Single-step multiphonon emission model of spin-dependent exciton formation in organic semiconductors

The maximum efficiency in organic light-emitting diodes depends on the ratio, $r=k_S∕k_T$, where $k_S$ $\left(k_T\right)$ is the singlet (triplet) exciton formation rate. Several recent experiments found that $r$ increases with increasing oligomer length starting from a value $r\approx 1$ in monomers and short oligomers. Here, we model exciton formation as a single recombination step accompanied by multiphonon emission. Our model is based on two assertions. (i) More phonons are emitted in triplet formation than in singlet formation. (ii) The Huang-Rhys parameter for this phonon emission is smaller in long oligomers than in short ones. We justify these assertions based on recent experimental and theoretical data.