Electroacoustic Modeling of Patterned Piezoelectric Micromachined Ultrasonic Transducers

Patterning the piezoelectric layer of a piezoelectric micromachined ultrasonic transducer (PMUT) plate usually leads to improved performance; however, modeling of such PMUT is not as straightforward as its conventional counterpart. This article presents an electroacoustic model for conventional as well as patterned PMUTs with square shaped membranes. Hamilton's principle is utilized to formulate the dynamics of the patterned PMUT. The derived mode shape is used to obtain the electrical, mechanical, and acoustic parameters to arrive at the complete electroacoustic model. The model is applied to eight different designs, where four are of conventional type with different electrode configurations and the other four are patterned designs with different patterning configurations. Using the proposed model, the electrode and patterning geometry for each PMUT design is optimized. Natural frequency, mode shape, the input impedance at the electrical port, and the transfer function from the electrical to the acoustic port calculated from this model are shown to be in good agreement with those obtained from finite-element analysis for all the studied designs. Moreover, the patterned PMUTs are shown to have superior performance, in terms of volume velocity per unit voltage, over conventional PMUTs operating at a given resonance frequency.