Strain-modulated defect engineering of two-dimensional materials

Strain- and defect-engineering are two powerful approaches to tailor the opto-electronic properties of two-dimensional (2D) materials, but the relationship between applied mechanical strain and behavior of defects in these systems remains elusive. Using first-principles calculations, we study the response to external strain of $h$-BN, graphene, MoSe$_2$, and phosphorene, four archetypal 2D materials, which contain substitutional impurities. We find that the formation energy of the defect structures can either increase or decrease with bi-axial strain, depending on the atomic radius of the impurity atom, which can be larger or smaller than that of the host atom. Analysis of the strain maps indicates that this behaviour is associated with the compressive or tensile local strains produced by the impurities that interfere with the external strain. We further show that the change in the defect formation energy is related to the change in elastic moduli of the 2D materials upon introduction of impurity, which can correspondingly increase or decrease. The discovered trends are consistent across all studied 2D materials and are likely to be general. Our findings open up opportunities for combined strain- and defect-engineering to tailor the opto-electronic properties of 2D materials, and specifically, the location and properties of single-photon emitters.