A nanometric needle sensor mounted in an Atomic Force Microscopy allows systematic picometer-range distance measurements. This force sensing device is used in Piezoresponse Force Microscopy (PFM) as a distance sensor, by employing the cantilever spring constant as the conversion factor opening a pathway to explore the piezoelectric effect at the nanoscale. The force-distance equivalence is achieved if the force sensor does not disturb the system to study, solely. In this manuscript we report a systematic study in which different Lead Zirconate Titanate (PZT) materials, having different d33 values, are measured following the standard theory available for PFM. Both in resonance and out of resonance measurements demonstrate that PFM cannot be considered quantitative. After performing the measurements, we propose a correction of the standard theory employed in PFM by considering the force exerted by the material as a variable. The g33 parameter, inherent to piezoelectricity, governs the amount of force available from the system. A comparison of piezoelectric stiffness for the case of a nanoscale site contact region, similar to the one it is found while performing PFM, is provided. Such stiffness is well below the cantilever stiffness, limiting and diminishing the material movement, as the piezoelectric material does not have enough stroke to induce the intended displacement. A correction factor, named Open Piezopotential Gauge, accounts for these effects, which is used to correct the measurements carried out in PZT materials towards a real quantitative PFM.
Download