Theory of Atom Scattering from Surface Phonon: The Role of Electron-Phonon Interaction

The forces that an He atom exerts on the atoms of a solid surface causing inelastic scattering have much in common with the interatomic forces that govern the dynamics of the lattice. The scattering theory, described in Chap. 7 based on two-body collisions, provides the correct interpretation of data for closed-shell surfaces, much as their lattice dynamics is well described by phenomenological interatomic potentials. The inelastic HAS experiments from metal surfaces, however, cannot be successfully described in the same way. In this Chapter the approaches developed for the lattice dynamics of metals, where the interatomic forces are mediated by free electrons, such as the Multipole Expansion (ME) and the Density Functional Perturbation Theory (DFPT) are introduced for the analysis of inelastic HAS intensities from metal surfaces. These theories have the important consequences that inelastic HAS intensities are directly proportional to the electron-phonon coupling strength for individual phonons and that HAS can detect deep sub-surface phonons. The propensity of HAS to excite certain phonons of conducting surfaces rather than others is found to depend on the electron-phonon interaction and the surface electron band structure.