Mathematical model, block-centered difference and numerical analysis on changing meshes of semiconductor device problem with heat and magnetic influences

Abstract

Numerical simulation of semiconductor device with heat and magnetic influences is a preliminary problem in information science. In this paper, mathematical model, numerical method and theoretical analysis are discussed. Four major physical unknowns (the potential, electron concentration, hole concentration, and the heat) are defined by several nonlinear PDEs, an elliptic equation, two convection–diffusion equations and a heat conductor equation. A block-centered numerical method with conservative nature is used to obtain the potential, and the computational accuracy is improved. An upwind block-centered difference method is adopted for solving other PDEs on changing meshes. The diffusion and convection operators are discretized by block-centered differences and upwind differences, respectively. Changing meshes are effective for simulating the status nearby P-N junction. The composite scheme avoids numerical dispersion and nonphysical oscillation, and the conservation is preserved. The unknowns and their adjoint vectors are computed at the same time. Some theoretical techniques such as energy norm estimates, the method of duality and mathematical induction are used to finish convergence analysis. Error results are concluded. Finally, numerical examples show the efficiency and possible application.