Quantum size effects in metal films: Energies and charge densities of Pb(111) grown on Cu(111)

Energies and electron densities of free-standing Pb(111) slabs consisting of 1 to 15 layers have been determined by means of ab initio total energy calculations, using periodic slab geometries and gradient-corrected density functional theory. Two sets of calculations were carried out, one with fixed slab geometries and another one where interlayer spacings were fully relaxed. We find quantum size effects (QSE's) for the total energies in agreement with experiments by Toennies et al. [Europhys. Lett. 10, 341 (1989)], who monitored the epitaxial growth of thin Pb films on a Cu(111) substrate. QSE's are also observed for the surface electron density of thin lead films which manifest themselves as different "apparent step heights" of the individual layers in high resolution helium atom scattering [Surf. Sci. 384, L858 (1997)]. For this second QSE, we find that the interplane relaxation but also the in-plane strain within the Pb layers imposed by the Cu(111) substrate, are important factors when it comes to a quantitative comparison between theory and experiment.