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研究生: 顏瑋廷
論文名稱: 對於垂直堆疊的量子點陣列之二階差分方程式的能階數值模擬
Numerical simulation of energy states for vertically aligned quantum dots array by second order finite di erence scheme
指導教授: 黃聰明
學位類別: 碩士
Master
系所名稱: 數學系
Department of Mathematics
論文出版年: 2005
畢業學年度: 94
語文別: 英文
論文頁數: 23
中文關鍵詞: 有限差分法薛丁格方程式能階十字特徵曲線反十字特徵曲線量子點陣列
英文關鍵詞: Finite di erence method, The Schr¨odinger equation, Energy states, crossing eigencurve, anti-crossing eigencurve, quantum dot array
論文種類: 學術論文
相關次數: 點閱:118下載:3
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  • 我們提出簡單的數值方法去研究由不同大小量子點所垂直堆疊的三維量子點序列的電子性質。我們利用有限差分法去離散所需的薛丁格方程式,而且證明了此方程式是二階快速收斂的。在這一篇論文中,我們提供數值方法去計算各種量子點序列結構的能階以及研究對於兩個碟狀同軸堆疊的不同大小量子點間的反十字與十字交叉特徵曲線之存在。

    We present a simple numerical method to investigate the electronic
    properties of a three-dimensional quantum dot array model formed
    by di
    erent size vertically aligned quantum dots. The corresponding
    Schr¨odin-ger equation is discretized using the finite di
    erence method
    with a constant electron mass and confinement potential. The scheme
    is 2nd order accurate and converges extremely fast. In this paper, we
    propose numerical schemes to compute the energy levels of various QDA
    structures and research the existence of the anti-crossing and crossing
    eigencurve for QDA formed by two disk-shaped co-axial QDs with different
    size.

    1. Introduction.............................1 2. Vertically aligned quantum dot array.....2 3. Finite di erence scheme..................4 4. Numerical results........................9 5. Conclusion...............................14 References..................................19

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