Light, Excitons, and transport in Organic Molecular Crystals

A small rubrene crystal.

Organic molecular crystals operate in a relatively unexplored region in the landscape of solid-state physics. This region is characterized by narrow bands with transport at the boundary between hopping and band transport, and by excitons with high binding energy that are an important hurdle towards free carrier photoexcitation. Often, the molecules in a molecular crystal are bound only Van-der-Waals interactions (no covalent bonding between molecules), essentially getting together until they touch. This then means that there is little overlap between excited state orbitals of one molecule and the next, which is what creates the narrow energy bands, and also what creates localized excitons with a large binding energy. One sees very much of the excitation spectrum of a molecule when that molecule is in a crystal. But it is still important to pay attention, because the crystal structure enforces a certain ordering of the molecules, and the direction of polarization of light will matter a lot (in contrast, for example, to molecules in solution).

Cartoon of an organic molecular crystal, where molecules do not interact much with each other.

These properties have a strong effect on the spectroscopy of absorption and fluorescence in such materials (example: rubrene). In addition, tightly bound excitons are the dominant result of photon absorption in these materials even at room temperature. Binding energies of the order of 1 eV mean that dissociation of excitons into free charge carriers can occurs only via interaction with defects and heterointerfaces, which is one important bottleneck towards using cheap and lightweight plastic components for harvesting solar light in organic photovoltaics.

The same properties also matter for the transport of energy in the form of excitons. This is particularly visible when long-lived triplet excitons are formed via a fission process from the photoexcited singlet exciton. The reason why something like this can occur is that exchange symmetry has a strong effect on Coulomb energy in organic molecules and it can be that the triplet state of an excited molecule (a triplet exciton in a crystal) has a much lower energy (by a factor of 2 or more) than the singlet state. Below what happens for just two electrons in a box:

Two-particle wavefunctions of two electrons that are put together to form an exciton inside an infinite square well, together with the corresponding energy. The wavefunctions are shown for the spin-1 triplet state (left) and the spin-0 singlet state (right). The fact that the electrons have a low probability to be at the same location decreases the Coulomb potential energy. The energy of the triplet state can become much lower than that of the singlet state as the size of the well in which the electrons are bound increases.

In an organic molecular crystal that consists of large organic conjugated molecules, the wavefunction of an electron in a frontier potential (ground state or first excited state) is so large that the energy of the triplet state is less than half that of the singlet state. Because of this, the spin-0 singlet excitons can undergo a (spin conserving!) fission process into two spin-1 triplet excitons. This is called singlet exciton fission.

Whenever a molecule's conjugated system is more or less the right size, the energy of the triplet state can be about half the energy of the singlet state. In this situation singlet exciton fission can still occur, but the reverse process of triplet exciton fusion can also happen. In this process, two triplet excitons that have a zero total spin can pool their energies to re-create a singlet exciton again. Never mind that the singlet exciton will then want to fission again, the possibility of re-forming the singlet state makes it so that short-lived singlet states can still be formed a long time after fission occurs.

Setup for triplet exciton microscopy. Blue light is focused on the surface of the crystal, where photoexcited singlet states undergo fission to create a population of long lived triplet excitons that diffuse. Such experiments can be used to study the diffusion length and its anisotropy of the triplet exciton dark states, by the light that they emit.

One very visible consequence of this is that the presence of a population of triplet excitons can be detected by the fluorescence that is emitted by rare triplet-triplet encounter events that lead to fusion and then photon emission. As an example, the combination of fission and fusion in rubrene allows to observe the triplet exciton diffusion length by the fluorescence that they emit via fusion events.

The diffusion of excitonic states is essentially an energy transport process. In organic photovoltaics, diffusion of excitons is tantamount to energy diffusion towards an appropriate harvester. Experiments of diffusion imaging, like that shown in the figure, can help answer the question of what physical processes are most responsible for limiting exciton diffusion length? Could one develop a molecular material where exciton diffusion lengths can reach distances of the order of micrometers and then build organic solar cells that do not have to rely on bulk heterojunctions? In fact, we have found that excitons in rubrene single crystals efficiently transform into triplet excitons that then have a long lifetime and a long diffusion length, of about 4 micrometers in one particular direction in the crystal.

The combined effect of singlet fission and triplet fusion also strongly influences the time dependence of fluorescence that is induced by short light pulses, and even the photoconductivity that arises after short pulse exposure. For either type of experiment, the triplet excitons are equivalent to a long-lived reservoir for excitations that can lead to a strong delayed fluorescence via triplet exciton fusion (in contrast to the prompt fluorescence that is associated to the radiative recombination of the photoexcited singlet excitons), and even a delayed onset of a strong photoconductivity via triplet exciton dissociation via an as yet not fully characterized mechanism.

In our research group, we do fundamental research that targets the physical mechanisms of exciton dynamics, diffusion, and dissociation in organic molecular crystals. Newly available high quality crystals like rubrene offer the opportunity to investigate these processes in a well-defined and controlled system. We regard the rubrene single crystal as an ideal system to establish a better fundamental understanding of exciton dynamics. This is because of several specific properties that are all found simultaneously in rubrene, such as highly efficient singlet-to-triplet and triplet-to-singlet conversion that allow the direct optical observation of triplet exciton diffusion (by imaging the light emitted by a triplet exciton gas because of triplet-triplet interactions), and the fact that triplet excitons can easily dissociate into free carriers thanks to interaction with defects.

Research on exciton dynamics in molecular crystals dates back to just after the invention of the laser, but many open questions remain today, not least because of modern potential optoelectronic applications (organic photovoltaics) and the fact that we are now in a position to apply new techniques to obtain new relevant experimental data.

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.

Old press releases:

• Taking inspiration from spilled milk.
• Physicists explore the key energy transport process underlying solar energy harvesting.

References:

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• 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).
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• P. Irkhin, I. Biaggio, “Two-photon absorption spectroscopy of rubrene single crystals,” Phys. Rev. B 89, 201202(R) (2014).
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• 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).
• D.M. Finton, E.A. Wolf, V.S. Zoutenbier, K.A. Ward, I. Biaggio, “Routes to singlet exciton fission in rubrene crystals and amorphous films,” AIP Advances 9 (9), 095027 (2019).
• 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).