Springer TAP vol98 ferroelectric thin films (springer 2005)

In Part I, the phase transition of a ferroelectric thin film is analyzed indetail on the basis of the Tilley–Zeks model, and its characteristic featuresare clarified.. Phase transitions in

Topics in Applied Physics

Volume 98

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Email: hans.koelsch@springer-sbm.com

Masanori Okuyama Yoshihiro Ishibashi (Eds.)

Ferroelectric Thin Films

Basic Properties and Device Physics

for Memory Applications

With 172 Figures

123

Professor Masanori Okuyama

Osaka University

Graduate School of Engineering Science

Department of Systems Innovation

1-3 Machikaneyama-cho, Toyonaka

560-8531 Osaka, Japan

okuyama@ee.es.osaka-u.ac.jp

Professor Yoshihiro Ishibashi

Aichi Shukutoku University

Nakakute-cho

480-1197 Aichi, Japan

yishi@asu.aasa.ac.jp

Library of Congress Control Number: 2004117860

Physics and Astronomy Classification Scheme (PACS):

68.55.-a, 77.80.-e, 81.15.-z, 77.84.-s, 77.22.-d

ISSN print edition: 0303-4216

ISSN electronic edition: 1437-0859

ISBN 3-540-24163-9 Springer Berlin Heidelberg New York

This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer Violations are liable for prosecution under the German Copyright Law.

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The prominent properties of ferroelectric materials such as polarization teresis, large dielectric constant, and remarkable piezoelectric, pyroelectricand electro-optical effects can all be applied in electronic devices Especially

hys-in the form of thhys-in films, ferroelectrics show excellent features when combhys-inedwith Si active electronic devices such as nonvolatile memories, capacitors,surface acoustic wave (SAW) filters, ultrasonic and infrared sensors, opticalmodulators, and switches Among these, nonvolatile memories utilizing fer-roelectric thin films have attracted special attention recently because of theirlow power dissipation and fast switching In order to realize the ultralargescale integration of ferroelectric thin-film memory devices, which might becompetitive with various current dynamic random access memories, compre-hensive studies of ferroelectric thin films ranging from basic physics to devicephysics are indispensable

A tremendous amount of research on ferroelectric thin films and theirapplication to memory devices has been carried out This book gathers to-gether remarkable research results relating to the basic physics of size effects,searches for new materials, the development of new preparation methods,microscopic and macroscopic characterization, and the fabrication and char-acterization of device structures

In Part I, the phase transition of a ferroelectric thin film is analyzed indetail on the basis of the Tilley–Zeks model, and its characteristic featuresare clarified In Part II, preparation methods for ferroelectric thin films such

as chemical solution, metal-organic chemical vapor deposition (MOCVD) andsputtering are described for the preparation of PZT and Bi-layer-structuredferroelectric thin films Island structures of nanometer size are observed inthe initial nucleation stage and their ferroelectric behavior is discussed InPart II, a description is also given of the spatial polarization distributionobserved by scanning nonlinear dielectric microscopy, which has ultrahighspatial resolution, and the applicability of the polarization domains to diskmemory with a size of the order of Tbits is proved In Part III, topics onrelaxor ferroelectrics showing dispersive dielectric phenomena are described.The colossal piezoelectric property is analyzed in the vicinity of the mor-photropic phase boundary Domain structures in relaxor ferroelectrics areanalyzed in detail, and the mechanism has been clarified by analyzing di-

VI Preface

electric properties of superlattice structures with various kinds of orderingperiodicity In Part IV, metal–ferroelectric–insulator–semiconductor (MFIS)structures in ferroelectric-gate FETs are studied The stability of the MFISstructure is analyzed theoretically, considering the space charge distribution.The memory retention of the MFIS structure has been analyzed, consider-ing leakage current through the ferroelectric junction, and long retention hasbeen achieved in structures using SrBi2Ta2O9 and YMnO3thin films.This book contains valuable information on both theoretical approachesand experimental efforts, and we hope that the book will offer some help notonly to beginners but also to specialists in ferroelectric physics and engineer-ing who would like to have an idea about the progress of research in the field

of ferroelectric thin films and devices

This work has been carried out under Grants-in-Aid for scientific research

in the priority area “Control of Material Properties of Ferroelectric ThinFilms and Their Application to Next-Generation Memory Devices”, spon-sored by the Ministry of Education, Culture, Sports, Science and Technology,Japan, for 2000–2004

Last but not least, we would like to express our sincere thanks toDrs Kaoru Yamashita and Takeshi Kanashima for their tremendous efforts

in arranging the manuscripts for this book and taking care of the researchproject Without their contribution, this book might not have come out indue time

This publication was supported by Grant-in-Aid for Publication of tific Research Results 165284, 2004, sponsored by the Japan Society for thePromotion of Science (JSPS)

Part I Theoretical Aspects

Theoretical Aspects of Phase Transitions in Ferroelectric

Thin Films

Yoshihiro Ishibashi 3

1 Introduction 3

2 The Tilley–Zeks Model 4

3 Transition Temperature and Polarization Profile 5

3.1 The Case of Zero Extrapolation Length (δ+= δ −= 0) 6

3.2 The Case of Positive Extrapolation Length (δ+= δ − = δ > 0) 9 3.3 The Case of Negative Extrapolation Length (δ+= δ − = δ < 0) 12 4 Asymmetric Films 14

4.1 The Positive–Positive Case (δ+> 0, δ − > 0) 15

4.2 The Negative–Negative Case (δ+< 0, δ − < 0) 15

4.3 The Mixed Case 15

4.3.1 The Case of|δ − | < |δ+| 16

4.3.2 The Case of|δ − | > |δ+| 16

5 Notes on Exact and Approximate Polarization Profiles 16

6 Concluding Remarks 19

References 20

Part II Preparation and Characterization of Ferroelectric Thin Films Theoretical Aspects of Phase Transitions in Ferroelectric Thin Films Shin-ichi Hirano, Takashi Hayashi, Wataru Sakamoto, Koichi Kikuta, Toshinobu Yogo 25

