Modeling of the elastic modulus of crystalline silicon based on a lattice dynamics approach

An augmented continuum theory, based on lattice dynamics theories, is developed to examine the elasticity of three-dimensional crystalline Si materials. The second-order elastic constants of Si can be expressed as the function of the force constants, with the modified Keating model. The phonon dispersion relations have been calculated by using the density functional perturbation (DFP) theory, from which the force constants can be extracted. Then the elastic modulus in any crystallographic directions can be calculated. The average deviation of Young's modulus from experiment is less than 3.8%. This approach is expected to be used in the design of silicon-based MEMS.