On the piezopotential properties of two-dimensional materials

The development of recently discovered two-dimensional (2D) piezotronics will benefit from the comprehensive understanding of the piezopotential properties of 2D materials. Taking two most widely studied 2D piezoelectric nanomaterials (PNMs), hexagonal boron nitride and molybdenum disulfide for examples, in this paper we investigate the piezopotential properties of 2D PNMs based on numerical simulations and analytical modelling. Our molecular dynamics (MD) simulations show that the piezopotential coefficients of 2D PNMs can be significantly enhanced by small-scale effects at the nanoscale, which becomes more aggressive as the length of 2D PNMs decreases. In addition, a complicated piezopotential distribution is also observed in the stretched 2D PNMs due to the influence of small-scale effects. The influence of small-scale effects on piezopotential properties of 2D PNMs is beyond the reach of previously widely used classical electromechanical theories. To consider the small-scale effects in the analytical modelling of 2D PNMs, we propose here a novel nonlocal electromechanical model based on Eringen's nonlocal theory. Analytical expressions of the piezopotential distribution and piezopotential coefficient of intrinsic 2D PNMs are obtained from the proposed nonlocal models, which show good agreements with MD simulation results. In addition to the electromechanical properties, small-scale effects can also affect the piezopotential of 2D PNMs by changing their semiconducting properties, since it is observed in our density functional theory calculations that the conduction band edges of 2D PNMs can be greatly downwards shifted by small-scale effects.