三维热传导型半导体问题的交替方向特征有限元方法及理论分析

１．引言 三维热传导型半导体器件瞬态问题的数学模型由四个非线性偏微分方程描述 ［１，２］．工程研究中一般考虑绝流边条件，由于绝流条件可以看作一反射条件来处理、为了数值分析方便，我们在此考虑三维周期问题： 其中，　＝［０，１］３，未知函数是电子位势　；电子，空穴浓度ｅ，ｐ；温度函数Ｔ．方程（１，１）－（１.４）中出现的系数均有正的上下界，且是　周期的． ａ＝Ｑ／ε，Ｑ，ε分别表示电子负荷和介电系数，均为正常数．Ｎ（ｘ）是给定的函数．Ｄｓ（ｘ）为扩散系数，μｓ（ｘ）为迁移率，ｓ＝ｅ，Ｐ．Ｒ（ｅ，ｐ，Ｔ）…

ALTERNATING-DIRECTION CHARACTERISTIC FIWITE ELEMENT METHODS AND ANALYSES FOR THE THREE-DIMENSIONAL SEMICONDUCTOR PROBLEM WITH HEAT-CONDUCTION

Alternating-direction methods are combined with characteristic finite element to treat the problem of three-dimensional transient behavior of semiconductor with heat-conduction, whose mathematical model is an initial and boundary problem of nonlinear partial differential equation system(Electric potential equation is approximated by mixed finite element method, concentration equations are approximated by alternating-direction characteristic finite element methods,and heatconduction equation is approximated by Galerkin alternating-direction method. Optimal order error estimates in L2 are demonstrated.