Modal-Transition-Induced Valleys of K² in Piezoelectric Bilayer Laterally Vibrating Resonators

Piezoelectric Laterally Vibrating Resonators (LVRs) have attracted significant attention as a potential technology for next-generation wafer-level multi-band filters. Piezoelectric bilayer structures such as Thin-film Piezoelectric-on-Silicon (TPoS) LVRs which aim to increase the quality factor (Q) or aluminum nitride and silicon dioxide (AlN/SiO₂) composite membrane for thermal compensation have been proposed. However, limited studies have investigated the detailed behaviors of the electromechanical coupling factor (K²) of these piezoelectric bilayer LVRs. Herein, AlN/Si bilayer LVRs are selected as an example, we observed notable degenerative valleys in K² at specific normalized thicknesses using two-dimensional finite element analysis (FEA), which has not been reported in the previous studies of bilayer LVRs. Moreover, the bilayer LVRs should be designed away from the valleys to minimize the reduction in K². Modal-transition-induced mismatch between electric and strain fields of AlN/Si bilayer LVRs are investigated to interpret the valleys from energy considerations. Furthermore, the impact of various factors, including electrode configurations, AlN/Si thickness ratios, the Number of Interdigitated Electrode (IDT) Fingers (NFs), and IDT Duty Factors (DFs), on the observed valleys and K² are analyzed. These results can provide guidance for the designs of piezoelectric LVRs with bilayer structure, especially for LVRs with a moderate K² and low thickness ratio.