Impact of bonding at multi-layer graphene/metal Interfaces on thermal boundary conductance

Abstract

We use density functional theory and the atomistic Green's function method (AGF) to study the effect of bonding on phonon transmission and thermal boundary conductance (TBC) at the interface of metals (Au, Cu, and Ti) and single layer graphene (SLG)/multi-layer graphene (MLG). Our analysis shows that the TBC across Ti/SLG/Ti interfaces (∼500 MW m⁻² K⁻¹) is significantly larger than the TBC across Cu/SLG/Cu (∼10 MW m⁻² K⁻¹) and Au/SLG/Au (∼7 MW m⁻² K⁻¹) interfaces. However, the TBC across Ti/MLG/Ti (∼40 MW m⁻² K⁻¹) is an order of magnitude lower compared to TBC at the Ti/SLG/Ti interface, whereas the TBC at Cu/MLG/Cu and Au/MLG/Au interfaces are similar to those of Cu/SLG/Cu and Au/SLG/Au, respectively. We find that this substantial decrease in TBC at the Ti/MLG/Ti interface is a result of phonon mismatch between the graphene layer bonded to Ti and the non-bonded graphene layers. The effect of number of graphene layers on TBC at Cu/MLG/Cu and Au/MLG/Au interfaces is relatively insignificant because of the weak interactions at these metal/graphene interfaces. It was observed that the moderate attenuation of Ti/C bonding strength can enhance the phonon coupling between the graphene layers bonded to Ti and non-bonded graphene layers, and can increase the TBC across Ti/MLG/Ti by ∼100%. This impact of interfacial bonding strength on TBC at metal/MLG interfaces, predicted by AGF calculations, is further confirmed by non-equilibrium molecular dynamics simulations which show the transition of thermal transport mechanism from metal/graphene dominated resistance to graphene/graphene dominated resistance as the metal/graphene bonding strength increases in the metal/MLG/metal structure.