Optimizing the electrode size of circular bimorph plates with different boundary conditions for maximum deflection of piezoelectric micromachined ultrasonic transducers.

The effect of plate electrode area on the deflection of a symmetric circular bimorph piezoelectric micromachined ultrasonic transducer (pMUT) with clamped and simply supported boundary conditions was studied for the first time. Distinct plate displacement shape functions were defined for the regions underneath and outside the active electrodes. The plate shape functions were solved analytically using classic plate theory in conjunction with the external boundary conditions and the internal ones between the two regions in order to calculate the exact plate displacement under both external voltage stimulus and acoustic pressure. The model was used to study the effect of the electrode area on the overall plate deflection per unit input voltage such that the electromechanical coupling is optimized. While the center plate deflection increased monotonically with the electrode area for a simply supported plate, it followed a parabolic shape for a clamped one with a maximum deflection when the electrode radius covered 60% of the total plate radius. The simply supported plate exhibited four times the plate deflection capability of its clamped counterpart, when both are operating at their optimal electrode size. Both an experimental clamped bimorph aluminum nitride (AlN) pMUT, recently reported in the literature, and Finite Element Modeling (FEM) were used to verify the developed model. The theoretical model predicted a static displacement per unit voltage of 10.9nm/V and a resonant frequency of 196.5kHz, which were in excellent agreement with the FEM results of 10.32nm/V and 198.5kHz, respectively. The modeling data matched well with the experimental measurements and the error ranged from 2.7-22% due to process variations across the wafer. As such, the developed model can be used to design more sensitive pMUTs or extract the flexural piezoelectric coefficient using piezoelectrically actuated circular plates.