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

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Handbook of dielectric, piezoelectric and ferroelectric materials550

sized silicon or latex spheres. See also Chu et al. (2004) and Alexe and

Hesse (2006). Self-assembly can be used to make nano-particles, nano-tubes

or nano-wires. In each case theoretical physicists have pursued the idea that

true finite-size effects might occur at dimensions slightly less than 100nm,

but this does not seem to be the case. In nano-spheres of BaTiO

the outside

shell is cubic (paraelectric) and the interior is (Tanaka and Makino, 1998)

tetragonal and ferroelectric (this shell–core structure resembles that in an

M&M candy). As diameter is reduced the nano-sphere is all cubic and not

ferroelectric. But this is just a surface chemistry effect and not a finite size

physics effect. Real finite size effects may occur for diameters < 3nm.

Most readers are familiar with carbon nanotubes. These are generally

good conductors, metallic or semiconducting. By comparison, ferroelectric

nanotubes are fairly good insulators. When a voltage is applied to them, they

expand, contract, or bend (piezoelectric). First fabricated by Hernandez

et al. (2002) in Colorado, Mishina et al. (2002, 2003) and Mishina (2005) in

Moscow, such oxide nanotubes have been most recently characterized by

Tenne (2004) and Mao et al. (2005). A brief review is given by Morrison

et al. (2003).

Note that the size distribution graph for the self-assembled nano-islands

of PZT in Fig. 18.11 is not a phase diagram (it is not a system in thermal

equilibrium). The distribution function for fractional percentage w of islands

of a certain volume V has

log(w) = a

V + b

1/3

+ c

2/3

18.4

assumed, with coefficients a

, b

, c

as fitted parameters. This gave very

18.11

PZT self assembly – AFM scan of PZT on SrTiO

(Dawber

et al

2003b).

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Ferroelectric nanostructures for device applications 551

good agreement with experiment. Physically this means that energy terms

proportional to nano-island volume, surface area, and edge lengths are included.

One could also add a term proportional to the number of vertices (as has

been done by J. Maier (Jamnik et al., 1995) in a different context for ionic

conductors), but that was not included.

The most interesting new developments expected in the coming year are

hybrid devices combining piezoelectric nanotubes with carbon nano-wires.

See Jang et al., (2005) for a preview of such designs.

18.4 Magnetoelectrics and magnetoelectric devices

The original idea that crystals could be simultaneously electrically and

magnetically ordered probably arose with Pierre Curie at the turn of the

twentieth century. However, crystals whose Hamiltonians or free energies

contained linear coupling between electric polarization P and magnetization

M were thought to be impossible after an era in the 1920s of their spurious

discovery in France by A. Perrier et al. in materials such as Ni in which the

effect is actually forbidden. This caused a black cloud to settle over the field

similar to the more recent case of ‘cold fusion’, and resulted in a hiatus in

‘magnetoelectricity’ R&D until the 1950s, when the Moscow groups, stimulated

by Shubnikov and understanding magnetic symmetry better than the rest of

the world, resurrected the problem. Dzyaloshinskii (1959) predicted such an

effect in antiferromagnetic Cr

, rapidly confirmed by Astrov (1960), and

also piezomagnetism, quickly found by Borovik-Romanov (1960). In contrast

to magnetostriction, which is a quadratic effect, piezomagnetism, like

piezoelectricity, is a linear vector response. Most physicists had thought that

the linear magnetoelectric effect and piezomagnetism were forbidden, because

the Hamiltonians that include them do not obey time-reversal symmetry (in

general, magnetism does not!). During the 1970s a successful search for

other linear magnetoelectrics (‘multiferroics’) was led by Hans Schmid in

Geneva. The primary device interest was multi-state logic elements for

computer bit storage that could be greater than binary. As such, it was imperative

to show switching of magnetic states with electric fields and/or of ferroelectric

states with magnetic fields. Hence the independence of, or coupling between,

magnetic and electric domain walls was of great importance. This work has

had a renaissance since 2000, with new work emphasizing Mn and Tb

compounds (Kimura et al., 2003; Hur et al., 2004). The study of

magnetoelectricity emphasizes two terms, given in Eq. [18.5]:

H = α

><M

> + β

ijk

><M

> 18.5

Note that due to the first term this Hamiltonian is not time-reversal invariant.

