量子力學等效電路模型之建立及其對元件模擬之探討

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研究生：	郭昭宏 Chao-Hung Kuo
論文名稱：	量子力學等效電路模型之建立及其對元件模擬之探討 An Equivalent Circuit Model of Quantum Mechanics and its Investigation to Device Simulation
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：	92
語文別：	英文
論文頁數：	42
中文關鍵詞：	量子力學等效電路、元件模擬
外文關鍵詞：	Quantum Mechanics, Equivalent Circuit Model, Device Simulation
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本論文是探討量子力學的物理特性與其在半導體元件上的模擬。為了描述量子力學模擬環境，首先我們必需開發一個有效率的特徵值與特徵向量的運算器來幫助我們解薛丁格波動方程式。這個高效率的運算器在本論文中稱之為QM-Solver。利用QM-Solver我們可以得到任意位能函數的特徵值和特徵向量，對於學習量子力學的原理，有很具體的幫助。其次，再配合我們建立的量子力學等效電路模型，來研究半導體元件中載子在量子井的運動情形。

In this thesis, we will study the quantum mechanics and its simulation on semiconductor devices. In order to handle the quantum mechanics simulation, we first need an efficient eigenvalue and eigenvector solver to help us solve the Schrödinger wave equation. This efficient solver in this thesis is called QM-solver. It is useful for us to study the quantum mechanics specifically by getting the eigenvalue and eigenvector from the QM-solver of any potential function. And the second, we use the equivalent circuit model of semiconductor device with quantum mechanics to observe the charge distribution in the quantum well.

Introduction........................................................1
The Development of Quantum Mechanics Solver.........................3
1 Introduction....................................................3
2 The Zero-Determinant Method.....................................4
3 The Equivalent Circuit Model of Schrödinger Equation............6
The Simulation Results of the QM-Solver............................11
1 The Infinite Quantum Well......................................11
2 The Simple Harmonic Oscillator.................................16
3 The Potential-Energy Barrier...................................19
4 The Triangular and the Two-Well Forms of Quantum Well..........22
The Electron Distribution in MOS Capacitor with Quantum Effects
by the QM-Solver...................................................25
1 The Equivalent Circuit Model of Decoupled Method...............28
2 Physical Fundamentals of the Electron Distribution.............32
3 The Simulation of MOS Capacitor................................33
Conclusion.........................................................41

                                

[1] D. A. Neamen, Semiconductor Physics & Devices, Chapter 2, McGraw-Hill, Inc., 1997.
[2] J. Sanny and W. Moebs, University Physics, Chapter 42, Times Mirror Higher Education Group, Inc., 1997.
[3] T. Janik and B. Majkusiak , “Analysis of the MOS transistor based on the self-consistent solution to the Schrodinger and Poisson equations and on the local mobility model,” IEEE Trans. Electron Devices, vol.45, p.1263 – 1271, 1998.
[4] H. C. Casey, Devices For Integrated Circuit, Chapter 7, John Wiley & Sons Inc., 1999.
[5] A. K. Ghatak, K. Thyagarajan, M.R. Shenoy “A novel numerical technique for solving the one-dimensional Schroedinger equation using matrix approach-application to quantum well structures,” IEEE Journal on Quantum Electronics, vol.24, p.1524 – 1531, 1988.
[6] S. Selberherr, Analysis and Simulation of Semiconductor Devices, New York: Springer, 1984.
[7] C.-L. Teng, “An equivalent circuit approach to mixed-level device and circuit simulation,” M. S. Thesis, Institute of EE, National Central University, Taiwan, Republic of China, Jun. 1997.
[8] J. W. Lee, “An equivalent circuit model for decoupled method in semiconductor device simulation,” M. S. Thesis, Institute of EE, National Central University, Taiwan, Republic of China, Jun. 2002.

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