Analytical study on effect of ring geometry on frequency shift of piezoelectric ring-shaped resonator

Ring-shaped resonators with one and fourpoint- outer-pinned supports have been designed in this work. The ring-shaped resonator reacts with a mass perturbation to provide eigenstate or frequency shifts which could transfer to electrical signals by piezoelectric effect. The aforementioned ring-shaped resonator is mainly comprised with a multilayer of Pt/Ti/PZT/Pt/Ti/SiO ₂ deposited on the silicon-on-insulator wafer and expected to be a contour mode. In order to estimate the sensitivity of the ring-shaped resonator against the mass perturbation, the theoretical analysis was conducted by ANSYS from two aspects including: (a) the view point of geometrical design and (b) the mass application methodology. When a mass perturbation (i.e., a liquid droplet) of 10 pg is homogeneously contacting on the top electrode of the resonator, frequency shifts from 2.11 to 4.07 kHz could be obtained when excited in the contour mode. Furthermore, the more stabled vibration behavior of resonator with four-pointpinned supports was approved by the computer stimulation of ANSYS analysis results.