Here the linear magnetoelectric effect due to α

vanishes above T

, the Neel

temperature) or T

(the Curie temperature), since <M> = 0; however, the

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Handbook of dielectric, piezoelectric and ferroelectric materials552

quadratic term due to β

ijk

is proportional to <M

> – the rms value of

magnetization – and remains finite well above T

(until T ~ 3T

in magnets

such as BaMnF

with [2D] planar spin ordering). Such quadratic

magnetoelectric effects in paramagnets were first discovered by Hou and

Bloembergen (1965).

If we wish to switch a magnetic domain with an electric field, we need to

know how much the magnetization M depends upon the polarization P. Does

reversing P influence M by 1%, 10% or 100%? The idea that ferroelectricity

could actually cause ferromagnetism (a 100% effect) was explained by Fox

and Scott (1977) and later by Privratska and Janovec (1997) and exemplified

with the BaMF

family (M = Mn, Ni, Co, Fe and mixed compounds

BaM

1–x

M′

). Fox and Scott made a semi-empirical quantitative estimate of

the effect by using known values of α in other Mn-compounds; Privratska

and Janovec used a group theory calculation which could not predict magnitudes

(or even whether the effect is large enough to measure), but they showed

which domain walls in which point group symmetries would permit it. By

producing a weak ferromagnetic moment (canting of antiferromagnetic spin

sublattices) M

= α

through the Dzyaloshinskii-Moriya anisotropic

exchange, the ferroelectric polarization can produce this effect in some

symmetry groups (e.g. 2′ in BaMnF

) but not others (e.g. 2 in BaCoF

). The

angle of spin canting (3 mrad = 0.17 degrees in BaMnF

) implies a plausible

value for the anisotropic exchange in comparison with off-diagonal α

other Mn

compounds.

This Fox–Scott mechanism has recently been rediscovered in BaNiF

and

developed in the context of ab initio models by Ederer and Spaldin (2006a,b);

it can also produce ferromagnetism within domain walls in antiferromagnets

(Privratska and Janovec, 1997). This mechanism is too weak to reconcile

conflicting BiFeO

magnetization data of Wang et al. (2003, 2005) with the

near-zero values reported by Eerenstein et al. (2005), and it is symmetry-

forbidden in the R3c structure of bismuth ferrite; however, a more general

model for ferromagnetism in antiferromagnetic domain walls which might

be stronger has been detailed by Privratska and Janovec (1997) which is

allowed for R3c. (Although the strong ferromagnetism initially reported in

Science by Wang et al. is not intrinsic to pure BiFeO

, it would appear that

not all of the discrepancy can be attributed to oxygen vacancies and resultant

mixed valence states for the Fe ions; perhaps some of the ferromagnetism is

due to net ferromagnetic moments in the antiferromagnetic domain walls.)

The Fox–Scott model is a bulk effect; weaker coupling between magnetic

and ferroelectric domain walls has been demonstrated by Cheong’s group at

Rutgers and is also of great theoretical interest.

Brown et al. (1968) showed that for direct magnetoelectric coupling,

explicit in the first term of Eq. [18.5], the square of the magnetoelectric

susceptibility cannot exceed the product of the electric susceptibility and the

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Ferroelectric nanostructures for device applications 553

magnetic susceptibility,

≤ χ

, making it uselessly weak for devices

(see also Ascher et al., 1966). However, that ignores indirect coupling through

strain. The latter can be important in a single material (i.e. piezoelectric

terms and electrostrictive terms such as sP and sP

plus piezomagnetic terms

such as sM and magnetostrictive terms sM

); and they permit binary structures

in which one substance has large piezoelectricity (or electrostriction) and the

other has large piezomagnetism or magnetostriction. By choosing two materials

in a laminated or nano-structured bimorph, one can cause large magnetostriction

in, say, terphenyl-d, and large piezoelectricity in, say, PZT. The result is a

prototype room temperature detector of weak magnetic fields, which might

be a very low-cost (uncooled) replacement for SQUID detectors. The best

result to date is a laminar bimorph of a ferromagnet (LSMO) and barium

titanate (Eerenstein et al., 2007). Unfortunately, the ‘Holy Grail’ of multiferroics

