Surface phonons in thin aluminum oxide films: Thickness, beam-energy, and symmetry-mixing effects

The surface-phonon (Fuchs-Kliewer) modes of thin α-${\mathrm{Al}}_2$ ${\mathrm{O}}_3$ films prepared on a Ru(001) substrate have been measured with high-resolution electron-energy-loss spectroscopy. An understanding of the differences in phonon spectra for thick cyrstals versus thin films is derived from calculations using dielectric theory and the infrared optical constants for α-${\mathrm{Al}}_2$ ${\mathrm{O}}_3$. In addition to the three characteristic phonon modes assigned previously at ∼400, ∼650, and ∼900 ${\mathrm{cm}}^{\mathrm{-}1}$ for ∼10-Å aluminum oxide films, our experiments and theoretical modeling confirm the presence of an additional mode at ∼800 ${\mathrm{cm}}^{\mathrm{-}1}$ and the splitting of the 400-${\mathrm{cm}}^{\mathrm{-}1}$ feature into two peaks at about 350 and 500 ${\mathrm{cm}}^{\mathrm{-}1}$ for our somewhat thicker 30-Å well-annealed α-${\mathrm{Al}}_2$ ${\mathrm{O}}_3$ films. The primary beam-energy dependence for the ∼900-${\mathrm{cm}}^{\mathrm{-}1}$ phonon is found experimentally to be ${\mathit{E}}^{\mathrm{-}0.9}$ while the dielectric theory predicts ${\mathit{E}}^{\mathrm{-}0.8}$, in contrast to the well known ${\mathit{E}}^{\mathrm{-}0.5}$ dependence for bulk ionic crystals. The 800- and 900-${\mathrm{cm}}^{\mathrm{-}1}$ features are related to the high-frequency surface-phonon branches corresponding to the 650-${\mathrm{cm}}^{\mathrm{-}1}$ bulk TO modes and are expected from dielectric theory for an ideal alumina layer on metal support. The 350-, 500-, and 650-${\mathrm{cm}}^{\mathrm{-}1}$ modes are related to the low-frequency surface-phonon branches, which are allowed due to a (ω,k)-dependent dispersion-related symmetry-mixing process. Successful modeling of these latter modes is carried out under the assumption of a ‘‘self-supported’’ alumina film.