Triplet Exciton Fusion

The two entangled triplet excitons created via singlet exciton fission have an energy that is about half that of the singlet exciton in rubrene. Because of this, the two triplet states can undergo fusion: If they have the right spin combination they can meet and re-create the singlet state. This newly created singlet exciton is in principle the same as the originally photoexcited singlet exciton, and will then behave in the same way, maybe emitting a photon, but most likely undergoing fission again.

Because of the high efficiency of singlet exciton fission in rubrene, photoexcitation in this material generally results in a dominant population of triplet excitons. The presence of triplet exciton fusion then has several remarkable effects, each one of them interesting for different reasons:

• When the excitation density is high enough, the vast majority of the fluorescence that we see from rubrene is due to triplet exciton fusion. The fluorescence quantum yield is then intensity dependent, because at low intensities only the photogenerated singlet states will contribute photons, while at higher intensities fusion from of the triplet generated by fission can also lead to fluorescence, and effect that is increasingly likely at higher excitation densities.
• A population of triplet excitons becomes visible because of the photons that are emitted upon a successful triplet-triplet meeting that results in photon emission. This can be used under localized steady-state illumination to visually observe the triplet exciton diffusion length.
• After pulsed excitation, the fluorescence due to triplet fusion will appear later, and will decay following characteristic power-law behavior that depends on the excitation density.
• When the two triplets that generated in a fission event meet each other again, we have the possibility of geminate fusion, which can lead to an oscillation in the fusion probability that creates quantum beats in the time-dependence of the fluorescence signal after pulsed illumination.

This crystal got defects implanted in the top part. This decreased the lifetime of triplet excitons and resulted ina lower fluorescence quantum yield under steady-state illumination.

Fluorescence yield at different excitation rates (expressed as singlets created per time and volume). A pristine rubrene crystal (blue) increases its yield by more than a factor of 10 as soon as the illumination intensity passes a few mW per square cm. In a crystal in which defects have been implanted the yield remains low until much higher intensities are reached.

The effect of triplet exciton fusion on luminescence yield in rubrene is dramatic. One can ask oneselves how is it possible that just a low density of defects in rubrene can dramatically alter the fluorescence quantum yield, or even sometimes the spectrum of the emitted fluorescence. Normally, if one has an ensemble of molecules and one swaps out 1 every 1000 molecules or so with a defective one, the normal molecules still determine the emission. But in rubrene, the dominant contribution to the emission can be the fusion of triplet excitons created by singlet fission, and these triplet exciton can diffuse around in the crystal. Any defect that destroys a triplet exciton that interacts with it would then effectively shorten the lifetime of triplet excitons and their ability to interact with each other. This in turn destroys that part of the luminescence that comes from triplet fusion, which can be more than an order of magnitude larger than that portion of the luminescence that is only due to the photoexcited singlet states.

Fluorescence dynamics after pulsed excitation in rubrene and in tetracene. At higher excitation intensities a clear power law with an exponent of -2 becomes visible, a sign of bimolecular effects: triplet-triplet fusion in a dense triplet population. At some point after long time, the density of the excitons becomes so small that bimolecular effects can be neglected and the decay becomes exponential. The exponential decay time for the fluorescence is 50 microseconds, corresponding to an average lifetime for an individual triplet exciton of 100 microseconds.

When the fluorescence is excited by short pulses, the fluorescence comes initially, for times shorter than the singlet exciton fission time, from the radiative recombination of the photoexcited singlet states. But the dominance of fission then implies that all the fluorescence in the nanosecond time scale and later originates from triplet exciton fusion. In practice, at sufficiently high initial excitation density, the vast majority of photons comes out at later times, and originate from that large “reservoir” of energy that is the triplet exciton population. One can say that the triplet exciton density is high enough that an individual triplet is free to collide with many other triplet excitons during its lifetime, a process that continues until one lucky collision creates that singlet state that then recombines radiatively rather than once again undergoing fission.

Something similar happens when looking at the photoconductivity that is induced by a short pulse exposure to light that creates an initial population of singlet excitons. These excitons immediately create a triplet exciton population by fission, and at low excitation densities this triplet population decays exponentially with a typical triplet exciton lifetime of 100 microseconds. Now, a triplet exciton is so tightly bound that it can certainly not dissociate when it is inside intrinsic rubrene. However, there are reasons to believe that such a triplet exciton can dissociate when it interacts with certain defects that are mostly localized near the surface of rubrene crystals. This then means that a high mobility hole can be generated by a triplet exciton as long as there are triplet excitons available. The consequence is that a pulsed photoconductivity measurement in rubrene is characterized by no immediate appearance of a photoconductivity. Instead, the photoconductivity grows with time as triplet excitons dissociate at defects, but stops growing once the triplet exciton population is depleted. This effectively gives a photoconductivity that has a rise time of about 100 microseconds, given by the average lifetime of a triplet exciton. We recognized the necessary presence of a “reservoir” that emptied itself into photoconductivity in our early papers on rubrene (the first three in the list below), but at the time there was still too little evidence of the required large singlet exciton fission efficiency in rubrene, and the required large triplet exciton lifetime, which is why those papers only talk generically about a reservoir of states that leads (slowly) to free charge carriers.

