A Modified Characteristics-mixed Finite Element for Semiconductor Device of Heat Conduction and Numerical Analysis

Abstract

Numerical simulation of a three-dimensional semiconductor device of heat conduction is a fundamental problem in modern information science. The mathematical model is formulated by a nonlinear system of initial-boundary problem, which is interpreted by four partial differential equations: an elliptic equation for electrostatic potential, two convection-diffusion equations for electron concentration and hole concentration, a heat conduction equation for temperature. The electrostatic potential appears within the latter three equations, and the electric field strength controls the concentrations and the temperature. The electric field potential is solved by a mixed finite element method, and the electric field strength is obtained simultaneously. The first order of the accuracy is improved for the latter. The concentrations and temperature are computed by the characteristics-finite element method, where the characteristic approximation is adopted for the hyperbolic term and finite element method is use to treat the diffusion. The composite computational scheme can solve the convection-dominated diffusion equations well because it can cancel numerical dispersion and nonphysical oscillation. The temperature is computed by finite element method, and an interesting simulation tool is proposed for solving semiconductor device problem numerically. By using the technique of a priori estimates of differential equations, an optimal order error estimates is obtained. A theoretical work is shown for numerical simulation of information science, and the actual problem is solved well.