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

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Handbook of dielectric, piezoelectric and ferroelectric materials610

with respect to the island distribution (particularly the spacing between the

self-patterning structures should be taken into account). The mechanical

imprint technique seems to be very attractive due to its efficient (cheap and

fast) way of application on a large-area scale.

20.3 Physical properties of the nano-islands

20.3.1 Structural investigation

For larger and smaller structures X-ray diffraction (XRD) analysis and/or

high-resolution transmission electron microscopy (HRTEM), respectively,

were performed to obtain structural information on the nanocrystals. XRD

diffraction patterns of PZT/STO nano-islands, obtained at 800 °C, show the

00l reflections from the STO substrate (cubic), and only the 00l reflections

of the tetragonal PZT (Fig. 20.9). This proves the epitaxial relationship

between the substrate and the nanostructures. No secondary phase peaks

were detected in the XRD patterns, confirming the formation of a good-

quality perovskite phase. XRD has shown that the PZT islands on STO have

a c-axis orientation. The XRD patterns obtained for PZT nano-islands grown

on (001) MgO substrate showed more diffraction peaks that could be indexed

as (h00) and (00l) reflections (Fig. 20.9). Obviously the larger lattice misfit

Intensity [a.u.]

MgO

STD

PZT

001

002

200

003

10 20 30 40 50 60 70

2θ [degrees]

20.9

X-ray diffraction pattern of PZT 52/48 nanocrystals on (001) STO

and (001) MgO substrates. The peaks labelled with circles indicate

substrate peaks originating from the remaining Cu K

radiation.

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Nanosized ferroelectric crystals 611

(PZT/MgO) results in the formation of epitaxial islands with both a- and c-

axis orientations.

Further structural information about the nanoislands was obtained from

TEM analysis (Figs 20.10 and 20.11). The low-magnification pictures (Fig.

20.10) show that all islands have a uniform height. Moreover, all the structures

have a well-defined truncated pyramidal shape with relatively sharp facets.

The facets preferably consist of {111} or {110} planes as the side walls of

the nanocrystals. The top facet of the island is parallel to the {001} substrate

plane. The appearance of such facets is related to previous research that

showed the ultra-thin film breaking up into small structures with lower energy

planes as result of microstructural instability and that in such a way the total

energy is reduced [12–14].

The HRTEM images of several PZT 52/48 /STO nano-islands have

confirmed that they are single crystals which are uniformly c-domain-oriented

without any 90° domains being present. All nano-islands have almost an

atomically flat surface. The rare steps observed on the top facet are related

to the substrate steps with a height of half a unit cell. The interface is

atomically flat, which indicates that any diffusion between the nanocrystal

and the substrate does not occur. The crystals are free from volume defects,

and the only defects are dislocations concentrated along the interface. They

are caused by stress relaxation-induced by the lattice mismatch between the

STO substrate and the PZT islands. The distance d between the dislocations

estimated on the basis of several tens of nano-islands gives values between

9 and 13 nm. This value is in agreement with the calculated spacing, d = a/

δ (where a is the lattice constant and δ is the value of the lattice misfit),

which is about 12 nm. It should be underlined that in each island there is a

50 nm

STO

PZT

~8 nm

~4 nm

4 nm

[010]

20.10

Low-magnification electron micrograph of PZT 52/48 on STO.

20.11

Cross-section HRTEM image of a single PZT 52/48 nanocrystal.

The distorted regions near misfit dislocations (showed by ‘T’) are

marked by dotted line.

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60 nm

= [220]

[010]

[100]

20.12

Plan-view HRTEM image of PZT 52/48 nano-islands on STO

substrate (the dislocation network is marked in the upper right

corner).

network of misfit dislocations present, the dislocations on average having a

mutual distance of 12 nm. The dislocation network is clearly visible on plan-

view TEM images (see Fig. 20.12).

20.3.2 The growth mechanism of the nano-islands

To investigate the growth mechanism of the PZT 52/48 nano-islands several

samples were prepared under different conditions: the crystallization

temperature was varied between 650 and 800 °C and the annealing time

between 5 min and 10 h. All experiments were carried out on samples with

the same thickness of the initial layer. Each sample was studied using HRTEM

(Fig. 20.13). In the early stage of nucleation the pre-existing holes penetrate

down to the substrate surface. As a result a non-faceted discontinuous layer

of about 3–4 nm thickness is formed. During longer heat treatments (650 °C

for 1 h) the nano-islands migrate on the substrate surface and coalesce into

larger irregular structures. The nanostructures crystallized at higher

temperatures (e.g. at 800 °C for 5 min) have a better thickness uniformity;

however, the coalescence process is not finished. An annealing as long as

1 h at 800 °C is required to form the equilibrium shape and distribution of the

islands. A thermal treatment at 800 °C longer than 1 h does not lead to significant

changes in island morphology, shape and distribution.

As it was previously shown, the nanostructure formation is connected

with the lowering of the interfacial energy [12–14]. In order to minimize the

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Nanosized ferroelectric crystals 613

PZT/STO interfacial energy, pre-existing ‘holes’ at the thin, amorphous CSD-

prepared PZT layer accumulate during annealing and then grow through the

PZT layer to uncover the STO substrate, leading to isolated islands with

misfit dislocations at the interface. At longer annealing times at high

temperatures, isolated PZT islands may coalesce into bigger ones,

simultaneously forming energetically favorable {111} and {110} facets.

