Ab Initio Prediction of Piezoelectricity in Two-Dimensional Materials

Two-dimensional (2D) materials present many unique materials concepts, including material properties that sometimes differ dramatically from those of their bulk counterparts. One of these properties, piezoelectricity, is important for micro- and nanoelectromechanical systems applications. Using symmetry analysis, we determine the independent piezoelectric coefficients for four groups of predicted and synthesized 2D materials. We calculate with density-functional perturbation theory the stiffness and piezoelectric tensors of these materials. We determine the in-plane piezoelectric coefficient d₁₁ for 37 materials within the families of 2D metal dichalcogenides, metal oxides, and III-V semiconductor materials. A majority of the structures, including CrSe₂, CrTe₂, CaO, CdO, ZnO, and InN, have d₁₁ coefficients greater than 5 pm/V, a typical value for bulk piezoelectric materials. Our symmetry analysis shows that buckled 2D materials exhibit an out-of-plane coefficient d₃₁. We find that d₃₁ for 8 III-V semiconductors ranges from 0.02 to 0.6 pm/V. From statistical analysis, we identify correlations between the piezoelectric coefficients and the electronic and structural properties of the 2D materials that elucidate the origin of the piezoelectricity. Among the 37 2D materials, CdO, ZnO, and CrTe₂ stand out for their combination of large piezoelectric coefficient and low formation energy and are recommended for experimental exploration.