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Hopping transport on a fractal: ac conductivity of porous silicon

M. Ben-Chorin, F. Möller, and F. Koch

W. Schirmacher and M. Eberhard

  • Physik-Department E16, Technische Universität München, D-85747 Garching, Germany

  • Physik-Department E13, Technische Universität München, D-85747 Garching, Germany

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Phys. Rev. B 51, 2199 – Published 15 January, 1995

DOI: https://doi.org/10.1103/PhysRevB.51.2199

Abstract

We have measured the frequency dependence of the conductivity and the dielectric constant of various samples of porous Si in the regime 1 Hz to 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 σ’ changes from an ω1/2 dependence to being proportional to ω. 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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Phys. Rev. B 51, 2199– Published 15 January, 1995
  • Received 2 September 1994

© 1995 American Physical Society

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