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

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Handbook of dielectric, piezoelectric and ferroelectric materials1020

These reactions proceed quickly and do not limit the vacancy formation

reaction. In contrast, O

has to meet another O

on the surface to form an

molecule, which then diffuses into the atmosphere. The reaction related

to O

that is suppressed at a higher

is the limiting factor of the vacancy

formation for BiT. Therefore, only model 3 can account for the

dependence

of weight loss. The formation of

′′′

Bi1

brings about

••

for charge

compensation in the crystal as expressed by eq. (33.1). High-

atmosphere

inhibits the reaction on the crystal surface, and thereby further creation of

••

is restricted, which prevents

′′′

Bi1

generation. Thus, a high

during

heating is effective for suppressing the vacancy formation in the lattice, i.e.

synthesizing high-quality BiT crystalline samples [19].

33.5 Domain structure

Figure 33.12 shows the domain structure in the a–b plane of a BiT crystal.

In the optical micrograph (Fig. 33.12a), taken in the transmission mode, a

striped 90° domain structure is clearly seen, similar to that reported for

BaTiO

single crystals [45] and PZT ceramics. Furthermore, a needle-like

domain structure is also observed, and the needlepoints are terminated at

domain walls. This kind of complex domain structure has been reported for

PbTiO

thin films [46] and predicted by Li et al. [47]. The striped domain

structures are observed at temperatures below the Curie temperature

= 675°C) and disappear above T

Figure 33.12(b) shows the piezoresponse-force microscope (PFM) image

for the area indicated by the dashed square in Fig. 33.12(a). White (the

strongest PFM signal) and black (the weakest one) areas have the domains

with P

oriented in upper and lower direction, respectively, while the gray

(a)

(b)

100µm

(

)

(

)

50µm

170 mV–160mV

33.12

(a) Domain structure of a BiT crystal in the

–

plane observed

with optical microscopy, and (b) piezoelectric-force microscopic

image of the area denoted by the dashed line in (a).

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Crystal structure and defect control 1021

color indicates the domain with P

oriented in the horizontal direction. The

dark lines observed in the optical micrograph are 90° domain walls. In

addition to the striped 90° domains, 180° domain walls with head-to-head

and tail-to-tail configurations are seen in some of needle-like 90° domains.

These ‘charged’ domain walls are known to strongly interact with

••

[11, 19].

Figure 33.13 shows the PFM images of Bi

4–x

(BLT, x = 0.85 and

1.2) crystals. La substitution led to a significant change in domain structure,

and the domain size decreases with an increase in La content (x). In contrast

to BiT, gentle and irregular curvatures were found, and striped 90° domain

structures are constructed in the area framed by the curvatures. The enlarged

micrographs of the dashed square denoted by ‘1’ and ‘2’ in Fig. 33.13(a) are

indicated in Fig. 33.13(c) and (d), respectively. Surprisingly, all the striped

90° domains are regularly terminated at the curvature, implying that not only

do domains interact with the neighbors but also that a widespread interaction

plays a crucial role in the formation of the domain structure in the BLT

crystals.

5 µm5µm

180°

domain

wall

50 µm50 µm

33.13

Piezoelectric-force microscopic images of BLT crystals: (a) BLT

(

= 0.85) and (b) BLT (

= 1.20). The enlarged micrographs of the

dashed square denoted by ‘1’ and ‘2’ in (a) are indicated in (c) and

(d), respectively.

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Handbook of dielectric, piezoelectric and ferroelectric materials1022

The curvature observed in the middle of Fig. 33.13(c) is composed of two

different parts. One is the wall between the domains with upper- and lower-

oriented P

, showing a tail-to-tail 180° domain wall. The other between these

180° domain walls is the part with no change in PFM signal, indicating that

the direction of P

does no change regardless of the curvature. If striped 90°

domains have a standard structural configuration with an alternative 90°

rotation of the a and b-axes, the domains with the same PFM signal separated

by the curvature should have the opposite b-axis distortion (the opposite

TiO

distortion along the b-axis, as discussed below). These domains can be

superimposed on each other after a translation operation of [1/2 1/2 0],

suggesting that the other part of the curvature is an antiphase domain boundary

(ADB), as observed in the ceramics of BLT [30] and SrBi

[48].

Furthermore, on the upper left in Fig. 33.13(c), a head-to-head 180° domain

wall as well as ADB is also observed.

