbrokenanddotted

linesusingthefollowingequationsforthemodelsofMakarov

WittryandKanayarespectively

2RmolineOdeg138

g(z)=exp(-(rarr元でi

g(z)=exp(-(

2Rmoline

Odeg125

-035

)2)

)2)

(Makarov)(2-1)

(Wittry)(2-2)

g(z)゜(RmolineOdeg242Rtri)2oline(2olineOrsquo242Rm)2(K゛3y8)゛(2lsquo3)

-17-

こrsquo

Aouepj^^auoiiDaii〇D

Fig2-4

10203040

Acceleratingvoltage

5060

Va(kV)

CollectニionefficiencynvsVacurves

GaAsSchottkydiodeThevaluesofLare505μmfromuppert0lowergroupofcurves

for

2and

respectivelyTheresultsusingtheMakarovrsquosWittry゛SandKanayarsquosmodelsareexpressedbythesolidbrokenanddottedlinesrespectivelyThevaluesofwandWare10nmand015ymrespectively^hedashedanddottedlineisinthecaseofw=50nmw=015umandL=2umusingtheWittryrsquosmode1

-18-

GaAs一一Makarov

--rdquo-Wittry

10Wf^=10nmhelliphelliphelliphellipKanayaL(pm)

rsquo≒゜ニ1こii4degこ7T`ヽヽヽ5

05万でヽこミア斗辿こTTZご

50nふyミ゛1helliphelliphelliphellip4゛`゛ζ゛ζ

Orsquo1capparacapcap

か4

5060

ThereareobviousdifferencesbetweenthesethreemodelsThe

MakarovrsquosandWittryrsquosmodelshavethelargesurfaceconcentration

butthepeakvalueatzRm゛Odeg13oftheMakarovrsquosmodelissmaller

thanthatoftheWittryrsquosmodelTheKanaya゛smodelhasmoreevenly

spreadeddistributionthantheothertwomodelsThisisbecause

theelectron-holepairconcentrationisassumedtobeuniformin

thesemi-sphereintheKanayarsquosmodelwhichisasimplefirst-

orderapproximationforthegenerationdistributionButinthe

actualcasetheelectron-holepairsareconcentratedaroundthe

centerofthesemi-sphereOnemustusetheimprovedelectron-hole

pairconcentrationmodelInsteadoftheuniformoneinorderto

expressthegenerationdistributionprecisely

InthecalculationofEBICtheabsolutevalueofRmustm

beneededSomereportedvaluesbyMakarovWittryandKanayaare

shownbythesolidbrokenanddottedlinesrespectively

inFig2-3forGaAsThedashedanddottedlineisderivedby

Everhart[6]anddiscussedlaterTherangesoftheWittryrsquosand

Kanayarsquosmodelsarealmostagreewitheachotherbutthatofthe

Makarovrsquosmodelisabout70ZofthoseoftheWittryrsquosandKanayarsquos

models

ThecalculatedEBICinGaAs(iethecollectionefficiency

nwhichbecomesunitywhenallthegeneratedcarrierscontribute

toEBIC)bythesamemethoddescribedinref[3]isshownIn

Fig2-4Thesolidbrokenanddottedlinesareforthemodelsof

MakarovWittryandKanayarespectivelyThevalueoftheacceler-

atlngvoltageva1Schangedfrom5t060kVThevalueofLIs50

20and05ymfromuppert0lowergroupofthecurvesrespectively

ThevaluesofWmandwdaretakenastypicalvaluesof10nmand

015ymrespectivelyTheelectronrange1SInverselyproportional

tothedensityofthematerialThemetalthicknessiscorrected

-19-

takingthedifferenceofthedensitiesbetweenthemetalandthe

bulksemiconductorinorderthatthesamplehasuniformdensityfrom

thesurfacetothebulkforasimpletheoreticalcalculationWhen

goldistakenastheSchottkycontactwmustbemultipliedby

pAupGaAS(゜3`゜6rsquopAudeg189andpGaASdeg5゛3

1cll3)

゛OIlecanestimateL

mainlyfromthegradientofthecurvebecausethegradientdecreases

monotonouslywithincreasingLupt05umTheestimatedvaluesof

LbyMakarovrsquosandWittry゛Smodelsarealmostequalbecausethe

gradientsofthecurvesagreewitheachotherforthesameLvalue

ThevalueofLlargerthan5μmcannotbedetermineddefinitely

becauseEBIChardlychangeswithvevenifLbecomeslargeThea

maximumvalueofLthatcanbedetermineddefinitelyincreasesas

thehighestvalueofvaincreasesbutanotherproblems(idegedeg

damagesofthesamplebyhighenergyelectronsetc)mayoccur

Theelectron-holepaircreatニionenergyEcanbeobtainedfrom

theabsolutevalueofEBICbytherelationndeg^C^EBIC^^B^

(IEBICmeasuredEBICIBprimarybeamcurrentkcorrectionfactニor

fortheenergylossduetobackscattニeredelectrons)[3]

TheabsolutevaluesoftニheMakarovrsquosmodelareabout10へj20Z

largerthanthoseoftheWittry゛smodelAndsothevalueofEpC

obtainedbytheformeris10へj20Zlargerthanthatbythelatter

ThegradientニSandtheabsolutevaluesofthecurvesoftheKanayarsquos

modelarequitedifferentfromthosebytwoothermodelsThe

reasonofthedifferenceisowingtotheassumptionoftheuniform

concentrationoftheelectron-holepairsinthesemi-sphereas

discussedbeforeTheKanayarsquosmodelisafirst-orderapproximation

forthegenerationdistributionandisnotsuitableforthe

accuratedeterminationofLandEThevalueofwdoesnotaffectpc(I

EBICsomuchfromtheresultsoftニhecalculation工fWbecomesm

largetheabsolutevalueofEBICat10wvaisdecreasedverymuch

-20-

butthegradientofthecurveintheregionofhighVadoesnot

changeasshowninFig2-4(thedashedanddottedlineisinthe

caseofwmdeg50nm゛wdrsquoOrsquo15pmandL=2ymusingtheWittry゛Smode1)

ThereforeLcanbedeterminedinanycaseofwm゛asfaraswm1S

sufficientlysmallinorderthattheelectronbeamcanenterinto

thebulkregion

ThenormalizeddepthdosefunctionsInSiexpressedbythe

followingequationsareshowninFig2-5bythesolidbroken

dottedanddashedanddottedlinesforthemodelsofMakarov

WittryKanayaandEverhartrespectively

zR-0261

g(z)=exp(-(-jyヲー-7)2)(Makarov)(2-4)

zR-0156

g(z)=exp(-(―q2L_一一

g(z)゜(RmolineOrsquo336Rm)2

g(z)=06+6212Re

(Wittry) (2-5)

(゛0336R)^(Kanay゛1)(2oline6)

oline12deg40(2Re)2+5lsquo69(zR

(Everhart)e)3

(2-7)

Makarovshowedthattheparameterszmlsquoanduhadvoltagedependencesl

andthetypicalvaluesatvadeg30kVaretakenItshouldbenoted

thatthedepthdosefunctionoftheEverhartrsquosmodelisnormalized

bytheextraporatedrangeRe(seeFiglsquo2-1)whichisdetermined

byextraporatingthestraightlineportionofthecurve

-21-

Fig2-5

11

u)6ua))iunjed

sjdiJieopdiejdud6lo」4sEコz

Normalizedgenerationdepth^rsquoRm

GenerationdistributionsinSiTheMakarov゛s

Witニビry゛sKanayarsquosandEverhart゛Smodelsare

expressedbythesolidbrokendottedanddashedanddottedlinesrespectivelyThegener-

atlondepthisnormalizedbythemaximumelectron

rangeRTheextraporatedrangesR゛SoftheMakarovrsquosWittryrsquosandEverhartrsquosmodelsare

takentobeagreedwitheachotherThetotニal

generatニionrateisnormalizedtobeunity

-22-

KUkarov

--一一-Wittry2deg

二ぷ芯t

15へ

゜¥レ臨べhellip

hellip

10rsquoS゛lsquoNhellip

helliphellip

05

hellip

helliphellip

1helliphellip

hellip

005

工nordertocomparetheEverhartrsquosmodelwithothersthe

extraporatedrangefortheGaussiandistributionisdeduced

(seefootnote)十andtheextraporatedrangesoftheMakarovrsquoS

WittryrsquosandEverhart゛Smodelsaretakentobeagreedwitheach

otherThepeakvaluesofthegenerationdistributionsofthe

MakarovrsquosWlttryrsquosandEverhartrsquosmodelsarealmostequalbut

thevalueofzRmatthepeakfortheWittryrsquosmodelisabout

015andsmallerthanthoseoftheothertwomodelsCzR=025)゜

ThegenerationdistributionoftheWittryrsquosmodelcomesnearerto

thesurfacethanthoseoftheMakarovrsquosandEverhartrsquosmodelsIt

isbecausetheWittryrsquosmodelisderivedInthecaseofGaAsand

ontheotherhandtheMakarovrsquosandEverhart゛Smodelsareconcerned

inthecaseofSiThedensityofG゛1AS(pGaAS゛5deg3gcm^)islarger

thanthatofS1(pSirsquo2deg3gcm^)andsotheWittry゛Smodelshows

themoresurfaceconcentrationthantheothersTheKanayarsquosmodel

isquitニedifferentwiththeotherthreemodelsowingtothesame

reasonasdiscussedinGaAs

- -

-- - - - -

- - - -

Gaussiandistribution(e゛p(oline((2oline2m)11)2))

showsthealmostlineardecreasearoundthepoint

ofinflection(zdegu゛Σ十zm)lsquoTheextraporatedrange

Re(1゛ersquothepointwithwhichthestraightline

atthepointofinflectioncrossesthezaxis)

becomes2u十zfromtheresultsofcalculationm

(seeFig2-5)゜TheextraporatedrangeRebecomes

078Rand062RfortheMakarovrsquosandWittryrsquosmm

modelrespectively

-23-

Fig2-6

0 102030

Acceleratin9

4050

voltage

60

va(kv)

CollectionefficiencynvsVacurvesforSiSchottkydiodeThevaluesofLare1052andlymfromuppert0lowergroupofcurvesrespectivelyTheresultsusingtheMakarovrsquosWittryrsquosKanayarsquosandEverhartrsquosmodelsareexpressedbythesolidbrokendottedanddashedanddottedlinesrespectivelyThevaluesofWandware10nmand05ymrespectivelymd

-24-

MakarovSi---rdquoWittry

Kanaya

----Everhart

ジhttpwwwL(pm)卜

)渫回ブモジミ穫

WmニlOnmrdquoミ4helliphellipで``rsquoヽ4゜

゛ゝ1rsquohelliphelliphellip

゛rsquoN

u1C

larrl

0E

501

Figure2-6showsthecollectionefficiencyinSiusing

thefourdifferentmodelsofMakarovWittryKanayaandEverhart

bythesolidbrokendottedanddashedanddottedlines

respectivelyThevalueofLIs1005020and10umfrom

uppert0lowergroupofcurvesrespectivelyThevaluesofW

andrdquodaretakenastypicalvaluesof10nmand05]imrespectively

Thevalueofwmismultipliedby821nthecalculationowingto

thedifferenceofdensitiesbetweenAuandS1

asdiscussedbeforeThevalueofLlargerthan10μmcannotbe

determinedaccuratelybecauseEBIChardlychangesevenifLvaries

ThegradientofthecurveoftheEverhartrsquosmodel1Sslightly

steeperthanthoseoftheMakarovrsquosandWittry゛smodelswhich

almostagreewitheachotニherAndsotheestimatedvalueofLby

theEverhartrsquosmodelbecomeslargerthanthatbytheMakarovrsquosor

Wittry゛smodelforthesamer)vSdegvaCurve(egL=lutnbythe

Everhartrsquosmodelbecomes07umiftheMakarov゛Smodel1Sused)

ThegradientofthecurveoftheKanayarsquosmodelisalmostequal

tothatニoftheEverhartrsquosmddelbuttheabsolutevalueofthe

formeris30Zsmallerthanthatofthelatterforthesamevalue

ofLThereforetheestimatedLbyKanayarsquosmodelalmostagree

withthatbytheEverhartrsquosmodelbutthevalueofE

pCuSing

theformeris30Zsmallerthanthatusingthelatter

Asmentionedbeforetheelectronrangeisinversely

proportionaltothedensityoftニhematerialTheelectronrange

derivedbyEverhartinSicanbeappliedtoGaAsconsideringthe

differenceofthedensitiesbetweenSiandGaAsThecalculated

valuesareplottedbythedashedanddottedlineinFig2-3

TherangesoftheMakarov゛SandWittry゛Smodelsarelargerthan

thatoftheEverhart゛smodelOneofthereasonsforthe

disagreementisthedifferentdefinitionsoftheelectronrange

-25-

ieMakarovandWittryusedthemaximumrangeRbutEverhart

usedtheextraporatedrangeRelsquoInordertニocomparethesevalues

theextraporatedrangesfortheMakarovrsquosandWittryrsquosmodels

inGaAsarededuced(seefootnoteinpage23)andbecome075Rm

andOlsquo62Rm゛respectivelylsquoForexampleinthecaseofvadeg30kv゛

thevaluesofRforMakarovrsquosandWittryrsquosmodelsare34andm

48ymandthenthevaluesofRebecome26and30ym

respectivelylsquoThevalueofReintheEverhartrsquosmodel(29umat

vadeg30kV)isslightlylargerthanthatoftheMakarovrsquosmodel

butagreeswiththatoftheWittryrsquosmodel

2-3 ExperimentalresultsinGaAs

AconventionalSEMwasusedfortheprimaryelectronbeam

whichwasmodulatedat3kHzwithachoppingcoilinsertedinto

thebeampathTheinducedcurrentwasmeasuredfromthevoltage

dropacrosstheloadresistancewhichwasconnectedtotheSchottky

barrierwithanohmiccontactThesignalwasdetectedbyalock-in

amplifierThebeamcurrentwasmeasuredbyaFaradaycageThe

beamwassomewhataefocussed(Φ|=10umφbeamdiameter)inorder

toavoidhighinjectionTheinducedcurrentwasnotchangedeven

ifthebeamwasirradiatedatthesamepointforanhour

TheSchottkybarrierwasrsquomadeonn-typeGaAs(Sndoped

ndeg62times1016cmoline3)byevaporatingAuofabout10nmthickina

vacuumofabout10oline7TorrTheohmiccontactwasobtainedby

evaporatingAu-Geandalloyingat400degCfor2mlnThecarrier

densityandthedepletionlayerwidthweredeterminedbyG-V

measurements

-26-

(Hiunqj≫)

U一SU

BeamcurrentIb(A)

Fig2-7

MeasuredEBICinGaAs(Sn-

dopedn=62)(1016cmoline3)Schottky

diodeatVa=10and50kVThe

beamcurrentwaschangedinthe

rangeof2)(10oline11≦I≦5)(10oline9A

-B-Theopenandsolidcirclesare

theexperimentalresultsforvadeg

10and50kVrespectivelyand

thegradientsofthesolidlines

areunity

Tab2-1

(s≫UコqjB)Aouapu

く1)

uoiioaiion

AcceleratingvoltageVa(kV)

Fig2-8

Curvefittingsoftheexperi-

mentalresultstothetheoretical

collectionefficienciesinGaAs

SchottkydiodeThesolidbroken

anddottedlinesaretheresultニS

usingtheMakarovrsquosWittry゛Sand

Kanayarsquosmodelsrespectively

Vaischangedfrom5t050kVwith

thefixedvalueofl゛10oline1oA

w=10nmandwmd

L(unj)Ec(ev)

Makarov

Wittry

Kanaya

03

03

05

48

41

41

二〇15um

ご洸竺詐比飛ぱ器ぶごぷ詣ぷ

-27-

000

5Gなfimf4ilvalu

0v≪>iakv

50

100

10

lylrsquo16rsquo1(i

acuteン゛tGaAs(Sndoed)

5n=62

lope

1二痙7

5Kanayao

21020304050

ThevalueofEBICatv=10and50kVareshownbythesolida

linesinFig2-7whenthebeamcurrentIBischangedintherange

of2)(10oline11≦I≦5)(10oline9AIftheminoritycarrier-B-

concentrationexceedsthethermalequilibriumconcentrationof

majoritycarriers(iehighinjection)theminoritycarrier

lifetimeisprolonged[12]ThereforeEBICbecomestoincrease

superlinearlywiththenumberofgeneratedcarriersie

withIBforafixedvalueofvarsquoInthisexperiment゛EBIC

increaseslinearlywithIBatbothvals゛WhichShoWsthe10w

injectionTheexperimentalresultsareshownbycirclesin

Fig2-8whenvischangedintherangeof5くVく50kVata=adeg

thefixedvalueofIBdeg10oline10A゛Theoreticalcollectionefficiencies

usingtheMakarovrsquosWitニtryrsquosandKanayarsquosmodelsareshownbythe

solidbrokenanddottedlinesrespectivelyinFig2-8The

valuesofLandEpcdeterminedbyfittingtheexperimentaldata

totニhetheoreticalcurvesaretabulatedinTab2-1forthethree

differentmodelsofMakarovWittryandKanayaThecollection

efficiencybytheMakarovrsquosmodelshowedfairlygoodagreement

withtheexperimentalresultsbutthatusingtheWittryrsquosmodel

isslightlylargerthantheexperimentalvaluesinthe10Wva

l`egioll(va≦10kV)Thediscrepancyinthelowvaregionbecomes

largeiftheKanaya゛SmodelisusedInthecaseofWittryrsquosand

Kanaya゛Smodelspoundheexperimentaldatawerefittedintherange

ofhighva(va≧15kv)TheestimatedvaluesofLis03urnby

usingboththeMakarovrsquosandtheWittryrsquosmodelsbutthatusing

theKanayarsquosmodelis05ymandabouttwiceoftheresultby

theMakarovrsquosandWittryrsquosmodelsThevaluesofEdeterminedpc

bytheMakarovrsquosWittryrsquosandKanaya゛Smodelsare4841and41

eVrespectivelyBythenormalincidencemetニhodofEBICWuand

Wittry[3]andKobayashieta1[L3]determinedEas468and457

eVrespectivelywhicharealmostequaltotheresultusingthe

Makarovrsquosmodelbutareabout10Zlargerthanthevalueobtained

bytheWittryrsquosandKanayarsquosmodels

-28-

2-4 Summary

ThevaluesofLandEcanbedeterminedfromthe

PC

ceofEBIConvbythenormalincidencemethodThe-

dependenceofEBIConVabythenormalincidencemethodThe

minoritycarriergenerationdistributionplaysanImportantrole

intheanalysisofEBICVariousgenerationdistributionmodels

arecomparedwitheachotherunitingthedifferentdefinitionsof

theelectronrange(Iemaximumrangeandextraporatedrange)

InGaAsGaussiandistributionsproposedbyMakarovand

Wittryhavelargesurfaceconcentrationsandthepeaksofthe

distributionsexistatabout0130fthemaximumelectronrange

Kanaya゛Smodelhasevenlyspreadeddistributionowingtothe

assumptionoftheuniformconcentrationofthegeneratedelectron-

holepairsThevalueofLlargerthan5μmcannotbedetermined

definitelybecauseEBIChardlychangesevenifLvariesThe

estimatedLbytheMakarovrsquosmodelalmostagreeswiththatblsquoythe

WittryrsquosmodelbutEdeterminedbytheformeris10へj20ZrdquoPC

largerthanthatbythelatter

InSithepeaksofthegenerationcistributionbecome

deeperthanthoseinGaAsbecausethedensityofS11Sabouthalf

ofthatofGaAsThelargestvalueofLthatcanbedetermined

definitelybecomestwiceofthatofGaAsbecausetheelectronrange

inSiisabouttwiceofthatinGaAsTheestimatedLbythe

MakarovrsquosorWittryrsquosmodelisabout30Zsmallerthanthatbythe

Everhartrsquosmodel

IntheexperimentsinGaAstheestimatedLbytheMakarovrsquos

modelagreedwiththatbytheWittryrsquosmodelbuttheestimated

Epcbytheformerwas48eVandabout17Zlargerthanthatbythe

latter

-29-

References

[1]

[2]

[5]

WCzajaJApplPhys374236(1966)

JFBresserdquoScanningElectronMicroscopy71972partlrdquo

(iiTRiChicago111)p105

CJWuandDBWittryJApplPhys丘旦2827(1978)

KKanayaandSOkayamaJPhysDApplPhys

543(1972)-

口EPosslnandCGKirkpatrickJApplPhys

5^4033(1979)

[6]TEEverhartandPHHoffJApplPhys

425837(1971)

[10]

[11]

[12]

[13]

GDArchardJApplPhys竪91505(1961)

DBWittryandDFKyserJApplPhys28375(1967)

TSRao-SahibandDBWittryJApplPhys

403745(1969)

VVMakarovSovPhysSemicond旦722(1975)

jVonAEGruenZNaturforsch12aHeft289(1957)-

JCornuRSittigandWZimmermannISolid-stateElectron

TKobayashiTSugitニaMKoyamaandSTakayanagi

IEEETransNuclSciNS-19324(1972)-

-30-

3-1

DETERMINATIONOFDIFFUSIONLENGTHSURFACERECOMBINATION

VELOCITYANDELECTRON-HOLEPAIRCREATIONENERGYBYTHE

LINESCANMETHOD

Introduction

Anelectronbeaminducedcurrent(EBIC)methodisa

convenienttechniquetomeasuretheminoritycarrierdiffusion

lengtニhLandthesurfacerecombinationvelocitysinsemi-

conductingmaterialsInthelinescanmethodLandScanbe

determinedfromthedependenceofEBIConthescanningdistance

whentheelectronbeamisscannedacrossthebarrierBerzand

Kuiken[1]gaveadetailedtheoryforthedeterminationofLand

sandOpdorp[2]investigatedexperimentallytheinfluenceof

surfacerecombinationonEBICJastrzebskieta1[31measured

Landsfordifferentgenerationdepthsbyvaryingtheaccelera-

tingvoltageofanelectronbeam

Inthosestudiesthegenerationsourcewasassumedto

beapointbutinpracticetheregionexcitedbytheelectron

beamhasafinitevolumeChiandGatos[4]determinedthe

junctiondepthbyanEBICtechniqueassumingafinitegeneration

volumeCzaja[5]andBresse[6]measuredthephysicalparameters

suchasLandtheelectron-holepaircreationenergyEpC゛when

theelectronbeamwasdirectednormaltothebarrierplane

Sheaeta1[7]investigatedtheresolutionlimitsoftheEBIC

linescanmethodtheyobtainedaone-dimensionallateraldose

functionandappliedittothemeasurementofLintheCuxSCdS

systemHowevertheydidnotdiscusstheeffectofsurface

recombinationonEBICSincethesurfacerecombination1S

stronglyconnectedwiththedepthofgenerationathree-

-31-

Fig3-1

Schematicviewof

anddefinitionsofthe

-32-

experimentalconditionscoordinatesystems

Electronbeam

Surfacecross-sectic

O゛9χ

Schottky哨Rbarrier

dimensionalgenerationdistributionmustbetakenforthedetailed

analysisofEBIC[81

Inthischapterfirstlywediscussthesurfacerecombi-

nationeffectonEBICassumingapointsourceandthendescribe

theinfluenceofthegenerationvolumeonEBICinthelinescan

methodtakingaccountofsurfacerecombinationWehavestudied

EB工Ctheoreticallyforthefinitevolumesourcewhichisdependent

ontheacceleratingvoltageandshowanimprovedmethodfor

thedeterminationofphysicalparametersofsemiconducting

materialsbasedonexperimentalresultsobtainedinSi

3-2 Surfacerecombinationeffectconsideringpointsource

ForsimpletheoreticalconsiderationwetakeaSchottky

diodeAsshowninFig3-1theSchottkybarrier1Sinthey-z

planeTheelectronbeamisincidentperpendiculartothesample

surfaceandthescanningdirectionisalongtheχ-axiswhichis

normaltothebarrierplane

Thegenerationsourceisconsideredtobeapointata

distancexgfromthebarrierandatadepthdfromthesurface

correspondingtotheacceleratingvoltagevarsquoThepositionis

XS

ぐi g゛ O゛dg)Thesteadystateexcessminoritycarrierdistribution

obtainedfromthefollowingdiffusionequation

pDnabla2pdeg - -

g6(x-゜cg゛yrsquo2olinedg)rsquo (3-1)

whereDisthediffusionconstantて1sthelifetimeandgisthe

generationrateofelectron-holepairsWhen

thesampledimensionsareassumedtobesufficientlylarge

-33-

3ta3

Normalizedscanningdistancex

(a)

Fig3-2

Fig3-3

U』

Normalizedscanningdistancex

(b)

3193

p≫Zl≫E』oz

Normalizrdscanningdistanceχ

(c)

PrimeNormalizedEBICvsnormalizedscanningdistanceχcurvesfordifferentvaluesofthesurfacerecombination

velocityparameter(seetext)SNormalizedgenerationdepthDis0001and10in(a)(b)and(c)

respectively

Oino

tou

iSu一uojsn}|ipMzireujjoZ

SurfacerecombinationvelocityparameterS

EstimateddiffusionlengthL大directlyfromthe

slopesofthecurvesbetweenthepointsatχ=2and3

Svariesfromoneto50

-34-

Dg=10

Dg=QO

151050

112345

Og<ao

161

S>0

21

Idrsquo

S5

10^

550

1必12345

135

sc^-at

SO⑤

バ宍

1012345

112345

SPg≪10

161

162S=0

SI

1(i3

1(541235

comparedwiththediffusionlengththeboundaryconditionsare

並Sz

χ=0

z=O゛

spl

z=0

=0

χ=+(x)

=0

(atthesurface) (3-2a)

(attheSchottkybarrier)(3-2b)

(3-2c)

Oncethedistributionp1SknowntheEBICcanbefound

asfollows

トeリンint]キレ

o4バ2rsquo(3-3)

whereeisthechargeofanelectronThevalueofjwascalculated

二二二二二二二エフエム2こ二言

J=

-eg

丁T

4oo

int

Dg

馴D戸

exp(-S(T-

S(司7)-

dT} (3-4)

wherexL゛DgdegdgLrsquoS=s(Lて)andTIsthevariablefor

integrationThefunctiony可7)1sthesecond-modified

first-orderBesselfunctionTheEBICisnormalizedtobeunity

whenallthegeneratedcarrierscontributetoEBIC

-35-

177FΞ-一一permil

(ぷ71

y))二1supe≧rsquo

四F

InFigs3-2(a)(b)and(c)thelogarithmofJis

plottedvsX(ΞxL)basedoneq(3-4)overtherangeofO≦X≦5一一

forS=へj50ThevalueofDgis0001and10in(a)(b)

and(c)respectivelyForS=0theintegralineq(3-4)leads

toJ=exp(-X)whichyieldsstraightlinesasshown

inFig3-20ntheotherhandallcurvesforS>Odeviate

fromthestraightlineThesurfacerecombinationgivesmuch

effectontheexcesscarrierdistributionasthegenerationdepth

becomessha110WerWhenDgis00and01thevaluesoflogJ

decreasesuperlinearlyovertheinterval0fO≦χ≦2and--

almostニlinearlyovertherangeofx≧2WhenDis10the一琴

surfacerecombinationhasaslightinfluenceandthevaluesof

logJdecreasealmostlinearlyovertheinterval0fO≦X≦5__

HowevertheslopesshowsubstantialdeviationfromunityThe

estimatedvaluesofdiffusionlengthdirectlyfromtheslopes

ofthecurvesinthelinearlydecreasingregion2≦X≦3are--

putasL火andplottedagainstSinFig3-3forDgdeg00and10

工nordinarysemiconductorsSvariesfromlt050Overthis

rangeL大Isabout80t090ZoftニherealvalueL

WhenweevaluatetheaccuratevaluesofLandSwemust

fittheexperimenpoundaldatatothetheoreticalcurvesoverthe

wholerangeofO≦X≦5WecanestimateSbyfitting--

particularlyovertheIntervalofO≦X≦2becausetheeffect--

ofthesurfacerecombinationappearsremarkablyinthisInterval

-36-

3-3 Analysisofelectronbeaminducedcurrenttakingthree-

dimensionalgenerationdistributionintoaccount

Insect3-2theminoritycarrierdistributionisassumedto

beapointButinpracticethegenerationdistributionhasa

finitevolumeinconnectionwithvThegenerationdistributiona

mustbetakenintoaccountwhentheextentofthegeneration

distributioncannotbeignoredcomparedwithL

Electronpenetratニionintosolidmaterialshasbeenstudied

bymanyauthorsTheminoritycarriergenerationdistribution

alongthedepthwasdiscussedindetailinChapterHWittry

andKyser[9]assumedthedepthdosefunctiontobeaGaussian

distributionandobtainedgoodagreementwithexperiments

EverhartandHoff[10]assumedapolynomialfunctiontoexplain

theirexperimentalresultsintheAl-SiO2-SisystemdegInthose

studiesonlythedistributionalongthezaxiswasdiscussedso

thedistributionalongthexaxiswasnotconsideredSheaeta1

[7]definedthelateraldosefunctionalongthexaxisfrom

VonGrlinrsquos[11]databutdidnotdiscusstheinfluenceofsurface

recombinationindetailSincetheinfluenceofsurfacerecombi-

nationonEBICdependsonthedepthfromthesurfacewemust

takethedistributionofgeneratedminoritycarriersinthe

x゛zplaneWeusethemodifieddiffusionmodelofKanayaand

Okayama[12]Themodel1Sverysimplebutissufficientfor

thefirst-orderapproximationtニothethree-dimensional

generationdistributionAccordingtothemodeltheelectrons

penetratestraightintothematerialtothemaximumenergy

dissipationdepthandthenscatterequallyinalldirections

makingelectron-holepairsTheshapeofthegenerationregion

becomesaspherepartofwhichisabovethesurface

-37-

Fig3-4

Tab3-1

11-

Schematicviewofelectronpenetrationisthemaximumenergydissipationdepth

a(W)

00000

1CMCO<rm

d(ym)

rdquo047

149

291

in<yi

vDVO

4VO

R(um)

100

295

13

74

20

Valuesofthecenterdgofthegeneration

volumeandtheradiusRinSiforseveralvalues

ofacceleratingvoltagevarsquo

-38-

IElectronbeam

O335

S`」「fdegce

uarrで0559j

10゛」

helliphelliphelliphelliphellip

Thecenterdgofthesphere(iethemaximumenergydissipation

depth)andtheradiusRaredependentontheacceleratingvoltage

va゛b゛lttheratiodgRisassumedtobeaconstantasshownin

Fig3-4evenWhenvaisvariedThevaluesofdgandRinSi

forseveralvaluesofvaaregiveninTab3-1calculatedwith

theaidoftheequationsofKanayaandOkayama[121

Wedividethesemi-sphereintomanysegmentsoflength

lessthanLandrepresenteachsegmentbyonepointsource

Thedensityoftheelectron-holepairsisassumedtobeuniform

withinthespheretosimplifytheanalysisThenthegeneration

strengthgofeachpointsourceisgivenbytニhefollowing

relation

Σg=G(3-5)

whereGisthewholegenerationstニrengthandΣexpressesthe

totalsummationwithinthesemi-sphereundertニhesamplesurface

TheEBICforthefinitevolumesourceisderivedby

summimgupthesolutionoftニhediffusionequationforeachpoint

sourcewhichisexpressedbyeq(3-4)Whenthedistance

betweenthebarrierandtheIrradiatedpointxbecomessmallerg

thanRsomeofthepointsourcesareforcedoutofthediode

andcannotcontributetoEBICThustheEBICdecreasesnearthe

barrierplaneWecallthisphenomenonanedgeeffectTosimplfy

thecalculationweassumethattheEBICcontributedbythe

forced-outsourcesiszeroThisedgeeffectmustbetakeninto

accountwhenthegenerationvolumeislargeincomparisonwith

thediffusionlengthWeshowanexampleforL=8ymandS=20

Whenvais10kVtheradiusRissmallcomparedwithLand

thegenerationsourcecanbeassumedasapointThelogarithm

-39-

Fig3-5

Qコー

山11

pdznpoi」oz

1020

Scanningdistanceχ

NormalizedEBICversusscanningdistanceχ

forthefinitevolumesourceThediffusionlengthLis8lsquoUmandthesurfacerecombinationvelocityparameterS(seetext)is20TheacceleratingvoltageVais50タ30and10kVfromuppertolowersolidcurverespectivelyThedottedcurveisthepointsourcesolutionforVa=50kVandtニhedashedlineisthegradientthereciprocal0fwhichgivesL=8um

-40-

1020304050(p『

゛X5入L=8μm

゛χS=20

2rsquoχyχ

゜χ

ldquoゝ5rdquo-Re-くiprocalsk)

rsquox9vesL=8|jm

rdquoゝ

2rsquo゜χ`Va=50KV

2rsquoχ

lsquoχ

lsquoゝ

5degχ

rsquoχ

rsquoχ2χ

30≒3rsquo

11diPointsourcelsquo

5solutionfor

va=50KV10

1020304050(μΓΥ

ofEBICJisplottedwithafullcurveasafunctionofthe

scanningdistancexinFig3-5logJdecreasessuperlinearlyover

theinterval0≦X≦2L(ie16uminthiscase)anddecreases--

almostlinearlyovertherangex≧2LTheslopeintherange-

O≦x≦2LisInfluencedverymuchbysurfacerecombination一一

〇necanestimateSbyfittingtheexperimentaldatatothe

theoreticalcurveinthisrangedegWhenva1S300r50kVthe

radiusRbecomesofthesameorderasLandthegeneration

volumecannotbeassumedasapointThenwedividethesemi-

sphereintomanysegmentsoflym^Thecalculatedvaluesof

EBICusingthefinitevolumesourcemethodareshowninFig3-5

ThelogJvsXcurvesshowamaximumnearthebarrierplane(

Xdeg4and7μmatvadeg30and50kVrespectively)andlogJdecreases

almostlinearlybeyondthesemaximumpointsThemaximumvalue

ofJbecomessmallasvincreasesThesurfacerecombinationadoesnotaffecttheshapeofthecurvesandsoLcanbedetermined

mainlyfromtheslopeofthelinearregionofthesecurves

independentlyofsThereciprocalslopeofthislinearportion

gives7ymwhichis87Zoftherealdiffusionlength

ThevalueofEpc゛rsquobywhichanelectron-holepairis

createdcanbedeterminedfromtheabsolutevalueofEBIC[13]

ThevalueofJinthecaseofS=501sabout70Zofthatinthe

caseofSdeg1whenvais50kv゛andsowemakelargeerrorsinthe

determinationofEifwedonotconsiderthesurfacerecomblna-pc

tioneffect

Thepointsourcesolutionatva゛50kVisshowninFig3-5

bythedottedlinewhenthegenerationoccursatthemaximum

energydissipationdepth(ie67ymfromTab3-1)

