Plasmon energy

In addition to dielectric property determinations, one also can measure valence electron densities from the low-loss spectrum. Using the simple free electron model one can show that the bulk plasmon energy E is governed by the equation ... 

P. Braun. Surf. Sci. 126,714,1983. VEELS study of bulk and surface plasmon energies across Al—Mg alloy phase diagram. 

In addition to primary features from copper in Eig. 2.7 are small photoelectron peaks at 955 and 1204 eV kinetic energies, arising from the oxygen and carbon Is levels, respectively, because of the presence of some contamination on the surface. Secondary features are X-ray satellite and ghost lines, surface and bulk plasmon energy loss features, shake-up lines, multiplet splitting, shake-off lines, and asymmetries because of asymmetric core levels [2.6]. 

By means of this combination of the cross section for an ellipsoid with the Drude dielectric function we arrive at resonance absorption where there is no comparable structure in the bulk metal absorption. The absorption cross section is a maximum at co = ojs and falls to approximately one-half its maximum value at the frequencies = us y/2 (provided that v2 ). That is, the surface mode frequency is us or, in quantum-mechanical language, the surface plasmon energy is hcos. We have assumed that the dielectric function of the surrounding medium is constant or weakly dependent on frequency. 

The alkali metals, with only one free electron per atom, have lower plasmon energies than those of divalent free-electron metals such as Mg and A1 because the plasma frequency decreases with decreasing electron density. Thus, surface plasmon energies for alkali metals are in or near the visible, whereas they are in the far ultraviolet for Mg, Al, and Pb. Surface plasmon energies of the divalent metals Ag, Au, and Cu are shifted toward and into the visible because of interband transitions (see Fig. 12.9d) this is also the cause of the large values of c" for Au and Cu. 

Solid Bulk Plasmon Energy (eV) Surface Plasmon Energy (eV) c" where c 2 Reference... 

XPS studies of surface plasmons of A1 have been made by Barrie (57) and by Baer and Busch (58). Figure 23 shows Barrie s 2s spectrum from a clean A1 film and from the film after heavy oxidation. At a 15.2 eV separation from the main peak, and at multiples of this, are peaks associated with bulk plasmons. At 10.7 eV is a small peak, observed with the clean film and not present after oxidation, which originates from excitation of the plasmon characteristic of a clean A1 metal surface. Barrie concluded that this plasmon energy is in accord with the prediction of Stern and Ferrell (59)... 

It has been found that for photon energies near and below plasmon energies ( 20 eV) and near other excitations, the electromagnetic fields are quite structured, both as a function of depth from the surface and as a function of energy./81 / For any quantitative structural studies, this situation is to be... 

To summarize, for photon energies above the plasmon energies (and away from other excitation energies), the electromagnetic fields can be described adequately with macroscopic dielectric theory. 

Kitson, S. C., Barnes, W. L., and Sambles, J. R. (1995). Surface plasmon energy gaps and photoluminescence. Phys. Rev. B 52 11441-11445. Gruhlke, R. H., Holland, W. R., and Hall, D. G. (1986). Surface-plasmon cross coupling in molecular fluorescence near a corrugated thin metal film. Phys. Rev. Lett. 56 2838-2841. 

Excitation and the relaxation (radiative and non radiative) processes of the Tryptophan solution and the colloids are represented in figure 18.7. The new relaxation pathways introduced by the metal nanoparticles (nonradiative decay rate, K p) are shown in figure 18.7(b). Although, one photon at 270nm and two-photons at 532nm are resonant with the excited states of the molecule, these wavelengths are not in resonance with the Plasmon energy level. 

The plasmon energy is given by the expression Ep = fia)p and the density of electrons in the valence band is given in Reference 18 as follows ... 

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.

In the theoretical approach used, there is only one free parameter r. In both cases, transmission and reflection, the experimental data are reproduced using Tg = 1.5. So, it is tempting to assume that in both cases comparable mechanisms are responsible for projectile energy loss. Moreover, = 1.5 is the value that one obtains considering the 2p and 2s electrons of F as free electrons. This value is also consistent with the measured bulk plasmon energy 25 eV [70]. We note that the value = 1.5 corresponds to a rather high electronic density for instance, it is larger than the electronic density of Al (r = 2.07). 

Table 7. Observed values of the surface plasmon energy ha>sp for Rb, Cs and some suboxides from Hel spectra. 40, 65). The concentration of free electrons N is derived from hcogp and yields the experimental number of electrons per formula unit ng which is corrected to set np (Rb,Cs)= 1. The expected values n. correspond to the bond model...

The experimental values of hcogp lead to the observed electron concentrations no (again referred to one formula unit), when using average values for Acc and the information about volumes taken from the crystal stmctures. (65) The expected values n are calculated on the basis of the bond model (Table 7). The experimentally derived values Uq are 20% smaller than the expected values Ug for the pure elements. In spite of the simplifications in the calculations, e.g. taking m instead of m, the determined electron deficiency seems to be real, as a decreased electron concentration is also calculated from the surface plasmon energies measured for Rb and Cs hy Kunz. 87)... 

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