System level modeling and design maps of PMUTs with residual stresses

We report a system level approach for design of Piezoelectric Micromachined Ultrasonic Transducers (PMUTs) with inclusion of residual tension. A multilayered circular plate model is used to derive the vibrational response of a PMUT subjected to, first a sinusoidal voltage input and second, a sinusoidal pressure load with frequencies near the first resonance of the PMUT. The model is simplified with the introduction of mode shape dependent nondimensional parameters that are found to change very little over a large range of design parameters. Introduction of these parameters leads to a tractable formulation for the forced response of the PMUT. Lumped model approach is used to derive expressions for overall performance parameters in terms of transfer functions of a PMUT acting as a transmitter, a receiver and a transceiver. These transfer functions are further used to develop parametric design maps of a PMUT with a given layer configuration (material and thickness of all layers) that enable us to easily track the effect of residual tension, vibrating area and the fundamental resonant frequency of the PMUT on the figure of merit in each of the three cases. Transition of PMUTs from plate regime to membrane regime on introduction of tensile residual stresses and corresponding difference in scaling of figure-of-merits with size have been verified experimentally. Using the design maps, we arrive at clear design inferences for a PMUT and show the difference in functional relationships between performance parameters and design parameters for plate type PMUTs and membrane type PMUTs.