Modelling of the elastic properties of crystalline silicon using lattice dynamics

Abstract

Based on lattice dynamics theories, an augmented continuum theory is developed to examine the elasticity of crystalline silicon. In the augmented continuum theory, the framework of continuum mechanics is used while the property of silicon from the atomistic description of the underlying local environment is extracted. The phonon dispersion relations are first calculated using the density functional perturbation theory, from which the force constants can be extracted. The second-order elastic constants of Si are then expressed as a function of the force constants. Combining the modified Keating model with the phonon dispersion relations, an analytic expression for certain high-symmetry k point phonon frequencies and the elastic constants of Si is obtained. The elastic modulus in any crystallographic directions in the (1 1 0) plane is calculated, and the average deviation of Young's modulus from experiments is less than 3.2%.