Analyzing piezoresponse force microscopy for reconstruction of probed ferroelectric structures

Abstract

Piezoresponse force microscopy (PFM) has emerged as the tool of choice for characterizing piezoelectric and ferroelectric materials at nanoscale, yet the interpretation of PFM remains to be difficult and sometimes ambiguous. Built on earlier works, we developed a numerical integration scheme to analyze the expected PFM response in ferroelectrics with arbitrary domain configurations, with the ultimate goal to accurately reconstruct the underlying ferroelectric structure from PFM measurements. Using such technique, we demonstrated that the relationship between the effective and intrinsic piezoelectric coefficients is sensitive to a variety of factors that are intrinsic to the probed materials, and showed that the PFM mapping is not only influenced by polarization distribution on the sample surface but also three-dimensional polarization distribution inside the material. While relatively simple domain structures were used for demonstration, the approach is general, and can be applied to ferroelectrics with arbitrary polarization distributions.

Piezoelectric Tensor of Collagen Fibrils Determined at the Nanoscale

“…Thus, the measured response is sensitive not only to piezoelectric, but also elastic moduli, and dielectric constants. 38 To determine each piezoelectric coefficient for collagen, the relationship between the measured (laboratory) and sample coordinate system must be considered. For a known sample orientation, the laboratory coordinate system ( ) can be related to the sample coordinate system ( ).…”

“…For a comprehensive discussion of lateral InvOLS calibration, see these reviews. − Furthermore, it is important to point out that convergence of local PFM and macroscopic piezoelectric measurements is unlikely due to the highly inhomogeneous electric field at the tip and corresponding locally confined deformation, which might be affected by sample-induced clamping. Thus, the measured response is sensitive not only to piezoelectric, but also elastic moduli, and dielectric constants …”

Polarization Domain Dynamics of Barium Titanate Ultrathin Films Using Piezoresponse Force Microscopy.

“…While the current investigation is focused on the expansion of the polarization domain in BTO, it is important to also consider the domain expansion as a good test for an accurate expression for the electric field due to an AFM tip. When the AFM tip is used to study the electromechanical response of materials, a good understanding of the expression for the electric field produced by the tip can be critical 27,28 . To find an analytic expression for the electric field due to the cone in the film we used the Laplace equation in the spherical coordinate system with electric field boundary conditions.…”

The effects of domain wall thickness on the nanoscale piezoresponse of ferroelectric domains

“…The typical 180 , uncharged 90 , and charged 90 domain walls have been analyzed based on the numerical scheme developed by us recently. 25 The paper is organized as follows. The electric field induced by the charged SPM tip and displacement response accounting for domain wall thickness are derived in Sec.…”