Resolution-function theory in piezoresponse force microscopy: Wall imaging, spectroscopy, and lateral resolution

Abstract

Oak Ridge, TN 37831 Piezoresponse Force M icroscopy (PFM ) has emerged as a primary tool for imaging, domain engineering, and switching spectroscopy on ferroelectric materials. Quantitative interpretation of PFM data including measurements of the intrinsic width of the domain walls, geometric parameters of the domain below the tip in local hysteresis loop measurements, as * Permanent address: V.Lashkaryov Institute of Semiconductor Physics, National Academy of Science of Ukraine, 41, pr. Nauki, 03028 Kiev, Ukraine † Corresponding author, sergei2@ornl.gov 2 well as interpretation of switching and coercive biases in terms of materials properties and switching mechanisms, requires reliable knowledge on electrostatic field structure produced by the tip. Using linear imaging theory, we develop a theoretical approach for interpretation of these measurements and determination of tip parameters from a calibration standard. The resolution and object transfer functions in PFM are derived and effect of materials parameters on resolution is determined. Closed form solutions for domain wall profiles in vertical and lateral PFM and signal from cylindrical domain in transversally isotropic piezoelectric are derived for point-charge and sphere-plane geometry of the tip. 3

Lateral signals in piezoresponse force microscopy at domain boundaries of ferroelectric crystals

“…Figure 2 shows the calculated line scans for LiNbO 3 from Ref. [15] in comparison with our experimental results obtained with a diamond coated tip of radius r = 60 nm (confirmed by scanning electron microscopy). Neither the amplitudes nor the shapes are well reproduced by the theoretical calculations.…”

“…15 In this work, the displacement of the sample surface underneath the tip is calculated, especially for scanning across 180 • domain boundaries. Here the tip is assumed to follow this displacement.…”

“…Here the tip is assumed to follow this displacement. In the model, 15 . A very recent publication investigated 70 nm thin PZT films and attributed the LS db to shear effects according to this model.…”

Piezoresponse force spectroscopy of ferroelectric-semiconductor materials

“…86 The reason for the faster response saturation is that the tip potential quickly vanishes for small R d leading to a strong decrease of the PFM response region ͑R max , h max ͒. The space outside the region ͑R max , h max ͒ is invisible to PFM, so when the domain radius reaches R max and height acquires h max , respectively, the response almost saturates.…”

Shear effects in lateral piezoresponse force microscopy at 180° ferroelectric domain walls

“…However, subsequent studies have questioned these scenarios after quantifying the resulting lateral force, and suggested instead the possibility of electrostatic effects arising from the electric field present around domain walls due to the buildup of opposite surface polarization charges. 14 Concurrently, numerical analyses in the framework of resolution-function theory showed that in a c-axis tetragonal film, local shear can occur at the domain wall, 15 potentially giving rise to a lateral PFM signal. Discriminating between these different contributions to identify the mechanism at the origin of the observed signal is all the more necessary as PFM becomes widely applied to more complex materials such as BiFeO 3 ͑BFO͒, presenting both in-plane and out-of-plane polarization components, and where all possible contributions to both vertical and lateral PFM signals have to be taken into account.…”