The origin of low-order and high-order impedance-coupled resonant modes in piezoelectric-excited millimeter-sized cantilever (PEMC) sensors: Experiments and finite element models

The characteristics of both low-order and high-order resonant modes exhibited by piezoelectric-excited millimeter-sized cantilever (PEMC) sensors were investigated to determine the coupling between electrical impedance and resonant modes observed experimentally. Experimentally measured frequency response spectra correlated well (<5% difference; n = 10 sensors) with three-dimensional (3D) finite element model (FEM) calculations. FEM frequency response and eigen frequency analyses revealed the sensorʹs resonant modes were complex, and characterized by combinations of transverse, torsional, longitudinal, buckling, and lateral motion. The magnitude of average integrated charge and current density change in the piezoelectric (lead zirconate titanate; PZT) layer at resonance directly correlated with coupling of resonant modes to electrical impedance measurement. Of the 32 resonant modes predicted by eigen frequency analysis in the frequency range 0–1 MHz, only a subset of 17 modes produced charge and current density changes in the PZT layer greater than off-resonance values. Thus, only the subset of resonant modes was coupled to electrical impedance changes and could be exploited for sensing. Transverse, longitudinal, and lateral motion of the piezoelectric layer coupled strongly with the PZT electrical impedance, while torsional and buckling motion did not. Electrically decoupled resonant modes were made measurable by introducing minor geometric asymmetry in composite layer alignment. High-order modes were shown experimentally to exhibit sub-femtogram sensitivity to mass-changes in air. Such modes consisted of combinations of transverse and longitudinal modes in both sensor layers.