适于半导体器件模拟的改进Gummel算法

A Modified Gummel Algorithm for Semiconductor Device Simulation

本文采用Ｓｌｏｔｂｏｏｍ变量把半导体器件模型归一化为奇异摄动问题．然后对该模型提出一种适于ｍ维（１≤ｍ≤３）数值计算的Ｇｕｍｍｅｌ算法，当外加偏压或器件测度（二维时如有效沟道长度，三维时如器件的有效体积等）足够小时，该算法是收敛的．数值例子表明，改进的Ｇｕｍｍｅｌ算法编程方便，收敛速度快．

Abstract This paper presents a singular perturbation model for semiconductor device equation in Slotboom variable.A modified Gummel map T is proposed for this model considering m-dimensional numerical computational reasons.For sufficiently small variation of biased potential or small measure of device body,the convergence of modified Gummel method is proved.A numerical example indicates that the new method converges faster than Gummel's one.