Carrier-density and field-dependent charge-carrier mobility in organic semiconductors with correlated Gaussian disorder

Recently, it has been demonstrated that for organic semiconductors with a Gaussian density of states (DOS) and with on-site energies that are spatially uncorrelated the hopping mobility of charge-carriers can be strongly carrier-density-dependent (extended Gaussian disorder model, EGDM). In the literature, it has been argued that for some materials, the on-site energies are actually spatially correlated. In this paper, we develop a full description of the mobility in a correlated Gaussian DOS (extended correlated disorder model, ECDM), using a master-equation method. We show that the mobility is less strongly carrier-density-dependent than in the EGDM, but that the field dependence is more pronounced. The field dependence is found to be described by a Poole-Frenkel factor, as has been deduced from empirical analyses of experimental data, but only in a limited field range. As an example of an application, we present a comparison between analyses of the current–voltage–temperature J(V,T) characteristics of a poly-phenylene-vinylene (PPV) based hole-only device using the EGDM and the ECDM. For both cases, excellent fits can be obtained, but with the EGDM a more realistic value of the intersite distance is found than in the case of the ECDM. We view this as an indication that site-energy correlations do not play an important role in PPV.