Heat transport in ultra-thin dielectric membranes and bridges

TL;DR

This paper models phonon modes in ultrathin dielectric membranes to analyze their heat capacity and conductivity, revealing dimensional effects and temperature-dependent behaviors in ultra-thin structures.

Contribution

It introduces a rigorous elasticity theory approach accounting for surface effects on phonon modes in ultrathin membranes, improving understanding of thermal transport at nanoscale.

Findings

Heat capacity $C_V$ is proportional to $T$ at low temperatures.

Heat conductivity $$ scales as $T^{3/2}$ in narrow bridges.

High temperature results match bulk three-dimensional behavior.

Abstract

Phonon modes and their dispersion relations in ultrathin homogenous dielectric membranes are calculated using elasticity theory. The approach differs from the previous ones by a rigorous account of the effect of the film surfaces on the modes with different polarizations. We compute the heat capacity of membranes and the heat conductivity of narrow bridges cut out of such membranes, in a temperature range where the dimensions have a strong influence on the results. In the high temperature regime we recover the three-dimensional bulk results. However, in the low temperature limit the heat capacity, $C_V$, is proportional with $T$ (temperature), while the heat conductivity, $\kappa$, of narrow bridges is proportional to $T^{3/2}$, leading to a thermal cut-off frequency $f_c=\kappa/C_V\propto T^{1/2}$.