Theslopeofthepointsourcesolutionovertherangex≧2LIs-

almostequaltothatofthevolumesourcesolutionbutthe

normalizedEBICis60Zofthatofthevolumesourcesolution

-41-

Fig3ldquo6

Chopping

こ011

Scanningcoil

Schematicdiagramoftheexperimentalset-up

-42-

コ4[Osc

lsquo~|-

|コt

||IElectronbeamReference

||

Sample

RL`Lock-inampχ-yrecorder

3-4 ExperimentalresultsinS1

Aschematicdiagramoftheexperimentalset-upisshown

inFig3-6Theacceleratingvoltage1Svariedfrom10t050kV

TheprimaryelectronbeamcurrentismeasuredbyaFaradaycage

andabout2times10oline10ATheinducedcurrentwasmeasuredfromthe

voltagedropacrosstheloadresistanceILdegThecurrentニIL

whichflowsthroughtheresistanceisexpressedasfollows

hdeg^sc-I{exp[(ekT)ILRL]-1} (3-6)

whereloisthebackwardsaturationcurrentand^scisthe

short-circuitcurrentwhichistherealEBICInordertoneglect

thesecondtermofeq(3-6)theEBICwasmeasuredinthefollowing

condition

h゛kTe (3-7)

InthepresentexperimenttheEB工Cwasmeasuredatroomtempera-

tureandso゛hhwaskeptlessthanlmvdeg

Theelectronbeamwaschoppedat3kHzwithachopping

coilinsertedintothebeampathSignalsassmallas1μVcould

bemeasuredwithagoodsignaltonoiseratiousingalock-in

amplifier

Thesamplesweren-typeSiwithresistivitypof10

and01ΩCm0hmiccontactsweremadebyevaporatingantimony-

dopedgoldontothesampleandalloyingat400degCfor2mln

Schottkycontactsweremadebyevaporatinggoldinavacuumas10W

as10oline7TorrThesamplewasinsertedintoavacuumchamberfor

EBICmeasurementimmediatelyafteritwascleavedandmeasured

-43-

3IS3

paziicuijoz

1020304050(pm)

Scanningdistancex

Fig3-7

Experimentalresultsfor

sampleA(p=lf2cin)whereL=

8μmandS=20Fullcurves

arethetheoreticalrsquoones

11(il

>P≪4<N1≪CM<Pq

1 1

3193paziipujjoZ

1164

50

Scanning

100

distance

Fig3-8

150

X(μm)

200

ExperimentalresultsforsampleB

(p=01f2cin)whereL=80urnandS=50

Fullcurvesarethetheoreticalones

Valueswithouttheinfluenceofan

ohmiccontニactareshownbydotted

curves

-44-

124(m)

5XExperimentalvaluesX---Va=50KV

2NNo30

1X一--10KV4

5しL=8pm

2χ

2χ

5χ

-Theoretical

5curve

41

50100150200

Experimentalvalues

--4=50Kv

lo―30KV

hellip-10KV

-ゝゝI゛゛゜゛ペヘヘ

helliphelliphelliphellipyhelliphelliphelliphellip

Theoreticalcurvehelliphelliphelliphellip9lsquorsquolsquo゜

Ldeg80μΓTlぶ

S=50

inavacuumas10was1times10oline8TorrTheresidualgasesonthe

cleavedsurfacewerecleanedbyargonionsputteringtoavoid

contaminationofthesurfacebyanirradiatニedelectronbeam

TheexperimentalresultsofsampleA(p=10ncm)are

showninFig3-7forva=1030and50kVrespectivelyEach

fullcurveisthetheoreticaloneforthecaseofL=8umandS=20

工fthediffusionconstantD1Stakenas16cm2Solinelthelifetime

てis4times10oline2μSandthesurfacerecombinationvelocitysis

4times105cmsolinelSurfacerecombinationhasagreatereffectasthe

generationdepthbecomesshallowerthatisVbecomeslower

AndsothevaluesofSandLcanbeestimatedmainlyfromthe

curvesforthelowestニandthehighestva(idege103゛d50kV

inthisexperiment)respectivelyTheexperimentalresultsfor

eachacceleratingvoltageagreeverywellwiththetheory

Theexperimentalcurvesforvadeg1030and50kVhaveamaximum

atxdeg02and4ymrespectivelyandeachmaximumvaluebecomes

smallerasvincreasesasdescribedinthetheoryHowevera

themaximumvalueandthepositionwheretheEBICshowsapeak

deviateslightlyfromthetheoryinthecasesofvadeg30and50kVdeg

Thisdiscrepancymaybeattributedtotheassumptionofuniform

densityofgenerationTheactualdistributionmaybelocalized

atthecenterofthegenerationvolume[9]andmoredetailed

treatmentforthegenerationshapeandthegenerationdensity

Isneeded

Inthecaseofthelocalizeddistributionofgeneration

wecanapplythesamemethodasdiscussedinsect3-3Ifthe

constantgischangedintoanappropriatevariablewhichexpresses

thelocalizeddistributionbetterresultswillbeobtained

HowevertheassumptionoftheunifoinndensityIssufficientfor

thequalitativeanalysisoftheInfluenceofthegenerationvolume

onEBIC

-45-

TheexperimentalresultsofsampleB(p=01ficm)are

indicatedinFig3-8inthesamewayassampleAThevalues

ofLandSare80ymand509respectivelyIfDis16cm2solinel

てis4ysandsis1)(105cmSoline11nthiscaseLisgreaterthan

thegenerationvolumeevenwhenvadeg50kVandthevolumesource

effectappearslessclearlythaninsampleAThediscrepancy

witニhintheinterval0<xく15urnisduetothesamereasonas

thatdiscussedInthecaseofsampleATheslopesofthecurves

overtherange15≦x≦100μmarelesssteepasvbecomes--a

higherbecausetheinfluenceofsurfacerecombinationdecreases

Theinfluenceofohmiccontactappearsovertherangex≧120μm-

sincethediffusionlengthisabouthalfofthesamplethickness

of200μmTheoreticalvaluescalculatedusingthemirror

imagemethod[14]discussedinChaptervareshownbyfull

curvesinFig3-8Valueswitニhoutニtheinfluenceofanohmic

contactarealsoshownbydottedcurves

Thescanningsurfacewasnotaffectedbyanelectronbeam

oftheorderof2times10oline10Abecausethesameresultwasobtained

forshallowexcitation(vadeg10kV)afterthesamplewasirradiated

for1hatV=10へ一50kVa

ThedepletionlayerwidthisnotbroughtIntoconsidera-

tionbecauseofitsnarrownesscomparedwiththescanningdistance

Theelectronbeamdiameterofabout50nminthisexperiment

1Snottakenintoaccountsinceitisverysmallincomparison

withthegenerationregionevenifvais10kvdeg

工fthebeamcurrentiskeptconstantthegeneration

densitydecreaseswithincreasingVbecausethegeneration

volumeincreasessuperlinearlywithvarsquo゜Whenthebeamcurrentis

2times10oline10Aandvais10kVtheexcessminoritycarrierdensity

-46-

atthegenerationpointisabout5times1014Cmoline3(themaximum

generationdensityinthisexperiment)followingthediscuss10n

inref[1]whichissmallerthanthemajoritycarrierdensity

1nthesamplesThereforethevalueofLismeasuredatthe

lowinjectlonlevel

3-5 Summary

Thegenerationvolumeofminoritycarriershasa

considerableeffectontheEBIClinescanprofilesespecially

whenItisequaltoorlargerthanthediffusionlengthWe

investigatedthedependenceofEBIConxforgeneralsurface

recombinationvelocityinthecaseofthefinitevolumesource

Whenvaislowandthegenerationdepthisshallow

surfacerecombinationhasalargeeffectonEBICWhenvaishigh

andthegeneratニiondepthisaslargeasthediffusionlengththe

generationregioncann0longerbeassumedasapointandthe

finitevolumesourceshouldbeusedintheanalysisThetheo-

reticalcalculationshowsthatsurfacerecombinationhasonlya

slighteffectontheshapeoflogJvsXcurvesbutaffectsthe

absolutevalueofJTheaccuratevaluesofLsandEshouldbepc

estimatedbyfittingtheexperimentaldatatothetheoretical

curvesforallacceleratingvoltagesExperimentalresultsinthe

measurementofLandSonS1Schottkydiodesshowedgoodagreement

withthetheoryatboth10Wandhighvadeg

TheexperimentalresultthatEBIChasamaximumnear

thebarrierplanewasexplainedqualitativelyusingthesimple

model0fthefinitevolumesourceItcouldnotbeexplainedby

thepointsourcesolutionFurtherinvestigationofthisedge

effectwillclarifythegenerationdistributionbyanelectronbeam

-47-

References

[1]

2]

31

[41

[7]

[8]

[9]

[10]

FBerzandHKKuikenSolid-stateElectron

437(1976)

19

CvanOpdorpPhilipsResRep_32192(1977)

LJastrzebskiJLagowskiandHCGatos

ApplPhysLett27537(1975)

JApplPhys481730(1977)

JYChiandHCGatosIEEETransElectronDev

ED-241366(1977)

WCzajaJApplPhys2Z^236(1966)

JFBresserdquoScanningElectronMicroscopy1972

Partlrdquo[SEM]nc工ITRIChicago)pp105-112

SpSheaLDPartニainandpJWarterrdquoScanning

ElectronMicroscopy1978Vol1rdquo(SEMIncAMFOrsquoHare)

pp435-444

GVSpivakGVSaparinandLFKomolova

rdquoScanningElectronMicroscopy1977rdquo(SEMInc

IITRIChicago)pp191-199

DBWittryandDFKyserJApplPhysj廻375

(1967)

TEEverhartandpHHoffJApplPhys

(1971)

-48-

42

-5837

[n] AEvonGriinZNaturforsch12a89(1957)

【12】KKanayaandSOkayamaJPhysDApplPhys

543(1972)

[13]CJWuandDBWlttryJApplPhys492827

(1978)

[1410vonROOSSolid-stateElectron111063(1978)

-49-

4-1

ANALYSISOFTHREE-DIMENSIONALGENERATIONDISTRIBUTION

BYTHECOMBINATIONOFTHENORMALINCIDENCEANDTHE

LINESCANMETHODS

Introduction

TheminoritycarrierdiffusionlengthLandthesurface

recombinationvelocityScanbedeterminedbyanEBICtechnique

withboththenormalincidenceandtニhelinescanmethodsusing

SEMasdiscussedinChapters皿andHITheminoritycarrier

generationdistributニionbyanelectronbeamplaysanimportant

roleintheanalysisofEBICWhenthedimensionofthegeneration

regioniscomparablewithorlargertニhanLthegenerationregion

cannotbeassumedasapointandthegenerationdistribution

mustbetakenintoaccount

Thegenerationdistributionbyanelectronbeamhasbeen

investigatedbyseveralauthorstheoretically[1]andexperimental-

1y[2-51Asregardstheone-dimensionaldistributionaGaussian

[2-3]orpolynomial[4]functionwasassumedforthedepthdose

functionandthecombinationofexponentialdecayfunctions[51

wasusedforthelateraldosefunctionInChapter工皿the

influenceofthethree-dimensionalgenerationdistributionon

EBICinthelinescanmethodswasstudiedassumingasimple

distribution(semisphere)withuniformminoritycarrierdensity

Ineachoftheseexperimentsonlyonemethodタeitherlinescan

ornomalincidencewastakenTheelectronpenetrationdepth

andthegenerationdistributiondifferedfromeachother

-50-

Schottky

barrier

Fig4-1

2P

Surfacecrosssection

「egion

Oneofthedividedsegments

Schematicviewofexperimentalconditionsandthedefinitionofthecoordinatesystem

-51-

Electronbeam

hottkySurfacecrossse

arrierOGene芯ion

Re゛region

Oneofthe

々dividedsegi

InthischapterwemeasuredEBICbyboththelinescan

andthenormalincidencemethodsinthesamesampleandclarified

thegenerationdistributionTheinfluenceofthethree-dimensional

generationdistributiononEBICisdiscussedassumingthatthe

electron-holepairsarelocalizedatニthecenterofthegeneration

regionTheexperimentニalresultsforGaAsSchottkydiodesare

alsoshown

4-2 Influenceofthree-dimensionalgenerationdistribution

onelectronbeaminducedcurrent

WeusedaSchottkydiodesinceitcanbeappliedforboth

thelinescanandthenormalincidencemethodsInthelinescan

methodtheEBICiscalculatedtakingtニhegenerationdistニrlbution

intoaccountbyasimilarmethoddiscussedinChapterⅡ工The

generationregionisdividedintomanysegmentsthesizeofwhich

issmallerthanLandeachsegmentisrepresentedbyonepoint

sourceTheEBICforthefinitevolumesourceisderivedby

summingupthesolutionofthediffusionequationforeachpoint

sourcersquo

Thedistributionisassumedtobesphericallysymmetric

asisshowninFig4-1Theelectron-holerdquopairsgeneratedbyan

electronbeanareconsideredtobelocalizedatthecenterRCof

thegenerationregionThegenerationstrengthgalonganyradius

vectorfromRc1Sassumedtobegivenby

gdeg^exp[-C(r2R2)] (4-1)

whereRisthedistancebetweenRandthemaximumelectronrange

CRm゛andristhedistancebetweenRCandeachdividedsegment

(seeFig4-1)

-52-

TheexponentCrelatestothedistributiondensityThedensity

becomesuniformasdiscussedinChapterl[EwhenC1Szeroand

theelectron-holepairslocalizenearRcwhenCbecomeslarge

Thedistributionisassumedinorderthatthedepthdosefunction

maybecomeGaussianasisreportedinthereferences[23]

ThevalueofLshouldbesmallinorderthatitcanbe

measuredbyboththelinescanandthenormalIncidencemethods

ThereforewetakeGaAsasanexampleInthelinescanmethodwe

calculatetheEBICintensity(whichiscalledthecollection

efficiencynandisnormalizedtobeunitywhenallthegenerated

carrierscontributetoEBIC)forseveralvaluesofCandR

The゛ilueofRmisgiven[2]by

町゜001A8Vノ゛フurn

cR

m゛

(4-2)

wherevaistheacceleratingvoltニageinkVThevaluesofCand

RRareassumedtobeconstantevenifvisvariedWhenvisCm

10and30kVaa

Rm

becomesOdeg74and4deg8ymrespectニivelyWetake

thetypicalvalueofLas1μminordertoexaminetheinfluence

ofthegenerationdistributiononEBICbecausethevalueofRm

issmallerthanLatva゛10kVbutlargerthanLatvadeg30kvrsquo

SincethesurfacerecombinationvelocitySofGaAsisoftheorder

of105-106cmSoline1[6-9]wetakevaluesofland50asthe

surfacerecombinationvelocityparameterSdefinedbySΞS(Lて)

(TisthelifetimeoforderofnS)

TheresultsofthecalculationareshowninFig4-2The

fullcurvesandthebrokencurvesareforCdeg8rsquo2゛RcRm゛Olsquo13and

C=54RR゜013respectivelyThesevaluesofCandRじmolinersquoCrsquom

thetypicalvaluesobtainedbythenormalincidencemethodin

GaAs[23]Thepointsourcesolutions(whichareobtainedby

assumingthatallthegenerationoccursatRc

-53-

are

)arealsoshownby

g`

A3U413Ud

COP≫no3

Fig4-2

ScanningdistanceX(pm)

j一次゜ごゴ野謡ごごご二ににごS

ご諧驚お謡謡S回読で昌翼麗

二竃Jeぎ驚謡じ雲Cにニごまふ(

ごごぶ謡1ば昌permilお穴混戮ずpermil

ぶぶごご1ここなSttedcdeges゛ecm

-54-

helliphellipl

]]1A

Ee

ビゲヤ

12

ss50

helliphelliphellipyJミ4sdeg50

dottedcurvesAtVa゛10kVthesizeofthedividedsegmentis

takenas005umwhichissmallerthanLsothateachdivided

segmentcanberepresentedbyonepointsourceIntheregion

05≦x≦15ymthelogarithmofEBICdecreasessuperlinearly--

anditdecreasesalmostlinearlyovertherangeofx≧15um-

ThetendencyappearsmoreapparentasSbecomeslargeThechange

oftheexponentCmakeslittledifferencetotheprofilesofthe

curvesTheabsolutevalueofnovertherangeofx≧05umis-

almostequaltothepointsourcesolutionwhenS1S1butbecomes

twicethatwhenSis50Thepeaksnearthebarrierareduetothe

edgeeffectasdescribedinChapterl工゛Atvadeg30kVthesizeof

thedividedsegmentistakenas02ymforthesamereasonas

Wit二hvadeg10kVThecurvesarequitedifferentfromthepointsource

solutionbothatS=1andS=50becausethedimensionsofthe

generationregionarelargeincomparisonwithLandthepoint

sourceassumptionisn0longervalidinthiscaseTheprofiles

ofthecurvesreflectthegeneratニiondistributionasoneseesthat

theprofilechangesifCvalsquotiesfrom54t082WhenSisvaried

fromlto50theprofiledoesnotchangeatthesameCvaluebutニ

ndecreasesbyabout30ZofthatofS=lItshouldbenotedthat

thesurfacerecombinationhasaninfluenceontheabsolutevalue

ofEBICevenifthevalueofRm(4deg8pm8tvadeg30kV)ismuch

greaterthanLThereforewecanevaluateLmainlyfromthe

slopeofthelinearregionat10Wvaconsideringthesurface

recombinationeffectandestimatethegenerationdistribution

fromtheprofilesofthecurvesinthecaseofhighva゛

-55-

Fig4-3

pasube

coipai

-O

Maximumelectronraり9eRm(μm)

AcceleratingvoltageVa(kv)

Experimentニalresultsofthenormalincidence

methodforthesampleA(SndopedGaAsn=62times1016

cm^L=03)Jm)andthesampleB(TedopedGaAs

ndeg80times1016cmoline3Ldeg07μm)Experimentalvaluesare

shownbycirclesThefullandbrokencurvesare

theoreticalcurvesforC=82RR=013andC=54

RcRmdeg013respectivelywdeg10cnmmandwddegOdeg151Jmdeg

-56-

12410oline

GaAsn(c「7i」

5A訟ばn

2ゝゝゝ

ゝゝ

ゝゝゝ

ゝゝゝrsquoL(pm)

1゛゛`ヽBO7J

yWヽ

5oline`olinersquo54013A03

≒旨

2φ

(52Schottkか

デ1テシフ)卜

1020304050

Theelectron-holepaircreationenergyEisobtained

fromthefollowingequation[101

n=ErdquordquoEBIC

pcIBvak(4-3)

whereIBisthebeamcurrentandkisthecorrectionfactorfor

theback-scatteredelectronsAsdescribedpreviouslythevalueof

nisinfluencedbySevenwhenVishighandsowemusttakeolinea`lsquorsquoolineolineolineolineolineolineolineolineolineolineoline

thesurfacerecombinationeffectintoaccountwhenweevaluateE

pc

4-3 Three-dimensionalgenerationdistributニioninGaAs

Thesameapparatusandthelock-intechniquewereused

asdescribedinsect3-4TheSchottkybarrierwasmadeonn-typeGaAs

wafersbyevaporatingAuofabout10nmthickinavacuumofabout

10rsquo7TorrTheohmiccontactwasobtainedbyevaporatingAu-Geand

alloyingat400degCfor2minThecarrierdensitynofeachsample

wasdeterminedbyc-vmeasurements

Theexperimentalresultsofthenormalincidencemethod

forthesampleA(Sndopedn=62times1016cmoline3)andthesampleB

(Tedopedn=80times1016cmoline3)areshowninFig4-3byfulland

opencirclesrespectivelyThevalueofvawaSvariedbetween5

and50kVTheEBICintensityincreasedlinearlywithIBwithin

therangeof1times10oline11≦IB≦-1times10oline9Awhenvawasfixed

whichsatisfiedthelowinjectionlevelconditionThecollection

efficiencynwascalculatedbythesamemethodreportedinref[10]

bychangi昭RcRmfrom01t0025andCfrom30to90

respectivelyThebestfitcurveswiththeexperimentalresults

wereobtainedInthecaseofL=03and07umforsamplesAandB

respectivelywhenRcRm゛O゛13andC=82wereusedThevaluesof

-57-

II

A3ua<3UduqjDaiion

ScanningdistanceX((jm)

Fig4-4

Experimentalresultsofthe

linescanmethodforthesampleA

[SndopedGaAsn=62times]016cmoline3)

Thefullandbrokencurvesare

ー い゛I

゛゛

ldquooU 5

Scanningdistancex(μm)

Fig4-5

ExperimentalresultニSofthe

linescanmetニhodforthesampleB

(TedopedGaAsn=80times1016cmoline3)

Thefullandbrokenlinesare

theoreticalcurvesforC=82RRtheoreticalcurvesforC=82R

=013andC=54RR=013cdeg=013andC=54RR=013c

respectivelyLdeg03cμmS゛20respectivelyLdeg07ymSdeg20

-58-

ぎ忌

五゛

olinelo

jV

ズごy

23

times1

GaAだj

j73C4Electron

L=07μmEbeam

2Sdeg20χ

1rsquo`

゛x

ya(W

2゛Va=30W

2_JE201

4一一―54013

5≒

脅χ

21`f

ゝ≒

ゝへ

5χ

147

RCRmandCagrees`゛iththerepoidegtedvalues[2]゜Thefulland

brokencurvesinthefigurearetheoreticalcurvesforC=82

RcRmdegOdeg13andC゛5deg4゛RcRmdegOlsquo13respectニivelylsquoThediscrepancy

betweenthetheoreticalcurvesandtheexperimentalvaluesat

10WvacanbeexplainedinthefollowingwaydegThegeneration

regionbecomesshallownearthesurfaceatlowVandtheEBIC

ismainlycontributedbytheseperatedelectron-holepairsin

thespace-chargeregionjustunderthesurfaceInthetheoretical

calculationitisassumedthatthere1Snorecombinationinthe

space-chargeregionButニinactualfactthecarriersrecomblne

throughthevarioustrapswhichreducestheEBIC

Theexperimentalresultsofthelinescanmethodforthe

samplesAandBareshownbycirclesinFigs4-4and4-5

respectivelyThetheoreticalcurvesareexpressedbythefull

(Cdeg82RcRmdeg013)andthebroken(C=54rsquoRcRmdegOdeg13)curves111

bothfiguresTheEBICintensityincreasedlinearlywithIBwitニhin

therange1times10oline11くrsquoIく1times10oline9Awhenvwasfixedat100r=B=a

30kVwhichsatisfiedthe10wInjectionlevelconditionasinthe

normalincidencemethodThetheoreticalcurvescalculatedusing

thesameparameterdeterminedbythenormalincidencemethodshow

goodagreementwiththeexperimentニalresultsatbothvadeg10and30

kVWhenwetakeintoaccountthattheexperimentalresultsat

vadeg30kVreflectthegenerationdistributiontheassumedgeneration

distributionbyeq(4-1)withC=5Aへ82andRcRmdegOdeg131s

consideredtobeappropriateforthethree-dimensionalgeneration

distributioninGaAs

Thevalueofkchangesfrom078to075whenvvariesa

from5t050kV[10]Whenwetaketheappropriatevalueofkfor

themeaSuredva゛Epccanbedeterminedbyeq(4-3)Thevaluesof

-59-

Normalincidence Line scan

V(kv)a

E(eV)GaAsCSndoped)pc

GaAs(Tedoped)

5-50

41

39

14

3 9

30

Tab4-1 Valuesoftheelectron-holepaircreationenergyEinGaAsdeterminedbytニhenormalincidenceandlinepc

scanmethods

-60-

Eobtainedbythenormalincidenceandthelinescanmethodsarepc

39Oi41eVand38へj44eVrespectivelyastabulatedin

Tab4-1BythenormalIncidencemethodWuandWittry[10]

determinedEpCas468eVwhichwasabout15Zlargerthanour

resultsOnereasonforthediscrepancy1Sthedifferenceofthe

generationdistributionsThemodifiedGaussiandistributionused

bythemslightlydifferedfromtheGaussiandistributionusedin

ouranalysisAnotニherreason1Stheaccuracyofmetalthickness

WeestimatethethicknessfromtheweightofthechargedAuwhich

1SevaporatedtomaketheSchottkybarrierThereforetニheobtained

valuemaybedifferentfromtherealthicknessInthelinescan

methodEBICbecomesinsensitivetothemetaltニhicknessandthe

trapsinthespace-chargeregionbutisinfluencedbysurface

recombinationasdiscussedbeforeAlferoveta1[11]andWittニry

andKyser[12]reportedEpcas32へj44eVand46eVrespectニive-

lyfromthepeakvalueofEBICwhentheelectronbeamcrossedthe

p-njunctionOurresultsof38へj44eVareinthemiddlerange

oft二heirvaluesIntheiranalysestheydidnottakethesurface

recombinationeffectintoaccountandsoourresultsareconsidered

tobemorereliablethantheirs

4-4 Summary

Thethree-dimensionalgenerationdistributionbyan

electronbeaminGaAswasinvestigatedbymeasuringEBICwitha

combinationofnormalincidenceandlinescanmethods

TheprofileoftheEBICcurvesinthelinescanmetニhod

expressesthegenerationdistributionwhenvaishighandthe

dimensionofthegenerationregionislargerthanLThesurface

-61-

recombinationdoesnotaffecttheprofileofEBICbutlowersthe

collectionefficiencyTheaccuratevalueoftheelectron-hole

paircreationenergymustbedeterminedbytakingthesurface

recombinationeffectintoaccount

TheexperimentalresultsinGaAsSchotニtkydiodeswith

differentdiffusionlengthsshowedthatthecenterofthe

generationregion(iethemaximumenergydissipationdepth)

waslocatedatthepointof0130fthemaximumelectronrange

andtheradialdistributionfromthecenterwasshowntobe

Gaussianwithaneχponentof54へ-82Theelectron-holepair

creationenergyinGaAswasdeterminedas38rsquoV44eV

References

[1]

[2]

[5]

[6]

KKanayaandSOkayamaJPhysDApplPhys

543(1972)

DBWittryandDFKyserJApplPhys旦旦375

(L967)

VVMakarovSovPhys-Semicond旦722(1975)

TEEverhartandpHHoffJApplPhysを

5837(1971)

SpSheaLDPartainandpJWarterrdquoScanning

ElectronMicroscopy71978V011uml(SEMIncAMFOrsquoHare)

pp435-444

LJastrzebskiHCGatosandJLagowski

JApplPhys481730(1977)

-62-

[7]

[81

[9]

[10]

[11]

[12]

LJastrzebskiJLagowskiandHCGatos

ApplPhysLettri537(1975)

MEttenbergHKresselandSLGilbert

JApplPhys44827(1973)

CAHoffmanKJarasiunasHJGerritsenand

AVNurmikkoApplPhysLett22536(1978)

CJWuandDBWlttryJApp1PhySpoundrsquo2827

(1978)

ZhIAlferovVMAndreevVIKorolrsquokovand

vIStreminSovPhys-Semlcond41113(1971)-

DBWittryandDFKyserJApplPhys

361387(1965)

-63-

5-1

ANALYSISOFELECTRONBEAMINDUCEDCURRENTCONSIDERING

SAMPLEDIMENSIONS

Introduction

Anelectronbeaminducedcurrent(EBIC)methodusing

ascanningelectronmicroscope(SEM)isaconvenienttechniqueto

measuretニheminoritycarrierdiffusionlengthLandthesurface

recombinationvelocitySinsemiconductorsTherehavebeenmany

theoreticalandexperimentalstudiesonthelinescanmethodof

EBICInChaptersI工andytheEBICwasanalyzedquantitatively

takingthethree-dimensionalgenerationdistributionintoaccount

bythedividingmethodandtheimprovedmethodtocharacterize

Landswassuggestedχihenthesampledimensionsarelessthan

oneortwodiffusionlengthstheminoritycarrierdistribution

isaffectedverymuchbysampledimensionsRoos[1]analyzed

EBICtheoreticallyinthecaseofthinlayersHecalculated

thedependenceofEBIConthescanningdistancexintherange

ofxL≪1inthesampleswithwL=land05(wlayerthickness)j

andshowedthatLcouldnotbedetermineddefinitelyfromthe

slopeofthelogarithmofEBICvsXcurve

InthischaptertoanalyzeEBICconsideringthesample

dimensionsgwediscussasimplemethodusinganimagesource-and-

sinkdistributionWeshowthedependenceofEBIConxoverafull

scanrangewhenthelengthbetweenapotニentialbarrierandan

ohmiccontactisequaltoandsmallerthanthediffusionlength

andmentionsomeimportantニpointstobenoticedinthedetermination

ofLandsTheexperimentalresultsinSiSchottkydiodesarealso

shown

-64-

Fig5-1

ySご

uarrj

Schottkybarrier

uarr

Ohmiccontact

Schematicviewofexperimentalconditionsanddefinitionofthecoordinatesystem

-65-

Electronbeam

-J-

レじ2「lingtrack_^一分

りhelliphelliphellipljc1お迄゛

IL

5-2 Determinationofdiffusionlengthandsurfacerecombination

velocity

ForsimpletheoreticalconsiderationwetakeaSchottky

barrierdiodeAsshowninFig5-1theSchottkybarrierisin

they-zplaneandtheelectronbeamisincidentニperpendicularto

thesamplesurface(χ-yplane)Thescanningdirectionisalong

theX-axiswhichisnormaltothebarrierplaneThegeneration

sourceisconsideredtobeapointニandislocatedat(゛grsquo

Thesteadystニateexcessminoritycarrierdistributionpis

obtainedfromthefollowingdiffusionequation

Dnabla2pdeg二T

-g6(x-xyz-d)rsquo

O゛dg)

(5-1)

whereDisthediffusionconstantンTisthelifetimeandgisthe

generationratニeofelectron-holepairs

工fthethicknesswbetweenthepotentialbarrierandthe

ohmiccontactismuchgreatニerthanLandtheotherboundariesin

theyandzdirectionsarebothmuchfurtherawayfromthe

generationsourceEBICiscalculatedunderthefollowingboundary

conditionsasdiscussedinsect3-2

3p-9z

χ=0

x=-H≫

Z=0

Z=0

=0(attheSchottkybarrier)

=0

wheresIsthesurfacerecombinationvelocity

-66-

(5-2a)

(5-2b)

(5-2c)

(5-4)d帽

wherexgrsquoLrsquoDgdegdLSdegs(Lて)andTisthevariablefor

-67-

integrationThevalueofJ(x)isnormalizedtobeunitywhena11

thegeneratedcarrierscontributetoEBICThefunctionK(ぺ7)

isthesecond-modifiedfirst-orderBesselfunction

FortheanalysisofEBICconsideringsampledimensions

wetakethefundamentalcasethatthediffusionlength1S

comparablewithorlargerthanthethicknessw(seeFig5-1)

OncethedistributionpisknownEBICcanbefoundasfollows

十(゛十(゜3p

j=eDintint-

0 -003χ

dydz

χ=0

(5-3)

whereeisthechargeofanelectronBerzeta1【2】solvedthe

diffusionequation(5-1)undertheboundaryconditions(5-2a)

(5-2b)and(5-2c)bythemirrorimagemethodInadditiontothe

reaLsourceatxg゛animagesinkwasintroducedatthesymmetric

position-XwithrespecttotheSchottkybarrier(seeFig5-2)

Whenthematerialextendstoχ=plusmndegdegthesolutionofeq(5-l)is

givenbypμ](゛゜土)゛WhentheSchottkybarrierisintroduced

theminoritycarrierdistribution1Sexpressedasp[x]十p[oline゛g]

inordertosatisfytheboundarycondition(5-2bplχ=OdegO)rsquo

andjisobtainedasfollows

J()゜

-eg-

-π

DgK(ぶ77F)

リinto

うと縦卜-dT

-H≫

十intexp(-S(T-D))

Dg

g ぜ)ケ

Thenonemustusethefollowingboundaryconditioninsteadof

(5-2c)

Ix=wdegO(attheohmiccontact) (5-2crsquo)

ThesolutionQfeq(5-1)undertheboundaryconditions(5-2a)

(5-2b)and(5-2crsquo)canbeobtainedbyextendingthemirrorimage

methodproposedbyBerz[2]andOpdorp[3]Inadditiontothereal

sourceatXafamilyofvirtuaLimagesourcesandsinksare

introducedatthesymmetricpositionswithrespecttothebarrier

andtheohmiccontact(seeFig5-2)Openandsolidcircles

representthesourcesandsinksrespectivelyThereforethe

sourcesareatX2w十Kg4W十xg゛゜rsquo゜lsquoand-(2w-x)-(4w-x)rdquoldquo゛

andthesinksareat-X-(2w十X)-(4w十X)and2゛゛olinersquo4゛olinersquo

respectivelyWhenthematerialextendstox=士≪>thesolution

ofeq(5-l)isgivenbyp【゛】(゛゜土゛grsquo士(2゛`7oline゛g)rsquo土(2W十)rdquorsquo゜rsquo)

(seeFig5-2)Iftニheinfluenceofohmiccontactニmustbetaken

intoaccounttheminoritycarrierdistributionisexpressedusing

thefollowinginfiniteseriesinordertosatisfytheboundary

conditions(5oline2brsquoplx=OdegO)811d(5oline2c≒Plx=wdegO)rsquo

p゛[゛g]゜jp[≒ 十p[oline

十p[2゛oline]十p[-(2W-X)

+p[2w十゛g]十p[-(2w十)

十一一一一一一-一一

9 (5-5)

Theinducedcurrentsbypairsofsourcesandsinksie

p[゛g]andp[oline゜cg]rsquop[2゛olineへ]andpr-(2w-x)]rsquop[2゛十]andp[-(2v゛十)]rsquo

areexpressedbyJ(x)-J(2v゛oline゜cg)J(2w十)゛rsquo゛゜゛rsquo

respectivelywiththeaidofeq(5-4)ThenthetotalEBICis

expressedintheinfiniteseriesasfollows

-68-

Fig5-2

Source

helliphelliphellipSink

Concentration

Sdηitky

barrier

Ohmic

contact

Schematicviewofexcessminoritycarrierconcentrationpatternforeachsourceandsinkwhicharerepresentedbytheopenandsolidcircles-respectively

