Post on 24-Jan-2021
Diffusion & OxidationDoping
Diffusion
1st Fick’s law
Fick's First Law is used in steady state diffusion, i.e., when the concentration within the diffusion volume does not change with respect to time.
( )
dxdnDJ
dxdnv
nnv
SdtdNJ
−=
−=−−−==3
)()(6
λλλ
⎟⎟⎠
⎞⎜⎜⎝
⎛−=
TkE
DDB
diffexp0 Ediff: activation energy for diffusion
Diffusion
2nd Fick’s lawFick's Second Law is used in non-steady state diffusion,i.e., when the concentration within the diffusion volume changes in time.
[ ]
2
2
)()(
:Continuity
xnD
dtdn
dxdJ
dtdn
dtdVdxdJSdtxxJxJdN
dxdnDJ
∂∂
=⇒−=
−=∆+−=
−=
DiffusionConstant source diffusion
“pre-deposition”Limited source diffusion
“drive-in”
( ) ∫∞
−=
⎟⎠
⎞⎜⎝
⎛=
x
x dxex
Dtxntxn
22erfc
;2
erfc),( 0
π
2
2exp),( ⎟
⎠
⎞⎜⎝
⎛=Dtx
DtQtxnπ
DtndxtxnSNtQ 0
0 32),()( Dose === ∫
∞
(complimentary error function)
DiffusionEnhanced diffusion:• Stress, electric field• Ionization• Grain boundaries (defects)
Parameters that affect diffusion:• Temperature• Pressure• Crystal direction (channeling)
Probability to escape in thermalactivation process:
⎟⎟⎠
⎞⎜⎜⎝
⎛ −−⋅⋅=
TkeaEWanPB
2/expω
w- attempt frequency
DiffusionIn gases:
D[cm2/s]
H2 in O2 0.7
CO2 in air 0.14
O2 in O2 0.18
sugar in water 3e-6
σσ PTv
nvvlD Bk~~~
scm][
2
=DxcDj
dd
−=
Mobility B, force F, drift velocity u of ionsBFu =
DLt
2
~Time of equalization
BTD Bk= Einstein's equation
L
Doping
Mechanism of Diffusion
a) substitutional diffusionb) impurity atom replaces Si atomc) impurity atom does not replace Si atom
Doping
O3HOB3OHB6BrO2B3O4BBr
3SiO4B3SiO2B
232262
23223
232
+→++→+
+→+
Uniformity on Wafers
O3HOP4O2PH6ClO2P3O4POCl
5SiO4P5SiO2P
25223
25223
252
+→++→+
+→+
⎟⎟⎠
⎞⎜⎜⎝
⎛∆
⎟⎟⎠
⎞⎜⎜⎝
⎛∆
==
DkrI
rr
DkrI
CrC
drrd
00
0
00
0
0
2
2)(
)1()/(
φ
Doping by thermal diffusion
Tool #433Rapid Thermal Processor (RTP) AG Heatpulse 610
a PC-controlled halogen lamp furnace. It accommodates 2", 3", and 4" wafers, or small pieces placed on a wafer.
It is typically used for alloying of ohmic contacts on III-V semiconductors. No other substrates than III-V are allowed.
Specifications:Protecting gas: N2Wafer size: pieces, 2", 3", 4“Max temperature:1000°CHeating rate: 120°C/secTemperature sensor: Thermocouple / Pyrometer
Diffusion
http://www.oki.com/
diffusion of dopant atoms in the direction parallel to the surface of semiconductor; undesired in device manufacturing as it causes distortion of the device geometry.
Thermal Oxidation of Si
222
22
2HSiOO2HSiSiOOSi
+→+→+
1. Oxygen is transported from the bulk of the gas phase to the gas-oxide interface2. Oxygen diffuses through the growing solid oxide film3. When oxygen reaches the Si/SiO2 interface, it chemically reacts with Si and forms SiO2
Interface Reaction Kinetics
)( sgggs CChJ −= sss CkJ =
sgsgs
gs JJ
hkC
C =+
= for 1
⎟⎠⎞
⎜⎝⎛−∝
RTEks exp
ks>>hg: mass transfer
ks<<hg: surface reaction
Interface Reaction Kinetics( )( )
iS
i
gg
CkJd
CCDJ
CChJ
=
−=
−=
3
0
02
01
constant ratereaction chemical SiOin oxygen of coeff. diff.
