1. Microelectronics Processing
Diffusion
Microelectronics processing - E. FinkmanEliezer Finkman

2. Doping Thermal diffusion
Doping is the process that puts specific amounts of dopants in the wafer surface through openings in the surface layers.
Thermal diffusion is a chemical process that takes place when the wafer is heated (~1000 C) and exposed to dopant vapor. In this process the dopants move to regions of lower concentration.
Doping Control is critical in MOS device scaling. (Scaling down the gate length requires equal scaling in doping profile)
Ion source
Thermal diffusion
Ion implantation
Microelectronics processing - E. FinkmanEliezer Finkman

3. Comparison of thermal diffusion and ion implantation
Microelectronics processing - E. FinkmanEliezer Finkman

4. Mathematics of diffusion: Fick’s First diffusion law
D is thermally activated

5. Mathematics of diffusion: Fick’s Second diffusion law
What goes in and does not go out,
stays there
C/t = (Fin-Fout)/ x

6. Fick’s diffusion law F F Concentration independent diffusion equation.
Often referred to as Fick’s second law.

7. Analytic solutions of the diffusion equations: Case of a spike delta function in infinite media
(x)

8. The evolution of a Gaussian diffusion profile
Peak concentration decreases as 1/√t and is given by C(0,t).
Approximate measure of how far the dopant has diffused (the diffusion length) is given by x=2√Dt which is the distance from origin where the concentration has fallen by 1/e

9. Carl Friedrich Gauss
( )

10. Analytic solutions of the diffusion equations: Case of a spike delta function near the surface
The symmetry of the problem is similar to previous case, with an effective dose of 2Q introduced into a (virtual) infinite medium.
The solution is thus:

11. Constant total dopant (number) diffusion: Impurity profile
Log scale
Linear scale
Three impurity profiles carried out under constant total dopant diffusion conditions. Note the reduction in the surface concentration C(0,t) with time, and the corresponding rise in the bulk density.

12. Analytic solutions of the diffusion equations: Case of an infinite source of dopant

13. The error function A related function is tabulated:
The solution of the diffusion equation from an infinite source is finally:

14. Constant surface concentration: diffusion depth
Log scale
Linear scale
Plots of C(x,t)/Cs vs diffusion depth x(µm) under constant surface concentration conditions for three different values of √Dt . This could mean either a change of temperature (i.e D(T)) or time, t.

15. Total number of impurities (predeposition dose)
As seen in the figure, the error function solution is approximately triangular. The total dose may be estimated by an area of triangular of height Cs and a base of 2√Dt, giving Q= Cs √Dt.
More accurately:
= Characteristic distance for diffusion.
CS = Surface concentration (solid solubility limit).

16. Two-step junction formation: (a) Predeposition from a constant source (erfc) (b) Limited source diffusion (Gaussian)

17. Shallow predep approximation
Solution of Drive-in profile:
In summary:
D1= Diffusivity at Predep temperature
t1= Predep time
D2= Diffusivity at Drive-in temperature
t2= Drive-in time

18. Two-step junction formation

19. Temperature dependence of D

20. Diffusion coefficients (constants) for a number of impurities in Silicon
Substitutional Interstitial

21. Typical diffusion coefficient values
Element
D0 (cm2/sec)
EA(eV) B
10.5
3.69 P As
0.32
3.56

22. The two principal diffusion mechanisms: Schematic diagrams
Vacancy diffusion
in a semiconductor.
Interstitial diffusion in a semiconductor.

23. Vacancy
Intersticial
                             
                             

24. Thermal diffusion – general comments
Schematic diagram of a furnace for diffusing impurities (e.g. phosphorus) into silicon.
Microelectronics processing - E. FinkmanEliezer Finkman

25. Rapid thermal annealing
a) Concept. b) Applied Materials 300 mm RTP system.

26. Dopant diffusion sources
Gas Source: AsH3, PH3, B2H6
Solid Sources: BN, NH4H2PO4, AlAsO4
Spin-on-glass: SiO2+dopant oxide
Liquid source:
A typical bubbler arrangement for doping a silicon wafer using a liquid source. The gas flow is set using mass flow controller (MFC).
Microelectronics processing - E. FinkmanEliezer Finkman

27. Junction depth
Microelectronics processing - E. FinkmanEliezer Finkman

28. Sheet resistance The resistance of a rectangular block is:
R = ρL/A = (ρ/t)(L/W) ≡ Rs(L/W)
Rs is called the sheet resistance. Its units are termed Ω/ .
L/W is the number of unit squares of material in the resistor.

29. Sheet resistance

30. Irving’s curves: Motivation to generate them
Microelectronics processing - E. FinkmanEliezer Finkman

31. Irving’s curves
Microelectronics processing - E. FinkmanEliezer Finkman

32. Figure illustrating the relationship of No, NB, xj, and Rs
Microelectronics processing - E. FinkmanEliezer Finkman

33. Diffusion of Gaussian implantation profileQ
Note: Q is the implantation dose.
Microelectronics processing - E. FinkmanEliezer Finkman