Contact resistance and shot noise in graphene transistors

Graphene’s distinctive band structure gives rise to exciting new transport properties and promising applications for carbon-based electronics.1–3 When measuring the conductance or current noise in a nanotube or a sheet of graphene, the properties of the contacts can matter as much as the electronic structure of the nanotube or graphene itself. In semiconducting nanotubes or graphene nanoribbons, it is known that Schottky barriers develop at the metallic contacts.4,5 Charge transfer between a metal and a wide graphene strips induces potential steps whose shape may differ strongly from usual Schottky barriers due to the semimetallic and twodimensional nature of graphene. The existence of such metal-induced potential steps was inferred experimentally from the transport properties of a graphene strip with various contact geometries.6 More direct evidence for these steps comes from optical mapping of the potential landscape across a graphene device.7 Recent theoretical work on graphene-metal interfaces has been performed within the atomistic tight-binding theory.8,9 In this paper, the conductance and the shot noise of graphene field effect transistors gFETs with extended contacts are derived using the Dirac Hamiltonian for graphene. Near a single contact, we assume that the Fermi energy in graphene varies monotonically over a characteristic length d, and we solve the corresponding scattering problem exactly. If the transport is ballistic between both contacts, we predict oscillations of the noise and conductance as the charge density is increased in the sheet. When the density exceeds the one under the contact, the noise minima might be zero and correspond to perfect transmission between the contacts. Such realizations of a noiseless gFET are caused by FabryPérot resonances and require low doping by the contacts. In the diffusive regime, we show how the total resistance and Fano factor of the whole gFET depend upon the contact resistance and Fano factor of each contact, which is relevant in interpreting recent experiments on shot noise in nonsuspended graphene.10,11 Before analyzing the gFETs’ properties, it is useful to investigate transport across a single graphene-metal contact. We thus consider that a metal electrode covers the left halfplane x 0 of an infinite graphene layer. We assume that the metal coating simply shifts the Fermi level of the graphene underneath while preserving its pristine Dirac cones.12 Far from the contact, the type n or p and density of charge carriers in the right half-plane x 0 are tuned by a distant metallic gate. A continuous Fermi wave-vector profile kF x must therefore develop near the contact edge to match the asymptotic values kF − =kF m under the metal and kF + =kF g in bare graphene. The dynamics of the massless fermions can be safely described by the single-valley twodimensional Dirac Hamiltonian,