The Concentration Limit for Solar Cells Based on Entropy Production
  The maximal concentration limit of solar radiation for photovoltaic applications is assumed to be constant, at Cmax\approx46,000 suns. This limit is easily found via a geometrical application of the 2nd law of thermodynamics to a radiation transfer system [A. Rabl, Sol. Energy vol. 18, pp. 93-111, 1976]. However, previous analysis did not include the generation of entropy in photovoltaic conversion. Here, we show a bandgap dependence of the maximal concentration limit for a semiconductor solar cell when taking this entropy generation into account, and show that the limit is reduced for low bandgap materials. This new concentration limit lies in contrast to the assumed invariance of the concentration limit, and we attribute this difference to a breakdown in the assumptions used to derive the traditional detailed-balance model. 
Ze'ev R Abrams, Xiang Zhang
cond-mat.mtrl-sci