由平面方程式求鈍角三角形內部向量及二維元件模擬

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姓名

許鈞凱(Jyun-Kai Hsu) 查詢紙本館藏

畢業系所

電機工程學系

論文名稱

由平面方程式求鈍角三角形內部向量及二維元件模擬
(Finding the internal vector from the plane equation in obtuse triangle element for 2D Semiconductor device simulation)

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摘要(中)

在本篇論文中，我們開發出新型重心版模組，能以任意三角形網格當基本元素，模擬二維的半導體元件，相對於以往需要避開或忽略鈍角三角形的產生，新版模組增加網格設定的彈性空間，並且有效減少模擬需要的節點數；首先我們利用簡易電阻驗證其理論電阻值，並且模擬PN二極體的特性曲線作驗證，接著將新版模組應用至圓柱形元件，開發出新形的梯形網格分割方式，探討其模擬精確值，最後分析當新版模組遇到大角度鈍角三角形網格時的模擬問題。

摘要(英)

In this thesis, we have successfully developed a new type module which is composed of any triangle mesh elements to simulate 2D semiconductor device. The new type module increases the flexibility to set up the mesh, and it can also effectively decreases the total amount of computation nodes. At first, a simple 2D resistor and PN diode will be simulated and compared to the theoretical for verification. Then, the new module will be applied to simulate the cylindrical semiconductor element by the new version of the trapezoidal mesh segmentation mode, and the simulation result will be compared to the exact value. Finally, we will discuss the problem when the new type module is used to simulate the large angle obtuse triangle mesh.

關鍵字(中)

★ 半導體
★ 模擬
★ 鈍角三角形
★ 二維
★ 三角形
★ 平面方程式

關鍵字(英)

★ semiconductor
★ simulation
★ obtuse triangle
★ two dimensional
★ triangle
★ plane equation

論文目次

目錄

摘要.....................i
Abstract................ii
目錄....................iii
圖目錄....................iv
表目錄....................vi
第一章簡介.................................1
第二章程式原理與架構介紹....................3
2.1 二維矩形網格模型介紹..............3
2.2 外心與重心於三角形網格之分析.......7
2.3 平面方程式於三角網格之分析.........9
第三章三角形網格於二維半導體之模擬...........18
3.1 包含鈍角三角形網格模組之電阻驗.........18
3.2 包含鈍角三角形網格模組的二極體之驗證....20
3.3 重心版與外心版模組之比較...............22
第四章梯形網格延伸與分裂之應用...............28
4.1 標準梯形元件之開發....................28
4.2 梯形分裂與標準梯形元件之比較...........33
4.3 大鈍角三角形的問題探討.................36
第五章結論.................................40
參考文獻 .....................................41

參考文獻

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指導教授

蔡曜聰(Yao-Tsung Tsai)

審核日期

2016-6-28

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