A refined quasi-static method for precise determination of piezoelectric coefficient of nanostructured standard and inclined thin films

Piezoelectric materials are key components for applications including non-destructive testing, medical imaging, energy harvesting, ultrasonic sensors, and actuators. Among different materials exhibiting piezoelectricity, crystalline thin films are proposed as alternative candidates to replace ceramics due to their high integrability in micro-/nano-scale devices and compatibility with non-conventional flexible/wearable substrates. To measure the piezoelectric response, Berlincourt (BC) quasi-static method is proposed as one of the simplest, however for thin films this method has not yet been explored in sufficient detail. This paper reports the effects of measuring BC parameters on the resulting piezoelectric coefficient (d₃₃) of sputter deposited ZnO with the shape of standard and inclined nanostructured thin films. Results provide comprehensive, reliable and repeatable information about true piezoelectric coefficient of thin films (6.0 ± 0.1 pC N⁻¹ for standard; 24 ± 1 pC N⁻¹ for inclined films) by selecting optimized parameters in BC measurements, including dynamic force (0.45 N_pp), static force (1 N) and frequency (110 Hz), utilizing the protocol here named Method 2 for clamping the film, and measuring after the stage of high variability has passed (t >1200 s). Additionally, this modified BC has allowed the indirect estimation of stress accumulated in the ZnO lattice during measurements, offering a reliable and repeatable method for the determination of true d₃₃ in crystalline thin films.