Influence of the spin-orbit split-off valence band in ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/${\mathrm{Al}}_{\mathit{y}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{y}}$As strained-layer quantum wells

Quantum-well ground and excited states are observed using wavelength-modulated reflectivity in ${\mathrm{In}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/${\mathrm{Al}}_{\mathit{y}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{y}}$As single-quantum-well structures. To account for the dependence of their energies on indium and aluminum concentrations, we find that it is necessary to include the coupling between the light-hole ${\mathrm{\Gamma }}_8$ valence band and the spin-orbit split-off ${\mathrm{\Gamma }}_7$ valence band. The calculation is performed using a two-band envelope-function approximation, and good agreement with experiment is obtained.