Effect of traps' adjacency on the electric field dependence of mobility in organic systems

In some organic materials, varying the finite distance between adjacent carrier traps modifies the Coulomb potential around each trap, resulting in a more complex field-dependence of mobility, differing from（but not incompatible with） the usually considered relationship of ln μ∝E^1/2, a relationship which has been successfully explained by the Poole–Frenkel effect. To investigate the influence of the adjacency of traps, a model system is proposed, which consists of two traps separated by distance α. Our numerical calculation shows that with increasing α, the dependence of mobility on the electric field changes from linear to exponential. Moreover, beyond a certain large α, i.e., as the distance to the nearest trap approaches infinity, the proposed model is essentially the same as the Poole–Frenkel effect. The proposed model accounts for the effect of the energy barrier shape, especially the effect of the location of the potential-energy maximum, a phenomenon which is not accommodated in the Poole–Frenkel model. Because the model assumes the Coulomb interaction between the adjacent traps, it applies to those charged traps which may exist in organic materials for various reasons.