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
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2005
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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.
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.
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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, Finite dierence method, The Schr¨odinger equation, Energy states, crossing eigencurve, anti-crossing eigencurve, quantum dot array