Diffusion #2

1. 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 @ 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 @ 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 @ 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 @ 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 • 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) where: = overall effective “Dt”

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 × 10-13 cm2/s. SOLUTION: where: Sw = 5 × 1013 cm-2 (Dt)w = (1.5 × 10-13 cm2/s)(3600s) = 5.4 × 10-10 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 = 273.3 min

18. Example (cont.) • If the n+ source/drain junction depth required is xj1 = 2.0 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 × 10-14cm2/s. Ignoring the contributions of the pre-dep, what is the approximate source/drain diffusion time (tnd)? SOLUTION: = 2.62 × 104 s = 436.8 min

21. Example (cont.) • If the boron diffusivity is 6.4 × 10-14 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 = 1.68 × 10-9 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. PhosphorusDiffusion

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.