The Effects of Surface Corrugation, or Surface Nonplanarity, on Electron Image-Potential Surface States on Metals.

A modified image potential is derived for arbitrary deformations of the plane metal surface using an expansion method in terms of a surface profile function h((')r(,(PARLL))). The interaction between an electron and a periodic or nonperiodic metallic surface is investigated. The Schrodinger equation describing the plane-surface image state is perturbed by both the image potential and a modified boundary condition. The previous work of A. M. Clogston and H. Feshbach is extended to treat this problem. In the case of a periodic corrugation, the modified image poten- tial and boundary condition result in a nearly -free-electron theory in the plane parallel to the surface. The energy-level shifts, effective mass, and wave functions, of the Rydberg state are calculated. In particular, the image-potential states on Cu, Au, and Ag (100) and (111) surfaces are correlated to the energy levels observed recently using angle-resolved inverse photoemission and two-photon photo- emission. The corresponding corrugation parameters, such as wavelength and amplitude, are determined and compared to the natural corrugation of the (100) and (111) surfaces. The qualitative results are at variance with N. Garcia et al. concerning the position and labeling of the image states. It is concluded that the lowest observed state corresponds to the n = 1 hydrogenic level. The quantum mechanics of a Rydberg state resonance in the presence of a general surface deformation is considered in the context of scattering. The asymptotic wave function is obtained by solving the Lippmann-Schwinger equation. The effect of breaking the translational symmetry is explored in cases of one- and two-dimensional surface structures. In the former case, the scattering amplitude of a Rydberg state in the presence of a surface defect is determined, while in the latter case the current density and trans - mission coefficient are obtained for the scattering from a single infinite step or track.