本篇論文最主要的目的在於使用三維圓柱座標下的梯形網路來模擬半導體元件p-n球接面的崩潰現象，文中分析p-n接面的I-V曲線的變化與電位的差異，並比較三維圓柱座標與三維直角座標之特性，三維圓柱座下的梯形網路對於p型半導體之半徑的模擬較直角座標精確，且模擬時間較短，並將模擬結果與理論做比較，驗證其正確性。接著再進行參數修改，如不同的接面半徑、摻雜濃度之差異及格子點差異，判斷其影響崩潰電壓的程度，最後總結出最佳的格子點設計之範圍，以達到最佳的模擬效果。In this thesis, the breakdown phenomenon of a spherical PN junction is studied in 3D cylindrical coordinates. We analyze the shift of I-V curve, potential deviation and compare the deviation between 3D cylindrical coordinates and 3D Cartesian coordinates. We develop the trapezoid 3D cube in cylindrical coordinates. The simulation speed and accuracy in 3D cylindrical coordinates is better than that in Cartesian coordinates. We also verify the simulation result with the theory. Then, we change different parameters such as the radius of a p-n junction, doping concentration and grid points to see the dependence of breakdown voltage on these parameters. Finally, we study how to find a better grid design and get a better simulation result.
