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Fundamentals of Industrial Process Measurement & Control (FG05M)
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AI Fundamentals & Applications
Find Rare Books Book Value. One example of a rotating analyzer ellipsometer RAE is shown in Figure 5. The incident energy range for these instruments is usually between 1. The RAE requires a light source, a fixed polarizer, a rotating analyzer, and a detector. After reflection from a surface, the light upon emerging from the analyzer has a time varying intensity that is detected.
The mechanical parts of RAE have two optical arms, which can be rotated within the plane of incidence of light typically between 45 and 90 o. The light beam a Xe high pressure lamp is collimated by a lens before reaching the polarizer. An electric shutter is used in order to be able to subtract external light. Both polarizer and analyzer are a Glan-Taylor type - two calcite prisms coupled on their hypotenuse faces.
The analyzer is rotated at a frequency w using a motor. A telescope is used for optical alignment. The first element of detection is an optical fiber, which carries the signal without any interference from room light to a monochromador coupled with a PMT tube The RAE uses the Fourier analysis to obtain a and b Fourier coefficients , which describe the phase and relative amplitude of the ac component of the varying light flux transmitted from the analyzer.
The intensity waveform obtained from the ellipsometric measurement has a sinusoidal form given by: I 0 is the intensity that is obtained by averaging the measured intensity I over a number of analyzer revolutions, A t is the instantaneous azimuth of the analyzer transmission axis, and w is the angular frequency of the rotating element.
The Fourier coefficients are related to the ellipsometric parameters Y and D as follows 19 : where P is the polarization azimuth that is obtained by the maximum and minimum intensity of light upon emerging the rotating analyzer. Although oxidation of Si occurs naturally in air, high-quality oxides with controllable properties and thickness are usually prepared by the thermal oxidation of extremely clean single crystal Si wafers at o C As an example, ellipsometric results have indicated that an intermediate layer exists as SiO x 21,22 between an atomically abrupt Si and SiO 2 interface.
However, the influence of this intermediate layer is negligible for modeling of thicker films as compared with a few nanometers thick SiO x Since the penetration depths of light into different materials varies considerably from nm to cm, an overlayer with only 0.
This phenomenon has been explained for transparent and rough overlayers The incident light transverses a transparent overlayer and reflects at the layer-substrate interface. After multiple reflections, the light beam that enters the detector is retarded with respect to one of the component of polarized light. As such, if only the s -component is totally reflected, the p -component is retarded inasmuch as it travels further. Concerning a rough layer, the light beam is depolarized after reflections due to light scattering from imperfections.
In this case, complementary techniques are necessary for structural characterization.
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The use of spectroscopic immersion ellipsometry, however, improves the sensitivity of ellipsometry to interfaces by using a transparent liquid with a refractive index that matches to the overlayer eliminating its optical contribution This technique enhances the interface sensitivity for values of D due to the presence of a liquid by an order of magnitude, and effects such as microscopic roughness can be studied at large areas as compared with small areas analyzed by atomic force microscopy AFM , for example.
Optical parameters of bare substrates Glass Although glass is commonly used as a substrate for thin films, its transparency in the visible energy range, and internal reflections, are of concern for ellipsometry. Since the light penetration depth in glasses is high e. While the latter solution includes more parameters making it more difficult to obtain a fit, it is an option for thin glass substrates, which are difficult to be abraded without breaking. The values of D are very high close to o or small close to 0 o at incident angles q 0 that are below and above, respectively, to the Brewster angle, q B , usually q B is near to o for most glasses Because of the difficulty in measuring D near o and 0 o , the data analysis can be made at different values of q 0 using only the Y values and ignoring the D values Au Among several examples of substrates, Au is one of the most often used in ellipsometry, a choice that is justifiable mainly due to its high reflectivity and conductivity, and stability to oxidation as compared with other metals.
The dielectric function of Au can be split into two regions at a threshold energy of about 2. These regions correspond to intraband transitions below 2. The same behavior was observed for bulk Au films with thickness ranging from 10 to 25 nm and 50 to nm, even after film annealing 30, As these results have indicated, ellipsometry is a powerful technique for characterizing Au surfaces, particularly because contaminant overlayers are a common reality for this metal under air exposure. Another topic of current interest is the study of adsorption processes of sulfur-containing monolayers and polymers on pre-treated Au substrates.
Here we only mention that these systems can be readily studied using ellipsometry along with techniques such as cyclic voltammetry, AFM and X-ray photoelectron spectroscopy XPS. Polymers Ellipsometry has been applied to the study of numerous polymer films, in particular those that are electrochemically obtained on optically smooth electrodes The examples presented here are: study of the conversion reaction of a polysulfonium precursor into poly- p -phenylenevinylene PPV films; and optical properties of transparent and absorbing conducting polymer films.
The precursor route is the most common method used to prepare light-emitting PPV films For this methodology, cast, spin-coat, or Langmuir-Blodgett films of a soluble precursor, poly- p -xylylidene tetrahydrothiophenium chloride, PTHT, can be prepared on different substrates These films are converted into PPV films under vacuum at around o C by eliminating sulfide groups. The effects of the thermal treatment on the optical properties of PTHT films deposited on Au can be observed in Figure 8 In particular, since k is directly related to the absorption coefficient, films converted at higher temperatures present higher values of k.
The conversion process of PTHT into PPV can be followed using ellipsometry and more details can be obtained using structural characterization techniques. Considering the optical properties of a transparent polymer, the modeling is straightforward in a wide range of energy. The film used for exemplifying this analysis is a poly-methacrylate derivative with a pendent anthracene chomophore, poly methylmethacrylate- co anthracenyl-methylmethacrylate , MDCPAC The absorption spectrum of this polymer shows the typical bands of anthracene between to nm; at longer wavelengths, the film is transparent.
The thickness obtained for this film was The use of ellipsometry for characterizing absorbing films demands more effort from the ellipsometer user. One method used for obtaining L, n and k of absorbing polymer films is the multiple-sample analysis.
A thicker film with a known value of L as obtained by profilometry or AFM, for example is analyzed by ellipsometry. Since L is known, the optical properties of the film can be fitted, and a new database is created.
finahargangpo.tk However, this method assumes that the optical properties are identical for all samples, which is not always the case. Other type of analysis is to find a range of transparency of films. A unique solution for optical properties and L is found only for films that are semi-transparent at about 1. A relatively new method called Arwin-Aspnes A-A method 44 has been proposed for analyzing several materials including polymers.
Limitations are if the film and substrate have peaks in the same spectral region, or the substrate spectrum is featureless A solution for finding both optical properties and L of absorbing films depends much from sample to sample, and talent and dedication and luck! The description of models and results is in a simplified form, but the reader can find more details about theoretical and experimental parts in the cited references.
The applications of ellipsometry in Materials Science are uncountable, however, the domain of this technique demands time experience of the user. Erroneous conclusions can be made without proper data analysis. Besides, high-quality samples and complementary techniques of characterization are certainly helpful tools to obtain satisfactory results. Irene, E.
Bulletin , 20 , Drude, P.
Rothen, A. Hauge, P. A , 5 , Azzam, R.
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Press, Hecht, E. Fowles, G. Pedrotti, F. Hummel, R. Aspnes, D. Landauer, R. Woollam, J.