縱向電場對第二類型異質結構激子態的影響

Abstract

在銻化鎵/砷化銦或銻化鎵/銻化鋁/砷化銦這種具有斷帶能隙的第二類型 異質結構中，其電子和電洞在空間上能夠被分離開來。在論文中，我們將 利用變易基底法來計算外加縱向電場對第二類型異質結構的激子態的影響 。變易基底法中有兩個參數a，b分別用來描述有效電洞和有效電子與界面 的距離。對含有變易參數的漢彌頓量H(a,b)，我們可以求出其對應的波函 數|Ψn(a,b)>。藉著最小化的過程，我們可以決定a，b的值。使用正交的 基底|Ψn(a,b)>再將漢彌頓矩陣對角化，即可以求得激子的能態。在我們 的計算中我們選擇了一組很有效的變易基底，使得我們激子基態的相對誤 差小於0.05%。我們也計算了方位角量子數m= 0,±1的較低激發態。 Electrons and holes can be spatially separated in type-II broken-gap heterostructures, which can be realized in GaSb-InAs or GaSb-AlSb-InAs interfaces. In this paper, we present a variation basis set approach to calculate the excitonic states in type-II heterostructures under the effect of an applied electric field. The approach contains two variation parameters a,b which correspond to the positions of the effective "electrons" and "holes". A variation hamiltonian H(a,b) is propose which eigenstates |Ψn(a,b)> can be solved. The The parameters a, b are determined by minimizing <ΨG(a,b)| H|ΨG(a, b)>, where |ΨG(a,b)> is the ground state of H(a,b) and H is the actual hamiltonian of the system. Using the orthogonal basis set |Ψn(a,b)> ,we diagonalized H to find the excitonic states. The sffectiveness of our choice of the the variation basis set is demostrated in our numerical examples. Besides, the relative error of the excitonic ground state is shown to be less than 0.05%. The low lying excitonic states are studied for both the azimuthal quantum number m=0,±1.