半導體奈米晶體與奈米柱系統之少電子理論

Abstract

本論文旨在建立一套針對奈米晶體/奈米柱系統之少體理論方法。我們採用三維的拋物線型位能模型，模擬並計算電子的運動行為與能譜結構。拋物線型位能兼具簡單、可與外加磁場偶合並解析、可在非等向系統中解析等優點，已在解釋二維系統中得到巨大的成功。首先我們分別計算單電子在(1)等向奈米晶體、(2)等向奈米晶體外加磁場以及(3)非等向之奈米柱等系統中之能譜結構；之後經由引入庫倫交互作用項，我們依據組態交互作用法建構少個電子的多體理論，此理論可以計算少量電子在這些奈米系統中的能譜及電子結構。在組態交互作用法中，我們選取有限數量的組態當作基底並依此基底建構系統的漢密頓矩陣，透過對角化漢密頓矩陣我們可以得到系統(在此有限組態近似下)的本徵能量與本徵態。最後，在兩個殼層的近似下，我們實際計算一個雙電子的奈米晶體/奈米柱系統，並且印證透過外加磁場及改變系統形狀來調控系統電子結構的可行性。

The purpose of this thesis is to develop a configuration interaction (CI) method for studying the few-body physics of interacting charged nanocrystal (NC) and nanorod (NR) systems. In the framework of the effective mass approximation, we develop a CI theory based on a three-dimensional (3D) parabolic model for the calculation of the few-electron spectrum of crystalline semiconductor nanoparticles with a size comparable to the effective Bohr radius. We derive the explicit formulation of the Coulomb matrix elements required in the theory and conducted the evaluations in a simple semi-analytical manner. We then apply this theory to three simple representative cases: (1) two mutually interacting electrons in a symmetric NC without a magnetic field, (2) two mutually interacting electrons in a symmetric NC under an external magnetic field, and (3) two mutually interacting electrons in an oblate or a prolate NC (NR) in the absence of a magnetic field. We calculate the ground states and the energy spectrum of two interacting electrons in nanosystems using the partial CI approach within the simple two-shell approximation and explore the possibility of singlet/triplet (S/T) state transitions, a physical phenomenon as the manifestation of particle-particle interaction, driven by magnetic fields and/or shape deformation.