Modeling and design of composite free-free beam piezoelectric resonators

A model is presented and experimentally validated for the design of asymmetrically layered piezoelectric free-free beam micromechanical resonators. The thin film resonators are composed of quad-symmetric torsional anchors connected to the nodal points of a free-free beam vibrating in its fundamental bending mode. The model provides analytical approximations for the resonance frequencies of the composite anchors and the free-free beam. Since dissipation in these devices is minimized when the mechanical impedances of the coupled structures are matched at resonance, i.e. when bending beam and torsional anchor resonance frequencies are equal, the model may be used to design resonators with optimized mechanical quality factors. The model is shown to successfully predict resonance frequencies in agreement with the results of finite element analysis and experimental results obtained for multi-layered lead zirconate titanate (PZT) piezoelectric microresonators with first natural frequencies in the range of 448 kHz to 1.1 MHz. The model is also validated as a tool for optimizing resonator quality factor.