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Ideal metallic films are expected to show a thickness-dependent work function at a level of 0.1 eV in a short thickness range (5 nm). We investigated the variation of the work function with film thickness during the evaporation of polycrystalline Cu films on glass and Ni substrates, using the vibrating capacitor (Kelvin-)method. An increase of the work function with increasing film thickness at 0.1 eV level has been observed at the vacuum-metal interface according to the theoretical expectations. The effect, however, ranges over large thicknesses ((10 ÷ 15) nm), i.e. comparable with electronic scattering lengths in metal films. This behaviour can be attributed to the violation of local charge neutrality in films with unlike surfaces.