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We present density functional theory (DFT) calculations for 6H-SiC$\{0001\}$surfaces with different surface stackings and terminations. We compare therelative stability of different $(0001)$ and $(000\bar1)$ surfaces in terms oftheir surface free energies. Removing surface and subsurface Si atoms, wesimulate the formation of graphene and graphene-like overlayers by Sievaporation. We find that overlayers with a different nature of bonding arepreferred at the two non-equivalent surface orientations. At $(0001)$, achemically bonded, highly strained and buckled film is predicted. At$(000\bar1)$, a van der Waals (vdW) bonded overlayer is preferred. We quantifythe vdW binding and show that it can have a doping effect on electron behaviorin the overlayer.

Relative stability of $6H$-SiC$\{0001\}$ surface terminations and formation of graphene overlayers by Si evaporation