Geometric and electronic structures of mono- and di-vacancies in phosphorene

The geometric structures, stabilities and diffusions of the monovacancy (MV) and divacancy (DV) in two-dimensional phosphorene, as well as their influences on their vibrational and electronic properties have been studied by first-principles calculations. Two possible MVs and 14 possible DVs have been found in phosphorene, in which the MV-(5|9) with a pair of pentagon-nonagon is the ground state of MVs, and the DV-(5|8|5) with a pentagon-octagon-pentagon structure is the most stable DV. All 14 DVs could be divided into four basic types based upon their topological structures and transform between different configurations via bond rotations. The diffusion of MV-(5|9) is found to exhibit an anisotropic character, preferring to migrate along the zigzag direction in the same half-layer. The introduction of MV and DV in phosphorene influences its vibrational properties, inducing the localized defect modes, which could be used to distinguish different vacancy structures. The MVs and DVs also have a significant influence on the electronic properties of phosphorene. It is found that the phosphorene with MV-(5|9) is a ferromagnetic semiconductor with the magnetic moment of 1.0 μB and a band gap of about 0.211 eV, while the DV induces a direct-indirect band gap transition. Our calculation results on the MV and DV in phosphorene are important for the promising application of the phosphorene in the nanoelectronics.