Electronic structure of vacancies in Si(111) unreconstructed surfaces

The electron states at vacancies in Si(111) unreconstructed surfaces are calculated by means of a tight-binding scheme. Vacancies at the surface layer and at the second and third layers are considered. The results for a vacancy at the surface layer show one state of $A_1$ symmetry below the surface dangling-bond band, and a doubly degenerate state of $E$ symmetry above it. Then, it is argued that as the Fermi level is fixed by the surface, the doubly degenerate state is empty and, as a consequence, the Jahn-Teller effect cannot take place. By means of a simplified version of the model, the possibilities for a local distortion of the Jahn-Teller type are examined. It is shown that the charge redistribution in the electronic spectrum caused by the eventual distortion leads to a gain in electronic energy proportional to the square of the displacements of the ions. The elastic energy is also estimated and shown to dominate the electronic energy. Thus it is concluded that vacancies in Si(111) surfaces are very likely stable to local distortions of the Jahn-Teller type.