The Shockley-Queisser limit and practical limits of nanostructured photovoltaics

Here we: (1) Briefly discuss the large variation of the so called Shockley-Queisser limit based on the assumptions used to calculate it (choice of incident spectrum, refractive index of the medium on each side of the cell, and the emissivity) and compare existing PV technologies to their theoretical limit. As opposed to many reports that compare the measured V_OC with the bandgap as a ratio (V_OC/E_g) or a difference (E_g-V_OC), we show how each technology compares to the maximum possible V_OC as determined by a detailed balance calculation (V_OC/V_OC,Max). (2) Present a new and simple model based on an integral form of the continuity equation (around an element of the nanostructure) and a novel transit time formulation that illuminates the practical limits and opportunities of nanostructured PV. The model accounts for Shockley-Read-Hall (SRH) bulk and interfacial recombination and the effect of reduced electric field strengths on the collection efficiency as a function of the length scale of the nanostructured pn junction. The model shows that for a given material (bulk lifetime, surface recombination velocity, dopant concentration, mobility, etc.) there exists an ideal length scale for nanostructuring. The model shows that in some cases a poor performing bulk material (5% efficient) may be turned into a high performing device (20% efficient). The model also shows the effects of multiple exciton generation.