“…Deviations of experimental observations from Langevin theory were reported to occur in two ways: (i) deviation from second-order dependence on charge carrier density and (ii) discrepancy in the rate constant, each of which will be addressed below: - Indeed, in many polymer–fullerene based devices, the charge-decay dynamics probed by charge extraction technique , and transient absorption spectroscopy , at open-circuit voltage , was found to exhibit approximately a third-order dependence on ρ( t ). Therefore, in order to be consistent with the experimental data, the rate constant (β) in the Langevin model has to depend on charge density (or, equivalently, on t ). , This third-order dependence of the BMR rate on charge density has been suggested to arise as a result of either a carrier lifetime dependence on charge density, , recombination via an exponential tail of density of states (DoS), − or carrier trapping in an inhomogeneous distribution of localized states. ,, Also, it was suggested that traps can sometimes enhance the dissociation of geminate pairs into free carriers but can act as recombination centers as well, leading to Shockley–Read–Hall (SRH) recombination dynamics. −
- Several experimental observations ,− indicate that even when second-order kinetics is operative, the experimental rate constant (β exp ) is smaller than that estimated according to the Langevin model, β L , by two to four orders of magnitude. Previous reports have attributed this overestimation to 2D recombination in the lamellar structure of conjugated polymer, charge carrier concentration gradient within the device, local dielectric constant difference, slow dynamics of charge carrier with smaller mobility, , delocalization of opposite charges in an encounter complex, phase separation, domain purity, and back electron transfer to triplet excitons concurrent with redissociation of charge-transfer (CT) states back to free carriers. ,
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