– a strong (uncanted) ferromagnet that is also ferroelectric at room temperature

– is still sought for. But it is unlikely to have device parameters superior to

PZT/terphenyl anyway. As a memory element, however, it would permit

electric WRITE operation and magnetic READ; this would eliminate the

need for a destructive read (and reset) for present-day FRAMs and make

possible fatigue-free memories. Its READ operation could be extremely fast

and low power. This very attractive possibility requires a ferroelectric (P >1

µC/cm

) that is also a strong ferromagnet (M ≥ 1 Bohr magneton/unit cell)

and has low electrical conductivity (<< 10

–6

ohm

–1

) at ambient

temperatures. Although BiFeO

doped to increase resistivity remains a possible

candidate, ferroelectric-ferromagnetic fluorides such as Sr

(FeF

)

or K

with respectively T

≈ 700K and 495K merit much more study (Abrahams,

1996, 1999; Abrahams et al., 1996; Ederer and Spaldin, 2006a,b).

From a device point of view, the advantage of a magnetoelectric RAM is

that it could be electrically written (fast, low power) but magnetically read

(non-destructive read-out, no re-set and little fatigue). Unfortunately, several

recent papers report magnetic effects on dielectric constants and interpret

them as evidence for magnetoelectricity (Hemberger et al., 2005); Catalan

and Scott (2007) have shown that this is usually not true and can arise from

magnetoresistance plus Maxwell–Wagner space charge in non-ferroelectrics,

including cubic spinels.

18.5 Toroidal and circular ordering of ferroelectric

domains in ferroics

Ferroic domains are usually rectilinear, although needle-like domain structures

are also common. However, circular or toroidal patterns can occur, and most

ferroelectrics (or antiferroelectrics) order with polarizations parallel or

antiparallel. As Kittel (1946) first pointed out, ferromagnets in nano-size

diameters will order with four 90° domains forming a circle or square. This

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Handbook of dielectric, piezoelectric and ferroelectric materials554

kind of topological spin defect (vortex) was treated theoretically by Mermin

(1979) in terms of winding numbers, and is commonly found in nano-magnets,

in both naturally occurring minerals (such as titanium-ilmenite) and synthetics

(Harrison et al., 2002). The latter authors achieved superb micrographs of

such vortex domains via electron holography. Typical size (diameter) of

these vortex domains is 100nm.

A completely different origin for circular or toroidal domains occurs in

magnetoelectrics, even in bulk. First analysed in detail by Ginzburg and by

Sannikov, this has been reviewed by several authors (Dubovik and Tugushev,

1990; Schmid, 1994; Fiebig, 2005; Eerenstein et al., 2006); and subject to a

flurry of recent papers (Naumov et al., 2004; Scott, 2005; Ponomareva et al.,

2005a,b; Prosandeev et al., 2006) but not yet unambiguously observed (a

newly recognized complication is that domain walls in antiferromagnets can

themselves be ferromagnetic). Such a system offers the possibility of very

high-density (Tbit/in

) memory and electrical WRITE with magnetic READ

operations. The read operations are facilitated by simultaneous application

of a large dc electric field, as recently shown by Prosandeev, et al. (2006).

Although permitted in bulk, the occurrence of such toroidal ordering in

ferroelectrics is favoured in nano-tubes and nano-disks (Naumov et al., 2004),

and recently Zhu et al. (2006) have fabricated such ferroelectric ‘doughnuts’

as small as 5nm inside diameter.

18.6 Electron emission from ferroelectrics

The fact that ferroelectrics emit copious electrons from their surfaces during

switching was discovered in Michigan (Rosenblum et al., 1974) and later

studied extensively in Sverdlovsk. Its use as synchronized electron sources

for accelerators was investigated by Gundel (1995; 1996) in CERN (now

Nantes), Le Bihan and others in France (Svirdov et al., 1998), Biedrzycki in

Poland, and several Russian/Israeli (Rosenman et al., 2000) and American

groups (Auciello et al., 1995). The prototype use as a synchronized, pulsed

electron source for accelerators was developed, but no commercial devices

were ever manufactured, primarily because of fatigue.

