Geminate Delayed Fluorescence by Anisotropic Diffusion-Mediated Reversible Singlet Fission and Triplet Fusion

Singlet fission (SF) occurs in molecular solids and is expected to increase the conversion efficiency of photons into electrons by transferring excitons or charges into low-band-gap semiconductors. The fundamental processes of SF and its reverse process of triplet fusion (TF) would have to be elucidated to characterize the effect of SF on the conversion efficiency. In situations in which TF occurs subsequent to SF within the same pair, a certain fraction of the excited singlets could be regenerated by TF and this may even happen repeatedly. Consequently, the excited singlets exhibit delayed fluorescence by geminate fusion of the triplets. In this study, we show that the exponent in the asymptotic power law decay of the geminate delayed fluorescence reflects the diffusional anisotropy. In molecular crystals, the difference in the ratio between the largest and smallest exciton diffusion constants can be orders of magnitude. By comparing the theoretical results and the fluorescence decay in tetracene and rubrene, we estimated the range of anisotropy in the triplet diffusion constants in these materials. We also show that the exponent of the power law decay changes as a function of time for certain values of the anisotropy ratio in the triplet diffusion constants.