Frohlich mode absorption

The dielectric function of a metal can be decomposed into a free-electron term and an interband, or bound-electron term, as was done for silver in Fig. 9.12. This separation of terms is important in the mean free path limitation because only the free-electron term is modified. For metals such as gold and copper there is a large interband contribution near the Frohlich mode frequency, but for metals such as silver and aluminum the free-electron term dominates. A good discussion of the mean free path limitation has been given by Kreibig (1974), who applied his results to interpreting absorption by small silver particles. The basic idea is simple the damping constant in the Drude theory, which is the inverse of the collision time for conduction electrons, is increased because of additional collisions with the boundary of the particle. Under the assumption that the electrons are diffusely reflected at the boundary, y can be written... 

Several predicted features of infrared surface mode absorption by small spheres are verified by the experimental results shown in Fig. 12.13. The frequency of peak absorption by spheres is shifted an appreciable amount from what it is in the bulk solid the e" curve peaks at 1070 cm", whereas the peak of the small-sphere absorption is at 1111 cm-1, very close to the frequency where e is — 2em (— 4.6 for a KBr matrix). The absorption maximum (absorption is nearly equal to extinction for these small particles) is very strong Qabs for a 0.1-jum particle is about 7 at the Frohlich frequency. 

Absorption resonances resulting from excitation of surface modes are accompanied by scattering resonances at approximately the same frequencies this was pointed out following (12.26). In most experiments transmission is measured to determine extinction, which is nearly equal to absorption for sufficiently small particles. However, surface mode resonances have been observed in spectra of light scattered at 90° by very small particles of silver, copper, and gold produced by nucleation of vapor in an inert gas stream (Eversole and Broida, 1977). The scattering resonance peak was at 3670 A, near the expected position of the Frohlich mode, for the smallest silver particles. Although peak positions were predictable, differences in widths and shapes of the bands were concluded to be the result of nonsphericity. 

Far-infrared absorption measurements gave an independent determination of the electron density from the position of the Frohlich mode near 9 meV ( 140 jum) a density of 2.3 X 1017 cm-3 was inferred. Other experiments on Sb-doped Ge and pure germanium irradiated at different powers showed appreciable changes in absorption band positions and shapes. Rose et al. 

The curves of Fig. 12.17 nicely illustrate the varied optical effects exhibited by small metallic particles in the surface mode region, both those explained by Mie theory with bulk optical constants and those requiring modification of the electron mean free path (see Section 12.1). Absorption by particles with radii between about 26 and 100 A peaks near the Frohlich frequency (XF — 5200 A), which is independent of size. Absorption decreases markedly at longer... 

For oxidized metal spheres, there is only one absorption band, near the vlo frequency of the coating material, as shown by the example of a Mg sphere with a MgO coating [298]. This is similar to the case of an ultrathin film on a metal plane substrate (Section 3.2). It follows that the usual SSR (Section 1.8.2) may also be applied to the surfaces of metal powders (see also the discussion in Section 3.9.4). Bamickel and Wokaun [314] reported that a dielectric coating shifts the resonance frequency of a metallic particle toward the red. Applying the MGEM dielectric function, Martin [315] calculated the reflection spectrum of an ensemble of S-pm Zn spheres coated with ZnO of variable thickness. He obtained the same qualitative result as Ruppin for the isolated particle [298], that in the limiting case of the absence of the core, the absorption maximum is at the Frohlich frequency. As the thickness of the coating decreases relative to the core radius, the surface-mode frequency increases and approaches vlo monotonicaUy. 

The wavenumber at which the Ti02 absorption band occurs in the measured infrared spectra (see Figure 7) is shifted from the wavenumber predicted by theory. The absorption maximum, which is usually coincident with the Frohlich frequency (Vp, the lowest-order surface mode) 20), can be calculated from the transverse optical mode of the material (Vyo), as long as the dielectric function is known for the material at zero (Cq) and infinite frequency and the dielectric function for the matrix (b ), according to 20) ... 

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