Measurement of nonlinear piezoelectric coefficients using a micromechanical resonator

We describe and demonstrate a method by which the nonlinear piezoelectric properties of a piezoelectric material may be measured by detecting the force that it applies on a suspended micromechanical resonator at one of its mechanical resonance frequencies. Resonators are used in countless applications; this method could provide a means for better-characterizing material behaviors within real MEMS devices. Further, special devices can be designed to probe this nonlinear behavior at specific frequencies with enhanced signal sizes. The resonators used for this experiment are actuated using a 1-$\mu$m-thick layer of aluminum nitride. When driven at large amplitudes, the piezoelectric layer generates harmonics, which are measurable in the response of the resonator. In this experiment, we measured the second-order piezoelectric coefficient of aluminum nitride to be $-(23.1\pm14.1)\times10^{-22}\ \mathrm{m/V^2}$.