Theory of singlet exciton yield in light-emitting polymers

Abstract

The internal electroluminescent quantum efficiency of organic light emitting diodes is largely determined by the yield of singlet excitons formed by the recombination of the injected electrons and holes. Many recent experiments indicate that in conjugated polymer devices this yield exceeds the statistical limit of 25% expected when the recombination is spin-independent. This paper presents a possible explanation for these results. We propose a theory of electron-hole recombination via inter-molecular inter-conversion from inter-molecular weakly bound polaron pairs (or charge-transfer excitons) to intra-molecular excitons. This theory is applicable to parallel polymer chains. A crucial aspect of the theory is that both the intra-molecular and inter-molecular excitons are effective-particles, which are described by both a relative-particle wavefunction and a center-of-mass wavefunction. This implies two electronic selection rules. (1) The parity of the relative-particle wavefunction implies that inter-conversion occurs from the even parity inter-molecular charge-transfer excitons to the strongly bound intra-molecular excitons. (2) The orthonormality of the center-of-mass wavefunctions ensures that inter-conversion occurs from the charge-transfer excitons to the lowest branch of the strongly bound exciton families, and not to higher lying members of these families. The inter-conversion is then predominately a multi-phonon process, determined by the Franck-Condon factors. These factors are exponentially smaller for the triplet manifold than the singlet manifold because of the large exchange energy. As a consequence, the inter-conversion rate in the triplet manifold is significantly smaller than that of the singlet manifold, and indeed it is comparable to the inter-system crossing rate. Thus, it is possible for the singlet exciton yield in conjugated polymers to be considerably enhanced over the spin-independent recombination value of 25%

Magnetic-Field Dependence of the Electroluminescence of Organic Light-Emitting Diodes: A Competition between Exciton Formation and Spin Mixing

“…This is in agreement with the claim of Segal et al that in PPV the S fraction is lower than 25% [14]. The result appears to be at odds with theoretical considerations about a faster formation rate of S than T excitons [24][25][26], based on different ionic characters and/or energies of S and T excitons. It is our assumption, however, that the step decisive for the final S fraction occurs in the very early stage of exciton formation, when these considerations may not yet apply.…”

Singlet Generation from Triplet Excitons in Fluorescent Organic Light-Emitting Diodes

“…These polarons are spin 1/2 particles. When oppositely charge polarons capture, they initially form some intermediate state, held by their mutual columbic potential well [50], before relaxing into an exciton (which can then emit). Before capture, the polarons are uncorrelated and so their spin states have random orientation with respect to one another.…”

Long-time deviations from exponential decay for inverse-square potentials

“…At this point we refrain from attempting a very general approach valid for the plethora of unstable systems with exponential decay at intermediate times. In particular, the process of excitonic decay in dissolved organic molecules is poorly understood, and present models explain only qualitatively the processes that lead to their emission spectra [21,22,23]. Hence we take refuge in a physical domain where full or sufficiently accurate analytical and numerical methods are available, namely, the decay of a wavepacket in a spherically symmetric potential well, in a given partial wave.…”