DIFFUSION

Diffusion

• Why impurity doping:• To change electrical properties.

• Methods:– Ion implantation– Diffusion

• Diffusion deep junction

• Ion implantation shallow junction

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.

Process:

• Cause: concentration gradient.

• Ambient: higher concentration

• Initially there are no impurities in the bulk crystal.

• Hence impurity atoms move inside crystal.

Mechanism:

• Substitution

• Interstitial

• Interstitialcy

Diffusion Mechanisms

• Vacancy model– For substitutional

impurities like P, B, As, Al, Ga

– Impurity atom exchanges position with a vacancy in the lattice

• Interstitial Diffusion

– For interstitial impurities like O, Au, Fe, Cu, Ni

– Rapid diffusion but impurities do not contribute to doping

The two principal diffusion mechanisms:Schematic diagrams

Vacancy diffusionin a semiconductor.

Interstitial diffusion in a semiconductor.

Diffusivity

• Intrinsic diffusivity is a function of temperature:

– D = D0exp(-Ea/kT)

Where Ea is the activation energy for the diffusion process

• 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

),(

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 ][

• 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).

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,

• Nature of the curve:

Constant total dopant

• Limited Source:

– C (x, 0) = 0; x ≠ 0 (initial condition)

– C ( , t) = 0

– Solution:

– Called drive-in diffusion

– Solution is Gaussian

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

• Diffusion Process: Pre-deposition followed by Drive-in.

• Pre-deposition:

• Drive-in:

• Finally,

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.

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.

• Disadvantages of Implantation over diffusion:– Expensive.– Damage creation.

• Can be annealed out. But…