Electron-Phonon Interaction in Dielectric Films. Application to Electron Energy Loss and Gain Spectra

Abstract

The classical analysis, due to Kliewer and Fuchs, of the optical polarization modes of an ionic crystal film in the long-wavelength limit is used to develop a quantum-mechanical treatment of the interaction between an electron and the optical-phonon field of the film. Retardation effects are neglected. The analog of Fröhlich's polaron Hamiltonian is obtained, but with explicit inclusion of surface effects. As a first application of this theory, the case of a fast electron is treated, and the electron-crystal energy-exchange spectra are derived. The classical energy-loss spectrum is recovered and involves processes resulting in one-phonon excitation. Quantum-mechanical two-phonon processes are evaluated. The gain spectrum is obtained for the first time and shows a strong temperature dependence. The results are in good agreement with experimental spectra in LiF crystal films. DOI: http://dx.doi.org/10.1103/PhysRevB.2.2488 © 1970 The American Physical Society