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EE143 – Ali Javey
Section 7: Diffusion
Jaeger Chapter 4
EE143 – Ali Javey
Dopant Diffusion Sources(a) Gas Source: AsH3, PH3, B2H6
(b) Solid SourceBN Si BN Si
(c) Spin-on-glass SiO2+dopant oxide
(d) Liquid Source.
EE143 – Ali Javey
Fick’s First Law of Diffusion
t coefficiendiffusion =DxNDJ
EE143 – Vivek Subramanian Slide 4-4
Fick’s Second Law of Diffusion
devicesmodernin situationsmany in t trueisn'which
t,independen-ionconcentrat is D Assumes
Eqn. Continuity with LawFirst Combine :Diffusion of Law Second sFick'
dimension) one(in
flux particle theof divergence theof negative the toequal ision concentrat of increase of Rate
:Flux Particlefor Equation Continuity
2
2
xND
tN
xJ
tN
EE143 – Ali Javey
B,P
As
10-6
Au
Cu
kTE
O
A
eDD
Diffusion Coefficients of Impurities in Si
SubstitutionalDiffusers Interstitial
Diffusers
EE143 – Ali Javey
Diffusion Coefficients
re temperatuabsolute=TJ/K x101.38=constant sBoltzmann'=k
energy activationE
ipRelationsh Arrhenius exp
23-
A
kTEDD A
O
EE143 – Ali Javey
(a) Interstitial Diffusion
Diffusion Mechanisms in Si
10-6 cm2/secAu
Cu
Fast DiffusionExample: Cu, Fe, Li, H
EE143 – Ali Javey
(b) Substitutional Diffusion
Diffusion Mechanisms in Si
(c) Interstitialcy DiffusionExample: Dopants in Si ( e.g. B, P,As,Sb)
EE143 – Vivek Subramanian Slide 4-9
Constant Source DiffusionComplementary Error Function Profiles
FunctionError ary Complement=erfctCoefficienDiffusion
ionConcentrat Surface
2, :Dose Total
2, :ionConcentrat
0
00
0
DN
DtNdttxNQ
DtxerfcNtxN
EE143 – Ali Javey
Limited Source DiffusionGaussian Profiles
ProfileGaussian tCoefficienDiffusion
ion Concentrat Surface
2exp
2exp,
:ionConcentrat
00
22
0
DDt
QNN
Dtx
DtQ
DtxNtxN
EE143 – Ali Javey
Two Step Dopant Diffusion (1) Predeposition dopant gas
SiO2SiO2
Si
dose control
(2) Drive-in Turn off dopant gasor seal surface with oxide
SiO2SiO2
Si
SiO2
Doped Si region
profile control(junction depth;concentration)
Note: Predeposition by diffusion can also be replaced by a shallow implantation step.
EE143 – Ali Javey
Predeposition Drive-in
Normalized Concentration versus depth
EE143 – Ali Javey
Diffusion of Gaussian Implantation Profile
EE143 – Ali Javey
istep
ieffective DtDtBudgetThermal
)()(Example
Dttotal of :
Well drive-in
and
S/D annealing
Temp (t)
time
welldrive-in
stepS/D
Annealstep
Temp (t)
time
welldrive-in
stepS/D
Annealstep
For a complete process flow, only those steps with high Dt values are important
Successive Diffusions: Thermal Budget
EE143 – Ali Javey
Solid Solubility Limits
• There is a limit to the amount of a given impurity that can be “dissolved” in silicon (the Solid Solubility Limit)
• At high concentrations, all of the impurities introduced into silicon will not be electrically active
EE143 – Ali Javey
High Concentration Diffusion Effects
Log C(x)
x
Low conc profile:Erfc or gaussian
Log C(x)
x
J large
J small
High conc. profile:D gets largerwhen C(x) is large
* C(x) looks “flatter”at high conc. regions
1) E-Field Enhanced Diffusion2) Charged point defects enhanced diffusion
EE143 – Ali Javey
Electric-field EnhancementExample: Acceptor Diffusion
Na(x)
Na(x)=Na-(x)
p(x)
hole gradient
x
Hole diffusion tendency
E build-in
Complete acceptorionization at diffusion temperature
At thermal equilibrium, hole current =0Hole gradient creates build-inelectric field to counteract the hole diffusion tendency
EE143 – Ali Javey
B-
+[p]holes tends to moveaway due to holeconcentration gradient
Ebuild-in
B- acceptorsexperiencean additionaldrift force
Enhanced Diffusion for B- acceptor atoms
Electric Field Enhancement
EE143 – Ali Javey
Asdiffusion
Uniform B conc in substrate
caused by Asconc gradient
B-
Electric Field Enhancement – Substrate Perturbation