Acoustic Confinement in XBARs

Although excited by interdigital transducers (IDTs), laterally excited bulk acoustic wave resonators (XBARS) rarely require the reflector gratings necessary for surface acoustic wave (SAW) devices. This is partially a consequence of the low group velocity of the XBAR mode which localizes it and prevents radiation off the IDT. In this article we elucidate how the group velocity enters the radiation equations, reduces the attenuation length, and sets a lower bound on the number of IDT fingers required to ignore radiation loss. Radiated power is calculated for a simplified XBAR model, and a scaling formula for anti-resonance Q with the number of IDT fingers is derived. The scaling is verified with simulations of devices with varying pitch and length, but the effective attenuation length required to match simulation is far smaller than one would expect based on group velocity considerations alone.