Abstract
The temperature dependences of the ac resistivity R and ac capacitance C of arsenic selenide were measured more than four decades ago [V. I. Kruglov and L. P. Strakhov, in Problems of Solid State Electronics, Vol. 2 (Leningrad Univ., Leningrad, 1968)]. According to these measurements, the frequency dependences are R ∝ ω−0.80±0.01 and ΔC ∝ ω−0.120±0.006 (ω is the circular frequency and ΔC is measured from the temperature-independent value C 0). According to fractal-geometry methods, R ∝ ω1−3/h and ΔC ∝ ω−2+3/h, where h is the walk dimension of the electric current in arsenic selenide. Comparison of the experimental and theoretical results indicates that the walk dimensions calculated from the frequency dependences of resistivity and capacitance are h R = 1.67 ± 0.02 and h C = 1.60 ± 0.08, which are in agreement with each other within the measurement errors. The fractal dimension of the distribution of conducting sections is D = 1/h = 0.6. Since D < 1, the conducting sections are spatially separated and form a Cantor set.
Similar content being viewed by others
References
V. I. Kruglov and L. P. Strakhov, in Problems of Solid State Electronics (Leningrad State University, Leningrad, 1968), Vol. 2, p. 80 [in Russian].
M. Pollak and T. Geballe, Phys. Rev. 192, 1742 (1961).
J. S. Blakemore, Solid State Physics (Cambridge University Press, Cambridge, 1985; Mir, Moscow, 1988).
R. White and T. Geballe, Long-Range Order in Solids (Academic, New York, 1979; Mir, Moscow, 1982).
S. S. Krylov and V. A. Lyubchich, Fiz. Zemli, No. 12, 14 (2002) [Izv., Phys. Solid Earth 38 (12), 1006 (2002)].
L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 1: Mechanics (Nauka, Moscow, 1973; Butterworth-Heinemann, Oxford, 1976).
G. Paladin and A. Vulpiani, in Proceedings of the Sixth International Symposium on Fractals in Physics, Trieste, Italy, July 9–12, 1985, Ed. by L. Pietronero and E. Tosatti (Elsevier, New York, 1986; Mir, Moscow, 1988).
A. Margolina, “Fractals in Physics,” in: Proceedings of the Sixth International Symposium on Fractals in Physics, Trieste, Italy, July 9–12, 1985, Ed. by L. Pietronero and E. Tosatti (Elsevier, New York, 1986; Mir, Moscow, 1988).
V. K. Balkhanov and Yu. B. Bashkuev, in Proceedings of the Sixth International Symposium on Electromagnetic Compatibility and Electromagnetic Ecology (EMC & EME), St. Petersburg, Russia, 2005 (St. Petersburg, 2005), p. 265.
V. K. Balkhanov, Yu. B. Bashkuev, V. I. Kozlov, and V. A. Mullayarov, Zh. Tekh. Fiz. 79(1), 152 (2009) [Tech. Phys. 54 (1), 151 (2009)].
V. K. Balkhanov and Yu. B. Bashkuev, Élektromagn. Volny Élektron. Sist., No. 6, 39 (2006).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.K. Balkhanov, Yu.B. Bashkuev, 2010, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2010, Vol. 137, No. 3, pp. 530–534.
Rights and permissions
About this article
Cite this article
Balkhanov, V.K., Bashkuev, Y.B. Fractal simulation of the resistivity and capacitance of arsenic selenide. J. Exp. Theor. Phys. 110, 469–472 (2010). https://doi.org/10.1134/S106377611003009X
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S106377611003009X