Frequency scaling of ac hopping transport in amorphous carbon nitride

The dynamics of hopping transport in amorphous carbon nitride is investigated in both Ohmic and non-linear regimes. Dc current and ac admittance were measured in a wide range of temperatures (90 K<T<300 K), electric fields (F<2 x 10(5) V cm(-1)) and frequencies (10(2)<f< 10(6) Hz). The dc Ohmic conductivity is described by a Mott law, i.e. a linear ln(sigma(OHMIC)) vs T-1/4 dependence. The scaling of field-enhanced conductivity as In (sigma/sigma(OHMIC))=phi[F-S/T] with S approximate to 2/3, observed for F> 3 x 10(4) V cm(-1) over 5 decades in sigma(T,F), is explained by band tail hopping transport; the filling rate, Gamma(F)(E-DL), of empty states at the transport energy is obtained with a "filling rate" method which incorporates an exponential distribution of localized states, with a non-equilibrium band tail occupation probability f(E) parametrized by an electronic temperature T-EFF (F)As the ac frequency and temperature increase, the increase in conductance G is accurately described by Dyre's model for hopping transport within a random spatial distribution of energy barriers. This model predicts a universal dependence of the complex ac conductivity of the form sigma(ac) = sigma(0)[i omega tau/ln (1 + i omega tau)], where sigma(O) is the zero frequency ac conductivity and tau(T,F) is a characteristic relaxation time. We find that the inverse characteristic time 1 /tau can also be described by a Mott law. It is compatible with the filling rate Gamma(F)(E-DL) at the transport energy, which governs the dc conductivity; this rate increases with increasing de field, as more empty states become available in the band tail for hopping transitions. This "universal" scaling law for the ac conductance provides a scaling parameter K(T,F) = tau(T,F) sigma(T,F,omega = 0)/epsilon which is found to decrease with increasing electric field from 5 to 0. 5, depending weakly on temperature. Our band tail hopping model predicts a high-field value of K(T,F) smaller than the Ohmic value, under the condition (eF gamma(-1)/E degrees)<=(kT/E degrees)(1/4), where gamma(-1) is the localization radius and E degrees the disorder energy of the band tail distribution. (C) 2007 Elsevier B.V. All rights reserved.