Theoretical study of quantum size effects in thin Al(100), Al(110), and Al(111) films

Abstract

We have carried out first-principles calculations for Al(100), Al(110), and Al(111) films up to 30 monolayers to study the oscillatory quantum size effects (QSEs) exhibited in the surface energy, work function, electron-phonon coupling constants, and superconductivity transition temperature ${T}_{c}$. Significant oscillatory QSEs on these physical properties are reported. These oscillations are correlated with the thickness dependence of the energies of confined electrons, which can be properly modeled by an energy-dependent phase shift of the electronic wave function upon reflection at the interface. The oscillations in the surface energy and work function for Al(111) and Al(110) films as a function of film thickness can be well fitted by a damped sinusoidal function with the periodicity determined by one Fermi wave vector along the [111] direction or a combination of three Fermi wave vectors along the [110] direction. A quantitative description of these QSE requires the full consideration of the crystal band structure.