Reflectance ellipsometry

The combined ellipsometry-reflectance method—three-parameter ellipsometry—has been subject to error analysis. Cahan showed that, while it is possible in principle to obtain an unambiguous solution for the optical constants and thickness of a film by three-parameter ellipsometry, the method does not guarantee that a solution can be obtained in practice. He also pointed out, by working with sample data from electrochemically produced films, that the numbers obtained as the solution are not necessarily physically real when the three-layer model is inadequate for the particular system. Chung, Lee, and Paik" studied the forward and reverse sensitivity analyses for three-parameter ellipsometry to obtain the forward sensitivity coefficients (dMldoi) > and the reverse sensitivity coefficients for a passive film on nickel (here... 

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. 

The detailed examination of the behavior of light passing through or reflected by an interface can, in principle, allow the determination of the monolayer thickness, its index of refiraction and absorption coefficient as a function of wavelength. The subjects of ellipsometry, spectroscopy, and x-ray reflection deal with this goal we sketch these techniques here. 

In ellipsometry monochromatic light such as from a He-Ne laser, is passed through a polarizer, rotated by passing through a compensator before it impinges on the interface to be studied [142]. The reflected beam will be elliptically polarized and is measured by a polarization analyzer. In null ellipsometry, the polarizer, compensator, and analyzer are rotated to produce maximum extinction. The phase shift between the parallel and perpendicular components A and the ratio of the amplitudes of these components, tan are related to the polarizer and analyzer angles p and a, respectively. The changes in A and when a film is present can be related in an implicit form to the complex index of refraction and thickness of the film. 

A newer and perhaps more useful application of ellipsometry to Langmuir films is their lateral characterization via ellipsometric microscopy [146], A simple modification of the nuU ellipsometer allows one to image features down to 10-/im resolution. Working with a fixed polarizer and analyzer, some domains are at extinction while others are not and appear bright. This approach requires no fluorescent label and can be applied to systems on reflective supports. 

ELL Ellipsometry [194, 195] Depolarization of reflected Thickness of adsorbed film... 

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]. 

RAIRS spectra contain absorption band structures related to electronic transitions and vibrations of the bulk, the surface, or adsorbed molecules. In reflectance spectroscopy the ahsorhance is usually determined hy calculating -log(Rs/Ro), where Rs represents the reflectance from the adsorhate-covered substrate and Rq is the reflectance from the bare substrate. For thin films with strong dipole oscillators, the Berre-man effect, which can lead to an additional feature in the reflectance spectrum, must also be considered (Sect. 4.9 Ellipsometry). The frequencies, intensities, full widths at half maximum, and band line-shapes in the absorption spectrum yield information about adsorption states, chemical environment, ordering effects, and vibrational coupling. 

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. 

Ellipsometry measurement of the characteristics of polarised light after reflection from a surface. 

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. 

In a reflectance or ellipsometry experiment, measurements are always referred to the physical plane of incidence, as defined in Fig. 27.24. If the polarization is parallel to this plane of incidence, the parameters related to it are denoted by the subscript p. For polarization perpendicnlar to the plane, the subscript s is used. When a linearly polarized beam is reflected, one often finds that the parallel and perpendicular components nndergo changes in amplitude and phase. Thus, two beams that are in... 

As discussed above, the reflection of linearly polarized light from a surface generally produces elliptically polarized light, because the parallel and perpendicular components are reflected with different efficiencies and different phase shifts. These changes in intensity and phase angle can be analyzed to characterize the reflecting system. This approach is called ellipsometry. 

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. 

Pleith, W., W. Kozlowski, and T. Twomey, Reflectance spectroscopy and ellipsometry of organic monolayers, in Adsorption of Molecules at Metal Electrodes, 3. Lipkowski and P. N. Ross, Eds., VCH, New York, 1992, p. 285. 

In a typical ellipsometry experiment a sample is irradiated with polarized light, which subsequently is reflected from the sample surface and detected after passing an analyzer. The ratio p of complex reflectances for perpendicularly (s) and parallelly (p) polarized light usually is represented as follows ... 

Ellipsometry is concerned with the measurement of the changes in polarisation state, as well as light intensity, on reflection since these parameters are highly sensitive probes of the thickness and refractive index, rtf, of a surface film. A full treatment of the principles involved in ellipsometric measurements can be found in any one of several excellent reviews (see references). 

Whereas the XSW technique takes advantage of the standing wave established on the total reflection of X-rays from a mirror surface, a conceptually more straightforward approach is that of simply specularly reflecting an X-ray beam from an electrode coated with the film of interest, measuring the ratio of the intensities of the incident and reflected rays, and fitting the data, using the Fresnel equations, to a suitable model an approach similar to optical ellipsometry. 

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