On the size-dependent elasticity of silicon nanocantilevers: impact of defects

Recent measurements have indicated that the elastic behaviour of silicon nanocantilevers and nanowires is size-dependent. Several theoretical models have been proposed to explain this phenomenon, mainly focused on surface stress effects. However, discrepancies are found between experiments and theories, indicating that there could be other influences in addition to surface effects. One of the important issues, which was experimentally confirmed and has not been considered, is accounting for the fact that experimentally tested nanocantilevers and nanowires are not defect free. In this paper molecular dynamics (MD) is utilized to study the effects of defects on the elasticity of silicon. The effective Young’s modulus Ẽ of [1 0 0] and [1 1 0] oriented silicon nanoplates is extracted in the presence of defects, showing that such defects significantly influence the size-dependent behaviour in Ẽ. The MD results are compared with the results of continuum theory, showing that continuum theory holds, even for very small defects. Taking into account the surface effects, native oxide layers together with fabrication-induced defects, the experimental measurements can be explained. The studied example involved nanocantilevers, but can be extended to nanowires. (Some figures in this article are in colour only in the electronic version) Due to advantages of miniaturization, such as smaller size, shorter time response, higher performance and reduced energy requirements, significant research efforts have been directed towards the developments of nanoelectromechanical systems (NEMS). The building blocks of NEMS are mostly nanocantilevers, nanoplates, nanowires and nanotubes. Due to their applications, their mechanical properties are of considerable interest. Recent experimental [1–4] and computational studies, including ab initio and density functional theory (DFT) [5–7], molecular dynamics (MD) [8–11] and modifications to continuum theory [12–15] revealed strong size-dependent mechanical properties as the characteristic dimensions of the structure approached nanometre scale. Li et al [1] measured the Ẽ of [1 1 0] silicon cantilevers with thicknesses ranging from 300 to 12 nm using the resonance frequency method. The Ẽ showed significant decrease from 167 to 53 GPa. Gordon et al [2] performed a new, multipoint bending protocol in an atomic force microscope in order to extract the elastic modulus of vertically aligned Si [1 1 1] nanowires (diameter ranges from 100 to 700 nm) in an as-grown state. Zhu et al [4] measured the effective Young’s modulus of silicon nanowires with diameters between 15 and 60 nm and lengths between 1.5 and 4.3μm. 0022-3727/11/072001+06$33.00 1 © 2011 IOP Publishing Ltd Printed in the UK & the USA J. Phys. D: Appl. Phys. 44 (2011) 072001 Fast Track Communication Figure 1. Measured effective Young’s modulus of silicon nanocantilevers for different thicknesses (squares [3] and stars [1]). The triangles are the results of direct MD simulation in extensional mode [22]. The solid line shows the prediction of size dependence when considering surface elasticity [15], and the dashed line shows the prediction when additional 2 nm native oxide layers are taken into account [21]. The nanowires, grown by the vapour–liquid–solid process, were subjected to tensile tests in situ inside a scanning electron