Full 3D FEM Simulation of Thickness Shear Bulk Acoustic Resonators on LN Assisted by Hierarchical Cascading Technique

This paper describes full three-dimensional (3D) simulation of transverse modes in thickness shear bulk acoustic resonators (TSBARs) on lithium niobate. The calculation is performed by the 3D finite element method (FEM) assisted by the hierarchical cascading technique (HCT). Owing to used rectangular-shaped electrodes, the HCT is applicable to the 3D FEM, and reduces required memory size and computational time significantly. It is shown that without apodization, transverse resonances can be suppressed almost completely by applying free side edges for X planes and standard piston mode design normal to the X direction. The result also indicates that the simple two-dimensional FEM simulation is enough for the standard piston mode design in this case. These conclusions are consistent with those obtained experimentally. The analysis is extended to influence of the edge ratio of the rectangular electrodes to the
$Q$
factor and spurious responses. The result indicates that the square shape is preferable in total.