Ellipsometry incident polarized light

Azzam RMA, Bashara NM (1977) Ellipsometry and polarized light. North Holland Physics, Amsterdam Haitjema H, Woerlee GF (1989) Analysis of tin dioxide coatings by multiple angle of incidence ellipsometry. Thin Solid Films 169(1) 1-16 Heavens OS (1991) Optical properties of thin solid films, 2nd edn. Dover, New York... 

Figure 7.25 Set-up for ellipsometry microscopy. Incident linearly polarized light reflects on the surface and becomes eiliptically polarized. The quarter wave plate converts the polarization from elliptical to linear. The analyzer is placed such that it extinguishes all light. If the reflection properties change because a gas is adsorbed, the polarization does not match the setting of the analyzer and light passes through it. Appropriate lenses project an image of the surface onto the CCD camera (adapted from Rotermund [72]).

Besides ellipsometry, reflectometry has proven its value. By this technique adsorbed masses can conveniently be obtained and. if the measurements are carried out with polarized light, also the orientation of the adsorbed molecules. Experiments are usually done at near-normal Incidence, when // Another variant, pertaining to adsorption from solution and sketched in fig. 2.15, can be made fast enough for the kinetics of adsorption to be followed. In the mode shown, fluid is admitted to the surface from bottom to top ("impinging jet") equations are available for the rate of supply in the stagnation point (the "core" of the fluid flow, which hits the surface perpendicularly). The quotient of the reflected Intensities = S is obtained by electronic division, it is... 

Ellipsometry is a technique that uses polari/.ed light to probe the dielectric properties of samples.- It is most commonly applied to the analysis of very thin films on surfaces. In ellipsometry, a polarized incident beam, often from a laser, is reflected from the film, and the reflected light is analyzed to determine a change in the state of polarization. The change in the amplitude and the phase of the reflected light are then related to properties such as film refractive index, absorptivity, optical anisotropy, and thickness. 

The two circular-polarized beams of the incident radiation (I, levorotatory r, dextrorotatory) not only can be influenced with respect to their direction of rotation, but also, in the region of an absorption band, can be absorbed to a different extent by the sample, so that in addition to so-called optical rotatory dispersion (ORD), circular dichroism (CD) or the Cotton effect is observed [35] - (38J. Along with these classical methods of analysis, modem methods for the analytical investigation of surfaces and boundary layers have become very important, including the use of polarized light in ellipsometry ( Surface Analysis) and surface plasmon resonance. Under the influence of external forces (e.g., a magnetic field), even optically inactive substances can be caused to produce magnetooptic rotation. 

Ellipsometry is based on the measurement of changes in the ellipticity of polarized light upon reflection at a surface. The ellipticity can be described by the ratio and phase difference of two plane-polarized light waves, one oscillating in parallel with the plane of incidence and the other perpendicular to it. When the two plane-polarized light waves have a phase shift of 90°, they are circularly polarized. 

For a general situation of optical anisotropy and sample orientation, the simple definition of p in Equation 13 is no longer a complete description, and the generalized ellipsometry approach is needed. In such instances. Equation 13 depends on the polarization state of the incident plane wave. The generalized elKpsometry parameters are then described by three ratios of the polarized-light reflection coefficients among the four available complex-valued elements of the Jones reflection matrix r [15, 36] ... 

Fig. 3.4. The geometry of an ellipsometry experiment. The linearly polarized incidence light beam becomes elliptically polarized after reflection at the sample surface. The plane of incidence is shown hatched. a is the angle of incidence...

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 ... 

A technique that can possibly measure the thickness of an anodic film is ellipsometry [21-23]. Figure 10.15 illustrates the setup of an ellipsometer and how is works. A light beam of known polarization reflects and passes through a sample. The polarization change between the incident and reflective beams, expressed as tan —the amplitude (of electrical filed, E) change upon reflection and A—the phase shift, is measured. Since... 

Ellipsometry and reflectometry have in common that information on the adsorbate is extracted from changes induced by this adsorbate in the properties of light after reflection from the surface. At any phase boundary the fractions of light that are reflected and transmitted depend on system properties (such as the refractive Indices of solvent, adsorbate and adsorbent, and the thickness of an adsorbed layer) and conditions that can, within some limits, be chosen (such as the angle of Incidence 8 (counted with respect to the normal to the surface), the wavelength and the polarization). Hence, in principle, adsorbate properties are accessible. 

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... 

Ellipsometry is an optical technique that detects the change of the polarization state when light is reflected from a surface. For rather simple systems like transparent films on reflecting substrates, film thickness and refractive index can be determined with high accuracy. More complicated samples (e.g., multilayer structures or layers with a graded index of refraction on a reflective carrier) can be characterized with a sufficient set of independent experimental data obtained for multiple angles of incidence and/or multiple wavelengths (spectroscopic ellipsometry). With a liquid cell, ellipsometry can be performed also in aqueous environments. 

The basic idea or ellipsometry is depicted in Fig. 1. Collimated light passes first through polarization optics, which define its polarization state. The beam is then incident on the test surface, which may be immersed in a transparent medium such as an electrolyte solution or etching medium. The light reflected at the specular angle is then analysed by further polarization optics. 

Ellipsometry was in fact the earliest optical technique to be applied to the study of electrode processes. It involves the determination of the change in polarisation state of an obliquely incident light beam upon specular reflection at a surface. In order to fully define a monochromatic light beam it is necessary, in addition to knowing the frequency, amplitude, and direction of propagation, to include information about the electric and magnetic vectors which describe the polarisation state. Since these vectors are orthogonal and related in amplitude it is, in fact, only necessary to consider one of them, and it is the electric vector that is usually chosen. If this vector lies in a plane then the beam is said to be plane polarized, and further if this plane lies parallel to the plane of incidence at a surface the beam is said to be p-polarised, whereas a beam polarised in a plane perpendicular to the plane of incidence is referred to as s-polarised. For any beam it is possible to resolve the electric vector into its s and p components, and when these components are of the same frequency but different phase and amplitude the beam is said to be elliptically polarised. This name arises from the... 

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