Diffusion-limited recombination in polymer-fullerene blends and its influence on photocurrent collection

We propose a model of charge recombination in interpenetrating two-phase systems, and apply it to blends of poly [2-methoxy-5-${(3\mathrm{}}^{\prime }{,7\mathrm{}}^{\prime }$-dimethyloctyloxy)-1-4-phenylene vinylene], (MDMO-PPV) and 1-(3-methoxycarbonyl)-propyl-1-phenyl-$\mathrm{}(6,6)\mathrm{}{\mathrm{C}}_{61}$ (PCBM). The main features of the model are that charge recombination is rate limited by the diffusion of positive polarons towards PCBM anions; that the density of polaron states contains a tail of deep traps which serve to delay recombination; and that polarons move between localized states largely by means of thermally activated hopping. The model is implemented using Monte Carlo simulations and is applied to reproduce the observed dependence of charge recombination kinetics on laser intensity, temperature, and background illumination, detected by transient optical spectroscopy. Modeling the experimental data yields a density of deep localized states in MDMO-PPV of order ${10}^{17}{\mathrm{cm}}^{-3},$ and a charge carrier lifetime of order 10 μs under solar illumination. An alternative model based on direct tunneling is ruled out by comparison with the observed temperature dependence. The recombination model is incorporated into a one-dimensional calculation of short-circuit photocurrent in a solar cell as a function of temperature and light intensity. We conclude that charge recombination is sufficiently slow not to limit photocurrent collection under solar intensities at short circuit, and propose that space charge effects may be responsible for the observed sensitivity of photocurrent to temperature.