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We analyse doping of graphene grown on SiC in two models which differ by the source of charge transfered to graphene, namely, from SiC surface and from bulk donors. For each of the two models, we find the maximum electron density induced in monolayer and bilayer graphene, which is determined by the difference between the work function for electrons in pristine graphene and donor states on/in SiC, and analyse the responsivity of graphene to the density variation by means of electrostatic gates.
We analyze a manifestation of the partial ordering transition of adatoms on graphene in resistivity measurements. We find that Kekule mosaic ordering of adatoms increases sheet resistance of graphene, due to a gap opening in its spectrum, and that critical fluctuations of the order parameter lead to a non-monotonic temperature dependence of resistivity, with a cusp-like minimum at T=T_c.