  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.
