Zuo-Guang. Ye Advanced Dielectric Piezoelectric and Ferroelectric Materials: Synthesis, Characterisation and Applications

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Handbook of dielectric, piezoelectric and ferroelectric materials780

with the polarization aligned perpendicular to the film’s plane (c-phase),

while for relatively large tensile strain values the polarization lies down in-

plane along the [110]

direction and the symmetry is orthorhombic (aa-

phase) (see Fig. 25.11). For zero and intermediate strain values and at low

temperatures, a low-symmetry phase (r-phase) occurs, which is, again, very

similar to that observed at the MPBs of PZT and related materials, discussed

in Section 25.4: it has no fixed symmetry axis so the polarization can rotate

in the plane defined by the [001]

and [110]

directions. The r-phase is

another example of a novel phase that does not exist in bulk BaTiO

but

could be stabilized in very thin films by strain engineering.

The case of PbTiO

has proved to be more complex and the different

predictions do not always agree with each other. While a similar r-phase is

predicted by the Landau–Devonshire approach (when single-domain films

are considered), in between the c-phase and the so-called a-phase (with

polarization in plane along [100]

) [126], the first-principles-based methods

predict the coexistence of the c and a phases at intermediate strain values,

with no r-phase [140, 141].

25.11

a) Temperature-misfit strain phase diagram of a single-domain,

five unit cell thick film of BaTiO

with realistic electrical boundary

conditions (96.3% charge compensation at the surfaces) and short

circuit conditions (no depolarizing field), as reported by Bo-Kuai Lai

et al

. [142] (b) The orientation of the polarization in the different

phases. Reused with permission from Bo-Kuai Lai, Igor A. Kornev, L.

Bellaiche, and G. J. Salamo,

Applied Physics Letters

, 86, 132904

(b)

–

c(K)

600

500

400

300

200

100

–100

–200

–3 –2 –1 0 1 2 3

Misfit strain (%)

–3 –2 –1 0 1 2 3

Misfit strain (%)

(a)

600

500

400

300

200

100

–100

–200

= 5, β/β

= 0.963

= 5, SC condition

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Symmetry engineering and size effects in ferroelectric thin films 781

For thin films, the electrical boundary conditions are also important in

order to determine the polarization state, as discussed in Sections 25.2 and

25.3. Formation of periodic stripe domains with opposite polarizations is

predicted in open-circuit conditions, in which the surface charges are not

compensated and large depolarizing fields are created. These domain variants

are elastically equivalent and the strain energy is, therefore, not modified

(the film is not relaxed) by the formation of stripes of 180° domains. In this

situation the net polarization of the materials is zero and, therefore, the film

is strictly speaking non-ferroelectric, despite the ferroelectric alignment of

the unit cells within each domain. It has been recently observed that the c/a

ratio of the films, typically linked to the squared polarization via c/a = (c/a)

+ aP

does not decrease monotonously with decreasing thickness (as expected

due to the increasing depolarizing field), but increases at very low thickness

(a few unit cells) [143]. This has been associated with the creation of stripe

domains at sufficiently large depolarizing fields. With the depolarizing fields

avoided in this way, the dipole moment per unit cell and the c/a ratio are

restored.

Other examples of the important influence of the electrical boundary

conditions when dealing with very thin films are given by first-principles

methods in BaTiO

[21, 142] and PbZr

0.5

[23] where the amount of

compensating charges is shown to influence the phase stability greatly. In

Fig. 25.11 the phase diagram of BTO has been calculated by Lai et al. for the

case with no depolarizing filed (ideal short circuit conditions) and for a

situation in which 96.3% of the surface charges are compensated. It can be

seen that such a seemingly small difference changes the phase diagram

considerably [142].

25.5.2 PbTiO

under tensile strain

Fully strained 5nm thin films of PbTiO

under small tensile strain have been

grown on DyScO

substrates, by using RHEED-assisted pulsed laser deposition

[134]. With this technique, thin films can be built unit cell-by-unit cell,

allowing a great control at the atomic level [144].

