  Density functional theory has been employed to study graphene on the (111),
(100) and (110) surfaces of silicon (Si) substrates. There are several
interesting findings. First, carbon atoms in graphene form covalent bonds with
Si atoms, when placed close enough on Si (111) and (100) surfaces, but not on
the (110) surface. The presence of a Si (111) surface shifts the Fermi level of
graphene into its conduction band, resulting in an increase of the work
function by 0.29 eV and of the electron density by three orders of magnitude.
The carrier density of graphene can also be increased by eighty times on a Si
(100) substrate without doping, due to the modification of the density of
states near the Dirac point. No interfacial covalent bond can be formed on Si
(110). These striking effects that different orientations of a silicon
substrate can have on the properties of graphene are related to the surface
density of the silicon surface. Applying the results to a real device of a
specific orientation requires further consideration of surface reconstructions,
lattice mismatch, temperature, and environmental effects.
