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

• 作者: Changfeng LI Huailing SONG Yirang YUAN
• 来源期刊: 数学物理学报（英文版）
• 年，卷（期）: 2020,（5）
• 页码范围: 1405-1428
• 页数: 24页
• 语种: 英文

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.