Recently, fabricated two dimensional (2D) phosphorene crystal structures have demonstrated great potential in applications of electronics. Mechanical strain was demonstrated to be able to significantly modify the electronic properties of phosphorene and few-layer black phosphorus. In this work, we employed first principles density functional theory calculations to explore the mechanical properties of phosphorene, including ideal tensile strength and critical strain. It was found that a monolayer phosphorene can sustain tensile strain up to 27% and 30% in the zigzag and armchair directions, respectively. This enormous strain limit of phosphorene results from its unique puckered crystal structure. We found that the tensile strain applied in the armchair direction stretches the pucker of phosphorene, rather than significantly extending the P-P bond lengths. The compromised dihedral angles dramatically reduce the required strain energy. Compared to other 2D materials, such as graphene, phosphorene demonstrates superior flexibility with an order of magnitude smaller Young's modulus. This is especially useful in practical large-magnitude-strain engineering. Furthermore, the anisotropic nature of phosphorene was also explored. We derived a general model to calculate the Young's modulus along different directions for a 2D system.

Recently fabricated two-dimensional phosphorene crystal structures have demonstrated great potential in applications of electronics. In this paper, strain effect on the electronic band structure of phosphorene was studied using first-principles methods including density functional theory (DFT) and hybrid functionals. It was found that phosphorene can withstand a tensile stress and strain up to 10 N/m and 30%, respectively. The band gap of phosphorene experiences a direct-indirect-direct transition when axial strain is applied. A moderate −2% compression in the zigzag direction can trigger this gap transition. With sufficient expansion (+11.3%) or compression (−10.2% strains), the gap can be tuned from indirect to direct again. Five strain zones with distinct electronic band structure were identified, and the critical strains for the zone boundaries were determined. Although the DFT method is known to underestimate band gap of semiconductors, it was proven to correctly predict the strain effect on the electronic properties with validation from a hybrid functional method in this work. The origin of the gap transition was revealed, and a general mechanism was developed to explain energy shifts with strain according to the bond nature of near-band-edge electronic orbitals. Effective masses of carriers in the armchair direction are an order of magnitude smaller than that of the zigzag axis, indicating that the armchair direction is favored for carrier transport. In addition, the effective masses can be dramatically tuned by strain, in which its sharp jump/drop occurs at the zone boundaries of the direct-indirect gap transition.

Two dimensional few-layer black phosphorus crystal structures have recently been fabricated and have demonstrated great potential in electronic applications. In this work, we employed first principles density functional theory calculations to study the edge and quantum confinement effects on the electronic properties of the phosphorene nanoribbons (PNR). Different edge functionalization groups, such as H, F, Cl, OH, O, S, and Se, in addition to a pristine case were studied for a series of ribbon widths up to 3.5 nm. It was found that the armchair-PNRs (APNRs) are semiconductors for all edge groups considered in this work. However, the zigzag-PNRs (ZPNRs) show either semiconductor or metallic behavior in dependence on their edge chemical species. Family 1 edges (i.e., H, F, Cl, OH) form saturated bonds with P atoms in the APNRs and ZPNRs, and the edge states keep far away from the band gap. However, Family 2 edges (pristine, O, S, Se) form weak unsaturated bonds with the p_z orbital of the phosphorus atoms and bring edge states within the band gap of the ribbons. For the ZPNRs, the edge states of Family 2 are present around the Fermi level within the band gap, which close up the band gap of the ZPNRs. For the APNRs, these edge states are located at the bottom of the conduction band and result in a reduced band gap.