ELEC 7364 Lecture Notes Summer 2008 - Home | …work7364/diffusion.pdf · ELEC 7364 Lecture Notes...
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The University of Michigan – Visiting Prof. HKU p. 1 S. W. Pang ELEC 7364 Lecture Notes Summer 2008 Dopant Diffusion by STELLA W. PANG from The University of Michigan, Ann Arbor, MI, USA Visiting Professor at The University of Hong Kong The University of Michigan – Visiting Prof. HKU p. 2 S. W. Pang Movement Due to Concentration Gradient
Transcript of ELEC 7364 Lecture Notes Summer 2008 - Home | …work7364/diffusion.pdf · ELEC 7364 Lecture Notes...
The University of Michigan – Visiting Prof. HKU p. 1 S. W. Pang
ELEC 7364 Lecture Notes Summer 2008
Dopant Diffusion
by STELLA W. PANG
from The University of Michigan, Ann Arbor, MI, USA
Visiting Professor at The University of Hong Kong
The University of Michigan – Visiting Prof. HKU p. 2 S. W. Pang
Movement Due to Concentration Gradient
The University of Michigan – Visiting Prof. HKU p. 3 S. W. Pang
Impurity Types
The University of Michigan – Visiting Prof. HKU p. 4 S. W. Pang
Movement of atoms through vacancies or interstitials of crystal lattice
Dopants (e.g. B, As, P): Big, Slow Diffusers through Vacancies
Metals (e.g. Na+, Li+, Fe+, …): Small, Ionic, Fast Diffusers through Interstitial
Dopant Diffusion
The University of Michigan – Visiting Prof. HKU p. 5 S. W. Pang
Assume no thermal or electrical gradient Fick's 1st Law (Concentration Gradient)
Flux
D = Diffusion Constant (cm2/s) C = Concentration of Impurities (atoms/cm3)
Fick's 2nd Law (Continuity and Matter Conservation)
Rate of Conc. Change Local Change in Diff Flux
Solve for C(x,t) using B. C.
Diffusion Process
€
J( atomscm2 − s
) = −D∂C∂x
€
∂C∂t
= −∂∂x(D∂C
∂x)
The University of Michigan – Visiting Prof. HKU p. 6 S. W. Pang
Surface concentration is held constant - Needs continuous supply of dopants (e.g. POCl3, B2H6, …)
B.C.: C(0,t) = Constant, C(∞,t) = 0; C(x,0) = 0 Solution: Complementary error function
at x=0: erfc(0)=1; C=Cs at x= : erfc(1)=0.16; C=0.16Cs
Diffusion Length LD =
Higher dose, deeper junction with longer diffusion time
Constant Source Diffusion
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C(x,t) = Cserfc(x
2 Dt)
€
erfc(y) = 1− 2π
e−η2
0
y
∫ dη
€
2 Dt
€
2 Dt
The University of Michigan – Visiting Prof. HKU p. 7 S. W. Pang
Junction Depth = xj At x = xj C(x) = Csub
Total Dose = Q
Constant Source - Junction Depth
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xj = 2 Dt erfc−1Csub
Cs
Q = C(x, t )dx = 2
π0
+∞
∫ Cs Dt
The University of Michigan – Visiting Prof. HKU p. 8 S. W. Pang
A fixed amount of dopants is deposited in the wafer before diffusion (e.g. ion implantation or drive-in after pre-deposition)
B.C.: C(∞,t) = 0 Known amount: (atoms/cm2)
Gaussian Solution:
Lower Cs, larger xj at longer diffusion time
Limited Source Diffusion
€
Qo = C(x,t)dx0
∞
∫
€
C(x,t) =Qo
πDte−x 2
4Dt
The University of Michigan – Visiting Prof. HKU p. 9 S. W. Pang
Surface Concentration decreases with time At x= 0:
At x= C = Cse-1
Junction Depth: at x= xj, C(x) = Csub
Limited Source - Junction Depth
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Cs =Qo
πDt
€
2 Dt
€
xj = 4Dt ln Cs
Csub
The University of Michigan – Visiting Prof. HKU p. 10 S. W. Pang
B in Si with Csub = 1.5x1016 cm-3 Constant Source Diffusion: Cs = 1.8x1020 cm-3 D = 3x10-15 cm2/s, t = 30 min
LD = = 4.7x10-6 cm
= 0.13 µm
Total amount of B in Si
= 4.7x1014 atoms/cm2
Diffusion Example
€
2 Dt
€
xj = 2 Dt erfc−1Csub
Cs
€
Q = C(x,t)dx =2π0
+∞
∫ Cs Dt
The University of Michigan – Visiting Prof. HKU p. 11 S. W. Pang
erfc(x) is steeper than exp(-x2)
Complementary Error and Gaussian Profiles
The University of Michigan – Visiting Prof. HKU p. 12 S. W. Pang
p-type: B atom, Diffuses as negatively charged atom - Intrinsic Diffusion Constant (Neutral Vacancies + Positively Charged Vacancies)
- At 1000 °C: - Relatively fast diffuser, need to limit thermal
budget for shallow junction n-type: As and P atoms
- For As: Slower Diffuser, more abrupt and shallow junction
- Intrinsic Diffusion Constant (Neutral Vacancies + Negatively Charged Vacancies)
- At 1000 °C:
Dopants in Si
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DBi = DBV
o +DBV+1
€
DBi ~10−14 cm
2
s
€
DAsi = DAs−V
o +DAs−V−1
€
DAsi ~10−15 cm
2
s
The University of Michigan – Visiting Prof. HKU p. 13 S. W. Pang
For P: Faster Diffuser, not as good for shallow junction
- Intrinsic Diffusion Constant (Neutral Vacancies)
- At 1000 °C: - P junctions form "kink" at high concentration
due to excess vacancies
Phosphorus in Si
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DPi = DP−V
o
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DPi ~10−14 cm
2
s
The University of Michigan – Visiting Prof. HKU p. 14 S. W. Pang
Faster Diffusion at Higher Temperature At any given temperature: Dsubstitutional << Dinterstitial
Control Diffusion Coefficient
The University of Michigan – Visiting Prof. HKU p. 15 S. W. Pang
Control No at the solid solubility limit: Wide process margin
At the solid solubility limit: Chemical concentration >Electrically active concentration
Control of high dose but shallow profile difficult
Control Surface Concentration
The University of Michigan – Visiting Prof. HKU p. 16 S. W. Pang
Similar to oxidation furnaces - Batch Processing Solid, liquid, gas dopant sources available
Diffusion Systems
The University of Michigan – Visiting Prof. HKU p. 17 S. W. Pang
Dominated by grain-boundary diffusion. Much faster (10-100 X) compared to diffusion in single crystal Si
Grain size varies (50-300 nm) and dopants can precipitate at grain boundaries and lower conductivity
Dopant Diffusion in Poly-Si
The University of Michigan – Visiting Prof. HKU p. 18 S. W. Pang
Usually xL ~ 0.8 xh
Need to minimize lateral diffusion: - Change Leff or cause punch through if S/D
overlap - Increase CGD and CGS due to diffusion under gate,
Result in increased parasitic and reduced speed
Lateral Diffusion