1 Introduction 25

1.1 The Chemical Solution Deposition Process 26

1.2 Representative Ferroelectric Thin Films for Memory Devices 28 1.3 Layer-Structured Bi4Ti3O12-Based Thin Films 28

2 Rare-Earth-Ion-Modified Bi Ti O Thin Films 29

VIII Contents

2.1 Chemical Processing of (Bi,R)4Ti3O12 Precursor Solutions,

Powders and Thin Films 29

2.2 Crystallization and Pyrolysis Behavior of (Bi,R)4Ti3O12Precursors 31

2.3 Crystallization of (Bi,R)4Ti3O12Thin Films 33

2.4 Surface Morphologies of (Bi,R)4Ti3O12 Films 35

2.5 Phase Transition and Ferroelectric Properties 36

2.6 Effect of Nd Content on Nd-Modified BIT (BNT) Thin Films 39 2.7 Effect of Processing Temperature on Nd-Modified BIT (BNT) Thin Films 41

3 Ge-Doped (Bi,Nd)4Ti3O12 Thin Films 43

3.1 Fabrication of (Bi,Nd)4(Ti,Ge)3O12Films 43

3.2 Microstructure and Electrical Properties of (Bi,Nd)4(Ti,Ge)3O12Films 45

4 UV Processing of (Bi,Nd)4Ti3O12 (BNT) Thin Films 46

4.1 Changes in the Chemical Bonding of Excimer-UV-Irradiated BNT Precursor Films 47

4.2 Effect of UV Light Irradiation on the Crystal Orientation of the Resultant Thin Films 48

4.3 Surface Morphology of UV-Light-Irradiated BNT Thin Films 50 4.4 Ferroelectric Properties of UV-Irradiated BNT Thin Films 51

4.5 Fatigue and Leakage Current Properties of UV-Irradiated BNT Thin Films 54

References 56

Pb-Based Ferroelectric Thin Films Prepared by MOCVD Masaru Shimizu, Hironori Fujisawa, Hirohiko Niu 59

1 Introduction 59

2 Experimental Procedure 61

3 Microscopic Observation of the Initial Growth Stages of PbTiO3 and PZT Thin Films on Various Substrates 62

3.1 Growth Process of PbTiO3 and PZT Thin Films on Polycrystalline Pt/SiO2/Si 62

3.2 Growth Process of PZT Thin Films on SrTiO3Single Crystals 64 3.3 Growth Process of PZT Thin Films on Epitaxial SrRuO3/SrTiO3 65

4 Epitaxial PZT Ultrathin Films 67

4.1 Preparation of PZT Ultrathin Films on SrRuO3/SrTiO3 67

4.2 Ferroelectric Properties of PZT Ultrathin Films 67

5 Self-Assembled PbTiO3and PZT Nanostructures and Their Ferroelectric Properties 71

5.1 Preparation of Self-Assembled PbTiO3 and PZT Nanostructures on Various Substrates 71

5.2 Piezoelectric and Ferroelectric Properties of PbTiO3 Nanostructures 72

Contents IX

References 74

Spontaneous Polarization and Crystal Orientation Control of MOCVD PZT and Bi4Ti3O12-Based Films Hiroshi Funakubo 77

1 Introduction 77

2 Spontaneous Polarization 77

2.1 PZT Films 78

2.2 Bi4Ti3O12-Based Films 80

3 Remanent Polarization of Polycrystalline Ferroelectric Films Prepared on Si Substrates 83

3.1 PZT Films 83

3.2 Bi4Ti3O12-Based Films 85

3.3 Low-Temperature Deposition 86

3.4 PZT Films 87

3.5 Bi4Ti3O12-Based Films 87

References 88

Rhombohedral PZT Thin Films Prepared by Sputtering Masatoshi Adachi 91

1 Introduction 91

2 Experimental Procedures 92

3 PZT Films on (Pb,La)TiO3 (PLT)/Pt/Ti/SiO2/Si and Ir/SiO2/Si 93

4 Rhombohedral PZT on (111) Ir/(111) SrTiO3 and (100) Ir/(100) SrTiO3Substrates 101

References 103

Scanning Nonlinear Dielectric Microscopy Yasuo Cho 105

1 Introduction 105

2 Principle and Theory of SNDM 106

2.1 Nonlinear Dielectric Imaging with Subnanometer Resolution 107 2.2 Comparison between SNDM Imaging and Piezoresponse Imaging 111

3 Higher-Order Nonlinear Dielectric Microscopy 112

3.1 Theory of Higher-Order Nonlinear Dielectric Microscopy 112

3.2 Experimental Details of Higher-Order Nonlinear Dielectric Microscopy 113

4 Three-Dimensional Measurement Technique 115

4.1 Principle and Measurement System 116

4.2 Experimental Results 117

5 Tb/in2 Ferroelectric Data Storage Based on SNDM 118

References 123

X Contents

Part III Relaxors

Analysis of Ferroelectricity and Enhanced Piezoelectricity

near the Morphotropic Phase Boundary

Makoto Iwata, Yoshihiro Ishibashi 127

1 Introduction 127

2 Free Energy and Phase Diagram 128

3 Dielectric Constants, Elastic Constants and Electromechanical Coupling Constants 131

4 Polarization Reversal 134

5 Enhanced Piezoelectricity Under an Oblique Field 140

6 Magnetostrictive Alloys of Rare-Earth–Fe2 Compounds 144

References 145

Correlation Between Domain Structures and Dielectric Properties in Single Crystals of Ferroelectric Solid Solutions Naohiko Yasuda 147

1 Introduction 147

2 Single-Crystal Preparation 148

2.1 Flux Method 148

2.2 Solution Bridgman Method 149

3 Measurement 150

4 Domain Structures in the PIN–PT Solid Solution 150

4.1 Temperature Dependence of the Permittivity, Domain Structure and Birefringence 150

4.2 The Effect of a dc Bias Field on the Domain Structure 152

5 Domain Structures in a (001) Plate of a PMN–PT Solid Solution 156

References 158

Relaxor Superlattices: Artificial Control of the Ordered– Disordered State of B-Site Ions in Perovskites Hitoshi Tabata 161

