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On the formula for the upper limit of photovoltaic solar energy conversion efficiency

The formula for the maximum efficiency of photovoltaic energy conversion in tandem solar cells is discussed. This formula is obtained by the use of a thermodynamically founded diode I-V characteristic, and is compared to a previously published formula which was based on the classical diode I-V characteristic within the framework of the theory of Shockley and Queisser (1961). Series expansions of the complicated efficiency formula are presented. They enable an easy and accurate computation of the maximum efficiency and provide more insight in the basic limit of the photovoltaic effect.