-69-

pr2wχ9]

plE【2w->り》】1

1rdquoMI

-E唇-

゜(2WdegO`92Wi

ミplE)rsquo゛p[2w-xg]

pl-《2w+x)】)゜91

s哺

(n

L1)

paziipEJoz

1 2 3

Normalizedscanningdistancex

0 5

M)DUd|UOISコ|}Ppazneaijoz

12 5 X)2050

Fig5-3

DependenceofEBIConthe

normalizedscanningdistanceχ(equivxL)

fullandbrokencurvesarefortニhecaseswithandwithouttheinflu-

enceofohmiccontニactrespectivelyThenormalizedsamplewidthwLis

1020and30andthenormalized

generationdepthDgisOdeg0Thevaluesofthesurfacerecombination

velocityparameterS(seetext)

areland10forupperandlower

groupofcurvesIrespectively

Fig5-4

Estimateddiffusionlength

fromthereciprocalgradientof

thecurveatthecenteroftニhe

scanningdistanceinthecaseof

DgdegOlsquoOandwLdeg1lsquoOSvaries

fromlt050L大andL訟are

forthecaseswithoutandwith

theinfluenceofohmiccontact

respectively

SurfacerecombinationvelKitypmmeterS

-70-

Dgdeg00

そー=10

L゛で

ヽ1慟1

111

25=1rsquo1

1`11

【flll

11

51s

degilOII

211`4

111

(flll゛

芒゜11゛|`

51S`|

11゛1

|ぎ=21`ヽ

||rsquo゜3|

(y

J(Xg)=J(x)-J(2v゛oline゛g

olineJ(匈゛≒

)十J(2wトxg

)十J(4wヽ4-xg

----

II

(5-6)

ThevalueofJ大convergestoacertainvalueandcanbecalculated

byacomputerincasesofanyvaluesofwLandS

InFig5-3thelogarithmofJisplottedbysolidlines

asafunctionofx(=xL)whetvwL1S1020and30and

Dgis00Thedashedlinesareforthecasewithouttheinfluence

ofohmiccontactTheupperandlowercurvesareforS=1and10

respectivelyThevaluesoflogJ大decreasesuperlinearlywithin

onediffusionlengthawayfromthebarrierThereforeonemakes

considerableerrorsifoneestimatesthevalueofLfromthe

reciprocalgradientofthecurveatarbitraryXInordertoshow

anextremeexampleweconsiderthecaseofw7Ldeg1゛08叫DgdegO`Odeg

Thereciprocalgradientofthecurveinthelinearregionat

xdeg05withoutandwiththeinfluenceofohmiccontactareputas

L大andLrespectivelyThevaluesofLandL幼thuSobtained

areplottedasafunctionofSinFig5-4WhenSisunityL

1Sabout68ZofLandL政isabout44ZofLThevaluesofL大

andL政reducetoonlyaboutonethirdofLwhenSis50

Themethodoftheanalysisforapointsourcementioned

abovecanbeeasilyappliedtothefinitegenerationdistribution

bythedividingmethoddiscussedinChaptersI工andHEspecially

inthecasesoflight-emittingdiodes(LEDrsquos)andlaserdiodes

(LDrsquos)usingGaAsandGaPthedimensionofthegenerationregion

istheorderofymforva゛20へrsquo30kVandiscomparablewiththe

thicknessoftheepitaxiallayersThereforethedividingmethod

becomesaneffectivemeanstomeasureLandSintheepitaxial

layers

-71-

Fig5-5

Q‐rsquoQ]

loline

11(52

ち5

0 50Scanningdistancex

100

(pm)

jDependenceofEBIConthescanningdistancexforn-SiSchottkydiodesThelengthWbetweenthe

barrierandtheohmiccontactis100Umthe

acceleratingvoltageVais50kVandLis20へj200lim

SolidandbrokenlinesareforSdeg104and105cmsec

respectニivelytakingthegenerationdistributioninto

accountThediffusionconstantDofholesis125

cm^sec

-72-

n-SiVa=50kVw00μm

5aD=iZ5cm2ss(cms)

1-helliphellip104

2゛l`4-----helliphellip105

`L(μm)

1へ`a-2001

≒yyhelliphelliphellip100i

5゛゛ぐ丈i

へ゛`恥i

`ヽ

`lsquolブjl

ゝゝjφ1

0h白contactム

2rsquo

5-3 ApplicationtoS1

ThediffusionlengthintheSibulkmaterialusedfor

solarcellsorLS工゛S1Scomparablewiththedimensionsofeach

elementAndsotheminoritycarrierdistributionisaffected

verymuchbyelementdimensionsTheSchottkydiodewastakenfor

afundamentalmodeltorevealtheinfluenceofsampledimensions

CalculatedEBICrsquosbythedividingmethodinthecaseof

n-Siforwdeg100umandva゛50kvareshowninFig5-5Thediffusion

constantDofholesistakenasatypicalvalueof125cm^sec

Solidanddashedlinesareforsdeg101゛and105cmsecrespectively

andLis20010050and20umforthecurvesfromupperto

lowerineachgroupThegenerationsourceisassumedtobeasemi-

sphereThenumberofthegeneratedelectron-holepairsatany

pointinthesemi-sphereisproportionaltoexp(-40(rR)2)

(rthedistancebetweenthepointandthecenterdRthe

radiusofthesemi-sphere)Thegenerationdistribution1Sassumed

inorderthatthedepthdosefunctionalongthez-axlsagreeswith

thatproposedbyEverhart[4]andthevaluesofdgandRare

5ymand11ymrespectively゛forvadeg50kvrsquo

AsshowninFig5-5theabsolutevalueofEB工Cincreases

withdecreasingSforthesameLvalueThecurvesconvergetoa

certaincurveforboths=10rsquoand105cmsecwhenLbecomesgreater

thanwForconveniencethelogJvsχcurvesaredividedinto

threepartsi

range(30≦X-

く一一

eA)nearthebarrier(0≦x≦30ym)B)middle--

70ym)andC)neartheohmiccontact(70≦x≦100--

μm)IntheregionA)peaksappearatxdeg6ymowingtotheedge

effectdescribedinsect3-3and10gヽJdecreasessuperlinearlybecause

ofthesurfacerecombinationeffectIntheregionC)logj大decreases

-73-

Fig5-6

゜1(il

四a3

U」

-01

Ddziieujjoz

゛D=1Z5cm2s巡付

1 03

orini=-

にuarrヤuarr

uarrにヤ

Ohmiccontactづ50100

Scanningdistancex(μm)

JDependenceofEBIConthescanningdistancex

forn-SiwhenLismuchgreaterthanWThesolid

linesareresultsbythethree-dimensionalsolutions

forsdeg1035times1031045)(104and105cmsec

respectivelyThedashedlineisEBICbyone-

dimensionalapproximationV=50kVw=100ymand

L=1000Uma

-74-

゛ぐpermil

゛`xズit

darrレ

rapidlybecausetheohmiccontactisacarriersinkInthemiddle

rangeB)logJ大decreasesalmostlinearlyThereciprocalgradient

ofthecurveincreasesasLbecomeslargeintherangeofL≦100pm-

Thegradientsofthecurvesarenotsoaffectedbysurface

recombinationIfvisloweredt010kVthesurfacerecombinationa

affectsEB工Cmuchmorethanforvadeg50kVbecausethegeneration

depthbecomesshallowerInfactthegradientsofthecurvesin

regionA)aresteeperthanthoseforv=50kVforthesameLvaluesa

ThereforeinthecaseofL≦100ymLandscanbedetermined-

mainlyfromtheslopesofthelinearlydecreasingregionforhigh

va(50kVinthiswork)andthesuperlinearlydecreasingregionnear

theSchottkybarrierfor10Wva(10kVinthiswork)respectively

takingtheinfluenceofohmiccontactintoaccountButinthe

caseofL≧100ymthevalueofLcannotbedetニermineddefinitely-

becausetheslopeofthecurveinthelinearlydecreasingregion

doesnotchangeevenifLvaries

WhenLbecomesmuchlargerthanwthecurvesofEBICvsX

convergetoacertaincurveCalculatedEBICrsquosinthecaseofn-Si

forva゛50kVwdeg100ymandLdeg1000ymareshownbysolidlines

1nFig5-6forsdeg1035times1031045times104and105cmsec

respectivelyThegenerationsource1Sassumedtobeapointatthe

depthdThedashedlineisasolutionofone-dimensionalg

approximation(seeappenditimes1nthischapter)Theabsolutevalueof

EBICbecomeslargerwithdecreasingSandthecurveforS40cmsec

approachestothesolutionofone-dimensionalapproximationItcan

beexplainedasfollowsInthecaseofs=Ocmsecthereisno

carrierrecombinationatthesurfaceHencethematerialcanbe

consideredtoextendtoz=_oobyintroducinganimagesourceat

(x0-d)EBICisobtainedbyintegratingdpdxinthey-zplane

atx=0AndsotheEBICbythepointsourceat(x

-75-

grsquoO゛plusmnd)using

JOoline1

Ig3paziieuijoz

Fig5-7

(a)

UI「rrsquo

a3

U」

rsquo一lsquo51 0

pdziieujjoz

Scanningdistance

(b)

X(pm)

ExperimentalresultsinSiSchottkydiodesfor

w゛200μmand83μminfigures(a)and(b)respectively

Vais1030and50kVSolidanddottニedlinesare

theoreticalresultsforL=80UmandS=50withand

withouttheinfluenceofohmiccontニactrespectively

-76-

inlsquoSiL=80μm

こ沼o

rsquoバ町「i「でなl`Jes

l悶

2卜Ohmiccontact今|

トj

rsquohelliphelliphelliphelliphellipi

15

≒|

2helliphellip1

0Scanningdistancex150(pm)00

へn-SiL=80μm

5゜`S=50

deg゜w=83um

degムExperimentalvalues2deg`4≒Vi=50kV

I゛lsquorsquo4≒oVadeg30kV

≒゜rdquoVa≪10kV

丿4

lrsquo

2lsquoo1

rsquo゜i

2degi

2Ohmiccontactrarr

050100

thethree-dimensionaldiffusionequationbecomesidenticaltothat

derivedbyone-dimensionaldiffusionequationconsideringthe

planarsourceatxrsquoxginthey-zplane[5]Howeverinpractice

SihasafinitevalueofSandsothethree-dimensionalsolution

mustbeneededinthecaseofL>wThevalueofscanbedeter-

minedfromtheabsolutevalueofEBICfollowingthediscussionof

sect4-2usingtheelectron-holepaircreationenergyE^^byan

electronbeam

TheexperimentalresultsinSiSchottkydiodeswith

w=200umand83μmmadefromonewaferareshowninFigs5-7(a)

and5-7(b)respectivelySamplepreparationsandmeasurement

procedureshavebeenalreadyshowninsect3-4Theresultsofthe

theoreticalcalculationusingL=80vimandS=50forthreedifferent

va゛s(10rsquo30and50kV)areshownbysolidlinesinbothfigures

Theresultsofthetheoreticalcalculationwithouttheinfluence

ofohmiccontactareshownbydottedlinesinFig5-7

Inthecaseofw=200ymthesamplewidthisthreetニimeslargerthan

Landsotheslopeofthelinearregion(50≦x≦120um)isnot--

verychangedbytheinfluenceofohmiccontactInthecaseof

Wdeg83umthecurvesarequitedifferentfromthoseforw=200ym

andthereciprocalgradientofthecurvesinthemiddlerange

(25≦x≦55ym)givesL=20ymwhichisaquarterofthereal--

diffusionlengthBothinFigs5-7(a)and(b)theoretical

calculationsshowgoodagreementwiththeexperimentalresuLts

whichshowsthatthemethoddiscussedinsect5-21Saneffective

meanstニoanalyzetheeffectofsampledimensions

-77-

5-4 Summary

Theminoritycarrierdistributionisaffectedverymuch

bythelengthwbetweenapotentialbarrierandanohmiccontact

ifWisequaltoorshorterthanthediffusionlengthLThe

dependenceofEBICJ大onthescanningdistancexwasinvestigated

byextendingthemirrorimagemethod

InthecaseofwL≧1logJ゛decreasesalmostlinearly-

inthemiddlerangeofthescanningdistancebuttheestimated

diffusionlengthfromthecurvesismuchshorterthanthereal

diffusionlength(eg30t044ZinthecaseofL=w)The

valuesofLandScanbedeterminedmainlyfromtheslopesof

thecurvesforhighand10Wva゛reSpectively゛takingtheinfluence

ofohmiccontニactintoaccount

工nthecaseofwLく1theslopeofthelinearly

decreasingregionoflogJvsXcurvesdoesnotchangeevenif

LvariesThedependenceofEBIConχconvergestoacertaincurve

ThevalueofLcannotbedetermineddefinitelybutthevalueofS

canbeobtニainedfromtheabsolutevalueofEBIC

TheexperimentalresultsinSiSchottkydiodesagreed

fairlywellwiththetheorywhichshowedthattheextendedmirror

imagemethodwaseffectiveinanalyzingEBICconsideringthesample

dimensions

-78-

References

[1]

[2]

[5]

OldwigvonRoosSolid-stateElectron

(1978)

211063

FBerzandHKKuikenSolid-stateElectron19

(1976)

437

CvanOpdorpPhilipsResRep32192(1977)

TEEverhartandPHHoffJApplPhys丘5837

(1971)

WHHackettJrJApplPhys

Appendix0nedegdimensionalapproximation

431649(1972)-

IfthediffusionlengthLisinfinitelylongminority

carriersdonotrecomblneuntiltheyflowintothebarrierorthe

ohmiccontactThereforethediffusioncurrentdoesnotvary

spatiallyTheminoritycarrierdistributionpcanbeexpressed

asalinearfunctionofχ1nthecaseofone-dimensional

approximation工fthepointsourceg1Slocatedatdegcgrsquop(゜c)is

putasfollows

p(x)=ax十b(a>00≦゛≦)rsquo

p(x)゜c゛十d(c<0X≦゛≦゛)゜

(5-Al)

(5-A2)

Thefactorsabcanddcanbedeterminedfromthefollowing

conditions

-79-

p(O)=0

p(w)=0

卵石

-卜-卵匹 ゜g

(5-A3)

(5-A4)

(5-A5)

(5-A6)

Theeq(5-A5)showsthecontinuityconditionatxdegxg゛andtheeq

(5-A6)givesthatallthegeneratedcarriersflowintothe

Schottニkybarrierandtheohmiccontactニwithoutrecombinationin

materialsThesolutionp(x)becomesasfoLlows

p(x)=

p(x)=

(1-ミj1)x(O≦x

--^(w-x)(Kg

NormalizedEBICJisexpressedby

J大=

-egeD

dp

-dxχ=0

=1-

こ)

3Wく

一一

Xく一一

(5-A7)

(5-A8)

X』

-80-

(5-A9)

6-1

DETERMINATIONOFLIFETIMEANDDIFFUSIONCONSTANT

BYPHASESHIFTTECHNIQUE

Introduction

Accuratedeterminationoflifetimeてofminoritycarriers

1Sveryimportantincharactニerizingsemiconductingmaterials

Thevalueofてcanbemeasureddirectlyfromthetransientresponse

aftertheinjectionofminoritycarriersTheradiativerecombina-

tionlifetimewasmeasuredinGaPandGaAsfromthedecayofphoto-

luminescence[1]cathodoluminescence[2]orelectroluminescence[3]

Thephotoconductancedecaymethod[4]Isthemostcommonlyused

techniquetomeasurelifetimeincludingradiatニiveandnon-

radiativeprocessesInthesemethodsmeasurementofTinsmall

areaoftheorderofym^isverydifficultbecausethesample

surfacemustberelativelywideinordertoobtainasufficient

signalThespatialvariationofてcouldbedeterminedfromthe

decayoftheelectronbeaminducedcurrent(EBIC)usinga

scanningelectronmicroscope(SEM)[5-8]Thevalueofてismuch

influencedbysurfacerecombinationsincelightoranelectron

beamforexcitationentersthroughthesurface

Thevalueofてcanbeobtainedfromthediffusionlength

LusingtherelationL=j5マThevalueofLcanbedeterminedbythe

spectralresponsemethodusingsolarcells[910rbythesurface

photovoltaicmethod[1011nbothmethodstheaccurateabsorption

coefficientmustbeneededtodeterminethevalueofL

AsdiscussedinChapters皿rsquov^VtheEBICmethodusingSEMisa

veryconvenienttechniquetomeasureLinsmallareaoftheorder

-81-

ofym^andtherehavebeenmanytheoretical【11-14】and

experimental[15-16]worksuptodateInthemetニhodhowever

thediffusionconstantDmustbegiveninordertoobtainT

Whentheintensityofexcitationforelectron-holepair

generationisrdquomodulatedthephaseofluminescenceorinducedcurrent

isshiftedfromthatoftheexcitationsourcebecauseofthe

recombinationofinjectedminoritycarriersinamaterialThe

valueofてcanbedeterminedfromtheamountofthephaseshift

Hwang[17]obtainedTinGaAsfromthephaseshiftofphoto-

luminescenceInthemethodtニhephaseshiftisinfluencedbythe

surfacerecombinationvelocityandtheabsorptioncoefficient

whichaffectminoritycarrierdistributionverymuchReichleta1

measuredでinSi[18-20]andGaAs[21]usingthephaseshiftin

photニ0-inducedcurrentMunakata[22]andOthmer[23]measuredて

bythephaseshiftofEBICinGeandSirespectivelyTheyused

tニhesolutionoftheone-dimensionaLdiffusionequationwithout

anyconsiderationofthesurfacerecombinationeffect

Ifsuchaphaseshiftmethodiscombinedwiththe

conventニionallinescanmethodofEBIC(iemeasurementofLusing

DCelectronbeam)thelifetimeandthediffusionconstantof

minoritycarriersinsmallareacanbedeterminedsimultaneously

Kammeta1[241determinedてandDinSiTheymadeaSchottky

barrierwithasilverpaintonSisurfacesandmeasuredEB工Cby

scanningtheelectronbeamonthesurfaceparalleltothebarrier

InthatmethodsurfacepreparationhasmucheffectonT[25]

andtheconfigurationusedbythemisnotconvenientwhenone

measuresてandDinmaterialswithsmallLTheanalysisisvery

complicatedandRoospointedouterrorsintheiranalysis[26]

andsuggestedasimpleconfiguration[271

-82-

Inthischapterwetaketheconfigurationthatthe

electronbeamscansonthesurfaceperpendiculartothebarrier

planeWiththisconfigurationtニhetime-dependentdiffusion

equationcanbesimplyreducedtothesteady-statediffusion

equationandthecomplicationintheanalysisthatRoosindicated

[26]canbeexcludedThisphaseshiftmethodcanbeappliedto

materialswithsmallLWesolvethethree-dimensionaltime-

dependentdiffusionequationtakingthesurfacerecombination

effectintoaccountandclarifytherelationofTandthephase

shifttheoreticallyWeshowthatthree-dimensionalsolutions

canbeexpressedbyone-dimensionalsolutionswithempirical

correctionfactorsandthatてandDcanbedeterminedwitニhout

anyrestrictionformodulationfrequencyExperimentalresults

inSiarealsoshown

6-2 Relationbetweenlifetimeandphaseshift

WetakeaSchottkydiodeasshowninFig6-1for

simpletheoreticalcalculationWeassumeapointgeneration

sourcewhichhastime-variabLepartgelωt(ω゜2TTfωangular

frequencyfmodulationfrequency)at(x゛0d)Whenthetldegeoline

variablepartofthenumberofminoritycarriers1Sputas

恥eiωt(isacomplexvariable)psatisfiestheconventional

steady-statediffusionequationbyintroducingthecompleχ

effectivediffusionlengthL゛eff(ΞL゛1171瓦JTL=ぷF)゜If

thetime-variablepartofEBICIsputasj`゛e(J゛1Scomplex-

EBIC)icanbeexpressedasfollowsbythemirrorImagemethod

asdiscussedinsect3-2

-83-

Fig6-1

ylご

uarrj

Schottkybarrier

uarr

Ohmiccontact

Schematicviewofeχperimentalconditionsand

definitionoftheco-ordinatesystem

-84-

Electronbeam

SOlyScanningtrack_xj

ズニに匹二oline-一一゛

lsquo9surface

lL-__--ang__helliphellip_

|`1

丑昌之

9gπLaf ―K

gdof

(ノダr7olineT

)酉ff

L大effl゛ぶ弓+T『

+0O

(-1(じ(lg)

)X[

jiご]ご

)ことりsube

dgDIL火eff

xlてこi7

dT

J(6-1)

whereeisthechargeofanelectronsisthesurfacerecombination

velocityandTisthevariableforintegratニionThefunctionK^

1sthesecond-modifiedfirst-orderBesselfunctionwithcomplex

variablesTheabsolutevalueofEBICnandthephaseshiftφ

fromthesourcearegivenasfollows

TI=

|」と

eg

φ=tan-1

Im一J

Rej゛

(6-2)

(6-3)

whereReandImstandforrealandimaginarypartsrespectively

Thevalueofnisnormalizedtobeunitywhenallthevariable

-partgcontributetothevariablepartofEB工CSincej火isa

functionofてthevalueofφbecomesafunctionofてThevalues

ofnandφcanbecalculatednumericallyWeassumeapointsource

forsimplecalculationbutthemethodmentionedabovecanbeeasily

appliedtothefinitegenerationdistributionbythedividing

methoddescribedinChapters工江andy

-85-

Fig6-2

Fig6-3

U2

Cχ310-rsquo

山5

ト2

10lsquo3

velocitysis

35225N

(Eu

一))

j^

9st^d

10

Jo}CIで噌」

ひpF

ぐりぐ

ごヽこ

W゛`みノー-

うて`゜ldegw-rsquo゜rsquordquorsquoPrime゛ご

゜二

゛゜〆ノ〆゛`゜

゜゛〆ノ

(MJD≪p)j

UMS

asEMd

ofEBICvsscanning

thealmostlinear

0 50 100 150

ScanningdistanceX(pm)

Normalizedintensityandphaseshift

distancexcurvesTheconcavecurvesand

linesarefortheIntensity(leftaxis)andthephaseshift

(rightaxis)respectivelyThesolidbrokenanddottedlines

areforf=10100and500kHz(ieωT=031314and157)

respectivelyLifetimeTistakenas5μSThediffusion

constantDis30_cm2Secandthesurfacerecombination

105CmSeC

S=105CmS

D=30ori^s

Lifetimeで(sec)

DependenceofgradientofphaseshiftdφdxonTD=30cmsecandrsquos=105cmsec

-86-

rsquoD=30crrfis

ωで=5f

5ヽ2MHz

ヽ1MHz

2`500kHz

1`

100kHz

``50kHz

`ヽ`10khtt

pwww

kHz

`ωで=01

1(jrsquo

825

1(i

725

1(jrsquo

6251(irsquo

525

10lsquo4

Mm2s)lsquo1-123lsquoj「rsquoQ心Hz」t

=10cms-10a3i

i=30kV-一一一一1003K

helliphelliphelliphelliphellip500157

Thevaluesofnandφwerecalculatedasafunction

ofscanningdistanceχforp-SiasanexampleTheresultsare

showninFig6-2whenてisputasatypicalvalueof5μs

Inthefiguretheconcavecurvesandthealmostlinearlines

areforn-χandφ-xrelationsrespectivelyThesolid

brokenanddottedlinesareforf=10100and500kHz(ie

ωT=031314and157)respectivelyThediffusionconstant

Disputas30cm^secThesurfacerecombinationvelocitysIs

takenas105cmsecsincetheordinarysurfacerecombination

velocitニyofSiis103へj105cmsecTheacceleratingvoltage

Isputas30kVThepointsourceisassumedtobelocatedat

themaximumenergydissipationdepthofabout3μmunderthe

surfacebasedonKanayarsquosmodel[28]forelectron-holepair

generationdistributニIon

Inthecaseofωてく01tニhedependenceofnonX

agreeswiththat-measuredbyaconventionallinescanmethod

usingDCelectronbeamThevalueofLcanbedeterminedfrom

theslopeofthen-χcurvestakingthesurfacerecombination-

effectintoaccountasdiscussedinChaptermThevalueof

L大effalmoStequaltoLandSOφbecomesnearlyzero

Inthecaseofωて≧01φincreasesalmostlinearly-

withxovertherangeofx≧Landthegradientdφdxbecomes-

largewithIncreasingfasshownInFig6-2Thegradient

dφdxisfoundtoIncreaseasてbecomeslargeforthesamefvalue

andnottochangeevenifSvariesfrom10^t0105cmsecfrom

thecalculationforvariousparametersFigure6-3showsthe

dependenceofdφdχonTwhenfisvariedfrom5kHzto2MHz

ThevaluesofDandsare30cm^secand105cmsecrespectively

ForeachvalueoffdφdxincreasesmonotonouslywithTwithin

therangeof01≦ωて≦5andapproachestoacertainvalue--

asymptoticallyovertherangeofωて≧5-

-87-

「ujopp」)

調uiusas^qdj〇}c心石司」

Fig6-4

Lifetimeて (sec)

10

Expressionofthedependenceofdφdxonてusingtheapproximatedsolutionsoftheone-

dimensionaldiffusioneuationinthecaseofD=30cm^secandf=10sectHzSolidlineisa

three-dimensionalsolutionLines(A)and(B)

aretheapproximatedone-dimensionalsolutionsand(Arsquo)and(Brsquo)aretheasymntotesforthethree-dimensionalsolutionThecorrectionfactorCforthethree-dimensionalsolutionis087

-88-

2(8)登ニ4F

helliphellipj(Å

(A)

D(EI)-(jじ硲ゴどこ二こhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip

2helliphelliphelliphelliphelliphelliphelliphellip(畿f3゛(c緊八(醤y3

d≫_Kii「」(A)石rsquo7『

5Ddeg30cm2sfdeg105Hz

c=087

Ursquo725J625_-52542

Ifwetakethesolutionsoftheone-dimensionaldiffusion

equationdφdxisgivenasfollows[241

O「

dφ

dx

助こ

Lω

2D

一 一 S

irfr

一万

(ωて≪1)

(ωT≫1)

(6-4)

(6-5)

Followingthethree-dimensionalsolution(eqs(6-l)(6-2)and

(6-3))asshowninFig6-3ydφdxincreasesproportionallyt07

intherangeofωてく05andreachestoacertainvalueoverthe

rangeofωて>5whichcanbeeχplainedqualitativelybyeqS

(6-4)and(6-5)respectivelyThedφdxvsTcurvesinFig6-3

canberepresentedbyonefunctionwiththecombinationofthe

approximatedsolutionsoftheone-dimensionaldiffusionequation

(eqs(6-4)and(6-5))Weshowanexampleinthecaseoff=105Hz

andD=30cm^secinFig6-4Thesolidlineisthethree-

dimensionalsolutionfromFig6-3andthedottedlines(A)and

(B)expresseqs(6-4)and(6-5)respectivelyThebrokenlines

(Arsquo)and(B゛)showtheasymptoticsolutionsofthethree-

dimensionalsolutionintherangesofωて<05andωて>5The

absolutevaluesof(A)and(Brsquo)becomeabout87Zofthoseof

(A)and(B)basedontheresultsofcalculationAsshownin

Fig6-4thethree-dimensionalsolutionisgivenbyacombination

ofthelines(Arsquo)and(Brsquo)andIsexpressedasfollows

-89-

「―」)畠一

uiMSaseudpazneaijoz

Fig6-5

rsquo0

ω^t「

NormalizedphaseshiftニLdφdxvSωてcurves

Solidlineisathree-dimensionalsolution

expressedbytheapproximatedone-dimensional

solutionswithempiricalcorrectionfactors

Brokenlineistheone-dimensionalsolution

-90-

2One-dimensionalノrsquosolution゛`4xrsquo

10バ

5acuteThree-dimensional

ぶacutesolution

2acute

(yl

言二分ヽ同r〔2μ(ldquoμ

゛1)rsquo1

5primeacute

cべ1251251cap25

dφ

dx

)=(c

TTfr TTf)ldquo゛十(c

yでワ

)rsquo゛

-91-

十1}3

(6-6)

(6-フ)

函rsquo

wherenisapositiveintegerWecalculatedeq(6-6)Inthe

casesofn=1へj5anddeterminednas31norderthatthe

solidcurveinFig6-4canbewellrepresentedbyeq(6-6)

Thevalueofc1Sthecorrectionfactorforthethree-dimensional

solutionandcisabout087asmentニionedabove

Fromeq(6-6)wecanderivethefollowingrelation

usingtheconventionaldiffusionlengthL

_

=pound石{2Σ(則2万

ThetermLdφdxisconsideredtobethenormalizedphaseshift

whichistheamountofthephaseshiftwhentheelectronbeam

scansoveronediffusionlengthItshouldbenotedthatLdφdx

isafunctニionofonlyωでFigure6-5showsthedependenceof

LdφdxonωてbythesolidlineIfthevaluesofLanddφdxare-

knownてcanbedeterminedfromthecurveforanymodulation

frequencyandDisalsoobtainedbytherelationofL=iF

Themodulationfrequencyfcanbechosenfreelyandthe

restrictionsofωΥ<050Γωて>5fortheapproximatIonneednot

tobetakenintoaccount

ThephaseshiftderivedbyMcKelvey[29]usingtheone-

dimensionaldiffusionequationisshownbythedashedlinein

Fig6-5Theestimatedvalueofωてbytheone-dimensional

solutionisabout76へ87Zofthatbythethree-dimensional

solutionforeveryvalueofLdφdxInthecaseoftheone-

dimensionalsolutionLisdetermineddirectlyfromthegradient

ofthelinearlydecreasingregionofEBICcurveandisabout

60へj80Zoftherealvaluefromtheresultsofthedetailanalysis

takingthesurfacerecombinationeffectintoaccount[14]

ThereforethevalueofωΥderivedbytheone-dimensionalsolution

isonly30へJ丁0Zoftherealvaluebecauseωてdecreases

proportionallytOLandL2intheregionsofLdφdxく03and

Ldφdx>2respectivelyOnemustusethethree-dimensional

solutioninordertodeterminetheaccuratevalueofて

6-3 ExperimentalresultsinSi

AconventionalSEMwasusedfortheprimaryelectron

beamwhichwasmodulatedat1rsquoj50kHzwiththedutyof05by

achoppingcoilinsertedintothebeampathThebeamcurrentwas

as10was10oline10AThemaximumminoritycarrierdensityinthis

experimentwasconsideredtobeabout3times1014Cmoline3andthe10w

injectionconditionwassatisfiedTheinducedcurrentwas

measuredbythevoltagedropacrosstheloadresistancewhich

wasconnectedtotheSchottkybarrierwithanohmiccontactThe

signalhadarectangularwaveformowingtothechoppedprimary

electronbeamandsothefundamentalfrequencycomponentinthe

Fourierseriesofthesignalwasdetectedbyanauto-phaselock-

inamplifierTheEBICnandthephaseshiftφfromthesource

wererecordedsimultaneously

ThediffusionlengthLisdeterminedinthecaseof

ωて<01takingthesurfacerecombinationeffectintoaccount

Thedependenceofnonxagreeswiththatニmeasuredbyaconventional

linescanmethodusingDCelectronbeamasdiscussedinsect6-2

-92-

Whenvaislowgivingtheshallowgenerationdepthsurface

recombinationhasalargeeffectonEBICWhenvaishigh

givingthedeepgenerationdepththesurfacerecombinationeffect

1SreducedTheaccuratevalueofLcouldbedeterminedbyfitting

experimentaldatatotheoreticalcurvesforboth10wandhighva゛S

(10and50kVrespectivelyInthiswork)asshownInsect3-3

Thevalueofdφdxisobtainedatanappropriate

modulationfrequencywhichsatisfiesωて>01AthighVthe

surfacerecombinationeffectIsreducedandsowechosetニhe

highestva(30kVinthiswork)asfarastheelectronbeamcould

bechoppedOncethevaluesofLanddφdxareknownthevalues

ofてandDcanbedeterminedfromthecurveinFig6-5

Sampleswerep-andn-typeSiwithtニheresistivitypof

10and01f2cmrespectivelyOhmiccontactsweremadeby

evaporatinggallium-dopedgoldandantimony-dopedgoldontothe

p-andn-typesamplesrespectivelySchottkycontactsweremade

byevaporatingaluminiumandgoldontothep-andn-typesamples

respectivelyinavacuumas10was10oline7TorrThesampleswere

insertedintoavacuumchamberforEBICmeasurementimmediately

aftertheywerecleaved

ThediffusionlengthLinp-typeSiwasdeterminedas

130μmfromthen-xcurvesinthecaseofωてく01The

experimentalresultsofthephaseshiftmethodareshownIn

Fig6-6bysolidlinesforf=5102030and50kHzrespectively

ThephaseshiftIncreaseswithxalmostlinearlyasdescribedin

sect6-2ThevaluesofてweredeterminedusingFig6-5as9595

8886and83ysfromthegradientsofthelinesinFig6-6

for5102030and50kHzrespectivelyTheobtainedvaluesof

てshowlittledifferencewitheachotherinanymeasurement

-93-

11

es^Md

Fig6-6

P-Si(r=10ncm)f=

20

1 0一

----n-Si(r=Q1ftcm)

Va=30kV

圭T

rdquo

------ニr二ご二二耳一一3

50100

Scanningdistance

150

Experimental

methodinp-(p=10

200

(μm)

resultsofthephaseshift

Ωcm)andn-type(p=01ncm)Si

-94-

rdquoolinersquordquooline`rsquolsquorsquoolinerdquordquoolinersquo50kHz

Vadeg30kVZ

10deg

30

FJ゛

一一20

〆がノrdquo〆〆〆

メノrdquo

〆〆〆〆〆ノ10

---rdquordquo|-sニニニldquo-notこ9

conditionfromωて=03(atf=5kHz)to30(atf=50kHz)

Itprovedthatthemodulationfrequencycouldbechosenfreelyas

mentionedinsect6-2Ifwetaketheaveragedvalueofて(ie

で89ys)thediffusionconstantDofelectronswasdeterminedas

19cra^secwhichalmostagreedwiththereportedvalue[301The

slightdeviationfromthestraightlineforf=50kHzmaycomefrom

unstablenessofthechoppedbeambecausethechoppingcoilused

inourexperimentwasnotdesignedforhighfrequencymodulation

above50kHz

Thediffusionlengthinn-SiwasobtainedasL=80ymand

thephaseshiftsareshowninFig6-6bybrokenlinesforf=3

10920and50kHzrespectivelyThedeterminedvaluesofてfrom

thegradientsofthelineswere889292and105usfor

fdeg3s1020and50kHzrespectivelyThevaluesofTalmost

equalwitheachotherasinthecaseofp-SiIfwetakethe

averagedvalueofT(ieで=94ps)tニhediffusionconstantD

ofholesbecomes7cm^secwhichalsoagreeswithtニhereported

value[301

Thegenerationdistributionisconsideredtobeasemi-

spheretheradiusofwhichisabout6ymatニvadeg30kVusingthe

Kanayarsquosmodel[28]Thedimensionsofgenerationdistribution

aresufficientlysmallincomparisonwiththediffusionlengthof

thesamplesThereforethepointsourceassumptioninthe

analysisisreasonable

-95-

6-4 Summary

Whentheintensitymodulatedelectronbeamisusedthe

phaseofinducedcurrent(EBIC)isshiftedfromthatofexcitation

sourcebecauseoftherecombinationinmaterialsWesolvedthe

three-dimensionaltime-dependentdiffusionequationtakingthe

surfacerecombinationeffectintoaccountandclarifiedthe

relationofてandthephaseshiftφtheoretically

Inthecaseofωて≧01φincreasesalmostlinearlywith-

Xovertherangeofx≧LThegradientdφdxbecomesafunction-

ofTandisnotaffectedbysurfacerecombinationTherelation

ofdφdxonてwasfoundtobeexpressedusingtheapproximated

solutionsoftheone-dimensionaldiffusionequatニionwithtニhe

empiricalcorrectionfactorsThenormalizedphaseshiftLdφdx

becomesafunctionofonlyωてIfthevaluesofLanddφdxare

knownてandDaredeterminedwiththeaidofLdφdxvsU3てcurve

withoutanyrestrictionformodulationfrequencyTheestimated

valueofてbytheone-dimensionalsolutionswithoutニthecorrection

factorsisonly30へノ70Zoftherealvaluederivedbythethree-

dimensionalsolution

Experimentalresultsinp-andn-typeSiSchottkydiodes

showedgoodagreementwiththetheoryandtheminoritycarrier

diffusionconstantsofelectronsandholesweredeterminedas

19and7cm^secrespectively

-96-

References

[11

[2]

