Physics of band-gap formation and its evolution in the pillar-based phononic crystal structures

In this paper, the interplay of Bragg scattering and local resonance is theoretically studied in a phononic crystal (PnC) structure composed of a silicon membrane with periodic tungsten pillars. The comparison of phononic band gaps (PnBGs) in three different lattice types (i.e., square, triangular, and honeycomb) with different pillar geometries shows that different PnBGs have varying degrees of dependency on the lattice symmetry based on the interplay of the local resonances and the Bragg effect. The details of this interplay is discussed. The significance of locally resonating pillars, specially in the case of tall pillars, on PnBGs is discussed and verified by examining the PnBG position and width in perturbed lattices via Monte Carlo simulations. It is shown that the PnBGs caused by the local resonance of the pillars are more resilient to the lattice perturbations than those caused by Bragg scattering.