A Surface Cauchy-Born model for silicon nanostructures

We present a Surface Cauchy-Born approach to modeling non-centrosymmetric, semiconducting nanostructures such as silicon that exist in a diamond cubic lattice structure. The model is based on an extension to the standard Cauchy-Born theory in which a surface energy term that is obtained from the underlying crystal structure and governing interatomic potential is used to augment the bulk energy. The incorporation of the surface energy leads naturally to the existence of surface stresses, which are key to capturing the size-dependent mechanical behavior and properties of nanomaterials. We present the approach in detail, then demonstrate its capabilities by calculating the minimum energy configurations of silicon nanowires due to surface stresses as compared to full scale atomistic calculations.