三维热传导型半导体器件瞬态模拟问题Crank-Nicolson差分-流线扩散有限元法及其数值分析  

C-N DIFFERENCE STREAMLINE DIFFUSION METHOD FOR THREE-DIMENSIONAL SEMICONDUCTOR PROBLEM WITH HEAT-CONDUCTION AND NUMERICAL ANALYSIS

作　　者：张争茹[1] 羊丹平[1] 

机构地区：[1]山东大学数学系,济南250100

出　　处：《应用数学学报》2002年第2期230-243,共14页Acta Mathematicae Applicatae Sinica

基　　金：国家重点基础研究规划项目(G1999032803);教育部高等院校骨干教师专项科研基金资助项目.

摘　　要：本文研究三维热传导型半导体器件瞬态模拟问题的数值方法.针对数学模型中各方程不同的特点,分别提出不同的有限元格式.特别针对浓度方程组是对流为主扩散问题的特点,使用Crank-Nicolson差分-流线扩散计算格式,提高了数值解的稳定性.得到的L2误差估计关于空间剖分步长是拟最优的,关于时间步长具有二阶精度.Abstract In this article, we study the numerical method for simulation of three-dimensional semiconductor problem with heat-conduction. Considering different types of partial differential equations arising from the model for the transient behavior of a semiconductor device, we present different finite element scheme respectively. Especially, we use Crank-Nicolson difference streamline diffusion method to treat convection-diffusion equations of the concentrations of electron and hole in the model. The numerical stability is improved by difference streamline diffusion method. An error estimate in L2 norm with quasi-optimal accuracy in space and second order accuracy in time is derived.

关 键 词：热传导型半导体器件 瞬态模拟问题 有限元法 数值分析 CRANK-NICOLSON格式 差分流线扩散法 误差估计 

分 类 号：TN303[电子电信—物理电子学] O241.82[理学—计算数学]