Waveguiding in supported phononic crystal plates

We investigate, with the help of the finite element method, the existence of absolute band gaps in the band structure of a free-standing phononic crystal plate and of a phononic crystal slab deposited on a substrate. The two-dimensional phononic crystal is constituted by a square array of holes drilled in an active piezoelectric (PZT5A or AlN) matrix. For both matrix materials, an absolute band gap occurs in the band structure of the free-standing plate provided the thickness of the plate is on the order of magnitude of the lattice parameter. When the plate is deposited on a Si substrate, the absolute band gap still remains when the matrix of the phononic crystal is made of PZT5A. The AlN phononic crystal plate losses its gap when supported by the Si substrate. In the case of the PZT5A matrix, we also study the possibility of localized modes associated with a linear defect created by removing one row of air holes in the deposited phononic crystal plate.