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Critical size for ferroelectricity

Chapter 3 Scaling effects in barium titanate

3.2 Critical size for ferroelectricity

Much of the theoretical work performed has focused on isolated particles unsuitable for devices, or on epitaxial films, however an understanding of these systems is an important step towards engineering better polycrystalline devices. Here we examine these two cases in order to better understand any expected intrinsic effects that may play a role in polycrystalline films. These intrinsic effects should arise purely due to changes in the dimension of the system and not due to strain, grain boundaries, defects, interfaces, or other changes that may be introduced during processing of the material.

Figure 3.3 shows reported BaTiO3 critical sizes by year, labeled for the system they were

studied in. These critical sizes refer to measurements that indicate spontaneous polarity, regardless of the magnitude or if an actual device was built. In nearly all cases distortions or properties decreased as this size was approached.

3.2.1 Ferroelectricity in nanoparticles

The study of BaTiO3 nanoparticles, while useful from a scientific perspective, does not directly

translate to practical devices due to differences in electromechanical boundary conditions and the difficulty in fabricating actual electronic devices. Nevertheless, these studies can help build an understanding of size effects at extreme scales.

Typically these studies exhibit similar behavior to ceramics work. The main point of agreement is decreasing tetragonal distortions that eventually result in a pseudo-cubic phase. These systems are typically studied by observing the crystal structure.

McCauley et al. studied BaTiO3 nanoparticles (20 - 83 nm) embedded in a glass matrix, a

system that could conceivably be used in devices. The nanoparticle size was varied by changing the sintering time. The composites showed typical broadening and lowering of the cubic-tetragonal phase transition. This system exists as an intermediary between polycrystalline ceramics and isolated nanoparticles. The glass matrix is expected to limit charge compensation and the depolarizing field should play a greater role than in similarly sized ceramics. By extrapolating dielectric measurements, a critical size for polarization stability was predicted as 17 nm.

Numerous other studies have found also found critical sizes below 40 nm.86–89,91,92,95–99 These studies almost exclusively rely on techniques that probe the local polarization or crystal structure. Examples include Raman,86,88,98 x-ray pair distribution function,89,92,95 second har- monic generation,87 and scanning probe microscopy.88,91 Generally these studies support the conclusion that a mix of polar and non-polar phases coexist in these fine particles, as they do for polycrystalline ceramics.

There is one report in the literature by Xu and Gao on the synthesis of tetragonal BaTiO3

powder with an average grain size of 70 nm that exhibits clear tetragonal peak splitting via x-ray diffraction.100 At this particle size the system typically indicates pseudo-cubic behavior.70 It is likely that improved processing resulted in the stabilization of the tetragonal distortion, and this finding is supported by their reported room temperature permittivity of greater than 6000.100

One challenge in nanoparticle systems is synthesizing particles and preventing grain growth. The synthesis often occurs at room temperature or with only minor thermal energy added.87,88,92 Challenges in synthesis of ceramics was previously identified by Freyet al. as responsible for some of the trends observed,70 and it is likely that these complex chemistry and low temperature techniques do not realize consistently high purity and crystallinity necessary for comparison between experiments.

Another key difference between these nano systems and polycrystalline devices is the lack of strain or mechanical clamping. Nanoparticles are typically not clamped by a substrate or surrounding grains, changing the electromechanical boundary conditions of the system in a way that is unrealistic for real devices.

3.2.2 Epitaxial thin films

A second approach to studying size effects is in epitaxial systems. These systems should allow extremely thin, high quality crystals to be grown and enable direct comparison with theory. This work was strongly motivated for the desire of high-K gate dielectrics, ferroelectric memories, and miniaturized MEMS.6 In practice these systems are complicated by the strains inherent in the system and in correct choice of contacts.

In 2003 first principle calculations predicted a critical grain size of 2.4 nm (6 unit cells) for the SrRuO3-BaTiO3-SrRuO3 stack.93 Incomplete screening at the interfaces led to a substantial

depolarization field that eventually destabilizes the ferroelectric phase. This finding was later investigated experimentally and hysteresis loops were demonstrated in 5 nm thick BaTiO3.101–103

As seen in bulk systems, the reduction of ferroelectric properties, such as remnant polarization, occurred smoothly towards zero.

Other ferroelectric systems have been similarly studied using first principles, with lead titanate exhibiting distortion down to 1.2 nm (3 unit cells)104. As seen in most systems, TC

decreased with decreasing thickness, however an actual device was not built so no ferroelectric or dielectric measurements were made.

The strength of the depolarizing field can be changed by adjusting the top contact. Plonkaet al., using epitaxial Ba1-xSrxTiO3 films on SrRuO3 showed changes inTC shifts and permittivity

with thickness by changing the top contact from SrRuO3 to Pt.105 The total device permittivity

was strongly dependent on top metal electrode, with SrRuO3 providing higher permittivities.

First principle studies with Pt and SrRuO3 contacts on SrTiO3 by Stengel and Spaldin showed

decreasing polarization and permittivity extending into films at the contact interfaces due to incomplete screening.106 Pt was found to provide more complete screening, however this finding

did not agree with literature results and was attributed to difficulties in growing high quality SrTiO3 on Pt. Stengel and Spaldin also showed that the dead layer at the contact interface

should lead to noticeable reductions (15%) in permittivity for films 75 nm thick.

This prediction is troubling for devices such as high-K dielectrics where it is desirable to have extremely fine layers, however for most applications polycrystalline films will typically be significantly thicker than this. This theoretical result was true even for the fully relaxed state, a result not found in experiment. Saadet al. fabricated a free-standing BaTiO3 device

by sectioning a 75 nm thick slice from a single crystal and recovered bulk-like properties.17

Dielectric measurements showed an extremely sharp transition at the expected temperature, with typical Curie-Weiss behavior above the transition. The high permittivity (greater than 25000) and lack of TC shifts or broadening seems to indicate that many of the size effects

reported in the literature are not intrinsic to reducing the scale, but rather extrinsic effects due to strain or difficulties in producing high quality material.

In a closely related study, Chang et al. sliced thin sheets of both BaTiO3 and SrTiO3 from

bulk single crystals.107Using Pt contacts no dead layer was observed in the BaTiO3device, while

equivalent SrTiO3 structures did exhibit a dead layer. First principle calculations confirm this

surprising finding and show that engineering of interface layers could mitigate dead layer effects and explains the difference in behavior between the various ferroelectric-contact systems.108 Additional simulations and experiments confirm that the interfaces of various ferroelectrics can indeed be engineered to avoid dead layer effects.85,109–111