Conversion efficiency limits and optimized designs for tandem solar cells with realistic sub-cell material quality

To examine practical efficiency limits of tandem solar cells, we calculated conversion efficiency (η_sc) and optimized sub-cell band-gap energies (E_g) in 1-, 2-, 3-, 4-, and 5-junction cells via a detailed-balance theory, taking account of the realistic internal luminescence quantum yields (y_int) of the sub-cell materials. We found that η_sc drastically decreases as the geometric mean y_int* of all sub-cells´ y_int drops from 1 to 0.1, and decreases proportionally to logy_int * in the low-y_int * region. Even with moderate material quality with y_int * = 0.001, η_sc above 30% (35%) should be still available in 2-junction (3-junction) tandem cells, though we need optimized designs with much higher E_g than those known for the ideal cases with y_int * = 1.