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We analytically study phonon transmission and localization in randomsuperlattices by using a Green's function approach. We derive expressions forthe average transmission rate and localization length, or Lyapunov exponent, interms of the superlattice structure factor. This is done by considering thebackscattering of phonons, due to the complex mass density fluctuations, whichincorporates all of the forward scattering processes. These analytical resultsare applied to two types of random superlattices and compared with numericalsimulations based on the transfer matrix method. Our analytical results showexcellent agreement with the numerical data. A universal relation for thetransmission fluctuations versus the average transmission is derivedexplicitly, and independently confirmed by numerical simulations. The transientof the distribution of transmission to the log-normal distribution for thelocalized phonons is also studied.Comment: 36 pages, Late

Phonon-transmission rate, fluctuations, and localization in random semiconductor superlattices: Green’s-function approach