Doping-induced effects on the band structure in n-type $3C-,$ $2H-,$ $4H-,$ $6H-\mathrm{S}\mathrm{i}\mathrm{C},$ and Si

Doping-induced energy shifts of the lowest conduction band and the uppermost valence band have been calculated for n-type $3C-,$ $2H-,$ $4H-,$ $6H-\mathrm{S}\mathrm{i}\mathrm{C},$ and Si. We present the resulting narrowing of the fundamental band gap and of the optical band gap as functions of donor concentration. The effects on the curvature of the lowest conduction band have been investigated in detail for $3C-$ and $6H-\mathrm{S}\mathrm{i}\mathrm{C}$ and, moreover, the effective electron masses in the vicinity of the conduction-band minimum have been calculated for all five materials. The calculations go beyond the common parabolic treatments of the ground-state energy dispersion by using energy dispersion and overlap integrals from band structure calculations. The nonparabolic valence-band curvatures especially strongly influence the self-energies, but also the double-well minimum of $6H-\mathrm{S}\mathrm{i}\mathrm{C}$ has effects on the self-energies and the resulting band curvatures. By comparing the total energy of the electron gas with the total energy of electrons in a nonmetal phase, we estimate the critical Mott concentration for the metal-nonmetal transition. The utilized method is based on a zero-temperature formalism within the random phase approximation with local field correction according to Hubbard.