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

NCUIR > College of Electrical Engineering & Computer Science > Graduate Institute of Electrical Engineering > Electronic Thesis & Dissertation > Item 987654321/86602

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/86602

Title:	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
Authors:	廖宇聰;Liao, Yu-Tsung
Contributors:	電機工程學系
Keywords:	半導體元件;模擬;有限元素法;SEMICONDUCTOR;SIMULATION;FINITE ELEMENT METHOD
Date:	2021-07-12
Issue Date:	2021-12-07 13:01:05 (UTC+8)
Publisher:	國立中央大學
Abstract:	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。;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.
Appears in Collections:	[Graduate Institute of Electrical Engineering] Electronic Thesis & Dissertation

Files in This Item:

File	Description	Size	Format
index.html		0Kb	HTML	78	View/Open

社群 sharing

Loading...