Optical, constants

Before we proceed, it would be useful to examine the magnitudes of the parameters )p and T that determine the optical constants. These are displayed in Table 24.2 for several metals and semiconductors. 

At short wavelengths, the real part of the dielectric approaches 1 and the imaginary part approaches 0. Near the plasma frequency, the real part crosses zero and becomes increasingly negative. The imaginary part starts to become increasingly negative. 

One can see that the definition of the ratio np-jmso as the plasma frequency becomes the dividing line where the metal goes from being transparent to an almost perfect reflector of 

Real (soUd) and imaginary (dashed) parts of the dielectric function for a conductive media with free electrons. 

Theoretical reflection for a free electron metal as a function of A /Ap. 

When reflectance spectroscopy was first used for the in situ study of electrode surfaces, the main emphasis was placed on monitoring the formation of adsorbates and thin films, e.g., the underpotential deposition of metals or the formation of oxides, because a rather strict correlation between coverage and adsorbate- or film-induced reflectance change was generally observed/ In the beginning of the seventies, the evaluation of adsorbate optical constants from measurements of with the help of stratified multilayer models 

The aim of this chapter is to provide some background on the theory of the optical properties of solids and to outline what we can learn from reflectance measurements with a brief survey of the various techniques. With respect to the first point, the review by Mclntyre is still highly recommended. The main emphasis of this article (and this may be the main difference to McIntyre s) is on the presentation and discussion of experimental results which are now available and which demonstrate that, indeed, new information can be obtained by this technique—information which is not accessible by purely electrochemical methods and yet is important for solving the puzzle about the microscopic structure of the electrochemical interface. 

The response of a medium to an incoming electromagnetic wave is in most cases sufficiently characterized by one frequency-dependent quantity, the 

Describing the electromagnetic plane wave by its time-dependent value of the electric vector, 

The first exp-term represents the exponential decay of the wave amplitude with penetration into the (absorbing) medium, while the second exponential term describes the time and phase dependence of the electromagnetic wave, traveling with phase velocity v - c/n. The two quantities n and k are called the refractive index and extinction coefficient, respectively, and are commonly referred to as the optical constants. 

The fundamental parameters that govern the absorption of radiation are the real and imaginary components of the complex refractive index  

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A) MEASUREMENT OF THE OPTICAL CONSTANTS OF MATERIALS USING ELLIPSOMETRY... 

Smectites are stmcturaUy similar to pyrophylUte [12269-78-2] or talc [14807-96-6], but differ by substitutions mainly in the octahedral layers. Some substitution may occur for Si in the tetrahedral layer, and by F for OH in the stmcture. Deficit charges in smectite are compensated by cations (usually Na, Ca, K) sorbed between the three-layer (two tetrahedral and one octahedral, hence 2 1) clay mineral sandwiches. These are held relatively loosely, although stoichiometricaUy, and give rise to the significant cation exchange properties of the smectite. Representative analyses of smectite minerals are given in Table 3. The deterrnination of a complete set of optical constants of the smectite group is usually not possible because the individual crystals are too small. Representative optical measurements may, however, be found in the Uterature (42,107). 

Early work in ellipsometry focused on improving the technique, whereas attention now emphasizes applications to materials analysis. New uses continue to be found however, ellipsometry traditionally has been used to determine film thicknesses (in the rang 1-1000 nm), as well as optical constants. " Common systems are oxide and nitride films on silicon v ers, dielectric films deposited on optical sur ces, and multilayer semiconductor strucmres. 

Ellipsometry is a very powerfiil, simple, and totally nondestructive technique for determining optical constants, film thicknesses in multilayered systems, sur ce and... 

The unknown parameters of the model, such as film thicknesses, optical constants, or constituent material fractions, are varied until a best fit between the measured P and A and the calculated P/ and A/ is found, where m signifies a quantity that is measured. A mathematical function called the mean squared error (MSE) is used as a measure of the goodness of the fit ... 

D. E. Aspnes. In Handbook of Optical Constants of Solids. (E. Palik, ed.) Academic Press, Orlando, 1985. Description of use of ellipsometry to determine optical constants of solids. 

Infrared ellipsometry is typically performed in the mid-infrared range of 400 to 5000 cm , but also in the near- and far-infrared. The resonances of molecular vibrations or phonons in the solid state generate typical features in the tanT and A spectra in the form of relative minima or maxima and dispersion-like structures. For the isotropic bulk calculation of optical constants - refractive index n and extinction coefficient k - is straightforward. For all other applications (thin films and anisotropic materials) iteration procedures are used. In ellipsometry only angles are measured. The results are also absolute values, obtained without the use of a standard. 

Determination of the optical constants and the thickness is affected by the problem of calculating three results from two ellipsometric values. This problem can be solved by use of the oscillator fit in a suitable wavenumber range or by using the fact that ranges free from absorption always occur in the infrared. In these circumstances the thickness and the refractive index outside the resonances can be determined - by the algorithm of Reinberg [4.317], for example. With this result only two data have to be calculated. 

Bertie JE, Lan Z. 1996. Infrared intensities of liquids. XX The intensity of the OH stretching band of liquid water revisited, and the best current values of the optical constants of H20(I) at 25 °C between 15,000 and 1 cm . Appl Spectrosc 50 1047-1057. 

Scott, G.D. Optical constants of thin film materials. J. opt. Soc. America... 

Figure 3.7 Curves (a) and lb) the variation in the optical constants of platinum with wavelength (from M.A. Barret and R. Parsons, Symp. Far. Soc4 (1970) 72). Curves (c) and (d) the variation with wavelength of the calculated optical constants of the strongly-bound hydrogen layer (from...

Huggins, M.L. and Sun, K.-H. (1943). Calculations of density and optical constants of a glass from its composition in weight percent. Journal of the American Ceramic Society. 26 4—11. 

It is the intensity of light transmitted by a sample of path length . It can be shown that t = (16 ir/3)R so that Eqs. (22) and (40) may be expressed with r in place of R0 and an optical constant H (= 16 jtK/3) in place of K. Although r is usually too small to be measured as such directly, some experimental results are often reported in the form of He/t even though Kc/Rg is the measured quantity. 

The expressions for scattered light intensity (and Rayleigh ratio) must be corrected by dividing by the appropriate Cabannes factor. Effectively this is equivalent to replacing the optical constant K as defined in Eq. (24) by Kf and by 2 Kfj for unpolarised and vertically polarised incident light respectively. 

From a practical point of view the consequences of TOF dispersion are important only for short intrinsic fluorescence decay times of to < 1 nsec. Figure 8.15 shows an example with to = 50 psec and realistic optical constants of the substrate. The intensity maximum in Fb(t) is formed at At 30 psec after (5-excitation. After this maximum, the fluorescence decays with an effective lifetime of r ff = 100 psec that increases after long times to t > > 500 psec. The long-lived tail disappears as soon as there is some fluorescence reabsorption, and for Ke = K there is practically no difference to the intrinsic decay curve (curve 3 in Figure 8.15). 

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