Dispersive aspects of the high-field hopping mobility of molecularly doped solids with dipolar disorder

The time-of-flight mobility of photoinjected charges in molecularly doped polymers obeys a Poole–Frenkel law, μ ∝ exp($\gamma \sqrt E $), which is commonly viewed as arising from hopping transport among sites with a large degree of energetic disorder. Recent theoretical investigations have focused on long-range correlations that characterize site energies when the dominant mechanism for energetic fluctuations is the interaction of charge carriers with randomly-oriented permanent dipoles of the dopant and host polymer. An exact calculation of the steady-state drift velocity v_d for a one-dimensional system with correlated dipolar disorder predicts a Poole–Frenkel law similar to that observed. In order to investigate another feature commonly observed in the high-field measurements, namely, the anomalous dispersion of the current–time transients, we have performed an exact calculation of the field-dependent diffusion constant D for the same dipolar disorder model. In the bulk limit we obtain an expression D = (KT/e) ?v_d/?E that generalizes the normal Einstein relation and predicts a strongly field-dependent diffusion constant. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2803–2809, 1997