[31

[4]

5]

6]

[10]

[11]

[12]

[13]

[14]

[15]

PDDapkusWHHackettJr0GLorimorandRZ

BachrachJApplPhys^54920(1974)

MBoulouandDBoisJApplPhysj旦4713(1977)

MEttenbergHKresselandSLGilbertJAppLPhys

44827(1973)

SWangrdquoSolid-stateElectronicsrdquo(McGraw一HillInc

1966)p300

WZimmermannphysstatsol(a)12671(1972)

DRHunterDHPaχmanMBurgessandGRBooker

rdquoScanningElectronMicroscopySystemsandApplications

1973rdquo(工nstPhysLondon)pp208-213

HKKuikenSolid-stateElectron19447(1976)-

AJakubowiczSolid-stateElectron22635(1980)

HTWeaverandRDNasbySolid-stateElectron

22687(1979)-

DLLileandNMDavisSolid-stateElectron

18699(1975)-

WvanRoosbroeckJApplPhys2plusmn380(1955)

WHHackettJr=JApplPhyspound1649(1972)

FBerzandHKKuikenSolid-stateElectron

19437(1976)

CvanOpdorpPhilipsResRept22192(1977)

DBWittryandDFKyserJApplPhys261387

(1965)

-97-

[16] CvanOpdorpRCPetersandMKlerkApplPhysLett

2h_125(1974)

[17]CJHwangJApplPhys4^4408(1971)

[18]

[19]

HReichlandHBerntSolid-stateElectron

18453(1975)

GSchwabHBerntandHReichlSolid-stateElectron

2091(1977)

[201JMiillerHBerntandHReichlSolid-stateElectron

21999(1978)

[211

[22]

JMiillerHReichlandHBerntSolid-stateElectron

22257(1979)

CMunakataandTEEverhartJpnJApplPhys

11913(1972)-

[23]SOthmerrdquoScanningElectronMicroscopy1978Vol1uml

(SEMIncOrsquoHare111)p727

[24] JDKaiiraiandHBerntSolid-stateElectron

21957(1978)-

【25】JDKammrdquoSemiconductorSilicon1977uml(The

ElectrochemicalSociety工nc)p491

[26] 0vonRoosSolid-stateElectron23177(1980)

[27]0vonRoosJApplPhys1^3738(1979)

[28]KKanayaandSOkayamaJPhysDApplPhys

543(1972)

[29]JpMckelveyrdquoSolidStateandSemiconductorPhysicsrdquo

(HarperandRowNewYork1966)pp439-440

[30]HFWolfrdquoSiliconSemiconductorDatardquo(Pergamon

PresslnC1969)

-98-

ⅥI

7-1

HEATTREATMENTEFFECTONDIFFUSIONLENGTHINS1

Introduction

Therehavebeenmanystudies[1]onthepropertiesofthe

processinducedfaults(PIFrsquos)Thedegradationoftheelectrical

performanceofthedeviceshasmuchconnectionwiththesegregated

impuritiesatPIFrsquosorthedecoratedfaultsofeachPIFRecently

thefaultproducedespeciallybytheoxidationathightemperatures

(IesocalledoxidationInducedstackingfault(OSF))has

receivedconsiderableattention[2-5]becausetheoxidationisa

fundamentalprocessinmakingLS工rsquosorcharge-coupleddevices(

CCDrsquos)Ravieta1[67]showedthattheelectricallyactive

OSF゛sincreasedtheleakagecurrentinprsquonjunctionsKimerllng[8]

determinedtheenergylevelofthefaultsfromtheelectron

beaminducedcurrent(EBIC)measurementsatvarioustemperatures

Generallythefaultsbecomerecombinationcentersanddecrease

thelifetimeandthediffusionlengthofminoritycarriers

Shimizu[9]showedthatthelifetimecouldbecontrolledpreferably

bytheintrinsicgetteringusingOSFrsquosRozgonyi[10]and

Tanikawa[11]reportedthattherelaxationtimeofMOScapacitors

decreasedasthedensityofOSFincreasedButtherehavebeen

alittlestudyonthequantitativeinformationofthedecreaseof

thediffusionlengthaftertheoxidationprocessathightemperatures

Inthischapterwemeasuredthechangesofthediffusion

lengthbyEBICmethodaftertheheattreatmentsathightemperature

andshowedthattheheattreatmentforafewminutescouldaffectthe

diffusionlengthatthesurfaceregionTheobservationofsurface

faultsbychemicaletchingwerealsoshown

-99-

(―)

<j)6udI

ColコこI()

Fig7-1

Heattreatmenttimet(min)

Diffusionlengthaftertheheattreatments

forvarioustimelengthsrangingfromlt0120minutesat1000degCOpenandsolidcirclesare

forthecasesindry02andArrespectivelyOriginaldiffusionlengthbeforeannealingis80pm

-100-

5ohellipumlindryO2

uml゜umlinArat1000degC

ol

12510251002

- W ゝ

rsquo _ l - ~ ヽ jS j - -

磨 卜

Fig7-2

(a)

(c)

rarr100Mm

ぶミ

卜`

r-^

rsquo

1Is

≪バ

rdquorsquo‐゛t

rsquo

grバ4≪

rsquo1

Surfacefaultsrevealedby

usingSirtletchantSamples(a)

wereannealedindryoat1000

and120minutesrespectively

-101-

い゛フバrdquo

゛para

`i

(b)

(d)

permilご}

->嗜

-゛

rsquo

III

`ヽご

いい

一J

t七

~貿で

rsquo

゛`1

鴫ヽ

rsquoq

-≪

ゝく

chemicaletching

(b)(c)and(d)

Cfor0830

一 一

- 一 一 -一 一

7-2

Experimentalresultsanddiscussions

Samplesaren-tニypeSigrownbyczmethodTheoriginal

resistivitybeforeannealingisaboutニ01ΩcmTheheattニreatment

wasdoneat1000degCintheflowofdry02andArrespectivelydeg

ThenthesampleswererinsedinHFforlmintoremovetheoxidized

layerandgoldwasevaporatedinordertomakeaSchottkybarrier

forEBICmeasurementsTheproceduresofthedeterminatニionofthe

diffusionlengthhavealreadybeendiscussedinChaptersmandでIV

Figure7-1showsthediffusionlengthaftertheheat

treatmentThetimetoftheheattreatmentwaschangedfromlto

120minutesTheopenandsolidcirclesareforthecaseIndryO2

andArrespectivelyTheoriginalvalueofdiffusionlengthis

80μmThediffusionlengthdecreasedtoabout7μmrapidlyas

tincreasedt05minandbecamealmostconstantovertherange

oft>5mlnThediffusionlengthdecreasedslightlymorerapidly

in02tニhaninArThelifetimechangedfrom5μsto003usif

thediffusionconstantofminoritycarrierswastakenasatypical

valueof125cmsecThesurfacefaultsofthesamplesannealed

indry02areSho゛linFigsdeg7-2(a)(b)(c)and(d)forlsquot゛

0830and120minrespectivelyThesampleswereetニchedby

SirtletchantforthesametimeThenumberoffaultsdidnotニ

increaseuntilt=8minbutbecameverylargeattdeg120min

ThesameresultwasobtainedforthesamplesannealedinAr

Itshouldbenotedthatthenumberoffaultsdidnotニchangedinthe

rangeofO≦t≦8minbutthediffusionlengthdecreasedrapidly--

inthesamerangeThelengthsbetweenthefaultsareverylarge

incomparisonwiththediffusionlengthinthesamplesannealed

for1くtく8minandsothediffusionlengthisconsidered

nottoberestrictedbytheaverageintervalbetweenthefaults

whenthefaultsareconsideredtobethecarriersink

-102-

TheuniformEBICwasobtainedwhentheelectニronbeamwasscanned

onthesurfacethroughtheSchottkybarrtersandthedarkpoints

correspondingtothefaultswerenotobserved

Therapiddecreaseofthediffusionlengthwasconsidered

tobecausedbytheformatonofnucleioffaultsattheearly

stageoftheheattreatmentTheverysmallnucleicanbecomethe

recombinationcenterseveniftheycannotberevealedbychemical

etchingIftheheattreatmenttimeissufficientlylongthe

nucleibecomelargeandcanberevealedbyetchingAsshownin

Fig7-2(d)thelengthbetweenthefaultsafterlongtimeheat

treatmentisthesameorderofthediffusionlengthTheformation

ofnucleiwasnotaffectedverymuchbytheoxidationbecausethe

decreaseofthediffusionlengthwasalsoobservedintheheat

treatmentinArAsisknowngenerallytheczgrownSIcontains

oversaturatedoxygenandtheformationofnucleiisrelatedtニO

theoxygenprecipitation[12]Thediffusionlengthdecreasedless

rapidlyinArthaninO2degOnereasonofthisphenomenonisconsidered

tobetheformationofSiOAnotherreasonistheoutdiffusion

ofoxygenbecauseoxygencanoutdiffusemorerapidlyinArthan

inO2degFurtherinvestigationmustbeneededfortheclarification

ofthenucleiformation

Inconclusionthediffusionlengthatthesurfaceregion

inSidecreasedtoabout10Zoftheoriginalvalueafterthevery

shortheattreatmentat1000degCforafewminutesNevertheless

thesurfacefaultsrevealedbychemicaletchingdidnotchange

Thenucleioffaultswereconsideredtobeformedattheearly

stageofheattreatmentandtheybecameminoritycarrier

recombinationcentersThedecreaseofthediffusionlengthwasnot

soaffectedbytheambientgases(ieoxygenorinertone)Much

attentionmustbepayedintheheattreatmentprocessathigh

temperatureevenifthetimeIsveryshort

-103-

i J I

References

[1]

21

31

71

81

[91

[10]

[n]

[12]

HFoilNGoreleandB0KolbesetirdquoSemiconductor

Silicon1977rdquo(JElectrochemicalSocietyInc

Prircetion1977)pp565-574

DJDThomasphysstatso1旦2261(1963)

CMMelliar-SmithrdquoCrystalcefectsinsiliconintegratニed

circuits-TheircauseandeffectrdquoinrdquoTreatieson

MaterialScienceandTechnologyrdquovol11(AcademicPress

NewYork1977)

KVRaviandCJVarkerJApplPhys45263(1974)

SMHuJApplPhys513666(1980)

KVRaviCJVarkerandCEVolk

JElectrochemSoc120533(1973)-

CJVarkerandKVRaviJApplPhys亘272(1974)

LCKlmerlingHJLeamyandJRPatel

ApplPhysLett30217(1977)

HShimizuAYoshinakaandYSuglta

JpnJApplPhys17767(1978)

GARozgonyiandRAKushner

JElectrochemSoc123570(1976)-

KTanikawaYItoandHSei

ApplPhysLett28285(1976)

JRPatelrdquoSemiconductorSilicon1977rdquo(The

ElectrochemicalSocietyIncPrinceton1977)

pp521-545

-104-

ⅧI CONCLUSIONS

InthepresentstudyEBICwasanalyzedquantitativelyby

solvingthesteady-stateortime-dependentthree-dimensional

diffusionequationsTheinfluenceofthefinitegenerationvolume

onEBICwasdiscussedandanImprovedmethodtocharacterize

thephysicalpropertiesinthesmallselectedareasofsemiconduc-

torswassuggestedTheobtニainedresultswereasfollows

InChapterHtheshortdiffusionlengthoftheorderof

ymcouldbedeterminedbythenormalincidencemethodofEBIC

Variousmodelsforgenerationdistributionusedintheanalysis

yieldedtheambiguityforthedeterminationofthediffusionlength

andtheelectron-holepaircreationenergybyanelectronbeam

Detailedinformationonthegenerationdistributionmustbe

necessarytoanalyzeEBICaccurately

InChaptニermthegenerationvolumeofminoritycarriers

hadrsquoaconsiderableeffectonEBICinthelinescanmethod

especiallywhenthedimensionsofthegenerationvolumewasequal

toorlargerthanthediffusionlengthWhentheaccelerating

voltagewaslowandsothegenerationdepthwasshallow

surfacerecombinationhadalargeeffectonEBICWhereaswhen

theacceleratingvoltagewashighandsothegenerationdepth

wasaslargeasthediffusionlengthsurfacerecombinationhad

aslighteffectonEBICTheaccuratevaluesofphysicalparameters

suchasthediffusionlengthshouldbedeterminedbyfittingthe

experimentaldatatothetニheoreticalcurvesforalltheaccelerating

voltagesTheexistenceofamaximuminEBICnearthebarriercould

beexplainedbythersquoedgeeffectrsquoattributedtothefinite

generationvolume

-105-

InChapter】5inthelinescanmethodthedependence

ofEBIConthescanningdistancerepresentedmainlythelateral

extentofthegenerationdistributionwhentheacceleratingvoltage

washighandwhenthedimensionsofthegeneratニionregionwere

largerthanthediffusionlengthThethree-dimensionalgeneration

distributionbasedupontheexperimentalresultsforthenormal

incidencecouldexplaintheexperimentalresultsofthelinescan

methodInGaAsthecenterofthegeneratニionregionwaslocated

atthepointof0130fthemaximumelectronrangeandthe

radialdistributionfromthecentニerwasshowntobeGaussianwith

anexponentニof54Q82Thevaluesof38へj44eVfortheelectron-

holepaircreationenergybyanelectronbeamwasobtainedtaking

thesurfacerecombinationeffectintニoaccount

InChapterVinthelinescanmethodtheminoritycarrier

distributionwasaffectedverymuchbyanohmiccontactwhenthe

lengthwbetweenthepotentialbarrierandtheohmiccontactwas

lessthanoneortwodiffusionlengthsTheslopeofthecurveof

EBICvsscanningdistancedidnotchangeevenwhentニhediffusion

lengthvariedandthediffusionlengthcouldnotbedetermined

definitelyfromtheslopeofthecurveTheabsolutevalueof

EBICwasdependentonthesurfacerecombinatニionvelocityand

thelengthW

InChapterⅥ[thephaseshiftbetweenthemodulated

electronbeamandEBICwasclarifiedbysolvingthethree-

dimensionaltime-dependentdiffusionequationTherelation

betweenthephaseshiftandthelifetimewasfoundtobeexpressed

usingtheapproximatedsolutionsoftheone-dimensionaldiffusion

equationwithempiricalcorrectionfactorsThelifetimeandthe

diffusionconstantofminoritycarrierscouldbedetermined

definitelywithoutanyrestrictionformodulationfrequency

-106-

InChapterVIIthediffusionlengthinthesurfaceregion

ofSiwasfoundtobedecreasedverymuchafterheattreatment

at1000degCforonlyafewminutesneverthelesssurfacefaults

revealedbychemicaletchingwerenotincreasedThenuclei

ofthefaultsmightbeformedattheearlystageofheattreatment

ThisinvestigationprovedthatEBICcouldbeanalyzed

quantitativelyinthesmallselectedareaconsideringthethree-

dimensionalgenerationdistributionbyanelectronbeamBut

thereexistsomepointstobestudiedfurtherasfollows

FirstbyEBICmethodthetotニalrecombinationlifetimeincluding

bothradiativeandnon-radiativeprocessescanbemeasuredBut

onecannotobservetheradiativerecombinatニionlifetimealone

whichIstheimportantparametニertocharacterizethellght-emittニing

diodesorlaserdiodes[1]Deeperunderstandingcanbeacquired

byinvestigatingtheluminescenceemitニtedbyrecombinationof

generatedelectron-holepairs(iecathodoluminescence)[23]

SecondlyEBICtechniquecannotrevealtheenergylevelsand

densitiesofimpuritiesandtrapsaccuratelywhichaffectthe

electricalpropertiesofmaterialsverymuchTherehavebeena

fewreports[4]todeterminetheenergylevelsoffaultsinSi

fromEBICmeasurementsatvarioustemperaturesButthe

experimentalaccuracyofEBICtニechnlqueisinferiortothat

ofthephotoluminescence[5]orthecapacitance[67]methods

Thirdly万thedoseofhighenergyelectronbeldquo万171万causesdamagesin

samplesSeveralinvestigationshaveshownthedecreaseoftニhe

tニhresholdvoltageinMOSdevices[8]andtheincreaseofthe

interfacestatedensitybetweentheoxideandthesemiconductors[9]

-107-

Improvementsofmeasurementtechniques(ieuseofthe10W

energyprimaryelectronbeam万orlthedecreaseoftニhetotal

amountofdose)wirsquollbenecessary

Electricalpropertiesofsemiconductorscanbecharacterized

collectivelybyEBICjointlywiththeothertechniqueswhich

complementtheweakpointsinEBICmethod

REFERENCES

[1]

[21

[5]

[6]

[7]

[8]

[9]

PDDapkusWHHackettJr0GLorimorandRZ

BachrachJApplPhys45

4920(1974)

DBHoltandBDChasephysstatS01(a)旦旦

135(1973)

MBoulouandDBoisJApplPhys 484713(1977)

LCKimerlingHJLeamyandJRPatel

ApplPhysLett30217(1977)

HBarryBebbandEWWilliamsrdquoSemiconductorsand

Semimetalsrdquo(edRKWillardsonandACBeer

AcademicPress1972)vol8pp182-392

SMSzerdquoPhysicsofSemiconductorDevicesrdquo(JohnWiley

SonsInc1969)

DVLangJApplPhys453023(1974)

WJKeeryK0LeedyandKFGallowayrdquoScanning

ElectronMicroscopy1976rdquo[IITR]Chicago)pp507-514

RHezelSolid-stateElectron11^

735(1979)

-108-

4i

rsquoII

LISTOFPUBLICAT工ONS

[1]

[21

[3]

[4]

[5]

[6]

Papers

Theinfluenceofthegenerationvolumeofminoritycarriers

onEBICrdquo

TFuyukiHMatsunamiandTTanaka

JPhysDApplPhys131093-1100(1980)

rdquoAnalysisofEB工CconsideringthegeneratニIondistribution

ofminoritycarriersrdquo

TFuyukiHMatsunamiandTTanaka

JPhysDApplPhys131503-1510(1980)

rdquoDeterminationoflifetimeanddiffusionconstantof

minoritycarriersbyaphaseshifttechniqueusing

electronbeaminducedcurrentrdquo

TFuyukiandHMatsunami

JApplPhys旦(1981)

rdquoAnalysisofelectronbeaminducedcurrentconsidering

sampledimensions一一-Measurementofdiffusionlength

andsurfacerecombinationvelocity-rdquo

TFuyukiandHMatsunami

JpnJApplPhys20(1981)No4

rdquoInfluenceofminoritycarriergenerationdistributionon

electronbeaminducedcurrentinthenormalincidencemethodrdquo

TFuyukiandHMatsunami

(tobepublished)

rdquoHeattreatmenteffectondiffusionlengthinSirdquo

TFuyukiandHMatsunami

(tobepublished)

-109-

[1]

[21

[3]

PublicationsintheInstituteofElectronicsandCommunication

EngineersofJapan

(inJapanese)

rdquoMeasurementofminoritycarrierdiffusionlengthby

EBICmethodrdquo

TFuyukiHMatsunamiandTTanaka

ReptTechSSD78-102(Feb1979)

rdquoCharacterizationofdiffusionlengthandlifetimebyEBICrdquo

TFuyukiandHMatsunami

ReptTechSSD79-103(Feb1980)

rdquoMeasurementoflifetimeanddiffusionconstantofminority

carriersbyphaseshifttechniqueinEBICrdquo

TFuyukiandHMatsunami

TransSectionJ63-C832-837(1980)

-110-

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Page 6: CHARACTERIZATION OF SEMICONDUCTORS BY Title ELECTRON …

ACKNOWLEDGEMENTS

Theauthorwishestoexi】resshisdeepgratitudetoformer

jブProfessorTetsuroTanakaforhiscontinuingguidanceandワバandrrsquoI

helliphellipノ1encouragementTheauthorwishestoexpresshis9万ざlltや1appreciation

toAssociateProfessorHiroyukiMatsuna万万mlforhispreciousguidance

andhelpfuladvicethroughouttニhepresentstudyTheauthor

acknowledgesProfessorAkiraKawabataforhisgenialguidanceand

encouragementTheauthorisgがIattilltoProfessorToshinoriTakagi

forhisstimulatingdiscussionsandusefulcriticismsonthemanuscript

TheauthorwouldalsoliketothankProfessorAkioSasakifora

criticalreadingofthemanuscriptandvaluablecomments

MuchattentionisduetoDrJuniiSaraieDrShigehiro

NishinoandDrAkiraSuzukifortheircontinuousencouragement

andstimulativediscussions

TheauthorthanksothermembersofSemiconductorLaboratory

fortheirconsiderableassistanceandexperimentalfacilities

一斑-

CONTENTS

ABSTRACT

ACKNOWLEDGEMENTS

L工STOFSYMBOLS

INTRODUCTION

References

i一m

VL

lVO

INFLUENCEOFMINORITYCARRIERGENERATIONDISTR工BUTION13

0NELECTRONBEAMINDUCEDCURRENTINTHENORMALINCIDENCE

METHOD

2-1

2-2

2-3

Introduction

Determinationofdiffusionlengthandelectron-

holepaircreationenergy

ExperimentalresultsinGaAs

2-4Summary

References

13

15

VOON

CMCM

30

DETERMINATIONOFDIFFUSIONLENGTHSURFACERECOMBINATION31

VELOCITYANDELECTRON-HOLEPAIRCREAT工ONENERGYBYTHE

LINESCANMETHOD

3-1Introduction31

3-2Surfacerecombinationeffectconsideringpoint33

source

3-3Analysisofelectronbeaminducedcurrenttaking37

tニhree-dimensionalgenerationdistributioninto

account

3-4ExperimentalresultsinSi

3-5Summary

References

一分-

`j7

44

48

】V

V江

ⅧI

ANALYSISOFTHREE-DIMENSIONALGENERATIONDISTRIBUTION50

BYTHECOMBINATIONOFTHENORMALINCIDENCEANDTHE

L工NESCANMETHODS

4-1Introduction

4-2 Influenceofthree-dimensionalgeneration

distributiononelectronbeaminducedcurrent

02

inin

4-3Three-dimensionalgenerationdistributioninGaAs57

4-4Summary

References

12

vOVD

ANALYSISOFELECTRONBEAMINDUCEDCURRENTCONSIDERING64

SAMPLEDIMENSIONS

5-1Introduction

5-2

5-3

Determinationofdiffusionlengthandsurface

recombinationvelocity

ApplicationtoSi

5-4Summary

References

Appendix

DETERMINATIONOFLIFETIMEANDDIFFUSIONCONSTANT

BYPHASESHIFTTECHNIQUE

6-1Introduction

6-2Relationbetweenlifetimeandphaseshift

6-3ExperimentalresultsinSi

6-4Summary

References

HEATTREATMENTEFFECTONDIFFUSIONLENGTHINS1

7-1Introduction

7-2Experimentalresultsanddiscussions

References

CONCLUS工ONS

References

LISTOFPUBLICATIONS

4vO

CVD

73

78

9VO>

77

81

lro

88

CNJVO

qNas

7O

O^(J

99

102

104

105

108

109

-V-

LISTOFSYMBOLS

Cl

cBC

ggpgBELOS嚢

cdDDeEfgGIIIIIlj一jJ

J大

correctionfactorwithwhichthethree-dimensionalsolutions

oftheヽgradientofphaseshiftcanbeexpressedbytheone-

dimensionalapproximations

exponentofGaussiandistribution

positionofgenerationsourcefromthesurfacealongthedepth

diffusionconstantofminoritycarriers

(equivdgL)normalizedgenerationdepth

chargeofanelectronz

electron-holepaircreationenergybyanelectronbeam

modulationfrequencyofprimaryelectronbeam

generationrateofactualpointsource

variablepartofgenerationsource

thewholegenerationstrengthinthegenerationregion

Imaginaryunit

primaryelectronbeamcurrent

measuredelectronbeaminducedcurrent

currentwhichflowsthroughtheloadresistance

backwardsaturationcurrent

shortcircuitcurrent

electronbeaminducedcurrent

variablepartofcomplexelectronbeaminducedcurrent

(≒n)normalizedelectronbeaminducedcurrentitbecomes

unitywhenallthegeneratedcarrierscontributeto

electニronbeaminducedcurrent

normalizedelectronbeaminducedcurrentconsideringthe

Influenceofohmiccontact

一吐-

誉~Lay

L大eff

p卵`μrRRCReRmSStTuva

correctionfactorfortheincidentbeamenergyconsidering

theenergylossduetobackscatteredelectrons

thermalvoltagersquo259mVatroomtemperature

second-modifiedfirst-orderBesselfunction

diffusionlengthofminoritycarriers

diffusionlengthestimateddirectlyfromtheslopeof

electronbeaminducedcurrentvsscanningdistancecurve

diffusionlengthestimateddirectlyfromtheslopeof

electronbeaminducedcurrentvsscanningdistancecurve

consideringtheinfluenceofohmiccontact

(ΞLJ百石iT)complexeffectivediffusionlength

distニributionofminoritニycarrierdensity

distributionofminoritycarrierdensityconsideringthe

influenceofohmiccontニact

variablepartofthedistributionofminoritycarrier

densitycomplexvariable

distancebetweenthecenteroftニhegenerationregionand

eachdividedsegment

radiusofgenerationregion

centerofgenerationregion

extraporatedelectronrange

loadresistance

maximumelectronrange

surfacerecombinationvelocity

(ΞS(Lて))surfacerecombinationvelocityparameter

time

variableforintegrat10n

para万7rdquo万eterforGaussiandistribution

acceleratingvoltageofprimaryelectronbeam

一吐-

rdquod

wm

Xxx

χy

ZZ

np

Pau

^GaAs

SpてφΦω

distancebetweenthepotentialbarrierandtheohmiccontact

depletionlayerwidth

metalthicknessofSchottkydiode

Cartesianco-ordinateofscanningdistance

(ΞxL)

distancebetweenthepotentialbarrierandthegeneration

pointalongthescanningdirection

(ΞL)

Cartesianco-ordinateonthescanningsurfacenormalto

thescanningdirection

Cartesianco-ordinatealongthedepth

peakoftheGaussiandistribution<

(=J)collectionefficiency

collectionefficiencyofthevariablepartニofthegeneration

source

resistivityofsemiconductors

massdensityofAu゜189gcm^

massdensityofGaAs゜53gcm^

massdensityofSi=23gcm^

minoritycarrierlifetime

phaseshiftbetweentheelectronbeaminducedcurrentand

tニhemodulatedgenerationsource

diameterofprimaryelectronbeam

angularfrequencyofmodulatedprimaryelectronbeam

-VnL-

IINTRODUCT工ON

Theremarkableprogressinthesolidstatedevicesisowing

totheadvancementinthecharacterizationtechniqueofthedevice

materialsWhenthedeviceshavingnewfunctionsaredevelopedthe

detailknowledgeofthephysicalpropertiesofthesemiconducting

material(bandgaplifetimeandmobilityofcarriersetc)mustbe

neededInparticularthosepropertiesmustbecharacterizedafter

theactualmanufacturingprocessbecausetheoriginalpropertiesmay

beaffectニedbythevariousprocessconditions

Inrecentyearstocharacterizeverysmalldevices(ie

LSI゛sorlaserdiodes)therehasbeenagrowinginteresttousea

finelyfocusedelectronbeamThetwodimensionalInformationofthe

materialpropertiescanbeobtainednon-destructivelywithhigh

spatialresolutionfromtheelectronbeamInteractionwithsamples

[121Surfacemorphologycanbeobservedwithgreatニdepthoffocus

byascanningelectronmicroscope(SEM)Crystaldefectsinthin

samplesaredetectedusingascanningelectrontransmission

microscope(STEM)[34]AscanningAugerelectronmicroscope(SAM)

[5]hasbecomeaveryusefultooltoanalyzethesurfaceandthe

interfaceregion

Themethodusinganelectronbeaminducedcurrent(EBIC)[6-10]

1saveryconvenienttechniquetodeterminethefundamentalparameters

(egthediffusionlengththelifetimeandthesurfacerecombination

velocityofminoritycarriers)whichcontroltheelectricalperfor-

manceofthedevicesTheelectron-holepairsgeneratedbyanelectron

beamareseperatedbytheinternalfieldInp-njunctionsorSchottky

barriersandthecurrent1SInducedIntheexternalcircuitThe

EBICdependsverymuchondiffusionandrecombinationofminority

carriersInsemiconductorsandthediffusionlengthetccanbe

-1-

Fig1-1

type

type

Primaryelectrbe≪m

^^trrttDepletionlayer

Electron-hotep弗i「6gerwrationregion

Primaryelectronbeam

rArrScanningdirection

(A)

(B)

Principalconfigurationstomeasurethe

electronbeaminducedcurrent(EBIC)

(A)normalincidencemethod

(B)linescanmethod

-2-

く二rArr|t夕

EBICく二rArr

-一一--

p-typentype

aver`

1ミミ二l∽rsquoebic

determinedfromtheanalysisofEBICInadditiontothetwodlmen-

sionalinformationofthediffusionlengthandthelifetimetheir

variationsalongthedeptニhcanbeobtainedforvariousgeneration

depthsbychangingtheacceleratingvoltageofanelectronbeam

TheprincipalconfigurationstomeasureEBICarethersquonormal

incidencemethodrsquoandthersquolinescanmethodrsquo(seeFig1-1)Inthe

normalincidencemethodtheelectronbeam1Sincidentnormaltothe

barrierplaneandisscannedonthesurfaceparalleltothatplane

ThedislocationsanddefectsinSiwereobservedinp-njunctionsand

Schottkybarrierdiodes[11-28]Inrecentyearselectricalactivity

ofoxidationinducedstackingfaults(OSF゛s)anditsrelationwith

deviceperformanceshavebeenstudied[29-35]Thenormalincidence

methodisalsousedforthefailureanalysisoftニheMOSdevices[36-

39]Usingthelinescanmethodthediffusionlengthandthesurface

recombinatニionvelocitycanbedeterminedfromthedependenceofEBIC

onthescanningdistancewhentheelectronbeamisscannedacrossthe

barrierTherehavebeenmanytheoretical[AO-46]andexperimental

[47-69]reportstomeasurethediffusionlengthandthesurface

recombinationvelocityinlight-emittingdiodes(LEDrsquos)andlaser

diodes

InalmostalltheworkssofarEB工Chasbeenanalyzedonly

qualitatively0rsemi-quantitativelyThediffusionlengthandthe

surfacerecombinationvelocityhavebeendeterminedunderrather

specialconditionsasmentionedbelowforthesimpletheoretical

calculationInthenormalincidencemethodtheyconsideredonly

theone-dimensionalgenerationdistributionalongthedepth[70-75]

undertheconfigurationthatthelateralextentofthegeneration

volumewasverysmallcomparedwithsampleareasInthelinescan

methodthegenerationvolumewasassumedtobeapoint[53546061]

undertheconditionthatthegenerationvolumewassufficiently

-3-

smallerthanthediffusionlengthandthesampledimensionsBut

intheactualcasethegenerationvolumehasafinitethree-

dimensionalextentreLatedtotheacceleratingvoltage[76-78]

Thelatestmicroelectronicdevices(ieLSIrsquosandthelaserdiodes

etc)havethesamedimensionsasthegenerationvolumeandS0

theanalysesconsideringtニhepointsourceortheone-dimensional

generationdistributニionareinaccuratetodeterminethediffusion

lengthandthesurfacerecombinationvelocityThenewmethodfor

thequantitativeanalysisofEBICmustbedevelopedtakingthethree-

dimensionalgenerationdistributionandtheinfluencesofthesample

dimensionsintoaccount[7980]

InthepresentstudyEBICisanalyzedquantitativelyby

solvingthesteady-stateortime-dependenttニhree-dimensionaldiffusion

equationsTheinfluenceofthefinitegenerationvolumeonEBICis

discussedwhentheextentofthegenerationvolumecannotbeignored

andimprovedmetニhodsaresuggestedtomeasurethephysicalproperties

(diffusionlengthlifetimeandsurfacerecombinationvelocityof

minoritycarrierselectron-holepaircreationenergybyanelectron

beametc)inthesmallselectニedareas

InChapternvariousmodelsforthegeneratニiondistribution

alongthedepth[7781-83]arecomparedwitheachotherandtニhe

influenceofthegenerationdistributiononthedeterminationofthe

diffusionlengthbythenormalincidencemethodisdiscussed

ChapterⅡIshowstheinfluenceofthegenerationvolumeon

EB工Cinthelinescanmethodtakingtニhesurfacerecombinationeffect

intoaccountAnimprovedmethodforthedeterminationofthe

diffusionlengthandthesurfacerecombinationvelocityisdescribed

-4-

InChapterVthree-dimensionalgenerationdistribution

isclarifiedbymeasuringEBICusingboththenormalincidenceand

thelinescanmethodsinthesamesamplewhichyieldsthe

quantitativeanalysisofEB工C

ChaptervdescribestheInfluenceofthesampledimensions

onEBICInthelinescanmethodEBICisInvestigatedbyextending

themirrorimagemethodlsquo[41-43]whenthediffusionlengthisof

theorderofthesampledimensions

InChapterWthephaseshifttechniqueinthemeasurement

ofEBIC[84-86]isdescribedTherelationbetweenthelifetime

andthephaseshiftisclarifiedbysolvingthethree-dimensional

time-dependentdiffusionequationThelifetimeandtニhediffusion

constantofminoritycarrierscanbedeterminedcombiningthe

phaseshifttechniquewiththeconventionallinescanmethod

Chaptervnshowstheheattreatmenteffectonthediffusion

lengthinSi

FinallyconclusionsandsuggestionsforfurtherInvestigation

aresummarizedinChaptervnr

ExperimentalresultsinSiandGaAsareshovmineverychapter

Themethoddiscussedinthesechapterscanbeappliedeasilyto

anysemiconductormaterialsbyconsideringthephysicalproperties

inherentinthematerials

-5-

References

[1

[21

[3]

4]

5]

6]

[7]

[8]

[9]

[10]