Here, domain structures are discussed in terms of ferroelectric and

ferroelastic distortions. 90° domains are formed to relieve mechanical stress

induced by ferroelectric distortion with sacrificing elastic strain energy at

domain walls. The formation of a new 90° domain wall requires the exchange

of the axis between a and b in the a–b plane. The strain energy is roughly

proportional to spontaneous deformation (S) expressed by S = a/b – 1. With

increasing La content (x), S decreases almost linearly from 0.007 (BiT) to

0.000 for BLT(x = 1.50), and orthorhombic distortion becomes smaller. The

close relation between S and the domain width of striped 90° domains is

revealed (see Fig. 33.14), and a smaller S results in a narrower domain

width, as can be clearly seen in Fig. 33.13. When S is lowered, the strain

energy density of domain walls decreases. Thus, this increases the density of

(= 1 –

)

0.0000.0020.0040.0060.008

90° domain width (mm)

BLT (

= 1.46)

BLT

(

= 0.85)

BLT

(

= 1.2)

BLT

(

= 0.46)

BiT

33.14

90° domain width as a function of spontaneous deformation

(

). The value of

is calculated from the structural data obtained by

the neutron diffraction Rietveld analysis.

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Crystal structure and defect control 1023

90° domain walls to attain a lower total energy. It can be said that S governs

90° domain structure in the a–b plane. However, the formation of ADB has

generally no relation to strain energy, and S does not affect the configuration

of ADB directly. Thus, we should consider local lattice distortion to elucidate

the nature of ADB.

Neutron diffraction study has revealed that La substitution leads to a

structural change in TiO

distortion along the b-axis as well as in the ferroelectric

distortion along the a-axis. While cooperative ionic displacements along the

a-axis result in the P

, the local dipole moments along the b-axis cancel each

other owing to the presence of glide plane. Now the TiO

rotation is focused

as a reference of local lattice distortion. BiT has two kinds of TiO

octahedron

as shown in Fig. 33.1; one is the octahedron at the middle of the perovskite

blocks (Ti1O

) and the other is the octahedron near Bi

layers (Ti2O

Here, only the octahedral distortion of Ti2O

is considered for simplicity.

For BiT, Ti2O

rotates by 8.7° around the a-axis in the b–c plane, while the

rotation angle around the b-axis in the a–c plane is only 2.4°. This indicates

that the local TiO

distortion is much larger in the b–c plane than that in the

a–c plane. La substitution causes a smaller TiO

rotation, and the rotation

angle for BLT (x = 0.75) is 8.2° in the b–c plane and 1.6° in the a–c plane.

In the single domain region, the phase of TiO

rotation is opposite for

adjacent octahedra that share oxide ions. The regular TiO

rotation does not

hold true at ADB, and the phase shift occurs by [1/2 1/2 0]. This irregular

TiO

rotation results in a large strain at ADB, and the strain energy becomes

less for a smaller TiO

rotation angle. The smaller TiO

distortion for BLT

seems to be a partial reason for the formation of ADB. The 90° domain

structure surrounded by ADB strongly suggests that the 90° domain is

constructed from ADB and the ADB acts as a nucleus of a new 90° domain,

as suggested by Ding et al. [30]. However, the formation of ADB as well as

90° domain is closely related to the phase transition from parent tetragonal

I4/mmm structure. Further study on the phase transition of BLT is required

to clarify the domain structure and its role in polarization switching.

33.6 Leakage current

The impedance spectroscopic analysis has shown that h

•

is the dominant

carrier for BiT crystals at relatively low temperatures [19]. During cooling

or annealing at intermediate temperatures, the crystals absorb oxygen into

the lattice, and the oxide ion occupies

••

with the formation of h

•

according

to the following reaction:

1/2O V O + 2

2O1

••

•

→

33.3

It has been reported that hole conduction becomes predominant over oxide-

ion conduction at relatively low temperatures [19]. It is reasonable to consider

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Handbook of dielectric, piezoelectric and ferroelectric materials1024

that hole conduction plays a detrimental role in leakage current at room

temperature. Figure 33.15 shows the leakage current (J) as a function of

electric field applied along the a-axis of the poled BiT crystals. For the

crystals grown in air, the ones annealed at 700°C in air had a relatively high

J of the order of 10

–7

to 10

–6

A/cm

. Note that annealing at 700°C under a

high

(35MPa) atmosphere resulted in a higher J in spite of reducing

oxygen vacancies. These results provide direct evidence that h

•

arising from

oxygen absorption is the dominant carrier for leakage current and hence

plays a detrimental role in the insulating properties of the BiT crystals at

room temperature.

