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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.


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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    Article  Google Scholar 

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

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    Article  Google Scholar 

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

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

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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

    ADS  Article  Google Scholar 

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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.

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

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

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Guillemoles, JF., Kirchartz, T., Cahen, D. et al. Guide for the perplexed to the Shockley–Queisser model for solar cells. Nat. Photonics 13, 501–505 (2019).

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