The extension to flat channel-plate structures with ferroelectric thin films

was studied in Nantes, but films gave inferior performance compared with

bulk ceramics. A good summary (yet unpublished) of the present situation

has been given by Kafadaryan (2006). Currents of tens of amps have been

obtained with synchronized, rather mono-energetic pulse lengths of 100ns

to 1µs. These are superior to thermionic cathodes in that they have higher

current densities and lifetimes and also have instant turn-on (thermionic

cathodes require a warm-up). The ferroelectric electron emitters can be operated

in poor vacuum and require no separate activation process. The commercial

drawbacks are that the intense electric fields cause micro-cracking and device

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Ferroelectric nanostructures for device applications 555

failure and that the effect is poorer in thin films than in bulk. Moreover, no

unambiguous theoretical model has been accepted for the basic emission

process. One published mechanism invokes a surface plasma layer creation

during switching that I regard as very unlikely (its supposed experimental

detection was actually to interference patterns similar to Newton’s rings and

not to plasmon reflectivity). Although fields of E = 10

V/cm are required for

good performance, this value has recently been achieved in FIB-cut single

crystals as well as PZT ceramics; note that 10

V/cm is a huge field (1GV/

m) but is only 50V across 50nm.

In my opinion this is an unexploited device area for which commercial

development of, for example, miniature high-power microwave devices that

could be made within a few years. Samsung explored in the 1990s the use of

this phenomenon for nano-lithography, and a comprehensive review was

published in 2000. Most recently this effect was used by Putterman’s group

for a kind of cold fusion (Naranjo et al., 2005) as a miniaturized source of

X-rays and neutrons.

18.7 Base–metal–electrode capacitors

The majority of all condensers used in electronics (billions/year) are barium–

titanate-based ceramic capacitors based on the original discovery by von

Hippel (1944). Leading producers include Kyocera in Kyoto and AVX Corp.

near Belfast. These are multi-layer capacitors (MLCs) with Ag/Pd electrode

stacks. Some of the electrodes are internal in an MLC and are ‘floating’ (no

contact to the external circuitry). Present efforts are to increase high-voltage

performance to higher breakdown voltages and to further reduce costs by

replacing silver-palladium with base metals, especially nickel. Electrode

separations d vary from submicrometre to ca. 20µm. Recently Milliken et al.

(2006b) and Scott (2006) have shown that the breakdown field varies as the

dc thermal model predicts (ignoring transient effects of applied field ramp

rate): E

= c

–1/2

for thicknesses above 1µm, but no theory exists for the

submicrometre-spaced devices, where electrode surface roughness may be

the limiting parameter. Progress would be expected in this high-volume

commercial area in the next five years: Ni replacement; higher breakdown

devices; and a reliable theory for both Ni–BaTiO

interfaces and the non-

monotonic dependence of breakdown voltage on the electrode separation d.

This has not been a fashionable research area in universities, but the financial

pay-off is potentially huge.

18.8 Electrocaloric cooling for mainframes and MEMs

The fact that ferroelectrics can be cooled by applying an electric field to

them under certain conditions has been known for 50 years. Termed the

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Handbook of dielectric, piezoelectric and ferroelectric materials556

‘electrocaloric effect’ after analogous magnetocaloric effects in magnets, the

mechanism was poorly analyzed for some years, with the three standard

texts on ferroelectricity by Jona and Shirane (1962), by Fatuzzo and Merz

(1962), and by Mitsui et al. (1969) giving three different predictions for

behaviour above and below T

. From Maxwell’s relations

(∂T/∂D)

= (∂E/∂S)

= (T/c

) (∂E/∂T)

18.6

where T is temperature; E, electric field; S, entropy; D, displacement vector;

and c, specific heat at constant displacement D. This gives in terms of the

Devonshire coefficient β from a Landau expansion of the free energy

(∂T/∂D)

= βDT/c

18.7

and, integrating over T, assuming T

– T

is small,

∆

βTTT

DD Tc PEP

= – =

( – ) [( /(2 )]([ ( )– (0)]

≈

18.8

The derivation above is misleading in popular textbooks (e.g. Lines and

Glass (1967)), because the field dependence P(E) is usually neglected at T

;

indeed T

is not shown in any diagram, and it is unclear whether the heat

cycle has three legs or four. The error lies in the fact that (∂P/∂E)

>> (∂P/

∂T)

. Thus significant effects also occur for T

and T

both above, or one

above and one below; and in fact the peak eletrocaloric effect can be 5–10

K above T

. It is complicated for first-order transitions, where a modest

applied field E can drive the crystal ferroelectric at temperatures well above

(e.g. up to T = T

+ 8.0K in barium titanate).

