On the Origin of High Couplings Two-Dimensional Modes of Vibration in Aluminum Nitride Plates

This work discusses, for the first time through the Lamb-Wave theory, the origin of the recently reported high electromechanical coupling coefficient values $(k_{t}^{2})$ in two-dimensional modes of vibration excited in Aluminum Nitride (AIN) plates. In particular, we investigate the operation of the recently demonstrated Two-Dimensional Mode Resonators (2DMRs) and Cross-Sectional Lamé Mode Resonators (CLMRs). Precisely, we show how 2DMRs consist of dispersive $\mathbf{s}_{1}$-mode resonators. In contrast, we demonstrate that CLMRs consist of multi-modal resonators relying on both the $\mathbf{S}_{0^{-}}$ and $\mathbf{S}_{1}$-modes of vibration by operating at higher resonance frequencies, for the $\mathbf{S}_{0}$-mode, than the dilatational frequency relative to the $\mathbf{S}_{1}$-mode.