以k．p法研究砷化銦/砷化鎵之奈米結構

Abstract

本論文以k．p法來研究砷化銦/砷化鎵量子結構(量子井、量子點)之電子結構。在價電帶的部分，我們採用四能帶的Luttinger k．p 理論，而導電帶的部分，我們採用單能帶的等效質量法。於應變(strain)部分，則是採用由Andreev et al.提出之應變張量於傅立葉空間中的解析解。於數值方法部分，我們採用較簡單的平面波展開法，我們可計算出量子結構於單載子情況下之能階，以及其波函數。而且我們根據單粒子電子結構的計算結果，進一步的計算單激子(exciton)之束縛能。 我們所採用的數值模擬方法，可運用於成長在(001)方向及(111)方向之量子井，和成長在(001)方向之量子點與帽層(capping layer)成份不同於位能障(barrier)之量子點。我們在計算時可考慮系統所受之應變以及壓電場，於位能障與量子點(量子井)界面之界面擴散(interdiffusion)效應也可納入我們的計算。並且把我們的模擬結果與實驗量測結果作個比較，有助於了解以砷化銦鎵為帽層之量子點基態發光波長紅移之現象。

In this thesis, we use k．p theory to study the electronic structure of InAs/GaAs nanostructure, such as quantum well and quantum dot. We present a numerical calculation to calculate the single particle properties of conduction electrons and valence holes of the strained quantum wells (QWs) and quantum dots(QDs), calculated by using one-band effective mass and four-band Luttinger theories, respectively. In the calculation for strain in dots, we adapt the analytic solution of strain tensor in the Fourier representation. In the numerical implementation, we take the plane wave basis to expand the single-particle wave function, and diagonalize the strained Hamiltonian matrix employing the “ARPACK” algorithm. Finally, we can calculate the exciton binding energy from the wave function we obtained. Our program is applied to two case studies: (001)、 (111)-orientated InGaAs/GaAs QWs and InAs/GaAs self-assembled QDs with InGaAs or GaAs capping layer. In the (111)-orientated QW, the piezoelectric effect reduces the transition energy. We study the InAs QD with InGaAs capping layer and we can find that the transition energy of InAs dots is red shift.