VEJohnson十Sm119151p763

0CWellsSEM1972p375

pMrdquoPetroffDVLangJLStrudelandRALogan

SEM71978pp325-332

CELymanSEM1978pp529-536

NCMcDonaldSEM1971p89

DBHoltrdquoQuantitativeScanningElectronMicroscopyrdquo

(DBHolteta1edsAcademicPress974)pp213-286

DBWittryrdquoMicroprobeAnalysisrdquo(CAAndersoned

JohnWileySonsNewYork1973)pp123-187

CJVarkerrdquoNondestructiveEvaluationofSemiconductor

MaterialsandDevicesrdquo(edJayNZemelNATOADVANCED

STUDYINST工TUTESSERIESSERIESBPhysicsvol46

PLENUMPRESS1979)pp515-580

HJLeamyLCKimerlingandSDFerris

SEM1978pp717-725

ThebibliographyonEBICislistedinthefollowing

K0LeedySolidStateTechnologyFeb1977pp45-48

--

-- - -

rdquo-

rdquo- - 言

争心- -

SEM19xxrdquoScanningElectronMicroscopyrdquoProceedingofAnnualConference

before1977(IITResearchInstituteChicago)

after1978(SEMIncAMFOrsquoHare)

-6-

[11]JJLanderHSchrelberJrTMBuckandJRMathews

ApplPhysLett旦206-207(1963)

[12]WCzajaandGHWheatleyJApplPhys亜

2782-2783(1964)

[13] WCzajaandJRPatelJApplPhys11476-1482

(L965)

[14]NFBNeveandPRThorntonSolid-stateElectron

旦900-901(1966)

[15]

[16]

[17]

[18]

[19]

[20]

[21]

[22]

[23]

[24]

IGDaviesKAHughesDVSulwayandPRThornton

Solid-stateElectron9275-279(1966)-

WCzajaJApplPhysyi918-919(1966)

DVSulwayPRThorntonandMJTurner

Soli-StateElectron11567-568C1968)-

AJRKockSDFerrisLCKimerlingandHJLeamy

ApplPhysLett27313-315(1975)

DBHoltandROgdenSolid-stateElectron1937-40(1976)-

HJLeamyLCKimerlingandSDFerris

SEM1976pp529-538

TKatoTMatsukawaandRShlmizu

ApplPhysLett26415-416(1975)

RBMarcusMRobinsonTTShengSEHaszkoand

SPMurarkaJElectrochemSOC124425-430(1977)

LCKimerlingHJLeamyandJRPatel

ApplPhysLett30217-219(1977)

DEIoannouandSMDavidson

physstatsol(a)丘旦K1-K4(1978)

-7-

[25]

[26]

HBlumtrittRGlelchmannJHeydenderichandH

Johansenphysstatsol(a)55611-620(1979)

HMennigerHRaidtandRGleichmann

physstat-sol(a)5旦173-180(1980)

[27]pAshburnandCJBullSolid-stateElectron

Tl_105-110(1979)

[28] pAshburnCJBullandJRABeale

JApplPhys503472-3477(1979)

[29]KVRaviCJVarkerandCEVolk

JElectrochemSoc120533-541(1973)-

[30]

【31】

[32]

[33]

[34]

[35]

[36]

[37]

[38]

[39]

[40]

CJVarkerandKVRaviJApplPhys45272-287(1974)

SKawadoYHayafujiandTAdachi

JpnJApplPhys14407-408(1975)

TESeidelSEHaszkoandDMMaher

JApplPhys485038-5042(1977)

AMurgaiJYChiandHCGatos

JElectrochemSoc1271182-1186(1980)-

SKawadqJpnJApplPhys191591-1602(1980)

JMDishmanSEHaszkoRBMarcusSPMurarka

andTTShengJApplPhys502689-2696(1979)

JLGatesand0KGriffith

ApplPhysLett27kZ-45(1975)

JFKatalanoSEM71976pp521-528

PRoltmanandWRBottomsSEM1977pp731-738

CLWilsonSolid-stateElectron23345-356(1980)-

WHHackettJrJApplPhys431649-1654(1972)

-8-

[41]

[42]

[431

[44]

[45]

【46】

[47]

[48]

[49]

[50]

FBerzandHKKuikenSolid-stateElectron

19437-445(1976)

CvanOpdorpPhilipsResKept32^192-249(1977)

0vonRoosSolid-stateElectron互lsquo1063-1067(1978)

0vonRoosSolid-StateElectron211069-1077(1978)

0vonRoosSolid-stateElectron22113-114and773-778-

(1979)

WvanRoosbroeckJApplPhys旦D380-391(1955)

DBWittryandDFKyserJApplPhysj11387-1389

(1965)

HHiguchiandHTamura

JpnJApplPhys4^

316-317(1965)

YuPDemidovRPGurovaYuMKushnirAIFrltner

andDVFetisovSovPhys-Semicond1030-1035(1968)

KMaedaAKasamiMToyamaandNWakamatsu

JpnJApplPhys旦65-75(1969)

[51]ZhIAlferovVMAndreevVIKorolrsquokovand

vIStreminSovPhys-Semicond41113-1116(1971)

[52]

[53]

[54]

[551

CJHwangSEHaszkoandAABergh

JApplPhys425117-5119(1971)

WHHackettJrRHSaulRWDiχonandGWKammlott

JApplPhys432857-2868(1972)

WZimmermannphysstatsol(a)^2671-678(1972)

MAvenJZDevineRBBolonandGWLudwlg

JApplPhys434136-4142(1972)

-9-

[56]

[57]

[58]

[59]

【60】

[61]

[62]

[63]

[64]

[65]

[66]

GLidgardSolid-stateElectron15159-164(1972)

DBHoltBDChaseandMCenslive

physstatsol(a)20459-467(1973)-

DBHoltandBDChasephysstatsol(a)2(

135-144(1973)

CvanOpdorpRCPetersandMKlerk

ApplPhysLett24125-126(1974)

LJBalkEKubalekandEMenzel

IEEETransED-22707^712(1975)-

LJastrzebskiJLagowskiandHCGatos

ApplPhysLett11_537-539(1975)

LJBalkEKubalekandEMenzelSEM71975pp447-455

JJOakesIGGreenfieldandDLPartaln

JApplPhys丘旦2548-2555(1977)

MLanirAHBVanderwyckandCCWang

JApplPhys496182-6184(1978)

DLPartainAGMilnesandLFVassamlllet

JElectrochemSoc1261584-1588(1979)-

NTohgeTMinamiandMTanaka

JpnJApplPhys172155-2156(1978)

【67】DLPartainAGMilnesandLFVassamillet

JElectronicMaterials旦493-499(1979)

[68]

[69]

DEIoannouandSMDavidson

JPhysDApplPhys昆1339-1344(1979)

ShengSLiWLWangPWLaiandRTOwen

JElectronicMaterials旦335-354(1980)

-10-

[70]

【71】

[72]

[73]

[74]

JFBresseSEM119111pp105-112

JFBresseSEM1977pp683-693

CJWuandDBWittryJApplPhyspound92827-2836(1978)

GEPossinSEM1979pp245-256

GEPossinandCGKirkpatrlck

JApplPhys旦4033-4041(1979)

[75]GEPossinandCGKirkpatrick

JVacSciTechnol161917-1920(1979)-

[76]

[77]

[78]

[79]

[80]

VonAEGruenZNaturforsch12aHeft289-95(1957)-

KKanayaandSOkayama

JPhysDApplPhys5A3-58(1972)

RShimizuYKataokaTIkutaTKoshikawaand

HHashimotoJPhysDApplPhys旦101-114(1976)

GVSpivakGVSaparinandLFKomolova

SEM1977pp191-199

CDonolatoandHKlann

-JApplPhys511624-1633(1980)

[81]DBWittryandDFKyser

JApplPhys2旦375-382(1967)

[82]

[83]

[84]

[85]

[86]

TEEverhartandPHHoff

JApplPhys425837-5846(1971)

VVMakarovSovPhys-Semicond旦in-llk(1975)

JDKannnandHBerntSolid-stateELectronヌ1957-964(1978)-

JDKammrdquoSemiconductorSilicon1977rdquo(JElectrochemical

Society)pp491-501

0vonRoosJApplPhys503738-3742(1979)

-n-

-L2-

2-1

INFLUENCEOFM工NORITYCARRIERGENERATIONDISTRIBUTION

ONELECTRONBEAMINDUCEDCURRENTINTHENOR^IALINCIDENCE

METHOD

Introduction

Accuratedeterminationofminoritycarrierdiffusionlength

LisveryimportanttocharacterizesemiconductorsOneofthe

convenientmethodstomeasureLIstheuseofelectronbeam

inducedcurrent(EBIC)Theelectron-holepairsgeneratedbyan

electronbeamareseperatedbyapotentialbarrier(egp-n

junctionorSchottkybarrier)andthecurrentisInducedinthe

externalcircuitThevalueofLcanbedeterminedfromthe

dependenceofEBIConthelengthzbetweenthepotentialbarrier

andthegenerationpointInthenormalIncidencemethodzis

variedbychangingtheacceleratingvoltagevaofanelectronbeam

andthesmallvalueofLoftheorderofumcanbedetermined

ThevalueofLintニhesmallregionisobtainedusingafocused

beamgeneratedbyascanningelectronmicroscope(SEM)lsquo

Czaja[1]measuredLinp-ndiodesofSiandGaPHe

assumedthegenerationdistributionasacombinationoftwo

exponentialfunctionsBresse[2]andWu[3]measuredLandthe

electron-holepaircreationenergyE^^inSiandGaAsTheyused

Schottkydiodesbecausetheelectronbeamenteredthroughthemetal

contactandthesurfacerecombinationeffectcouldbeneglected

IntheiranalysesBresseusedthesemi-sphericalgeneration

distrlbutionproposedbyKanayaeta1[4]andWuassumedGaussian

distリbutlonPossineta1[5]analyzedEBICindetailtakingthe

influencesofthesurfacerecombinationandtheinternalfield

-13-

Metal

Depletio

layer

Primaryelectronbeam

Numberofgeneratedcarriers

Fig2-1Schematicviewofexperimentalconditions

jusingSchottkydiodesMetalthicknessis

wanddepletionlayerwidthiswright-handillustぷふこsthedぶdosefunctionRandR

-givethemaxiraum

andextraporaiedmelectrSnolinerangerespectively

-14-

0generatedcarrier

に_---___1

我_______Iuarrヽ

y重ダ

1ごpermil

andestimatedthedepthdistributionoflifetimeinion-implantedSi

TheylsquousedthepolynomialfunctionderivedbyEverhart[6]forthe

generationdistribution

工ntheanalysisofEBICtheminoritycarriergeneration

distributionplaysanimportantroletodeterminetheaccurate

valueofLandEHoweverthedistributionmodelsusedinthepc

analysesaredifferentwitheachotherasmentionedaboveIntニhis

chapterwecomparevariousmodelsforthegenerationdistribution

inGaAsandSiWecalculateEBICandclarifytheinfluenceofthe

generationdistributiononthedeterminationofLandEpc

Experimentalresultsarealsopresented

2-2 Determinationofdiffusionlengthandelectron-holepair

creationenergy

ASchottkybarrierdiodeisusedinordertoneglectthe

influenceofthesurfacerecombinationTheelectronbeamis

irradiatednormallytothebarrierplanethroughthemetalas

shownInFig2-1Thethicknessofthemetalandthedepletion

layerareputaswmandwd゛respectivelyTheminoritycarrier

generationdistributionalongthedepth(Socalledthedepthdose

function)isIllustratedalso1nFig2-1TheEBICiscalculated

basedonthefollowingassumptions1)Theminoritycarriers

generatedinthemetal(regionI)cannotcontributetoEBIC

2)Theelectron-holepairsgeneratedinthedepletionlayer(

regionlsquoTL)areseperatedquicklybythefieldofthedepletion

layerandwhollycontributetoEBIC3)Theminoritycarriers

generatedinthebulk(regionⅡI)partlycontributetoEBICie

theminoritycarrierswhichreachtotheedgeofthedepletion

-15-

mDiwi)iunMd

SMtjjesp≫)ejAU≫6|o』ψsEコz

Normalizedgenerationdepth^rsquoRm

Fig2-2

Generationdistribution

inGaAsTheMakarov゛SWittryrsquos

andKanayarsquosmodelsareexpressed

bytニhesolidbrokenanddotted

linesrespectivelyThegener-

atlondepthisnormalizedby

themaximumelectronrangeR

ThetotalgenerationrateiSm

normaLlzedtobeunity

-16-

2 0

1 05

(Efi)≪MJO^M

d6ue」

CO』oa3

rdquorsquo5102050Acceleratingvoltageva(kv)

Fig2-3

ElectronrangesinrsquoGaAsforvariousmodelsThesolidbrokendottedanddashedanddottedlinesaretheresultsusingMakarovrsquosWitニtryrsquosKanayarsquosandEverhartrsquosmodels

respectively

rdquoゝゝGaAs

χ

`Makarov20χ

----Wittry

χhelliphelliphellipKanaya

11S

15

゛S≒

rsquoχ≒

χrsquo

10trsquolsquo

卜卜゜χ゛

卜ゝrsquo

05χrsquo゛rsquoゝ

ゝrsquoゝ1

ゝゝrsquoゝゝ

ゝゝ

00

50

GaAso々

タグrsquo

Makarov

15-rsquo一一Wittry

ノKanaya

12

---Everhart

13yelr(2゛十`゛dinFig2-1)bydiffusioncanflowintothemetal

bythefieldofthedepletionlayer

Therehavebeenmanytheoretical147]andexperimental

[68-11】worksonthegenerationdistributionKanayaand

Okayama[4]proposedasemi-sphericalgenerationdistribution

usingthemodifieddiffusionmodel0fArchard[7]Wittryeta1

assumedGaussiandistributionandappliedtoGaAs[89]

EverhartandHoffl6]derivedapolynomialfunctionfromtheir

experimentsIntheA1olineSi02olineSisystemdegMakarov[10]showedthat

thegenerationdistributioncouldbeexpressedasGaussianlike

(exp(-((z-z)u)2))andthep8゛゜eters2manduvariedaccording

totheatomicnumberandthedensityofthematerialInorderto

comparethesedistributionsnormalizeddepthdosefunctionwas

introducedGruen[11]showedthattheshapeofthedepthdose

curveispracticallyinvariantifthepenetrationdepthis

normalizedbytheelectronrange

ThedepthdosefunctioninGaAsnormalizedbythemaximum

electronrangeRm(atwhichnoelectronentersintothematerial

seeFig2-1)areshowninFig2-2bythesolidbrokenanddotted

linesusingthefollowingequationsforthemodelsofMakarov

WittryandKanayarespectively

2RmolineOdeg138

g(z)=exp(-(rarr元でi

g(z)=exp(-(

2Rmoline

Odeg125

-035

)2)

)2)

(Makarov)(2-1)

(Wittry)(2-2)

g(z)゜(RmolineOdeg242Rtri)2oline(2olineOrsquo242Rm)2(K゛3y8)゛(2lsquo3)

-17-

こrsquo

Aouepj^^auoiiDaii〇D

Fig2-4

10203040

Acceleratingvoltage

5060

Va(kV)

CollectニionefficiencynvsVacurves

GaAsSchottkydiodeThevaluesofLare505μmfromuppert0lowergroupofcurves

for

2and

respectivelyTheresultsusingtheMakarovrsquosWittry゛SandKanayarsquosmodelsareexpressedbythesolidbrokenanddottedlinesrespectivelyThevaluesofwandWare10nmand015ymrespectively^hedashedanddottedlineisinthecaseofw=50nmw=015umandL=2umusingtheWittryrsquosmode1

-18-

GaAs一一Makarov

--rdquo-Wittry

10Wf^=10nmhelliphelliphelliphellipKanayaL(pm)

rsquo≒゜ニ1こii4degこ7T`ヽヽヽ5

05万でヽこミア斗辿こTTZご

50nふyミ゛1helliphelliphelliphellip4゛`゛ζ゛ζ

Orsquo1capparacapcap

か4

5060

ThereareobviousdifferencesbetweenthesethreemodelsThe

MakarovrsquosandWittryrsquosmodelshavethelargesurfaceconcentration

butthepeakvalueatzRm゛Odeg13oftheMakarovrsquosmodelissmaller

thanthatoftheWittryrsquosmodelTheKanaya゛smodelhasmoreevenly

spreadeddistributionthantheothertwomodelsThisisbecause

theelectron-holepairconcentrationisassumedtobeuniformin

thesemi-sphereintheKanayarsquosmodelwhichisasimplefirst-

orderapproximationforthegenerationdistributionButinthe

actualcasetheelectron-holepairsareconcentratedaroundthe

centerofthesemi-sphereOnemustusetheimprovedelectron-hole

pairconcentrationmodelInsteadoftheuniformoneinorderto

expressthegenerationdistributionprecisely

InthecalculationofEBICtheabsolutevalueofRmustm

beneededSomereportedvaluesbyMakarovWittryandKanayaare

shownbythesolidbrokenanddottedlinesrespectively

inFig2-3forGaAsThedashedanddottedlineisderivedby

Everhart[6]anddiscussedlaterTherangesoftheWittryrsquosand

Kanayarsquosmodelsarealmostagreewitheachotherbutthatofthe

Makarovrsquosmodelisabout70ZofthoseoftheWittryrsquosandKanayarsquos

models

ThecalculatedEBICinGaAs(iethecollectionefficiency

nwhichbecomesunitywhenallthegeneratedcarrierscontribute

toEBIC)bythesamemethoddescribedinref[3]isshownIn

Fig2-4Thesolidbrokenanddottedlinesareforthemodelsof

MakarovWittryandKanayarespectivelyThevalueoftheacceler-

atlngvoltageva1Schangedfrom5t060kVThevalueofLIs50

20and05ymfromuppert0lowergroupofthecurvesrespectively

ThevaluesofWmandwdaretakenastypicalvaluesof10nmand

015ymrespectivelyTheelectronrange1SInverselyproportional

tothedensityofthematerialThemetalthicknessiscorrected

-19-

takingthedifferenceofthedensitiesbetweenthemetalandthe

bulksemiconductorinorderthatthesamplehasuniformdensityfrom

thesurfacetothebulkforasimpletheoreticalcalculationWhen

goldistakenastheSchottkycontactwmustbemultipliedby

pAupGaAS(゜3`゜6rsquopAudeg189andpGaASdeg5゛3

1cll3)

゛OIlecanestimateL

mainlyfromthegradientofthecurvebecausethegradientdecreases

monotonouslywithincreasingLupt05umTheestimatedvaluesof

LbyMakarovrsquosandWittry゛Smodelsarealmostequalbecausethe

gradientsofthecurvesagreewitheachotherforthesameLvalue

ThevalueofLlargerthan5μmcannotbedetermineddefinitely

becauseEBIChardlychangeswithvevenifLbecomeslargeThea

maximumvalueofLthatcanbedetermineddefinitelyincreasesas

thehighestvalueofvaincreasesbutanotherproblems(idegedeg

damagesofthesamplebyhighenergyelectronsetc)mayoccur

Theelectron-holepaircreatニionenergyEcanbeobtainedfrom

theabsolutevalueofEBICbytherelationndeg^C^EBIC^^B^

(IEBICmeasuredEBICIBprimarybeamcurrentkcorrectionfactニor

fortheenergylossduetobackscattニeredelectrons)[3]

TheabsolutevaluesoftニheMakarovrsquosmodelareabout10へj20Z

largerthanthoseoftheWittry゛smodelAndsothevalueofEpC

obtainedbytheformeris10へj20Zlargerthanthatbythelatter

ThegradientニSandtheabsolutevaluesofthecurvesoftheKanayarsquos

modelarequitedifferentfromthosebytwoothermodelsThe

reasonofthedifferenceisowingtotheassumptionoftheuniform

concentrationoftheelectron-holepairsinthesemi-sphereas

discussedbeforeTheKanayarsquosmodelisafirst-orderapproximation

forthegenerationdistributionandisnotsuitableforthe

accuratedeterminationofLandEThevalueofwdoesnotaffectpc(I

EBICsomuchfromtheresultsoftニhecalculation工fWbecomesm

largetheabsolutevalueofEBICat10wvaisdecreasedverymuch

-20-

butthegradientofthecurveintheregionofhighVadoesnot

changeasshowninFig2-4(thedashedanddottedlineisinthe

caseofwmdeg50nm゛wdrsquoOrsquo15pmandL=2ymusingtheWittry゛Smode1)

ThereforeLcanbedeterminedinanycaseofwm゛asfaraswm1S

sufficientlysmallinorderthattheelectronbeamcanenterinto

thebulkregion

ThenormalizeddepthdosefunctionsInSiexpressedbythe

followingequationsareshowninFig2-5bythesolidbroken

dottedanddashedanddottedlinesforthemodelsofMakarov

WittryKanayaandEverhartrespectively

zR-0261

g(z)=exp(-(-jyヲー-7)2)(Makarov)(2-4)

zR-0156

g(z)=exp(-(―q2L_一一

g(z)゜(RmolineOrsquo336Rm)2

g(z)=06+6212Re

(Wittry) (2-5)

(゛0336R)^(Kanay゛1)(2oline6)

oline12deg40(2Re)2+5lsquo69(zR

(Everhart)e)3

(2-7)

Makarovshowedthattheparameterszmlsquoanduhadvoltagedependencesl

andthetypicalvaluesatvadeg30kVaretakenItshouldbenoted

thatthedepthdosefunctionoftheEverhartrsquosmodelisnormalized

bytheextraporatedrangeRe(seeFiglsquo2-1)whichisdetermined

byextraporatingthestraightlineportionofthecurve

-21-

Fig2-5

11

u)6ua))iunjed

sjdiJieopdiejdud6lo」4sEコz

Normalizedgenerationdepth^rsquoRm

GenerationdistributionsinSiTheMakarov゛s

Witニビry゛sKanayarsquosandEverhart゛Smodelsare

expressedbythesolidbrokendottedanddashedanddottedlinesrespectivelyThegener-

atlondepthisnormalizedbythemaximumelectron

rangeRTheextraporatedrangesR゛SoftheMakarovrsquosWittryrsquosandEverhartrsquosmodelsare

takentobeagreedwitheachotherThetotニal

generatニionrateisnormalizedtobeunity

-22-

KUkarov

--一一-Wittry2deg

二ぷ芯t

15へ

゜¥レ臨べhellip

hellip

10rsquoS゛lsquoNhellip

helliphellip

05

hellip

helliphellip

1helliphellip

hellip

005

工nordertocomparetheEverhartrsquosmodelwithothersthe

extraporatedrangefortheGaussiandistributionisdeduced

(seefootnote)十andtheextraporatedrangesoftheMakarovrsquoS

WittryrsquosandEverhart゛Smodelsaretakentobeagreedwitheach

otherThepeakvaluesofthegenerationdistributionsofthe

MakarovrsquosWlttryrsquosandEverhartrsquosmodelsarealmostequalbut

thevalueofzRmatthepeakfortheWittryrsquosmodelisabout

015andsmallerthanthoseoftheothertwomodelsCzR=025)゜

ThegenerationdistributionoftheWittryrsquosmodelcomesnearerto

thesurfacethanthoseoftheMakarovrsquosandEverhartrsquosmodelsIt

isbecausetheWittryrsquosmodelisderivedInthecaseofGaAsand

ontheotherhandtheMakarovrsquosandEverhart゛Smodelsareconcerned

inthecaseofSiThedensityofG゛1AS(pGaAS゛5deg3gcm^)islarger

thanthatofS1(pSirsquo2deg3gcm^)andsotheWittry゛Smodelshows

themoresurfaceconcentrationthantheothersTheKanayarsquosmodel

isquitニedifferentwiththeotherthreemodelsowingtothesame

reasonasdiscussedinGaAs

- -

-- - - - -

- - - -

Gaussiandistribution(e゛p(oline((2oline2m)11)2))

showsthealmostlineardecreasearoundthepoint

ofinflection(zdegu゛Σ十zm)lsquoTheextraporatedrange

Re(1゛ersquothepointwithwhichthestraightline

atthepointofinflectioncrossesthezaxis)

becomes2u十zfromtheresultsofcalculationm

(seeFig2-5)゜TheextraporatedrangeRebecomes

078Rand062RfortheMakarovrsquosandWittryrsquosmm

modelrespectively

-23-

Fig2-6

0 102030

Acceleratin9

4050

voltage

60

va(kv)

CollectionefficiencynvsVacurvesforSiSchottkydiodeThevaluesofLare1052andlymfromuppert0lowergroupofcurvesrespectivelyTheresultsusingtheMakarovrsquosWittryrsquosKanayarsquosandEverhartrsquosmodelsareexpressedbythesolidbrokendottedanddashedanddottedlinesrespectivelyThevaluesofWandware10nmand05ymrespectivelymd

-24-

MakarovSi---rdquoWittry

Kanaya

----Everhart

ジhttpwwwL(pm)卜

)渫回ブモジミ穫

WmニlOnmrdquoミ4helliphellipで``rsquoヽ4゜

゛ゝ1rsquohelliphelliphellip

゛rsquoN

u1C

larrl

0E

501

Figure2-6showsthecollectionefficiencyinSiusing

thefourdifferentmodelsofMakarovWittryKanayaandEverhart

bythesolidbrokendottedanddashedanddottedlines

respectivelyThevalueofLIs1005020and10umfrom

uppert0lowergroupofcurvesrespectivelyThevaluesofW

andrdquodaretakenastypicalvaluesof10nmand05]imrespectively

Thevalueofwmismultipliedby821nthecalculationowingto

thedifferenceofdensitiesbetweenAuandS1

asdiscussedbeforeThevalueofLlargerthan10μmcannotbe

determinedaccuratelybecauseEBIChardlychangesevenifLvaries

ThegradientofthecurveoftheEverhartrsquosmodel1Sslightly

steeperthanthoseoftheMakarovrsquosandWittry゛smodelswhich

almostagreewitheachotニherAndsotheestimatedvalueofLby

theEverhartrsquosmodelbecomeslargerthanthatbytheMakarovrsquosor

Wittry゛smodelforthesamer)vSdegvaCurve(egL=lutnbythe

Everhartrsquosmodelbecomes07umiftheMakarov゛Smodel1Sused)

ThegradientofthecurveoftheKanayarsquosmodelisalmostequal

tothatニoftheEverhartrsquosmddelbuttheabsolutevalueofthe

formeris30Zsmallerthanthatofthelatterforthesamevalue

ofLThereforetheestimatedLbyKanayarsquosmodelalmostagree

withthatbytheEverhartrsquosmodelbutthevalueofE

pCuSing

theformeris30Zsmallerthanthatusingthelatter

Asmentionedbeforetheelectronrangeisinversely

proportionaltothedensityoftニhematerialTheelectronrange

derivedbyEverhartinSicanbeappliedtoGaAsconsideringthe

differenceofthedensitiesbetweenSiandGaAsThecalculated

valuesareplottedbythedashedanddottedlineinFig2-3

TherangesoftheMakarov゛SandWittry゛Smodelsarelargerthan

thatoftheEverhart゛smodelOneofthereasonsforthe

disagreementisthedifferentdefinitionsoftheelectronrange

-25-

ieMakarovandWittryusedthemaximumrangeRbutEverhart

usedtheextraporatedrangeRelsquoInordertニocomparethesevalues

theextraporatedrangesfortheMakarovrsquosandWittryrsquosmodels

inGaAsarededuced(seefootnoteinpage23)andbecome075Rm

andOlsquo62Rm゛respectivelylsquoForexampleinthecaseofvadeg30kv゛

thevaluesofRforMakarovrsquosandWittryrsquosmodelsare34andm

48ymandthenthevaluesofRebecome26and30ym

respectivelylsquoThevalueofReintheEverhartrsquosmodel(29umat

vadeg30kV)isslightlylargerthanthatoftheMakarovrsquosmodel

butagreeswiththatoftheWittryrsquosmodel

2-3 ExperimentalresultsinGaAs

AconventionalSEMwasusedfortheprimaryelectronbeam

whichwasmodulatedat3kHzwithachoppingcoilinsertedinto

thebeampathTheinducedcurrentwasmeasuredfromthevoltage

dropacrosstheloadresistancewhichwasconnectedtotheSchottky

barrierwithanohmiccontactThesignalwasdetectedbyalock-in

amplifierThebeamcurrentwasmeasuredbyaFaradaycageThe

beamwassomewhataefocussed(Φ|=10umφbeamdiameter)inorder

toavoidhighinjectionTheinducedcurrentwasnotchangedeven

ifthebeamwasirradiatedatthesamepointforanhour

TheSchottkybarrierwasrsquomadeonn-typeGaAs(Sndoped

ndeg62times1016cmoline3)byevaporatingAuofabout10nmthickina

vacuumofabout10oline7TorrTheohmiccontactwasobtainedby

evaporatingAu-Geandalloyingat400degCfor2mlnThecarrier

densityandthedepletionlayerwidthweredeterminedbyG-V

measurements

-26-

(Hiunqj≫)

U一SU

BeamcurrentIb(A)

Fig2-7

MeasuredEBICinGaAs(Sn-

dopedn=62)(1016cmoline3)Schottky

diodeatVa=10and50kVThe

beamcurrentwaschangedinthe

rangeof2)(10oline11≦I≦5)(10oline9A

-B-Theopenandsolidcirclesare

theexperimentalresultsforvadeg

10and50kVrespectivelyand

thegradientsofthesolidlines

areunity

Tab2-1

(s≫UコqjB)Aouapu

く1)

uoiioaiion

AcceleratingvoltageVa(kV)

Fig2-8

Curvefittingsoftheexperi-

mentalresultstothetheoretical

collectionefficienciesinGaAs

SchottkydiodeThesolidbroken

anddottedlinesaretheresultニS

usingtheMakarovrsquosWittry゛Sand

Kanayarsquosmodelsrespectively

Vaischangedfrom5t050kVwith

thefixedvalueofl゛10oline1oA

w=10nmandwmd

L(unj)Ec(ev)

Makarov

Wittry

Kanaya

03

03

05

48

41

41

二〇15um

ご洸竺詐比飛ぱ器ぶごぷ詣ぷ

-27-

000

5Gなfimf4ilvalu

0v≪>iakv

50

100

10

lylrsquo16rsquo1(i

acuteン゛tGaAs(Sndoed)

5n=62

lope

1二痙7

5Kanayao

21020304050

ThevalueofEBICatv=10and50kVareshownbythesolida

linesinFig2-7whenthebeamcurrentIBischangedintherange

of2)(10oline11≦I≦5)(10oline9AIftheminoritycarrier-B-

concentrationexceedsthethermalequilibriumconcentrationof

majoritycarriers(iehighinjection)theminoritycarrier

lifetimeisprolonged[12]ThereforeEBICbecomestoincrease

superlinearlywiththenumberofgeneratedcarriersie

withIBforafixedvalueofvarsquoInthisexperiment゛EBIC

increaseslinearlywithIBatbothvals゛WhichShoWsthe10w

injectionTheexperimentalresultsareshownbycirclesin

Fig2-8whenvischangedintherangeof5くVく50kVata=adeg

thefixedvalueofIBdeg10oline10A゛Theoreticalcollectionefficiencies

usingtheMakarovrsquosWitニtryrsquosandKanayarsquosmodelsareshownbythe

solidbrokenanddottedlinesrespectivelyinFig2-8The

valuesofLandEpcdeterminedbyfittingtheexperimentaldata

totニhetheoreticalcurvesaretabulatedinTab2-1forthethree

differentmodelsofMakarovWittryandKanayaThecollection

efficiencybytheMakarovrsquosmodelshowedfairlygoodagreement

withtheexperimentalresultsbutthatusingtheWittryrsquosmodel

isslightlylargerthantheexperimentalvaluesinthe10Wva

l`egioll(va≦10kV)Thediscrepancyinthelowvaregionbecomes

largeiftheKanaya゛SmodelisusedInthecaseofWittryrsquosand

Kanaya゛Smodelspoundheexperimentaldatawerefittedintherange

ofhighva(va≧15kv)TheestimatedvaluesofLis03urnby

usingboththeMakarovrsquosandtheWittryrsquosmodelsbutthatusing

theKanayarsquosmodelis05ymandabouttwiceoftheresultby

theMakarovrsquosandWittryrsquosmodelsThevaluesofEdeterminedpc

bytheMakarovrsquosWittryrsquosandKanaya゛Smodelsare4841and41

eVrespectivelyBythenormalincidencemetニhodofEBICWuand

Wittry[3]andKobayashieta1[L3]determinedEas468and457

eVrespectivelywhicharealmostequaltotheresultusingthe

Makarovrsquosmodelbutareabout10Zlargerthanthevalueobtained

bytheWittryrsquosandKanayarsquosmodels

-28-

2-4 Summary

ThevaluesofLandEcanbedeterminedfromthe

PC

ceofEBIConvbythenormalincidencemethodThe-

dependenceofEBIConVabythenormalincidencemethodThe

minoritycarriergenerationdistributionplaysanImportantrole

intheanalysisofEBICVariousgenerationdistributionmodels

arecomparedwitheachotherunitingthedifferentdefinitionsof

theelectronrange(Iemaximumrangeandextraporatedrange)

InGaAsGaussiandistributionsproposedbyMakarovand

Wittryhavelargesurfaceconcentrationsandthepeaksofthe

distributionsexistatabout0130fthemaximumelectronrange

Kanaya゛Smodelhasevenlyspreadeddistributionowingtothe

assumptionoftheuniformconcentrationofthegeneratedelectron-

holepairsThevalueofLlargerthan5μmcannotbedetermined

definitelybecauseEBIChardlychangesevenifLvariesThe

estimatedLbytheMakarovrsquosmodelalmostagreeswiththatblsquoythe

WittryrsquosmodelbutEdeterminedbytheformeris10へj20ZrdquoPC

largerthanthatbythelatter

InSithepeaksofthegenerationcistributionbecome

deeperthanthoseinGaAsbecausethedensityofS11Sabouthalf

ofthatofGaAsThelargestvalueofLthatcanbedetermined

definitelybecomestwiceofthatofGaAsbecausetheelectronrange

inSiisabouttwiceofthatinGaAsTheestimatedLbythe

MakarovrsquosorWittryrsquosmodelisabout30Zsmallerthanthatbythe

Everhartrsquosmodel

IntheexperimentsinGaAstheestimatedLbytheMakarovrsquos

modelagreedwiththatbytheWittryrsquosmodelbuttheestimated

Epcbytheformerwas48eVandabout17Zlargerthanthatbythe

latter

-29-

References

[1]

[2]

[5]

WCzajaJApplPhys374236(1966)

JFBresserdquoScanningElectronMicroscopy71972partlrdquo

(iiTRiChicago111)p105

CJWuandDBWittryJApplPhys丘旦2827(1978)

KKanayaandSOkayamaJPhysDApplPhys

543(1972)-

口EPosslnandCGKirkpatrickJApplPhys

5^4033(1979)

