Doping Graphene with Metal Contacts

Making devices with graphene necessarily involves making contacts with metals. We use density functional theory to study how graphene is doped by adsorption on metal substrates and find that weak bonding on Al, Ag, Cu, Au, and Pt, while preserving its unique electronic structure, can still shift the Fermi level with respect to the conical point by $\sim 0.5\mathrm{eV}$. At equilibrium separations, the crossover from $p$-type to $n$-type doping occurs for a metal work function of $\sim 5.4\mathrm{eV}$, a value much larger than the graphene work function of 4.5 eV. The numerical results for the Fermi level shift in graphene are described very well by a simple analytical model which characterizes the metal solely in terms of its work function, greatly extending their applicability.

Figure 1

The most stable configurations of graphene (a) on Cu, Ni, and Co (111) with one carbon atom on top of a metal atom (A site), and the second carbon on a hollow site (C site) and (b) on Al, Au, Pd, and Pt(111) in a unit cell with 8 carbon atoms and 3 metal atoms per layer.

Figure 2

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 $p_z$ character is indicated by the blackness of the bands. The conical point corresponds to the crossing of predominantly $p_z$ 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 3

Calculated Fermi energy shift with respect to the conical point, $\Delta E_{\mathrm{F}}$ (dots), and change in the work function $W-W_{\mathrm{G}}$ (triangles) as a function of $W_{\mathrm{M}}-W_{\mathrm{G}}$, the difference between the clean metal and graphene work functions. The lower (black) and the upper [gray (green)] results are for the equilibrium ($\sim 3.3\AA$) and a larger (5.0 Å) separation of graphene and the metal surfaces, respectively. The solid line and the dashed line follow from the model of Eq. (1) with ${\Delta }_{\mathrm{c}}=0$ for $d=5.0\AA$. The insets illustrate the position of the Fermi level with respect to the conical point.

Figure 4

Left: Schematic illustration of the parameters used in modeling the interface dipole and potential step formation at the graphene-metal interface. Right: Plane-averaged difference electron density $\Delta n(z)=n_{\mathrm{M}|\mathrm{G}}(z)-n_{\mathrm{M}}(z)-n_{\mathrm{G}}(z)$ showing the charge displacement upon formation of the graphene-Pt(111) interface.

Figure 5

Fermi level shifts $\Delta E_{\mathrm{F}}(d)$ as a function of the graphene-metal surface distance. The dots give the calculated DFT results, the solid lines give the results obtained from the model, Eq. (1) [23].