本篇論文主要是建構球面網格的架構，將其進行半導體元件的電性模擬，運用 C語言來撰寫程式，模型的單位是以四面體為基礎，先使用四面體建構傳統的六面體元件，再建構出球殼模型，因四面體是在三維模型中最小的單位，在組成其它形狀時的靈活度會最高，理論的部分則是使用有限元素法、重心法、來建構出四面體，在使用帕松方程式(Poisson’s Equation)、電子連續方程式(Electron continuity equation)電洞連續方程式(Hole continuity equation)來模擬半導體元件的擴散、飄移、產生、複合等特性，在運算架構部分，我們是使用牛頓拉福森法來來進行運算，開發出一套可以模擬半導體元件特性的模型架構。結果的部分，我們分別模擬了六面體所組成的串聯電阻與二極體，也模擬了使用四面體所組成球體電阻與球殼二極體，結果也符合我們的預期，可以確定我們的模擬是可行的。 ;This thesis is mainly about the electrical simulation of semiconductor components by using C language program of spherical mesh structure. The unit of the model is based on tetrahedron. First, we use tetrahedron to construct basic hexahedral components, and then the model of the spherical shell, since the tetrahedron is the smallest unit in the three-dimensional model, it has the highest flexibility when composing other models. The theoretical part uses the finite element method and the center of gravity method to construct the tetrahedron. We use Poisson’s Equation, Electron continuity equation, and Hole continuity equation to simulate the diffusion, drift, generation, recombination, and other characteristics of semiconductor components. In the computing architecture part, we use Newton-Raphson′s method to perform calculations, and developed a model architecture that can simulate the characteristics of semiconductor components. In the results part, we simulated the series resistance、diode、MOS capacitance composed of hexahedrons, spherical resistance and the spherical shell diode composed of tetrahedra. The results are also in line with our expectations, and we can confirm that our simulation is feasible.
