Does below-bandgap absorption improve solar cell efficiency?

The Shockley-Queisser (S-Q) model assumes that the absorptance spectrum of a solar cell is a Heaviside step-function centered at the bandgap energy, i.e. zero below and unity above the bandgap. The absorptance of a practical solar cell is always non-zero below the absorber bandgap. For example, the Urbach tail of bulk semiconductors makes the absorptance an exponential decay function below the bandgap. The presence of an Urbach tail reduces the efficiency when the absorber's bandgap is lower than the optimum value of 1.3 eV predicted by the S-Q model. A very small efficiency improvement (≤ 0.17 %) is possible only for those solar cells with bandgaps greater than 1.3 eV, of which their theoretical efficiency limits are substantially below the S-Q limit. A proof is presented to show that the maximum efficiency is obtained when the absorptance spectrum is a Heaviside step-function centered at the optimum bandgap given by the S-Q model; any other absorptance spectra will not beat this efficiency. A similar approach can be applied to the case of low dimensional structures such as quantum wells, quantum wires/nano wires, and quantum dots.