University of Groningen

Structural domains in thin films of ferroelectrics and multiferroicsVenkatesan, Sriram

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CHAPTER 1

Introduction This chapter briefly introduces the fundamentals of ferroelectric materials and their

underlying physical concepts. The application of ferroelectric materials within memory

devices and the associated challenges are also briefly described. At the end, a concise

introduction to the field of multiferroics and the research objective of this thesis are

presented.

1.1 INTRODUCTION

The Greek philosopher Plato quotes “necessity is the mother of invention”. The quest

in search for materials of primitive men made them to cross several civilizations from the

stone age era. The field of materials science is aimed at a better understanding of the

naturally existing materials in order to create new materials with desired properties for

the betterment of human life. Today sophisticated technologies are the result of the

discovery of such “smart”- intelligent materials and they found a vital role in the basic

needs of men. As history dates back to several thousand years, humans learned to make

earthenware like pottery products, table ware using clay, which are known to be the first

man-made ceramics. The word ceramics is derived from the Greek word “keromos”

meaning “burnt earth” [1,2]. Ceramics in general are polycrystalline material and have

many different identities when they are applied, from household products to the modern

electronics industry.

Classification of ceramics can be based on many aspects like shapes, properties,

application, processing methods etc. In general, ceramics can be classified into two broad

categories, traditional ceramics and advanced ceramics. The traditional ceramics found to

have innumerable applications in our daily life such as hard porcelain, electrical

insulators, sanitary ware, semivitreous white ware, tiles, dental porcelain and many more.

Advanced ceramics can be again classified into structural and functional ceramics. The

1

Chapter 1

structural ceramics are mainly related to their mechanical performance, like tribological

behaviour, cutting tools, abrasives, chemical inertness, withstanding high thermal

environments etc. Some examples for structural ceramics are; Alumina (Al2O3), Zirconia

(ZrO2), silicon carbide (SiC), silicon nitride (SiN), Spinel (MgAl2O4), SiAlON, Corderite

(Mg2Al2Si4O18). The polycrystalline bulk form of ceramics are basically designed by

modifying the micro structural aspects of their grain boundary phenomena [1,2]. The

grain boundary phenomena include electrical and ionic conductivity. The functional

ceramics became the crucial part in many technological areas including energy, medical,

manufacturing industry, transportation and information technology. Figure 1.1 shows the

structural and functional applications of ceramics. Research on ceramics covers extensive

areas of science like physics, chemistry, materials science and also strongly

interdisciplinary like bio-materials as well as engineering.

Figure 1.1: Structural and functional applications of advanced ceramics [3].

2

Introduction

In the 20th century, large vacuum tubes relied on ceramic materials. As the electronic

industry grew rapidly, semiconductor Integrated Circuits (IC) became the core

component of today’s electronic devices. IC’s in the devices are protected by ceramics

packages. The IC’s are highly sensitive to external moisture and strong light. Ceramic

packages protect these delicate instruments against the surrounding atmosphere and make

them cost effective by reduction in size. In the area of functional ceramics, the electro-

ceramics contribution to the electronic industry is enormous, specifically ferroelectric

ceramics are technically highly important. They are known for their unique properties

such as high dielectric permittivity and piezoelectricity. The focus of this thesis is on the

single crystalline thin films which fall under the category of functional ceramics,

explicitly on functional oxides in thin film form.

1.2 FERROELECTRICITY

Ferroelectricity was first discovered by Valasek [4,5] in 1921 in a complex compound

called Rochelle salt (Sodium potassium tartrate tetrahydrate). At that time it was the only

material possessing the extraordinary property of reversible polarization. Later around

1935 ferroelectricity was observed in potassium dihydrogen phosphate (KH2PO4). The

most popular and classical ferroelectric material BaTiO3 was discovered during World

War II in 1941 [4,5]. BaTiO3 originally looked as a potential material for capacitors

because of its high dielectric constant (> 1200). Later the work of Wul, Goldman [6] and

Von Hippel [7] and others explained that the high dielectric constant originates from the

ferroelectric nature of BaTiO3. The physical quantity corresponding to the stored electric

energy per unit area is called electric displacement D; it is related to the electric field E

by the following simple expression

D= ε0E +P = εε0E (1.1)

where ε and ε0 are the material’s relative permittivity and permittivity of the vacuum

respectively and P is the dielectric polarization, respectively.