[6]TEEverhartandPHHoffJApplPhys

425837(1971)

[10]

[11]

[12]

[13]

GDArchardJApplPhys竪91505(1961)

DBWittryandDFKyserJApplPhys28375(1967)

TSRao-SahibandDBWittryJApplPhys

403745(1969)

VVMakarovSovPhysSemicond旦722(1975)

jVonAEGruenZNaturforsch12aHeft289(1957)-

JCornuRSittigandWZimmermannISolid-stateElectron

TKobayashiTSugitニaMKoyamaandSTakayanagi

IEEETransNuclSciNS-19324(1972)-

-30-

3-1

DETERMINATIONOFDIFFUSIONLENGTHSURFACERECOMBINATION

VELOCITYANDELECTRON-HOLEPAIRCREATIONENERGYBYTHE

LINESCANMETHOD

Introduction

Anelectronbeaminducedcurrent(EBIC)methodisa

convenienttechniquetomeasuretheminoritycarrierdiffusion

lengtニhLandthesurfacerecombinationvelocitysinsemi-

conductingmaterialsInthelinescanmethodLandScanbe

determinedfromthedependenceofEBIConthescanningdistance

whentheelectronbeamisscannedacrossthebarrierBerzand

Kuiken[1]gaveadetailedtheoryforthedeterminationofLand

sandOpdorp[2]investigatedexperimentallytheinfluenceof

surfacerecombinationonEBICJastrzebskieta1[31measured

Landsfordifferentgenerationdepthsbyvaryingtheaccelera-

tingvoltageofanelectronbeam

Inthosestudiesthegenerationsourcewasassumedto

beapointbutinpracticetheregionexcitedbytheelectron

beamhasafinitevolumeChiandGatos[4]determinedthe

junctiondepthbyanEBICtechniqueassumingafinitegeneration

volumeCzaja[5]andBresse[6]measuredthephysicalparameters

suchasLandtheelectron-holepaircreationenergyEpC゛when

theelectronbeamwasdirectednormaltothebarrierplane

Sheaeta1[7]investigatedtheresolutionlimitsoftheEBIC

linescanmethodtheyobtainedaone-dimensionallateraldose

functionandappliedittothemeasurementofLintheCuxSCdS

systemHowevertheydidnotdiscusstheeffectofsurface

recombinationonEBICSincethesurfacerecombination1S

stronglyconnectedwiththedepthofgenerationathree-

-31-

Fig3-1

Schematicviewof

anddefinitionsofthe

-32-

experimentalconditionscoordinatesystems

Electronbeam

Surfacecross-sectic

O゛9χ

Schottky哨Rbarrier

dimensionalgenerationdistributionmustbetakenforthedetailed

analysisofEBIC[81

Inthischapterfirstlywediscussthesurfacerecombi-

nationeffectonEBICassumingapointsourceandthendescribe

theinfluenceofthegenerationvolumeonEBICinthelinescan

methodtakingaccountofsurfacerecombinationWehavestudied

EB工Ctheoreticallyforthefinitevolumesourcewhichisdependent

ontheacceleratingvoltageandshowanimprovedmethodfor

thedeterminationofphysicalparametersofsemiconducting

materialsbasedonexperimentalresultsobtainedinSi

3-2 Surfacerecombinationeffectconsideringpointsource

ForsimpletheoreticalconsiderationwetakeaSchottky

diodeAsshowninFig3-1theSchottkybarrier1Sinthey-z

planeTheelectronbeamisincidentperpendiculartothesample

surfaceandthescanningdirectionisalongtheχ-axiswhichis

normaltothebarrierplane

Thegenerationsourceisconsideredtobeapointata

distancexgfromthebarrierandatadepthdfromthesurface

correspondingtotheacceleratingvoltagevarsquoThepositionis

XS

ぐi g゛ O゛dg)Thesteadystateexcessminoritycarrierdistribution

obtainedfromthefollowingdiffusionequation

pDnabla2pdeg - -

g6(x-゜cg゛yrsquo2olinedg)rsquo (3-1)

whereDisthediffusionconstantて1sthelifetimeandgisthe

generationrateofelectron-holepairsWhen

thesampledimensionsareassumedtobesufficientlylarge

-33-

3ta3

Normalizedscanningdistancex

(a)

Fig3-2

Fig3-3

U』

Normalizedscanningdistancex

(b)

3193

p≫Zl≫E』oz

Normalizrdscanningdistanceχ

(c)

PrimeNormalizedEBICvsnormalizedscanningdistanceχcurvesfordifferentvaluesofthesurfacerecombination

velocityparameter(seetext)SNormalizedgenerationdepthDis0001and10in(a)(b)and(c)

respectively

Oino

tou

iSu一uojsn}|ipMzireujjoZ

SurfacerecombinationvelocityparameterS

EstimateddiffusionlengthL大directlyfromthe

slopesofthecurvesbetweenthepointsatχ=2and3

Svariesfromoneto50

-34-

Dg=10

Dg=QO

151050

112345

Og<ao

161

S>0

21

Idrsquo

S5

10^

550

1必12345

135

sc^-at

SO⑤

バ宍

1012345

112345

SPg≪10

161

162S=0

SI

1(i3

1(541235

comparedwiththediffusionlengththeboundaryconditionsare

並Sz

χ=0

z=O゛

spl

z=0

=0

χ=+(x)

=0

(atthesurface) (3-2a)

(attheSchottkybarrier)(3-2b)

(3-2c)

Oncethedistributionp1SknowntheEBICcanbefound

asfollows

トeリンint]キレ

o4バ2rsquo(3-3)

whereeisthechargeofanelectronThevalueofjwascalculated

二二二二二二二エフエム2こ二言

J=

-eg

丁T

4oo

int

Dg

馴D戸

exp(-S(T-

S(司7)-

dT} (3-4)

wherexL゛DgdegdgLrsquoS=s(Lて)andTIsthevariablefor

integrationThefunctiony可7)1sthesecond-modified

first-orderBesselfunctionTheEBICisnormalizedtobeunity

whenallthegeneratedcarrierscontributetoEBIC

-35-

177FΞ-一一permil

(ぷ71

y))二1supe≧rsquo

四F

InFigs3-2(a)(b)and(c)thelogarithmofJis

plottedvsX(ΞxL)basedoneq(3-4)overtherangeofO≦X≦5一一

forS=へj50ThevalueofDgis0001and10in(a)(b)

and(c)respectivelyForS=0theintegralineq(3-4)leads

toJ=exp(-X)whichyieldsstraightlinesasshown

inFig3-20ntheotherhandallcurvesforS>Odeviate

fromthestraightlineThesurfacerecombinationgivesmuch

effectontheexcesscarrierdistributionasthegenerationdepth

becomessha110WerWhenDgis00and01thevaluesoflogJ

decreasesuperlinearlyovertheinterval0fO≦χ≦2and--

almostニlinearlyovertherangeofx≧2WhenDis10the一琴

surfacerecombinationhasaslightinfluenceandthevaluesof

logJdecreasealmostlinearlyovertheinterval0fO≦X≦5__

HowevertheslopesshowsubstantialdeviationfromunityThe

estimatedvaluesofdiffusionlengthdirectlyfromtheslopes

ofthecurvesinthelinearlydecreasingregion2≦X≦3are--

putasL火andplottedagainstSinFig3-3forDgdeg00and10

工nordinarysemiconductorsSvariesfromlt050Overthis

rangeL大Isabout80t090ZoftニherealvalueL

WhenweevaluatetheaccuratevaluesofLandSwemust

fittheexperimenpoundaldatatothetheoreticalcurvesoverthe

wholerangeofO≦X≦5WecanestimateSbyfitting--

particularlyovertheIntervalofO≦X≦2becausetheeffect--

ofthesurfacerecombinationappearsremarkablyinthisInterval

-36-

3-3 Analysisofelectronbeaminducedcurrenttakingthree-

dimensionalgenerationdistributionintoaccount

Insect3-2theminoritycarrierdistributionisassumedto

beapointButinpracticethegenerationdistributionhasa

finitevolumeinconnectionwithvThegenerationdistributiona

mustbetakenintoaccountwhentheextentofthegeneration

distributioncannotbeignoredcomparedwithL

Electronpenetratニionintosolidmaterialshasbeenstudied

bymanyauthorsTheminoritycarriergenerationdistribution

alongthedepthwasdiscussedindetailinChapterHWittry

andKyser[9]assumedthedepthdosefunctiontobeaGaussian

distributionandobtainedgoodagreementwithexperiments

EverhartandHoff[10]assumedapolynomialfunctiontoexplain

theirexperimentalresultsintheAl-SiO2-SisystemdegInthose

studiesonlythedistributionalongthezaxiswasdiscussedso

thedistributionalongthexaxiswasnotconsideredSheaeta1

[7]definedthelateraldosefunctionalongthexaxisfrom

VonGrlinrsquos[11]databutdidnotdiscusstheinfluenceofsurface

recombinationindetailSincetheinfluenceofsurfacerecombi-

nationonEBICdependsonthedepthfromthesurfacewemust

takethedistributionofgeneratedminoritycarriersinthe

x゛zplaneWeusethemodifieddiffusionmodelofKanayaand

Okayama[12]Themodel1Sverysimplebutissufficientfor

thefirst-orderapproximationtニothethree-dimensional

generationdistributionAccordingtothemodeltheelectrons

penetratestraightintothematerialtothemaximumenergy

dissipationdepthandthenscatterequallyinalldirections

makingelectron-holepairsTheshapeofthegenerationregion

becomesaspherepartofwhichisabovethesurface

-37-

Fig3-4

Tab3-1

11-

Schematicviewofelectronpenetrationisthemaximumenergydissipationdepth

a(W)

00000

1CMCO<rm

d(ym)

rdquo047

149

291

in<yi

vDVO

4VO

R(um)

100

295

13

74

20

Valuesofthecenterdgofthegeneration

volumeandtheradiusRinSiforseveralvalues

ofacceleratingvoltagevarsquo

-38-

IElectronbeam

O335

S`」「fdegce

uarrで0559j

10゛」

helliphelliphelliphelliphellip

Thecenterdgofthesphere(iethemaximumenergydissipation

depth)andtheradiusRaredependentontheacceleratingvoltage

va゛b゛lttheratiodgRisassumedtobeaconstantasshownin

Fig3-4evenWhenvaisvariedThevaluesofdgandRinSi

forseveralvaluesofvaaregiveninTab3-1calculatedwith

theaidoftheequationsofKanayaandOkayama[121

Wedividethesemi-sphereintomanysegmentsoflength

lessthanLandrepresenteachsegmentbyonepointsource

Thedensityoftheelectron-holepairsisassumedtobeuniform

withinthespheretosimplifytheanalysisThenthegeneration

strengthgofeachpointsourceisgivenbytニhefollowing

relation

Σg=G(3-5)

whereGisthewholegenerationstニrengthandΣexpressesthe

totalsummationwithinthesemi-sphereundertニhesamplesurface

TheEBICforthefinitevolumesourceisderivedby

summimgupthesolutionoftニhediffusionequationforeachpoint

sourcewhichisexpressedbyeq(3-4)Whenthedistance

betweenthebarrierandtheIrradiatedpointxbecomessmallerg

thanRsomeofthepointsourcesareforcedoutofthediode

andcannotcontributetoEBICThustheEBICdecreasesnearthe

barrierplaneWecallthisphenomenonanedgeeffectTosimplfy

thecalculationweassumethattheEBICcontributedbythe

forced-outsourcesiszeroThisedgeeffectmustbetakeninto

accountwhenthegenerationvolumeislargeincomparisonwith

thediffusionlengthWeshowanexampleforL=8ymandS=20

Whenvais10kVtheradiusRissmallcomparedwithLand

thegenerationsourcecanbeassumedasapointThelogarithm

-39-

Fig3-5

Qコー

山11

pdznpoi」oz

1020

Scanningdistanceχ

NormalizedEBICversusscanningdistanceχ

forthefinitevolumesourceThediffusionlengthLis8lsquoUmandthesurfacerecombinationvelocityparameterS(seetext)is20TheacceleratingvoltageVais50タ30and10kVfromuppertolowersolidcurverespectivelyThedottedcurveisthepointsourcesolutionforVa=50kVandtニhedashedlineisthegradientthereciprocal0fwhichgivesL=8um

-40-

1020304050(p『

゛X5入L=8μm

゛χS=20

2rsquoχyχ

゜χ

ldquoゝ5rdquo-Re-くiprocalsk)

rsquox9vesL=8|jm

rdquoゝ

2rsquo゜χ`Va=50KV

2rsquoχ

lsquoχ

lsquoゝ

5degχ

rsquoχ

rsquoχ2χ

30≒3rsquo

11diPointsourcelsquo

5solutionfor

va=50KV10

1020304050(μΓΥ

ofEBICJisplottedwithafullcurveasafunctionofthe

scanningdistancexinFig3-5logJdecreasessuperlinearlyover

theinterval0≦X≦2L(ie16uminthiscase)anddecreases--

almostlinearlyovertherangex≧2LTheslopeintherange-

O≦x≦2LisInfluencedverymuchbysurfacerecombination一一

〇necanestimateSbyfittingtheexperimentaldatatothe

theoreticalcurveinthisrangedegWhenva1S300r50kVthe

radiusRbecomesofthesameorderasLandthegeneration

volumecannotbeassumedasapointThenwedividethesemi-

sphereintomanysegmentsoflym^Thecalculatedvaluesof

EBICusingthefinitevolumesourcemethodareshowninFig3-5

ThelogJvsXcurvesshowamaximumnearthebarrierplane(

Xdeg4and7μmatvadeg30and50kVrespectively)andlogJdecreases

almostlinearlybeyondthesemaximumpointsThemaximumvalue

ofJbecomessmallasvincreasesThesurfacerecombinationadoesnotaffecttheshapeofthecurvesandsoLcanbedetermined

mainlyfromtheslopeofthelinearregionofthesecurves

independentlyofsThereciprocalslopeofthislinearportion

gives7ymwhichis87Zoftherealdiffusionlength

ThevalueofEpc゛rsquobywhichanelectron-holepairis

createdcanbedeterminedfromtheabsolutevalueofEBIC[13]

ThevalueofJinthecaseofS=501sabout70Zofthatinthe

caseofSdeg1whenvais50kv゛andsowemakelargeerrorsinthe

determinationofEifwedonotconsiderthesurfacerecomblna-pc

tioneffect

Thepointsourcesolutionatva゛50kVisshowninFig3-5

bythedottedlinewhenthegenerationoccursatthemaximum

energydissipationdepth(ie67ymfromTab3-1)

Theslopeofthepointsourcesolutionovertherangex≧2LIs-

almostequaltothatofthevolumesourcesolutionbutthe

normalizedEBICis60Zofthatofthevolumesourcesolution

-41-

Fig3ldquo6

Chopping

こ011

Scanningcoil

Schematicdiagramoftheexperimentalset-up

-42-

コ4[Osc

lsquo~|-

|コt

||IElectronbeamReference

||

Sample

RL`Lock-inampχ-yrecorder

3-4 ExperimentalresultsinS1

Aschematicdiagramoftheexperimentalset-upisshown

inFig3-6Theacceleratingvoltage1Svariedfrom10t050kV

TheprimaryelectronbeamcurrentismeasuredbyaFaradaycage

andabout2times10oline10ATheinducedcurrentwasmeasuredfromthe

voltagedropacrosstheloadresistanceILdegThecurrentニIL

whichflowsthroughtheresistanceisexpressedasfollows

hdeg^sc-I{exp[(ekT)ILRL]-1} (3-6)

whereloisthebackwardsaturationcurrentand^scisthe

short-circuitcurrentwhichistherealEBICInordertoneglect

thesecondtermofeq(3-6)theEBICwasmeasuredinthefollowing

condition

h゛kTe (3-7)

InthepresentexperimenttheEB工Cwasmeasuredatroomtempera-

tureandso゛hhwaskeptlessthanlmvdeg

Theelectronbeamwaschoppedat3kHzwithachopping

coilinsertedintothebeampathSignalsassmallas1μVcould

bemeasuredwithagoodsignaltonoiseratiousingalock-in

amplifier

Thesamplesweren-typeSiwithresistivitypof10

and01ΩCm0hmiccontactsweremadebyevaporatingantimony-

dopedgoldontothesampleandalloyingat400degCfor2mln

Schottkycontactsweremadebyevaporatinggoldinavacuumas10W

as10oline7TorrThesamplewasinsertedintoavacuumchamberfor

EBICmeasurementimmediatelyafteritwascleavedandmeasured

-43-

3IS3

paziicuijoz

1020304050(pm)

Scanningdistancex

Fig3-7

Experimentalresultsfor

sampleA(p=lf2cin)whereL=

8μmandS=20Fullcurves

arethetheoreticalrsquoones

11(il

>P≪4<N1≪CM<Pq

1 1

3193paziipujjoZ

1164

50

Scanning

100

distance

Fig3-8

150

X(μm)

200

ExperimentalresultsforsampleB

(p=01f2cin)whereL=80urnandS=50

Fullcurvesarethetheoreticalones

Valueswithouttheinfluenceofan

ohmiccontニactareshownbydotted

curves

-44-

124(m)

5XExperimentalvaluesX---Va=50KV

2NNo30

1X一--10KV4

5しL=8pm

2χ

2χ

5χ

-Theoretical

5curve

41

50100150200

Experimentalvalues

--4=50Kv

lo―30KV

hellip-10KV

-ゝゝI゛゛゜゛ペヘヘ

helliphelliphelliphellipyhelliphelliphelliphellip

Theoreticalcurvehelliphelliphelliphellip9lsquorsquolsquo゜

Ldeg80μΓTlぶ

S=50

inavacuumas10was1times10oline8TorrTheresidualgasesonthe

cleavedsurfacewerecleanedbyargonionsputteringtoavoid

contaminationofthesurfacebyanirradiatニedelectronbeam

TheexperimentalresultsofsampleA(p=10ncm)are

showninFig3-7forva=1030and50kVrespectivelyEach

fullcurveisthetheoreticaloneforthecaseofL=8umandS=20

工fthediffusionconstantD1Stakenas16cm2Solinelthelifetime

てis4times10oline2μSandthesurfacerecombinationvelocitysis

4times105cmsolinelSurfacerecombinationhasagreatereffectasthe

generationdepthbecomesshallowerthatisVbecomeslower

AndsothevaluesofSandLcanbeestimatedmainlyfromthe

curvesforthelowestニandthehighestva(idege103゛d50kV

inthisexperiment)respectivelyTheexperimentalresultsfor

eachacceleratingvoltageagreeverywellwiththetheory

Theexperimentalcurvesforvadeg1030and50kVhaveamaximum

atxdeg02and4ymrespectivelyandeachmaximumvaluebecomes

smallerasvincreasesasdescribedinthetheoryHowevera

themaximumvalueandthepositionwheretheEBICshowsapeak

deviateslightlyfromthetheoryinthecasesofvadeg30and50kVdeg

Thisdiscrepancymaybeattributedtotheassumptionofuniform

densityofgenerationTheactualdistributionmaybelocalized

atthecenterofthegenerationvolume[9]andmoredetailed

treatmentforthegenerationshapeandthegenerationdensity

Isneeded

Inthecaseofthelocalizeddistributionofgeneration

wecanapplythesamemethodasdiscussedinsect3-3Ifthe

constantgischangedintoanappropriatevariablewhichexpresses

thelocalizeddistributionbetterresultswillbeobtained

HowevertheassumptionoftheunifoinndensityIssufficientfor

thequalitativeanalysisoftheInfluenceofthegenerationvolume

onEBIC

-45-

TheexperimentalresultsofsampleB(p=01ficm)are

indicatedinFig3-8inthesamewayassampleAThevalues

ofLandSare80ymand509respectivelyIfDis16cm2solinel

てis4ysandsis1)(105cmSoline11nthiscaseLisgreaterthan

thegenerationvolumeevenwhenvadeg50kVandthevolumesource

effectappearslessclearlythaninsampleAThediscrepancy

witニhintheinterval0<xく15urnisduetothesamereasonas

thatdiscussedInthecaseofsampleATheslopesofthecurves

overtherange15≦x≦100μmarelesssteepasvbecomes--a

higherbecausetheinfluenceofsurfacerecombinationdecreases

Theinfluenceofohmiccontactappearsovertherangex≧120μm-

sincethediffusionlengthisabouthalfofthesamplethickness

of200μmTheoreticalvaluescalculatedusingthemirror

imagemethod[14]discussedinChaptervareshownbyfull

curvesinFig3-8Valueswitニhoutニtheinfluenceofanohmic

contactarealsoshownbydottedcurves

Thescanningsurfacewasnotaffectedbyanelectronbeam

oftheorderof2times10oline10Abecausethesameresultwasobtained

forshallowexcitation(vadeg10kV)afterthesamplewasirradiated

for1hatV=10へ一50kVa

ThedepletionlayerwidthisnotbroughtIntoconsidera-

tionbecauseofitsnarrownesscomparedwiththescanningdistance

Theelectronbeamdiameterofabout50nminthisexperiment

1Snottakenintoaccountsinceitisverysmallincomparison

withthegenerationregionevenifvais10kvdeg

工fthebeamcurrentiskeptconstantthegeneration

densitydecreaseswithincreasingVbecausethegeneration

volumeincreasessuperlinearlywithvarsquo゜Whenthebeamcurrentis

2times10oline10Aandvais10kVtheexcessminoritycarrierdensity

-46-

atthegenerationpointisabout5times1014Cmoline3(themaximum

generationdensityinthisexperiment)followingthediscuss10n

inref[1]whichissmallerthanthemajoritycarrierdensity

1nthesamplesThereforethevalueofLismeasuredatthe

lowinjectlonlevel

3-5 Summary

Thegenerationvolumeofminoritycarriershasa

considerableeffectontheEBIClinescanprofilesespecially

whenItisequaltoorlargerthanthediffusionlengthWe

investigatedthedependenceofEBIConxforgeneralsurface

recombinationvelocityinthecaseofthefinitevolumesource

Whenvaislowandthegenerationdepthisshallow

surfacerecombinationhasalargeeffectonEBICWhenvaishigh

andthegeneratニiondepthisaslargeasthediffusionlengththe

generationregioncann0longerbeassumedasapointandthe

finitevolumesourceshouldbeusedintheanalysisThetheo-

reticalcalculationshowsthatsurfacerecombinationhasonlya

slighteffectontheshapeoflogJvsXcurvesbutaffectsthe

absolutevalueofJTheaccuratevaluesofLsandEshouldbepc

estimatedbyfittingtheexperimentaldatatothetheoretical

curvesforallacceleratingvoltagesExperimentalresultsinthe

measurementofLandSonS1Schottkydiodesshowedgoodagreement

withthetheoryatboth10Wandhighvadeg

TheexperimentalresultthatEBIChasamaximumnear

thebarrierplanewasexplainedqualitativelyusingthesimple

model0fthefinitevolumesourceItcouldnotbeexplainedby

thepointsourcesolutionFurtherinvestigationofthisedge

effectwillclarifythegenerationdistributionbyanelectronbeam

-47-

References

[1]

2]

31

[41

[7]

[8]

[9]

[10]

FBerzandHKKuikenSolid-stateElectron

437(1976)

19

CvanOpdorpPhilipsResRep_32192(1977)

LJastrzebskiJLagowskiandHCGatos

ApplPhysLett27537(1975)

JApplPhys481730(1977)

JYChiandHCGatosIEEETransElectronDev

ED-241366(1977)

WCzajaJApplPhys2Z^236(1966)

JFBresserdquoScanningElectronMicroscopy1972

Partlrdquo[SEM]nc工ITRIChicago)pp105-112

SpSheaLDPartニainandpJWarterrdquoScanning

ElectronMicroscopy1978Vol1rdquo(SEMIncAMFOrsquoHare)

pp435-444

GVSpivakGVSaparinandLFKomolova

rdquoScanningElectronMicroscopy1977rdquo(SEMInc

IITRIChicago)pp191-199

DBWittryandDFKyserJApplPhysj廻375

(1967)

TEEverhartandpHHoffJApplPhys

(1971)

-48-

42

-5837

[n] AEvonGriinZNaturforsch12a89(1957)

【12】KKanayaandSOkayamaJPhysDApplPhys

543(1972)

[13]CJWuandDBWlttryJApplPhys492827

(1978)

[1410vonROOSSolid-stateElectron111063(1978)

-49-

4-1

ANALYSISOFTHREE-DIMENSIONALGENERATIONDISTRIBUTION

BYTHECOMBINATIONOFTHENORMALINCIDENCEANDTHE

LINESCANMETHODS

Introduction

TheminoritycarrierdiffusionlengthLandthesurface

recombinationvelocityScanbedeterminedbyanEBICtechnique

withboththenormalincidenceandtニhelinescanmethodsusing

SEMasdiscussedinChapters皿andHITheminoritycarrier

generationdistributニionbyanelectronbeamplaysanimportant

roleintheanalysisofEBICWhenthedimensionofthegeneration

regioniscomparablewithorlargertニhanLthegenerationregion

cannotbeassumedasapointandthegenerationdistribution

mustbetakenintoaccount

Thegenerationdistributionbyanelectronbeamhasbeen

investigatedbyseveralauthorstheoretically[1]andexperimental-

1y[2-51Asregardstheone-dimensionaldistributionaGaussian

[2-3]orpolynomial[4]functionwasassumedforthedepthdose

functionandthecombinationofexponentialdecayfunctions[51

wasusedforthelateraldosefunctionInChapter工皿the

influenceofthethree-dimensionalgenerationdistributionon

EBICinthelinescanmethodswasstudiedassumingasimple

distribution(semisphere)withuniformminoritycarrierdensity

Ineachoftheseexperimentsonlyonemethodタeitherlinescan

ornomalincidencewastakenTheelectronpenetrationdepth

andthegenerationdistributiondifferedfromeachother

-50-

Schottky

barrier

Fig4-1

2P

Surfacecrosssection

「egion

Oneofthedividedsegments

Schematicviewofexperimentalconditionsandthedefinitionofthecoordinatesystem

-51-

Electronbeam

hottkySurfacecrossse

arrierOGene芯ion

Re゛region

Oneofthe

々dividedsegi

InthischapterwemeasuredEBICbyboththelinescan

andthenormalincidencemethodsinthesamesampleandclarified

thegenerationdistributionTheinfluenceofthethree-dimensional

generationdistributiononEBICisdiscussedassumingthatthe

electron-holepairsarelocalizedatニthecenterofthegeneration

regionTheexperimentニalresultsforGaAsSchottkydiodesare

alsoshown

4-2 Influenceofthree-dimensionalgenerationdistribution

onelectronbeaminducedcurrent

WeusedaSchottkydiodesinceitcanbeappliedforboth

thelinescanandthenormalincidencemethodsInthelinescan

methodtheEBICiscalculatedtakingtニhegenerationdistニrlbution

intoaccountbyasimilarmethoddiscussedinChapterⅡ工The

generationregionisdividedintomanysegmentsthesizeofwhich

issmallerthanLandeachsegmentisrepresentedbyonepoint

sourceTheEBICforthefinitevolumesourceisderivedby

summingupthesolutionofthediffusionequationforeachpoint

sourcersquo

Thedistributionisassumedtobesphericallysymmetric

asisshowninFig4-1Theelectron-holerdquopairsgeneratedbyan

electronbeanareconsideredtobelocalizedatthecenterRCof

thegenerationregionThegenerationstrengthgalonganyradius

vectorfromRc1Sassumedtobegivenby

gdeg^exp[-C(r2R2)] (4-1)

whereRisthedistancebetweenRandthemaximumelectronrange

CRm゛andristhedistancebetweenRCandeachdividedsegment

(seeFig4-1)

-52-

TheexponentCrelatestothedistributiondensityThedensity

becomesuniformasdiscussedinChapterl[EwhenC1Szeroand

theelectron-holepairslocalizenearRcwhenCbecomeslarge

Thedistributionisassumedinorderthatthedepthdosefunction

maybecomeGaussianasisreportedinthereferences[23]

ThevalueofLshouldbesmallinorderthatitcanbe

measuredbyboththelinescanandthenormalIncidencemethods

ThereforewetakeGaAsasanexampleInthelinescanmethodwe

calculatetheEBICintensity(whichiscalledthecollection

efficiencynandisnormalizedtobeunitywhenallthegenerated

carrierscontributetoEBIC)forseveralvaluesofCandR

The゛ilueofRmisgiven[2]by

町゜001A8Vノ゛フurn

cR

m゛

(4-2)

wherevaistheacceleratingvoltニageinkVThevaluesofCand

RRareassumedtobeconstantevenifvisvariedWhenvisCm

10and30kVaa

Rm

becomesOdeg74and4deg8ymrespectニivelyWetake

thetypicalvalueofLas1μminordertoexaminetheinfluence

ofthegenerationdistributiononEBICbecausethevalueofRm

issmallerthanLatva゛10kVbutlargerthanLatvadeg30kvrsquo

SincethesurfacerecombinationvelocitySofGaAsisoftheorder

of105-106cmSoline1[6-9]wetakevaluesofland50asthe

surfacerecombinationvelocityparameterSdefinedbySΞS(Lて)

(TisthelifetimeoforderofnS)

TheresultsofthecalculationareshowninFig4-2The

fullcurvesandthebrokencurvesareforCdeg8rsquo2゛RcRm゛Olsquo13and

C=54RR゜013respectivelyThesevaluesofCandRじmolinersquoCrsquom

thetypicalvaluesobtainedbythenormalincidencemethodin

GaAs[23]Thepointsourcesolutions(whichareobtainedby

assumingthatallthegenerationoccursatRc

-53-

are

)arealsoshownby

g`

A3U413Ud

COP≫no3

Fig4-2

ScanningdistanceX(pm)

j一次゜ごゴ野謡ごごご二ににごS

ご諧驚お謡謡S回読で昌翼麗

二竃Jeぎ驚謡じ雲Cにニごまふ(

ごごぶ謡1ば昌permilお穴混戮ずpermil

ぶぶごご1ここなSttedcdeges゛ecm

-54-

helliphellipl

]]1A

Ee

ビゲヤ

12

ss50

helliphelliphellipyJミ4sdeg50

dottedcurvesAtVa゛10kVthesizeofthedividedsegmentis

takenas005umwhichissmallerthanLsothateachdivided

segmentcanberepresentedbyonepointsourceIntheregion

05≦x≦15ymthelogarithmofEBICdecreasessuperlinearly--

anditdecreasesalmostlinearlyovertherangeofx≧15um-

ThetendencyappearsmoreapparentasSbecomeslargeThechange

oftheexponentCmakeslittledifferencetotheprofilesofthe

curvesTheabsolutevalueofnovertherangeofx≧05umis-

almostequaltothepointsourcesolutionwhenS1S1butbecomes

twicethatwhenSis50Thepeaksnearthebarrierareduetothe

edgeeffectasdescribedinChapterl工゛Atvadeg30kVthesizeof

thedividedsegmentistakenas02ymforthesamereasonas

Wit二hvadeg10kVThecurvesarequitedifferentfromthepointsource

solutionbothatS=1andS=50becausethedimensionsofthe

generationregionarelargeincomparisonwithLandthepoint

sourceassumptionisn0longervalidinthiscaseTheprofiles

ofthecurvesreflectthegeneratニiondistributionasoneseesthat

theprofilechangesifCvalsquotiesfrom54t082WhenSisvaried

fromlto50theprofiledoesnotchangeatthesameCvaluebutニ

ndecreasesbyabout30ZofthatofS=lItshouldbenotedthat

thesurfacerecombinationhasaninfluenceontheabsolutevalue

ofEBICevenifthevalueofRm(4deg8pm8tvadeg30kV)ismuch

greaterthanLThereforewecanevaluateLmainlyfromthe

slopeofthelinearregionat10Wvaconsideringthesurface

recombinationeffectandestimatethegenerationdistribution

fromtheprofilesofthecurvesinthecaseofhighva゛

-55-

Fig4-3

pasube

coipai

-O

Maximumelectronraり9eRm(μm)

AcceleratingvoltageVa(kv)

Experimentニalresultsofthenormalincidence

methodforthesampleA(SndopedGaAsn=62times1016

cm^L=03)Jm)andthesampleB(TedopedGaAs

ndeg80times1016cmoline3Ldeg07μm)Experimentalvaluesare

shownbycirclesThefullandbrokencurvesare

theoreticalcurvesforC=82RR=013andC=54

RcRmdeg013respectivelywdeg10cnmmandwddegOdeg151Jmdeg

-56-

12410oline

GaAsn(c「7i」

5A訟ばn

2ゝゝゝ

ゝゝ

ゝゝゝ

ゝゝゝrsquoL(pm)

1゛゛`ヽBO7J

yWヽ

5oline`olinersquo54013A03

≒旨

2φ

(52Schottkか

デ1テシフ)卜

1020304050

Theelectron-holepaircreationenergyEisobtained

fromthefollowingequation[101

n=ErdquordquoEBIC

pcIBvak(4-3)

whereIBisthebeamcurrentandkisthecorrectionfactorfor

theback-scatteredelectronsAsdescribedpreviouslythevalueof

nisinfluencedbySevenwhenVishighandsowemusttakeolinea`lsquorsquoolineolineolineolineolineolineolineolineolineolineoline

thesurfacerecombinationeffectintoaccountwhenweevaluateE

pc

4-3 Three-dimensionalgenerationdistributニioninGaAs

Thesameapparatusandthelock-intechniquewereused

asdescribedinsect3-4TheSchottkybarrierwasmadeonn-typeGaAs

wafersbyevaporatingAuofabout10nmthickinavacuumofabout

10rsquo7TorrTheohmiccontactwasobtainedbyevaporatingAu-Geand

alloyingat400degCfor2minThecarrierdensitynofeachsample

wasdeterminedbyc-vmeasurements

Theexperimentalresultsofthenormalincidencemethod

forthesampleA(Sndopedn=62times1016cmoline3)andthesampleB

(Tedopedn=80times1016cmoline3)areshowninFig4-3byfulland

opencirclesrespectivelyThevalueofvawaSvariedbetween5

and50kVTheEBICintensityincreasedlinearlywithIBwithin

therangeof1times10oline11≦IB≦-1times10oline9Awhenvawasfixed

whichsatisfiedthelowinjectionlevelconditionThecollection

efficiencynwascalculatedbythesamemethodreportedinref[10]

bychangi昭RcRmfrom01t0025andCfrom30to90

respectivelyThebestfitcurveswiththeexperimentalresults

wereobtainedInthecaseofL=03and07umforsamplesAandB

respectivelywhenRcRm゛O゛13andC=82wereusedThevaluesof

-57-

II

A3ua<3UduqjDaiion

ScanningdistanceX((jm)

Fig4-4

Experimentalresultsofthe

linescanmethodforthesampleA

[SndopedGaAsn=62times]016cmoline3)

Thefullandbrokencurvesare

ー い゛I

゛゛

ldquooU 5

Scanningdistancex(μm)

