三维半导体器件问题在时空局部加密复合网格上的有限差分格式

A FINITE DIFFERENCE SCHEME FOR THREE-DIMENSIONAL SEMICONDUCTOR DEVICE ON GRIDS WITH LOCAL REFINEMENT IN TIME AND SPACE

半导体器件的瞬时状态由三个方程组成的非线性偏微分方程组的初边值问题决定,电子位势方程是椭圆型的,电子和空穴浓度方程是抛物型的．依据实际数值模拟的需要,提出了一类三维半导体问题在时间和空间上进行局部加密的复合网格上的有限差分形式,并给出了电子和空穴浓度的最大模误差估计,最后给出了数值算例．

The momentary state of a semiconductor device is described by a system of three nonlinear partial differential equations. One elliptic equation is for the electrostatic potential, and two parabolic equations are for the electron concentration and the hole concentration. According to the necessary of practical numerical simulations, a finite difference scheme for three-dimensional transient behavior of a semiconductor device on grids with local refinement in time and space is constructed and studied. Error analysis is presented and is illustrated by a numerical example.