The Light A Solar Cell Throws Away

A solar cell in bright sunlight is an emitter. Not metaphorically: an operating silicon or organic cell radiates light out of its front surface, faintly, continuously, and the better the cell is the more it radiates. This is not a defect to be engineered away. It is the price of admission, written into the same physics that lets the cell absorb in the first place, and it is why no single-junction cell will ever reach a hundred per cent. What is negotiable is the direction of that glow, and on 5 October researchers at ICFO — the Institute of Photonic Sciences in Castelldefels, near Barcelona — reported an organic solar cell built as an optical cavity specifically to stop most of it escaping sideways.

The paper, published in Energy & Environmental Science, is titled "Inhibited photon emission to overcome Boltzmann losses in an organic solar cell with a cavity configuration". The authors are Francisco Bernal-Texca, Chiara Cortese, Mariia Kramarenko, Quan Liu and Jordi Martorell. The claim they make for it is large and carefully phrased: not that they have beaten the Shockley–Queisser limit, but that they have demonstrated a route that could.

Start with a body at room temperature that absorbs strongly at some wavelength. Thermodynamics requires that it also emit strongly at that wavelength, otherwise you could point two such bodies at each other and watch one spontaneously heat the other — Kirchhoff's law, in its usual form. A solar cell absorbs above its bandgap by design, so above its bandgap it must emit.

Under illumination at open circuit the bookkeeping becomes exact. Charge is not leaving the device, so every absorbed photon must eventually be accounted for, and in an ideal cell the only channel is radiative recombination: an electron and a hole meet, and a photon of roughly bandgap energy leaves. At open circuit the cell therefore emits a photon for every photon it absorbs. The separation between the electron and hole quasi-Fermi levels — which is what the voltmeter reads as the open-circuit voltage — settles at exactly the value that makes those two rates equal.

That last sentence is where the loss lives. The emission rate depends not only on how many carriers are present but on how many optical modes are available for the photon to leave by. Open more escape routes and the cell has to hold more carriers to keep emission in balance with absorption — but the carrier density is pinned by the illumination, so instead the voltage falls. Fewer escape routes, higher voltage. The cell is being taxed for the size of its own exit.

Now count the exits. Sunlight arrives at the Earth from a disc about half a degree across — an angular radius of about 0.27°, since the Sun is 1.39 million kilometres wide and 149.6 million kilometres away. A flat cell pointed at it accepts light from that narrow cone and essentially nothing else. But the same flat cell, left to itself, emits into the entire forward hemisphere: every direction above the plane of the device, a full 180 degrees of escape.

The mismatch is enormous and it is straightforward to put a number on. In the étendue bookkeeping that governs this exchange, what matters is the squared sine of the half-angle. For the Sun's cone that is sin²(0.267°) ≈ 2.2 × 10⁻⁵; for the full hemisphere it is 1. The cell is emitting into roughly forty-six thousand times more angular space than it is absorbing from. The voltage penalty is the thermal voltage times the logarithm of that ratio, and at 300 K the thermal voltage is 25.9 millivolts, so the cost is 25.9 mV × ln(46,000) ≈ 278 millivolts.

Nearly three-tenths of a volt, thrown away by geometry alone. For a cell whose open-circuit voltage is around 0.9 V, that is not a correction. It is a third of the budget. This is the quantity the field calls the Boltzmann loss, and it is a standard term in detailed-balance accounting rather than anything ICFO has discovered — what is unusual is treating it as an engineering target rather than a constant of nature.

There has always been one well-known way to recover it: concentrate the sunlight. Put the cell at the focus of a large mirror or lens and the acceptance cone widens until it matches the emission cone, the logarithm collapses, and the voltage comes back. Concentrator photovoltaics has been exploiting this for decades. The cost is a tracker, a mirror, a cooling system and a plant that only works in direct sun. The alternative — restrict the emission angle instead of widening the acceptance angle — gets to the same place thermodynamically, and ICFO's work is a demonstration of it inside the device stack rather than in front of it.

Figure 1. The voltage a solar cell loses to the mismatch between the cone it absorbs from and the cone it emits into, as a function of the emission half-angle. Schematic drawn from standard detailed-balance relations at 300 K, not from data in the paper. Credit: Photonics Insider.

The device is an inverted organic solar cell based on PM6:Y6, the donor–acceptor blend that has carried most of the efficiency records in organic photovoltaics over the past several years. Nothing exotic there; it is the standard high-performance workhorse of the field, and choosing it makes the comparison clean.

