Encounter-Limited Charge-Carrier Recombination in Phase-Separated Organic Semiconductor Blends

The theoretical effects of phase separation on encounter-limited charge carrier recombination in organic semiconductor blends are investigated using kinetic Monte Carlo simulations of pump-probe experiments. Using model bulk heterojunction morphologies, the dependence of the recombination rate on domain size and charge carrier mobility are quantified. Unifying competing models and simulation results, we show that the mobility dependence of the recombination rate can be described using the power mean of the electron and hole mobilities with a domain-size-dependent exponent. Additionally, for domain sizes typical of organic photovoltaic devices, we find that phase separation reduces the recombination rate by less than one order of magnitude compared to the Langevin model and that the mobility dependence can be approximated by the geometric mean.

Figure 1

(a) Hole concentration transients and (b) time-dependent mobilities for $d=15\mathrm{nm}$ with varying hole hopping rates.

Figure 2

The effect of the domain size on the mobility dependence of the simulated recombination rate coefficient compared to the Langevin, harmonic mean, and minimum mobility models.

Figure 3

Depiction of the two extreme recombination regimes: (a) very small domain size and (b) very large domain size. One charge is depicted with a dotted circle around it that represents the Coulomb capture radius ($R_C$). The other charge is shown with a green path that illustrates one of the most likely pathways to enter the capture sphere.

Figure 4

Fitted values for the prefactor ($f_1$) and the power mean exponent ($g$) as a function of the domain size.