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Charge density dependent nongeminate recombination in organic bulk heterojunction solar cells

Apparent recombination orders exceeding the value of two expected for bimolecular recombination have been reported for organic solar cells in various publications. Two prominent explanations are bimolecular losses with a carrier concentration dependent prefactor due to a trapping limited mobility, and protection of trapped charge carriers from recombination by a donor--acceptor phase separation until reemission from these deep states. In order to clarify which mechanism is dominant we performed temperature and illumination dependent charge extraction measurements under open circuit as well as short circuit conditions at poly(3-hexylthiophene-2,5-diyl):[6,6]-phenyl-C$_{61}$butyric acid methyl ester (P3HT:PC$_{61}$BM) and PTB7:PC$_{71}$BM (Poly[[4,8-bis[(2-ethylhexyl)oxy]benzo[1,2-b:4,5-b']dithiophene-2,6-diyl][3-fluoro-2-[(2-ethylhexyl)carbonyl]thieno[3,4-b]thiophenediyl]]) solar cells in combination with current--voltage characteristics. We show that the charge carrier density $n$ dependence of the mobility $μ$ and the recombination prefactor are different for PC$_{61}$BM at temperatures below 300K and PTB7:PC$_{71}$BM at room temperature. Therefore, in addition to $μ(n)$ a detrapping limited recombination in systems with at least partial donor--acceptor phase separation is required to explain the high recombination orders.