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A realistic smooth potential is constructed for the Si(111) surface both with and without relaxation of the surface atoms. In both cases, a single band of surface states whose charge is highly localized in "dangling bonds" is found in the energy gap. In the relaxed case, two new bands of surface states appear, lying 2.0-3.6 eV and 10.7-12.9 eV below the valence-band maximum, and localized in the back bonds of the surface atoms.
Appelbaum et al. (Mon,) studied this question.