  Phosphorene, a monolayer of black phosphorus, is promising for nanoelectronic
applications not only because it is a natural p-type semiconductor but also it
possesses a layer-number dependent direct bandgap (in the range of 0.3 eV~1.5
eV). On basis of the density functional theory calculations, we investigate
electronic properties of the bilayer phosphorene with different stacking
orders. We find that the direct bandgap of the bilayers can vary from 0.78 -
1.04 eV with three different stacking orders. In addition, a vertical electric
field can further reduce the bandgap down to 0.56 eV (at the field strength 0.5
V/{\AA}). More importantly, we find that when a monolayer of MoS_2 is
superimposed with the p-type AA- or AB-stacked bilayer phosphorene, the
combined tri-layer can be an effective solar-cell material with type-II
heterojunction alignment. The power conversion efficiency is predicted to be
~18% or 16% with AA- or AB-stacked bilayer phosphorene, higher than reported
efficiencies of the state-of-the-art trilayer graphene/transition metal
dichalcogenide solar cells.
