Ferroelectric Thin Films: Basic Properties and Device Physics for Memory Applications (Topics in Applied Physics)

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Topics in Applied Physics Volume 98

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Topics in Applied Physics Topics in Applied Physics is a well-established series of review books, each of which presents a comprehensive survey of a selected topic within the broad area of applied physics. Edited and written by leading research scientists in the field concerned, each volume contains review contributions covering the various aspects of the topic. Together these provide an overview of the state of the art in the respective field, extending from an introduction to the subject right up to the frontiers of contemporary research. Topics in Applied Physics is addressed to all scientists at universities and in industry who wish to obtain an overview and to keep abreast of advances in applied physics. The series also provides easy but comprehensive access to the fields for newcomers starting research. Contributions are specially commissioned. The Managing Editors are open to any suggestions for topics coming from the community of applied physicists no matter what the field and encourage prospective editors to approach them with ideas.

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Dr. Hans J. Koelsch

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Assistant Editor Adelheid H. Duhm Springer-Verlag GmbH Tiergartenstr. 17 69121 Heidelberg Germany Email: [email protected]

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 [email protected]

Professor Yoshihiro Ishibashi Aichi Shukutoku University Nakakute-cho 480-1197 Aichi, Japan [email protected]

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. Springer is a part of Springer Science+Business Media springeronline.com © Springer-Verlag Berlin Heidelberg 2005 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: DA-TEX · Gerd Blumenstein · www.da-tex.de ockler GbR, Leipzig Production: LE-TEX Jelonek, Schmidt & V¨ Cover design: design & production GmbH, Heidelberg Printed on acid-free paper

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543210

Preface

The prominent properties of ferroelectric materials such as polarization hysteresis, large dielectric constant, and remarkable piezoelectric, pyroelectric and electro-optical effects can all be applied in electronic devices. Especially in the form of thin films, ferroelectrics show excellent features when combined with Si active electronic devices such as nonvolatile memories, capacitors, surface acoustic wave (SAW) filters, ultrasonic and infrared sensors, optical modulators, and switches. Among these, nonvolatile memories utilizing ferroelectric thin films have attracted special attention recently because of their low power dissipation and fast switching. In order to realize the ultralarge scale integration of ferroelectric thin-film memory devices, which might be competitive with various current dynamic random access memories, comprehensive studies of ferroelectric thin films ranging from basic physics to device physics are indispensable. A tremendous amount of research on ferroelectric thin films and their application to memory devices has been carried out. This book gathers together 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 characterization of device structures. In Part I, the phase transition of a ferroelectric thin film is analyzed in detail on the basis of the Tilley–Zeks model, and its characteristic features are clarified. In Part II, preparation methods for ferroelectric thin films such as chemical solution, metal-organic chemical vapor deposition (MOCVD) and sputtering are described for the preparation of PZT and Bi-layer-structured ferroelectric thin films. Island structures of nanometer size are observed in the initial nucleation stage and their ferroelectric behavior is discussed. In Part II, a description is also given of the spatial polarization distribution observed by scanning nonlinear dielectric microscopy, which has ultrahigh spatial resolution, and the applicability of the polarization domains to disk memory with a size of the order of Tbits is proved. In Part III, topics on relaxor ferroelectrics showing dispersive dielectric phenomena are described. The colossal piezoelectric property is analyzed in the vicinity of the morphotropic phase boundary. Domain structures in relaxor ferroelectrics are analyzed in detail, and the mechanism has been clarified by analyzing di-

VI

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electric properties of superlattice structures with various kinds of ordering periodicity. In Part IV, metal–ferroelectric–insulator–semiconductor (MFIS) structures in ferroelectric-gate FETs are studied. The stability of the MFIS structure is analyzed theoretically, considering the space charge distribution. The memory retention of the MFIS structure has been analyzed, considering leakage current through the ferroelectric junction, and long retention has been achieved in structures using SrBi2 Ta2 O9 and YMnO3 thin films. This book contains valuable information on both theoretical approaches and experimental efforts, and we hope that the book will offer some help not only to beginners but also to specialists in ferroelectric physics and engineering 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 Thin Films and Their Application to Next-Generation Memory Devices”, sponsored 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 to Drs. Kaoru Yamashita and Takeshi Kanashima for their tremendous efforts in arranging the manuscripts for this book and taking care of the research project. Without their contribution, this book might not have come out in due time. This publication was supported by Grant-in-Aid for Publication of Scientific Research Results 165284, 2004, sponsored by the Japan Society for the Promotion of Science (JSPS). Osaka, Nagoya, January 2005

Masanori Okuyama Yoshihiro Ishibashi

Contents

Part I Theoretical Aspects Theoretical Aspects of Phase Transitions in Ferroelectric Thin Films Yoshihiro Ishibashi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 The Tilley–Zeks Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Transition Temperature and Polarization Profile . . . . . . . . . . . . . . . . . 3.1 The Case of Zero Extrapolation Length (δ+ = δ− = 0) . . . . . . . 3.2 The Case of Positive Extrapolation Length (δ+ = δ− = δ > 0) 3.3 The Case of Negative Extrapolation Length (δ+ = δ− = δ < 0) 4 Asymmetric Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 The Positive–Positive Case (δ+ > 0, δ− > 0) . . . . . . . . . . . . . . . . 4.2 The Negative–Negative Case (δ+ < 0, δ− < 0) . . . . . . . . . . . . . . 4.3 The Mixed Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 The Case of |δ− | < |δ+ | . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 The Case of |δ− | > |δ+ | . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Notes on Exact and Approximate Polarization Profiles . . . . . . . . . . . 6 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 3 4 5 6 9 12 14 15 15 15 16 16 16 19 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 The Chemical Solution Deposition Process . . . . . . . . . . . . . . . . . 1.2 Representative Ferroelectric Thin Films for Memory Devices . 1.3 Layer-Structured Bi4 Ti3 O12 -Based Thin Films . . . . . . . . . . . . . 2 Rare-Earth-Ion-Modified Bi4 Ti3 O12 Thin Films . . . . . . . . . . . . . . . . .

25 25 26 28 28 29

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2.1

Chemical Processing of (Bi,R)4 Ti3 O12 Precursor Solutions, Powders and Thin Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Crystallization and Pyrolysis Behavior of (Bi,R)4 Ti3 O12 Precursors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Crystallization of (Bi,R)4 Ti3 O12 Thin Films . . . . . . . . . . . . . . . 2.4 Surface Morphologies of (Bi,R)4 Ti3 O12 Films . . . . . . . . . . . . . . 2.5 Phase Transition and Ferroelectric Properties . . . . . . . . . . . . . . 2.6 Effect of Nd Content on Nd-Modified BIT (BNT) Thin Films 2.7 Effect of Processing Temperature on Nd-Modified BIT (BNT) Thin Films . . . . . . . . . . . . . . . . . . . 3 Ge-Doped (Bi,Nd)4 Ti3 O12 Thin Films . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Fabrication of (Bi,Nd)4 (Ti,Ge)3 O12 Films . . . . . . . . . . . . . . . . . . 3.2 Microstructure and Electrical Properties of (Bi,Nd)4 (Ti,Ge)3 O12 Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 UV Processing of (Bi,Nd)4 Ti3 O12 (BNT) Thin Films . . . . . . . . . . . . 4.1 Changes in the Chemical Bonding of Excimer-UV-Irradiated BNT Precursor Films . . . . . . . . . . . . 4.2 Effect of UV Light Irradiation on the Crystal Orientation of the Resultant Thin Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Surface Morphology of UV-Light-Irradiated BNT Thin Films . 4.4 Ferroelectric Properties of UV-Irradiated BNT Thin Films . . . 4.5 Fatigue and Leakage Current Properties of UV-Irradiated BNT Thin Films . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pb-Based Ferroelectric Thin Films Prepared by MOCVD Masaru Shimizu, Hironori Fujisawa, Hirohiko Niu . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Microscopic Observation of the Initial Growth Stages of PbTiO3 and PZT Thin Films on Various Substrates . . . . . . . . . . . . . . . . . . . . . 3.1 Growth Process of PbTiO3 and PZT Thin Films on Polycrystalline Pt/SiO2 /Si . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Growth Process of PZT Thin Films on SrTiO3 Single Crystals 3.3 Growth Process of PZT Thin Films on Epitaxial SrRuO3 /SrTiO3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Epitaxial PZT Ultrathin Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Preparation of PZT Ultrathin Films on SrRuO3 /SrTiO3 . . . . . 4.2 Ferroelectric Properties of PZT Ultrathin Films . . . . . . . . . . . . 5 Self-Assembled PbTiO3 and PZT Nanostructures and Their Ferroelectric Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Preparation of Self-Assembled PbTiO3 and PZT Nanostructures on Various Substrates . . . . . . . . . . . . . 5.2 Piezoelectric and Ferroelectric Properties of PbTiO3 Nanostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

29 31 33 35 36 39 41 43 43 45 46 47 48 50 51 54 56 59 59 61 62 62 64 65 67 67 67 71 71 72

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References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Spontaneous Polarization and Crystal Orientation Control of MOCVD PZT and Bi4 Ti3 O12 -Based Films Hiroshi Funakubo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Spontaneous Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 PZT Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Bi4 Ti3 O12 -Based Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Remanent Polarization of Polycrystalline Ferroelectric Films Prepared on Si Substrates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 PZT Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Bi4 Ti3 O12 -Based Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Low-Temperature Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 PZT Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Bi4 Ti3 O12 -Based Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rhombohedral PZT Thin Films Prepared by Sputtering Masatoshi Adachi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Experimental Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 PZT Films on (Pb,La)TiO3 (PLT)/Pt/Ti/SiO2/Si and Ir/SiO2 /Si . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Rhombohedral PZT on (111) Ir/(111) SrTiO3 and (100) Ir/(100) SrTiO3 Substrates . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scanning Nonlinear Dielectric Microscopy Yasuo Cho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Principle and Theory of SNDM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Nonlinear Dielectric Imaging with Subnanometer Resolution . 2.2 Comparison between SNDM Imaging and Piezoresponse Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Higher-Order Nonlinear Dielectric Microscopy . . . . . . . . . . . . . . . . . . . 3.1 Theory of Higher-Order Nonlinear Dielectric Microscopy . . . . . 3.2 Experimental Details of Higher-Order Nonlinear Dielectric Microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Three-Dimensional Measurement Technique . . . . . . . . . . . . . . . . . . . . . 4.1 Principle and Measurement System . . . . . . . . . . . . . . . . . . . . . . . 4.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Tb/in2 Ferroelectric Data Storage Based on SNDM . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77 77 77 78 80 83 83 85 86 87 87 88 91 91 92 93 101 103 105 105 106 107 111 112 112 113 115 116 117 118 123

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Part III Relaxors Analysis of Ferroelectricity and Enhanced Piezoelectricity near the Morphotropic Phase Boundary Makoto Iwata, Yoshihiro Ishibashi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Free Energy and Phase Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Dielectric Constants, Elastic Constants and Electromechanical Coupling Constants . . . . . . . . . . . . . . . . . . . . . 4 Polarization Reversal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Enhanced Piezoelectricity Under an Oblique Field . . . . . . . . . . . . . . . 6 Magnetostrictive Alloys of Rare-Earth–Fe2 Compounds . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Correlation Between Domain Structures and Dielectric Properties in Single Crystals of Ferroelectric Solid Solutions Naohiko Yasuda . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Single-Crystal Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Flux Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Solution Bridgman Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Domain Structures in the PIN–PT Solid Solution . . . . . . . . . . . . . . . . 4.1 Temperature Dependence of the Permittivity, Domain Structure and Birefringence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 The Effect of a dc Bias Field on the Domain Structure . . . . . . 5 Domain Structures in a (001) Plate of a PMN–PT Solid Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Relaxor Superlattices: Artificial Control of the Ordered– Disordered State of B-Site Ions in Perovskites Hitoshi Tabata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Relaxor Behavior in Perovskite-Type Dielectric Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Artificial Control of the Ordered/Disordered State of B-Site Ions in Ba(Zr,Ti)O3 by a Superlattice Technique . . . . . . . . . . . . . . . . . . . . 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

127 127 128 131 134 140 144 145

147 147 148 148 149 150 150 150 152 156 158

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References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 Part IV Ferroelectric–Insulator–Semiconductor Junctions Physics of Ferroelectric Interfaces: An Attempt at Nanoferroelectric Physics Yukio Watanabe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Spontaneous Polarization and the Ferroelectric Surface . . . . . . . . . . . 2 Electric Field in and Arising from a Ferroelectric . . . . . . . . . . . . . . . . 2.1 Ferroelectric Covered by Metal (M/F) . . . . . . . . . . . . . . . . . . . . . 2.2 Ferroelectric Covered by Semiconductor (S/F) . . . . . . . . . . . . . . 2.3 Ferroelectric Covered by Insulator or Nothing (I/F), and Depolarization Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Surface Relaxation Modeling of I/F Structure and Generalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Ferroelectric Field Effect Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Domains, Depolarization Instability, and Memory Retention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Epitaxial Strain and the Surface Relaxation ∇P Effect . . . . . . . . . . . 5.1 Epitaxial Strain vs. Depolarization Instability . . . . . . . . . . . . . . 5.2 The Surface Relaxation ∇P Effect Can Be Unimportant . . . . . 6 Finite Band Gap Energy and Redefinition of “Insulator” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Reexamination of the Depolarization Field . . . . . . . . . . . . . . . . . 6.2 Relaxation Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Insulator Under Static Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Ferroelectric Under Static Field . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 The Natural Choice of a Ferroelectric . . . . . . . . . . . . . . . . . . . . . 7 Modeling of F/I/S Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Mathematical Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Comparison with Experiments: Leakage Current and Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Numerical Results for Typical Structures . . . . . . . . . . . . . . . . . . 8.2 Retention and Leakage Current . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3 Contradiction and Solution: Miller–McWhorter Theory . . . . . . 9 Intrinsic 2D Electron Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Ferroelectric Coupled to Free Electrons: Ferroelectric 2D Metal . . . 11 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

177 177 178 178 179 179 180 181 181 183 183 184 185 185 186 186 186 187 188 188 191 191 191 192 193 195 196 196 196

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Preparation and Properties of Ferroelectric–Insulator– Semiconductor Junctions Using YMnO3 Thin Films Norifumi Fujimura, Takeshi Yoshimura . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Material Design of Ferroelectric and Insulator Layers for MF(I)S Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Fabrication of YMnO3 Epitaxial Films . . . . . . . . . . . . . . . . . . . . . . . . . 4 Fabrication and Properties of Y2 O3 Films on Si . . . . . . . . . . . . . . . . . 5 Fabrication of YMnO3 /Y2 O3 /Si Capacitors . . . . . . . . . . . . . . . . . . . . . 6 Investigation of Retention Characteristics of YMnO3 /Y2 O3 /Si Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Influence of Leakage Current on the Retention Characteristics of YMnO3 /Y2 O3 /Si Capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

199 199 200 204 206 208 210 211 217

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 SiO2 Film . . . . . . . . . . . . . . . 230 4 Experimental Improvement of Retention Time by O2 Annealing . . . 231 4.1 Effect of O2 Annealing 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 O2 Annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

Contents

4.5 More Improvement by Rapid Thermal Annealing . . . . . . . . . . . Photoyield Spectroscopic Studies on SBT Thin Films . . . . . . . . . . . . 5.1 Principle of Photoyield Spectroscopy of SBT Films . . . . . . . . . . 5.2 Effects of O2 Annealing on SBT Thin Films Studied by UV-PYS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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234 235 235 236 238

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 [email protected] 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 the second order. A surface is characterized by an extrapolation length δ, 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 negative δ 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 extensive use 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 of the data on bulk ferroelectrics, it was natural that extension to surfaces, films and superlattices should be sought. In fact, Kretschmer and Binder [4] set out a framework for semi-infinite materials by including in the free energy functional a contribution from the inhomogeneity of the polarization p, treating p as a function of the coordinate z. Tilley and Zeks [5, 6, 7, 8, 9] extended the study of Kretschmer and Binder, mostly to symmetric-surface cases, and their coworkers have also performed detailed analyses of the model to cases where the phase transition in the bulk is of the second order as well as of the first order [10, 11, 12, 13, 14, 15]. In this Chapter, for convenience, we refer to the form of the free energy functional adopted by Tilley and Zeks as the Tilley–Zeks model. There are several important quantities for specifying the physical properties of thin films. These are the dependences of the transition temperature and the polarization profile in the film on the film thickness and other parameters involved in the model. At present the Tilley–Zeks model is almost the only well-defined model with which most of the questions mentioned above can be answered without much ambiguity and much approximation. However, there may still be some need to improve the Tilley–Zeks model or to produce new, better models in order to discuss the experimental data in detail. In this situation, in the present review we first present what can be concluded from the original Tilley–Zeks model about phase transitions in ferroM. Okuyama, Y. Ishibashi (Eds.): Ferroelectric Thin Films, Topics Appl. Phys. 98, 3–23 (2005) © Springer-Verlag Berlin Heidelberg 2005

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Yoshihiro Ishibashi

electric thin films, and then mention an extension of the model to incorporate asymmetric 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 2 L/2 p2− α 2 β 4 κ ∂p κ p2+ 1 p + p + + dζ + , (1) f= L 4 2 ∂ζ 2 δ+ δ− −L/2 2 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 the extrapolation length. In (1), it is assumed that α = a (T − T0 )

(2)

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 αc and the polarization profile p (z) below the transition temperature. For this purpose let us minimize the free energy, i.e., δf = 0; δp (z)

(3)

we then obtain a differential equation called the Euler–Lagrange equation, and have to solve it under given boundary conditions. The boundary conditions in the present case are ∂p− p− = ∂z δ−

at z = −L/2

(4)

and p+ ∂p+ =− ∂z δ+

at z = L/2 .

(5)

The physical meaning of the term “extrapolation length” or why it is called the extrapolation length will be easily understood from Fig. 1. The 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+ and p− , and the extrapolation lengths δ+ and δ−

is larger than that in the bulk for a negative extrapolation length, while it is smaller 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 κ , (6) ξ= |α| which is composed of a material constant κ and the temperature α, an external parameter. The phase transition and the physical properties of the present 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 derived from (2): αp + βp3 − κ

∂2p = 0, ∂z 2

(7)

integration of which yields κ 2

∂p ∂z

2 =

α 2 β 4 p + p + c, 2 4

(8)

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− .

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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 in the sense that we can obtain a simple but general idea about the effect of thickness 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., p (0) = pc ,

(9)

and then the integration constant c is given by c=

α 2 β 4 p + p . 2 c 4 c

(10)

On denoting the polarization of the bulk by pb as p2b = −

α β

(11)

and on putting k2 =

p2c , 2p2b − p2c

(12)

c can be rewritten as c = −βp4b

k2 (1 + k 2 )2

.

(13)

Let us now put P (z) = pc sin θ(z) , and then θ(z) can be obtained from z α 1 + k2 θ dθ − dz = . 2κ −L/2 2 0 1 − k 2 sin2 θ Thus, we can find p(z) by using (15), as −α L p(z) = pc sn z + , z < 0, κ (1 + k 2 ) 2

(14)

(15)

(16)

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


7

Fig. 2. Polarization profiles in the case of δ = 0 for various film thicknesses; the thickness can be seen from the z-value where p becomes zero

−κ 1 + k 2 K(k) α = 2ξ 1 + k 2 K(k) ,

L=2

(17)

where K(k) is the complete elliptic integral of the first kind. This equation implies that the relationship between the two length scales ξ and L is expressible in terms of a parameter k at a given temperature. The critical thickness Lc , below which pc becomes zero or ferroelectricity is totally lost, is given as −κ π (18) Lc = α by putting k = 0 into (17). Namely, it is found that the critical thickness decreases with decreasing temperature (|α| increasing). The value of p(z) for various thicknesses L can be obtained from (14)–(16) and is shown in Fig. 2, where the z-coordinate where p vanishes corresponds to L/2. The average energy density is obtained from 2κ f¯ = L

0

−L/2

dp dz

2 dz + c ,

which can be reduced to 2k βκ 2 f¯ = pc p2b I(k) + c , L 2 1 + k2

(19)

(20)

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Yoshihiro Ishibashi

Fig. 3. The average free energy as a function of the inverse film thickness in the case of δ = 0

where I(k) is defined as π/2 cos2 θ 1 − k 2 sin2 θ dθ . I(k) =

(21)

0

The thickness dependence of f¯ is shown in Fig. 3. If we regard the disappearance of the polarization with decreasing thickness as a “thickness transition”, 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 multiplying 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 infinite space. The average polarization is given by 2pc 0 sin θ(z) dz , (22) p¯ = L −L/2 which can be reduced to the form 2 2κ p¯ = kJ(k) , L β

(23)

where J(k) is defined by J(k) =

1 1+k ln . 2k 1 − k

(24)

The thickness dependence of p¯ is shown in Fig. 4. The temperature dependence of the spontaneous polarization in thne vicinity of the transition temperature obviously indicates that the transition is of the second order.


9

Fig. 4. The average polarization as a function of inverse film thickness in the case of δ = 0

3.2 The Case of Positive Extrapolation Length (δ+ = δ− = δ > 0) In this case, by symmetry, we write the surface polarization as p+ = p− = ps

(25)

(the subscript “s” means “surface”), and it is obtained by using (8) and (4) as

2 2 2 2 (26) ps = pb + pe − (p2b + p2e ) + (p4c − 2p2b p2c ) , where use has been made of a polarization pe , composed of the model parameters, defined by p2e =

κ . βδ 2

(27)

As in the previous case, p(z) is obtained from p(z) = pc sin θ(z) , and θ is given by z 1 + k2 θ dθ α − dz = , 2κ −L/2 2 θs 1 − k 2 sin2 θ

(28)

(29)

where, in the r.h.s. of (29), the lower limit of integration is not zero, but θs , defined by ps = pc sin θs .

(30)

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Yoshihiro Ishibashi

Fig. 5. Polarization profiles for δ = 1 for various film thicknesses; the thickness can be seen from the z-value where the p-curves terminate

The θs can be expressed, using (26), as pb θs = sin−1 2 pb + p2e

(31)

for pc pb . The critical thickness Lc below which ferroelectricity is lost can be obtained as follows: −κ π (32) − θs Lc = 2 α 2 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 2 βκ 2 κ 2 2 f¯ = (33) kpc pb Is (k) + ps , L 2 1 + k2 2δ where

π/2

cos2 θ

Is (k) =

1 − k 2 sin2 θ dθ .

(34)

θs

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).


11

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

Fig. 7. The average polarization as a function of inverse film thickness for several positive values of δ

The relation between the critical thickness, the temperature and the extrapolation length is shown in Fig. 8. It is readily seen that the critical thickness becomes thinner with increasing extrapolation length for a given temperature (see the α < 0 part of Fig. 8). The thickness transition is found to be also of second order.

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Yoshihiro Ishibashi

Fig. 8. The relation between the critical temperature and thickness for various values of δ

3.3 The Case of Negative Extrapolation Length (δ+ = δ− = δ < 0) In this case the surface polarization is larger than that in the bulk. The transition temperature is higher than that of the bulk. Let us put ps = pc cosh θ(z) ,

(35)

and define θ at the surfaces, θs , by ps = pc cosh θs .

(36)

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, and therefore (4) and (5) can be approximated at the surfaces as κ ps 2 α 2 ps − p2c = , 2 2 δ

(37)

ignoring the fourth-order terms in pc . By using (36) this can be reduced to α sinh2 θs =

κ cosh2 θs . δ2

(38)

Thus, the condition that the above approximation is valid is tanh2 θs =

κ ≤ 1. αδ 2

On the other hand, θ and z are related through

(39)


L/2

dz = 0

√

2κ 0

θ

dθ

.

2α + βp2c cosh2 θ + 1

13

(40)

Therefore, putting pc = 0, we find the relation between L and θs to be κ θs . (41) L=2 α Thus, the critical thickness is given by κ κ −1 Lc = 2 tanh . α αδ 2

(42)

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., pb < pc .

(43)

In this case the surface polarization is given by

2 p2s = p2b + p2e + (p2b + p2e ) + p4c − 2p2c p2b . The z-dependence of θ can be expressed as θ z 2κ dθ

dz = ,

β 0 0 −2p2 + p2 cosh2 θ + 1 b

(44)

(45)

c

and by taking the upper limits of the integration as L/2 and θ, (45) is reduced to θs L/2 2κ dθ

(46) dz =

. β 0 0 −2p2b + p2c cosh2 θ + 1 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 extrapolation length. Before concluding the present section, comments seem to be in order on the negative extrapolation length. It has been reported that the polarization is enhanced near the surface in 4 nm thick PbTiO3 and 12 nm thick BaTiO3 films [16, 17]. This feature of surface-enhanced polarization can certainly be reproduced by the Tilley–Zeks model with a negative extrapolation length. At the same time, however, the model predicts a surface-enhanced polarization not only in thin films but also in bulk materials as well, leading then to a confusing situation where the transition temperature in the “bulk” obtained

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Yoshihiro Ishibashi

by this model is higher (α > 0 for 1/L = 0 in Fig. 8) than that (α = 0) presupposed as the “bulk” transition temperature. This is quite different from the 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 repeatedly mentioned, a negative extrapolation length leads to a higher transition temperature, and the smaller it is in its absolute value the higher the transition temperature becomes. If this trend is extrapolated, an infinitely high transition temperature will result for an infinitely thin film, which, however, seems to the present author to be unphysical. Thus, the case of a negative extrapolation length may be only of academic interest, and to apply the model to more realistic cases, avoiding this sort of confusing and unphysical situation, some sort of amendment of the Tilley–Zeks model or new models to replace it may be needed.

4 Asymmetric Films Following the historical track of the development of theories of thin films, we have so far placed emphasis on thickness transitions at a given temperature and considered cases where the extrapolation length at both surfaces is the same, that is, we have considered symmetric films. But a symmetric film is nothing but a special case of an asymmetric one, and it is probably more appropriate to study asymmetric films, since asymmetry in the extrapolation 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 critical points in terms of the sample thickness and temperature for various cases of the extrapolation length [14]. The mathematical procedures are as follows. After substituting (6) into (1), the average free energy is rewritten as 2 p2− ∂p κ p2+ 1 κ dz + c + + f= L ∂z 2 δ+ δ− 2 2 p ∂p 1 κ p+ = + − . (47) κ dp + c + L ∂z 2 δ+ δ− The integration constant c is given by c=

α 2 β 4 pm + pm 2 4

(48)

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 pm as


f=

A 2 B pm + p4m + · · · , 2 4

15

(49)

where pm plays the role of an effective order parameter [14, 15]. Thus, we have been able to obtain an effective Landau-type free energy function (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 ⎛ ⎞ √ −ακ ⎝ p p b b ⎠, π − sin−1

A= α+ − sin−1

L 2 2 2 p +p p + p2 b

e+

b

(50)

e−

where use has been made of κ 2 , βδ+ κ = 2 . βδ−

p2e+ =

(51)

p2e−

(52)

The transition temperature is always lower than that in the bulk, and is found to decrease with decreasing thickness of the film. 4.2 The Negative–Negative Case (δ+ < 0, δ− < 0) Putting the minimum value of the polarization equal to pm , and adopting a similar procedure, we obtain √ ακ κ κ −1 + tanh . (53) tanh−1 A= α− 2 2 L αδ− αδ+ 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 our previous work [14].

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Yoshihiro Ishibashi

Fig. 9. The order parameter ph adopted in cases of asymmetric extrapolation length with mixed signs

4.3.1 The Case of |δ− | < |δ+ | In this case the minimum value of the polarization is located at z > L/2, outside the film. The coefficient A is given by √ ακ κ κ −1 A= α− − tanh . (54) tanh−1 2 2 L αδ− αδ+ It is found that the transition temperature increases with decreasing thickness. 4.3.2 The Case of |δ− | > |δ+ | In this case the maximum value of the polarization is located at z < −L/2, outside the film. The coefficient A is given by ⎛ ⎞ √ −ακ ⎝ −1 pb p b ⎠. − sin−1

A= α+ sin

(55) L 2 2 2 p +p p + p2 b

e−

b

e+

It is found that the transition temperature decreases with decreasing thickness. 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 the Euler–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.


Tilley and Zeks adopted a polarization profile z p = p0 cos ξ

17

(56)

to obtain the relation between Lc , δc and ξc at the critical point (the subscript “c” means “critical”), and from the boundary condition, the critical relation ξc Lc = (57) tan 2ξc δc is obtained. The polarization profile (56) and, therefore, the relation (57) are both exact only at the critical point. But we may need a further consideration, since the left-hand side of (57) is a periodic function. For example, for a 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 ξc should 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 a higher energy. The necessity for such a selection of a valid unique solution based upon physical considerations as mentioned above, originates from the fact that the polarization 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 method for considering the system, in particular one that is not periodic as in the present 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 the polarization profile of one 180◦ wall in an infinite system, obtained by solving exactly the same Euler–Lagrange equation (7) under a different boundary condition, is of the form z (58) p = p0 tanh √ , 2ξ √ where it should be noted that a factor 1/ 2 appears in the argument of the tanh function. In the light of (58), let us use, instead of (56), z (59) p = p0 cos h , ξ introducing an adjustable parameter h. Since h is a mathematical parameter, nothing to do with physical values set experimentally, we may confine its range to

18

Yoshihiro Ishibashi

0≤h≤

π ξ. L

(60)

The parameter h must be determined by the boundary conditions such that tan

hL ξ = . 2ξ hδ

(61)

When δ = 0, h must be h=

πξ , L

(62)

and so (59) is reduced to p = p0 cos

πz . L

(63)

The critical relation is then easily given as Lc = πξc ,

(64)

which of course coincides with the result from (57). On the other hand, h must vanish when δ = ∞, and then (56) and (59) are both reduced to p = p0 , just a constant. 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 lengths are mutually related by the boundary condition, this is certainly only an appearance. However, it may be useful to pursue the above line further, since the exact solution is not always available. Let us just write the polarization profile with a parameter K as p = p0 cos Kz ,

(65)

instead of (59), confining the range of K to 0 ≤ K ≤ π/L .

(66)

Then, the boundary condition becomes K tan

KL 1 = , 2 δ

and it turns out, therefore, that L 1 K= g , L δ

(67)

(68)

where g is a function only of L/δ. Using K, the critical relation, including temperature, can be obtained as


1 − ξc Kc = 0 .

19

(69)

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 extrapolation 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 understood from the following. Let us now write the polarization profile, including the higher harmonics, as p = a1 cos Kx + a3 cos 3Kx + · · · . Then, the boundary condition becomes

3KL K a1 sin KL 1 2 + 3a3 sin 2 + · · · = , 3KL δ a1 cos KL + a cos + · · · 3 2 2

(70)

(71)

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. This situation is quite similar to the temperature variation of the modulation wavelength 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 same correct relation. Therefore, it seems to be just a matter of mathematical taste which expression one should adopt. However, the situation becomes a little different at general points different from the critical point. For the sake of clarity, let us take, as an example, (14) in [13], which, when we adopt the expression (56), gives an approximate free energy in the ferroelectric phase a little below the critical point. In this case, one is not allowed to change the temperature, thickness or extrapolation length independently, but instead they must be varied so as to keep a definite mutual relation demanded by the boundary condition. On the other hand, if one adopts the expression (59) or (65), one becomes able to choose such physical parameters independently regardless of the others, since the deviation from the relation demanded by the 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 from the Tilley–Zeks model for the equilibrium state of thin films. Here we have considered mainly cases where the transition in the bulk is of the second order,

20

Yoshihiro Ishibashi

though much work has been published on first-order transition cases [11, 12, 19, 20]. As a special phenomenon appearing only in the first-order case, two-step transitions have been reported, one attributed to the transition at the surface and the other to that in the bulk [19]. Recently, however, Ishibashi and Iwata [20] raised a question regarding the validity of assigning two transitions in the way that Scott et al. did, pointing out that there is only one transition parameter in the Tilley–Zeks model, and the surface and bulk polarizations are 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 transitions, using the effective Landau potential expanded to the tenth order in the polarization p, but the reducibility of the Landau–Ginzburg potential of the Tilley–Zeks model in the first-order transition case to such an effective Landau potential has not yet been clarified. Depolarization fields may play an important role in thin films, especially when the polarization is perpendicular to the surface; in other words, the spatial modulation of the polarization is longitudinal [4, 9, 21]. The depolarization field may suppress the transition into the ferroelectric phase, or cause the ferroelectric thin film to be divided into many 180◦ domains if the surface charges are not completely compensated. However, we shall not get into the details here, though they are certainly important, so interested readers are referred 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 been reported. Interested readers are also referred to [21]. Acknowledgements I would like to express sincere thanks to Professor D. R. Tilley, who introduced me to his interesting model of ferroelectric thin films, for critical reading of the manuscript and correcting many misunderstandings of mine, and to Professor H. Orihara, Hokkaido University, for his stimulating arguments in the course of cooperative analyses of the model and of writing this review.

References [1] [2] [3] [4] [5] [6]

J. Scott, C. A. Araujo: Science 246, 1400 (1989) 3 J. Scott: Ferroelectr. Rev. 1, 1 (1998) 3 J. Scott: Ferroelectric Memories (Springer, Berlin 2000) 3, 16 R. Kretschmer, K. Binder: Phys. Rev. B 20, 1065 (1979) 3, 20 D. Tilley, B. Zeks: Solid State Commun. 49, 823 (1984) 3 D. Tilley: Solid State Commun. 65, 657 (1988) 3


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. Butlerand, 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

Index

average polarization, 8 complete elliptic integral, 7 critical point, 14 critical thickness, 7 depolarization field, 20 effective Landau free energy, 14 Euler–Lagrange equation, 4 extrapolation length, 3 ferroelectric thin films, 3 film thickness, dependence of ferroelectric properties on, 3 Jacobian elliptic function, 6

Landau free energy, 4 Landau–Devonshire theory, 3 Landau–Ginzburg free energy functional, 14 length scale, 5 longitudinal polarization modulation, 20 phase transition, 3 polarization profile, 3, 5 spatial modulation, 4 surface polarization, 4 thickness transition, 12 Tilley–Zeks model, 3 two-step transition, 20

Chemical Solution Deposition of Layer-Structured Ferroelectric Thin Films Shin-ichi Hirano1 , Takashi Hayashi2, Wataru Sakamoto3 , Koichi Kikuta1 , and Toshinobu Yogo3 1

2

3

Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan {hirano,kik}@apchem.nagoya-u.ac.jp Department of Materials Science and Engineering, Shonan Institute of Technology 1-1-25 Tsujido-Nishikaigan, Fujisawa, Kanagawa 251-8511, Japan [email protected] 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 Bi4 Ti3 O12 thin films have been successfully prepared on Si-based substrates by using metallo-organic precursor solutions. The pyrolysis behavior of (Bi,R)4 Ti3 O12 precursors depends upon the starting rare earth source, which strongly affects the surface morphology of the synthesized film. Among the (Bi,R)4 Ti3 O12 films, BNT thin films reveal the most homogeneous and smooth surfaces. Single-phase (Bi,R)4 Ti3 O12 films of Bi-layered perovskite have been crystallized on Si-based substrates. Rare-earth-doped BIT thin films show different crystal orientations dependent upon the substituent ion. BIT and BLT thin films exhibit strong (00l) peaks, while BNT, BST and BGT thin films have a marked (117) preferred orientation. Among the rare-earth-doped BIT thin films, BNT thin films show the best saturation properties of the ferroelectrics with a large Pr and small Ec for low applied voltages. However, low-temperature-processed BNT films do not exhibit enough ferroelectricity. From further investigation of BNT films, the surface morphology and ferroelectric properties can be improved by optimization of the Ge doping in the BNT, particularly in the case of BNT-based thin films prepared at low temperatures. Furthermore, excimer UV irradiation of as-deposited films is very effective in removing the residual organic groups in the precursor film and in improving the microstructure and ferroelectric properties of the resultant BNT thin film. The use of excimer UV irradiation, further, leads to the easy formation of single-phase BIT-based thin films exhibiting excellent ferroelectric properties and a homogeneous microstructure with uniform fine grains at low temperatures. The layer-structured ferroelectric (Bi,R)4 Ti3 O12 films developed in this study, especially the BNT-based films, are found to have potential for application in several electric thin-film devices utilizing ferroelectricity, such as the FeRAM.

1 Introduction Thin-film processing is quite important for the development of the miniaturization and hybridization of electronic devices with low consumption of M. Okuyama, Y. Ishibashi (Eds.): Ferroelectric Thin Films, Topics Appl. Phys. 98, 25–59 (2005) © Springer-Verlag Berlin Heidelberg 2005

26

Shin-ichi Hirano et al.

energy (low operating voltage). In this case, functional materials with desired properties are required for applications at a submicron level or less. Processing techniques for thin films have also been receiving great attention for applications in semiconductor memories, optoelectronic devices, electronic components, display devices, magnetic devices, sensors and emerging areas. Low-temperature thin-film processing also requires precise control of chemical composition and high crystallinity. The various techniques available today for the fabrication of thin films are noticeably more varied in type and in sophistication than those of several decades ago. Better equipment and more advanced techniques have, undoubtedly, led to higher-quality films, and indeed may be a primary factor in the now routine achievement of desired functionalities in thin films (50 nm or greater) prepared by a selection of different methods. 1.1 The Chemical Solution Deposition Process The chemical solution deposition (CSD) process, which includes the sol–gel process, is one of the most common processes used as a fabrication method for thin films. This process can be widely used for optical, electrical, magnetical, mechanical and catalyst applications. The important advantages of the chemical solution process are high purity, good homogeneity, lower processing temperatures, precise composition control for the preparation of multicomponent compounds, versatile shaping, and preparation with simple and cheap apparatus, compared with other methods. However, the more the number of elements, the more complicated the solution chemistry, leading to difficult problems in obtaining the desired crystalline phase. Therefore, it is required to design the metal-organic precursors through reaction control of the metal–oxygen–carbon bonds of the component substances and to investigate solutions of multicomponent systems. Also, the crystallization behavior of precursor films is complicated, so the investigation of the crystallization process is key for the synthesis of thin films with high quality. The first report on chemical solution processing of ferroelectric thin film was published for the synthesis of BaTiO3 films by Fukushima [1] in 1976. Fukushima used a mixture of metal alkoxide and inorganic-salt precursors for the 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. Ferroelectric thin films ranging from polycrystalline to texture-oriented polycrystalline and epitaxial in nature have been synthesized for 20 years. Similary to other thin-film deposition techniques, the CSD process, including sol–gel, is essentially a mass transport process. The transformation of a liquid solution to a solid crystalline film is accomplished through three steps:

Chemical Solution Deposition

27

Fig. 1. Process flow diagram for the fabrication of ferroelectric thin films by chemical solution deposition

1. Precursor materials are dissolved in a homogeneous solution, thus assuring molecular-level mixing of different precursor compounds. 2. Mass transport is completed by spin- and dip-coating of a thin layer of the solution onto the substrate surface. A thin layer of an amorphous gel film 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, an electric furnace or a focused infrared-light furnace under a controlled atmosphere is usually used; sometimes a UV light irradiation process is also applied to cause the condensation and pyrolysis of the precursor thin film 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 appropriate chemical modification of the metallo-organic complexes, leading to the development of new molecular engineering. The chemically designed new precursors allow chemical solution preparation of the desired materials in the form of fine powders, fibers or films. Figure 1 illustrates the general flow diagram for the fabrication of thin films by chemical solution processing via metalloorganics. The intermediate compound, for example a complex alkoxide, can usually be described as a homogeneous solution, which is very important and effective for preparing chemically homogeneous thin films.

28


1.2 Representative Ferroelectric Thin Films for Memory Devices Ferroelectric thin films have been receiving significant attention for various 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 for FeRAMs are required to have excellent ferroelectric properties (large remanent 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(Zrx Ti1−x )O3 (PZT) and SrBi2 Ta2 O9 (SBT) thin films have been studied extensively [4, 5]. Although PZT thin films have many advantages, such as a large remanent polarization and low processing temperature, PZT thin films on Pt electrodes are known to show ferroelectric fatigue phenomena [5]. In addition, PZT thin films contain a toxic and volatile element (Pb). On the other hand, although SBT thin films have excellent fatigue-free properties [5], SBT films tend to crystallize to an undesirable phase, such as a fluoride phase, during the crystallization process and have a higher crystallization temperature compared with PZT. 1.3 Layer-Structured Bi4 Ti3 O12 -Based Thin Films Among several candidates for ferroelectric materials, Bi4 Ti3 O12 (BIT) is attracting significant attention. Similar to SBT, BIT has a layered perovskite structure consisting of triple TiO6 octahedra in perovskite-like layers separated by Bi2 O2 layers. BIT has a large remanent polarization, small coercive field and high Curie temperature. Furthermore, BIT thin films are known to crystallize at a lower temperature compared with SBT thin films. However, in its structure, BIT contains unstable Bi ions, which are easily evaporated during the heating process. This volatility of Bi ions affects the ferroelectric and fatigue characteristics of thin films. Bi3+ ions in the perovskite blocks of BIT can be preferentially substituted by trivalent rare earth ions, such as La3+ , Nd3+ and Sm3+ , for the improvement of the ferroelectric properties. Recently, improvement of the electrical properties of BIT thin films by rare earth ion modification has been reported by many researchers [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26]. In addition, the substitution of Bi3+ by rare earth ions with a smaller ionic radius is expected to be effective in improving the ferroelectric properties. In such cases, the chemical solution deposition method described in the previous section is considered to be very suitable for the fabrication of ferroelectric BIT-based thin films, because this process has several advantages over 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 properties depends strongly upon the factor of the synthesis of an appropriate precursor, such as the selection of the starting materials and the optimization of


29

the chemical composition, as well as the coating and crystallization conditions, 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-temperature annealing process is not acceptable for high-density memory devices, because the designed structure in a silicon semiconductor device is often seriously 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-modified BIT thin films on Si-based substrates, especially from the viewpoint of ferroelectric-memory applications, by the CSD method using metallo-organic precursor solutions, and the resulting properties. Furthermore, the doping of Ge into BIT and ultraviolet (UV) light irradiation processes for the low-temperature processing of BIT-based thin films, particularly Nd-modified BIT thin films with high quality, are described.

