An approximation of semiconductor device by mixed finite element method and characteristics-mixed finite element method

The mathematical model of a semiconductor device is described by a system of three quasi-linear partial differential equations for initial boundary value problem. The electric potential is governed by an elliptic equation. The electron and hole concentrations are governed by two equations of convection-dominated diffusion type. Standard mixed finite element is used for the electric potential equation. A characteristics-mixed finite element method is presented for the concentration equations. This scheme conserves mass locally. In order to derive the optimal L2L2-norm error estimates, a post-processing step is included in the approximation to the scalar concentration. Numerical experiment is presented finally to validate the theoretical analysis.