Adaptive meshing schemes for simulating dopant diffusion

Two adaptive meshing schemes for the efficient simulation of dopant diffusion in silicon using the finite element method are presented. The first scheme is based on an adaptation criterion which is obtained by computing a local error estimate derived from the finite element solution itself. The second scheme is based on a mesh adaption criterion which uses physical diffusion parameters. A comparison is then made between the results obtained using the two different meshing schemes. Results obtained using both schemes are in very good agreement with each other; however, the remeshing scheme based on the physical criterion is easier to implement and reduces computation time by a factor of five as compared to the remeshing based on error evaluation. It is thus shown that a computationally efficient adaptive meshing strategy for dopant diffusion problems can be developed by employing a spatial discretization which limits the variation of the diffusion coefficient over an element