Atomistic Insight into the Formation of Metal-Graphene One-Dimensional Contacts

Motivated by the need to control the resistance of metal-graphene interfaces, we have simulated the structural and transport properties of edge contacts upon their formation. Our first-principles calculations reveal that the contacts evolve in a nontrivial way depending on the type of metal and the chemical contamination of the graphene edge. In particular, our results indicate that the origin of the low experimental resistance of chromium-graphene edge contacts is related to their weaker variation upon contamination and defect formation. In summary, by analyzing the distance dependence of the graphene-metal interaction and the relation between the reactivity and forces at the graphene edge, we shed new light on the mechanisms responsible for the diverse performance of experimentally fabricated graphene edge contacts.

Figure 1

(a) Side (left) and top (right) view of a model $\mathrm{M}$-$\mathrm{Gr}$ edge contact. (b) Calculated contact resistance at 300 K as a function of gate voltage ($V_G$) for different graphene edge contacts with different metals, namely $\mathrm{Ni}$ (orange), $\mathrm{Cr}$ (brown), $\mathrm{Ti}$ (brown), and $\mathrm{Au}$ (cyan). The intrinsic resistance of free-standing graphene is included as reference (black curve). A gate voltage of $V_G=\pm 0.2\mathrm{V}$ corresponds to a doping level of approximately $4\times {10}^{12}{\mathrm{cm}}^{-2}$.

Figure 2

Forces in the $z$ direction on the atoms of the graphenic subsystem, for four selected contacts at maximum-force conformation. Blue (red) shades indicate forces pointing towards (away from) the metal surface. The forces for the following contacts are shown: (a) $\mathrm{Ni}$-$\mathrm{Gr}$, (b) $\mathrm{Ni}$-$\mathrm{O}$-$\mathrm{Gr}$, (c) $\mathrm{Ni}$-$\mathrm{F}$-$\mathrm{Gr}$, and (d) $\mathrm{Cr}$-$\mathrm{F}$-$\mathrm{Gr}$.

Figure 3

(a),(b) Side and top views of two $\mathrm{Ti}\text{−}{\mathrm{F}}_2\text{−}\mathrm{Gr}$ interfaces with different contacting sites (marked with horizontal dashed lines). Top panels: maximum-force conformations before structural optimization. Lower panels: contact geometry upon relaxation, together with the corresponding resistance at $T=300\mathrm{K}$ and $V_G=0\mathrm{V}$.

Figure 4

(a) Schematic illustration of the three equilibrium conformations for transition-metal-based contacts. (b) Histogram of the contact resistance at $T=300\mathrm{K}$ and $V_G=0\mathrm{V}$, as obtained for different metals ($\mathrm{Ni}$, $\mathrm{Cr}$, $\mathrm{Ti}$, and $\mathrm{Au}$) and graphene edge contaminations (O, F).

Figure 5

(a) Schematic model of a corrugated metal-graphene 1D contact. The distances $d^1$, $d^2$, and $d^3$ denote metal-graphene distances at minimum energy, maximum force, and maximum force distance plus 1 Å, respectively. The corresponding resistances are denoted by $R_C^1$, $R_C^2$, and $R_C^3$. (b),(c) show the histograms of contact resistance at $T=300\mathrm{K}$ and $V_G=0\mathrm{V}$ for the clean (gray), O- (red), F- (blue), and ${\mathrm{F}}_2$- (light blue) contaminated $\mathrm{Ni}$ and $\mathrm{Cr}$ electrodes.

Figure 6

Spin-up ($\uparrow$) and spin-down ($\downarrow$) calculated density of states projected onto the interface atoms of the $\mathrm{Cr}$-$\mathrm{F}$-$\mathrm{Gr}$ contact, at distances $d^1$ (top panel), $d^2$ (middle panel), and $d^3$ (bottom panel). In the bottom panel the corresponding PDOS of a graphene zigzag edge is shown for comparison. For visualization purposes, the PDOS of F has been multiplied by 4.