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研究生： 洪嘉良
Jia-liang Hong
論文名稱： 利用線性零組件建構2-D半導體元件模擬及應用
Analysis and Simulation of 2-D Semiconductor Device by Linear Components
指導教授： 蔡曜聰
Yao-Tsung Tsai
口試委員:
學位類別： 碩士
Master
系所名稱： 資訊電機學院 - 電機工程學系
Department of Electrical Engineering
畢業學年度： 98
語文別： 中文
論文頁數： 49
中文關鍵詞： 線性零組件
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    • 在這篇論文中，我們利用基本的線性零組件，來完成非線性元件的模擬，我們使用的基本線性包含零組件電壓源、電容以及電壓控制電流源。我們更進一步將元件內部參數，置於主程式中，便於使用者辨識及做調整。為了用線性零組件進行2-D元件的模擬，我們利用線性電壓控制電流源這個線性零組件，再利用牛頓-拉夫森法將運算得到的電流以及轉導，置入矩陣ADV = B，經由牛頓-拉夫森法可以求解到DV ，這個未知向量，利用此觀念，逐步取代二維模擬器(2D mixed-level simulator)中使用之非線性特殊零組件，在牛頓拉夫森建立公式ADV = B中，A矩陣含微分項，微分項可用解析解或數值解來得到，我們分別運用解析解及數值解完成二維元件模擬，並進行解析解與數值解結果驗證與時間比較。

    In this thesis, the basic linear components, which consist of voltage source, capacitor, and voltage-control current source, are employed to simulate the non-linear devices. The circuit parameters are explicitly defined at the main program for easier recognition and adjustment.To simulate 2-D semiconductor devices by linear elements, the nonlinear Poisson equation and the nonlinear carrier continuity equations are replaced by the linear voltage-controlled current source in the environment of the Newton-Raphson iteration. The matrix A in ADV = B include partial differentiation items which are obtained by both numerical differentiation and analytical differentiation in this thesis. The simulation results show a good accuracy
    between two methods.

    中文摘要..........................................I ABSTRACT .........................................II 目錄..............................................III 圖表索引..........................................IV 第一章簡介........................................1 第二章線性零組件與牛頓-拉夫森法之關係.............3 2.1 線性零組件與牛頓-拉夫森法之運算關係...........3 2.2 線性零組件描述外顯式二極體....................8 2.3 外顯式二極體串聯電阻之暫態響應................11 第三章利用線性零組件完成二維元件模擬..............13 3.1 2D 等效電路模型...............................13 3.2 VCCS 線性零組件與牛頓拉夫森...................17 3.3 以VCCS 線性零組件替換非線性零組件.............19 第四章 2-D半導體元件模擬解析解與數值解比較........23 4.1 線性壓控電流源取代非線性特殊電容..............23 4.2 波松方程式解析模型之推導......................25 4.3 電子漂移擴散解析模型之推導....................27 4.4 電子復合解析模型之推導........................29 4.5 電洞漂移擴散解析模型之推導....................30 4.6 電洞復合解析模型之推導........................32 4.7 結果驗證與時間比較............................34 第五章結論........................................40 參考文獻..........................................41

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