Dipolar lattice model of disorder in random media analytical evaluation of the gaussian disorder model

Abstract

One contribution to the distribution of site energies (DOS) in a random medium with localized charge-transport sites is the electrostatic potential of randomly placed and randomly oriented dipolar species nearby. This contribution has recently been modelled using a lattice on which a certain fraction (f) of the points is occupied by dipoles with random orientations. Simulations indicated that the DOS is close to a Gaussian distribution as long as f is not too small. This fact was taken to justify the application of the Gaussian disorder model (GDM) of charge transport in situations where dipolar contributions to the disorder are important. Analytical results on this model are presented here, including an expression for the r.m.s. width of the DOS that differs considerably from the previous result. While the central portion of the DOS is well approximated by a Gaussian distribution in many cases, the low- and high-energy tails generally deviate from this distribution. A simple principle is introduced to evaluate the effect of these deviations on the mobility of charge carriers. The resulting corrections to the predictions of the GDM are sometimes large. Low concentrations of large dipoles probably lead to non-equilibrium transport on the time scale of conventional experiments.