Electrical Transport Studies of Electro Optically Active Semiconductors
CHARACTERIZATION OF SEMICONDUCTORS BY Title ELECTRON …
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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
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CHARACTERIZATIONOFSEMICONDUCTORS
BY
ELECTRONBEAMINDUCEDCURRENT
BY
TAKASHIFUYUKI
JANUARY1981
DEPARTMENTOFELECTRONICS
KYOTOUNIVERSITY
KYOTOJAPAN
j
犬CHARACTERIZATIONOFSEMICONDUCTORS
IBY
ELECTRONBEAMINDUCEDCURRENT
BY
TAKASHIFUYUKI
JANUARY1981
DOC
1981
1
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-
S
hellipJVi_--Wrsquordquo>>-trsquomjrsquordquordquo^>-≫^
f1
t
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
I
江
Ⅲ
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
Ⅵ
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
C
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-
k
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-
W
rdquod
wm
Xxx
g
g
χy
ZZ
m
n
np
Pau
^GaAs
I
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-
p
n
Fig1-1
type
type
Primaryelectrbe≪m
^^trrttDepletionlayer
Electron-hotep弗i「6gerwrationregion
Primaryelectronbeam
rArrScanningdirection
(A)
-
(B)
Principalconfigurationstomeasurethe
electronbeaminducedcurrent(EBIC)
(A)normalincidencemethod
(B)linescanmethod
-2-
-
ぶ
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
十
--
-- - -
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-
皿
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
i
Numberofgeneratedcarriers
Fig2-1Schematicviewofexperimentalconditions
jusingSchottkydiodesMetalthicknessis
wanddepletionlayerwidthiswright-handillustぷふこsthedぶdosefunctionRandR
-givethemaxiraum
andextraporaiedmelectrSnolinerangerespectively
-14-
0generatedcarrier
に_---___1
我_______Iuarrヽ
y重ダ
Z
1ごpermil
氷
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
t
χ
`Makarov20χ
----Wittry
χhelliphelliphellipKanaya
11S
15
゛S≒
rsquoχ≒
χrsquo
10trsquolsquo
卜卜゜χ゛
1
卜ゝrsquo
05χrsquo゛rsquoゝ
ゝrsquoゝ1
ゝゝrsquoゝゝ
ゝゝ
00
50
D
GaAso々
5
タグrsquo
2
万
1
ぶ
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
ぐ
二ぷ芯t
15へ
゜¥レ臨べhellip
hellip
10rsquoS゛lsquoNhellip
helliphellip
05
hellip
helliphellip
1helliphellip
hellip
005
芦
o
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
-
十
- -
-- - - - -
- - - -
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
>
ざ
u1C
larrl
0E
2
き
(
501
-
Figure2-6showsthecollectionefficiencyinSiusing
thefourdifferentmodelsofMakarovWittryKanayaandEverhart
bythesolidbrokendottedanddashedanddottedlines
respectivelyThevalueofLIs1005020and10umfrom
uppert0lowergroupofcurvesrespectivelyThevaluesofW
m
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
2
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]
3
4
[5]
WCzajaJApplPhys374236(1966)
JFBresserdquoScanningElectronMicroscopy71972partlrdquo
(iiTRiChicago111)p105
CJWuandDBWittryJApplPhys丘旦2827(1978)
KKanayaandSOkayamaJPhysDApplPhys
543(1972)-
口EPosslnandCGKirkpatrickJApplPhys
5^4033(1979)
[6]TEEverhartandPHHoffJApplPhys
425837(1971)
7
8
9
[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-
Ⅲ
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
Z
Schematicviewof
anddefinitionsofthe
-32-
experimentalconditionscoordinatesystems
Electronbeam
Surfacecross-sectic
O゛9χ
Schottky哨Rbarrier
y
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
1
1
2
Normalizedscanningdistancex
(a)
Fig3-2
Fig3-3
U
四
S
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
S
Og<ao
2
161
S>0
S
21
Idrsquo
S5
2
10^
550
2
1必12345
135
sc^-at
SO⑤
バ宍
1012345
112345
SPg≪10
2
161
S
2
162S=0
SI
1
1(i3
5
2
1(541235
comparedwiththediffusionlengththeboundaryconditionsare
D
p
p
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=
j
-eg
+
2
一
丁T
4oo
int
Dg
馴D戸
0
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
d
g
11-
Schematicviewofelectronpenetrationisthemaximumenergydissipationdepth
a(W)
00000
1CMCO<rm
d(ym)
rdquo047
149
291
in<yi
vDVO
4VO
R(um)
-
100
295
5
9
13
74
20
2
Valuesofthecenterdgofthegeneration
volumeandtheradiusRinSiforseveralvalues
ofacceleratingvoltagevarsquo
-38-
IElectronbeam
O335
j
S`」「fdegce
uarrで0559j
10゛」
helliphelliphelliphelliphellip
上
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
1
pdznpoi」oz
1
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
2
4
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
1
1
1
-
1020304050(pm)
Scanningdistancex
Fig3-7
Experimentalresultsfor
sampleA(p=lf2cin)whereL=
8μmandS=20Fullcurves
arethetheoreticalrsquoones
1
5
11(il
>P≪4<N1≪CM<Pq
1 1
3193paziipujjoZ
5
2
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
2
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
5
6
[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-
E
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
1
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-
心
helliphellipl
l
]]1A
Ee
ビゲヤ
2
12
ss50
4
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
U
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
ビ
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
-
ド
ー い゛I
い
゛゛
w
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
j
②
五゛
゛
`
olinelo
jV
ズごy
こ
l
x
1
23
times1
l
U
5
GaAだj
(
j73C4Electron
L=07μmEbeam
2Sdeg20χ
1rsquo`
5
゛x
鹸
ya(W
2゛Va=30W
2_JE201
4一一―54013
5≒
脅χ
21`f
3
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-
W
Normalincidence Line scan
V(kv)a
E(eV)GaAsCSndoped)pc
GaAs(Tedoped)
5-50
41
39
4
0
14
3 9
30
3
3
9
8
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]
3
4
[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-
V
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
X
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
D
p
p
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()゜
j
-eg-
2
-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-
X
pr2wχ9]
plE【2w->り》】1
1rdquoMI
-E唇-
゜(2WdegO`92Wi
ミplE)rsquo゛p[2w-xg]
pl-《2w+x)】)゜91
Q
s哺
(n
L1)
1
paziipEJoz
1 2 3
-
Normalizedscanningdistancex
哺
0 5
M)DUd|UOISコ|}Ppazneaijoz
0
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
て
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-
W
Fig5-5
5
Q‐rsquoQ]
loline
11(52
2
ち5
Z
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
y
へ
`ヽ
`lsquolブjl
ゝゝjφ1
2
0h白contactム
ヤ
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
5
2
゜1(il
四a3
U」
5
-01
Ddziieujjoz
2
0
゛D=1Z5cm2s巡付
1 03
orini=-
にuarrヤuarr
i
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
士
darrレ
よ
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
1
JOoline1
―
Ig3paziieuijoz
Fig5-7
(a)
1
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
1
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]
3
4
[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
D
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=
1
-egeD
dp
-dxχ=0
=1-
<
こ)
3Wく
一一
Xく一一
(5-A7)
(5-A8)
X』
W
-80-
(5-A9)
Ⅶ
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
X
Schematicviewofeχperimentalconditionsand
definitionoftheco-ordinatesystem
-84-
Electronbeam
SOlyScanningtrack_xj
ズニに匹二oline-一一゛
lsquo9surface
lL-__--ang__helliphellip_
|`1
I
丑昌之
9gπLaf ―K
gdof
E
(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
1
U2
Cχ310-rsquo
山5
D
ト2
い
10lsquo3
velocitysis
35225N
(Eu
J
一))
^
n
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
g
