Ellipsometry amplitude ratio

Ellipsometry [112, 113 Ellipsometry is one of the earliest optical technique to be applied to the study of adsorption processes [112, 113]. It involves the analysis of the phase change and the change in amplitude ratio of polarized light reflected from a surface. 

The properties of adsorbed layers at liquid interfaces can be determined either indirectly by thermodynamic methods or directly by means of some particular experimental techniques, such as radiotracer and ellipsometry. For adsorbed layers of synthetic polymers or biopolymers the advantages of the ellipsometry technique become evident as it yields information not only on the adsorbed amount but also on the thickness and refractive index of the layer. The theoretical background of ellipsometry with regard to layers between two bulk phases has been described in literature quite frequently (243). In brief, the principle of the method assumes that the state of polarization of a light beam is characterized by the amplitude ratio Ep E and the phase difference (8 — 8g) of the two components of the electric-field vector E. These two components Ep and E are parallel (p) and normal (s) to the plane of incidence of the beam and given by... 

Optical constants of samples are determined from the change in the polarization state by reflection (or transmission) in ellipsometry. The ellipsometry parameters (vp. A) represent the amplitude ratio and phase difference between p>- and s-polarization However, ellipsometry parameters generally show complicated variations with changes in optical constants and film thicknesses for the investigated samples. Since the ellipsometry parameters can t be related to what we interested directly, some mathematical analysis should be done to get information such as dielectric function, film thickness and so on. 

The technique of ellipsometry provides an independent measurement of the thickness of an adsorbed film and the amount of material in that film. It relies on the fact that the state of polarization of light changes after reflection from a surface. When elliptically polarized light is reflected from a bare surface, there is a change in both the amplitude ratio and the phase difference of the components. This can be expressed mathematically in the following way... 

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. 

In ellipsometry two parameters are determined. These are A, the phase angle between the leading and trailing components in Fig. 27.24, and the ratio of the electric field amplitudes E and E, which defines the second parameter, /. IE I/IEJ = tan /. A and r may be recorded as functions of other experimental variables, such as potential and time. 

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 ... 

Where, y/ and A are also called ellipsometry parameters. The ratio of the modulus of the amplitude reflection coefficients is given by tan y/, and the phase difference between p- and s-polarized reflected light is given by A. The two ellipsometry parameters y/ and A are obtained directly from the measurement of ellipsometry. 

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