Dielectric constant of metals

Dielectric constants of metals, semiconductors and insulators can be detennined from ellipsometry measurements [38, 39]. Since the dielectric constant can vary depending on the way in which a fihn is grown, the measurement of accurate film thicknesses relies on having accurate values of the dielectric constant. One connnon procedure for detennining dielectric constants is by using a Kramers-Kronig analysis of spectroscopic reflectance data [39]. This method suffers from the series-tennination error as well as the difficulty of making corrections for the presence of overlayer contaminants. The ellipsometry method is for the most part free of both these sources of error and thus yields the most accurate values to date [39]. 

In expression (5), sm is the high-frequency dielectric constant of metal caused by interband transitions. The value sm in the first approximation can be taken to be equal to 1 [16]. The imaginary part of coefficient at E in the formula (4) represents dielectric losses s" from conductivity electrons... 

Several of the amorphous alloys made by vapour quenching were investigated by means of substrate-incident magneto-optical measurements. The substrate-incident Kerr effect (different from the film-incident Kerr effect. The substrate-incident Kerr effect, in the absence of interference, can be obtained from eq. (6) by substitution of z /2/ns and 81/2/ns for e1/2 and 81/2, respectively (ns is the refractive index of the substrate). For the red and the infrared region, where the dielectric constant of metals is much larger than unity, one obtains... 

Dielectric constant is a complex entity. The real part of dielectric constant of metal should be negative and its magnitude should be greater than the value of... 

L. Kleinman, New approximation for screened exchange and the dielectric constant of metals, Phys. Rev. 160, 585-90 (1967). 

Dielectric Constant The dielectric constant of material represents its ability to reduce the electric force between two charges separated in space. This propei ty is useful in process control for polymers, ceramic materials, and semiconduc tors. Dielectric constants are measured with respect to vacuum (1.0) typical values range from 2 (benzene) to 33 (methanol) to 80 (water). TEe value for water is higher than for most plastics. A measuring cell is made of glass or some other insulating material and is usually doughnut-shaped, with the cylinders coated with metal, which constitute the plates of the capacitor. 

If a piece of metal, such as silver, is dipping into a solvent, and a positive atomic core is taken from the surface into the solvent, the ion is again surrounded by its electrostatic field but free energy has been lost by the dielectric, and a relatively small amount of work has had to be done. The corresponding potential-energy curve (Fig. 96) is therefore much less steep and has a much shallower minimum than that of Fig. 9a. For large distances d from a plane metal surface this curve is a plot of — c2/4td where t is the dielectric constant of the medium at the temperature considered The curve represents the work done in an isothermal removal of the positive core. 

Solvent effects on the rate of the decarbonylation of MeCOMn(CO)5 were examined by Calderazzo and Cotton (50) and are presented in part in Table IV. In general they are very small, and no regular trends can be discerned. This virtual lack of dependence of the rate on the nature of the solvent and very little correlation between the rate and the dielectric constant of the solvent are typical of substitution reactions of metal carbonyls (J). In the light of the foregoing, a qualitative observation that CpFe(CO)2-COMe decarbonylates much more readily on treatment at reflux in nonpolar heptane or cyclohexane than in polar dioxane is somewhat intriguing 219). 

The third-order optical Kerr susceptibility of nanocomposites, Xeff. formed by a non-absorbing matrix, with dielectric constant containing metal nanoclusters with low volume fraction p (i.e., filling factor) is given [95] by ... 

Treating the free electrons in a metal as a collection of zero-frequency oscillators gives rise51 to a complex frequency-dependent dielectric constant of 1 - a>2/(co2 - ia>/r), with (op = (47me2/m)l/2 the plasma frequency and r a collision time. For metals like Ag and Au, and with frequencies (o corresponding to visible or ultraviolet light, this simplifies to give a real part... 

With the proper definitions of ex and k0, this equation is applicable to the metal as well as to the electrolyte in the electrochemical interface.24 Kornyshev et al109 used this approach to calculate the capacitance of the metal-electrolyte interface. In applying Eq. (45) to the electrolyte phase, ex is the dielectric function of the solvent, x extends from 0 to oo, and x extends from L, the distance of closest approach of an ion to the metal (whose surface is at x = 0), to oo, so that kq is replaced by kIo(x — L). Here k0 is the inverse Debye length for an electrolyte with dielectric constant of unity, since the dielectric constant is being taken into account on the left side of Eq. (45). For the metal phase (x < 0) one takes ex as the dielectric function of the metal and limits the integration over x ... 

Non-Aqueous Colloidal Metal Solutions. It has been difficult to prepare colloidal gold in non-aqueous media due to limitations in preparative methods (low salt solubilities, solvent reactivity, etc.), and the fact that the low dielectric constant of organic solvents has hindered stabilization of the particles. In aqueous solution the gold particles are stabilized by adsorption of innocent ions, such as chloride, and thus stabilized toward flocculation by the formation of a charged double layer, which is dependent on a solvent of high dielectric constant. Thus, it seemed that such electronic stabilization would be poor in organic media. 

As was pointed out in Chapters 2 and 3, a dipole layer exists at the surface of a metal, which gives rise to a concomitant surface dipole potential x- The magnitude of this potential changes in the presence of an external electric field. A field E directed away from the surface induces an excess charge density, o e0e E, where e is the dielectric constant of the medium outside the metal. The field E pushes the electrons into the metal, producing the required excess charge, and decreasing the dipole potential (see Fig. 3.4). This has consequences for the interfacial capacity. 

Morris et al. carried out extensive studies [20] of the acidity of metal hydrides in tetrahydrofuran (THF), including metal hydrides of very low acidity as well as dihydrogen complexes that are reactive with CH3CN. The dielectric constant of THF is low compared to that of CH3CN, so ion-pairing issues must be taken into account [21], though these measurements in THF provide useful comparisons to data in CH3CN and other solvents. 

The measurement of properties such as the resistivity or dielectric constant of PS requires some kind of contact with the PS layer. Evaporation of a metal onto the PS film-covered silicon sample produces a metal/PS/Si sandwich, which behaves like an MIS structure with an imperfect insulator. Such sandwich structures usually exhibit a rectifying behavior, which has to be taken into account when determining the resistivity [Si3, Bel4]. This can be circumvented by four-terminal measurements of free-standing PS films, but for such contacts the applied electric field has to be limited to rather small values to avoid undesirable heating effects. An electrolytic contact can also be used to probe PS films, but the interpretation of the results is more complicated, because it is difficult to distinguish between ionic and electronic contributions to the measured conductivity. The electrolyte in the porous matrix may short-circuit the silicon filaments, and wetting of PS in-... 

The macroscopic dielectric constant of PS is very sensitive to the frequency range investigated. For very high frequencies the dielectric constant can be obtained by optical measurements. In this regime the effective medium approximation has been found to be an adequate description [Th3]. For lower frequencies the dielectric constant e is commonly obtained by capacitance measurements of metal/PS/ Si structures. AC conductivity measurements of such structures indicate a hop-... 

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