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We address the stability of the surface phases that occur on the C-side of3C-SiC($\bar{1} \bar{1} \bar{1}$) at the onset of graphene formation. In thisgrowth range, experimental reports reveal a coexistence of several surfacephases. This coexistence can be explained by a Si-rich model for the unknown(3$\times$3) reconstruction, the known (2$\times$2)$_{C}$ adatom phase, and thegraphene covered (2$\times$2)$_{C}$ phase. By constructing an $ab$ $initio$surface phase diagram using a van der Waals corrected density functional, weshow that the formation of a well defined interface structure like the"buffer-layer" on the Si side is blocked by Si-rich surface reconstructions.

physical review. b, condensed matter and materials physics

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$3)-3C-SiC($\bar{\text{1}}\bar{\text{1}}\bar{\text{1}}$)  reconstruction