Ellipsometric coefficients

This complex ratio, also called the ellipsometric coefficient, is often conveniently written as... 

Fig. 4.3. The temperature dependence of the ellipsometric coefficient at the Brewster angle pb for A — n — octyl — 4 — cyanobiphenyl (8CB). Phase transition temperature Tjvz is at 315.3 K. The solid line is a fit to (4.5) and (4.6) with...

Brewster angle ellipsometry (BAE) and surface optical second harmonic generation (SHG, see Chap. 5) were used to study the growth of 8CB films, evaporated in air onto glass (BK7) substrates, covered with a 15 nm thick film of poly(vinyl cinnamate) (PVCN) [48]. As the thickness of 8CB on PVCN layers was far below the optical wavelengths, the Drude formula for the ellipsometric coefficient at the Brewster angle, ps, (4.3), was used. The ellipticity coefficient of the 8CB adsorbate was calculated as... 

EUipsometry has already been cited as the method that first established that passivity was associated with the presence of a very thin oxide film. Later it was measured (Jovancicevic, 1987) by means of ellipsometric spectroscopy and it was thus found possible to evolve an extinction coefficient that varied characteristically with the wavelength at which the ellipsometry was carried out (Fig. 12.66). The interpre-... 

Ellipsometry. Determination of h(u>) by KK analysis and coupled measurements of 1Z and T are affected, respectively, by the problem of the tails added to the experimental R(u>) spectra and by the need to perform 7Z and T measurements separately These problems, which introduce some uncertainty, can be solved by spectroscopic ellipsometry. The technique involves analyzing the polarization of a light beam reflected by a surface. The incident beam must be linearly polarized and its polarization should be allowed to rotate. A second linear polarizer then analyzes the reflected beam. The roles of polarizer and analyzer can be exchanged. The amplitudes of the s and p components of the reflected radiation are affected in a different way by reflection at the surface. The important function describing the process is the ellipsometric ratio p, which is defined as the polarization of the reflected wave with respect to the incident wave, expressed as the ratio between the Fresnel coefficients for p and s polarizations ... 

Finally, n was determined by spectroscopic ellipsometry. The main drawback with this technique when applied to anisotropic samples is that the measured ellipsometric functions tanlF and cos A are related both to the incidence angle and the anisotropic reflectance coefficient for polarizations parallel and perpendicular to the incidence plane. The parameters thus have to be deconvolved from a set of measurements performed with different orientations of the sample [see (2.15) and (2.16)]. The complex refractive index determined by ellipsometry is reliable only in the spectral region where the sample can be considered as a bulk material. In fact, below the absorption... 

Ellipsometric measurements were carried out on LB films of [tetrakis-(3,3-dimethyl-l-butoxycarbonyl)] CuPc in the presence of dry air, toluene, and tetrachlo-roethene. The relative thickness, the normalized refractive index, and extinction coefficient at a fixed wavelength were changed, when these films are exposed to different concentrations of toluene and tetrachloroethene [46],... 

The three-medium problem is the simplest surface problem to be solved one unknown thin film on a substrate immersed in an ambient. The optical properties of each medium are defined by wavelength dependent refractive indices Wj and real absorption coefficients kj. As the properties of the ambient and substrate are usually known or measured before the formation of the surface thin film, the goal of the ellipsometric measurement is to determine the unknowns n, k2 d the thickness of the thin film. 

At planar interfaces there are four main types of linear optical signals that are detected by different techniques. Three of them are related to reflection and one to attenuated total reflection. In reflection methods the basic measurable parameters are related to rp and rs - the complex am-phtudes of the reflection coefficients of the light polarized parallel p) and perpendicular s) to the incidence plane, respectively (Fig. 17). These are reflection coefficient = rs(p), phase of reflected light 5j(p) = (l/2/)lnK(p)/rf(p), ellipsometric parameters = tan rp/rs and A =... 

This equation is the so-called basic ellipsometric equation. It contains R and R which depend on the optical properties of the reflecting system, the wavelength of the light X the angle of incidence cp and the experimentally measurable parameters Pand A. For the reflection at a clean interface, the Rp and R are the Fresnel coefficients (246) of the single uncovered interface. They depend only on the refractive indices of the two adjacent phases and the angle of incidence. For systems that do not absorb light the optical constants of the two bulk phases (ambient and substrate media) are usually obtained from the experimental values of P and A for the clean interface (denoted by subscript 0 via Eq. (111). For a layer-covered interface, multiple reflections and refractions take place within the layer (Fig. 24). 

Preliminary analysis indicates a layer thickness of 3.09 nm and a complex permittivity of (2.34 + 0.25 i), corresponding to a refractive index, n, of 1.53 and absorption coefficient, k, of 0.08. These values are in agreement with figures produced by ellipsometric analysis of multilayer films (7 to 29 layers) of the same material [9]. The film thickness also coincides with the molecular length of 3.0 nm, measured from a precision space-filled model, suggesting vertical alignment of the molecules within the layers. 

The refractive index, n, and extinction coefficient, k, values were calculated from the measured values of ellipsometric angles P and A, using equation (2) ... 

In the following section a procedure for a calculation of the reflectivity coefficients rp and (and consequently the ellipsometric angles) first published by Lekner [6] will be described. 

A number of methods have been used to measure the EO coefficients and ni of the poled polymer samples. These EO measurements are made by detecting the change in refractive index of the poled polymer sample when a modulating electric field is applied to the sample. Mach-Zehnder [42,43]. Fabry-Perot [44,45], and Mich-elson [46] interferometric techniques have been used to evaluate the EO coefficients. Other techniques, such as an attenuated total reflection technique [47,48] and an ellipsometric technique [49-51], have also been employed to determine the r coefficients. 

Fig. 26.5 The experimental arrangement for measurement of the EO coefficient using the ellipsometric technique.

---