Ellipsometry, as defined by R. A. Azzam and N. M. Bashara in Ellipsometry and Polarized Light, published by North-Holland Physics Publishing, 1987 edition, is an optical technique for the characterization and observation of events at an interface or film between two media and is based on exploiting the polarization transformation that occurs as a beam of polarized light is reflected from or transmitted through the interface or film. Two factors make ellipsometry particularly attractive: (1) its essential non-perturbing character (when the wavelength and intensity of the light beam are properly chosen) hence its suitability for in-situ measurements, and (2) its remarkable sensitivity to minute interfacial effects, such as the formation of a sparsely distributed sub-monolayer of atoms or molecules. The great diversity of situations in nature and man-made systems where interfaces and films play an important role has lead to the application of ellipsometry in a wide spectrum of fields such as physics, chemistry, materials and photographic science, biology, as well as optical, electronic, mechanical, metallurgical and biomedical engineering.
Ellipsometry is sometimes referred to as polarimetry, generalized polarimetry, or complete polarimetry. The latter names are more common especially when interaction with the sample involves transmission of light through the bulk of the sample and the polarization transformation depends on bulk sample properties as well as surface properties and films.
Azzam and Bashara further state in their aforementioned book that ellipsometry can be generally defined as the measurement of the state of polarization of a polarized vector wave. Ellipsometry is generally conducted in order to obtain "information" about an "optical system" that modifies the state of polarization. In a general scheme of ellipsometry, a polarized light-wave is allowed to interact with an optical system under investigation. The interaction changes the state of polarization of the wave. Measurement of the initial and final states of polarization, repeated for an adequate number of different initial states, leads to the determination of the law of transformation of polarization by the system as described, for example, by its Jones or Mueller matrix. To extract more fundamental information about the optical system than is conveyed by its Jones or Mueller matrix, it is necessary to examine light-matter interaction within the system by the electromagnetic theory of light. In other words, it is necessary to study the details of the internal polarization-modifying processes that are responsible for the external behavior as described by the measured Jones or Mueller matrix of the system.
An operational diagram of a general ellipsometer arrangement as shown in Ellipsometry and Polarized Light is shown in FIG. 1 of the drawings. A beam from a suitable light source (L) is passed through a variable polarizer (P) to produce light of known polarization. This light interacts with the optical system (S) under study and its polarization is modified. The modified state of polarization at the output of the system is measured (analyzed) by a polarization analyzer (A) followed by a photodetector (D). If the light interaction with the sample under study varies with wavelength, a monochromatic light source must be used or a means of isolating quasimonochromatic portions (with known wavelengths) of the light must be provided.
One way in which the light wave can interact with the optical system is by being reflected from a surface of the optical system (S). This reflection causes the state of polarization to be changed abruptly. Such a change can be explained using the Fresnel reflection coefficients for the two linear polarizations parallel (p) and perpendicular (s) to the plane of incidence. Another way the light wave can interact with the optical system is transmission through the material of the optical system. When the polarization state change depends on the angle of interaction of the light beam and the sample under study, as for example with reflection from (or oblique transmission through) a sample, the incident light should be as collimated as possible so only a single angle of incidence is measured at one time.
Azzam and Bashara explain that, since the time of Drude, reflection ellipsometry has been recognized as an important tool for the study of surfaces and thin films. Among the many useful applications of ellipsometry are: (1) measurement of the optical properties of materials and their frequency dependence (wavelength dispersion), the materials may be in the liquid or solid phase, may be optically isotropic or anisotropic, and can be either in bulk or thin-film form; (2) monitoring of phenomena on surfaces that involve either the growth of thin films starting from a submonolayer (e.g., by oxidation, deposition, adsorption or diffusion of impurities), or the removal of such films (e.g., by desorption, sputtering or diffusion); and (3) measurement of physical factors that affect the optical properties such as electric and magnetic fields, stress or temperature.
A description of the principles of ellipsometry, and a discussion of the reflection process, the measurement process, and data reduction can be found in "Ellipsometry A Century Old New Technique" by Dr. Richard F. Spanier, Industrial Research, September 1975, which article is incorporated herein by reference. A diagram of a conventional ellipsometer from Dr. Spanier's article is shown in FIG. 2B. Many additional types of automated and manually operated ellipsometers are known in the art. Dr. Spanier states in the article that ellipsometry involves the measurement of tan .psi., the change in the amplitude ratio upon reflection, and .DELTA., the change in the phase difference upon reflection. The quantities .DELTA. and .psi. are functions of the optical constants of the surface, the wavelength of the light used, the angle of incidence, the optical constants of the ambient medium, and for film-covered surfaces, the thicknesses and optical constants of the films.
Thus, in order to be able to compute the information about a sample's properties which cause a polarization state change in the reflected light, it is necessary to convert the polarization state change together with the angle of incidence and wavelength into physical properties of the sample according to some mathematical model. Properties such as refractive index, thickness, and absorption index of films on a surface or the optical constants of bare surfaces can be computed, for example. Similarly, in the case of transmitted light, properties such as the birefringence of the bulk material can be computed. Each ellipsometric measurement of polarization state change yields one value for .DELTA. and one value for .psi.. Thus, at best, two of the properties of the surface (whether or not film covered) or two properties of the bulk (in the case of transmitted light) can be computed if values for the remaining properties are known from other sources.
Frequently, in the art, one can compute more of these properties, of film covered surfaces, for example, if one has values for .DELTA. and values for .psi., at more than one angle of incidence; preferably, at many angles of incidence. Theoretically, one property can be computed for each independent .DELTA. and one property can be computed for each independent .psi. measured but it is better to overdetermine the unknowns with extra values of .DELTA. and .psi.. Accordingly, it is advantageous to measure as many angles of incidence on a particular sample as possible. However, this has not been done frequently in the past because it is so cumbersome to get the data by making separate successive measurements at each angle through the use of a scanning technique.
It has also been proposed to provide ellipsometers with a plurality of duplicate setups with multiple beams all of different, discrete angles in order to simultaneously obtain information for light at different angles of incidence. These ellipsometers essentially combine several ellipsometers of the known type and use them simultaneously. This technique is limited in the number of angles that can be simultaneously measured because of the need for a plurality of ellipsometers, which can add considerably to the initial cost and maintenance of such a system.
The following U.S. patents are cited of interest for their disclosures relating to ellipsometry and ellipsometers.
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