The Effects of Doping on Transport in Organic Electronics: Analyzing the Dopant-Induced Disorder

Organic electronic materials, specifically conjugated polymers, are a cost-effective and environmentally friendly alternative to inorganics. However, their low intrinsic conductivity means they must be doped to increase the number of free carriers. Characterizing the effects of doping on organic thermoelectrics has proven to be a long-standing problem. Doping introduces both structural and energetic changes to the polymer, changing the shape of the electronic Density of States (DOS) through the creation of band tails and widening the DOS, resulting in a type of energetic disorder termed dopant-induced disorder (DID). The shape of the DOS resulting from doping can be captured through two parameters: the width of the DOS, termed energetic disorder, and the shape of the DOS, which is quantified by a shape parameter p, which can take on values of 1 for an exponential DOS to 2 for a Gaussian one. In our previous work, we showed that DID causes energetic disorder to increase while the p value simultaneously decreases from 2 to below 1 in heavily doped polymers, implying heavy tails. The resulting carrier mobility is impaired by the presence of heavy tails and the deep trap states in them. Doping then simultaneously increases DID, affecting the shape of the DOS, but fills the deepest tail states first, partially countering their effect.<br/><br/>To decouple the influences of each of these effects, we fix the shape of the DOS to simulate doping without DID. We then compute both conductivity and thermoelectric Seebeck coefficient at each DOS and carrier concentration using a numerical simulation of phonon-assisted carrier hopping between localized states. The simulation iteratively solves the Pauli master equation with Miller-Abrahams hopping rates. The iteration converges on an out-of-equilibrium distribution function, from which carrier and energy currents are computed, from which we extract conductivity and Seebeck coefficient, respectively. The Seebeck coefficient is a convenient and readily measurable proxy for the carrier concentration as it scales with the position of the Fermi level in the DOS. The Seebeck vs conductivity plot thus reveals the tradeoff induced by doping and captures the impact of the DOS on transport. We find distinct behavior of the Seebeck vs conductivity relation across doping regions, and these behaviors can be described in terms of carrier concentration in conjunction with the key parameters of the DOS: its width (energetic disorder) and shape parameter. The distinct regions on the Seebeck-conductivity curve come from surprisingly simple relationships between doping and several transport parameters, which also allow us to provide qualitative expressions for difficult-to-measure quantities like carrier concentration and carrier-dependent mobility. Ultimately, this analysis clearly displays the underlying effects of doping without the simultaneous obfuscation of DID, allowing us to gain a clearer understanding of the effects of both influences. This work will impact the design of polymer-dopant complexes for reaching higher carrier mobility in future organic electronics.