鈍角三角形的邊線向量與內部向量探討及其在二維元件模擬之應用

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姓名

沈韋廷(Wei-ting Shen) 查詢紙本館藏

畢業系所

電機工程學系

論文名稱

鈍角三角形的邊線向量與內部向量探討及其在二維元件模擬之應用
(Finding internal vector from the edge vector in obtuse triangle element for 2D Semiconductor Device Simulation)

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摘要(中)

本篇論文中，我們利用C語言模擬半導體元件特性。發現在切割網格時會如果出現180°切角，這會造成模擬上的誤差，而為了減少這誤差產生，我們將180°切角切割成不同角度，其中會出現鈍角三角形網格，所以我們開發了鈍角三角形模組來解決這問題。先利用單一鈍角三角形模組驗證，再經由模擬電阻與實際電阻值比較，及二極體的模擬驗證來確保模擬的正確性，最後應用在包含鈍角三角形網格的相關應用，例如:MOS電容器、180°切角的改善、局部網格加密時會出現的180°切角問題，都不會造成過大的誤差，並且成功改善了鈍角三角形網格模擬上的誤差。

摘要(英)

In this thesis, we use C language to simulate semiconductor device characteristics. We found that the 180°-angle mesh will cause simulation problem. It may have a triangle mesh with an obtuse angle if we divide the 180° angle into two angles. In order to simulate the obtuse triangle mesh, it’s necessary to develop an obtuse triangle model for 2D device simulation. The validity of a single obtuse triangle model is verified by numerical experiment. We simulate a resister and compare its result to the theoretical value. Finally, applying this obtuse model to many applications, such as MOS capacitor, 180°-angle problem, in mesh regrid.

關鍵字(中)

★ 半導體模擬
★ 二維

關鍵字(英)

★ semiconductor simulation
★ two-dimensional

論文目次

摘要...............................................i
Abstract..........................................ii
圖目錄.............................................iv
表目錄.............................................vi
第一章簡介.........................................1
第二章二維鈍角三角形模組等效電路開發與驗證.............2
2.1 簡單網格分析概念.................................2
2.2 封閉面規劃及討論.................................3
2.2.1利用外心定義封閉面..............................3
2.2.2外心在鈍角三角形出現的問題.......................5
2.2.3利用重心定義封閉面..............................6
2.3 利用邊線電場求其內部電場..........................6
2.4 二維數值鈍角三角形驗證...........................12
2.4.1二維數值鈍角三角形內電場驗證.....................12
2.4.2二維數值鈍角三角形內電子流密度與電洞流密度驗證.....16
第三章半導體元件特性模擬與驗證.......................21
3.1簡單電阻模擬與分析................................21
3.2簡單電阻模擬之外心與重心比較.......................23
3.3二極體接面特性模擬與討論...........................25
第四章半導體元件應用與討論...........................30
4.1 MOS電容器特性模擬................................31
4.2 180°切角的改善...................................34
4.3 尺寸微縮時出現鈍角三角形問題.......................38
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

2016-6-28

推文