Coulomb problem for graphene with the gapped electron spectrum

The characteristics of charge carriers in graphene with dopants having charge $Z$ and deposited onto a SiC substrate are analyzed. The closed set of explicit equations determining the spectrum of charge carriers are obtained for the case of the Coulomb potential modified at small distances. The critical values $Z_{cr}$ of the dopant charge at which the energy level with the given quantum numbers crosses the valence band boundary are determined. At $Z<Z_{cr}$, for the lowest values of the orbital angular momentum, the position of the energy level corresponding to the bound state is obtained as a function of charge $Z$. For $Z>Z_{cr}$, the position and width of the quasistationary state are calculated. The problem concerning the screening of the impurity charge is also considered.