半导体瞬态问题的修正迎风有限体积格式  

MODIFIED UPWIND FINITE VOLUME SCHEME FOR SEMICONDUCTOR DEVICE

作　　者：杨青[1] 

机构地区：[1]山东师范大学数学科学院,济南250014

出　　处：《系统科学与数学》2008年第6期725-738,共14页Journal of Systems Science and Mathematical Sciences

基　　金：山东省自然科学基金(Z2006A02);山东省中青年科学家科研奖励基金(BS01009)资助项目

摘　　要：半导体器件的瞬时状态由包含三个拟线性偏微分方程所组成的方程组的初边值问题来描述.其中电子位势方程是椭圆型的,电子和空穴浓度方程是对流扩散型的.对电子位势方程采用一次元有限体积法来逼近,对电子浓度和空穴浓度方程采用修正的迎风有限体积方法来逼近,并进行详细的理论分析,关于位势得到O(h+Δt)阶的H^1模误差估计结果,关于浓度得到O(h^2+Δt)阶的L^2模误差估计结果.最后,给出数值例子.The mathematical model of the semiconductor device is described by the initial boundary value problem for a system of three quasilinear partial differential equations, where the electrostatic potential equation is elliptic, the electronic conservation equation and the hole concentration equation are convection-dominated diffusive. The electrostatic potential equation is approximated with the aid of finite volume method, while the electron and hole concentration equations are approximated with modified upwind finite volume schemes. Error order O（h ＋ △t） in H^1-norm and error order O（h^2 ＋ At） in L^2-norm are obtained, respectively for potential and concentration.

关 键 词：半导体 初边值问题 修正迎风格式 有限体积法 误差估计 

分 类 号：O241.82[理学—计算数学]