Direct Measurement of Inverse Piezoelectric Effects in Thin Films Using Laser Doppler Vibrometry

This study highlights efforts to develop an accurate, simple methodology to assess the electromechanical response in thin-film heterostructures, using laser Doppler vibrometry to measuring surface displacements smaller than 1 nm. The work demonstrates how to use the measured values to extract the piezoelectric coefficient ${d}_{33}$ for a generic thin-film system by means of finite-element modeling. Finally, the work shows how to assess the electromechanical figure of merit for thin films, and offers a procedure for how to compare them to their bulk counterparts via the electromechanical coupling coefficient ${k}_{33}$.