Elucidating the origin of spurious modes in aluminum nitride microresonators using a 2-D finite-element model

In this work, an approach has been developed to predict the location of large spurious modes in the resonant response of aluminum nitride (AlN) microelectromechanical systems (MEMS) resonators over a wide range of desired operating frequencies. This addresses significant challenges in the design of more complex AlN devices, namely the prediction and elimination of spurious modes in the resonance response. Using the finite element method (FEM), the dispersion curves at wavelengths ranging from 8 to 20 μm were computed. It was determined that the velocities of symmetric Lamb (S0) and high-order antisymmetric (A) modes overlap at specific wavelengths. A 2-D FEM analysis showed that both the S0 and higher order A modes are mutually excited at a common operating wavelength. From this analysis, the coupling-of-modes (COM) parameters were extracted and used to compute the P-matrix and S-parameters using a 6-port transmission matrix. The P-matrix simulation was able to predict the electrical response of the S0 and nearby spurious modes. This work identified specific wavelength regions where COM has limited accuracy because of mode conversion. In these regions, the reflection (κ(p)) and transduction (ζ(p)) parameters change rapidly.