A mapping of the reciprocal space performed by synchrotron X-ray

diffraction on those films (see Fig. 25.12) has revealed an intensity modulation

with in-plane periodicity of about 30 nm (70 unit cells), which is due to polar

stripe domains, similar to those observed by Streiffer and coworkers [8,

145]. The reciprocal space points around which the satellites are shown

reveal the symmetry of the polarization inside the stripes, while the direction

of the modulation tells us about the orientation of the stripes.

The measurements have revealed that the stripes carry in-plane, as well as

out-of-plane components of the polarization. Thus, it is shown that when

PbTiO

is grown under a small tensile strain (of about 1%), the polarization

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Handbook of dielectric, piezoelectric and ferroelectric materials782

tilts away from the substrate normal but does not reach a full in-plane

configuration. This would be consistent with a phase of the type r, as the one

predicted for BaTiO

. As explained above, if the polarization has a larger

freedom to deform, piezoelectric and dielectric responses could be drastically

enhanced. Work is in progress to determine whether this is the case.

This work demonstrates that controlling the growth of thin films at the

atomic level allows novel phases to be created even in chemically simple

compounds. Some of these phases do not exist in bulk or cannot be synthesized

by standard means. The epitaxial growth of thin films gives us access to tune

the symmetry of materials at the unit cell level, which is crucial for defining

their functional responses and to build model materials designed for specific

functionalities.

25.12

Selected regions of the reciprocal space in the (hk0) plane,

around (100), (200), (010) and (110) Bragg peaks, of a PbTiO

thin film

deposited under tensile strain on a DyScO

substrate. The

measurements were obtained by synchrotron X-ray scattering in

grazing incidence geometry. Next to the sharp Bragg reflections,

broad intensity maxima are observed revealing a second periodicity

of about 30nm, which is due to polar stripe 180° domains. The same

in-plane periodicity is observed in the (h0l) scattering plane. The

orientation of these modulations and the Bragg peaks around which

they appear indicate that the polarization in the stripes has both in-

plane and out-of-plane component and it is, therefore, tilted away

from the substrate normal (see ref. [134]).

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Symmetry engineering and size effects in ferroelectric thin films 783

25.5.3 Strain relaxation and domain formation

As already discussed, above certain critical thickness, the strain will relax.

The system PbTiO

on DyScO

described above is a very special one because

at the growth temperature (around 600 °C), above the Curie temperature, the

in-plane lattices parameters of a [110]-oriented DyScO

substrate and the

bulk PbTiO

are very close to each other [146]. This means that the films can

grow coherently and without forming dislocations. Upon cooling below T

the spontaneous strain will appear, but by then there is not enough energy to

nucleate the dislocations. Hence, strain will be relaxed either through a

transition to a new phase with tilted polar vectors, as in the ultra-thin films

described in the previous section, or, for sufficiently thick films (above 5

nm) relaxation may take place by forming twins or 90° domains [147].

As explained by Pompe and collaborators in a series of seminal papers, a

configuration of periodic a/c/a domain (with the c and a domains having

polarization perpendicular and parallel, respectively, to the plane of the films)

can relax the lattice mismatch [52, 148, 149]. The volume ratio of a-domains

will depend on the so-called effective mismatch strain, with which dislocations

that are created above the ferroelectric phase transition are taking into account

to lower the nominal mismatch [52, 148, 149].

Recently, phase field models have been used to predict domain patterns

under different strain conditions: under biaxial strain, under anisotropic

substrates, etc. [150–152]. On the face of it, theory would appear to be

slightly ahead of experiment; this is partly because it is difficult to find the

right combination of real substrates and films that will allow the growth

under the necessary conditions to replicate the theoretical calculations. On

top of that, in the real world dislocations appear which relax strain, and

adsorbates stick to the surfaces screening depolarizing fields, so results can,

and often do, differ from predictions. Furthermore, even if dislocations can

be prevented (as in [134]) and adsorbates minimized (as in [8, 144]), other

subtle effects such as surface symmetry [4, 5] and electrode screening length

[143] all contribute to the final polarization state of the films, so experimental

results may disagree with theoretical predictions even under ideal growth

conditions. Resolving the problem of domain states and polar symmetry in

ferroelectric thin films is therefore going to require a two-way approach with

experimentalists and theoreticians feeding off each other’s findings and ideas.

