diffusion in vlsi
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Contains a full description. Read all other presentations in the "l*" series to get a full understanding of VLSI fab process.* indicates numberTRANSCRIPT
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DIFFUSION
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Diffusion
• Why impurity doping:• To change electrical properties.
• Methods:– Ion implantation– Diffusion
• Diffusion deep junction
• Ion implantation shallow junction
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Basic Process
• Ambient:– Carefully controlled– High temperature quartz tube furnace– Gas mixture containing desired dopants.
• Temperature range: 800-12000C• P-type: boron n-type: phosphorous • Uses liquid sources.
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Process:
• Cause: concentration gradient.
• Ambient: higher concentration
• Initially there are no impurities in the bulk crystal.
• Hence impurity atoms move inside crystal.
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Mechanism:
• Substitution
• Interstitial
• Interstitialcy
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Diffusion Mechanisms
• Vacancy model– For substitutional
impurities like P, B, As, Al, Ga
– Impurity atom exchanges position with a vacancy in the lattice
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• Interstitial Diffusion
– For interstitial impurities like O, Au, Fe, Cu, Ni
– Rapid diffusion but impurities do not contribute to doping
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The two principal diffusion mechanisms:Schematic diagrams
Vacancy diffusionin a semiconductor.
Interstitial diffusion in a semiconductor.
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Diffusivity
• Intrinsic diffusivity is a function of temperature:
– D = D0exp(-Ea/kT)
Where Ea is the activation energy for the diffusion process
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• Fick’s Laws of Diffusion:– 1st Law: Flux of dopants is proportional to
concentration gradient
– 2nd Law: Rate of change of concentration is proportional to change of concentration gradient with depth
– Constant of proportionality is called diffusivity or diffusion constant which is dependent on temperature
dx
txdCDJ
),(
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Fick’s 2nd law:
Change in flux with position = rate of change of concentration at given point
)(.. 12 JJAdt
dCdxA
dx
Dd
dx
dJ
dt
dC dxdC ][
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• Depending on D, diffusion can be of 2 types:– Constant surface concentration-/constant
source-/infinite source- diffusion.– Constant total dose diffusion
• Case 1: D is constant
• Case 2: D depends on x (position).
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Infinite source diffusion
• Boundary condition:– C (0, t) = Cs– C ( , t) = 0
• Initial condition– C (x, 0) = 0
• Solving for Fick’s law (subjected to these conditions):
tD
xerfcCtxC s
2,
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• Nature of the curve:
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Constant total dopant
• Limited Source:
– C (x, 0) = 0; x ≠ 0 (initial condition)
– C ( , t) = 0
– Solution:
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– Called drive-in diffusion
– Solution is Gaussian
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Junction depth (Xj)
When concentration of impurity is equal to background doping concentration, that depth is junction depth
• Case 1: pre-deposition diffusion
• Case 2: drive-in diffusion
s
Bj C
CerfcDtx 1..2
)ln(..4DtC
QDtx
B
Tj
Where CB is the background concentration
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• Diffusion Process: Pre-deposition followed by Drive-in.
• Pre-deposition:
• Drive-in:
• Finally,
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At the mask edge…
• Impurities will diffuse downwards and sideways.
• This is lateral diffusion.
• Ratio of lateral to vertical penetration:– 75% for constant total dopant.– 65-70% for concentration dependant.
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A comparison with Ion-Implantation:• Advantages of implantation over diffusion;
– Lesser contamination.– Better control over the process.– Room temperature process.– Better flexibility.– Not governed by solid solubility or
concentration gradient.
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• Disadvantages of Implantation over diffusion:– Expensive.– Damage creation.
• Can be annealed out. But…