Structural origin of gap states in semicrystalline polymers and the implications for charge transport

We quantify the degree of paracrystalline disorder in the \ensuremath{\pi}-\ensuremath{\pi} stacking direction of crystallites of a high performing semicrystalline semiconducting polymer with advanced x-ray line-shape analysis. Using density functional theory calculations to provide input to a simple tight-binding model, we obtain the density of states of a system of \ensuremath{\pi}-\ensuremath{\pi} stacked polymer chains with increasing amounts of paracrystalline disorder. We find that, for an aligned film of PBTTT, the paracrystalline disorder is 7.3%. This type of disorder induces a tail of trap states with a breadth of \ensuremath{\sim}100 meV as determined through calculation. This finding agrees with previous device modeling and provides physical justification for the mobility edge model.