Hopping transport on a fractal: ac conductivity of porous silicon

Ben-Chorin, M.; Möller, F.; Koch, F.; Schirmacher, W. and Eberhard, Marc A. (1995). Hopping transport on a fractal: ac conductivity of porous silicon. Physical Review B, 51 (4), pp. 2199-2213.


We have measured the frequency dependence of the conductivity and the dielectric constant of various samples of porous Si in the regime 1 Hz-100 kHz at different temperatures. The conductivity data exhibit a strong frequency dependence. When normalized to the dc conductivity, our data obey a universal scaling law, with a well-defined crossover, in which the real part of the conductivity sigma' changes from an sqrt(omega) dependence to being proportional to omega. We explain this in terms of activated hopping in a fractal network. The low-frequency regime is governed by the fractal properties of porous Si, whereas the high-frequency dispersion comes from a broad distribution of activation energies. Calculations using the effective-medium approximation for activated hopping on a percolating lattice give fair agreement with the data.

Publication DOI: https://doi.org/10.1103/PhysRevB.51.2199
Divisions: Engineering & Applied Sciences > Electrical, electronic & power engineering
Engineering & Applied Sciences > Adaptive communications networks research group
Uncontrolled Keywords: frequency dependence,porous Si,conductivity,universal scaling law
Published Date: 1995-01-15


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