Low thermal conductance of metal contacts is one of the main challenges in thermal management of nanoscale devices of graphene and other 2D materials. Previous attempts to search for metal contacts with high thermal conductance yielded limited success due to incomplete understanding of the origins of the low thermal conductance. In this paper, we carefully study the intrinsic thermal conductance across metal/graphene/metal interfaces to identify the heat transport mechanisms across graphene interfaces. We find that unlike metal contacts on diamond, the intrinsic thermal conductance of most graphene interfaces (except Ti and TiNx) is only about 50 % of the phonon radiation limit, suggesting that heat is carried across graphene interfaces mainly through elastic transmission of phonons. We thus propose a convenient approach to substantially enhance the phononic heat transport across metal contacts on graphene, by better matching the energy of phonons in metals and graphene, e.g., using metallic nitrides. We test the idea with TiNx, with phonon frequencies of up to 1.18*10^14 rad/s, 47 % of the highest phonon frequencies in graphene of 2.51*10^14 rad/s . Interestingly, we obtain a huge thermal conductance of 270 MW m-2 K-1 for TiNx/graphene interfaces, which is about 140 % of the phonon radiation limit. The huge thermal conductance could be partially attributed to inelastic phonon transport across the TiNx/graphene interface. Our work provides guidance for the search for good metal contacts on 2D materials and devices.
