First-principles calculation of mechanical properties of Si⟨001⟩ nanowires and comparison to nanomechanical theory

Abstract

We report the results of first-principles density functional theory calculations of the Young's modulus and other mechanical properties of hydrogen-passivated Si 001 nanowires. The nanowires are taken to have predominantly {100} surfaces, with small {110} facets according to the Wulff shape. The Young's modulus, the equilibrium length and the constrained residual stress of a series of prismatic beams of differing sizes are found to have size dependences that scale like the surface area to volume ratio for all but the smallest beam. The results are compared with a continuum model and the results of classical atomistic calculations based on an empirical potential. We attribute the size dependence to specific physical structures and interactions. In particular, the hydrogen interactions on the surface and the charge density variations within the beam are quantified and used both to parameterize the continuum model and to account for the discrepancies between the two models and the first-principles results.

Size and temperature effects on the fracture mechanisms of silicon nanowires: Molecular dynamics simulations

“…The Young's modulus of a [0 0 1]-oriented NW with D = 2 nm is about 26% smaller than the bulk value (122.5 GPa). Even though the NWs in Lee and Rudd (2007) have a different orientation from the NWs in this study, the consistency in the general trend in the size dependence is encouraging. It suggests that a common mechanism is responsible for the reduction of the Young's modulus for Si NWs with different orientations.…”

“…Similarly, the Young's modulus of the [1 1 1] NW of D = 2 nm is reduced by 33% from the bulk value (168 GPa at 300 K for the MEAM model). Lee and Rudd (2007) calculated the Young's modulus of [0 0 1]-oriented NWs by first-principle density functional theory. They also reported a monotonic reduction of Young's modulus as NW diameter decreases.…”

Mechanics of Nanoelectromechanical Systems: Bridging the Gap Between Experiment and Theory

“…The existence of scale-dependent behavior has been confirmed by experimental measurements, including resonance frequency tests [6], tensile testing in scanning electron microscope (SEM) [7], transmission electron microscope (TEM) [8,9], atomic force microscope (AFM) [10,11] and nanoindenter [12] and also theoretical investigations, including ab initio and density functional theory (DFT) [13,14,15], molecular dynamics (MD) [16,17,18,19] and modifications to continuum theory [20,21,22,23]. Although scale-dependence has been observed by both theory and experiment, a considerable discrepancy still remains between the experiments and models.…”

“…The surface atoms have lower coordination numbers and electron densities and therefore tend to adopt equilibrium lattice spacing differently from the bulk ones [48,23]. On the other hand, the epitaxial relationship from bulk to surface has to be maintained, therefore, bulk atoms strain the atoms near the surface and create the so-called surface stress [13,23,36,49]. Consequently, the surface atoms like to reconstruct and can deviate easily from their original ideal situations, and therefore, have different elasticity compared to the bulk, known as surface elasticity [41,47,20,23].…”

“…and not defect free (such as single crystal defects, fabrication induced imperfections etc.) in contrast to the perfect mono-crystalline structures studied using atomistic simulations [19,17,14,13]. The goal of this chapter is to try to determine to what extent these effects influence the effective elastic modulus of nanosystems, to try to reduce the existing gap between the experiments and theory of scale-dependence, and to determine the origin of the scale-dependence in silicon nanosystems.…”