Mathematical foundations of information processing methods for dielectric spectroscopy of thin films

A. G. Karpov ; V. A. Klemeshev ; V. V. Trofimov

Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 4 (2015), pp. 13-26

Résumé

Complex permittivity contains information about the structure and functional properties of the dielectric material. Therefore, the method of spectral measurement and analysis permittivity can serve as a useful tool for research and diagnostics. The original method for computing the real and imaginary parts of permittivity is proposed to process dielectric measurement data in real time. It may be implemented in a compact computing device included in the process control system. This method is based on the use of quadrature formulas for the calculation of integrals. The real and imaginary parts of the permittivity calculated for the frequency values arranged in a geometric progression. Optical properties of the specimen are directly related to the permittivity. The mathematical model to determine the absorption and refractive indices of thin films on a transparent substrate is proposed on the basis of the said relation. Determination of optical properties and thickness of thin films is incorrect inverse problem. The two-step algorithm based on the steepest descent method is proposed to solve it. The method of selecting the initial parameter values is proposed. More stable solutions are obtained for the initial value corresponding to the minimum transmittance in the short wavelength range, when interference effects play an insignificant role. The study of the optical properties of thin films efficient emitters of interest in practical applications was performed. Refs 19. Figs 3.

Détail

Keywords: mathematical model, permittivity, thin film, optical properties.

Bibliographie

[1] Hyde P. J., “Wide-frequency-range dielectric spectrometer”, Proc. IEE, 117:9 (1970), 1891–1901

[2] Klemeshev S. A., Petrov M. P., Shalygin A. K., Trusov A. A., Voitylov A. V., Vojtylov V. V., “Electro-optical effects in disperse systems in strong electric fields of arbitrary shape”, Colloids and Surfaces A: Physicochemical and Engineering Aspects, 456 (2014), 114–119 | DOI

[3] Macdonald J. R., Brachman M. K., “Linear-System Integral Transform Relations”, Rev. Mod. Phys., 28 (1956), 393–422 | DOI | MR | Zbl

[4] Karpov A. G., Egorov N. V., “Automated dielectrometer”, Instruments and Experimental Techniques, 1999, no. 6, 63–67 (In Russian)

[5] Almazov A. A., Egorov N. V., Reznikov M. A. et al., “The microprocessor system of timekeeping dielectric relaxation”, Methods and tools for the diagnosis of bearing capacity of composite articles: Practice of creating and applying, v. 2, 2 ed., ed. V. A. Lotishchenko, Zinatne Publ., Riga, 1991, 125–131 (In Russian) | MR

[6] Karpov A. G., Egorov N. V., Almazov A. A., “Analysis of the surface status information in real time”, The Journal of Surface Investigation. X-ray, Synchrotron and Neutron Techniques, 1999, no. 10, 22–27 (In Russian)

[7] Karpov A. G., Egorov N. V., “Basic elements of information expert system for parameter identification of dielectric response”, The Journal of Surface Investigation. X-ray, Synchrotron and Neutron Techniques, 2005, no. 5, 69–76 (In Russian) | MR

[8] Gavrilenko V. I., Grekhov A. M., Korbutiak D. V., Litovchenko V. G., Optical properties of semiconductors, a guide, Naukova dumka Publ., Kiev, 1987, 608 pp. (In Russian)

[9] Kondratov V. E., Optics photocathodes, Nauka Publ., M., 1976, 208 pp. (In Russian)

[10] Sizelove J. R., Love III J. A., “Analysis of Translucent and Opaque Photocathodes”, Appl. Optics, 6 (1967), 356–357 | DOI

[11] Siushe Zh.-P., Chemical physics of semiconductors, Van Nostrand, London, 1965, 197 pp.

[12] Kiselev V. P., Chaldyshev V. A., “The optical properties of the crystal Na$_2$KSb”, Semiconductors, 17 (1983), 587 (In Russian)

[13] Tikhonov A. N., Goncharskii A. V., Stepanov V. V., Iagola A. G., Regularizing algorithms and a priori information, Nauka Publ., M., 1987, 180 pp. (In Russian)

[14] Babadzanjanz L., Voitylov A., “Numerical methods for inverse problems in electrooptics of polydisperse colloids”, Colloids and Surfaces B: Biointerfaces, 56 (2007), 121–125 | DOI

[15] Kossel D., Deutscher K., Hirshberg K., “Interference photocathodes”, Advances in electronics and electron physics, 28a (1969), 419–431 | DOI

[16] Szozyrlowski J., “Determination of optical constants of real thin films”, J. Phys. D: Appl. Phys., 11 (1978), 583–594 | DOI

[17] Tiurin Iu. N., Makarov A. A., Statistical analysis of the data on the computer, Infra-M Publ., M., 1998, 528 pp. (In Russian)

[18] Dai Y. H., Yuan Y., “Convergence properties of the Fletcher–Reeves method”, The IMA Journal of Numerical Analysis, 16 (1996), 155–164 | DOI | MR | Zbl

[19] Kiselev V. P., Konev V. V., Chaldyshev V. A., “Secondary electron transport in photoemission from films”, Soviet Physics Journal, 28:6 (1985), 517–520 | DOI