| Abstract Scope |
Rational design of organic semiconductors, as well as thorough modeling of structure and charge transport in devices requires a detailed understanding of molecular packing and structural imperfections. It is often assumed that charge transport in films of both small molecule and polymer semiconductors is limited by defects at grain boundaries and by inter-grain morphology. While chemically the intra-grain packing motif can be tuned, it is still assumed that transport within a grain is much more efficient than between grains. Thus, little attention is paid to the degree of ordering in the crystalline regions. To this end, we measure the intra-crystalline order in high performance organic semiconductors. We utilize an X-ray peak shape analysis method developed by Warren and Averbach (1950), and incorporate a rigorous error propagation routine to establish confidence bounds in the results. This analysis yields information on grain size, and static, cumulative disorder called paracrystalline disorder. With this tool we investigate three prototypical organic semiconductors: the high performing n-type polymer P(NDI2OD-T2) (Polyera ActivInkN220), p-type polythiophene PBTTT, and p-type small molecule TIPS-Pentacene. By analyzing the paracrystalline disorder of three different materials in a variety of crystallographic directions, new insight is gained regarding the nature of molecular packing and transport in this class of materials. For the first time, we quantify the degree of paracrystalline disorder in a charge transport relevant (crystallographic) direction. We find that PBTTT π-stacking has a large, 7.3% paracrystalline disorder (where <1% is considered highly crystalline, and 15% is considered amorphous). For a high performing (up to 1 cm<sup>2</sup>/Vs) polymer that is so often regarded as highly ordered due to its terraced topography and strongly diffracting lamellar stacks, the π-stacking direction is surprisingly disordered. We find that such high disorder dominates peak broadening, and we formulate a disorder-induced correlation length. Furthermore, by modeling the band structure of a collection of π-stacked PBTTT segments with different degrees of paracrystalline disorder, we show that, compared to the ideal completely ordered microstructure, the experimentally determined disorder introduces a tail of localized states which can act as traps for charge transport. These calculations provide physical justification for the mobility edge model. |