Surprisingly, crystals grown in O

atmosphere (O

crystals) exhibit a

significantly lower J of the order of 10

–9

A/cm

, which is consistent with the

results of La-substituted BiT thin films [49].

As described above, heat treatment

at high temperatures inevitably creates

••

as well as

′′′

Bi1

in the BiT lattice.

Crystal growth under a higher

atmosphere suppresses the defect formation,

and the O

crystals have a smaller number of these vacancies compared with

those grown in air. High-

annealing (700°C, 35MPa) also increases J of

the O

crystals. This increase in J shows that the vacancies are present even

in the O

crystals; a further defect control could lead to a lower J in the BiT

system.

Figure 33.16 shows the leakage current properties of BLT (x = 0.46)

crystals along the a-axis. The BLT crystals were grown in air. Note that BLT

(x = 0.46) crystals annealed in air at 700°C showed an extremely low J of the

order of 10

–9

A/cm

. The high-pressure oxygen annealing (

= 35 MPa) at

(kV/cm)

806040200

(A/cm

)

–9

–8

–7

–6

–5

–4

Grown in air

Grown in O

25°C,

-axis

Annealed in air

Annealed at

high

Annealed at

high

33.15

Leakage current density (

) as a function of electric field (

)

applied along the

-axis at 25°C for the BiT crystals grown in air and

atmosphere. The annealing at 700 °C under a high

of 35MPa

led to an increase in

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Crystal structure and defect control 1025

700°C increases J. Even though the oxygen annealing indeed decreases

••

, the annealed crystals have a higher J. The oxygen annealing did not

change the metal composition of the crystals. The fact of the high J caused

by the oxygen annealing shows that the incorporation of oxygen into the

lattice caused by the annealing generates h

•

, as expressed by Eq. (33.3). It is

concluded that h

•

is the detrimental carrier in BLT crystals. The concentration

of h

•

is determined by the excess oxygen that is absorbed from the ambient

during annealing or cooling [19]. The La substitution reduces

••

in the

perovskite layers owing to the high chemical stability of oxide ions near La

in the perovskite layers, and thus decreases h

•

. The chemical stabilization of

oxide ions by La substitution is the origin of the high insulating property

observed for the BLT crystals.

33.7 Polarization properties

Figure 33.17 shows the polarization hysteresis loops of the BiT crystals with

air annealing (700°C, 5h) along the a(b)-axis. The air-grown crystals exhibit

a P

of 37µC/cm

and a coercive field (E

) of 35–40kV/cm. This P

value is

lower than those given in the previous reports [4, 5]. The O

crystals consistently

show a larger P

of 48µC/cm

. It is well known that a small P

of BiT

ceramics and thin films is a result of domain pinning caused by oxygen

vacancies [11, 50]. The improvement of P

observed for the O

crystals is a

result of domain depinning due to fewer

••

associated with the high insulating

property.

Figure 33.18 shows the polarization hysteresis loops of the BLT (x = 0.46)

crystals at 25°C. The high-

annealing (

= 35MPa, 700°C, 10h)

(kV/cm)

806040200

(A/cm

)

–9

–8

–7

–6

–5

–4

Annealed in air

Annealed at

high

BLT (

= 0.46)

25°C,

-axis

Grown in air

33.16

Leakage current density (

) as a function of electric field (

)

applied along the

-axis at 25°C for Bi

4–

(BLT,

= 0.46)

crystals. The annealing at 700°C under a high

of 35 MPa led to

an increase in

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Handbook of dielectric, piezoelectric and ferroelectric materials1026

improves the rectangularity of the hysteresis and increases P

from 25 to 36

µC/cm

. One of the reasons why the high-

annealing leads to the larger

is a weak pinning of domains for the annealed crystals due to the small

number of

••

. The air-annealed crystals still have a certain amount of

••

in the perovskite layers, and

••

acts as a pinning center of the domain wall.

The oxygen annealing increases the number of switchable domains by applying

an electric field. The high-

annealing is demonstrated to be effective for

improving polarization properties in the BLT system with a high insulating

property.

