1. ECE/ChE 4752: Microelectronics Processing Laboratory
Diffusion #2
ECE/ChE 4752: Microelectronics Processing Laboratory
Gary S. May
February 5, 2004

2. Outline Objectives Double Diffusions Concentration-Dependent Diffusion
Diffusion in Silicon
Lateral Diffusion

3. Objectives
Discuss the concept of double diffusions, an important part of how we fabricate our CMOS transistors in the lab.
Introduce some “second-order” diffusion effects.

4. Outline Objectives Double Diffusions Concentration-Dependent Diffusion
Diffusion in Silicon
Lateral Diffusion

5. After p-well Diffusion

6. After NMOS Source/Drain n+ Diffusion

7. Notation: p-well Pre-dep
Boron doping
Pre-Dep: Tpp => Dpp, Cspp
tpp = p-well pre-dep time
Tpp = p-well pre-dep temperature
Dpp = p-well diffusion constant at pre-dep temperature
Cspp = surface concentration for p-well pre-dep

8. Notation: p-well Drive-in
Tpd => Dpd
tpd = p-well drive-in time
Tpd = p-well drive-in temperature
Dpd = p-well diffusion constant at drive-in temperature

9. Notation: n+ Source/Drain Pre-dep
Phosphorus doping
Pre-Dep: Tnp => Dnp, Csnp; Dp1
tnp = n+ source/drain pre-dep time
Tnp = n+ source/drain pre-dep temperature
Dnp = n+ source/drain diffusion constant at pre-dep temperature
Csnp = surface concentration for n+ source/drain pre-dep
Dp1 = boron diffusion constant at source/drain pre-dep temperature

10. Notation: n+ Source/Drain Drive-in
Tnd => Dnd; Dp2
tnd = n+ source/drain drive-in time
Tnd = n+ source/drain drive-in temperature
Dnd = n+ source/drain diffusion constant at drive-in temperature
Dp2 = boron diffusion constant at source/drain drive-in temperature

11. Profile: After p-well Diffusion
where:
= well dose
= well “Dt”
There is a pn-junction xj0 where NA(x) = Csub

12. Profile: After n+ Source/Drain Diffusion
where:
= source/drain dose
= source/drain “Dt”
BUT: now the well profile has changed to…

13. New Well Profile where: = overall effective “Dt”
There is a pn-junction xj1 where ND(x) = NA(x)
There is a new pn-junction xj2 where NA(x) = Csub (where xj2 > xj0)

14. Example
Suppose we want to design a p-well CMOS diffusion process with a well depth of xj2 = 2.5 mm. Assume the n-type substrate doping is 1015 cm-3.

15. Example (cont.)
If we start with a boron pre-dep with a dose of 5 × 1013 cm-2, followed by a 1-hr drive-in at 1100 oC, what is the initial junction depth (xj0)? Neglect the depth of the pre-dep. The B diffusivity at this temperature is 1.5 × cm2/s.
SOLUTION:
where: Sw = 5 × 1013 cm-2
(Dt)w = (1.5 × cm2/s)(3600s) = 5.4 × cm2
NA(xj0) = 1015 cm-3 =>
= 1.24mm

16. Example (cont.)
Find the necessary (Dt)eff for the p-well to reach the desired junction depth of xj2 = 2.5 mm.
SOLUTION (This must be solved by iteration!!!):
where: x = xj2 = 2.5 mm
NA(xj2) = 1015 cm-3
Sw = 5 × 1013 cm-2
=> (Dt)eff = 2.46 × 10-9 cm-2

17. Example (cont.)
What is the approximate p-well drive-in time needed if all steps are carried out at 1100 oC?
SOLUTION:
= 1.64 × 104 s = min

18. Example (cont.)
If the n+ source/drain junction depth required is xj1 = mm, what is the p-well doping at the source/drain junction?
SOLUTION:
where: x = xj1 = 2.0 mm
(Dt)eff = 2.46 × 10-9 cm2
=> NA(xj1 = 2.0 mm) = 9.76 × 1015 cm-3

