The structure and elastic properties of phosphorene edges.

We investigated the edge atomic structures and elastic properties of defect-free phosphorene nanoribbons (PNRs). Density functional tight binding simulations were used to optimize two main edge configurations: armchair (AC) and zigzag (ZZ). It was found that the energy relaxation of PNRs leads to the noticeable changes in edge atomic configurations. The effective width of the edge region, which includes all the atoms involved in the edge relaxation, was found to contain approximately three atomic rows near the edge for both AC and ZZ PNRs. We further extracted the edge stress and modulus for the ZZ and AC edges. Both the AC and ZZ edge stresses of PNRs are positive, indicating tensile stress at the edges. In addition, both the AC and ZZ edge moduli are positive. However, the edge elastic modulus and edge stress of ZZ PNRs are about three times larger than those of AC PNRs. Furthermore, we showed that the tensile edge stresses along ZZ and AC edges are able to cause distortion in freestanding phosphorene nanoribbons. Our results highlight the importance of accounting for edge stresses in the design and fabrication of PNRs.