Shockley: Queisser detailed balance limit after 60 years

Abstract

The year 2021 marks the 60th anniversary of the Shockley–Queisser paper which laid the theoretical foundations for the fundamentals of solar cell operation. This article reviews the principal results of the Shockley‐Queisser paper and the developments that followed. Starting with links to the earlier radiative balance laws of Kirchhoff and Planck, we discuss the nature of the detailed balance between the incident and emitted photon beams. The resulting efficiency limit is juxtaposed with another popular limit due to Trivich and Flinn. The dependence of the Shockley–Queisser limit on the intensity and sizes (étendues) of the two beams—in other words, on the concentration of sunlight—is discussed in some detail. This article then takes a broader view of the detailed balance with the help of the generalized Planck law and the refinements that this implies for the efficiency and the current–voltage characteristic of the cell. A natural extension of the Shockley–Queisser detailed balance into the realms of thermodynamics is outlined by considering the photon entropy in the two beams. This produces the detailed balance limit in a typical thermodynamic form, similar to the result for a heat engine, where the efficiency losses are expressed in terms of entropy generation. The paper concludes with a brief discussion of how the results can be extended to the operation of practical solar cells with a more realistic description of light absorption and nonradiative recombination. A brief overview is also given of mechanisms for how the Shockley–Queisser limit can be exceeded.