Surface phonon dispersion curves of thin Pb films on Cu(111)

Abstract

Thin films of lead have been grown on the Cu(111) surface and their structure and phonon dispersion curves have been investigated with high-resolution helium atom scattering. The diffraction pattern of the first monolayer (ML) indicates a $p(4\ifmmode\times\else\texttimes\fi{}4)$ structure. Films consisting of $N=3$, 4, 5, and bulklike 50 ML all have a regular $(1\ifmmode\times\else\texttimes\fi{}1)$ structure with the same lattice constant as the bulk and small superimposed $p(4\ifmmode\times\else\texttimes\fi{}4)$ peaks for the thinnest films. The time-of-flight spectra reveal an unusually large number of inelastic peaks for all the films. The results have been analyzed in terms of dispersion curves which exhibit more than $\frac{1}{2}$ the total number of expected two $N$ modes active in the planar scattering geometry. Dispersion curves for an unannealed 5 ML film are also reported. A force-constant model fitted to the bulk dispersion curves can only qualitatively reproduce some of the data but help to explain some features. Along the $\overline{\ensuremath{\Gamma}}\ensuremath{-}\overline{K}$ direction, a Kohn anomaly is identified for the 3, 4, and 5 ML films at nearly the same wave vector as in the bulk along the equivalent direction.