However, a certain amount of thermal energy (equivalent to the 1 h treatment

at 800 °C) is required to reach the equilibrium state in which well-defined

facets appear.

20.3.3 Ferroelectric properties

Owing to the small size of the nanocrystals, their characterization cannot be

achieved using conventional measurement techniques. For this purpose,

scanning probe techniques, in particular piezoresponse force microscopy

(PFM), have proven to be most valuable. The local polarization state and the

electromechanical properties of the ferroelectric nanostructures can be probed

via the converse piezoelectric effect using the AFM technique combined

with a lock-in technique. This method is based on the detection of local

vibrations of a ferroelectric sample induced by a testing a signal applied

between the conductive tip of the PFM and the bottom electrode of the

sample [7, 23]. The role of the bottom electrode is usually played by a

conductive substrate; in the case of PZT nano-islands Nb-doped STO substrates

allowed to study the ferroelectric properties. Because of the strong relation

between the piezoelectric coefficient and the spontaneous polarization the

material expands or contracts under the applied electric field. The sign of the

piezoelectric coefficient is determined by the direction of the spontaneous

polarization with respect to that of the applied electric field.

(a) (b)

(c)

20.13

Cross-sectional HRTEM micrographs of PZT nano-islands

grown on STO substrates (a) at 650 °C for 1 h, (b) at 800 °C for 5 min

and (c) at 800 °C for 1 h. The dashed lines in (a) and (b) show the

coalescence of two neighboring islands.

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The PZT 52/48/STO:Nb islands with heights above 25 nm or with a large

lateral size show a well-developed piezoelectric hysteresis loop. Figure 20.14

shows the topography and piezoresponse images proving the switching of

the polarization in crystals with a height of 15 nm. The grain marked by the

dashed contour was successively polarized negatively (polarization pointing

into the sample, Fig. 20.14b), and then positively (Fig. 20.14c) by the biased

AFM tip. It was also possible to record a loop on an island of irregular shape.

Similar loops were obtained for islands with heights above 25 nm and smaller

lateral size and for the structures after mechanical imprint. For smaller structures

(smaller island volume, e.g. low height and low lateral size) there were

problems in obtaining a hysteresis loop.

20.3.4 Impact of the misfit dislocations on the

ferroelectric switching

In order for switching to occur it is necessary that the crystal possesses more

than a critical number of unit cells with the proper crystallographic structure.

The PZT/STO nano-islands have relatively large regions affected by the

dislocation network (see Figs 20.11 and 20.12). In order to investigate the

long-range strain fields associated with the dislocation, a geometric phase

Signal (a.u.)

Bias (V)

–30 –20 –10 0 10 20 30

(d)

500 nm

(a)

(b) (c)

20.14

Switching of an individual nanocrystal by PFM: (a) topography

(

-scale 25nm) and piezoresponse images after applying (b) a

negative and (c) a positive dc voltage. (d) Hysteresis loop recorded

on the structure in the middle of the image (a).

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Nanosized ferroelectric crystals 615

analysis of HRTEM images was performed. Based on this analysis, the

details of which are given in Chu et al. [24], the in-plane (ε

), shear (ε

) and

out-of-plane (ε

) strain fields have been determined. The strain, associated

with the misfit dislocations, is predominantly localized on the PZT side. The

estimation has shown that the strain extends into the PZT phase for about 4

nm from the dislocation core (Fig. 20.15). Based on this value it is possible

to calculate the partial volume (V

) affected by the dislocations. In the case

of PZT 52/48 nano-islands on STO, with a base length of about 50 nm and

a height of about 9 nm, V

can be estimated to about 50% of the total volume

of the island. Because ferroelectricity is a cooperative phenomenon of a

sufficiently large number of non-centrosymmetric unit cells, this significant

value could influence the ferroelectric properties. In the affected regions, the

PZT lattice deviates from the regular tetragonal structure, and the long-range

correlations of the local polarization may thus break down, leading to a

polarization instability. As a result, ferroelectric switching was not observed

in these nano-islands using PFM. By contrast, in PZT 52/48 islands with a

double height of ~20 nm, V

is only about 25% and in this case a well-

defined piezoresponse loop has been recorded (see Fig. 20.14).

To distinguish the impact of a purely intrinsic size effect (which in principle

may occur in structures with a height of only about 10 nm) from the influence

of dislocations, dislocation-free islands were fabricated and investigated.

20.15

Cross-sectional HRTEM image of a PZT nano-island with the

distorted regions near misfit dislocations (dashed line). The

additional half-plane on the substrate side is marked as a solid line.

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Handbook of dielectric, piezoelectric and ferroelectric materials616

One of such systems is PT/STO, where the calculated spacing between misfit

dislocations (about 195 nm) is much larger than the island size. HRTEM

studies have proven that the PT/STO interface is atomically sharp and misfit

dislocations are not present (see Fig. 20.16). An individual PT island on STO

has shown a piezoelectric hysteresis loop, proving the switching behavior of

10 nm high PT structures (Fig. 20.17). This result is also in good agreement

with recent results showing the ferroelectric properties of thin lead titanate

film with thickness of several unit cells [25, 26].

