Temperature-dependent electrical conduction in porous silicon: Non-Arrhenius behavior

A model for the temperature dependence of electrical conduction in a porous silicon (PS) layer is introduced based on the consideration that the onset of electrical conduction is dependent on the formation of a continuous network of conducting sites extending the entire thickness of a PS layer. At an arbitrary temperature, a PS layer consists of both unblocked and blocked sites (blocking energies are larger than thermal fluctuation energy). The fraction of unblocked sites increases with temperature. At low temperatures (T T2), a PS layer is mainly dominated by a continuous network of unblocked sites, while discrete blocked sites do not form any continuous network extending the entire thickness of a PS layer. Contrary to the prevalent views, the overall temperature dependence of the electrical conductivity of a PS is not always Arrhenius: it obeys a Vogel-Tammann-Fulcher (VTF) law at T > T2, becomes insulating at T T > T1. Both T1 and T2 are found to increase with the decrease silicon nanocrytallites sizes. The VTF behavior was derived using the mean-field approximation for Ising model and found to agree with experimental evidences.