本篇論文中，我們藉由加入離子衝撞游離模型於二維元件模擬器內，來模擬半導體元件內部載子雪崩崩潰之現象。首先，我們比較兩種不同結構，第一種為圓弧形PN接面，另一種為直線併圓弧PN接面，模擬不同接面深度與接面半徑對二極體崩潰特性的影響。再者，為了解釋曲率效應造成二極體崩潰電壓差異，我們引入圓柱坐標系之波松方程式搭配半導體物理觀念，進一步推導圓柱形陡峭PN 二極體之理論電場及電位公式，並分析理論計算與程式模擬數據差異，針對造成兩者數據差異的原因予以改善，同時驗證二維元件模擬器之可靠性。最後，為了讓使用者能快速驗證設計元件結構和全面性變化，我們將位階顯示概念整合於二維元件模擬器中，並以相同基準點設計圓弧形PN二極體與直線併圓弧PN二極體兩種結構，透過位階顯示器檢視兩者結構間差異，同時探討直線接面結構對電性影響。

In this thesis, we design a 2-D device simulator which includes the impact-ionization model to simulate the avalanche breakdown. First, we discuss two device structures. One is cylindrical P-N junction and the other is plane and cylindrical P-N junction. We also simulate various junction depths and radiuses for studying the curvature effect on breakdown characteristics. Second, to explain about curvature effect on diode breakdown, we derive electric field and electric potential formula from Poisson’s equation at cylindrical coordinates by using semiconductor physics. Also, we analyze and improve the difference between analytical equation and numerical simulation to verify the validity of 2-D device simulator. Finally, in order to quickly verify the device structure and simulation results, we design a 2-D levelized indicator. The levelized indicator can be used to quickly check the 2-D simulation results of the above-mentioned two device structures. Besides, the levelized indicator is a very useful tool for user to obtain an overall 2-D distribution such as potential distribution.

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