tcoefficien transportmassinterface Si/SiO at theoxygen ofion concentrat interface gas/SiO at theoxygen ofion concentrat
gas in theoxygen ofion concentrat
2
20
2
−−
−−−
−
S
g
i
g
kD
hCC
C
Ddk
hk
DdkC
CS
g
S
Sg
0
0
0
1
1
++
⎟⎠⎞
⎜⎝⎛ +
=
Ddk
hk
CC
S
g
S
gi
01 ++=
growth) state-(steady 321 JJJ ==
Interface Reaction Kinetics
Ddk
hk
DdkC
CS
g
S
Sg
0
0
0
1
1
++
⎟⎠⎞
⎜⎝⎛ +
=
Ddk
hk
CC
S
g
S
gi
01 ++=
( )00 limitedreaction 1
dkD
hk
CCC S
G
S
gi >>
+=≈
( )00 limiteddiffusion :0 ; dkDCCC Sig <<≈≈
)(
)(
020
00
τ+=+
=
tBAdd
NCktd
dtd iSthe actual growth
depends on J3:
Interface Reaction Kinetics
)(
)(
020
00
τ+=+
=
tBAdd
NCktd
dtd iS
the actual growthdepends on J3:
[ ]( )
any) (if thicknessoxide initial
/;/2);(2
cm (wet) 104.4 (dry) 102.22
011
322220
−
+==+=
××=−−
−
i
iigSg
d
BAddNDCBkhDA
N
τ
BAttABtd
BAtBttdBA
tAtd
4/),()(
4/,)(
14/
12
)(
20
20
20
<<++≅
>>≅
−+
+=
ττ
τ
Oxide ExpansionCracks – lower breakdown voltage (5-10 MV/cmLeakageTrapped charges
Mechanical Relaxation Effectsduring oxide growth (expansion)
Stress relaxation: Strain relaxation:
( )
212
2110
21
21
21
s/cmdyn 108.2dyn/cm 106.6for
/expstrain)(constant
;
⋅⋅=
⋅=
−=−=
==
+=
η
ησσεε
ησεσε
εεε
Y
Yt
Y
x
xx
T
&&
& ( )[ ]ησε /exp10 YtY
−−=
Si substrate
SiO2
Usually a mixtureof strain and stressrelaxations
τ ~ 4 sec
A volume change of ~200%!
Diffusion Along Grain BoundariesStressDefects
easier diffusion along grain boundaries
http://shasta.mpi-stuttgart.mpg.de/research/thinfilmcnt/thinfilms.htm
Interdiffusion & Transformationsin Thin Films
Electro-migration
Interdiffusion is crucialin multilayers
MoSimultilayers
•EUV lithography •EUV metrology •EUV microscopy •synchrotron optics •x-ray astronomy •soft x-ray lasers •element analysis •plasma physics
M. Ohring: Materials Science of thin filmshttp://www.iof.fraunhofer.de/departments/optical-coatings/
Si Crystal Structurediamond structure
Two interleaving FCC cells offset by 1/4 of the cube diagonal
Isotropic vs Anisotropic Wet Etching
Chemicals IsotropicHF:HNO3:CH3COOH:H20HFHF:NH4F Masking Materials
Photoresist (Acids Only)Si3N4SiO2Anisotropic
KOHEDP (Ethylenediamine Pyrocatechol)CsOHNaOHN2H4-H20 (Hydrazine)
Chemicals KOH EtchingEtch rate
(110) > (100) > (111)(111) > (110) > (111) w/ IPA
Varies with T and concentration
MasksSi3N4: is the best, very slow etch rate, selectivity > 1000SiO2 :selectivity >> 100
Application of Anisotropic Etch
Pits
Steps
Holes
Cantilevers
Bridges
MicromachiningM. Madou “Fundamentals of microfabrication”
Etch Stop Layers
Boron Stops Etching~1020 cm-3 reduces etch rate 1000 times
Boron-doped Layer
masking
Laser-Assisted Wet Etching
M. Madou, Fundamentals of Microfabrication
Macroporous Si http://www.macroporous-silicon.com/
Photogenerated minority carriers (in the case of n-type Si this means "holes") diffuse from the back side of the sample to the pore (etch) pits and promote dissolution there, because of the enhanced electrical field in the space charge layer (SCL). www-tkm.physik.uni-karlsruhe.de/