  The Shockley-Queisser (S-Q) theory defines the thermodynamic upper limits for
Jsc, Voc, FF, and efficiency of a solar cell. The classical calculation assumes
an abrupt onset of absorption at the band-edge, perfect absorption for all
energies above the bandgap, and absence of non-radiative recombination. These
assumptions are never satisfied for any practical solar cell. In this paper, we
explain how the S-Q limits are redefined in the presence of the non-ideal
optical effects, and we provide closed-form analytical expressions for the new
limits for Jsc, Voc, and FF. Remarkably, these new limits can be achieved to a
very high degree, even with significantly imperfect materials.