Fig4-5

ExperimentalresultニSofthe

linescanmetニhodforthesampleB

(TedopedGaAsn=80times1016cmoline3)

Thefullandbrokenlinesare

theoreticalcurvesforC=82RRtheoreticalcurvesforC=82R

=013andC=54RR=013cdeg=013andC=54RR=013c

respectivelyLdeg03cμmS゛20respectivelyLdeg07ymSdeg20

-58-

ぎ忌

五゛

olinelo

jV

ズごy

23

times1

GaAだj

j73C4Electron

L=07μmEbeam

2Sdeg20χ

1rsquo`

゛x

ya(W

2゛Va=30W

2_JE201

4一一―54013

5≒

脅χ

21`f

ゝ≒

ゝへ

5χ

147

RCRmandCagrees`゛iththerepoidegtedvalues[2]゜Thefulland

brokencurvesinthefigurearetheoreticalcurvesforC=82

RcRmdegOdeg13andC゛5deg4゛RcRmdegOlsquo13respectニivelylsquoThediscrepancy

betweenthetheoreticalcurvesandtheexperimentalvaluesat

10WvacanbeexplainedinthefollowingwaydegThegeneration

regionbecomesshallownearthesurfaceatlowVandtheEBIC

ismainlycontributedbytheseperatedelectron-holepairsin

thespace-chargeregionjustunderthesurfaceInthetheoretical

calculationitisassumedthatthere1Snorecombinationinthe

space-chargeregionButニinactualfactthecarriersrecomblne

throughthevarioustrapswhichreducestheEBIC

Theexperimentalresultsofthelinescanmethodforthe

samplesAandBareshownbycirclesinFigs4-4and4-5

respectivelyThetheoreticalcurvesareexpressedbythefull

(Cdeg82RcRmdeg013)andthebroken(C=54rsquoRcRmdegOdeg13)curves111

bothfiguresTheEBICintensityincreasedlinearlywithIBwitニhin

therange1times10oline11くrsquoIく1times10oline9Awhenvwasfixedat100r=B=a

30kVwhichsatisfiedthe10wInjectionlevelconditionasinthe

normalincidencemethodThetheoreticalcurvescalculatedusing

thesameparameterdeterminedbythenormalincidencemethodshow

goodagreementwiththeexperimentニalresultsatbothvadeg10and30

kVWhenwetakeintoaccountthattheexperimentalresultsat

vadeg30kVreflectthegenerationdistributiontheassumedgeneration

distributionbyeq(4-1)withC=5Aへ82andRcRmdegOdeg131s

consideredtobeappropriateforthethree-dimensionalgeneration

distributioninGaAs

Thevalueofkchangesfrom078to075whenvvariesa

from5t050kV[10]Whenwetaketheappropriatevalueofkfor

themeaSuredva゛Epccanbedeterminedbyeq(4-3)Thevaluesof

-59-

Normalincidence Line scan

V(kv)a

E(eV)GaAsCSndoped)pc

GaAs(Tedoped)

5-50

41

39

14

3 9

30

Tab4-1 Valuesoftheelectron-holepaircreationenergyEinGaAsdeterminedbytニhenormalincidenceandlinepc

scanmethods

-60-

Eobtainedbythenormalincidenceandthelinescanmethodsarepc

39Oi41eVand38へj44eVrespectivelyastabulatedin

Tab4-1BythenormalIncidencemethodWuandWittry[10]

determinedEpCas468eVwhichwasabout15Zlargerthanour

resultsOnereasonforthediscrepancy1Sthedifferenceofthe

generationdistributionsThemodifiedGaussiandistributionused

bythemslightlydifferedfromtheGaussiandistributionusedin

ouranalysisAnotニherreason1Stheaccuracyofmetalthickness

WeestimatethethicknessfromtheweightofthechargedAuwhich

1SevaporatedtomaketheSchottkybarrierThereforetニheobtained

valuemaybedifferentfromtherealthicknessInthelinescan

methodEBICbecomesinsensitivetothemetaltニhicknessandthe

trapsinthespace-chargeregionbutisinfluencedbysurface

recombinationasdiscussedbeforeAlferoveta1[11]andWittニry

andKyser[12]reportedEpcas32へj44eVand46eVrespectニive-

lyfromthepeakvalueofEBICwhentheelectronbeamcrossedthe

p-njunctionOurresultsof38へj44eVareinthemiddlerange

oft二heirvaluesIntheiranalysestheydidnottakethesurface

recombinationeffectintoaccountandsoourresultsareconsidered

tobemorereliablethantheirs

4-4 Summary

Thethree-dimensionalgenerationdistributionbyan

electronbeaminGaAswasinvestigatedbymeasuringEBICwitha

combinationofnormalincidenceandlinescanmethods

TheprofileoftheEBICcurvesinthelinescanmetニhod

expressesthegenerationdistributionwhenvaishighandthe

dimensionofthegenerationregionislargerthanLThesurface

-61-

recombinationdoesnotaffecttheprofileofEBICbutlowersthe

collectionefficiencyTheaccuratevalueoftheelectron-hole

paircreationenergymustbedeterminedbytakingthesurface

recombinationeffectintoaccount

TheexperimentalresultsinGaAsSchotニtkydiodeswith

differentdiffusionlengthsshowedthatthecenterofthe

generationregion(iethemaximumenergydissipationdepth)

waslocatedatthepointof0130fthemaximumelectronrange

andtheradialdistributionfromthecenterwasshowntobe

Gaussianwithaneχponentof54へ-82Theelectron-holepair

creationenergyinGaAswasdeterminedas38rsquoV44eV

References

[1]

[2]

[5]

[6]

KKanayaandSOkayamaJPhysDApplPhys

543(1972)

DBWittryandDFKyserJApplPhys旦旦375

(L967)

VVMakarovSovPhys-Semicond旦722(1975)

TEEverhartandpHHoffJApplPhysを

5837(1971)

SpSheaLDPartainandpJWarterrdquoScanning

ElectronMicroscopy71978V011uml(SEMIncAMFOrsquoHare)

pp435-444

LJastrzebskiHCGatosandJLagowski

JApplPhys481730(1977)

-62-

[7]

[81

[9]

[10]

[11]

[12]

LJastrzebskiJLagowskiandHCGatos

ApplPhysLettri537(1975)

MEttenbergHKresselandSLGilbert

JApplPhys44827(1973)

CAHoffmanKJarasiunasHJGerritsenand

AVNurmikkoApplPhysLett22536(1978)

CJWuandDBWlttryJApp1PhySpoundrsquo2827

(1978)

ZhIAlferovVMAndreevVIKorolrsquokovand

vIStreminSovPhys-Semlcond41113(1971)-

DBWittryandDFKyserJApplPhys

361387(1965)

-63-

5-1

ANALYSISOFELECTRONBEAMINDUCEDCURRENTCONSIDERING

SAMPLEDIMENSIONS

Introduction

Anelectronbeaminducedcurrent(EBIC)methodusing

ascanningelectronmicroscope(SEM)isaconvenienttechniqueto

measuretニheminoritycarrierdiffusionlengthLandthesurface

recombinationvelocitySinsemiconductorsTherehavebeenmany

theoreticalandexperimentalstudiesonthelinescanmethodof

EBICInChaptersI工andytheEBICwasanalyzedquantitatively

takingthethree-dimensionalgenerationdistributionintoaccount

bythedividingmethodandtheimprovedmethodtocharacterize

Landswassuggestedχihenthesampledimensionsarelessthan

oneortwodiffusionlengthstheminoritycarrierdistribution

isaffectedverymuchbysampledimensionsRoos[1]analyzed

EBICtheoreticallyinthecaseofthinlayersHecalculated

thedependenceofEBIConthescanningdistancexintherange

ofxL≪1inthesampleswithwL=land05(wlayerthickness)j

andshowedthatLcouldnotbedetermineddefinitelyfromthe

slopeofthelogarithmofEBICvsXcurve

InthischaptertoanalyzeEBICconsideringthesample

dimensionsgwediscussasimplemethodusinganimagesource-and-

sinkdistributionWeshowthedependenceofEBIConxoverafull

scanrangewhenthelengthbetweenapotニentialbarrierandan

ohmiccontactisequaltoandsmallerthanthediffusionlength

andmentionsomeimportantニpointstobenoticedinthedetermination

ofLandsTheexperimentalresultsinSiSchottkydiodesarealso

shown

-64-

Fig5-1

ySご

uarrj

Schottkybarrier

uarr

Ohmiccontact

Schematicviewofexperimentalconditionsanddefinitionofthecoordinatesystem

-65-

Electronbeam

-J-

レじ2「lingtrack_^一分

りhelliphelliphellipljc1お迄゛

IL

5-2 Determinationofdiffusionlengthandsurfacerecombination

velocity

ForsimpletheoreticalconsiderationwetakeaSchottky

barrierdiodeAsshowninFig5-1theSchottkybarrierisin

they-zplaneandtheelectronbeamisincidentニperpendicularto

thesamplesurface(χ-yplane)Thescanningdirectionisalong

theX-axiswhichisnormaltothebarrierplaneThegeneration

sourceisconsideredtobeapointニandislocatedat(゛grsquo

Thesteadystニateexcessminoritycarrierdistributionpis

obtainedfromthefollowingdiffusionequation

Dnabla2pdeg二T

-g6(x-xyz-d)rsquo

O゛dg)

(5-1)

whereDisthediffusionconstantンTisthelifetimeandgisthe

generationratニeofelectron-holepairs

工fthethicknesswbetweenthepotentialbarrierandthe

ohmiccontactismuchgreatニerthanLandtheotherboundariesin

theyandzdirectionsarebothmuchfurtherawayfromthe

generationsourceEBICiscalculatedunderthefollowingboundary

conditionsasdiscussedinsect3-2

3p-9z

χ=0

x=-H≫

Z=0

Z=0

=0(attheSchottkybarrier)

=0

wheresIsthesurfacerecombinationvelocity

-66-

(5-2a)

(5-2b)

(5-2c)

(5-4)d帽

wherexgrsquoLrsquoDgdegdLSdegs(Lて)andTisthevariablefor

-67-

integrationThevalueofJ(x)isnormalizedtobeunitywhena11

thegeneratedcarrierscontributetoEBICThefunctionK(ぺ7)

isthesecond-modifiedfirst-orderBesselfunction

FortheanalysisofEBICconsideringsampledimensions

wetakethefundamentalcasethatthediffusionlength1S

comparablewithorlargerthanthethicknessw(seeFig5-1)

OncethedistributionpisknownEBICcanbefoundasfollows

十(゛十(゜3p

j=eDintint-

0 -003χ

dydz

χ=0

(5-3)

whereeisthechargeofanelectronBerzeta1【2】solvedthe

diffusionequation(5-1)undertheboundaryconditions(5-2a)

(5-2b)and(5-2c)bythemirrorimagemethodInadditiontothe

reaLsourceatxg゛animagesinkwasintroducedatthesymmetric

position-XwithrespecttotheSchottkybarrier(seeFig5-2)

Whenthematerialextendstoχ=plusmndegdegthesolutionofeq(5-l)is

givenbypμ](゛゜土)゛WhentheSchottkybarrierisintroduced

theminoritycarrierdistribution1Sexpressedasp[x]十p[oline゛g]

inordertosatisfytheboundarycondition(5-2bplχ=OdegO)rsquo

andjisobtainedasfollows

J()゜

-eg-

-π

DgK(ぶ77F)

リinto

うと縦卜-dT

-H≫

十intexp(-S(T-D))

Dg

g ぜ)ケ

Thenonemustusethefollowingboundaryconditioninsteadof

(5-2c)

Ix=wdegO(attheohmiccontact) (5-2crsquo)

ThesolutionQfeq(5-1)undertheboundaryconditions(5-2a)

(5-2b)and(5-2crsquo)canbeobtainedbyextendingthemirrorimage

methodproposedbyBerz[2]andOpdorp[3]Inadditiontothereal

sourceatXafamilyofvirtuaLimagesourcesandsinksare

introducedatthesymmetricpositionswithrespecttothebarrier

andtheohmiccontact(seeFig5-2)Openandsolidcircles

representthesourcesandsinksrespectivelyThereforethe

sourcesareatX2w十Kg4W十xg゛゜rsquo゜lsquoand-(2w-x)-(4w-x)rdquoldquo゛

andthesinksareat-X-(2w十X)-(4w十X)and2゛゛olinersquo4゛olinersquo

respectivelyWhenthematerialextendstox=士≪>thesolution

ofeq(5-l)isgivenbyp【゛】(゛゜土゛grsquo士(2゛`7oline゛g)rsquo土(2W十)rdquorsquo゜rsquo)

(seeFig5-2)Iftニheinfluenceofohmiccontactニmustbetaken

intoaccounttheminoritycarrierdistributionisexpressedusing

thefollowinginfiniteseriesinordertosatisfytheboundary

conditions(5oline2brsquoplx=OdegO)811d(5oline2c≒Plx=wdegO)rsquo

p゛[゛g]゜jp[≒ 十p[oline

十p[2゛oline]十p[-(2W-X)

+p[2w十゛g]十p[-(2w十)

十一一一一一一-一一

9 (5-5)

Theinducedcurrentsbypairsofsourcesandsinksie

p[゛g]andp[oline゜cg]rsquop[2゛olineへ]andpr-(2w-x)]rsquop[2゛十]andp[-(2v゛十)]rsquo

areexpressedbyJ(x)-J(2v゛oline゜cg)J(2w十)゛rsquo゛゜゛rsquo

respectivelywiththeaidofeq(5-4)ThenthetotalEBICis

expressedintheinfiniteseriesasfollows

-68-

Fig5-2

Source

helliphelliphellipSink

Concentration

Sdηitky

barrier

Ohmic

contact

Schematicviewofexcessminoritycarrierconcentrationpatternforeachsourceandsinkwhicharerepresentedbytheopenandsolidcircles-respectively

-69-

pr2wχ9]

plE【2w->り》】1

1rdquoMI

-E唇-

゜(2WdegO`92Wi

ミplE)rsquo゛p[2w-xg]

pl-《2w+x)】)゜91

s哺

(n

L1)

paziipEJoz

1 2 3

Normalizedscanningdistancex

0 5

M)DUd|UOISコ|}Ppazneaijoz

12 5 X)2050

Fig5-3

DependenceofEBIConthe

normalizedscanningdistanceχ(equivxL)

fullandbrokencurvesarefortニhecaseswithandwithouttheinflu-

enceofohmiccontニactrespectivelyThenormalizedsamplewidthwLis

1020and30andthenormalized

generationdepthDgisOdeg0Thevaluesofthesurfacerecombination

velocityparameterS(seetext)

areland10forupperandlower

groupofcurvesIrespectively

Fig5-4

Estimateddiffusionlength

fromthereciprocalgradientof

thecurveatthecenteroftニhe

scanningdistanceinthecaseof

DgdegOlsquoOandwLdeg1lsquoOSvaries

fromlt050L大andL訟are

forthecaseswithoutandwith

theinfluenceofohmiccontact

respectively

SurfacerecombinationvelKitypmmeterS

-70-

Dgdeg00

そー=10

L゛で

ヽ1慟1

111

25=1rsquo1

1`11

【flll

11

51s

degilOII

211`4

111

(flll゛

芒゜11゛|`

51S`|

11゛1

|ぎ=21`ヽ

||rsquo゜3|

(y

J(Xg)=J(x)-J(2v゛oline゛g

olineJ(匈゛≒

)十J(2wトxg

)十J(4wヽ4-xg

----

II

(5-6)

ThevalueofJ大convergestoacertainvalueandcanbecalculated

byacomputerincasesofanyvaluesofwLandS

InFig5-3thelogarithmofJisplottedbysolidlines

asafunctionofx(=xL)whetvwL1S1020and30and

Dgis00Thedashedlinesareforthecasewithouttheinfluence

ofohmiccontactTheupperandlowercurvesareforS=1and10

respectivelyThevaluesoflogJ大decreasesuperlinearlywithin

onediffusionlengthawayfromthebarrierThereforeonemakes

considerableerrorsifoneestimatesthevalueofLfromthe

reciprocalgradientofthecurveatarbitraryXInordertoshow

anextremeexampleweconsiderthecaseofw7Ldeg1゛08叫DgdegO`Odeg

Thereciprocalgradientofthecurveinthelinearregionat

xdeg05withoutandwiththeinfluenceofohmiccontactareputas

L大andLrespectivelyThevaluesofLandL幼thuSobtained

areplottedasafunctionofSinFig5-4WhenSisunityL

1Sabout68ZofLandL政isabout44ZofLThevaluesofL大

andL政reducetoonlyaboutonethirdofLwhenSis50

Themethodoftheanalysisforapointsourcementioned

abovecanbeeasilyappliedtothefinitegenerationdistribution

bythedividingmethoddiscussedinChaptersI工andHEspecially

inthecasesoflight-emittingdiodes(LEDrsquos)andlaserdiodes

(LDrsquos)usingGaAsandGaPthedimensionofthegenerationregion

istheorderofymforva゛20へrsquo30kVandiscomparablewiththe

thicknessoftheepitaxiallayersThereforethedividingmethod

becomesaneffectivemeanstomeasureLandSintheepitaxial

layers

-71-

Fig5-5

Q‐rsquoQ]

loline

11(52

ち5

0 50Scanningdistancex

100

(pm)

jDependenceofEBIConthescanningdistancexforn-SiSchottkydiodesThelengthWbetweenthe

barrierandtheohmiccontactis100Umthe

acceleratingvoltageVais50kVandLis20へj200lim

SolidandbrokenlinesareforSdeg104and105cmsec

respectニivelytakingthegenerationdistributioninto

accountThediffusionconstantDofholesis125

cm^sec

-72-

n-SiVa=50kVw00μm

5aD=iZ5cm2ss(cms)

1-helliphellip104

2゛l`4-----helliphellip105

`L(μm)

1へ`a-2001

≒yyhelliphelliphellip100i

5゛゛ぐ丈i

へ゛`恥i

`ヽ

`lsquolブjl

ゝゝjφ1

0h白contactム

2rsquo

5-3 ApplicationtoS1

ThediffusionlengthintheSibulkmaterialusedfor

solarcellsorLS工゛S1Scomparablewiththedimensionsofeach

elementAndsotheminoritycarrierdistributionisaffected

verymuchbyelementdimensionsTheSchottkydiodewastakenfor

afundamentalmodeltorevealtheinfluenceofsampledimensions

CalculatedEBICrsquosbythedividingmethodinthecaseof

n-Siforwdeg100umandva゛50kvareshowninFig5-5Thediffusion

constantDofholesistakenasatypicalvalueof125cm^sec

Solidanddashedlinesareforsdeg101゛and105cmsecrespectively

andLis20010050and20umforthecurvesfromupperto

lowerineachgroupThegenerationsourceisassumedtobeasemi-

sphereThenumberofthegeneratedelectron-holepairsatany

pointinthesemi-sphereisproportionaltoexp(-40(rR)2)

(rthedistancebetweenthepointandthecenterdRthe

radiusofthesemi-sphere)Thegenerationdistribution1Sassumed

inorderthatthedepthdosefunctionalongthez-axlsagreeswith

thatproposedbyEverhart[4]andthevaluesofdgandRare

5ymand11ymrespectively゛forvadeg50kvrsquo

AsshowninFig5-5theabsolutevalueofEB工Cincreases

withdecreasingSforthesameLvalueThecurvesconvergetoa

certaincurveforboths=10rsquoand105cmsecwhenLbecomesgreater

thanwForconveniencethelogJvsχcurvesaredividedinto

threepartsi

range(30≦X-

く一一

eA)nearthebarrier(0≦x≦30ym)B)middle--

70ym)andC)neartheohmiccontact(70≦x≦100--

μm)IntheregionA)peaksappearatxdeg6ymowingtotheedge

effectdescribedinsect3-3and10gヽJdecreasessuperlinearlybecause

ofthesurfacerecombinationeffectIntheregionC)logj大decreases

-73-

Fig5-6

゜1(il

四a3

U」

-01

Ddziieujjoz

゛D=1Z5cm2s巡付

1 03

orini=-

にuarrヤuarr

uarrにヤ

Ohmiccontactづ50100

Scanningdistancex(μm)

JDependenceofEBIConthescanningdistancex

forn-SiwhenLismuchgreaterthanWThesolid

linesareresultsbythethree-dimensionalsolutions

forsdeg1035times1031045)(104and105cmsec

respectivelyThedashedlineisEBICbyone-

dimensionalapproximationV=50kVw=100ymand

L=1000Uma

-74-

゛ぐpermil

゛`xズit

darrレ

rapidlybecausetheohmiccontactisacarriersinkInthemiddle

rangeB)logJ大decreasesalmostlinearlyThereciprocalgradient

ofthecurveincreasesasLbecomeslargeintherangeofL≦100pm-

Thegradientsofthecurvesarenotsoaffectedbysurface

recombinationIfvisloweredt010kVthesurfacerecombinationa

affectsEB工Cmuchmorethanforvadeg50kVbecausethegeneration

depthbecomesshallowerInfactthegradientsofthecurvesin

regionA)aresteeperthanthoseforv=50kVforthesameLvaluesa

ThereforeinthecaseofL≦100ymLandscanbedetermined-

mainlyfromtheslopesofthelinearlydecreasingregionforhigh

va(50kVinthiswork)andthesuperlinearlydecreasingregionnear

theSchottkybarrierfor10Wva(10kVinthiswork)respectively

takingtheinfluenceofohmiccontactintoaccountButinthe

caseofL≧100ymthevalueofLcannotbedetニermineddefinitely-

becausetheslopeofthecurveinthelinearlydecreasingregion

doesnotchangeevenifLvaries

WhenLbecomesmuchlargerthanwthecurvesofEBICvsX

convergetoacertaincurveCalculatedEBICrsquosinthecaseofn-Si

forva゛50kVwdeg100ymandLdeg1000ymareshownbysolidlines

1nFig5-6forsdeg1035times1031045times104and105cmsec

respectivelyThegenerationsource1Sassumedtobeapointatthe

depthdThedashedlineisasolutionofone-dimensionalg

approximation(seeappenditimes1nthischapter)Theabsolutevalueof

EBICbecomeslargerwithdecreasingSandthecurveforS40cmsec

approachestothesolutionofone-dimensionalapproximationItcan

beexplainedasfollowsInthecaseofs=Ocmsecthereisno

carrierrecombinationatthesurfaceHencethematerialcanbe

consideredtoextendtoz=_oobyintroducinganimagesourceat

(x0-d)EBICisobtainedbyintegratingdpdxinthey-zplane

atx=0AndsotheEBICbythepointsourceat(x

-75-

grsquoO゛plusmnd)using

JOoline1

Ig3paziieuijoz

Fig5-7

(a)

UI「rrsquo

a3

U」

rsquo一lsquo51 0

pdziieujjoz

Scanningdistance

(b)

X(pm)

ExperimentalresultsinSiSchottkydiodesfor

w゛200μmand83μminfigures(a)and(b)respectively

Vais1030and50kVSolidanddottニedlinesare

theoreticalresultsforL=80UmandS=50withand

withouttheinfluenceofohmiccontニactrespectively

-76-

inlsquoSiL=80μm

こ沼o

rsquoバ町「i「でなl`Jes

l悶

2卜Ohmiccontact今|

トj

rsquohelliphelliphelliphelliphellipi

15

≒|

2helliphellip1

0Scanningdistancex150(pm)00

へn-SiL=80μm

5゜`S=50

deg゜w=83um

degムExperimentalvalues2deg`4≒Vi=50kV

I゛lsquorsquo4≒oVadeg30kV

≒゜rdquoVa≪10kV

丿4

lrsquo

2lsquoo1

rsquo゜i

2degi

2Ohmiccontactrarr

050100

thethree-dimensionaldiffusionequationbecomesidenticaltothat

derivedbyone-dimensionaldiffusionequationconsideringthe

planarsourceatxrsquoxginthey-zplane[5]Howeverinpractice

SihasafinitevalueofSandsothethree-dimensionalsolution

mustbeneededinthecaseofL>wThevalueofscanbedeter-

minedfromtheabsolutevalueofEBICfollowingthediscussionof

sect4-2usingtheelectron-holepaircreationenergyE^^byan

electronbeam

TheexperimentalresultsinSiSchottkydiodeswith

w=200umand83μmmadefromonewaferareshowninFigs5-7(a)

and5-7(b)respectivelySamplepreparationsandmeasurement

procedureshavebeenalreadyshowninsect3-4Theresultsofthe

theoreticalcalculationusingL=80vimandS=50forthreedifferent

va゛s(10rsquo30and50kV)areshownbysolidlinesinbothfigures

Theresultsofthetheoreticalcalculationwithouttheinfluence

ofohmiccontactareshownbydottedlinesinFig5-7

Inthecaseofw=200ymthesamplewidthisthreetニimeslargerthan

Landsotheslopeofthelinearregion(50≦x≦120um)isnot--

verychangedbytheinfluenceofohmiccontactInthecaseof

Wdeg83umthecurvesarequitedifferentfromthoseforw=200ym

andthereciprocalgradientofthecurvesinthemiddlerange

(25≦x≦55ym)givesL=20ymwhichisaquarterofthereal--

diffusionlengthBothinFigs5-7(a)and(b)theoretical

calculationsshowgoodagreementwiththeexperimentalresuLts

whichshowsthatthemethoddiscussedinsect5-21Saneffective

meanstニoanalyzetheeffectofsampledimensions

-77-

5-4 Summary

Theminoritycarrierdistributionisaffectedverymuch

bythelengthwbetweenapotentialbarrierandanohmiccontact

ifWisequaltoorshorterthanthediffusionlengthLThe

dependenceofEBICJ大onthescanningdistancexwasinvestigated

byextendingthemirrorimagemethod

InthecaseofwL≧1logJ゛decreasesalmostlinearly-

inthemiddlerangeofthescanningdistancebuttheestimated

diffusionlengthfromthecurvesismuchshorterthanthereal

diffusionlength(eg30t044ZinthecaseofL=w)The

valuesofLandScanbedeterminedmainlyfromtheslopesof

thecurvesforhighand10Wva゛reSpectively゛takingtheinfluence

ofohmiccontニactintoaccount

工nthecaseofwLく1theslopeofthelinearly

decreasingregionoflogJvsXcurvesdoesnotchangeevenif

LvariesThedependenceofEBIConχconvergestoacertaincurve

ThevalueofLcannotbedetermineddefinitelybutthevalueofS

canbeobtニainedfromtheabsolutevalueofEBIC

TheexperimentalresultsinSiSchottkydiodesagreed

fairlywellwiththetheorywhichshowedthattheextendedmirror

imagemethodwaseffectiveinanalyzingEBICconsideringthesample

dimensions

-78-

References

[1]

[2]

[5]

OldwigvonRoosSolid-stateElectron

(1978)

211063

FBerzandHKKuikenSolid-stateElectron19

(1976)

437

CvanOpdorpPhilipsResRep32192(1977)

TEEverhartandPHHoffJApplPhys丘5837

(1971)

WHHackettJrJApplPhys

Appendix0nedegdimensionalapproximation

431649(1972)-

IfthediffusionlengthLisinfinitelylongminority

carriersdonotrecomblneuntiltheyflowintothebarrierorthe

ohmiccontactThereforethediffusioncurrentdoesnotvary

spatiallyTheminoritycarrierdistributionpcanbeexpressed

asalinearfunctionofχ1nthecaseofone-dimensional

approximation工fthepointsourceg1Slocatedatdegcgrsquop(゜c)is

putasfollows

p(x)=ax十b(a>00≦゛≦)rsquo

p(x)゜c゛十d(c<0X≦゛≦゛)゜

(5-Al)

(5-A2)

Thefactorsabcanddcanbedeterminedfromthefollowing

conditions

-79-

p(O)=0

p(w)=0

卵石

-卜-卵匹 ゜g

(5-A3)

(5-A4)

(5-A5)

(5-A6)

Theeq(5-A5)showsthecontinuityconditionatxdegxg゛andtheeq

(5-A6)givesthatallthegeneratedcarriersflowintothe

Schottニkybarrierandtheohmiccontactニwithoutrecombinationin

materialsThesolutionp(x)becomesasfoLlows

p(x)=

p(x)=

(1-ミj1)x(O≦x

--^(w-x)(Kg

NormalizedEBICJisexpressedby

J大=

-egeD

dp

-dxχ=0

=1-

こ)

3Wく

一一

Xく一一

(5-A7)

(5-A8)

X』

-80-

(5-A9)

6-1

DETERMINATIONOFLIFETIMEANDDIFFUSIONCONSTANT

BYPHASESHIFTTECHNIQUE

Introduction

Accuratedeterminationoflifetimeてofminoritycarriers

1Sveryimportantincharactニerizingsemiconductingmaterials

Thevalueofてcanbemeasureddirectlyfromthetransientresponse

aftertheinjectionofminoritycarriersTheradiativerecombina-

tionlifetimewasmeasuredinGaPandGaAsfromthedecayofphoto-

luminescence[1]cathodoluminescence[2]orelectroluminescence[3]

Thephotoconductancedecaymethod[4]Isthemostcommonlyused

techniquetomeasurelifetimeincludingradiatニiveandnon-

radiativeprocessesInthesemethodsmeasurementofTinsmall

areaoftheorderofym^isverydifficultbecausethesample

surfacemustberelativelywideinordertoobtainasufficient

signalThespatialvariationofてcouldbedeterminedfromthe

decayoftheelectronbeaminducedcurrent(EBIC)usinga

scanningelectronmicroscope(SEM)[5-8]Thevalueofてismuch

influencedbysurfacerecombinationsincelightoranelectron

beamforexcitationentersthroughthesurface

Thevalueofてcanbeobtainedfromthediffusionlength

LusingtherelationL=j5マThevalueofLcanbedeterminedbythe

spectralresponsemethodusingsolarcells[910rbythesurface

photovoltaicmethod[1011nbothmethodstheaccurateabsorption

coefficientmustbeneededtodeterminethevalueofL

AsdiscussedinChapters皿rsquov^VtheEBICmethodusingSEMisa

veryconvenienttechniquetomeasureLinsmallareaoftheorder

-81-

ofym^andtherehavebeenmanytheoretical【11-14】and

experimental[15-16]worksuptodateInthemetニhodhowever

thediffusionconstantDmustbegiveninordertoobtainT

Whentheintensityofexcitationforelectron-holepair

generationisrdquomodulatedthephaseofluminescenceorinducedcurrent

isshiftedfromthatoftheexcitationsourcebecauseofthe

recombinationofinjectedminoritycarriersinamaterialThe

valueofてcanbedeterminedfromtheamountofthephaseshift

Hwang[17]obtainedTinGaAsfromthephaseshiftofphoto-

luminescenceInthemethodtニhephaseshiftisinfluencedbythe

surfacerecombinationvelocityandtheabsorptioncoefficient

whichaffectminoritycarrierdistributionverymuchReichleta1

measuredでinSi[18-20]andGaAs[21]usingthephaseshiftin

photニ0-inducedcurrentMunakata[22]andOthmer[23]measuredて

bythephaseshiftofEBICinGeandSirespectivelyTheyused

tニhesolutionoftheone-dimensionaLdiffusionequationwithout

anyconsiderationofthesurfacerecombinationeffect

Ifsuchaphaseshiftmethodiscombinedwiththe

conventニionallinescanmethodofEBIC(iemeasurementofLusing

DCelectronbeam)thelifetimeandthediffusionconstantof

minoritycarriersinsmallareacanbedeterminedsimultaneously

Kammeta1[241determinedてandDinSiTheymadeaSchottky

barrierwithasilverpaintonSisurfacesandmeasuredEB工Cby

scanningtheelectronbeamonthesurfaceparalleltothebarrier

InthatmethodsurfacepreparationhasmucheffectonT[25]

andtheconfigurationusedbythemisnotconvenientwhenone

measuresてandDinmaterialswithsmallLTheanalysisisvery

complicatedandRoospointedouterrorsintheiranalysis[26]

andsuggestedasimpleconfiguration[271

-82-

Inthischapterwetaketheconfigurationthatthe

electronbeamscansonthesurfaceperpendiculartothebarrier

planeWiththisconfigurationtニhetime-dependentdiffusion

equationcanbesimplyreducedtothesteady-statediffusion

equationandthecomplicationintheanalysisthatRoosindicated

[26]canbeexcludedThisphaseshiftmethodcanbeappliedto

materialswithsmallLWesolvethethree-dimensionaltime-

dependentdiffusionequationtakingthesurfacerecombination

effectintoaccountandclarifytherelationofTandthephase

shifttheoreticallyWeshowthatthree-dimensionalsolutions

canbeexpressedbyone-dimensionalsolutionswithempirical

correctionfactorsandthatてandDcanbedeterminedwitニhout

anyrestrictionformodulationfrequencyExperimentalresults

inSiarealsoshown

6-2 Relationbetweenlifetimeandphaseshift

WetakeaSchottkydiodeasshowninFig6-1for

simpletheoreticalcalculationWeassumeapointgeneration

sourcewhichhastime-variabLepartgelωt(ω゜2TTfωangular

frequencyfmodulationfrequency)at(x゛0d)Whenthetldegeoline

variablepartofthenumberofminoritycarriers1Sputas

恥eiωt(isacomplexvariable)psatisfiestheconventional

steady-statediffusionequationbyintroducingthecompleχ

effectivediffusionlengthL゛eff(ΞL゛1171瓦JTL=ぷF)゜If

thetime-variablepartofEBICIsputasj`゛e(J゛1Scomplex-

EBIC)icanbeexpressedasfollowsbythemirrorImagemethod

asdiscussedinsect3-2

-83-

Fig6-1

ylご

uarrj

Schottkybarrier

uarr

Ohmiccontact

Schematicviewofeχperimentalconditionsand

definitionoftheco-ordinatesystem

-84-

Electronbeam

SOlyScanningtrack_xj

ズニに匹二oline-一一゛

lsquo9surface

lL-__--ang__helliphellip_

|`1

丑昌之

9gπLaf ―K

gdof

(ノダr7olineT

)酉ff

L大effl゛ぶ弓+T『

+0O

(-1(じ(lg)

)X[

jiご]ご

)ことりsube

dgDIL火eff

xlてこi7

dT

J(6-1)

whereeisthechargeofanelectronsisthesurfacerecombination

velocityandTisthevariableforintegratニionThefunctionK^

1sthesecond-modifiedfirst-orderBesselfunctionwithcomplex

variablesTheabsolutevalueofEBICnandthephaseshiftφ

fromthesourcearegivenasfollows

TI=

|」と

eg

φ=tan-1

Im一J

Rej゛

(6-2)

