橢球形狀量子點內類氫雜質的束縛能的計算

Abstract

本論文的主旨在研究內含類氫雜質的量子點結構中電子束縛能的變化趨勢 。我們使用的邊界位障令為無窮大，我們主要分三個方向來研究束縛能的 變化，(一)在QD伸長或縮短時產生的影響，(二)雜質位置偏移球心時的影 響，(三)QD體積固定但形狀從球漸變為橢球時束縛能的變化。本文的計算 方法是以1989年時Gorecki和Byers Brown所提的理論為基礎。我們對這個 理論做了部分的改進，不僅可以得到較好的結果，而且適用範圍也擴大了 。由我們的數值結果可以看出，隨著QD的伸長，束縛能很快地趨近於定值 。如果考慮固定一QD的體積的問題，結果顯示，束縛能隨著形狀的變化不 明顯，主要影響的因素是體積的大小。 In this thesis we study the change of electronic binding energy of hydrogenic impurity in the QD(quantum dot) with infinite potential boundary barrier. We take three different cases to survey the tendency of change of binding energy:(i) The QD is lengthened or shortened (ii) the position of impurity deviates from the center of the QD (iii) the volume of the QD is kept constant but the shape of the QD can be gradually chang. The calculational method used in this thesis is based on the theory proposed by Gorecki and Byers Brown in 1989. We improve the contour function so that we get better results. Besides, with our improvement, we can deal prolate QDs problems. No matter where the impurity is, the numerical results show that the binding energy converge quickly. If we fix the volumes of QDs, and lengthen or shorten them, we find that the binding energies change slowly. It reveals that the binding energy and the volume of the QD are closely correlated.