1. ECE/ChE 4752: Microelectronics Processing Laboratory
Diffusion #1
ECE/ChE 4752: Microelectronics Processing Laboratory
Gary S. May
January 29, 2004

2. Outline Introduction Apparatus & Chemistry Fick’s Law Profiles
Characterization

3. Definition
Random walk of an ensemble of particles from regions of high concentration to regions of lower concentration
In general, used to introduce dopants in controlled amounts into semiconductors
Typical applications:
Form diffused resistors
Form sources/drains in MOS devices
Form bases/emitters in bipolar transistors

4. Basic Process Source material transported to surface by inert carrier
Decomposes and reacts with the surface
Dopant atoms deposited, dissolve in Si, begin to diffuse

5. Outline Introduction Apparatus & Chemistry Fick’s Law Profiles
Characterization

6. Schematic

7. Dopant Sources Inert carrier gas = N2 Dopant gases:
P-type = diborane (B2H6)
N-Type = arsine (AsH3), phosphine (PH3)
Other sources:
Solid = BN, As2O3, P2O5
Liquid = BBr3, AsCl3, POCl3

8. Solid Source Example reaction: 2As2O3 + 3Si → 4As + 3SiO2
(forms an oxide layer on the surface)

9. Liquid Source
Carrier “bubbled” through liquid; transported as vapor to surface
Common practice: saturate carrier with vapor so concentration is independent of gas flow
=> surface concentration set by temperature of bubbler & diffusion system
Example: 4BBr3 + 3O2 → 2B2O3 + 6Br
=> preliminary reaction forms B2O3, which is deposited on the surface; forms a glassy layer

10. (oxygen is carrier gas that initiates preliminary reaction)
Gas Source
Examples:
a) B2H6 + 3O2 → B2O3 + 3H2O (at 300 oC)
b) i) 4POCl3 + 3O2 → 2P2O5 + 6Cl2
(oxygen is carrier gas that initiates preliminary reaction)
ii) 2P2O5 + 5Si → 4P + 5SiO2

11. Outline Introduction Apparatus & Chemistry Fick’s Law Profiles
Characterization

12. Diffusion Mechanisms
Vacancy: atoms jump from one lattice site to the next.
Interstitial: atoms jump from one interstitial site to the next.

13. Vacancy Diffusion Also called “substitutional” diffusion
Must have vacancies available
High activation energy (Ea ~ 3 eV  hard)

14. Interstitial Diffusion
“Interstitial” = between lattice sites
Ea = eV  easier

15. First Law of Diffusion C = dopant concentration/unit volume
F = flux (#of dopant atoms passing through a unit area/unit time)
C = dopant concentration/unit volume
D = diffusion coefficient or diffusivity
Dopant atoms diffuse away from a high-concentration region toward a lower-concentration region.

16. Conservation of Mass
1st Law substituted into the 1-D continuity equation under the condition that no materials are formed or consumed in the host semiconductor

17. Fick’s Law
When the concentration of dopant atoms is low, diffusion coefficient can be considered to be independent of doping concentration.

18. Temperature Effect Diffusivity varies with temperature
D0 = diffusion coefficient (in cm2/s) extrapolated to infinite temperature
Ea = activation energy in eV

19. Outline Introduction Apparatus & Chemistry Fick’s Law Profiles
Characterization

20. Solving Fick’s Law 2nd order differential equation
Need one initial condition (in time)
Need two boundary conditions (in space)

21. Constant Surface Concentration
“Infinite source” diffusion
Initial condition: C(x,0) = 0
Boundary conditions:
C(0, t) = Cs
C(∞, t) = 0
Solution:

22. Key Parameters Complementary error function:
Cs = surface concentration (solid solubility)

23. Total Dopant Total dopant per unit area:
Represents area under diffusion profile

24. Example
For a boron diffusion in silicon at 1000 °C, the surface concentration is maintained at 1019 cm–3 and the diffusion time is 1 hour. Find Q(t) and the gradient at x = 0 and at a location where the dopant concentration reaches 1015 cm–3.
SOLUTION:
The diffusion coefficient of boron at 1000 °C is about 2 × 1014 cm2/s, so that the diffusion length is

25. Example (cont.)
When C = 1015 cm–3, xj is given by

26. Constant Total Dopant “Limited source” diffusion
Initial condition: C(x,0) = 0
Boundary conditions:
C(∞, t) = 0
Solution:

27. Example
Arsenic was pre-deposited by arsine gas, and the resulting dopant per unit area was 1014 cm2. How long would it take to drive the arsenic in to xj = 1 µm? Assume a background doping of Csub = 1015 cm-3, and a drive-in temperature of 1200 °C. For As, D0 = 24 cm2/s and Ea = 4.08 eV.
SOLUTION:

28. Example (cont.) t • log t – 10.09t + 8350 = 0
The solution to this equation can be determined by the cross point of equation:
y = t • log t and y = 10.09t – 8350.
Therefore, t = 1190 seconds (~ 20 minutes).

29. Diffusion Profiles

30. xj = junction depth (where C(x)=Csub)
Pre-Deposition
Pre-deposition = infinite source
xj = junction depth (where C(x)=Csub)

31. Drive-In
Drive-in = limited source
After subsequent heat cycles:

32. Multiple Heat Cycles
where: (for n heat cycles)

33. Outline Introduction Apparatus & Chemistry Fick’s Law Profiles
Characterization

34. Junction Depth
Can be delineated by cutting a groove and etching the surface with a solution (100 cm3 HF and a few drops of HNO3 for silicon) that stains the p-type region darker than the n-type region, as illustrated above.

35. Junction Depth
If R0 is the radius of the tool used to form the groove, then xj is given by:
In R0 is much larger than a and b, then:

36. 4-Point Probe
Used to determine resistivity

37. 4-Point Probe 1) Known current (I) passed through outer probes
2) Potential (V) developed across inner probes
r = (V/I)tF
where: t = wafer thickness
F = correction factor (accounts for probe geometry)
OR: Rs = (V/I)F
where: Rs = sheet resistance (W/)
=> r = Rst

38. Resistivity where: s = conductivity (W-1-cm-1) r = resistivity (W-cm)
mn = electron mobility (cm2/V-s)
mp = hole mobility (cm2/V-s)
q = electron charge (coul)
n = electron concentration (cm-3)
p = hole concentration (cm-3)

39. Resistance

40. Sheet Resistance 1 “square” above has resistance Rs (W/square)
Rs is measured with the 4-point probe
Count squares to get L/w
Resistance in W = Rs(L/w)

41. Sheet Resistance (cont.)
Relates xj, mobility (m), and impurity distribution C(x)
For a given diffusion profile, the average resistivity ( = Rsxj) is uniquely related to Cs and for an assumed diffusion profile.
Irvin curves relating Cs and have been calculated for simple diffusion profiles.

42. Irvin Curves