本篇論文中主要使用C語言，建立一套基於球體座標系統的三維梯形網格來模擬元件的特性，並在程式裡加入離子撞擊游離模型，可用來觀察不同球狀接面的崩潰電壓與電流。將梯形網格建立完畢後，首先要定義如何找出外心來分割網格，以利於後續求出電流通過的截面積與體積，並推導三種方向的電阻公式，再與模擬結果做比較即可得知網格是否設計正確。最後除了球體二極體元件以外，也將網格應用在圓柱和直角這兩種座標系統，分別模擬環繞式電晶體電容與矩形PN二極體，在輸入方式上則新增GPS座標的定位方式，所有的模擬結果皆證實了此系統應用的廣泛性和可靠度。;In this thesis, we have successfully developed a three-dimensional trapezoidal model written in C and based on spherical coordinates for device simulation. We can also observe both breakdown voltage and breakdown current happened in spherical curvature with impact-ionization model added into this equivalent circuit. As the first step in our analysis, we will provide a detailed explanation to define circumcenters of a trapezoid. In order to ensure that our software is reliable and the model is correct, it’s necessary to derive three kinds of resistance formulas and then compare those with simulation results. The data summarized indicate strong relationship between theory and simulation. In addition, it is important to emphasize that this trapezoidal model not only can be applied to spherical PN diode but also can be applied to cylindrical Gate-All-Around MOS capacitor and rectangular PN diode. Moreover, we introduce GPS coordinates into our program, making it more flexible and easy to use. These results lead us to the conclusion that the beauty of our program is its universality and reliability.