2 Rare-Earth-Ion-Modified Bi4 Ti3 O12 Thin Films In this section, mainly the synthesis of thin films rare-earth-ion-modified BIT, (Bi,R)4 Ti3 O12 (R = La, Nd, Sm, Gd), on Si-based substrates by the CSD method is described. The pyrolysis and crystallization behavior of metalloorganic precursor powders and films is investigated. The ferroelectric properties and microstructure of the CSD-derived (Bi,R)4 Ti3 O12 films are also evaluated. Table 1. Metallo-organic compounds used for the synthesis of (Bi,R)4 Ti3 O12 R source BIT (Bi4 Ti3 O12 ) BLT (Bi3.25 La0.75 Ti3 O12 ) BNT (Bi3.25 Nd0.75 Ti3 O12 ) BST (Bi3.25 Sm0.75 Ti3 O12 ) BGT (Bi3.25 Gd0.75 Ti3 O12 )

– La(Oi Pr)3 Nd(OAc)3 Sm(OAc)3 Gd(Oi Pr)3

Bi source t

Bi(O Am)3 Bi(Ot Am)3 Bi(Ot Am)3 Bi(Ot Am)3 Bi(Ot Am)3

Ti source Ti(Oi Pr)4 Ti(Oi Pr)4 Ti(Oi Pr)4 Ti(Oi Pr)4 Ti(Oi Pr)4

2.1 Chemical Processing of (Bi,R)4 Ti3 O12 Precursor Solutions, Powders and Thin Films Figure 2 illustrates the experimental procedure used for the preparation of (Bi,R)4 Ti3 O12 precursor solutions, powders and thin films. Table 1 shows the starting sources of the (Bi,R)4 Ti3 O12 precursor solutions. Nd(OAc)3 and Sm(OAc)3 were prepared from Nd(CH3 COO)3 · H2 O and

30


Fig. 2. Experimental procedure for preparation of (Bi,R)4 Ti3 O12 powders and films by chemical solution deposition

Sm(CH3 COO)3 · 4H2 O by dehydration at 110 ◦ C for 4 h under vacuum. The required amounts of Ti(Oi Pr)4 , Bi(Ot Am)3 with a 3% Bi excess composition, and the rare earth source were dissolved in 2-methoxyethanol. The effect of excess Bi on the fabrication of Bi4 Ti3 O12 -based thin films has been reported previously [18]. Acetylacetone was added to the solution as a stabilizing agent. In this case, a (Bi,R)4 Ti3 O12 precursor solution including 6 equivalents of acetylacetone (acetylacetone/BNT precursor = 6) was found to have sufficient long-term stability as a coating solution. Then, the mixed solution was refluxed for 20 h, yielding a 0.1 M homogeneous precursor solution. Films were fabricated using the precursor solution by spin-coating on Pt(200 nm)/TiOx (50 nm)/SiO2 /Si substrates. As-deposited precursor films were dried on a hotplate at 150 ◦C for 5 min and calcined at 500 ◦C for 10 min in an O2 flow, and then crystallized at temperatures between 600 ◦C and 750 ◦ C for 30 min in an O2 flow by rapid thermal annealing (RTA) at a heating rate of 150 ◦C/min. The thickness of (Bi,R)4 Ti3 O12 films was adjusted to be approximately 200 nm by repeating the coating/calcining cycle.


31

Fig. 3. XRD profiles of (a) Bi4.12 Ti3 O12 (BIT), (b) Bi3.35 La0.75 Ti3 O12 (BLT), (c) Bi3.35 Nd0.75 Ti3 O12 (BNT), (d) Bi3.35 Sm0.75 Ti3 O12 (BST) and (e) Bi3.35 Gd0.75 Ti3 O12 (BGT) powders heat-treated at various temperatures

2.2 Crystallization and Pyrolysis Behavior of (Bi,R)4 Ti3 O12 Precursors Homogeneous and stable rare-earth-doped BIT ((Bi,R)4 Ti3 O12 ) precursor solutions were prepared by controlling the reaction of the starting metalloorganic compounds in 2-methoxyethanol with a key additive of acetylacetone. To investigate the crystallization behavior of rare-earth-doped BIT precursors, their crystallized powders were prepared by heat treatment at various temperatures. Figure 3 shows XRD profiles of (a) Bi4.12 Ti3 O12 (BIT), (b) Bi3.35 La0.75 Ti3 O12 (BLT), (c) Bi3.35 Nd0.75 Ti3 O12 (BNT), (d) Bi3.35 Sm0.75 Ti3 O12 (BST) and (e) Bi3.35 Gd0.75 Ti3 O12 (BGT) powders. In the case of BIT, the precursor powder began to crystallize directly into the

32


Fig. 4. DTA-TG curves of (a) BIT, (b) BLT, (c) BNT, (d) BST and (e) BGT precursors (Endo., endothermic; Exo., exothermic)

Bi4 Ti3 O12 structure at 500 ◦C. On the other hand, the BLT, BNT, BST and BGT precursor powders crystallized into Bi-layered perovskite structures at the higher temperature of 600 ◦C. Although the substitution of rare earth ions on the Bi sites of BIT resulted in a higher crystallization temperature, the rare-earth-doped BIT precursors also crystallized directly into the BIT single-phase without the intermediate formation of undesired phases such as pyrochlore.


33

The quality of films prepared by the CSD method is affected by the decomposition and burnout behavior of the organic species contained in the precursor film during heating. Therefore, the pyrolysis behavior of (Bi,R)4 Ti3 O12 precursors was investigated by differential thermal analysis-thermogravimetry (DTA-TG), which is suitable for understanding the pyrolysis and crystallization behavior on the basis of thermal and weight balance during the heating process. Figure 4 illustrates DTA-TG curves of (a) BIT, (b) BLT, (c) BNT, (d) BST and (e) BGT precursors. The decomposition and burnout behavior of the organic species in the precursors was found to depend upon the kind of starting rare earth source. When metal alkoxide was used as a rare earth source (La(Oi Pr)3 or Gd(Oi Pr)3 ), the precursor decreased in weight gradually with increasing temperature up to 600 ◦C, as shown in Figs. 4(b) and 4(e). A similar change in weight was observed for nonsubstituted BIT (Fig. 4(a)). In the first stage, remaining solvents were evaporated at around 100 ◦ C to 150 ◦C, and then residual organic species were decomposed between 150 ◦ C and 550 ◦ C. The exothermic peaks at around 200 ◦C to 300 ◦ C and 400 ◦ C to 500 ◦C observed in DTA corresponded to the combustion of organic species in the precursors. The small exothermic peak at around 600 ◦C was due to the crystallization and burnout of residual organic species. On the other hand, the pyrolysis behavior of precursors formed from rare earth acetates (Nd(OAc)3 and Sm(OAc)3 ) was quite different from that of the BIT, BLT and BGT precursors. As shown in Figs. 4(c) and 4(d), a sharp exothermic peak with rapid weight loss was observed at 150 ◦C to 180 ◦ C. In this stage, the evaporation of residual organic solvent, and the decomposition and burnout of organics in the precursors occured simultaneously. The broad exothermic peaks followed by a gradual weight loss at 270 ◦C in the BNT precursor and at 350 ◦C in the BST precursor were attributed to the combustion of residual organic species. The small exothermic peak at around 550 ◦C was considered to be due to crystallization. It is noteworthy that little weight loss was detected during crystallization in the BNT precursor above 400 ◦ C. The optimization of the molecular design of precursors is considered to be a key for the low-temperature synthesis of high-quality BIT-based ferroelectric films. 2.3 Crystallization of (Bi,R)4 Ti3 O12 Thin Films On the basis of the data on the crystallization and pyrolysis behavior of the precursors, BIT, BLT, BNT, BST and BGT thin films were fabricated on Pt/TiOx /SiO2 /Si substrates. All as-deposited films crystallized to a Bilayered perovskite single phase above 600 ◦C. As the annealing temperature increased, the full width at half maximum of each diffraction peak gradually decreased, indicating that the films increased in crystallinity. In order to clarify the effect of rare earth substitution in the BIT structure on the ferroelectric properties of the resultant films, the full-crystallization temperature

34


Fig. 5. XRD profiles of (a) BIT, (b) BLT, (c) BNT, (d) BST and (e) BGT thin films prepared at 750 ◦ C on Pt/TiOx /SiO2 /Si substrates

was selected to be 750 ◦C. Figure 5 illustrates XRD patterns of rare-earthdoped BIT thin films heat-treated at 750 ◦ C. The thin films showed different orientations with high crystallinity. The BIT and BLT thin films exhibited strong 00l diffraction peaks, whereas the BNT, BST and BGT thin films revealed a random orientation with a strong 117 reflection. The ferroelectricity of the BNT, BST and BGT films with a (117) preferred orientation is expected to be larger than that of the (00l)-oriented BIT and BLT, because the spontaneous polarization for these materials along the a-axis is known to be much larger than that along the c-axis [25]. Bi-layered perovskite materials such as BIT tend to show an (00l) preferred orientation on Pt(111). When a rare earth ion is doped into BIT, the distortion of the crystal structure results in a change in film orientation. La has a relatively large ionic radius (136 pm), which is close to that of the Bi ion. Thus, similarly to BIT films, BLT thin films show a (00l) preferred orientation with anisotropic grain growth, as described in the next section. When the smaller rare earth ions such as Nd, Sm and Gd are substituted in BIT, the orientation of the film changes because of the increasing lattice mismatch between the (111) plane of Pt on TiOx /SiO2 /Si and the (00l) plane of (Bi,R)4 Ti3 O12 with decreasing ionic radius of the substituted rare earth ion. The smallest mismatch, of about 1.3%, is calculated on the basis of an atomic alignment between the (111) plane of Pt and the (001) plane of BIT. Thus, BNT, BST and BGT thin films show a random orientation with an enhanced 117 reflection. This behavior can also be explained by the fact that the lattice constants of (Bi,R)4 Ti3 O12 powders calculated from the XRD data decrease with decreasing rare earth ion size. This result is consistent with that reported by Pineda-Flores et al. [26].


35

Fig. 6. AFM images of (a) BIT, (b) BLT, (c) BNT, (d) BST and (e) BGT thin films prepared at 750 ◦ C on Pt/TiOx /SiO2 /Si substrates

2.4 Surface Morphologies of (Bi,R)4 Ti3 O12 Films The surface morphology of synthesized films is one of the most important factors for achieving the desired electrical properties. Figure 6 shows AFM images of (a) BIT, (b) BLT, (c) BNT, (d) BST and (e) BGT thin films syn-

36


thesized at 750 ◦C. The BIT thin films consisted of large grains with rough surfaces, as shown in Fig. 6(a). The BLT thin films were composed of rod-like, large anisotropic grains [Fig. 6(b)]. This microstructure of the film originates from the (00l) preferred orientation. The microstructure of the BNT, BST and BGT films reflected the crystal orientation. The BNT, BST and BGT films were composed of closely packed grains, as shown in Figs. 6(c)–6(e), and these films showed a random orientation with a strong 117 reflection. In particular, the BNT thin film had a homogeneous, smooth surface with a larger grain size of about 200 nm, whereas the BST and BGT thin films had smaller grain sizes than those of the BNT thin films. The microstructure of the films might be attributable to the kind of starting material. The (Bi,R)4 Ti3 O12 precursors showed differences in the decomposition and burnout behavior of the organics, which depended upon the starting rare earth source, as described in Sect. 2.2. 2.5 Phase Transition and Ferroelectric Properties It is known that the Curie temperature of single-crystal BIT is 675 ◦C [25] and is decreased by the substitution of A-site cations (Bi) by rare earth ions [12, 26]. Therefore, in order to confirm the ferroelectric phase transition behavior of rare-earth-modified BIT, differential scanning calorimetry (DSC) measurements were conducted on fully crystallized (Bi,R)4 Ti3 O12 powders at 900 ◦ C, because DSC analysis is useful for detecting exothermic and endothermic behavior of ferroelectrics during phase transition. Figure 7 illustrates DSC curves of (a) BLT, (b) BNT, (c) BST and (d) BGT powders from 100 ◦ C to 600 ◦C. The phase transition from a ferroelectric to a paraelectric is endothermic. The DSC curves were broadened by the substitution with the rare earth ion, as shown in Fig. 7, because Bi4−x Rx Ti3 O12 tends to exhibit a relaxor behaviour when the amount of substitution, x, is above 0.8, as reported by Pineda-Flores et al. [26]. As a result, the Curie temperatures of the BLT, BNT, BST and BGT powders were found to be in the range from 400 ◦ C to 450 ◦ C. Rare-earth-modified BIT is expected to maintain a high Curie temperature and exhibit ferroelectric characteristics over a wide temperature range. In order to examine the ferroelectricity of synthesized films, the P –E hysteresis was also measured for (Bi,R)4 Ti3 O12 thin films on Pt/TiOx /SiO2 /Si substrates crystallized at 750 ◦ C. Figure 8 shows P –E hysteresis loops of 200 nm-thick (Bi,R)4 Ti3 O12 thin films measured at room temperature. These thin films showed ferroelectric P –E hysteresis loops at applied voltages of above 5 V. The remanent polarization (Pr ) and coercive field (Ec ) of the thin films varied considerably depending upon the substituent ions. Among the films, the BNT thin film revealed superior Pr and Ec and a superior degree of squareness of the hysteresis loop to the others. BNT thin films showed a Pr of 21.6 µC/cm2, which was higher than those of the BIT and BLT thin films, 7.1 µC/cm2 and 15.9 µC/cm2, respectively, at an applied voltage of 5 V. This


37

Fig. 7. DSC curves of (a) BLT, (b) BNT, (c) BST and (d) BGT powders (Endo., endothermic; Exo., exothermic)

can be explained by both the change of the TiO6 octahedra in the structure and the crystal orientation of the synthesized films. Ferroelectricity is known to be based upon the displacement of an atom from its original position along one axis. The substitution of A-site ions in the Bi4 Ti3 O12 structure by rare earth ions with a smaller ionic radius promotes the rotation of TiO6 octahedra in the a–b plane, accompanied by a tilt of the octahedra along the c-axis [13]. Also, in this case, the orientation of the film depended upon the substituent ions. Since the polar axis of these materials is almost along the aaxis, the ferroelectricity of the BNT film with a (117) preferred orientation was superior to BIT and BLT with a (00l) preferred orientation. Figure 9 shows the changes in saturation properties of the (Bi,R)4 Ti3 O12 films with applied voltage. The values of Pr [Fig. 9(a)] and Ec [Fig. 9(b)] were measured

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Fig. 8. P –E hysteresis loops of rare-earth-doped BIT thin films prepared at 750 ◦ C on Pt/TiOx /SiO2 /Si substrates (thickness 200 nm, applied voltage 5 V)

Fig. 9. Saturation properties of (a) remanent polarization (Pr ) and (b) coercive field (Ec ) for rareearth-doped BIT thin films prepared at 750 ◦ C on Pt/TiOx /SiO2 /Si substrates as a function of applied voltage (film thickness 200 nm)


39

Fig. 10. XRD patterns of Bi4−x Ndx Ti3 O12 [(a) x = 0.0, (b) x = 0.5, (c) x = 0.75 and (d) x = 1.0] thin films on substrates, Pt/TiOx /SiO2 /Si prepared at 700 ◦ C

at various voltages from 1 V to 15 V. From Fig. 9, the BNT film was found to show excellent saturation properties, with higher Pr and lower Ec values in comparison with the other rare-earth-doped BIT films. Although the BST and BGT films had a (117) preferred orientation, these films were found to have a smaller Pr and larger Ec than the values for BNT. Because the grain sizes of the BST and BGT thin films were smaller than that of the BNT thin films, large applied voltages were required to obtain large ferroelectricity, as shown in Fig. 9. 2.6 Effect of Nd Content on Nd-Modified BIT (BNT) Thin Films From the results in the previous sections, Nd-doped BIT (BNT) thin films were found to show excellent microstructure and ferroelectric properties. Therefore, further investigations of BNT films were performed to achieve ferroelectric BIT-based thin films with high performance. Figure 10 shows XRD profiles of Bi4−x Ndx Ti3 O12 (BNT) (x = 0.0, 0.5, 0.75, 1.0) thin films prepared at 700 ◦ C on Pt/TiOx/SiO2 /Si substrates. Bi4−x Ndx Ti3 O12 thin films crystallized in a single phase of Bi-layered perovskite BIT without any formation of a second phase. Nonsubstituted BIT thin films exhibited a (00l) preferred orientation, as shown in Fig. 10(a). On the other hand, BNT (x = 0.5, 0.75, 1.0) thin films showed high crystallinity with a random orientation, having a strong 117 diffraction peak, as shown in Figs. 10(b)– 10(d). The change in the crystal orientation due to the Nd substitution was clearly observed. Compared with the nonsubstituted BIT films, the BNT (x = 0.5 to 1.0) films showed a decreased intensity of 00l reflections, and had an almost random orientation. BIT-based materials have a layered perovskite structure and exhibit strongly anisotropic physical properties. The spontaneous polarization of BIT along the c-axis is known to be much smaller than that along

40


Fig. 11. AFM images of the surfaces of Bi4−x Ndx Ti3 O12 [(a) x = 0.0, (b) x = 0.5, (c) x = 0.75 and (d) x = 1.0] thin films on Pt/TiOx /SiO2 /Si substrates, prepared at 700 ◦ C

the a-axis [25]. From this viewpoint, randomly oriented films are considered to be more favorable than c-axis-oriented films. The BNT films in this study, therefore, have a more suitable orientation in comparison with nonsubstituted BIT films for achieving large ferroelectricity. Figure 11 shows AFM images of the surfaces of BNT (x = 0.0–1.0) thin films prepared at 700 ◦C on Pt/TiOx /SiO2 /Si substrates. The nonsubstituted BIT thin films exhibited an inhomogeneous microstructure consisting of relatively large grains with a statistical roughness, root mean square (RMS), of approximately 24.4 nm. Among the films considered here, the BNT (x = 0.75) thin films showed the most homogeneous microstructure, with a uniform grain size around 200 nm (RMS roughness 12.0 nm), as shown in Fig. 11(c). The values of the RMS roughness decreased from 24.4 nm for BIT (x = 0.0) to 11.4 nm for BNT (x = 1.0). The improved microstructures of the BNT (x ≥ 0.75) films in Figs. 11(c) and (d) may be attributable to the optimum amount of Nd substitution. Nd modification is found to be effective in improving the surface morphology of synthesized films, because the precursor films undergo optimized nucleation and growth process, producing films with a ho-


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Fig. 12. P –E hysteresis loops of Bi4−x Ndx Ti3 O12 [(a) x = 0.0, (b) x = 0.5, (c) x = 0.75 and (d) x = 1.0] thin films on Pt/TiOx /SiO2 /Si substrates, prepared at 700 ◦ C (applied voltage 5 V)

mogeneous and dense microstructure. Also, the homogeneous microstructure of the BNT films may affect the ferroelectric properties, because the voltage can be applied uniformly to the films. Figure 12 shows P –E hysteresis loops of BNT (x = 0.0 to 1.0) thin films prepared at 700 ◦ C. In order to clarify the effect of Nd substitution on the ferroelectric properties of the resultant films, the full-crystallization temperature was selected to be 700 ◦ C. From Fig. 12, the ferroelectric properties such as Pr , Ec and the degree of squareness of the hysteresis loops for Ndsubstituted BIT thin films were found to be greatly improved in comparison with those of nonsubstituted BIT thin films. Well-saturated P –E hysteresis loops with a large Pr and a low Ec were observed for the BNT (x = 0.75, 1.0) films. Among these films, the BNT (x = 0.75) thin films showed the highest remanent polarization (Pr ), of 22 µC/cm2 , and a relatively low coercive electric field (Ec ) of 80 kV/cm. This large ferroelectricity may be attributable to the change in crystal orientation from the (00l) preferred orientation to the random orientation with a strong (117) reflection, and to the tilting of TiO6 octahedra derived from the substitution of Nd3+ , which has a smaller ionic radius than Bi3+ [13, 16, 20, 22]. Figure 13 shows saturation properties of P –E hysteresis curves at applied voltages from 1 V to 10 V for BNT (x = 0.0–1.0) thin films prepared at 700 ◦ C. BNT (x = 0.75, 1.0) thin films exhibited Pr values of around 15 µC/cm2 , even when the applied voltage was as low as 3 V. Furthermore, a well-saturated behavior of the P –E hysteresis loops was obtained for BNT (x = 0.75, 1.0) thin films, which had high Pr and low Ec values, as shown in Fig. 13. The optimization of the Nd content in BIT thin films is found to be a key for improving the ferroelectric properties of the resultant films. 2.7 Effect of Processing Temperature on Nd-Modified BIT (BNT) Thin Films BNT (x = 0.75) thin films were found to exhibit the most excellent properties among the Bi4−x Ndx Ti3 O12 films described in the previous section. There-

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Fig. 13. Saturation property of remanent polarization (Pr ) of P –E hysteresis loops for Bi4−x Ndx Ti3 O12 [(a) x = 0.0, (b) x = 0.5, (c) x = 0.75 and (d) x = 1.0] thin films on Pt/TiOx /SiO2 /Si substrates, prepared at 700 ◦ C (applied voltage 1 V to 10 V)

Fig. 14. XRD profiles of Bi3.35 Nd0.75 Ti3 O12 (BNT) thin films on Pt/TiOx /SiO2 /Si substrates, prepared at (a) 600 ◦ C, (b) 650 ◦ C and (c) 700 ◦ C

fore, low-temperature processing of BNT thin films was also examined, mainly for the x = 0.75 composition of BNT. As-deposited BNT (x = 0.75) precursor films were found to crystallize in a BIT single phase at 600 ◦ C and to exhibit a random orientation with weak 00l diffraction peaks, as shown in Fig. 14. The (117) preferred orientation of the films became dominant with increasing annealing temperature. The same crystallization behavior was observed for BNT (x = 0.5, 1.0) thin films. From AFM images of the surface morphology of BNT (x = 0.75) thin films, BNT thin films prepared at 600 ◦ C were found to exhibit inhomogeneous, bimodal grain microstructures that consisted of fine and large grains with an RMS roughness of approximately 10 nm, as described later in Sects. 3.2 and 4.3. In addition, well-saturated P –E hysteresis curves (Pr approximately 20 µC/cm2 ) were obtained for BNT (x = 0.75) thin


43

films prepared above 650 ◦C. However, BNT (x = 0.75) thin films prepared at 600 ◦ C exhibited much lower Pr values (approximately 10 µC/cm2 ) than those of BNT (x = 0.75) films prepared above 650 ◦C. Therefore, an improvement of the microstructure and ferroelectric properties of low-temperature-processed BNT films, particularly BNT films synthesized below 600 ◦ C, is very much needed.

3 Ge-Doped (Bi,Nd)4 Ti3 O12 Thin Films Recently, rare-earth-modified BIT thin films have been studied to improve their ferroelectric properties [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]. Among them, Nd-substituted BIT (BNT) thin films have been attractive because their ferroelectric properties are superior to those of other rare-earth-substituted BIT thin films [13, 15, 19, 20, 22, 24]. However, the fabrication of BNT thin films at low temperature is still difficult, because of problems such as insufficient ferroelectric properties and inhomogeneous microstructure. Recently, Kijima and coworkers reported that Si-substituted BIT thin films could be fabricated at low temperatures with good surface morphology [27, 28]. Since germanium is quite similar to silicon, Nd- and Gecodoped BIT thin films are expected to reduce the processing temperature and to show excellent properties with a good surface morphology. This section describes the fabrication of Ge-doped Bi3.25 Nd0.75 Ti3 O12 (Bi3.25 Nd0.75 Ti3−x Gex O12 ) thin films by chemical solution deposition. The effects of Ge doping in Bi3.25 Nd0.75 Ti3 O12 on the crystallization of precursor films and the surface morphology of crystallized films have been examined. The ferroelectric properties of synthesized thin films have also been evaluated [29]. 3.1 Fabrication of (Bi,Nd)4 (Ti,Ge)3 O12 Films Ge-doped (Bi,Nd)4 Ti3 O12 thin films were fabricated by chemical solution deposition as described in Sect. 2.1. The desired amounts of Bi(Ot C5 O11 )3 , Ti(Oi C3 H7 )4 , dehydrated Nd(CH3 COO)3 and Ge(OC2 H5 )4 corresponding to three Bi3.35 Nd0.75 Ti3−x Gex O12 (BNTGx ) compositions [x = 0.0, 0.1, 0.3] (with 3% of excess Bi) were dissolved in absolute 2-methoxyethanol, and acetylacetone was then added to the solution as a stabilizing agent. The solution was refluxed for 18 h, yielding a homogeneous solution. BNTGx precursor films were prepared using the BNTGx precursor solutions by spin-coating onto Pt(200 nm)/TiOx (50 nm)/SiO2 /Si substrates. As-deposited precursor films were dried on a hotplate at 150 ◦ C for 5 min, and then calcined at 500 ◦ C for 10 min in an O2 flow, followed by crystallization between 600 ◦ C and 700 ◦ C for 30 min at a heating rate of 150 ◦C/min using rapid thermal annealing (RTA) in an O2 flow.

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Fig. 15. XRD profiles of (a) Bi3.35 Nd0.75 Ti3 O12 (BNT), (b) Bi3.35 Nd0.75 Ti2.9 Ge0.1 O12 (BNTG0.1 ) and (c) Bi3.35 Nd0.75 Ti2.7 Ge0.3 O12 (BNTG0.3 ) thin films prepared at 700 ◦ C on Pt/TiOx /SiO2 /Si substrates

Figure 15 illustrates XRD profiles of BNT, BNTG0.1 and BNTG0.3 thin films prepared at 700 ◦ C on Pt/TiOx /SiO2 /Si substrates. In order to fabricate Bi4 Ti3 O12 (BIT) single-phase thin films, the BNT, BNTG0.1 and BNTG0.3 compositions are selected, because these compositions have been confirmed to have the BIT structure on the basis of Raman spectroscopic data for the Bi4 Ge1−x Tix O12 ceramic system [30]. Also, the amount of Nd substitution on the Bi sites of BNTGx is determined according to a previous study [24] described in Sect. 2.7. These films crystallized into the BIT single phase and exhibited a random orientation with a strong (117) reflection, because no change in the diffraction peaks with Ge doping was observed, as shown in Figs. 15(a)–15(c). Figures 16(a) and 16(b) show the XRD profiles of BNTG0.1 and BNTG0.3 thin films prepared at 600 ◦C and 700 ◦ C. The BNTG0.1 and BNTG0.3 thin films crystallized into the BIT single phase with a (117) preferred orientation above 600 ◦C. These films were found to exhibit similar crystallization behavior, without any formation of a second phase. Similar diffraction patterns were also observed for BNT films prepared at 600 ◦ C, as shown in Fig. 14. These results indicate that the synthesized films in this study crystallized into the BIT single phase above 600 ◦ C and showed a random orientation with a strong (117) reflection. Kawashima et al. reported on germanate (Bi2 GeO5 )added (Bi,La)4 Ti3 O12 (BLT) thin films prepared by chemical solution deposition [31]. However, these films exhibited a random orientation with strong 00l reflections. The ferroelectricity of the current BNTGx thin films with a (117) preferred orientation is expected to be larger than that of the (00l)oriented Bi2 GeO5 -added BLT films, because the spontaneous polarization of BIT along the a-axis is much larger than that along the c-axis. The crystal


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Fig. 16. XRD profiles of (a) BNTG0.1 and (b) BNTG0.3 thin films prepared at 600 ◦ C and 700 ◦ C on Pt/TiOx /SiO2 /Si substrates

orientation is also related with improving the surface morphology of BITbased films, as described in Sect. 2.4. Furthermore, Nd-substituted BIT thin films have been reported to show a higher Pr than La-substituted BIT thin films [16, 20, 22]. 3.2 Microstructure and Electrical Properties of (Bi,Nd)4 (Ti,Ge)3 O12 Films Figures 17(a)–17(c) show AFM images of BNT, BNTG0.1 and BNTG0.3 thin films prepared at 600 ◦C and 700 ◦C on Pt/TiOx /SiO2 /Si substrates. The BNT thin films prepared at 600 ◦C and 700 ◦C showed different surface mor-

46


phologies and grain sizes, as shown in Fig. 17(a). The RMS roughness values of the BNT thin films prepared at 600 ◦C and 700 ◦C were approximately 6.2 nm and 13.0 nm, respectively. On the other hand, the BNTG0.1 thin films showed a good surface morphology. Also, the BNTG0.1 thin films prepared at 600 ◦ C and 700 ◦ C had similar surface morphologies and grain sizes, as shown in Fig. 17(b). The RMS roughness values of BNTG0.1 thin films prepared at 600 ◦ C and 700 ◦C were approximately 4.6 nm and 5.8 nm, respectively. Also, the grain size and shape of the BNTG0.1 thin films were uniform compared with those of nondoped BNT thin films, particularly those of BNT thin films crystallized at 600 ◦C. However, the BNTG0.3 thin films showed inhomogeneous microstructures, as shown in Fig. 17(c). It turns out, as seen from Fig. 17, that the nucleation and growth process in the BNTGx thin film during heating can be optimized by controlling the amount of Ge. This finding is important for fabricating thinner BNT-based films with high performance at low temperatures. The dielectric constants of BNT, BNTG0.1 and BNTG0.3 films on Pt/TiOx /SiO2 /Si substrates at 10 kHz were found to be about 320, 290 and 240, respectively, with a loss tangent of approximately 3%. This change may be due to the Ge doping in the BNT structure. Figure 18 shows P –E hysteresis loops of the BNT, BNTG0.1 and BNTG0.3 thin films crystallized at 600 ◦ C and 700 ◦ C. These films were approximately 200 nm thick. P –E hysteresis measurements were performed at an applied voltage of 5 V and a frequency of 100 Hz. The remanent polarization (Pr ) and coercive field (Ec ) of the BNT thin films prepared at 700 ◦C were 21 µC/cm2 and 67 kV/cm, respectively. On the other hand, the BNTG0.1 and BNTG0.3 thin films exhibited lower Pr values of 16 µC/cm2 and 10 µC/cm2, respectively. However, at a crystallization temperature of 600 ◦ C, the Pr value of 15 µC/cm2 for BNTG0.1 thin films was higher than the value of 10 µC/cm2 for BNT thin films. The lower Pr value of the BNT thin films at 600 ◦C was due to the inhomogeneous microstructure, consisting of fine grains (10 nm to 20 nm) and large grains (100 nm to 250 nm), as shown in Fig. 17(a). On the other hand, the BNTG0.1 thin films at crystallization temperatures of both 600 ◦ C and 700 ◦ C had dense and homogeneous surface morphologies with uniform grains (100 nm to 150 nm, Fig. 17(b)) and similar Pr values (Fig. 18(b)). However, the BNTG0.3 thin films showed lower Pr values than those of the BNT and BNTG0.1 thin films. From these results, we conclude that the surface morphology and ferroelectric properties can be improved by optimization of the Ge doping in BNT, particularly in the case of low-temperature preparation of BNT-based thin films.

4 UV Processing of (Bi,Nd)4 Ti3 O12 (BNT) Thin Films Only a few studies of the preparation of BNT thin films by CSD, including a sol–gel method, have been reported up to now. The preparation of BNT thin


47

films by the CSD method using nitrates or acetates as starting materials has been studied [15, 16], but the processing temperature is as high as 650 ◦C to 800 ◦ C. A high-temperature heating process is not suitable for the fabrication of high-density memory devices, because silicon semiconductor devices are often seriously damaged during the annealing process. Recently, excimer UV light irradiation, involving a photolysis reaction of organic species on as-deposited precursor films, has been reported to be very useful for preparing BLT thin films with improved microstructure and improved ferroelectric properties at a low temperature of 600 ◦ C [18]. In order to lower the processing temperature, a new process for film preparation using an excimer laser or an Hg or Xe UV lamp to induce a photolysis reaction of the organic species and crystallization has also been actively investigated [32, 33, 34]. On the other hand, Bi4−x Ndx Ti3 O12 (BNT) thin films have been attracting a significant amount of attention for their ferroelectric properties, which are superior to those of other rare-earth-doped BIT thin films [13, 15, 19, 20, 22, 24]. In this section, we describe the application of excimer UV processing to the chemical preparation of BNT thin films. The effects of excimer UV light irradiation of as-deposited precursor films on the crystallization, microstructure and ferroelectric properties of the resultant thin films have been investigated for the fabrication of ferroelectric BNT films at low processing temperatures [35]. 4.1 Changes in the Chemical Bonding of Excimer-UV-Irradiated BNT Precursor Films As-deposited BNT precursor films were dried at 150 ◦C for 5 min on a hotplate, and were then irradiated with a Xe excimer UV lamp (172 nm) at 300 ◦ C for 30 min in an O2 atmosphere. These processes were repeated several times to obtain films of the desired thickness. The excimer-UV-processed BNT films were heat-treated at 500 ◦ C for 10 min in an O2 flow and then crystallized at 550 ◦C or 600 ◦ C for 30 min at a heating rate of 150 ◦ C/min by rapid thermal annealing. To investigate the pyrolysis behavior of the organic groups of BNT precursor films induced by excimer UV irradiation, Fourier transform infrared spectrometer (FT-IR) measurements were performed. Figure 19 shows FTIR spectra of as-deposited BNT precursor films with and without excimer UV irradiation at 300 ◦ C for 30 min in an O2 atmosphere. Absorbance peaks assigned to stretching vibrations of C–H and C=O (carbonyl) groups were observed for the samples calcined at 300 ◦C without excimer UV irradiation at approximately 2900 cm−1 and 1600 cm−1, respectively. On the other hand, for excimer UV irradiation at a temperature of 300 ◦C in an O2 atmosphere, the organic species in the BNT precursor films were completely removed during an irradiation time of 30 min, and a peak assigned to metal–oxygen bonds in oxides was observed at around 600 cm−1 . Thus, UV light irradiation of the BNT precursor films was found to be effective in forming –M-O–M–O–

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Fig. 17. AFM images of (a) BNT, (b) BNTG0.1 and (c) BNTG0.3 thin films prepared at 600 ◦ C and 700 ◦ C on Pt/TiOx /SiO2 /Si substrates

bonds in the precursor films through bond cleavage by a photolysis reaction before crystallization. This may be attributable to the easier decomposition of organic groups by oxidation reactions with O2 and with O3 formed by UV irradiation, as well as the photolysis reaction. This behavior is very similar to that of BLT films previously reported [18]. 4.2 Effect of UV Light Irradiation on the Crystal Orientation of the Resultant Thin Films Figure 20 shows XRD patterns of BNT thin films prepared on Pt/TiOx /SiO2 /Si substrates at 550 ◦C and 600 ◦ C with and without excimer


49

Fig. 18. P –E hysteresis loops of (a) BNT, (b) BNTG0.1 and (c) BNTG0.3 thin films prepared at 600 ◦ C and 700 ◦ C on Pt/TiOx /SiO2 /Si substrates

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Fig. 19. FT-IR spectra of as-deposited BNT precursor films with and without excimer UV irradiation at 300 ◦ C for 30 min in O2 atmosphere

UV irradiation. The BNT precursor films crystallized at 550 ◦ C in a BIT single phase in the case of both excimer UV nonirradiation and irradiation. However, the crystal orientation of the synthesized BNT thin films was changed by the excimer UV irradiation. In addition, BNT thin films prepared at 550 ◦ C with excimer UV irradiation showed a stronger 117 reflection and a weaker 200 reflection compared with those without excimer UV irradiation. Furthermore, BNT thin films prepared at 600 ◦C revealed a random orientation with a strong 117 reflection, and the 200 diffraction intensity of the films was reduced for excimer-UV-derived films. The excimer UV irradiation in an O2 atmosphere has been found to be effective for increasing the 117 reflection intensity of BNT thin films. 4.3 Surface Morphology of UV-Light-Irradiated BNT Thin Films Figure 21 shows AFM images of the surface morphology of BNT thin films prepared at 550 ◦ C and 600 ◦C with and without excimer UV irradiation. BNT thin films prepared at 550 ◦ C and 600 ◦ C without excimer UV irradiation exhibited inhomogeneous, bimodal grain microstructures that consisted of fine and large grains with a RMS roughness of approximately 7 nm to 10 nm. On the other hand, the BNT thin films prepared at 550 ◦C with excimer UV irradiation consisted of uniform grains with sizes of approximately 150 nm and a homogeneous, smooth surface microstructure with an RMS roughness of approximately 5.8 nm the film grew to larger grains of size 200 nm with annealing at 600 ◦ C. Excimer UV irradiation has been found


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Fig. 20. XRD patterns of BNT thin films prepared on Pt/TiOx /SiO2 /Si substrates: without excimer UV irradiation, (a) 550 ◦ C, (b) 600 ◦ C; and with excimer UV irradiation, (c) 550 ◦ C, (d) 600 ◦ C

to be effective for the improvement of the surface morphology of BNT thin films. This fact, shown in Fig. 21, is very important for achieving uniform properties in microsized areas of films. 4.4 Ferroelectric Properties of UV-Irradiated BNT Thin Films Figure 22 shows P –E hysteresis loops of BNT thin films prepared at 550 ◦ C and 600 ◦C with and without excimer UV irradiation, measured at an applied voltage of 10 V. 550 ◦C-annealed BNT thin films without excimer UV irradiation did not show a well-saturated P –E hysteresis loop, while 600 ◦ C-annealed

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Fig. 21. AFM images of the surface morphology of BNT thin films: without excimer UV irradiation, (a) 550 ◦ C, (b) 600 ◦ C; and with excimer UV irradiation, (c) 550 ◦ C, (d) 600 ◦ C

films exhibited a comparatively saturated P –E hysteresis loop. The values of Pr and Ec for the 600 ◦C-annealed films were 8.7 µC/cm2 and 102 kV/cm, respectively. On the other hand, BNT thin films prepared with excimer UV irradiation exhibited well-saturated P –E hysteresis loops with larger Pr and smaller Ec values. BNT thin films prepared at 600 ◦ C with excimer UV irradiation showed a Pr value of 16.9 µC/cm2 and a reduced Ec value of 93 kV/cm, to be compared with the values for films without excimer UV irradiation. Also, 550 ◦ C-annealed BNT thin films prepared with excimer UV irradiation showed good ferroelectric properties similar to those of 600 ◦ C-annealed BNT thin films, as shown in Fig. 22. The values of Pr and Ec were 16.1 µC/cm2 and 102 kV/cm, respectively. Figure 23 shows the relationship between the Pr value and the applied voltage for BNT thin films prepared at 550 ◦C and 600 ◦ C with and without excimer UV irradiation. The BNT thin films exhibited good saturation properties, and the Pr values gradually approached saturation beyond an applied voltage of 5 V. The BNT thin films synthesized


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Fig. 22. P –E hysteresis loops of BNT thin films at an applied voltage of 10 V: without excimer UV irradiation, (a) 550 ◦ C, (b) 600 ◦ C; and with excimer UV irradiation, (c) 550 ◦ C, (d) 600 ◦ C

Fig. 23. Relationship between the Pr value and the applied voltage for BNT thin films: without excimer UV irradiation, (a) 550 ◦ C, (b) 600 ◦ C; and with excimer UV irradiation, (c) 550 ◦ C, (d) 600 ◦ C

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using excimer UV irradiation exhibited much higher Pr values compared with those prepared without excimer UV irradiation over the measurement range of applied voltage, as shown in Fig. 23. This may be attributable to the smooth surface and the homogeneous BNT grains that are obtained by irradiating with excimer UV, as described in Sect. 4.3. 4.5 Fatigue and Leakage Current Properties of UV-Irradiated BNT Thin Films For the purpose of practical memory device applications, the fatigue endurance and leakage current properties of synthesized ferroelectric thin films are also significant factors. Figure 24 shows the polarization fatigue properties of BNT thin films prepared at 550 ◦C and 600 ◦ C using excimer UV irradiation, measured at a frequency of 100 kHz under an applied voltage of 5 V before and after 109 switching cycles. The fatigue of the BNT thin films was initiated at around 107 cycles. The Pr values of the BNT thin films prepared at 600 ◦C decreased by 14% after a fatigue measurement with 109 switching cycles, as shown in Fig. 24. BNT thin films prepared at 550 ◦ C with excimer UV irradiation exhibit fatigue endurance similar to that of the 600 ◦ C-annealed samples. The low-temperature-processed BNT thin films did not show a high degree of fatigue endurance compared with BLT thin films prepared with excimer UV irradiation [18]. This polarization fatigue was found to be completely recovered by annealing at 400 ◦C. Further improvement of the fatigue properties of the BNT thin films in this study is required for ferroelectric memory device applications. Figure 25 shows the leakage current properties of BNT thin films prepared at 550 ◦ C and 600 ◦C with excimer UV irradiation. The BNT thin films prepared at 550 ◦C showed leakage current properties superior to those of the 600 ◦ C-annealed films. The leakage current density of the 550 ◦ C-annealed BNT thin films was below 10−6 A/cm2 up to an applied voltage of 3 V. This may be attributable to the increased roughness involving grain growth, as shown in Fig. 21. The optimization of the microstructure has been found to be a key for the improvement of the leakage current properties of CSD-derived BNT thin films.


55

Fig. 24. The polarization fatigue properties of BNT thin films prepared at (a) 550 ◦ C and (b) 600 ◦ C with excimer UV irradiation

Fig. 25. Leakage current properties of BNT thin films prepared at (a) 550 ◦ C and (b) 600 ◦ C with excimer UV irradiation

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Index

Bi3.35 Gd0.75 Ti3 O12 , 31 Bi3.35 La0.75 Ti3 O12 , 31 Bi3.35 Nd0.75 Ti3 O12 , 31 Bi3.35 Sm0.75 Ti3 O12 , 31 Bi4 Ti3 O12 , 44 (Bi,Nd)4 (Ti,Ge)3 O12 , 43 (Bi,R)4 Ti3 O12 , 29

Ge-doped (Bi,Nd)4 Ti3 O12 , 43 layered perovskite structure, 39 metal-organic precursors, 26 rare-earth-ion-modified BIT, 29

chemical solution deposition, 26 CSD, 26 excimer UV light irradiation, 47 fatigue, 54 ferroelectric thin films, 26

sol–gel deposition, 26 spin-coating, 30 surface morphology, 35 UV processing, 46

Pb-Based Ferroelectric Thin Films Prepared by MOCVD Masaru Shimizu, Hironori Fujisawa, and Hirohiko Niu Graduate School of Engineering, University of Hyogo, 2167, Shosha, Himeji, Hyogo 671-2201, Japan {mshimizu,fujisawa}@eng.u-hyogo.ac.jp Abstract. This Chapter focuses on the preparation and ferroelectric properties of Pb-based thin films and nanostructures. First, the growth behavior of MOCVDdeposited PbTiO3 and PbZrx Ti1−x O3 (PZT) thin films on various substrates, such as polycrystalline Pt(111)/SiO2 /Si(100), SrTiO3 (100) single crystals and epitaxial SrRuO3 (100)/SrTiO3 (100), has been investigated. SEM, AFM and TEM observations revealed that PbTiO3 and PZT showed the V–W (Volmer–Weber) growth mode when they were grown on polycrystalline Pt-covered Si substrates. From AFM observations, it was found that PZT grown on etched SrTiO3 (100) with a surface terminated by TiO2 and on the TiO2 planes of annealed SrTiO3 (100) showed the S– K (Stranski–Krastanov) growth mode. The V–W growth mode was also observed for PZT on the SrO planes of annealed SrTiO3 (100). When PZT was grown on epitaxial SrRuO3 (100)/SrTiO3 (100), the S–K growth mode was observed. Epitaxial PZT ultrathin films 20 nm thick were successfully grown on SrRuO3 (100)/SrTiO3 (100) with a terrace and step structure. Only when PZT films were grown on SrRuO3 with a terrace and step structure did they exhibit good ferroelectric hysteresis loops, with remanent polarizations (Pr ) of 29 µC/cm2 to 33 µC/cm2 and coercive fields (Ec ) of 340 kV/cm to 370 kV/cm. A 15 nm-thick PZT film showing an unsaturated hysteresis loop was also studied. The ferroelectricity and local current flow of PZT ultrathin films with thicknesses smaller than 10 nm were investigated by SPM techniques. V–W growth was observed for PbTiO3 and PZT on epitaxial Pt/SrTiO3 and Pt/MgO substrates. Pyramidal-shaped, triangular-prism-shaped and squareshaped PbTiO3 and PZT self-assembled nanostructures were successfully prepared on epitaxial Pt/SrTiO3 (111), (110) and (100) substrates, respectively, demonstrating structural control. Piezoresponse measurements using SPM proved that PbTiO3 and PZT nanoislands prepared on various substrates had ferroelectricity even before they became films. The minimum volume of a PbTiO3 nanostructure was 1.9 × 103 nm3 (38 nm width × 1.7 nm height). This result has led us to a new study and development, of self-assembled and self-organized ferroelectric nanostructure technology.