1 Relaxor Behavior in Perovskite-Type Dielectric Compounds 161

1.1 Introduction 161

1.2 Experimental Procedure 162

1.3 Results and Discussion 163

1.4 Conclusions 167

2 Artificial Control of the Ordered/Disordered State of B-Site Ions in Ba(Zr,Ti)O3 by a Superlattice Technique 167

2.1 Introduction 167

2.2 Experimental 168

2.3 Results and Discussion 170

Contents XI

References 172

Part IV Ferroelectric–Insulator–Semiconductor Junctions Physics of Ferroelectric Interfaces: An Attempt at Nanoferroelectric Physics Yukio Watanabe 177

1 Spontaneous Polarization and the Ferroelectric Surface 177

2 Electric Field in and Arising from a Ferroelectric 178

2.1 Ferroelectric Covered by Metal (M/F) 178

2.2 Ferroelectric Covered by Semiconductor (S/F) 179

2.3 Ferroelectric Covered by Insulator or Nothing (I/F), and Depolarization Field 179

2.4 Surface Relaxation Modeling of I/F Structure and Generalization 180

3 Ferroelectric Field Effect Devices 181

4 Domains, Depolarization Instability, and Memory Retention 181

5 Epitaxial Strain and the Surface Relaxation∇P Effect 183

5.1 Epitaxial Strain vs Depolarization Instability 183

5.2 The Surface Relaxation∇P Effect Can Be Unimportant 184

6 Finite Band Gap Energy and Redefinition of “Insulator” 185

6.1 Reexamination of the Depolarization Field 185

6.2 Relaxation Semiconductors 186

6.3 Insulator Under Static Field 186

6.4 Ferroelectric Under Static Field 186

6.5 The Natural Choice of a Ferroelectric 187

7 Modeling of F/I/S Interfaces 188

7.1 Mathematical Formulation 188

7.2 Approximations 191

8 Comparison with Experiments: Leakage Current and Dynamics 191

8.1 Numerical Results for Typical Structures 191

8.2 Retention and Leakage Current 192

8.3 Contradiction and Solution: Miller–McWhorter Theory 193

9 Intrinsic 2D Electron Layers 195

10 Ferroelectric Coupled to Free Electrons: Ferroelectric 2D Metal 196

11 Concluding Remarks 196

References 196

XII Contents

Preparation and Properties of Ferroelectric–Insulator–

Norifumi Fujimura, Takeshi Yoshimura 199

1 Introduction 199

2 Material Design of Ferroelectric and Insulator Layers for MF(I)S Capacitors 200

3 Fabrication of YMnO3 Epitaxial Films 204

4 Fabrication and Properties of Y2O3 Films on Si 206

5 Fabrication of YMnO3/Y2O3/Si Capacitors 208

6 Investigation of Retention Characteristics of YMnO3/Y2O3/Si Capacitors 210

7 Influence of Leakage Current on the Retention Characteristics of YMnO3/Y2O3/Si Capacitors 211

References 217

Improvement of Memory Retention in Metal–Ferroelectric– Insulator–Semiconductor (MFIS) Structures Masanori Okuyama, Minoru Noda 219

1 Introduction 220

2 Theoretical Analysis of Memory Retention in MFIS Structures 220

2.1 Capacitance Retention Characteristics 220

2.2 Theoretical Studies of Band Profile and Retention Degradation of MFIS Capacitors 222

2.2.1 Construction of MFIS Model and Analysis Method 222

2.2.2 Calculated Band Diagrams 224

2.3 Effects of Currents Through the Ferroelectric and Insulator Layers on Retention Characteristics of MFIS Structures 225

2.3.1 Effects of Schottky Current Through Insulator Layer 225

2.3.2 Effects of Schottky Current Through Ferroelectric Layer 226 2.3.3 Effects of Absorption Current in Ferroelectric Layer 227

2.3.4 Discussion of Current Reduction 228

3 Advanced Structures to Improve Retention Time 228

3.1 Enhancement of Barrier Height 228

3.2 Insertion of Ultrathin Insulator Layer Between Metal and Ferroelectric Layers 228

3.3 High-k Insulator Layer Instead of SiO2Film 230

4 Experimental Improvement of Retention Time by O2 Annealing 231

4.1 Effect of O2Annealing on Physical Properties of SBT Thin Films on (111) Pt/Ti/SiO2/Si Substrates 231

4.2 Polarization Retention Characteristics of Pt/SBT/Pt Capacitors 231

4.3 Current Conduction in SBT Films 232

4.4 Retention Improvement of MFIS Structures by O Annealing 233

Contents XIII4.5 More Improvement by Rapid Thermal Annealing 234

5 Photoyield Spectroscopic Studies on SBT Thin Films 2355.1 Principle of Photoyield Spectroscopy of SBT Films 2355.2 Effects of O2 Annealing on SBT Thin Films Studied

by UV-PYS 236References 238

Index 241

Theoretical Aspects of Phase Transitions

in Ferroelectric Thin Films

Yoshihiro Ishibashi

Faculty of Business, Aichi Shukutoku University,

Nagakute-cho, Aichi Prefecture 480-1197, Japan

yishi@asu.aasa.ac.jp

Abstract Phase transitions in ferroelectric thin films are discussed theoretically

on the basis of the Tilley–Zeks model for the case where the transition is of thesecond order A surface is characterized by an extrapolation lengthδ, which is a

key concept of the model For a positive δ the ferroelectric phase transition tends

to be suppressed, with a decreasing transition temperature, while for a negativeδ

ferroelectricity tends to be enhanced, with an increasing transition temperature.Not only symmetric-surface cases, but also asymmetric-surface cases are discussed