The different conclusions about the electrocaloric effect in textbooks has

been reviewed by Scott (1993) and studied in careful detail by Tuttle and

Payne (1981), Strukov (1967) and Shebanov and Borman (1992), but because

the effect was small in bulk (measured in millidegrees/volt), it remained a

laboratory curiosity. However, Mischenko et al. (2006) inferred ∆T = 12K at

25V across 350 nm for cooling (Fig. 18.12) in ferroelectric thin films, sufficient

to design a prototype cooler for MEMs or even computer mainframes, which

has stimulated a burst of R&D on the subject. There are two subtleties: first,

the thermal cycle has only three legs and not four as is sometimes shown for

magnetoelectric cooling. The first step is to turn on the field at T = T

and

isothermally reduce the entropy S by increasing polarization P from zero to

. The second step is to turn the field off. Although this lowers E to zero

almost instantly, it certainly does not drop P to zero as quickly; instead, P

relaxes slowly (and approximately adiabatically). This adiabatic cooling lowers

T to T

and P to zero. The third leg of the heat cycle is to warm up from T

to T

by extracting heat from the surrounding system; this is at constant

(zero) polarization and is hence ‘isochoric’. Secondly, this heat cycle is more

complicated for a first-order phase transition slightly above the transition

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Ferroelectric nanostructures for device applications 557

temperature T

. In BaTiO

up to T = T

+ 8.0K ferroelectricity can be

induced by the applied field. Hence switching the field on at T

< T < T

8K can produce extremely large changes in entropy due to domain formation

and consequently large changes in temperature. In such cases the maximum

electrocaloric effect can occur above T

, contrary to the conclusion in some

textbooks or in Strukov’s papers on triglycine sulphate (which is second-

order).

18.9 Interfacial phenomena

Ferroelectrics in some ways are more complicated than ferromagnets, simply

because magnets can be measured in air with no electrical contact, whereas

ferroelectric electrical measurements generally must be made on a sandwich

consisting of two electrodes around a dielectric (Valasek, 1921). The interface

between the metal electrodes and the semiconducting ferroelectric is very

complex, involving screening in the metal (Dawber et al., 2003a, 2005a) and

instabilities at ca. 3nm dielectric thickness (Junquera and Ghosez, 2003),

reduced perhaps to 1nm by electrode-ferroelectric ionic interactions more

complex than simple Fermi–Thomas screening (Gerra et al., 2006). There

are rather subtle differences in the behaviour of ferroelectric thin films with

elemental metal electrodes (Pt, Au, Ni) and oxide metal electrodes, such as

SrRuO

, IrO

or RuO

. The primary criterion for good electrodes is a large

(°C)

30025020015010050

∆

(°C)

480

∆

(kV/cm)

380

280

180

18.12

Electrocaloric effect in lead scandium tantalate PST (Mischenko

et al

, 2006).

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Handbook of dielectric, piezoelectric and ferroelectric materials558

work function (ca. 5.0–5.5eV), to prevent ohmic or near-ohmic contacts on

the dielectrics (which typically have electron affinities of 3.5eV and bandgaps

of 3–4eV, so that the Pt 5.3 eV work function nicely puts the Pt Fermi level

at mid-gap in the dielectric). Full oxidation of most oxide electrodes is

therefore important, because, for example, the work function of RuO

is at

4.95eV, but unoxidized elemental Ru nano-islands in the electrode deposited

below ca. 840K are at 4.65eV, causing ‘hot spots’ and leakage (Hartmann et

al., 2000).

