Continuum models calibrated with atomistic simulations for the transverse vibrations of silicon nanowires

We have conducted Molecular Dynamics (MD) simulations with the Environment-Dependent Interatomic Potential (EDIP) to obtain the natural frequency of ultra-thin Silicon Nanowires (SiNWs) with various crystallographic structures, boundary conditions and dimensions. As expected, results show that the mechanical properties of SiNWs are size-/orientation-dependent. The observed phenomena are ascribed to the surface effects which become dominant due to the large surface-to-volume number of atoms at the investigated range of dimensions. Due to their accuracy, atomistic simulations are widely accepted for the investigations of such nano-scaled systems; however, they suffer from high computational costs. In this regard, continuum models are appreciated due to their efficacy; but they are not accurately applicable in very small nano-scales where the basic assumptions of continuity are undermined. Nevertheless, we aim in this paper to propose and prove that suitably improved continuum models are still applicable for these systems. In order to account for the surface effects, including the surface elasticity and surface stress, we have proposed a shell-core composite continuum model; at which the bulk core is modeled by the Euler-Bernoulli or Timoshenko beams, while the thin bonding surface layers with different elastic parameters are added to incorporate with the surface effects. We have estimated the surface stress and the surface elastic parameters using our MD simulations results; then we have shown that the calibrated continuum models are capable of predicting the vibrational behavior of SiNWs having thicknesses larger than 2 nm.