Isotope scattering of large-wave-vector phonons in GaAs and InSb: Deformation-dipole and overlap-shell models

Scatterings of near-zone-boundary phonons by isotopic disorder in diatomic GaAs InSb crystals are studied theoretically. In multiatomic lattices the scattering rate depends importantly on the vibrational amplitudes of constituent atoms. We find that the wave-vector dependences of these amplitudes, which are predicted by some lattice models, show quite dissimilar behaviors as compared to others. The typical examples investigated in this paper are the deformation-dipole model and the overlap-shell model. With the use of these models the frequency dependence of the relaxation time of phonons is calculated. Both models, however, predict the relaxation time of about 0.1 {μ}sec for 1-THz TA phonons in GaAs, which is at least 1 order of magnitude shorter than the lifetime reported by Ulbrich et al.