Quantum Size Effects (QSE) in thin metal films, where electrons are confined in the perpendicular direction, were first predicted by Sandomirskii 40 years ago and reveal themselves, as oscillations in many physical properties with the film thickness. This is produced by the systematic variation in the Density Of States (DOS) at the Fermi level due to its periodic crossing by the Quantum Well States (QWS) created by the confinement of electrons. Many physical properties of metallic films have been predicted to oscillate with the thickness with a periodicity of few monolayers. We may cite bulk properties, such as the electron density, the electrical resistivity, the Hall coefficient, or the superconducting transition temperature, surface properties, such as the work function, the chemical reactivity, or the activation barrier for surface diffusion and thermodynamic properties, such as the equilibrium height distribution of islands.
For thin films of Pb deposited onto substrates that confine electrons within the Pb film, He atom scattering indicated the presence of QSE-induced oscillations in the apparent step height. Oscillations in the interlayer distances from XRD data obtained for Pb/Si(111) have been recently reported. The changes in the interlayer distances (typically 0.02-0.03 nm) affect the whole thin film, but are mostly concentrated close to the substrate and the external surface. STM images of Pb islands on Si(111) recorded at positive sample bias have shown a pair of oscillations in the step height with an amplitude of 0.03 nm. The measured step heights, however, were always below the bulk value.
We report the oscillatory behavior of the apparent step height, as measured by STM, for ultrathin films of Pb deposited at low temperatures on Cu(111). Experiments and first principles calculations for isolated Pb(111) slabs agree in detail. The observed oscillations in the apparent step height are mostly due to QWS-induced, layer-dependent, changes in the electronic DOS at the Fermi level. The step height oscillations mirror the oscillatory behavior of the roughening temperature for the same system. The thicknesses those are more unstable thermally, as a consequence of their larger DOS at the Fermi level, show larger apparent step heights.
|