Example: Diffusion

This problem considers the thermally driven diffusion of a dopant into a solid from a constant masked source. Parameters have been chosen to be those typically encountered in semiconductor diffusion. The PDE is just the diffusion equation:

dt(C) = div(D*grad(C)) ,

where C is the concentration and D is the diffusivity. At early times, the solution near the source can be compared to the analytic solution for 1D diffusion.

Concentration contours at time = 1 hour.

Comparison of numerical and exact solutions (C/C0) along center line.

Concentration (C/C0) vs. time at various points along the center line.