When the centre of the positive and negative charges in the crystal structure do not

coincide naturally (without application of any external field) such crystals are said to

possess a spontaneous polarization. When, upon applying an electric field, such a

spontaneous polarization can be reversed then the material is called ferroelectric. As a

3

Chapter 1

standard definition ferroelectrics are simply defined as the “class of materials which

exhibits spontaneous electric polarization (in the absence of electric field) which

reversible by applying an electric field”. The term ferro in the ferroelectrics has nothing

to do with the ferrous i.e., iron content in the materials, rather this term used to explain

that this class of materials exhibit spontaneous electric polarization and electric

hysteresis, analogous to the ferromagnetic properties of spontaneous magnetization and

magnetic hysteresis. A typical polarization versus electric field loop of a ferroelectric

material is shown in figure 1.2. These materials exhibit a Curie temperature Tc,

(temperature above which the spontaneous polarization disappears and the material

becomes paraelectric as explained in a later section). The ferroelectric nature of a

material depends crucially on the atomic structure. The detailed classification of the 32

crystal groups of importance for piezoelectric, pyroelectric (generate electricity when

heated) and ferroelectric behaviour is shown in figure 1.3.

Figure 1.2: Polarization Vs electric field hysteresis loop for typical ferroelectrics.

4

Introduction

After a long scientific journey into bulk ferroelectrics with e.g. the discovery of many

new interesting ferroelectric materials like Lead zirconate titanate (PZT), Lead lanthanum

zirconate titanate (PLZT), Lithium niobate (LiNbO3), and relaxors like Lead magnesium

niobate (PMN) (in which the dielectric anomaly at Tc is not sharp and a frequency

dependence is found) and different properties, in the late 70’s ferroelectric thin films

were developed. Starting from the 80’s many of the ferroelectric materials discovered in

bulk form were also produced in the form of thin films. The invention of thin film

processing led to the miniaturization of the electronic devices and allowed the

replacement of its bulky form components by miniaturized devices. The details of thin

film growth methods are explained in the next chapter.

32 Crystal classes (Point groups)

21 Non-Centrosymmetry 11 Centrosymmetry

20 Piezoelectric 1 Non Piezoelectric

10 Pyroelectric (spontaneously polarized)

Ferroelectric (Only if Polarization

Is reversible)

Figure 1.3: Classification of 32 crystal classes.

5

Chapter 1

1.2.1 Crystal Structure

Figure 1.4: An ideal cubic ABO3 perovskite structure unit cell.

The materials discussed in this thesis belong to the category of the so-called

perovskite structure. The most commonly studied ferroelectric oxides have a cubic

perovskite structure (when they are in the paraelectric state) with chemical formula ABO3

(Fig 1.4). Conventionally it is viewed such that the larger cation (A) occupies the corner

sites of the cube while the smaller cation(B) occupies the body centre and three oxygen

anion atoms per unit cell occupy the face centres of the cube. The main advantage of the

perovskite structure is the large flexibility in tailoring the chemical composition and

lattice parameter(s) of the system by substituting the different cations present at both the

A and B sites without changing the overall structure completely. A wide range of solid

solutions can thus be formed easily and one can synthesize materials of interest in order

to tune the different properties like piezoelectricity and Curie temperature [8]. The main

developments of new compounds within the perovskite family can be achieved by

understanding the tolerance factor. To classify the formation of perovskite type

compounds, Goldschmidt proposed the following tolerance factor t [9]:

t = rA+rO / 2 (rB+rO) (1.2)

6

Introduction

where rA and rB are the radii of the A site and B site cations, respectively, and rO is the

radius of the oxygen anion. Almost all the perovskites have t values in-between 0.75 and

1. The ideal cubic perovskite has a tolerance factor of 1, but most of the cubic perovskites

have t values in-between 0.8 and 0.9. However, distorted perovskite structures have a

wide range of t values. The model system lead titanate (PbTiO3) investigated in this thesis

has a tolerance factor of 0.95.

1.2.2 Classification and origin of ferroelectrics

The origin of ferroelectricity can be attributed to different mechanisms in different

types of ferroelectrics. Conventionally, ferroelectrics are classified broadly into two

major types [10].

1. Displacive ferroelectrics: This type of ferroelectrics is most commonly found in

ionic materials with typical perovskite structure. The ions attain equilibrium positions,

corresponding to a non-polar state above Tc (where a net dipole moment is not present).

However, below Tc some of the ions shift such that a polar state is introduced in the

material i.e. mutually displacing the centres of positive and negative charge and thus

creating a net dipole moment in the system. Examples are BaTiO3 and PbTiO3 (see

Fig.1.5.)

