開放式量子異質結構之準穩態研究

Abstract

在本論文中，我們研究粒子在不同量子異質結構中的準穩態行為。首先，我們使用一個簡單的時域模型考慮電子在開放式耦合量子井中之準穩態的生命期。利用轉換矩陣法及特殊邊界給定可以得到一複變數色散方程並從而求得共振能階與生命期。 對於開放式量子線與量子點系統，我們引進了合超流幾何函數-複變引數之惠特克函數。利用此函數來表示電子在上述系統中的波函數，在異質介面邊界滿足特殊連續條件及假設等效質量近似條件下，我們可以得到一複數固有能量值色散方程式。所有的準穩態的共振能階與生命期可以被精確求得。求解此複變方程式需使用牛頓法在複數平面勘根求解。 此外，我們也使用微擾法研究激子在多層半導體量子點中的行為。我們發現等效介電常數法在許多情況下不適用。激子在開放式量子點的生命期近似的等於電子生命期。 最後，我們用自洽法研究場發射二極體的電性。場發射二極體的陰極表面電場只與材料表面功函數有關。

In this dissertation, we study the quasistationary states in open quantum heterostructures. The quasistationary states of an electron in an open coupled quantum well, an open quantum wire, and an open quantum dot are investigated. A simple time-dependent model is presented to investigate lifetimes of the quasistationary states in open coupled quantum wells. A complex-eigenenergy solver is presented to determine both the resonance positions ER and the corresponding lifetimes τ of the system for the latter two cases. In the eigen-solver, the wave functions are expressed in terms of the Whittaker functions with complex arguments, and the effective-mass Schrödinger equation is solved analytically. The quasistationary states in terms of the complex eigen-energies, ER-iħ/(2τ), are extracted numerically in the complex plane by Newton's method. All the quasistationary states of the system can be determined. The system of an exciton in spherically N-layered semiconductor quantum dots is also investigated via the perturbation method. Finally, the quasistationary states of a relativistic field-emission-limited diode are investigated via a self-consistent approach.