标题：NUMERICAL METHOD OF MIXED FINITE VOLUME-MODIFIED UPWIND FRACTIONAL STEP DIFFERENCE FOR THREE-DIMENSIONAL SEMICONDUCTOR DEVICE TRANSIENT BEHAVIOR PROBLEMS
作者：Yuan, Yirang; Yang, Qing; Li, Changfeng; Sun, Tongjun
作者机构：[YUAN, Y] Institute of Mathematics, Shandong University, Jinan, 250100, China;[ YANG, Q] School of Mathematical Sciences, Shandong Normal University, 更多
通讯作者地址：[Yuan, YR]Shandong Univ, Inst Math, Jinan 250100, Peoples R China.
关键词：three dimensional transient behavior of heat conduction problem;mixed finite volume element;modified upwind fractional step difference;second-order error estimate in L2 norm;numerical computation
摘要：Transient behavior of three-dimensional semiconductor device with heat conduction is described by a coupled mathematical system of four quasi-linear partial differential equations with initial-boundary value conditions.The electric potential is defined by an elliptic equation and it appears in the following three equations via the electric field intensity.The electron concentration and the hole concentration are determined by convection-dominated diffusion equations and the temperature is interpreted by a heat conduction equation.A mixed finite volume element approximation,keeping physical conservation law,is used to get numerical values of the electric potential and the accuracy is improved one order.Two concentrations and the heat conduction are computed by a fractional step method combined with second-order upwind differences.This method can overcome numerical oscillation,dispersion and decreases computational complexity.Then a three-dimensional problem is solved by computing three successive one-dimensional problems where the method of speedup is used and the computational work is greatly shortened.An optimal second-order error estimate in L2 norm is derived by using prior estimate theory and other special techniques of partial differential equations.This type of mass-conservative parallel method is important and is most valuable in numerical analysis and application of semiconductor device.