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研究生： 夏浚清
Chun-Ching Hisa
論文名稱： 電腦輔助推導Kronig-Penney模型及量子井的模擬
Computer-Aided Kronig-Penney Model Derivation and Multiple Quantum Well Simulation
指導教授： 蔡矅聰
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： 94
語文別： 英文
論文頁數： 44
中文關鍵詞： 能帶 、量子井
外文關鍵詞： bandgap, Quantum Well Simulation
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    • 本論文研究用等效電路法模擬量子力學系統。推導Kronig-Penney公式過程十分冗長，為了解決這類問題，我們提出人機互動電腦輔助推導的概念。在本文的最後，我們會討論到量子井系統。過程中我們發現Kronig-Penney模型似乎有一些問題存在。我們研究出另一個模型去改正這個問題。

    In this thesis, we will use the equivalent-circuit method to simulate the quantum mechanical systems. It is tedious to derive the formulation of the Kronig-Penney model. In order to solve the problem more effectively, we propose the computer-aid derivation which is based on the interaction between human and computer. Finally, we introduce the quantum well system. We find the problem in the Kronig-Penney model. We search new model for the potential function to improve the problem.

    Contents 1. Introduction……………………………………………1 2. Solving Schrödinger equation by equivalent circuit………….....3 2.1 Introduction………………………………………………3 2.2 The Schrodinger equation in the Equivalent-Circuit Model………4 2.3 Example for infinite quantum well…………………………………8 3. Computer-aided derivation of the analytic Kronig-Penny model…………14 3.1 Introduction…………………………………………..…14 3.2 The Kronig-Penny model ……15 3.3 The evolution of the Kronig-Penny………………21 3.4 Summary…………27 4. Finding the allowed energy bandwidth in confined multiple QW system.29 4.1 The E vs. k diagram in a one-dimensional crystal…..…………..……29 4.2 Simulation of equivalent-circuit method in the confined QW………..30 4.3 The parabolic model of the QW…………………………………..………..36 4.4 Summary……………………………………………………………42 5. Conclusion…………………………43 List Of Reference…………………………………………………………….44

    [1] C. H. Kao, “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.
    [2] 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.
    [3] J. P. Mckelvey, Solid State and Semiconductor Physics, Robert E. Kreger, Inc., 1966
    [4] D. A. Neamen, Semiconductor Physics & Devices, Chapter 2, McGraw-Hill, Inc., 2003.
    [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] B. Aethur, Concepts of modern physics, McGraw-Hill, Inc., McGraw-Hill, Inc., 2003.
    [7] N. Zettli, Quantum mechanics : concepts and applications, New York : Wiley, 2001.
    [8] H. Craig Casey, jr. Devices For Integrated Circuits ,Chapter2, John Wiley & Sons, Inc. 1998.

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