Dynamics of Null and Electrostatic Blind Spots for Quantitative Piezoresponse Force Microscopy

Abstract

Piezoresponse force microscopy (PFM) is a cornerstone technique for probing nanoscale electromechanical phenomena, yet quantitative─and in some cases qualitative─interpretation remains hindered by parasitic electrostatic forces coupled through cantilever dynamics. Recent approaches aim to suppress these artifacts by operating at resonance-defined null spots (NS) or electrostatic blind spots (ESBS), but their quantitative separation and evolution under realistic measurement conditions remain insufficiently characterized. Here, combining analytical beam models, geometrically faithful finite-element simulations, and automated interferometric measurements, we show that NS and ESBS are fundamentally different operating conditions. The NS is a modal zero at contact resonance where sensitivity to the selected mode vanishes for both excitation pathways, whereas the ESBS is a quasistatic position where only the distributed electrostatic response is suppressed. Automated measurements reveal that both conditions evolve with the tip–sample boundary condition yet remain spatially separated under realistic experimental conditions. While beam models capture the dominant cantilever mechanics, finite-element simulations and experiments show that quantitative prediction of near-tip behavior requires realistic three-dimensional probe electrostatics and mechanics. These findings identify NS and ESBS as condition-dependent sensing locations and provide a practical framework for advancing interferometric PFM toward truly quantitative electromechanical metrology.