Hopping transport on a fractal: ac conductivity of porous silicon

Ben-Chorin, M., Möller, F., Koch, F., Schirmacher, W. and Eberhard, Marc A. 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.


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