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

We quantify the degree of paracrystalline disorder in the π-π 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 π-π 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 ∼100 meV as determined through calculation. This finding agrees with previous device modeling and provides physical justification for the mobility edge model.

Figure 1

(a) Grazing incidence x-ray scattering of aligned ribbon phase PBTTT in the π-π stacking direction (circles). Fits used to isolate the π-π stacking peaks (0$k$0): the peaks in question are shown (solid lines), chain backbone related peaks (dotted lines), background (dashed-dotted line), and the complete fit (dashed line). Inset: The general packing motif of PBTTT, with the π-π stacking and lamellar stacking direction indicated. (b) The Fourier transforms of the isolated (010) and (020) peaks with the fit to the Warren-Averbach model. Inset: Normalized (0$k$0) peaks showing order-dependent broadening.

Figure 2

(a) Change in the position of the valence band maximum for a distorted PBTTT crystal as obtained with DFT calculations. (b) Slope of the exponential tails of the DOS obtained with the tight-binding model simulations. (c) Density of states for different values of paracrystalline disorder as determined by the simplified Hamiltonian. The energy $E_{\mathrm{VBM}}$ corresponds to the valence band maximum in a perfectly ordered crystalline region.