A BLOCK-CENTERED UPWIND APPROXIMATION OF THE SEMICONDUCTOR DEVICE PROBLEM ON A DYNAMICALLY CHANGING MESH  

作　　者：Yirang YUAN Changfeng LI Huailing SONG 袁益让;李长峰;宋怀玲(Institute of Mathematics,Shandong University,Jinan 250100,China;Shandong Applied Financial Theory and Policy Research Base,Jinan 250100,China;School of Economics,Shandong University,Jinan 250100,China;College of Mathematics and Econometrics,Hunan University,Changsha 410082,China)

机构地区：[1]Institute of Mathematics,Shandong University,Jinan 250100,China [2]Shandong Applied Financial Theory and Policy Research Base,Jinan 250100,China [3]School of Economics,Shandong University,Jinan 250100,China [4]College of Mathematics and Econometrics,Hunan University,Changsha 410082,China

出　　处：《Acta Mathematica Scientia》2020年第5期1405-1428,共24页数学物理学报（B辑英文版）

基　　金：supported the Natural Science Foundation of Shandong Province(ZR2016AM08);Natural Science Foundation of Hunan Province(2018JJ2028);National Natural Science Foundation of China(11871312).

摘　　要：The numerical simulation of a three-dimensional semiconductor device is a fundamental problem in information science. The mathematical model is defined by an initialboundary nonlinear system of four partial differential equations: an elliptic equation for electric potential, two convection-diffusion equations for electron concentration and hole concentration, and a heat conduction equation for temperature. The first equation is solved by the conservative block-centered method. The concentrations and temperature are computed by the block-centered upwind difference method on a changing mesh, where the block-centered method and upwind approximation are used to discretize the diffusion and convection, respectively. The computations on a changing mesh show very well the local special properties nearby the P-N junction. The upwind scheme is applied to approximate the convection, and numerical dispersion and nonphysical oscillation are avoided. The block-centered difference computes concentrations, temperature, and their adjoint vector functions simultaneously.The local conservation of mass, an important rule in the numerical simulation of a semiconductor device, is preserved during the computations. An optimal order convergence is obtained. Numerical examples are provided to show efficiency and application.

关 键 词：three-dimensional semiconductor device of heat conduction block-centered upwind difference on a changing mesh local conservation of mass convergence analysis numerical computation 

分 类 号：O175.29[理学—数学] TN303[理学—基础数学]