Unoccupied electronic states and surface barriers at Cu surfaces

Abstract

The surface potential barrier shape of the low-index faces of copper was determined by an analysis of inverse photoemission and two-photon photoemission measurements making use of the one-step model of photoemission. The barrier potentials obtained in this way allow for a consistent description of the energetic positions and effective masses of all known surface states for the various faces. It is found, in agreement with previous theoretical predictions that the most open surface, Cu(110), exhibits the strongest saturation of the image potential with an image plane lying nearest to the topmost atomic layer and with the weakest image force outside the crystal. A comparison with theoretical slab calculations shows that in these calculations the position of the image plane is always significantly further outside the crystal than derived in the present study. Dynamical effects in the effective potential are found to be negligible for electronic states up to 6 eV above the Fermi level E_F,but are probably responsible for systematic discrepancies between theory and experiment for unoccupied bulk states in the energy range 10-15 eV above E_F.