1 Introduction In the past decade, one of the major and most exciting areas of ferroelectric applications has been nonvolatile ferroelectric random access memories (FeRAMs), including DRAM-type memories and ferroelectric-gate FET-type M. Okuyama, Y. Ishibashi (Eds.): Ferroelectric Thin Films, Topics Appl. Phys. 98, 59–77 (2005) © Springer-Verlag Berlin Heidelberg 2005

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memories. For the development and realization of FeRAMs, the importance of the thin-film physics and thin-film technology of ferroelectric materials has increased extensively, because ferroelectric thin films are combined with Si integrated-circuit chips. This combination of a ferroelectric thin film with a bulk semiconductor chip raises practical issues due to the properties of the ferroelectric thin film itself and to process integration. Much effort has been made to solve a variety of issues, such as fatigue resulting from polarization reversal, imprinting, interfaces between ferroelectrics and metals or semiconductors, the processing of ferroelectric thin films, electrode and barrier materials, and degradation caused by processing in reducing gas atmospheres. For the deposition of ferroelectric thin films, a variety of techniques, such as reactive evaporation, sputtering (ion beam, rf diode and rf magnetron), pulsed laser deposition (PLD) (another term, “laser ablation”, is also widely used), sol–gel, metal-organic deposition (MOD) and metal-organic chemical vapor deposition (MOCVD), have been reported. Among these techniques, the MOCVD method has excellent potential because of good compositional control, high film density, high film uniformity, high deposition rate, the possibility of a low processing temperature and good compatibility with Si LSI processes. Moreover, MOCVD can offer good step coverage characteristics, which is very important for deposition on three-dimensional surfaces. The first attempt at CVD of perovskite Pb-based ferroelectric thin films was reported in 1982 [1]. Reports on MOCVD of PbTiO3 and Pb(Zr,Ti)O3 (PZT) thin films, using Pb(C2 H5 )4 , Zr(O-tC4 H9 ) and Ti(O-iC3 H7 )4 as precursors, were first published in 1988 [2, 3] and 1990 [4], respectively. After the publication of these pioneering works, a lot of papers on MOCVD of ferroelectric thin films, including PbTiO3 , PZT, (Pb,La)(Zr,Ti)O3 (PLZT), BaTiO3 , SrTiO3 , Bax Sr1−x TiO3 , Bi4 Ti3 O12 , and SrBi2 Ta2 O12 , have been published. For the realization of FeRAMs with high integration and low-voltage operation, high-quality thin films require preparation at low growth temperatures. To obtain high-quality ferroelectric thin films, understanding of the growth mechanism is very important. However, the growth mechanisms of ferroelectric thin films, in particular Pb-based films, prepared by MOCVD have rarely been examined, except for a few reports [5, 6]. Section 3 presents observations of the initial growth stages of PbTiO3 and PZT thin films prepared on various substrates by MOCVD. From the point of view of device performance, thinner ferroelectric films are required. Ferroelectric properties and the ultimate potential of ferroelectric ultrathin films have also attracted interest not only from the point of view of device applications, but also from that of the thin-film size effect. Therefore, a variety of studies on the thickness dependence of the ferroelectric properties and on the preparation of ferroelectric ultrathin films have been reported [7, 8, 9, 10, 11, 12]. Section 4 describes the preparation of PZT

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ultrathin films and the effect of the surface flatness of the substrate on the crystalline and ferroelectric properties of the PZT ultrathin films. In the past several years, interest in ferroelectric nanostructures on substrates has increased greatly, not only from the point of view of nanoelectronics, such as Gbit or Tbit FeRAMs and nanoactuators, but also from the point of view of the three-dimensional size effect. Various techniques have been utilized to prepare ferroelectric nanostructures, such as electron beam direct writing [13,14], electron beam lithography [15], focused-ion-beam milling [16, 17], imprint lithography [18], self-assembled processes (another term, “self-organized processes”, is also widely used in the literature) [19] and self-patterning processes [20,21]. Among these techniques, self-assembled processes have provided nanostructures smaller than 50 nm. Generally, in the initial growth stages of PbTiO3 and PZT grown on Pt-covered substrates, self-assembled nanoislands have been observed. Section 5 presents a brief description of the preparation and structural control of self-assembled nanostructures, and their ferroelectric properties.

2 Experimental Procedure PbTiO3 and PZT thin films and nanostructures were prepared on various substrates at 370 ◦ C to 560 ◦ C by MOCVD using Pb(C2 H5 )4 , (C2 H5 )3 PbOCH2 C(CH3 )3 , Zr(O-tC4 H9 )4 and Ti(O-iC3 H7 )4 as precursors and O2 as an oxidant. Details of our MOCVD technique have already been reported elsewhere [22,23,24]. The substrates used were Pt(111)/SiO2/Si(100); SrTiO3 (100); Pt/SrTiO3 (111), (110) and (100); Pt/MgO(111), (110) and (100); and SrRuO3 (100)/SrTiO3(100). Pt and SrRuO3 were deposited by rf magnetron sputtering at substrate temperatures of 550 ◦C to 630 ◦ C and 560 ◦ C, respectively. In order to obtain atomically flat surfaces, the SrTiO3 single-crystal substrates were either etched with BHF (buffered NH4 F–HF, 0.1 mol/l, pH = 4.5) solution or annealed in air at 1150 ◦C for 6 h. The initial growth stages and surface morphologies of films were observed mainly using scanning electron microscopy (SEM) (Hitachi S-900), atomic force microscopy (AFM) (Seiko Instruments Inc. SPI-3800N) and transmission electron microscopy (TEM) (JEOL JEM2010FEG). The crystalline structure was examined using the X-ray diffraction method (PANalytical X’pert-MRD). The ferroelectric and dielectric properties of films were measured with an electrometer (Keithley 6517), a pulse generator (NF WF1946), a digitizing oscilloscope (HP 54602B) and a Sawyer–Tower circuit. The piezoelectric and ferroelectric properties of nanosized islands and ultrathin films were examined by piezoresponse force microscopy (PFM) using AFM.

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Fig. 1. Schematic diagram of the three growth modes. (a) Volmer–Weber (V–W), (b) Frank–van der Merwe (F–M) and (c) Stranski–Krastanov (S–K) growth modes

3 Microscopic Observation of the Initial Growth Stages of PbTiO3 and PZT Thin Films on Various Substrates 3.1 Growth Process of PbTiO3 and PZT Thin Films on Polycrystalline Pt/SiO2 /Si In the theory of thin-film growth, three growth modes are traditionally distinguished. They are the Volmer–Weber (V–W) [25], Frank–van der Merwe (F–M) [26] and Stranski–Krastanov (S–K) growth modes [27]. They are also referred to as island growth (3D), layer-by-layer growth (2D) and layer-bylayer plus island growth. These growth modes are illustrated schematically in Fig. 1. The particular growth mode for a given system depends on the interface energies and lattice mismatch [28]. In order to observe the initial growth stages of PbTiO3 and PZT films deposited on metal-covered substrates, the films were grown at 560 ◦ C on Pt/SiO2 /Si(100) for various deposition times, in the range 2 s to 600 s. Pt deposited by rf magnetron sputtering at 550 ◦C was polycrystalline and had a strong (111) orientation. Figure 2 shows AFM images of PbTiO3 and PbZr0.24 Ti0.76 O3 deposited on Pt(111)/SiO2/Si(100) for 2 s to 480 s. At very early stages, small nuclei were observed (Fig. 2(a) and (d)). They grew gradually, and pyramidal-shaped islands were observed (Fig. 2(b) and (e)). As the deposition time increased, pyramidal-shaped islands grew laterally until finally they covered the entire substrate surface (Fig. 2(c) and (f)). The average width and height of the PbTiO3 and PZT islands increased with deposition time. The pyramidal-shaped islands of both PbTiO3 and PZT showed a (111) orientation. However, the in-plane orientation was random and the islands were randomly distributed, because the Pt was polycrystalline and had a random in-plane orientation.


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Fig. 2. AFM images of PbTiO3 deposited on Pt(111)/SiO2 /Si(100) for (a) 2 s, (b) 35 s and (c) 480 s, and of PZT deposited for (d) 30 s, (e) 60 s and (f ) 420 s

Fig. 3. Cross-sectional TEM image of a PbTiO3 island grown on polycrystalline Pt(111)/SiO2 /Si(100)

The microstructure of PbTiO3 and PZT islands was observed by TEM. Figure 3 shows a typical cross-sectional TEM image of a PbTiO3 island on Pt/SiO2 /Si. TEM observations showed that islands grew three-dimensionally on Pt and that they did not grow after several layers of PbTiO3 and PZT [29,

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30]. Therefore the growth mode of PbTiO3 and PZT islands on Pt-covered Si was the Volmer–Weber mode, as illustrated in Fig. 1(a). In TEM images, it was observed that the PbTiO3 islands had stripes inclined at 30◦ to 40◦ to the Pt substrate surface and that lattice planes which were normal to the substrate surface were also tilted at the stripe line. TEM observations and crystallographic considerations showed that the stripe lines correspond to (101) twin boundaries [29,30], which are a–c (90◦ ) domain boundaries due to the tetragonal structure. Nanosize islands of PbTiO3 and PZT were also shown to have tetragonal and rhombohedral phases [30], and therefore the islands could have spontaneous polarization. 3.2 Growth Process of PZT Thin Films on SrTiO3 Single Crystals In order to investigate the growth process of PZT thin films on single-crystal substrates, PZT films were grown on SrTiO3 (100) single crystals. When the SrTiO3 (100) single-crystal substrate was etched with BHF solution, the surface showed a terrace–step structure and was terminated with TiO2 atomic planes, as described in Sect. 4 [31, 32, 33]. Figure 4 shows AFM images of PZT (Zr-rich) grown on etched SrTiO3 for 5 s to 50 s. The AFM images at early stages showed layer growth and no three-dimensional growth (Fig. 4(a) and (b)). The surface of the SrTiO3 was uniformly covered with one atomic layer of PZT because the PZT thickness of 0.42 nm, which was calculated from the growth rate of 5 nm/min and deposition time of 5 s, was just equal to the height of one unit cell of PZT. In the next stage, three-dimensional islands were formed after some layers, as shown in Fig. 4(c) and (d). This suggests that the growth mode of PZT on etched SrTiO3 (100) was the Stranski– Krastanov mode, as illustrated in Fig. 1(c). This was also supported by a line profile measurement using AFM. When the SrTiO3 (100) surface was annealed in air at 1150 ◦C, the surface of the SrTiO3 was terminated with both SrO and TiO2 atomic planes [34]. Figure 5 shows AFM and FFM (friction force microscopy) images of the surface of an annealed SrTiO3 (100) surface, and an AFM image of the surface after PZT has been deposited for 5 s. In the FFM image of Fig. 5(b), bright- and dark-contrast terraces correspond to high- and low-friction terraces, respectively. The topmost SrTiO3 surface is composed of either an SrO or a TiO2 atomic plane [34, 35]. Coaxial-impact-collision ion-scattering spectroscopy (CAICISS) and FFM studies have shown that the bright- and dark-contrast terraces correspond to SrO- and TiO2 -terminated terraces, respectively [35]. When PZT was deposited on this annealed SrTiO3 substrate, it showed a different growth mode on the SrO planes from the TiO2 planes, as can be seen in Fig. 5(c). Three-dimensional island growth was observed on a bright-contrast region in the FFM image of Fig. 5(b), i.e. an SrO plane (V– W mode). On the other hand, on the dark-contrast region in Fig. 5(b), i.e.


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Fig. 4. AFM images of PZT deposited on etched SrTiO3 (100) single crystal for (a) 5 s, (b) 10 s, (c) 30 s and (d) 50 s. The square dark-contrast areas correspond to etch pits

Fig. 5. (a) AFM image and (b) FFM image of the surface of an annealed SrTiO3 (100) single crystal, and (c) AFM image of PZT deposited at 560 ◦ C for 5s

a TiO2 plane, two-dimensional growth and subsequent island growth (S–K mode) were observed [36]. 3.3 Growth Process of PZT Thin Films on Epitaxial SrRuO3 /SrTiO3 The growth behavior of PZT thin films on SrRuO3 /SrTiO3 (100) was also investigated. SrRuO3 (100) was epitaxially grown on SrTiO3 (100) by rf magnetron sputtering at 560 ◦C. Figure 6 shows surfaces of PZT thin films deposited on epitaxial SrRuO3 /SrTiO3 (100) for various deposition times. When

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Fig. 6. AFM images of PZT deposited on epitaxial SrRuO3 (100)/SrTiO3 (100) at 560 ◦ C for (a) 10 s, (b) 60 s and (c) 90 s

Fig. 7. Dependence of surface roughness of PZT films on SrRuO3 (100)/ SrTiO3 (100) on the deposition time

PZT (Zr-rich) was deposited on SrRuO3 /SrTiO3 at 560 ◦ C, in the initial growth stages three-dimensional island growth was not observed, as shown in Fig. 6(a). In this growth stage, PZT layers had already been formed, and this fact was confirmed by X-ray fluorescence analysis. Afterwards, as shown in Figs. 6(b) and (c), three-dimensional growth was observed. Figure 7 shows the dependence of the surface roughness of PZT films grown on SrRuO3 /SrTiO3 on the deposition time. The root mean square (rms) roughness did not change for deposition times up to 50 s, but after that it increased dramatically. These results means that S–K growth mode (layerby-layer growth plus island growth) occurred for PZT grown on epitaxial SrRuO3 /SrTiO3 [37], as observed for PZT on MgO [6].


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4 Epitaxial PZT Ultrathin Films 4.1 Preparation of PZT Ultrathin Films on SrRuO3 /SrTiO3 In this section, we describe an investigation of the preparation of PZT ultrathin films and the influence of the surface flatness of SrTiO3 (100) singlecrystal substrates on the crystalline and ferroelectric properties of PZT ultrathin films [38, 39]. In the first stage, in order to obtain atomically flat surfaces on the SrTiO3 (100) single-crystal substrates, SrTiO3 (100) was etched with BHF solution and afterwards annealed at 950 ◦C [31,33]. Figure 8 shows AFM images of surfaces untreated and treated SrTiO3 single-crystal substrates, and line profiles. From Fig. 8(a), we can see that the SrTiO3 surface without surface treatment shows corrugations and no terrace–step structure. On the other hand, the surface of treated SrTiO3 has atomically flat terraces and steps with a height of 0.4 nm, as shown in Fig. 8(c). This step height corresponds to one unit cell length of SrTiO3 , which shows that SrTiO3 has an atomically flat surface. In the second stage, 25 nm-thick SrRuO3 thin films were deposited as a bottom electrode on untreated and treated SrTiO3 substrates by rf magnetron sputtering. When SrRuO3 was deposited on untreated SrTiO3 , it showed no distinct terraces or steps, as shown in Fig. 8(b). On the other hand, SrRuO3 deposited on treated SrTiO3 had terraces and steps, as shown in Fig. 8(d). X-ray diffraction measurements showed that the SrRuO3 (100) films were epitaxially grown on both the treated and untreated SrTiO3 (100) substrates. In the final stage, 20 nm-thick PZT thin films were deposited on SrRuO3 (25 nm)/SrTiO3 with and without a terrace and step structure. AFM images and line profiles of PZT surfaces on SrRuO3 /SrTiO3 with and without a terrace and step structure are shown in Fig. 9. PZT ultrathin films showed terrace and step structures only when they were grown on SrRuO3 /SrTiO3 with a terrace and step structure. The surface morphology of the PZT reflected that of the SrRuO3 , because the thickness of PZT was very thin. X-ray diffraction results showed that the PZT and SrRuO3 were epitaxially grown on both the treated and the untreated SrTiO3 . Figure 10 shows X-ray diffraction profiles of the 20 nm-thick PZT ultrathin films grown on SrRuO3 /treated SrTiO3 with a terrace and step structure. The FWHM value for the PZT ultrathin film on treated SrTiO3 , 0.5◦ , was smaller than that for PZT on untreated SrTiO3 , 0.9◦ , indicating that the PZT ultrathin film grown on a substrate with an atomically flat surface showed better crystalline structure than the film grown on a substrate without a flat surface. 4.2 Ferroelectric Properties of PZT Ultrathin Films Ferroelectric properties were measured for PZT ultrathin-film capacitors with Pt top and SrRuO3 bottom electrodes. D–E hysteresis loops for 20 nm-thick

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Fig. 8. AFM images of surfaces, and line profiles, of SrTiO3 (100) single crystals and SrRuO3 films on SrTiO3 (100). (a) Untreated SrTiO3 substrate, (b) SrRuO3 grown on untreated SrTiO3 , (c) treated SrTiO3 substrate and (d) SrRuO3 grown on treated SrTiO3

PZT films grown on SrRuO3 with and without a terrace and step structure are shown in Fig. 11. When the PZT thin films were prepared on SrRuO3 without a terrace and step structure, poor hysteresis loops were observed, as shown in Fig. 11(a), owing to a high leakage current. In contrast, PZT films grown on SrRuO3 with a terrace and step structure showed saturated hysteresis loops with a good square shape, as can be seen in Fig. 11(b). The


69

Fig. 9. AFM images of surfaces, and line profiles, of 20 nm-thick PZT films grown on (a) SrRuO3 /untreated SrTiO3 and (b) SrRuO3 /treated SrTiO3 with terrace and step structures

Fig. 10. X-ray diffraction profiles of 20 nm-thick PZT films grown on SrRuO3 /treated SrTiO3 with terrace and step structures. (a) θ–2θ profile and (b) φscan profile

remanent polarization (Pr ) and coercive electric field (Ec ) were 29 µC/cm2 to 33 µC/cm2 and 340 kV/cm to 370 kV/cm, respectively. Figure 12 shows current–voltage characteristics of 20 nm-thick PZT films grown on SrRuO3 with and without a terrace and step structure. The leakage current density of the PZT film with a terrace and step structure was smaller than that of the

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Fig. 11. D–E hysteresis loops of 20 nm-thick PZT ultrathin films on (a) SrRuO3 /untreated SrTiO3 and (b) SrRuO3 /treated SrTiO3

Fig. 12. Current–voltage characteristics of 20 nm-thick PZT ultrathin films on (a) SrRuO3 /untreated SrTiO3 and (b) SrRuO3 /treated SrTiO3

film without a terrace and step structure and was approximately 10−3 A/cm2 at +1 V [38]. These results reveal that the surface flatness of the substrate is very important for the preparation of ultrathin PZT films with good ferroelectric properties. The 15 nm-thick PZT ultrathin films grown on SrRuO3 with a terrace and step structure showed unsaturated hysteresis loops owing to high leakage current densities [39]. In our experiments, conventional D–E hysteresis measurements to observe ferroelectricity were not applied for PZT ultrathin films with thicknesses smaller than 15 nm, owing to the high leakage current and film breakdown. For PZT ultrathin films, piezoresponse force microscopy (PFM) is one


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of most promising approaches to measuring ferroelectric and piezoelectric properties [9, 10]. Using this technique, ultrathin PZT films with thicknesses smaller than 10 nm have been found to have ferroelectricity [10, 40]. Local current flow in PZT films was observed by current-sensitive atomic force microscopy (CS-AFM) [41, 42]. This CS-AFM measurement for PZT ultrathin films with thicknesses under 10 nm revealed that large local currents flowed at the step edges of SrRuO3 bottom electrodes [40].

5 Self-Assembled PbTiO3 and PZT Nanostructures and Their Ferroelectric Properties 5.1 Preparation of Self-Assembled PbTiO3 and PZT Nanostructures on Various Substrates As mentioned in Sect. 3, in the initial growth stages of PbTiO3 and PZT grown on polycrystalline Pt/SiO2 /Si, self-assembled nanoislands were observed [30, 43]. When films were grown on epitaxial Ptcovered SrTiO3 substrates, different types of nanostructures were observed in the initial growth stages [44, 45]. Figure 13 shows PbTiO3 nanoislands formed on Pt/SrTiO3 (111), (110) and (100) substrates. On epitaxial Pt(111)/SrTiO3(111), pyramidal-shaped nanostructures were grown, as shown in Fig. 13(a). Compared with those grown on polycrystalline Ptcovered Si substrates, as demonstrated in Fig. 2, the nanostructures grown on Pt/SrTiO3 (111) were arranged laterally, because the Pt was epitaxially grown on SrTiO3 (111) and had a good in-plane orientation. Triangular-prism-shaped and square-shaped PbTiO3 nanostructures were grown by self-assembly on epitaxial Pt(110)/SrTiO3(110) and Pt(100)/SrTiO3 (100) substrates, as shown in Fig. 13(b) and (c), respectively. The three types of nanostructure mentioned above were also prepared on epitaxial Pt-covered MgO(111), (110) and (100) substrates. PZT nanostructures were also observed on Pt-covered SrTiO3 and MgO substrates.

Fig. 13. AFM images of PbTiO3 nanostructures prepared on (a) Pt/SrTiO3 (111), (b) Pt/SrTiO3 (110) and (c) Pt/SrTiO3 (100)

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Fig. 14. Typical piezoelectric hysteresis loops of PbTiO3 nanostructures prepared on (a) Pt/SiO2 /Si(100), (b) Pt/SrTiO3 (111) and (c) Pt/SrTiO3 (110), measured by SPM

XRD studies showed that the PbTiO3 and PZT nanoislands were epitaxially grown on these substrates [44]. This result means that structural control was successfully performed using epitaxial relations. 5.2 Piezoelectric and Ferroelectric Properties of PbTiO3 Nanostructures The observation of domain structures in PbTiO3 and PZT islands by TEM suggests indirectly the possibility of ferroelectricity in those islands, as described in Sect. 3 [29, 30]. In order to examine directly whether the nanostructures have ferroelectricity or not, a piezoresponse measurement using SPM (scanning probe microscopy) was performed. The piezoresponse technique using SPM is one of the most promising and important approaches to piezoelectric and ferroelectric phenomena in ferroelectric nanostructures prepared on various substrates [45]. Some details of piezoresponse measurements for PZT have already been reported elsewhere [42, 43, 46]. Piezoelectric hysteresis loops with polarization reversal were observed in nanostructures prepared on Pt-covered SrTiO3 (see Fig. 13), as well as on Si substrates (see Fig. 2). Figure 14 shows typical piezoelectric hysteresis loops observed for PbTiO3 nanostructures grown on Pt/SiO2 /Si(100) and on Pt/SrTiO3 (111) and (110). These piezoelectric hysteresis loops reveal that the PbTiO3 nanostructures on the polycrystalline and epitaxial Ptcovered substrates have ferroelectricity. PbTiO3 nanostructures on epitaxial Pt-covered MgO(111), (110) and (100) and PZT nanostructures on epitaxial Pt-covered SrTiO3 (111) and (100) also showed piezoresponse hysteresis loops, indicating their ferroelectricity. In order to investigate the minimum size of a PbTiO3 nanostructure that would show ferroelectricity, control of the size of the structures was attempted. The sizes of the nanostructures were controlled by changing the deposition temperature and deposition time. The average size of nanostruc-


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Fig. 15. Piezoresponse hysteresis loops of PbTiO3 nanostructures on Pt/SiO2 /Si with (a) a width of 38 nm and a height of 1.7 nm, and (b) a width of 29 nm and a height of 4.1 nm

tures increased as the deposition temperature and deposition time increased. When PbTiO3 was grown on Pt/SiO2 /Si, the average width and height were 41 nm and 3.6 nm, respectively, for PbTiO3 islands prepared at 390 ◦ C, and 49 nm and 19 nm for islands prepared at 560 ◦C, respectively. Figure 15 shows piezoresponse hysteresis loops observed for PbTiO3 nanoislands with heights of 1.7 nm and 4.1 nm and widths of 38 nm and 29 nm which were prepared at 390 ◦ C [47]. These piezoelectric hysteresis loops evidently prove the presence of ferroelectricity. It is surprising that the minimum height of 1.7 nm corresponds to only 4 unit cells of PbTiO3 . To our knowledge, these values are the minimum size of PbTiO3 in which ferroelectricity has been experimentally observed. In addition, in this study, piezoelectric hysteresis loops cannot be obtained from PbTiO3 islands smaller than 1.9×103 nm3 owing to several difficulties in the measurements, such as breakdown under high electrical fields (> MV/cm), degradation of the conductive coating of the SPM tip and drift of the X–Y scanner. Therefore, the critical volume for ferroelectricity may be smaller than the minimum volume of 1.9 × 103 nm3 obtained in this study. Acknowledgements The authors would like to thank greatly Dr. K. Honda (Fujitsu Lab. Co. Ltd.) for TEM observations and helpful discussions, and Messrs. H. Nonomura and M. Okaniwa for sample preparation and electrical measurements.

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Index

a–c (90◦ ) domain, 64 atomic force microscopy (AFM), 61 atomically flat surface, 67 CAICISS, 64 coaxial-impact-collision ion-scattering spectroscopy, 64 ferroelectric nanostructures, 61 ferroelectric ultrathin films, 60 ferroelectricity, 72 FFM, 64 friction force microscopy, 64 initial growth stages, 60, 62 islands, 62 layer growth, 64 metal-organic chemical vapor deposition, 60, 61 MOCVD, 60, 61 nanostructures, 61, 71 nuclei, 62

PbTiO3 nanoislands, 71 PbTiO3 nanostructures, 71, 72 PbTiO3 thin films, 61 PFM, 61 piezoresponse force microscopy, 61 piezoresponse hysteresis loop, 72 piezoresponse measurement, 72 PZT nanostructures, 71, 72 PZT thin films, 61 PZT ultrathin films, 60, 67 Sawyer–Tower circuit, 61 self-assembled nanoislands, 71 self-assembled process, 61 self-organized process, 61 Stranski–Krastanov growth mode, 64, 66 structural control, 72 terrace and step structure, 67 three-dimensional island growth, 64, 65 two-dimensional growth, 64 Volmer–Weber growth mode, 64

Spontaneous Polarization and Crystal Orientation Control of MOCVD PZT and Bi4Ti3 O12 -Based Films Hiroshi Funakubo Department of Innovative and Engineered Materials, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology, G1-32, 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8502, Japan [email protected] Abstract. The spontaneous polarization (Ps ) and the remanent polarization (Pr ) of films deposited on Si substrates are compared for PZT and Bi4 Ti3 O12 -based films. PZT has many advantages compared with Bi4 Ti3 O12 -based ferroelectrics. However, the ferroelectric properties of PZT cannot be tailored, because they vary basically only with the Zr/Ti ratio in the film, except for the effect of processing conditions. In spite of that, the ferroelectric properties can be designed by the so-called “site-engineered concept” [1], the concept of designing properties by the substitution of the pseudoperovskite sites of the Bi4 Ti3 O12 structure, for Bi4 Ti3 O12 -based films. This makes these materials good candidates for FeRAM applications.

1 Introduction In this Chapter, we describe mainly a comparison of properties between PZT and Bi4 Ti3 O12 -based ferroelectrics [1]. Tetragonal PZT ferroelectrics and Bi4 Ti3 O12 -based ferroelectrics, especially lanthanide-substituted Bi4 Ti3 O12 , are prime candidates for ferroelectric random access memories (FeRAM). We summarize the present data on such films prepared by MOCVD and discuss the future scope of these materials on the basis of these data. We have selected the MOCVD process because of its ability to make high-quality films, the low deposition temperature and the good step coverage, which make this process the most suitable one for high-density FeRAM fabrication.

2 Spontaneous Polarization Among the many characteristics of ferroelectric materials, the spontaneous polarization (Ps ) is the most basic one. It also corresponds to the maximum remanent polarization (Pr ), which is directly connected to the switching charge in an FeRAM. However, it has hardly been discussed because of the lack of single-crystal data. M. Okuyama, Y. Ishibashi (Eds.): Ferroelectric Thin Films, Topics Appl. Phys. 98, 77–91 (2005) © Springer-Verlag Berlin Heidelberg 2005

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Fig. 1. (a) XRD pattern and (b) pole figure plot at a fixed angle 2θ corresponding to the PZT 111 diffraction peak for a 50 nm-thick Pb(Zr0.35 Ti0.35 )O3 film grown on a (100) SrRuO3 ||(100) SrTiO3 substrate at 570 ◦ C

2.1 PZT Films During recent decades, epitaxial PZT films have been grown by various growth methods with film thicknesses ranging from 10 nm to 5 µm. Single crystals of SrTiO3 , MgO, LaAlO3 etc., together with Si, have been used as substrates for this epitaxial growth. The films are grown above the Curie temperature, so that the film transforms from a cubic to a tetragonal symmetry during the cooling process. Therefore, these films generally include not only 180◦ domains, but also 90◦ domains in order to release the strain arising from the substrate [2]. This means that the domains whose polar axes lie in the plane (a-domains) exist together with domains whose polar axes are perpendicular to the film surface (c-domains). In this case, c-domains contribute to the polarization when the electric field is applied along the surface normal direction, while a-domains do not make any contribution [3, 4]. We already estimated the Ps value of tetragonal Pb(Zr0.35 Ti0.65 )O3 having a mixed structure of a- and c-domains for 200 nm-thick films by assuming no 90◦ domain switching for the a-domains caused by the applied field. To evaluate the Ps of PZT films more accurately, the growth and characterization of perfectly polar-axis-oriented films are essential. However, this has hardly been reported, except for a report of Pb(Zr0.5 Ti0.5 )O3 films by Ishida et al. [5]. We have successfully grown perfectly c-axis-oriented Pb(Zr0.35 Ti0.35 )O3 films for the first time by decreasing the film thickness down to 80 nm and growing at high temperature on (100) SrTiO3 substrates [6]. Figure 1(a) shows XRD data for a perfect c-axis-oriented film. Epitaxial growth of this film with a c-axis orientation has been demonstrated. Figure 2 shows an X-ray reciprocal-space map around the SrTiO3 204 spot. The PZT 402 spot corresponding to a-domains is hardly observed, suggesting that the film has a perfect polar-axis orientation.

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Fig. 2. X-ray reciprocal-space map around SrTiO3 204 spot for the same film as shown in Fig. 1

Fig. 3. (a) P –E hysteresis loops, and saturation properties of Pr and Ec values versus the maximum applied voltage for the same film as shown in Figs. 1 and 2

Figure 3 shows P –E hysteresis loops of the same film and the value of Pr and the coercive field (Ec ) versus the maximum applied voltage. A large Pr value above 80 µC/cm2 with a good saturation property is observed. The saturation polarization value (Psat ) of this film directly corresponds to the Ps value of this film because the film has a perfect polar-axis orientation. This large Ps value is in good agreement with the value estimated from films consisting of a mixture of a- and c-domains on the basis of the assumption

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Fig. 4. (a) TEM micrograph and (b) Fourier-filtered image using Bi4 Ti3 O12 007 spot for a (100)/(010)-oriented Bi4 Ti3 O12 film grown on a (101) TiO2 substrate

that a-domains do not switch to c-domains, differently from the data for sintered bodies. These results suggest that a large Pr value is expected when the film orientation can be controlled. 2.2 Bi4 Ti3 O12 -Based Films Films of Bi4 Ti3 O12 -based ferroelectrics, including lanthanide substituted ones, are novel candidates for FeRAMs because of their relatively large Pr values and lead-free composition. However, their Ps values have hardly been reported, because of the lack of single-crystal data. Differently from the PZT case, this crystal has a large anisotropy in the growth rate along the c-axis because it has a layer-structure stacking of bismuth oxide and pseudoperovskite layers along the c-axis; however, its Ps is along the a-axis. We have already estimated the Ps value by making (104)/(014)-oriented epitaxial films. However, in this case, the volume fractions of (104) and (014) are difficult to estimate by XRD because of the close lattice parameters of the a- and b-axes. Therefore, a measurement of ferroelectric properties using (100)/(010)-oriented films or films whose c-axes lie in the plane is necessary for a precise estimation. These film orientations are just those of (100)/(001)-oriented films of PZT [7]. However, the long c-axis lattice parameter of about 3.3 nm must lie in the plane for films of this orientation to be made. In the case of oxide superconductors, a-axis-oriented films of YBa2 Cu3 O7 with a c-axis lattice parameter of 1.2 nm have been achieved, but this has not been done for Bi2 Ba2 CaCu2 O8 films with a c-axis lattice parameter of 3.7 nm. We have found that the (101)-oriented plane of the rutile structure is useful as a substrate for making (100)/(010)-oriented Bi4 Ti3 O12 films [8, 9,


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Table 1. Summary of ferroelectric properties of (110)- and (100)/(010)oriented films Orientation Ec ( kV/cm) Pr ( µC/cm2 ) Psat ( µC/cm2 ) Ps//a-axis ( µC/cm2 ) (110) 136 34 41 58 (100)(010) 138 31 40* 58 *Using X-ray diffraction, the volume fraction a/b was evaluated to be 67/33.

Fig. 5. Schematic view [(a) plan view and (b) bird’s eye view] of the lattice matching of 1 unit of Bi4 Ti3 O12 with 7 units of TiO2

10]. Figure 4 shows TEM micrographs of Bi4 Ti3 O12 films with a (100)/(010) orientation. Figure 4(a) shows a cross-sectional TEM image in the (100)/(010) direction. A clear layer structure grown perpendicular to the substrate surface has been demonstrated, as shown in Fig. 4(a). Taking account of the possible combinations of the (100)/(010) planes of the Bi4 Ti3 O12 -based film and (101) TiO2 , a long-range lattice matching of 7 unit cells of TiO2 with 1 unit cell of the Bi4 Ti3 O12 over 3.3 nm is the most reasonable possibility, as shown in Fig. 5. In this case, one possible scenario is that the Ti top layer of TiO2 matches the oxide bottom layer of the Bi4 Ti3 O12 , as shown in Fig. 5, where the lattice matching decreases to 2.8%, as shown in Fig. 4(b). In such a way, (110)- and (100)/(010)-oriented Nd-substituted Bi4 Ti3 O12 films have been grown on (100) and (101) RuO2 layers, respectively [11]. Figure 6 shows the P –E hysteresis of these films. Well-saturated hysteresis loops are obtained for both films. Table 1 summarizes the ferroelectric properties of these films. According to the volume fractions of (100)/(010) estimated

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Fig. 6. P –E hysteresis loops of (a) (110)- and (b) (100)/(010)-oriented Bi4 Ti3 O12 films grown on (110) and (101) RuO2 layers, respectively

Fig. 7. Relationship between the Curie temperature and the spontaneous polarization (Ps )

from XRD, the Ps value, assuming that (010) domains do not switch to (100) domains because of the applied electric field, is 58 µC/cm2 . This value is plotted in Fig. 7, which shows the relationship between the Curie temperature (Tc ) and Ps . The present Ps value is larger than that reported for singlecrystal Bi4 Ti3 O12 . Moreover, the Ps value above 50 µC/cm2 is matched to the guideline of the FeRAM road map up to 2009. There are two possible reasons for the larger Ps value of Nd-substituted Bi4 Ti3 O12 than for singlecrystal Bi4 Ti3 O12 . One is an overestimation of the Ps value of Nd-substituted Bi4 Ti3 O12 due to switching of (010) domains to (100) ones. The other is the small polarization of single-crystal Bi4 Ti3 O12 due to domain pinning, as Noguchi et al. [12] pointed out for Bi4 Ti3 O12 sintered bodies.


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Fig. 8. (a) XRD patterns and (b) P –E hysteresis loops for PZT films deposited at various deposition temperatures

3 Remanent Polarization of Polycrystalline Ferroelectric Films Prepared on Si Substrates In the above section, the Ps value, which corresponds to the maximum Pr value of a ferroelectric material, has been discussed. In real cases, polycrystalline films deposited on a Si substrate together with electrodes are used. In this section, the present status of the Pr values of polycrystalline films deposited on Si substrates is discussed. 3.1 PZT Films PZT films are known to have a relatively large Pr value even if they are deposited on Si substrates. Figure 8 shows XRD patterns of PZT films deposited on (111) Pt-coated Si substrates [3]. When the deposition temperature is as high as 580 ◦ C, the PZT film has a (111) orientation, originating from local epitaxial growth of (111) PZT on (111) Pt. For this orientation, the Pr value is expected to reach 56% of the Ps value. If the Ps value is 90 µC/cm2, as shown in Fig. 3(a), the Pr value of (111)-oriented films is expected to reach 50 µC/cm2 , in good agreement with the data shown in Fig. 8(b). The advantage of this orientation is the single-domain structure of (111) [2], suggesting that the properties are stable against heat treatment after the deposition. As shown in Fig. 8(b), the film orientation changed from (111) to (100)/(001) when the deposition temperature decreased. In the latter orientation, the Pr value depends strongly on the volume fractions of the (100) and (001) domains, because a (100)-oriented film does not shows any ferroelectricity, although (001) domains show 100% of the Ps value. The volume ratio depends on the strain applied to the film [13]. For a simple capacitor structure, the volume fraction of (001) domains is estimated to be 38–50%, depending on the film thickness and the deposition temperature. However, it may possibly be changed by heat treatment above the Curie temperature. In the PZT

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Fig. 9. Remanent polarization (Pr ) as a function of the volume fraction of (001) domains, V (001)/[V (001) + V (100)], in (100)/(001)-oriented Pb(Zr0.35 Ti0.65 )O3 films

Fig. 10. XRD analysis of Nd- and V-cosubstituted and Nd-substituted Bi4 Ti3 O12 films on (111) Pt-coated Si substrates. (a) θ–2θ scan, (b) ψ–2θ/θ scan, (c) ψ scan

case, (111)- and (100)/(001)-oriented films are often reported, while reports of a random orientation are limited, suggesting that the orientation control technique is less effective (Fig. 9), which is different from the situation for Bi4 Ti3 O12 -based films, where, for example, the orientation can be controlled by changing the kind of bottom electrodes (Fig. 10).


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Fig. 11. (a) XRD patterns and (b) ψ angular scan of Nd- and V-cosubstituted Bi4 Ti3 O12 films deposited on (001) Ru/SiO2 /Si and (111) Pt/Ti/SiO2 /Si substrates

3.2 Bi4 Ti3 O12 -Based Films Differently from the PZT case, the orientation control of Bi4 Ti3 O12 -based films depends strongly on various preparation factors. Polycrystalline films with a Pr value of 35 µC/cm2 are observed for Nd-substituted Bi4 Ti3 O12 films prepared by CSD methods [14]. On the other hand, a (104)/(014) orientation, which is crystallographically comparable to the (111) orientation of a PZT film, is obtained by local epitaxial growth with a (111) Pt bottom electrode by MOCVD [15]. The Pr value also depends on the volume fractions of (104) and (014) domains. The film orientation can be controlled by changing the top surface of the substrate. Figure 11 shows an XRD comparison of films deposited on (111) Pt- and (001) Ru-coated Si substrates [1]. When the bottom electrode is changed to a (001) Ru-coated one, films with a (110) and (101) preferred orientation are obtained, instead of the (104)/(014) orientation obtained on a (111) Pt-coated substrate. This orientation is expected to have a larger Pr value than for the (104)/(014) orientation. Indeed, a larger Pr value is obtained for (110)- and (100)/(010)-oriented films prepared on (001) Ru-coated substrates, as shown in Fig. 12. However, in spite of the successful growth of (100)/(010)- and (110)-oriented films on single-crystal substrates, it is rather difficult to prepare polycrystalline in-plane c-axis-oriented films on Si. Recently, Matsuda et al. [16] reported on the successful preparation of inplane c-axis-oriented films, i.e. (100)/(001)-oriented films, of Pr-substituted Bi4 Ti3 O12 . The large Pr value of 46 µC/cm2 for these films strongly suggests a (100) preferred orientation, similarly to epitaxial La-substituted films grown on (100) Si substrates [17]. This suggests that the mechanism that determines the volume fraction of (100) and (010) domain is different from that for (100) and (001) domains in PZT films [7]. An understanding of the mechanism determining the domain alignment in Bi4 Ti3 O12 -based films is the next important step in obtaining large Pr values in polycrystalline films.

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Fig. 12. (a) P –E hysteresis of the same films as shown in Fig. 11, and (b) the fatigue endurance of films deposited on (001) Ru-coated substrates

Fig. 13. (a) XRD pattern, (b) P –E hysteresis and (c) saturation properties of Pr and Ec of a RuO2 /PZT/Pt/RuO2 capacitor. The PZT film was deposited at 395 ◦ C

3.3 Low-Temperature Deposition Lowering of the deposition temperature is one of the most important key issues in realizing high-density FeRAMs. This is because of the reduction of in-


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Fig. 14. (a) XRD pattern and (b) P –E hysteresis loops of a Pr -substituted Bi4 Ti3 O12 -based film prepared on a (001) Ru-covered Si substrate at 500 ◦ C

terdiffusion of the layers in the devices. The research activity on SrBi2 Ta2 O9 , one of the candidates for FeRAM, has dramatically shrunk during last five years owing to the difficulty of low-temperature deposition [16], together with the small Ps value of below 25 µC/cm2 . In this section, the possibility of low-temperature deposition, especially in the case of MOCVD processes, is summarized. 3.4 PZT Films Some groups [3, 18, 19] have succeeded in preparing PZT films with good ferroelectric properties by MOCVD at low temperature. One of the advantages of low-temperature deposition is the possibility of combination with Ru-based electrodes. Ru electrodes have many advantages because of their superior etching properties. Figure 13 shows an XRD plot and the ferroelectric properties of a RuO2 /PZT/Pt/RuO2 capacitor made using a PZT film deposited at 395 ◦C [20]. By inserting a 10 nm-thick Pt layer, the crystallinity of the PZT film is dramatically improved, and good ferroelectricity with good saturation properties is obtained. This capacitor has been ascertained to have fatigue-free characteristics up to 1010 switching cycles. These data show that high-reliability capacitors applicable to high-density FeRAM cell arrays can be prepared using low temperature-deposited PZT films [20, 21, 22]. 3.5 Bi4 Ti3 O12 -Based Films In the case of Bi4 Ti3 O12 -based films, low-temperature deposition has also been achieved on Ru substrates (Fig. 14). A relatively large Pr value of 16 µC/cm2 has been obtained for films deposited at 500 ◦C [22] (Fig. 14). This temperature is about 100 ◦ C lower than that for SrBi2 Ta2 O9 [16] and it can be decreased further by optimization of the conditions. This capacitor has also been ascertained to have fatigue-free characteristics up to 8 × 1010 switching cycles.

