Carbon rehybridization at the graphene/SiC(0001) interface: Effect on stability and atomic-scale corrugation

We address the energetic stability of the graphene/SiC(0001) interface and the associated binding mechanism by studying a series of low-strain commensurate interface structures within a density functional scheme. Among the structures with negligible strain, the $6\sqrt{3}\times 6\sqrt{3}R{30}^{\circ }$ SiC periodicity shows the lowest interface energy, providing a rationale for its frequent experimental observation. The interface stability is driven by the enhanced local reactivity of the substrate-bonded graphene atoms undergoing $s{p}^2$-to-$s{p}^3$ rehybridization (pyramidalization). By this mechanism, relaxed structures of higher stability exhibit more pronounced graphene corrugations at the atomic scale.

Figure 1

Interface energy $E_{\mathrm{int}}$ vs graphene/SiC rotation angle $\alpha$. The structures are distinguished by the strain $s$ in the graphene layer: very weak strain with $\left|s\right|⩽0.2\%$ (circles), tensile strain with $s>0.2\%$ (diamonds), and compressive strain with $s<-0.2\%$ (squares). The dashed line is a linear fit of $E_{\mathrm{int}}$ for the structures with $\left|s\right|⩽0.2\%$.

Figure 2

Distribution of the pyramidalization angle ${\theta }_{\mathrm{p}}$ of the C atoms in the buffer layer for the interface structures with $\left|s\right|⩽0.2\%$. The solid bars refer to Si-bonded graphene C atoms identified by a cutoff distance of 2.3 Å, while the open bars refer to nonbonded C atoms. The graphene/SiC rotation angle $\alpha$, the interface energy $E_{\mathrm{int}}$, and the fraction $f_{\mathrm{Si}}$ of Si-bonded graphene C atoms are indicated for each structure. In the bottom panel, the inset illustrates the $\pi$-axial vector ${\mathbf{v}}_{\pi }$ and the pyramidalization angle ${\theta }_p$.

Figure 3

(a) Atomistic configuration used to compute $E_{\mathrm{C}-\mathrm{Si}}$ as a function of the pyramidalization angle ${\theta }_{\mathrm{p}}$ [only the top of the SiC pyramid construction (Ref. 16) is shown]. (b) Calculated $E_{\mathrm{C}-\mathrm{Si}}$ vs ${\theta }_{\mathrm{p}}$ and fit according to Eq. (2) (dashed line). We used a fixed C-Si distance $d_{\mathrm{C}-\mathrm{Si}}$ of 2.05 Å, corresponding to typical C-Si bond distances at the graphene/SiC(0001) interface.

Figure 4

Sticking energy $E_{\mathrm{stick}}$ of the graphene buffer layer vs model energy $E_{\mathrm{rehyb}}$ accounting for the C $\pi$-orbital local rehybridizations. Both energies are given per surface Si atom. The structures are distinguished according to strain, as in Fig. 1.