1 Introduction

The fundamental question of the way in which ferroelectric properties depend

on thickness in thin films has recently become important because extensiveuse is being made of very thin ferroelectric films in memory devices [1,2,3].Since the Landau–Devonshire theory gives a very good account of much ofthe data on bulk ferroelectrics, it was natural that extension to surfaces, films

and superlattices should be sought In fact, Kretschmer and Binder [4] setout a framework for semi-infinite materials by including in the free energy

functional a contribution from the inhomogeneity of the polarization p, ing p as a function of the coordinate z Tilley and Zeks [5,6,7,8,9] extendedthe study of Kretschmer and Binder, mostly to symmetric-surface cases, andtheir coworkers have also performed detailed analyses of the model to caseswhere the phase transition in the bulk is of the second order as well as of thefirst order [10,11,12,13,14,15] In this Chapter, for convenience, we refer

treat-to the form of the free energy functional adopted by Tilley and Zeks as theTilley–Zeks model

There are several important quantities for specifying the physical erties of thin films These are the dependences of the transition temperatureand the polarization profile in the film on the film thickness and other para-meters involved in the model At present the Tilley–Zeks model is almost theonly well-defined model with which most of the questions mentioned abovecan be answered without much ambiguity and much approximation However,there may still be some need to improve the Tilley–Zeks model or to producenew, better models in order to discuss the experimental data in detail

prop-In this situation, in the present review we first present what can be cluded from the original Tilley–Zeks model about phase transitions in ferro-

con-M Okuyama, Y Ishibashi (Eds.): Ferroelectric Thin Films,

Topics Appl Phys 98, 3–23 (2005)

4 Yoshihiro Ishibashi

electric thin films, and then mention an extension of the model to incorporateasymmetric surfaces We conclude the review with some remarks

2 The Tilley–Zeks Model

In this section we consider a thin film, which extends from−L/2 to L/2, and

undergoes a second-order phase transition if there is no surface effect (i.e., it

is like the bulk case) The Landau free energy then can be written as

which is composed of the local energy (the α- and β-terms in the integrand),

a contribution due to the spatial modulation inside the film (the κ-term) and

a contribution from the surfaces governed by the surface polarization and theextrapolation length In (1), it is assumed that

as usual; β and κ are both positive constants, i.e., β > 0; κ > 0; p+ and

δ+denote the polarization and the extrapolation length, respectively, at z = L/2; and p − and δ − denote the corresponding quantities at z = −L/2 Our task is to find the transition temperature αcand the polarization pro-

file p (z) below the transition temperature For this purpose let us minimize

the free energy, i.e.,

extrapolation length here is regarded as a material constant like β and κ, and

can be either positive or negative As a general rule, the surface polarization

Theoretical Aspects of Phase Transitions in Ferroelectric Thin Films 5

Fig 1 Surface polarizations p+ andp −, and the extrapolation lengthsδ+andδ −

is larger than that in the bulk for a negative extrapolation length, while it issmaller for a positive extrapolation length

It should be noted that there are four length scales in the present

model, namely, the film thickness L, the extrapolation lengths δ+, δ −, and a

length scale ξ; the latter is given by

ξ =



κ

which is composed of a material constant κ and the temperature α, an

ex-ternal parameter The phase transition and the physical properties of thepresent model are governed by the interplay of such length scales

3 Transition Temperature and Polarization Profile

In this section we obtain the solutions by minimizing the free energy given

in (1) To do so, we have to solve the Euler–Lagrange equation derivedfrom (2):

where c is an integration constant.

In what follows in this section, we consider only cases with a symmetric

extrapolation length, i.e., the case where δ+= δ −

6 Yoshihiro Ishibashi

3.1 The Case of Zero Extrapolation Length (δ+ =δ −= 0) [ 9 ]

This is one of the simplest cases, but it is nevertheless quite illustrative inthe sense that we can obtain a simple but general idea about the effect ofthickness on the transition and physical properties of ferroelectric thin films

A zero extrapolation length means that the surface value of the polarization

is fixed to zero, and the maximum of polarization, pc, is located at the center

of the film, where dp/dz = 0, i.e.,

where sn is the Jacobian elliptic function The thickness L can be expressed,

by putting z = 0 and θ = π/2 into the upper limits of the integration

in (15), as

Theoretical Aspects of Phase Transitions in Ferroelectric Thin Films 7

Fig 2 Polarization profiles in the case of δ = 0 for various film thicknesses; the

thickness can be seen from thez-value where p becomes zero

disappear-it is of the second-order nature This is easily verified by taking the derivative

of ¯f with respect to L at L = Lc, which will turn out to be zero

A comment is in order here It is interesting to note that the factor

mul-tiplying 1/L in the first term of the r.h.s in (20) when k approaches unity (1/L approaching zero) is just the wall energy when a single wall exists in an

depen-Theoretical Aspects of Phase Transitions in Ferroelectric Thin Films 9

Fig 4 The average polarization as a function of inverse film thickness in the case

ofδ = 0

3.2 The Case of Positive Extrapolation Length (δ+ =δ −=δ > 0)

In this case, by symmetry, we write the surface polarization as

10 Yoshihiro Ishibashi

Fig 5 Polarization profiles for δ = 1 for various film thicknesses; the thickness

can be seen from thez-value where the p-curves terminate

The θscan be expressed, using (26), as

θs= sin−1 pb

p2

b+ p2 e

Omitting tedious mathematics, we present p(z) graphically in Fig. 5,

where the z-coordinate where the p(z) curve terminates corresponds to L/2 The thickness dependence of f is given by

The average free energy ¯f is shown in Fig.6 for several values of δ.

