An analytical solution for curved piezoelectric micromachined ultrasonic transducers with spherically shaped diaphragms

An analytical solution for piezoelectrically actuated spherically shaped diaphragms has been developed to study their dynamic behavior with targeted applications in piezoelectric micromachined ultrasonic transducers (pMUT). The analytical model starts with a curved pMUT composed of a piezoelectric diaphragm with a nominal radius in size, a radius of curvature in shape, and under both possible actuation sources of radial pressure and electric potential. The diaphragm has the piezoelectric material polarized in the direction perpendicular to its surface and sandwiched between two metal electrodes. When an electric field is applied between the two electrodes, the in-plane piezoelectric strain can cause larger out-of-plane deflections than a flat unimorph piezoelectric diaphragm because of the diaphragm's spherical curvature with a clamped periphery for high electromechanical coupling factor. Key performance parameters, including mechanical mode shapes, resonant frequencies, dynamic responses, and displacements, with respect to the curvature and size of the diaphragm have been investigated. Both analytical derivations and numerical simulations using finite element analysis have been performed for the optimal design of the electromechanical coupling factor, with varying factors such as mechanical resonant frequency, radius of curvature, nominal radius, and thickness. As such, this work provides theoretical foundations for the design of curved pMUTs with high electromechanical coupling factor compared with planar-shape pMUTs.