Observation of high-index excitonic states in ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/AlAs ternary-alloy quantum wells by two-photon spectroscopy

The application of two-photon absorption spectroscopy allows us to observe exciton states associated with high-index light-hole subbands in ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As/AlAs ternary-alloy quantum wells, which cannot be resolved in linear optical spectroscopy due to alloy broadening. The 2p-1s splitting energy of heavy-hole excitons up to the i=4 subband is determined to be 10 meV. Based on the observed energy separation between 2p light- and heavy-hole excitons with Δi=0 we derive a valence-band offset of Δ${\mathit{E}}_{\mathit{v}}$=340±15 meV for the x=0.37 ternary-alloy quantum wells. In addition, we provide experimental determination of the two-photon absorption coefficient ${\mathrm{\beta }}^{\mathrm{}\left(2\right)\mathrm{}}$ in quantum wells.