Potential‐barrier model at metal surfaces: Thin films and its dependence on the film thickness

Abstract

We propose a model for the potential of thin metal films, in which (1) we reproduce self-consistent effective potentials (i.e., Lang and Kohn), in fact, better than any approximation in the existing literature, (2) we parameterize the potential as a function of the film thickness, and (3) we approach the classical image potential for large separation from the surfaces. Our potential does not diverge as the electron approaches the surfaces and takes into account the effect of the two surfaces. It reproduces the first peak in the effective potential, which is a Friedel oscillation. We present a simple dependence of the potential with the film thickness that (1) allows a direct description of the quantum size effects and (2) shows how the bulk surface potential is reached. This makes our model useful in the interpretation of tunnel experiments, field emission, and scanning tunneling microscopy.