Tunneling in graphene-metal contacts and intercalated graphite

We develop a theory for electron tunneling in graphene/metal electrical contacts with applications in graphene-based electronics and intercalated graphite in battery anodes. A temperature-dependent, momentum-resolved tunneling theory is proposed to explain the contact resistance for Pt/graphene, Cu/graphene, and Au/graphene contacts. Electron transport studied in sandwich structures involving a Pt (111) surface, an intermediate graphene layer, and a Cu (111) surface demonstrates that the contact potential between the metal electrode and graphene layer strongly influences the electronic density of states available for out-of-plane tunneling between dissimilar metals. By expressing the conductivity in terms of the work function of the metal electrodes, the theory is generalized to a range of metal surfaces. The sensitivity of out-of-plane conductivity to metal surface is probed; the out-of-plane conductivity in graphene is therefore not ‘intrinsic’ but is instead determined by the interaction and surface morphology of the contacting metal electrodes. The tunneling theory is then applied to alkali-metal intercalated graphite in lithium-ion battery anodes to elucidate the mechanism of out-of-plane conductivity.