(kV/cm)

–100 –50 0 50 100

(µC/cm

)

–60

–40

–20

25°C, 1Hz

(

)-axis

Grown in O

(annealed in air)

Grown in air

(annealed in air)

33.17

Polarization hysteresis loops along the

-axis measured at

25 °C for the BiT crystals.

33.18

Polarization hysteresis loops along the a axis measured at

25°C for Bi

4–

(BLT,

= 0.46) crystals.

(kV/cm)

–100 –50 0 50 100

–60

–40

–20

(µC/cm

)

25°C, 1Hz

(

) axis

grown in air

Annealed

at high

Annealed

in air

BLT

(

= 0.46)

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Crystal structure and defect control 1027

33.8 Effects of La and Nd substitutions on the

electronic band structure and chemical

bonding

The electronic structure of BNT (x = 2.0) was calculated for both the paraelectric

I4/mmm and the ferroelectric B2cb structures. The calculated band structure

of BNT (x = 2.0) near E

is almost the same as that of BiT (see Fig. 33.5a).

The calculation for the paraelectric BNT (x = 2.0) shows that the fundamental

is indirect (valence band maximum at P and conduction band minimum

at Γ), which is consistent with the result in the reported calculations [34]. In

contrast, our calculations suggest that the ferroelectric BNT (x = 2.0) has a

direct band gap, with the valence band maximum and conduction band

minimum lying at Brillouin-zone center Γ. Our calculation suggests that

BNT (x = 2.0) gives a narrower E

g(DFT)

of 2.4eV compared with BiT (E

g(DFT)

= 2.6eV), which is in good agreement with the results of the optical

measurements [35].

Figure 33.6(c) shows the total DOS between –25 and 7.5eV of BNT (x =

2.0) with B2cb ferroelectric structure. In this calculations, Nd is assumed to

occupy at the A site in the perovskite layers. The valence band consists

mainly of the O 2p states, while the Ti3d states form the conduction band.

The width of the valence band was approximately 5.5eV. Two kinds of Bi

for BiT result in two localized states of Bi 6s band near –10 eV, whereas

BNT has one peak of the Bi 6s band attributed to the Bi in the Bi

layers.

BiT and BNT indicate a similar low-lying O 2s band (–19 to –16eV), and the

broad Nd 5d states overlap with the O 2p band for BNT.

Figure 33.7(c) presents the PDOS of BNT (x = 2.0) with B2cb ferroelectric

structure. For both BiT and BNT, the Bi

layers show similar electronic

character, and the Bi2 and O2 in the Bi

layers do not have DOS near the

Fermi energy (E

). Thus, the perovskite layers play an essential role in the

electronic structure near the band gap, and E

is determined by the orbital

interaction in the perovskite layers. As in the case for BiT (see Fig. 33.7b),

the electronic structure of BNT shows that the valence band maximum mainly

consists of the O 2p orbitals. The conduction band minimum is composed of

the empty 3d orbitals of Ti in the perovskite layers. There is a strong

hybridization with Ti and Bi. This behavior reflects the strong hybridization

of the Ti3d and O2p orbitals in the perovskite layers, as is common for ABO

perovskites [51].

Interestingly, the Bi1 at the perovskite A site has a key role in the electronic

structure of the valence band for BiT. The antibonding orbitals are composed

of the 6s of the Bi1 and the 2p of the adjacent oxide ions form and constitute

the large DOS just below the E

. Furthermore, the orbital hybridization with

O2p leads to considerable DOS of the Bi1 6p states in the valence band. This

behavior is unexpected in a simplified ionic picture, but has been demonstrated

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Handbook of dielectric, piezoelectric and ferroelectric materials1028

also for α-PbO [52, 53], PbTiO

[51] and BiScO

-PbTiO

solid solution

[54]. The hybridization of the Bi1 6p-O 2p orbitals results in the bonding

states in the valence band, and the occupation of the Bi 6p electrons in the

valence band stabilizes the ferroelectric distortion in BiT.

Here, we discuss the role of Nd at the perovskite A site in view of electronic

structure and oxygen stability. The Nd 5d states found in the valence band is

a result of the orbital interaction with O 2p in the perovskite layers. Furthermore,

the substitution of Nd causes a significant change in DOS just below the E

The oxide ions in the perovskite layers (O1, O3, O5, O6) have a large DOS

near the E

in BiT, which are the antibonding states caused by the Bi1 6s–

O 2p hybridization. The Nd substitution decreases DOS near the E

due to

the lack of the Bi 6s–O 2p interaction and contributes to stabilizing the oxide

ions in the perovskite layers. The total/partial density of states (DOS) analysis

of BLT (x = 2.0) suggests that the La 5d is hybridized with the O 2p of the

adjacent oxygen. The covalent bonding between La and O in the perovskite

layers creates the DOS of the La 5d states in the valence band near the Fermi

level (–5~0eV), which is a possible origin of the high chemical stability of

oxygen in BLT.

