半导体器件模拟中求解线性系统的预条件处理方法  

Precondition Methods for Solving Linear Systems in Semiconductor Device Simulation

作　　者：刘其贵[1] 吴金[1] 肖志强[1] 魏同立[1] 

机构地区：[1]东南大学微电子中心,南京210096

出　　处：《东南大学学报（自然科学版）》2001年第4期14-17,共4页Journal of Southeast University：Natural Science Edition

基　　金：国家自然科学基金 ( 6980 60 0 2 );江苏省自然科学基金 (BK970 0 6)资助项目

摘　　要：对半导体器件模拟中求解线性方程组的预条件处理方法 ,即不完全LU分解方法进行了研究 .首先介绍了ILU分解的理论基础 ,说明了采用预条件处理方法对解决线性方程组迭代求解收敛的重要性 .然后介绍了由ILU方法发展而来的ILUV方法 ,并在对ILU和ILUV方法的理论研究和算法分析的基础上 ,提出了兼容以上 2种方法优点的ILUVP方法 ,解决了ILUV方法中参数 ψ的选取无法兼顾计算量和收敛速度不同要求的难题 .最后通过对一个存在陡峭层分布的漂移扩散方程进行求解的实例 ,验证了算法的可行性和有效性 .This paper discusses the pre condition methods (that is, the ILU methods) for solving the linear system in semiconductor device simulation.First, with the introduction to the theoretical foundation of ILU methods, the importance of applying pre condition methods to solve the iterative convergence problem of linear equations is illustrated. Then, the ILUV methods, which were developed from the ILU methods are introduced. Based on the theoretical study and algorithmic analysis of those ILU and ILUV methods, the ILUVP method, which maintains the merits of those two methods and solves the problem that the selection of the parameter ψ in the ILUV method can not meet the different demands for both calculating amount and the convergence rate, is put forward. Finally, through an example of a drift and diffusion equation with steep distribution, the feasibility and effectivity of this algorithm are proved.

关 键 词：半导体器件 ILU ILUV ILUVP 预条件 线性系统 

分 类 号：TN303[电子电信—物理电子学]