NUMERICAL METHOD OF MIXED FINITE VOLUME-MODIFIED UPWIND FRACTIONAL STEP DIFFERENCE FOR THREE-DIMENSIONAL SEMICONDUCTOR DEVICE TRANSIENT BEHAVIOR PROBLEMS

doi:10.1016/S0252-9602(16)30129-1

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (1): 259-279.doi: 10.1016/S0252-9602(16)30129-1

NUMERICAL METHOD OF MIXED FINITE VOLUME-MODIFIED UPWIND FRACTIONAL STEP DIFFERENCE FOR THREE-DIMENSIONAL SEMICONDUCTOR DEVICE TRANSIENT BEHAVIOR PROBLEMS

袁益让¹, 杨青², 李长峰³, 孙同军³

1. Institute of Mathematics, Shandong University, Jinan 250100, China;
2. School of Mathematical Sciences, Shandong Normal University, Jinan 250014, China;
3. School of Economics, Shandong University, Jinan 250100, China

收稿日期:2014-08-31 修回日期:2016-02-03 出版日期:2017-02-25 发布日期:2017-02-25
作者简介:Yirang YUAN,E-mail:yryuan@sdu.edu.cn;Qing YANG,E-mail:sd-yangq@163.com;Changfeng LI,E-mail:cfli@sdu.edu.cn;Tongjun SUN,E-mail:tjsun@sdu.edu.cn
基金资助:
This work is supported by National Natural Science Foundation of China (11101244, 11271231), National Tackling Key Problems Program (20050200069), and Doctorate Foundation of the Ministry of Education of China (20030422047).

NUMERICAL METHOD OF MIXED FINITE VOLUME-MODIFIED UPWIND FRACTIONAL STEP DIFFERENCE FOR THREE-DIMENSIONAL SEMICONDUCTOR DEVICE TRANSIENT BEHAVIOR PROBLEMS

Yirang YUAN¹, Qing YANG², Changfeng LI³, Tongjun SUN³

1. Institute of Mathematics, Shandong University, Jinan 250100, China;
2. School of Mathematical Sciences, Shandong Normal University, Jinan 250014, China;
3. School of Economics, Shandong University, Jinan 250100, China

Received:2014-08-31 Revised:2016-02-03 Online:2017-02-25 Published:2017-02-25
About author:Yirang YUAN,E-mail:yryuan@sdu.edu.cn;Qing YANG,E-mail:sd-yangq@163.com;Changfeng LI,E-mail:cfli@sdu.edu.cn;Tongjun SUN,E-mail:tjsun@sdu.edu.cn
Supported by:
This work is supported by National Natural Science Foundation of China (11101244, 11271231), National Tackling Key Problems Program (20050200069), and Doctorate Foundation of the Ministry of Education of China (20030422047).

摘要/Abstract

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.

关键词: three dimensional transient behavior of heat conduction problem, mixed finite volume element, modified upwind fractional step difference, second-order error

Abstract:

Key words: three dimensional transient behavior of heat conduction problem, mixed finite volume element, modified upwind fractional step difference, second-order error

袁益让, 杨青, 李长峰, 孙同军. NUMERICAL METHOD OF MIXED FINITE VOLUME-MODIFIED UPWIND FRACTIONAL STEP DIFFERENCE FOR THREE-DIMENSIONAL SEMICONDUCTOR DEVICE TRANSIENT BEHAVIOR PROBLEMS[J]. 数学物理学报(英文版), 2017, 37(1): 259-279.

Yirang YUAN, Qing YANG, Changfeng LI, Tongjun SUN. NUMERICAL METHOD OF MIXED FINITE VOLUME-MODIFIED UPWIND FRACTIONAL STEP DIFFERENCE FOR THREE-DIMENSIONAL SEMICONDUCTOR DEVICE TRANSIENT BEHAVIOR PROBLEMS[J]. Acta mathematica scientia,Series B, 2017, 37(1): 259-279.

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NUMERICAL METHOD OF MIXED FINITE VOLUME-MODIFIED UPWIND FRACTIONAL STEP DIFFERENCE FOR THREE-DIMENSIONAL SEMICONDUCTOR DEVICE TRANSIENT BEHAVIOR PROBLEMS

NUMERICAL METHOD OF MIXED FINITE VOLUME-MODIFIED UPWIND FRACTIONAL STEP DIFFERENCE FOR THREE-DIMENSIONAL SEMICONDUCTOR DEVICE TRANSIENT BEHAVIOR PROBLEMS

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