本論文主要透過C語言，以四面體以及重心法的概念建立三維的四面體網格結構，並以帕松方程式、電子連續方程式以及電洞連續方程式來建立三維的四面體等效電路模型，再以四面體等效電路模型為基礎，建構出半球球體以及半球球殼網格結構，最後以牛頓 – 拉福森法來進行迭代求值，完成半導體元件模擬。模擬過程我們展示了如何以四面體網格結構在三維空間中正確建立等效電路模型，除了三角柱、六面體等網格之建立，我們也利用重心法建立之四面體在三維中形狀自由度高、模擬彈性大的特性，建立以球體為核心概念的半導體模型，並模擬出其電位和電流 – 電壓特性曲線，其模擬結果也符合我們的預期，證明此半球面網格架構之半導體元件模擬是成功建立的。

The purpose of the study is to use C language to establish a three-dimensional tetra-hedral mesh structure with the concepts of tetrahedron method and center of gravity model. And also we establish a three-dimensional tetrahedral equivalent circuit model with the poisson equation, the electrons and holes continuity equa-tions.Furthermore, we construct hemispherical sphere and hemispherical spherical shell mesh structure. Finally complete the simulation of semiconductor components by Newton – Raphson method. During the simulation, we show how to establish the equivalent circuit model in 3D space with the tetrahedral mesh structure correctly. In addition to the establishment of triangular prism, hexahedron and other meshes, we also use the gravity-center method to establish the spherical semiconductor model. This is because the gravity-center method has the characteristic of shape freedom. And we simulate its potential and current-voltage characteristic curves, the simula-tion results are also in line with our expectations, proving the semi-spherical grid structure semiconductor device simulation is successfully established.

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