Confinement Effects in Two-Dimensional Silicon Structures

Two-dimensional silicon structures are currently attracting a great deal of attention due to their potential application in the electronic and energy sectors. Most published works have employed simple face-centered cubic (fcc) models in determining dispersion curves and density of states for silicon. In this paper we address confinement effects in silicon using a two- and three-body environment-dependent interatomic potential (EDIP). Dispersion curves for silicon thin films under free-standing boundary conditions are theoretically computed by means of the dynamical equation. We show how size confinement causes the emergence of new energy levels and a flattening of the dispersion curves, explaining the reduction of phonon group velocities with respect to bulk, and the change in the volumetric specific heat. Our results indicate when confinement effects begin to play a primary role in the dynamical behavior of the structure and allow the prediction of the number of atomic layers above which a silicon film can be considered thick in terms of its dynamical behavior.