▎ 摘　　要

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's 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 Green's 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 >> 1 for sub-diffusive or localized phonons, and beta = 1 only in the case where the transport is diffusive. The overall Wb 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. Published by AIP Publishing.