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Substrate Coupling Suppresses Size Dependence of Thermal Conductivity in Supported Graphene

Thermal conductivity $κ$ of both suspended and supported graphene has been studied by using molecular dynamics simulations. Obvious length dependence is observed in $κ$ of suspended single-layer graphene (SLG), while $κ$ of supported SLG is insensitive to the length. The simulation result of room temperature $κ$ of supported SLG is in good agreement with experimental value. In contrast to the decrease in $κ$ induced by inter-layer interaction in suspended few-layer graphene (FLG), $κ$ of supported FLG is found to increase rapidly with the layer thickness, reaching about 90% of that of bulk graphite at six layers, and eventually saturates at the thickness of 13.4 nm. More interestingly, unlike the remarkable substrate dependent $κ$ in SLG, the effect of substrate on thermal transport is much weaker in FLG. The underlying physics is investigated and presented.