Reflection energy loss spectra

The term 3(— l/e q, co)) is referred to as the dielectric loss function. Structures in this function can be correlated to bulk plasmon excitations. In the vicinity of a surface the differential cross section for inelastic scattering has to be modified to describe the excitation of surface plasmons. The surface energy loss function is proportional to 3(—l/e(, cu) + 1). In general, the dielectric function is not known with respect to energy and momentum transfer. Theoretical approaches to determine the cross section therefore have to rely on model dielectric functions. Experimentally, cross sections are determined by either optical absorption experiments or analysis of reflection energy loss spectra [107,108] (see Section 4.3). 

Figure Bl.6.10 Energy-loss spectrum of 3.5 eV electrons specularly reflected from benzene absorbed on the rheniiun(l 11) surface [H]. Excitation of C-H vibrational modes appears at 100, 140 and 372 meV. Only modes with a changing electric dipole perpendicular to the surface are allowed for excitation in specular reflection. The great intensity of the out-of-plane C-H bending mode at 100 meV confimis that the plane of the molecule is parallel to the metal surface. Transitions at 43, 68 and 176 meV are associated with Rli-C and C-C vibrations.

Structural Information from EELS. Besides yielding chemical composition, EELS is also capable of providing structural information on an atomic scale. It has been known (54) for some time that the fine-structure in the energy-loss spectrum close to an ionization edge reflects the energy dependence of the density of electronic states above the Fermi level. 

Figure 8.2.4 Electron energy loss spectrum for a 10 layer MnO(lOO) film on Pt(lll). A primary electron energy of 36 eV and a specular reflection geometry (Ak = 0) had been used. The low-lying excitations are dominated by the MnO Fuchs-Kliewer phonon...

It should be noted that low-loss spectra are basically connected to optical properties of materials. This is because for small scattering angles the energy-differential cross-section dfj/dF, in other words the intensity of the EEL spectrum measured, is directly proportional to Im -l/ (E,q) [2.171]. Here e = ei + iez is the complex dielectric function, E the energy loss, and q the momentum vector. Owing to the comparison to optics (jqj = 0) the above quoted proportionality is fulfilled if the spectrum has been recorded with a reasonably small collection aperture. When Im -l/ is gathered its real part can be determined, by the Kramers-Kronig transformation, and subsequently such optical quantities as refraction index, absorption coefficient, and reflectivity. 

The basic experiment in HREELS in the backscattering geometry is straightforward [37], A monochromatized electron beam of 1-10 eV is directed toward the surface and the energy distribution of the reflected electrons is measured in an electron analyzer with a resolution of up to 7 meV. The spectrum consists of the elastic peak and peaks due to energy losses to the sample surface by the excitation of molecular vibrations. If plotted as wave numbers, these vibrations are very similar to those observed in IR techniques. The resolution achievable in this technique is, however, considerably less than in IR, which becomes clear if one considers that 1 meV = 8.066 cm , so the spectral resolution in HREELS is of the order of 100 cm (in IR the resolution is typically around 4 cm" or better). Detection of crystallinity or other high-resolution details as is possible in IR is therefore currently not achievable in HREELS. 

It can be seen from Eq. (1.82) that an IR spectrum of a thin film depends essentially on the TO and LO energy loss functions of the film substance (1.1.18°, 1.1.19°) for 5- and p-polarization, respectively, the reflectivity values are positive, and the reflection spectrum is like the absorption spectrum. Moreover, the absorption of i -polarized radiation, 1 — Rs, is greater at small angles of incidence, whereas the quantity — Rp exhibits a maximum at grazing angles of incidence. This is not the case for a dielectric substrate [Eqs. (1.80) and (1.81)] (see Sections 2.2 and 2.3 for more detail). 

Let us compare the thin-film approximation formulas for (1) the transmissivity (1.98) (2) the reflectivities for the external reflection from this film deposited onto a metallic substrate (1.82) (3) the internal reflection at (p > (pc (1.84) and (4) the external reflection from this film deposited on a transparent substrate (dielectric or semiconducting) (1.81) (Table 1.2). In all cases s-polarized radiation is absorbed at the frequencies of the maxima of Im( 2), vroi (1.1.18°), whereas the jo-polarized external reflection spectrum of a layer on a metallic substrate is influenced only by the LO energy loss function Im(l/ 2) (1.1.19°). The /7-polarized internal and external reflection spectra of a layer on a transparent substrate has maxima at vro as well as at vlq. Such a polarization-dependent behavior of an IR spectrum of a thin film is manifestation of the optical effect (Section 3.1). 

This balance is achieved by introducing a finite cavity which reflects all waves perfectly. As well as excluding any energy loss, the cavity guarantees normalizability of all waves. Furthermore, it splits up the continuous frequency spectrum of the Hertzian multipoles. It is a discrete set of coupled ingoing and outgoing modes, which interacts with the particles under consideration. 

Figure 1 An overview of high resolution electron energy loss spectroscopy. Top left the incident electron beam is shown as a narrow, intense peak on the intensity vs energy loss axes. The specularly reflected beam is shown with loss peaks due to adsorbed molecules, with modes tuo. Centre The scattering mechanism is illustrated with the three diatomic molecules adsorbed on the sur ce with perpendicular and parallel orientation relative to the sur ce. Mode has a dynamic dipole moment pa which is perpendicular to the sur ce, and induces a second image dipole in the same direction, so that the electron scatters from a combined dipole moment of 2p . This is the dipole scattering process. The mode o>2 is parallel to the surface, and the induced image dipole cancels the molecular dynamic dipole moment. The mode is screened and is not present in the spectrum if there is no impact contribution to the scattering. Mode (03 is shown with the dynamic dipole moment equal to zero (the orientation is not relevant). The mode will be observed as an impact mode.

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