Thermal transport in graphene nanoribbons supported on SiO2

Abstract

We present a theoretical model for thermal transport in graphene nanoribbons (GNRs) on SiO${}_{2}$ based on solving the phonon Boltzmann transport equation. Thermal transport in supported GNRs is characterized by a complex interplay between line edge roughness (LER) and internal scattering, as captured through an effective LER scattering rate that depends not only on the surface roughness features, but also on the strength of internal scattering mechanisms (substrate, isotope, and umklapp phonon scattering). Substrate scattering is the dominant internal mechanism, with a mean free path (mfp) of approximately 67 nm. In narrow supported GNRs ($Wl130$ nm, i.e., roughly twice the mfp due to substrate scattering), phonon transport is limited by LER and spatially anisotropic. For intermediate widths ($130\phantom{\rule{0.16em}{0ex}}\mathrm{nm}lWl1$ $\ensuremath{\mu}$m) a competition between LER and substrate scattering governs transport, while thermal transport in wide GNRs ($Wg1\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}$m) is dominated by substrate scattering and spatially isotropic. Thermal transport in supported GNRs can be tailored by controlling the ribbon width and edge roughness. We conclude that narrow ribbons act as longitudinal heat conduits while wide ribbons act as good omnidirectional heat spreaders.