Thermal Stability of Corrugated Epitaxial Graphene Grown on Re(0001)

We report on a novel approach to determine the relationship between the corrugation and the thermal stability of epitaxial graphene grown on a strongly interacting substrate. According to our density functional theory calculations, the C single layer grown on Re(0001) is strongly corrugated, with a buckling of 1.6 Å, yielding a simulated C $1s$ core level spectrum which is in excellent agreement with the experimental one. We found that corrugation is closely knit with the thermal stability of the C network: C-C bond breaking is favored in the strongly buckled regions of the moiré cell, though it requires the presence of diffusing graphene layer vacancies.

Figure 1

(a) LEEM images at low (left) and high (right) magnification clearly show the homogeneity of the single-layer graphene film. The dark curved lines correspond to monoatomic steps of the substrate. (b) Line profile of the $\mu$-LEED pattern of $\mathrm{GR}/\mathrm{Re}(0001)$ (shown in the inset). (c) Top and side views of the simulated structure of $\mathrm{GR}/\mathrm{Re}(0001)$. The color scale reflects the separation between C and the substrate beneath. (d) Distribution of the C-Re distances in the moiré cell.

Figure 2

(a) C $1s$ spectrum measured at normal emission and $h\nu =400\mathrm{eV}$ (empty circles) together with the simulated spectrum (solid line) and the calculated spectral distribution originated by the 200 C atoms. (b) BE of nonequivalent C atoms on the C-Re distance. The color scale in the model reflects the BEs of the different C $1s$ components.

Figure 3

(a) C $1s$ spectral evolution of the GR-covered sample at 1110 K. The components, associated to strongly and weakly interacting regions, are shown below the image plot. (b) Time evolution of the intensities of the $S$ and $W$ components. (c) Arrhenius plot of the decay rate of the $S$ population.

Figure 4

 Reaction path for GR layer breaking in the presence of a C vacancy in the strongly interacting region of the moiré cell as obtained from NEB simulations. Initial (IS), transition (TS), and final state (FS) structural geometries are shown.