Phonon Transmission Rate, Fluctuations, and Localization in Random Semiconductor Superlattices: Green's Function Approach

TL;DR

This paper develops an analytical Green's function method to study phonon transmission, fluctuations, and localization in random superlattices, providing insights into phonon transport and disorder effects.

Contribution

It introduces a novel analytical framework for phonon transport in disordered superlattices, linking structure factors to transmission and localization properties.

Findings

Analytical expressions match numerical simulations.

Universal relation for transmission fluctuations derived.

Transmission distribution approaches log-normal form for localized phonons.

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.