Model of Frequency-Modulated Atomic Force Microscopy for Non-Contact Piezoresponse Applications

Piezoresponse force microscopy (PFM) is a local probe method based on atomic force microscopy (AFM), where a surface displacement of a piezoelectric sample after application of an external electric field can be measured based on its effect on the AFM force sensor. A long-lasting issue concerning piezoelectric effect evaluation is the concurrent presence of electrostatic forces. A number of strategies have been introduced aiming at reducing electrostatic crosstalk. Recently, a non-contact PFM method based on frequency-modulation (FM) dynamic mode with constant excitation (CE) was introduced, with the aim of estimating piezoresponse of soft materials with reduced influence of electrostatic background. In this work, an analytical model describing the behavior of the probe of an AFM operated in CE-FM mode is presented, with the aim of rationalizing the results obtained in such non-contact PFM mode. Numerical solutions of the derived equations provide insight for improving the measurement accuracy of surface displacements by CE-FM-PFM. Its rather general applicability helps also to quantify the residual electrostatic contributions, that are anticipated as strongly mitigated in this PFM mode.