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Acknowledgements I gratefully acknowledge the important contributions of M. Miyayama and Y. Noguch (University of Tokyo); M. Osada (JNIRIM), K. Saito and M. Mizuhira (Philips Japan); K. Suzuki, Y. Nishi and M. Fujimoto (Taiyo Yuden Co.); and especially for the students in my laboratory.

References [1] H. Funakubo, T. Watanabe, T. Kojima, T. Sakai, Y. Noguchi, M. Miyayama, M. Osada, M. Kakihana, K. Saito: J. Cryst. Growth 248, 180 (2003) 77, 85 [2] K. Saito, T. Kurosawa, T. Akai, T. Oikawa, H. Funakubo: J. Appl. Phys. 93, 545 (2003) 78, 83 [3] M. Aratani, T. Oikawa, T. Ozeki, H. Funakubo: Appl. Phys. Lett. 79, 1000 (2001) 78, 83, 87 [4] H. Funakubo, M. Aratani, T. Oikawa, K. Tokita, K. Saito: J. Appl. Phys. 92, 6788 (2002) 78 [5] J. Ishida, T. Yamada, A. Sawabe, K. Okuwada, K. Saito: Appl. Phys. Lett. 80, 467 (200) 78 [6] H. Morioka, G. Asano, T. Oikawa, H. Funakubo, K. Saito: Appl. Phys. Lett. 82, 4761 (2003) 78 [7] T. Watanabe, H. Morioka, S. Okamoto, M. Takahashi, Y. Noguchi, M. Miyayama, H. Funakubo: Proc. Mater. Res. Soc. 784, C4.2.1 (2004) 80, 85 [8] T. Watanabe, H. Funakubo, K. Saito, T. Suzuki, M. Fujimoto, M. Osada, Y. Noguchi, M. Miyayama: Appl. Phys. Lett. 81, 660 (2002) 80 [9] T. Watanabe, T. Sakai, H. Funakubo, K. Saito, M. Osada, M. Yoshimoto, A. Sasaki, J. Liu, M. Kakihana: Jpn. J. Appl. Phys. 41, L1478 (2002) 80 [10] T. Watanabe, K. Saito, M. Osada, T. Suzuki, M. Fujimoto, M. Yoshimoto, A. Sasaki, J. Liu, M. Kakihana, H. Funakubo: Proc. Mater. Res. Soc. 748, U2.4, 69 (2003) 81 [11] T. Watanabe, T. Kojima, H. Uchida, H. Funakubo: Jpn. J. Appl. Phys. 42, L309 (2004) 81 [12] Y. Noguchi, M. Miyayama: Appl. Phys. Lett. 78, 1903 (2001) 82 [13] M. Otsu, H. Funakubo, K. Shinozaki, N. Mizutani: Trans. Mater. Res. Soc. Jpn. 14A, 1655 (1994) 83 [14] H. Uchida, H. Yoshikawa, I. Okada, H. M. T. Iijima, T. Watanabe, T. Kojima, H. Funakubo: Appl. Phys. Lett. 81, 2229 (2002) 85 [15] T. Watanabe, K. Saito, H. Funakubo: J. Cryst. Growth 235, 389 (2002) 85 [16] H. Lee, D. Hesse, N. Zakharov, U. Goesele: Science 296, 2006 (2002) 85, 87 [17] H. Matsuda, S. Ito, T. Iijima: Appl. Phys. Lett. 83, 5023 (2003) 85 [18] N. Nukaga, M. Mitsuya, T. Suzuki, Y. Nishi, M. Fujimoto, H. Funakubo: Jpn. J. Appl. Phys. 40, 5595 (2001) 87 [19] H. Funakubo, K. T. T. Oikawa, M. Aratani, K. Saito: J. Appl. Phys. 92, 5448 (2002) 87 [20] G. Asano, H. Morioka, H. Funakubo, T. Shibutami, N. Ohshima: Appl. Phys. Lett. 83, 5056 (2003) 87


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[21] G. Asano, T. Oikawa, K. Tokita, K. Okada, H. Funakubo: Trans. Mater. Res. Soc. Jpn. 27, 223 (2002) 87 [22] G. Asano, T. Oikawa, H. Funakubo: Jpn. J. Appl. Phys. 42, 2801 (2003) 87

Index

(104)/(014) orientation, 85 (111) Pt, 83 a-domain, 78 Bi4 Ti3 O12 , 77 Bi4 Ti3 O12 -based ferroelectrics, 80 c-domain, 78 coercive field, 79 Curie temperature, 78

low-temperature deposition, 77, 87 metal-organic chemical vapor deposition, 77 MOCVD, 77 orientation control, 84 P –E hysteresis loop, 79 polar-axis-oriented films, 78 pole figure plot, 78 PZT, 77

epitaxial film, 78, 80 FeRAM, 77 ferroelectric random access memory, see FeRAM lanthanide-substituted Bi4 Ti3 O12 , 77 local epitaxial growth, 83 long-range lattice matching, 81

Ru-based electrode, 87 RuO2 /PZT/Pt/RuO2 , 86 rutile structure, 80 site-engineered concept, 77 spontaneous polarization, 77 SrTiO3 , 78 substitution in Bi4 Ti3 O12 , 77

Rhombohedral PZT Thin Films Prepared by Sputtering Masatoshi Adachi Department of Electronics and Informatics, Faculty of Engineering, Toyama Prefectural University, 5180 Kurokawa, Kosugimachi, Toyama 939-0398, Japan [email protected] Abstract. PZT thin films with a rhombohedral perovskite structure were successfully grown on (111) PLT/Pt/Ti/SiO2 /Si and (111) Ir/SiO2 /Si substrates. The crystal structures of the films were sensitive to the substrate temperature Ts . PZT films with a completely rhombohedral structure were obtained at a Ts of 630 ◦ C to 660 ◦ C on PLT/Pt/Ti/SiO2 /Si substrates, a wider Ts range than on Ir/SiO2 /Si substrates. The composition of the PZT film can be easily adjusted by changing the area ratio of the PbO/Zr/Ti target. Films deposited on both PLT/Pt/Ti/SiO2 /Si and Ir/SiO2 /Si substrates yielded the same electrical-property results. When the Zr content was increased from 0.8 to 0.97, the dielectric constant, remanent polarization and Curie temperature of the rhombohedral PZT films monotonically decreased, and were similar to those of PZT ceramics. A phase transition between two rhombohedral ferroelectric phases was observed in some highly (111)-oriented PZT films. The fatigue characteristics were also measured. The PZT films maintained their initial switching-charge value over 1012 switching cycles. The possibility of an engineered domain configuration was examined in (100)oriented rhombohedral PZT single-crystal films. Highly (111)- and (100)-oriented rhombohedral PZT (Zr/Ti = 80/20) single-crystal films were obtained by RF magnetron sputtering on (111) Ir/(111) SrTiO3 and (100) Ir/(100) SrTiO3 substrates. The ferroelectric hysteresis curve of the (100)-oriented rhombohedral PZT film showed a square-like shape, and the (111)-oriented film showed a slanted loop. The coercivity Ec of the (100)-oriented film was smaller than that of the (111)-oriented film. These results show the possibility of an engineered domain configuration in [001]-oriented rhombohedral PZT single-crystal films. This structure may be advantageous for improvement of the fatigue properties of FeRAMs.

1 Introduction Recently, with the progress in thin-film technology, intensive efforts have been made to prepare ferroelectric thin films such as lead-based perovskites and nonlead bismuth layered structures for ferroelectric random access memories (FeRAMs) and also for gate insulators in metal–ferroelectric–semiconductor (MFS) gate structures [1, 2, 3, 4, 5]. For dielectric capacitor films in dynamic random access memories (DRAMs), only a high dielectric constant and a lower leakage current density are required [6]. Hence, highly nonpolar-axisoriented (Pb,La)TiO3 thin films with a La-rich composition, as well as the M. Okuyama, Y. Ishibashi (Eds.): Ferroelectric Thin Films, Topics Appl. Phys. 98, 91–105 (2005) © Springer-Verlag Berlin Heidelberg 2005

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dielectric SrTiO3 , (Sr,Ba)TiO3 and ferroelectric Pb(Zr,Ti)O3 , are available for DRAMs, because a polar-axis-oriented film possesses a smaller dielectric constant than do others. Pb(Zr,Ti)O3 is a solid solution between PbTiO3 and PbZrO3 . The structure and properties of PZT have been well characterized. From a study of the phase diagram, PZT is known to be tetragonal when the Zr/Ti ratio is less than 52/48, and the lattice constant ratio c/a increases as the Zr/Ti ratio decreases [7]. When the Zr/Ti ratio is larger than 53/47, PZT is in the rhombohedral form. The boundary between the tetragonal and rhombohedral phases is nearly independent of temperature; this boundary is referred to as the morphotropic phase boundary (MPB). PZT shows peculiar dielectric, ferroelectric and piezoelectric characteristics around the MPB composition [8]. On the other hand, the Zr-rich PZT bulk ceramic becomes an orthorhombic antiferroelectric phase when the Zr/Ti ratio is larger than 94/6 [7]. At the composition near 95/5, however, the PZT thin film has a rhombohedral ferroelectric phase transition near room temperature, because the phase boundary between orthorhombic antiferroelectric and rhombohedral ferroelectric phases shifts toward more Zr-rich PZT composition due to the stress in the film. Further, the spontaneous polarization shows a marked step change which leads to a high pyroelectric coefficient at room temperature. In addition, Zr-rich PZT can be applied in FeRAMs, because its coercive field is very small [9,10]. In this Chapter, the growth of rhombohedral PZT thin films prepared by sputtering is described, together with their properties.

2 Experimental Procedures An RF magnetron sputtering apparatus with three cathodes was used to prepare metal electrodes and ferroelectric PZT thin films, as shown in Fig. 1. Such ferroelectric oxide films require electrically conducting surfaces as both bottom and top electrodes for electrical measurements. The selection criteria for the substrate and the underlying metal electrode require the following: 1. 2. 3. 4.

minimum interdiffusion with other regions; resistance to oxidation; good matching of thermal expansion coefficients; an ability to promote the growth of crystalline ferroelectrics;

For semiconductor applications based on silicon substrates, the metallization and buffer layers must have adequate electrical properties and also act as an effective diffusion barrier to isolate the components of the ferroelectric film from the underling silicon substrate. Platinum and iridium show good resistance to oxidation. However, Pt has weak adhesion to Si oxide and reacts chemically with bare Si. A dense microstructure in the platinum

Rhombohedral PZT Thin Films Prepared by Sputtering

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Fig. 1. Schematic drawing of the magnetron sputtering system with three magnetic cathodes

film and a bonding layer of titanium are necessary to ensure good mechanical integrity with oxidized silicon wafers. However, platinum tends to react with PbO, forming an alloy which segregates into islands on the substrate surface, and porosity in the platinum film leads to undesirable interdiffusion with the underlying silicon substrate. In the experiments described here, PLT/Pt/Ti/SiO2/Si and Ir/SiO2 /Si were used as substrates. In order to grow ferroelectric films, epitaxially, Ir/SrTiO3 substrates were also used.

3 PZT Films on (Pb,La)TiO3 (PLT)/Pt/Ti/SiO2/Si and Ir/SiO2 /Si Zr-rich ferroelectric PZT (x = 0.54–0.96) belongs to the rhombohedral system and its polarization axis is parallel to the (111) direction. PZT thin films were prepared on PLT/Pt/Ti/SiO2/Si or (111) Ir/SiO2 /Si substrates. In order to prepare high-quality PZT thin films, a highly (111)-oriented PLT film, as thin as 5 nm to 10 nm, was deposited as a buffer layer on the (111) Pt/Ti/SiO2 /Si substrate prior to the deposition of the PZT film. The multitarget used in this experiment is shown in Fig. 2. The target consisted of PbO pellets (12 mm diameter and 2 mm thickness) and pure Ti metal chips (10 mm2 × 10 mm2 or 5 mm2 ×5 mm2 , 0.5 mm thickness, 99.5% purity) positioned on a pure Zr metal target of diameter 76.2 mm and thickness 5 mm (98% purity), all of which were produced by High Purity Chemicals Co., Ltd. The PbO pellets were prepared by a conventional oxide calcination technique using PbO powder.

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Fig. 2. Schematic diagram of the multitarget

Table 1. Typical sputtering conditions for PZT thin films Substrate Target Input power Gas pressure Sputtering gas Target–substrate distance Film thickness Growth rate

(111) Pt/Ti/SiO2 /Si (111) Ir/SiO2 /Si Zr metal + Ti chips + PbO Pellets, substrate temperature 620 ◦ C to 660 ◦ C 100 W 4–12×10−3 Torr Ar = 8, O2 = 2 sccm 65 mm 300 nm to 1200 nm 5 nm/min

By arranging an appropriate number of pellets and Ti metal chips, we could easily control the Pb and Zr contents of the PZT films. Typical sputtering conditions are listed in Table 1. Figure 3 shows XRD patterns of PZT films deposited on (111) PLT/Pt/ Ti/SiO2 /Si and (111) Ir/SiO2 /Si substrates at 640 ◦C and 638 ◦C, respectively. The PZT film, with a perovskite structure, on Ir/SiO2 /Si is more highly (111)-oriented than that on PLT/Pt/Ti/SiO2/Si. Figure 4 shows the crystalline structure of PZT as a function of the substrate temperature Ts ; the PZT films were deposited on Ir/SiO2 /Si and PLT/Pt/Ti/SiO2/Si substrates at 5–9 × 10−3 Torr. In Fig. 4, Ipero and Ipyro represent the XRD intensities of the (hkl) reflections corresponding to the perovskite and the pyrochlore structures, respectively. The PZT films on Ir/SiO2 /Si had a mixture of pyrochlore and perovskite structures below 635 ◦ C and above 652 ◦ C. PZT films with a completely perovskite structure were obtained at a Ts of 635 ◦ C to 652 ◦ C.


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Fig. 3. XRD patterns of PZT (Zr/Ti = 94/6) thin films deposited on PLT/Pt/Ti/SiO2 /Si and Ir/SiO2 /Si substrates at 638 ◦ C and 640 ◦ C

The PZT films on PLT/Pt/Ti/SiO2/Si contained a mixture of pyrochlore and perovskite structures below 625 ◦ C and above 660 ◦ C. It should be noted that the crystalline structure of the PZT films is clearly improved by depositing a very thin PLT buffer layer on the substrate. It is considered that without the PLT layer, zirconium oxide or the pyrochlore structure adheres to the surface of the platinum bottom cathode in the initial stages of the PZT deposition and disturbs the growth of the perovskite phase, whereas PZT films can be successfully grown on a PLT layer, which is formed easily on the substrate owing to the absence of Zr. On the other hand, PZT films with a completely perovskite structure were obtained on Ir/SiO2 /Si at a Ts of 635 ◦C to 652 ◦ C. PZT films with a mixture of pyrochlore and perovskite structures were formed below 630 ◦C and above 655 ◦C. PZT films with a completely perovskite structure were deposited on PLT/Pt/Ti/SiO2/Si and Ir/SiO2 /Si at a Ts of 630 ◦ C to 660 ◦C and 635 ◦ C to 652 ◦ C, respectively. Figure 5 shows the temperature dependence of the relative dielectric constant and of tan δ for the PZT films. The films were deposited on PLT/Pt/Ti/SiO2/Si and Ir/SiO2 /Si below 5– 9 × 10−3 Torr at a Ts of 635 ◦C to 645 ◦C, and the film thickness was 600 nm. For the PZT films with Zr contents of 0.94 and 0.85 on PLT/Pt/SiO2/Si, the values of the dielectric constant and tan δ at 28 ◦ C are almost equal to 386 and 2.4%, respectively. However, the dielectric constants show anomalies at the transition points around 223 ◦C and 255 ◦ C. For the film with a Zr content of 0.936 on the Ir/SiO2 /Si substrate, the dielectric constant and tan δ at 28 ◦ C are 390 and 2.4%, respectively. The Curie temperature of this film was

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Fig. 4. Perovskite ratio of PZT films (Zr/Ti = 94/6) as a function of substrate temperature

Fig. 5. Temperature dependence of the dielectric constant and tan δ of PZT (Zr/Ti = 85/15, 93.6/6.4 and 94/6) films

224 ◦ C. The dielectric constant of this PZT/Ir/SiO2/Si film near the transition temperature is smaller than that of the PZT/PLT/Pt/Ti/SiO2/Si film. It is considered that the measured value is the dielectric constant for a series capacitor made up of a PZT film and a PLT buffer layer.


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Fig. 6. Zr content dependence of the dielectric constant and tan δ of PZT films at room temperature; f = 100 kHz

Figure 6 shows the dependence of the relative dielectric constant and tan δ of PZT films on the Zr content at room temperature. The dependence of the dielectric constant observed here is very similar to that of PZT ceramics, while the values for the films are smaller than those for ceramics. The value of tan δ for the PZT films ranges from 1.8% to 4%. Pyroelectric currents were observed in the PZT films even without a poling treatment, in the direction from the upper to the lower electrode. The temperature dependence of the pyroelectric coefficients of the PZT (Zr/Ti = 96/4 and 93.6/6.4) films is shown in Fig. 7. The pyroelectric coefficient is about 15 nC/cm2 K. The pyroelectric coefficient shows two peaks, at 47 ◦ C and 87 ◦ C. These peak at the lower temperature corresponds to the phase transition from the low-temperature rhombohedral ferroelectric phase FR(LT) to the high-temperature rhombohedral ferroelectric phase FR(HT) , and the peak at the higher temperature of arround 220 ◦C are also observed, which are the phase transition from FR(HT) to the paraelectric phase Pc . Further, the phase transition between the two rhombohedral ferroelectric phases was not often observed, in some poor (111)-oriented films. This may be due to self-poling of the ferroelectric domains in the highly (111)-oriented film. Figure 8 shows the Zr content dependence of the phase transition temperature of the PZT films from rhombohedral FR(LT) to FR(HT) and from FR(HT) to the paraelectric Pc phase. The Curie temperature Tc and the phase transition temperature from FR(LT) to FR(HT) of the films are lower than those for PZT ceramics with the same composition. This may be attributed to the stress in the film. Figures 9(a) and (b) show D–E hysteresis loops of a Pb(Zr0.94 Ti0.06 )O3 film deposited on a PLT/Pt/Ti/SiO2/Si substrate and of a Pb(Zr0.936 Ti0.064 )O3 film deposited on an Ir/SiO2 /Si substrate. The coercive field Ec

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Fig. 7. Temperature dependence of the pyroelectric coefficients of PZT (96/4 and 93.6/6.4) films

Fig. 8. Zr content dependence of the phase transition temperature of PZT films from rhombohedral FR(LT) to rhombohedral FR(HT) and from FR(HT) to paraelectric Pc


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Fig. 9. D–E hysteresis loops of rhombohedral PZT films. (a) Zr/Ti = 94/6 on a PLT/Pt/Ti/SiO2 /Si substrate (x-axis, 62 kV/div; y-axis, 40 (µC/cm2 )/div) (b) Zr/Ti = 93.6/6.4 on an Ir/SiO2 /Si substrate (x-axis, 62 kV/div; y-axis, 40 µC/cm2 )/div

and remanent polarization Pr are 38 kV and 20 µC/cm2 , and 38 kV and 23.6 µC/cm2, respectively. The ferroelectric properties are significantly affected by the Zr content. Most hysteresis loops observed were asymmetric because of the existence of an internal bias field in the film. When a sputtered film was cooled from Ts to room temperature, passing through Tc , some spontaneous polarizations in the film adopted the same orientation, that is, the growth direction, resulting in a net polarization and bias. These asymmetrical hysteresis loops prevented accurate measurement of the remanent polarization. The values of (+Pr ) + (−Pr ) and the average coercive field (the average absolute value of the positive and negative coercive fields) were estimated to characterize the ferroelectricity of the films. Figure 10 shows the dependence of (+Pr )+ (−Pr ) and the coercive field on the Zr content. The remanent polarization decreases monotonically and the coercive field increases with increasing Zr content. The value of (+Pr ) + (−Pr ) is equivalent to the effective output polarization signal of a ferroelectric nonvolatile memory. The polarization-switching characteristics of rhombohedral Pb (Zr0.94 Ti0.064 )O3 /PLT/Pt/Ti/SiO2/Si and Pb(Zr0.936 Ti0.064 )O3 /Ir/SiO2/Si were also measured using double bipolar pulses. Large positive and negative switching currents and nonswitching transient currents were clearly observed. The switching times of the two PZT films were 320 ns and 260 ns, respectively. The fatigue characteristics of the remanent polarization (switching charge) are shown in Fig. 11. A slight asymmetry of the loops for the switching charges indicates that the D–E hysteresis loops are slightly asymmetrical. Only a minimal decay of polarization was observed up to 108 switching cycles. The Pr value of the films decreased by 5% to 7% when they were subjected to a bipolar stress of 1012 cycles. This suggests that the rhombohedral PZT films sputtered on PLT/Pt/Ti/SiO2/Si and Ir/SiO2 /Si substrates have the same endurance and are suitable for applications in memory devices.

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Fig. 10. Zr content dependence of the sum of the positive and negative remanent polarizations [(+Pr ) + (−Pr )] and the average coercive field of PZT films

Fig. 11. Fatigue characteristics of PZT (94/6) films


101

4 Rhombohedral PZT on (111) Ir/(111) SrTiO3 and (100) Ir/(100) SrTiO3 Substrates In rhombohedral PZT films, the spontaneous polarization is in the 111 direction, so that a large remanent polarization is expected in (111)-oriented PZT films. But in this case, a relatively high electric field is needed to reverse the polarization. If a (100)-oriented single crystal PZT film could be obtained, the idea of an engineered domain configuration, as reported for some bulk crystals [11] might be possible to put into practice. Figure 12 shows a schematic domain configuration in a [001]-oriented rhombohedral single-crystal film. In this configuration, with an electric field parallel to the c-axis, four equivalent polarization directions ([111], [¯111], [1¯11] and [¯1¯11]) in a (100)-oriented PZT film will act just like one polarization parallel to the c-axis, and therefore the electric field required to reverse the polarization will be expected to be smaller than that for (111)-oriented films [12, 13]. This structure may be advantageous for improvement of the fatigue properties of FeRAMs, because one possible reason for fatigue originates in stress, which is caused by polarization reversal under the influence of the electric field between the ferroelectric layer and electrode layer. XRD patterns of PZT/Ir(100)/SrTiO3(100) and PZT/Ir(111)/SrTiO3 (111) films are shown in Fig. 13. (100)- and (111)-oriented Ir films could be easily grown on SrTiO3 (100) and SrTiO3 (111) substrates, respectively, and highly (100)- and (111)-oriented rhombohedral PZT films could be grown on Ir(100)/SrTiO3(100) and Ir(111)/SrTiO3(111) substrates, respectively. Each PZT film contained only the perovskite structure, without any pyrochlore phase. The compositions of the films measured by EPMA were Pb/(Zr + Ti) = 1 and Zr/(Zr + Ti) = 0.8, so the (100)- and (111)-oriented PZT films ob-

Fig. 12. Schematic domain configuration in a [001]-oriented rhombohedral single crystal

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Fig. 13. XRD pattern of PZT (Zr/Ti = 80/20) films grown on (a) Ir(100)/SrTiO3 (100) and (b) Ir(111)/SrTiO3 (111) substrates

Fig. 14. Surface images of (100)- and (111)-oriented PZT (Zr/Ti = 80/20) films grown on (a) Ir(100)/SrTiO3 (100) and (b) Ir(111)/SrTiO3 (111) substrates

tained had a stoichiometric composition in the rhombohedral region. Surface images of PZT films obtained by a digital microscope are shown in Fig. 14. The (100)-oriented PZT film had a larger grain size and a larger roughness compared with the (111)-oriented PZT film. D–E hysteresis curves of (100)- and (111)-oriented PZT films of thickness 600 nm are shown in Fig. 15. The (100)-oriented film shows a square-like shape (Fig. 15(a)). On the other hand, the (111)-oriented film shows a slanted loop (Fig. 15(b)). The remanent polarization (Pr ) and coercive field (Ec ) were 16.5 µC/cm2 and 50 kV/cm, respectively, for the PZT(100) film, and 25.5 µC/cm2 and 60 kV/cm, respectively, for the PZT(111) film. The value of Ec for the (100)-oriented film was smaller than that for the (111)-oriented film. Those results show the possibility of an engineered domain configuration in [001]-oriented rhombohedral PZT single-crystal films.


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Fig. 15. D–E hysteresis curves of (100)- and (111)-oriented PZT (Zr/Ti = 80/20) films grown on (a) Ir(100)/SrTiO3 (100) and (b) Ir(111)/SrTiO3 (111) substrates (scale units: x-axis, 50 kV/cm/div; y-axis, 15 µC/cm/div)

References [1] K. Abe, H. Tomita, H. Toyoda, M. Imai, Y. Yokote: Jpn. J. Appl. Phys. 30, 2152 (1991) 91 [2] K. Torii, H. Kawakami, H. Miki, K. Kushida, Y. Fujisaki: J. Appl. Phys. 81, 2755 (1997) 91 [3] K. Aoki, Y. Fukuda, K. Numata, A. Nishimura: Jpn. J. Appl. Phys. 35, 2210 (1996) 91 [4] T. Hirai, K. Teramoto, K. Nagashima, H. Koike, S. Matsuno, S. Tanimoto, Y. Tarui: Jpn. J. Appl. Phys. 35, 4016 (1996) 91 [5] S. Horita, T. Kawada, Y. Abe: Jpn. J. Appl. Phys. 35, L1357 (1996) 91 [6] H. Yamaguchi, P. Y. Lesaicherre, T. Sakuma, Y. Miyasaka, A. Ishitani, M. Yoshida: Jpn. J. Appl. Phys. 32, 4069 (1993) 91 [7] V. Gavrilyachenko, R. Spinko, M. Martynenko, E. Fesenko: Sov. Phys. Solid. State 12, 1203 (1970) 92 [8] B. Jaffe, R. Roth, S. Marzullo: J. Res. Natl. Bur. Stand. 55, 239 (1955) 92 [9] M. Adachi, A. Hachisuka, N. Okumura, T. Shiosaki, A. Kawabata: Jpn. J. Appl. Phys. 26, 68 (1987) 92 [10] Y. Ushida, J. Lian, T. Shiosaki, A. Kawabata: Jpn. J. Appl. Phys. 26, 72 (1987) 92 [11] S. Wada, S. Suzuki, T. Noda, T. Suzuki, M. Osada, M. Kakihana, S. E. Park, L. Cross, T. Shrout: Jpn. J. Appl. Phys. 38, 5501 (1999) 101 [12] X. H. Du, U. Belegundu, K. Uchino: Jpn. J. Appl. Phys. 36, 5580 (1997) 101 [13] S. Kalpat, X. Du, I. Abothu, A. Akiba, H. Goto, K. Uchino: Jpn. J. Appl. Phys. 40, 713 (2001) 101

Index

engineered domain configuration, 101, 103 FeRAM, 91, 92, 101 Ir/SiO2 /Si, 93–95, 99, 100 MFS structure, 91 morphotropic phase boundary, 92 MPB, 92

perovskite, 91, 94, 103 PLT, 93 pyroelectric coefficient, 96 PZT, 92, 93, 101 rhombohedral phase, 92, 93, 96, 97, 99, 101 rhombohedral PZT, 92 sputtering, 92

Scanning Nonlinear Dielectric Microscopy Yasuo Cho Research Institute of Electrical Communication, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan [email protected]

Abstract. In this Chapter, we first describe the development of subnanometerresolution scanning nonlinear dielectric microscopy (SNDM) for the observation of ferroelectric polarization. We demonstrate that the resolution of SNDM is higher than that of conventional piezoresponse imaging. We also describe the theoretical resolution of SNDM and quantitative measurement techniques using SNDM. This theoretical result predicts that an atomic-scale image can be taken by SNDM. Next, we report a new SNDM technique detecting the higher nonlinear dielectric constants ε3333 and ε33333 . It is expected that higher-order nonlinear dielectric imaging will provide higher lateral and depth resolution. Using this higher-order nonlinear dielectric microscopy technique, we have successfully investigated the surface layers of ferroelectrics. Moreover, a new type of scanning nonlinear dielectric microscope probe, called the ε311 -type probe, and a system to measure the ferroelectric polarization component parallel to the surface have been developed. Finally, the formation of artificial small, inverted domains is reported to demonstrate that the SNDM system is very useful as a nanodomain engineering tool. Nanosize domain dots were successfully formed in a LiTaO3 single crystal. This means that we can obtain a very high density of ferroelectric data storage, with a density above 1 Tb/in2 . Therefore, we have concluded that SNDM is very useful for observing ferroelectric nanodomains and the local crystal anisotropy of dielectric materials with subnanometer resolution and also has a quite high potential as a nanodomain engineering tool.

1 Introduction Recently, ferroelectric materials, especially in thin-film form, have attracted the attention of many researchers. Their large dielectric constants make them suitable as dielectric layers of microcapacitors in microelectronics. They have also been investigated for application in nonvolatile memories using the switchable dielectric polarization of the ferroelectric material. To characterize such ferroelectric materials, a high-resolution tool is required for observing the microscopic distribution of the remanent (or spontaneous) polarization of ferroelectric materials. With this background, we have proposed and developed a new, purely electrical method for imaging the state of the polarization in ferroelectric and piezoelectric materials and their crystal anisotropy. It involves the measurement of point-to-point variations of the nonlinear dielectric constant M. Okuyama, Y. Ishibashi (Eds.): Ferroelectric Thin Films, Topics Appl. Phys. 98, 105–126 (2005) © Springer-Verlag Berlin Heidelberg 2005

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of a specimen and is termed “scanning nonlinear dielectric microscopy” (SNDM) [1, 2, 3, 4, 5, 6, 7]. This is the first successful purely electrical method for observing ferroelectric polarization distribution without the influence of the shielding effect of free charges. The resolution of this microscope has been improved down to the subnanometer order. Here we describe the theory for detecting the polarization and the technique for the nonlinear dielectric response, and report results for the imaging of ferroelectric domains in single crystals and thin films using SNDM. In particular, in a measurement of a PZT thin film, it has been confirmed that the resolution is of subnanometer order. We also describe the theoretical resolution of SNDM. Moreover, we demonstrate that the resolution of SNDM is higher than that of conventional piezoresponse imaging by using scanning force microscopy (SFM) techniques [8, 9]. Next, we report a new SNDM technique. In the above conventional SNDM technique, we measure the lowest-order nonlinear dielectric constant ε333 , which is a 3rd-rank tensor. To improve the performance and resolution of SNDM, we have modified the technique such that the higher nonlinear dielectric constants ε3333 (4th-rank tensor) and ε33333 (5th-rank tensor) are detected. It is expected that higher-order nonlinear dielectric imaging will provide higher lateral and depth resolution. We have confirmed this improvement over conventional SNDM imaging experimentally, and used the technique to observe the growth of a superficial paraelectric layer on periodically poled LiNbO3 [10, 11, 12]. In addition to this technique, a new type of scanning nonlinear dielectric microscope probe, called the ε311 -type probe, and a system to measure the ferroelectric polarization component parallel to the surface have been developed. This is achieved by measuring the ferroelectric material’s nonlinear dielectric constant ε311 instead of ε333 , which is measured in conventional SNDM. Experimental results show that the probe can satisfactorily detect the direction of the polarization parallel to the surface. Finally, the formation of artificial small, inverted domains is reported to demonstrate that the SNDM system is very useful as a nanodomain engineering tool. Nanosize domain dots have been successfully formed in a LiTaO3 single crystal. This means that we can obtain a very high density of ferroelectric data storage, with a density above Tb/in2 [13].

2 Principle and Theory of SNDM First, we briefly describe the theory of the detection of polarization. Precise descriptions of the principle of the microscope have been reported elsewhere (see [3, 4]). We also report the results of the imaging of ferroelectric domains in single crystals and in thin films using SNDM. In particular, in the case of a PZT thin-film measurement, we succeeded in obtaining a domain image with a subnanometer resolution.

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Fig. 1. Schematic diagram of scanning nonlinear dielectric microscope

2.1 Nonlinear Dielectric Imaging with Subnanometer Resolution Figure 1 shows the system setup of a scanning nonlinear dielectric microscope using an LC lumped constant-resonator probe [4]. In the figure, Cs (t) denotes the capacitance of the specimen under the center conductor (the tip) of the probe. Cs (t) is a function of time because of the nonlinear dielectric response to an applied alternating electric field Ep3 (= Ep cos ωp t, fp = 5−100 kHz). The ratio of the alternating variation of the capacitance ∆Cs (t) to the static value of the capacitance Cs0 without a time dependence is given by [3] ∆Cs (t) ε333 ε3333 2 = Ep cos 2ωp t + E cos 2ωp t , Cs0 ε33 4ε33 p

(1)

where ε33 is a linear dielectric constant and ε333 and ε3333 are nonlinear dielectric constants. An even-rank tensor, including the linear dielectric constant ε33 , does not change with a 180◦ rotation of the polarization. On the other hand, the lowest order of the nonlinear dielectric constant, ε333 , is a third-rank tensor, similar to the piezoelectric constant, so that there is no ε333 in a material with a center of symmetry, and the sign of ε333 changes with inversion of the spontaneous polarization. The LC resonator is connected to an oscillator tuned to the resonance frequency of the resonator. The electrical parts (i.e. needle, ring, inductance and oscillator) are assembled into a small probe for performing SNDM. The oscillation frequency of the probe (or oscillator) (around 1.3 GHz) is modulated by the change of the capacitance ∆Cs (t) due to the nonlinear dielectric response to the applied electric field. As a result, the probe (oscillator) produces a frequency-modulated (FM) signal. By detecting this FM signal using an FM demodulator and lock-in amplifier, we obtain a voltage signal proportional to the capacitance variation. The signals corresponding to ε333 and ε3333 were obtained by setting the reference signal of the lock-in amplifier to the frequency ωp of the applied electric field and to the doubled frequency 2ωp ,

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Fig. 2. A two-dimensional image of a 90◦ a–c domain in a BaTiO3 single crystal and a cross-sectional (one-dimensional) image along the line A–A

respectively. Thus we can detect the nonlinear dielectric constant just under the needle and can obtain a fine resolution determined by the diameter of the pointed end of the tip and the linear dielectric constant of the specimen. The capacitance variation caused by the nonlinear dielectric response is quite small (∆Cs (t) /Cs0 is in the range from 10−3 to 10−8 ). Therefore the sensitivity of the SNDM probe must be very high. The measured value of the sensitivity of a lumped constant probe of the type described above is 10−22 F. For the study described here, the needle of the lumped constant-resonator probe was fabricated using electrolytic polishing of a tungsten wire or a metalcoated conductive cantilever. The radius of curvature of the tip was 1 µm– 25 nm. To check the performance of the new scanning nonlinear dielectric microscope, first we measured the macroscopic domains in a multidomain BaTiO3 single crystal. Figure 2 shows a two-dimensional image of a so-called 90◦ a–c


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Fig. 3. Images of a PZT film on a SrTiO3 substrate. (a) Domain patterns by SNDM, (b) surface morphology by AFM

domain, which was obtained by a coarse scanning over a large area. The sign of the nonlinear dielectric constant ε333 of the +c-domain is negative, whereas it is positive in the −c-domain. Moreover the magnitude of ε111 = ε222 is zero in the a-domain, because BaTiO3 belongs to the tetragonal system at room temperature. Thus, we can easily distinguish the types of domains. To demonstrate that this type of microscopy is also useful for domain measurement of thin ferroelectric films, we measured a PZT thin film. Figure 3 shows (a) and AFM (b) images taken from the same location in a PZT thin film deposited on a SrTiO3 (STO) substrate using metal-organic chemical vapor deposition. From the figure, it is apparent that the film is polycrystalline (from Fig. 3(b)) and that each grain in the film is composed of several domains (from Fig. 3(a)). From X-ray diffraction analysis, this PZT film is in the tetragonal phase, and diffraction peaks corresponding to both the c-axis and the a-axis were observed. Moreover, in Fig. 3(a), the observed signals were partially of zero amplitude, and partially positive. Thus, the images show that we have succeeded in observing 90◦ a–c domain distributions in a single grain of the film. These images of the film were taken from a relatively large area. Therefore, we also tried to observe very small domains in the same PZT film on an STO substrate. The results are shown in Figs. 4(a) and 4(b). The bright areas and the dark areas correspond to a negative polarization and a positive polarization, respectively. This shows that we can successfully observe a nanoscale 180◦ c–c domain structure. Figure 4(b) shows a cross-sectional image taken along the line A–A in Fig. 4(a).

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Fig. 4. Nanoscale ferroelectric domains in a PZT thin film: (a) domain image, (b) cross-sectional (one-dimensional) image of phase signal along the line A–A

Fig. 5. Theoretical images of a 180◦ c–c domain boundary

As shown in this figure, we have measured a c–c domain with a width of 1.5 nm. Moreover, we have found that the resolution of the microscope is less than 0.5 nm. To clarify the reason why such a high resolution can be easily obtained, even if a relatively thick needle is used for the probe, we show calculated results for a one-dimensional image of a 180◦ c–c domain boundary lying at y = 0 (we have chosen the y direction as the scanning direction) [7, 14].


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Fig. 6. Simultaneously taken images of a PZT film. (a) Topography by AFM, (b) domain patterns by SNDM and (c) domain patterns by SFM (piezoimaging)

Figure 5 shows the calculated results, where Y0 is the tip position normalized with respect to the tip radius a. The resolution of the SNDM image is heavily dependent on the dielectric constant of the specimen. For example, for the case of ε33 /ε0 = 1000 and a = 10 nm, it will be possible to take an atomicscale image by SNDM. 2.2 Comparison between SNDM Imaging and Piezoresponse Imaging Another frequently reported high-resolution tool for observing ferroelectric domains is piezoelectric-response imaging using SFM [8, 9]. From the viewpoint of resolution for ferroelectric domains, SNDM will surpass the piezoresponse imaging because SNDM measures the nonlinear response of a dielectric material, which is proportional to the square of the electric field, whereas the piezoelectric response is linearly proportional to the electric field. The concentration of the distribution of the square of the electric field in the specimen underneath the tip is much higher than that of the linear electric field. Thus, SNDM can resolve smaller domains than those measured by the piezoimaging technique. To prove this fact experimentally, we have also performed simultaneous measurements of the same location of the above-mentioned PZT film sample by using AFM (topography), SNDM and piezoimaging, as shown in Fig. 6. These images were taken under just same conditions using the same metal-coated cantilever. From the images, we can prove that SNDM can resolve greater detail than can conventional piezoresponse imaging using the SFM technique.

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3 Higher-Order Nonlinear Dielectric Microscopy A higher-order nonlinear dielectric microscopy technique with higher lateral and depth resolution than conventional nonlinear dielectric imaging has been investigated. The technique has been demonstrated to be very useful for observing surface layers of the order of a unit cell thickness on ferroelectric materials. 3.1 Theory of Higher-Order Nonlinear Dielectric Microscopy Equation (2) is a polynomial expansion of the electric displacement D3 as a function of the electric field E3 : 1 1 1 D3 = Ps3 + ε33 E3 + ε333 E32 + ε3333 E33 + ε33333 E34 + · · · 2 6 24

(2)

Here, ε33 , ε333 , ε3333 and ε33333 correspond to the linear and nonlinear dielectric constants and are tensors of 2nd, 3rd, 4th and 5th rank, respectively. Even-ranked tensors, including the linear dielectric constant ε33 , do not change with polarization inversion, whereas the sign of odd-ranked tensors reverses. Therefore, information regarding the polarization can be elucidated by measuring odd-ranked nonlinear dielectric constants such as ε333 and ε33333 . Considering the effect up to E 4 , the ratio of the alternating variation of the capacitance ∆Cs underneath the tip to the static capacitance Cs0 is given by ∆Cs (t) ε333 1 ε3333 2 ≈ Ep cos ωp t + E cos 2ωp t Cs0 ε33 4 ε33 p 1 ε33333 3 + E cos 3ωp t + · · · . 24 ε33 p

(3)

This equation shows that alternating capacitances of different frequencies corresponds to different orders of the nonlinear dielectric constant. Signals corresponding to ε333 , ε3333 and ε33333 were obtained by setting the reference signal of the lock-in amplifier in Fig. 1 to frequencies ωp , 2ωp and 3ωp , respectively, where ωp is the frequency of the applied electric field. Next, we consider the resolution of SNDM. From (2), the resolution of SNDM is found to be a function of the electric field E. We note that the electric field under the tip becomes more highly concentrated as ε33 increases [15], and the distributions of the E 2 , E 3 and E 4 fields underneath the tip become much more concentrated, in accordance with their power, than that of the E field, as shown in Fig. 7. From this figure, we can see that higher-order nonlinear dielectric imaging has a higher resolution than lower-order nonlinear dielectric imaging.


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Fig. 7. Distribution of E, E 2 , E 3 and E 4 fields under a needle tip; a denotes the tip radius

Fig. 8. (a) ε333 and (b) ε33333 images of PZT thin film

3.2 Experimental Details of Higher-Order Nonlinear Dielectric Microscopy We have experimentally confirmed that ε33333 imaging has a higher lateral resolution than ε333 imaging using an electroconductive cantilever with a radius of 25 nm as a tip. Figures 8(a) and (b) show ε333 and ε33333 images of the two-dimensional distribution of a lead zirconate titanate (PZT) thin film. The two images can be correlated, and it is clear that the ε33333 image resolves greater detail than does the ε333 image owing to the higher lateral and depth resolution.

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Fig. 9. ε333 , ε3333 and ε33333 images of (a) virgin PPLN, (b) immediately after polishing, and (c) 1 h after polishing


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Next, we investigated the surface layer of periodically poled LiNbO3 (PPLN) by ε333 , ε3333 and ε33333 imaging. Figure 9(a) shows ε333 , ε3333 and ε33333 signals of virgin, unpolished PPLN. In this figure, only ε333 imaging detects the c–c domain boundaries, while ε33333 imaging does not. The ε3333 signal shows weak peaks at domain boundaries. This is because ε3333 and ε33333 imaging is affected by the surface paraelectric layer. To prove the existence of a surface paraelectric layer, we polished the PPLN and then performed measurements on it. Figure 9(b) shows the resulting images. In this figure, it is clear that ε33333 imaging can detect the c–c domain boundaries after removal of the paraelectric layer. Moreover, ε3333 imaging can also detect periodic signals, in contrast to our expectation. The nonlinear dielectric signals from a positive area of PPLN are stronger than those from a negative area immediately after polishing, possibly because the negative area is more easily damaged than the positive area and has already been covered by a very thin surface paraelectric layer with a weak nonlinearity, even immediately after polishing. One hour after polishing, we conducted the ε333 , ε3333 and ε33333 imaging again, and the results are shown in Fig. 9(c). In this figure, the ε33333 signal disappears and the ε3333 signal becomes flat again, whereas the ε333 imaging clearly detects the c–c domain boundaries (as seen in Fig. 9(a)). This implies that the entire surface area of the PPLN is covered by a surface paraelectric layer again. From theoretical calculations for a LiNbO3 substrate, ε33333 and ε3333 imaging has sensitivities down to depths of 0.75 nm and 1.25 nm, respectively, whereas ε333 imaging has sensitivity down to a depth of 2.75 nm when a tip of radius 25 nm is used. Thus, we conclude that the thickness of the surface paraelectric layer ranges between 0.75 nm and 2.75 nm. From these results, we have succeeded in observing the growth of the surface layer and we have confirmed that the negative areas of LiNbO3 can be more easily damaged than the positive areas.