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
5
`ヽ`10khtt
pwww
kHz
て
三
千
名
`ωで=01
2
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
|
-
〆
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-
o
「―」)畠一
uiMSaseudpazneaijoz
Fig6-5
rsquo0
1
1
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
ぶ
大
言二分ヽ同r〔2μ(ldquoμ
゛1)rsquo1
5primeacute
2
cべ1251251cap25
(
dφ
-
dx
煙
-
)=(c
TTfr TTf)ldquo゛十(c
yでワ
)rsquo゛
D
-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
0
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
X
Experimental
methodinp-(p=10
200
(μm)
resultsofthephaseshift
Ωcm)andn-type(p=01ncm)Si
-94-
rdquoolinersquordquooline`rsquolsquorsquoolinerdquordquoolinersquo50kHz
Vadeg30kVZ
乙
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]
7
8
9
[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
1
-
Heattreatmenttimet(min)
Diffusionlengthaftertheheattreatments
forvarioustimelengthsrangingfromlt0120minutesat1000degCOpenandsolidcirclesare
forthecasesindry02andArrespectivelyOriginaldiffusionlengthbeforeannealingis80pm
-100-
5ohellipumlindryO2
uml゜umlinArat1000degC
0
ol
5
0
12510251002
-
-
- W ゝ
rsquo _ l - ~ ヽ jS j - -
』
磨 卜
Fig7-2
(a)
(c)
S
ぐ
rarr100Mm
4
ぶミ
ぎ
1
ゝ
卜`
r-^
rsquo
1Is
≪バ
rdquorsquo‐゛t
rsquo
grバ4≪
rsquo1
ゝ
Surfacefaultsrevealedby
usingSirtletchantSamples(a)
wereannealedindryoat1000
and120minutesrespectively
-101-
囁
い゛フバrdquo
゛para
`i
(b)
ゝ
¥
i
(d)
ゝ
permilご}
゜
->嗜
-゛
寸
か
rsquo
III
`ヽご
いい
I
一J
J
t七
~貿で
ぜ
rsquo
j
゛`1
鴫ヽ
rsquoq
-≪
ゝく
タ
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
4
5
6
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
3
4
[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
`
メ
{
LISTOFPUBLICAT工ONS
I
[1]
[21
[3]
[4]
[5]
[6]
Papers
H
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-
J
皿
[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-
1
j
- page1
- page2
- page3
- page4
- page5
- page6
- page7
- page8
- page9
- page10
- page11
- page12
- page13
- page14
- page15
- page16
- page17
- page18
- page19
- page20
- page21
- page22
- page23
- page24
- page25
- page26
- page27
- page28
- page29
- page30
- page31
- page32
- page33
- page34
- page35
- page36
- page37
- page38
- page39
- page40
- page41
- page42
- page43
- page44
- page45
- page46
- page47
- page48
- page49
- page50
- page51
- page52
- page53
- page54
- page55
- page56
- page57
- page58
- page59
- page60
- page61
- page62
- page63
- page64
- page65
- page66
- page67
- page68
- page69
- page70
- page71
- page72
- page73
- page74
- page75
- page76
- page77
- page78
- page79
- page80
- page81
- page82
- page83
- page84
- page85
- page86
- page87
- page88
- page89
- page90
- page91
- page92
- page93
- page94
- page95
- page96
- page97
- page98
- page99
- page100
- page101
- page102
- page103
- page104
- page105
- page106
- page107
- page108
- page109
- page110
- page111
- page112
- page113
- page114
- page115
- page116
- page117
- page118
- page119
- page120
-
いvl}丿
CHARACTERIZATIONOFSEMICONDUCTORS
BY
ELECTRONBEAMINDUCEDCURRENT
BY
TAKASHIFUYUKI
JANUARY1981
DEPARTMENTOFELECTRONICS
KYOTOUNIVERSITY
KYOTOJAPAN
j
犬CHARACTERIZATIONOFSEMICONDUCTORS
IBY
ELECTRONBEAMINDUCEDCURRENT
BY
TAKASHIFUYUKI
JANUARY1981
DOC
1981
1
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-
S
hellipJVi_--Wrsquordquo>>-trsquomjrsquordquordquo^>-≫^
f1
t
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
I
江
Ⅲ
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
Ⅵ
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
C
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-
k
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-
W
rdquod
wm
Xxx
g
g
χy
ZZ
m
n
np
Pau
^GaAs
I
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-
p
n
Fig1-1
type
type
Primaryelectrbe≪m
^^trrttDepletionlayer
Electron-hotep弗i「6gerwrationregion
Primaryelectronbeam
rArrScanningdirection
(A)
-
(B)
Principalconfigurationstomeasurethe
electronbeaminducedcurrent(EBIC)
(A)normalincidencemethod
(B)linescanmethod
-2-
-
ぶ
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
十
--
-- - -
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-
皿
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
i
Numberofgeneratedcarriers
Fig2-1Schematicviewofexperimentalconditions
jusingSchottkydiodesMetalthicknessis
wanddepletionlayerwidthiswright-handillustぷふこsthedぶdosefunctionRandR
-givethemaxiraum
andextraporaiedmelectrSnolinerangerespectively
-14-
0generatedcarrier
に_---___1
我_______Iuarrヽ
y重ダ
Z
1ごpermil
氷
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
t
χ
`Makarov20χ
----Wittry
χhelliphelliphellipKanaya
11S
15
゛S≒
rsquoχ≒
χrsquo
10trsquolsquo
卜卜゜χ゛
1
卜ゝrsquo
05χrsquo゛rsquoゝ
ゝrsquoゝ1
ゝゝrsquoゝゝ
ゝゝ
00
50
D
GaAso々
5
タグrsquo
2
万
1
ぶ
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
ぐ
二ぷ芯t
15へ
゜¥レ臨べhellip
hellip
10rsquoS゛lsquoNhellip
helliphellip
05
hellip
helliphellip
1helliphellip
hellip
005
芦
o
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
-
十
- -
-- - - - -
- - - -
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
>
ざ
u1C
larrl
0E
2
き
(
501
-
Figure2-6showsthecollectionefficiencyinSiusing
thefourdifferentmodelsofMakarovWittryKanayaandEverhart
bythesolidbrokendottedanddashedanddottedlines
respectivelyThevalueofLIs1005020and10umfrom
uppert0lowergroupofcurvesrespectivelyThevaluesofW
m
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
2
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]
3
4
[5]
WCzajaJApplPhys374236(1966)
JFBresserdquoScanningElectronMicroscopy71972partlrdquo
(iiTRiChicago111)p105
CJWuandDBWittryJApplPhys丘旦2827(1978)
KKanayaandSOkayamaJPhysDApplPhys
543(1972)-
口EPosslnandCGKirkpatrickJApplPhys
5^4033(1979)
[6]TEEverhartandPHHoffJApplPhys
425837(1971)
7
8
9
[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-
Ⅲ
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
Z
Schematicviewof
anddefinitionsofthe
-32-
experimentalconditionscoordinatesystems
Electronbeam
Surfacecross-sectic
O゛9χ
Schottky哨Rbarrier
y
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
1
1
2
Normalizedscanningdistancex
(a)
Fig3-2
Fig3-3
U
四
S
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
S
Og<ao
2
161
S>0
S
21
Idrsquo
S5
2
10^
550
2
1必12345
135
sc^-at
SO⑤
バ宍
1012345
112345
SPg≪10
2
161
S
2
162S=0
SI
1
1(i3
5
2
1(541235
comparedwiththediffusionlengththeboundaryconditionsare
D
p
p
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=
j
-eg
+
2
一
丁T
4oo
int
Dg
馴D戸
0
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
d
g
11-
Schematicviewofelectronpenetrationisthemaximumenergydissipationdepth
a(W)
00000
1CMCO<rm
d(ym)
rdquo047
149
291
in<yi
vDVO
4VO
R(um)
-
100
295
5
9
13
74
20
2
Valuesofthecenterdgofthegeneration
volumeandtheradiusRinSiforseveralvalues
ofacceleratingvoltagevarsquo
-38-
IElectronbeam
O335
j
S`」「fdegce
uarrで0559j
10゛」
helliphelliphelliphelliphellip
上
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
1
pdznpoi」oz
1
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
2
4
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
1
1
1
-
1020304050(pm)
Scanningdistancex
Fig3-7
Experimentalresultsfor
sampleA(p=lf2cin)whereL=
8μmandS=20Fullcurves
arethetheoreticalrsquoones
1
5
11(il
>P≪4<N1≪CM<Pq
1 1
3193paziipujjoZ
5
2
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