Figure 1.5: Relative displacements of ions in barium titanate and lead titanate systems.

Pb2

Ti4

BaTiO PbTiO3

O2

0.05 Å

+ +

+ +

++

++

+

+ Ba2

O2

Ti4

0.47 Å

0.04 Å 0.3 Å 0.1 Å

+

+

c a

7

Chapter 1

2. Order –Disorder ferroelectrics: This type of ferroelectrics is typically observed in

crystals with hydrogen bonds. In these systems hydrogen atoms jump around some multi

potential well configurations above Tc such that there is no net dipole moment. Below Tc

hydrogen atoms jump around some ordered subset of potential wells in such a way that a

net dipole moment is produced in the unit cell. An example is KH2PO4.

Another classification of ferroelectrics is based on their unit cell structure. The four

general categories distinguished and their examples are:

1. Perovskite or Oxygen octahedral group - BaTiO3, PbTiO3

2. Tungsten bronze group - PbNb2O6, SrNb2O6

3. Layered structure - Bi4Ti3O12

4. Pyrochlore group - CdNb2O7

Although the ferroelectric material considered in this thesis, PbTiO3, falls

conventionally under the category of displacive ferroelectric, its mechanism for

ferroelectricity differs from the one in BaTiO3. In the case of barium titanate the

ferroelectricity comes into play due to the off-centering of the B site cation with respect

to the oxygen cage. On the other hand, in lead titanate the strong ferroelectricity is due to

a mechanism driven by the A site, i.e. the 6s2 electrons of Pb2+ hybridize with the O-2p

electrons to form strong covalent bonds which also give rise to a relative displacement of

the Pb2+ cage with respect to the O-octahedron. This mechanism is also known as the

lone pair driven mechanism and leads to a strong ferroelectric behaviour observed for

PbTiO3 [11].

1.2.3 Curie point and phase transitions

All ferroelectric materials have a transition temperature called the Curie temperature

(Tc). At a temperature T > Tc the crystal does not exhibit ferroelectricity, while for T < Tc

it is ferroelectric. Upon decreasing the temperature through the Curie point, a

ferroelectric crystal undergoes a phase transition from a non-ferroelectric to a

ferroelectric phase. The nonferroelectric phase above the Curie temperature is called as

paraelectric phase. If there are more than one ferroelectric phases, the temperature at

which the crystal transforms from one ferroelectric phase to another is called the

transition temperature. These are structural phase transition is accompanied by changes in

8

Introduction

structure and most often symmetry. The dielectric, thermal, optical and elastic properties

show anomalous behaviour around the Curie temperature. The temperature dependence

of the dielectric constant in ferroelectric crystals with continuous phase transitions

(second order) is governed by the Curie-Weiss law above the Curie point (T > Tc):

ε−ε 0 = C/(T-Tc) (1.3)

Where ε is the permittivity of the material, ε0 is the permittivity of vacuum, C is the Curie

constant and Tc is the Curie temperature. The dielectric constant increases with an

increase in temperature and reaches a maximum at Tc and drops down above Tc following

Curie-Weiss law. The spontaneous polarization in most ferroelectric crystals is highest at

temperatures well below Tc (theoretically at 0 K) and decreases to zero at Tc. In typical

ferroelectrics, the spontaneous polarization decreases as the temperature increases and

disappears continuously or discontinuously at Tc. Depending on this continuous or

discontinuous jump in the spontaneous polarization, the phase transitions are classified as

second or first order respectively as shown in the Figure. 1.6. The free energy as a

function of spontaneous polarization for first and second order transitions in ferroelectrics

is shown in figure 1.7. Understanding the first and second order structural phase

transitions through a thermodynamical approach was first given by Landau [12,13] in

1937. Landau theory served as a phenomenological theory using symmetry based

arguments for macroscopic entities. Later in 1949 Devonshire applied Landau theory for

BaTiO3 [14].

Figure 1.6: Spontaneous polarization as the function of (a) second order and (b) first order phase transitions.

(b) (a)

9

Chapter 1

(b) (a)

Figure 1.7: Free energy as a function of spontaneous polarization for (a) second order and (b) first order phase transitions [15].

1.2.4 Piezoelectricity

All ferroelectric materials are piezoelectric (but the reverse is not true).

