Dielectric function of aluminum

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... 

In order to excite SPP in a metallic tip, the metal is required to have an optical property that has a negative real and minimal imaginary part in the dielectric function at the excitation wavelength [98] as discussed in Sect. 4.2. As a plasmonic material in the UV region, aluminum can be used instead of silver and gold. The dielectric function of aluminum shows a reasonably small imaginary part while the real part keeps negative in the UV. 

Fig. 8.1 Dielectric functions of aluminum [10], indium [11], and silver [10]. Dashed-dotted line represents = -2...

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... 

The imaginary part of the dielectric function of SiC at its Frohlich frequency in the infrared (about 932 cm- ) is close to that of aluminum at 8.8 eV. So Fig. 2Aa also shows the field lines of the Poynting vector around a small SiC sphere illuminated by light of frequency 932 cm-1. At nearby frequencies, 900... 

Despite of its simplicity the Drude model correctly describes the optical properties of simple metals. In Fig. 1.4 we report the experimental dielectric constant, the refractive index and the reflectance for aluminum. Figure 1.4 closely resembles Fig. 1.3 with (Op 15 eV. The best agreement of the dielectric function of metal with that obtained in the framework of the free electron model can be obtained for the alkali metals (Li, Na, K, Cs, Rb), whose response seems to be weakly affected by the contribution from the core electrons. Notably, alkali metals, such as sodium, have an almost free-electron-like response and thus, in accordance... 

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. 

In addition to that of aluminum, the dielectric function of indium is also shown in Fig. 8.1 [10, 11]. Indium behaves as a plasmonic metal at wavelengths down to 170 nm. The imaginary part of the dielectric function is reasonably small, similar to that of aluminum. DUV-SERS using indium has been also demonstrated [17]. 

The reflectance, dielectric functions, and refractive indices, together with calculations based on the Drude theory, for the common metal aluminum are shown in Fig. 9.11. Aluminum is described well by the Drude theory except for the weak structure near 1.5 eV, which is caused by bound electrons. The parameters we have chosen to fit the reflectance data, hu>p = 15 eV and hy = 0.6 eV, are appreciably different from those used by Ehrenreich et al. (1963), hup = 12.7 eV and hy = 0.13 eV, to fit the low-energy (hu < 0.2 eV) reflectance of aluminum. This is probably caused by the effects of band transitions and the difference in electron scattering mechanisms at higher energies. The parameters we use reflect our interest in applying the Drude theory in the neighborhood of the plasma frequency. 

The dielectric function and reflectance of aluminum, which were displayed in Fig. 9.11, are shown over a broader energy range in Fig. 10.2 note that two... 

Figure 10.2 Dielectric functions and reflectance of aluminum (Hagcmann ct al., 1974).

Note that there is no bulk absorption band in aluminum corresponding to the prominent extinction feature at about 8 eV. Indeed, the extinction maximum occurs where bulk absorption is monotonically decreasing. This feature arises from a resonance in the collective motion of free electrons constrained to oscillate within a small sphere. It is similar to the dominant infrared extinction feature in small MgO spheres (Fig. 11.2), which arises from a collective oscillation of the lattice ions. As will be shown in Chapter 12, these resonances can be quite strongly dependent on particle shape and are excited at energies where the real part of the dielectric function is negative. For a metal such as aluminum, this region extends from radio to far-ultraviolet frequencies. So the... 

Figure 12.6 Calculated absorption spectra of aluminum spheres, randomly oriented ellipsoids (geometrical factors 0.01, 0.3, and 0.69), and a continuous distribution of ellipsoidal shapes (CDE). Below this is the real part of the Drude dielectric function.

Extinction calculations for aluminum spheres and a continuous distribution of ellipsoids (CDE) are compared in Fig. 12.6 the dielectric function was approximated by the Drude formula. The sum rule (12.32) implies that integrated absorption by an aluminum particle in air is nearly independent of its shape a change of shape merely shifts the resonance to another frequency between 0 and 15 eV, the region over which e for aluminum is negative. Thus, a distribution of shapes causes the surface plasmon band to be broadened, the... 

EDM is thermal erosion for electrically conductive materials, which is based on electrical discharging (sparking) between the tool (electrode) and a conductive work-piece. Therefore, every electrically conductive material can be processed, especially steel and aluminum, in mold making. This applies particularly for very hard materials where the limit can be reached with traditional machining processes. Both the workpieces as well as the mold are immersed in a non-conductive liquid medium, the so-called dielectric fluid (usually oil or deionized water). This dielectric fluid is necessary for the functionality of EDM. 

Henry DJ et al (2011) Reactivity and regioselectivity of aluminum nanoclusters insights from regional density functional theory. J Phys Chem C 115 1714-1723 49. Fukushima A, Senami M, Tsuchida Y, Tachibana A (2010) Local dielectric property of cubic hafnia. Jpn J Appl Phys 49 111504... 

In this contribution, we employ local dielectric spectroscopy (LDS), a method recently used to characterize relaxation dynamics of ultrathin polymer films at nanometer scale [45 7], to study the evolution of irreversibly adsorbed layers in poly(vinyl acetate) films deposited on different solid substrates, i.e. aluminum, gold and silicon, under annealing above the Tg [30, 41, 48]. After describing the setup and sample preparation in Sect. 7.2, we present, in Sect. 7.3, our results on the growth of the layer as a function of the interfacial interaction. The influence of the adsorbed layer on the relaxation dynamics of nano-confined PVAc films and their capacity to absorb moisture in various degrees of relative humidity is studied in details. 

We apply the concepts discussed in the last few sections to the case of a C aperture in aluminum. The thickness of the alumimun film is chosen to be 100 nm. The dimensions of the C aperture are as follows aperture length 155nm, aperture width 70 run, tongue width 25 nm, and gap width 25 nm. The incident field is X-polarized. The XZ plane is a mirror symmetry plane for the C aperture. The surrounding dielectric is assumed to be ifee space. The normalized scattering and absorption cross sections as a function of wavelength are shown in Fig. 43. 

Figure 7.8 shows a capacitive electrode system. One half-cell is an ordinary indifferent electrolyte-skin electrode. In the other half-cell, the electrolyte has been replaced by a dielectric so that there is no galvanic coupling between the electrode metal plate and the skin. The dielectric is usually a thin layer of a chloride or oxide of the metal in the electrode plate. The metal plate functions as a substrate for the thin dielectric that can be made from anodizing or oxidizing silver, aluminum, silicon, or titan. The dielectric must be robust and endure humidity and sweat arriving from the skin. The capacitance between the metal plate and the skin is dependent on contact area, dielectric thickness, and... 

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