Theoretical study of the elasticity of ultra-thin finite silicon nanowires. I. Semiempirical model considerations

We present a theoretical framework towards the development of a hybrid theoretical technique for the mixed ab initio and semiempirical calculation of the elastic modulus of ultra thin hydrogenated silicon nanowires. The present approach achieves accurate results at low computational cost by combining ab initio and semiempirical theoretical techniques. Here we describe the basic steps of such a theoretical scheme which combines continuum models like Timoshenko and Euler-Bernoulli beam theory with ab initio and semiempirical methods. Our current modified beam-method-like technique is implemented through accurate real space density functional theory, using the PBE functional, which calibrates semiempirical results from AM1. The present results for the Young's modulus of [1 1 0] NWs range from 148-156 GPa, comparable to results in the literature obtained by methods of very high computational cost.