Persistent quantum-size effect in aluminum films up to twelve atoms thick

Total energies and work functions have been calculated for unrelaxed, free-standing Al(111) films, 1–12 layers thick, using the all-electron, full-potential linear combination of Gaussian-type orbitals–fitting-function technique. The work function exhibits a significant quantum-size effect (at least 0.1 eV) over the entire range of thickness considered. This result contradicts an old prediction that the work function of an Al(111) N-layer film will converge to within a few hundredths of an eV by N=6. The present result, which is consistent with earlier jellium calculations, demonstrates the risk of mistaking an accidental coincidence of work functions for two films, differing in thickness by one layer, for a true convergence with respect to thickness. The implications for thin-film calculations of surface properties are discussed. A linear fit to the film binding energy vs thickness is used to extract the Al(111) surface energy (0.45 eV) and the binding energy of bulk Al (4.06 eV). © 1996 The American Physical Society.