內外側摻雜濃度變化對圓柱接面之電場公式的推導與模擬驗證

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姓名

陳廷宇(Ting-Yu Chen) 查詢紙本館藏

畢業系所

電機工程學系

論文名稱

內外側摻雜濃度變化對圓柱接面之電場公式的推導與模擬驗證
(Derivation and Verification of Electric-Field Equation in Low-high-doping Cylindrical PN Junction)

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摘要(中)

本篇論文主要重點為在內側濃度低於外側濃度時，電場大小比較會呈現相反順序。平面接面最大，圓柱型接面次之，球型接面最小。傳統的設計是內側濃度高於外側濃度，電場大小會呈現球型接面最大，圓柱型接面次之，平面接面最小。電場越大元件就越容易崩潰，所以曲面的設計跟元件的崩潰電壓有重要的關係。我們主要是藉由建立曲面對稱性相對較優的梯形網格，來模擬比較圓柱形接面在摻雜濃度P − N+與P+ − N情況下電場的關係，並用簡單的幾何模型來推導電場解析公式。而梯形網格是由兩個三角形網格模組所組成的，分別是銳角三角形與鈍角三角形，以此來模擬圓柱形接面的電場，並比較兩種不同摻雜濃度所得結果，最後會比較平面、圓柱型與球型接面電場之間的關係，並將程式模擬之比較結果呈現出來。

摘要(英)

This thesis discusses the electric-field comparison between the plan junction, the cylindrical junction, and the spherical junction. If the inside concentration is lower than the outside, the electric-field comparison will be reversed. The plane junction is the largest, the
cylindrical junction is the second, and the spherical junction is the smallest. When the inside concentration of the traditional design is higher than the outside, the electric field of the spherical junction will show the largest, the cylindrical junction the second, and the planar junction the smallest. The larger the electric field, the smaller the breakdown voltage. Therefore,
the design of the curved surface has an important relationship with the breakdown voltage of the PN junction. Our main simulation is on the electric field of the cylindrical junction with P − N+ and P+ − N. We establish a trapezoidal grid which is composed of acute triangle and obtuse triangle to simulate electric field, and use a simple geometric model to derive the
analytical electric-field equations with P − N+ and P+ − N Finally, we compare the relationship between the three junctions.

關鍵字(中)

★ 蔡曜聰
★ 電場公式
★ 摻雜濃度變化
★ 程式模擬
★ 模擬驗證
★ 圓柱接面

關鍵字(英)

論文目次

摘要 ................. i
Abstract ............ ii
誌謝 ................ iii
目錄 ................ iv
圖目錄 ............... v
表目錄 .............. vi
第一章簡介 .......... 1

第二章圓柱形單邊陡接面之理論物理與公式解析 .. 4
2-1 摻雜濃度與接面結構對接面電場之影響 .. 4
2-2 平面單邊陡接面之理論電場解析公式推導 .. 7
2-3 圓柱形單邊陡接面之理論電場解析公式推導 .. 11

第三章圓柱形單邊陡接面之模擬驗證 .. 18
3-1 梯形網格結構定義 .. 18
3-2 圓柱形P − N+與P+ − N接面之模擬驗證 ..21
3-3 摻雜濃度變化對圓柱形單邊陡接面之影響 .. 24

第四章球型單邊陡接面之理論物理與公式解析 .. 28
4-1 球型單邊陡接面之理論電場解析公式推導 .. 28
4-2 平面、圓柱型、球型單邊陡接面電場之關係探討 .. 36
4-3 平面與圓柱型單邊陡接面電場之模擬比較與探討 .. 39

第五章結論 .. 42

參考文獻 .. 43

參考文獻

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指導教授

蔡曜聰

審核日期

2020-7-2

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