On the channel width-dependence of the thermal conductivity in ultra-narrow graphene nanoribbons

TL;DR

This paper investigates how the thermal conductivity of ultra-narrow graphene nanoribbons depends on their width, revealing that the relationship varies with phonon transport regimes and is influenced by channel length.

Contribution

It demonstrates that the width dependence of thermal conductivity in graphene nanoribbons varies across different phonon transport regimes and depends on channel length, which was not previously understood.

Findings

The width dependence exponent varies with phonon transport regime.

Ballistic, diffusive, and localized phonons show different width scaling.

Channel length influences the width dependence of thermal conductivity.

Abstract

The thermal conductivity of low-dimensional materials and graphene nanoribbons in particular, is limited by the strength of line-edge-roughness scattering. One way to characterize the roughness strength is the dependency of the thermal conductivity on the channel width in the form W^{\beta}. Although in the case of electronic transport this dependency is very well studied, resulting in W^6 for nanowires and quantum wells and W^4 for nanoribbons, in the case of phonon transport it is not yet clear what this dependence is. In this work, using lattice dynamics and Non-Equilibrium Greens Function simulations, we examine the width dependence of the thermal conductivity of ultra-narrow graphene nanoribbons under the influence of line edge-roughness. We show that the exponent {\beta} is in fact not a single well-defined number, but it is different for different parts of the phonon spectrum depending on whether phonon transport is ballistic, diffusive, or localized. The exponent {\beta} takes values {\beta} < 1 for semi-ballistic phonon transport, values {\beta} >> than 1 for sub-diffusive or localized phonons, and {\beta} = 1 only in the case where the transport is diffusive. The overall W^{\beta} dependence of the thermal conductivity is determined by the width-dependence of the dominant phonon modes (usually the acoustic ones). We show that due to the long phonon mean-free-paths, the width-dependence of thermal conductivity becomes a channel length dependent property, because the channel length determines whether transport is ballistic, diffusive, or localized.