TY - JOUR

T1 - Energy spectrum of excitons in square quantum wells

AU - Belov, P. A.

PY - 2019/8/1

Y1 - 2019/8/1

N2 - Energies of the ground and excited states of excitons in GaAs/AlGaAs and InGaAs/GaAs finite square quantum wells (QWs) of various widths are calculated. This is achieved by studying the three-dimensional Schrodinger equation for the exciton in a QW and, in particular, by determining the lower energy boundary of the continuous spectrum of the corresponding differential operator. The eigenvalue problem for the Schrodinger equation is solved numerically by the finite-difference method properly taking into account discontinuities of the material parameters at the interfaces of the QW. The calculated bound states of electron-hole pairs are classified based on the types of their dominant in-plane and quantum-confinement one-dimensional functions of the wave function factorized form. A dependence of energy levels on a QW width as a parameter is thoroughly studied for widths up to 100 nm. The accurate radiative decay rates for calculated s-like exciton states are also obtained. Calculated energy spectra are confronted with the experimental reflectance spectra measured for high-quality InGaAs/GaAs heterostructures with QWs. The ground and, at least, a few excited states of the heavy-hole exciton in QW are identified in the experimental spectra.

AB - Energies of the ground and excited states of excitons in GaAs/AlGaAs and InGaAs/GaAs finite square quantum wells (QWs) of various widths are calculated. This is achieved by studying the three-dimensional Schrodinger equation for the exciton in a QW and, in particular, by determining the lower energy boundary of the continuous spectrum of the corresponding differential operator. The eigenvalue problem for the Schrodinger equation is solved numerically by the finite-difference method properly taking into account discontinuities of the material parameters at the interfaces of the QW. The calculated bound states of electron-hole pairs are classified based on the types of their dominant in-plane and quantum-confinement one-dimensional functions of the wave function factorized form. A dependence of energy levels on a QW width as a parameter is thoroughly studied for widths up to 100 nm. The accurate radiative decay rates for calculated s-like exciton states are also obtained. Calculated energy spectra are confronted with the experimental reflectance spectra measured for high-quality InGaAs/GaAs heterostructures with QWs. The ground and, at least, a few excited states of the heavy-hole exciton in QW are identified in the experimental spectra.

KW - Energy spectrum

KW - Exciton

KW - Finite-difference method

KW - Quantum well

KW - Radiative decay rate

KW - Schrödinger equation

KW - SEMICONDUCTORS

KW - OPTICAL-PROPERTIES

KW - OSCILLATOR-STRENGTH

KW - LATTICE BAND-STRUCTURE

KW - SHALLOW

KW - Schrodinger equation

KW - BOUND-STATES

KW - SPECTROSCOPY

KW - MASS

KW - BINDING-ENERGY

KW - RESONANCES

UR - http://www.scopus.com/inward/record.url?scp=85064659942&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/energy-spectrum-excitons-square-quantum-wells

U2 - 10.1016/j.physe.2019.04.008

DO - 10.1016/j.physe.2019.04.008

M3 - Article

AN - SCOPUS:85064659942

VL - 112

SP - 96

EP - 108

JO - Physica E: Low-Dimensional Systems and Nanostructures

JF - Physica E: Low-Dimensional Systems and Nanostructures

SN - 1386-9477

ER -