Phonons at Intedaces and Superiattices G. Benedek Gruppo Nazionale di Struttura della Materia del Consiglio Nazionale delle Ricerche, Dipartimento di Fisica dell 'Universita, Via Celoria 16 1-20133 Milano, Italy V. R. Velasco Instituto de Fisica del [stado Sol ido, Consejo Superior de Investigaciones Cientificas, Serrano 123, [-28006 Madrid, Spain 1. Introduction Since the discovery of surface waves in semi-infinite isotropic elastic media by Lord RAYLEIGH 111 until recently the dynamics of surfaces was in most cases confined to the realm of the theory of elasticity. In the meantime the theory of surface waves has been applied to the study of anisotropic media 121 and it has evolved from its original geophysical and seismological grounds 131 to te- chnical applications in delay lines, signal-processing, opto-acoustic, and acousto-electronic devices, etc. 141. On the other hand the surface lattice dynamics in the dispersive range, where the microscopic effects and the discrete character of the lattice become important, was centered mainly on theoretical studies devised for ideal, unre- laxed surfaces 15,61. These simple models were the main source of information, as long as no spectroscopy of surface phonons was available. the de- termination of the dispersion curves of surface phonons was considered much more difficult than for bulk phonons, since the standard probes of lattice vibrations, such as thermal neutrons, do not work so well for surfaces due to their large penetration depth and consequent lack of sensitivity. The turning point in surface phonon spectroscopy was achieved less than four years ago by means of high-resolution measurements of atom beam scattering. Thanks to the development of intense, highly monochromatic helium beam sources 171.the dispersion relations of Rayleigh modes in different crystal surfaces were observed for the first time 18-121, thus confirming earlier theoretical predictions 113-151. Another important breakthrough has been made recently by means of electron energy-loss spectroscopy (EELS). The dispersion curves of Rayleigh waves on a clean Ni(OOl) surface and of the adsorbate vibrational modes for a c(2x2) oxygen overlayer on Ni(OOl) have been measured with fair resolution 116,171. These techniques cannot be used for solid-solid interfaces, in thin films and superlattices. For these systems the optical techniques, such as Brillouin and Raman scattering, and infrared absorption, are more suitable. In the parti- cular case of superlattices, a fairly vast amount of experimental information is emerging from Raman scattering experiments 118-211. The theoretical study of the surface lattice dynamics has been approached by means of several methods. One method is based on the construction of a trial so lution for the semi-infinite lattice 1221 in the same spirit as in the elastic - wave theory 121. This method was later extended to crystals with long-range forces 1231 and used for the study of metal surfaces 1241. 66 F. Nizzoli et al. (eds.), Dynamical Phenomena at Surfaces, Interfaces and Superlattices © Springer-Verlag Berlin Heidelberg 1985