Reflectance study of the oscillator strength of excitons in semiconductor quantum wells

The oscillator strength of excitons is investigated systematically in lattice-matched GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As, strained-well ${\mathrm{In}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs, and strained-well GaAs/${\mathrm{GaAs}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{P}}_{\mathit{x}}$ quantum wells (QW’s) using Fourier-transform reflectance spectroscopy. The oscillator strength in GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As QW’s increases as the well width is reduced, in agreement with the existing theory, while those in ${\mathrm{In}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs and GaAs/${\mathrm{GaAs}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{P}}_{\mathit{x}}$ QW’s show a maximum at a certain well width. The well-width dependence of the band nonparabolicity and the overlap of the electron and hole wave functions is responsible for this behavior. The oscillator strengths in ${\mathrm{In}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs and GaAs/${\mathrm{GaAs}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{P}}_{\mathit{x}}$ QW’s are differently dependent on the alloy composition; this is also explained in terms of the band nonparabolicity and the wave-function overlap. The temperature dependence of the oscillator strength in these structures is well described by a modified Debye-Waller expression with an averaged phonon mode. The exciton-phonon interaction, deduced from the temperature dependence of the oscillator strength of the zero-phonon line, is mainly determined by confined phonons in GaAs/${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As QW’s, and by quasi-three-dimensional phonons in ${\mathrm{In}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/GaAs QW’s.