Size modulation electronic and optical properties of phosphorene nanoribbons: DFT-BOLS approximation.

DFT and BOLS approximations were carried out to study the electronic and optical properties of different sizes of black phosphorus nanoribbons (PNRs) with either zigzag- or armchair-terminated edges. PNRs exhibit a nearly direct bandgap, the size of which is strongly increased because of quantum effects. Meanwhile, the bandgap energies of these two kinds of edge PNRs reveal an excellent size dependency. We reconcile the size-dependence of the bandgap energy shifts for PNRs with respect to stimulated bond relaxation, and quantification of the bond length, the bond strength, and the bond nature index. Our calculations suggest that atomic under-coordination shortens the length and increases the stiffness of the P-P bond, which widens the bandgap.