Regarding the average polarization, we present the results only graphically

in Fig 7, without showing the concrete form of the formula corresponding

to (23)

Theoretical Aspects of Phase Transitions in Ferroelectric Thin Films 11

Fig 6 The average free energy as a function of the inverse film thickness for several

ex-perature (see the α < 0 part of Fig. 8) The thickness transition is found to

be also of second order

First, we consider the case α > 0 At the thickness transition pc must

vanish, or in the vicinity of the thickness transition pc must be small, andtherefore (4) and (5) can be approximated at the surfaces as

Theoretical Aspects of Phase Transitions in Ferroelectric Thin Films 13

Next, we consider the case of α < 0 Obviously, there is no thickness

transition in this case, because the bulk is already ferroelectric and the surface

is more so, and pc must be larger than pb, i.e.,

The value of pc can be obtained from (46) when L and δ are given In this

way we can find polarization profiles for the case of a negative extrapolationlength

Before concluding the present section, comments seem to be in order onthe negative extrapolation length It has been reported that the polarization

is enhanced near the surface in 4 nm thick PbTiO3 and 12 nm thick BaTiO3films [16,17] This feature of surface-enhanced polarization can certainly bereproduced by the Tilley–Zeks model with a negative extrapolation length

At the same time, however, the model predicts a surface-enhanced tion not only in thin films but also in bulk materials as well, leading then to aconfusing situation where the transition temperature in the “bulk” obtained

polariza-14 Yoshihiro Ishibashi

by this model is higher (α > 0 for 1/L = 0 in Fig.8) than that (α = 0)

pre-supposed as the “bulk” transition temperature This is quite different fromthe case of positive extrapolation length, where all curves merge into the

point 1/L = α = 0 In addition, it should be noted that, as has been

repeat-edly mentioned, a negative extrapolation length leads to a higher transitiontemperature, and the smaller it is in its absolute value the higher the tran-sition temperature becomes If this trend is extrapolated, an infinitely hightransition temperature will result for an infinitely thin film, which, however,seems to the present author to be unphysical Thus, the case of a negative ex-trapolation length may be only of academic interest, and to apply the model

to more realistic cases, avoiding this sort of confusing and unphysical ation, some sort of amendment of the Tilley–Zeks model or new models toreplace it may be needed

situ-4 Asymmetric Films

Following the historical track of the development of theories of thin films, wehave so far placed emphasis on thickness transitions at a given temperatureand considered cases where the extrapolation length at both surfaces is thesame, that is, we have considered symmetric films But a symmetric film isnothing but a special case of an asymmetric one, and it is probably moreappropriate to study asymmetric films, since asymmetry in the extrapola-

tion length will be more common in practical circumstances Ishibashi et al.

have developed a method for deriving an effective Landau free energy from

a Landau–Ginzburg free energy functional like (1), and discussed the criticalpoints in terms of the sample thickness and temperature for various cases ofthe extrapolation length [14]

The mathematical procedures are as follows After substituting (6) into(1), the average free energy is rewritten as

in terms of pm, the extremum value in the polarization profile, located at

z = zm, where dp/ dz = 0 All of the terms in (47) turn out to be expressible

in terms of pm, and therefore the free energy (1) can be expanded into a

power series in p as

Theoretical Aspects of Phase Transitions in Ferroelectric Thin Films 15

where pmplays the role of an effective order parameter [14,15]

Thus, we have been able to obtain an effective Landau-type free energyfunction (with no coordinate-dependent term) from the Landau–Ginzburg

free energy functional (with coordinate-dependent terms) The coefficient A

is important, since A = 0 gives the critical point [14]

4.1 The Positive–Positive Case (δ+ > 0, δ − > 0)

The target coefficient A is given by

4.2 The Negative–Negative Case (δ+ < 0, δ − < 0)

Putting the minimum value of the polarization equal to pm, and adopting asimilar procedure, we obtain

αδ2

−

+ tanh−1 κ

αδ2 +



The transition temperature is found to increase with decreasing thickness

4.3 The Mixed Case

Without loss of generality, we can assume that δ+ > 0 and δ − < 0 (Fig.9).

There are two different cases, depending upon the absolute value of δ − In

the following, we show only the results Interested readers are referred to ourprevious work [14]

It is found that the transition temperature decreases with decreasing ness

thick-The coefficient B in (49) can be obtained in a similar way, and it has been

reported that B is found to be proportional to β, and therefore positive, when

A = 0 for any of the cases studied above, implying that the transition of in

the present model is of second order [3,15]

5 Notes on Exact and Approximate Polarization Profiles

As mentioned above, in the Tilley–Zeks model the exact solutions of theEuler–Lagrange equation are available in terms of Jacobian elliptic functions.Apart from analyses of such exact solutions, the following considerations may

be of some help for a better understanding of the model

Theoretical Aspects of Phase Transitions in Ferroelectric Thin Films 17Tilley and Zeks adopted a polarization profile

p = p0cosz

to obtain the relation between Lc, δc and ξc at the critical point (the script “c” means “critical”), and from the boundary condition, the criticalrelation

fixed Lc (i.e., experimentally, taking a sample of a certain thickness), there

are many possible values of ξc which satisfy (57), and so a question may

arise: Which ξcshould we take? In this case, obviously, we should take the ξc

corresponding to the highest temperature For a fixed ξc(i.e., experimentally,

at a fixed temperature), there are also many possible values of Lc= Lc,min+

2πξc (= 0, 1, 2, ) which satisfy (55), and so a question may arise: Which

Lc should we take? In this case we should obviously take Lc,min, because a

larger Lc corresponds to more polarization modulations and therefore to ahigher energy

The necessity for such a selection of a valid unique solution based uponphysical considerations as mentioned above, originates from the fact that thepolarization profile is expressed only in terms of a physically given (fixed)

parameter ξ, without any adjustable parameters To avoid this inconvenience

(although it is not a big one), we can adopt a different mathematical methodfor considering the system, in particular one that is not periodic as in thepresent case An example of such cases is the problem of the 180◦ wall,

which is concerned with a half-period, with the order parameter p extending

from −pb to pb (not further back to −pb) The well-known solution for thepolarization profile of one 180◦wall in an infinite system, obtained by solving

exactly the same Euler–Lagrange equation (7) under a different boundarycondition, is of the form

p = p0tanh√ z

where it should be noted that a factor 1/ √

2 appears in the argument of thetanh function

In the light of (58), let us use, instead of (56),

p = p0cos h z

introducing an adjustable parameter h Since h is a mathematical parameter,

nothing to do with physical values set experimentally, we may confine itsrange to

