Delocalization Enhances Conductivity at High Doping Concentrations

Many applications of organic semiconductors require high electrical conductivities and hence high doping levels. Therefore, it is indispensable for effective material design to have an accurate understanding of the underlying transport mechanisms in this regime. In this study, own and literature experimental data that reveal a power-law relation between the conductivity and charge density of strongly p-doped conjugated polymers are combined. This behavior cannot consistently be described with conventional models for charge transport in energetically disordered materials. Here, it is shown that the observations can be explained in terms of a variable range hopping model with an energy-dependent localization length. A tight-binding model is used to quantitatively estimate of the energy-dependent localization length, which is used in an analytical variable range hopping model. In the limit of low charge densities, the model reproduces the well-known Mott variable range hopping behavior, while for high charge densities, the experimentally observed superlinear increase in conductivity with charge density is reproduced. The latter behavior occurs when the Fermi level reaches partially delocalized states. This insight can be anticipated to lead to new strategies to increase the conductivity of organic semiconductors