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姓名	湯惟策(Wei-tse Tan)  查詢紙本館藏	畢業系所	數學系
論文名稱	(An Inexact Newton Method for Drift-DiffusionModel in Semiconductor Device Simulations)
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摘要(中)	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。
摘要(英)	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.
關鍵字(中)	★ semiconductor ★ GMRES ★ finite difference ★ drift-diffusion ★ Newton's method	關鍵字(英)	★ drift-diffusion ★ Newton's method ★ finite difference ★ GMRES ★ semiconductor
論文目次	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
參考文獻	[1] S. Aˇsmontas, J. Gradauskas, A. Suˇzied˙elis, and G. Valuˇsis. Submicron semiconductor structure for microwave detection. Microelectronic Engineering, 53(1-4):553– 556, 2000. [2] J.F. Burgler, W.M. Coughran Jr, and W. Fichtner. An adaptive grid refinement strategy for the drift-diffusionequations. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 10(10):1251–1258, 1991. [3] R.C. Chen and J.L. Liu. An iterative method for adaptive finite element solutions of an energy transport model of semiconductor devices. Journal of Computational Physics, 189(2):579–606, 2003. [4] R.C. Chen and J.L. Liu. Monotone iterative methods for the adaptive finite element solution of semiconductor equations. Journal of Computational and Applied Mathematics, 159(2):341–364, 2003. [5] R.C. Chen and J.L. Liu. A quantum corrected energy-transport model for nanoscale semiconductor devices. Journal of Computational Physics, 204(1):131–156, 2005. [6] R.C. Chen and J.L. Liu. An accelerated monotone iterative method for the quantum-corrected energy transport model. Journal of Computational Physics, 227(12):6226–6240, 2008. [7] R.S. Dembo, S.C. Eisenstat, and T. Steihaug. Inexact newton methods. SIAM Journal on Numerical Analysis, 19:400–408, 1982. [8] S.C. Eisenstat, H.F. Walker, S.C. Eisenstatt, and F. Walker. Choosing the forcing terms in an inexact Newton method. SIAM J. Sci. Comput, 1996. [9] H. K. GUMMEL. A Self -Consistent Iterative Scheme for One-Dimensional Steady State Transistor Calculations. IEEE Trans, ED-11(2):455–465, 1964. [10] M. Hansen. Maxwells Equations. 2004. [11] L. Hsiao and S. Wang. Quasineutral limit of a time-dependent drift–diffusion– Poisson model for pn junction semiconductor devices. Journal of Differential Equations, 225(2):411–439, 2006. [12] Joseph W. Jerome. Semiconductor models: Their mathematical study and approximation, 1992. [13] J.W. Jerome. Consistency of semiconductor modeling: an existence/stability analysis for the stationary van Roosbroeck system. SIAM Journal on Applied Mathematics, 45:565–590, 1985. [14] P.A. Markowich, C.A.
指導教授	黃楓南(Feng-Nan Hwang)	審核日期	2009-7-23
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