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Finite Temperature Quasicontinuum Method for Thermal and Mechanical Analysis of Silicon Nanostructures

Z. Tang, H. Zhao, G. Li and N.R. Aluru
University of Illinois at Urbana-Champaign, US

Keywords:
multiscale, finite temperature, quasicontinuum, quasiharmonic models

Abstract:
We formulate a finite temperature quasicontinuum method to calculate the thermodynamic and elastic properties of crystalline silicon as well as the mechanical response of silicon nanostructures subjected to externally applied forces. We solve the continuum elasticity governing equations at the continuum level and calculate the material constitutive relations at the atomistic level where the silicon atoms are described by the Tersoff interatomic potential. At finite temperature, the continuum constitutive relation is computed through the Helmholtz free energy density at the representative atoms. The Helmholtz free energy density is calculated by using the quantum-mechanical lattice dynamics with a local quasiharmonic approximation (LQHM) and a k-space quasiharmonic approximation (QHMK) of the Tersoff potential. In the k-space quasiharmonic model, a semi-local approximation of the vibrational component of the Helmholtz free energy is proposed. To demonstrate the method, we first calculate the variation of the lattice parameter, the Helmholtz free energy, the entropy and the elastic constants as a function of temperature. We then compute the deformation response of silicon nanostructures for various external loads by using the proposed finite temperature quasicontinuum method.

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