Image and adsorbate state dependence on the adsorbate coverage in the Na/Cu(1 1 1) system

A model is developed to describe the adsorbate coverage dependence of excited state (image states and adsorbate-localised states) on a metal surface. It is applied to the case of Na adsorbates on a Cu(1 1 1) surface. It allows to define in a consistent way (i) an effective potential, which is only function of the electron-surface distance representing the average perturbation introduced by a large set of alkali adsorbates on the surface and (ii) the local perturbation induced around each adsorbate. It can be applied up to moderate coverages, typically for Na-induced work function changes below 1.5 eV. In this range, its predictions reproduce the experimental findings of Fischer et al. [Surf. Sci. 314 (1994) 89] for the energy of the image states and Na-localised state.