A genuine correlation in piezoelectric properties of two-dimensional materials: a high-throughput computational study

The rational design of two-dimensional piezoelectric materials has recently garnered increasing interest because of harnessing these materials in technological applications, including sensor technology, actuating devices, energy harvesting, and medical applications. Several materials possessing high piezoelectric response have been reported so far, but a high-throughput first-principles approach to estimate the piezoelectric potential of layered materials has not been performed yet. In this respect, we systematically investigated the piezoelectric ($e_{11}$, $d_{11}$) and elastic (C$_{11}$ and C$_{12}$) properties of 108 thermodynamically stable two-dimensional (2D) semiconductor materials by employing first-principle methods. Our calculations found a notable difference between the relaxed ion coefficients calculated with GGA and LDA functionals, indicating a strong exchange-correlation functional dependence. Nevertheless, both functionals yield the same trends for the elastic constants and piezoelectric coefficients. Our high-throughput approach demonstrates that the materials containing Group-\textrm{V} elements produce notably high piezoelectric strain constants, $d_{11}$ $>$ 40 pmV$^{-1}$, and 42 of considered materials have the $e_{11}$ coefficient higher than MoS$_{2}$ insomuch as BrSSb has one of the largest $d_{11}$ with a value of 503.6 pmV$^{-1}$. Besides, we established simple empirical models to estimate the $d_{11}$ coefficients by utilizing the relative ionic motion in the unit cell and the polarizability of the individual elements in the compounds. The proposed models, tested for both exchange-correlation functionals, are successful in estimating the piezoelectric constants of the studied materials with sufficient accuracy.