2
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
5
6
[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-
E
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
1
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-
心
helliphellipl
l
]]1A
Ee
ビゲヤ
2
12
ss50
4
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
U
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
ビ
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
-
ド
ー い゛I
い
゛゛
w
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
j
②
五゛
゛
`
olinelo
jV
ズごy
こ
l
x
1
23
times1
l
U
5
GaAだj
(
j73C4Electron
L=07μmEbeam
2Sdeg20χ
1rsquo`
5
゛x
鹸
ya(W
2゛Va=30W
2_JE201
4一一―54013
5≒
脅χ
21`f
3
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-
W
Normalincidence Line scan
V(kv)a
E(eV)GaAsCSndoped)pc
GaAs(Tedoped)
5-50
41
39
4
0
14
3 9
30
3
3
9
8
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]
3
4
[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-
V
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
X
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
D
p
p
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()゜
j
-eg-
2
-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-
X
pr2wχ9]
plE【2w->り》】1
1rdquoMI
-E唇-
゜(2WdegO`92Wi
ミplE)rsquo゛p[2w-xg]
pl-《2w+x)】)゜91
Q
s哺
(n
L1)
1
paziipEJoz
1 2 3
-
Normalizedscanningdistancex
哺
0 5
M)DUd|UOISコ|}Ppazneaijoz
0
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
て
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-
W
Fig5-5
5
Q‐rsquoQ]
loline
11(52
2
ち5
Z
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
y
へ
`ヽ
`lsquolブjl
ゝゝjφ1
2
0h白contactム
ヤ
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
5
2
゜1(il
四a3
U」
5
-01
Ddziieujjoz
2
0
゛D=1Z5cm2s巡付
1 03
orini=-
にuarrヤuarr
i
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
士
darrレ
よ
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
1
JOoline1
―
Ig3paziieuijoz
Fig5-7
(a)
1
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
1
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]
3
4
[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
D
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=
1
-egeD
dp
-dxχ=0
=1-
<
こ)
3Wく
一一
Xく一一
(5-A7)
(5-A8)
X』
W
-80-
(5-A9)
Ⅶ
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
X
Schematicviewofeχperimentalconditionsand
definitionoftheco-ordinatesystem
-84-
Electronbeam
SOlyScanningtrack_xj
ズニに匹二oline-一一゛
lsquo9surface
lL-__--ang__helliphellip_
|`1
I
丑昌之
9gπLaf ―K
gdof
E
(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
1
U2
Cχ310-rsquo
山5
D
ト2
い
10lsquo3
velocitysis
35225N
(Eu
J
一))
^
n
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
g
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
5
`ヽ`10khtt
pwww
kHz
て
三
千
名
`ωで=01
2
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
|
-
〆
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-
o
「―」)畠一
uiMSaseudpazneaijoz
Fig6-5
rsquo0
1
1
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
ぶ
大
言二分ヽ同r〔2μ(ldquoμ
゛1)rsquo1
5primeacute
2
cべ1251251cap25
(
dφ
-
dx
煙
-
)=(c
TTfr TTf)ldquo゛十(c
yでワ
)rsquo゛
D
-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
0
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
X
Experimental
methodinp-(p=10
200
(μm)
resultsofthephaseshift
Ωcm)andn-type(p=01ncm)Si
-94-
rdquoolinersquordquooline`rsquolsquorsquoolinerdquordquoolinersquo50kHz
Vadeg30kVZ
乙
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]
7
8
9
[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
1
-
Heattreatmenttimet(min)
Diffusionlengthaftertheheattreatments
forvarioustimelengthsrangingfromlt0120minutesat1000degCOpenandsolidcirclesare
forthecasesindry02andArrespectivelyOriginaldiffusionlengthbeforeannealingis80pm
-100-
5ohellipumlindryO2
uml゜umlinArat1000degC
0
ol
5
0
12510251002
-
-
- W ゝ
rsquo _ l - ~ ヽ jS j - -
』
磨 卜
Fig7-2
(a)
(c)
S
ぐ
rarr100Mm
4
ぶミ
ぎ
1
ゝ
卜`
r-^
rsquo
1Is
≪バ
rdquorsquo‐゛t
rsquo
grバ4≪
rsquo1
ゝ
Surfacefaultsrevealedby
usingSirtletchantSamples(a)
wereannealedindryoat1000
and120minutesrespectively
-101-
囁
い゛フバrdquo
゛para
`i
(b)
ゝ
¥
i
(d)
ゝ
permilご}
゜
->嗜
-゛
寸
か
rsquo
III
`ヽご
いい
I
一J
J
t七
~貿で
ぜ
rsquo
j
゛`1
鴫ヽ
rsquoq
-≪
ゝく
タ
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
4
5
6
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
3
4
[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
`
メ
{
LISTOFPUBLICAT工ONS
I
[1]
[21
[3]
[4]
[5]
[6]
Papers
H
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-
J
皿
[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-
1
j
- page1
- page2
- page3
- page4
- page5
- page6
- page7
- page8
- page9
- page10
- page11
- page12
- page13
- page14
- page15
- page16
- page17
- page18
- page19
- page20
- page21
- page22
- page23
- page24
- page25
- page26
- page27
- page28
- page29
- page30
- page31
- page32
- page33
- page34
- page35
- page36
- page37
- page38
- page39
- page40
- page41
- page42
- page43
- page44
- page45
- page46
- page47
- page48
- page49
- page50
- page51
- page52
- page53
- page54
- page55
- page56
- page57
- page58
- page59
- page60
- page61
- page62
- page63
- page64
- page65
- page66
- page67
- page68
- page69
- page70
- page71
- page72
- page73
- page74
- page75
- page76
- page77
- page78
- page79
- page80
- page81
- page82
- page83
- page84
- page85
- page86
- page87
- page88
- page89
- page90
- page91
- page92
- page93
- page94
- page95
- page96
- page97
- page98
- page99
- page100
- page101
- page102
- page103
- page104
- page105
- page106
- page107
- page108
- page109
- page110
- page111
- page112
- page113
- page114
- page115
- page116
- page117
- page118
- page119
- page120
-
j
犬CHARACTERIZATIONOFSEMICONDUCTORS
IBY
ELECTRONBEAMINDUCEDCURRENT
BY
TAKASHIFUYUKI
JANUARY1981
DOC
1981
1
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-
S
hellipJVi_--Wrsquordquo>>-trsquomjrsquordquordquo^>-≫^
f1
t
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
I
江
Ⅲ
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
Ⅵ
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
C
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-
k
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-
W
rdquod
wm
Xxx
g
g
χy
ZZ
m
n
np
Pau
^GaAs
I
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-
p
n
Fig1-1
type
type
Primaryelectrbe≪m
^^trrttDepletionlayer
Electron-hotep弗i「6gerwrationregion
Primaryelectronbeam
rArrScanningdirection
(A)
-
(B)
Principalconfigurationstomeasurethe
electronbeaminducedcurrent(EBIC)
(A)normalincidencemethod
(B)linescanmethod
-2-
-
ぶ
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
十
--
-- - -
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-
皿
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
i
Numberofgeneratedcarriers
Fig2-1Schematicviewofexperimentalconditions
jusingSchottkydiodesMetalthicknessis
wanddepletionlayerwidthiswright-handillustぷふこsthedぶdosefunctionRandR
-givethemaxiraum
andextraporaiedmelectrSnolinerangerespectively
-14-
0generatedcarrier
に_---___1
我_______Iuarrヽ
y重ダ
Z
1ごpermil
氷
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
t
χ
`Makarov20χ
----Wittry
χhelliphelliphellipKanaya
11S
15
゛S≒
rsquoχ≒
χrsquo
10trsquolsquo
卜卜゜χ゛
1
卜ゝrsquo
05χrsquo゛rsquoゝ
ゝrsquoゝ1
ゝゝrsquoゝゝ
ゝゝ
00
50
D
GaAso々
5
タグrsquo
2
万
1
ぶ
