Temperature dependence of electrical conductivity

Abstract

It has been shown that the temperature dependence of electrical conductivity for widely different classes of materials can be reproduced by use of the derivative of the Fermi function, G (Ê, T); as the probability density function in place of the Fermi function, f(Ê, T) [1]. The G(Ê, T) function has been found to be applicable to low-dimensional synthetic metallic conductors, semi-conductors, and vitreous insulators. The temperature dependence of electrical conductivity is simulated by curve-fitting the G(Ê, T) function to experimental conductivity versus temperature data in terms of the parameter, E ̂ = E − E F is the energy of the bottom of the conduction band and E F is the Fermi energy. It is shown that Ê, which lies in the band gap region, corresponds to experimentally observable absorption of energy in compounds such as (TMTSF) 2 PF 6, and single crystalline germanium. The quantity Ê can be considered as a sub-band gap activation energy. The derivation of the G(Ê, T) function is briefly discussed. The standard derivation of the Fermi function should yield a cumulative probability function rather than the probability density function.