Electron confinement in nanostrucutres at surfaces has received a great attention in the last years (see e.g. [1,2]). Quantum size effects are found to occur when the size of the nanostructure becomes comparable to the de Broglie wave-length of electrons confined within it. Two effects are expected in the confinement of excited electronic states: (i) increase of the electronic state energy and (ii) decrease of the state lifetime by decay at the borders of the confinement region. A large number of theoretical and experimental works have been focused on quantum size effects in different systems such as quantum well states confined inside metal islands, surface state confinement in quantum corrals and vacancy islands [1-7]. The knowledge on confinement effects on image potential states is much more scarce.
In this communication we present a theoretical study of confinement of the image potential states in patches of the clean Cu(100) surface otherwise covered with 1ML Ar. With the wave packet propagation method [8] we have evaluated different properties of the image potential states localized on clean surface islands. In particular, an analysis of the energies, lifetimes and wave functions of confined electrons will be presented as function of the island size. The wave packet propagation results will be compared with predictions of the simple and physically transparent "particle in a box model". The present results are compared with previous studies of the image potential states localized on Ar islands on a Cu(100) surface [6] and Ar monolayer on a Cu(100) surface [9]. In the case of an incomplete adsorbate coverage of the surface, electron confinement is different on adsorbate islands and on clean substrate patches.
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