Ballistic-diffusive model for heat transport in superlattices and the minimum effective heat conductivity

TL;DR

This paper develops a thermodynamic model combining ballistic and diffusive heat fluxes to explain the minimum effective thermal conductivity observed in superlattices at nanometric scales.

Contribution

It introduces a novel theoretical framework using Guyer-Krumhansl equations to analyze heat transport in superlattices, explaining the thermal conductivity minimum.

Findings

Effective heat conductivity exhibits a minimum at nanometric periods.

Dispersion relations derived from the model match experimental observations.

The model clarifies the roles of ballistic and diffusive heat fluxes in superlattices.

Abstract

There has been much interest in semiconductor superlattices because of showing very low thermal conductivities. This makes them especially suitable for applications in a variety of devices for thermoelectric generation of energy, heat control at the nanometric length scale, etc. Recent experiments have confirmed that the effective thermal conductivity of superlattices at room temperature have a minimum for very short periods (in the order of nanometers) as some kinetic calculations had anticipated previously. This work will show advances on a thermodynamic theory of heat transport in nanometric 1D multilayer systems by considering the separation of ballistic and diffusive heat fluxes, which are both described by Guyer-Krumhansl constitutive equations. The dispersion relations, as derived from the ballistic and diffusive heat transport equations, are used to derive an effective heat conductivity of the superlattice and to explain the minimum of the effective thermal conductivity.