(6-3)

whereReandImstandforrealandimaginarypartsrespectively

Thevalueofnisnormalizedtobeunitywhenallthevariable

-partgcontributetothevariablepartofEB工CSincej火isa

functionofてthevalueofφbecomesafunctionofてThevalues

ofnandφcanbecalculatednumericallyWeassumeapointsource

forsimplecalculationbutthemethodmentionedabovecanbeeasily

appliedtothefinitegenerationdistributionbythedividing

methoddescribedinChapters工江andy

-85-

Fig6-2

Fig6-3

U2

Cχ310-rsquo

山5

ト2

10lsquo3

velocitysis

35225N

(Eu

一))

j^

9st^d

10

Jo}CIで噌」

ひpF

ぐりぐ

ごヽこ

W゛`みノー-

うて`゜ldegw-rsquo゜rsquordquorsquoPrime゛ご

゜二

゛゜〆ノ〆゛`゜

゜゛〆ノ

(MJD≪p)j

UMS

asEMd

ofEBICvsscanning

thealmostlinear

0 50 100 150

ScanningdistanceX(pm)

Normalizedintensityandphaseshift

distancexcurvesTheconcavecurvesand

linesarefortheIntensity(leftaxis)andthephaseshift

(rightaxis)respectivelyThesolidbrokenanddottedlines

areforf=10100and500kHz(ieωT=031314and157)

respectivelyLifetimeTistakenas5μSThediffusion

constantDis30_cm2Secandthesurfacerecombination

105CmSeC

S=105CmS

D=30ori^s

Lifetimeで(sec)

DependenceofgradientofphaseshiftdφdxonTD=30cmsecandrsquos=105cmsec

-86-

rsquoD=30crrfis

ωで=5f

5ヽ2MHz

ヽ1MHz

2`500kHz

1`

100kHz

``50kHz

`ヽ`10khtt

pwww

kHz

`ωで=01

1(jrsquo

825

1(i

725

1(jrsquo

6251(irsquo

525

10lsquo4

Mm2s)lsquo1-123lsquoj「rsquoQ心Hz」t

=10cms-10a3i

i=30kV-一一一一1003K

helliphelliphelliphelliphellip500157

Thevaluesofnandφwerecalculatedasafunction

ofscanningdistanceχforp-SiasanexampleTheresultsare

showninFig6-2whenてisputasatypicalvalueof5μs

Inthefiguretheconcavecurvesandthealmostlinearlines

areforn-χandφ-xrelationsrespectivelyThesolid

brokenanddottedlinesareforf=10100and500kHz(ie

ωT=031314and157)respectivelyThediffusionconstant

Disputas30cm^secThesurfacerecombinationvelocitysIs

takenas105cmsecsincetheordinarysurfacerecombination

velocitニyofSiis103へj105cmsecTheacceleratingvoltage

Isputas30kVThepointsourceisassumedtobelocatedat

themaximumenergydissipationdepthofabout3μmunderthe

surfacebasedonKanayarsquosmodel[28]forelectron-holepair

generationdistributニIon

Inthecaseofωてく01tニhedependenceofnonX

agreeswiththat-measuredbyaconventionallinescanmethod

usingDCelectronbeamThevalueofLcanbedeterminedfrom

theslopeofthen-χcurvestakingthesurfacerecombination-

effectintoaccountasdiscussedinChaptermThevalueof

L大effalmoStequaltoLandSOφbecomesnearlyzero

Inthecaseofωて≧01φincreasesalmostlinearly-

withxovertherangeofx≧Landthegradientdφdxbecomes-

largewithIncreasingfasshownInFig6-2Thegradient

dφdxisfoundtoIncreaseasてbecomeslargeforthesamefvalue

andnottochangeevenifSvariesfrom10^t0105cmsecfrom

thecalculationforvariousparametersFigure6-3showsthe

dependenceofdφdχonTwhenfisvariedfrom5kHzto2MHz

ThevaluesofDandsare30cm^secand105cmsecrespectively

ForeachvalueoffdφdxincreasesmonotonouslywithTwithin

therangeof01≦ωて≦5andapproachestoacertainvalue--

asymptoticallyovertherangeofωて≧5-

-87-

「ujopp」)

調uiusas^qdj〇}c心石司」

Fig6-4

Lifetimeて (sec)

10

Expressionofthedependenceofdφdxonてusingtheapproximatedsolutionsoftheone-

dimensionaldiffusioneuationinthecaseofD=30cm^secandf=10sectHzSolidlineisa

three-dimensionalsolutionLines(A)and(B)

aretheapproximatedone-dimensionalsolutionsand(Arsquo)and(Brsquo)aretheasymntotesforthethree-dimensionalsolutionThecorrectionfactorCforthethree-dimensionalsolutionis087

-88-

2(8)登ニ4F

helliphellipj(Å

(A)

D(EI)-(jじ硲ゴどこ二こhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip

2helliphelliphelliphelliphelliphelliphelliphellip(畿f3゛(c緊八(醤y3

d≫_Kii「」(A)石rsquo7『

5Ddeg30cm2sfdeg105Hz

c=087

Ursquo725J625_-52542

Ifwetakethesolutionsoftheone-dimensionaldiffusion

equationdφdxisgivenasfollows[241

O「

dφ

dx

助こ

Lω

2D

一 一 S

irfr

一万

(ωて≪1)

(ωT≫1)

(6-4)

(6-5)

Followingthethree-dimensionalsolution(eqs(6-l)(6-2)and

(6-3))asshowninFig6-3ydφdxincreasesproportionallyt07

intherangeofωてく05andreachestoacertainvalueoverthe

rangeofωて>5whichcanbeeχplainedqualitativelybyeqS

(6-4)and(6-5)respectivelyThedφdxvsTcurvesinFig6-3

canberepresentedbyonefunctionwiththecombinationofthe

approximatedsolutionsoftheone-dimensionaldiffusionequation

(eqs(6-4)and(6-5))Weshowanexampleinthecaseoff=105Hz

andD=30cm^secinFig6-4Thesolidlineisthethree-

dimensionalsolutionfromFig6-3andthedottedlines(A)and

(B)expresseqs(6-4)and(6-5)respectivelyThebrokenlines

(Arsquo)and(B゛)showtheasymptoticsolutionsofthethree-

dimensionalsolutionintherangesofωて<05andωて>5The

absolutevaluesof(A)and(Brsquo)becomeabout87Zofthoseof

(A)and(B)basedontheresultsofcalculationAsshownin

Fig6-4thethree-dimensionalsolutionisgivenbyacombination

ofthelines(Arsquo)and(Brsquo)andIsexpressedasfollows

-89-

「―」)畠一

uiMSaseudpazneaijoz

Fig6-5

rsquo0

ω^t「

NormalizedphaseshiftニLdφdxvSωてcurves

Solidlineisathree-dimensionalsolution

expressedbytheapproximatedone-dimensional

solutionswithempiricalcorrectionfactors

Brokenlineistheone-dimensionalsolution

-90-

2One-dimensionalノrsquosolution゛`4xrsquo

10バ

5acuteThree-dimensional

ぶacutesolution

2acute

(yl

言二分ヽ同r〔2μ(ldquoμ

゛1)rsquo1

5primeacute

cべ1251251cap25

dφ

dx

)=(c

TTfr TTf)ldquo゛十(c

yでワ

)rsquo゛

-91-

十1}3

(6-6)

(6-フ)

函rsquo

wherenisapositiveintegerWecalculatedeq(6-6)Inthe

casesofn=1へj5anddeterminednas31norderthatthe

solidcurveinFig6-4canbewellrepresentedbyeq(6-6)

Thevalueofc1Sthecorrectionfactorforthethree-dimensional

solutionandcisabout087asmentニionedabove

Fromeq(6-6)wecanderivethefollowingrelation

usingtheconventionaldiffusionlengthL

_

=pound石{2Σ(則2万

ThetermLdφdxisconsideredtobethenormalizedphaseshift

whichistheamountofthephaseshiftwhentheelectronbeam

scansoveronediffusionlengthItshouldbenotedthatLdφdx

isafunctニionofonlyωでFigure6-5showsthedependenceof

LdφdxonωてbythesolidlineIfthevaluesofLanddφdxare-

knownてcanbedeterminedfromthecurveforanymodulation

frequencyandDisalsoobtainedbytherelationofL=iF

Themodulationfrequencyfcanbechosenfreelyandthe

restrictionsofωΥ<050Γωて>5fortheapproximatIonneednot

tobetakenintoaccount

ThephaseshiftderivedbyMcKelvey[29]usingtheone-

dimensionaldiffusionequationisshownbythedashedlinein

Fig6-5Theestimatedvalueofωてbytheone-dimensional

solutionisabout76へ87Zofthatbythethree-dimensional

solutionforeveryvalueofLdφdxInthecaseoftheone-

dimensionalsolutionLisdetermineddirectlyfromthegradient

ofthelinearlydecreasingregionofEBICcurveandisabout

60へj80Zoftherealvaluefromtheresultsofthedetailanalysis

takingthesurfacerecombinationeffectintoaccount[14]

ThereforethevalueofωΥderivedbytheone-dimensionalsolution

isonly30へJ丁0Zoftherealvaluebecauseωてdecreases

proportionallytOLandL2intheregionsofLdφdxく03and

Ldφdx>2respectivelyOnemustusethethree-dimensional

solutioninordertodeterminetheaccuratevalueofて

6-3 ExperimentalresultsinSi

AconventionalSEMwasusedfortheprimaryelectron

beamwhichwasmodulatedat1rsquoj50kHzwiththedutyof05by

achoppingcoilinsertedintothebeampathThebeamcurrentwas

as10was10oline10AThemaximumminoritycarrierdensityinthis

experimentwasconsideredtobeabout3times1014Cmoline3andthe10w

injectionconditionwassatisfiedTheinducedcurrentwas

measuredbythevoltagedropacrosstheloadresistancewhich

wasconnectedtotheSchottkybarrierwithanohmiccontactThe

signalhadarectangularwaveformowingtothechoppedprimary

electronbeamandsothefundamentalfrequencycomponentinthe

Fourierseriesofthesignalwasdetectedbyanauto-phaselock-

inamplifierTheEBICnandthephaseshiftφfromthesource

wererecordedsimultaneously

ThediffusionlengthLisdeterminedinthecaseof

ωて<01takingthesurfacerecombinationeffectintoaccount

Thedependenceofnonxagreeswiththatニmeasuredbyaconventional

linescanmethodusingDCelectronbeamasdiscussedinsect6-2

-92-

Whenvaislowgivingtheshallowgenerationdepthsurface

recombinationhasalargeeffectonEBICWhenvaishigh

givingthedeepgenerationdepththesurfacerecombinationeffect

1SreducedTheaccuratevalueofLcouldbedeterminedbyfitting

experimentaldatatotheoreticalcurvesforboth10wandhighva゛S

(10and50kVrespectivelyInthiswork)asshownInsect3-3

Thevalueofdφdxisobtainedatanappropriate

modulationfrequencywhichsatisfiesωて>01AthighVthe

surfacerecombinationeffectIsreducedandsowechosetニhe

highestva(30kVinthiswork)asfarastheelectronbeamcould

bechoppedOncethevaluesofLanddφdxareknownthevalues

ofてandDcanbedeterminedfromthecurveinFig6-5

Sampleswerep-andn-typeSiwithtニheresistivitypof

10and01f2cmrespectivelyOhmiccontactsweremadeby

evaporatinggallium-dopedgoldandantimony-dopedgoldontothe

p-andn-typesamplesrespectivelySchottkycontactsweremade

byevaporatingaluminiumandgoldontothep-andn-typesamples

respectivelyinavacuumas10was10oline7TorrThesampleswere

insertedintoavacuumchamberforEBICmeasurementimmediately

aftertheywerecleaved

ThediffusionlengthLinp-typeSiwasdeterminedas

130μmfromthen-xcurvesinthecaseofωてく01The

experimentalresultsofthephaseshiftmethodareshownIn

Fig6-6bysolidlinesforf=5102030and50kHzrespectively

ThephaseshiftIncreaseswithxalmostlinearlyasdescribedin

sect6-2ThevaluesofてweredeterminedusingFig6-5as9595

8886and83ysfromthegradientsofthelinesinFig6-6

for5102030and50kHzrespectivelyTheobtainedvaluesof

てshowlittledifferencewitheachotherinanymeasurement

-93-

11

es^Md

Fig6-6

P-Si(r=10ncm)f=

20

1 0一

----n-Si(r=Q1ftcm)

Va=30kV

圭T

rdquo

------ニr二ご二二耳一一3

50100

Scanningdistance

150

Experimental

methodinp-(p=10

200

(μm)

resultsofthephaseshift

Ωcm)andn-type(p=01ncm)Si

-94-

rdquoolinersquordquooline`rsquolsquorsquoolinerdquordquoolinersquo50kHz

Vadeg30kVZ

10deg

30

FJ゛

一一20

〆がノrdquo〆〆〆

メノrdquo

〆〆〆〆〆ノ10

---rdquordquo|-sニニニldquo-notこ9

conditionfromωて=03(atf=5kHz)to30(atf=50kHz)

Itprovedthatthemodulationfrequencycouldbechosenfreelyas

mentionedinsect6-2Ifwetaketheaveragedvalueofて(ie

で89ys)thediffusionconstantDofelectronswasdeterminedas

19cra^secwhichalmostagreedwiththereportedvalue[301The

slightdeviationfromthestraightlineforf=50kHzmaycomefrom

unstablenessofthechoppedbeambecausethechoppingcoilused

inourexperimentwasnotdesignedforhighfrequencymodulation

above50kHz

Thediffusionlengthinn-SiwasobtainedasL=80ymand

thephaseshiftsareshowninFig6-6bybrokenlinesforf=3

10920and50kHzrespectivelyThedeterminedvaluesofてfrom

thegradientsofthelineswere889292and105usfor

fdeg3s1020and50kHzrespectivelyThevaluesofTalmost

equalwitheachotherasinthecaseofp-SiIfwetakethe

averagedvalueofT(ieで=94ps)tニhediffusionconstantD

ofholesbecomes7cm^secwhichalsoagreeswithtニhereported

value[301

Thegenerationdistributionisconsideredtobeasemi-

spheretheradiusofwhichisabout6ymatニvadeg30kVusingthe

Kanayarsquosmodel[28]Thedimensionsofgenerationdistribution

aresufficientlysmallincomparisonwiththediffusionlengthof

thesamplesThereforethepointsourceassumptioninthe

analysisisreasonable

-95-

6-4 Summary

Whentheintensitymodulatedelectronbeamisusedthe

phaseofinducedcurrent(EBIC)isshiftedfromthatofexcitation

sourcebecauseoftherecombinationinmaterialsWesolvedthe

three-dimensionaltime-dependentdiffusionequationtakingthe

surfacerecombinationeffectintoaccountandclarifiedthe

relationofてandthephaseshiftφtheoretically

Inthecaseofωて≧01φincreasesalmostlinearlywith-

Xovertherangeofx≧LThegradientdφdxbecomesafunction-

ofTandisnotaffectedbysurfacerecombinationTherelation

ofdφdxonてwasfoundtobeexpressedusingtheapproximated

solutionsoftheone-dimensionaldiffusionequatニionwithtニhe

empiricalcorrectionfactorsThenormalizedphaseshiftLdφdx

becomesafunctionofonlyωてIfthevaluesofLanddφdxare

knownてandDaredeterminedwiththeaidofLdφdxvsU3てcurve

withoutanyrestrictionformodulationfrequencyTheestimated

valueofてbytheone-dimensionalsolutionswithoutニthecorrection

factorsisonly30へノ70Zoftherealvaluederivedbythethree-

dimensionalsolution

Experimentalresultsinp-andn-typeSiSchottkydiodes

showedgoodagreementwiththetheoryandtheminoritycarrier

diffusionconstantsofelectronsandholesweredeterminedas

19and7cm^secrespectively

-96-

References

[11

[2]

[31

[4]

5]

6]

[10]

[11]

[12]

[13]

[14]

[15]

PDDapkusWHHackettJr0GLorimorandRZ

BachrachJApplPhys^54920(1974)

MBoulouandDBoisJApplPhysj旦4713(1977)

MEttenbergHKresselandSLGilbertJAppLPhys

44827(1973)

SWangrdquoSolid-stateElectronicsrdquo(McGraw一HillInc

1966)p300

WZimmermannphysstatsol(a)12671(1972)

DRHunterDHPaχmanMBurgessandGRBooker

rdquoScanningElectronMicroscopySystemsandApplications

1973rdquo(工nstPhysLondon)pp208-213

HKKuikenSolid-stateElectron19447(1976)-

AJakubowiczSolid-stateElectron22635(1980)

HTWeaverandRDNasbySolid-stateElectron

22687(1979)-

DLLileandNMDavisSolid-stateElectron

18699(1975)-

WvanRoosbroeckJApplPhys2plusmn380(1955)

WHHackettJr=JApplPhyspound1649(1972)

FBerzandHKKuikenSolid-stateElectron

19437(1976)

CvanOpdorpPhilipsResRept22192(1977)

DBWittryandDFKyserJApplPhys261387

(1965)

-97-

[16] CvanOpdorpRCPetersandMKlerkApplPhysLett

2h_125(1974)

[17]CJHwangJApplPhys4^4408(1971)

[18]

[19]

HReichlandHBerntSolid-stateElectron

18453(1975)

GSchwabHBerntandHReichlSolid-stateElectron

2091(1977)

[201JMiillerHBerntandHReichlSolid-stateElectron

21999(1978)

[211

[22]

JMiillerHReichlandHBerntSolid-stateElectron

22257(1979)

CMunakataandTEEverhartJpnJApplPhys

11913(1972)-

[23]SOthmerrdquoScanningElectronMicroscopy1978Vol1uml

(SEMIncOrsquoHare111)p727

[24] JDKaiiraiandHBerntSolid-stateElectron

21957(1978)-

【25】JDKammrdquoSemiconductorSilicon1977uml(The

ElectrochemicalSociety工nc)p491

[26] 0vonRoosSolid-stateElectron23177(1980)

[27]0vonRoosJApplPhys1^3738(1979)

[28]KKanayaandSOkayamaJPhysDApplPhys

543(1972)

[29]JpMckelveyrdquoSolidStateandSemiconductorPhysicsrdquo

(HarperandRowNewYork1966)pp439-440

[30]HFWolfrdquoSiliconSemiconductorDatardquo(Pergamon

PresslnC1969)

-98-

ⅥI

7-1

HEATTREATMENTEFFECTONDIFFUSIONLENGTHINS1

Introduction

Therehavebeenmanystudies[1]onthepropertiesofthe

processinducedfaults(PIFrsquos)Thedegradationoftheelectrical

performanceofthedeviceshasmuchconnectionwiththesegregated

impuritiesatPIFrsquosorthedecoratedfaultsofeachPIFRecently

thefaultproducedespeciallybytheoxidationathightemperatures

(IesocalledoxidationInducedstackingfault(OSF))has

receivedconsiderableattention[2-5]becausetheoxidationisa

fundamentalprocessinmakingLS工rsquosorcharge-coupleddevices(

CCDrsquos)Ravieta1[67]showedthattheelectricallyactive

OSF゛sincreasedtheleakagecurrentinprsquonjunctionsKimerllng[8]

determinedtheenergylevelofthefaultsfromtheelectron

beaminducedcurrent(EBIC)measurementsatvarioustemperatures

Generallythefaultsbecomerecombinationcentersanddecrease

thelifetimeandthediffusionlengthofminoritycarriers

Shimizu[9]showedthatthelifetimecouldbecontrolledpreferably

bytheintrinsicgetteringusingOSFrsquosRozgonyi[10]and

Tanikawa[11]reportedthattherelaxationtimeofMOScapacitors

decreasedasthedensityofOSFincreasedButtherehavebeen

alittlestudyonthequantitativeinformationofthedecreaseof

thediffusionlengthaftertheoxidationprocessathightemperatures

Inthischapterwemeasuredthechangesofthediffusion

lengthbyEBICmethodaftertheheattreatmentsathightemperature

andshowedthattheheattreatmentforafewminutescouldaffectthe

diffusionlengthatthesurfaceregionTheobservationofsurface

faultsbychemicaletchingwerealsoshown

-99-

(―)

<j)6udI

ColコこI()

Fig7-1

Heattreatmenttimet(min)

Diffusionlengthaftertheheattreatments

forvarioustimelengthsrangingfromlt0120minutesat1000degCOpenandsolidcirclesare

forthecasesindry02andArrespectivelyOriginaldiffusionlengthbeforeannealingis80pm

-100-

5ohellipumlindryO2

uml゜umlinArat1000degC

ol

12510251002

- W ゝ

rsquo _ l - ~ ヽ jS j - -

磨 卜

Fig7-2

(a)

(c)

rarr100Mm

ぶミ

卜`

r-^

rsquo

1Is

≪バ

rdquorsquo‐゛t

rsquo

grバ4≪

rsquo1

Surfacefaultsrevealedby

usingSirtletchantSamples(a)

wereannealedindryoat1000

and120minutesrespectively

-101-

い゛フバrdquo

゛para

`i

(b)

(d)

permilご}

->嗜

-゛

rsquo

III

`ヽご

いい

一J

t七

~貿で

rsquo

゛`1

鴫ヽ

rsquoq

-≪

ゝく

chemicaletching

(b)(c)and(d)

Cfor0830

一 一

- 一 一 -一 一

7-2

Experimentalresultsanddiscussions

Samplesaren-tニypeSigrownbyczmethodTheoriginal

resistivitybeforeannealingisaboutニ01ΩcmTheheattニreatment

wasdoneat1000degCintheflowofdry02andArrespectivelydeg

ThenthesampleswererinsedinHFforlmintoremovetheoxidized

layerandgoldwasevaporatedinordertomakeaSchottkybarrier

forEBICmeasurementsTheproceduresofthedeterminatニionofthe

diffusionlengthhavealreadybeendiscussedinChaptersmandでIV

Figure7-1showsthediffusionlengthaftertheheat

treatmentThetimetoftheheattreatmentwaschangedfromlto

120minutesTheopenandsolidcirclesareforthecaseIndryO2

andArrespectivelyTheoriginalvalueofdiffusionlengthis

80μmThediffusionlengthdecreasedtoabout7μmrapidlyas

tincreasedt05minandbecamealmostconstantovertherange

oft>5mlnThediffusionlengthdecreasedslightlymorerapidly

in02tニhaninArThelifetimechangedfrom5μsto003usif

thediffusionconstantofminoritycarrierswastakenasatypical

valueof125cmsecThesurfacefaultsofthesamplesannealed

indry02areSho゛linFigsdeg7-2(a)(b)(c)and(d)forlsquot゛

0830and120minrespectivelyThesampleswereetニchedby

SirtletchantforthesametimeThenumberoffaultsdidnotニ

increaseuntilt=8minbutbecameverylargeattdeg120min

ThesameresultwasobtainedforthesamplesannealedinAr

Itshouldbenotedthatthenumberoffaultsdidnotニchangedinthe

rangeofO≦t≦8minbutthediffusionlengthdecreasedrapidly--

inthesamerangeThelengthsbetweenthefaultsareverylarge

incomparisonwiththediffusionlengthinthesamplesannealed

for1くtく8minandsothediffusionlengthisconsidered

nottoberestrictedbytheaverageintervalbetweenthefaults

whenthefaultsareconsideredtobethecarriersink

-102-

TheuniformEBICwasobtainedwhentheelectニronbeamwasscanned

onthesurfacethroughtheSchottkybarrtersandthedarkpoints

correspondingtothefaultswerenotobserved

Therapiddecreaseofthediffusionlengthwasconsidered

tobecausedbytheformatonofnucleioffaultsattheearly

stageoftheheattreatmentTheverysmallnucleicanbecomethe

recombinationcenterseveniftheycannotberevealedbychemical

etchingIftheheattreatmenttimeissufficientlylongthe

nucleibecomelargeandcanberevealedbyetchingAsshownin

Fig7-2(d)thelengthbetweenthefaultsafterlongtimeheat

treatmentisthesameorderofthediffusionlengthTheformation

ofnucleiwasnotaffectedverymuchbytheoxidationbecausethe

decreaseofthediffusionlengthwasalsoobservedintheheat

treatmentinArAsisknowngenerallytheczgrownSIcontains

oversaturatedoxygenandtheformationofnucleiisrelatedtニO

theoxygenprecipitation[12]Thediffusionlengthdecreasedless

rapidlyinArthaninO2degOnereasonofthisphenomenonisconsidered

tobetheformationofSiOAnotherreasonistheoutdiffusion

ofoxygenbecauseoxygencanoutdiffusemorerapidlyinArthan

inO2degFurtherinvestigationmustbeneededfortheclarification

ofthenucleiformation

Inconclusionthediffusionlengthatthesurfaceregion

inSidecreasedtoabout10Zoftheoriginalvalueafterthevery

shortheattreatmentat1000degCforafewminutesNevertheless

thesurfacefaultsrevealedbychemicaletchingdidnotchange

Thenucleioffaultswereconsideredtobeformedattheearly

stageofheattreatmentandtheybecameminoritycarrier

recombinationcentersThedecreaseofthediffusionlengthwasnot

soaffectedbytheambientgases(ieoxygenorinertone)Much

attentionmustbepayedintheheattreatmentprocessathigh

temperatureevenifthetimeIsveryshort

-103-

i J I

References

[1]

21

31

71

81

[91

[10]

[n]

[12]

HFoilNGoreleandB0KolbesetirdquoSemiconductor

Silicon1977rdquo(JElectrochemicalSocietyInc

Prircetion1977)pp565-574

DJDThomasphysstatso1旦2261(1963)

CMMelliar-SmithrdquoCrystalcefectsinsiliconintegratニed

circuits-TheircauseandeffectrdquoinrdquoTreatieson

MaterialScienceandTechnologyrdquovol11(AcademicPress

NewYork1977)

KVRaviandCJVarkerJApplPhys45263(1974)

SMHuJApplPhys513666(1980)

KVRaviCJVarkerandCEVolk

JElectrochemSoc120533(1973)-

CJVarkerandKVRaviJApplPhys亘272(1974)

LCKlmerlingHJLeamyandJRPatel

ApplPhysLett30217(1977)

HShimizuAYoshinakaandYSuglta

JpnJApplPhys17767(1978)

GARozgonyiandRAKushner

JElectrochemSoc123570(1976)-

KTanikawaYItoandHSei

ApplPhysLett28285(1976)

JRPatelrdquoSemiconductorSilicon1977rdquo(The

ElectrochemicalSocietyIncPrinceton1977)

pp521-545

-104-

ⅧI CONCLUSIONS

InthepresentstudyEBICwasanalyzedquantitativelyby

solvingthesteady-stateortime-dependentthree-dimensional

diffusionequationsTheinfluenceofthefinitegenerationvolume

onEBICwasdiscussedandanImprovedmethodtocharacterize

thephysicalpropertiesinthesmallselectedareasofsemiconduc-

torswassuggestedTheobtニainedresultswereasfollows

InChapterHtheshortdiffusionlengthoftheorderof

ymcouldbedeterminedbythenormalincidencemethodofEBIC

Variousmodelsforgenerationdistributionusedintheanalysis

yieldedtheambiguityforthedeterminationofthediffusionlength

andtheelectron-holepaircreationenergybyanelectronbeam

Detailedinformationonthegenerationdistributionmustbe

necessarytoanalyzeEBICaccurately

InChaptニermthegenerationvolumeofminoritycarriers

hadrsquoaconsiderableeffectonEBICinthelinescanmethod

especiallywhenthedimensionsofthegenerationvolumewasequal

toorlargerthanthediffusionlengthWhentheaccelerating

voltagewaslowandsothegenerationdepthwasshallow

surfacerecombinationhadalargeeffectonEBICWhereaswhen

theacceleratingvoltagewashighandsothegenerationdepth

wasaslargeasthediffusionlengthsurfacerecombinationhad

aslighteffectonEBICTheaccuratevaluesofphysicalparameters

suchasthediffusionlengthshouldbedeterminedbyfittingthe

experimentaldatatothetニheoreticalcurvesforalltheaccelerating

voltagesTheexistenceofamaximuminEBICnearthebarriercould

beexplainedbythersquoedgeeffectrsquoattributedtothefinite

generationvolume

-105-

InChapter】5inthelinescanmethodthedependence

ofEBIConthescanningdistancerepresentedmainlythelateral

extentofthegenerationdistributionwhentheacceleratingvoltage

washighandwhenthedimensionsofthegeneratニionregionwere

largerthanthediffusionlengthThethree-dimensionalgeneration

distributionbasedupontheexperimentalresultsforthenormal

incidencecouldexplaintheexperimentalresultsofthelinescan

methodInGaAsthecenterofthegeneratニionregionwaslocated

atthepointof0130fthemaximumelectronrangeandthe

radialdistributionfromthecentニerwasshowntobeGaussianwith

anexponentニof54Q82Thevaluesof38へj44eVfortheelectron-

holepaircreationenergybyanelectronbeamwasobtainedtaking

thesurfacerecombinationeffectintニoaccount

InChapterVinthelinescanmethodtheminoritycarrier

distributionwasaffectedverymuchbyanohmiccontactwhenthe

lengthwbetweenthepotentialbarrierandtheohmiccontactwas

lessthanoneortwodiffusionlengthsTheslopeofthecurveof

EBICvsscanningdistancedidnotchangeevenwhentニhediffusion

lengthvariedandthediffusionlengthcouldnotbedetermined

definitelyfromtheslopeofthecurveTheabsolutevalueof

EBICwasdependentonthesurfacerecombinatニionvelocityand

thelengthW

InChapterⅥ[thephaseshiftbetweenthemodulated

electronbeamandEBICwasclarifiedbysolvingthethree-

dimensionaltime-dependentdiffusionequationTherelation

betweenthephaseshiftandthelifetimewasfoundtobeexpressed

usingtheapproximatedsolutionsoftheone-dimensionaldiffusion

equationwithempiricalcorrectionfactorsThelifetimeandthe

diffusionconstantofminoritycarrierscouldbedetermined

definitelywithoutanyrestrictionformodulationfrequency

-106-

InChapterVIIthediffusionlengthinthesurfaceregion

ofSiwasfoundtobedecreasedverymuchafterheattreatment

at1000degCforonlyafewminutesneverthelesssurfacefaults

revealedbychemicaletchingwerenotincreasedThenuclei

ofthefaultsmightbeformedattheearlystageofheattreatment

ThisinvestigationprovedthatEBICcouldbeanalyzed

quantitativelyinthesmallselectedareaconsideringthethree-

dimensionalgenerationdistributionbyanelectronbeamBut

thereexistsomepointstobestudiedfurtherasfollows

FirstbyEBICmethodthetotニalrecombinationlifetimeincluding

bothradiativeandnon-radiativeprocessescanbemeasuredBut

onecannotobservetheradiativerecombinatニionlifetimealone

whichIstheimportantparametニertocharacterizethellght-emittニing

diodesorlaserdiodes[1]Deeperunderstandingcanbeacquired

byinvestigatingtheluminescenceemitニtedbyrecombinationof

generatedelectron-holepairs(iecathodoluminescence)[23]

SecondlyEBICtechniquecannotrevealtheenergylevelsand

densitiesofimpuritiesandtrapsaccuratelywhichaffectthe

electricalpropertiesofmaterialsverymuchTherehavebeena

fewreports[4]todeterminetheenergylevelsoffaultsinSi

fromEBICmeasurementsatvarioustemperaturesButthe

experimentalaccuracyofEBICtニechnlqueisinferiortothat

ofthephotoluminescence[5]orthecapacitance[67]methods

Thirdly万thedoseofhighenergyelectronbeldquo万171万causesdamagesin

samplesSeveralinvestigationshaveshownthedecreaseoftニhe

tニhresholdvoltageinMOSdevices[8]andtheincreaseofthe

interfacestatedensitybetweentheoxideandthesemiconductors[9]

-107-

Improvementsofmeasurementtechniques(ieuseofthe10W

energyprimaryelectronbeam万orlthedecreaseoftニhetotal

amountofdose)wirsquollbenecessary

Electricalpropertiesofsemiconductorscanbecharacterized

collectivelybyEBICjointlywiththeothertechniqueswhich

complementtheweakpointsinEBICmethod

REFERENCES

[1]

[21

[5]

[6]

[7]

[8]

[9]

PDDapkusWHHackettJr0GLorimorandRZ

BachrachJApplPhys45

4920(1974)

DBHoltandBDChasephysstatS01(a)旦旦

135(1973)

MBoulouandDBoisJApplPhys 484713(1977)

LCKimerlingHJLeamyandJRPatel

ApplPhysLett30217(1977)

HBarryBebbandEWWilliamsrdquoSemiconductorsand

Semimetalsrdquo(edRKWillardsonandACBeer

AcademicPress1972)vol8pp182-392

SMSzerdquoPhysicsofSemiconductorDevicesrdquo(JohnWiley

SonsInc1969)

DVLangJApplPhys453023(1974)

WJKeeryK0LeedyandKFGallowayrdquoScanning

ElectronMicroscopy1976rdquo[IITR]Chicago)pp507-514

RHezelSolid-stateElectron11^

735(1979)

-108-

4i

rsquoII

LISTOFPUBLICAT工ONS

[1]

[21

[3]

[4]

[5]

[6]

Papers

Theinfluenceofthegenerationvolumeofminoritycarriers

onEBICrdquo

TFuyukiHMatsunamiandTTanaka

JPhysDApplPhys131093-1100(1980)

rdquoAnalysisofEB工CconsideringthegeneratニIondistribution

ofminoritycarriersrdquo

TFuyukiHMatsunamiandTTanaka

JPhysDApplPhys131503-1510(1980)

rdquoDeterminationoflifetimeanddiffusionconstantof

minoritycarriersbyaphaseshifttechniqueusing

electronbeaminducedcurrentrdquo

TFuyukiandHMatsunami

JApplPhys旦(1981)

rdquoAnalysisofelectronbeaminducedcurrentconsidering

sampledimensions一一-Measurementofdiffusionlength

andsurfacerecombinationvelocity-rdquo

TFuyukiandHMatsunami

JpnJApplPhys20(1981)No4

rdquoInfluenceofminoritycarriergenerationdistributionon

electronbeaminducedcurrentinthenormalincidencemethodrdquo

TFuyukiandHMatsunami

(tobepublished)

rdquoHeattreatmenteffectondiffusionlengthinSirdquo

TFuyukiandHMatsunami

(tobepublished)

-109-

[1]

[21

[3]

PublicationsintheInstituteofElectronicsandCommunication

EngineersofJapan

(inJapanese)

rdquoMeasurementofminoritycarrierdiffusionlengthby

EBICmethodrdquo

TFuyukiHMatsunamiandTTanaka

ReptTechSSD78-102(Feb1979)

rdquoCharacterizationofdiffusionlengthandlifetimebyEBICrdquo

TFuyukiandHMatsunami

ReptTechSSD79-103(Feb1980)

rdquoMeasurementoflifetimeanddiffusionconstantofminority

carriersbyphaseshifttechniqueinEBICrdquo

TFuyukiandHMatsunami

TransSectionJ63-C832-837(1980)

-110-

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Page 7: CHARACTERIZATION OF SEMICONDUCTORS BY Title ELECTRON …
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