二维热传导型半导体问题的一个二阶格式

Finite Difference Method and Analysis For Two-dimensional Semiconductor Device of Heat Conduction

热传导型半导体器件瞬态问题的数学模型由四个拟线性偏微分方程所组成的方程组的初边值问题来描述 .其中电子位势方程是椭圆型的 ,电子和空穴浓度方程是对流扩散型的 ,温度方程为热传导型的 .本文对二维热传导型半导体的一类混合初边值问题利用降阶法给出了一个二阶差分格式 ,并对其进行了详细的理论分析 ,得到了离散的 l2

The mathematical model of the two- dimensional semiconductor devices of heat condition is described by a system of four quasilinear partial differential equations for ini- tial boundary value problem.One equation in elliptic form is for the electric potential;two equations of convection- dominated diffusion type are for the electron and hole concentra- tion;and one heatconduction equation is for temperature.A scheme that has convergence rate of second orderis derived by the method of reduction of orderforthis system,and the analysis of convergence is presented.