Analysis and Guideline for Determining Piezoelectric Coefficient for Films with Substrate Constraint

Piezoelectric films including coatings are widely employed in various electromechanical devices. Precise measurement for piezoelectric film properties is crucial for both piezoelectric material development and design of the piezoelectric devices. However, substrate constraint on the deformation of piezoelectric films could cause significant impacts on the reliability and accuracy of the piezoelectric coefficient measurement. Through both theoretical finite element analysis and experimental validation, here we have identified three important factors that strongly affect the measurement results: ratio of Young's modulus of substrate to piezoelectric film, ratio of electrode size to substrate thickness, and test frequency. Our investigations show that a relatively smaller substrate's Young's modulus to film, and a larger ratio of electrode size to substrate thickness would cause a larger substrate bending effect and thus potentially more significant measurement errors. Moreover, intense transversal displacement fluctuation can be excited at excessively high frequencies, leading to unreliable measurements. Various well-established piezoelectric measurement methods are compared with outstanding measurement issues identified for those commonly used piezoelectric films and substrates. We further establish the guidelines for piezoelectric coefficient measurements to achieve high reliability and accuracy, thus important to the wide technical community with interests in electromechanical active materials and devices.