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
ぐ
二ぷ芯t
15へ
゜¥レ臨べhellip
hellip
10rsquoS゛lsquoNhellip
helliphellip
05
hellip
helliphellip
1helliphellip
hellip
005
芦
o
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
-
十
- -
-- - - - -
- - - -
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
>
ざ
u1C
larrl
0E
2
き
(
501
-
Figure2-6showsthecollectionefficiencyinSiusing
thefourdifferentmodelsofMakarovWittryKanayaandEverhart
bythesolidbrokendottedanddashedanddottedlines
respectivelyThevalueofLIs1005020and10umfrom
uppert0lowergroupofcurvesrespectivelyThevaluesofW
m
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
2
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]
3
4
[5]
WCzajaJApplPhys374236(1966)
JFBresserdquoScanningElectronMicroscopy71972partlrdquo
(iiTRiChicago111)p105
CJWuandDBWittryJApplPhys丘旦2827(1978)
KKanayaandSOkayamaJPhysDApplPhys
543(1972)-
口EPosslnandCGKirkpatrickJApplPhys
5^4033(1979)
[6]TEEverhartandPHHoffJApplPhys
425837(1971)
7
8
9
[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-
Ⅲ
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
Z
Schematicviewof
anddefinitionsofthe
-32-
experimentalconditionscoordinatesystems
Electronbeam
Surfacecross-sectic
O゛9χ
Schottky哨Rbarrier
y
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
1
1
2
Normalizedscanningdistancex
(a)
Fig3-2
Fig3-3
U
四
S
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
S
Og<ao
2
161
S>0
S
21
Idrsquo
S5
2
10^
550
2
1必12345
135
sc^-at
SO⑤
バ宍
1012345
112345
SPg≪10
2
161
S
2
162S=0
SI
1
1(i3
5
2
1(541235
comparedwiththediffusionlengththeboundaryconditionsare
D
p
p
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=
j
-eg
+
2
一
丁T
4oo
int
Dg
馴D戸
0
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
d
g
11-
Schematicviewofelectronpenetrationisthemaximumenergydissipationdepth
a(W)
00000
1CMCO<rm
d(ym)
rdquo047
149
291
in<yi
vDVO
4VO
R(um)
-
100
295
5
9
13
74
20
2
Valuesofthecenterdgofthegeneration
volumeandtheradiusRinSiforseveralvalues
ofacceleratingvoltagevarsquo
-38-
IElectronbeam
O335
j
S`」「fdegce
uarrで0559j
10゛」
helliphelliphelliphelliphellip
上
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
1
pdznpoi」oz
1
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
2
4
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
1
1
1
-
1020304050(pm)
Scanningdistancex
Fig3-7
Experimentalresultsfor
sampleA(p=lf2cin)whereL=
8μmandS=20Fullcurves
arethetheoreticalrsquoones
1
5
11(il
>P≪4<N1≪CM<Pq
1 1
3193paziipujjoZ
5
2
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
2
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
5
6
[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-
E
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
1
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-
心
helliphellipl
l
]]1A
Ee
ビゲヤ
2
12
ss50
4
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
U
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
ビ
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
-
ド
ー い゛I
い
゛゛
w
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
j
②
五゛
゛
`
olinelo
jV
ズごy
こ
l
x
1
23
times1
l
U
5
GaAだj
(
j73C4Electron
L=07μmEbeam
2Sdeg20χ
1rsquo`
5
゛x
鹸
ya(W
2゛Va=30W
2_JE201
4一一―54013
5≒
脅χ
21`f
3
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-
W
Normalincidence Line scan
V(kv)a
E(eV)GaAsCSndoped)pc
GaAs(Tedoped)
5-50
41
39
4
0
14
3 9
30
3
3
9
8
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]
3
4
[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-
V
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
X
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
D
p
p
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()゜
j
-eg-
2
-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-
X
pr2wχ9]
plE【2w->り》】1
1rdquoMI
-E唇-
゜(2WdegO`92Wi
ミplE)rsquo゛p[2w-xg]
pl-《2w+x)】)゜91
Q
s哺
(n
L1)
1
paziipEJoz
1 2 3
-
Normalizedscanningdistancex
哺
0 5
M)DUd|UOISコ|}Ppazneaijoz
0
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
て
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-
W
Fig5-5
5
Q‐rsquoQ]
loline
11(52
2
ち5
Z
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
y
へ
`ヽ
`lsquolブjl
ゝゝjφ1
2
0h白contactム
ヤ
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
5
2
゜1(il
四a3
U」
5
-01
Ddziieujjoz
2
0
゛D=1Z5cm2s巡付
1 03
orini=-
にuarrヤuarr
i
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
士
darrレ
よ
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
1
JOoline1
―
Ig3paziieuijoz
Fig5-7
(a)
1
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
1
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]
3
4
[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
D
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=
1
-egeD
dp
-dxχ=0
=1-
<
こ)
3Wく
一一
Xく一一
(5-A7)
(5-A8)
X』
W
-80-
(5-A9)
Ⅶ
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
X
Schematicviewofeχperimentalconditionsand
definitionoftheco-ordinatesystem
-84-
Electronbeam
SOlyScanningtrack_xj
ズニに匹二oline-一一゛
lsquo9surface
lL-__--ang__helliphellip_
|`1
I
丑昌之
9gπLaf ―K
gdof
E
(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
1
U2
Cχ310-rsquo
山5
D
ト2
い
10lsquo3
velocitysis
35225N
(Eu
J
一))
^
n
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
g
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
5
`ヽ`10khtt
pwww
kHz
て
三
千
名
`ωで=01
2
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
|
-
〆
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-
o
「―」)畠一
uiMSaseudpazneaijoz
Fig6-5
rsquo0
1
1
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
ぶ
大
言二分ヽ同r〔2μ(ldquoμ
゛1)rsquo1
5primeacute
2
cべ1251251cap25
(
dφ
-
dx
煙
-
)=(c
TTfr TTf)ldquo゛十(c
yでワ
)rsquo゛
D
-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
0
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
X
Experimental
methodinp-(p=10
200
(μm)
resultsofthephaseshift
Ωcm)andn-type(p=01ncm)Si
-94-
rdquoolinersquordquooline`rsquolsquorsquoolinerdquordquoolinersquo50kHz
Vadeg30kVZ
乙
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]
7
8
9
[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
1
-
Heattreatmenttimet(min)
Diffusionlengthaftertheheattreatments
forvarioustimelengthsrangingfromlt0120minutesat1000degCOpenandsolidcirclesare
forthecasesindry02andArrespectivelyOriginaldiffusionlengthbeforeannealingis80pm
-100-
5ohellipumlindryO2
uml゜umlinArat1000degC
0
ol
5
0
12510251002
-
-
- W ゝ
rsquo _ l - ~ ヽ jS j - -
』
磨 卜
Fig7-2
(a)
(c)
S
ぐ
rarr100Mm
4
ぶミ
ぎ
1
ゝ
卜`
r-^
rsquo
1Is
≪バ
rdquorsquo‐゛t
rsquo
grバ4≪
rsquo1
ゝ
Surfacefaultsrevealedby
usingSirtletchantSamples(a)
wereannealedindryoat1000
and120minutesrespectively
-101-
囁
い゛フバrdquo
゛para
`i
(b)
ゝ
¥
i
(d)
ゝ
permilご}
゜
->嗜
-゛
寸
か
rsquo
III
`ヽご
いい
I
一J
J
t七
~貿で
ぜ
rsquo
j
゛`1
鴫ヽ
rsquoq
-≪
ゝく
タ
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
4
5
6
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
3
4
[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
`
メ
{
LISTOFPUBLICAT工ONS
I
[1]
[21
[3]
[4]
[5]
[6]
Papers
H
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-
J
皿
[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-
1
j
- page1
- page2
- page3
- page4
- page5
- page6
- page7
- page8
- page9
- page10
- page11
- page12
- page13
- page14
- page15
- page16
- page17
- page18
- page19
- page20
- page21
- page22
- page23
