半导体器件瞬态模拟的对称正定混合元方法  

A SYMMETRIC POSITIVE DEFINITE MIXED FINITE ELEMENT METHOD FOR TRANSIENT SIMULATION OF A SEMICONDUCTOR DEVICE

作　　者：羊丹平[1] 

机构地区：[1]山东大学数学所,济南250100

出　　处：《应用数学学报》2000年第3期444-456,共13页Acta Mathematicae Applicatae Sinica

基　　金：国家重点基础研究规则项目;教育部博士点专项科研基金;"跨世纪优秀人才计划"基金

摘　　要：提出具有对称正定特性的混合元格式求解非稳态半导体器件瞬态模拟问题．提出一个最小二乘混合元方法、一个新的具有分裂和对称正定性质的混合元格式和一个解经典混合元方程的对称正定迭代格式求解电场位势和电场强度方程；提出一个最小二乘混合元格式求解关于电子与空穴浓度的非稳态对流扩散方程，浓度函数和流函数被同时求解；采用标准的有限元方法求解热传导方程．建立了误差分析理论。in this article, we present some symmetric positive definite mixed finite element methods to solve transient simulation of a semiconductor device with heat conduction. Three mixed element procedures are introduced to treat equations of the electronic potential and intensity. The first is a least-squares mixed finite element scheme, the second is a new mixed element algorithm with splitting and symmetric positive definite properties and the third is a symmetric positive definite iterative algorithm for the classical mixed finite element method. A least--squares mixed finite element method is used to solve time-dependent convection- diffusion equations on concentrations of electron and hole, in which concentration equations and flux functions are solved simultaneously. A standard finite element method is used to solve equation of heat conduction. Convergence analysis of the numerical method is given.

关 键 词：半导体器件 数值模拟 对称正定混合元 瞬态模拟 

分 类 号：TN303[电子电信—物理电子学]