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

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20.1 Introduction

Functional materials in real applications have the form of patterned structures

rather than 2D infinite thin films. For example, piezoelectric micro-sensors

and micro-actuators involve piezoelectric thin films patterned into structures

of micrometer-range sizes. For future applications, e.g. memories, ferroelectric

films should be patterned into structures with lateral sizes in the nanometer

range. For example, in a prospective 10 Gbit non-volatile ferroelectric random

access memory (NV-FeRAM), the lateral area of the whole memory cell,

consisting of a capacitor and a transistor, should not exceed 100 nm, implying

ferroelectric capacitors having lateral sizes well below 100 nm [1, 2]. It is

well known that many materials change or even lose their useful properties

as soon as their sizes fall below a certain limit [3, 4]. During the past decade

a large amount of effort has been made to understand whether electroceramic

cells of 100 nm lateral sizes can still show piezo- or ferroelectric properties.

Most investigations were performed on ultra-thin films, but these can lead to

conclusions that are not always true for geometrically confined structures

such as islands, nanotubes or nanorods. In this case the relatively large

proportion of surfaces and interfaces can lead to domain pinning or to other

surface-related problems.

On the other hand the properties of nanostructures can also depend on the

route of their preparation. Different preparation methods can impose a certain

degree of specific defects, a certain porosity level, the incorporation of foreign

atoms or, for example, hydroxyl groups, interfacial stresses, etc. Additional

problems can occur during conventional and non-conventional patterning

processes when part of the continuous film is removed in order to obtain

separate structures [5–7]. Self-patterning methods seem to be appealing for

the production of good-quality structures that can be used for basic

investigations (e.g. for size–effect-related issues). Additional advantages of

such methods are usually lower fabrication costs (compared with, e.g.,

lithography-based routes) and relatively fast preparation time (compared

Nanosized ferroelectric crystals

I SZAFRANIAK-WIZA, Poznan University of

Technology, Poland and M ALEXE and D HESSE,

Max Planck Institute of Microstructure Physics, Germany

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Nanosized ferroelectric crystals 601

with, e.g., direct e-beam processes) [8]. That can make them attractive from

the point of view of potential applications. As one possible self-patterning

route, the formation of islands during very early stages of film formation has

been investigated [9–11].

In the middle of the 1990s, it was observed that the preparation of ultra-

thin epitaxial films by chemical solution deposition (CSD) is hindered by a

microstructural instability [12, 13]. Oxide thin films with a thickness below

a critical value break into islands after a high-temperature annealing. The

driving force of this process is an excess of the total free energy of the

continuous film compared with a film that only partially covers the substrate.

The free energy is minimized by (i) the film–substrate system through the

formation of surfaces of low energy [14], and eventually (ii) the formation of

islands, which lowers the interface area and thus the interface energy. Although

this effect has initially been regarded as an undesirable effect occurring

during the preparation of ultra-thin epitaxial films, it can favorably be applied

for the preparation of nano-islands. First attempts were focused on the

fabrication of lead titanate nanograins [15–17]. However, the choice of the

substrate, which was platinum-coated silicon, resulted in a random orientation

of the nanograins. The analysis of the size effect of such randomly oriented

nanograins can be rather complicated if there is no information on the crystal

orientation of each grain, because ferroelectric and piezoelectric properties

are closely connected with the crystallographic orientation [18]. A detailed

analysis of lead titanate and ferroelectric lead zirconate titanate nanostructures,

prepared on Pt-coated Si wafers, has shown that they do not possess single-

crystal quality, since twin boundaries were observed by transmission electron

microscopy (TEM) [9]. Therefore, it can be difficult to distinguish between

the intrinsic and extrinsic size effects associated with crystal imperfections.

The best way to investigate size effects in ferroelectrics is to produce single-

crystal, defect-free, monodomain nanostructures with controlled size and

orientation. The present chapter considers the preparation and properties of

single-crystal ferroelectric nanostructures obtained by the self-patterning

method based on the instability of ultra-thin films.

