Properly-tuned continuum and atomistic models for vibrational analysis of the silicon nanoplates

Abstract

The high computational costs of atomistic simulations for the investigation of nanostructures, despite their accuracy, necessitate efforts to develop efficient continuum models. Since the classical continuum mechanics assume the matter as continuous and ignore the size dependency of material properties, these theories fail to capture the behavior of materials at the nanoscale. Size-dependencies of nanostructures could result in the emergence of surface effects. This paper, for the first time, aims to develop and tune surface-enhanced continuum models to predict the vibrational properties of nanoplates which are inherently discrete at the nanoscale. Regarding this aim, we use a composite core-shell modeling scheme for integrating Kirchhoff and Mindlin plate theories with the surface effects. We have performed Molecular Dynamics (MD) simulations to determine the accurate vibrational behavior of silicon nanoplates. We present a systematic procedure for obtaining continuum model parameters, including the surface elastic parameters and surface-induced stress, from our MD simulation results. In doing so, this simulation method benefits from the merits of both continuum- and atomistic-based modeling. We further examine the validity of the developed continuum models by comparing the results achieved using calibrated continuum models and the validation set of MD results. It is demonstrated that properly tuned continuum models, especially the Mindlin plate theory with surface effects, can accurately predict the vibrational behavior of ultrathin Si nanoplates. Furthermore, our calibrated continuum models based on the Mindlin plate theory offer an effective tool for capturing higher natural frequencies of Si nanoplates, introducing new paradigms in nanomechanical resonators.