Substrate Coupling Suppresses Size Dependence of Thermal Conductivity in Supported Graphene

Thermal conductivity $\kappa$ of both suspended and supported graphene has been studied by using molecular dynamics simulations. Obvious length dependence is observed in $\kappa$ of suspended single-layer graphene (SLG), while $\kappa$ of supported SLG is insensitive to the length. The simulation result of room temperature $\kappa$ of supported SLG is in good agreement with experimental value. In contrast to the decrease in $\kappa$ induced by inter-layer interaction in suspended few-layer graphene (FLG), $\kappa$ 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 $\kappa$ in SLG, the effect of substrate on thermal transport is much weaker in FLG. The underlying physics is investigated and presented.