Piezoelectricity is the ability of a certain class of material to develop an electric charge in

response to an applied external mechanical stress. This is called the direct piezoelectric

effect. All piezoelectric materials also show a converse piezoelectric effect corresponding

to geometrical strain in the material when a voltage is applied. Understanding the internal

structure and the detailed crystallographic symmetry elements in the materials is essential

to understand piezoelectricity. Figure 1.3 shows how piezoelectricity relates to the

detailed classification of 32 crystallographic point groups. The basic equations describing

the direct and converse piezoelectric effects can be expressed in terms of electric and

elastic properties as follows [8]:

D = dE + εσE (1.2)

S = sEσ + dE (1.3)

Where D is the dielectric displacement, σ the stress, E the electric field, S the strain, d the

piezoelectric coefficient, s the material compliance constant (inverse of the elastic

constant) and ε is the material’s dielectric constant (permittivity). The superscript in the

equations indicates that the quantity is held constant. In the case of εσ stress is held

constant which implies that the piezoelectric element is mechanically unconstrained and

in the case of sE, the electric field is held constant which implies electrodes on the

elements are mutually shortened.

10

Introduction

The direct and converse piezoelectric effects can also be conveniently expressed in terms

of following tensor notations [16]:

Pi = d ijk σ jk (1.4)

Xij = d kij Ek (1.5)

In case of the direct piezoelectric effect Pi is the polarization generated along the i-axis,

which is proportional to the applied stress σjk through the piezoelectric coefficients dijk.

For the converse piezoelectric effect Xij is the strain generated in a particular orientation

of the crystal when an electric field Ek is applied along a certain k-axis.

1.3 DOMAIN STRUCTURES IN FERROELECTRIC THIN FILMS

So far we have discussed the basic concepts of ferroelectrics, now the focus is on the

domain structures present in epitaxial perovskite thin films, which is the subject of this

thesis. In order to understand the discussions in the later chapters it is a prerequisite to

have knowledge of epitaxial thin films and structural domain related concepts applying to

lead titanate films on strontium titanate substrates.

Materials in thin film form are explored because of their unique functionalities and

applications such as hard coatings, IC’s, filters, reflective, anti-reflective coatings etc.,

when compared to the bulk form of the same material. A thin film is defined as having a

thickness in the range from a few monolayers to several hundredths of nanometers and

being deposited on a solid substrate. A crystalline thin film grown on a single crystal

substrate, having certain crystallographic orientation relationship with the underlying

substrate is called an epitaxial thin film. Perovskite ferroelectric thin films are strongly

affected by the epitaxial strain. The intrinsic coupling between the strain and polarization

by the substrate clamping effect (i.e. imposing the strain to the film via the substrate by

utilizing the substrate–film lattice mismatch differences) can be used to tune the

electronic configuration and bonding of the complex oxide films to achieve enhanced

functional properties. Noheda et al. [17] have shown in their work that chemical pressure

can be used to obtain a monoclinic phase along the morphotropic phase boundary in the

Lead Zirconate Titanate system (PZT) and this phase may be responsible for the giant

piezoelectric and dielectric response of PZT. Pertsev et.al. [18] have shown that a similar

11

Chapter 1

morphotropic phase boundary can be obtained in pure lead titanate films under epitaxial

strain.

The misfit strain between the film and substrate can be defined by

d sub – d film (1.6)Um = ----------------

d sub

where dsub and dfilm are the in-plane lattice parameters of the substrate and the film,

respectively. Maintaining the epitaxial strain is of common interest from the application

point of view. However it is not straightforward, because the system as a whole is

thermodynamically highly energetic. When the thickness of the film is increased, strain

energy builds up. At a certain thickness the system needs to relax the developed strain.

The thickness at which the relaxation process starts is called the critical thickness.

In ferroelectric thin films, the relaxation of the strained films generally takes places

during cooling, after the phase transition from the paraelectric to ferroelectric phase

occured, where also symmetry is broken and differences in lattice parameters are

introduced. Ferroelectric thin films are generally grown at high temperatures above the

phase transition temperature (TC) holding for the bulk ferroelectric. During cooling to

room temperature the thin film crosses TC, where the symmetry is lowered, due to the

cubic to tetragonal phase transition. This symmetry lowering can lead to a preferential

domain formation that is able to relieve the accumulated stress in the film.

