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

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Abstract
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.