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姓名	李思儒(Szu-Ju Li)  查詢紙本館藏	畢業系所	電機工程學系
論文名稱	使用含量子效應的等效電路模型模擬半導體元件之特性 (Semiconductor Device Simulation with Equivalent Circuit Model including Quantum Effect)
相關論文	★ 表面電漿共振效應於光奈米元件之數值研究 ★ 金氧半電容元件的暫態模擬之數值量測 ★ 雙載子電晶體在一維和二維空間上模擬的比較 ★ 改善後的階層化不完全LU法及其在二維半導體元件模擬上的應用 ★ 一維雙載子接面電晶體數值模擬之驗證及其在元件與電路混階模擬之應用 ★ 階層化不完全LU法及其在準靜態金氧半場效電晶體電容模擬上的應用 ★ 探討分離式簡化電路模型在半導體元件模擬上的效益 ★ 撞擊游離的等效電路模型與其在半導體元件模擬上之應用 ★ 二維半導體元件模擬的電流和電場分析 ★ 三維半導體元件模擬器之開發及SOI MOSFET特性分析 ★ 元件分割法及其在二維互補式金氧半導體元件之模擬 ★ 含改良型L-ILU解法器及PDM電路表述之二維及三維元件數值模擬器之開發 ★ 含費米積分之高效率載子解析模型及其在元件模擬上的應用 ★ 量子力學等效電路模型之建立及其對元件模擬之探討 ★ 適用於二維及三維半導體元件模擬的可調變式元件切割法 ★ 整合式的混階模擬器之開發及其在振盪電路上的應用
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摘要(中)	在目前最新奈米級半導體元件的發展上，量子力學扮演了相當重要的角色，同時在元件模擬與設計上也同樣要予以考量。因此開發一個包含量子效應的元件模擬器是必要的。在本論文中，我們將介紹一維薛丁格(Schrodinger)計算與密度梯度模型(density gradient model) 來模擬量子效應。首先我們提出了等效電路法與高效率特徵值解法器來解薛丁格波動方程式，根據這個薛丁格等效電路模型，我們可以建立柏松─薛丁格互解方程式等效電路模型來模擬金氧半(MOS)元件在反轉區的量子效應。此外，我們也將分別使用簡化數值法與等效電路法來模擬克若尼-潘尼(Kronig-Penney)模型，以觀察半導體元件中能帶的特性。在元件模擬中，為了使所有變數都能有相同數量級而不需比例縮放參數(scaling factor)，我們提出了對數比例法(log-scale)以幫助其在牛頓疊代法的收斂。為了解決記憶體空間不足的問題，我們也提出了帶狀不完全LU(Banded incomplete LU)法來改善這問題。最後，我們將建立起密度梯度公式的等效電路模型，並利用分離模式(decoupled method)與對數比例法來解量子飄移擴散模型(quantum drift-diffusion model)。
摘要(英)	In up-to-date development of nanoscale semiconductor devices, quantum mechanisms play an important role and have to be properly taken into account in the simulation and design. Therefore, it is necessary to develop the device simulator including quantum effects. The 1-D Schrodinger computation and density gradient model for quantum effect simulations will be introduced in this dissertation. We propose a simplified equivalent circuit model to solve the Schrodinger equation and an efficient eigenvalue and eigenvetor solver to solve the eigenvalue problem. Based on the equivalent circuit model of Schrodinger equation, the equivalent circuit model of the Poisson-Schrodinger equation can be created and can be simulated to show that the MOS device features of the quantum effects at strong inversion. Moreover, the Kronig-Penney approximation will be also applied to reveal the essential features of the energy band structure of semiconductors with the simplified numerical method and the equivalent circuit method. To make all variables in similar orders without scaling factors, we propose a log-scale method to help Newton-Raphson iterations to easily converge in device simulations. Also, we will propose a matrix solver using Banded incomplete LU method to improve the problem that the memory space is insufficient. Finally, the density gradient model will be converted to an equivalent circuit form and we use the decoupled method with a log-scale method to solve the self-consistent quantum drift-diffusion model.
關鍵字(中)	★ 量子效應 ★ 等效電路模型 ★ 克若尼-潘尼模型 ★ 薛丁格波動方程式 ★ 帶狀不完全LU法	關鍵字(英)	★ quantum mechanisms ★ equivalent circuit model ★ Kronig-Penney model ★ Schrodinger equation ★ Banded incomplete LU method
論文目次	1. Introduction 1 2. Equivalent-Circuit Modeling of Schrodinger Equation 6 2.1 Overview of Schrodinger Equation Solution 7 2.2 Development of Equivalent Circuit Model 8 2.2.1 1D Equivalent Circuit Model 9 2.2.2 2D Equivalent Circuit Model 13 2.3 Simulations on Quantum Well Device 15 3. Development of Schrodinger – Poisson Self-Consistent Solver and MOS Capacitor Device Simulation 20 3.1 Equivalent Circuit Model of Schrodinger – Poisson Equation 21 3.2 Simulation in MOS Inversion Layer 26 4. Simplified Numerical Method and Equivalent Circuit Method for Kronig-Penney Model Simulations 31 4.1 Kronig-Penney Model Formulation and Numerical Solver 32 4.2 Equivalent Circuit Method for Kronig-Penney Model Simulation 36 4.3 Comparison of Simulations in Simplified Numerical Method and Equivalent Circuit Method 38 4.3.1 Simulation with Simplified Numerical Method 39 4.3.2 Simulation with Equivalent Circuit Method and its Comparison with Simplified Numerical Method 43 5. Log-Scale Method with Equivalent Circuit Model in Device Simulation 49 5.1 Log-Scale Variable Method and Large-Scale Variable Method 50 5.2 Equivalent Circuit Method with Log-Scale Variable Method 52 5.3 Device Simulations with Log-Scale Variable Method 55 6. Banded incomplete LU factorization and its applications in semiconductor device simulation 59 6.1 Banded Incomplete LU Method 61 6.2 Simulation Results and Comparisons 65 7. Quantum-Corrected Drift-Diffusion Modeling with Equivalent Circuit Method 68 7.1 Drift-Diffusion Model and Density-Gradient Model 69 7.2 Equivalent Circuit Method for QDD Model 72 7.3 Device Simulations with QDD Model 76 7.3.1 Numerical Algorithm for QDD Model Simulation 76 7.3.2 Boundary Conditions for QDD model 77 7.3.3 Device Simulation Results 80 8. Conclusion 83 Reference 87 Appendix A 94 Appendix B 96 Appendix C 100
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指導教授	蔡曜聰(Yao-Tsung Tsai)	審核日期	2007-7-12
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