Abstract
Analytical expressions for calculating the tensor of the effective permittivity of a matrix-type heterogeneous medium with inclusions of random ellipsoidal shape, which are a small deviation from the average spheroidal shape, are obtained. The orientations of the inclusions are probabilistically distributed; rotation group representations are used for their consideration. It is shown that the developed method is a generalization of the Maxwell–Garnett approximation for the given medium type. Based on this method, the frequency- induced dielectric properties of porous silicon are simulated in the range of 103–108 Hz.
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References
A. G. Fokin, Sov. Tech. Phys. 16, 849 (1971).
A. G. Fokin, Sov. Tech. Phys. 18, 44 (1973).
T. D. Shermergor, Theory of Elasticity of Micro-Inhomogeneous Media (Nauka, Moscow, 1977) [in Russian].
V. B. Yakovlev, V. V. Bardushkin, I. V. Lavrov, et al., Izv. Vyssh. Uchebn. Zaved., Elektron.,No. 3, 7 (2013).
V. I. Kolesnikov, V. B. Yakovlev, V. V. Bardushkin, I. V. Lavrov, A. P. Sychev, and E. N. Yakovleva, Dokl. Phys. 58, 379 (2013).
S. Giordano, Int. J. Eng. Sci. 43, 1033 (2005).
S. Giordano, J. Electrost. 64, 655 (2006).
E. N. Ivanov and I. V. Lavrov, Oboron. Kompleks Nauch.-Tekh. Progressu Rossii.,No. 1, 73 (2007).
I. V. Lavrov, Ekol. Vestn. Nauch. Tsentrov Chernomor. Ekon. Sotrudn.,No. 1, 52 (2009).
I. Lavrov, Dielectric and Conductive Properties of Inhomogeneous Media with Texture (LAP Lambert Academic, Saarbr¨¹cken, 2011) [in Russian].
C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1998; Mir, Moscow, 1986).
I. E. Protsenko, O. A. Zaimidoroga, and V. N. Samoilov, J. Opt. A: Pure Appl. Opt. 9, 363 (2007).
M. V. Borovkov and T. I. Savyolova, Normal Distributions on SO(3) (Mosk. Inzhen. Fiz. Inst., Moscow, 2002) [in Russian].
I. M. Gelfand, R. A. Minlos, and Z. Ya. Shapiro, Representations of the Rotation and Lorentz Groups and their Applications (Pergamon, Oxford, 1963; Fizmatgiz, Moscow, 1958).
Physical Values, the Handbook, Ed. by I. S. Grigor’ev and E. Z. Meilikhov (Energoatomizdat, Moscow, 1991) [in Russian].
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Original Russian Text © M.I. Zavgorodnyaya, I.V. Lavrov, A.G. Fokin, 2015, published in Izvestiya vysshikh uchebnykh zavedenii. Elektronika, 2014, Vol. 109, No. 5, pp. 3–14.
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Zavgorodnyaya, M.I., Lavrov, I.V. & Fokin, A.G. Analytical approach to calculating the effective dielectric characteristics of heterogeneous textured materials with randomly shaped inclusions. Semiconductors 49, 1718–1726 (2015). https://doi.org/10.1134/S1063782615130163
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DOI: https://doi.org/10.1134/S1063782615130163