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Polymer Engineering and Science, Vol.47, No.5, 545-550, 2007
Effect of the separation of Coulomb centers on the activation energy in electronic hopping transport: A reinterpretation in poly-N-vinylcarbazole
The effect of the separation of Coulomb centers in the activation energy for the electronic hopping transport of noncrystalline organic materials was studied. The theoretical analysis was carried out in absence of an applied electric field, using a simple one-dimensional model of two centers separated by a distance R. It was found that the height of the potential well is reduced by an amount e(2)/4 pi epsilon epsilon R-0 due to the overlapping of the Coulomb centers. This reduction defines an effective activation energy given by (Delta E)(0) - e(2)/4 pi epsilon epsilon R-0, where (Delta E)(0) is the height of the nonperturbed potential well. As an experimental application of this result, current-voltage characteristic in poly-N-vinylcarbazole at different temperatures was obtained, from which the conductivity at zero electric field was estimated by extrapolation to zero field in Poole-Frenkel plots. The correspondent activation energy was estimated from Arrhenius plots in the order of 0.65 eV. Because the carriers transport in this polymer occurs by hopping between the molecules of carbazole whose mean separation is in the order of 6.5 x 10(-10) m, the height of the nonperturbed Coulomb barrier of a single hopping site in this material would be really estimated in 1.18 eV.