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Phonon-interface scattering in multilayer graphene on an amorphous support

Significance The thermal conductivity of suspended graphene can be even higher than the basal-plane value of graphite, which is among the highest found in solids. However, when graphene is in contact with an amorphous material, the thermal conductivity is suppressed considerably. This paper reports that the thickness of multilayer graphene supported on an amorphous substrate needs to be more than 30 atomic layers to recover the graphite thermal conductivity. The finding is explained by long phonon mean free paths in graphite even along the cross-plane direction, and is used to clarify interface leakage of phonons as an important mechanism for the observed suppression. The result is relevant for the application of graphene for electronics, thermal management, and other applications. The recent studies of thermal transport in suspended, supported, and encased graphene just began to uncover the richness of two-dimensional phonon physics, which is relevant to the performance and reliability of graphene-based functional materials and devices. Among the outstanding questions are the exact causes of the suppressed basal-plane thermal conductivity measured in graphene in contact with an amorphous material, and the layer thickness needed for supported or embedded multilayer graphene (MLG) to recover the high thermal conductivity of graphite. Here we use sensitive in-plane thermal transport measurements of graphene samples on amorphous silicon dioxide to show that full recovery to the thermal conductivity of the natural graphite source has yet to occur even after the MLG thickness is increased to 34 layers, considerably thicker than previously thought. This seemingly surprising finding is explained by long intrinsic scattering mean free paths of phonons in graphite along both basal-plane and cross-plane directions, as well as partially diffuse scattering of MLG phonons by the MLG-amorphous support interface, which is treated by an interface scattering model developed for highly anisotropic materials. Based on the phonon transmission coefficient calculated from reported experimental thermal interface conductance results, phonons emerging from the interface consist of a large component that is scattered across the interface, making rational choice of the support materials a potential approach to increasing the thermal conductivity of supported MLG.