Substrate-induced cross-plane thermal propagative modes in few-layer graphene
Résumé
We report the layer-number dependence of the averaged interlayer thermal resistances (Rint) 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 Rint 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.