Phonon modes in Si [111] nanowires

We solve a long standing question concerning the boundary conditions for optical phonons in nanowires. The controversy between the so-called clamped and free conditions is well documented in standard literature. We answer this question of the boundary conditions by presenting a spring-and-mass model of the Stillinger and Weber type to calculate optical and acoustic phonons in Si [111] nanowires. Our results show that this model, in parallel to the bulk case, is sufficient to describe important features of the phonon spectrum. Furthermore, our results predict that optical phonons in nanowires are subject to clamped boundary conditions.