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

The mathematical model for semiconductor devices of heat conduction is numerically discretized. The physical variables are the electrostatic potential, the electron and hole concentrations, and the temperature. Standard mixed finite element is used for the elliptic electric potential equation. A characteristics-mixed finite element method is presented for the two convection-dominated concentration equations. Standard finite element is used for the temperature equation of parabolic type. This scheme conserves mass locally for the concentrations. In order to derive the optimal L2L2-norm error estimates, a post-processing step is included in the approximation to the scalar concentrations. Numerical experiment is presented finally to validate the theoretical analysis.