Local polarization dynamics in ferroelectric materials

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Rep. Prog. Phys. 73 (2010) 056502 The minimum writable domain size is not necessarily related to the information limit in PFM and can be either larger or smaller. This follows from the fact that while the signal generation volume in PFM is independent of the tip bias, the written domain size, and in particular, the critical size of the nucleated domain, has a strong bias dependence, i.e. minimum writable domain size can be smaller than the PFM resolution. This suggests that in some cases the resolution is a limiting factor precluding experimental observation of smaller domains created by PFM. Clearly, this conclusion is non-universal and strongly depends on the material, e.g. in polycrystalline films, the grain-by-grain switching will result in minimal writable bit sizes being larger than the resolution. The resolution effect will clearly affect the analysis of the parameters such as domain size distributions in the disordered materials or geometry of the fractal and self-affine domain walls. For example, the structure factor will be S(q) = S ′ (q)R(q), where S ′ (q) is the intrinsic structure factor of the interface and R(q) is the transfer function defining microscope resolution. Practically, R(q) = 1 for q ≪ q c and R(q) = q −n for q ≫ q c , where power law n is determined by the image formation mechanism. For ultrathin interfaces such as ferroelectric walls, q c ∼ 1/w c . Correspondingly, the fractal properties h(x) for length scales below w c are likely dominated by the scanner noise along the slow scan axis (which can be established from the topographic imaging of appropriate calibration standard, e.g. step edge of a cleaved graphite surface), and by the tails of the transfer function for the fast scan axis, rather than the intrinsic wall geometry [219]. 3. Local polarization switching in ferroelectric materials by PFM 3.1. Polarization dynamics at the nanoscale The key characteristic of ferroelectric materials is that the direction of spontaneous polarization can be reversed by the application of sufficient electric field. Not surprisingly, SPM of ferroelectrics has attracted considerable attention due to its potential to manipulate ferroelectric materials at the nanoscale by creating ferroelectric domains, studying their dynamics during growth and relaxation and mapping their interaction with structural and morphological defects [107, 108, 110]. In this section, we summarize the existing results on the kinetics of domain formation and relaxation, as well as theoretical models for the description of the domain growth process in the rigid ferroelectric approximation. 3.2. Experimental aspects of tip-induced polarization switching 3.2.1. Domain growth kinetics. PFM allows a straightforward approach to study the kinetics of domain formation and relaxation by combining the writing step of applying a bias pulse of preselected duration and magnitude, and the reading stage at which the size of the resulting domain is imaged. These studies have received a significant impetus in the context of ferroelectric data storage [25], and have been S V Kalinin et al stimulated by the availability of high-quality epitaxial thin films that have low (below 10 V) switching voltages. A broad range of studies of domain wall growth on sol– gel [220–223] ferroelectric films have been reported. The implementation of high-voltage PFM [224] has allowed studies of domain dynamics in single crystals as well, and particularly has enabled the kinetic studies as a function of pulse parameters [225–232]. As an example, shown in figure 22 is the morphology of ferroelectric domains in LNO single crystal. While for low bias pulses the domains are nearly round, large domains adopt well-defined crystallographic shapes, mirroring surface tension driven rounding of nanoparticles. The radii of domains fabricated in lithium niobate single crystals were found to scale linearly with applied field and approximately logarithmically with time [226]. Similar scaling was found for other materials, suggesting the universality of this rate law. The time dependence of domain-wall velocity was studied by several groups [128, 233, 234] in an attempt to relate domain growth kinetics to the dominant wall pinning mechanisms. The first link between wall velocity and disorder was established in the seminal papers by Tybell et al [64] and Paruch et al [234] and since then was actively studied by several groups [233, 235]. Domain growth in epitaxial films has also been compared with macroscopic measurements on capacitor structures [380]. Significant efforts have been directed at fabricating ultrasmall domains and the determination of minimal stable domain size and associated lifetimes. Recently, 8 nm domain arrays have been fabricated and detected using scanning nonlinear dielectric microscopy [237, 238] (figure 23(a)). The Cho group has also demonstrated the formation of 7 nm arrays and 2.8 nm domains (see figure 23(b)) and has written images using the technique (figure 23(c)) [236]. This impressive result corresponds to a density of 160 Tb inch −2 (10 Tb inch −2 for 8 nm array), approaching molecular storage level [239]. One of the key uncertainties for the characterization of domain growth kinetics is the lack of quantitative information on the electrostatic field structure produced by the probe. In most studies to date, the field is approximated as a single point charge, a model well validated for tip apex at large separations from the contact area. On larger length scales, the conical part of the tip provides a slow-decaying field component, which is, however, attenuated by the dielectric gap effect. Furthermore, the point charge model is clearly inapplicable for small tip–surface separations of the order of the tip size (which in turn is related to the domain wall width, as discussed in section 2.3, on which the field is uniform). The second factor affecting domain growth kinetics is the effect of mobile surface charges, screening and liquid bridge formation, as discussed in section 3.3. 3.2.2. Domain relaxation and retention. The retention behavior of ferroelectric domains following local polarization reversal presents obvious interest for data storage and ferroelectric lithography applications. Retention behavior in epitaxial and polycrystalline PZT [240], the thermal stability [228] and the retention behavior [229] of fabricated domains 23
Rep. Prog. Phys. 73 (2010) 056502 S V Kalinin et al Figure 22. (a) PFM phase image of domains written in a lithium niobate crystal by varying the voltage pulse amplitude. Plots of domain radius versus (b) pulse amplitude and (c) pulse duration in a lithium niobate crystal. (e) Domain size as a function of pulse duration for a 370 Å thick PZT film. (d) Domain wall speed as a function of the inverse applied electric field for three PZT films of different thicknesses. Panels (a)–(c) reproduced with permission from [226], copyright 2005, American Institute of Physics, and panels (d),(e) reproduced with permission from [64], copyright 2002, American Physical Society. Figure 23. (a) 8 nm array of domains, (b) 2.8 nm domain and (c) nanoscale domains written to construct an image. (a) Reproduced from [52], copyright 2006 IOP Publishing and (b), (c) from [236], copyright 2007, Institute of Pure and Applied Physics. 24
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