20.3.5 Dislocations and domain wall formation

During the analysis of nanoislands with different interfacial strain, a few

islands were found that contain a twin boundary [27]. The HREM image of

PZT ~ 10 nm

PZT ~ 20 nm

PT ~ 9 nm

Applied bias (V)

–10 –5 0 5 10

PFM signal (a.u.)

–100

–50

100

150

20.17

PFM measurements of local hysteresis loop of three different

islands.

20.16

HRTEM image of PT nanocrystal on STO.

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Nanosized ferroelectric crystals 617

such an island is shown in Fig. 20.18. This island is slightly larger than those

discussed before. The PZT 40/60 island shows an epitaxial c-axis orientation

with respect to the substrate; however, a small region (on the top right on

Fig. 20.18) possesses an a-axis orientation. Between these two regions a

90 °C domain wall is observed. The estimated angular separation (α) between

these two regions is about 1°

which is smaller than the calculated value of 2°.

This suggests that the ferroelastic strain distribution near the domain wall is

rather complex. The defect analysis has shown that – besides the dislocations

related to the relaxation of the lattice mismatch (with an extra half plane on

the substrate side) – there is a dislocation related to another extra half plane

in the substrate which is parallel to the interface, i.e. a dislocation with a

Burger’s vector perpendicular to the plane of the interface.

The geometric phase analysis of HRTEM images was used in order to

determine the strain near the domain wall. The corresponding details were

published in Chu et al. [27]. In the region far from the interface the strain

distorts both the a- and c-domain regions. The wall region exhibits a

compressively strained area embedded in a relatively strain-free surrounding.

The estimated thickness of the domain wall, based on this analysis, is about

1.5 nm (close to four unit cells). A more complicated situation prevails near

the interface. The 90° domain wall does not end directly on the edge dislocation,

but on a distance of about 2 nm from it. The strain distribution in this region

20.18

Cross-sectional HRTEM image of a PZT 40/60 island showing

the twin wall. Bottom: Magnified section of the region close to the

interfacial dislocation.

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Handbook of dielectric, piezoelectric and ferroelectric materials618

is more complicated. Near the edge dislocation with a perpendicular Burger’s

vector a tensile strain is observed. Near the interface and the wall, this

tensile strain is reduced by the compressive strain caused by the presence of

the twin wall. This elastic coupling by partial strain annihilation qualitatively

minimizes the long-range electromechanical energy. The slight deviation

between the calculated and the observed value of the angular separation and

the gentle broadening of the wall width near the dislocation core can be

understood as effects of the interaction of long-range strain fields of the twin

wall and the dislocation core. More important for future PZT applications is

the fact that the switching behavior of the islands containing a twin wall is

different. If an electric field is applied perpendicularly to the interface of the

island, switching of the single c-domain state has to be accomplished by

removing the twin wall from the island. This electric field-driven movement

is, however, difficult, since the long-range strain field of the interfacial

dislocation imposes a potential barrier on the twin wall. This fact can cause

difficulties in mobilizing the twin wall by applying electric fields. As a

consequence, the twin wall in the islands should thus not be electrically

active. Indeed the nano-islands, investigated by PFM, show large regions

where the PFM signal is about zero (see Fig. 20.19a). This value suggests the

presence of the 90° domains. Figure 20.19(b) shows the hysteresis loop

acquired on the structure in the middle of the image. Its shape reveals the

huge imprint, which can be associated also with the domain pinning.

20.4 Conclusions and future trends

The self-patterning method is a new appealing way of nano-island fabrication.

The lateral size and the height of the nanostructures can be controlled by

adjustments of the deposited film thickness, of the crystallization conditions

and a proper choice of the substrate. The dislocations present in such structures

can have a large impact on the final properties. The network of misfit

dislocations forming as a result of lattice mismatch relaxation affects a relatively

large volume of the island. Such islands are not switchable and they lose the

useful properties for an application as memories or storage devices. Dislocations

with a Burger’s vector perpendicular to the interface and connected with a

twin wall can render the system electrically inactive. Thus the formation of

such defects has to be avoided, if ferroelectric oxides with nanometer-size

sizes are to be employed for future applications that require ferroelectric

switching.

It appears that an ‘interface engineering’ is required for epitaxial nano-

islands, if the latter should retain their ferroelectric properties, in particular

polarization switchability. The substrate should be carefully chosen, not only

under the aspect of chemical stability (avoiding interfacial diffusion and

reaction processes at the processing temperatures), but also adapting the

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Nanosized ferroelectric crystals 619

(a)

20.19

(a) AFM image of PZT 40/60 nano-islands on STO (200 × 200

range 10 nm). The marked regions have shown a PFM signal

about zero. (b) Hysteresis loop recorded on the structure in the

middle of the image (a).

Applied bias (V)

(b)

–2–4 0 2 4

–30

–40

–20

–10

(pm/V)

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