Can Mobility Negative Temperature Coefficient Be Reconciled with the Hopping Character of Transport in Conducting Polymers?

Poly(3,4-ethylenedioxythiophene) (PEDOT) is a conducting polymer that is used in a wide range of applications such as electronics, optoelectronics, and bioelectronics, where the fundamental understanding of the charge transport, and in particular of the electrical conductivity σ, is a prerequisite to develop new high performance devices. There are many reports in the literature where the conductivity of archetypical conducting polymer PEDOT doped with tosylate (PEDOT:TOS) exhibits a negative temperature coefficient, dσdT<0, which is strikingly different from the activated-type behavior with dσdT>0 commonly observed in most conducting polymers. This unusual temperature dependence was attributed to the transition from the photon-assisted hopping to the metallic behavior, which is however difficult to rationalize taking into account that this transition occurs at high temperatures. In order to understand the origin of this unusual behavior, multiscale mobility calculations in PEDOT:TOS for the model of hopping transport were performed, where changes in the morphology and the density of states (DOS) with the temperature were explicitly taken into account. The morphology was calculated using the Molecular Dynamics simulations, and the hopping rates between the chains were calculated quantum-mechanically following the Miller-Abrahams formalism. Our results reproduce the observed negative temperature coefficient, where however the percolation analysis shows that this behavior mainly arises because of the changes in morphology upon heating when the system becomes less ordered. This results in a less efficient π–π stacking and hence lower mobility in the system. We therefore conclude that experimentally observed negative mobility temperature coefficient in conducting polymers at high temperatures is consistent with the hopping transport, and does not necessarily reflect the transition to a metallic band-like transport. Based on our multiscale modeling, we introduce a simple Gaussian Disorder Model for the efficient mobility calculations, where the DOS broadening is a function of the temperature, and where the transfer integral distribution is a bimodal distribution evolving with temperature.