Impact of Tortuosity on Charge-Carrier Transport in Organic Bulk Heterojunction Blends

The impact of the tortuosity of the charge-transport pathways through a bulk heterojunction film on the charge-carrier mobility is theoretically investigated using model morphologies and kinetic Monte Carlo simulations. The tortuosity descriptor provides a quantitative metric to characterize the quality of the charge-transport pathways, and model morphologies with controlled domain size and tortuosity are created using an anisotropic domain growth procedure. The tortuosity is found to be dependent on the anisotropy of the domain structure and is highly tunable. Time-of-flight charge-transport simulations on morphologies with a range of tortuosity values reveal that tortuosity can significantly reduce the magnitude of the mobility and the electric-field dependence relative to a neat material. These reductions are found to be further controlled by the energetic disorder and temperature. Most significantly, the sensitivity of the electric-field dependence to the tortuosity can explain the different experimental relationships previously reported, and exploiting this sensitivity could lead to simpler methods for characterizing and optimizing charge transport in organic solar cells.

Figure 1

Cross-sectional images ($y\text{−}z$ plane) of morphologies with 8-nm average domain size. (a) an anisotropic morphology with horizontally elongated domains created with $\mathrm{\Delta }{J}_{xy}=0.1$ giving $\tau =1.15$, (b) an isotropic morphology created with $\mathrm{\Delta }{J}_{xy}=0$ giving $\tau =1.07$, and (c) an anisotropic morphology with vertically aligned domains created with $\mathrm{\Delta }{J}_{xy}=-0.05$ giving $\tau =1.05$.

Figure 2

(top) Domain anisotropy evolution as domains grow during phase separation and (bottom) the resulting average tortuosity of the charge-transport pathways.

Figure 3

Electric-field dependence of the normalized mobility in a neat film (left), a medium tortuosity blend (middle), and a high tortuosity blend (right) for different temperatures and energetic disorder values.

Figure 4

Fit parameters quantifying the deviation in the mobility behavior from the neat film due to the tortuosity of the BHJ morphologies with dashed lines to guide the eye.