Normalized reflection spectra in GaAs/${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As single quantum wells: Structure characterizations and excitonic properties

A systematic study of GaAs/${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As single quantum wells is performed in two sets of samples with different alloy concentrations (namely, x=9% and 18.5%) and well thicknesses ranging from 15 to 250 Å. These samples are grown by the molecular-beam-epitaxy facility and characterized by ‘‘normalized reflection spectroscopy.’’ Accurate calculations of exciton energies are computed in the effective-mass approximation by a variational wave function expanded in electron-hole subbands taking into account the four-band Lüttinger Hamiltonian and strain tensor energy. Maxwell’s equations of the system are exactly solved in order to compute the optical response in polaritonic framework. Model calculations well compare in energies and line shapes with normalized reflectivity for quantum-well thicknesses lower than 70 Å. For larger samples it is necessary to hypothesize a certain degree of strain relaxation and nonhomogeneous indium concentration in the sample in order to explain some discrepancies between theory and experiments.