At a glance when we look at (56) and (59), only ξ seems to be treated

as special in relation to other quantities Since, of course, all three lengthsare mutually related by the boundary condition, this is certainly only anappearance However, it may be useful to pursue the above line further, sincethe exact solution is not always available Let us just write the polarization

profile with a parameter K as

where g is a function only of L/δ Using K, the critical relation, including

temperature, can be obtained as

Theoretical Aspects of Phase Transitions in Ferroelectric Thin Films 19

Here, it should be noted that (68) has been derived upon the basis of

a harmonic approximation of the polarization profile Namely, within this

approximation K seems to be governed only by the thickness and the

ex-trapolation length, and to be independent of temperature But this is not the

case, and K is temperature-dependent through the function g in (68), which

is indeed found to be a function also of temperature, as is easily understoodfrom the following Let us now write the polarization profile, including thehigher harmonics, as

and thus it turns out that K depends upon higher harmonic components in

the polarization profile, which in turn depend upon how far the thickness,temperature and extrapolation length deviate from the critical point Thissituation is quite similar to the temperature variation of the modulationwavelength in an incommensurate structure [18]

As mentioned above, as far as the critical relation between the thickness,temperature and extrapolation length is concerned, it does not matter which

of (56), (59) or (65) is adopted for the polarization profile, all giving the samecorrect relation Therefore, it seems to be just a matter of mathematical tastewhich expression one should adopt However, the situation becomes a littledifferent at general points different from the critical point For the sake ofclarity, let us take, as an example, (14) in [13], which, when we adopt theexpression (56), gives an approximate free energy in the ferroelectric phase alittle below the critical point In this case, one is not allowed to change thetemperature, thickness or extrapolation length independently, but insteadthey must be varied so as to keep a definite mutual relation demanded bythe boundary condition On the other hand, if one adopts the expression (59)

or (65), one becomes able to choose such physical parameters independentlyregardless of the others, since the deviation from the relation demanded bythe boundary condition is all absorbed in a mathematical parameter such as

h or K This seems important from the viewpoint of experiments.

6 Concluding Remarks

In this review, we have described some theoretical consequences derived fromthe Tilley–Zeks model for the equilibrium state of thin films Here we haveconsidered mainly cases where the transition in the bulk is of the second order,

in the way that Scott et al did, pointing out that there is only one transitionparameter in the Tilley–Zeks model, and the surface and bulk polarizationsare not independent quantities, but rather are uniquely interrelated by a

function governed by L, δ, α and some material constants such as β and κ.

Ishibashi and Iwata presented another interpretation of these two-step sitions, using the effective Landau potential expanded to the tenth order in

tran-the polarization p, but tran-the reducibility of tran-the Landau–Ginzburg potential of

the Tilley–Zeks model in the first-order transition case to such an effectiveLandau potential has not yet been clarified

Depolarization fields may play an important role in thin films, especiallywhen the polarization is perpendicular to the surface; in other words, thespatial modulation of the polarization is longitudinal [4,9,21] The depolar-ization field may suppress the transition into the ferroelectric phase, or causethe ferroelectric thin film to be divided into many 180◦domains if the surface

charges are not completely compensated However, we shall not get into thedetails here, though they are certainly important, so interested readers arereferred to [4] and [21]

It may also be of interest to examine the influence on Tilley–Zeks films

of an applied field, weak or strong, and several studies have already beenreported Interested readers are also referred to [21]

Acknowledgements

I would like to express sincere thanks to Professor D R Tilley, who troduced me to his interesting model of ferroelectric thin films, for criticalreading of the manuscript and correcting many misunderstandings of mine,and to Professor H Orihara, Hokkaido University, for his stimulating argu-ments in the course of cooperative analyses of the model and of writing thisreview

in-References

[1] J Scott, C A Araujo: Science 246, 1400 (1989) 3

[2] J Scott: Ferroelectr Rev 1, 1 (1998) 3

[3] J Scott:Ferroelectric Memories (Springer, Berlin 2000) 3,16

[4] R Kretschmer, K Binder: Phys Rev B 20, 1065 (1979) 3,20

[5] D Tilley, B Zeks: Solid State Commun 49, 823 (1984) 3

[6] D Tilley: Solid State Commun 65, 657 (1988) 3

Theoretical Aspects of Phase Transitions in Ferroelectric Thin Films 21

[7] D Tilley, B Zeks: Ferroelectrics 134, 313 (1992) 3

[8] D Tilly:Ferroelectric Ceramics (Birkh¨auser, Basel 1993) p 163 3

[9] D Tilley: Ferroelectric Thin Films (Gordon and Breach, Amsterdam 1996)

p 12 3,6,20

[10] Y Ishibashi, H Orihara, D Tilley: J Phys Soc Jpn 67, 3292 (1998) 3

[11] E K Tan, J Osman, D Tilley: Solid State Commun 116, 61 (2000) 3,20

[12] E K Tan, J Osman, D Tilley: Solid State Commun 117, 59 (2001) 3,20

[13] L H Ong, J Osman, D Tilley: Phys Rev B 63, 144109 (2001) 3,19

[14] Y Ishibashi, H Orihara, D Tilley: J Phys Soc Jpn 71, 1471 (2002) 3,14,

15

[15] K H Chew, Y Ishibashi, F Shin, H Chan: J Phys Soc Jpn 72, 2974 (2003)

