橢球形狀量子點內偏心類氫雜質的能譜

Abstract

本論文主要研究內含類氫雜質的量子點結構中基態與第一激發態的電子能 階.而且量子點的邊界的位能勢為無窮大.我們分三個方向來探討,(一)在 球形量子點,雜質處於球心,能階能量對球形半徑大小的變化,(二)在橢球 形量子點內,雜質位置偏移幾何中心對能階能量的影嚮,(三)固定量子點的 體積,但形狀從球變為橢球時能階能量的變化.本文的計算方法是以1989年 時Gorecki和Brown所提的理論為基礎.我們針對原先他們的variational boundary perturbation theory中,再作一個線性疊加的變分,使得這個方 法在雜質接近邊界的時候,可以得到不錯的基態能量結果.除此之外,還可 以算出激發態的能量,使得G-B理論更具一般性和實用性.而且我們分析了 庫倫位能勢和邊界無窮位能勢相互競爭的現象.還可以從波函數平方的等 值面分佈情形,了解低維量子系統的量子尺寸效應. In this thesis we study the electronic eigenenergies of ground state and the first excited state of a hydrogenic impurity in a quantum dot. The potential at the boundary of the quantum dot in our present work is set to be infinite. And we survey this problem in three case. (i) the tendency of change of the eigenenergies when the impurity is located at the center of this dot (ii) the change of elliptical quantum dot is shifted along a principal axis (iii) the change of eigenenergies when the volume of the quantum dot is fixed but the shape of quantum dot is gradually changed from sphere to ellipsoid. The calculation method used in our work is based on the theory proposed by Gorecki and Brown in 1989. We extend the original ideal of Gorecki and Brown to include more basis functions to evaluate the eigenvalue. And our improved especially when the position of method can also get excited energies which makes the G-B's variational method more general to other problems. From the coefficients of basis functions and the equal-value contour surface of eigenfunctions got in our numerical calculation, we show the effect from coulomb potential and that from boundary pontential compete with each other. And we also find the size effect of quantum dot apparently influence the eigenenergies.