Influence of surface corrugations on hydrogenic image-potential states

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Abstract
An electron can be bound to a surface by the Coulomb attraction to its positive image charge. The resulting Rydberg-type series of image-potential surface states has been observed in the band gaps of free-electron-like s,p bands for several metal surfaces. The binding energy for the first member of the series (n=1) is very nearly hydrogenic for the dense (111) crystallographic surfaces, but appears to depart significantly from the hydrogenic value for the more strongly corrugated (100) surfaces. Variational calculations are performed to determine the energy-level shifts due to surface corrugations, assuming a simple model potential and coincident image plane, hard-wall boundary, and corrugated surface. The binding energy is found to be decreased only slightly by the surface structure, contrary to recent theoretical results obtained by perturbation theory, but consistent with the standard phase-shift analysis of the experimental data.