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DIFFUSION.PDE

This problem considers the thermally driven diffusion of a dopant into a solid from a constant source. Parameters have been chosen to be those typically encountered in semiconductor diffusion.

surface concentration = 1.8e20 atoms/cm^2
diffusion coefficient = 3.0e-15 cm^2/sec

The natural tendency in this type of problem is to start off with zero concentration in the material, and a fixed value on the boundary. This implies an infinite curvature at the boundary, and an infinite transport velocity of the diffusing particles. It also generates over-shoot in the solution, because the Finite-Element Method tries to fit a step function with quadratics.

A better formulation is to program a large input flux, representative of the rate at which dopant can actually cross the boundary, (or approximately the molecular velocity times the concentration deficiency at the boundary).

Here we use a masked source, in order to generate a 2-dimensional pattern. This causes the result to lag a bit behind the analytical Plane-diffusion result at late times.

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