In this work, PbTiO3 is grown at 570°C, where the TC of bulk PbTiO3 is 490°C. The

stress is generally relieved by forming misfit dislocations and by breaking up into

different ferroelastic domains [19-21]. Epitaxial strain, thermal strain and phase

transformation strain contribute substantially to the strain driving the relaxation

mechanism(s)[22]. It is to be noted that the term domain used in this thesis refers to

crystallographic domains and not to the domains where only the polarization reverses.

Pompe and Speck [23-25] in their papers explained the different domain configurations

of PbTiO3 thin films on SrTiO3 substrates. Figure 1.8a shows the polydomain structures

due to the multiple misfit relaxation mechanisms. There are three possible domain

configurations for a nearly matched tetragonal cell on the (001) face of a cubic substrate.

c and a in the figure represents the lattice parameters of the tetragonal ferroelectric phase.

b represents the lattice parameter of the cubic substrate. c-domains are oriented such that

12

Introduction

their c-axis is normal to the film/substrate interface; a1 and a2 domains are oriented such

that their c-axis is parallel to the film/substrate interface and aligned with the [100] and

[010] directions of the substrate respectively.

Since the a lattice parameter of PbTiO3 (at room temperature) is slightly smaller than

b lattice parameter of the SrTiO3, the mismatch can be relieved by introducing a small

amount of domains with the c lattice parameter of PbTiO3 parallel to the interface. In this

way a small volume fraction of a-domains is introduced by a twinning mechanism in the

predominant c oriented film. Figure 1.8 (b) shows the domain wall twin plane (101)

between the 90° domains (or a- domain and c- domain) in the tetragonal phase.

(a)

(b)

Figure 1.8: (a) Domain configurations within an epitaxial tetragonal psubstrate as shown by Pompe and Speck [25]. (b) The schematic represen90° domains (or a- domain) and c- domains in the tetragonal phase [26].

The crystallographic domain pattern in perovskite thin films

structures (PbTiO3 and PZT) grown on different substrates l

LaAlO3 etc. were studied by many authors using TEM

Piezoresponse Force Microscopy (PFM) [27-30].

(101)

hase on a (001)-oriented cubic tation of a domain wall between

, particularly on tetragonal

ike SrTiO3, MgO, KTaO3,

, X-ray Diffraction and

13

Chapter 1

Figure 1.9: Variation of c domain abundance as a function of temperature for PbTiO3 films grown on a MgO substrate measured using a in-situ x-ray diffraction [34].

The parameter α is denoted in the literature to quantify the volume fraction of c-

domains. It is found that the parameter α depends on the thickness of the film (h), film

composition and the substrate. The experimental data in the literature show both

increasing and decreasing values of α with increasing h values. The ratio of a- and c-

domains can be quantified from TEM and AFM images. The temperature dependence of

α has also been studied by different authors for PbTiO3 and (Pb,La)TiO3 systems on

different substrates [31-34]. Their results show the reduction of α with increasing

temperature. The results of Lee and Baik [34] for a PbTiO3 thin film with h=300 nm on a

MgO substrate is shown in figure 1.9 as an example for the reduction of α with increasing

temperature. These reports on a/c domains constitute as fundamental literatures for our

work, as discussed in more detail in chapter 4. However there is very limited work done

on mono-domain films, where the polarization has the preferred orientation perpendicular

to the interface. Mono-domain films will be extensively discussed in chapter 3.

1.4 FERROELECTRIC MEMORIES

Ferroelectric materials received much attention not only because of fundamental

scientific interest but also because of their potential technological applications utilizing

their unique properties like dielectric, piezoelectric, pyroelectric and electro-optic

properties. Here we focus on the application of thin film ferroelectrics as a Ferroelectric

Random Access Memory (FeRAM or FRAM). Currently semiconductor memory formats

14

Introduction

like Dynamic Random Access Memory (DRAM) and Static Random Access Memory

(SRAM) dominate the market. However the disadvantage of these memories is their

volatility i.e., the loss of stored data upon power failure. Today’s non-volatile memories

available commercially are Complementary Metal Oxide Semiconductors (CMOS) using

battery as backup, Electrically Erasable Programmable Read Only Memory (EEPROM)

and Flash memory. The FRAM is a non volatile memory using a ferroelectric thin film

capacitor for storing data. As described before, ferroelectric materials spontaneously

polarize in such a way that the magnitude and direction of polarization can be reversed by

the application of an external electric field. FRAM's make use of this phenomena to store

data i.e., the upward and downward polarizations in the unit cell are referred to “0” and

“1” state or vice versa. Currently perovskite lead zirconate titanate (PZT) and layer-

structured strontium bismuth tantalate (SBT) are employed as ferroelectric RAM’s

[35,36]. The FRAM cell design is based on a capacitor structure integrated with a

transistor, i.e. a 1T1C or 2T2C architecture as shown in the figure below, where BL

denotes Bit Line, WL denotes Word Line, PL denotes Plate Line, BLB denotes

complementary Bit Line and FE denotes Ferroelectric capacitor.