Our calculations show that La and Nd substitutions at the perovskite A

site lead to a decrease in oxygen vacancy. The lower concentration of oxygen

vacancies is verified in BLT compared with BiT (see Fig. 33.10), which

originates from the orbital interaction between La and O in the perovskite

layers. The high stability of oxide ions are also expected for BNT, and this

is consistent with the results of a leakage-current density of the order of

–9

A/cm

of BNT crystals [35]. Compared with BiT, BLT and BNT crystals

exhibit a much lower leakage current, suggesting that defects such as oxygen

vacancies and electron holes are lower in the BLT and BNT crystals. It is

recognized that oxygen vacancies act as pinning site of domain wall and

impedes polarization switching [11, 50]. The suppression of domain pinning

results in a larger P

and high fatigue endurance, which have been achieved

for BNT thin films [24]. The results obtained in this study indicate that the

substitution of La and Nd is effective for stabilizing oxide ions in the perovskite

layers.

33.9 Summary

The crystal structures of Bi

in the ferroelectric and paraelectric states

have been analyzed, and the ferroelectric distortion has been discussed in

terms of ionic displacement of the constituent ions. The off-center Ti

displacements in TiO

octahedra play a minor role in spontaneous polarization,

while the entire shift of the TiO

octahedra with respect to heavy Bi ions

results in a large spontaneous polarization along the a-axis. The bond valence

analysis shows that the underbondings of Bi1 at the A site and Bi2 in the

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Crystal structure and defect control 1029

layers in the paraelectric state at 700°C is recovered to the satisfactory

bonding by the ferroelectric transition. The analysis of partial density of

states indicates that the ferroelectric transition originates from a strong

hybridization between the Bi1 6s(p) and the O3 2p states.

The defect structure and the mechanism of leakage current at room

temperature of Bi

, and the role of La and Nb in Bi

on the

ferroelectric-related properties are discussed. La and Nd substations at the

perovskite A site improve the chemical stability of the adjacent oxide ions

and reduces the concentration of oxygen vacancies. The results of the leakage

current properties of the single crystals reveal that electron holes arising

from the incorporation of oxygen at oxygen vacancies in the perovskite

layers act as detrimental carriers for leakage current at room temperature in

the Bi

system. A high insulating property at room temperature was

obtained for the La- and Nb-substituted Bi

crystals as a result of the

small number of electron holes due to fewer oxygen vacancies.

The substitutions of La and Nd give rise to a smaller remanent polarization

compared with Bi

, which is in good qualitative agreement with the

spontaneous polarization estimated from the structural data determined by

neutron diffraction analysis. Electronic band structure calculations and the

optical transmission data show direct band gap for the ferroelectric phases in

the Bi

system. The analysis of the electronic density of states of RE-

substituted lattice indicates that the orbital interaction of the RE 5d and O 2p

states stabilizes oxide ions in the perovskite layers, which is consistent with

the much lower leakage current observed for the RE-substituted crystals.

The observations of domain structure show that striped 90° domain walls

as well as head-to-head and tail-to-tail 180° domain walls are present in the

and La-substituted crystals. The substitution of La leads to a marked

decrease in the 90° domain width. Piezoelectric-force microscope observations

reveal that the antiphase domain boundary is formed only for La-substituted

crystals. The antiphase domain boundary is suggested to play an important

role in the formation of 90° domains.

33.10 Future trends

La and Nd substitutions into Bi

are effective for improving chemical

stability of oxide ions in the perovskite layers and thereby the leakage current

is suppressed to a very low value of the order of ~10

–9

A/cm

. These

substitutions, however, lead to a marked decrease in spontaneous polarization,

and thus the superior leakage-current properties due to less oxygen vacancies

are achieved by sacrificing the spontaneous polarization of Bi

Here, a definite guide for achieving polarization switching as well as a

low leakage current is proposed for the Bi

-based devices. Although

the processing temperature of the Bi

films is about ~ 700°C which is

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