Effects of size and surface on the elasticity of silicon nanoplates: Molecular dynamics and semi-continuum approaches

In this paper, the size effects on the elastic behavior of single crystal silicon nanoplates terminated by {100} surfaces is studied by means of molecular dynamics (MD) using a modified embedded atom method. The results indicate that the {100} surfaces undergo 2 × 1-type reconstruction, which significantly influences the mechanical properties of nanoplates. The simulations are carried out at room temperature and structural relaxation is performed. The effective Young's modulus, in extensional mode, is determined for different thicknesses. The surface energy, surface stress and surface elasticity of layers near the surfaces (non-bulk layers) are obtained. These surface properties are used as inputs for a recently developed two-dimensional plane-stress semi-continuum framework. The framework can be seen as the link between the surface effects calculated by atomistic simulations and the overall elastic behavior. The surface properties of nanoplates of a few layers are shown to deviate from thicker plates, suggesting a size dependence of surface parameters and, especially, surface energy. For thicknesses below 3 nm, there is a difference between the effective Young's modulus, calculated by the semi-continuum approach and that calculated directly by MD. The difference is due to the size dependence of surface parameters.