Acoustic meta-materials in MEMS BAW resonators

This paper presents a meta-material-based design method for bulk acoustic wave (BAW) resonators with enhanced characteristics compared to those obtained with the typical bulk material implementation. We demonstrate the novel use of empty inclusions (i.e., ‘holes’) in bulk materials for engineering their acoustic (mechanical) properties (e.g. Young’s modulus E, Poisson’s ratio ν and mass density ρ) to tune and achieve optimal acoustical performance/characteristics. Inclusions have been demonstrated before to produce phononic band gaps for wave trapping. We focus on the propagation characteristics of the meta-materials brought into being by these inclusions. We implement patterns of holes with different sizes and distributions, to effectively scatter acoustic waves in bar-type BAW resonators and to devise the desired resonator properties, e.g., the resonant frequency. While the available bulk material is homogeneous and isotropic, the bar consists of an equivalent non-homogeneous material that can for example be distributed by design in order to shrink the overall resonator size, enhance electromechanical transduction coefficients or reject spurious modes. Our paper compares two extraction methods for the equivalent material properties of a periodically hole-punched material: the steady-state mechanical simulation of a unit cell and its ‘phase delay’ counterpart. We discuss their validity and practical use for the design of bar resonators.