Maximizing phonon thermal conductance for ballistic membranes

TL;DR

This paper calculates the ballistic phonon conductance in membranes, revealing that materials with lower sound speeds maximize conductance, especially at low temperatures where phonon transport is ballistic.

Contribution

It introduces a theoretical calculation of phonon conductance considering the transition from 3D to 2D, highlighting the counter-intuitive role of sound speed.

Findings

Lower sound speed materials have higher ballistic conductance.

Conductance depends on temperature and membrane thickness.

Transition from 3D to 2D affects phonon transport properties.

Abstract

At low temperatures, phonon scattering can become so weak that phonon transport becomes ballistic. We calculate the ballistic phonon conductance G for membranes using elasticity theory, considering the transition from three to two dimensions. We discuss the temperature and thickness dependence and especially concentrate on the issue of material parameters. For all membrane thicknesses, the best conductors have, counter-intuitively, the lowest speed of sound.