Validity of the dielectric approximation in describing electron-energy-loss spectra of surface and interface phonons in thin films of ionic crystals

Abstract

The dielectric approximation has proven useful in interpreting experimental data obtained by electron-energy-loss spectroscopy (EELS) in specular geometry at the surface of a large variety of materials, including artificial (multi)layered systems. This approximation can no longer be applied to very thin films as the concept of a bulk dielectric function—the only input required in this approach—breaks down when used for a slab of a few atomic planes. In this paper, a formalism is developed allowing microscopic calculations of the phonon surface response function relevant to specular EELS in the case of thin films of ionic materials. Two test cases are analyzed in some detail: ${\mathrm{CaF}}_2$(111) isolated films and RbF(001) layers on a thick Ge substrate. EELS spectra are obtained from shell-model, lattice-dynamical calculations for relaxed films and compared with the predictions of the dielectric approximation. It is shown that the dielectric approximation reproduces the essential features of the phonon response when the layer thickness exceeds 20–30 Å. However, even for films having that thickness, small contributions of microscopic surface phonons survive and these may not be negligible. It is shown, in particular, that the ${\mathrm{S}}_2$ surface microscopic phonon of RbF(001) is responsible for doubling the intensity of the loss structure in the region of the ‘‘interface’’ macroscopic Fuchs-Kliewer phonon predicted by the dielectric approximation in RbF/Ge.