Bridging the gap between experimental measurements and atomistic predictions of the elastic properties of silicon nanowires using multiscale modeling

In the present work, we have applied recently developed nonlinear multiscale finite element techniques which account for nanoscale surface stress and surface elastic effects to investigate the elastic properties of silicon nanowires as obtained through bending deformation. The numerical results are used to clarify the factors underlying the current disconnect between atomistic simulations and experiments as to the nanowire sizes at which deviation from bulk elastic properties due to surface effects are observed. In particular, we demonstrate that when nanowires with aspect ratios (defined as the axial length divided by the square cross sectional length) larger than about 15 are considered, the elastic softening that has been observed experimentally for larger (i.e. > 20 nm diameter) nanowires is observed. In contrast, when smaller aspect ratios are considered, very little deviation from the bulk elastic properties are observed, in agreement with existing atomistic calculations. Furthermore, we demonstrate that the elastic softening is strongly boundary condition dependent, where fixed/fixed silicon nanowires exhibit a strong aspect ratio-dependent softening, while little variation in the elastic properties of fixed/free nanowires are observed. Comparisons are made with existing surface elastic theories and experiments to bring further insights into the boundary condition dependence in elastic properties.