20.2 Preparation of nano-islands

Nanosize lead zirconate titanate epitaxial crystals were prepared by a

conventional chemical solution deposition. However, the film thickness was

much smaller compared with the conventional method, and the post-annealing

treatment was performed at slightly higher temperatures than usual [19]. The

amorphous ultra-thin films were deposited by spin-coating. Different single

crystals such as (001)-oriented SrTiO

(STO) (from CrysTec GmbH, Berlin),

(001)-oriented MgO and (001)-oriented LaAlO

(LAO) (both from Crystal

GmbH, Berlin) were used as substrates. For electrical measurements, STO

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substrates with a niobium doping were used. The Nb concentration of 0.5%

ensures some conductivity, so that the substrate can also take the role of a

bottom electrode. Two types of solutions were used, viz. a commercial precursor

(PZT9906, Chemat Technology, Inc.) for Pb(Zr

0.52

0.48

(denoted as PZT

52/48) and metalorganic solutions for lead zirconate titanate with different

Zr/Ti contents (denoted, e.g., PZT 20/80 for Pb(Zr

0.2

0.8

). The initial

film thickness was determined by the degree of dilution of the raw precursors

in their solvents (butanol in the case of the commercial precursor, and xylene

for metalorganic ones) within a wide range (e.g. from 1:10 to 1:50 for

Pb(Zr

0.52

0.48

), and by adjusting the spinning speed from 3000 to 6000 rpm.

The gel film obtained was dried on a hot plate at 80 °C for 5 min, pyrolized

at 300 °C for 5 min, and finally crystallized at 600–1100 °C for 5 min–10 h

in a lead-rich atmosphere. Energy dispersive spectroscopy (EDS) analysis in

a scanning electron microscope (SEM) was used to control the PZT

compositions. In all cases the composition after crystallization agreed well

with the nominal composition of the raw precursors.

20.2.1 The control of size and distribution of the nano-

islands

The growth of nanostructures was firstly investigated as a function of the

initial film thickness, the crystallization temperature, and the lattice mismatch

between the substrate and the nano-islands. The initial thickness of the deposited

amorphous layers has been adjusted by the combination of spinning speed

and dilution of the raw precursors. After crystallization at 800 °C for 1 h, the

final morphology of the layers was examined in SEM and by atomic force

microscopy (AFM). Figure 20.1 shows the SEM images of the final structures

of PZT 52/48 and lead titanate (PbTiO

, denoted as PT). The deposition

conditions were kept the same, only the precursor dilution was changed. All

AFM investigations have shown that the nano-islands obtained by this method

have similar height. As expected, thicker PZT 52/48 films, with an initial

thickness below the critical value, have transformed into films with faceted

holes after the crystallization. A deposition using a higher dilution results in

ultra-thin films, which, after the high-temperature crystallization, break up

into small single-crystal islands, as shown in Fig. 20.1. For the highest

dilution (1:40) the resulting islands have a height of about 9 nm and lateral

sizes of 40–90 nm with a relatively narrow distribution in size (Fig. 20.1d).

The islands are distributed on the substrate with a high density of about 150

crystals on an area of 1 µm

. Thicker layers obtained with lower dilution

(1:25) result in islands that are both larger and higher (Fig. 20.1b). Their

height increases to about 25 nm, and the distance between close neighbours

increases as well, resulting in a low areal density of the islands of about

30/µm

. If the initial film thickness is just below a critical value, larger

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islands of irregular shape form, as shown in Fig. 20.1a. The smallest structures

obtained in this way have a height of about 3–4 nm and a lateral size of 30–

40 nm according to the AFM investigation shown in Fig. 20.2.

Similar behavior has been observed for the PT structures. If the initial

film thickness is just above a critical value (dilution 1:5), faceted holes

develop in the film (Fig. 20.1e). The thinner initial layer (1:10) has broken

Initial layer thickness

PZT

(a) (b) (c) (d)

(e) (f) (g) (h)

20.1

Scanning electron images of final PZT 52/48 (a)–(d) and PbTiO

(e)–(h) structures obtained after 1 h crystallization of ultra-thin films

at 800 °C.

20.2

AFM image of the smallest PZT 52/48 islands on STO (image

size 500 × 500 nm

, z range 10 nm).

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up into relatively large islands. The islands have a different shape from the

PZT islands; they have formed elongated stripes, as shown in Fig. 20.1f. The

islands have an average height of 15 nm and a wide distribution in lateral

sizes, up to more than a few hundred micrometres. As it was observed

previously, thinner layers compared with thicker ones create more regular

islands that are both higher and laterally larger up to a height of about 20nm

(Fig. 20.1g) and their areal density is lower. The smallest islands obtained

from the 1:25 diluted precursor have a height of about 10 nm and lateral

sizes of about 50 nm with a relatively narrow distribution in size (Fig.

20.1h).

20.2.2 The influence of the crystallization temperature

The crystallization temperature plays an important role in the morphology of

the final structures. It was found that, in order to obtain uniform islands, a

thermal treatment at 800 °C for 1 h is necessary. The annealing at higher

temperature results in the formation of larger islands. For instance, as Fig.

