Piezoelectric-AlN resonators at two-dimensional flexural modes for the density and viscosity decoupled determination of liquids

A micromachined resonator immersed in liquid provides valuable resonance parameters for determining the fluidic parameters. However, the liquid operating environment poses a challenge to maintaining a fine sensing performance, particularly through electrical characterization. This paper presents a piezoelectric micromachined cantilever with a stepped shape for liquid monitoring purposes. Multiple modes of the proposed cantilever are available with full electrical characterization for realizing self-actuated and self-sensing capabilities. The focus is on higher flexural resonances, which nonconventionally feature two-dimensional vibration modes. Modal analyses are conducted for the developed cantilever under flexural vibrations at different orders. Modeling explains not only the basic length-dominant mode but also higher modes that simultaneously depend on the length and width of the cantilever. This study determines that the analytical predictions for resonant frequency in liquid media exhibit good agreement with the experimental results. Furthermore, the experiments on cantilever resonators are performed in various test liquids, demonstrating that higher-order flexural modes allow for the decoupled measurements of density and viscosity. The measurement differences achieve 0.39% in density and 3.50% in viscosity, and the frequency instability is below 0.05‰. On the basis of these results, design guidelines for piezoelectric higher-mode resonators are proposed for liquid sensing.