4 Three-Dimensional Measurement Technique A new type of scanning nonlinear dielectric microscope probe, named the ε311 -type probe, and a system to measure the ferroelectric polarization component parallel to the surface using SNDM have been developed [16]. This is achieved by measuring the nonlinear dielectric constant ε311 of the ferroelectric material instead of ε333 , which is measured in conventional SNDM. Experimental results show that the probe can detect the polarization direction parallel to the surface with high spatial resolution. Moreover, we propose an advanced measurement technique using a rotating electric field. This technique can be applied to measure three-dimensional polarization vectors.

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Fig. 10. Capacitance variation with alternating electric field: (a) ε333 measurement, and (b) ε311 measurement

Fig. 11. Schematic configuration of (a) the new ε311 probe and (b) the measurement system

4.1 Principle and Measurement System Figure 10 shows parallel-plate models of nonlinear-dielectric-constant measurements. Since a precise description of the ε333 measurement has been provided above, we explain only the ε311 measurement here. We consider ¯3 with an amplithe situation in which a relatively large electric field E tude Ep and angular frequency ωp is applied to a capacitance Cs , producing a change of the capacitance resulting from the nonlinear dielectric response. We detect the capacitance variation ∆Cs perpendicular to the polarization direction (z-axis) by a high-frequency electric field with ˜1 ), as shown in Fig. 10(b). (In the a small amplitude along the x-axis (E ε333 measurement, we detect ∆Cs along the direction of the spontaneous ¯ is perpendicular to polarization Ps3 .) That is, in the ε311 measurement, E ˜ We call this kind of measurement, which uses crossed electric fields, E. an “ε311 -type” measurement. In this case, the final formula is given by ∆Cs (t) ε311 ε3311 2 = Ep cos ωp t + E cos 2ωp t , Cs0 ε11 4ε11 p

(4)

where ε11 is the linear dielectric constant, and ε311 and ε3311 are nonlinear dielectric constants. From this equation, by detecting the compo-


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nent of capacitance variation with the angular frequency of the applied electric field ωp , we can detect the nonlinear dielectric constant ε311 . According to this principle, we have developed an ε311 -type probe for measuring the polarization direction parallel to the surface. Figure 11 shows a schematic diagram of the measurement system. We put four electrodes ¯ which causes the nonaround the probe tip to supply the electric field E, ¯ linear effect. Electrodes A and B supply E3 , which is along the z-axis, ¯2 , which is along the y-axis. We apand electrodes C and D supply E ¯2 ply voltages to the electrodes, such as to satisfy the condition that E ¯ and E3 just under the tip become parallel to the surface without becoming concentrated at the tip, as shown in Fig. 11(b). (In Fig. 11(b), the component related to the y-direction is omitted for simplification.) On the ˜ for measuring the capacitance variation is other hand, the electric field E concentrated at the probe tip, as in the conventional measurement. It is ˜ because we have consufficient to consider only the x-component of E, ˜ firmed that most of E underneath the tip is perpendicular to the surface. Moreover, we can obtain any electric field vector E¯ with an arbitrary ¯2 and E ¯3 . Therefore, we rotation angle by combining the amplitudes of E need not rotate the specimen to detect a lateral polarization with an arbitrary direction. 4.2 Experimental Results Figure 12 shows measurement results of a PZT thin film where the direction ¯ was varied. In Fig. 12(a), when E ¯ is parallel of the applied electric field E to the polarization direction, a pattern corresponding to the polarization is ¯ is observed, while no pattern is observed in Fig. 12(b), because in this case E perpendicular to the polarization direction. Figures 12(c) and (d) show cases ¯ is applied along intermediate directions. The pattern can be obwhere E served in both Fig. 12(c) and Fig. 12(d), because the vector E¯ can be divided by the component along the polarization direction. However, opposite contrast was obtained because the signs of the component along the polarization are opposite. Moreover, the new probe can measure both ε311 and ε333 independently. Figure 12(e) shows an ε333 image, which corresponds to the perpendicular component of the polarization. From the same positions in Fig. 12(a), signals are observed. This means that the polarization has both parallel and perpendicular components, that is, the polarization is tilted with respect to the surface. Figure 12(f) is a topographic image, which was measured simultaneously. From these results, we have confirmed that the new probe and system can be applied to three-dimensional polarization measurements.

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Fig. 12. Images of PZT thin film: (a)–(d) ε311 images, (e) ε333 image and (f ) topography

5 Tb/in2 Ferroelectric Data Storage Based on SNDM Nanosized inverted domain dots in ferroelectrics are expected to play a major role in the storage of information in the next-generation ultrahigh-density recording systems. As high-density recording media, ferroelectric materials are considered to be superior to the ferromagnetic materials widely used at present because the domain wall thickness of typical ferroelectric materials is of the order of a few lattice spacings, far less than that of ferromagnetic materials [17]. Scanning probe microscopy (SPM) has been extensively investigated as a method of forming and detecting small inverted domain dots in ferroelectric thin films such as lead zirconate titanate [18]. In this technique, domain dots are switched by applying a relatively large dc pulse to the probe, creating an electric field at the tip of the probe cantilever. These dots can then be detected via an ac surface displacement (vibration) of the ferroelectric material based on the piezoelectric response to an ac electric field applied by the same tip [8]. This technology has clear implications for bit storage in ultrahigh-density recording systems, with anticipated storage densities of the order of Tb/in2 . Although current techniques are capable of forming and detecting dots of around 100 nm in size, this falls far short of the 1 Tb/in2 thought to be possible [18, 19]. The limiting factors involved are the resolution of the piezoimaging method and the physical properties of the ferroelectric medium. For example, even if very small nanodots less than 10 nm in size could be formed successfully, a detection method with a resolution finer than 1 nm would be required to detect such dots with sufficient accuracy. Therefore, it is of pri-


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mary importance to improve the resolution of the domain detection device such that the smallest formable domain sizes can be resolved. The resolution of our scanning nonlinear dielectric microscope is in the subnanometer range, much higher than that of other SPM methods used for observing polarization distributions. Moreover, our SNDM technique is a purely electrical method, allowing domain information to be read at much higher speed than is possible by piezoimaging, the read speed of which is limited by the mechanical resonant frequency of the atomic force microscopy (AFM) cantilever (typically around 100 kHz). More recently, the present authors have studied the formation of smalldomain inverted dots in PZT thin films using SNDM, and have successfully produced and observed a domain inverted dot with a radius of 12.5 nm [15]. However, single-crystal material is expected to be more suitable for studying nanodomain engineering quantitatively with good reproducibility, because current thin films still suffer from atomic-scale nonuniformities that prevent switching in the nanodomains in which they occur. To date, barium titanate (BaTiO3 ) is the only material that has been studied as a single-crystal material for nanodomain switching [19]. Although BaTiO3 is a typical ferroelectric material, it is not suitable as a recording medium for a number of reasons. Most importantly, single-crystal BaTiO3 belongs to the tetragonal system, with the result that it has two possible domains in which to store bits, a 90◦ a–c domain and a 180◦ c–c domain. Such a structure introduces a level of complexity not desired at present. Furthermore, the phase transition from the tetragonal phase to the orthorhombic phase occurs at 5 ◦ C, which is dangerously close to room temperature for a storage medium, possibly resulting in data loss as a result of ambient-temperature drift. Lastly, it is difficult to fabricate large, high-quality, practically usable BaTiO3 single crystals at low cost. A ferroelectric nanodomain engineering material suitable for practical application as a storage medium should have a single 180◦ c–c domain and an adequately high Curie point without phase transitions below the Curie point, and be producible as large single crystals with good homogeneity at low cost. Lithium tantalate (LiTaO3 ) single crystals satisfy all these conditions, and have been used widely in optical and piezoelectric devices. The development of nanodomain engineering techniques based on single-crystal LiTaO3 will have applications not only in ultrahighdensity data storage, but also in various electrooptical, integrated optical and piezoelectric devices. In our study, we investigated the formation of small inverted domain dots in single-crystal LiTaO3 using our SNDM nanodomain engineering system. A schematic diagram of the SNDM domain engineering system is shown in Fig. 13. In the case of single-crystal LiTaO3 , the signal-to-noise ratio is sufficiently high to eliminate the need for the lock-in amplifier, and nanodomains can be easily detected using a normal oscilloscope. The use of a

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Fig. 13. Ferroelectric nanodomain engineering system based on scanning nonlinear dielectric microcopy

lock-in amplifier seriously limits the reading speed, and so discarding that requirement is expected to result in very high reading speeds. An SNDM ferroelectric data storage system using single-crystal LiTaO3 is therefore a strong candidate for ultrahigh-density storage. The two types of single-crystal LiTaO3 available commercially, stoichiometric lithium tantalate (SLT) and congruent lithium tantalate (CLT), were examined. Both forms have a good rectangular hysteresis loop suitable for memory applications [20]. SLT has fewer point defects owing to the lower Li content compared with CLT, with the direct result that the coercive electric field of SLT is about 1/13 that of CLT. The natural domain size of CLT, on the other hand, is smaller than that of SLT. Therefore, SLT is expected to offer faster switching and a lower switching voltage, while CLT is suitable for higher-density storage with smaller domain dots and stable retention. CLT has the additional, not insignificant benefit of being much less expensive than SLT, as almost all commercially available LiTaO3 crystals are grown from a congruent-composition melt. The ferroelectric domain dots were produced using a pulse generator newly installed in the SNDM system, similar to what has been done for ferroelectric data storage based on piezoimaging for potential application as a data storage medium. For the formation of very small domain dots, we fabricated and used very thin SLT and CLT single-crystal plates of thickness 70−150 nm. As a preliminary investigation of this method of domain engineering, we clarified the variation in the inverted-domain size in SLT with the duration of application of the voltage. In order that the application of the voltage pulse in the nanosecond range was not affected by the high impedance of the tip–sample contact, a 50 Ω terminal resistance was connected in par-


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Fig. 14. Typical shapes of nanodomain dots for voltage application times of (a) 500 ns, (b) 100 ns and (c) 60 ns using a voltage of 15 V and a 100 nm-thick SLT plate. The upper figures are mixed-signal (A cos θ) images, and the lower figures are phase (cos θ) images

allel between the tip (ground) and the back electrode of the sample (metal stage). Thus, the resultant load resistance between the tip and the metal stage was fixed at 50 Ω and the nanosecond pulses were applied accurately. Figure 14 shows the typical shapes of nanodots formed in a 100 nm-thick SLT plate as seen in mixed-signal (A cos θ) and phase (cos θ) images for three voltage application times at 15 V. The phase image shows only the sign of the domain, and was used to define the size of the nanodots. As expected, the smallest inverted-domain dot among these examples, with a radius less than 10 nm, was obtained at the shortest voltage application time of 60 ns. The smallest SLT dot obtained in this study is shown in Fig. 15. The shape of this domain is irregular rather than round. Therefore, we calculated an equivalent radius of a circle with the same area as this domain. The value obtained was 6 nm, which corresponds to a memory density of 4 Tb/in2 if the dots are close-packed. These nanodomain dots in SLT were confirmed to be stable over time through continuous measurements over the first 24 h and further measurements 1 month later. The dots exhibited no measurable change during this period. Single-crystal CLT was also examined as a practical data storage medium. CLT was employed for this application because Li vacancy defects in CLT ef-

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Fig. 15. Smallest single nanodot obtained in this study (phase image), with an equivalent radius of 6 nm. This dot was formed by application of a 15 V, 60 ns pulse to a 100 nm-thick SLT plate

Fig. 16. Nanodomain characters written at 14 V on a 70 nm-thick CLT film (normalized amplitude). The large characters were using 10 µs pulses, and the small characters were written using 5 µs pulses

fectively pin the sites of domains, and the smaller size of the natural domains allows higher memory densities. The controllability of nanosized domain inversion was demonstrated on a 70 nm-thick CLT plate by writing domains to form the words “TOHOKU UNIV.”, as shown in Fig. 16. Two sizes of characters were written; both are shown in the figure at the same magnification. The larger characters were written with 10 µs pulses, and the smaller characters were written with 5 µs pulses, both at 14 V. The average size of one of the smaller characters is about 120 nm. The pulse application time for CLT was necessarily much longer than in the case of SLT, reflecting the lower switching speed of CLT.


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Fig. 17. SNDM images of close-packed arrays of domain dots (normalized amplitude) at a data density of (a) 0.62 Tb/in2 (11 V, 10 µs) and (b) 1.50 Tb/in2 (12 V, 80 ns) formed using 70 nm-thick single-crystal CLT

Ultrahigh-density bit storage was then performed at a data density of 1 Tb/in2 using the 70 nm CLT plate. Figure 17 shows SNDM images of close-packed arrays of positive- and negative-domain dots at densities of 0.62 Tb/in2 and 1.50 Tb/in2 . The 0.62 Tb/in2 array was formed at 11 V with 10 µs pulses, and the 1.50 Tb/in2 array was formed at 12 V with 80 ns pulses. The average radius of the dots in the 1.50 Tb/in2 array is 10.4 nm. Although the dots in the 1.50 Tb/in2 array may not be resolvable with sufficient accuracy for practical data storage, this system is fully expected to become practically applicable as a storage system after further refinement. We have thus demonstrated, using a ferroelectric medium and nanodomain engineering, that rewritable bit storage at a data density of more than 1 Tb/in2 is achievable. To the best of our knowledge, this is the highest density reported for rewritable data storage, and this is expected to stimulate renewed interest in this approach to the next generation of ultrahigh-density rewritable electric data storage systems.

References [1] Y. Cho, A. Kirihara, T. Saeki: Denshi Joho Tsushin Gakkai Ronbunshi J78C-1, 593 (1995) 106 [2] Y. Cho, A. Kirihara, T. Saeki: Electronics and Communication in Japan, vol. 2 (Scripta Technica 1996) p. 79 106 [3] Y. Cho, A. Kirihara, T. Saeki: Rev. Sci. Instrum. 67, 2297 (1996) 106, 107

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[4] Y. Cho, S. Atsumi, K. Nakamura: Jpn. J. Appl. Phys. 36, 3152 (1997) 106, 107 [5] Y. Cho, S. Kazuta, K. Matsuura: Appl. Phys. Lett. 72, 2833 (1999) 106 [6] H. Odagawa, Y. Cho: Surf. Sci. 463, L621 (2000) 106 [7] H. Odagawa, Y. Cho: Jpn. J. Appl. Phys. 39, 5719 (2000) 106, 110 [8] A. Gruverman, O. Auciello, R. Ramesh, H. Tokumoto: Nanotechnology 8, A38 (1997) 106, 111, 118 [9] L. Eng L, H. J. G¨ u, G. A. Schneider, U. K¨ opke, J. S. na Mu˜ noz: Appl. Phys. Lett. 74, 233 (1999) 106, 111 [10] Y. Cho, K. Ohara, A. Koike, H. Odagawa: Jpn. J. Appl. Phys. 40, 3544 (2001) 106 [11] K. Ohara, Y. Cho: Jpn. J. Appl. Phys. 40, 5833 (2001) 106 [12] Y. Cho, K. Ohara: Appl. Phys. Lett. 79, 3842 (2001) 106 [13] Y. Cho, K. Fujimoto, Y. Hiranaga, Y. Wagatsuma, A. Onoe, K. Terabe, K. Kitamura: Appl. Phys. Lett. 81, 4401 (2002) 106 [14] Y. Cho, K. Ohara, S. Kazuta, H. Odagawa: J. Eur. Ceram. Soc. 21, 2135 (2001) 110 [15] K. Matsuura, Y. Cho, H. Odagawa: Jpn. J. Appl. Phys. 40, 3534 (2001) 112, 119 [16] H. Odagawa, Y. Cho: Appl. Phys. Lett. 80, 2159 (2002) 115 [17] F. Jona, G. Shirane: Ferroelectric Crystals (Pergamon, New York 1962) p. 46 118 [18] P. Pauch, T. Tybell, J. M. Triscone: Appl. Phys. Lett. 79, 530 (2001) 118 [19] L. Eng, M. Bammerlin, C. Loppacher, M. Guggisberg, R. Bennewitz, R. L¨ uthi, E. Meyer, T. Huser, H. Heinzelmann, H. J. G¨ untherodt: Ferroelectrics 222, 153 (1999) 118, 119 [20] K. Kitamura, Y. Furukawa, K. Niwa, V. Gopalan, T. Mitchell: Appl. Phys. Lett. 73, 3073 (1998) 120

Index

a–c (90◦ ) domain, 109 BaTiO3 single crystal, 109 c–c (180◦ ) domain, 109 ferroelectric data storage, 118

higher-order nonlinear dielectric microscopy, 112

scanning nonlinear dielectric microscopy, 106 SNDM, 106

Analysis of Ferroelectricity and Enhanced Piezoelectricity near the Morphotropic Phase Boundary Makoto Iwata1 and Yoshihiro Ishibashi2 1

2

Department of Engineering Physics, Electronics and Mechanics, Graduate School of Engineering, Nagoya Institute of Technology, Nagoya 466-8555, Japan [email protected] Faculty of Business, Aichi Shukutoku University, Nagakute-cho, Aichi Prefecture 480-1197, Japan [email protected]

Abstract. In this Chapter, we discuss the phase diagram, dielectric constants, elastic constants, piezoelectricity and polarization reversal in the vicinity of a morphotropic phase boundary (MPB) in perovskite-type ferroelectrics and rare-earth– Fe2 compounds from a theoretical viewpoint based on a Landau-type free-energy function. It has been clarified that the instability of the order parameter perpendicular to the radial direction in the order-parameter space near the MPB is induced by the isotropy or small anisotropy of the free-energy function; this is called the transverse instability. It should be noticed that the origins of the enhancement of the responses near the MPB both in the perovskite-type ferroelectrics and the rare-earth–Fe2 compounds are the same. At the end of this Chapter, we point out that the transverse instability is a common phenomenon, appearing not only in the perovskite-type ferroelectric oxides, but also in magnetostrictive alloys consisting of rare-earth–Fe2 compound [1], in the low-temperature phase of hexagonal BaTiO3 [2] and in shape memory alloys [3, 4].

1 Introduction Solid solutions of perovskite-type ferroelectrics whose composition is in the vicinity of the morphotropic phase boundary (MPB) show excellent properties for applications such as electrostrictive actuators and sensors, because of the large dielectric constant and high electromechanical coupling constant [5, 6, 7, 8, 9]. The physical origins of these properties had not been clarified for many years until Ishibashi and Iwata [10] proposed in 1998, on the basis of a Landau–Devonshire-type potential with terms up to the fourth order in the polarization, that such a large dielectric response in the MPB region is induced by an instability perpendicular to the spontaneous polarization, called the transverse instability. They explained not only the large dielectric and elastic-compliance constants but also the significant piezoelectric response, on the basis of the concept of transverse instability [1, 11, 12, 13, 14, 15, 16]. They also discussed a field-induced monoclinic M. Okuyama, Y. Ishibashi (Eds.): Ferroelectric Thin Films, Topics Appl. Phys. 98, 127–148 (2005) © Springer-Verlag Berlin Heidelberg 2005

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Makoto Iwata and Yoshihiro Ishibashi

phase and a field-induced transition in an engineered domain configuration in the MPB region [17, 18]. It should be noticed that the field-induced monoclinic phase can be explained by a Landau–Devonshire-type potential with terms up to the fourth order in the polarization. Recently, Noheda et al. found that a monoclinic structure exists between the tetragonal and rhombohedral phases in the MPB region, and they pointed out that the monoclinic structure can be pictured as providing a “bridge” between the tetragonal and rhombohedral structures [19, 20, 21, 22]. Vanderbilt and Cohen [23] pointed out that an eighth-order term in the polarization, p8 , is required to explain the transition from the cubic to the monoclinic phase in terms of a Landau–Devonshire-type potential. On the other hand, Fu and Cohen [24] reported that a polarization-rotation path exists under an electric field on the basis of first-principles calculations, and pointed out that the polarization rotation can result in a significant piezoelectric response. It should be noticed that the appearance of the monoclinic phase and the giant piezoelectric response can be explained as a consequence of the transverse instability. It is known that perovskite-type relaxor ferroelectrics and related materials such as Pb(Zn1/3 Nb2/3 )O3 –PbTiO3 (PZN–PT) show excellent properties for applications such as electrostrictive actuators and sensors [25, 26, 27, 28, 29]. One of the most important properties for applications in relaxors and related materials is the giant dielectric response, which means a large dielectric constant and high electromechanical coupling constant. The giant dielectric response is considered to be due to a transverse instability in the MPB region [27]. In the present chapter, we discuss the theory of ferroelectricity and enhanced piezoelectricity near the MPB on the basis of a Landau–Devonshiretype free energy.

2 Free Energy and Phase Diagram In the solid-solution systems to be studied here, the paraelectric phase is cubic, and as a result of a temperature-driven phase transition to the ferroelectric phase, a tetragonal, rhombohedral or orthorhombic phase appears. All ferroelectric phases are piezoelectric, and an increase of the piezoelectric constants close to the MPB is one of the most important features. Let us start with the free-energy function, written in terms of the polarization components and the strain components as [30, 31, 32, 33]

Ferroelectricity and Enhanced Piezoelectricity

f = + + + + + +

β α 2 p1 + p22 + p23 + 1 p41 + p42 + p43 2 4 γ1 6 β2 2 2 2 2 2 2 p1 p2 + p2 p3 + p3 p1 + p1 + p62 + p63 2 2 2 γ2 4 2 2 4 p p + p3 + p2 p3 + p21 + p43 p21 + p22 2 1 2 γ3 2 2 2 c11 2 p1 p2 p3 + u1 + u22 + u23 + c12 (u1 u2 + u2 u3 + u3 u1 ) 2 2 c44 2 2 u + u + u26 + Q11 u1 p21 + u2 p22 + u3 p23 2 4 5 Q12 u1 p22 + p23 + u2 p23 + p21 + u3 p21 + p22 Q44 (u4 p2 p3 + u5 p3 p1 + u6 p1 p2 ) ,

129

(1)

where α is temperature-dependent in the form α = a (T − T0 ); β1 , β2 , γ1 , γ2 and γ3 are all constant; cij are the elastic stiffness constants; and Qij are the electrostrictive constants. To stabilize the tetragonal, orthorhombic and rhombohedral phases which appear as the result of the phase transition from the cubic phase, γ1 , γ2 and γ3 have to satisfy the conditions that γ1 > 0,

γ1 + 3γ2 > 0,

γ1 + 6γ2 + γ3 > 0.

(2)

By using the equilibrium conditions for strain components ∂f /∂ui = 0 (i = 1, 2, . . . , 6), the strain components as a function of the polarization components are given by 2 (c11 + c12 ) Q11 − 2c12 Q12 2 c12 Q11 − c11 Q12 p + u1 = − p + p23 , (c11 − c12 ) (c11 + 2c12 ) 1 (c11 − c12 ) (c11 + 2c12 ) 2 2 (c11 + c12 ) Q11 − 2c12 Q12 2 c12 Q11 − c11 Q12 p2 + p3 + p21 , u2 = − (c11 − c12 ) (c11 + 2c12 ) (c11 − c12 ) (c11 + 2c12 ) 2 (c11 + c12 ) Q11 − 2c12 Q12 2 c12 Q11 − c11 Q12 u3 = − p3 + p1 + p22 , (c11 − c12 ) (c11 + 2c12 ) (c11 − c12 ) (c11 + 2c12 ) Q44 Q44 Q44 u4 = − p2 p3 , u 5 = − p3 p1 , u 6 = − p1 p2 . (3) c44 c44 c44 Using (3), the free-energy function can be reduced to β1 4 β2 2 2 α 2 p + p22 + p23 + p + p42 + p43 + p1 p2 + p22 p23 + p23 p21 f = 2 1 4 1 2 γ2 4 2 γ1 6 + p1 + p62 + p63 + p1 p2 + p23 + p42 p23 + p21 + p43 p21 + p22 2 2 γ3 2 2 2 p p p , (4) + 2 1 2 3 where 2 2 c11 Q11 + 2Q212 + c12 Q211 − 4Q11 Q12 , β1 = β1 − D Q2 2 β2 = β2 − c11 2Q11 Q12 + 2Q212 − c12 Q211 + 2Q211 − 44 , (5) D c44 D = (c11 − c12 ) (c11 + 2c12 ) .

130


Fig. 1. Phase diagrams with second-order transitions from the cubic phase. Solid and dotted lines indicate second- and first-order transitions, respectively. (a) β1 = 1, γ1 = 1, γ2 = 6/5, γ3 = 17/25. (b) β1 = 1, γ1 = 1, γ2 = 11/12, γ3 = 15/8. (c) β1 = 1, γ1 = 1, γ2 = 13/12, γ3 = 5/2 [11]

Now, it is known that an MPB appears when the β1 and β2 above are equal, within a model where terms only up to the fourth order are taken into account, because the free-energy function becomes isotropic in the space spanned by p1 , p2 and p3 , i.e., the free energy becomes a function only of p21 + p22 + p23 . It is clear, however, that their signs have nothing to do with the appearance of the MPB. In other words, whether the transition from the cubic phase is of the second order or of the first order is not significant. In the following, we first discuss second-order transitions and then first-order transitions. It has been clarified that for β1 > β2 and β1 + 2β2 > 0, a cubic– rhombohedral transition of the second order occurs, and for β2 > β1 > 0 a cubic–tetragonal transition of the second order also occurs. Depending on the values of the coefficients of the sixth-order terms, γ1 , γ2 and γ3 , several different phase diagrams are obtained, as shown in Fig. 1 [11]. Regarding the method used for assigning values, readers are referred to [32] and [33]. All of the transitions between the rhombohedral, orthorhombic and tetragonal phases must be of first order for reasons of symmetry. If β1 and β2 satisfy the condition that β1 < 0 or β1 + 2β2 < 0, the transition from the cubic phase is of first order. The transition temperatures to the tetragonal, orthorhombic and rhombohedral phases are given by αT =

3 β12 , 16 γ1

αO =

3 (β1 + β2 ) , 16 γ1 + 3γ2

αR =

3 (β1 + 2β2 ) , 16 γ1 + 6γ2 + γ3

(6) 2

(7) 2

(8)


131

Fig. 2. Phase diagrams with first-order transitions from the cubic phase. Dotted lines indicate first-order transitions. (a) β1 = −1, γ1 = 1, γ2 = 6/5, γ3 = 17/25. (b) β1 = −1, γ1 = 1, γ2 = 11/12, γ3 = 15/8. (c) β1 = −1, γ1 = 1, γ2 = 13/12, γ3 = 5/2 [11]

respectively, and the actual transition occurs to the phase with the highest transition temperature. Here again, several phase diagrams are obtained depending on the values of γ1 , γ2 and γ3 , as shown in Fig. 2 [11].

3 Dielectric Constants, Elastic Constants and Electromechanical Coupling Constants In this section, we derive the dielectric constants, the piezoelectric constants and the elastic constants on the basis of the free energy in (1) [10, 11, 12]. By adopting a “golden rule”, we obtain the Hessian, which in the present case is a 9 × 9 matrix composed of the second derivatives of the free energy with respect to the order parameters: ⎞ ⎛ f11 . . . f19 ⎝ ... ... ... ⎠ , (9) f91 . . . f99 0 where fij = ∂ 2 f /∂qi ∂qj (qi = u1 , . . . , u6 for i = 1, . . . , 6 and qi = p1 , . . . , p3 for i = 7, . . . , 9), and the symbol 0 outside the matrix implies that the equilibrium values of the order parameters have to be substituted. For the tetragonal phase, where p1 = p2 = 0 and p23 = p2 = 0, the dielectric susceptibilities, piezoelectric constants and elastic constants can be obtained from the free-energy function given by (1), in a straightforward manner without any transformation of coordinates, as

132


1 1 = = α + β2 p2 + γ2 p4 = (β2 − β1 ) p2 + (γ2 − γ1 ) p4 , χ11 χ22 1 = α + 3β1 p2 + 5γ1 p4 , χ33 α311 = α322 = 2Q12 p,

(10)

α333 = 2Q11 p, α223 = α131 = Q44 p, c11 = c22 = c011 −

2Q212 , β1 + 2γ1 p2

2Q211 , β1 + 2γ2 p2 2Q212 = c012 − , β1 + 2γ2 p2 2Q11 Q12 = c23 = c012 − , β1 + 2γ2 p2

c33 = c011 − c12 c13

c44 = c55 = c044 −

Q44 β1 − β 2 −

Q244 c244

+ (γ1 − γ2 ) p2

,

c66 = c044 . Here p is the spontaneous polarization, which satisfies α + β1 p2 + γ1 p4 = 0.

(11)

(To avoid confusion, the suffixes of the third-rank tensor have not been reduced.) For the rhombohedral phase, where p21 = p22 = p23 = r2 = 0, the dielectric constants, piezoelectric constants and elastic stiffness constants are transformed by ⎞⎛ ⎞ ⎛ ⎞ ⎛ √1 √ −1 0 a a 2 2 1 1 −2 ⎟ ⎝ b ⎠ = ⎜ (12) ⎝ √6 √6 √6 ⎠ ⎝ b ⎠ , √1 √1 √1 c c 3

3

3

where (a, b, c) are coordinates. We obtain


133

1 1 = = A − B = α + 3β1 r2 + (5γ1 + 6γ2 − γ3 ) r4 χ11 χ22 = 2 (β1 − β2 ) r2 + 2 (2γ1 − γ3 ) r4 , 1 = A + 2B = α + 3 (β1 + 2β2 ) r2 + 5 (γ1 + 6γ2 + γ3 ) r4 , χ33 2r 1 α311 = α322 = √ (C + 2D − E − 2F ) = √ (Q11 − Q44 + 2Q12 ) , 3 3 2r 1 α333 = √ (C + 2D + 2E + 4F ) = √ (Q11 + 2Q44 + 2Q12 ) , (13) 3 3 2r 1 α211 = −α222 = α112 √ (C − D + 2E − 2F ) = √ (Q11 − Q44 − Q12 ) , 6 6 r 1 α223 = α131 = √ (C − D − E + F ) = √ (2Q11 − Q44 − 2Q12 ) , 3 3 c11 = c22 2

2

2 (Q11 + Q12 − Q44 ) c011 + c012 (Q11 − Q12 − Q44 ) + c011 − − , 2 3B 3C c0 + 2c012 + 4c044 2 (Q11 + 2Q12 + Q44 )2 = 11 + , 3 3C 2 (Q11 − Q12 − Q44 ) c0 + 5c012 − 2c044 + = 11 6 3B 2 2 (Q11 + 2Q12 − Q44 ) − , 3C = c23 2 (Q11 + 2Q12 + 2Q44 ) (Q11 + 2Q12 − Q44 ) c0 + 2c012 − 4c044 − , = 11 3 3C 2 (2Q11 − 2Q12 + Q44 ) c0 − c012 + c044 − , = c55 = 11 3 6B c0 − c012 + 4c044 (Q11 − Q12 − Q44 )2 = 11 − , 6 3B = c56 = −c24 (2Q11 − 2Q12 + Q44 ) (Q11 − Q12 − Q44 ) c0 − c012 − 2c044 √ √ − , = 11 3 2 3 2B =

c33 c12

c13

c44 c66 c14

where r is the spontaneous polarization, which satisfies α + (β1 + 2β2 ) r2 + (γ1 + 6γ2 + γ3 ) r4 = 0.

(14)

We omit the result for the orthorhombic phase owing to lack of space (see [11, 12]). Let us now discuss the inverse transverse dielectric susceptibilities predicted by (10) and (14). It is found that the transverse dielectric susceptibility at the MPB diverges if the power series expansion in terms of the polarization is truncated at the fourth order; the increase is related to the isotropy of

134


the free-energy function. In actual situations, however, no divergence is to be expected there, because the transition across the MPB must be of first order for reasons of symmetry. Indeed, the divergence will be suppressed by a contribution from higher-order terms. The sixth-order terms become isotropic when γ1 = γ2 = γ3 /2.

(15)

Next, let us discuss the electromechanical coupling constants. In the ferroelectric phases, there appears induced piezoelectricity. The nonzero components of the piezoelectric constants are governed by the crystal symmetry. In general, in the piezoelectric phase the energy due to fluctuations in the polarization p and strain u can be written as f=

1 1 2 p + apu + cp u2 , u 2χ 2

(16)

where χu , a and cp are the susceptibility under constant strain, the piezoelectric constant, and the elastic constant under constant polarization, respectively (to simplify the discussion, we have taken only one polarization component and one strain component). Then, the electromechanical coupling constant k can be defined as χu k=a . (17) cp The elastic constant under constant field is obtained as c E = c p − χu a 2 = c p 1 − k 2 .

(18)

Note that all elastic constants obtained in the present section are under constant field. Some of them (for example, c44 in (2)) are exactly zero when the condition β1 = β2 and γ1 = γ2 = γ3 /2 holds. In the vicinity of the MPB, where this condition almost holds (though not exactly), cE will be small, and therefore the corresponding electromechanical constant will become large, or close to unity. This is indeed observed in the vicinity of the MPB.

4 Polarization Reversal Let us consider polarization reversal due to an external field [13, 15]. For the sake of simplicity, the free energy f , written in terms of the polarization components p1 , p2 and p3 and truncated at the fourth order, is discussed, i.e., β1 4 α 2 p1 + p22 + p23 + p1 + p42 + p43 f = 2 4 β2 2 2 2 2 2 2 p1 p2 + p2 p3 + p3 p1 , (19) + 2


135

where α is temperature-dependent in the form α = a (T − T0 ), and β1 and β2 are constants. To explain experimental findings related to the MPB and the p– e hysteresis loop more satisfactorily, it is desirable to include the sixth-order terms. Nevertheless, we shall use (18) for the present, because substantial aspects of the MPB can be reproduced in a transparent manner even without the sixth-order terms. We consider the p–e hysteresis loop in the low-frequency limit near the MPB using the free-energy function (19). The hysteresis loop is determined by the equilibrium conditions, i.e., ∂f = ei ∂pi

(i = 1, 2, 3),

(20)

where ei (i = 1, 2, 3) are the components of the external electric field, and the stability conditions are that all the principal minors of the Hessian matrix ⎞ ⎛ ∂2f ∂2f ∂2f 2

⎜ ∂∂p2 f1 ⎜ ⎝ ∂p2 ∂p1 ∂2f ∂p3 ∂p1

∂p1 ∂p2 ∂p1 ∂p3 ⎟ ∂2f ∂2f ⎟ 2 ∂p ∂p ∂p2 2 3⎠ ∂2f ∂2f 2 ∂p3 ∂p2 ∂p3

(21)

are positive definite. First, we consider the tetragonal phase, where, in the absence of an external field, the spontaneous polarization ps is oriented along the [001] direction such that p3 = ps ,

p1 = p2 = 0.

(22)

When an electric field e3 along the same [001] direction is applied to the sample, the relation between the polarization p (= p3 ) and the electric field is reduced from the equilibrium condition (20) to e3 = αp + β1 p3 .

(23)

This equation gives the hysteresis curve in the p–e3 plane within the region in which the stability condition (21) is satisfied. Note that this equation does not depend on β2 . The electric field em for which the slope ∂p/∂e3 of the p–e3 curve diverges is obtained from 2 (−α)3/2 , em = √ 3 3β1

1≤

β2 . β1

(24)

This field, which is derived only from consideration of the instability along the direction of the spontaneous polarization, is usually regarded as the coercive field in the hysteresis loop of a ferroelectric. It should be noted, however, that this is not always the case. The stability conditions are obtained as α + β2 p23 > 0

and α + 3β1 p23 > 0.

(25)

136


Fig. 3. p–e hysteresis loops for the tetragonal phase near the MPB. The numerical values α = −1, β1 = 1, and (a) β2 = 4, (b) β2 = 1.5, (c) β2 = 1.1 have been adopted. The parts drawn with dotted lines represent the range where the polarization becomes unstable [13]

The former and latter inequalities come from the stability conditions in the directions perpendicular and parallel, respectively, to the [001] direction. When these conditions are not fulfilled, the resulting instabilities are called transverse and longitudinal instabilities, respectively. We emphasize that the transverse instability is more important for the hysteresis loop near the MPB, even though this is often overlooked in the consideration of the hysteresis loops of the usual ferroelectrics. In the present chapter, we shall show theoretically that near the MPB, the transverse instability is more easily induced by an external field than is the longitudinal instability. From the conditions (23) and (25), the coercive field ec in the p–e3 loop is given by

3/2 −α β2 , 1< < 3, (26) ec = (β2 − β1 ) β2 β1 2 β2 (−α)3/2 , 3 ≤ . (27) ec = √ β1 3 3β1 For 3 ≤ β2 /β1 , the polarization instability is induced along the [001] direction, while for 1 < β2 /β1 < 3 it is induced in a direction perpendicular to [001]. It is easily seen from (26) and (27) that for 3 ≤ β2 /β1 , the coercive field coincides with em , while for 1 < β2 /β1 < 3 the coercive field induced by the transverse instability is smaller than em . Figures 3(a)–3(c) show typical hysteresis loops for the tetragonal phase, where the numerical values α = −1, β1 = 1, and β2 = 4, 1.5 and 1.1 have been adopted [13]. Dotted lines represent the range where the polarization becomes unstable. The coercive field is observed to decrease upon approaching the MPB. Next, let us consider the hysteresis loops for the rhombohedral phase. In the absence of an external field, the polarization along the [111] direction can be taken as p1 = p2 = p3 = rs ,

(28)


137

where the spontaneous polarization along the [111] direction is obtained from √ √ 3rs . When an electric field 3er along the [111] direction (e1 = e2 = e3 = er ) is applied to the sample, the equilibrium condition (20) is reduced to er = αr + (β1 − 2β2 ) r3 ,

(29)

where r is the polarization as a function of the external field. This equation gives the hysteresis curve in the r–e plane within the region where the stability condition (21) is satisfied. The electric field for which the slope ∂r/∂er of the r–er curve diverges is given by 2 (−α)3/2 , erm = 3 3 (β1 + 2β2 )

−

1 β2 < ≤ 1. 2 β1

(30)

√ We emphasize that in the rhombohedral phase also, although the field 3erm is usually regarded as the coercive field in a ferroelectric, because of the transverse instability this is not always the case. The stability condition (21) for the polarization r is reduced to β2 < 1, β1 β2 1 α + 3 (β1 + 2β2 ) r2 > 0, − < ≤ 0. 2 β1 α + 3β1 r2 > 0,

0
0. The Landau–Khalatnikov e = (0, 0, e), where p0 = (−α/β1 ) equation of motion for the free energy in (19) is

138


Fig. 4. p–e hysteresis loops for the rhombohedral phase near the MPB. The numerical values α = −1, β1 = 1 and (a) β2 = 0.9, (b) β2 = 0.5, (c) β2 = −0.3 have been adopted. The parts drawn with dotted lines represent the range where the polarization becomes unstable [13]

∂f dp1 =− = −αp1 − β1 p31 − β2 p22 + p23 p1 , dt ∂p1 ∂f dp2 =− γ = −αp2 − β1 p32 − β2 p21 + p23 p2 , dt ∂p2 dp3 ∂f γ =− = −αp3 − β1 p33 − β2 p21 + p22 p1 + e, dt ∂p3

γ

(35)

where γ is a kinetic coefficient. If the initial condition is p = (0, 0, −p0), the dipole moment does not know to which side it should “rotate” under the action of the electric field e = (0, 0, e). Therefore, we artificially assume that the dipole moment is tilted slightly to p = (δp, 0, −p0 ) at t = 0, where δp p0 . Then, the path of polarization will be restricted to within the xz plane. Figure 5 shows a typical result for the variation of the polarization components as a function of time for a stepped electric field in the region ec < e < em , where ec and em are defined in (26) and (24), respectively. The parameter values adopted were α = −1, β1 = 1, β2 = 1.1, e = 0.3, p0 = 1, γ = 1, and (1) δp = 10−5 , (2) δp = 10−4 and (3) δp = 10−3 , where ec ≈ 0.0867 and em ≈ 0.385. Figure 6 shows the field dependence of the path of the polarization in the reversal process. The strength of the electric field e applied was 0.3, 0.4, 0.41 and 0.43 in the case of curves (1), (2), (3) and (4), respectively. It is seen from Figs. 5 and 6 that two processes occur; one is a process parallel to the electric field and the other is a process perpendicular to the spontaneous polarization, and the path of the polarization follows an arc in the xz plane after a fast process parallel to the electric field for a weak electric field. In the present section, only the polarization reversal process in a homogeneous system has been considered. Therefore, the validity of the present theory is limited because the spatial inhomogeneity of the polarization that appears during an actual switching process is not taken into account. The polarization reversal process in a real ferroelectric is a heterogeneous one in-


139

Fig. 5. Typical solutions for the polarization components p1 and p3 for several processes. The parameter values adopted were α = −1, β1 = 1, β2 = 1.1, e = 0.32, p0 = 1, γ = 1, and (1) δp1 = 10−5 , (2) δp1 = 10−4 and (3) δp1 = 10−3 . The values of τ1 , τ2 and τ3 show the polarization reversal times for the curves (1), (2) and (3), respectively; τ is defined as the time at which p3 (t) becomes zero [15]

Fig. 6. Field dependence of the path of the polarization reversal. The parameter values adopted were α = −1, β1 = 1, β2 = 1.1, e = 0.3, p0 = 1, γ = 1, δ1 = 10−4 , and (1) e = 0.3, (2) e = 0.3, (3) e = 0.4 and (4) e = 0.43 [15]

140


volving the motion of many dipole moments, and the nucleation-and-growth process of ferroelectric domains plays an important role in the polarization reversal process [34, 35, 36]. For more quantitative considerations in the case of real ferroelectrics, a computer simulation on the basis of a lattice model is required.

