A formula for the admittance of laterally excited bulk wave resonators (XBARs)

The recently invented laterally excited bulk wave resonators (XBARs) demonstrate outstanding parameters suitable for the design of low loss filters for the fifth generation of mobile phones. The operation of XBARs can be interpreted as an excitation of anti-symmetric Lamb mode A1 by the interdigital transducer. However, it can also be seen as the generation of fundamental plate resonances in a set of parallelly connected quasi-independent resonators, excited by a lateral electric field created by narrow electrodes with alternating polarity. By exploiting this latter interpretation, we propose a formula for the admittance of multi-layered membranes, including the main piezoelectric layer of suitable orientation and different additional dielectric layers on both sides of the membranes. The structure can be asymmetric and the excitation of all shear wave thickness resonances, not only with odd numbers, is described. The formula can be used for the one-dimensional modelling and optimisation of XBARs and the estimation of the resonance frequency dependence on the deposited trimming thin layers.