Model calculation of surface states in silicon

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Abstract
Bands of localized states have been calculated for the ideal (100), (110), and (111) surfaces of silicon. The three-parameter local pseudopotential method has been used to calculate energy bands for complex wavevectors normal to the surface, and the corresponding wavefunctions and their normal derivatives are matched to appropriate vacuum functions. Interpolation between the states calculated at points of high symmetry is provided by the approximate description of the energy bands in the bulk material developed by Heine and Jones (1969). Two bands of surface states occur in the neighbourhood of the energy gap, though there are notable differences between the results for the three faces. In particular, the glide plane present in the (110) surface leads to a doubly degenerate band along an edge of the two dimensional Brillouin. Consequences of the results for the interpretation of experimental data, and the validity of the model as a guide to surface states at real surfaces are discussed.