Calculation of the mobility of two-dimensional excitons in a GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As quantum well

We have calculated the mobility of two-dimensionally free excitons in a quantum well by considering various scattering processes. The relaxation times are derived by using a variational wave function for the 1s exciton in the lowest subband in an infinitely deep well. The calculated mobilities for the GaAs well at first increase with temperature due to the predominance of the interface-roughness scattering, then attain a peak, and finally decrease with temperature as the deformation-potential scattering dominates. The piezoelectric scattering has less importance. The calculated values agree with the experimental data for 8- and 15-nm-wide wells up to about 150 K; however, the disagreement between the values for a 4-nm-wide well indicates that the effect of a finite barrier should be considered. The polar-optic-phonon scattering has been included to explain the rapid decrease of the experimental data above 150 K; however, the single-subband approximation gives too high a value for the mobility, while the values for bulk excitons are quite low compared to the experimental data.