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

doi:10.1007/s10473-020-0514-x

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (5): 1405-1428.doi: 10.1007/s10473-020-0514-x

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

袁益让¹, 李长峰^2,3, 宋怀玲⁴

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

收稿日期:2019-01-14 修回日期:2020-05-13 出版日期:2020-10-25 发布日期:2020-11-04
通讯作者: Changfeng LI E-mail:cfli@sdu.edu.cn
作者简介:Yirang YUAN,E-mail:yryuan@sdu.edu.cn;Huailing SONG,E-mail:shling@hnu.edu.cn
基金资助:
This research was supported the Natural Science Foundation of Shandong Province (ZR2016AM08), Natural Science Foundation of Hunan Province (2018JJ2028), National Natural Science Foundation of China (11871312).

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

Yirang YUAN¹, Changfeng LI^2,3, Huailing SONG⁴

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

Received:2019-01-14 Revised:2020-05-13 Online:2020-10-25 Published:2020-11-04
Contact: Changfeng LI E-mail:cfli@sdu.edu.cn
Supported by:
This research was 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/Abstract

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 initial-boundary 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

Abstract: The numerical simulation of a three-dimensional semiconductor device is a fundamental problem in information science. The mathematical model is defined by an initial-boundary 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.

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

中图分类号:

65M06

袁益让, 李长峰, 宋怀玲. A BLOCK-CENTERED UPWIND APPROXIMATION OF THE SEMICONDUCTOR DEVICE PROBLEM ON A DYNAMICALLY CHANGING MESH[J]. 数学物理学报(英文版), 2020, 40(5): 1405-1428.

Yirang YUAN, Changfeng LI, Huailing SONG. A BLOCK-CENTERED UPWIND APPROXIMATION OF THE SEMICONDUCTOR DEVICE PROBLEM ON A DYNAMICALLY CHANGING MESH[J]. Acta mathematica scientia,Series B, 2020, 40(5): 1405-1428.

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

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

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