Transport in correlated and uncorrelated random media, with applications to molecularly doped polymers

The commonly observed Poole-Frenkel field dependence; of the mobility of photo-injected charges in molecularly-doped polymers has been shown to arise from the spatially-correlated, Gaussian energy distribution of transport sites encountered by charges moving through the material. Experimental current-time transients obtained for molecularly-doped polymers exhibit universality with respect to electric field and a metal-insulator-like transition from non-dispersive to dispersive transport, features usually identified with multiple trapping models that assume an uncorrelated exponential distribution of trap energies. For materials that exhibit both sets of features the possibility arises that both kinds of disorder coexist. We study here, analytically and numerically, transport in a random medium containing two kinds of energetic disorder, i.e., a spatially correlated Gaussian component and a spatially uncorrelated exponential component associated with traps. The essential question addressed is the degree to which the uncorrelated component of disorder alters or destroys the Poole-Frenkel field dependence associated with the correlated component. In our hybrid model, the bulk mobility theoretically drops to zero when the typical trap depth exceeds the thermal energy, causing a metal-insulator-like transition. In a finite sample this corresponds to a transition to the dispersive transport regime, in which carriers can never equilibrate. For a finite 3D computational sample, the behavior above and below the transition point shows different finite size scaling with the number of sites in the lattice. In agreement with experimental observations, the Poole-Frenkel field dependence of the charge carrier mobility, and the associated temperature dependence observed in a trap-free sample, is unaffected as the transition to dispersive transport is approached from the conducting side --Abstract, page iii