Why graphene growth is very different on the C face than on the Si face of SiC: Insights from surface equilibria and the $(3\times 3)-3C-\mathrm{SiC}\left(\overline{1}\overline{1}\overline{1}\right)$ reconstruction

We address the stability of the surface phases that occur on the C side of $3C-\mathrm{SiC}\left(\overline{1}\overline{1}\overline{1}\right)$ at the onset of graphene formation. In this growth range, experimental reports reveal a coexistence of several surface phases. This coexistence can be explained by a Si-rich model for the unknown $(3\times 3)$ reconstruction, the known $(2\times 2{)}_{\text{C}}$ adatom phase, and the graphene-covered $(2\times 2{)}_{\text{C}}$ phase. By constructing an ab initio surface phase diagram using a van der Waals corrected density functional, we show that the formation of a well defined interface structure like the “buffer layer” on the Si side is blocked by Si-rich surface reconstructions.

Figure 1

Comparison of the surface energies relative to the bulk-terminated ($1\times 1$) phase as a function of the C chemical potential within the allowed ranges (given by diamond Si and graphite C). Shaded areas indicate chemical potential values outside the strict thermodynamic stability limits. The surface energy diagram includes structure models proposed earlier for the C face [(b) [23], (d) [21], (e) and (h) [20], (f) [27], (g) 35] and models adapted from the Si face [(a) [17] and (c) 36].

Figure 2

I: The (a) and (b) phases from Fig. 1 calculated using the HSE06 exchange-correlation functional with fully relaxed structures and unit cells. II: The geometry of the Si twist model and simulated constant current STM images for occupied and empty state of the Si twist model (unit cell shown in red). The three points of interest (A, B, C) marked by arrows are labeled according to Hiebel et al. [27]. III: Spin-polarized density of states.

Figure 3

Comparison of the surface energies for four different interface structures of $3C$-SiC($\overline{1}\overline{1}\overline{1}$), relative to the bulk-truncated ($1\times 1$) phase, as a function of the C chemical potential within the allowed ranges (given by diamond Si, diamond C, or graphite C, respectively), using the graphite limit as zero reference. In addition, the known ($2\times 2$)${}_{\text{C}}$ reconstruction and the ($3\times 3$) Si twist model are shown.