- page24
- page25
- page26
- page27
- page28
- page29
- page30
- page31
- page32
- page33
- page34
- page35
- page36
- page37
- page38
- page39
- page40
- page41
- page42
- page43
- page44
- page45
- page46
- page47
- page48
- page49
- page50
- page51
- page52
- page53
- page54
- page55
- page56
- page57
- page58
- page59
- page60
- page61
- page62
- page63
- page64
- page65
- page66
- page67
- page68
- page69
- page70
- page71
- page72
- page73
- page74
- page75
- page76
- page77
- page78
- page79
- page80
- page81
- page82
- page83
- page84
- page85
- page86
- page87
- page88
- page89
- page90
- page91
- page92
- page93
- page94
- page95
- page96
- page97
- page98
- page99
- page100
- page101
- page102
- page103
- page104
- page105
- page106
- page107
- page108
- page109
- page110
- page111
- page112
- page113
- page114
- page115
- page116
- page117
- page118
- page119
- page120
-
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-
S
hellipJVi_--Wrsquordquo>>-trsquomjrsquordquordquo^>-≫^
f1
t
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
I
江
Ⅲ
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
Ⅵ
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
C
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-
k
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-
W
rdquod
wm
Xxx
g
g
χy
ZZ
m
n
np
Pau
^GaAs
I
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-
p
n
Fig1-1
type
type
Primaryelectrbe≪m
^^trrttDepletionlayer
Electron-hotep弗i「6gerwrationregion
Primaryelectronbeam
rArrScanningdirection
(A)
-
(B)
Principalconfigurationstomeasurethe
electronbeaminducedcurrent(EBIC)
(A)normalincidencemethod
(B)linescanmethod
-2-
-
ぶ
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
十
--
-- - -
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-
皿
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
i
Numberofgeneratedcarriers
Fig2-1Schematicviewofexperimentalconditions
jusingSchottkydiodesMetalthicknessis
wanddepletionlayerwidthiswright-handillustぷふこsthedぶdosefunctionRandR
-givethemaxiraum
andextraporaiedmelectrSnolinerangerespectively
-14-
0generatedcarrier
に_---___1
我_______Iuarrヽ
y重ダ
Z
1ごpermil
氷
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
t
χ
`Makarov20χ
----Wittry
χhelliphelliphellipKanaya
11S
15
゛S≒
rsquoχ≒
χrsquo
10trsquolsquo
卜卜゜χ゛
1
卜ゝrsquo
05χrsquo゛rsquoゝ
ゝrsquoゝ1
ゝゝrsquoゝゝ
ゝゝ
00
50
D
GaAso々
5
タグrsquo
2
万
1
ぶ
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
ぐ
二ぷ芯t
15へ
゜¥レ臨べhellip
hellip
10rsquoS゛lsquoNhellip
helliphellip
05
hellip
helliphellip
1helliphellip
hellip
005
芦
o
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
-
十
- -
-- - - - -
- - - -
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
>
ざ
u1C
larrl
0E
2
き
(
501
-
Figure2-6showsthecollectionefficiencyinSiusing
thefourdifferentmodelsofMakarovWittryKanayaandEverhart
bythesolidbrokendottedanddashedanddottedlines
respectivelyThevalueofLIs1005020and10umfrom
uppert0lowergroupofcurvesrespectivelyThevaluesofW
m
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
2
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]
3
4
[5]
WCzajaJApplPhys374236(1966)
JFBresserdquoScanningElectronMicroscopy71972partlrdquo
(iiTRiChicago111)p105
CJWuandDBWittryJApplPhys丘旦2827(1978)
KKanayaandSOkayamaJPhysDApplPhys
543(1972)-
口EPosslnandCGKirkpatrickJApplPhys
5^4033(1979)
[6]TEEverhartandPHHoffJApplPhys
425837(1971)
7
8
9
[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-
Ⅲ
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
Z
Schematicviewof
anddefinitionsofthe
-32-
experimentalconditionscoordinatesystems
Electronbeam
Surfacecross-sectic
O゛9χ
Schottky哨Rbarrier
y
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
1
1
2
Normalizedscanningdistancex
(a)
Fig3-2
Fig3-3
U
四
S
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
S
Og<ao
2
161
S>0
S
21
Idrsquo
S5
2
10^
550
2
1必12345
135
sc^-at
SO⑤
バ宍
1012345
112345
SPg≪10
2
161
S
2
162S=0
SI
1
1(i3
5
2
1(541235
comparedwiththediffusionlengththeboundaryconditionsare
D
p
p
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=
j
-eg
+
2
一
丁T
4oo
int
Dg
馴D戸
0
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
d
g
11-
Schematicviewofelectronpenetrationisthemaximumenergydissipationdepth
a(W)
00000
1CMCO<rm
d(ym)
rdquo047
149
291
in<yi
vDVO
4VO
R(um)
-
100
295
5
9
13
74
20
2
Valuesofthecenterdgofthegeneration
volumeandtheradiusRinSiforseveralvalues
ofacceleratingvoltagevarsquo
-38-
IElectronbeam
O335
j
S`」「fdegce
uarrで0559j
10゛」
helliphelliphelliphelliphellip
上
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
1
pdznpoi」oz
1
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
2
4
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
1
1
1
-
1020304050(pm)
Scanningdistancex
Fig3-7
Experimentalresultsfor
sampleA(p=lf2cin)whereL=
8μmandS=20Fullcurves
arethetheoreticalrsquoones
1
5
11(il
>P≪4<N1≪CM<Pq
1 1
3193paziipujjoZ
5
2
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
2
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
5
6
[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-
E
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
1
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-
心
helliphellipl
l
]]1A
Ee
ビゲヤ
2
12
ss50
4
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
U
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
ビ
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
-
ド
ー い゛I
い
゛゛
w
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
j
②
五゛
゛
`
olinelo
jV
ズごy
こ
l
x
1
23
times1
l
U
5
GaAだj
(
j73C4Electron
L=07μmEbeam
2Sdeg20χ
1rsquo`
5
゛x
鹸
ya(W
2゛Va=30W
2_JE201
4一一―54013
5≒
脅χ
21`f
3
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-
W
Normalincidence Line scan
V(kv)a
E(eV)GaAsCSndoped)pc
GaAs(Tedoped)
5-50
41
39
4
0
14
3 9
30
3
3
9
8
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]
3
4
[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-
V
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
X
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
D
p
p
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()゜
j
-eg-
2
-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-
X
pr2wχ9]
plE【2w->り》】1
1rdquoMI
-E唇-
゜(2WdegO`92Wi
ミplE)rsquo゛p[2w-xg]
pl-《2w+x)】)゜91
Q
s哺
(n
L1)
1
paziipEJoz
1 2 3
-
Normalizedscanningdistancex
哺
0 5
M)DUd|UOISコ|}Ppazneaijoz
0
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
て
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-
W
Fig5-5
5
Q‐rsquoQ]
loline
11(52
2
ち5
Z
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
y
へ
`ヽ
`lsquolブjl
ゝゝjφ1
2
0h白contactム
ヤ
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
5
2
゜1(il
四a3
U」
5
-01
Ddziieujjoz
2
0
゛D=1Z5cm2s巡付
1 03
orini=-
にuarrヤuarr
i
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
士
darrレ
よ
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
1
JOoline1
―
Ig3paziieuijoz
Fig5-7
(a)
1
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
1
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]
3
4
[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
D
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=
1
-egeD
dp
-dxχ=0
=1-
<
こ)
3Wく
一一
Xく一一
(5-A7)
(5-A8)
X』
W
-80-
(5-A9)
Ⅶ
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
X
Schematicviewofeχperimentalconditionsand
