Surface Fuchs-Kliewer modes

The surface Fuchs-Kliewer modes, like the Rayleigh modes, should be regarded as macroscopic vibrations, and may be predicted from the bulk elastic or dielectric properties of the solid with the imposition of a surface boundary condition. Their projection deep into the bulk makes them insensitive to changes in local surface structure, or the adsorption of molecules at the surface. True localised surface modes are those which depend on details of the lattice dynamics of near surface ions which may be modified by surface reconstruction, relaxation or adsorbate bonding at the surface. Relatively little has been reported on the measurement of such phonon modes, although they have been the subject of lattice dynamical calculations [61-67],... 

At the time of a recent review [9], there remained very few examples of vibrational studies of adsorbate, or localised substrate modes, at metal oxide surfaces. By far the majority of studies concerned the characterisation by HREELS of phonon modes (such as Fuchs-Kliewer modes) pertaining to the properties of the bulk structure, rather than the surface, or to electronic transitions. Such studies have been excluded from this review in order to concentrate on the vibrational spectroscopy of surface vibrations on well-characterised metal oxide surfaces such as single crystals or epitaxially grown oxide films, for which there is now a substantial literature. Nevertheless, it is important to briefly describe the electronic and phonon properties of oxides in order to understand the constraints and difficulties in carrying out RAIRS and HREELS with sufficient sensitivity to observe adsorbate vibrations, and more localised substrate vibrational modes. 

Localised phonon excitations are in principle best studied by neutral-atom scattering, or off specular HREELS, in order to reduce the strong dipole excitation of Fuchs-Kliewer modes. Two off specular HREELS measurements on MgO(lOO) have been reported [25, 68], however there is some disagreement concerning the energy and assignment of the substrate derived loss peaks. Since the microscopic surface modes are expected to be sensitive to the surface structure, it has been suggested [9] that the differences may be associated with differences in surface preparation. 

Fig. 9. The HREELS spectrum of clean Cr2 03(0001) and Cr2 03(0001) [67]. The loss at 21.4meV in the spectrum of Cr2 O3(110) disappears on exposure to CO or O2, and is ascribed to a localised surface mode. Its isotopic shift of 2.4% is predicted theoretically, and is significantly smaller than that observed for the Fuchs-Kliewer modes of 4.5-6%.

In dielectric layers, where a surface phonon mode may occur, or in ionic crystals, multiple scattering from the surface phonon mode can result in Poisson replicas of the no-loss peak. These modes are referred to as Fuchs- Kliewer modes they are a general feature of HREELS spectra of ionic and polar materials, and metal oxides. Ordered overlays on surfaces can also exhibit collective modes, but at submonolayer coverages the HREELS loss peaks are due almost exclusively to single oscillations of the fundamentals. Substrate (silver) phonon modes are shown at 10 meV (83 cm ) in Figure 7. 

Cr2 03(0001) surface is characterised by losses at 21.4, 51.7, 78.6, 85.0 and 88.5meV, and combinations of these losses at higher energies. The latter four are identified as Fuchs-Kliewer phonon modes, and the intensity and energy of these modes are found to be uninfluenced by the adsorption of CO or O2 at 90K. 

Fig. 4.1. Phonon dispersion curves in MgO(lOO) (according to Chen et ai, 1977). Hatched zones are the projection of the bulk modes. Surface modes S are indexed by n (1 < n < 7) the Rayleigh mode is Si the Fuchs and Kliewer modes have a frequency close to 12x10 rad s S3 is an example of a microscopic mode.

As in the case of metals and semi-conductors, there exist specific surface excitations in insulating oxides. Three types of surface phonon modes may be distinguished the Rayleigh mode, the Fuchs and Kliewer modes and the microscopic surface modes. The first two modes have a long penetration length into the crystal. They are located below the bulk acoustic branches and in the optical modes, respectively. The latter are generally found in the gap of the bulk phonon spectrum. 

Fuchs and Kliewer (1965) have predicted the existence of macroscopic surface optic modes in ionic crystals. We give here a simplified derivation of their result, based on the formalism of the dielectric constant. In the phonon frequency range, the bulk dielectric constant e( )) approximately varies with co as ... 

More precisely, Fuchs and Kliewer have shown that there exist two modes ft)FK+ and layer thickness, increases. Their common value is intermediate between wto and colo- At the zone centre, the surface mode is uniform in the whole slab. In MgO, for example, it has a frequency close to 1.2 x 10 rad s ... 

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