Nanotech 2006 Vol. 1
Nanotech 2006 Vol. 1
Technical Proceedings of the 2006 NSTI Nanotechnology Conference and Trade Show, Volume 1

Nanoscale Modeling Chapter 7

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

Authors: Z. Tang, H. Zhao, G. Li and N.R. Aluru

Affilation: University of Illinois at Urbana-Champaign, United States

Pages: 625 - 628

Keywords: multiscale, finite temperature, quasicontinuum, quasiharmonic models

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.

ISBN: 0-9767985-6-5
Pages: 871
Hardcopy: $119.95