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

Experiment and simulation validated analytical equivalent circuit model for piezoelectric micromachined ultrasonic transducers

“…In support of some analytical modeling endeavors, finite element models have been successfully implemented [22]- [27]. However, analytical approaches have yet to be proven by experiment because of discrepancies commonly attributed to residual stress [1], [3], [25], [29]. For an analytical model useful to future pMUT design, the model must be extensively confirmed with experimental results and use relevantly simplified lumped parameters for ease of use in design optimization.…”

A two-port piezoelectric micromachined ultrasonic transducer

“…The prototype dynamic response was theoretically studied using analytical model previously derived [9]. The material properties of AlN and Mo are listed in Tables I and II, respectively.…”

“…The first harmonic amplitude of the plate flexural vibration as a function of the radius for a two-port pMUT is theoretically derived as [9]:…”

“…where Y 0,p , d 31,p , Z p , D, Λ k , O k (x), Ψ k (x), α k , and α are a function of the material properties, plate geometry, and frequency of operation [9]. The second harmonic amplitude of the plate oscillatory displacement is related to the voltageinduced, in-plane, piezoelectric tensioning and is analytically presented as [11]:…”

“…Recently, our group has developed the analytical solution for a circular, unimorph pMUT with multiple top electrodes using the approach of Green's function [8] and this technique has been generalized to include the influence of residual stress [9]. We have further derived the lumped circuit model including the tension of a diaphragm due to the in-plane piezoelectric stress under an applied voltage [10,11], and optimized the electrode size for maximum pressure outputs from a typical conventional one-port pMUT [12].…”