由軸線法及平面法求四面體內部向量及其在三維半導體元件模擬

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姓名

施定國(Ding-Guo Shih) 查詢紙本館藏

畢業系所

電機工程學系

論文名稱

由軸線法及平面法求四面體內部向量及其在三維半導體元件模擬
(Finding internal vector from the plane equation and axis method in tetrahedron element for 3D semiconductor Device Simulation)

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摘要(中)

在本篇論文中，我們使用重心版模組來開發四面體等校電路模型，此模組能以任意四面體當基本元素，模擬三維的半導體元件；我們主要為開發電場的方法，在三維平面法的開發中，我們克服了以往二維提升至三維所遭遇的維度問題，並且另外開發了軸線法的程式，利用兩種方法做簡單電場驗證且求得我們核心方程式所需之參數，接著驗證電子流、電洞流密度，最後將四面體組成單顆立方體電阻及複數顆電阻做驗證，證實四面體網格之可靠性。

摘要(英)

In this thesis, we use barycenter module to develop equivalent circuit model of tetrahedron. This module can be applied to any tetrahedron mesh elements to simulate 3D semiconductor devices. We develop two methods for the internal electric field in each tetrahedron. The two methods include the plane method and the axis method. We solved the difficult problems to use the plane method in 3D application. Additionally, we developed the axis method. The two methods are used for the verification of the electric field, the electron current density, and the hole current density. Finally, we verify the two methods by a 3D resistor which is composed of many tetrahedrons.

關鍵字(中)

★ 軸線法
★ 平面法

關鍵字(英)

論文目次

摘要………………………………………………………………………………i
Abstract…………………………………………………………………………ii
目錄……………………………………………………………………………..iii
圖目錄…………………………………………………………………………..iv
第一章簡介…………………………………………………………………….1
第二章三維四面體網格模組建構…………………………………………….3
2-1 立方體基本網格結構介紹……………………………………………………….3
2-2 重心及外心在四面體網格之分析……………………………………………….6
2-3 四面體等效電路之架構………………………………………………………….8
第三章四面體內部之電場開發……………………………………………...15
3-1 平面法求其內部向量之分析…………………………………………………...15
3-2 軸線法求其內部向量之分析…………………………………………………21
3-3 平面法及軸線法在四面體之模組驗證………………………………………...23
3-4 平面法及軸線法之問題探討…………………………………………………...27
第四章三維半導體元件特性模擬與驗證………………………………….30
4.1 四面體等效電路模組電子流密度驗證…………………………………………30
4.2 四面體等效電路模組電洞流密度驗證…………………………………………33
4.3 立方體電阻模擬分析……………………………………………………………35
第五章結論………………………………………………………………….39
參考文獻……………………………………………………………………….40

參考文獻

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指導教授

蔡曜聰(Yao-Tsung Tsai)

審核日期

2018-7-5

推文