1. Section 7: Diffusion
Jaeger Chapter 4
EE143 – Ali Javey

2. Dopant Diffusion Sources
(a) Gas Source: AsH3, PH3, B2H6 BN Si BN Si
(b) Solid Source
(c) Spin-on-glass
SiO2+dopant oxide
(d) Liquid Source.
EE143 – Ali Javey

3. Fick’s First Law of Diffusion
EE143 – Ali Javey

4. Fick’s Second Law of Diffusion
EE143 – Vivek Subramanian

5. Diffusion Coefficients of Impurities in Si
10-6 Au Cu
Substitutional
Diffusers
Interstitial
Diffusers
B,P As
EE143 – Ali Javey

6. Diffusion Coefficients
EE143 – Ali Javey

7. Diffusion Mechanisms in Si
(a) Interstitial Diffusion
Example: Cu, Fe, Li, H
Fast Diffusion Cu
10-6 cm2/sec Au
EE143 – Ali Javey

8. Diffusion Mechanisms in Si
(b) Substitutional Diffusion
(c) Interstitialcy Diffusion
Example: Dopants in Si ( e.g. B, P,As,Sb)
EE143 – Ali Javey

9. Constant Source Diffusion Complementary Error Function Profiles
EE143 – Vivek Subramanian

10. Limited Source Diffusion Gaussian Profiles
EE143 – Ali Javey

11. Two Step Dopant Diffusion
(1) Predeposition
dopant gas
dose control
SiO2
SiO2
Doped Si region Si
(2) Drive-in
Turn off dopant gas
or seal surface with oxide
profile control
(junction depth;
concentration)
SiO2
SiO2
SiO2 Si
Note: Predeposition by diffusion can also be replaced by a shallow implantation step.
EE143 – Ali Javey

12. Normalized Concentration versus depth
Predeposition
Drive-in
EE143 – Ali Javey

13. Diffusion of Gaussian Implantation Profile
EE143 – Ali Javey

14. Successive Diffusions: Thermal Budget
Example
Dttotal of :
Well drive-in
and
S/D annealing
Temp (t)
Temp (t)
well
well
drive
drive - - in in
S/D
S/D
step
step
Anneal
Anneal
step
step
time
time
For a complete process flow, only those steps with high Dt values are important
EE143 – Ali Javey

15. 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

16. High Concentration Diffusion Effects
E-Field Enhanced Diffusion
Charged point defects enhanced diffusion
Log C(x) x
Low conc profile:
Erfc or gaussian
J large
J small
High conc. profile:
D gets larger
when C(x)
is large
* C(x) looks “flatter”
at high conc. regions
EE143 – Ali Javey

17. Electric-field Enhancement
Example: Acceptor Diffusion
Na(x)
p(x)
Na(x)=Na-(x)
hole gradient
Hole diffusion
tendency
E build-in x
At thermal equilibrium, hole current =0
Hole gradient creates build-in
electric field to counteract the hole
diffusion tendency
Complete acceptor
ionization at diffusion temperature
EE143 – Ali Javey

18. Electric Field Enhancement
holes tends to move
away due to hole
concentration gradient
+[p] B-
Ebuild-in
B- acceptors
experience
an additional
drift force
Enhanced
Diffusion for B- acceptor atoms
EE143 – Ali Javey

19. Electric Field Enhancement – Substrate PerturbationAs
diffusion
caused by As
conc gradient
Uniform B conc in substrate B-
EE143 – Ali Javey