Both leakage currents and charge injection are serious problems and can

produce artefacts in switching data. The resulting leakage current in PZT

films can be Schottky-limited in a partially depleted film (Pintilie and Alexe,

2005; Pintilie et al., 2005) for somewhat conducting lead zirconate titanate

(PZT) but Poole–Frenkel limited in a fully depleted PZT film from the

Samsung 32 Mbit production line (Zubko et al., 2006a,b). These differences

in conduction mechanisms were very well illustrated in an early paper by Li

and Lu (1991). Understanding and optimizing interfacial phenomena are

paramount to the commercialization of thin film memories and ferroelectric

DRAM capacitors, and have been reviewed by Auciello (2006). Early problems

with fatigue, primarily due to perovskite-pyrochlore conversion (Lou et al.,

2006) in FRAMs have now been overcome via oxide electrodes.

18.10 Phased-array radar

Phased-array radar devices produce an angular scanning of the horizon without

mechanical rotation of the antenna. This can be achieved by a voltage-

dependent phase shift in the antenna elements. Such shifts can be generated

in bulk ferroelectrics, but only at very high voltages (kV), which entails

large sizes and weights. It would be desirable to produce phased array radar

devices with ferroelectric thin films, since this could entail very low voltages

(5V) compatible with silicon chip technology, and hence embodiments with

small size and weight. Thin-film ferroelectrics exhibit a large decrease in

dielectric constant with application of modest voltages, typically 25–60% at

5V. This suggested that they could be used as the active phase-shift element

in phased-array radar, a project studied carefully in the 1990s by researchers

at Grumman and TRW in the USA and by Vendik’s group in Leningrad.

Unfortunately the dielectric loss tangent in these films remains too large for

acceptable insertion losses in such devices, so nothing has been made

commercially. There is hope that this loss is not intrinsic, since it is orders of

magnitude smaller in bulk. Therefore significant efforts to improve the quality

of thin films have been underway, with perhaps the best results obtained at

Penn State University. A status report was published recently by Miranda et

al. (2002).

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Ferroelectric nanostructures for device applications 559

18.11 Focal-plane arrays

All ferroelectrics are pyroelectric and hence application of thin-film ferroelectric

technology to pyroelectric detectors, including focal-plane arrays, is of interest.

This may be enhanced by the fact that high-quality films can be deposited on

curved substrates via chemical vapor deposition or misted CSD (chemical

solution deposition). This was shown both at Symetrix and at SONY in 1997

(Isobe et al., 1997; Solayappan et al., 1997). No breakthroughs have been

reported in the open literature, although LG Electronics has reported using

the mist system for DRAM capacitors (Kim et al., 1997).

18.12 Ferroelectric superlattices

The study of artificially layered ferroelectric superlattices, such as BaTiO

SrTiO

is of great current interest (Tenne et al., 2006). Such superlattices can

produce enhanced polarization P and dielectric constant ε. Their physics is

generally very well understood but remains somewhat enigmatic at very

small repeat distances of one to three unit cells (Dawber et al., 2005b).

PbTiO

/SrTiO

is particularly interesting because it has a near-perfect lattice

constant match. A surprising phenomenon is that in BaTiO

/SrTiO

the

polarization flops from along [001] to [110] in the relaxed superlattice (Jiang

et al., 2003; Rios et al., 2003; Johnston et al., 2005). Jiang et al. (2002) also

showed that PbZr

1–x

/PbZr

1–y

(all-PZT) superlattices with x >> y

had significant Maxwell–Wagner space charge at the layer interfaces that

influenced fatigue. ‘Tri-color’ superlattices are particularly interesting; these

materials have a stacking sequence of ABCABCABC… that lacks inversion

symmetry.

A related topic is periodically poled crystals of LiNbO

and other non-

linear optical materials (Walker et al., 2005; Glickman et al., 2006). Here the

superlattice consists not of different chemical compositions such as BaTiO

SrTiO

, but of +P and –P domains. Such materials provide highly efficient

phase-matching for non-linear optics. The quest at present is to produce

shorter wavelengths (< 1µm) and to understand domain widths and stability

(the positive +P domains are not always the same width as the negative –P

domains, and the widths can vary with time).

18.13 Ultra-thin single crystals

Until very recently the conventional wisdom with regard to ferroelectric thin

films was that for thicknesses much below 1.0µm, the dielectric peak persus

temperature χ(T) was greatly broadened and shifted to much lower (hundreds

of degrees) temperatures. Most scientists assumed that this was due to intrinsic

size effects, theoretically predicted. However, we now know that for thicknesses

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