Comparison of Solar Cell Efficiencies of Black Phosphorus and Silicon at the Nano and Micro Scales from First-Principles Calculations

Density functional theory and many-body (GW+BSE) calculations of transmittance, absorbance, and reflectance are performed on silicon and black phosphorus (BP). We find that a damping value of 0.01 used in the dielectric function calculation is the optimal for calculating the solar cell efficiency of Si. Our calculations indicate that the solar cell efficiency of a 100 {\mu}m thick Si slab is 27.4% while the efficiency of BP for the same thickness is 2.33% and 1.94% for light polarized along the zigzag and armchair directions, respectively. For 100 nm thick materials, we obtain that Si presents a 0.8% solar cell efficiency and BP exhibits a 0.14% and 1.02% efficiency for light polarized along the the zigzag and armchair directions, respectively, indicating that BP performs better than Si at these small scales. Our results underscore the important effect of the material thickness on solar cell efficiencies.