Γ-Xmixing effects on pseudodirect exciton transitions in GaAs/AlAs type-II superlattices

We report on an experimental study of Γ-X mixing effects on the optical transition of the no-phonon-assisted (pseudodirect) exciton consisting of the n=1 AlAs-${\mathit{X}}_{\mathit{z}}$ electron and the n=1 GaAs-Γ heavy hole in [001]-(GaAs${)}_{\mathit{m}}$/(AlAs${)}_{\mathit{m}}$ type-II superlattices (m=8–13 monolayers) by using cw- and time-resolved-photoluminescence spectroscopies and photoluminescence-excitation spectroscopy. We have estimated the relative oscillator strength of the pseudodirect transition to the direct transition between the n=1 Γ electron and Γ heavy-hole states from the relative photoluminescence-excitation intensity, the relative photoluminescence intensity, and the relative photoluminesence decay rate. The values of the relative oscillator strength estimated from these three kinds of experimental results, which are around 1×${10}^{\mathrm{-}4}$, are mutually consistent, and they are almost independent of the layer thickness. We evaluate the Γ-X mixing factor from the relative oscillator strength, using a first-order perturbation theory, as a function of the layer thickness and show that the mixing factor is mainly determined by the overlap of the envelope functions of the Γ and ${\mathit{X}}_{\mathit{z}}$ electrons.