博碩士論文 109521112 詳細資訊




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姓名 趙一杰(I-Chieh,Chao)  查詢紙本館藏   畢業系所 電機工程學系
論文名稱 半球面網格的構建及半導體元件的模擬
(Construction of Hemispherical Mesh and Simulation of Semiconductor Devices)
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摘要(中) 本論文主要透過C語言,以四面體以及重心法的概念建立三維的四面體網格結構,並以帕松方程式、電子連續方程式以及電洞連續方程式來建立三維的四面體等效電路模型,再以四面體等效電路模型為基礎,建構出半球球體以及半球球殼網格結構,最後以牛頓 – 拉福森法來進行迭代求值,完成半導體元件模擬。模擬過程我們展示了如何以四面體網格結構在三維空間中正確建立等效電路模型,除了三角柱、六面體等網格之建立,我們也利用重心法建立之四面體在三維中形狀自由度高、模擬彈性大的特性,建立以球體為核心概念的半導體模型,並模擬出其電位和電流 – 電壓特性曲線,其模擬結果也符合我們的預期,證明此半球面網格架構之半導體元件模擬是成功建立的。
摘要(英) The purpose of the study is to use C language to establish a three-dimensional tetra-hedral mesh structure with the concepts of tetrahedron method and center of gravity model. And also we establish a three-dimensional tetrahedral equivalent circuit model with the poisson equation, the electrons and holes continuity equa-tions.Furthermore, we construct hemispherical sphere and hemispherical spherical shell mesh structure. Finally complete the simulation of semiconductor components by Newton – Raphson method. During the simulation, we show how to establish the equivalent circuit model in 3D space with the tetrahedral mesh structure correctly. In addition to the establishment of triangular prism, hexahedron and other meshes, we also use the gravity-center method to establish the spherical semiconductor model. This is because the gravity-center method has the characteristic of shape freedom. And we simulate its potential and current-voltage characteristic curves, the simula-tion results are also in line with our expectations, proving the semi-spherical grid structure semiconductor device simulation is successfully established.
關鍵字(中) ★ 半導體元件模擬
★ 半球面網格
★ 四面體網格
★ 二極體
關鍵字(英) ★ semiconductor device simulation
★ Hemispherical mesh
★ tetrahedral mesh
★ diode
論文目次 摘要 i
abstract ii
誌謝 iii
目錄 iv
圖目錄 vi
表目錄 viii
第一章 簡介 1
第二章 元件模擬方法架構 3
2-1 有限元素法與重心法之架構 3
2-2等效電路模型及牛頓 - 拉福森法 8
2-3 四面體建立之三角柱、六面體三維網格網格模型 19
第三章 四面體半球球面網格建構及模擬 24
3-1 四面體半球網格模型之建構 24
3-2 四面體半球網格之改良 27
3-3 四面體半球網格電阻模擬 28
第四章 四面體半球球殼網格建構與模擬 30
4-1四面體建立半球球殼網格建構 30
4-2四面體建立半球球殼網格模擬 35
4-3三角柱疊層球殼網格結構與模擬 38
第五章 結論 43
參考文獻 44
參考文獻 [1] B. W. Kernighan,and D.M. Ritchie, “C Programming Language, 2nd Edition”,Prentice Hall ,Mar.1988.
[2] J Sanny and W.Moebs, Samuel J. Ling, “University Physics Volume 2”, 12th Media Services,Jun.2016
[3] J. Jin, “The Finite Element Method in Electromagnetics, 3rd Edition”, Wiley-IEEE Press ,Mar.2014
[4] X.S.Raymond “Elementary Introduction to the Theory of Pseudodifferential Operators, 1st Edition”, CRC Press,Sep.1991
[5] Y. T. Liao, “3D Bridged Cube Element and Matrix Coefficient Verification and Its Applications to Semiconductor Device Simulation”, National Central University,M. S. Thesis, Jun. 2021.
[6] E.Deleersnijder, G.Lebon, “Enforcing the continuity equation in numerical models of geophysical fluid flows”, Elsevier, doi:10.1016/S0893-9659(01)00057-X, Oct.2001
[7] J. C.Volmer , Tom W.J.de Geus , Ron H.J.Peerlings ,“Improving the initial guess for the Newton-Raphson protocol in time-dependent simulations” Journal of Computational Physics, doi: 10.1016/j.jcp.2020.109721,Nov.2020
[8] J.F.Lee, “2D Grounded Triangle Element and Matrix Coefficient Verification and Its Applications to Semiconductor Device Simulation”, National Central Univer-sity,M.S. Thesis, Jun. 2021.
[9] Y.P.Chen, “3D grounded cube element and matrix coefficient verification and its applications to semiconductor device simulation”, National Central University, M.S. Thesis, Jun. 2021.
[10]L.Y.Lu, “Animation of Non-convex polyhedron”, National Tsing Hua University,M.S. Thesis, Jun. 2008.
指導教授 蔡曜聰(Yao-Tsung Tsai) 審核日期 2022-7-5
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