Electronic structure of phosphorene nanoflakes. A theoretical insight

Abstract

Abstract Phosphorene nanoflakes of different shapes and sizes were studied at the hybrid BHandHLYP level of theory. This functional accurately reproduces the experimental bond lengths and valence angles of black phosphorus. All nanoflakes were found to have a singlet ground state and their band gaps (Egs) decrease linearly with 1/N, where N is the number of P atoms in the nanoflakes. It seems that the topology of the nanoflake edges does not affect Eg. The ionization potentials (IPs) and electron affinities (EAs) generally grow smaller with increasing nanoflake size. The change in IPs and EAs with size correlate with the delocalization pattern of polaron cations and anions. The shape and nature or the longest edge (zig-zag or armchair) affect both the IP and EA. Nanoflakes with a long zigzag edge have higher IPs and lower EAs compared to square systems. Low theoretically calculated hole reorganization energies (less than 0.1 eV) are in agreement with the experimentally determined high hole mobility in phosphorene. The low hole reorganization energies are due to the better ability of phosphorene nanoflakes to delocalize polaron cations compared to polaron anions.