Energy-Temporal Pathways of Free-Charge Formation at Organic Bilayers: Competition of Delocalization, Disorder, and Polaronic Effects

We investigated the charge separation process in organic semiconductor bilayers from the moment of creation of a donor exciton to the time when all charge pairs have either recombined or reached external contacts. The system was modeled using a one-dimensional microscopic Hamiltonian that includes the effects of carrier delocalization, electron-hole interaction, static disorder, and carrier-phonon interaction. Transition rates between excitonic states were modeled using modified Redfield approach which takes into account polaronic effects by exact treatment of diagonal exciton-phonon interaction. An efficient numerical scheme was developed that enabled us to obtain the time dependence of energy-resolved populations of relevant exciton states on a time scale as long as 1 mu s. Our results indicated that charge separation proceeds via the so-called cold pathway in which donor excitons convert to relaxed charge-transfer excitons which further transform to the states of separated charges. We found that for lower disorder strengths the time scale for conversion of donor excitons to charge transfer excitons is similar to(1-10) ps, while further separation to free charges takes place on the time scale reaching similar to 1 ns. These time scales are extended for larger disorder strengths because diffusion of donor excitons to the interface and transport of separated charges toward external contacts are slowed down. We also found that charge separation yield has a rather weak dependence on electron phonon interaction strength.