FINITE ELEMENT ANALYSIS OF THE ONE-DIMENSIONAL FULL DRIFT-DIFFUSION SEMICONDUCTOR MODEL

摘要

This paper analyzes an explicit finite element procedure for the simulation of the transient behavior of the drift-diffusion semiconductor devices, which consist of three quasilinear partial differential equations, one formally of elliptic type for the potential and two formally of parabolic type for the electron and hole concentrations, and include the recombination-generation rates and velocity saturation mobilities. The procedure is based on the use of a mixed finite element method for the potential and discontinuous upwinding finite element method for the electron and hole concentration equations. The method for the concentration equations is proven to satisfy a maximum principle and to be total variation bounded. The Kuznetsov approximation theory for scalar conservation laws is applied to show that asymptotic error estimates of optimal order can be obtained and that the constants for the error estimates are independent of the small diffusion coefficients of the concentration equations. Numerical experiments are presented to test the performance of the scheme and to indicate the asymptotic behavior of the solution as a function of mobilities, generation rates, and diffusion terms. [References: 28]