On Earth we make our photovoltaic panels out of semiconductors, separating the positive and negative charge collection nets with the depletion region of a reverse-biased pn semiconductor junction, but in space we could use photoemission across a vacuum gap; this will probably give less power per unit area but more power per unit mass than silicon solar cells, but will be thoroughly dominated by thin-film cells.
I got this idea from a discussion with Luke Parrish, who suggested that for space-based PV panels you could just use vacuum, and contributed several other key ideas to what follows.
We were discussing aerographite, which has recently been mooted as a possible solar sail material with 1 kPa UTS and 180 g/m³. As it happens, aerographite is fairly conductive (0.2 S/m at that density).
You could make a large photoemissive solar panel, like old vacuum-tube electric eyes but backward-biased. WP claims that cesium on a silver oxide support gives photoemissivity down into the infrared, so you could plate such a mixture on the sunward side of the aerographite support to make a photoemissive cathode, potentially a gigantic one; photon energy beyond what is needed to overcome the work function becomes electron kinetic energy, which can push the electron uphill against a potential difference to an electron collector grid anode, which needs to be porous, to let light through, and spaced far enough away from the cathode with insulating supports to prevent field emission from stealing the electrons back to the cathode. The spacing can be any distance that is small relative to the mean free path in the vacuum medium.
The spaces in the electron collector grid through which light comes will also permit the loss of some photoelectrons, perhaps the majority. Assuming no charge transfer to the solar wind, the lost electrons will eventually fall back to the positively-charged PV panel, some striking the cathode and others the anode. If it’s desired to maximize efficiency per area rather than efficiency per mass, you can extend the grid sunward into a honeycomb which lets almost all of the light through, while capturing all of the electrons, except for those emitted at a very small angle to the incoming light. However, extending the grid “vertically” in this way runs into diminishing returns very quickly; to maximize the electrons captured per unit mass of panel, the thickness should be only a little thicker than the width of the “wires” in the grid in the “horizontal” direction.
This means that the mesh of the grid should be as fine as possible, but its holes still need to be large relative to the wavelength of light and relative to the thickness of its “wires”. I suspect that hole diameter on the order of 1–10 μm will be optimal, with “wires” on the order of 0.1–1 μm “horizontally” and 0.1–3 μm “vertically”. An omnitriangulated mesh would be optimal for rigidity; a hexagonal mesh would be optimal for compliance and wire-to-hole ratio; a square mesh is in between these extremes.
This works out to be on the order of 1 g/m² for the mesh if it is made of something like aluminum (2 · 0.3 μm · 1 μm · 3 μm / (3 μm)² · (3 g/cc) = 0.6 g/m²), corresponding to the areal density of a uniform sheet of about 100 nm. These dimensions are too small to make use of the lower density of aerographite itself, because those result from heterogeneity at larger scales than that.
If the cathode has 50 nm of low-work-function photoemissive material plated onto the front of it, which I think is realistic, backed by the low-density aerographite mentioned above with an areal density of ½ g/m², it would be about 2.8 mm in average thickness. You would of course want to give both this cathode and the anode thicker and thinner parts, like the veins of a dicotyledon leaf or the threads of ripstop nylon, to reduce their electrical resistance and mechanical compliance.
It may be important to keep the electrodes cool to avoid loss of the electrodes from the anode mesh. Using a high-work-function surface for the anode and the non-sunward side of the cathode may be helpful to reduce such losses. Also, if you’re using volatile metals like cesium, you need to keep the electrode cool or it will evaporate off into space.
This adds up to an areal density for our orbiting solar panels on the order of 2 g/m² or 2 tonnes per km², roughly a hundred times lighter than conventional silicon solar panels at 100 μm thickness; typically in space multijunction cells with efficiency around 30% are used.
A km² of sunlight is about 1400 megawatts at Earth’s orbital distance, or much more if you’re closer to the sun, but how much of that can we really gather?
This depends on the quantum efficiency of photoemission from the cathode (what fraction of photons eject an electron) and the reverse bias voltage we demand the electrons fight against. Photons whose energy is precisely the work function plus the bias voltage are converted with 100% efficiency; photons at any lower energy are entirely wasted; any excess photon energy over that minimum is wasted. (We could imagine multiple cleverly shaped anodes whose electric fields guide most electrons to the highest-energy anode they’d be able to reach, but let’s assume we don’t do that.)
So, too high a bias voltage will produce zero current, but lowering the bias voltage will eventually produce insufficient additional current to make up for the energy loss per electron; there’s some voltage at which we see the maximum power. (This closely corresponds to spectrum losses in conventional PV panels.) This MPPT bias voltage will be a little lower than the energy of the average photon, which is probably about 700 nm; h c/700 nm = 1.2398 eV/0.7 ≈ 1.8 eV, so probably the right bias voltage is on the order of 1.8 V, which is a conveniently tractable voltage; the Shockley-Queisser limit is an efficiency of 33% at a semiconductor bandgap of 1.34 eV, which I think corresponds to a bias voltage of 1.34 V in this photoemissive panel.
(Note: the above is incorrect, and energy efficiency calculations hereafter erroneously assume that the bias voltage between the electrodes is 1.8 V, which is wrong. 1.34 V or 1.8 V is the amount of energy per electron lost in overcoming the work function of the photocathode material; the energy remaining to be harvested at the anode is whatever the photon energy is, minus that work function. So the right bias voltage might be 0.5 V or 1 V or something. I should fix this but I don’t have time this year. It means that the main efficiency conclusions below are too high by some unknown factor probably between 1 and 4.)
I think the recombination losses found in semiconductor PV cells do not have much of an analogue in this device; the space charge is entirely negative, and the only way electrons can “recombine” after leaving the cathode is to fall back onto it, either because they lacked the energy to reach the anode or because they went through holes in the anode twice. Presumably there is at least some probability that they will be “emitted” into the cathode material, though, where they will immediately “recombine”.
