Nanocomposites and nanomaterials

Evolution of low-frequency dispersion in solids 
with change of temperature 
Fliunt O. Ye.
Faculty of Electronics and Computer Technologies, Ivan Franko National University of Lviv, Dragomanov Str., 50, Lviv-79005, Ukraine 
E-mail: Orest.Fliunt@lnu.edu.ua

Strong by many orders of magnitude increasing of both dielectric constant and dielectric loss toward low frequencies is termed low-frequency dispersion (LFD)  or quasi-DC conductivity. Frequency spectra of dielectric constant and loss in the region dominating by LFD obey power fractional law with small value of exponent n. In the time domain discharging current very weakly depends on time obeying power law t-n. Many experimental works giving dielectric frequency spectra in low and infra-low regions confirm dominating of LFD on dielectric spectra in different class of dielectric and semiconducting materials, often even without direct indication. LFD represents partial case of universal fractional power law (jω)-(1-n), where j is imaginary unit and ω is circular frequency, with small side values of exponent from range 0<n<1. In the case of LFD frequency dependence of dielectric loss is very close to frequency dependence of dielectric loss caused usual DC current, but with the important difference, that it is accompanied with accumulation of anomalously high amount of electrical charge. 
In this work a model of temperature behavior of LFD or q-DC conductivity has been proposed. The model is based on distribution of relaxation times of effective dipoles, formed by elementary hopping charge localization over wide temporal range. The model gives possibility to explain revealed transition of LFD from low to high-temperature regime. In high temperature regime LFD shows thermally activated Arrhenius law shift with temperature independent shape in log-log scale. Calculated values of activation energy of LFD obtained from frequency shift of spectra with changing of temperature are close to experimental values. Drastic temperature change of exponent n from values above 0.4 to small values below 0.25 in narrow transition region of LFD has been explained. The low-resistivity GaSe layered crystals show high-temperature regime of LFD with n= 0.19 and activation energy Ea= 0.19 eV, nevertheless dominating below 150 K temperature, that is in accordance with proposed model. Thereby, gap of experimental values of exponent n can be explained by thermally activated behavior of distributed effective dipoles under the condition of their continuous distribution according to power law.