Surface dynamics of the wetting layers and ultrathin films on a dynamic substrate: (0.5-4) ML Pb/Cu(111)

The growth of Pb ultrathin films on Cu(111) has been long studied in connection with electronic quantum-size effects and for the different temperature-dependent growth kinetics. At low temperature the formation of a wetting layer (1 monolayer (ML)), is followed by an instability of the 2 ML film and a regular layer-by-layer growth is then only observed for more than two monolayers. The 2 ML film was, however, shown to be stabilized by alloying Pb with 20% Tl. This work presents a theoretical study of the dynamics of the wetting layer as well as for 2 ML Pb0.8Tl0.2, 3 and 4 ML Pb on Cu(111) in the 4 × 4 commensurate phase, for which detailed inelastic Helium atom scattering (HAS) spectra have been measured. The present calculations based on the embedded atom method (EAM) include the dynamics of the substrate. Besides leading to a detailed interpretation of the HAS experimental data, the present results are compared with a previous density-functional perturbation theory (DFPT) study for 3 to 7 ML Pb on a rigid substrate. The comparison reveals the role played by the substrate dynamics at the smallest thicknesses, despite the large mass and stiffness differences between Pb and Cu. Also the different thermal expansion of the film with respect to the substrate is shown to cause appreciable anomalies in the temperature and thickness dependence of the phonon dispersion curves.