Semiconductor Surface States Considered on the Hubbard Model; Correlation with Electron Paramagnetic Resonance Data

The occurrence of a strong electron paramagnetic resonance (EPR) signal from clean Si surfaces, and its sensitivity to gas exposures, indicates the presence of a high density of unpaired electrons (about ${\text{2×10}}^{14}\hspace{0.17em}{\mathrm{cm}}^{\text{−2}}$ ) in the surface region. Previously this has not been correlated closely with other surface experiments. It is shown that the application of ordinary Hartree-Fock (H-F) band theory to the unpaired electron states leads to serious difficulties in accounting for the EPR results. This problem is considered and shown to result from the inadequate treatment of correlations in H-F theory, which is serious when electron densities lower than in the bulk are encountered. By applying the improved treatment developed by Hubbard for such cases, some difficulties are shown to be removed. One obtains a natural explanation of the two narrow surface state bands deduced by Allen and Gobeli from Si surface photoelectric data. The approach should generally be applicable to all semiconductor surfaces. It is predicted that where two surface state bands are formed by this mechanism, their separation will be of the order of, or greater than, the surface bandwidths.