Toward photocurrent enhancement by singlet fission

Humans are unlikely to consider an anticipated crisis significant until it is at the door, and our collective response to the threat of impending climate change is no exception. Hence, the full consequences of releasing carbon dioxide into the atmosphere by burning of fossil fuels are unavoidable unless technological breakthroughs make large-scale renewable energy economically preferable. A substantial improvement in the cost efficiency of solar cells is, therefore, needed urgently.

Important reasons for the low efficiency of current semiconductor cells are that only photons with at least the energy of the bandgap are absorbed and that the excess energy of those with more is lost as heat. For sunlight, a material with the best compromise size of bandgap, ∼1.1eV, has a maximum theoretical efficiency (that assumes no losses) just below 1/3, the so-called Shockley-Queisser limit.¹

We can try to minimize losses and approach this limit as closely as possible, and we can also try to circumvent it. The latter has been done by using more than one bandgap (one absorbing material) in series. The photons that have the highest energy are absorbed in the first material and give the highest voltage, those of lower energy are absorbed in the next one and give a lower voltage that is added to the first one, and so forth. However, doing this right is complicated and requires a matching of the currents generated in the various materials. In fact, it is so difficult that the efficiency-to-cost ratio actually drops.

We have designed a molecular solid to inexpensively circumvent the Shockley-Queisser limit. It permits photons with energy at least twice that of the bandgap to produce two positive and two negative charges and so contribute double to the current. The theoretical efficiency limit for a simple overlay of an ordinary and current-doubling absorbing material, without any expensive current-matching requirements, approaches 1/2.²

The first step in photocurrent doubling in molecular materials is known as singlet fission (see Figure 1).³ In this process, the initially excited singlet molecule (S₁, with all its electron spins paired) shares some of its energy with a ground-state (S₀) neighbor and both convert to their less excited triplet states (T₁, with two of the electron spins unpaired). The energy of the triplets is sufficient for the second step dashcharge separation dashprovided that the redox levels of the two materials involved are chosen to have the right relative position on the energy scale.

Singlet fission has long been known in rare molecular crystals, conjugated polymers, and oligomers. Unfortunately, other processes compete successfully and the triplet yields were mostly a few percent instead of the theoretical 200%. Note that the whole point of singlet fission is to make more than one excitation out of each photon absorbed, and so a yield below 100% is not helpful in our context. However, very recently, T₁ yields near 200% were reported for an aggregate⁴ and two molecular solids,^{5, 6} including our own, and charge separation yields over 100% were reported for a third.^{7, 8}

Figure 1. Energy diagram representing the singlet fission process, the first step in photocurrent doubling. The initially excited singlet molecule (S₁) shares energy with a ground-state molecule (S₀). This results in both transforming into their less excited triplet states (T₁). A’ and A” are the two chromophores (species whose electrons can be excited) involved.

We designed a new material specifically for high T₁ yield, using the principles of quantum mechanics.^{3, 5, 9} While a 200%T₁ is important, the main significance of our result is that it shows it is possible to design new classes of highly efficient singlet-fission materials. This is essential to obtain the necessary properties for a practical solar cell, such as proper alignment of redox potentials, and long-term stability in sunlight. Efficient materials known at present, including ours, provide a proof of concept, but are far from practical.

We have used several design principles. First, the process should be approximately isoergic, that is, to release or absorb a negligible amount of energy. This requires the T₁-S₁ and S₀-T₁ energy differences to be about equal, a highly unusual situation. Quantum theory suggests two classes of conjugated π-electron structures likely to meet this requirement. The first is large alternant hydrocarbons (no odd-membered rings), familiar from Hückel theory. Due to orbital pairing, the overlap density of the highest occupied and the lowest unoccupied molecular orbitals is unusually large and makes the splitting of S₁ and T₁ large as well. Indeed, all systems in which singlet fission was found in the past were alternant hydrocarbons or their simple derivatives.

Our material belongs to the other class suggested by theory, biradicaloids. These structures lie halfway between the usually extremely reactive biradicals, species with two electrons in two non-bonding orbitals and similar S₀ and T₁ energies, and stable ordinary molecules, in which S₀ lies far below T₁ and S₁. When the two non-bonding orbitals of a biradical are split by a suitable structural perturbation to produce a biradicaloid, both electrons go into the more stable orbital, S₀ is stabilized, and T₁ destabilized. With a perturbation of the right strength, the S₀-T₁ and T₁-S₁ gaps become equal.

The second design principle results from the application of the Fermi golden rule. Singlet fission will be fast if the Hamiltonian matrix element between the initial S₁S₀ state and the final T₁T₁ state is large. In the first approximation, this requires the maximization of a difference between two integrals involving overlap charge repulsion, which can be done by visual inspection of the spatial relation between the orbitals of the two interacting partners and verified by computation. It is detrimental to have the two aromatic planes stacked directly above each other. However, if one plane is slipped sideways relative to the other, the spatial relation becomes favorable. This is the relation found within the crystal of our material.

In summary, we have demonstrated that certain principles can be applied to the design of molecular and crystal structures to double the current produced from the absorption of a single photon. With the first verification of these design rules in hand, we can now extend the search to many other structures for the interacting materials. We can also synthesize absorbing materials with the optimal spatial relation (mutual orientation and distance) between the two molecules involved in the singlet fission process to avoid relying on the vagaries of crystal structures. These aspects represent the focus of our future work.