Origin of piezoelectric response under a biased scanning probe microscopy tip across a 180∘ferroelectric domain wall

Abstract

PACS number(s): 77.80.Fm, 77.22.Ej The piezoelectric response of a material under a nanoscale biased tip scanned across a sample in piezoelectric force microscopy (PFM) provides insight into the structure and dynamics of domain walls in ferroelectrics. While the vertical displacements of the tip under piezoelectric deformations of the sample has been reasonably explained, the origin of the lateral twisting of the tip remains unclear.

Thermotropic phase boundaries in classic ferroelectrics

“…The finite element method (FEM) was utilized to model the piezoresponse in the PFM experiments 65,66 , using the commercial ANSYS software. In the present simulations, the tip was modelled as a truncated cone (tip height 10 mm, full cone angle 30°) with a circular contact area (50 nm) with the sample surface 66 . The BaTiO 3 sample was modelled in an XYZ reference frame as a rectangular slab of 8 Â 8 Â 1 mm.…”

“…The BaTiO 3 sample was modelled in an XYZ reference frame as a rectangular slab of 8 Â 8 Â 1 mm. A decoupled approximation was assumed [65][66][67][68] ; first, the electric field distribution in the sample was calculated, which was then used as input in the subsequent calculation of the piezoresponse. For different polarization rotation values, the latter used appropriate dielectric and piezoelectric property tensors extracted from the multi-domain phase-field simulations.…”

Nanoscale studies of ferroelectric domain walls as pinned elastic interfaces

“…PFM thus allows the position of individual ferroelectric domain walls to be mapped with sub-10 nm resolution over areas essentially limited only by the scan range (10s-100s µm). Moreover, novel domain-wall-specific functional properties can be readily identified, including characteristic lateral piezoresponse features in out-of-plane polarised samples [69,70,71], and, with additional conductive tip current measurements, domain wall electrical conduction in these otherwise insulating materials [72,73,74,75,76].…”

“…A crucial step is determining the spatial distribution of this highly inhomogeneous electric field, variously considered in a point-charge or spherical approximation, or with more realistic shapes in analytical or numerical models [86,87,16,18,83,71]. Moreover, the presence of adsorbates on the ferroelectric surface can significantly influence the electric field, and screen certain types of defects, thus strongly affecting polarisation switching dynamics.…”

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

“…[109][110][111][112][113][114][115] Similar approaches were pursued by other groups. [116][117][118][119][120] These analyses were extended to quantitatively describe a ferroelectric domain wall profile in vertical and lateral PFM 115,121,122 , orientational dependence of the PFM signal, 112,123 and to quantify piezoresponse spectroscopy 124 , as will be discussed below. Perhaps even more importantly, the PFM signal (more rigorously, electromechanical surface displacement) was shown to be independent of contact area, ensuring that PFM, unlike force based SPMs, can be an intrinsically quantitative technique.…”