But then, that is the way it always has been in science.

25.6 Conclusion and future trends

This chapter aims at showing some of the current research trends regarding

the interplay between size, symmetry and functional properties in ferroelectric

thin films. It seems clear that, at the laboratory level, the ultimate limits for

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Handbook of dielectric, piezoelectric and ferroelectric materials784

size minimization in ferroelectric thin films have been reached (basically,

there is no limit!). And the basic ingredients of the physics of ferroelectric

thin films are also known: strain, strain relaxation and depolarization fields.

The interplay between these can lead to new polar symmetries and/or new

domain geometries, while the domain size is dictated by Kittel’s law down

to the nanometre regime.

In recent times some new research trends are emerging in the area of

ferroelectrics. At present these are incipient, but look likely to grow in

importance; below we list a few, with the aim not so much of discussing their

physics, but rather inspiring the reader along new lines of work.

• Non-planar nanoferroelectrics: pioneering work has been done on

ferroelectric nanotubes [153, 154], ferroelectric nanorods [155] and

ferroelectric nanocolumns [156]. At present most of the work is just

‘proof of principle’ showing that these structures can be made and are

indeed ferroelectric. Almost nothing is known yet, however, about the

polar orientation, the depolarization effects, the existence of new polar

symmetries, including vortex states [157], and the ultimate ferroic size

limit in these confined geometries. One of the first new insights has been

the analysis of domain size scaling in single-crystal 3D nanoferroelectrics,

where an extension of the original Kittel’s law has been proposed [158].

Three-dimensional effects in small ferroelectrics have more than just

academic interest. As the size of planar ferroic structures is laterally

reduced in order to increase the storage density of devices, even planar

geometries begin to experience edge effects. Furthermore, in order to

increase the storage density, 3D nanostructures are the only way forward,

and indeed the International Technology Roadmap for Semiconductors

indicates that these should reach the prototype stage by 2010 [159].

• Self-organized ferrodevices: as the drive towards miniaturization pushes

on, new strategies for the fabrication of large arrays of very small

ferrodevices become more urgent. An interesting idea is the use of self-

organization or self-patterning. Self-organized arrays of ferroelectric

islands [160, 161] and metallic electrodes on top of ferroelectric films

[162] have been reported. The self-patterning in these structures is achieved

through strain interactions via the substrate, leading to a distinct size and

shape distribution of the resulting nano-islands [161].

But there are other approaches. Gregg and co-workers have achieved

self-organized Tbit/inch

arrays by filling in self-organized nanoporous

alumina with Pt electrodes [163]. They are also actively working with

other strategies such as the use of close-packing spheres as templates.

The achievement of well-registered self-organized nano-patterns is as

much an engineering problem as a scientific one, with difficulties ranging

from the mere fabrication to the addressing of the individual devices and

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Symmetry engineering and size effects in ferroelectric thin films 785

the modelling of the properties. But overcoming the difficulties has a big

prize in terms of potential economic impact, so it is expected that research

in this area will continue.

• Domain walls: domain walls have their own symmetry, distinct from

that of the domains. They also have, accordingly, their own properties:

recent reports suggest that domain walls in some piezoceramics have

enhanced electromechanical properties owing to their low dimensionality.

And while domain walls are very thin in typical ferroelectrics, there is

reason to suspect that they may not be so in relaxors and multi-ferroics.

Moreover, they can be broaden by the applied electric field [110].

