Phonon Transmission Rates in Randomly Stacked Superlattices

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I have numerically and analytically investigated phonon transmission rates in randomly stacked superlattices fabricated of semiconducting materials (AlAs and GaAs), using the transfer matrix method and Green's functions.The transmission rates which are numerically obtained show sharp peaks and dips with respect to frequency, whose pattern is peculiar to configuration of constituent layrs of random superlattices, resulting in a finger print of random superlattices.The average transmission rates over a number of possible configurations of constituent layrs exhibit similar frequency dependence to that of squared absolute structure factor of the random superlattices without multiple scattering at the interfaces between the constituent layrs.I have analytically derived the averaged transmission rates over the sample of random superlattices by means of Green's functions.I exhibit that the Lyapunovexponent, which is inverse of the localization length of phonons, is proportional to the squared absolute structure factor of the random superlattices and that the averaged transmission rates and related quantities such as universal transmission fluctuations can be described in terms of the ratio of system length to localization length.