19. Example (cont.)
Suppose the source/drain dose (Ssd) is 5 × 1014 cm-2. What is the surface concentration in the source/drain regions and the source/drain diffusion (Dt)sd?
SOLUTION:
where: x = xj1 = 2.0 mm
ND(x = xj1) = 9.76 × 1015 cm-3
(Solving by iteration): (Dt)sd = 1.52 × 10-9 cm2
(ii) Surface Concentration:
= 7.24 × 1018 cm-3

20. Example (cont.)
The phosphorus source/drain regions are deposited and driven in at 1050 oC. At this temperature, the phosphorus diffusivity is 5.8 × cm2/s. Ignoring the contributions of the pre-dep, what is the approximate source/drain diffusion time (tnd)?
SOLUTION:
= 2.62 × 104 s = min

21. Example (cont.)
If the boron diffusivity is 6.4 × cm2/s at 1050 oC, correct for the p-well diffusion time to account for the extra diffusion during the source/drain drive-in. (Neglect the contributions of pre-dep steps).
SOLUTION:
Dp2tnd = × cm2
( “Dt” accumulated by boron during source/drain diffusion).
=> Initial p-well drive-in may be reduced by this amount, or:
= 86.9 min

22. Outline Objectives Double Diffusions Concentration-Dependent Diffusion
Diffusion in Silicon
Lateral Diffusion

23. Vacancies
When host atom acquires sufficient energy to leave its lattice site, a vacancy is created.
Vacancy density of a given charge state (# vacancies/unit volume, CV) has temperature dependence similar to carrier density:
where Ci = intrinsic vacancy density, EF = Fermi level, and Ei = intrinsic Fermi level

24. Vacancy-Dependent Diffusion
If diffusion is dominated by the vacancy mechanism, D is proportional to vacancy density.
At low doping concentrations (n < ni), EF = Ei, and CV = Ci (independent of doping), so
D (which is proportional to CV = Ci ), also independent of doping concentration.
At high concentrations (n > ni), [exp(EF – Ei)/kT] becomes large, which causes CV and D to increase.

25. Intrinsic and Extrinsic Diffusion

26. Effect on Diffusivity Cs = surface concentration
Ds = diffusion coefficient at the surface
g = parameter to describe concentration dependence

27. Diffusion Profiles

28. Junction Depth For g > 0, D decreases with concentration
Increasingly steep box-like profiles result
Therefore, highly abrupt junctions are formed
Junction depth is virtually independent of
background concentration
= 1
= 2
= 3

29. Outline Objectives Double Diffusions Concentration-Dependent Diffusion
Diffusion in Silicon
Lateral Diffusion

30. Concentration Dependence
Boron, arsenic: g ≈ 1
Gold, platinum: g ≈ -2
Phosphorus: g ≈ 2 (sort of)

31. Phosphorus Diffusion

32. Phosphorus Diffusion (cont.)
When surface concentration is low, diffusion profile is an erfc (curve a).
As concentration increases, the profile begins to deviate (b and c).
At high concentration (d), profile near the surface is similar b, but at ne, kink occurs, followed by rapid diffusion in tail region.
Because of high diffusivity, phosphorus is used to form deep junctions, such as the n-tubs in CMOS.

33. Outline Objectives Double Diffusions Concentration-Dependent Diffusion
Diffusion in Silicon
Lateral Diffusion

34. The Problem
1-D diffusion equation is not adequate at the edge of the mask window.
There, impurities diffuse downward and sideways (i.e., laterally).
In this case, we must consider a 2-D diffusion equation and use numerical techniques to get the diffusion profiles under different initial and boundary conditions.

35. Diffusion Contours
Contours of constant doping concentration for a constant Cs, assuming D is independent of concentration.

36. Interpretation
Variation at far right corresponds to erfc distribution.
Example: at C/Cs = 10–4, the vertical penetration is about 2.8 µm, whereas the lateral penetration is about 2.3 µm (i.e., the penetration along the diffusion mask-semiconductor interface).

37. Implications
Because of lateral diffusion, the junction consists of a central plane (or flat) region with approximately cylindrical edges with a radius of curvature rj.
If the mask has sharp corners, the shape of the junction near the corner will be roughly spherical.
Since the electric-field intensities are higher for cylindrical and spherical junctions, the avalanche breakdown voltages of such regions can be substantially lower than that of a plane junction.