臺灣博碩士論文加值系統

本篇論文中主要使用C語言，設計一套四面體的網格來模擬元件的特性，根據分

析後，我們選擇使用重心來開發模組，因為重心法可以適用任意四面體，首先使用邊

線向量的方法來求得核心方程式所需要的參數，接著驗證電場、電子流密度、電洞流

密度的正確性，最後將四面體組合成立方體應用在N型矽半導體、P-N二極體、球座

標的球座標網格應用，並且將這些應用做理論的推導與程式模擬的結果作比較分析，

所有的模擬結果皆證實此四面體網格的廣泛性及可靠度。

In this thesis, we use C++ language to develop a tetrahedron element for 3-D device simulation. Barycenter method can be applied to arbitrary tetrahedron, and we use the edge vector to obtain the parameters needed by the core equation, and verify the electric field, current density and hole current density. Finally, the tetrahedrons are combined into cube applied to the N-type silicon semiconductors, PN diodes, and the spherical coordinate. In addition, these applications are used for theoretical derivation and compared with the program simulation. All the simulation results confirm the reliability of this tetrahedron mesh.

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 三維四面體網格與等效電路模型分析.........3
2-1. 立方體網格結構與分析...................3
2-2. 外心在四面體網格出現的問題..............7
2-3. 重心在四面體網格之分析..................8
2-4 邊線電場求其內部電場....................8
第三章 三維半導體元件特性模擬與驗證.............18
3-1. 四面體模組電場驗證.....................18
3-2. 四面體模組電子流密度與電洞流密度驗證.....22
3-3. 立方體簡單電阻模擬分析..................29
3-4. 四面體模組的二極體之模擬分析.............32
第四章 三維四面體網格球座標之應用................34
4-1. R方向電阻推導與驗證.....................34
4-2. θ方向電阻推導與驗證.....................36
4-3. φ方向電阻推導與驗證.....................39
第五章 結論....................................41
參考文獻 ........................................42

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