Calculation of intervalley scattering rates in ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As: Effects of alloy and phonon scattering

The lifetime broadening of an electron at the bottom of the Γ conduction-band valley in ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As is calculated for 0≤x≤1. The parameter-free calculations take into account both electron-alloy scattering and electron-phonon scattering, with realistic models for the electronic band structures and phonon spectra. Second-order perturbation theory and the coherent-potential approximation are employed to evaluate the broadening. Intervalley scattering dominates the contributions to the lifetime in indirect-gap ${\mathrm{Al}}_{\mathit{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As (x≥0.45). The calculations give a fastest intervalley scattering time at temperature 10 K of 16 fs at x=0.81, with approximately twice as many transfers going to the L valleys as to the X valleys. Results are compared with lifetime broadenings obtained from spectroscopic ellipsometry, time-resolved photoluminescence, and Raman measurements.