Shockley-Queisser triangle predicts the thermodynamic efficiency limits of arbitrarily complex multijunction bifacial solar cells

As monofacial, single-junction solar cells approach their fundamental limits, there has been significant interest in tandem solar cells in the presence of concentrated sunlight or tandem bifacial solar cells with back-reflected albedo. The bandgap sequence and thermodynamic efficiency limits of these complex cell configurations require sophisticated numerical calculation. Therefore, the analyses of specialized cases are scattered throughout the literature. In this paper, we show that a powerful graphical approach called the normalized Shockley-Queisser (S-Q) triangle (i.e., i(mp) =1 - v(mp)) is sufficient to calculate the bandgap sequence and efficiency limits of arbitrarily complex photovoltaic (PV) topologies. The results are validated against a wide variety of specialized cases reported in the literature and are accurate within a few percent. We anticipate that the widespread use of the S-Q triangle will illuminate the deeper physical principles and design trade-offs involved in the design of bifacial tandem solar cells under arbitrary concentration and series resistance.