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I recall reading somewhere that solar power - already marginal at Jupiter - will cease to produce any power whatsoever at distances much further out than Saturn. Unfortunately I can not now find the source of that, so I'd like to explore it here.

As far as I understand the photoelectric effect (which is, I think, related to how PV cells work), the intensity of radiation does not affect whether an electron is released, only the wavelength of the light. Because of this, it didn't make sense to me why photovoltaics might cease to produce light altogether at distances far from the sun.

So I'd like to ask, whether, at some point far from the Sun, the output of solar panels starts dropping much faster than the inverse square law suggests. If it does, is this due to a lack of light intensity, or some other effect?

As a bonus, what would the shape of that drop-off look like?

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    $\begingroup$ The farther out from the Sun the less dense the photon flux is: fewer photons per square meter. At some point the electricity generated by the decreasing number of photons per unit area will not be enough to overcome internal electrical resistance of the electrical generating system. $\endgroup$
    – Fred
    Feb 9, 2023 at 6:21
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    $\begingroup$ Very highly related, if not a duplicate: How far from the Sun can solar power be used as a reliable energy source? $\endgroup$ Feb 9, 2023 at 8:43
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    $\begingroup$ The issue is not that solar cells stop working. This issue is that power generated falls with the inverse square law. That means a hugely increasing solar array size (and hence mass) for missions far from the Sun. Moreover, getting something that far away requires a lot of propulsive capability. $\endgroup$ Feb 9, 2023 at 8:45
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    $\begingroup$ "I recall reading"...where? It was almost certainly either misinformation or a misunderstanding. Solar could be extended far, far past Jupiter, even if the photovoltaics had a minimum intensity requirement, just by adding reflectors to concentrate the light. It just won't provide as much for a given mass as alternatives like RTGs. $\endgroup$ Feb 9, 2023 at 17:32
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    $\begingroup$ @ChristopherJamesHuff - I don't recall exactly where I read it, but it was most likely in a discussion about the realism of solar panels in Kerbal Space Program. If not, it will have been in the NASASpaceflight forums, or in an article on nasa.gov. DavidHammen - I'm not thinking of the inverse-square law. This effect (if it actually exists) is something different; a sharp(ish?) cutoff, not a gradual decline in power. $\endgroup$ Feb 9, 2023 at 20:03

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Good SE questions deserve good answers. I'm not a PV expert but I can at least get the ball rolling.

At some point far from the Sun does the output of solar panels start dropping much faster than inverse square?

Yes!

If so, how fast?

tl;dr: efficiency at Saturn's 10 AU might be one third that at 1 AU, and about a quarter at Neptune.

I recall reading somewhere that solar power - already marginal at Jupiter - will cease to produce any power whatsoever at distances much further out than Saturn.

This, not unlike Mark Twain's death while he was still alive, seems to be greatly exaggerated. :-)


Single crystal silicon as an example

It depends on the semiconductor material in question (silicon, III-V (GaAs InP), perovskites(?), exotics etc.) material quality, defect density/radiation damage, etc. but basically at a low rate of carrier (electron-hole pairs) production there are competing processes that allow them to recombine locally inside the material such that they can't make it out and be used to produce a current.

The simplest way to characterize these processes is with a single parameter called shunt resistance that tries to lump all of these loss mechanisms into a number.

Mathematical models used for terrestrial PV applications are going to focus on sunny to cloudy/overcast days:

...and may not be very accurate at Saturn (10 AU) and beyond, and experimental data for cells optimized for terrestrial applications may be worse at Saturn than those optimizes for very low light levels, but with those caveats, let's take a look at some data anyway.

From Crystalline silicon cell performance at low light intensities September 2009 Solar Energy Materials and Solar Cells 93(9):1471-1481 DOI:10.1016/j.solmat.2009.03.018 Figure 2b shows a measured efficiency curve of some single crystal silicon PV cells. Eyeballing the measured efficiency curve I get about 7% at 1 AU (1361 W/m^2) 4% at Saturn's 10 AU (13.61 W/m^2) and 2% at Neptune's 30 AU (1.5 W/m^2):

open-circuit voltage, fill factor ( FF ) and efficiency at maximum power point voltage measured between 0.01 and 1000 W/m 2 irradiance intensity for the mc-Si cell

Fig. 2 (a) Apparent shunt and series resistances ( R Se , 1 D and R Sh , 1 D ) as obtained from irradiance intensity measurement, (b) open-circuit voltage, fill factor ( FF ) and efficiency at maximum power point voltage measured between 0.01 and 1000 W/m 2 irradiance intensity for the mc-Si cell.

See also Evaluating Crystalline Silicon Solar Cells at Low Light Intensities Using Intensity-Dependent Analysis of I–V Parameters (paywalled)

Need more? Concentrate!

If you're going to be wandering out at Saturn and beyond and need to get back to PV efficiencies similar to those at 1 AU, then concentrate! By thinking harder, you'll realize you can concentrate the light as well.

While you're out there at Saturn hopefully you've either brought Wikipedia along or can still link to it and read its Concentrator photovoltaics article.

You can build one giant concentrator; say a 100 square meter aluminized polymer film reflector (like a solar sail-looking thing) for every 10 square meters of PV area, or use a high granularity system with small lenses or reflectors on thousands of small cells.

Further reading:

and related:

Yes colder is better so there's a "hot" penalty circa 1 AU

Answers to Temperature of photovoltaic cells vs efficiency - is it ever actively controlled? explain that the recombination losses are increased at elevated temperatures. Closer to Earth at 1 AU this will actually show a drop in efficiency going towards the Sun if the panels are not provided a good way to cool (they're "in the sun" so will get toasty). But out near Saturn at 10 AU they're going to be quite cold, this will not be a significant factor.

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  • $\begingroup$ Let me suggest to replace the first image with figure 1 from the same source as your second one. This first paper looks rather fishy to me and even contradicts itself (check table 1 which states the opposite...) $\endgroup$
    – asdfex
    Feb 11, 2023 at 10:31
  • $\begingroup$ You may want to add something about manufacturing quality which plays a major role. The purer the silicon crystal is, the better the low light performance. Compare figure 1 in DOI:10.1016/j.solmat.2009.03.018 - some lose 85% at 3W/m², some only 25%. $\endgroup$
    – asdfex
    Feb 11, 2023 at 10:34
  • $\begingroup$ @asdfex I'll just pull the first image out - it was just meant to illustrate that some work only covers the sunny-to-cloudy day range. For your second point "It depends on the semiconductor material in question (silicon, III-V (GaAs InP, perovskites(?), exotics etc.) material quality, defect density/radiation damage, etc." is meant to show that it's a pretty big topic and I won't be going into details. Once a PV cell has been exposed to deep space for a while I think that radiation damage will make the issue of initial high quality moot. $\endgroup$
    – uhoh
    Feb 11, 2023 at 11:02
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    $\begingroup$ This is a very good answer, but, as you've noted, my recollection of the effect is slightly different. I'll wait a few more days before accepting - just on the off-chance that there actually is some other effect more similar to what I recall hearing of. $\endgroup$ Feb 13, 2023 at 3:16
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    $\begingroup$ @Infinite_Maelstrom oh take your time! I know just what you mean - sometimes it takes me years to get to the bottom of something I can't quite recall... :-) $\endgroup$
    – uhoh
    Feb 13, 2023 at 3:53

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