第二類型雙量子井中的激子態

Abstract

變分基底法可被用來研究第二型異質接面所形成的的激子能態，例如：砷 化銦╱銻化鎵，或砷化銦╱銻化鋁╱銻化鎵結構。這種結構下的導電電子 和電洞可以穩定的分離，形成一激子態。我們使用這種逼近法來研究這種 第二型雙量子井的基態及激發態束縛能。基於物理的直覺，電子及電洞兩 者的波函數可以近乎正確的比擬成相對的粒子及另一粒子固 ，如此我們 就找到一個單一乘積的波函數基底，作為變分法 用函數。經由一個矩陣 對角化的過程，我們可以在有限個數的試用函數狀態下，得到比傳統變分 法更精確的結果。在這個逼近方法下，我們發現單一乘積波函數所給出的 能量和微擾過後的最佳結果相比，只有百分之零點一左右的差別，顯示出 我們所選擇的變分試用函數是相當接近真實情況的。在計算中，所有的電 子電洞質量比都是被允許的，我們並沒有假設電洞的等效質量遠大於電子 。此外，我們也對不同的量子井寬度及方位角量子數做計算及比較。 A variation basis set approach is applied to study the excitonic in type-II broken-gap heterojunctions, which can be realized in or GaSb-AlSb-InAs interfaces. Such type-II broken- gap have a special characteristic that the conduction electrons and spatially separated, even in their equilibrium configuration. We study the excitonic binding energy and the low lying states. The specific structures we studied are the type-II broken-gap well structures. Based on physical intuitions, a variation hamiltonian H(a,b) is in which the electron and the hole are each acted upon by an fix-centered point charge which locates on the other side of the junctions. The variation parameters a,b are the perpendicular distances of effective ``fixed electron'' and the effective ``fixed hole'' from the junction. The values of a,b are obtained by minimizing the ground state value for hamiltonian H. where H is the actual Hamiltonian of the system. Using the variation complete set of the electron-hole of H(a,b), we diagonalize H and find the excitonic states. With this approach, we obtain a better ground state energy as the excited state energies of the exciton. We find that |.PSI._G(a,b)> already gives a very good ground And the relative error of our best results only in the range of In this calculation, we have not assumed the condition m_h over than 1. In fact, our method applies equally well for any m_h over m_e Finally, the dependence of the excitonic state on the width ofl and different azimuthal quantum numbers m are also studied.