20.3 shows, the height of nanocrystals obtained from the 1:40 diluted precursor

increases from 9 nm after a treatment at 800 °C up to 20 nm after an annealing

at 1100 °C. The area density drastically decreases down to 15–20 islands per

1 µm

. Most probably at higher temperature the mobility and surface diffusion

are enhanced and that allows the deposited material to migrate and to coalesce

into larger islands. As a result the PZT nano-islands are higher and more

separated.

The mechanism of nano-island formation can be described similarly to

that used to produce semiconductor quantum nanostructures in materials like

Ge on Si, in which the shape and distribution obeys the Shchukin–Williams

theory [20, 21]. This theory predicts the formation of three different kinds of

structure (pyramids, domes and superdomes) as a function of the coverage

(a) (b) (c)

20.3

AFM images (size: 2 × 2 µm

) of PZT 52/48 nanocrystals on

SrTiO

crystallized at (a) 800 °C (

range 20 nm), (b) 950 °C (

range

20 nm), and (c) 1100 °C (

range 35 nm).

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Nanosized ferroelectric crystals 605

and the crystallization temperature. The detailed analysis of the influence of

the thickness of the amorphous layer and the crystallization temperature on

the final shape of the PZT islands was presented in Dawber et al. [22]. For

large thicknesses superdomes are dominant; as the thickness is decreased the

coexistence of domes and superdomes changes to a dominance of domes.

The domes and superdomes can be distinguished both on the basis of size

(superdomes are significantly larger than domes) and the kind of facets

present (superdomes have steeper side facets and a larger flat top facet than

domes). After processing at higher temperatures (e.g. 1100 °C) even for the

thinnest amorphous layers the superdomes become dominant. This may be

advantageous for the fabrication of an array of superdomes which are further

spaced from each other, thus avoiding the formation of merged domes which

drastically reduce the degree of registration in an array of nanocrystals.

On the other hand a crystallization at higher temperatures can cause

undesirable effects. Quite often losses of volatile elements or compounds,

which become more important at higher temperature, have a big impact on

the final composition and the phase contents (e.g. pyrochlore phases are

formed instead of the perovskite phase). An additional disadvantage of this

treatment is the possibility of diffusion through layer/substrate interfaces,

which may result in the formation of solid solutions. Because of these facts

the lowest possible crystallization temperature (e.g. 800 °C) was chosen for

the fabrication of uniform nanostructures, the physical properties of which

have been investigated.

20.2.3 The effect of the lattice mismatch

As is clear from Fig. 20.1, the shape of the islands depends on the composition

of the deposited layer. The Zr/Ti ratio has an influence on the tetragonality

(i.e. the ratio c/a of the lattice parameters) and therefore the lattice mismatch

varies with the Zr/Ti composition (Fig. 20.4). The influence of the lattice

mismatch on the growth mechanism has been the subject of detailed studies

during recent decades [4]. The influence of the lattice mismatch on the

formation of nanoislands was investigated as well. For these investigations

several samples of different compositions were prepared, and all were

crystallized at 800° C for 1 h. The wide range of PZT compositions (Zr

contents between 0 and 48%) of islands deposited on single crystal STO,

LAO and MgO substrates provided a variation of the lattice mismatch δ (δ =

island

– a

substrate

)/a

substrate

, where a are the respective lattice constants of

island or substrate) between 6.5% and 0.2%. It was shown that PT islands on

(001) STO substrates formed elongated structures (see Fig. 20.1), whereas

thin layers of PZT with higher Zr concentration broke up into smaller structures.

In the case of PZT/STO and PZT/LAO, small structures were obtained with

an average height of 10 nm and a lateral size of about 50 nm. The deposition

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of PZT onto LAO substrates produced two types of islands – smaller and

larger ones having a more square shape (Fig. 20.5). In both cases the islands

are distributed on the substrate with a high density of about 150–200 crystals

on an area of 1 µm

. PZT islands on MgO substrates became both laterally

larger and higher (Fig. 20.5). Their height increases to about 25 nm, and the

lateral size may reach a few hundred nanometers. Again due to the conservation

of the total volume, the distance between close neighbors increased resulting

in a low area density of the islands.

0.8 1.00.60.4

Ti/Zr

3.9

4.0

4.1

4.2

Unit cell parameter

- and

-orientation preferred

MgO

-orientation preferred

SrTiO

20.4

Schematic diagram of the lattice mismatch and possible

orientations of PZT.

