A General Analytical Formulation for the Motional Parameters of Piezoelectric MEMS Resonators

This paper reports on a general analytical expression for the motional resistance (R
_m
) of an arbitrary mode in a piezoelectric microelectromechanical system resonator with parallel plate electrode geometry. After applying simplifying assumptions and using analytical modes shapes, expressions for the R
_m
of modes with out-of-plane flexure as the primary displacement are presented. These modes include free-free transverse beam flexure (TBF), unclamped disk flexure resonators (DFRs), and antisymmetric A
₀
Lamb modes. For verification, R
_m
is extracted from resonators fabricated in a lead zirconate titanate on silicon process. Predicted R
_m
of TBF and DFR modes is validated using on-wafer extracted e
₃₁
constants, analytical modal properties, and independently measured material properties.