三維橋接式四面體網格開發及矩陣係數驗證與半導體元件模擬

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姓名

廖宇聰(Yu-Tsung Liao) 查詢紙本館藏

畢業系所

電機工程學系

論文名稱

三維橋接式四面體網格開發及矩陣係數驗證與半導體元件模擬
(3D Bridged Cube Element and Matrix Coefficient Verification and Its Applications to Semiconductor Device Simulation)

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摘要(中)

本論文研究之主旨在於開發一套用以模擬三維半導體元件之程式模擬架構，我們的模擬架構建立在有限元素法的理論上，使用了四面體網格重心法模型來劃分網格內各個節點區域的空間電荷體積與電場高斯面，以此來運算各項等效電流值。而我們使用重心法模型的目的在於四面體之重心必定在模型內部，所以我們的網格模型能容許各種形狀的四面體。在模擬架構之精確性方面，藉由比對等效電流的矩陣係數之理論值與實驗值來進行矩陣係數的驗證，可以判斷我們的模擬程式是否正確，若比對結果之誤差過大，表示程式存在缺陷，此時我們可以藉由觀察是哪一項矩陣係數出現誤差，快速找出對應的位置來除錯，因此驗證矩陣係數的目的在於可以確認程式是否存在缺陷並且幫助我們更簡單地對程式進行除錯。在論文最後的部分，我們模擬了PN junction diode、MOS capacitor以及Bipolar junction transistor之特性曲線，其模擬結果符合我們的預期，證實了三維橋接式四面體網格之模擬架構用於半導體元件模擬是足夠可靠的。

摘要(英)

The main purpose of this thesis is to develop a simulation framework for simulating three-dimensional semiconductor devices. Our simulation framework is based on the theory of finite element method. We use the center of gravity model for the tetrahedral cube to create the equivalent circuit model. The purpose of using the center of gravity model is that the center of gravity of the tetrahedron is always inside the cube, so our mesh model can tolerate tetrahedrons of various shapes. In terms of the accuracy of the simulation framework, we can verify the matrix coefficients by comparing the theoretical values and experimental values of the equivalent current matrix coefficients to determine whether our simulation program is correct. If the error of the comparison result is too large, it means that the program is defective. At this time, we can quickly find the corresponding position to debug by observing which matrix coefficient has the error. Therefore, the purpose of verifying the matrix coefficient is it can confirm whether the program has defects and help us debug the program more easily. In the last part of the thesis, we simulated the characteristic curves of PN junction diode, MOS capacitor and Bipolar junction transistor. The simulation results are in line with our expectations. It is proved that the simulation framework of the three-dimensional bridged tetrahedral mesh is reliable enough for the simulation of semiconductor devices.

關鍵字(中)

★ 半導體元件
★ 模擬
★ 有限元素法

關鍵字(英)

★ SEMICONDUCTOR
★ SIMULATION
★ FINITE ELEMENT METHOD

論文目次

摘要 i
Abstract ii
誌謝 iii
目錄 iv
圖目錄 v
表目錄 vii

第一章簡介 1
第二章三維模擬方法之架構 3
2.1 有限元素法之基本原理 3
2.2 三維橋接式等效電路模型之運算方程式推導 5
2.3 三維四面體重心法元素之模型架構 9
2.4 重心法與外心法之優缺點比較 11
第三章三維橋接式矩陣係數驗證 13
3.1 三維橋接式四面體元素之內部等效電場分析 13
3.2 三維橋接式四面體元素之矩陣係數架構 18
3.3 三維橋接式四面體元素之矩陣係數驗證 32
第四章四面體元素在半導體元件模擬之應用 37
4.1 PN junction diode之模擬應用 37
4.2 MOS capacitor之模擬應用 39
4.3 Bipolar junction transistor之模擬應用 42
第五章結論 44
參考文獻 45

參考文獻

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指導教授

蔡曜聰(Yao-Tsung Tsai)

審核日期

2021-7-12

推文