5 Enhanced Piezoelectricity Under an Oblique Field In the previous sections, it has been pointed out that the dielectric response perpendicular to the spontaneous polarization is larger than the response parallel to the spontaneous polarization in the MPB region. It may be conjectured that the piezoelectricity is enhanced if the electric field applied includes an element perpendicular to the spontaneous polarization. In the present section, we discuss the effect of an oblique field on the enhancement of the piezoelectricity, where an oblique field is defined as an external field not parallel to the spontaneous polarization. It has been reported that in a single crystal with rhombohedral 3 m symmetry, piezoelectric activity is enhanced under a dc electric field along the [001] direction, which is not parallel to the spontaneous polarization, because of the appearance of a stable domain structure, called an engineered domain configuration, where four kinds of domains with polarizations along the [111], [¯ 111], [1¯ 11] and [¯ 1¯ 11] directions coexist in the crystal, and the domain walls cannot be moved by an external field along the [001] direction [37, 38, 39, 40], since the four domains are energetically equally stable with respect to the applied field. Furthermore, recently, another engineered domain configuration in the tetragonal phase has also been proposed, where three kinds of domains with polarization directions along [100], [010] and [001] coexist under a field along the [111] direction [41]. In the case of an engineered domain configuration, two possibilities for the origin of the enhanced piezoelectricity must be considered. One is the response of a domain wall itself, and the other is the transverse instability of the bulk crystal due to the oblique field. In the present section, we discuss the contribution from the oblique field to the enhanced piezoelectricity for an engineered domain configuration [16, 17, 18]. We start with the free-energy function g written in terms of the polarization components pi and the stress components Xj , in the form [17, 42]


g= + − − − −

β1 4 α 2 p1 + p22 + p23 + p1 + p42 + p43 2 4 β2 2 2 2 2 2 2 p1 p2 + p2 p3 + p3 p1 2 s011 2 X1 + X22 + X32 − s012 (X1 X2 + X2 X3 + X3 X1 ) 2 s044 2 X4 + X52 + X62 − B11 X1 p21 + X2 p22 + X3 p23 2 B12 X1 p22 + p23 + X2 p23 + p21 + X3 p21 + p22 B44 (X4 p2 p3 + X5 p3 p1 + X6 p1 p2 ) ,

141

(36)

where α is temperature-dependent in the form α = a(T − T0 ), β1 and β2 are constants, s0ij are the elastic compliance constants in the paraelectric phase and Bij are the electrostrictive constants. The relationship between the free-energy functions g(pi , Xj ) in (36) and f (pi , uj ) in (1) is given in [17]. In order to investigate the contribution from the bulk properties to the enhancement of the piezoelectricity for an engineered domain configuration, it is certainly desirable to include the sixth-order terms, because some perovskite ferroelectrics undergo a first-order paraelectric–ferroelectric phase transition. However, we shall use the free-energy equation (36) without the sixth-order terms in order to reproduce substantial aspects of the behavior of engineered domain configurations near the MPB. By using the free-energy (36), we expand the electric field ei and the strain uik in terms of small deviations of the polarization ∆pm and of the stress ∆Xim as ∂2g ∂ 2g ∆pm + ∆Xlm ∂pi ∂pm ∂pi ∂Xlm = βim ∆pm − gilm ∆Xlm ,

ei =

(37) −∂ g ∂ g ∆pm + ∆Xlm ∂Xik ∂pm ∂Xik ∂Xlm = gjkm ∆pm + sjklm ∆Xlm , 2

2

uik =

where gilm are the piezoelectric constants and βim the inverse dielectric constants, and the strain components are given by ukl = −∂g/∂Xkl . (No confusion should occur regarding the notation gilm here, although g is also used in (36).) It can be seen that the piezoelectric constants gilm can be directly obtained from the free energy (36), while the piezoelectric relationships are given by ∆uij = sijlm Xmn + dijm em , (38) ∆pk = dkmn Xmn + εkm em ,

142


where εkm are the dielectric constants under constant stress and sijkm are the elastic compliance constants under constant electric field. To explain the contribution from the bulk properties to the behavior of an engineered domain configuration [37, 38, 39, 40, 41], calculation of the piezoelectric constants dilm is required. Using (37) and (38), the piezoelectric constants dilm are given by dilm = εij gjlm .

(39)

In the present chapter, we discuss the temperature and concentration dependence of the piezoelectric constants dilm . Let us consider the piezoelectric constants in the tetragonal phase. Before the calculation of the piezoelectric constant along the [111] direction, the piezoelectric constant along the direction of the spontaneous polarization (the [001] direction), i.e., d333 , is calculated. In the present calculation, we assume that the spontaneous polarization lies along the [001] direction (p1 = p2 = 0 and p3 = p). If a weak electric field is applied along the [001] direction, the piezoelectric constant along the electric field in cubic coordinates is given by d333 = ε31 g133 + ε32 g233 + ε33 g333 (40) 2B11 p B11 = = √ , 2 α + 3β1 p −αβ1 where α + β1 p2 = 0.

(41)

√ Next, let us consider the case in which an electric field 3e along the [111] direction of the cubic coordinates is applied to a tetragonal sample (e1 = e2 = e3 = e). In the calculation of the piezoelectric constant along the electric field, we adopt hexagonal coordinates, where the transformation of the coordinates for (a, b, c) is given by ⎞⎛ ⎞ ⎛ ⎞ ⎛ √1 √ −1 0 a a 2 2 1 1 −2 ⎟ ⎝ b ⎠ = ⎜ (42) ⎝ √6 √6 √6 ⎠ ⎝ b ⎠ . √1 √1 √1 c c 3

3

3

After transformation of the coordinates, the dielectric constants and piezoelectric constants in rhombohedral coordinates corresponding to d∗333 are obtained as


ε31 = 0, √ 2 β2 − 3β1 ε32 = , 3 2α (β2 − β1 ) −β2 − 3β1 ε33 = , 6α (β2 − β1 ) √ 2 2 g233 = √ [−B11 − 2B12 + B44 ] p, 3 3 2 g333 = √ [B11 + 2B12 + 2B44 ] p, 3 3

143

(43)

where the asterisk in d∗333 denotes the piezoelectric constant for an engineered domain configuration. The piezoelectric constant along the electric field d∗333 is given by d∗333 = ε31 g133 + ε32 g233 + ε33 g333

1 4B44 = √ B11 + 2B12 + , β2 /β1 − 1 3 −3αβ1

(44)

where p2 is obtained from (41). Note that the piezoelectric constant d333 in rhombohedral coordinates does not depend on the spatial distribution of equivalent domains in the engineered domain configuration. Therefore, the value of d333 for a [001] ferroelectric domain obtained in (44) coincides with the piezoelectric constant averaged over the three kinds of equivalent domains, as long as the effect of domain boundaries is ignored. It is found that the piezoelectric constant d∗333 in an engineered domain configuration gradually increases on approaching the MPB and diverges at the MPB for our free-energy function (36). The ratio between the piezoelectric constants d∗333 and d333 is given by

B11 + 2B12 1 d∗333 1 4B11 √ = . (45) 1+ d333 3B11 B11 + 2B12 β2 /β1 − 1 3 It is seen that this ratio is also enhanced on approaching the MPB, i.e., β2 /β1 → 1. In the present section, we have shown that substantial aspects of the piezoelectric properties for an engineered domain configuration near the MPB are well reproduced on the basis of a Landau–Devonshire-type free-energy function which is truncated at the fourth order with respect to the polarization. For a more quantitative discussion, however, a free-energy function including sixth-order terms would be required. On the other hand, in the present theory, we have only discussed the effect of an oblique field on the enhanced piezoelectricity for an engineered domain configuration, without the contribution from the domain boundaries. Theories taking the contribution from the domain boundaries into account are required.

144


6 Magnetostrictive Alloys of Rare-Earth–Fe2 Compounds Magnetostrictive alloys belonging to the rare-earth–iron ternary compound family are known to show interesting phase diagrams including an MPB [9, 43, 44]. For example, Tb1−x Dyx Fe2 at the x = 0 end undergoes a phase transition from a cubic paramagnetic phase to a rhombohedral ferromagnetic (strictly speaking, ferrimagnetic) phase, while at the x = 1 end the compound undergoes a transition to a tetragonal phase [45]. The ferromagnetic MPB between the rhombohedral and tetragonal phases exists at about x = 0.7 at room temperature [2]. It is known that the alloy Tb1−x Dyx Fe2 in the vicinity of the MPB manifests excellent properties as a magnetostrictive actuator. Because of its importance in applications, the origins of such properties have been studied intensively, and theoretical analyses of the large magnetostrictive effect in these alloys have been put forward by Clark and coworkers [43, 44]. Ishibashi and Iwata [1] have pointed out that the phase diagrams of the rare-earth–Fe2 compound family are equivalent to those of the PbTiO3 –PbZrO3 solid solution system discussed in previous sections. These authors have applied a theory based on the Landau–Devonshire free energy to phase transitions in the rare-earth–Fe2 compound family, where the Landau-type free energy written in terms of the magnetization components m1 , m2 and m3 and the strain components ui (i = 1–6) is given by f = + + + + +

β α 2 m1 + m22 + m23 + 1 m41 + m42 + m43 2 4 γ1 6 β2 2 2 2 2 m1 m2 + m2 m3 + m23 m21 + m1 + m62 + m63 2 2 2 γ2 4 2 2 4 m1 m2 + m3 + m2 m3 + m21 + m43 m21 + m22 2 γ3 2 2 2 c11 2 m1 m2 m3 + u1 + u22 + u23 + c12 (u1 u2 + u2 u3 + u3 u1 ) 2 2 c44 2 2 u + u + u26 + Q11 u1 m21 + u2 m22 + u3 m23 2 4 5 Q12 u1 m22 + m23 + u2 m23 + m21 + u3 m21 + m22

(46)

+ Q44 (u4 m2 m3 + u5 m3 m1 + u6 m1 m2 ) . Here α is temperature-dependent in the form α = a (T − T0 ); β1 , β2 , γ1 , γ2 and γ3 are all constant; cij are the elastic stiffness constants; and Qij are the magnetostrictive constants. It should be noted that the free energy as a function of the magnetization components in (46) is the same as the free energy in (1) if magnetization components are substituted for polarization components. It has been shown that the physical properties of large magnetic susceptibility, large elastic compliance constants and high magetomechanical coupling constants can be explained in the same manner as discussed in the previous sections. The physical properties of magnetostrictive alloys near the


145

MPB can also be explained by a transverse instability due to the fact that the free-energy function becomes more isotropic.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33]

Y. Ishibashi, M. Iwata: J. Phys. Soc. Jpn. 68, 1353 (1999) 127, 144 Y. Ishibashi: Ferroelectrics 264, 197 (2001) 127, 144 Y. Ishibashi, M. Iwata: J. Phys. Soc. Jpn. 72, 1675 (2003) 127 M. Iwata, Y. Ishibashi: J. Phys. Soc. Jpn. 72, 2834 (2003) 127 B. Jaffe, J. W. J. Crook, H. Jaffe: Piezoelectric Ceramics (Academic Press, London 1971) 127 B. Jaffe, R. Roth, S. Marzullo: J. Res. Natl. Bur. Stand. 55, 239 (1955) 127 E. Sawaguchi: J. Phys. Soc. Jpn. 8, 615 (1953) 127 J. Kuwata, K. Uchino, S. Nomura: Jpn. J. Appl. Phys. 21, 1298 (1982) 127 R. Newnham: Mater. Res. Soc. Bull. 22, 20 (1997) 127, 144 Y. Ishibashi, M. Iwata: Jpn. J. Appl. Phys. 37, L985 (1998) 127, 131 Y. Ishibashi, M. Iwata: Jpn. J. Appl. Phys. 38, 800 (1999) 127, 130, 131, 133 Y. Ishibashi, M. Iwata: Jpn. J. Appl. Phys. 38, 1454 (1999) 127, 131, 133 M. Iwata, Y. Ishibashi: Jpn. J. Appl. Phys. 38, 5670 (1999) 127, 134, 136, 137, 138 Y. Ishibashi: Ferroelectrics 264, 197 (2001) 127 M. Iwata, H. Orihara, Y. Ishibashi: Jpn. J. Appl. Phys. 40, 708 (2001) 127, 134, 139 M. Iwata, H. Orihara, Y. Ishibashi: Ferroelectrics 266, 57 (2002) 127, 140 M. Iwata, H. Orihara, Y. Ishibashi: Jpn. J. Appl. Phys. 40, 703 (2001) 128, 140, 141 M. Iwata, Y. Ishibashi: Jpn. J. Appl. Phys. 39, 5156 (2000) 128, 140 B. Noheda, D. Cox, G. Shirane, J. Gonzalo, L. Cross, S. E. Park: Appl. Phys. Lett. 74, 2059 (1999) 128 R. Guo, L. Cross, S. E. Park, B. Noheda, D. Cox, G. Shirane: Phys. Rev. Lett. 84, 5423 (2000) 128 B. Noheda, J. Gonzalo, L. Cross, R. Guo, S. E. Park, D. Cox, G. Shirane: Phys. Rev. B 61, 8687 (2000) 128 B. Noheda, D. Cox, G. Shirane, R. Guo, B. Jones, L. Cross: Phys. Rev. B 63, 141301 (2000) 128 D. Vanderbilt, M. Cohen: Phys. Rev. B 63, 94108 (2001) 128 H. Fu, R. Cohen: Nature 403, 281 (2000) 128 J. Kuwata, K. Uchino, S. Nomura: Ferroelectrics 37, 579 (1981) 128 J. Kuwata, K. Uchino, S. Nomura: Jpn. J. Appl. Phys. 21, 1298 (1982) 128 M. Iwata, T. Araki, M. Maeda, I. Suzuki, H. Ohwa, N. Yasuda, H. Orihara, Y. Ishibashi: Jpn. J. Appl. Phys. 41, 7003 (2002) 128 L. Cross: Ferroelectrics 76, 241 (1987) 128 L. Cross: Ferroelectrics 151, 305 (1994) 128 A. Devonshire: Philos. Mag. 40, 1040 (1949) 128 A. Devonshire: Philos. Mag. 42, 1065 (1950) 128 K. Fujita, Y. Ishibashi: Jpn. J. Appl. Phys. 36, 5214 (1997) 128, 130 K. Fujita, Y. Ishibashi: Jpn. J. Appl. Phys. 36, 254 (1997) 128, 130

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[34] Y. Ishibashi: J. Phys. Soc. Jpn. 59, 4148 (1990) 140 [35] T. Nagaya, Y. Ishibashi: J. Phys. Soc. Jpn. 60, 4331 (1991) 140 [36] D. Ricinschi, Y. Ishibashi, M. Iwata, M. Okuyama: Jpn. J. Appl. Phys. 40, 4990 (2001) 140 [37] S. E. Park, T. Shrout: IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44, 1140 (1997) 140, 142 [38] S. E. Park, T. Shrout: J. Appl. Phys. 82, 1804 (1997) 140, 142 [39] S. Wada, S. E. Park, L. Cross, T. Shrout: J. Kor. Phys. Soc. 32, S1290 (1998) 140, 142 [40] S. Wada, S. Suzuki, T. Noma, T. Suzuki, M. Osada, M. Kakihana, S. E. Park, L. Cross, T. Shrout: Jpn. J. Appl. Phys. 38, 5505 (1999) 140, 142 [41] S. E. Park, S. Wada, L. Cross, T. Shrout: J. Appl. Phys. 86, 2746 (1999) 140, 142 [42] A. Amin, R. Newnham, L. Cross: Phys. Rev. B 34, 1595 (1986) 140 [43] A. E. Clark: Handbook on the Physics and Chemistry of Rare Earth (NorthHolland, Amsterdam 1979) Chap. 15, p. 231 144 [44] A. Clark: Ferromagnetic Materials 1 (North-Holland, Amsterdam 1980) p. 531 144 [45] U. Atzmony, M. Daniel, E. Bauminger, D. Lebenbaum, I. Nowik, S. Offer: Phys. Rev. B 7, 4220 (1973) 144

Index

coercive field, 135 dielectric susceptibility, 131 elastic constants, 131 electromechanical coupling constants, 134 electrostrictive constants, 129 engineered domain configuration, 140 equilibrium conditions for strain components, 129 ferromagnetic magnetostrictive alloys, 144 free-energy function, 128 Hessian, 131 hexagonal BaTiO3 , 127 hysteresis loop, 135 Landau–Devonshire type potential, 127

magnetostrictive actuators, 144 magnetostrictive alloys, 144 morphotropic phase boundary, 127 MPB, 127 oblique field, 140 Pb(Zn1/3 Nb2/3 )O3 –PbTiO3 , 128 phase diagram, 130 piezoelectric constants, 131 polarization reversal, 134 PZN–PT, 128 rare-earth–Fe2 compound family, 144 stability condition, 135, 136 Tb1−x Dyx Fe2 , 144 transverse instability, 127

Correlation Between Domain Structures and Dielectric Properties in Single Crystals of Ferroelectric Solid Solutions Naohiko Yasuda Department of Electrical and Electronic Engineering, Gifu University, Gifu 501-1193, Japan [email protected] Abstract. In the present chapter, the growth of single crystals in relaxor–PbTiO3 (PT) solid solution system by the flux method and the solution Bridgman method, the observation of domain wall structures under an electric field, optical birefringence, and the correlation between the domain structure and the permittivity are described. By the flux method and the solution Bridgman method, high-quality PIN–PT single crystals with a composition near the morphotropic phase boundary (MPB) with a high Curie temperature have been grown. In a (100) plate of a 0.72PIN–0.28PT single crystal with a composition near the MPB, complex domain structures were observed under no bias field, where coexistence of the rhombohedral and tetragonal phases was found. It was found from observations of the domain structure under a dc electric field that a fieldinduced R-to-T phase transition starts to take place abruptly in the (110) planes at about 6 kV/cm. The phase boundary between the R and T phases along a (110) plane moves in such a way that the T region expands at the expense of the R region, and the R and T phases coexist in a dc field range from 6 kV/cm to 12 kV/cm. The temperature dependence of the birefringence of 0.72PIN–0.28PT is also presented. It was found in the crystal system (1 − x)PMN–xPT that the field dependence of the dielectric constant (E < 25 kV/cm) in crystals with x = 0.06 and 0.1 is reversible, while in a crystal x = 0.15 it is not reversible. Observation of domain structures and simultaneous permittivity measurement was performed on a (001) plate of a 0.85PMN–0.15PT crystal under various dc electric fields E. It was found that the dielectric constant decreases abruptly as the ferroelectric domain wall structure grows under a biasing field of about 1.6 kV/cm.

1 Introduction In solid solutions between relaxor lead-based ferroelectrics and the normal ferroelectric PbTiO3 (PT) with compositions near a morphotropic phase boundary (MPB), it has been reported both experimentally [1, 2, 3] and theoretically [4] that the giant piezoelectric response may be due to a polarization rotation. It was also reported that, in this solid solution system with a near-MPB composition, the mechanism of the enhanced electromechanical properties is M. Okuyama, Y. Ishibashi (Eds.): Ferroelectric Thin Films, Topics Appl. Phys. 98, 147–161 (2005) © Springer-Verlag Berlin Heidelberg 2005

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due to an instability perpendicular to the spontaneous polarization, named the transverse instability [5, 6]. On the other hand, the extremely high electromechanical coupling factors and piezoelectric coefficients in this solid solution system with a near-MPB composition can also be interpreted in terms of an engineered domain structure, where the ferroelectric domain wall structure is stabilized by an oblique electric field, that is a 001 electric field for the rhombohedral phase and a 111 field for the tetragonal phase (all directions refer to cubic coordinates) [7, 8, 9, 10, 11]. It is known that in a relaxor–PT solid solution system, the size of the domain wall structure depends on the concentration of PT. Namely, the domain size in the relaxor is known to be of the order of a nanometer, while the domains in PT are of the normal size for domains (of the order of a micrometer) [12, 13, 14, 15]. Because of the small domain size, the relaxor seems to be cubic even in the ferroelectric phase, as observed by using a polarizing microscope, and a lowering of the symmetry on a macroscopic scale starts to be observed with increasing PT content [16, 17]. Application of an electric field to the relaxor ferroelectric Pb(Mg1/3 Nb2/3 )O3 (PMN) induces a ferroelectric phase, with the formation of macroscopic polar domains [18, 19]. To clarify the macroscopic properties of these materials for device applications, such as the permittivity, piezoelectricity and switching behavior, studies of the ferroelectric domain wall structure are important. Simultaneous observations of domain structures and of dielectric properties for relaxor-based ferroelectric solid solution single crystals are especially required. In this Chapter, the growth of single crystals, the observation of domain wall structures under a dc field, optical birefringence, and the correlation between domain structures and permittivity in the solid solution of a relaxor– PT system are described.

2 Single-Crystal Preparation 2.1 Flux Method Single crystals of lead-based relaxor–normal-ferroelectric (PT) solid solutions were obtained by a conventional flux method using a PbO–PbF2–B2 O3 flux [20, 21, 22, 23]. The temperature profile used for the crystal preparation consisted of rapid heating to 1200 ◦C, soaking at this temperature for 5 h, and then cooling to 850 ◦ C at a rate of 1 K to 5 K/h. The crystals obtained are shown in Fig. 1(a). Some wafers cut parallel to the (001) plane are shown in Fig. 1(b). The Ti concentration of the relaxor–PT solid solution was determined using an inductive-charge-plasma (ICP) chemical analysis. The single crystals grown were confirmed by X-ray powder diffraction studies to consist of a single perovskite phase.

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Fig. 1. (a) As-grown crystals and (b) wafers cut parallel to the (001) plane of 0.72PIN–0.28PT [20, 21]

Fig. 2. (a) Coagulated solid solution and (b) wafer cut at 2 mm from the bottom of the 0.72PIN–0.28PT crystal [24]

2.2 Solution Bridgman Method A single crystal of the solid solution (1 − x)Pb(In1/2 Nb1/2 )O3 –xPT (PIN– PT) with a composition near the MPB was obtained by a solution Bridgman method using a PbO–B2O3 flux [24, 25, 26], where the composition PIN/PT of the charge was 63/37 mole% for x = 0.37. The by-weight ratio of PIN– PT:PbO:B2 O3 was 53:53:1. A total charge of 50 g was put into a Pt crucible 15 mm in diameter and 100 mm in length. The Pt crucible was sealed with a Pt lid to prevent lead evaporation loss during crystal growth. An electric furnace with two heating zones, where the upper zone was controlled at 1370 ◦C and the lower zone at 350 ◦C, was used to grow the single crystal. The Pt crucible was suspended and driven down through the zones at a rate of 0.4 mm/h after soaking for 10 hour. The operational parameters to set the temperature and the driving rate were determined according to thermodynamic data for the melting behavior. No seed material was used to nucleate the crystal. Both heating zones were maintained for 297 h, and then cooled to room temperature at a rate of 100 K/h. The crystals were extracted from the matrix by dissolution in hot dilute nitric acid. The coagulated solid solution resulting from the growth is shown in Fig. 2(a). A yellowish wafer cut out at 2 mm from the bottom of the asgrown PIN–PT crystal is shown in Fig. 2(b).

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Fig. 3. Schematic side view of an electroded sample plate for domain structure observation [27, 28, 29, 30]

3 Measurement For domain wall observation, thin samples are necessary because of the complexity of the domain structure in relaxor–PT solid solutions with a nearMPB composition. Plate-like samples were cut out and polished with a polishing sheet (0.3 µm size). The orientation of the crystal axis was determined with an X-ray diffractometer. To investigate the effect of an electric field on the domain configuration, top and bottom electrodes were formed with deposited semi-transparent gold layers, or a bottom electrode was formed with a transparent conductive glycerin layer, as seen in Fig. 3 [27, 28, 29, 30, 31]. Gold leads were attached to the sample with silver paste (Dupont No. 4922). The domain structures were analyzed by means of a polarizing light microscope (Olympus BX60). A heating/cooling stage (Japan High Tech LK-600) mounted on the microscope was used for observing the change in the domain structures with temperature and a dc biasing electric field. The optical retardation of the domains for the e-line (λ = 546.1 nm) was measured using a tilting U-CTB compensator, and the birefringence was calculated. The electrical capacitance was measured using an LCR meter (HP-4274) at 10 kHz with a probe field weaker than 23 V/cm.

4 Domain Structures in the PIN–PT Solid Solution 4.1 Temperature Dependence of the Permittivity, Domain Structure and Birefringence In the solid solution (1 − x)PIN–xPT, an MPB is known to exist at about x = 0.37 at room temperature. Figure 4 shows the temperature dependence of the dielectric constant of 0.72PIN–0.28PT [22,28]. From the characteristics of


151

Fig. 4. Permittivity of a (001) plate of 0.72PIN–0.28PT at 1 kHz [20]

the dielectric constant, this crystal, with a near-MPB composition, is found to exhibit successive phase transitions from rhombohedral (R) to tetragonal (T) to cubic (C) with increasing temperature. Some domain structures in a (001) plate of 0.72PIN–0.28PT are presented in Fig. 5 for various temperatures, [28, 29], and are found to be very complex and to contain very fine domains. These are similar to those in the PMN–PT [16, 32] and Pb(Zn1/3 Nb2/3 )O3 – PT (PZN–PT) [33, 34] systems with near-MPB compositions. In Fig. 5(b), two kinds of domains are observed (denoted by (1) and (2)). One domain pattern looks bright, with interference colors, when observed with crossed polarizers parallel to the 100 direction; this is assigned to a rhombohedral domain characterized by a (110) indicatrix orientation (see the domain marked by an ellipse, labeled (1)). The other domain pattern shows darkness; this is assigned to a tetragonal domain with the extinction position parallel to the 100 direction (see the domain marked by an ellipse, labeled (2)). The extinction of the rhombohedral domains is not completely homogeneous, implying that the extinction directions of the domains deviate slightly from the regular crystallographic axes. It has been pointed out that this may result from the internal stresses created by lattice mismatching between the rhombohedral and tetragonal phases [16, 28, 29, 33, 34]. With heating, the rhombohedral domain structure starts to change to a tetragonal domain structure at the expense of the rhombohedral phase, as presented in Figs. 5(a), (b) and (c). With further heating, the tetragonal

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Fig. 5. Domain structures in a (001) plate of 0.72PIN–0.28PT at various temperatures [28]

phase changes to the cubic phase, with the growth of isotropic region visible as the wedge-type dark areas in Fig. 5(d) and (e). At 300 ◦C, the whole crystal is in the cubic phase, as presented in Fig. 5(f). Figure 6 presents the temperature dependence of the spontaneous birefringence for the domains (1) and (2) in Fig. 5(b). With heating, the birefringence of the domain (1) decreases gradually, and then discontinuously at about 125 ◦C. The first-order phase transition from the rhombohedral to the tetragonal phase takes place at a temperature Tt . With further heating, the birefringence decreases gradually and disappears at the tetragonal-to-cubic phase transition temperature Tc about 285 ◦C. The birefringence of the domain (2) decreases gradually and disappears at Tc , at about 290 ◦ C. 4.2 The Effect of a dc Bias Field on the Domain Structure Figure 7(A) presents the domain structure in a (001) plate of 0.72PIN–0.28PT plate under various dc electric fields (E) applied along the 010 direction [29, 30]. The whole crystal, under no bias field, is in the rhombohedral phase in room temperature. Figure 7(B) presents a schematic illustration of (A). Straight, broad domain stripes are observed in Figs. 7(A)(a) and (B)(b) along the (110) planes, and in them, fine domains along the (010) and (100)


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Fig. 6. Birefringence of the domains (1) and (2) in a (001) plate of 0.72PIN–0.28PT. See Fig. 5 for (1) and (2) [28]

planes are observed alternately. The configuration of these domain structures in the rhombohedral phase does not change with an electric field below 4 kV/cm. At about 6 kV/cm, a new phase with straight, broad domain stripes along the (110) planes abruptly appears, as seen in Figs. 7(A)(c) and (B)(c). The new phase has a fine domain wall structure inclined at 45◦ relative to the fine domains along the (010) and (100) planes in the rhombohedral phase. From its extinction behavior in the (001) plate, the new phase was identified as tetragonal. It is found that the electric-field-induced R-to-T phase transition starts to take place at about 6 kV/cm. The boundary between the R and T phases along a (110) plane moves in such a way that the T region expands at the expense of the R region. The R and T phases coexist over a wide range of the applied electric field, from 6 kV/cm to 12 kV/cm. Such an electric-fieldinduced R-to-T phase transition occurs very slowly. With a further increase in the dc electric field, the wall density in the T phase decreases. At 20 kV/cm, the whole crystal is in the T phase, as seen in Figs. 7(A)(f) and (B)(f). Once the R phase has transformed into the T phase with increasing electric field, the T phase remains even after the applied electric field is removed. When the field is applied along the 0¯10 direction after it has been applied along 010, a polarization reversal in the T phase takes place, as shown in Fig. 8. The whole crystal under zero field along the 0¯10 direction is in the tetragonal phase, as presented in Fig. 8(a). At about 4 kV/cm, corresponding to the coercive field, the polarization reversal starts to take place, as presented in Fig. 8(b). With increasing field, the domain walls move along the (110)

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Fig. 7. (A) Changes in the domain structure in a (001) plate of 0.72PIN–0.28PT with dc fields [29, 30]. (B) Schematic illustration of (A)


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Fig. 8. Changes in the domain structure in a (001) plate of 0.72PIN–0.28PT with polarization reversal [29]

Fig. 9. Normalized permittivity in a (001) plate of (1 − x)PMN–xPT for x = 0.06 and 0.1 measured with dc fields [17]

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planes, and the wall density decreases, as seen in Figs. 8(c), (d) and (e). With further increase of the dc field, the wall density decreases, and the walls tend to vanish, as seen in Fig. 8(f).

5 Domain Structures in a (001) Plate of a PMN–PT Solid Solution The relationship between the domain structure and the permittivity in (1 − x)PMN–xPT has been studied by Yasuda et al. [17]. Figure 9 shows the field dependence of the dielectric constant ε for x = 0.06 and 0.1. In single crystals with x = 0.06 and 0.1, which show optical isotropy, the permittivity has a broad maximum at dc fields Em = 12 kV/cm and 7.5 kV/cm, respectively, with increasing E. No hysteresis in the permittivity versus electric field is found either for an increasing or for a decreasing dc electric field. Figure 10 presents the relative permittivity as a function of E along the 001 direction in 0.85PMN–0.15PT both for increasing and for decreasing runs. With increasing E in the virgin state, the permittivity increases gradually (region I), and at 1.6 kV/cm drops abruptly and then decreases gradually (region II), for run 1 . After that, the permittivity increases slightly with decreasing E, for run 2 . With increasing E applied in the opposite direction, the permittivity shows a peak at −0.8 kV/cm and then decreases slightly, for run 3. The change in the domain structures in the (001) plate of 0.85PMN– 0.15PT with E applied along the 001 direction was observed simultaneously with dielectric measurements, as shown in Fig. 10. Figure 11 shows photographs of the crystal plate taken by a polarizing microscope, corresponding to run 1 of Fig. 10. The polarized light under crossed Nicol prisms is not transmitted at lower E (see Fig. 11(a)), which corresponds to region I (higher permittivity) of run 1 in Fig. 10.

Fig. 10. Permittivity in a (001) plate of 0.85PMN–0.15PT measured with dc fields [17]


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At 1.6 kV/cm, the polarized light under crossed Nicol prisms starts to be transmitted as presented in Fig. 11(b), where stripes and broad domain walls along the (100) planes are seen. Figures 11(c) and (d) also show stripes and broad domains for a further increase in E, corresponding to region II for run 1 in Fig. 10. When E is decreased in run 2 in Fig. 10, the stripes and broad domain walls along the (100) planes remain. Namely, during run 2 , no change of the domain pattern is observed, and the domain pattern is memorized. Figure 12 shows photographs of the crystal plate taken by the polarizing microscope, corresponding to run 3 of Fig. 10. When E is increased in the opposite direction, stripes and broad domain walls along the (010) planes start to appear, corresponding to the permittivity peak in run 3 (see Fig. 10), as seen in Fig. 12(b) in the region where stripes and broad domain walls along the (100) planes are seen in Fig. 12(a). With a further increase in E, the stripes and broad patterns grow, as seen in Figs. 12(c) and (d). On the basis of the experimental results, the permittivity has been found to decrease with the formation of a macroscopic domain structure.

Fig. 11. Changes in the domain structure of a 0.85PMN–0.15PT (001) plate at (a) 0 kV/cm, (b) 1.6 kV/cm, (c) 4.9 kV/cm and (d) 8.2 kV/cm, corresponding to run 1 of Fig. 10 [17]

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Fig. 12. Changes in the domain structure of a 0.85PMN–0.15PT (001) plate at (a) 0 kV/cm, (b) −0.8 kV/cm, (c) −4.9 kV/cm and (d) −8.2 kV/cm, corresponding to run 3 of Fig. 10 [17]

Memorandum The author would like to devote this chapter to his late mother Reiko Watanabe.

References [1] B. Noheda, D. Cox, G. Shirane, J. Gonzalo, L. Cross, S. Park: Appl. Phys. Lett. 74, 2059 (1999) 147 [2] B. Noheda, J. Gonzalo, L. Cross, R. Guo, S. P. D. Cox, G. Shirane: Phys. Rev. B 63, 141301 (2000) 147 [3] Y. Uesu, M. Masuda, Y. Yamada, K. Fujishiro, D. Cox, B. Noheda, G. Shirane: J. Phys. Soc. Jpn. 71, 960–965 (2002) 147 [4] H. Fu, R. Cohen: Nature 403, 281–283 (2000) 147 [5] Y. Ishibashi, M. Iwata: Jpn. J. Appl. Phys. 37, L985–L987 (1998) 148 [6] Y. Ishibashi, M. Iwata: Jpn. J. Appl. Phys. 38, 800–804 (1999) 148 [7] J. Kuwata, K. Uchino, S. Nomura: Ferroelectrics 37, 579–582 (1981) 148 [8] S. Park, T. Shrout: Mater. Res. Innovat. 1, 20–25 (1997) 148 [9] S. Wada, S. Suzuki, T. Noma, T. Suzuki, M. Osada, M. Kakihara, S. Park, L. Cross, T. Shrout: Jpn. J. Appl. Phys. 38, 5505–5511 (1999) 148


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[10] V. Bornand, S. Trolier-McKinstry, K. Takemura, C. Randall: J. Appl. Phys. 87, 3965–3972 (2000) 148 [11] N. Yasuda, H. Ohwa, A. Nakada, K. Fujita, M. Iwata, Y. Ishibashi, W. Sakamoto, T. Yogo, S. Hirano: in Proc. 1st International Meeting on Ferroelectric Random Access Memories, ed. by H.Ishihara and M.Okuyama (Research and Development Association for Future Electronic Devices, Tokyo 2001) pp. 103–104 148 [12] L. Cross: Ferroelectrics 151, 305–320 (1987) 148 [13] C. Randall, A. Bhalla: Jpn. J. Appl. Phys 29, 327–333 (1990) 148 [14] C. Randall, D. Barber, P. Groves, R. Whatmore: J. Mater. Sci. 23, 3678–3682 (1988) 148 [15] Z. G. Ye, Y. Bing, J. Gao, A. Bokov, P. Stephens, B. Noheda, G. Shirane: Phys. Rev. B 67, 104104 (2003) 148 [16] Z. Ye, M. Dong: J. Appl. Phys. 87, 2312–2319 (2000) 148, 151 [17] N. Yasuda, A. Nishihata, T. Kamiyama, N. Uemura, H. Ohwa, M. Iwata, Y. Ishibashi: in Abstracts of the 10th European Meeting on Ferroelectricity (Cambridge 2003) p. 365 148, 155, 156, 157, 158 [18] Z. G. Ye, H. Schmid: Ferroelectrics 145, 83–108 (1993) 148 [19] G. Galvarin, E. Husson, Z. G. Ye: Ferroelectrics 165, 349–358 (1995) 148 [20] N. Yasuda, H. Ohwa, M. Kume, Y. Yamashita: Jpn. J. Appl. Phys. 39, L66– L68 (2000) 148, 149, 151 [21] N. Yasuda, H. Ohwa, M. Kume, K. Hayashi, Y. Hosono, Y. Yamashita: J. Cryst. Growth 229, 299–304 (2003) 148, 149 [22] N. Yasuda, H. Ohwa, M. Kume, Y. Hosono, Y. Yamashita, S. Ishino, H. Terauchi, M. Iwata, Y. Ishibashi: Jpn. J. Appl. Phys. 40, 5664–5667 (2001) 148, 150 [23] H. Ohwa, M. Iwata, H. Orihara, N. Yasuda, Y. Ishibashi: J. Phys. Soc. Jpn. 70, 3149–3154 (2001) 148 [24] N. Yasuda, N. Mori, H. Ohwa, Y. Hosono, Y. Yamshita, M. Iwata, M. Maeda, I. Suzuki, Y. Ishibashi: Jpn. J. Appl. Phys. 41, 7007–7010 (2002) 149 [25] K. Harada, S. Shimanuki, T. Kobayashi, S. Saitoh, Y. Yamashita: Key Eng. Mater. 157–158, 95–102 (1999) 149 [26] S. Shimanuki, S. Saitoh, Y. Yamashita: Jpn. J. Appl. Phys. 37, 3382–3385 (1998) 149 [27] M. Mulvihill, L. Cross, W. Cao, K. Uchino: J. Am. Ceram. Soc. 80, 1462–1468 (1997) 150 [28] N. Yasuda, N. Uemura, H. Ohwa, Y. Yamashita, M. Iwata, M. Maeda, I. Suzuki, Y. Ishibashi: J. Korean Phys. Soc. 42, S1261–S1265 (2003) 150, 151, 152, 153 [29] N. Yasuda, N. Uemura, N. Osaki, H. Ohwa, M. Iwata, Y. Ishibashi: Trans. Mater. Res. Soc. Jpn. 28, 161–164 (2003) 150, 151, 152, 154, 155 [30] N. Yasuda, M. Sakaguchi, Y. Itoh, H. Ohwa, Y. Yamashita, M. Iwata, Y. Ishibashi: Jpn. J. Appl. Phys. 42, 6205–6208 (2003) 150, 152, 154 [31] E. Sawaguchi, M. Charters: Phys. Rev. 117, 465–469 (1960) 150 [32] G. Xu, H. Luo, H. Xu, D. Li, P. Wang, Z. Yin: Ferroelectrics 261, 125–130 (2001) 151 [33] K. Fujishiro, R. Vlokh, Y. Uesu, Y. Yamada, J. Kiat, B. Dkhil, Y. Yamashita: Jpn. J. Appl. Phys. 37, 5246–5248 (1998) 151

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[34] Z. Ye, M. Dong, L. Zhang: Ferroelectrics 229, 223–228 (1999) 151

Index

birefringence, 147, 148

optical retardation, 150

domain size, 148 domain wall structure, 148, 153

Pb(In1/2 Nb1/2 )O3 –xPT, 149 Pb(Mg1/3 Nb2/3 )O3 , 148 PIN–PT, 149 PMN, 148 PMN–PT, 151 polarizing light microscope, 150, 156

engineered domain configuration, 148 extinction directions, 152 field-induced R-to-T phase transition, 147 flux method, 147 indicatrix orientation, 151 macroscopic domain structure, 158 macroscopic polar domains, 148

relaxor lead-based ferroelectrics, 147 rhombohedral domains, 151 solution Bridgman method, 147 stripes and broad domain walls, 156 tetragonal domains, 151

Relaxor Superlattices: Artificial Control of the Ordered–Disordered State of B-Site Ions in Perovskites Hitoshi Tabata Institute of Scientific and Industrial Research, Osaka University, 8-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan [email protected] Abstract. We have developed a new superlattice technique to artificially control the B-site ordering state. The technique has been applied to Ba(Zr0.2 Ti0.8 )O3 , in which B-site ions are not naturally ordered. XRD measurements and theoretical calculations of the XRD patterns with a step model indicated that the BZT superlattices were well constructed. We also carried out measurement of dielectric properties for samples in various B-site ordering states. The existence of relaxor behavior in BZT with x = 0.2 was confirmed in a superlattice sample with an ordering ratio below 25%. For the homovalent-system compound BZT, we have succeeded in controlling the B-site ordering state and have demonstrated the influence of the order–disorder transition for the first time. We believe that this technique could be a key method for investigating the exact origin of relaxor behavior.

1 Relaxor Behavior in Perovskite-Type Dielectric Compounds Relaxor behavior has been widely reported in perovskite-type materials. Among them, Ba(Zr,Ti)O3 is one of the candidate materials for elucidating the mechanism of relaxor phenomena. It has homovalent B-site ions Zr4+ and Ti4+ . Therefore, there is no driving force to push the ions into an ordered structure. On the other hand, there is the possibility of coexistence of multiple phases. In the case of the bulk state, it has been found that the relaxor behavior is strongly affected by the annealing conditions. To make clear the intrinsic parameters of the relaxor, we have demonstrated the artificial control of the positioning of the B-site ions. The stacking periodicity and the compositional combination of BaTiO3 and BaZrO3 were changed systematically with this method and the signature of a relaxor was detected. 1.1 Introduction Relaxor-type dielectric materials are treasure boxes for both basic physics and practical applications. Since the discovery of dielectric relaxation behavior in M. Okuyama, Y. Ishibashi (Eds.): Ferroelectric Thin Films, Topics Appl. Phys. 98, 161–175 (2005) © Springer-Verlag Berlin Heidelberg 2005

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Pb(Mg,Nb)O3 , a number of studies have been performed on A(B ,B )Otype ferroelectrics [1, 2] with heterovalent B-site ions (Table 1). The colossal dielectric constant, diffusive phase transition and large piezoelectric effect are quite interesting not only for practical applications but also for fundamental physics. In spite of extensive research efforts, the mechanism for the dielectric properties of relaxor ferroelectrics has not been fully elucidated. However, one of the important key parameters is the ordered–disordered distribution of the B-site cations, which introduces various chemical and/or structural inhomogeneities. Table 1. Typical relaxors with heterovalent B-site ions 2+/5+ Pb(Mg,Nb)O3 Pb(Zn,Nb)O3 Pb(Mg,Ta)O3 3+/5+ Pb(Sc,Nb)O3 Pb(Sc,Ta)O3

(PMN) (PZN) (PMT) (PSN) (PST)

(PMN) (PZN) (PMT) (PSN) (PST)

The formation of superlattices is a powerful technique for controlling the atomic ordering of A-site and B-site ions artificially [3, 4]. By using this technique, strained superlattices and “asymmetric” structured superlattices of BaTiO3 /SrTiO3 have been constructed which enhance the dielectric properties and the remanent polarization, respectively [5, 6, 7, 8, 9]. Furthermore, new functionality can be generated [10, 11, 12, 13]. We have demonstrated the formation of superlattices of BaTiO3 and BaZrO3 on SrTiO3 (111) substrates where the B-site ordering state is controlled by a laser MBE technique. Recently, it has been reported that Ba(Zr4+ ,Ti4+ )O3 shows relaxor behavior in the bulk state [14]. It is well known that the ordering of B-site ions in the 111 direction is a key factor for showing relaxor properties. However, there is no driving force to generate an ordered structure of B-site ions in Ba(Ti,Zr)O3 , owing to its homovalent character. In this Chapter, the relation between the B-site ion ordering and relaxor behavior is discussed. 1.2 Experimental Procedure Bulk materials were fabricated by a standard solid-state reaction technique. BaTiO3 and BaZrO3 powders were mixed in the correct ratio, and sintered at 1000 ◦C to 1300 ◦C for 24 h under atmospheric conditions. Films and superlattices of BaTiO3 –BaZrO3 (BT–BZ) with various periods were prepared by pulsed laser deposition (PLD) with multiple targets using an ArF excimer laser with a wavelength of 193 nm at 650 ◦C under an oxygen pressure PO2 of 1 Pa. The substrate used was a Nb-doped SrTiO3 (111) conductive single crystal, which was also used as the bottom electrode in a metal–insulator–metal structure. The ordered superlattices varied in their stacking periodicity; the

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shortest periodicity corresponded to 5 unit cells of BT (BaTiO3 ) and 5 unit cells of BZT (Ba(Ti0.4 Zr0.6 )O3 ), denoted by “5/5”. Other superlattices had periodicities 10/10, 20/20, 50/50 and 100/100. In these superlattices the total composition is Ti : 80% and Zr : 20%. The reason why we selected composition of Zr = 0.2 was that a pinching effect is reported at this point [14]. We controlled the thickness of each layer of the superlattices by adjusting the deposition time on the assumption that the deposition rate was constant. The stacking periodicity was confirmed by diffraction peaks from the superlattices due to the Laue function. We showed that the total thickness of the superlattices was about 300 nm by use of a contact-type thickness profiler. Pt top electrodes were deposited by dc sputtering using a stainless-steel shadow mask and annealed at 650 ◦ C to remove oxygen defects and improve the character of the interface between the metal and the oxide. For each superlattice, the relative dielectric constant and P –E hysteresis loop were measured by an HP 4194 A impedance analyzer and a Sawyer– Tower test system, respectively. Crystal structure analysis was carried out by X-ray diffraction (XRD) with Cu Kα radiation, and reflection high-energy electron diffraction (RHEED). 1.3 Results and Discussion [15] First, the dielectric constants of bulk samples were measured. Figure 1(a) shows the temperature dependence of the dielectric constant (εr ) of Ba(Zrx Ti1−x )O3 (x = 0–0.2) annealed at 1000 ◦C for an applied frequency varying from 1 kHz to 1 MHz. The critical temperatures indicating the phase transitions from cubic to tetragonal and tetragonal to orthorhombic decreased systematically with increasing Zr composition. Up to a Zr concentration of x = 0.15, the graphs show sharp peaks with no frequency distribution. At a concentration of x = 0.2, on the other hand, the peak shape changes dramatically. The graph now shows a broad peak and a variation with the applied frequency, which is a typical feature of a relaxor material. At this composition of x = 0.2, multiple phases such as the cubic, tetragonal, orthorhombic and rhombohedral phases come together. After annealing at 1300 ◦C, on the other hand, the relaxor-like behavior disappears and the XRD pattern shows sharp peaks. BZT (x = 0.2) is not a relaxor (Fig. 1(b)). This suggests that coexistence of multiple phases is one of the key features of a relaxor. Therefore, when we investigate the characteristics of a relaxor, we should optimize the sintering conditions to obtain a single phase at each composition. After checking the optimum annealing temperature, we measured the dielectric properties of BZT with various compositions (x = 0–1.0) systematically. BZT shows relaxor-like character from x = 0.3 to 0.8 (Fig. 2). In case of the BZT films, relaxor-like character was not observed up to x = 0.3 (Fig. 3(a)). A BZT (x = 0.35) film, on the other hand, shows a relaxor-like dispersion of the dielectric constant with respect to the frequency (Fig. 3(b)).

