In order to find an upper theoretical limit for the efficiency of p‐n junction solar energy converters, a limiting efficiency, called the detailed balance limit of efficiency, has been calculated for an ideal case in which the only recombination mechanism of hole‐electron pairs is radiative as required by the principle of detailed balance. The efficiency is also calculated for the case in which radiative recombination is only a fixed fraction fc of the total recombination, the rest being nonradiative. Efficiencies at the matched loads have been calculated with band gap and fc as parameters, the sun and cell being assumed to be blackbodies with temperatures of 6000°K and 300°K, respectively. The maximum efficiency is found to be 30% for an energy gap of 1.1 ev and fc = 1. Actual junctions do not obey the predicted current‐voltage relationship, and reasons for the difference and its relevance to efficiency are discussed.
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A treatment of photovoltage, but not solar‐cell efficiency free of such limitations, has been carried out by
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This discrepancy appears to have been first emphasized by Pfann and van Roosbroeck (see footnote 2), who point out that the forward current varies as with values of A as large as three.
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Once a photon exceeds about three times the energy gap the probability of producing two or more hole‐electron pairs becomes appreciable:
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17.
See footnote 16, p. 305;
18.
Equations like (3.16) occur in published treatments of solar‐cell efficiency. The difference is that the term in due to which is small but required by the principle of detailed balance, is included, and the coefficient of is related to the fundamental minimum reverse saturation current rather than to a semi‐empirical value.
19.
As for Eq. (3.16), factors like υ have been introduced by various authors, most recently by M. Wolf (see footnote 6). However, the forms are dependent upon additional semiempirical quantities so that they cannot be used for the purposes given in the introduction.
20.
Similar maximization of the output power has been carried out in terms of the maximum area rectangle on the I‐V plot by various authors, in particular W. G. Pfann and W. van Roosbroeck (See footnote 2). The results do not, however, appear to have been published in analytic form in which the matching factor m is shown to be a function solely of the variable
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W. Shockley, U.S. Patent 2,569,347, issued September 25, 1951.
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M. Wolf and M. B. Prince (see footnote 27), p. 1186.
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