Example : DiffusionThis 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. |
