Ellipsometry method

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]. 

Of interest are the results obtained in studies not of the excess electrons themselves, but of solvent (e.g. hexamethylphosphotriamide) molecules on introducing the solvated electrons. In the Raman spectrum, obtained by the coherent ellipsometry method, with the introduction of solvated electrons a positive shift in the C—H bond vibrational frequency is observed This has been attributed to the appearance of increased electron density at the C—H bond when a hexamethylphosphotriamide molecule enters into the solvate shell of an electron. 

Thin surface-induced ordered liquid crystalline layers can also be observed by measuring their birefringence, which is a sort of ellipsometry method, used to analyze the polarization properties of directly transmitted waves. The method has been used in the pioneering linear optics experiments at solid-liquid crystal interfaces [16-24] and later in [25,26]. 

The direct technique of polarization and hysteresis loops measurements is well-known Souer-Tower method [31]. It allows to measure the average polarization in a sample and its dependence on the temperature and external electric field. To investigate the polarization profile, i.e. its values at different distances from the surface, the indirect methods are necessary. One of such indirect methods is so-called ellipsometry method, which allows to study the spatial distribution of optical refraction index (see [32] and references therein). The distribution (profile) of polarization can be obtained in the supposition, that the coupling between polarization and optical refraction index is determined primarily by quadratic... 

The metal Sm has a complicated nine-layer hexagonal structure. Its optical conductivity, as determined by Knyazev and Noskov (1970) for a bulk polycrystal surface using the ellipsometry method, is compared in fig. 3.40 with Gd and Dy. Clearly all three metals have very similar properties, even though the Sm band structure is expected to be much more complicated. As pointed out before, the measured optical conductivity of Gd by the authors is too low, possibly due to surface contamination. The differences between Sm and other rare earths should be studied with clean single crystal surfaces using polarized light. 

Figure 2 presents the dependence of the ellipsometric parameters and A on the incidence angle for the Epiclon-derived Pis. The shape of this dependence is important in electing the correct mathematical model for determination of the optical constants. Using the principal angle ellipsometry method (A = -tc 12) [37], the equation (2) becomes as shown in relation (3) ... 

Regions of practically immobile states of a meniscus are shown in Fig. 25 by arrows on the pressure axis for solution concentration Co = 5 x 10 (curves 3) and 5 x 10 M (curves 4). This makes it possible to assess static values of contact angles. Because of small hysteresis (the regions shown by arrows are short) the mean value of static contact angle is equal to 40° for C = 5 X 10 M and 36° at 5 x 10 M. The calculated values are close to those measured using captive bubbles [45] and differential ellipsometry method [46] on quartz surface for the same solutions. 

The thicknesses of the surface layers of some elastomers are 100 A and depend on the surface nature. For elastomers the formation of more dense and less dense layers was also observed. The loose layer has the greatest thickness. The values determined by the ellipsometry method depend on temperature, because with growing temperature the molecular mobihty of chains increases, and because of the increase in the surface of the molecular contact, the density of the layer increases. Much less data are available on packing density in filled crosshnked polymers. For cured epoxy resin it was formd that the properties of the surface layer at the interface with a sohd depend on the curing conditions. The ordered surface layer has a thickness of 0.5-0.6x10 m, which is by one order higher when compared with hnear polymers. 

This chapter summarizes the optical principles involved in ellipsometry and reviews some typical applications in electrochemical systems. Newly developing areas of application and recent developments in the experimental approach and instrumentation will also be dealt with. Some emphasis will be on modified techniques, including the combined reflectance-ellipsometry method. Ellipsometry is a broad field that includes various techniques and a wide range of applications. The chapter is mostly devoted to showing what can be done with ellipsometry for the purpose of investigating electrochemical interfaces. Readers are referred to other sources of information on specific subjects. A thorough treatment of polarized light and ellipsometry has been published by Azzam and Bashara. The technique as applied to electrochemistry has also been subject to various reviews " and symposia. 

Combined Reflectance-Ellipsometry (Three-Parameter Ellipsometry) Method... 

The optical principles and equations used in the technique are concisely summarized. The combined reflectance-ellipsometry (three-parameter ellipsometry) method and spectroscopic ellip-sometry are expected to be applied to an increasing number of studies in interfacial electrochemistry. The importance of proper experimental conditions, especially the proper choice of incidence angle is emphasized. Instrumentation, experimental methods, and error and sensitivity problems are dealt with. Some typical and recent applications in electrochemistry are reviewed. 

