On the upper limit of the energy conversion efficiency in tandem solar cells

Abstract

The efficiency of solar energy conversion in a photovoltaic device consisting of an infinite number of solar cells is examined in detail. A mathematical analysis of the complicated functional dependence of the efficiency on temperature and light concentration ratio is presented. Although an infinite tandem seems, at first sight, only of academic interest, it is shown that the various approximate expressions obtained for the complicated efficiency function can give some more insight into the basic limits of the photovoltaic conversion, and can enable easy predictions of an upper limit of the efficiency of tandem structures with a finite number of solar cells.

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

“…It is striking that these analytical expressions are much simpler than those of the corresponding coefficients Q, a3, u4, a5 of the series (8), as published in a preceding paper (Grosjean and De Vos 1981). Nevertheless, the numerical values differ little:…”

“…up to terms of third and higher orders. Applying the method previously used to calculate the coefficients bl, c l , b2 and c2 of the series (9) (Grosjean and De Vos 1981), we obtained (see appendix 2): J but we were not able to find B2 and C2 in this manner because of the appearance of a divergent integral solely to be ascribed to the inadequacy of the method when it is applied to equations ( 12)-( 13), and therefore not to the coefficients B2 and C2 being infinite. The proof of this statement lies in the fact that, using other more powerful techniques of series development based upon an exhaustive mathematical study of the system (12)-(13) (Grosjean, unpublished results), one of us was able to show after laborious calculations that 15 5…”

“…From the theoretical point of view, it is of interest to let t vary from 0 to 1. In a previous paper, Grosjean and De Vos (1981) gave a mathematical analysis of the function qsQ(t) defined by the set of equations ( 6 ) and ( 7 ) . In particular, they obtained a few initial terms of two series expansions of qsQ(t), namely, a power series in the vicinity of t = 1 (where ~S Q = 0) and a more complicated series in the vicinity of t = 0 (where ~S Q = 1):…”

“…It could therefore be expected that with increasing order oft, one would sooner or later encounter integrals with respect to U whose integrands contain such powers of U in the denominator that their behaviour in the vicinity of the lower bound U = 0 becomes approximately proportional to the first or a higher power of l / u , which of course entails divergence. In the calculations outlined in appendix 2 of the paper of Grosjean and De Vos (1981), no divergent integrals occur in the coefficients of the terms of the first and the second order in t, but if one attempted to use the method to calculate coefficients such as b3, c3, . .…”

Singlet fission in organic crystals : ultrafast spectroscopic study

“…The Shockley-Queisser limit predicts the maximal theoretical efficiency for one single p-n junction solar cell to be about 31% based on the assumption that the sub-bandgap photons remain unabsorbed and the excess energy of supra-bandgap photons is wasted as heat [27]. A number of different approaches have been used to significantly exceed this limit, e.g., tandem (multijunction) cells [28,29], hot carrier capture [30], and multiple exciton generation (MEG) [31]. Among them, the MEG is a process which creates multiple electron-hole pairs per absorbed photon with energy at least twice larger than the semiconductor's bandgap.…”