Conversion efficiency limits and bandgap designs for multi-junction solar cells with internal radiative efficiencies below unity

We calculated the conversion-efficiency limit η_sc and the optimized subcell bandgap energies of 1 to 5 junction solar cells without and with intermediate reflectors under 1-sun AM1.5G and 1000-sun AM1.5D irradiations, particularly including the impact of internal radiative efficiency (η_int) below unity for realistic subcell materials on the basis of an extended detailed-balance theory. We found that the conversion-efficiency limit η_sc significantly drops when the geometric mean η_int∗ of all subcell η_int in the stack reduces from 1 to 0.1, and that η_sc degrades linearly to logη_int∗ for η_int∗ below 0.1. For η_int∗<0.1 differences in η_sc due to additional intermediate reflectors became very small if all subcells are optically thick for sun light. We obtained characteristic optimized bandgap energies, which reflect both η_int∗ decrease and AM1.5 spectral gaps. These results provide realistic efficiency targets and design principles.