自組式量子點中激子動態行為的理論研究

Abstract

由於擁有高度量化的電子結構，自組式量子點展現出優異發光特性。此前瞻性的奈 米材料可以應用在各種光量子資訊的應用，例如量子遠傳、量子密碼學和量子光源發射 器。在自組式量子點的量子光學應用中(如單光子、糾纏態光子對發射器)，光激子的動 態行為在光學元件的操作上扮演決定性的角色。然而，在固態材料中無法避免的量子鬆 弛(relaxation)效應與量子同調性(coherence)的破壞，往往大幅地限制了量子點在光量子 資訊上的應用。 在本計畫中，我們將藉由解析方法與大型的數值計算程式，建構出一套激子在量子 侷限中的動態行為理論。在解析方法中我們已經完成了激子在三維簡諧振盪模型中自旋 鬆弛時間的理論，其中完整考慮了電子電洞的交換能、自旋軌道耦合與核子自旋的作用 力。在這個理論架構下，我們將發展一個有效的數值模擬方法－8 能帶kp 模型－來計 算應力自組式量子點帶有自旋混成的電子結構，其中涵蓋了所有可能的自旋軌道耦合及 應力效應。以kp 模型所計算的單一電子及電洞能階為基礎，進而利用組態相互作用法 來解決多激子的問題，並考慮所有可能的粒子間交互作用，尤其是自旋相關的電子電洞 庫倫交互作用。 量子點中激子鬆弛時間的研究，可藉由求解電子與電洞對自發性復合的速率方程 (rate equation)與黃金費米定則(Fermi’s golden rule)來了解。量子點中亮激子發去相 (de-phasing time)時間的計算則可從求解自旋的運動方程得到，並將同調性破壞的原 因：包括聲子或核子自旋交互作用，作有系統的研究。此理論將比對並解釋時間解析光 譜的實驗結果，以及變溫光譜的分析。本研究可以對量子點中激子動態行為提供理論的 基礎進而有效的設計或控制量子點光源元件

With highly quantized energy spectrum and excellent optical properties, self-assembled quantum dots are promising nanostructures for optical implementation of quantum information technology, e.g. quantum teleportation, quantum cryptography, and quantum light sources. In photo-excited self-assembled quantum dots (QDs), the dynamical properties of photo-generated exciton play an essential role in the quantum operations of dot-based photonic devices, e.g. on-demand single photon sources, or entangled photon pair emitters. However, inevitable population relaxation and losing of quantum coherence of photo-excited carriers in a quantum dot due to both of intrinsic or extrinsic mechanisms limit the usability of the do-based photonic devices. In this project, we shall carry out a comprehensive theoretical investigation of dynamical properties of quantum-confined excitons in strained self-assembled quantum dots by using both analytical and large-scale numerical approaches. A theory for the spin relaxation times of excitons in a quantum dot in a 3D parabolic model is being developed with the full consideration of e-h exchange interactions, spin-orbital and hyperfine interactions. In the theoretical framework, we shall develop an efficient numerical simulator based on 8-band kp model for the calculation of the spin-mixed electronic structures of strained self-assembled quantum dots, taking into account all possible spin-orbital couplings and strain. Based on the kp -calculated single particle levels, the configuration interaction (CI) method will be employed to solve interacting multi-exciton problems with the full consideration of all possible inter-particle interactions, remarkably including spin-relevant e-h exchang interactions. The relaxation times of exciton states of a quantum dot then will be studied by solving the rate equations and using Fermi’s golden rules, which are mainly determined by spontaneous e-h recombination rate but interfered by bright-to-dark exciton state transitions. The de-phasing times of the optically active bright excitons in the dot are evaluated by solving the equation of motion for spin exciton where the fluctuation of phonon-bath or nuclear spin field as perturbations are treated as sources of de-coherence. The theoretical results will be compared with and used to account for measured time-resolved photoluminescence (PL) and analysis of the temperature-dependence of single-dot PL line widths. These studies of dynamical properties of excitons in a photo-excited quantum dot shall provide useful guidelines for optimal design of the dot-based quantum light source devices.