3,15,16

[16] P Ghosez, K Rabe: Appl Phys Lett 76, 2767 (2000) 13

[17] N Yanase, K Abe, N Fukushima, T Kawakubo: Jpn J Appl Phys 38, 5305

(1999) 13

[18] Y Ishibashi, V Dvorak: J Phys Soc Jpn 44, 32 (1978) 19

[19] J Scott, H Duiker, P Beale, B Pouligny, K Dimmler, M Parris, D

But-lerand, S Eaton: Physica B 150, 160 (1988) 20

[20] Y Ishibashi, M Iwata: J Phys Soc Jpn 71, 2576 (2002) 20

[21] W Zhong, B Qu, P Zhang, Y Wang: Phys Rev B 50, 12375 (1994) 20

film thickness, dependence of

ferroelec-tric properties on,3

Jacobian elliptic function,6

Landau free energy,4

Chemical Solution Deposition

of Layer-Structured Ferroelectric Thin Films

Shin-ichi Hirano1, Takashi Hayashi2, Wataru Sakamoto3,

Koichi Kikuta1, and Toshinobu Yogo3

1 Graduate School of Engineering, Nagoya University,

Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan

{hirano,kik}@apchem.nagoya-u.ac.jp

2

Department of Materials Science and Engineering,

Shonan Institute of Technology

1-1-25 Tsujido-Nishikaigan, Fujisawa, Kanagawa 251-8511, Japan

hayashi@mate.shonan-it.ac.jp

3 EcoTopia Science Institute, Nagoya University,

Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan

{sakamoto,yogo}@esi.nagoya-u.ac.jp

Abstract Ferroelectric rare-earth-doped Bi4Ti3O12thin films have been fully prepared on Si-based substrates by using metallo-organic precursor solutions.The pyrolysis behavior of (Bi,R)4Ti3O12precursors depends upon the starting rareearth source, which strongly affects the surface morphology of the synthesized film.Among the (Bi,R)4Ti3O12films, BNT thin films reveal the most homogeneous andsmooth surfaces Single-phase (Bi,R)4Ti3O12 films of Bi-layered perovskite havebeen crystallized on Si-based substrates Rare-earth-doped BIT thin films showdifferent crystal orientations dependent upon the substituent ion BIT and BLTthin films exhibit strong (00l) peaks, while BNT, BST and BGT thin films have

success-a msuccess-arked (117) preferred orientsuccess-ation Among the rsuccess-are-esuccess-arth-doped BIT thin films,BNT thin films show the best saturation properties of the ferroelectrics with a large

Prand smallEcfor low applied voltages However, low-temperature-processed BNTfilms do not exhibit enough ferroelectricity From further investigation of BNT films,the surface morphology and ferroelectric properties can be improved by optimiza-tion of the Ge doping in the BNT, particularly in the case of BNT-based thin filmsprepared at low temperatures Furthermore, excimer UV irradiation of as-depositedfilms is very effective in removing the residual organic groups in the precursor filmand in improving the microstructure and ferroelectric properties of the resultantBNT thin film The use of excimer UV irradiation, further, leads to the easy forma-tion of single-phase BIT-based thin films exhibiting excellent ferroelectric propertiesand a homogeneous microstructure with uniform fine grains at low temperatures.The layer-structured ferroelectric (Bi,R)4Ti3O12films developed in this study,especially the BNT-based films, are found to have potential for application in severalelectric thin-film devices utilizing ferroelectricity, such as the FeRAM

1 Introduction

Thin-film processing is quite important for the development of the turization and hybridization of electronic devices with low consumption of

minia-M Okuyama, Y Ishibashi (Eds.): Ferroelectric Thin Films,

Topics Appl Phys 98, 25–59 (2005)

26 Shin-ichi Hirano et al.

energy (low operating voltage) In this case, functional materials with sired properties are required for applications at a submicron level or less.Processing techniques for thin films have also been receiving great attentionfor applications in semiconductor memories, optoelectronic devices, electroniccomponents, display devices, magnetic devices, sensors and emerging areas.Low-temperature thin-film processing also requires precise control of chemi-cal composition and high crystallinity The various techniques available todayfor the fabrication of thin films are noticeably more varied in type and in so-phistication than those of several decades ago Better equipment and moreadvanced techniques have, undoubtedly, led to higher-quality films, and in-deed may be a primary factor in the now routine achievement of desiredfunctionalities in thin films (50 nm or greater) prepared by a selection ofdifferent methods

de-1.1 The Chemical Solution Deposition Process

The chemical solution deposition (CSD) process, which includes the sol–gelprocess, is one of the most common processes used as a fabrication methodfor thin films This process can be widely used for optical, electrical, magnet-ical, mechanical and catalyst applications The important advantages of thechemical solution process are high purity, good homogeneity, lower processingtemperatures, precise composition control for the preparation of multicompo-nent compounds, versatile shaping, and preparation with simple and cheapapparatus, compared with other methods However, the more the number

of elements, the more complicated the solution chemistry, leading to ficult problems in obtaining the desired crystalline phase Therefore, it isrequired to design the metal-organic precursors through reaction control ofthe metal–oxygen–carbon bonds of the component substances and to investi-gate solutions of multicomponent systems Also, the crystallization behavior

dif-of precursor films is complicated, so the investigation dif-of the crystallizationprocess is key for the synthesis of thin films with high quality

The first report on chemical solution processing of ferroelectric thin filmwas published for the synthesis of BaTiO3 films by Fukushima [1] in 1976.Fukushima used a mixture of metal alkoxide and inorganic-salt precursors forthe fabrication of BaTiO3 films Application of sol–gel processing for PZT

thin films started in 1984 with a report by Fukushima et al [2], followed

by Budd et al [3] in 1985 Meanwhile, the chemical processing of thin films

of other ferroelectric oxides has made remarkable progresses Ferroelectricthin films ranging from polycrystalline to texture-oriented polycrystalline andepitaxial in nature have been synthesized for 20 years

Similary to other thfilm deposition techniques, the CSD process, cluding sol–gel, is essentially a mass transport process The transformation

in-of a liquid solution to a solid crystalline film is accomplished through threesteps:

Chemical Solution Deposition 27

Fig 1 Process flow diagram for the fabrication of ferroelectric thin films by

chem-ical solution deposition

1 Precursor materials are dissolved in a homogeneous solution, thus ing molecular-level mixing of different precursor compounds

assur-2 Mass transport is completed by spin- and dip-coating of a thin layer ofthe solution onto the substrate surface A thin layer of an amorphous gelfilm is formed on the substrate

3 The as-deposited thin film, together with the substrate, is then heated

to cause densification and crystallization of the film In this process, anelectric furnace or a focused infrared-light furnace under a controlledatmosphere is usually used; sometimes a UV light irradiation process isalso applied to cause the condensation and pyrolysis of the precursor thinfilm to proceed

