Responsivity and sensitivity of piezoelectric MEMS resonators at higher order modes in liquids

Micromachined resonators completely submerged in liquids suffer from high viscous damping and low measurement signals compared to the operation in gaseous environment or in vacuum, which drastically decreases the sensing performance. A promising approach to decrease damping is the utilization of higher order modes. However, with the increase in mode order also the fluid-structure interaction decreases. In this context, it is unclear how the use of higher order modes helps, when targeting the characterization of fluid properties such as density and viscosity. In this paper, we demonstrate how the use of higher order modes affects both the responsivity and sensitivity of resonantly excited MEMS sensors when operated in liquids. The latter two key device parameters are experimentally investigated with respect to the inverse viscosity-density product (ρfluid·μfluid)-0.5 for the quality factor Q, the electrical conductance peak height ΔG and for the resonance frequency fres in standardized liquids with dynamic viscosity values ranging from 5 to 700 mPa∙s. It is observed, that an increase in mode order significantly increases the quality factor by a factor of 7, when comparing 1st to 10th order mode in a sample fluid with a dynamic viscosity of 5 mPa∙s), allowing the characterization of high viscous liquid with a dynamic viscosity up to 700 mPa∙s. Even so, no influence on the relative responsivity of Q and ΔG is observed. In fact, a decrease in the relative responsivity of fres is observed, so that no gain in response is achieved for all three parameters when the mode order is increased. However, higher order modes show significantly improved strain profiles on the surface of the resonating structure, resulting in increased ΔG values for the piezoelectric readout mechanism. Therefore, the sensitivity is substantially increased resulting in an improvement by a factor of ˜30, when comparing the 1st and 10th order mode. Even higher factors of ˜50 are obtained for Q and ΔG, what enables a minimal detectable (ρ·μ)−0.5 value of 0.000998 (mPa·s·kg/l)−0.5in a high viscous sample fluid with (ρ·μ)−0.5 = 0.040 (mPa·s·kg/l)−0.5 (for comparison: a common engine oil such as SAE 5W-40 has (ρ·μ)−0.5 = 0.039 (mPa·s·kg/l)−0.5at 0 °C).