A nonlocal continuum model for the piezopotential of two-dimensional semiconductors

Owing to the intrinsic nanoscale dimension of two-dimensional (2D) piezoelectric semiconductors, the small-scale effects on their piezopotential properties are inevitable in their piezotronic applications. In this work, based on the nonlocal constitutive relations and the phenomenological theory of piezoelectric semiconductors, the small-scale effects are incorporated into the continuum modelling of the piezopotential for 2D semiconductors. After a linearized analysis is performed to the newly proposed nonlocal continuum model, the analytical expression of the piezopotential for 2D semiconductors is achieved, which is found to agree well with the density functional theory (DFT) results by choosing an appropriate characteristic nonlocal length. It is shown in our nonlocal continuum model that the small-scale effects can significantly enhance the piezopotential of 2D semiconductors, which tends to be more aggressive in 2D semiconductors with a smaller length or a larger initial carrier concentration. In addition, our DFT simulations also reveal that the influence of small-scale effects on the piezopotential properties of 2D semiconductors is attributed to the existence of nonlocal polarization, which originates from the end effects due to the finite length of their structures.