中心處具有雜質之球形複層量子點電子能階的研究

Abstract

本論文研究中心處具有雜質之球形複層量子點的能階受幾何和材料因素的影響。經由求解Schroedinger方程式，可以得到系統能階滿足的方程式和解析形式的波函數。數值計算結果顯示，對於複層量子點而言，選擇不同的的幾何和材料因素將導致功函數和Coulomb交互作用相互間的重要性有所不同，因此對電子能階有很大的影響。束縛態的能階視電子所在區域範圍而定：範圍愈大，能階愈低。若複層外的位能太低會有量子穿隧效應。

The ground state energy of an impurity located at the center of a multi-layer spherical quantum dot (MLSQD) is studied within the framework of effective mass approximation. It is found the material properties and geometric parameters would influence the ground state energy prominently. By solving the Schroedinger's equation analytically, the eigen-state energies can be obtained and the corresponding wave functions can be expressed in terms of Hypergeometric functions. The numerical results shows that by varying the materials in different layer and the geometry of the dot, the potentials and the ground state energies will be influenced deeply. To a bound state problem, the ground state energy directly relates to the thickness of the layer where the electron can stay steadily. The narrower the layer, the lower the ground state energies. On the contrary, quantum tunneling effect would occur if the potential can not allow any bound state to exist.