Abstract
A mathematical model is necessary to analyze sensor performance and optimize its design. However, most of the existing models of piezoelectric micro-machined hydrophones are incomplete and too complex to understand. There has been no mathematical model for the sensitivity of piezoelectric hydrophones. To address this shortcoming, this paper proposes a mathematical model of a piezoelectric micro-machined hydrophone. The stresses in the piezoelectric layer and static displacement of the diaphragm under uniform sound pressure are derived. In addition, the resonant frequency and sensitivity of the hydrophone are analyzed. The finite element simulation is used to verify the validity of the proposed mathematical model. On the basis of the mathematical model and simulation, the diaphragm radius, top electrode area, and piezoelectric film thickness are optimized. Furthermore, the hydrophone is fabricated, and its morphology is observed. The impedance-frequency spectrum of the hydrophone is measured by HIOKI IM3536 LCR impedance analyzer. The tested resonant frequency is 0.5 MHz, which is relatively close to the calculated result of 0.537 MHz, so the validity of the proposed mathematical model is further validated. Also, the reason why the test result is less than the calculated result is explained. The effective electromechanical coupling coefficient derived from the impedance curve is 7.5%. The developed mathematical model can provide a useful guide for designing high performance piezoelectric micromachined hydrophone and make preliminary predictions of its characteristics.
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