Piezoelectric stepped-plate resonators vibrating at lateral modes for direct viscosity determination in liquids

Precise viscosity measurement in liquid media remains a critical challenge for micromachined resonant sensors. This primarily results from the inherent coupling between viscosity and density in hydrodynamic interactions, which limits independent quantification of viscosity. This work presents an aluminum nitride (AlN) piezoelectric microresonator vibrating at in-plane lateral mode for direct viscosity sensing in liquids. The resonator features cantilevered dual-plate structure with a wide step to leverage width-dependent effects on resonant frequency and quality factor. Through fluid-structure interaction modeling, the resonator is optimized to enhance vibrational characteristics while increasing linearity with respect to liquid viscosity. In experiments, the resonator incorporates fully electrical interfaces by combining self-actuation and self-sensing capabilities under liquid immersion. Furthermore, a significantly linear relationship between the quality factor and liquid viscosity is demonstrated. This linearity enables direct viscosity quantification through simultaneously measuring the resonant frequency and quality factor, which eliminates the need for prior density calibration required by conventional methods. The fabricated resonator achieves a mean absolute relative deviation of 2.65% with a maximum stability deviation of 3.43%. These results establish microplate-based laterally vibrating resonators as promising solutions for high-precision viscosity determination in compact liquid monitoring systems.