The mobility in disordered molecular systems with energies given by a charge-induced dipoles interaction

We investigate the field dependence of the mobility in a model for a disordered molecular system containing spatial and energetic disorders. In this model we assign an isotropic polarizability to each site and take the site energies to be the site polarization energies, the interaction energy of a charge in the given site with the induced dipoles in the neighboring sites. This model was shown, in a previous publication, to contain short-ranged energetic correlations and we show in this work that this correlation produces a charge mobility proportional to the exponential of the square root of the applied field, the Poole-Frenkel dependence observed in various disordered organic materials, over a significant range of fields. We present an expression for the field dependence of the mobility in terms of the average intersite separation and of the isotropic polarizability of the electronic states, the two model parameters.