Effect of a Metal Contact on Surface Phonons and on Electron Energy Losses in Dielectric Films

Abstract

We consider a dielectric film which is bounded on one side by a semi-infinite metal and by vacuum on the other side. We analyze the effect of the electronic screening, due to the free electrons in the metal, on the surface optical-phonon modes in the dielectric film and calculate the energy loss experienced by fast electrons in passing through such a film. The dielectric is represented by the usual continuum-model frequency-dependent dielectric constant including the bulk phonons, and the free electrons in the metal are treated within the Thomas-Fermi approximation. Whereas the high-frequency surface mode is not much affected by the presence of the metal, except at long wavelengths, the low-frequency mode experiences a drastic relaxation up to wavelengths of the order of the Thomas-Fermi screening length. These effects are accompanied by a strong enhancement of the interaction of electrons with the high-frequency surface mode, in most of its frequency range, and a similarly strong reduction of the interaction with the low-frequency mode. As a result, the energy loss of fast electrons due to the excitation of the high-frequency mode is redistributed over the frequency range covered by this mode, in such a way that the intensity is lowered very close to the LO-phonon frequency and strongly enhanced at lower frequencies down to the limiting surface-mode frequency of the unperturbed film. On the other hand, the energy loss associated with the excitation of the low-frequency surface mode is negligible in this case. Numerical results for typical cases indicate that the predicted effects should be experimentally observable.