Hopping transport on a fractal: ac conductivity of porous silicon

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

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)2199-2213
Number of pages15
JournalPhysical Review B
Issue number4
Publication statusPublished - 15 Jan 1995


  • frequency dependence
  • porous Si
  • conductivity
  • universal scaling law


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