Coming back to the fluorescence, it is interesting to study it in the limit where it is guaranteed that any signal we detect comes from “geminate” fluorescence: the photons originating by the fusion of the two members of a the triplet exciton pair that were created by singlet fission. We found that this geminate fluorescence can be a useful tool to open a window on triplet exciton transport, the way that the triplet excitons move around in the crystal. This is because the two triplet excitons diffuse independently, each with its own random walk inside the crystal lattice, and they must meet again by chance in order for fusion to even be attempted. Therefore, the geminate fluorescence signal depends on the product of the probability of the two triplets meeting again and the probability of fusing once they meet. But since the probability of hopping in different directions varies by a large amount in an organic crystal, the two excitons in the pair initially must diffuse in only one dimension, along a molecular column, and only later, after many unsuccessful attempts, will they have a good chance to jump out of the molecular column in which they were born and start diffusing in two dimensions. In the same vein, true diffusion in three dimensions will happen on much later time scales.

In work supported by the DOE Office of Science (Office of Basic Energy Sciences), we have shown that by observing the power-law dynamics of geminate fluorescence one can identify the time-scales over which the excitons diffuse with a given dimensionality, and also determine the probability per unit time that characterizes hopping in different directions. More details are in the 2021 paper in the list below, which also discusses how these changes in the dimensionality of diffusion can be an important factor in determining the efficiency of the singlet fission process: If the two excitons have even a small probability of undergoing annihilation instead of just fusion, then a long period of one-dimensional diffusion after being born will basically doom them to death, because there is a 100 percent probability to meet again in one-dimensional diffusion. If this manner of transport lasts too long, then the two excitons may meet many many times, and their probability of surviving many encounters will rapidly go to zero.

Further work with geminate fusion fluorescence is on-going. It turns out that it can be used to evaluate the persistence of spin-entanglement in the triplet-pair generated by singlet exciton fission. By observing the quantum beats created by quantum interference when the spin-entangled exciton meet again and fuse, it has now become possible to find out lots of things about how triplet excitons move in a crystal lattice. Such things as the ability of triplet exciton to localize on a certain family of the molecules in the crystal lattice (in rubrene, there are two inequivalent molecules in the unit cell), and the average time a triplet exciton needs to hop between these two families. As an example, we have recently found that triplet excitons indeed move between inequivalent molecules with an average time of the order of 100-200 ps that corresponds to when triplet diffusion goes from one-dimensional to two-dimensional. We also found that this hopping leads to a stochastic dephasing of the spin-wavefunction during triplet exciton transport, which leads to a global decoherence in a triplet-pair population despite the fact that individual triplet pairs still remain entangled. While this transport-induced dephasing (TID) effect leads to the complete suppression of any quantum beats, we have shown how the application of a magnetic field along specific symmetry directions completely removes TID and resuscitates the quantum beats. By tuning the magnetic field direction a few degrees away from these specific directions that nullify TID it is then possible to tune the amount of global decoherence and measure how much time it takes for the quantum beats to be destroyed by it. It is this ability that ultimately allows to measure such things as a 100 ps hopping time for the triplet excitons. There is much more about this here . This work supported by the DOE Office of Science (Office of Basic Energy Sciences).

More information:

• H. Najafov, I. Biaggio, V. Podzorov, M. F. Calhoun, M. E. Gershenson, “Primary Photoexcitations and the Origin of the Photocurrent in Rubrene Single Crystals,” Phys. Rev. Lett. 96, 0566004 (2006).
• H. Najafov, B. Lyu, I. Biaggio, V. Podzorov, “Investigating the origin of the high photoconductivity of rubrene single crystals,” Phys. Rev. B 77, 125202 (2008).
• P. Irkhin and I. Biaggio, “Direct imaging of anisotropic exciton diffusion and triplet diffusion length in rubrene single crystals,” Phys. Rev. Lett. 107, 017402 (2011).
• A. Ryasnyanskiy and I. Biaggio, “Triplet exciton dynamics in rubrene single crystals,” Phys. Rev. B 84, 193203 (2011).
• I. Biaggio, P. Irkhin, “Extremely efficient exciton fission and fusion and its dominant contribution to the photoluminescence yield in rubrene single crystals,” Appl. Phys. Lett. 103(26), 263301 (2013).
• P. Irkhin, I. Biaggio, T. Zimmerling, M. Döbeli, B. Batlogg, “Defect density dependent photoluminescence yield and triplet diffusion length in rubrene,” Appl. Phys. Lett. 108(6), 063302 (2016).
• Eric A. Wolf, Drew M. Finton, Vincent Zoutenbier, Ivan Biaggio, “Quantum beats of a multiexciton state in rubrene single crystals,” Appl. Phys. Lett. 112, 083301 (2018).
• Eric A. Wolf, Ivan Biaggio, “Geminate exciton fusion fluorescence as a probe of triplet exciton transport after singlet fission,” Phys. Rev. B Letters 103 (20), L201201 (2021).
• Gerald Curran III, Zachary Rex, Casper Xallan Wilson, Luke J. Weaver, Ivan Biaggio, Ivan Biaggio, “Persistence of spin coherence in a crystalline environment,” Phys. Rev. Lett. 133, 056901 (2024).

See also:

• Light, Excitons, and transport in Organic Molecular Crystals.
• The rubrene crystal.
• Absorption and luminescence spectroscopy.
• Singlet Exciton Fission.
• Triplet Exciton Fusion.
• Quantum Beats.
• Triplet Exciton Diffusion and Fusion.
• Global Spin Decoherence in a Triplet-Pair population.