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Ideal solar cell efficiencies

Nature Photonics volume 15, pages 163–164 (2021)Cite this article

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To the Editor — In a recent paper, Guillemoles et al.1 attempt to clarify and explain the often cited paper by Shockley and Queisser2 (SQ), which defines the limits to photovoltaic conversion by a single-junction solar cell. The SQ paper is not easy to read and is therefore easily misunderstood. As modern solar cells approach theoretical efficiency limits, the fundamentals become particularly important and the effort by Guillemoles et al. is therefore to be welcomed. However, in doing so, the authors have fallen into several pitfalls, and the aim of the present note is to clarify a number of misconceptions and correct some errors in that paper for specialists and non-specialists alike to help disentangle the complexities of the SQ paper.

Guillemoles et al. claim to consider only the SQ curve that corresponds to one sun illumination. This leads them to ascribe — incorrectly — a major part of the voltage drop from the ‘ideal’ value of Eg/q to electrical losses in transferring a charge carrier between the contacts (labelled as ‘isothermal losses’ in ref. 1). In fact, the largest part of this loss is of optical nature, a fundamental and unavoidable loss contained in the SQ theory and visible in Fig. 1 as the difference between the maximum-concentration and one sun efficiencies, due to the expansion in size (étendue) from the incident to emitted beam. Sometimes called optical entropy generation6,7, this is a subtle but important loss, with an origin closer to Planck’s radiation thermodynamics8 than to traditional optics, that is easily misunderstood9. Emitted photons are in thermal equilibrium with the electron–hole pairs that emit them, and with which they share the common temperature and chemical potential. The optical entropy generation — which implies that heat is absorbed from the low temperature heat bath that cannot be converted to useful work — reduces the chemical potential of the emitted photons. This, in turn, reduces the voltage that the electron–hole pairs can generate, at or away from the open circuit. The magnitude of this loss is about 0.28 V in voltage terms; the resulting efficiency loss exceeds the non-radiative and residual radiative losses (in other words, the difference of the measured efficiency from the SQ one sun curve) in the best solar cells (see Fig. 1), and is similar to these losses in standard production cells. It is important to emphasize that this loss cannot be reduced by changing the electronic parameters of the solar cell but only by manipulating the incident and emitted beams. Interestingly, irreversible entropy generation is also at the root of the loss of full power at short circuit, not always discussed in the textbooks on photovoltaics in any detail.

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Fig. 1: The most frequently quoted Shockley–Queisser efficiency curves shown alongside the best measured solar cell efficiencies (points).

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Acknowledgements

The Centre for Advanced Photovoltaics is supported by the Czech Ministry of Education, Youth and Sport under grant number CZ.02.1.01/0.0/0.0/15_003/0000464.

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  1. Solar Energy Laboratory, Faculty of Engineering and Physical Sciences, University of Southampton, Southampton, UK

    Tom Markvart

  2. Centre for Advanced Photovoltaics, Faculty of Electrical Engineering, Czech Technical University in Prague, Prague, Czech Republic

    Tom Markvart

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Markvart, T. Ideal solar cell efficiencies. Nat. Photonics 15, 163–164 (2021). https://doi.org/10.1038/s41566-021-00772-4

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