A theory of thin metal films: electron density, potentials and work function

Abstract

Electron densities, potentials, and work functions of thin metal films are calculated self-consistently. The planar uniform-background model and the density-functional formalism are used similarly as in the theory of metal surfaces by Lang and Kohn. Electron densities and potentials are discussed for r s = 4 both as function of the position in the film and of film thickness. Numerical results for the dependence of the work function on film thickness are given for r s = 2, 3, 4, 5, 6. As functions of film thickness electron densities, potentials and work functions show oscillations with a period of one-half the Fermi wavelength. The amplitude of the oscillations in potentials and work functions is about 1 eV for one monolayer and 0.1 eV for films of 20 Å thickness. A comparison with non-self-consistent calculations reveals the necessity of self-consistent computations. The relevance of the results to work function measurements and to investigations of thermodynamic and transport properties are discussed. The influence of the film geometry on calculations designed for surfaces per se is examined.