In the CSD process, the starting raw materials are not only mixed at

a molecular level in the solution, but also reacted to cause an appropriatechemical modification of the metallo-organic complexes, leading to the devel-opment of new molecular engineering The chemically designed new precur-sors allow chemical solution preparation of the desired materials in the form

of fine powders, fibers or films Figure1 illustrates the general flow diagramfor the fabrication of thin films by chemical solution processing via metallo-organics The intermediate compound, for example a complex alkoxide, canusually be described as a homogeneous solution, which is very important andeffective for preparing chemically homogeneous thin films

28 Shin-ichi Hirano et al.

1.2 Representative Ferroelectric Thin Films for Memory Devices

Ferroelectric thin films have been receiving significant attention for ous applications, such as ferroelectric random access memories (FeRAMs).FeRAMs are extremely attractive memories because of their nonvolatility,lower working voltage and higher access speed [4] Ferroelectric thin films forFeRAMs are required to have excellent ferroelectric properties (large rema-

vari-nent polarization (Pr), small coercive field (Ec) and fatigue-free properties)and the ability to be crystallized at a low processing temperature

As candidate materials for FeRAMs, Pb(ZrxTi1−x)O3 (PZT) andSrBi2Ta2O9 (SBT) thin films have been studied extensively [4,5] AlthoughPZT thin films have many advantages, such as a large remanent polarizationand low processing temperature, PZT thin films on Pt electrodes are known

to show ferroelectric fatigue phenomena [5] In addition, PZT thin films tain a toxic and volatile element (Pb) On the other hand, although SBT thinfilms have excellent fatigue-free properties [5], SBT films tend to crystallize

con-to an undesirable phase, such as a fluoride phase, during the crystallizationprocess and have a higher crystallization temperature compared with PZT

1.3 Layer-Structured Bi 4 Ti 3 O 12 -Based Thin Films

Among several candidates for ferroelectric materials, Bi4Ti3O12(BIT) is tracting significant attention Similar to SBT, BIT has a layered perovskitestructure consisting of triple TiO6 octahedra in perovskite-like layers sep-arated by Bi2O2 layers BIT has a large remanent polarization, small co-ercive field and high Curie temperature Furthermore, BIT thin films areknown to crystallize at a lower temperature compared with SBT thin films.However, in its structure, BIT contains unstable Bi ions, which are easilyevaporated during the heating process This volatility of Bi ions affects theferroelectric and fatigue characteristics of thin films Bi3+ ions in the per-ovskite blocks of BIT can be preferentially substituted by trivalent rare earthions, such as La3+, Nd3+ and Sm3+, for the improvement of the ferroelec-tric properties Recently, improvement of the electrical properties of BITthin films by rare earth ion modification has been reported by many re-searchers [6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26]

at-In addition, the substitution of Bi3+ by rare earth ions with a smaller ionicradius is expected to be effective in improving the ferroelectric properties

In such cases, the chemical solution deposition method described in theprevious section is considered to be very suitable for the fabrication of fer-roelectric BIT-based thin films, because this process has several advantagesover other fabrication methods [7,10,16,18,19,20] In the CSD process,the preparation of high-quality films with the desired crystallographic phase,crystallinity, crystal orientation, microstructure and ferroelectric propertiesdepends strongly upon the factor of the synthesis of an appropriate precur-sor, such as the selection of the starting materials and the optimization of

Chemical Solution Deposition 29the chemical composition, as well as the coating and crystallization condi-tions, as shown in Fig 1 Although the preparation of BIT-based films by

a CSD method using nitrates as starting materials has been reported [16],the processing temperature is as high as 650◦C to 800◦C A high-temper-

ature annealing process is not acceptable for high-density memory devices,because the designed structure in a silicon semiconductor device is often seri-ously damaged during the heating process Thus, low-temperature processing

of BIT-based thin films with excellent ferroelectricity is strongly required

In this Chapter, we deal with the fabrication of rare-earth-ion-modifiedBIT thin films on Si-based substrates, especially from the viewpoint of fer-roelectric-memory applications, by the CSD method using metallo-organicprecursor solutions, and the resulting properties Furthermore, the doping of

Ge into BIT and ultraviolet (UV) light irradiation processes for the perature processing of BIT-based thin films, particularly Nd-modified BITthin films with high quality, are described

low-tem-2 Rare-Earth-Ion-Modified Bi4Ti3O12 Thin Films

In this section, mainly the synthesis of thin films rare-earth-ion-modified BIT,

(Bi,R)4Ti3O12 (R = La, Nd, Sm, Gd), on Si-based substrates by the CSD

method is described The pyrolysis and crystallization behavior of organic precursor powders and films is investigated The ferroelectric prop-

metallo-erties and microstructure of the CSD-derived (Bi,R)4Ti3O12 films are alsoevaluated

Table 1 Metallo-organic compounds used for the synthesis of (Bi,R)4Ti3O12

R source Bi source Ti source

BLT (Bi3.25La0.75Ti3O12) La(OiPr)3 Bi(OtAm)3 Ti(OiPr)4

BNT (Bi3.25Nd0.75Ti3O12) Nd(OAc)3 Bi(OtAm)3 Ti(OiPr)4

BST (Bi3.25Sm0.75Ti3O12) Sm(OAc)3 Bi(OtAm)3 Ti(OiPr)4

BGT (Bi3.25Gd0.75Ti3O12) Gd(OiPr)3 Bi(OtAm)3 Ti(OiPr)4

2.1 Chemical Processing of (Bi,R)4 Ti 3 O 12 Precursor Solutions, Powders and Thin Films

Figure 2 illustrates the experimental procedure used for the

prepara-tion of (Bi,R)4Ti3O12 precursor solutions, powders and thin films ble 1 shows the starting sources of the (Bi,R)4Ti3O12 precursor solutions.Nd(OAc) and Sm(OAc) were prepared from Nd(CH COO) · H O and