A quite different means for the experimental determination of surface excess quantities is ellipsometry. The technique is discussed in Section IV-3D, and it is sufficient to note here that the method allows the calculation of the thickness of an adsorbed film from the ellipticity produced in light reflected from the film covered surface. If this thickness, t, is known, F may be calculated from the relationship F = t/V, where V is the molecular volume. This last may be estimated either from molecular models or from the bulk liquid density. 

In this chapter we review some of the most important developments in recent years in connection with the use of optical teclmiques for the characterization of surfaces. We start with an overview of the different approaches available to tire use of IR spectroscopy. Next, we briefly introduce some new optical characterization methods that rely on the use of lasers, including nonlinear spectroscopies. The following section addresses the use of x-rays for diffraction studies aimed at structural detenninations. Lastly, passing reference is made to other optical teclmiques such as ellipsometry and NMR, and to spectroscopies that only partly depend on photons. 

Band gaps in semiconductors can be investigated by other optical methods, such as photoluminescence, cathodoluminescence, photoluminescence excitation spectroscopy, absorption, spectral ellipsometry, photocurrent spectroscopy, and resonant Raman spectroscopy. Photoluminescence and cathodoluminescence involve an emission process and hence can be used to evaluate only features near the fundamental band gap. The other methods are related to the absorption process or its derivative (resonant Raman scattering). Most of these methods require cryogenic temperatures. 

Ellipsometry is a method of measuring the film thickness, refractive index, and extinction coefficient of single films, layer stacks, and substrate materials with very high sensitivity. Rough surfaces, interfaces, material gradients and mixtures of different materials can be analyzed. 

The number of measurable layers of a stack is limited only by the optical contrast between the different layers. In practice stacks of ten layers and more can be analyzed by ellipsometry. Further advantages of ellipsometry compared with other metrological methods are the non-invasive and non-destructive character of the optical method, the low energy entry into the sample, the direct measurement of the dielectric function of materials, and the possibility of making the measurement in any kind of optical transparent environment. 

Measurements of the adsorption of inhibitors on corroding metals are best carried out using the direct methods of radio-tracer detection and solution depletion measurements . These methods provide unambiguous information on uptake, whereas the corrosion reactions may interfere with the indirect methods of adsorption determination, such as double layer capacity measurements", coulometry", ellipsometry and reflectivity Nevertheless, double layer capacity measurements have been widely used for the determination of inhibitor adsorption on corroding metals, with apparently consistent results, though the interpretation may not be straightforward in some cases. 

In recent years, high-resolution x-ray diffraction has become a powerful method for studying layered strnctnres, films, interfaces, and surfaces. X-ray reflectivity involves the measurement of the angnlar dependence of the intensity of the x-ray beam reflected by planar interfaces. If there are multiple interfaces, interference between the reflected x-rays at the interfaces prodnces a series of minima and maxima, which allow determination of the thickness of the film. More detailed information about the film can be obtained by fitting the reflectivity curve to a model of the electron density profile. Usually, x-ray reflectivity scans are performed with a synchrotron light source. As with ellipsometry, x-ray reflectivity provides good vertical resolution [14,20] but poor lateral resolution, which is limited by the size of the probing beam, usually several tens of micrometers. 

Optical Methods Reflectance and ellipsometry snffer from lack of a theory at the molecnlar level. The same is true for SERS and SHG. The main advances will be in the nse of far-IR spectroscopy and SFG. SFG measurements performed with femtosecond lasers open np new possibilities for time-resolved adsorbate stndies. 

During the anodic polarization of platinum to potentials of about 3.0 V (RHE), one or several layers (but no more than three) of chemisorbed oxygen are formed, which sometimes are called the a-oxide of platinum. The limiting thickness of these layers is about 1.3 nm. They can be studied both by electrochemical methods and by ellipsometry. At more positive potentials phase-oxide surface layers, the p-oxides are formed. The quantitative composition and structure of these layers and the exact limits of potential for their formation depend on many factors composition of the electrolyte solution, time of polarization, surface history, and often remain unknown. 

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