Phonon surface loss function of ionic-crystal films: A comparison between microscopic and macroscopic approaches
The surface loss function is an important quantity in the description of reflection electron-energy-loss spectroscopy (EELS) in near-specular geometry. In this paper, lattice-dynamics calculations of the surface energy-loss function associated with optical excitations in ionic-crystal slabs are performed. Test calculations are carried out for both NaF isolated films and NaF slabs onto a semi-infinite substrate. In the latter case, a continuum dielectric theory is used to describe the response of the substrate, emphasis being on long-wavelength optical phonons. We compare the results of the microscopic formulation of the surface loss function of the film with those deduced from the so-called dielectric theory, where a bulk-like dielectric response of the slab is assumed. The legitimacy of the use of a bulk response is a central question in applications of the dielectric theory to a very thin slab. It is shown that the latter provides a valid description of the surface energy-loss function for the wave vectors predominantly probed in EELS when the film thickness exceeds ~ 2 nm (about 10 atomic planes). For very thin, relaxed films (less than 8 atomic layers), the dielectric theory fails in producing the correct frequency positions of the surface energy-loss peaks; by contrast the intensities of the loss peaks are more accurately predicted.