Method to Further Improve Sensitivity for High-Order Vibration Mode Mass Sensors With Stepped Cantilevers

Using high-order vibration mode has been regarded as an effective way to improve the sensitivity of piezoelectric resonant cantilever mass sensors. To further improve the high-order mode sensitivity without reducing the overall dimension, a new shape design method was proposed to improve the sensitivity at the desired high-order vibration mode by optimizing the multi-stepped thickness along the cantilever axis. With the proposed method, a new fourth-order mode mass sensor is proposed incorporating a three-stepped piezoelectric-elastic composite cantilever. The effect of structural parameters on the vibration modes and also the sensitivity is analyzed. With the optimized three-stepped cantilever, the sensitivity can be at least 3.0 times that of the uniformed cantilever sensor also operated in the fourth-order vibration mode. Then, a piezoelectric mass sensor is fabricated with the step thickness ratio and step length ratio of 0.5 and 0.29. The experimental results show that the fourth-order mode sensitivity can achieve $185.41\times 10^{4}$ Hz/g, which is nearly 19.5 times and 3.0 times greater than those of the custom uniform cantilever sensor working in the first and fourth vibration modes. Meanwhile, the quality factor is 82.65 about 3.5 times as great as that of the rectangular uniform cantilever sensor. The nearly consistency between simulation and experiments fully validates the feasibility and effectiveness of the newly proposed sensitivity improving method.