Substrate-induced cross-plane thermal propagative modes in few-layer graphene

We report the layer-number dependence of the averaged interlayer thermal resistances (R-int) of the suspended and supported few-layer graphene (FLG), simulated by equilibrium molecular dynamics (EMD). The existence of a silicon dioxide substrate significantly decreases the R-int of FLG at low layer number. We use the model of long-wavelength dynamics of a nanolayer adsorbed on a deformable crystal [Kosevich and Syrkin, Phys. Lett. A 135, 298 (1989)] to explain the appearance of the substrate-induced gaps in the FLG dispersion curves and phonon radiation into the deformable substrate from these gap modes. The enhanced thermal conductance in the cross-plane direction is ascribed to the phonon radiation from FLG into the deformable substrate, which partially transfers the flow of phonon energy in FLG from the in-plane to the cross-plane direction and to the substrate. To confirm this, we calculate the cross-plane thermal resistance of three-layer graphene supported by an effective SiO2 substrate in which atomic masses are increased by a factor of 1000. This makes the substrate almost immovable and suppresses phonon radiation from the supported FLG by complete phonon reflection at the interface. The cross-plane thermal resistance of three-layer graphene supported on such a substrate is found to be the same as its suspended counterpart.