Phonon Universal Transmission Fluctuations and Localization in Semiconductor Superlattices with a Controlled Degree of Order

TL;DR

This paper investigates how phonon transmission and localization fluctuate in semiconductor superlattices with varying degrees of order, revealing universal fluctuation behavior across different disorder types through analytical and numerical methods.

Contribution

It introduces a unified analytical framework for phonon transmission fluctuations in partially ordered superlattices, demonstrating universal fluctuation behavior regardless of disorder specifics.

Findings

Transmission fluctuations follow a universal curve.

Localization length varies with superlattice order.

Analytical expressions match numerical simulations.

Abstract

We study both analytically and numerically phonon transmission fluctuations and localization in partially ordered superlattices with correlations among neighboring layers. In order to generate a sequence of layers with a varying degree of order we employ a model proposed by Hendricks and Teller as well as partially ordered versions of deterministic aperiodic superlattices. By changing a parameter measuring the correlation among adjacent layers, the Hendricks- Teller superlattice exhibits a transition from periodic ordering, with alterna- ting layers, to the phase separated opposite limit; including many intermediate arrangements and the completely random case. In the partially ordered versions of deterministic superlattices, there is short-range order (among any $N$ conse- cutive layers) and long range disorder, as in the N-state Markov chains. The average and fluctuations in the transmission, the backscattering rate, and the localization length in these multilayered systems are calculated based on the superlattice structure factors we derive analytically. The standard deviation of the transmission versus the average transmission lies on a {\it universal\/} curve irrespective of the specific type of disorder of the SL. We illustrate these general results by applying them to several GaAs-AlAs superlattices for the proposed experimental observation of phonon universal transmission fluctuations.