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研究生:湯惟策
研究生(外文):Wei-tse Tan
論文名稱:An Inexact Newton Method for Drift-Diffusion Model in Semiconductor Device Simulations
論文名稱(外文):An Inexact Newton Method for Drift-Diffusion Model in Semiconductor Device Simulations
指導教授:黃楓南
指導教授(外文):Feng-Nan Hwang
學位類別:碩士
校院名稱:國立中央大學
系所名稱:數學研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
畢業學年度:97
語文別:英文
論文頁數:44
中文關鍵詞:semiconductorGMRESfinite differencedrift-diffusionNewton''s method
外文關鍵詞:drift-diffusionNewton''s methodfinite differenceGMRESsemiconductor
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本篇論文針對半導體儀器作數值模擬,運用 inexact Newton''s method 對 drift-diffusion model 求解。考慮原型的 drift-diffusion model 包含:電子電壓,電子濃度,電洞濃度等三個未知變數。數值實驗使用 drift-diffusion model 模擬一個一維的二極體幾何模型。我們討論兩個不同的 non-dimensionalization approach 對 Newton''s method 的影響並分析 GMRES method 使用不同的 preconditioner 在 Newton''s method 的結果。實驗結果顯示使用不同的 non-dimensionalization approach 將影響 Newton''s method 的收斂情形。在實驗中我們使用 US non-dimensional approach (Uniform Scaling non-dimensional approach) 有效的提供 Newton''s method 一個良好的環境。根據實驗結果發現增加 block Jacobi preconditioner 中 block 的數量幾乎不影響 Newton''s method 的迭代次數,更甚者即便是增加網格點的數目 Newton''s method 的迭代次數依然不受影響。
The aim of this thesis to employ an inexact Newton''s method to solve discrete drift-diffusion model in semiconductor device simulations, where the drift-diffusion model in the primitive form consists of the electrostatic potential , the electron concentrations and the hole concentrations. Consider a 1D diode simulations modeled by drift-diffusion as a test case. We discuss the effect on Newton''s method by two non-dimensionalization approaches and the application of GMRES method without/ with diagonal and block Jacobi. It is true that the non-dimensional approach will affect the converge of Newton''s method. In our case, we choose US non-dimensional approach (Uniform Scaling non-dimensional approach) and it will make a great environment for Newton''s method. From numerical experiment, we find that increasing number of blocks for a block Jacobi preconditioner almost doesn''t affect the number of Newton''s iterations and decreasing grid size for a block Jacobi preconditioner also doesn''t affect the Newton''s iterations neither.
Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 The drift-diffusion model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 The drift-diffusion model in semiconductor devices . . . . . . . . . . . . 2
2.2 Two Non-dimensionalization approaches . . . . . . . . . . . . . . . . . . 3
3 Numerical method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.1 Finite difference method . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.2 The inexact Newton method with backtracking for semiconductor algorithm 8
4 Numerical result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.1 The drift-diffusion model for the n
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