Piezo-micro-ultrasound-transducers for air-coupled arrays: Modeling and experiments in the linear and non-linear regimes

The paper is focused on the multi-physics modeling, via the finite element method (FEM), of a 4 × 4 air-coupled array of Piezoelectric Micromachined Ultrasonic Transducers (PMUTs), and on its mechanical and acoustic validation by means of the comparison, in the time domain, with experimental results. A two-stage numerical procedure is employed, in order to evaluate the complete performance of the device, by means of two FEM models. In the first stage, the electro-mechanical-acoustic (EMA) problem is solved for the stand-alone transducer, taking into account the fabrication induced residual stresses and the multiple couplings between different physics. The numerical results are compared with the experimental ones in terms of initial deflection and time histories of pressure, in the linear and non-linear regime: the proposed model correctly captures the reported phenomena and perfectly matches the experimental trends. The second stage is devoted to the simulation of the 4 × 4 PMUTs array performance, belonging to the silicon die. The vibrating plates are modeled as equivalent rigid pistons. The acceleration histories, computed in the first stage, are imposed on the pistons, while a rigid baffle condition is enforced on the remaining part of the die surface. The model is adopted to predict the pressure field for different patterns of the array's activation.