Structural properties of the multilayer graphene/$4H\text{−}\mathrm{Si}\mathrm{C}\left(000\overline{1}\right)$ system as determined by surface x-ray diffraction

We present a structural analysis of the multilayer graphene/$4H\mathrm{Si}\mathrm{C}\left(000\overline{1}\right)$ system using surface x-ray reflectivity. We show that graphene films grown on the C-terminated $\left(000\overline{1}\right)$ surface have a graphene-substrate bond length that is very short $\left(1.62\mathrm{\AA }\right)$. The measured distance rules out a weak van der Waals interaction to the substrate and instead indicates a strong bond between the first graphene layer and the bulk as predicted by ab initio calculations. The measurements also indicate that multilayer graphene grows in a near turbostratic mode on this surface. This result may explain the lack of a broken graphene symmetry inferred from conduction measurements on this system [C. Berger et al., Science 312, 1191 (2006)].

Figure 1

(a) Schematic drawing of the reflectivity geometry. Incident wave ${\mathbf{k}}_i$ strikes the sample surface at an angle $ϴ+\omega$. The diffracted wave, ${\mathbf{k}}_f$, is kept fixed at $2ϴ$ from ${\mathbf{k}}_i$. $\mathbf{q}$ is “rocked” through the $\left(00\ell \right)$ rod by rotating the sample through an angle $\pm \omega$. (b) Model of multilayer graphene islands grown on a SiC substrate with a reconstructed SiC interface layer. For specular reflectivity, all $n$-layer islands can be represented as one island with a fractional surface coverage parameter $p_n$.

Figure 2

A schematic model of multilayer graphene grown on the $4\mathrm{H}\text{−}\mathrm{Si}\mathrm{C}\left(000\overline{1}\right)$ substrate. Dashed lines are the bulk SiC lattice planes before interface relaxation ($\Delta$’s). The fifth (adatom) layer is displaced ${\delta }_{\mathit{ad}}$ from the last interface layer. (●) are carbon atoms and (엯) are silicon atoms. The shaded circles in the top three layers of the interface can be either carbon or silicon atoms depending on which of the two models, carbon corrugated or carbon rich, is used.

Figure 3

(Color online) Specular reflectivity vs $q_{\perp }$ (in r.l.u.) for a graphitized $4\mathrm{H}\text{−}\mathrm{Si}\mathrm{C}\left(000\overline{1}\right)$ C-face surface with nine graphene layers. Shaded circles are the data. The solid line is the best fit to the structural model (described in text) with a smooth graphene layer $({\sigma }_G=0.0\mathrm{\AA })$. The dashed line is the best fit with a corrugated graphite layer $({\sigma }_G=0.25\mathrm{\AA })$. The dotted line is the best fit if the graphene-substrate distance $D_0$ is reduced by 10%.

Figure 4

Schematic ball models of bulk, C-corrugated, and C-rich interface layers between the substrate and the graphene film. Shaded circles are carbon atoms and open circles are silicon atoms. Hatched atoms are carbon atoms in the first graphene layer. Interlayer spacings and densities (relative to bulk SiC) are shown.

Figure 5

(Color online) Specular reflectivity for graphitized $4\mathrm{H}\text{−}\mathrm{Si}\mathrm{C}\left(000\overline{1}\right)$ C-face surface. Shaded circles are the data. The solid line is the best fit to the carbon-corrugated top layer. The dashed line show the fit for the same model if the Si layer density is fixed at the bulk value $({\rho }_{1a}=1)$. The dotted line is a fit when the carbon corrugation in the top layer is removed but the total density remains the same (“smooth C layer”).

Figure 6

(Color online) A comparison of the calculated reflectivity vs $q_{\perp }$ (in r.l.u.) for different first bilayer models. The solid line is the best-fit structure with bulk bilayer parameters. The dashed line is a fit with ${\rho }_{2\mathrm{Si}}$ fixed at a value 25% less than the bulk. The dotted line is a best fit with the both ${\Delta }_{2\mathrm{Si}}$ and ${\Delta }_{2\mathrm{C}}$ relaxed toward the bulk by 5%.