Fractal simulation of the resistivity and capacitance of arsenic selenide

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 ∝ ω^1−3/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.