Furthermore, according to Kittel’s law, the density of domain walls

increases as film thickness decreases, so in very thin films of the right

materials the properties of the domain walls may dominate the physics.

This idea is already being explored in relation to multi-ferroics [164],

and it is likely to attract increased attention in the near future.

The above list is by no means exhaustive: hybrid materials and nano-

composites, flexoelectricity and graded ferroelectrics, integration with carbon

nanotubes, non-oxide multiferroics, etc. are other promising areas of incipient

research. The number of scientists working in ferroelectrics or multi-ferroics,

and the number of high-impact articles being published suggest that this is a

very dynamic and exciting area of research at the moment. Whether the

interest will be sustained or whether it will fizzle out remains to be seen. But,

from our point of view, there is promise in the factor that ferroelectric

nanodevices (memories, micro-electromechanical sensors and actuators

(MEMS), etc.) are already being made and marketed. The combination of

exciting physics and commercial applications offers a solid platform to build

upon. Our bet is that nanoferroelectrics are is here to stay.

25.7 Further reading

In order to expand in the topics discussed here, we advise reading the following

books on thin films and heteroepitaxy, deposition techniques and X-ray

diffraction techniques applied to thin films:

Thin Films: Heteroepitaxial Systems, edited by W.K. Liu and M.B. Santos

(Series on Directions in Condensed Matter Physics, vol. 15), World Scientific

UK, 1999.

Thin Films and Heterostructures for Oxide Electronics by Satishchandra

B. Ogale (Multifunctional Thin Films Series, Editors: O. Auciello and R.

Ramesh), Springer, 2005.

High Resolution X-Ray Scattering: From Thin Films to Lateral

Nanostructures by U. Pietsch, V. Holy and T. Baumbach (Series: Advanced

Texts in Physics), Springer-Verlag, Second Edition, 2004.

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Handbook of dielectric, piezoelectric and ferroelectric materials786

We also recommend reading the following excellent, recent review articles

(some of which are also referred to in the general list of references):

M. Dawber, K. M. Rabe, J. F. Scott, ‘Physics of thin-film ferroelectric

oxides’, Rev. Mod. Phys. 77, 1083 (2005).

D. Damjanovic, ‘Contributions to the piezoelectric effect in ferroelectric

single crystals and ceramics’, Journal of the American Ceramic Society, 88,

2663 (2005).

N. Setter et al. ‘Ferroelectric thin films: Review of materials, properties,

and applications’, J. Appl. Phys. 100, 051606 (2006).

J. F. Scott, ‘Applications of modern ferroelectrics’, Science 315, 955

(2007).

M. Davis, ‘Picturing the elephant: giant piezoelectric activity and the

monoclinic phases of relaxor-ferroelectric single crystals’, Journal of

Electroceramics (2007) DOI: 10.1007/s 10832-007-9046-1.

Other reviews on the subject of Section 25.4 include:

B. Noheda, ‘Structure and high-piezoelectricity in lead oxide solid solutions’,

Current Opinion in Solid State & Materials Science, 6, 27 (2005)

B. Noheda and D. E. Cox, ‘Bridging phases at the morphotropic boundaries

of lead oxide solid solutions’, Phase Transitions, 79, 5–20 (2006)

25.8 Acknowledgements

Much of our pulsed laser deposition work has been done in collaboration

with Arjen Janssens, Guus Rijnders and Dave H. A. Blank, of the University

of Twente, and Ard Vlooswijk, Gijsbert Rispens and Christophe Daumont of

the University of Groningen. Section 25.4 is based on an intensive collaboration

with Dave E. Cox and the late Gen Shirane, which has been most rewarding

from professional and personal points of view. We are also grateful to Oliver

Seeck and Wolfgang Caliebe for their help at the beamlime W1 in HASYLAB

(DESY-Hamburg). We acknowledge the support of the Dutch Foundation for

Fundamental Research (FOM) and the Dutch Science Organization (NWO).

One of us (G.C.) acknowledges the financial support of a Marie Curie

Fellowship.

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