Modern solar panel technology is pretty damned awesome. I say this from personal experience, since my roof is pretty much maxed out. I may even move the inverter into the lounge to replace the television as my visual entertainment of choice.

Most people don't view solar panels as a source of entertainment, though. They want power, and the big thing that everyone talks about when it comes to power is the panels' efficiency: how many photons that hit them liberate electrons. The usual answer is... not many.

There is a fundamental limitation, called detailed balance, that helps limit the efficiency. Essentially, absorption of a photon and emission of a photon are the same thing (you just reverse the direction of time). So, if something is good at absorbing photons, it's also good at emitting photons. When your solar panel absorbs a lot of photons, there are lots of excited electrons around, and many of them will lose their energy by emitting other photons. In the end, where these two processes balance out helps set the maximum possible efficiency of a standard solar cell.

Now, you shouldn't worry about that too much when it comes to the panels used outside of the lab, because other factors ensure that they are nowhere near that ideal limit. In the lab, it's a different story; there are experimental solar cells that get close to the limit. So research is now turning to ways to beat detailed balance. It turns out that you can do this by using conservation laws to prevent electrons from radiating the energy they just absorbed. Getting it to work is a bit delicate, however, and even understanding why it works is difficult. So what follows may be a bit confusing.

Hiding in the dark

When I described the process of turning light into electrical energy above, the limit is given by the balance between absorption of a photon and emission of a photon. What if an electron was unable to emit a photon?

Let's look at an example of that. A molecule, which is basically a cloud of electrons, is sitting around minding its own business, when a photon collides with it. The photon is absorbed by the molecule and, as a result, one of the electrons gets excited and moves to a state with higher energy. But, the electron can't choose just any state, because the photon has also given it some angular momentum. So, the new state must match both the change in energy and the change in angular momentum. If nothing else was going on, the electron could then emit a photon with the right energy and angular momentum, allowing it to return from whence it came.

However, usually an electron has more than one choice in how it loses energy. So, it can also lose a small amount of energy and angular momentum to enter a state with less energy, but still more than it had originally. That leaves the electron stuck. It still has energy to lose, but the only way to return to its lowest energy state is to emit a photon with no angular momentum, which is impossible.

From an outside perspective, you can think of it like this: the molecule absorbs a photon, emits a photon, absorbs a photon, emits a photon, absorbs a photon... and disappears. The molecule no longer emits or absorbs, because the electron has trapped itself in a state from which it cannot escape. This is called a dark state.

Imperfections are beautiful

Once the molecule is trapped in the dark state, it cannot absorb any more photons, but it can deliver the trapped electron to an electrical load to do work (got to get rid of that energy somehow). This works even if there is no energy difference between the dark state and the state which the electron was originally driven into by the photon. Under these circumstances, you do beat detailed balance (it's actually more complicated than this, but this is the core idea).

In nature, entering a dark state is commonly associated with some energy loss, but can be used to energy from one molecule to another. Think of photosynthesis, where antennas gather photons in one location and transfer charge to reaction centers that are, from a molecular perspective, on another continent. Even though the molecules that make up the chain that the energy travels along might have identical structures, their environments are different enough that they can't be considered identical.

But, so far, all the calculations on using dark states to beat detailed balance have assumed identical molecules. Does this dark state trick still work when nature comes along and breaks this assumption? Researchers from the UK set out to answer that question using a kind of general model.

The model abstracts molecules as a series of energy levels and rates. The rates represent how fast an electron can move between two levels, while the levels represent the energy required to (or given up) by an electron that transfers between two states. The model and also includes a pair of states where electrical work is done by a load—cases where an electron that decays from the upper load state to the lower load state has done some useful work in the outside world.

The model allowed the researchers to compare the amount of work the molecular pair can do under a variety of conditions. The researchers compared molecular pairs with a dark state and without a dark state. For the case with a dark state, they could vary the match between the energy levels of the two molecules, and the rates of transfer between energy levels in order to see what combinations provided the largest amount of electrical work.

Dark and undark

Let's follow the energy. As before, one molecule absorbs a photon, which excites an electron, which can then emit a photon, returning to where it started. But there's an alternative: the whole molecule shakes itself up, losing some of the energy in mechanical vibrations. The electron moves to a slightly lower energy, which just happens to match the energy that the second molecule wants to absorb. So, instead of emitting a photon, the remaining energy is transferred from one molecule to another (via a process that I won't go into detail about). The electron, having given up its energy, falls back to the ground state and is ready to absorb another photon.

The second molecule, however, has a different structure, so the electron that was excited by this close range transfer process finds itself unable to emit a photon to lose energy. Instead, it can transfer its energy to the load and return to the ground state. But, the dark state is not perfect, so there is a chance of the electron directly emitting a photon and returning to the ground state without doing any work (naughty electron!).

The question: how much freedom do we have to vary these different rates and generate more power than predicted by detailed balance? This turns out to have a rather strange answer.

Slower is faster, up is down

If you compare the rate at which energy leaks uselessly out of the dark state to the rate at which energy is transferred to the electrical load, you'll get a bit confused: the slower the rate of transfer to the load is, the better. That is, slowing down the transfer means that more electrons go via the load than leak directly to ground. If that rate is around 100 times slower than the energy leakage, then you exceed the fundamental limit of detailed balance by a factor of about ten (the precise number depends on a lot of details, but ten is a good round number).

What does this actually mean? I discussed this with one of the paper authors. Then, I spent a sleepless night puzzling over it. And then spent a great deal more time re-reading the paper and contemplating my navel. And, what's really annoying is that this model is nearly identical to something that I've investigated myself for different purposes, so I should understand what's going on. Despite this, I'm still not sure I've got it right.

My sense is that it's not just about rates. The probability of a transition depends on the rate and the population difference between the two states. When an electron enters the dark state, it sees two choices: the fastest available transition is direct to the ground state. If the ground state is almost fully populated, then that is actually a highly unfavourable transition. In contrast, the upper state of the load has a population that is about half that of the dark state. The natural flow of electrons is to equalize populations (or rather an equality that is weighted by the transition rates), so the electron heads to the load rather than directly to the ground state.

The trick then is to maintain these population differences. If the rate of transfer to the load is high, then the population difference gets smaller, and the drive to transfer electrons reduces. As a result, more electrons escape directly to the ground state. However, if the rate of transfer is slow, the population difference remains large, and electrons will hang on in the dark state until they get a chance to head for that invitingly empty load.

That also means that the load has to be carefully matched to the molecule. A load that was very slow to use its electrons will allow population to build up at the top of the load, reducing the drive. For the electrical engineers among us, you can almost think of this like matching the load to a transmission line to enable maximum power transfer. For the rest of us, well I'm afraid I'm out of analogies.

The lesson you should take home is that you cannot hang any old device off a solar cell like this and expect excellent performance. Instead, one needs to have some intermediate device that presents the right interface.

Going beyond calculations

Researchers have been working on this concept for six or seven years now, but there has been nothing beyond calculations. But, for me, this is where this paper really stands up. Although the calculation is quite general, the researchers obtained parameters from real molecular systems. They produced vast tables of organic molecules and found optimum matches that might be used to demonstrate an organic solar cell with a dark side to it. This gives me hope.

Physical Review Letters, 2016, DOI: 10.1103/PhysRevLett.117.203603