The role of Coulombic coupling in electroabsorption of square quantum wells

Abstract

The impact of Coulombic coupling between different subband pairs, on the quantum confined Stark effect in square quantum wells, has been studied. It is shown, via detailed comparison between electroabsorption spectra obtained from a full excitonic Green function calculation, a decoupled excitonic Green function calculation and measurement, that inclusion of the Coulombic coupling between different subband pairs is generally required for correct prediction of electroabsorption in square wells, especially for shallow or narrow square quantum wells. These results are of particular significance for the accurate calculation of electrorefraction, by Kramers-Kronig transformation, of quantum well electroabsorption spectra.

Transition from two-dimensional to three-dimensional electroabsorption in extremely shallow quantum wells

“…The use of discretized states to model the quasi-continua brings the need to ensure that a sufficient number of these subbands are included and that their energy spacing is small enough to model accurately the Coulomb interaction of excitons in extremely shallow quantum wells. Previous work has shown that when a sufficient number of outer well subbands are included and their energy spacing is appropriate, both the resonant and continuum parts of the calculated excitonic spectrum tend to saturate at a maximum level [12,13]. Further, once these conditions are met the model reproduces the measured tendency of absorption spectra for different applied electric field strengths to cross at approximately the same energy in the continuum part of the spectra [9,13].…”

“…Instead, the exciton peaks are assumed to have a modified Lorentzian shape with a low energy Urbach tail, in agreement with observation [12][13][14] and detailed calculations of lineshape [24]. In this approximation, the broadening parameter in equation ( 4) takes the form [26]…”

“…The importance of using an accurate description of the Coulombic interaction in the electron-hole pair for valid calculations of excitonic absorption is now well established [11,12,[15][16][17][18]. The appropriate Schrödinger equation for the exciton problem can be solved in real space [17,19] or in momentum space [15,16,20].…”

“…In extremely shallow wells, extensive Coulombic coupling between bound and unbound states the quasicontinua is expected [14]. In this work, the contribution from quasi-continuum states above the shallow quantum well is modelled by placing the wells centrally in an infinitely deep, much wider outer well [12]. This has the effect of discretizing the continuum states, enabling the use of well-defined eigenstates to describe quantum well resonances at finite applied fields.…”

“…However, more subband pairs of different index must be included as the 3D limit is approached. More recent studies of the quantum confined Stark effect in finite Al x Ga 1−x As/GaAs quantum wells have revealed that, in general, accurate simulation of measured electroabsorption spectra also requires the inclusion of Coulombic mixing between a wide range of subbands of different index, including the quasi-continua [12][13][14]. The strength of the contribution to the absorption edge exciton from Coulombic mixing between subband pairs of higher (and different) index than 2 depends on the energy separation of the confined particle states and their separation from the quasicontinua.…”