Direct and indirect transition in (GaAs)n/(AlAs)nsuperlattices withn=1–15

Photoreflectance and photoluminescence measurements are carried out in (GaAs${)}_{\mathit{n}}$/(AlAs${)}_{\mathit{n}}$ superlattices with n ranged from 1 to 15 at room temperature. Analysis of photoreflectance spectra gives several critical-point energies with a high accuracy which coincide with the photoluminescence peak energies in superlattices with n≥10. In superlattices with n<10 the lowest transition energy determined from photoreflectance analysis is found to be larger than the lowest peak energy of photoluminescence, whereas the higher-energy peak of photoluminescence agrees well with the transition energy obtained from the photoreflectance analysis. The present results strongly suggest an existence of crossover of direct and indirect transition in the superlattices around n=10. Energy-band structures and momentum-matrix elements are calculated by tight-binding method based on ${\mathit{sp}}^3$ ${\mathit{s}}^{\mathrm{*}}$ with including the second-nearest-neighbor interactions, which show a crossover of direct and indirect transition around n=8. The lowest peak energies of photoluminescence data agree with the lowest calculated indirect band gaps in superlattices with n<10 and with the lowest direct band gaps for n≥10. The lowest transition energies determined from the photoreflectance analysis exhibit a feature similar to the layer-number dependence of the calculated direct band gaps in the whole range of n, but a disagreement in the energy values between the two exists in the range of n from 5 to 10. A disagreement between the present and previous data for n=5 is explained in terms of layer-number fluctuation, which is supported by the energy-band calculation of a long-period superlattice such as (GaAs${)}_{\mathit{n}}$/(AlAs${)}_{\mathit{n}}$/(GaAs${)}_{\mathit{n}+1\mathrm{}}$/(AlAs${)}_{\mathit{n}}$.