FE FEFE

Figure 1.10: Schematic diagram of 1T1C (left) and 2T2C (right) FRAM bit cells

FRAM is not the single contender in today’s prototype non volatile memory cells; there

are other memories such as Magnetic RAM (MRAM), and Phase-change RAM (PRAM).

Table 1.11 compares the current status of different baseline and prototypic memories and

their technical details according to the international technology road map for

semiconductors in 2009. In addition to non-volatility, FRAM has a high writing speed, a

15

Chapter 1

low power consumption, and a high endurance, making FRAM superior to the present

DRAM and SRAM [35,36].

1.4.1 Challenges

Like any other memories FRAM has, apart from its advantages, also challenges that

have to be addressed.

1. Polarization Fatigue: The loss of polarization under electric field cycling is a key issue

in RAM’s using lead zirconate titanate. After a continuous cycling of negative and

positive bias i.e., cyclic read and write operation the material using platinum as a

electrode becomes subjected to polarization fatigue, resulting in a reduced remanent

polarization [35,36]. Research work to solve the problem is in progress and it appears that

the use of conductive oxide electrodes, e.g. SrRuO3, is an effective solution. For high

density memory applications PZT remains the preferred material.

2. Retention Loss: Like fatigue, a ferroelectric material cannot retain the polarization

ideally for a long time due to a reduction of the residual polarization, because of a

reduced difference between the switching and non switching charges. The retention time

in mono-domain PbTiO3 thin films using piezo force microscopy is discussed in

chapter 3.

3. Imprint: This is the tendency of one polarization state to be more stable than the

opposite one which results in the loss of polarization. The imprint affects the ferroelectric

nature by shifting the ferroelectric hysteresis loop resulting in loss of the remanent

polarization which makes it difficult to distinguish and address the write and read modes.

Other issues, like problems associated with the integration of ferroelectric materials with

CMOS technology also persist [35,36].

The theoretical concept of FRAM, on paper for the last two decades, has now been

translated into commercial memory products. Many large semiconductor companies, like

Fujitsu, Infineon, Toshiba, Ramtron, Samsung, Matsushita and Symmetrix, have reported

results of their research efforts on FRAM technology, and some of them already run a

16

Introduction

Table 1.11: Table taken from the international technology road map for semiconductors 2009 (ITRS) showing the current status of baseline and prototype memories [41].

business based on FRAM products. The scaling of ferroelectrics is of special importance,

because ferroelectric behaviour is proved to exist down to a thickness of 1.2 nm for

PbTiO3 [37], and 4 nm for PZT [38]. Epitaxially strained films can be polarized and

switched locally using conductive atomic force microscopes. It is estimated that a high

integrated density upto 40 Gbit/cm2 can be achieved by using the so-called Millipede

technology (an array of atomic force probe tips is used for reading and writing the bits)

[39,40]. Even after travelling such a long journey, the commercial exploitation of

17

Chapter 1

ferroelectric memories is still an emerging field that can prosper if the critical issues

mentioned above are solved. However, despite the clear potential of FRAM, for another

decade the dominancy of flash memories is expected to continue leading the industry.

1.5 MULTIFERROICS

Mutual control of magnetism and electricity was first postulated by Pierre Curie in

1894 [42]. More than half a century later in 1959, the same concept was predicted

theoretically by Dzyaloshinskii [42]. This result was followed in 1960 by experimental

evidence reported for Cr2O3 by Astrov [44]. Also, a few others reported the magneto-

electric effect in the 70’s [45-47]. In later years magnetoelectric materials received much

less attention, probably due to the lack large responses of such materials in nature.