definitionoftheco-ordinatesystem
-84-
Electronbeam
SOlyScanningtrack_xj
ズニに匹二oline-一一゛
lsquo9surface
lL-__--ang__helliphellip_
|`1
I
丑昌之
9gπLaf ―K
gdof
E
(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
1
U2
Cχ310-rsquo
山5
D
ト2
い
10lsquo3
velocitysis
35225N
(Eu
J
一))
^
n
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
g
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
5
`ヽ`10khtt
pwww
kHz
て
三
千
名
`ωで=01
2
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
|
-
〆
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-
o
「―」)畠一
uiMSaseudpazneaijoz
Fig6-5
rsquo0
1
1
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
ぶ
大
言二分ヽ同r〔2μ(ldquoμ
゛1)rsquo1
5primeacute
2
cべ1251251cap25
(
dφ
-
dx
煙
-
)=(c
TTfr TTf)ldquo゛十(c
yでワ
)rsquo゛
D
-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
0
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
X
Experimental
methodinp-(p=10
200
(μm)
resultsofthephaseshift
Ωcm)andn-type(p=01ncm)Si
-94-
rdquoolinersquordquooline`rsquolsquorsquoolinerdquordquoolinersquo50kHz
Vadeg30kVZ
乙
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]
7
8
9
[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
1
-
Heattreatmenttimet(min)
Diffusionlengthaftertheheattreatments
forvarioustimelengthsrangingfromlt0120minutesat1000degCOpenandsolidcirclesare
forthecasesindry02andArrespectivelyOriginaldiffusionlengthbeforeannealingis80pm
-100-
5ohellipumlindryO2
uml゜umlinArat1000degC
0
ol
5
0
12510251002
-
-
- W ゝ
rsquo _ l - ~ ヽ jS j - -
』
磨 卜
Fig7-2
(a)
(c)
S
ぐ
rarr100Mm
4
ぶミ
ぎ
1
ゝ
卜`
r-^
rsquo
1Is
≪バ
rdquorsquo‐゛t
rsquo
grバ4≪
rsquo1
ゝ
Surfacefaultsrevealedby
usingSirtletchantSamples(a)
wereannealedindryoat1000
and120minutesrespectively
-101-
囁
い゛フバrdquo
゛para
`i
(b)
ゝ
¥
i
(d)
ゝ
permilご}
゜
->嗜
-゛
寸
か
rsquo
III
`ヽご
いい
I
一J
J
t七
~貿で
ぜ
rsquo
j
゛`1
鴫ヽ
rsquoq
-≪
ゝく
タ
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
4
5
6
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
3
4
[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
`
メ
{
LISTOFPUBLICAT工ONS
I
[1]
[21
[3]
[4]
[5]
[6]
Papers
H
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-
J
皿
[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-
1
j
- page1
- page2
- page3
- page4
- page5
- page6
- page7
- page8
- page9
- page10
- page11
- page12
- page13
- page14
- page15
- page16
- page17
- page18
- page19
- page20
- page21
- page22
- page23
- page24
- page25
- page26
- page27
- page28
- page29
- page30
- page31
- page32
- page33
- page34
- page35
- page36
- page37
- page38
- page39
- page40
- page41
- page42
- page43
- page44
- page45
- page46
- page47
- page48
- page49
- page50
- page51
- page52
- page53
- page54
- page55
- page56
- page57
- page58
- page59
- page60
- page61
- page62
- page63
- page64
- page65
- page66
- page67
- page68
- page69
- page70
- page71
- page72
- page73
- page74
- page75
- page76
- page77
- page78
- page79
- page80
- page81
- page82
- page83
- page84
- page85
- page86
- page87
- page88
- page89
- page90
- page91
- page92
- page93
- page94
- page95
- page96
- page97
- page98
- page99
- page100
- page101
- page102
- page103
- page104
- page105
- page106
- page107
- page108
- page109
- page110
- page111
- page112
- page113
- page114
- page115
- page116
- page117
- page118
- page119
- page120
-
Thephysicalpropertiessuchasthediffusionlengthin
thesmallselectedareascouldbecharacterizedbyEBIC
consideringthethree-dinensionalgenerationdistributionbyan
electronbeamandthesampledimensionsExperimentalresults
inSiandGaAsshowedgoodagreementwiththetheoryandthe
generationdistributionsinSiandGaAswererevealedWitニh
experiments
一旦-
S
hellipJVi_--Wrsquordquo>>-trsquomjrsquordquordquo^>-≫^
f1
t
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
I
江
Ⅲ
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
Ⅵ
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
C
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-
k
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-
W
rdquod
wm
Xxx
g
g
χy
ZZ
m
n
np
Pau
^GaAs
I
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-
p
n
Fig1-1
type
type
Primaryelectrbe≪m
^^trrttDepletionlayer
Electron-hotep弗i「6gerwrationregion
Primaryelectronbeam
rArrScanningdirection
(A)
-
(B)
Principalconfigurationstomeasurethe
electronbeaminducedcurrent(EBIC)
(A)normalincidencemethod
(B)linescanmethod
-2-
-
ぶ
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
十
--
-- - -
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-
皿
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
i
Numberofgeneratedcarriers
Fig2-1Schematicviewofexperimentalconditions
jusingSchottkydiodesMetalthicknessis
wanddepletionlayerwidthiswright-handillustぷふこsthedぶdosefunctionRandR
-givethemaxiraum
andextraporaiedmelectrSnolinerangerespectively
-14-
0generatedcarrier
に_---___1
我_______Iuarrヽ
y重ダ
Z
1ごpermil
氷
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
t
χ
`Makarov20χ
----Wittry
χhelliphelliphellipKanaya
11S
15
゛S≒
rsquoχ≒
χrsquo
10trsquolsquo
卜卜゜χ゛
1
卜ゝrsquo
05χrsquo゛rsquoゝ
ゝrsquoゝ1
ゝゝrsquoゝゝ
ゝゝ
00
50
D
GaAso々
5
タグrsquo
2
万
1
ぶ
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
ぐ
二ぷ芯t
15へ
゜¥レ臨べhellip
hellip
10rsquoS゛lsquoNhellip
helliphellip
05
hellip
helliphellip
1helliphellip
hellip
005
芦
o
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
-
十
- -
-- - - - -
- - - -
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
>
ざ
u1C
larrl
0E
2
き
(
501
-
Figure2-6showsthecollectionefficiencyinSiusing
thefourdifferentmodelsofMakarovWittryKanayaandEverhart
bythesolidbrokendottedanddashedanddottedlines
respectivelyThevalueofLIs1005020and10umfrom
uppert0lowergroupofcurvesrespectivelyThevaluesofW
m
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
2
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]
3
4
[5]
WCzajaJApplPhys374236(1966)
JFBresserdquoScanningElectronMicroscopy71972partlrdquo
(iiTRiChicago111)p105
CJWuandDBWittryJApplPhys丘旦2827(1978)
KKanayaandSOkayamaJPhysDApplPhys
543(1972)-
口EPosslnandCGKirkpatrickJApplPhys
5^4033(1979)
[6]TEEverhartandPHHoffJApplPhys
425837(1971)
7
8
9
[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-
Ⅲ
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
Z
Schematicviewof
anddefinitionsofthe
-32-
experimentalconditionscoordinatesystems
Electronbeam
Surfacecross-sectic
O゛9χ
Schottky哨Rbarrier
y
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
1
1
2
Normalizedscanningdistancex
(a)
Fig3-2
Fig3-3
U
四
S
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
S
Og<ao
2
161
S>0
S
21
Idrsquo
S5
2
10^
550
2
1必12345
135
sc^-at
SO⑤
バ宍
1012345
112345
SPg≪10
2
161
S
2
162S=0
SI
1
1(i3
5
2
1(541235
comparedwiththediffusionlengththeboundaryconditionsare
D
p
p
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=
j
-eg
+
2
一
丁T
4oo
int
Dg
馴D戸
0
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
d
g
11-
Schematicviewofelectronpenetrationisthemaximumenergydissipationdepth
a(W)
00000
1CMCO<rm
d(ym)
rdquo047
149
291
in<yi
vDVO
4VO
R(um)
-
100
295
5
9
13
74
20
2
Valuesofthecenterdgofthegeneration
volumeandtheradiusRinSiforseveralvalues
ofacceleratingvoltagevarsquo
-38-
IElectronbeam
O335
j
S`」「fdegce
uarrで0559j
10゛」
helliphelliphelliphelliphellip
上
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
