Model dielectric function plasmons

In the IR spectral region, DFs i(ui) are sensitive to phonon and plasmon contributions. Hence, IR model dielectric functions (MDFs) are written as the sum of lattice and free-charge-carrier fcc(u ) contributions [73]... 

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). 

In the infrared spectral region, the dielectric function ej(o)) is sensitive to phonon and plasmon contribution. Therefore, the infrared model dielectric function can be written as a sum of lattice, sj (co) and free-charge carrier. 

As an example of extinction by spherical particles in the surface plasmon region, Fig. 12.3 shows calculated results for aluminum spheres using optical constants from the Drude model taking into account the variation of the mean free path with radius by means of (12.23). Figure 9.11 and the attendant discussion have shown that the free-electron model accurately represents the bulk dielectric function of aluminum in the ultraviolet. In contrast with the Qext plot for SiC (Fig. 12.1), we now plot volume-normalized extinction. Because this measure of extinction is independent of radius in the small size... 

Fig. 7. Contour plot of the inverse of the dielectric function imaginary part Im[—l/efr/, co)I for an unperturbed electron gas of Tj = 2, as a function of the momentum transfer q and the transition energy co. All quantities in atomic units. The dielectric function is calculated using the Mermin model. The contour plot is in logarithmic scale. The KS eigenenergies of the 2p orbital for Ne and N ions embedded in the electron gas are shown with circles for different electronic configurations (all of them with a K-shell hole and a given number of electrons in the L shell). The value of the plasmon energy is also shown with a thick solid line.

Figure 4a illustrates the spectral dependence of ellipsometric parameters and A for the hybrid sample Ag/APTES/Si. Experimental spectra were fitted by the optical response of one effective layer. According to model calculations for this sample, the thickness of the effective layer and APTES film was 5.3 and 11.5 nm, respectively. The spectral dependence of the dielectric function for the effective layer (Fig. 4b) possesses two features. The low-energy peak at 2.2 eV can be attributed to the residual material of the solution containing the P VP-coated Ag nanoparticles. The peak can be also contributed by the interparticle dipole-dipole couplings of nanoparticles on solid substrates. The peak at the 3.4 eV is related to the surface plasmon resonance of metal nanoparticles and corresponds to the absorption peak of Ag colloidal solution (Fig. 4b). In the spectra of hybrid samples Ag/DNA/APTES/Si, the peak at 4.5 eV originated from the contribution of DNA was additionally observed.

Earlier observations by Cesario et al. [60] of a decay in fluorescence for arrays of Au nanoparticles spaced above a Ag film by a Si02 layer of increasing thickness, were interpreted as due to the finite vertical extent of the evanescent fields associated with a surface plasmon. In this model the coupling results in an enhanced interaction between individual localized plasmons at individual nanostructures [61] and thus an enhancement in the radiative efficiency increasing the spacer layer thickness moves the nanowires out of the evanescent field of the surface plasmon. A possible physical mechanism for the experimentally observed decay involves nonradiative decay of the excited states. The aluminum oxide deposited in these experiments was likely to be nonstoichio-metric, and defects in the oxide could act as recombination centers. Thicker oxides would result in higher areal densities of defects, and decay in fluorescence. A definitive assignment of the mechanism for the observed fall off of fluorescence would require determination of the complex dielectric function of our oxides (as deposited onto an Ag film), and inclusion in the field-square calculations. Finally it should be noted that at very small thicknesses quenching of the fluorescence is expected [38,62] consistent with observations of an optimum nanowire-substrate spacer thickness. 

Free-charge carriers in semiconductors form collective excitation modes, the so-called plasma mode (plasmon). The plasma modes will couple to the LO lattice modes and form the so-called coupled LO plasmon-phonon (LPP) modes. Depending on the strength of the coupling, the free carriers thereby influence the dielectric function. A possible contribution from free carriers to the dielectric functions is also accounted for by virtue of the classical Drude model [38] ... 

In its basic expression, the Drude model does not predict that the absorption bandwidth is affected by particle size. Experimentally, colloidal systems having a weak cluster-matrix interaction show a well-established inverse correlation with respect to the plasmon bandwidth with particle size. In order to describe the bandwidth dependency on particle size. Hovel et al. [47] proposed a classical view of free-electron metals here, the scattering of electrons with other electrons, phonons, lattice defects and impurities leads to a damping of the Mie resonance. Briefly, in realistic metals, the dielectric function is composed of contributions from both interband transitions and the free-electron portion [48]. The free-electron dielectric function can be modified by the Dmde model to account for this dependency, giving [47-50]... 

The calculated enhancement of this purely physical EM effect as function of the distance of the molecule from the spere, reflects the long range nature of this model The enhancement depends strongly upon the particle shape and the dielectric constants and 3 For small spheres, in resonance with the localized surface plasmons,... 

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