Magnetoelectric coupling is closely related to “multiferroism”. In 1994 the term

multiferroics was coined by Schmid [48]. Almost four decades later, a renaissance began

in the field of multiferroics due to the discovery of the magneto-electric effect in rare

earth doped manganites and seminal paper on multiferroics by Nicola. A. Spaldin [49]. In

2007, Science magazine placed the field of multiferroics on the "Break through of the

year" list and in 2008 on the "Areas to watch" list [50].The multiferroics can be defined

as the class of materials which exhibits two or more ferroic order parameters (i.e.

ferroelectricity, ferromagnetism, ferroelasticity) simultaneously in a single phase. It is

relatively easy to find coexistence of two of these ferroic orderings, but it is more

difficult to have a large coupling between two of them. In particular, it is not easy to find

large magnetoelectric coupling. It is important to note that not all magnetoelectric

materials are multiferroics and also the reverse is not always true. For example Cr2O3 is a

magnetoelectric material which exhibits antiferromagnetism without any electric

ordering, whereas hexagonal YMnO3 is a multiferroic material which exhibits

ferroelectricity and antiferromagnetism but the linear magnetoelectric effect is forbidden

by symmetry. Although there are few ferroelectric anti-ferromagnets, materials that

exhibit both ferroelectricity and ferromagnetism are scarcely available in nature. In order

18

Introduction

Figure 1.12: The relation between multiferroic and magnetoelectric materials [51].

to understand the reason for this scarcity one should have a clear understanding of the

origin of ferroelectricity and ferromagnetism. We have seen in the beginning of this

chapter that for ferroelectricity the centers of the positive and the negative ions within the

unit cell do not coincide, but now it is also essential to know the reason for this lack of

centrosymmetry. For conventional perovskite ferroelectrics a formal requirement is that

cations have an empty “d” shell configuration [49], but then the question arises why we

need this empty d-shell for off centering the transition metal ions? To answer this let’s

consider the classical displacive type ferroelectric barium titanate. The empty d state of

the transition metal ion Ti4+ in BaTiO3, is used to establish a strong covalent bond with

neighboring oxygen atoms and hence it is favorable to shift the Ti atom from the centre

of the O6 octahedra to form covalent bonds with part of the oxygen atoms at the expense

of the other oxygen atoms. On the other hand, for a net magnetic moment, a partially

filled d-shell is a requirement. As soon as one or more electrons start to occupy the

d-shell the perovskite will loose it ferroelectric nature [52,53]. In order to have these

mutually exclusive events, i.e. magnetism and ferroelectricity in a single phase, several

routes were proposed. Most of the mechanisms proposed for co-existence of

ferroelectricity and ferromagnetism are based on an alternative mechanism for

ferroelectricity whereas the alternative (non d electron) of searching for new mechanism

for magnetism remained largely unexplored. Smolenskii [54] proposed to synthesize

19

Chapter 1

mixed systems consisting of magnetic ions i.e., cations with partially filled d- shell and

ferroelectric transition metal ions satisfying the empty d-shell requirement for

ferroelectricity. They successfully synthesized PbFe1/23+Nb1/2

5+O3 or PbFe2/33+W1/3

6+O3.

These systems were found to have a low ferroelectric Curie temperature or Neel

temperature and a weak magnetoelectric coupling. Other systems are generally classified

on the basis of their mechanisms leading to multiferroic behaviour [51,52,55,56].

Lone pair multiferroics

One of the alternative mechanisms uses the stereo-chemical activity of the A-site ions

to couple the magnetism and ferroelectricity in a single phase. Examples of multiferroic

materials using this mechanism are BiFeO3, BiMnO3 and PbVO3. The Bi3+ or Pb2+ ion

has a stereo-chemically active 6s2 lone pair electron, which displaces this ion from the

centrosymmetric position with respect to the coordinated oxygen ions. Then, the A-site

Bi or Pb ion is responsible for ferroelectricity and the B-site Fe ion is responsible for the

magnetism in a single phase. These systems exhibit proper ferroelectricity. BiFeO3 is a

material of interest to many researchers because of its room temperature multiferroic

behaviour. Still, BiFeO3 is an antiferromagnet. To find ferroelectric ferromagnets remains

very challenging.

Geometric ferroelectrics

In this type of materials, the ferroelectricity is achieved by a complex lattice

distortion. The hexagonal rare earth manganites RMnO3 (R = Ho-Lu, Y) exhibit a net

dipole moment due to the enlargement of the unit cell by lattice distortions such as

buckling in the R-O plane and manganese-oxygen bipyramids [57]. Other examples

falling into this category are K2 SeO4 and Cs2CdI4.

Charge ordered ferroelectrics

Charge ordering gives rise to the ferroelectricity in certain materials [58]. Only a few

compounds have been proposed in which this charge ordering or electronic

ferroelectricity occurs. The prominent examples are Fe3O4 and LuFe2O4. The

ferroelectricity in LuFe2O4 [58] arises from electron correlations such that the Fe ions in

each layer form a triangular lattice with an ordered arrangement of valence states of Fe2+

and Fe3+. This charge ordering occurs below 350K.