1
pdznpoi」oz
1
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
2
4
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
1
1
1
-
1020304050(pm)
Scanningdistancex
Fig3-7
Experimentalresultsfor
sampleA(p=lf2cin)whereL=
8μmandS=20Fullcurves
arethetheoreticalrsquoones
1
5
11(il
>P≪4<N1≪CM<Pq
1 1
3193paziipujjoZ
5
2
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
2
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
5
6
[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-
E
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
1
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-
心
helliphellipl
l
]]1A
Ee
ビゲヤ
2
12
ss50
4
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
U
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
ビ
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
-
ド
ー い゛I
い
゛゛
w
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
j
②
五゛
゛
`
olinelo
jV
ズごy
こ
l
x
1
23
times1
l
U
5
GaAだj
(
j73C4Electron
L=07μmEbeam
2Sdeg20χ
1rsquo`
5
゛x
鹸
ya(W
2゛Va=30W
2_JE201
4一一―54013
5≒
脅χ
21`f
3
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-
W
Normalincidence Line scan
V(kv)a
E(eV)GaAsCSndoped)pc
GaAs(Tedoped)
5-50
41
39
4
0
14
3 9
30
3
3
9
8
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]
3
4
[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-
V
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
X
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
D
p
p
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()゜
j
-eg-
2
-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-
X
pr2wχ9]
plE【2w->り》】1
1rdquoMI
-E唇-
゜(2WdegO`92Wi
ミplE)rsquo゛p[2w-xg]
pl-《2w+x)】)゜91
Q
s哺
(n
L1)
1
paziipEJoz
1 2 3
-
Normalizedscanningdistancex
哺
0 5
M)DUd|UOISコ|}Ppazneaijoz
0
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
て
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-
W
Fig5-5
5
Q‐rsquoQ]
loline
11(52
2
ち5
Z
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
y
へ
`ヽ
`lsquolブjl
ゝゝjφ1
2
0h白contactム
ヤ
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
5
2
゜1(il
四a3
U」
5
-01
Ddziieujjoz
2
0
゛D=1Z5cm2s巡付
1 03
orini=-
にuarrヤuarr
i
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
士
darrレ
よ
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
1
JOoline1
―
Ig3paziieuijoz
Fig5-7
(a)
1
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
1
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]
3
4
[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
D
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=
1
-egeD
dp
-dxχ=0
=1-
<
こ)
3Wく
一一
Xく一一
(5-A7)
(5-A8)
X』
W
-80-
(5-A9)
Ⅶ
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
X
Schematicviewofeχperimentalconditionsand
definitionoftheco-ordinatesystem
-84-
Electronbeam
SOlyScanningtrack_xj
ズニに匹二oline-一一゛
lsquo9surface
lL-__--ang__helliphellip_
|`1
I
丑昌之
9gπLaf ―K
gdof
E
(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
1
U2
Cχ310-rsquo
山5
D
ト2
い
10lsquo3
velocitysis
35225N
(Eu
J
一))
^
n
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
g
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
5
`ヽ`10khtt
pwww
kHz
て
三
千
名
`ωで=01
2
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
|
-
〆
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-
o
「―」)畠一
uiMSaseudpazneaijoz
Fig6-5
rsquo0
1
1
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
ぶ
大
言二分ヽ同r〔2μ(ldquoμ
゛1)rsquo1
5primeacute
2
cべ1251251cap25
(
dφ
-
dx
煙
-
)=(c
TTfr TTf)ldquo゛十(c
yでワ
)rsquo゛
D
-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
0
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
X
Experimental
methodinp-(p=10
200
(μm)
resultsofthephaseshift
Ωcm)andn-type(p=01ncm)Si
-94-
rdquoolinersquordquooline`rsquolsquorsquoolinerdquordquoolinersquo50kHz
Vadeg30kVZ
乙
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]
7
8
9
[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
1
-
Heattreatmenttimet(min)
Diffusionlengthaftertheheattreatments
forvarioustimelengthsrangingfromlt0120minutesat1000degCOpenandsolidcirclesare
forthecasesindry02andArrespectivelyOriginaldiffusionlengthbeforeannealingis80pm
-100-
5ohellipumlindryO2
uml゜umlinArat1000degC
0
ol
5
0
12510251002
-
-
- W ゝ
rsquo _ l - ~ ヽ jS j - -
』
磨 卜
Fig7-2
(a)
(c)
S
ぐ
rarr100Mm
4
ぶミ
ぎ
1
ゝ
卜`
r-^
rsquo
1Is
≪バ
rdquorsquo‐゛t
rsquo
grバ4≪
rsquo1
ゝ
Surfacefaultsrevealedby
usingSirtletchantSamples(a)
wereannealedindryoat1000
and120minutesrespectively
-101-
囁
い゛フバrdquo
゛para
`i
(b)
ゝ
¥
i
(d)
ゝ
permilご}
゜
->嗜
-゛
寸
か
rsquo
III
`ヽご
いい
I
一J
J
t七
~貿で
ぜ
rsquo
j
゛`1
鴫ヽ
rsquoq
-≪
ゝく
タ
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
4
5
6
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
3
4
[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
`
メ
{
LISTOFPUBLICAT工ONS
I
[1]
[21
[3]
[4]
[5]
[6]
Papers
H
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-
J
皿
[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-
1
j
- page1
- page2
- page3
- page4
- page5
- page6
- page7
- page8
- page9
- page10
- page11
- page12
- page13
- page14
- page15
- page16
- page17
- page18
- page19
- page20
- page21
- page22
- page23
- page24
- page25
- page26
- page27
- page28
- page29
- page30
- page31
- page32
- page33
- page34
- page35
- page36
- page37
- page38
- page39
- page40
- page41
- page42
- page43
- page44
- page45
- page46
- page47
- page48
- page49
- page50
- page51
- page52
- page53
- page54
- page55
- page56
- page57
- page58
- page59
- page60
- page61
- page62
- page63
- page64
- page65
- page66
- page67
- page68
- page69
- page70
- page71
- page72
- page73
- page74
- page75
- page76
- page77
- page78
- page79
- page80
- page81
- page82
- page83
- page84
- page85
- page86
- page87
- page88
- page89
- page90
- page91
- page92
- page93
- page94
- page95
- page96
- page97
- page98
- page99
- page100
- page101
- page102
- page103
- page104
- page105
- page106
- page107
- page108
- page109
- page110
- page111
- page112
- page113
- page114
- page115
- page116
- page117
- page118
- page119
- page120
-
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
I
江
Ⅲ
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
Ⅵ
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
C
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-
k
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-
W
rdquod
wm
Xxx
g
g
χy
ZZ
m
n
np
Pau
^GaAs
I
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-
p
n
Fig1-1
type
type
Primaryelectrbe≪m
^^trrttDepletionlayer
Electron-hotep弗i「6gerwrationregion
Primaryelectronbeam
rArrScanningdirection
(A)
-
(B)
Principalconfigurationstomeasurethe
electronbeaminducedcurrent(EBIC)
(A)normalincidencemethod
(B)linescanmethod
-2-
-
ぶ
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
十
--
-- - -
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-
皿
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
i
Numberofgeneratedcarriers
Fig2-1Schematicviewofexperimentalconditions
jusingSchottkydiodesMetalthicknessis
wanddepletionlayerwidthiswright-handillustぷふこsthedぶdosefunctionRandR
-givethemaxiraum
andextraporaiedmelectrSnolinerangerespectively
-14-
0generatedcarrier
に_---___1
我_______Iuarrヽ
y重ダ
Z
1ごpermil
氷
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
t
χ
`Makarov20χ
----Wittry
χhelliphelliphellipKanaya