So, what about the quantum efficiency? Evidently in silicon PV it’s around 0.8, but these photoemissive panels might be much worse. If their quantum efficiency were, say, 10⁻⁶, they would produce less electrical energy per mass than conventional silicon cells, rendering them useless. Wikipedia says that phototubes typically produce microamperes, and they typically have a cathode area around 10 cm² and are typically illuminated by an infrared beam that can’t be much more than 10 W/m² (or we’d feel it on our skin and possibly damage our eyes), which puts a lower bound on their QE of about 10 cm² · 10 W/m² / 1.7 eV / (μA/e) ≈ 1/6000. At this QE we would expect 33% · 1400 W/m² / 6000 ≈ 77 mW/m², which is high enough to be useful but not high enough to compete with conventional solar cells; dividing by the estimate above of 2 g/m², we get 39 mW/g, which is much lower than the areal efficiency of conventional multijunction silicon solar cells, 30% · 1400 W / m² / (230 g/m²) ≈ 1800 mW/g, 46 times higher.
So this approach can be mass-competitive with multijunction silicon solar cells if the photoemissive cathode quantum efficiency is more than about 1/130, i.e., 0.8%.
In fact the cesium-antimony photocathodes used in the first commercially successful photomultiplier tubes have a quantum efficiency of 12% at 400 nm, though the quantum efficiency of earlier silver-oxide-cesium photocathodes peaked at 0.4% at 800 nm. This information seems to come from p. 4 of the Photomultiplier Handbook; on p. 11 it says, “on the best sensitized commercial photosurfaces, the maximum yield reported is as high as one electron for three light quanta,” which would work out to 33% QE. This would give an overall solar cell efficiency of 33% · 33% = 11%, but that’s probably for a single wavelength; a few of the QEs of different materials plotted on p. 15 are above 10% at 555 nm, and some, like Na₂KSb, are above 20% at 450 nm, so maybe 33% · 15% ≈ 5% is more realistic. In Table I on p. 16, Na₂KSb’s responsivity to tungsten light at 2856 K is given as 43 μA/lumen, while K₂CsSb (nominally 33% QE) is given as 90 μA/lumen. Nominally lower QE materials with longer-wavelength peaks are even higher: GaAs:Cs-O is said to have 720 μA/lumen despite only a 12% QE due to an 800-nm response peak, and semitransparent Na₂KSb:Cs on a reflecting substrate is 300 μA/lumen with 16% QE with a 530-nm response peak, which matches sunlight better than it does a tungsten lightbulb. Presumably these are all in a forward-biased condition, as they are used in PMTs, not back-biased, but hopefully the correction is small.
Rechecking the calculation from a different angle, 1000 W/m² is about 128000 lux, so the above-the-atmosphere 1400 W/m² should be about 180 klux = 180 klm/m², which at 300 μA/lm would be 54 A/m²; at 1.8 V that would be 97 W/m², which is 6.9% efficiency, close to the 6% I estimated above.
So it seems likely that, using new ultralight electrode materials like aerographite, coated with modern (semiconducting?) multialkali photocathode materials, this photoemissive generator can probably beat silicon PV in power per unit mass by a factor of, say, 20 or so (50 W/g instead of 1.8 W/g), but it will be five times worse in power per unit area (6% efficiency rather than 30%).
Thin-film semiconductor PV cells like CIGS can probably beat it in power per unit mass, too.
Moreover, the Photomultiplier Handbook says, “Semiconductors, therefore, are superior to metals in all three steps of the photoemissive process: they absorb a much higher fraction of the incident light, photoelectrons can escape from a greater distance from the vacuum interface, and the threshold wavelengths can be made longer than those of a metal. Thus, it is not surprising that all photoemitters of practical importance are semiconducting materials.” So in a sense this gadget is a semiconductor thin film solar cell.
10.1088/1361-648X/aa79bd “Super low work function of alkali-metal-adsorbed transition metal dichalcogenides” claims work functions as low as 0.7 V with a potassium film on a strained tungsten telluride backing.
Interestingly, the “semitransparent” photocathode materials are “deposited on a transparent medium,” with typical film thicknesses around 30 nm, so as to emit electrons in the opposite direction from the incident light. That suggests the possibility of reversing the positions of the cathode and anode and making the anode opaque, so there is no question of electrons escaping through holes in it. Conceivably supporting the photocathode thin film in a vacuum on a sparse grid like the anode grid described earlier, covering what would be holes in the grid, would get photoelectrons coming out both sides, so that by placing anodes on both sides you could increase the quantum efficiency, perhaps doubling it. That might boost you to 14% efficiency or so, but still not enough to compete with existing CIGS and similar solid-state thin-film PV cells.
Most of the mass of the cathode in the above setup comes from the thin-film cathode (and then I just calculated on the assumption that the anode mesh would have comparable mass). An interesting way to reduce the mass further is to use a photocathode mesh or foam rather than a solid layer. A mesh with holes significantly smaller than the wavelength of light can be essentially opaque to the light if it’s sufficiently conductive, so you could use a photocathode mesh with 100-nm-wide pores separated by 1-nm-wide “wires”, thus reducing the necessary areal density of the cathode by 98%.
Parrish commented that existing systems are about an order of magnitude heavier than the number I was using above as a silicon-solar-cell comparison:
The ISS uses 8 solar array wings massing about 1 ton each that get 84–120kW average or up to 240 in direct sunlight. So about 30W/kg in direct sunlight. We’re talking 3 orders of magnitude improvement.
Apparently photoelectric solar power is a thing, and I should read about how well it works, but I don’t have time this year.
