自組式量子點中單一激子的庫倫交互作用

Abstract

本篇論文主要是利用數值積分方法去驗證電子－電洞交互作用的解析結果，它包括了電子－電洞的直接庫倫作用及電子－電洞的交換作用。一般認為，電子－電洞的交換作用是造成所謂的精細結構匹裂(fine structure splitting，FSS)的主要原因，而精細結構匹裂則是阻礙實現量子點作為糾纏光子對光源的主要原因[5,6]。

在這篇論文裡，我們首先回顧文獻[7]的理論工作：在三維非等向性拋物線位能下，直接庫倫作用與交換作用的推導過程，藉此了解電子－電洞交換作用背後的物理，影響交換作用的主要原因有三：材料特性、量子點的尺寸以及激子波函數形狀的不對稱。

接著利用數值方法來驗證三維模型的準確性，除了藉此確認三維模型的正確與否，還可以定量的給出理論公式的適用範圍，也可以進一步的討論理論公式所無法涵蓋的部份，最後模擬各種不同尺寸量子點的直接庫倫作用與交換作用的趨勢與能量尺度。

In this thesis, the electron-hole direct Coulomb interactions and exchange inter- actions in quantum dots are both simulated by using numerical integration method and analytical mean. The electron-hole exchange interaction is often regarded as the main consequence for the fine structure splitting (FSS) of quantum dots. The FSS have been confirmed as a main obstacle for the fabrication of dot-based entangled photon pair emitters.[5,6]

In order to understand the underlying physics of the FSS, we present a theory for the electron-hole Coulomb interaction based on 3D asymmetry parabolic model [7]. According to theoretical studies, the FSS is attributed to several underlying mechanisms: material properties, the size of quantum dots and the lateral deformation of exciton wave function.

By using the numerical integration method and analytical mean, we identify the the size-dependence of the electron-hole Coulomb interactions in a quantum dot with arbitrary aspect ratio. Finally we use the numerical integration method to find the tendency and the energy scale of electron-hole Coulomb interactions between different sizes of quantum dots.