Simulation of solidly mounted BAW resonators using FEM combined with BEM and/or PML

Finite element method (FEM) has become an important approach in the modeling of bulk acoustic wave (BAW) resonators. Unfortunately FEM is not capable of describing unbounded regions, the substrate and the sides of the resonator. Perfectly matched layer (PML) can be used to prevent artificial reflection of the wave on the clamped sides, while the substrate is traditionally modeled by a boundary element method (BEM). This work presents numerical simulation of solidly mounted BAW resonators where both PML and BEM are used to model the substrate. With the correct adjustment of PML parameters, the resonator impedance computed with the FEM/PML model approaches the FEM/BEM results, both are in good agreement with the measured data.