本篇文章中，我們討論為什麼會形成圓弧 PN 接面，並推導出理論公式，接著建立二維數值模擬器來幫助分析，我們將帕松方程式及電流連續方程式利用等效電路的方式以設計出二維數值模擬器，接著我們考慮用圓柱座標分析圓弧接面，我們用梯形網格去取代方塊網格，並設定最佳化角度來降低誤差，最後我們利用泰勒級數分別將峰值電場、空乏區寬度和崩潰電壓的公式模型化，利用理論公式對曲率的斜率，我們可以了解當接面半徑變小時，各公式變化的方向，再藉由二維數值模擬器的驗證，證明理論公式解析模型是正確的。 In this thesis, we discuss why we will form a curved PN junction, and derive theoretical formula, then build the two-dimensional mixed level simulator to help analysis. In order to design the two-dimensional mixed level simulator, we have transformed Poisson’s equation and the current continuity equation into equivalent circuit, then we consider using cylindrical coordinates to analyze curved PN junction. We use trapezoid mesh to replace square mesh, and set optimization angle to reduce error. Finally, we use Taylor series to obtain the analytical model for understanding the electric field dependence on the junction radius. From the analytical model, we can understand the change direction of the electric field magnitude at the PN junction if we reduce the junction radius. The analytical model is also verified by the two-dimensional mixed level simulator.
