The influence of Coulomb interaction on the spectrum of the surface states of a semiconductor in relation to the degree of their occupation

A theoretical study is presented of the influence of Coulomb interaction on the spectrum of monoenergetic donor centers on the surface of an MOS structure. It is found that the principal contribution to the dispersion of the potential is from the small-scale potential with a characteristic size of the order of the mean distance between the charges. The energy distribution of the donor centers is computed as a function of the degree of occupation of the centers. In the case of low concentrations of the charge centers a gap exists between the free and occupied states which disappears with increase of the charge concentration. It is shown that the presence of a gap in the state density is due to the ordering of charged donors, i.e., Wigner crystallization.