High-resolution parametric characterization of snap-through behaviour in bistable PiezoMEMS membranes

Abstract

This study presents a novel parameter space representation of bistable PiezoMEMS (piezoelectric micro-electromechanical systems) devices characterized by fractal tongue-like patterns similar to Arnold tongues. The parameter space is measured by analysing the snap-through trajectory of a compressively pre-stressed bistable thin film aluminium nitride (AlN) based PiezoMEMS membrane. The snap-through initiation is achieved by applying parameterized electrical signals comprised of rectangular pulses, frequency range is swept from 60 to 120 kHz covering the first resonance mode and peak-to-peak voltage starting from 15 and reaching 72.5 V. Several measurements were performed for 2, 3, 4, 5 and 20 pulses. The results show how different key metrics depend on both frequency and amplitude, but also develop while increasing the number of excitation pulses. For 2 and 3 pulses, uncluttered and organized patterns emerge, which tend towards seemingly more chaotic configurations for higher numbers of pulses. Our work discusses four different metrics of behaviour: probability of permanent switching, number of snap-throughs, correlation relation of the velocity trajectories and the time needed for the first snap-through. Finally, a simple simulation of a Duffing equation is presented that showed highly comparable results, when stimulated for a high number of pulses, to that of the 20 electrical pulses measurements. We reached significant displacement values of 8 to $10\mu m$ when moving from one ground state to another with membranes having a thickness of $3.2\mu m$ and diameters ranging from 600 to $800\mu m$. These features make those bistable devices great candidates for PiezoMEMS actuators like ultrasonic emitters.