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Fig. 1. Temperature dependence of εr of Ba(Zrx Ti1−x )O3 (x = 0–0.2) bulk samples annealed at 1200 ◦ C (a) and 1300 ◦ C (b), measured at various frequencies

Figure 4 shows the temperature dependence of the relative dielectric constant εr and the dielectric loss tan δ of solid-solution films and order– disorder-controlled superlattices for various applied frequencies. In the case of a Ba(Ti,Zr)O3 solid-solution film and the BaTiO3 –BaZrO3 superlattices (above a stacking periodicity of 100/100), the dielectric constant decreases monotonically with increasing temperature from room temperature (R.T.) to 120 ◦ C (Figs. 4(a), (b)). The dispersion character of tan δ above 120 ◦ C is due to incomplete contact between the top electrode and the metal probe. The relative dielectric constant of the 20/20 superlattice at R.T. increases as the stacking-layer thickness decreases. The maximum value of the relative dielectric constant is about 300, which is larger than that of the 100/100 superlattice (εr = 280). There is no dielectric dispersion with frequency in the


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Fig. 2. Temperature dependence of εr of Ba(Zrx Ti1−x )O3 (x = 0–1.0) bulk samples annealed at 1300 ◦ C to 1400 ◦ C

Fig. 3. Temperature dependence of εr of Ba(Zrx Ti1−x )O3 films: (a) x = 0.3 and (b) x = 0.35

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Fig. 4. Temperature dependence of the relative dielectric constant εr and dielectric loss tan δ as a function of applied electric frequency for a solid-solution film (a), 100/100 superlattice (b) and 20/20 superlattice (c)


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superlattices with a stacking periodicity above 100/100. Below a periodicity of 20/20, on the other hand, a small diffuse transition is observed (Fig. 4(c)). These results suggest the possibility of relaxor behavior even in the case of homovalent materials at the B-sites. It should be noted that when the superlattice shows relaxor behavior in the dielectric constant (the real part of the capacitance), the dielectric loss (tan δ) indicates a divergent character of up to several percent. 1.4 Conclusions The dielectric properties of Ba(Ta,Zr)O3 have been studied in bulk samples, films and superlattices. The results suggest that the relaxor behavior is strongly correlated with the presence of several phases and the ordering state of the B-site ions. To elucidate the mechanism of the relaxor behavior from an experimental point of view, the samples should be formed under the same conditions. In the next section, we shall discuss the results for relaxor superlattices systematically and in more detail.

2 Artificial Control of the Ordered/Disordered State of B-Site Ions in Ba(Zr,Ti)O3 by a Superlattice Technique To elucidate the mechanism of the relaxor behavior, we have used artificial control of the ordering of the B-site ions by creating superlattices. The relaxor behavior of a ferroelectric material depends on the order state of the constituent ions in the crystal. To clarify the mechanism of this relaxor behavior, Ba(Zr,Ti)O3 was chosen as the target material because its B-site ions are not naturally ordered. The superlattice samples were prepared by using a pulsed laser deposition technique. The observed X-ray diffraction patterns of the superlattices and theoretical calculations of these patterns revealed that the degree of order was well controlled by our technique. Relaxor behavior occurs in a Ba(Zr0.15 Ti0.85 )O3 /Ba(Zr0.25 Ti0.75 )O3 superlattice but not in other ones suggesting that the combination of B-site compositions is a key factor in determining the origin of the relaxor behavior. 2.1 Introduction The properties of relaxors, such as a large dielectric constant and a large piezoelectric effect, are quite interesting in practical applications for smallsize capacitors and microactuators [16, 17] and in fundamental physics for clarifying the origin of relaxor properties [18]. Since the discovery of relaxor behavior, such as a diffusive phase transition and a frequency dispersion, in Pb(Mg2/3 Nb1/2 )O3 (PMN) [19], extensive research has been carried out on complex perovskite compounds of the formula A(B ,B )O3 (where A represents the A-site ions, and B and B represent the B-site ions) to elucidate the

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Fig. 5. Schematic crystal structure of a perovskite material (a), and schematic illustration of an ordercontrolled superlattice made with a combination of two kinds of targets (b)

mechanism of relaxor behavior (Fig. 5(a)). The exact mechanism of relaxor behavior, however, is still unclear. Previous studies have suggested several models, such as the super-paraelectric model [18], the dipole glass model [20] and the quenched random-field model [21]. In a previous study, Setter and Cross proposed the influence of an order– disorder transition in the ion arrangement in a typical relaxor material such as Pb(Sc0.5 Ta0.5 )O3 (PST) [22]. According to their report, PST exhibits relaxor behavior when these ions randomly occupy the B-sites. On the other hand, the phase transition becomes of first-order type, similar to that of normal ferroelectric materials, when the B-site ions Sc and Ta are arranged alternately in a 111 direction. This result suggests that the degree of the order on the B-sites is a key factor for the appearance of relaxor behavior. In this Chapter, the dielectric properties of Ba(Zr0.2 Ta0.8 )O3 (BZT, x = 0.2) thin films and superlattice films are compared. The samples were analyzed by an X-ray diffraction measurement to detect the crystal structure and the ion arrangement. The dielectric properties of these samples were measured using an impedance analyzer (HP 4194A). 2.2 Experimental We chose BZT with x = 0.2 as the target material in our studies. Ravez et al. reported relaxor behavior in BZT with x = 0.15 in a bulk solid solution


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for the first time [23]. After that report, some other researchers investigated the relaxor behavior of BZT [24, 25]. The results are quite interesting from the point of view of the valence state of the B-site ions because the difference in valence state between the two kinds of B-site ions, such as in 5+ 3+ 5+ Pb(Mg2+ 2/3 Nb1/3 )O3 and Pb(Sc0.5 Ta0.5 )O3 , is not an intrinsic factor here in the origin of relaxor behavior. However, the effect of the valence state (homovalent vs. heterovalent) and the order–disorder state of the B-site ions has not been clearly discussed for BZT systems. So far, it has been impossible to order the B-site ions, because Zr4+ and Ti4+ have the same valence state in BZT. Hence, using superlattice techniques, we have controlled the B-site ordering state systematically, and elucidated the influence of the order–disorder state on the relaxor properties. Table 2. Nominal chemical compositions of combinations of target pairs for samples of various order degrees. The total composition of Zr and Ti is the same for all the superlattices Target No.

100 75 50 25 0

Target pair Layer a

Layer b

BaTiO3 Ba(Zr0.05 Ti0.95 )O3 Ba(Zr0.1 Ti0.9 )O3 Ba(Zr0.15 Ti0.85 )O3 Ba(Zr0.2 Ti0.8 )O3

Ba(Zr0.4 Ti0.6 )O3 Ba(Zr0.35 Ti0.65 )O3 Ba(Zr0.3 Ti0.7 )O3 Ba(Zr0.25 Ti0.75 )O3 Ba(Zr0.2 Ti0.8 )O3 (solid solution)

The B-site ordering state can be controlled by combining pairs of layers such as A(B y B 1−y )O3 and A(B 2x−y B 1−2x+y )O3 . Figure 5(b) shows a schematic diagram of the stacking used. This structure can be achieved by using a superlattice technique [26, 27]. For BZT with x = 0.2, the target compositions calculated for various B-site ordering states are shown in Table 2. The target pellets were prepared by the following process. Mixed powders of BaZrO3 and BaTiO3 with the various compositions shown in Table 2 were ball-milled first and pressed into disks 10 mm in diameter and 3 mm in thickness. Each disk was sintered at 1300 ◦C for 24 h. In order to confirm the homogeneity of the target composition, the d value of the (101) planes (d101 ) and the Curie point (Tc ) of the bulk sample used as the target were estimated for the various compositions. The d101 value increased linearly with increasing Zr concentration, and Tc decreased systematically with increasing Zr concentration in our Ba(ZrxTi1−x )O3 , as well as in the previous reports in [28, 29]. So we could assume that a homogeneous target material was obtained for each composition. The BZT superlattice films, with a total composition of x = 0.2, were fabricated on Nb-doped SrTiO3 (STO) (111) single crystals by a pulsed laser

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Fig. 6. XRD profiles of superlattices formed from various kinds of targets: (a) No. 100, (b) No. 50 and (c) No. 25

deposition technique. An ArF excimer laser with a 193 nm wavelength was used. The growth rate of the films was 3.5 nm/min. The films were fabricated at a substrate temperature of 650 ◦ C in an O2 with 8% of O3 atmosphere (1 Pa). The crystalline and periodic units were examined by X-ray diffraction. The thicknesses of the films were all 300 nm in this study. 2.3 Results and Discussion [30] Figure 6 shows XRD patterns of superlattices (experimental and calculated) that were designed to have a stacking periodicity of 47/47 nm and a B-site ordering state of (a) 100%, (b) 50% and (c) 25%. A significant peak (main peak) was observed at around 2θ = 80 ◦ C in each spectrum, which arises from diffraction from the (222) planes in a BZT film with a perovskite structure. In addition, some satellite peaks corresponding to the superlattice structure were observed at both sides of the main peak. The period of the superlattice structure can be evaluated from the diffraction angles of the main peak and satellite peaks from [31] dSL =

λ , 2 (sin θL − sin θL−1 )

(1)

where dSL is the stacking periodicity of the superlattice, L is the diffraction order of the satellite peak, θ is the diffraction angle and λ is the wavelength of the X-rays (Cu Kα , λ = 1.5405 nm). The dSL values for the superlattices calculated from (1) are in good agreement with the design value of 47 nm. Here, we demonstrate an interesting feature of the intensities of the satellite peaks in the XRD pattern. The intensity ratio I−1st /Imain increases with increasing B-site ordering; this is observed in these superlattice samples up to a stacking periodicity of 12/12 nm. Setter and Cross confirmed this kind of


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variation for the intensity of the satellite peaks in the PST system [22]. Setter and Cross prepared the PST as a bulk sample while systematically varying the sintering time, and measured XRD patterns for their samples. Some satellite peaks corresponding to the superlattice structure were observed, and the peak intensity increased with increasing sintering time. These authors concluded that this was due to changes in the order state of the B-site ions. Our result is similar to that of Setter and Cross. Therefore it is concluded that the ordering condition of the B-site ions can be controlled systematically by our technique without any postsintering treatment. On the other hand, the intensity decrease with decreasing stacking periodicity is mainly due to the increasing cycle number of stacking units (layer a and layer b). As we set the film thickness to 300 nm in this study, the cycle number increased with decreasing stacking periodicity to obtain the total thickness of 300 nm. Finally, we describe the typical dielectric properties for a superlattice with a stacking periodicity of 47/47 nm and a repetition cycle number of 32. Figure 7 shows the dielectric constants of superlattices with B-site ordering states of (a) 25% and (b) 50% as a function of temperature (εr – T curves). The relative dielectric constant is 350 for both samples in the temperature range between −30 ◦C and 150 ◦ C. This value is similar to a previously reported value for a BZT thin film [25]. A broad phase transition and a frequency dispersion are observed in the εr –T curve for the sample with 25% ordering (Fig. 7(a)). Furthermore, the inset of Fig. 7(a) shows the dielectric loss as a function of temperature (tan δ–T curve), and the peak position in the tan δ–T curve shifts to a higher temperature range with increasing measurement frequency. This indicates that frequency dispersion occurs in this sample. For the sample with a B-site ordering of 50%, on the other hand, a point of inflection is maintained at a temperature of 80 ◦ C in the εr –T curve. It seems that there is no broad phase transition and no frequency dispersion. The inset figure apparently shows the absence of frequency dispersion in the tan δ–T curve. A sample with an ordering of over 50% also exhibited the same behavior in terms of dielectric properties. This result suggests that the B-site ordering state in BZT and PST influences the relaxor behavior, and that the B-site ordering state (ratio of ordered to disordered) is one of the important key factors in determining the origin of relaxor behavior. A better interpretation of the systematic change in dielectric properties will be described in a future article.

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Fig. 7. Temperature dependence of the dielectric constant (εr ) of superlattices with B-site ordering values of (a) 25% and (b) 50%. The insets represent the dielectric loss (tan δ) as a function of temperature

References [1] G. Smolenski, V. Isupov, A. Agranovskaya, S. Popov: Sov. Phys. Solid State 1, 147 (1958) 162 [2] G. Somolenski: J. Phys. Soc. Jpn. 28 Suppl., 26 (1970) 162 [3] K. Ueda, H. Tabata, T. Kawai: Science 280, 1064 (1998) 162 [4] K. Ueda, H. Tabata, T. Kawai: Phys. Rev. B. 60, R12561 (1999) 162 [5] H. Tabata, H. Tanaka, T. Kawai: Appl. Phys. Lett. 65, 1970 (1994) 162 [6] T. Tsurumi, T. Suzuki, M. Yamane, M. Daimon: Jpn. J. Appl. Phys. 33, 5192 (1994) 162 [7] H. Tabata, T. Kawai: Appl. Phys. Lett. 70, 321 (1997) 162 [8] T. Zhao, A. H. Chen, F. Chen, W. S. Shi, H. B. Lu, G. Z. Yangal: Phys. Rev. B 60, 1697 (1999) 162


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[9] Z. Wang, T. Yasuda, S. Hatatani, S. Oda: Jpn. J. Appl. Phys. 38, 6817 (1999) 162 [10] J. Mantese, N. Schubring, A. Micheli, M. Mohammed, R. Naik, G. Auner: Appl. Phys. Lett. 71, 2047 (1997) 162 [11] H. M. Christen, E. Specht, D. Norton, M. Chisholm, L. Boatner: Appl. Phys. Lett. 72, 2535 (1998) 162 [12] O. Nakagawara, T. Shimuta, T. Makino, S. Arai, H. Tabata, T. Kawai: Appl. Phys. Lett. 77, 3257 (2000) 162 [13] T. Shimuta, O. Nakagawara, T. Makino, S. Arai, H. Tabata, T. Kawai: J. Appl. Phys. 91, 2290 (2002) 162 [14] P. Dobal, A. Dixit, R. Katiyar, Z. Yu, R. Guo, A. Bhalla: J. Appl. Phys. 89, 8085 (2001) 162, 163 [15] H. Tabata, Y. Hotta, T. Kawai: J. Korean. Phys. Soc. 42, S1199 (2002) 163 [16] F. Uchikoba, T. Ito, S. Nakajima: Jpn. J. Appl. Phys. 34, 2374 (1995) 167 [17] Y. Yamashita, K. Harada, T. Tao, N. Ichinose: Integr. Ferroelectr. 13, 17 (1996) 167 [18] L. Cross: Ferroelectrics 76, 241 (1987) 167, 168 [19] G. Smolensky, A. Agranovskaja: Sov. Phys. Tech. Phys. 3, 1380 (1958) 167 [20] D. Viehland, S. Jang, L. Cross, M. Wutting: J. Appl. Phys. 68, 2916 (1990) 168 [21] V. Westphal, W. Kleemann, M. Glinchuk: Phys. Rev. Lett. 68, 847 (1992) 168 [22] N. Setter, L. Cross: J. Appl. Phys. 51, 4356 (1980) 168, 171 [23] J. Ravez, C. Broustera, A. Simon: J. Mater. Chem. 9, 1609 (1999) 169 [24] Y. Zhi, A. Chen, R. Guo, A. Bhalla: J. Appl. Phys. 92, 2655 (2002) 169 [25] A. Dixit, S. Majumder, R. Katiyar, A. Bhalla: Appl. Phys. Lett. 82, 2679 (2003) 169, 171 [26] K. Ueda, H. Tabata, T. Kawai: Science 280, 1064 (1998) 169 [27] H. Tabata, H. Tanaka, T. Kawai: Appl. Phys. Lett. 65, 1970 (1994) 169 [28] P. Dobal, A. Dixit, R. Katiyar, Z. Yu, R. Guo, S. Bhalla: J. Appl. Phys. 89, 8085 (2001) 169 [29] K. H. Hellwege, A. Hellwege: Landolt-B¨ ornstein III/16a, Ferroelectric and Related Substances (Springer, Berlin 1981) p. 422 169 [30] Y. Hotta, G. Hassink, T. Kawai, H. Tabata: Jpn. J. Appl. Phys. 42, 5908 (2003) 170 [31] C. Hammond: The Basics of Crystallography and Diffraction (International Union of Crystallography, Oxford 1997) p. 157 170

Index

A(B ,B )O-type ferroelectrics, 162 artificial control of ordering state, 161 B-site ordering, 162, 169–171 Ba(Zr,Ti)O3 , 161, 162, 167 BaTiO3 , 161–164, 169 BaZrO3 , 162, 164, 169 BZT, see Ba(Zr,Ti)O3 diffusive phase transition, 162 dipole glass model, 168 frequency distribution in graph of dielectric constant, 163 heterovalent ions, 169 homovalent ions, 162

Pb(Mg,Nb)O3 , 162 Pb(Mg,Ta)O3 , 162 Pb(Sc,Nb)O3 , 162 Pb(Sc,Ta)O3 , 162 Pb(Zn,Nb)O3 , 162 perovskite, 161 PLD, 162, 167, 169 pulsed laser deposition, 162, 167, 169 quenched random-field model, 168 relaxor, 161–163, 167–169, 171 RHEED, 163

metal–insulator–metal structure, 162

super-paraelectric model, 168 superlattice, 162–164, 167–171

ordered–disordered distribution of B-site cations, 162

XRD, 163

Physics of Ferroelectric Interfaces: An Attempt at Nanoferroelectric Physics Yukio Watanabe Kyushu University, Department of Physics, Hakozaki 6-10-1, Higashi-Ku, Fukuoka, Fukuoka 812-8581, Japan

Abstract. Experiments on devices can be regarded as part of basic physics. Here, theoretical analyses of devices using the interface in a ferroelectric junction reveal novel basic properties unknown in conventional experiments. Devices using interfaces in ferroelectric junctions are grouped into two types: (1) the lateral-type, or field-effect, devices that use the transconductance, i.e., the conduction parallel to the interface; and (2) the vertical-type, or diode-like, devices, in which the conduction is perpendicular to the interface and the current flows through the ferroelectric. The discussion below concentrates on the field-effect type (1). On the other hand, the other type of devices [1, 2, 3, 4, 5, 6] have recently attracted intense interest due to the resistance RAM (R-RAM). Additionally, modulation of the tunneling current and the photovoltaic effect have been demonstrated [7, 8, 9]. Details of these topics will be discussed elsewhere. We start our journey by assuming for the present that the ferroelectric is an ideal insulator.

1 Spontaneous Polarization and the Ferroelectric Surface Although ferroelectrics are often discussed in terms of their special lattice structure and phonon dynamics, they are defined by the spontaneous polarization PS . PS is an electric polarization that is nonzero even under no applied voltage Eappl , and is reversible. The macroscopic charge distribution in a ferroelectric is exactly the same as in a nonferroelectric insulator under a finite Eappl . For example, in the one-dimensional case, its charge distribution is exactly same as that for a dielectric in a parallel-plate capacitor under an external field, as described in elementary textbooks on electrostatics. Let us take the Cartesian coordinate x parallel to PS and assume that PS is homogeneous, i.e., constant. The macroscopic charge distribution ρ (x) in the ferroelectric for Eappl = 0 is then ρf (x) = PS δ (x) − PS δ(x − lf ) (where δ is the delta function); x = 0 and x = lf correspond to the top and bottom surfaces, and lf is the thickness of the ferroelectric. That is to say, the property that characterizes ferroelectrics exists only at the surfaces, and all other parts M. Okuyama, Y. Ishibashi (Eds.): Ferroelectric Thin Films, Topics Appl. Phys. 98, 177–199 (2005) © Springer-Verlag Berlin Heidelberg 2005

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Fig. 1. Charge distribution in a ferroelectric (a), in a metal/ferroelectric/metal (M/F/M) system (b), and in a semiconductor/ferroelectric/semiconductor (S/F/S) system (c). In an M/F/M system, the location and value of ρm agree completely with those of ρf if M is an ideal metal. In an S/F/S system, the shielding charge ρs is effectively separated from ρf , which is the cause of the depolarization field

are electrically the same as in dielectrics (Fig. 1). This simple consideration indicates the special importance of the surface in the physics and applications of ferroelectrics. An ideal ferroelectric, as well as a dielectric, is considered here to be a simple insulator. Combining this assumption with the charge distribution ρf (x) = PS δ(x) − PS δ(x − lf ), we conclude that the ferroelectric should be extremely sensitive to the material contacting the ferroelectric surface, directly, i.e., the interface. In the discussion below, we assume that the ferroelectric surface is perpendicular to PS and that the dimensions of the surface, i.e., the lengths along the y- and z-axes, is infinite.

2 Electric Field in and Arising from a Ferroelectric The surface charge due to PS is huge. Therefore, it would be quickly shielded or effectively reduced. For the time being, we assume that the ferroelectric is monodomain. 2.1 Ferroelectric Covered by Metal (M/F) If a ferroelectric (F) is covered by a metal (M), PS is shielded by electrons and holes/ions in the metal (the metal is grounded). In the discussion of ρf , we approximate the thickness of the surface lattice as zero. Accordingly, we approximate the Thomas–Fermi screening length λTF , which is 0.01 nm to 0.1 nm, as zero. Namely, we approximate the metal as a perfect conductor and the charge density in the metal as ρm (x) = −PS δ(x) + PS δ(x − lf ) (PS ≤ PS ). For λTF = 0 we have PS = PS , no net charge density exists, and no electric field exists inside or outside of the ferroelectric. Therefore, the ferroelectric properties are not affected or constrained by ρf (Fig. 2). The properties of the metal are expected to change with contact because of PS , because electrons are accumulated or depleted in the metal. This change modulates the conductance of the metal, although the effect is negligibly small. This is the principle of the field-effect transistor (FET) using a ferroelectric.

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Fig. 2. Geometry of M/I/F/I/M system (a), the charge distribution (b), and potential distribution (c)

2.2 Ferroelectric Covered by Semiconductor (S/F) If the ferroelectric is covered by a sufficiently thick semiconductor (S), ρf is compensated by the shielding charge in the semiconductor as in an M/F/M system. However, its screening length λD 1 cannot be approximated as zero. Namely, the total charge in the semiconductor is almost the same as that in the metal, but the center of the charge is separated from the ferroelectric surface by λD . Therefore, an electric field exists in the semiconductor. The M/F interface is a limiting case of an S/F interface where λD = 0. Let us simplify the charge distribution in the semiconductor to ρs (x) = −PS δ (x + λD ) + PS δ (x − lf − λD ). Therefore, the S/F interface is modeled as an M/I/F system, with the thickness of the insulator I being very small. In this case, an electric field exists also in the ferroelectric, as shown in the discussion of the I/F interface below. When the semiconductor is not thick enough, the absolute value of the total charge in the semiconductor is smaller than PS . 2.3 Ferroelectric Covered by Insulator or Nothing (I/F), and Depolarization Field A ferroelectric covered by an insulator or a dielectric layer is modeled by an I/F/I system. For a monodomain insulating ferroelectric, the electric field at the surface of the I layer is the same as that at the surface of the F layer. This electric field will be shielded by various charges, though the degree of shielding depends on the shielding mechanism. Therefore, a more appropriate model of an I/F interface is M/I/F or S/I/F. For example, a water layer containing many ions can be regarded as a metal, and air can be regarded as a semiconductor with an appropriate band-gap energy Eg and impurity density. 1

PS is usually very large, and therefore the shielding carriers are degenerate within a distance of λTF from the S/F interface. At distances from the S/F interface exceeding λTF , the field is reduced so that the carriers are nondegenerate. However, the field still exists beyond this distance and is shielded on a characteristic length scale of λD (λD λTF ).

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We consider first an M/I/F interface, where M is grounded and the thickness of the insulator is li . For simplicity we take the relative dielectric constant of the insulator εi as unity (Fig. 2). The charge distribution is given by ρ (x) = PS δ (x) − PS δ (x − lf ) − PS δ (x + li ) + PS δ (x − lf − li ). The potential Ψ (x) for this charge distribution is obtained from the continuity of the electric flux and Ψ (x), as previously done in [10, 11, 12]. (Integration of ε0 dE/dx = ρ = −PS δ (x + li ) in the vicinity of x = −li gives PS = ε0 |Ei | < PS for Eappl = 0.) The continuity of the electric flux is expressed by ε0 Ef −PS = ε0 Ei , where ε0 is the vacuum permittivity, and Ef and Ei are the electric fields in the ferroelectric and the insulator, respectively. The continuity of Ψ (x) is expressed by Ei li + Ef lf + Ei li = 0. Therefore, we obtain Ef = PS / [ε0 (1 + lf /2li)], Ei = −PS / [ε0 (1 + 2li /lf )], and PS = PS / (1 + 2li /lf ). The electric field in the ferroelectric Ef has a polarity such that it tends to decrease PS and hence is called the depolarization field. 2.4 Surface Relaxation Modeling of I/F Structure and Generalization An insulator/ferroelectric structure can be regarded as a ferroelectric with a nonferroelectric surface layer, i.e., a surface relaxation (∇P ) layer [11]. Therefore, it can also be described by the result of Kretschmer and Binder [13]

E (x) = P (x) −

L

P (x ) dx/L /ε0 ,

(1)

0

where L = lf + 2li . For an I/F/I structure, we have E (x) = Ei and P (x) = 0 for −li < x < 0 and l < x < lf + li , and E (x) = Ef and P (x) = PS for 0 < x < lf . The substitution of these expressions in (1) yields the same expressions for Ef and Ei as in the previous subsection. For εi = 1, we replace Ei by εi Ei in the equation of continuity of the electric flux. To keep the equation of continuity of the potential correct, we substitute li by li /εi . After these transformations, we have Ef = PS / [ε0 (1 + εi lf /2li )] and Ei = −PS / [ε0 (1 + 2li /lf εi )]. As discussed in the previous section, a semiconductor/ferroelectric (S/F) interface can be modeled by a metal/insulator/ferroelectric (M/I/F) interface. Namely, the charge distribution ρ (x) in an S/F/S interface is approximated by an M/I/F/I/M structure, where li is replaced by λD . Therefore, a depolarization field exists in an S/F/S interface; Batra and colleagues attributed the instability of a ferroelectric field-effect transistor using a metal/ferroelectric/semiconductor (MFS) structure to this field [14]. The preceding paragraphs show the approximation of an S layer as an M/I layer. Therefore, an S/I/F interface can be modeled by an M/I /F interface, where the insulator I consists of two insulating layers.


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3 Ferroelectric Field Effect Devices The charge ρm induced by PS in an F/M interface can change the transverse conductance of the metal. This change is important only if the thickness of the metal layer is comparable to λTF . The same argument is applicable to the F/S and the F/I/S interface: the effect of the induced charge ρS is significant for a semiconductor thickness < λD , and this condition is easily achieved. This is the principle of the ferroelectric TFT (thin-film transistor) and of ferroelectric field-effect adaptive resistors. When the conduction is limited by pn junctions at the channel–source/ drain boundaries as in the usual Si FET devices, another device principle exists. Suppose that the channel is acceptor-doped with an acceptor density NA . If the PS -induced negative charge density ρs exceeds NA , the carrier type changes. This change leads to the disappearance of the pn junction, and, therefore, the conduction is no longer limited by the pn junction. This is the principle of MFS and MFIS devices, which have an F/S and an F/I/S interface, respectively. Here, we have added “M” to “FS” and “FIS”, according to the convention for the MIS (metal–insulator–semiconductor) device, although the physical essence is F/S or F/I/S.

4 Domains, Depolarization Instability, and Memory Retention A simple example of an I/F/I structure is a ferroelectric crystal plate in vacuum or dry air. In the conventional theory, a multidomain structure forms to reduce the depolarization field. An example is a c–c stripe domain, where the spontaneous-polarization vector is perpendicular to the surface, and its polarity in each stripe domain changes alternately from one to the next (Fig. 3). The electrostatic energy reduces with decreasing domain width W [15]. The reduction of the electrostatic energy by domain formation is limited by the domain wall energy, which increases linearly with the density of domain walls. Therefore, the sum of the electrostatic energy and the domain wall . It is easy to show that energy always has a nonzero minimum energy Emin√ the value of W for Emin decreases in proportion to lf . For a short lf , for example 50 nm, however, Emin is larger than the freeenergy difference between the ferroelectric and the paraelectric phase. This poses a limitation on the minimum lf of the stable ferroelectric phase (lfd min ) determined by the depolarization field. Experimentally, lfd min can only be observed in a ferroelectric with clean surfaces in ultrahigh vacuum, which has not yet been tested so far. Nonetheless, the value of lfd min of 50 nm seems too thick; this will be discussed later. If we apply this thermodynamic instability to MFIS devices, which have an F/I/S interface, we conclude that for li thicker than a certain value, the

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Fig. 3. A ferroelectric platelet in vacuum (a) is an I/F/I structure (b). Its electrostatic energy is reduced by forming domains (c)

Fig. 4. Reduction of Curie–Weiss temperature of a stress-free, ideally insulating PbTiO3 film in an M/F/I/M structure, representing the decrease of free energy vs. the width of a stripe domain at a given insulator thickness li

Fig. 5. The domain width at the minimum free energy (a), and the stability (b) of the stress-free ferroelectric phase in an MFIM device. F = PbTiO3 (TC = 478.8 ◦ C), I = SiO2 . Below lf , where the δT curve touches the abscissa, the ferroelectric phase is unstable for a given li [10]


183

ferroelectric phase in the MFIS destabilizes below a critical lf . An example is shown in Figs. 4 and 5. In field effect devices and other ferroelectric memory devices, the polarity of a domain corresponds to a memory state of 0 or 1. The most important mechanism determining the minimum domain size is the c–c domain wall width, which is of the order of one lattice unit. In addition, the preceding discussion shows that the depolarization field determines the stable domain configuration in MFIS and other devices using an F/I interface. In other words, an artificially formed domain may be unstable. This domain instability becomes important as lf decreases.

5 Epitaxial Strain and the Surface Relaxation ∇P Effect 5.1 Epitaxial Strain vs. Depolarization Instability Ferroelectricity in a given ferroelectric substance corresponds uniquely to a special crystallographic structure. This implies that enhancement of the crystallographic symmetry of the ferroelectric phase can encourage the ferroelectricity. For example, enhancement of the tetragonality of BaTiO3 , i.e., the ratio of the length of the c-axis to the a-axis, increases the Curie temperature TC . This crystallographically controlled ferroelectricity has been confirmed in bulk single-crystal samples. If the ferroelectric undergoes a depolarization field instability, its crystallographic structure changes also. Unless the ferroelectric is freestanding, such a structural change may be suppressed by the adjacent material. This effect is significant in epitaxial thin films (Fig. 6). Therefore, we cannot compare the depolarization field instabilities and other ferroelectric instabilities with experiments without discussing the effect of strain. Crystallographically controlled ferroelectricity has become progressively important in thin films. The lattice mismatch between the substrate and the ferroelectric layer yields a two-dimensional in-plane stress. Indeed, enhancement of the ferroelectricity by the epitaxial strain has been reported [16, 17]. It is easy to show by the Ginzburg–Landau (GL) theory that the effect of the two-dimensional in-plane strain in tetragonal phase can be expressed by an

Fig. 6. Enhancement and stabilization of ferroelectricity by compressive strain

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Fig. 7. Classification of the effect of substrate stress on a ferroelectric film. In the frozen-phase limit, the phase is fixed by the substrate, but the energy of given domain configurations can be estimated. The freestanding case is regarded as a weak-stress limit [12, 19]. Here, for a ferroelectric film to be categorized as epitaxial, the lengths of its in-plane lattice constants are at least the same as those of the substrate. This should ocurr at at any ambient temperature for pefect epitaxy

increase of the effective TC when PS is perpendicular to the surface [10, 12]. In the general case, Pertsev et al. have shown that a strain-driven phase appears [18]. In the case of perfect epitaxy, we can regard the ferroelectric thin film as a frozen phase and assume that the ferroelectric phase undergoes no phase transition caused by the depolarization field [19] (Fig. 7). 5.2 The Surface Relaxation ∇P Effect Can Be Unimportant Ferroelectricity should disappear when the number of mutually interacting unit cells (or unit lattice cells) that constitute the ferroelectric is below a certain value, because ferroelectricity is a cooperative phenomenon. The number of unit cells (or unit lattice cells) that interact with the surface unit cells (or unit lattice cells) is less than that inside. Therefore, we expect a reduction of ferroelectricity at the surface, and this effect is called the ferroelectricsurface-relaxation ∇P effect (Fig. 8). The ∇P effect has conventionally been studied using ferroelectric particulates. These studies indicate that the ferroelectricity disappears below 10 nm, which is attributed to ∇P [20]. However, we would expect that studies using conventional ferroelectric particulates would encounter various experimental difficulties. On other hand, recent studies of ferroelectric surfaces and thin films demonstrate that ferroelectricity can exist even near the surface [1, 2, 3, 4, 5, 6, 21, 22]. Therefore, the intrinsic ∇P probably occurs only on a very short length scale, for example a few lattice spacings. This implies that most of the degraded properties observed so far in thin films and particulates are extraneous. It is worth adding that the reduction of ferroelectricity in thin films, such as the reduced PS and dielectric constant ε, has been attributed to the ∇P effect. However, it is also attributable to strain effects.


185

Fig. 8. Cooperative phenomena at a surface (a) and in a cluster (b). The graph of PS (c) can be regarded as PS vs. size or PS vs. distance from the surface

6 Finite Band Gap Energy and Redefinition of “Insulator” 6.1 Reexamination of the Depolarization Field We have discussed the importance of strain in thin films. Nonetheless, some properties related to the depolarization field are still inexplicable by strain only. Here, we should note that the unscreened depolarization field is as high as 0.1 GV/cm to 1 GV/cm, so that it can change the ferroelectric phase into the paraelectric phase. One puzzle is the experimental observation of quasi-stable domain configurations in MFIS devices. If unshielded, an enormous electric field is expected to exist at the F/I/S interface. Therefore, this field would change an artificially written domain configuration to the stable one discussed in Sect. 4. Such a change has not been observed so far, which can be explained by various mechanisms, including the shielding of the depolarization field. Moreover, the domain configuration of single crystals has been examined only in air. Therefore, the c–c domain configuration in Sect. 4, drawn for an unshielded depolarization field, has little experimental support. Additionally, a freestanding 100 nm thick PbTiO3 platelet possesses lattice parameters similar to those of the bulk [23], suggesting that the platelet is free from the depolarization instability. Therefore, we cannot assume a priori that a ferroelectric is a good insulator. Indeed, most of the oxide perovskite ferroelectrics have an Eg of 3 eV to 4 eV, which is similar to the values of wide-gap semiconductors, for example GaN. Moreover, ferroelectric thin-film heterostructures exhibit various semiconductor properties such as pn junctions (p hole carrier type; n electron carrier type), tunneling junctions, and the photovoltaic effect [1,2,3,4,5,6,7,8,9]. Therefore, we may postulate that a thin ferroelectric may be treated appropriately as a semiconductor.

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6.2 Relaxation Semiconductors If we take this view, we encounter a gap between the understanding of bulk single-crystal ferroelectrics and that of small-size ferroelectrics such as thin films. Indeed, the dielectric constant is well defined only when the leakage current is absent. If ferroelectrics or dielectrics were conductive, most devices in which ferroelectrics and dielectrics are applied, such as capacitors and piezoelectric actuators, would be unusable. To bridge this gap, we may return to the old studies of wide-band-gap semiconductors [24]. In those days, wide-gap semiconductors such as the III– V compound semiconductors were called relaxation semiconductors, because they exhibit large dielectric relaxation. In other words, the intrinsic carrier concentration in these semiconductors is low, and hence the carrier conduction is small so that the dielectric response is evident when an external field is applied to them. Oxide ferroelectrics have a extremely high permittivity, and a carrier mobility far lower than those of the III–V compounds. Therefore, oxide ferroelectrics can be regarded as an extreme limit of a relaxation semiconductor, and their response to a external field is dominated by the dielectric response, unless they are not heavily doped. This inference agrees with our experience. We should remember that this experience and the inference are for dynamical cases. We may need to think differently about the response of a ferroelectric to a static or extremely slowly varying electric field. 6.3 Insulator Under Static Field In standard solid-state physics, the distinction between a semiconductor and an insulator is merely semantic. On the other hand, the formation of a conductive layer by doping and by an electric field is an essential feature of the applications of semiconductors. Here, the origin of the conductive layer is the accumulation of electrons and holes due to band bending. Can all insulators form a conductive layer on their surface under the influence of an electric field like standard semiconductors? We doubt this possibility for insulators possessing a large Eg , for example 6 eV. The value of Eg is important because atoms would move, deform and shield the electric field before the conductive layer was formed, if the electric field was larger than or comparable to the atomic binding energy or chemical energy. 6.4 Ferroelectric Under Static Field Now, the values of Eg of ferroelectrics are close to those of standard semiconductors. Do they form a conductive layer under the influence of a field? We cannot answer yet, because the electric charge can be shielded at least locally by the dielectric response, i.e., the displacement of the bound charges. Indeed, the dielectric response of the ferroelectric is significant.


187

Fig. 9. A pair of metal sheets under a bias voltage in vacuum (a) has the same charge distribution as that in a ferroelectric without a shielding mechanism (b). In a dielectric, the electric field due to these charges can be shielded by the dielectric response, which is due to local atomic displacements and deformation, and is represented by a macroscopic polarization

Suppose we have a pair of sheet charges in a vacuum. Such charges are easily provided by a pair of metal sheets biased with an external voltage (Fig. 9). The electric field from the charges is partially shielded if we insert a dielectric or a ferroelectric. If the permittivity of the dielectric or ferroelectric is infinite, the electric field is completely shielded. Many ferroelectrics possess a very large linear permittivity for a small electric field. Therefore, a small electric field is almost completely screened out by the dielectric response of a ferroelectric inserted between the charges. Consequently, we expect that a conductive layer will not be formed by the electric field on the ferroelectric surface. However, the mechanism of shielding of the charge is only a drastic change of PS , where the sheet charge density is of order PS and with the sign same as PS . Such shielding is not always possible. In the case of the depolarization field, the field originates from PS . The only way for a monodomain ferroelectric to shield the depolarization field substantially is to polarize itself in the opposite direction. This means that the net spontaneous polarization is PS − PS = 0. This can be only possible when the ferroelectric undergoes instability to a paraelectric phase. 6.5 The Natural Choice of a Ferroelectric Now, our ferroelectric has three choices: (1) the depolarization field exists almost unshielded, and the net polarization is close to the value of PS under no depolarization field; (2) the ferroelectric changes to a paraelectric; (3) the depolarization field is screened by mechanisms other than the dielectric response that is the local deformation and displacement of atoms or lattices. As lf decreases (Fig. 4), the second choice becomes energetically more favorable than the first, if the ferroelectric is strain-free. Is the ferroelectricity then

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vulnerable to destroying its microscopic origin by its own macroscopic properties? The ferroelectricity can be rescued if charged defects and vacancies segregate at the surface or if charged impurity ions etc. move towards the surface. However, these processes are very slow and take a long time to shield the field. Alternatively, field-induced formation of a conductive layer by band bending could be an effective and fast shielding mechanism, if it exists. By examining experimental data on MFIS devices [10,12], we have proposed that a conductive layer should exist, and explained the MFIS data as discussed later [11, 12]. Although no theory supporting this possibility existed in those days, we knew that perovskite oxides with an Eg of 2 eV did form conductive layers because of PS [25, 26]. Therefore, it would not be unreasonable to assume that perovskite ferroelectrics with an Eg of 3 eV did so also. Here, we should note some pioneering Russian theoretical work that considered the possible formation of a conductive layer in ferroelectrics [27].

