Boltzmann Transport in Nanostructures as a Friction Effect

TL;DR

This paper introduces a hydrodynamic framework based on the Boltzmann transport equation to understand surface scattering effects on thermal transport in nanostructures, challenging traditional mean free path assumptions.

Contribution

It develops a novel approach using relaxon basis to model heat flow as a frictional hydrodynamic phenomenon in nanostructures, applicable to various materials and geometries.

Findings

Heat flow behaves as a viscous fluid slowed by surface friction.

Method applied to molybdenum disulphide nanostructures to estimate thermal conductivity.

Framework can be extended to electrons and other low-dimensional systems.

Abstract

Surface scattering is the key limiting factor to thermal transport in dielectric crystals as the length scales are reduced or when temperature is lowered. To explain this phenomenon, it is commonly assumed that the mean free paths of heat carriers are bound by the crystal size and that thermal conductivity is reduced in a manner proportional to such mean free paths. We show here that these conclusions rely on simplifying assumptions and approximated transport models. Instead, starting from the linearized Boltzmann transport equation in the relaxon basis, we show how the problem can be reduced to a set of decoupled linear differential equations. Then, the heat flow can be interpreted as a hydrodynamic phenomenon, with the relaxon gas being slowed down in proximity of a surface by friction effects, similar to the flux of a viscous fluid in a pipe. As an example, we study a ribbon and a trench of monolayer molybdenum disulphide, describing the procedure to reconstruct the temperature and thermal conductivity profile in the sample interior and showing how to estimate the effect of nanostructuring. The approach is general and could be extended to other transport carriers, such as electrons, or extended to materials of higher dimensionality and to different geometries, such as thin films.