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Predeposition Equations

A predeposition diffusion is defined as a diffusion with an unlimited source of impurities (in excess of that required to reach the solid solubility limit of the substrate).

The distribution of the impurities within the substrate is found by solving Fick's Laws with the following initial and boundary conditions:

Initial condition:
N(x=0⁺,t=0) = 0 (no impurity in the substrate at the start of the predep)

Boundary conditions:
N₀ = constant = N_sl (surface concentration is limited by the solid solubility)

N_∞ = 0 (limited time so that impurity does not diffuse through the material)

The solution to Ficks Laws:

where:
N₀ = N_sl (the surface concentration = solid solubility limit of the dopant/substrate system)
x = position within the substrate where N is evaluated
D = diffusion coefficient of the impurity (temperature and dopant specific)
t = time of the diffusion

Dose (Q)

The dose is the # impurity atoms/cm² and is found by integrating the flux crossing the surface of the substrate over the length of the predep.

Processing Equations

· Four Point Probe

· Oxidation

· Photolithography

· Phase Diagrams

· Predeposition Diffusion

· Junctions

· Drive Diffusion

· CVD

· Ion Implantation

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