What the group changed is the optics around it. They made the cell into a cavity, putting silver at both ends: a reflective back electrode, as inverted organic cells normally have, and a silver front electrode thin enough to let sunlight in while still presenting high reflectivity across a broad range of angles. The two mirrors turn the active layer into a Fabry–Pérot resonator, and a resonator has a strongly angle-dependent response. Light can couple out efficiently only near the resonance condition, which for a thin cavity means near normal incidence; at large angles the cavity simply will not support an escaping mode. Emission that would have gone sideways has nowhere to go, and the photon stays in until it is reabsorbed.

The physical chain is short enough to state in one line: fewer escape directions, lower radiative emission at fixed carrier density, larger quasi-Fermi-level splitting, higher open-circuit voltage.

ICFO puts the Shockley–Queisser limit for a single-junction cell at 33.16 per cent. Narrow the emission cone to match the cone the sunlight arrives in, Bernal Texca says, and "solar cells will, in principle, be able to approach efficiencies close to 43%". Martorell adds that "the underlying principle is not specific to organic materials" — the same cavity argument applies to silicon, to perovskites, to anything whose voltage is limited by radiative recombination into a hemisphere.

Two things, and the release is quiet about both.

The first is current. A silver front electrode that reflects well at large angles is a silver front electrode that reflects somewhat at small angles too, and every photon it turns away at the front surface is a photon the cell never absorbs. Angle restriction is always a trade between voltage and current: narrow the cone and you gain millivolts while losing milliamps. The net gain in power conversion efficiency is the only figure that settles the argument, and ICFO's announcement does not give it. Bernal Texca's point that "the simplicity of the cavity cell design does not introduce any additional fabrication complexity" speaks to manufacturability, not to the balance of the trade. The measured efficiency of the cavity cell against its reference is in the paper; it is not in the press release, and Energy & Environmental Science is a hybrid journal, so whether the paper is readable without a subscription depends on what the authors chose.

The second is the sky. A cell that only accepts light from a narrow cone can only use light that arrives in that cone — which means direct beam, and which means tracking. Diffuse radiation, scattered out of the cone by cloud and atmosphere, is typically a fifth to a half of annual irradiance depending on latitude and climate, and a strongly angle-restricted cell loses most of it. That is precisely the objection that has kept concentrator photovoltaics a niche technology despite its higher efficiencies, and angle restriction inherits it, cavity or no cavity. Partial restriction — a cone of, say, twenty degrees rather than half a degree — keeps most of the diffuse light and recovers a smaller share of the voltage, and is the regime where this is most likely to be useful in practice.

Readers who make optical coatings will have recognised the device by now. An angularly selective filter — transmitting near normal, reflecting at large angles, over a defined band — is a thin-film design problem of a type the coating industry has solved many times, in rugate filters, in angular-selective solar-control glass, in the collimating stacks used on some detectors. What is new is not the filter. It is putting it inside the device, in the same deposition sequence as the electrode, so that it costs nothing extra to make.

That framing is worth holding onto because it sets the real difficulty. A dielectric stack can be made far more angularly selective than a thin silver layer, but it has to do this across the whole absorption band of the cell, at every wavelength from roughly 500 to 900 nanometres for PM6:Y6, without introducing the transmission ripple that would cost current. A single metal layer is a blunt instrument that happens to be cheap, robust and already part of the process. The gap between those two — a blunt cheap cavity and a sophisticated expensive one — is where the engineering of the next few years will sit.

Not the limit. Shockley and Queisser's number stands, because it was always a statement about a cell exchanging radiation with a hemisphere, and nobody has violated it; the cavity changes the boundary condition rather than the thermodynamics. What has changed is that the angular term in that calculation now has a device attached to it, made of materials already in use, in a geometry that does not add a process step.

The honest summary is that ICFO has shown a mechanism and published a ceiling, and has not yet published, in public, the thing that will decide whether anyone uses it — the measured efficiency, and how much of the 278 millivolts actually came back. For the photonics industry the interesting part is independent of that answer. A solar cell has just been redesigned as a resonator, and the quantity being optimised is not absorption but the angular distribution of emission. If that framing takes hold, the people who will be asked to supply the next generation of photovoltaic front surfaces are not the ones who make transparent conductors. They are the ones who make filters.