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