Why the apparent order of bimolecular recombination in blend organic solar cells can be larger than two: A topological consideration

The apparent order δ of non-geminate recombination higher than δ = 2 has been evidenced in numerous experiments on organic bulk heterojunction (BHJ) structures intensively studied for photovoltaic applications. This feature is claimed puzzling, since the rate of the bimolecular recombination in organic BHJ systems is proportional to the product of the concentrations of recombining electrons and holes and therefore the reaction order δ = 2 is expected. In organic BHJ structures, electrons and holes are confined to two different material phases: electrons to the acceptor material (usually a fullerene derivative) while holes to the donor phase (usually a polymer). The non-geminate recombination of charge carriers can therefore happen only at the interfaces between the two phases. Considering a simple geometrical model of the BHJ system, we show that the apparent order of recombination can deviate from δ = 2 due solely to the topological structure of the system.