Stabilized finite elements for semiconductor device simulation

Abstract.

This work deals with the numerical simulation of the so-called Drift-Diffusion model for semiconductors. It includes two current continuity equations which are scalar convection-diffusion equations, with possibly dominating convection. To face this problem we have resorted to two main strategies. We use the Streamline–Upwind/Petrov-Galerkin (SUPG) method with a shock-capturing technique which increases the amount of numerical dissipation in the neighbourhood of layers without loosing the high accuracy in regions where the solution is smooth. This strategy is carried out along with adaptive grid refinement which reduces the mesh size only where needed. Numerical results for cases of physical interest in two dimensions on unstructured grids are presented. Total Variation Diminishing (TVD) methods and Mixed Finite Volumes (MFV) are tested as well.