Nanomechanical Modeling of the Bending Response of Silicon Nanowires

Understanding the mechanical behavior of silicon nanowires is essential for the implementation of advanced nanoscale devices. Although bending tests are predominantly used for this purpose, their findings should be properly interpreted through modeling. Various modeling approaches tend to ignore parts of the effective parameter set involved in the rather complex bending response. This oversimplification is the main reason behind the spread of the modulus of elasticity and strength data in the literature. Addressing this challenge, a surface-based nanomechanical model is introduced in this study. The proposed model considers two important factors that have so far remained neglected despite their significance: (i) intrinsic stresses composed of the initial residual stress and surface-induced residual stress and (ii) anisotropic implementation of surface stress and elasticity. The modeling study is consolidated with molecular dynamics-based study of the native oxide surface through reactive force fields and a series of nanoscale characterization work through in situ three-point bending test and Raman spectroscopy. The treatment of the test data through a series of models with increasing complexity demonstrates a spread of 85 GPa for the modulus of elasticity and points to the origins of ambiguity regarding silicon nanowire properties, which are some of the most commonly employed nanoscale building blocks. A similar conclusion is reached for strength with variations of up to 3 GPa estimated by the aforementioned nanomechanical models. Precise consideration of the nanowire surface state is thus critical to comprehending the mechanical behavior of silicon nanowires accurately. Overall, this study highlights the need for a multiscale theoretical framework to fully understand the size-dependent mechanical behavior of silicon nanowires, with fortifying effects on the design and reliability assessment of future nanoelectromechanical systems.