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In this paper we present a comprehensive model for the tunneling current ofthe metal-insulator-graphene heterostructure, based on the Bardeen TransferHamiltonian method, of the metal-insulator-graphene heterostructure. As aparticular case we have studied the metal-graphene junction, unveiling the roleplayed by different electrical and physical parameters in determining thedifferential contact resistance.

Model of the Electrostatics and Tunneling Current of Metal-Graphene Junctions and Metal-Insulator-Graphene Heterostructures