An analytical analysis of the sensitivity of circular piezoelectric micromachined ultrasonic transducers to residual stress

In this work, a novel Green´s function technique is used to solve for plate deflection of a piezoelectric micromachined ultrasonic transducer (pMUT) under the influence of residual stress. The pMUT is modelled as a clamped, circular diaphragm consisting of a stack of structural and piezoelectric material actuated by an arbitrary number of circular electrodes. From classic plate theory, the equation of motion for axisymmetric bending is derived based on residual stress considering external pressure, voltage applied across the piezoelectric material, and electrode geometry. With Green´s function, the equation of motion is analytically solved where the plate impedance shows a considerable increase in bandwidth and center deflection for a plate under compressive stress. The static zero-bias deflection of a microfabricated pMUT with a center electrode covering ≈60% of the plate radius agrees well with the model prediction. Based on the model and confirmed by experiment, it is suggested that an outer dummy electrode extending to the plate edge should be added to the pMUT design to prevent zero-bias deflection.