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.
