Measuring the transport of electrons through a graphene sheet necessarily involves contacting it with metal electrodes. We studied the adsorption of graphene on metal substrates using ﬁrst-principles calculations at the level of density-functional theory . The bonding of graphene to Al, Ag, Cu, Au, and Pt (111) surfaces is so weak that its unique “ultrarelativistic” electronic structure is preserved (Fig.1). The interaction does, however, lead to a charge transfer that shifts the Fermi level by up to 0.5 eV with respect to the conical points. The crossover from p-type to n-type doping occurs for a metal with a work function ~5.4 eV, a value much larger than the work function of free-standing graphene, 4.5 eV. We developed a simple analytical model that describes ΔEF, the Fermi-level shift in graphene, very well in terms of WM−WG, the metal substrate work function relative to that of graphene (Fig.2). Graphene interacts with and binds more strongly to Co, Ni, Pd, and Ti (Fig.1). This chemisorption involves hybridization between graphene pz states and metal d states that opens a band gap in graphene, and reduces its work function considerably. The supported graphene is effectively n-type doped because in a current-in-plane device geometry the work-function lowering will lead to electrons being transferred to the unsupported part of the graphene sheet.
[1[ G. Giovannetti, P.A. Khomyakov, G. Brocks, V.M. Karpan, J. van den Brink and P.J. Kelly, Doping graphene with metal contacts, Phys. Rev. Lett. 101, 026803 (2008); P. A. Khomyakov, G. Giovannetti, P.C. Rusu, G. Brocks, J. van den Brink and P.J. Kelly, First-principles study of the interaction and charge transfer between graphene and metals, Phys. Rev. B 79, 195425 (2009).
Figure 1. Band structures of graphene absorbed upon Al, Pt, and Co (111) substrates. The bottom left and right panels correspond, respectively, to majority and minority spin band structures. The Fermi level is at zero energy. The amount of carbon pz character is indicated by the blackness of the bands. The conical point corresponds to the crossing of predominantly pz bands at K. Note that on doubling the lattice vectors (for Al and Pt), the K point is folded down onto the K point of the smaller Brillouin zone.
Figure 2. Calculated Fermi energy shift with respect to the conical point, EF (dots), and the work function W−WG (crosses) as a function of the clean metal-graphene work-function difference WM−WG. The lower (black) and the upper (green/gray) points are for the equilibrium (d~3.3 Å) and large (d=5.0 Å) graphene-metal-surface separations, respectively. The solid and dashed lines follow from the analytical model with d = 3.3 and 5.0 Å, respectively. The insets illustrate the position of the Fermi level with respect to the conical point.