(a) (b) (c)

20.5

AFM images of PZT 20/80 nanoislands with the same initial

thickness deposited on (a) (001) STO, (b) (001) MgO and (c) (001)

LAO. The images were taken from 500 × 500 nm

area,

range is

20 nm.

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Nanosized ferroelectric crystals 607

The results clearly show that a certain value of the lattice mismatch strain

helps the total system to break up into islands. The smallest strain of PT/STO

(0.2%) allows elongated stripe-like structures to be prepared. The islands

obtained in such systems where the lattice mismatch is relatively large are

usually bigger, and their density on the surface is smaller; however, in this

case the islands usually possess two possible orientations (see Section 20.3.1

below).

20.2.4 Multi-step deposition

In order to control the sizes of the nano-islands more precisely, a multi-step

deposition procedure has been applied. Figure 20.6 shows the morphology

of PZT 20/80 structures on MgO after each deposition step, whereas Fig.

20.7 shows the deposition of PZT 52/48 on STO. The first deposited amorphous

layers with a thickness below the critical value were crystallized at 800 °C.

The films broke up to form nano-islands during the crystallization stage and

then samples were recoated with an amorphous layer having the same thickness

as the first layer. Again the film broke up during the thermal treatment. It

was observed that most of the ‘old’ islands increased their lateral size but

(a) (b) (c)

(d) (e)

40 nm

0 nm

20.6

PZT 20/80 nano-islands after (a) first, (b) second, (c) third, (d)

fourth and (e) fifth deposition on (001) MgO substrates. The scanning

area was 2 × 2µm

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Handbook of dielectric, piezoelectric and ferroelectric materials608

new ones appeared with the same lateral size as those obtained previously. It

was possible to repeat this procedure several times until the islands started

to coalesce. Owing to the lower density of relatively big islands on the MgO

substrate it was possible to repeat the procedure up to five times, but in the

case of the very dense islands on STO the procedure was limited because

coalescence started already during the third step.

Generally this procedure can be repeated several times until a coalescence

process starts. From a practical point of view it is easier to use a multi-step

deposition procedure in the case of islands with a relatively large distance

between neighbors. A precise control of the island size could be possible

using a more diluted precursor; however, each deposition cycle (solution

deposition, pyrolysis, and crystallization step) could also increase the number

of dust particles and impurities on the sample surface. As a result such a thin

film would not be deposited homogeneously, resulting in large structures,

(a) (b)

20.7

PZT 52/48 nano-islands after (a) first, (b) second, (c) third and (d)

fourth deposition on (001) STO substrates. The images were taken

from 2 × 2 µm

area,

-range 20 nm.

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Nanosized ferroelectric crystals 609

often with a somewhat strange shape, or even in continuous films around

imperfections.

20.2.5 Towards nano-island registration

One of the disadvantages of self-assembly methods is the random distribution

of the final structures on the substrate. As expected, nanostructures obtained

by this method did not show an ordered arrangement in their positions. The

initial thin film broke up at random places, and formed a collection of irregularly

spaced nanocrystals. Because nanostructures are formed as the result of film

breaking, it is possible to introduce defects that could play an essential role

in creating discontinuities in the film during thermal treatment before the

crystallization process would start. Up to now the influence of two types of

defects has been investigated. In both cases the initial thin layer of PZT 52/

48 was deposited and dried at 80 °C. Then defect sites at regular spatial

intervals were intentionally introduced. During the first experiment defects

were created by mechanical imprint using a stamp with a regular array of

pyramidal SiN

structures. The height of the pyramids was about 260nm and

the spacing between them 0.5 µm. In the second experiment the defect sites

were imposed by an electron beam. In both cases the final structures obtained

after defect introduction and crystallization (Fig. 20.8) are apparently different

from the previous structures. The islands are larger and higher and they have

a well-defined rectangular shape. Their edges are parallel to the [110] and

[110]

crystallographic directions of the substrate. The distances between

nearest neighbors are much larger than in the case of non-treated samples. It

seems that the introduction of defects can be used as a method for registration;

however, the presented registration is still relatively poor. Most probably it

could be improved by optimizing the distance between the introduced detects

(a) (b) (c)

20.8

PZT 52/48 nanostructrures obtained after crystallization of the

same thick amorphous layer (a) not treated, (b) mechanically

imprinted (area 10 × 10 µm

range 50 nm), (c) periodically exposed

with 1000 µC/cm

doses and 1 µm pitch with the same initial

thickness.

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