Potential-barrier model at metal surfaces: Application to analyses of low-energy electron-diffraction fine-structure experiments

Abstract

We propose a model for the potential barrier for electrons crossing a metal surface, in which (1) we reproduce the effective potential of Lang and Kohn, in fact, better than any approximation in the existing literature and (2) we approach the classical image potential for large separation from the surface. Our potential does not diverge as the electron approaches the surface and goes over smoothly to the electron-electron interaction potential in the bulk. It reproduces the first peak in the e6'ective potential of Lang and Kohn, which is a Friedel oscillation. %'e achieve better agreement with the Lang-Kohn potential than Jennings, Jones, and Weinert in their barrier model. This makes our model useful in the analysis of low-energy electron-diFraction Gne-structure experiments. Our simple barrier model allows analytical solutions of the Schrodinger equation in the density-functional formalism.

Analytical Representation of the Lang-Kohn Density Profiles by the Numerical Fitting

“…The effective potential V(x) of Lang and Kohn was fitted by saturated image barrier [6] and more recently by the analytical potentials given by Mola et al [7] which reproduce the first peak in the potential of LK (which is a Friedel oscillation) and approach the classical image potential for large separation from the surface as well.…”