Frequency scaling of ac hopping transport in amorphous carbon nitride

Abstract

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 × 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( σ OHMIC) vs T − 1/4 dependence. The scaling of field-enhanced conductivity as ln( σ / σ OHMIC) = ϕ[ F S / T] with S ≈ 2/3, observed for F > 3 × 10 4 V cm − 1 over 5 decades in σ( T, F), is explained by band tail hopping transport; the filling rate, Γ 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 σ ac = σ(0)[ iωτ / ln(1 + iωτ)], where σ(0) is the zero frequency ac conductivity and τ( T, F) is a characteristic relaxation time. We find that the inverse characteristic time 1 / τ can also be described by a Mott law. It is compatible with the filling rate Γ F ( E DL) at the transport energy, which governs the dc conductivity; this rate increases with increasing dc 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) = τ( T, F) σ( T, F, ω = 0) / ɛ 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 ( eFγ − 1 / E°) ≤ ( kT / E°) 1/4, where γ − 1 is the localization radius and E° the disorder energy of the band tail distribution.