Tunneling conduction, variable range

In(frequency) curves the value of the exponent is estimated to be 0.9 for the last two cases, which shows a possibility of variable range hopping phenomena [84]. This quantum mechanical tunneling or correlated barrier hopping is based on the pair approximation in which the motion of the carriers is contained within a pair of sites. If the DC and AC conductivities arise from the same hopping mechanism, the pair approximation cannot be applied [85]. Scher and Lax [86] proposed the continuous random network [65]. The frequency-dependent conductivity is given by... 

In the following sections several models elaborated for conducting disordered systems are presented most of them are based on variable range hopping (VRH) and/or on tunneling mechanisms. One has to stress that usually it is not easy to determine which model best describes the conductivity mechanism in the given investigated material, since experimental data (e.g., temperature dependence of the dc conductivity) can often be fitted by several theoretical equations. Therefore, there is a need to analyze the different experimental implications of the models. 

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