20

Introduction

Magnetic ordering ferroelectrics

An entirely new mechanism proposed for invoking ferroelectricity is due to magnetic

ordering in the material instead of structural distortions, charge ordering, or stereo-

chemical activity. TbMnO3 discussed in chapter 5 of this thesis belongs to the category of

materials showing this mechanism. The breaking of inversion symmetry and the electric

polarization is the result of a long-range spin-spiral magnetic ordering. When this spin

spiral occurs, ferroelectricity thus becomes possible with a strong coupling to the

magnetic order [59].

1.6 OUTLINE OF THE THESIS

For any thin film device it is essential to fabricate high quality films. Knowledge of

the microstructural aspects of thin films is very important for understanding their

functional properties. Microstructural aspects include (i) possible defects (e.g. impurities,

oxygen vacancies, dislocations) in the structure at the atomic scale, (ii) the quality of the

electrode/film and film/substrate interfaces, (iii) structural domains and domain walls,

(iv) grains and grain boundaries and (v) the quality of the surface. All the above

mentioned aspects contribute substantially to fatigue, imprint and retention loss of the

ferroelectric films as discussed in section 1.4.1. The objective of this thesis is to gain

insight in the domain structure and its formation in ferroelectric and multiferroic thin

films on a microscopic scale. Transmission Electron Microscopy (TEM) is potentially a

powerful tool to visualize the thin films with thickness in the order of nanometers. We

used TEM to study the important microstructural aspects described above, with a

particular attention for the domain structure, formation and evolution. PbTiO3 thin films

were taken as a model ferroelectric system for our investigations and TbMnO3 thin films

were studied for the case of multiferroics.

As discussed in section 1.2.1 the properties of ferroelectric materials like

piezoelectricity and Curie temperature can be tuned by substituting different cations. In

perovskite thin films the functional properties can in addition be controlled and tuned by

imposing strain in the thin film by using the substrate-film lattice mismatch as the tuning

parameter (i.e. removing the need to add any dopants as for the bulk case). This

21

Chapter 1

dissertation is organized as follows: The general concepts of (a-)domain formation in

perovskite thin films and related issues are the focus of chapter 2 along with a detailed

description of the experimental methods used in this research work. Chapter 3 focuses on

the growth of thick PbTiO3 films with complete c-axis orientation, in order to have the

desired polarization completely out of plane. The application of strain to the thin films via

the substrate-film lattice mismatch is used to increase the Curie temperature to much

higher values than those of the bulk. We found a huge increase never reported before for

the relatively thick (130 nm – 280 nm) films we studied. Many groups had previously

worked on this particular system of PbTiO3 thin films on SrTiO3 substrates, but there

were no clear reports on critical thickness for complete strain relaxation and domain

formation. In chapter 3 we address the experimental boundary conditions for growing

strained films (without a-domains) and relaxed films (with a-domains). The discrepancies

in calculating the critical thickness by different models are also addressed in this chapter.

A general misconception existed that PbTiO3 films on SrTiO3 substrates relax their strain

for a film thickness beyond of few tens of nanometer, but we showed that thick PbTiO3

thin films on SrTiO3 substrates can be grown directly in a strained ferroelectric (single-

domain) state at temperatures clearly above the Curie temperature for bulk PTO.

Chapter 4 focuses on the substrate influence on a-domain formation and their

microstructural details in PbTiO3 thin films grown on SrTiO3 and DyScO3 substrates.

Chapter 5 aims to explain the detailed nano-domain structure observed in thin films

of multiferroic TbMnO3. As discussed in the multiferroics section 1.5, TbMnO3 is an

interesting system showing multiferroic behaviour, because of a new mechanism by

which ferroelectricity and magnetism can coexist. TbMnO3 thin films under epitaxial

strain on SrTiO3 substrates have been first reported by Daumont et al. [60]. A detailed

microstructural analysis of the nano-scale domains present in epitaxial TbMnO3 thin

films using TEM is reported for the first time by us in this thesis. The evolution of the

domain structure with film thickness and the various strain relaxation mechanism active

in the epitaxial TbMnO3 thin films are discussed in detail in Chapter 5. At an end the

summary and outlook of this dissertation is presented in chapter 6.

22

Introduction

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