Analytic solution for N-electrode actuated piezoelectric disk with application to piezoelectric micromachined ultrasonic transducers

Abstract

In this work, the deflection equation of a piezoelectrically-driven micromachined ultrasonic transducer (PMUT) is analytically determined using a Green's function approach. With the Green's function solution technique, the deflection of a circular plate with an arbitrary circular/ring electrode geometry is explicitly solved for axisymmetric vibration modes. For a PMUT with one center electrode covering ≈60% of the plate radius, the Green's function solution compares well with existing piece-wise and energy-based solutions with errors of less than 1%. The Green's function solution is also simpler than them requiring no numerical integration, and applies to any number of axisymmetric electrode geometries. Experimentally measured static deflection data collected from a fabricated piezoelectric micro ultrasonic transducer (PMUT) is further used to validate the Green's function model analysis. The center deflection and deflection profile data agree well with the Green's function solution over a range of applied bias voltages (5 to 21 V) with the average error between the experimental and Green's function data less than 9%.

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

“…Some work has begun to address the analytical model gap by focusing on the development of plate theory based electromechanical models [1], [3], [13], [22]- [28]. In [3], [22], explicit analytical equations for effective electromechanical coupling k 2 ef f are defined based on material constants and geometric parameters enabling optimized design for high k 2 ef f .…”

“…With developed analytical models, electrode size optimization performed for high k 2 ef f and deflection [3], [26], [28], [29] demonstrates the usefulness of analytical approaches for more flexible, straight-forward performance optimization via tailored geometry. In support of some analytical modeling endeavors, finite element models have been successfully implemented [22]- [27].…”

“…Building on a previously discussed Green's function deflection model for a 31 mode unimorph pMUT [28], we present a general, analytical Mason equivalent circuit model of an arbitrary electrode and axisymmetric mode system. The model explicitly defines electrical, mechanical and acoustic domain parameters based on geometry, material properties, and defined mode constants.…”

A Column-Row-Parallel ASIC architecture for 3D wearable / portable medical ultrasonic imaging

“…The piezoelectric micromachined ultrasonic transducers (PMUTs) also emerge as another possible 2D transducer solution for 3D imaging [47][48][49][50][51]. It combines the piezoelectric material with micromachining techniques, trying to exploit the benefits from both worlds.…”

“…As a technology in its early research phase, it has shown initial success of a 5x5 working array [47]. More works are being done to address problems with this technology, including how to enhance the device bandwidth to generate images with better axial resolution; and how to reduce the intrinsic device parasitic capacitance from the high permittivity of the piezoelectric material [48,49,51].…”