Quantification of surface displacements and electromechanical phenomena via dynamic atomic force microscopy

Abstract

Detection of dynamic surface displacements associated with local changes in material strain provides access to a number of phenomena and material properties. Contact resonance-enhanced methods of atomic force microscopy (AFM) have been shown capable of detecting ∼1-3 pm-level surface displacements, an approach used in techniques such as piezoresponse force microscopy, atomic force acoustic microscopy, and ultrasonic force microscopy. Here, based on an analytical model of AFM cantilever vibrations, we demonstrate a guideline to quantify surface displacements with high accuracy by taking into account the cantilever shape at the first resonant contact mode, depending on the tip-sample contact stiffness. The approach has been experimentally verified and further developed for piezoresponse force microscopy (PFM) using well-defined ferroelectric materials. These results open up a way to accurate and precise measurements of surface displacement as well as piezoelectric constants at the pm-scale with nanometer spatial resolution and will allow avoiding erroneous data interpretations and measurement artifacts. This analysis is directly applicable to all cantilever-resonance-based scanning probe microscopy (SPM) techniques.

Ferroelectric or non-ferroelectric: Why so many materials exhibit “ferroelectricity” on the nanoscale

“…This shows that at different values of surface potentials, the value of C' is not constant, but rather indicates a peak in this case near ~0.5V. A procedure to enable quantitative measurements independent of the chosen cantilever is detailed in Balke et al 349 This method was used to determine the effective d33 values of a LiNbO3 single crystal, but requires quantitative determination of the electrostatic and piezoelectric contributions to the response. The amplitude of the displacement Dac for two different cantilevers A and B is shown in (a) for two differently oriented domains.…”

“…99,335,346 A straightforward way to separate these contributions is to consider potentialdependence of forces acting on the junction in contact, i.e. to consider the so-called on-field observables.…”

“…This is especially true for resonance-enhanced measurements, where the common force-distance based calibration of the detector sensitivity in the atomic force microscope yields inaccurate results. The systematic procedure detailed in reference 349 takes into account the detailed shape of the eigenmode that is excited on resonance, the cantilever geometry, its spring constant and several other accountable properties. The cantilever dynamics can be largely accounted for in the so-called shape factor ξ, which allows to correct the experimental data to make the cantilever independent, and subsequently allowing quantitative comparison of the displacements measured with different cantilevers.…”

“…The associated theory was developed in the context of atomic force acoustic microscopy (AFAM) 196,[350][351][352][353] and later adapted to PFM. 333,349,354 For ferroelectric materials, classical 180° domain switching does not change the elastic properties of the system. However, non-180° domain switching, tip-induced phase transitions, or electrochemical processes all are expected to shift resonance frequency due to a change in mechanical properties.…”

Non-piezoelectric effects in piezoresponse force microscopy

“…3. Such local and non-local electrostatic effects can arise from the various electrical interactions between the AFM tip/cantilever and sample surface, such as the capacitive interaction, [80,81] the CPD, [79,82] the application of an external voltage to the entire sample, and the corresponding injected charges on the sample surface. [83][84][85] Hong et al reported a significant influence of the electrostatic effect on piezoresponse hysteresis loop measurements.…”