在本篇論文中，我們藉由泰勒級數法開發出了一套三角形網格模組，並利用此三角形網格模組去進行了半導體元件模擬，以驗證我們所開發出的模組是可行的，且利用泰勒級數法能夠更迅速更簡單地求出三角形內部電場。其中我們討論了零件掃描法應用於計算封閉面的優點，並利用矩型網格去做簡單的概念推導，接著再進入本論文的核心，介紹如何利用泰勒級數去求出三角形內部電場並開發出完整的三角形網格模組，最後再藉由程式去進行模擬驗證，包括三角形內部電場、電子電洞流密度與單顆矩型電阻，待確認我們所開發出的程式是有效的後，再將此三角形網格應用於其他半導體元件如PN二極體與BJT等，並模擬其特性曲線。

In this thesis, we successfully develop a triangular module by using the Taylor series, and use this module to simulate semiconductor devices and verify its validity. Furthermore, using the Taylor series to calculate the electric field of the triangular module is easy and simple. First of all, we discuss that using the element-by-element method in calculating the Gaussian surface is better than the node-by-node method, and we use the rectangular mesh module to explain a simple concept derivation. Then we introduce how to use the Taylor series to calculate the electric field, drift and diffusion current and verify the values. We also simulate a simple resistor and compare the value with the theoretical value. After confirming the resistor validity, we apply it to other semiconductor devices such as PN diodes and BJTs, and simulate their characteristic curves.

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