Phonon-assisted Γ-Xtransfer in (001)-grown GaAs/AlAs superlattices

A theory of phonon-assisted intervalley {Γ}-X transfer in periodic heterostructures GaAs/AlAs is developed on the basis of the envelope-function approximation. Matrix elements of intervalley transitions are expressed through the overlap integrals of {Γ} and X envelope functions with use of {Γ}-X intervalley deformation potential constants of bulk GaAs and AlAs. The phonon spectrum of an ideal GaAs/AlAs periodic heterostructure is studied in a microscopic approach. It is shown that phonons responsible for intervalley transitions are GaAs-like and AlAs-like X-point LO phonons, confined within GaAs and AlAs layers, respectively. {Γ}-X transfer times due to phonon-assisted scattering are calculated for the problem of photoexcited-electron relaxation in the type-II GaAs/AlAs superlattices and compared with the transfer times due to the phononless transition mechanism ({Γ}-X mixing). Both phonon-assisted {Γ}-X scattering and {Γ}-X mixing are important for the determination of {Γ}-X transfer times. The calculated values of {Γ}-X transfer times and their dependence on GaAs and AlAs layer thicknesses are in agreement with the experimental data.