用泰勒級數求三角形內部向量及二維元件模擬

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姓名

陳慧瑜(Hui-Yu Chen) 查詢紙本館藏

畢業系所

電機工程學系

論文名稱

用泰勒級數求三角形內部向量及二維元件模擬
(Finding internal vector from the Taylor series in arbitrary triangle element for 2D semiconductor device simulation)

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摘要(中)

在本篇論文中，我們藉由泰勒級數法開發出了一套三角形網格模組，並利用此三角形網格模組去進行了半導體元件模擬，以驗證我們所開發出的模組是可行的，且利用泰勒級數法能夠更迅速更簡單地求出三角形內部電場。其中我們討論了零件掃描法應用於計算封閉面的優點，並利用矩型網格去做簡單的概念推導，接著再進入本論文的核心，介紹如何利用泰勒級數去求出三角形內部電場並開發出完整的三角形網格模組，最後再藉由程式去進行模擬驗證，包括三角形內部電場、電子電洞流密度與單顆矩型電阻，待確認我們所開發出的程式是有效的後，再將此三角形網格應用於其他半導體元件如PN二極體與BJT等，並模擬其特性曲線。

摘要(英)

In this thesis, we successfully develop a triangular module by using the Taylor series, and use this module to simulate semiconductor devices and verify its validity. Furthermore, using the Taylor series to calculate the electric field of the triangular module is easy and simple. First of all, we discuss that using the element-by-element method in calculating the Gaussian surface is better than the node-by-node method, and we use the rectangular mesh module to explain a simple concept derivation. Then we introduce how to use the Taylor series to calculate the electric field, drift and diffusion current and verify the values. We also simulate a simple resistor and compare the value with the theoretical value. After confirming the resistor validity, we apply it to other semiconductor devices such as PN diodes and BJTs, and simulate their characteristic curves.

關鍵字(中)

★ 半導體元件
★ 泰勒級數
★ 元件模擬

關鍵字(英)

論文目次

目錄
摘要.......................................i
Abstract...................................ii
圖目錄......................................v
表目錄......................................vii
第一章簡介.................................1
第二章泰勒級數與三角型模型開發...............4
2.1零件掃描法之優點..........................4
2.2 二維矩型網格介紹.........................7
2.3 利用泰勒級數法求內部電場之模型開發........11
第三章泰勒級數與三角型模型驗證...............22
3.1內部電場驗證.............................22
3.2電子流與電洞流密度驗證....................25
3.3單顆矩形電阻模擬與驗證....................31
第四章泰勒級數與二維半導體元件之應用.........34
4.1多顆矩型電阻模擬與驗證....................34
4.2 PN二極體與其特性曲線模擬.................36
4.3簡化的二維BJT模擬分析與討論...............41
第五章結論.................................46
參考資料....................................47

參考文獻

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指導教授

蔡曜聰

審核日期

2019-7-19

推文