### 博碩士論文 962201029 完整後設資料紀錄

 DC 欄位 值 語言 DC.contributor 數學系 zh_TW DC.creator 湯惟策 zh_TW DC.creator Wei-tse Tan en_US dc.date.accessioned 2009-7-23T07:39:07Z dc.date.available 2009-7-23T07:39:07Z dc.date.issued 2009 dc.identifier.uri http://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN=962201029 dc.contributor.department 數學系 zh_TW DC.description 國立中央大學 zh_TW DC.description National Central University en_US dc.description.abstract 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。 zh_TW dc.description.abstract 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. en_US DC.subject semiconductor zh_TW DC.subject GMRES zh_TW DC.subject finite difference zh_TW DC.subject drift-diffusion zh_TW DC.subject Newton's method zh_TW DC.subject drift-diffusion en_US DC.subject Newton's method en_US DC.subject finite difference en_US DC.subject GMRES en_US DC.subject semiconductor en_US DC.title An Inexact Newton Method for Drift-DiffusionModel in Semiconductor Device Simulations en_US dc.language.iso en_US en_US DC.type 博碩士論文 zh_TW DC.type thesis en_US DC.publisher National Central University en_US