The Si(2 × 1) surface: A theory of its spectroscopy

The metastable reconstructed form of the Si(111) surface produced by cleavage is studied. Modifications of Haneman's model for the detailed geometry of the reconstruction are proposed to explain recent spectroscopic measurements. In the modified model, the bonds between the first and second layers are alternately lengthened and shortened as first-layer atoms are raised and lowered. The results of detailed calculations for realistic models of unreconstructed surfaces with such bond-length modifications are reported. The dangling-bond surface states are found to be lower in energy, narrower in bandwidth, and more ${\mathrm{sp}}^3$-like in shape for the raised atoms. A new band of surface states associated with the lengthened bonds is found to lie 0 to 4.0 eV below the valence-band maximum, and to have its density of states and shape consistent with the energy and azimuthal angular structure of surface-state photoemission in this range. Since both the dangling-bond and stretched-bond surface states will depend primarily on their local environment, a two-dimensional tight-binding picture is invoked to estimate the positions and widths of the hybridized surface-state bands on the 2 × 1 surface. These are shown to be consistent with infrared absorption and other measurements. While it explains the spectroscopy of the surface, the present model appears energetically unfavorable, and we propose that the steps invariably formed upon cleavage may be necessary to render it metastable.