Carrier screening controls transport in conjugated polymers at high doping concentrations

Abstract

Transport properties of doped conjugated polymers (CPs) have been widely analyzed with the Gaussian Disorder Model (GDM) in conjunction with hopping transport between localized states. These models reveal that even in highly doped CPs, a majority of carriers are still localized because dielectric permittivity of CPs is well below that of inorganic materials, making Coulomb interactions between carriers and dopant counter-ions much more pronounced. However, previous studies within the GDM did not consider the role of screening the dielectric interactions by carriers. Here we implement carrier screening in the Debye-H\"uckel formalism in our calculations of dopant-induced energetic disorder, which modifies the Gaussian density of states (DOS). Then we solve the Pauli Master Equation using Miller-Abrahams hopping rates with states from the resulting screened DOS to obtain conductivity and Seebeck coefficient across a broad range of carrier concentrations and compare them to measurements. Our results show that screening has significant impact on the shape of the DOS and consequently on carrier transport, particularly at high doping. We prove that the slope of Seebeck coefficient vs electric conductivity, which was previously thought to be universal, is impacted by screening and decreases for systems with small dopant-carrier separation, explaining our measurements. We also show that thermoelectric power factor is underestimated by a factor of $\sim10$ at higher doping concentrations if screening is neglected. We conclude that carrier screening plays a crucial role in curtailing dopant-induced energetic disorder, particularly at high carrier concentrations.