The effect of correlations on the non-ohmic behavior of the small-polaron hopping conductivity in 1D and 3D disordered systems

Abstract

According to percolation theory the investigation of charge transport in disordered systems is equivalent to the study of the possibility of the passage of the carriers through a random network of impedances which interconnect the different lattice sites. When the site energies are not the same, the energy of a site affects the incoming as well as the outgoing impedances connected to the given site and this gives rise to correlations between neighboring impedances. This new condition characterizes the transport process and imposes the evaluation of the average number of sites accessible by a bond from a given site for all possible configurations of sites that satisfy the percolation condition. The generalized molecular crystal model, appropriate for the study of small-polaron hopping transport in disordered systems, and the Kubo formula permit the evaluation of these impedances. Taking correlations into account, theoretical percolation considerations applicable to one-dimensional and three-dimensional disordered systems, lead to analytical expressions for the temperature and electric field dependence of the DC conductivity at high (multi-phonon-assisted hopping) and low (few-phonon-assisted hopping) temperatures. The theoretical analysis reveals the effect of correlations on the non-ohmic behavior of the small-polaron hopping conductivity and permits the evaluation of the maximum hopping distance. Quantitative estimates of this effect are presented comparing the theoretical results, including correlations with those ignoring them, previously reported, applying them to recent experimental data for a wide temperature range and from low up to moderate electric fields.

Density of states and extent of wave function: two crucial factors for small polaron hopping conductivity in 1D

“…Figure 9(I) presents the conductivity for different densities of states N 0 = 10 9 -10 11 eV −1 m −1 as a function of the applied electric field. For low up to moderate electric fields the conductivity follows nicely the F 2 -behaviour, as we expected from the analytical expression previously reported [24,26]. Specifically, when the condition F 2 /g(T ) ≪ 1 is satisfied, i.e.…”

“…These conclusions were in a qualitative agreement with theoretical results referred to variable range hopping [22,23,25]. Dimakogianni and Triberis [26] also investigated the effect of correlations on the non-ohmic behaviour of the small polaron hopping conductivity in 1D and 3D disordered systems. They concluded that the inclusion of correlations results to a much stronger dependence of the conductivity on the magnitude of the applied electric field compared to the uncorrelated case.…”

“…From these results we realize that the T −1/2 -behaviour of σ [26] holds for low up to moderate electric fields. For the smaller densities of states, i.e.…”

“…In total, in this specific example, augmenting DOS by two orders of magnitude increases the conductivity by approximately tens of orders of magnitude. From these results we realize that the T −1/2 -behaviour of σ [26] holds for low up to moderate electric fields. For higher values of F the conductivity deviates from the T −1/2 -behaviour as T decreases and this deviation appears to be larger the stronger the electric field is.…”

“…F = (5 × 10 3 -1 × 10 8 ) Vm −1 . Again, we depict our results as a function of T −1/2 in order to compare them with the analytically obtained formula ln σ ∝ T −1/2 which holds for low up to moderate electric fields and was previously obtained by two of us [26] following a different theoretical treatment and taking into account the effect of correlations, namely…”