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

Abstract

We analytically study phonon transmission and localization in random superlattices by using a Green's function approach. We derive expressions for the average transmission rate and localization length, or Lyapunov exponent, in terms of the superlattice structure factor. This is done by considering the backscattering of phonons, due to the complex mass density fluctuations, which incorporates all of the forward scattering processes. These analytical results are applied to two types of random superlattices and compared with numerical simulations based on the transfer matrix method. Our analytical results show excellent agreement with the numerical data. A universal relation for the transmission fluctuations versus the average transmission is derived explicitly, and independently confirmed by numerical simulations. The transient of the distribution of transmission to the log-normal distribution for the localized phonons is also studied.

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“…25,26 ). Additional analogies, not discussed here, also exist with the transport and localization of phonons in different kinds of periodic and random one-dimensional structures 27,28,29 .…”

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“…10 More recently, intentionally disordered SL's, in which disordering is artificially created by random thickness fluctuations, have received much attention. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] These intentionally disordered SL's were grown with the main aim of observing Anderson localization and mobility edges. The reported enhancement of photoluminescence ͑PL͒ was attributed to electron and hole localization due to disorder.…”

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