外加磁場下二維拋物線量子點中激子的研究

Abstract

本文乃是針對量子點中的激子在外加磁場作用下之能階性質來做研究，激子的行為受到拋物線束縛位能入外加磁場的影響，同時考慮電子電洞均被束縛以及電子被束縛但電洞不被束縛兩種情形。理論的推導是由等效質量近似的能量算符出發，能量算符包括三個部份：質心座標部份、相對座標部份及混合質心座標與相對座標部份。在質心座標部份，只包含拋物線束縛位能，不會受到磁場和庫倫作用力的影響，是一個二維空間的簡諧振盪。在相對座標部份，受到拋物線束縛位能、磁場及庫倫作用力的共同影響。混合質心座標與相對座標部份，在整個系統行為中我們將之視為微擾項。研究結果發現在磁場作用下，能階值會隨磁場強度增加而增大，且能階次序在強磁場作用下會產生反轉。

In this thesis, we study the properties of an exciton in the two dimensional parabolic quantum dot under the external magnetic field. field. For simplicity, we consider the two dimensional parabolic confinement of electron and hole. In our calculations, we also include the case that the hole is unconfined in the two dimensional plane. The effective mass Hamiltonian approach is employed in our calculation. The Hamiltonain is divided into three components: center-mass coordinate part; relative coordinate part and the mixture of center-mass and relative coordinate part. The first part is the well-known two dimensional harmonic oscillator which is not affected by magnetic field and Coulomb interaction. The second part is the two-dimensional parabolic confinement potential system under a magnetic field as well as Coulomb interaction. The third part is treated as a perturbation term in our calclation. Our result shows that the exciton energy is affected prominently by the magneticfield. The order of the energy levels may bereversed as the strength of the magnetic field becomes stronger.