Guide for the perplexed to the Shockley–Queisser model for solar cells

The Shockley–Queisser model is a landmark in photovoltaic device analysis by defining an ideal situation as reference for actual solar cells. However, the model and its implications are easily misunderstood. Thus, we present a guide to help understand and to avoid misinterpreting it.

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Fig. 1: Explanation of the key concepts used in the SQ model.
Fig. 2: Power losses as a function of bandgap and applied voltage in the SQ model.

References

  1. 1.

    Shockley, W. & Queisser, H. J. J. Appl. Phys. 32, 510–519 (1961).

  2. 2.

    Prince, M. B. J. Appl. Phys. 26, 534–540 (1955).

  3. 3.

    Loferski, J. J. J. Appl. Phys. 27, 777–784 (1956).

  4. 4.

    Wolf, M. Proc. IRE 48, 1246–1263 (1960).

  5. 5.

    Nayak, P. K., Mahek, S., Snaith, H. J. & Cahen, D. Nat. Rev. Mater. 4, 269–285 (2019).

  6. 6.

    Krogstrup, P. et al. Nat. Photon. 7, 306–310 (2013).

  7. 7.

    Stolterfoht, M. et al. Energ. Environ. Sci. 10, 1530–1539 (2017).

  8. 8.

    Würfel, P. Physics of Solar Cells: From Basic Principles to Advanced Concepts 2nd edn (Wiley-VCH, 2009).

  9. 9.

    Araujo, G. L. & Marti, A. Sol. Energy Mater. Sol. Cells 33, 213–240 (1994).

  10. 10.

    Hirst, L. C. & Ekins-Daukes, N. J. Prog. Photovolt. Res. Appl. 19, 286–293 (2011).

  11. 11.

    Würfel, U., Cuevas, A. & Würfel, P. IEEE J. Photovolt. 5, 461–469 (2015).

  12. 12.

    Asbeck, P. J. Appl. Phys. 48, 820–822 (1977).

  13. 13.

    Bridgman, P. W. Phys. Rev. 31, 101–102 (1928).

  14. 14.

    Markvart, T. Phys. Status Solidi A 205, 2752–2756 (2008).

  15. 15.

    Green, M. A. Prog. Photovolt. Res. Appl. 9, 123–135 (2001).

  16. 16.

    Green, M. A. Solid State Electron. 24, 788–789 (1981).

  17. 17.

    Tiedje, T., Cebulka, J. M., Morel, D. L. & Abeles, B. Phys. Rev. Lett. 46, 1425–1428 (1981).

  18. 18.

    Nayak, P. K. et al. Energ. Environ. Sci. 5, 6022–6039 (2012).

  19. 19.

    Vandewal, K. et al. Nat. Mater. 13, 63–68 (2014).

  20. 20.

    Rau, U., Blank, B., Müller, T. C. M. & Kirchartz, T. Phys. Rev. Appl. 7, 044016 (2017).

  21. 21.

    Rau, U. Phys. Rev. B 76, 085303 (2007).

  22. 22.

    Xu, Y., Gong, T. & Munday, J. N. Sci. Rep. 5, 13536 (2015).

  23. 23.

    Schweiger, M., Herrmann, W., Gerber, A. & Rau, U. IET Renewable Power Generation 11, 558–565 (2017).

  24. 24.

    Green, M. A. & Ho-Baillie, A. W. Y. ACS Energy Lett. 4, 1639−1644 (2019).

  25. 25.

    Liu, Z. et al. ACS Energy Lett. 4, 110–117 (2019).

  26. 26.

    Green, M. A. Prog. Photovolt. Res. Appl. 26, 3–12 (2018).

  27. 27.

    Polman, A. et al. Science 352, aad4424 (2016).

  28. 28.

    Braly, I. L. et al. Nat. Photon. 12, 355–361 (2018).

  29. 29.

    Marti, A., Balenzategui, J. L. & Reyna, R. F. J. Appl. Phys. 82, 4067–4075 (1997).

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Acknowledgements

J.-F.G. thanks the French programme of “investment for the future” (ANR-IEED-002-0). D.C. thanks the Inst. PV d’Ile de France for a visiting professorship and the Ullmann family foundation (via the Weizmann Institute) for support. T.K. and U.R. acknowledge the Helmholtz Asssociation for funding via the PEROSEED project.

Author information

Correspondence to Jean-Francois Guillemoles or Thomas Kirchartz or David Cahen or Uwe Rau.

Supplementary Information

Supplementary Information

Supporting data for the application of the SQ model to actual photovoltaic technologies.

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