| FINITE DIFFERENCE FRACTIONAL STEP METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE |
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| 作者姓名： | 袁益让 |
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| 作者单位： | InstituteofMathematics,ShandongUniversity,Jinan250100,China |
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| 基金项目： | 国家重点基础研究发展计划(973计划)，国家自然科学基金，the Doctorate Foundation of the Ministry of Education of the Ministry of Education of China |
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| 摘 要： | Characteristic finite difference fractional step schemes are put forward. The electric potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are treated by a kind of characteristic finite difference fractional step methods. The temperature equation is described by a fractional step method. Thick and thin grids are made use of to form a complete set. Piecewise threefold quadratic interpolation, symmetrical extension, calculus of variations, commutativity of operator product, decomposition of high order difference operators and prior estimates are also made use of. Optimal order estimates in l2 norm are derived to determine the error of the approximate solution. The well-known problem is thorongley and completely solred.
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| 关 键 词： | 普通半导体装置 三维加热 有限差分特征 平行函数 误差估计 数学物理 |
| 收稿时间： | 25 November 2002 |
FINITE DIFFERENCE FRACTIONAL STEP METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE |
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| YUAN Yirang.FINITE DIFFERENCE FRACTIONAL STEP METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE[J].Acta Mathematica Scientia,2005,25(3):427-438. |
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| Authors: | YUAN Yirang |
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| Institution: | 1. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon;2. School of Basic Sciences and Humanities German Jordanian University, Amman, Jordan |
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| Abstract: | Characteristic finite difference fractional step schemes are put forward. The electric Potential equation is described by a seven-point finite difference scheme, and the electron and hole concentration equations are treated by a kind of characteristic finite difference fractional step methods. The temperature equation is described by a fractional step method. Thick and thin grids are made use of to form a complete set. Piecewise threefold quadratic interpolation, symmetrical extension, calculus of variations, commutativity of operator product, decomposition of high order difference operators and prior estimates are also made use of. Optimal order estimates in l2 norm are derived to determine the error of the approximate solution. The well-known problem is thorongley and completely solred. |
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| Keywords: | General region semiconductor device 3-dimensional heat conduction characteristic finite difference parallel fractional steps l2 error estimate |
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