11S
15
゛S≒
rsquoχ≒
χrsquo
10trsquolsquo
卜卜゜χ゛
1
卜ゝrsquo
05χrsquo゛rsquoゝ
ゝrsquoゝ1
ゝゝrsquoゝゝ
ゝゝ
00
50
D
GaAso々
5
タグrsquo
2
万
1
ぶ
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
ぐ
二ぷ芯t
15へ
゜¥レ臨べhellip
hellip
10rsquoS゛lsquoNhellip
helliphellip
05
hellip
helliphellip
1helliphellip
hellip
005
芦
o
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
-
十
- -
-- - - - -
- - - -
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
>
ざ
u1C
larrl
0E
2
き
(
501
-
Figure2-6showsthecollectionefficiencyinSiusing
thefourdifferentmodelsofMakarovWittryKanayaandEverhart
bythesolidbrokendottedanddashedanddottedlines
respectivelyThevalueofLIs1005020and10umfrom
uppert0lowergroupofcurvesrespectivelyThevaluesofW
m
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
2
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]
3
4
[5]
WCzajaJApplPhys374236(1966)
JFBresserdquoScanningElectronMicroscopy71972partlrdquo
(iiTRiChicago111)p105
CJWuandDBWittryJApplPhys丘旦2827(1978)
KKanayaandSOkayamaJPhysDApplPhys
543(1972)-
口EPosslnandCGKirkpatrickJApplPhys
5^4033(1979)
[6]TEEverhartandPHHoffJApplPhys
425837(1971)
7
8
9
[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-
Ⅲ
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
Z
Schematicviewof
anddefinitionsofthe
-32-
experimentalconditionscoordinatesystems
Electronbeam
Surfacecross-sectic
O゛9χ
Schottky哨Rbarrier
y
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
1
1
2
Normalizedscanningdistancex
(a)
Fig3-2
Fig3-3
U
四
S
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
S
Og<ao
2
161
S>0
S
21
Idrsquo
S5
2
10^
550
2
1必12345
135
sc^-at
SO⑤
バ宍
1012345
112345
SPg≪10
2
161
S
2
162S=0
SI
1
1(i3
5
2
1(541235
comparedwiththediffusionlengththeboundaryconditionsare
D
p
p
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=
j
-eg
+
2
一
丁T
4oo
int
Dg
馴D戸
0
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
d
g
11-
Schematicviewofelectronpenetrationisthemaximumenergydissipationdepth
a(W)
00000
1CMCO<rm
d(ym)
rdquo047
149
291
in<yi
vDVO
4VO
R(um)
-
100
295
5
9
13
74
20
2
Valuesofthecenterdgofthegeneration
volumeandtheradiusRinSiforseveralvalues
ofacceleratingvoltagevarsquo
-38-
IElectronbeam
O335
j
S`」「fdegce
uarrで0559j
10゛」
helliphelliphelliphelliphellip
上
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
1
pdznpoi」oz
1
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
2
4
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
1
1
1
-
1020304050(pm)
Scanningdistancex
Fig3-7
Experimentalresultsfor
sampleA(p=lf2cin)whereL=
8μmandS=20Fullcurves
arethetheoreticalrsquoones
1
5
11(il
>P≪4<N1≪CM<Pq
1 1
3193paziipujjoZ
5
2
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
2
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
5
6
[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-
E
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
1
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-
心
helliphellipl
l
]]1A
Ee
ビゲヤ
2
12
ss50
4
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
U
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
ビ
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
-
ド
ー い゛I
い
゛゛
w
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
j
②
五゛
゛
`
olinelo
jV
ズごy
こ
l
x
1
23
times1
l
U
5
GaAだj
(
j73C4Electron
L=07μmEbeam
2Sdeg20χ
1rsquo`
5
゛x
鹸
ya(W
2゛Va=30W
2_JE201
4一一―54013
5≒
脅χ
21`f
3
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-
W
Normalincidence Line scan
V(kv)a
E(eV)GaAsCSndoped)pc
GaAs(Tedoped)
5-50
41
39
4
0
14
3 9
30
3
3
9
8
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]
3
4
[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-
V
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
X
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
D
p
p
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()゜
j
-eg-
2
-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-
X
pr2wχ9]
plE【2w->り》】1
1rdquoMI
-E唇-
゜(2WdegO`92Wi
ミplE)rsquo゛p[2w-xg]
pl-《2w+x)】)゜91
Q
s哺
(n
L1)
1
paziipEJoz
1 2 3
-
Normalizedscanningdistancex
哺
0 5
M)DUd|UOISコ|}Ppazneaijoz
0
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
て
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-
W
Fig5-5
5
Q‐rsquoQ]
loline
11(52
2
ち5
Z
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
y
へ
`ヽ
`lsquolブjl
ゝゝjφ1
2
0h白contactム
ヤ
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
5
2
゜1(il
四a3
U」
5
-01
Ddziieujjoz
2
0
゛D=1Z5cm2s巡付
1 03
orini=-
にuarrヤuarr
i
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
士
darrレ
よ
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
1
JOoline1
―
Ig3paziieuijoz
Fig5-7
(a)
1
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
1
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]
3
4
[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
D
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=
1
-egeD
dp
-dxχ=0
=1-
<
こ)
3Wく
一一
Xく一一
(5-A7)
(5-A8)
X』
W
-80-
(5-A9)
Ⅶ
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
X
Schematicviewofeχperimentalconditionsand
definitionoftheco-ordinatesystem
-84-
Electronbeam
SOlyScanningtrack_xj
ズニに匹二oline-一一゛
lsquo9surface
lL-__--ang__helliphellip_
|`1
I
丑昌之
9gπLaf ―K
gdof
E
(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
1
U2
Cχ310-rsquo
山5
D
ト2
い
10lsquo3
velocitysis
35225N
(Eu
J
一))
^
n
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
g
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
5
`ヽ`10khtt
pwww
kHz
て
三
千
名
`ωで=01
2
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
|
-
〆
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-
o
「―」)畠一
uiMSaseudpazneaijoz
Fig6-5
rsquo0
1
1
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
ぶ
大
言二分ヽ同r〔2μ(ldquoμ
゛1)rsquo1
5primeacute
2
cべ1251251cap25
(
dφ
-
dx
煙
-
)=(c
TTfr TTf)ldquo゛十(c
yでワ
)rsquo゛
D
-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
0
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
X
Experimental
methodinp-(p=10
200
(μm)
resultsofthephaseshift
Ωcm)andn-type(p=01ncm)Si
-94-
rdquoolinersquordquooline`rsquolsquorsquoolinerdquordquoolinersquo50kHz
Vadeg30kVZ
乙
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]
7
8
9
[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
1
-
Heattreatmenttimet(min)
Diffusionlengthaftertheheattreatments
forvarioustimelengthsrangingfromlt0120minutesat1000degCOpenandsolidcirclesare
forthecasesindry02andArrespectivelyOriginaldiffusionlengthbeforeannealingis80pm
-100-
5ohellipumlindryO2
uml゜umlinArat1000degC
0
ol
5
0
12510251002
-
-
- W ゝ
rsquo _ l - ~ ヽ jS j - -
』
磨 卜
Fig7-2
(a)
(c)
S
ぐ
rarr100Mm
4
ぶミ
ぎ
1
ゝ
卜`
r-^
rsquo
1Is
≪バ
rdquorsquo‐゛t
rsquo
grバ4≪
rsquo1
ゝ
Surfacefaultsrevealedby
usingSirtletchantSamples(a)
wereannealedindryoat1000
and120minutesrespectively
-101-
囁
い゛フバrdquo
゛para
`i
(b)
ゝ
¥
i
(d)
ゝ
permilご}
゜
->嗜
-゛
寸
か
rsquo
III
`ヽご
いい
I
一J
J
t七
~貿で
ぜ
rsquo
j
゛`1
鴫ヽ
rsquoq
-≪
ゝく
タ
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
4
5
6
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
3
4
[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
`
メ
{
LISTOFPUBLICAT工ONS
I
[1]
[21
[3]
[4]
[5]
[6]
Papers
H
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-
J
皿
[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-
1
j
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-