Molecular geometry fluctuations and field-dependent mobility in conjugated polymers

Many conjugated polymers exhibit an electric field-dependent mobility of approximately the Poole-Frenkel form. We propose a model to describe transport in dense films of these materials in which thermal fluctuations in the molecular geometry modify the energy levels of localized electronic charged states in the material. Based on quantum chemistry calculations we argue that the primary restoring force for these fluctuations in molecular geometry is steric in origin, which leads to spatially correlated fluctuations in the on-site energy of the charged electronic states. The phenylene ring torsion, in PPV-like conjugated polymers, is an example of this kind of spatially correlated thermal fluctuation. Using a Master equation approach to calculate the mobility, we show that the model can quantitatively explain the experimentally observed field-dependent mobility in conjugated polymers. We examine typical paths taken by carriers and find that at low fields, the paths are three-dimensional, whereas at high fields the paths become essentially one-dimensional along the applied field. Thus, one-dimensional transport models can be valid at high fields but not at low fields. Effects of deep traps, the site energy correlation length, temperature, and asymmetric and small polaron rates are studied.