Principles of Ellipsometry

Ellipsometry is a high-precision optical characterization technique, the potential of which has not yet been sufficiently exploited in polymer science. It is a rapid and nondestructive experimental method for the analysis of surfaces and thin films. Besides the determination of film thickness with high sensitivity ( 0.1 nm), optical parameters related to material properties can also be evaluated [1]. The facts that ellipsometric measurements can be performed under any ambient conditions, and require no special sample preparation procedures, provide a definite advantage over other surface science techniques [2—4]. 

In spectroscopic ellipsometry, (i/ , A) spectra are measured by changing the wavelength of light. In general, the spectroscopic ellipsometry measurement is carried out in the ultraviolet (UV)-visible region, although measurements in the infrared (IR) region have also been performed. 

The Ip and A measured from ellipsometry are defined from the ratio (p) of reflection coefficients for p- and s-polarization (tp, Tj)  

This is the principal equation of ellipsometry, where the reflection coefficients are a function of the complex refractive indices (N) of the materials, the film 

Characterization of Polymer Blemk Miscibility, Morphology, and Interfaces, First Edition. 

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The principles of ellipsometry have been set forth in sec. 1.7.10b. For the ellipsometric thickness of an interlayer over which the index of refraction n changes with position we gave the following Drude equation... 

The system described here is based on the principles of ellipsometry (47). Figure 8 gives a block diagram of our experimental setup. The Psi-meter consists of a 2 mW helium-neon polarized laser source, a quarter wave retardation plate to generate circularly polarized light, a synchronously rotating polarizer to... 

In order to calculate the optical generation rates in the organic absorbers (see appendix 1), it is necessary to determine the complex refractive index n = n + ik of all layers. The most useful method to obtain this data is spectroscopic ellipsometry, which allows us to determine the real part n and imaginary part k of the refractive index. The general measurement principle of ellipsometry is to measure the polarization of an output beam after the polarized input beam has interacted with the sample. From the change in polarization we derive the optical properties of the layer by fitting the measured output polarization to a model of the optical response of the material [144]. 

Actually, the principle of ellipsometry was established one hundred years ago, but... 

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. 

R.M.A. Azzam, N.M. Bashara Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977) E. Echt Optics (Addison-Wesley, Reading, 1990) M. Born, M. Wolf Principles of Optics (Pergamon, Oxford, 1970)... 

Consider surfaces that are inert and may be made (molecularly) smooth, so that, optically speaking, they may be treated as Fresnel surfaces. Mica, certain polished glasses, quartz and silicon wafer surfaces may belong to this category. For such well-defined systems the optical techniques introduced in sec. 1.7.10 come to mind reflectometry, ellipsometry, and (to study the dynamics) fluorescence recovery after photobleaching (FRAP). The principles of these techniques have been outlined in that section. 

Independent of all the efforts to implement ellipsometry to pulse-heating systems, a second branch of measurements has been jointly developed at NRLM-NMIJ [17] and NIST [101] to obtain the total hemispherical emittance. The principle of this technique is to interrupt the heating process of a pulse calorimeter and to create a short steady-state temperature condition by using the pyrometer as a feedback device. The energy input to maintain this steady-state equals the total radiative losses and thus can be related to the total hemispherical emittance, assuming that no convection occurs during the short steady-state time. 

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... 

In the first two Sections, the basics of the Brewster angle ellipsometry and the operation principles of the photoelastic modulator (PEM) based ellipsometer will be overviewed. In the following, three different ellipsometric studies of the solid-liquid crystal interface wiU be presented. 

Infrared Imaging and Mapping for Biosensors, Fig. 3 (a) Principle of IR synchrotron mapping ellipsometry. Due to reflection at the sample, the polarization of the radiation is changed. For example, the incident linearly polarized radiation becomes elliptically polarized. The sample Is moved by a two-dimensional mapping table, and a spectrum Is taken for every probed spot. The elllpsometiic parameters defined by the quantity p, which is the ratio of the complex reflection coefficients Tp and r, are measured for every spot. A is the phase shift... 

In principle matrix methods analogous to the ones discussed in the section about neutron reflectivity can be applied to calculate ellipsometric angles for an arbitrary refractive index profile (Lekner 1987) and analytical approximations have also been developed (Charmet and de Gennes 1983). In practice the use of ellipsometry to obtain fine details of the structure of interfaces at the level of tens of angstrom units is likely to be difficult and to require extreme care. 

The principle of the reflectance spectroscopy technique is to shine a monochromatic light beam, usually polarised in a plane parallel or perpendicular to the plane of incidence, at an electrode surface at a known angle of incidence and to record the intensity of the reflected beam as a function of either wavelength, potential or time. The data obtained are then compared to model calculations made using the same three layer model as is used in ellipsometry, i.e. bulk electrode/interfacial region/bulk solution. These calculations are based on the Fresnel equations [19] and assume that all phases are isotropic. 

In this chapter, we will provide an overview of principles, measurement techniques, data analysis procedures for ellipsometry, and introduce the related applications of ellipsometry, especially in the field of stoichiometry. 

This chapter introduces the principles, measurement techniques, data analysis procedures for ellipsometry, and provides the related applications of ellipsometry, esp>ecially in the field of stoichiometry. As examples, we give an overview of the various eUijjsometiy applications in stoichiometry for surface and interfaces, alloys and compwsites, etc. It s shown that ellipsometry, either alone or in combination with other techniques, is now a mature technique which has been successfully applied to large variety applications. There will be a bright future for ellipsometry as its combine accuracy, speed, and proven reliability with the huge advantage of nondestructive characterization. 

Some of the basic facts of optics pertaining to ellipsometry will be presented briefly in this and the following subsections. Detailed treatment of the optical principles and the derivation of the equations for the reflection and the refraction of light can be found in standard textbooks on optics or electromagnetic radiation. A short summary of optical principles for ellipsometry was presented in a previous review on ellipsometric optics with special reference to electrochemical systems by the present author. ... 

Since dp is at most a few micrometers in the IR region, an ATR spectrum provides information regarding the sample s surface. Thus, the ATR method is especially applicable to the case of thin macromolecular materials such as fibers and fabrics, and also to thin polymer layers (especially coatings and laminates) which often fail to yield useful transmission spectra. Other sophisticated methods that are useful for examining thin polymer layers include infrared ellipsometry IRE) and infrared reflection absorption spectroscopy IRRAS) the principles of these techniques are briefly described in Section 2.2.5.1. 

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). 

A chemical sensor is a device that transforms chemical information into an analytically useful signal. Chemical sensors contain two basic functional units a receptor part and a transducer part. The receptor part is usually a sensitive layer, therefore a well founded knowledge about the mechanism of interaction of the analytes of interest and the selected sensitive layer has to be achieved. Various optical methods have been exploited in chemical sensors to transform the spectral information into useful signals which can be interpreted as chemical information about the analytes [1]. These are either reflectometric or refractometric methods. Optical sensors based on reflectometry are reflectometric interference spectroscopy (RIfS) [2] and ellipsometry [3,4], Evanescent field techniques, which are sensitive to changes in the refractive index, open a wide variety of optical detection principles [5] such as surface plasmon resonance spectroscopy (SPR) [6—8], Mach-Zehnder interferometer [9], Young interferometer [10], grating coupler [11] or resonant mirror [12] devices. All these optical... 

Thus, in principle, one can obtain the complex index of refraction from the upper left-hand quarter of the optical tensor M= [My, (i,j = 1,..., 3)]. We now explain how these optical constants can be derived from ellipsometry. 

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