Bulk plasmons

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 ... 

The degree of surface cleanliness or even ordering can be determined by REELS, especially from the intense VEELS signals. The relative intensity of the surface and bulk plasmon peaks is often more sensitive to surface contamination than AES, especially for elements like Al, which have intense plasmon peaks. Semiconductor surfaces often have surface states due to dangling bonds that are unique to each crystal orientation, which have been used in the case of Si and GaAs to follow in situ the formation of metal contacts and to resolve such issues as Fermi-level pinning and its role in Schottky barrier heights. 

Sometimes it is possible to distinguish surface and bulk plasmons by lowering Eq so that the bulk plasmon will decrease in intensity more rapidly than the surface plasmon. However both surface states and interband transitions can show the same behavior. 

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]. 

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

At the surface of metals, the surface plasmon-polaritons, also called "surface plasmons," are not the same as the "bulk" plasmons these surface plasmons are affected (i.e., shifted slightly in energy) by monolayer adsorbates thus Surface Plasmon Resonance (SPR) spectroscopy yields information about the nature of the binding of the adsorbates onto a metal surface. The surface plasmons are excited by a p-polarized electromagnetic wave (polarized in the plane of the film) that crosses a glass medium (1), such as a prism, and is partially reflected by a metallic film (2) and back into the glass medium the dispersion relation is... 

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)... 

Fig. 1 presents the EELS data for silicon growth (Vsi=0.17 nm/min at substrate temperature 150°C) atop 2D Mg2Si with structure (2/3)V3-R30°. It is apparent, that surface phase does not destroy at Si overgrowth and 2 nm of Si completely cover the silicide phase. However, the surface plasmon shifted to lower energy at 20 nm of Si thickness, while position of bulk plasmon corresponded to the monocrystalline silicon. The main cause of the given difference is the strong surface relief Therefore in this case the known relation between bulk and surface plasmons for atomically clean surface is not valid. 

The XPS spectra clearly indicated the presence of SiC, as seen in Figures 11.54 [364]. These data should be compared with those of Figure 10.7 [2]. In their XPS energy loss spectra for C(ls) core level, shown in Figure 11.55 [363], there was a known bulk plasmon band at 34 eV and the surface plasmon band at 24 eV. In addition, a band due to SiC was observed at 20 eV. 

Figure 11.55. XPS energy loss spectra of C(ls) core level. For the specimen area covered by the bright plasma, the energy loss spectrum is typical for diamond (bulk plasmon at 34 eV, and surface plasmon at 24 eV) [364].

Figure 23 Spherical crystallite of aluminium with oxide layer on carbon support. Point analyses within the particle show sharp bulk plasmon at 15 eV and from oxide layer diffuse loss feature a/ 23 eV...

Again, the mode spectrum depends on Zq. In the limit Zq -> 00, we obtain and = p/2, where describes the coupling of the 3D bulk and 2D plasmons deep in the medium (z 00), and, separately, a describes the decoupled, distant surface plasmon. However, in the limit z 0, we have col = and col = coyi + cay = col + o)2D where is now the decoupled bulk plasmon deep in the medinm, and, separately, describes the conpling of the surface plasmon with the 2D plasmon. For finite, nonvanishing Zq these hybridized plasmon modes are admixed as given by Eq.(31). 

The screened susceptibility x(q, m z, z ) appearing in equation (23) is a smooth function of the spatial coordinates that interpolates from zero very far from the surface to the bulk value. It contains the spectrum of the single-pai ticle and collective modes and their coupling. This coupling, known as Landau-damping, depends on distance and it is the only channel that allows decaying of a collective mode in the jellium theory. Surface plasmons of parallel momentum q different from zero are Landau-damped but bulk plasmons cannot decay into electron-hole pairs below a critical frequency in this linear theory. Collective modes can show up in electron emission spectra [28,29] because they are coupled to electron-hole pairs. 

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). 

Werner, W. S. M., Ruocco, A., Offi, F., lacobucci, S., Smekal, W, Winter, H., and Stefani, G. 2008. Role of surface and bulk plasmon decay in secondary electron emission. Phys. Rev. B 78 233403. 

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). 

The dipolar response of a large sodium sphere can be calculated from the experimental bulk dielectric function as discussed in the context of Eq. (6). The calculated width is To = 0.19 eV. This asymptotic experimental width is due to a structure in the dielectric function which is caused by an interband transition [55]. The collective oscillation can decay by exciting a single electron to a higher electronic band. The same mechanism occurs in the damping of the bulk plasmon. In this case, the width can be well correlated with the strength of the pseudopotential (see Figure 9 of Ref. [48]). 

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