A Simplified and Wafer-Level Thin Film Characterization of Transverse Piezoelectric Coefficient

Characterizing material properties of piezoelectric thin films is crucial for optimizing the design and fabrication of piezoelectric MEMS devices. In this paper, we present a simplified, wafer-level method to measure the effective transverse piezoelectric coefficient ( e<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">31,f</inf> ). By applying the unimorph plate model, we derive an equation that establishes a quadratic relationship between deflection and electrode radii. This allows us to calculate e<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">31,f</inf> by measuring the electric field-induced deflection across multiple circular electrodes on piezoelectric films deposited on a silicon substrate. Finite element method (FEM) analysis confirms the feasibility of this approach. Furthermore, the e<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">31,f</inf> values of polycrystalline PZT (p-PZT) and ScAlN obtained with this method align closely with those from the conventional cantilever method, demonstrating the reliability of our wafer-level characterization technique.