Quantum size effects in metal nanofilms: Comparison of an electron-gas model and density functional theory calculations

Abstract

Effects of quantum confinement of electrons in metal nanofilms are analyzed using a noninteracting electron-gas model. Electrons are confined within a potential well with infinite-height barrier. The positions of the barrier are at a fixed distance away from the geometric boundaries of the film such that the surface-charge neutrality requirement is maintained at the bulk limit. The model predicts oscillations in basic physical properties such as the Fermi energy, electron density, surface free energy, and dipole layer moment as a function of film thickness. We compare predictions of this electron-gas model with first-principles density functional theory (DFT) for ten metal films. For Ag(110), Ag(100), Mg(0001), Al(111), Al(110), and Pb(111) films, the oscillation features obtained from the model are in good quantitative agreement with those from DFT calculations. However, for Al(100), Pb(110), and Pb(100) films, oscillation behavior in the model differs from DFT calculations. For Ag(111), the electron-gas model predicts weak oscillations, in contrast to the DFT calculations, in which no noticeable regular oscillations are observed.