7 Modeling of F/I/S Interfaces A rigorous treatment of the charge density and the electric field, including those in the semiconductor, is indispensable here, although the essence of the F/I/S interface is the F/I interface, as discussed in Sect. 2 (see Fig. 2). Therefore, we employ a band diagram model of the semiconductor heterostructure (Fig. 10). 7.1 Mathematical Formulation In the GL thermodynamic theory, the free energy density F0 for a bulk ferroelectric with an inhomogeneous PS (or P ) distribution under a homogeneous 2-dimensional stress in the a–b plane is written as [11, 19] F0 + η (∇P ) = αP 2 + βP 4 + γP 6 + Fσ (S) × P 2 + η (∇P ) . 2

2

(2)

The coefficients α ( = (T − θ) /2ε0 C), β, γ, and η are thought conventionally to be determined by a local atomic potential and a long-range electrostatic force, where T and θ are the ambient temperature and the Curie–Weiss temperature (close to the Curie temperature TC ), respectively. Fσ (S) is determined by the stress tensor S. We use the bulk value of the coefficients, because their change due to thermal fluctuations has been shown to be important only for a size smaller than 1 nm [28]. Equation (2) also contains the domain wall energy EW . The free energy F of the M/F/I/S structure contains terms representing the electrostatic energy EES and the kinetic energy EK in addition to (2). When the stress is not very large, the stress term Fσ (S) × P 2 can be renormalized to yield an effective change of θ. However, for a frozen phase


189

Fig. 10. Model, and definition of the coordinates and parameters (a); potential distribution (b); and band diagram (c). The tilted dashed line in (b) is for an insulating ferroelectric [11, 19]

(see Fig. 7), we can estimate only the stable domain configuration and the value of the induced charge in the semiconductor, and not the phase stability nor PS . Therefore, if stress is not very large the part of the free energy F dependent on the polarization P that should be compared with the bulk value F0 × 2W lf is written as W 0 2 F = dy dx F0 + η (∇P ) + EES + EK −W

−lf

W

= −W

EES =

0

dy −lf

W

∞

dy −W

−∞

2 dx F0 + η (∇P ) + EW + EES + EK ,

(3)

dx ε (x, y) ε0 E 2 (x, y) /2,

(4)

where ε (x, y) is the relative permittivity and is constant in each layer, for example ε = 1 in the the F layer, ε = εi in the I layer, and ε = εs in the S layer. 2 The contribution of the η (∇P ) term from the domain walls is separated 2 and is included in EW , and the η (∇P ) term includes only the effect of surface relaxation in (3). The electric field E = −∇Ψ is given by Poisson’s equation with the boundary conditions Ψ (∞, y) = 0 and Ψ (−lf , y) = Ve + δφms ,

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− ∆Ψ (x, y) = e ND+ − NA− + p − n /εs ε0 , + − −∆Ψ (x, y) = eNDf − eNAf + epf − enf − ∇P + Q /ε0 ,

(5) (6)

where ND+ , NA− , p, and n are the ionized-donor density, the ionized-acceptor density, the hole density, and the electron density in the semiconductor, respectively, and Q is the ionic charge induced by the field. The similar symbols with the subscript “f” in (5)–(8) are the corresponding quantities for the ferroelectric. By noting that Ψ (∞, y) = 0, we can relate n, nf , p, and pf to Ψ by n = NC F1/2 ((EF − EC (x, y)) /kT ) , p = NV F1/2 ((EV (x, y) − EF ) /kT ) , nf = NCf F1/2 ((EF − δφ − ECf (x, y)) /kT ) ,

(7)

pf = NVf F1/2 ((EVf (x, y) − EF + δφ) /kT ) ,

(8)

EC (x, y) − ECf (x, y) −

0 0 EC = EV (x, y) − EV = −eΨ, 0 0 ECf = EVf (x, y) − EVf = −eΨ,

where EF is the Fermi level, F1/2 is the Fermi function of order 1/2,2 k is the Boltzmann constant, EC and EV (= EC − Eg ) are the energy levels of the conduction and the valence band, respectively, and NC and NV are the effective densities of states of the conduction and the valence band,2 respectively. The superscript 0 denotes a quantity very deep from the surface, for example 0 0 = EC (∞, y), and EV = EV (∞, y). δφ, δφms , and Ve are the difference EC between the work functions of the semiconductor and the ferroelectric, the difference between the work functions of the semiconductor and the metal, 0 is determined by (5) with Ψ = 0, and the external bias, respectively. EF − EC 0 and EF − ECf is determined similarly. We have derived this formulation of the work function difference and confirmed its correctness by considering a double Schottky structure (metal/ semiconductor/metal), for which the solution is known [29]. EK is the sum of the kinetic energies of electrons and holes. For example, denoting the wave vector by k, we can express the kinetic energy of an electron in the ferroelec0 0 0 0 0 tric as ¯h2 k 2 /2 m + ECf − EF . Here, we use EC , EV , ECf , and EVf instead of EC (x, y), EV (x, y), ECf (x, y), and EVf (x, y), because the use of the latter means a double counting of EES . For a given W and a given functional form of P (x), (5)–(8) can be solved with boundary conditions such as εi ε0 Ei = ε0 Ef + P at x = 0 and the continuity of Ψ , as in Sect. 2. The best solution is given by the trial function of P (x) that minimizes (3). EW can be calculated as previously done [10, 12]. 2

√ √ F1/2 (x) = (2/ π) ∫0∞ dE E/ (1 + exp (E − x)) . For a 3-dimensional elec3/2

3/2

tron gas, NC = 2 2πme kT /h2 and NV = 2 2πmh kT /h2 , where h is the Planck constant (¯ h = h/2π), me is the electron band mass, and mh is the hole band mass.


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The free energy F in (3) can be calculated using the solution, and the P (x) and W that yield the minimum F are the final solutions. 7.2 Approximations When we are discussing the properties of MFIS devices and thin films of practical interest, we can simplify the above formulation by using approximate estimations of the ∇P effect and the kinetic term. ∇P is nonzero near the surface, as discussed in Sect. 5. However, the thickness of the nonzero region is typically 1 nm [1, 2, 3, 4, 5, 6, 21, 22], whereas the ferroelectric layer is thicker than 10 nm in most cases of interest. If we are interested in the properties of a ferroelectric layer or an MFIS device as one entity, we can ignore the details of this surface region. Therefore, we may approximate the ferroelectric layer as a multilayer consisting of a sublayer with a constant P and a thin surface sublayer with P = 0 [11, 19, 30, 31]. The surface conductive layer is expected to be very thin: the carriers are confined in the direction of the depth (x). Therefore, we should consider the quantization of the motion in the x direction [32]. The major changes due to this effect are a change in the carrier distribution at the surface, for example within 1 nm to 2 nm from the surface, and an increase in the kinetic energy. If we are interested in the overall properties of an MFIS device or a ferroelectric layer thicker than 10 nm, we can approximate the quantization effect by (i) an effective change of the ferroelectric to an insulating surface layer and a ferroelectric, and (ii) a renormalization of the effective mass [19]. An example of a rigorous solution without these approximations shows that the above approximations are acceptable [33]. More seriously, however, we have reservation about models that are too sophisticated, because ∇P and the quantization depend critically on the conditions in the region within a few lattice spacings from the surface, which is far from ideal so far, especially in thin-film structures. In short, the most important part of the approximation is the renormalization of lf and li .

8 Comparison with Experiments: Leakage Current and Dynamics 8.1 Numerical Results for Typical Structures Using the formulation in Sect. 7, we have estimated the thermodynamic stability of the system and the charge induced in the semiconductor, which is equal to D = εi ε0 Ei and corresponds to the memory signal. The results below can be compared with results obtained by assuming the ferroelectric to be an ideal insulator, i.e., Eg = ∞ (Fig. 5) [10]. The estimation of the kinetic energy depends critically on the quality of the F/I interface. For example, we can neglect the kinetic energy EK when

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defects, dislocations, and vacancies exist at the F/I interface, because we may assume, approximately, that electrons and holes exist in the gap. This situation is very probable, because most MFIS devices use a crystallographically unmatched (nonperovskite) oxides as an interfacial layer, on which the ferroelectric is grown nonepitaxially. Moreover, if the interface is dominated by an excessive amount of imperfections, we should regard the MFIS device effectively as an M/F/M/I/S structure, as suggested previously [10]. Additionally, we encounter a fundamental issue in evaluating EK , because of the polaron effect, which would substantially reduce the value of EK estimated from free-carrier statistics. On the other hand, results neglecting EK overestimate the effect of the finite Eg . Therefore, to illustrate and emphasize the effect of the finite Eg , we show results for a monodomain ferroelectric with EK = 0 and, for simplicity, Q = 0 and no stress [11]. Here, for many experimental results using polycrystalline ferroelectric layers, the strain-free condition would be an acceptable approximation. In this case, the ferroelectric phase of PbTiO3 , as evidenced by PS , is stable to at least lf = 10 nm for all values of li (Fig. 11(b)). D is almost independent of lf and is determined by semiconductor and structure para− meters such as li , NA− , NAf , and Ve . However, D for large values of li is a small fraction of PS = 75 µC/cm2 . The results contrast strikingly with the results for which the finite Eg is ignored (Fig. 11(a)) [10]. The result for a finite Eg , i.e., assuming semiconductivity, agrees satisfactory with the experimental data [34, 35, 36] (Fig. 12(a)). 8.2 Retention and Leakage Current The ferroelectric phase and PS of a stress-free insulating PbTiO3 layer with li ≥ 3 nm (SiO2 ) are theoretically unstable even for lf ≥ 400 nm [10]. Therefore, D, which represents the memory state of an MFIS device, is also unstable. We can translate this conclusion into corresponding conclusions for other insulators by changing the nominal li to a renormalized thickness 3.9li /εi . (Note that εi for SiO2 is 3.9.) This conclusion contradicts the experimental short-period stability of many MFIS devices [34, 35, 36, 37]. On the other hand, if we consider the effect of a finite Eg of the ferroelectric, we find no intrinsic instability for the practical range of parameters, for example lf , even without stress, and can explain the experimental transient stability. Theory [11] predicts that the induced charge D is intrinsically a small fraction of PS (EK > 0 increases D but reduces the stability of PS ). So, why are the memory states of MFIS devices experimentally unstable? We pointed out for the first time in Sect. VI of [10] that an MFIS device with an excessive amount of defects, etc. should be regarded as an MFMIS device, and hence the retention in MFIS devices is limited by the leakage current (Fig. 13(a)). Namely, carriers accumulate at the F/I interface with little energy cost and reduce D when it has many imperfections, and the


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Fig. 11. Dependence of induced charge (D) in Si on lf in a metal/PbTiO3 /SiO2 /Si structure for a given li under no stress. The finite-Eg effect is not included in (a) [10], but is included in (b) [11]. The kinetic energy EK is neglected. (c) Demonstration of 10 months’ retention of a memory state by an MFS device [25, 26]

only mechanism that suppresses this carrier accumulation is the speed of the carrier transportation, i.e., the electrical resistance. Indeed, Okuyama and colleagues have recently succeeded in improving the retention by reducing the leakage current [37]. The above discussion suggests also that the retention can be substantially improved if the imperfections in the F/I interface are improved. 8.3 Contradiction and Solution: Miller–McWhorter Theory Our theory appears to succeed in explaining the major static properties of MFIS experiments. However, it appears to fail in explaining the dynamic properties of MFIS devices such as the polarization (D–E) hysteresis curves. Here, the theory by Miller and McWhorter [38], which assumes the ferroelectric to be an ideal insulator, explains the D–E curves well [34, 35, 36]. Why is the effect of the formation of a conductive layer invisible in D–E curves? The capacitance vs. voltage (C–V ) curves of MIS devices give an answer [40]. At high frequencies with inversion, the carriers at the interface

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− Fig. 12. (a) Dependence of D on li for given NA− , NAf , and Ve , compared with the experimental value under no stress. The kinetic energy is neglected, which corresponds to a slightly nonideal F/I interface. Different curves are for different sets of parameters. The arrows show the range of the experimental data [11]. (b) Example of carrier distribution obtained by a 2-dimensional calculation [19]

cannot move from the interface, and therefore the net dynamic response of charges is unaffected by the carriers, even if they exist. Namely, the carriers are invisible at high frequencies. Now, typical ferroelectrics are an extreme limit of a relaxation semiconductor. Their relaxation time is calculated to be of the order of 103 s, the carrier density is negligibly small and the carriers are immobile in the ferroelectric except in an atomically thin layer at the surface. Therefore, the ferroelectric behaves as an insulator in a D–E measurement (Fig. 13(b)).


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Fig. 13. (a) Importance of leakage current or resistance in retention and in the D–E curve [10]. (b) The carriers can only move very slowly. Therefore, they are invisible in D–E curves

9 Intrinsic 2D Electron Layers The comparisons with experiments in the preceding section are indirect concerning the surface carrier layer (e.g., Fig. 12(b)). We need direct evidence for this layer at the F/I interface. If this layer is conductive, we should easily be able to detect it experimentally. To answer this, we need to investigate the details of the distribution of P and ρ on a nanometer scale. For this purpose, we include the quantization of the motion and the ∇P effect. Figure 14(a) shows an example of such a calculation and shows that a dense, narrow carrier layer exists slightly below the surface [33]. This suggests that the scattering of the carriers by surface imperfections may be suppressed and the layer can be conductive. This prediction is experimentally supported (Fig. 14(b)) [40].

Fig. 14. (a) Theoretical distribution of electron density and P at the minimum energy in an electrodeless, single-domain, pure BaTiO3 platelet with P parallel to the surface [33]. (b) Experimental surface conduction of BaTiO3 in ultrahigh vacuum, supporting the calculation [40]

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Fig. 15. Conventionally, ferroelectrics are modeled by cooperative dipoles (a). The coupling of PS to electrons via a macroscopic or mesoscopic field leads to the formation of a new state of the electrons and of the lattice (b)

10 Ferroelectric Coupled to Free Electrons: Ferroelectric 2D Metal The surface carrier layer above consists of 2-dimensional (2D) electrons/holes that are intrinsically coupled to PS . This layer can be regarded as a ferroelectric 2D metal, which may also exist at domain boundaries [41] (Fig. 15).

11 Concluding Remarks A study of ferroelectric interfaces with special attention to MFIS devices has guided us to an understanding of the ferroelectric surface in an extreme limit that has not been much studied so far. The formulation discussed here may be too much idealized to treat real MFIS devices. However, the essence, such as the existence of carriers at a clean F/I interface, the intrinsic reduction of D, and the stabilization of PS by these carriers, should remain valid. The study has also revealed a new state where PS and electrons/holes are coupled to form a new 2D system. The changes in the basics of the physics of ferroelectrics due to these effects appear to be small but will still remain important.

References [1] [2] [3] [4] [5]

Y. Watanabe, et al.: Physica 739, C235–240 (1994) 177, 184, 185, 191 Y. Watanabe, et al.: Appl. Phys. Lett. 78, 3738 (2001) 177, 184, 185, 191 Y. Watanabe: Phys. Rev. B 59, 11257 (1999) 177, 184, 185, 191 Y. Watanabe: Appl. Phys. Lett. 66, 28 (1995) 177, 184, 185, 191 Y. Watanabe, D. Sawamura, M. Okano: Appl. Phys. Lett. 72, 2415 (1998) 177, 184, 185, 191

Physics of Ferroelectric Interfaces [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43]

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M. Okano, Y. Watanabe: Appl. Phys. Lett. 233 (2000) 177, 184, 185, 191 Y. Watanabe: Phys. Rev. B 57, R5563 (1998) 177, 185 Y. Watanabe, M. Okano: Appl. Phys. Lett. 78, 1906 (2001) 177, 185 Y. Watanabe, M. Okano: J. Appl. Phys. 94 (2003) 177, 185 Y. Watanabe: J. Appl. Phys. 83, 2179 (1998) erratum 180, 182, 184, 188, 190, 191, 192, 193, 195 Y. Watanabe: Phys. Rev. B 57, 789 (1998) 180, 188, 189, 191, 192, 193, 194 Y. Watanabe: J. Appl. Phys. 84, 3428 (1998) 180, 184, 188, 190 R. Kretschmer, K. Binder: Phys. Rev. B 20, 1065 (1979) 180 P. Batra, P. Wurfel, B. Silverman: Phys. Rev. Lett. 30, 384 (1973) 180 M. Lines, A. Glass: Principles and Applications of Ferroelectrics and Related Materials (Oxford 1977) 181 T. Kawakubo, et al.: Jpn. J. Appl. Phys. 37, 5108 (1998) 183 Y. Watanabe, et al.: Jpn. J. Appl. Phys. 33, 5182 (1994) 183 N. Pertsev, Zembilgotov, A. Tagantsev: Phys. Rev. Lett. 80, 1988 (1998) 184 Y. Watanabe, A. Masuda: Jpn. J. Appl. Phys. 40, 5610 (2001) 184, 188, 189, 191, 194 K. Ishikawa, K. Yoshikawa, N. Okada: Phys. Rev. B 37, 5852 (1988) 184 H. Fujisawa, et al.: J. Eur. Ceram. Soc. 24, 1641 (2004) 184, 191 P. Ghoosez, K. Rabe: Appl. Phys. Lett. 76, 2767 (2000) 184, 191 K. Wasa: private communication 185 W. van Roosbroeck, H. Casey(Jr.): Phys. Rev. B 5, 2154 (1972) 186 Y. Watanabe, D. Sawamura: Jpn. J. Appl. Phys. 36, 6162 (1997) 188, 193 Y. Watanabe: Appl. Phys. Lett. 66, 1770 (1995) 188, 193 Y. Watanabe, M. Tanamura, Y. Matsumoto: Jpn. J. Appl. Phys. 35, 1564 (1996) ,Y. Watanabe, U.S. Patent No. 5422338 (1995) 188 B. Vul, G. Guro, I. Ivanchik: Sov. Phys. Semicond. 4, 128 (1970) 188 A. Bell: Ferroelectr. Lett. 15, 133 (1993) 190 M. Sze, D. Coleman(Jr.), A. Loya: Solid State Electron. 14, 1209 (1971) 191 Y. Watanabe: Appl. Surf. Sci. 130 – 132, 610 (1998) 191 Y. Watanabe, A. Masuda: Ferroelectrics 217, 53 (1998) 191 T. Ando, A. Fowler, F. Stern: Rev. Mod. Phys. 54, 437 (1982) 191, 195 Y. Watanabe, A. Masuda: Ferroelectrics 267, 379 (2002) 192, 193 T. Hirai, et al.: Jpn. J. Appl. Phys. 33, 5219 (1994) 192, 193 T. Hirai, et al.: Jpn. J. Appl. Phys. 33, 4163 (1995) 192, 193 E. Tokumitsu, et al.: Jpn. J. Appl. Phys. 33, 5202 (1995) 192, 193 K. Kodama, et al.: Jpn. J. Appl. Phys. 41, 2639 (2002) 193 S. Miller, P. McWhorter: J. Appl. Phys. 72, 5999 (1992) S. Sze: Physics of Semiconductor Devices (Wiley, New York 1981) 193, 195 Y. Watanabe, M. Okano, A. Masuda: Phys. Rev. Lett. 86, 332 (2001) 196 Y. Watanabe, et al.: in Proc. 25th Int. Conf. Phys. Semicond. (2001) p. 1623 M. Okano, Y. Watanabe, S. Cheong: Appl. Phys. Lett. 82, 1923 (2003)

Index

all-oxide ferroelectric FET, 193 band diagram, 189 C–V curve, 193 capacitance–voltage curve, 193 conductive layer on surface of ferroelectric, 191 Debye screening length, 179 depolarization field, 177, 183, 185, 187 depolarization instability, 181 domains, 181 electron statistics, 189 energy band diagram, 189 epitaxial strain, 183 ferroelectric 2D metal, 195 ferroelectric-gate FET, 178 field, effect on ferroelectric, 177, 186 finite-size effect, see size effect FIS interface, 188 frozen phase, 184 Ginzburg–Landau free energy, see asoLandau–Ginzburg free energy functional183 GL theory, see Ginzburg–Landau free energy IF interface, 179 IFI structure, 182 insulator–ferroelectric interface, see IF interface

memory retention, 183, 192 metal–ferroelectric interface, see MF interface MF interface, 178 MFIM structure, 182 MFIS structure, 188, 189 MFM structure, 178 MFS structure, 191 MIFIM structure, 179 Miller–McWhorter theory, 193 polaron effect, 192 relaxation semiconductor, 186 screening, see asoDebye screening length; Thomas–Fermi screening length180, see asoDebye screening length; Thomas–Fermi screening length185, see asoDebye screening length; Thomas–Fermi screening length187, see asoDebye screening length; Thomas–Fermi screening length191 semiconductor–ferroelectric–interface, see SF interface SF interface, 179 SFS structure, 178 shielding, see screening size effect, 185 surface and spontaneous polarization, 177 surface relaxation of ferroelectric, 177, 180, 184, 191

kinetic energy, 188, 192 leakage current, 192

Thomas–Fermi screening length, 178, 181

Preparation and Properties of Ferroelectric–Insulator–Semiconductor Junctions Using YMnO3 Thin Films Norifumi Fujimura and Takeshi Yoshimura Department of Applied Materials Science, College of Engineering, Osaka Prefecture University, 1-1 Gakuen-cho, Sakai, Osaka 599-8531 Japan {fujim,tyoshi}@ams.osakafu-u.ac.jp Abstract. On the basis of consideration of the design of materials for MFIS-FETs, the application of YMnO3 and Y2 O3 films as the ferroelectric and insulator layers, respectively, is proposed. After process optimization for the YMnO3 and Y2 O3 films, an YMnO3 /Y2 O3 capacitor with an epitaxial structure was developed. The use of epitaxial films drastically improves the dielectric and ferroelectric characteristics, and a relatively long memory retention time exceeding 104 s was successfully obtained. A relationship between memory retention and the polarization state or leakage current is proposed.

1 Introduction Semiconductor memory devices using a ferroelectric material are important candidates for new nonvolatile memory devices [1]. These memory devices are called ferroelectric random access memories (FeRAMs). FeRAMs are classified into two types. One consists of one transistor and one capacitor (1T– 1C type) [2]. In the 1T–1C type, information is stored by the ferroelectric capacitor. Information is read destructively by sensing the transient current that arises when an external voltage is applied to the capacitor, because the transient current when the polarity of the remanent polarization is reversed is larger than when it is not reversed. Since the structure of the 1T–1C type resembles that of a DRAM, a low-density (below 256 Mb) 1T–1C type has already been put into industrial production. However, ferroelectric materials with a remanent polarization larger than 30 µC/cm2 are required to produce high-density 1T–1C-type FeRAMs. Another type of FeRAM is called the ferroelectric-gate field effect transistor, and has a metal–ferroelectric–insulator–semiconductor (MFIS) structure [3, 4]. The ferroelectric thin film is used as a gate insulator in the FET and the insulator layer is inserted as a buffer layer. In this structure, the channel conductivity of the FET is directly controlled by the polarity of the remanent polarization because the electrostatic charge density of the remanent polarization modulates the surface potential of the semiconductor. To modulate the surface potential of the semiconductor, the required electrostatic charge density is only 0.1 µC/cm2 . Therefore, the ferroelectric material M. Okuyama, Y. Ishibashi (Eds.): Ferroelectric Thin Films, Topics Appl. Phys. 98, 199–220 (2005) © Springer-Verlag Berlin Heidelberg 2005

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does not need to have a large remanent polarization. Since a large dielectric capacitance of the ferroelectric gate insulator is not required for operating the MFIS-FET, the memory cell can be downsized. Compared with the 1T–1C type, the MFIS-FET has several advantages, such as nondestructive readout and a decreased memory cell size. To make high-density FeRAMs equivalent to DRAMs, the MFIS-FET type is desirable. MFS-FETs require the direct deposition of a ferroelectric thin film on a Si substrate. The film needs to maintain its ferroelectric properties on the Si substrate. The interface state density at the film/Si interface must be small enough to allow normal MOSFETs to be operated. Thin films of various ferroelectric materials have been investigated for MFS-FETs [5, 6, 7, 8, 9]. Although these materials usually exhibit good ferroelectric properties on metal electrodes such as Pt and Ir, it is difficult to form ferroelectric films directly on Si substrates because of interdiffusion between the film and the Si and the formation of a SiO2 layer with a low dielectric constant [10]. First, we describe electromagnetic calculations performed to design materials suitable for an MFIS structure. On the basis of the material design, the application of YMnO3 [11, 12, 13, 14] and Y2 O3 in MFIS-FETs is discussed. Finally, the effects of the polarization state and the leakage current of the YMnO3 on the memory retention time, which is considered to be the most serious issue for this device, are discussed.

2 Material Design of Ferroelectric and Insulator Layers for MF(I)S Capacitors In this section, the electrical behavior of an MFIS capacitor is simulated. The bias voltage applied to the top electrode is divided between the ferroelectric film, the insulator and the surface of the semiconductor. The distribution ratio depends on the dielectric capacitances of the ferroelectric film and of the semiconductor. Since the relationship between the dielectric constant of a ferroelectric material and the electric field is nonlinear, the P –E curve of the ferroelectric film was assumed to be given by Miller ’s formula [15, 16, 17] in this study. Figure 1 shows the energy band diagram and the potential distribution in the MFIS capacitor. The bias voltage applied to the top electrode (VG ) is described as follows: VG = VF + VI + ψS ,

(1)

where VF and VI are the voltages applied to the ferroelectric film and the insulator respectively, and ψS is the surface potential of the semiconductor. If the MFIS capacitor is ideal and excludes interface traps, space charge, etc., (2) is applicable according to Gauss’s law: QS = QF ,

(2)

Ferroelectric–Insulator–Semiconductor Junctions

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Fig. 1. (a) Potential distribution and (b) energy band diagram of an MFIS capacitor

where QS and QF are the surface charge densities of the semiconductor and the ferroelectric film, respectively. The QF defined by Miller’s formula is described by (3): VF /dF ± EC QF = ε0 εF VF /dF tanh , (3) ±EC / ln (1 + Pr /Ps ) / (1 − Pr /Ps ) where ε0 is the permittivity of free space, εF is the linear dielectric constant, Pr is the remanent polarization, Ps is the spontaneous polarization, EC is the coercive field and dF is the thickness of the ferroelectric film. The relationship between QS and ψS is given by 2εS kT qψS qψS − 1 × exp − QS = ∓ + 1/2 kT kT εS q 2kT 2 pp0 q 1/2 np0 qψS qψS + −1 , (4) exp − − pp0 kT kT where k is the Boltzmann constant, T is the absolute temperature, q is the magnitude of the electronic charge, εS is the permittivity of silicon, and np0 and pp0 are the carrier density of electrons and holes, respectively [18]. Since the surface charge density on the insulator (QI ) is also equal to QF according to Gauss’s law, the relationship between QF and VI is given by ε0 εI VI /dI = QF ,

(5)

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Fig. 2. Calculated results for (a) the relationship between VG (bias voltage) and VF , (b) the relationship between VG and the polarization of the ferroelectric layer, and (c) the high-frequency C–V curve. The thickness of the insulator layer is 0 nm (thick solid line), 30 nm (broken line) and 60 nm (thin solid line)

where εI and dI are the dielectric constant and the thickness of the insulator, respectively. Using these equations, the relationships between VG , QF , VF and ψS can be obtained. A calculation was performed for an MFIS capacitor consisting of a ferroelectric film with Ps = 1 µC/cm2 , Pr = 0.9 µC/cm2, EC = 50 kV/cm and εF = 20, an insulator film with εI = 14, which is equal to the dielectric constant of Y2 O3 , and an n-type semiconductor with a carrier density of 3 × 1015 cm−3 . The thickness of the ferroelectric film was fixed at 300 nm, and that of the insulator film was varied from 0 to 60 nm. Figure 2(a) shows the relationship between VG and VF . As dI becomes larger, the value of VG required to polarize the ferroelectric film becomes larger. Moreover, when VF is lower than the coercive voltage, the depolarization voltage is applied to the ferroelectric film. The depolarization voltage increases as dI increases. Figure 2(b) shows the relationship between VG and the polarization of the ferroelectric film (QF ). All the calculated loops have a kink near 0 µC/cm2 . The kink originates from the formation of a depletion layer at the surface of the semiconductor. As the thickness of the insulator increases, the hysteresis loop becomes inclined. Although the coercive volt-


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Fig. 3. Calculated results for (a) the relationship between the negative remanent polarization and PS , and (b) the relationship between PS and the VG required to apply twice the coercive voltage (3 V) to the ferroelectric layer. The thickness of the insulator layer was varied from 0 nm to 100 nm

age does not change, the absolute value of the remanent polarization for the MFIS capacitor (Pr ) decreases. Actually, it is impossible to measure such a P –E hysteresis in an MFIS capacitor. Recently we succeeded in measuring such a hysteresis using a low-frequency P –E measurement under light illumination [18]. High-frequency C–V curves were calculated using a theoretical equation reported by Sah et al. [19]. Figure 2(c) shows a calculated highfrequency C–V curve. With increasing dI , although the capacitance in the accumulation region decreases, no other changes are observed. It can be seen that the memory window of the C–V curve does not depend on the thickness of the insulator, because the memory window should be equal to twice the coercive voltage of the ferroelectric film (2EC × dF ). From the calculations of C–V curves, an increase in the thickness dI does not seem to affect the operation of the MFIS-FET. Together with the results shown in Figs. 2(a) and (b), however, an increase in dI makes the operating voltage higher and the remanent polarization lower, and cause a serious problem with the memory retention. To understand the effects of dI and Ps on the operation of MFIS capacitors in detail, the above calculations were replotted to show the relationship between Pr or Vg and Ps . Figure 3(a) shows the relationship between the negative Pr and Ps . dI is varied from 0 to 100 nm. From (4), since a negative Pr above 0.03 µC/m2 is required to make a strong inversion layer, a Ps above 0.2 µC/m2 is required. The negative Pr increases with increasing Ps . But the increase of Pr becomes smaller at larger dI . Figure 3(b) shows the relationship between Ps and the VG required to apply twice the coercive voltage (3 V) to the ferroelectric film. The required VG increases with increasing Ps and dI . If dI is 0 nm (namely an MFS capacitor) and ferroelectric films with a Ps larger than 10 µC/m2 can be used, ferroelectric films with large Ps become disad-

204


vantageous as dI increases. From Figs. 3(a) and (b), in this MFIS capacitor, a ferroelectric film with Ps ranging from 0.2 to 2 µC/m2 is desirable, and dI is allowed to be up to about 30 nm in the case. On the basis of these calculations, YMnO3 , with a Ps of 5.5 µC/m2 and an εr of 20, was selected as the ferroelectric material for the MFIS structure to be fabricated, and Y2 O3 was selected for the insulator layer.

3 Fabrication of YMnO3 Epitaxial Films YMnO3 thin films were deposited on (111) MgO, and (111) Pt/(0001) sapphire and [111]-oriented Pt/ZrO2/SiO2 /Si by a pulsed-laser-deposition (PLD) method. The MgO substrates were annealed at 1000 ◦C for 10 h in an oxygen flow to obtain a clean, stepped surface. A KrF excimer laser with a 248 nm wavelength was used. To measure the P –E hysteresis, epitaxial (111) Pt/(0001) sapphire substrates were used. The substrate temperature and the oxygen gas pressure were varied from 700 to 850 ◦C and 1 ×10−5 to 10−2 Torr, respectively. In some cases, ozone was introduced at a concentration of 4% in the O2 gas using an ozone generator. The laser power density was varied from 1.9 to 2.8 J/cm2. The thickness of the YMnO3 thin films was varied from 10 to 300 nm. The crystal structure of the films was analyzed by X-ray diffraction with CuKα radiation, and by reflection high-energy electron diffraction (RHEED). The surface morphology of the films was evaluated using atomic force microscopy (AFM) and scanning electron microscopy (SEM). The composition of the films was evaluated using energy-dispersive X-ray spectroscopy (EDX). Dielectric and ferroelectric measurements were conducted using MFM or MFIS configurations with a platinum top electrode with an area of 900 µm2 sputtered through a shadow mask. The leakage current was measured using a picoampere meter. The capacitance was measured using an LCR meter with a small ac amplitude of 25 mV at frequencies ranging from 20 Hz to 1 MHz. Measurements of the polarization and memory retention of MFM capacitors were performed using a Sawyer–Tower circuit or a ferroelectric test system (Radiant, RT66 A). The RHEED pattern of the film at the thickness of 10 nm showed a diffuse streak pattern, which indicates that an orientation distribution exists in the initial stages of YMnO3 growth. Therefore, the compositional deviation and crystallization process of the YMnO3 films in the initial stages were studied. The change in the film composition (Y/Mn ratio) with increasing thickness revealed that a Y-rich layer existed at film thicknesses below 50 nm. To optimize the film composition at a fixed thickness of 10 nm, the dependence on the laser power density and gas pressure were studied. A laser power density of more than 2.4 J/cm2 or an oxygen pressure of more than 1 ×10−3 Torr makes the YMnO3 stoichiometry correct at a thickness of 10 nm. It was also recognized that the use of ozone (4% in O2 ) improves the stoichiometry of the film. The optimized deposition conditions are as follows: a gas pressure


205

Fig. 4. XRD (a) and RHEED (b) and (c) patterns of epitaxial YMnO3 /Pt deposited under optimized conditions. The directions of the incident electron beam, (b) and (c) correspond to 1100 and 1¯ 210, respectively

(containing 4% ozone in oxygen) of 1 ×10−3 Torr, a laser power density of 2.4 J/cm2, a substrate temperature of 800 ◦ C and a laser repetition rate of 5 Hz. By optimizing the deposition conditions, highly oriented epitaxial films can be obtained. As shown in Fig. 4(a), the XRD intensity drastically increases, and the FWHM of the 0004 XRD rocking curve is also improved from 2◦ to 0.7◦ . The RHEED pattern shows an excellent streak pattern, as shown in Fig. 4(b). In the case of epitaxial YMnO3 /Pt, saturated P –E hysteresis was obtained, as shown in Fig. 5. Values of Pr of 1.7 µC/cm2 and Ec of 80 kV/cm are obtained, although the hysteresis is a little imprinted. The imprint phenomenon is caused by localized space charge, probably due to nonstoichiometry, including that of the oxygen. Although it has been revealed that a small amount of compositional distribution still remains, highly oriented epitaxial films with relatively square P –E hysteresis were obtained. The Pr and Ec of the epitaxial YMnO3 /Pt obtained are quite suitable for the operation of an MFIS capacitor. Other fundamental characteristics of the ferroelectric for memories, such as the endurance characteristics and the retention characteristics, were also evaluated for the epitaxial YMnO3 /Pt. The detailed results have been reported elsewhere [20]. Figure 6 shows the endurance characteristics of the epitaxially grown YMnO3 /Pt/sapphire at elevated temperatures. Since a pulse giving a field higher than Ec and longer than the domain-switching time is necessary to obtain the correct endurance property, a sine wave voltage giving an electric field of 600 kV/cm, with a frequency of 100 kHz, was applied to switch the polarization. It is encouraging that no degradation was observed for up to 1010 measured cycles even at 200 ◦C.

206


Fig. 5. P –E hysteresis of the epitaxial YMnO3 film on a Pt/sapphire substrate

Fig. 6. Endurance characteristics at elevated temperatures

4 Fabrication and Properties of Y2 O3 Films on Si We have succeeded in obtaining ferroelectric layers with suitable dielectric properties for an MFIS structure on epitaxially grown Pt on sapphire. However, ferroelectric layers with identical dielectric properties need to be obtained on Si. To obtain an excellent YMnO3 layer on Si, a Y2 O3 layer was inserted between the YMnO3 and the Si as an insulator [18]. Y2 O3 is known to have an Ia3-type crystal structure with a lattice constant of a = 1.0604 nm. The lattice mismatch between (0001) YMnO3 and (111) Y2 O3 is about 9%. This section describes the fabrication and the dielectric properties of epitaxial Y2 O3 layers on Si.


207

Fig. 7. RHEED patterns of Y2 O3 deposited at oxygen pressures of 1.0 ×10−5 Torr, (a) and 1.0 ×10−8 Torr (b) and (c). The directions of the incident electron beam in (b) and (c) correspond to 1¯ 11 and 11¯ 2, respectively

Y2 O3 thin films with a thickness of 20 nm were deposited by a pulsedlaser deposition method on n-type (111) Si substrates. The (111) Si substrates were chemically cleaned in a hot solution of NH4 OH:H2 O2 (1:1) and soaked in a hot solution of HCl:H2 O2 (2:1). Finally, dipping in a 1% HF solution to remove the surface oxide was performed. The substrate temperature was fixed at 500 ◦C. An unfocused laser beam, with an energy density of 0.4 J/cm, was used for deposition with a pulse rate of 1 Hz. O2 gas mixed with O3 (less than 4% O3 , total gas pressure 1.0 ×10−8 Torr to 5.0 ×10−2 Torr) was introduced during deposition. For some samples, rapid thermal annealing (RTA) was performed at 1 atm in an O2 ambient. The C–V characteristics were measured using an LCR meter. Figure 7 shows RHEED patterns of Y2 O3 films grown at different oxygen gas pressures during deposition. At a gas pressure of 1.0 ×10−5 Torr, the observed streak pattern does not change for any direction of incidence of the electron beam. This means that the Y2 O3 film is not epitaxial but a [111]oriented polycrystalline film. In contrast, at a gas pressure of 1.0 ×10−8 Torr, the streak pattern changes with the direction of the incident electron beam, as shown in Figs. 7(b) and (c). This indicates that the film grows epitaxially on the Si substrate. The surface morphology of the Y2 O3 /Si epitaxial film observed by SEM was flat and smooth, and an RMS roughness of 0.14 nm was obtained by AFM measurements. C–V measurements revealed that the dielectric permittivity was about 15, which suggests that there is no SiO2 layer at the interface. Transmission electron micrographs and diffraction patterns also supported the proposition that the film is epitaxial without an SiO2 layer [20]. However, a flat-band shift of −3.4 V due to oxygen deficiency was observed. The C–V curve also indicated a charge-injection-type hysteresis with an interfacial state density of 1.1 ×1013 /cm2 , which is much higher than that of thermal silicon oxide. In order to compensate the oxygen deficiency of the film, postannealing in an O2 ambient was attempted at various temperatures. When the annealing temperature was increased, although the flat-band voltage increased, the capacitance in the accumulation region decreased. These results must be caused by the presence of an interfacial SiO2 layer, which is formed before compensating the oxygen deficiency of Y2 O3 . It may be indispensable to compensate the oxygen vacancies during deposition, while maintaining epitaxial growth.

208


Fig. 8. C–V curve of Y2 O3 deposited directly on Si with 3 ML-thick initial layer. Annealing in forming gas was carried out at 500 ◦ C. The equivalent oxide thickness (EOT) is calculated to be 1.33 nm

Therefore, we introduced a two-step growth process. An initial Y2 O3 layer was deposited in an O2 ambient of 1.0 ×10−8 Torr to protect against surface oxidation of the Si substrate, and subsequent Y2 O3 deposition was performed in an oxygen atmosphere ranging from 1 ×10−7 Torr to 1 ×10−2 Torr. The thickness of the initial layer was varied from 0.5 to 5 monolayers. Insitu RHEED observations revealed that epitaxial films could be grown when the thickness of the initial layer was larger than 1 monolayer. Moreover, the RHEED pattern for a film with three initial monolayers apparently exhibited sharp streaks, which means that the crystallinity of this sample has been considerably improved. As for the electrical properties, the C–V characteristics of films with three initial monolayers which were prepared at an oxygen pressure of 5.0 ×10−2 Torr showed a shift of the flat-band voltage from the theoretical C–V curve of −1.37 V. In addition to this, the observed dielectric constant (εr = 15) is well matched to that of bulk Y2 O3 . However, the interfacial state density (1.0 ×1013 /cm2 ) changed very little, in comparison with films made without the two-step process [21]. After annealing in forming gas (5% H2 in N2 ), a Pt/Y2 O3 /Si capacitor with excellent dielectric properties could be obtained (Fig. 8). The chargeinjection-type hysteresis disappeared and the decreasing in the capacitance in the accumulation region was not observed. The leakage current density was around 1 ×10−6 A/cm2 at 1 V.

5 Fabrication of YMnO3 /Y2 O3 /Si Capacitors To prepare he epitaxially grown (0001) YMnO3 films on (111) Y2 O3 /(111) Si capacitors, YMnO3 films were deposited on the epitaxial (111) Y2 O3 /(111) Si described in Sect. 4. The thickness of the Y2 O3 layer was fixed at 20 nm


209

Fig. 9. XRD pattern (a) and RHEED patterns (b) and (c) of epitaxially grown 100 YMnO3 /Y2 O3 /Si. The incident electron beam in (b) and (c) corresponds to 1¯ and 1¯ 210, respectively

in order to obtain the fully polarized ferroelectric domain structure calculated in Sect. 2. The memory retention characteristics of MFIS capacitors were measured using an LCR meter. The retention characteristics were characterized by the change in the capacitance at the flat-band voltage after a polarizing voltage was applied. The retention time was defined as the time when the ratio of the capacitances after the capacitor had been charged by a positive and a negative electric field became 50% of the initial difference. Since nonferroelectric polarizations such as a space charge and an interfacial polarization might be included in the capacitor, a short-pulsed voltage (100 ms) was used to minimize these effects. Figure 9 shows (a) an XRD pattern, and (b) and (c) RHEED patterns of a YMnO3 film on epitaxial Y2 O3 /Si. An epitaxially grown YMnO3 film was obtained on (111) Si. The crystallinity of the epitaxial YMnO3 film is quite excellent even on Si. The FWHM of the XRD rocking curves of the epitaxial and oriented YMnO3 was 0.7◦ and 2.2◦ , respectively. The FWHM value for the epitaxial film on Si is identical to that for an epitaxial film on sapphire. On the basis of these XRD and RHEED measurements, it can be stated definitely that the crystallinity of the epitaxial YMnO3 on Si is equivalent to that of YMnO3 on sapphire. Figure 10(a) shows the C–V characteristics of the epitaxial YMnO3 on Y2 O3 /Si. A ferroelectric type C–V hysteresis loop with a memory window of 4.8 V can be recognized. This value is nearly equal to that of 2Vc in the P –E hysteresis of epitaxial YMnO3 on Pt/sapphire. The memory window width is also identical to that measured by pulsed C–V measurement, which can subtract the effect of space charge [14]. The change in the memory window width with increasing applied voltage behaves as predicted from the behavior of epitaxial YMnO3 on Pt/sapphire. Both of these systems have a similar

210


Fig. 10. (a) Conventional C–V and (b) pulsed C–V curves of an epitaxial YMnO3 /Y2 O3 /Si capacitor

tendency and saturate above 13 V. This result indicates that the ferroelectric domain state as a function of the applied voltage is identical and that it is fully polarized even in YMnO3 on Y2 O3 /Si. These results support the adequacy of our simulations described in Sect. 2.

6 Investigation of Retention Characteristics of YMnO3 /Y2 O3 /Si Capacitors As described in Sect. 2, a small depolarization field (Ed ) compared with Ec of the ferroelectric layer is required for obtaining a long memory retention time. Decreasing the thickness of the ferroelectric layer and increasing the insulator thickness and the carrier density of the semiconductor cause Ed to increase [22, 23, 24, 25, 26, 27]. The ferroelectric domain structure in the ferroelectric layer might be also important for long retention. If the ferroelectric domains are not polarized fully, the polarization might become unstable and easy to depolarize. Recently, the relationship between the retention properties and the leakage current has been discussed because the retention properties depend on the retained charge density in the ferroelectric layer. In this section, the influence of the ferroelectric domain structure on the retention properties is studied. Dielectric measurements were conducted using MFM or MFIS configurations with an area of 900 µm2 sputtered through a shadow mask. The influence of the polarization state on the retention properties was investigated. We selected a polarizing voltage of ±5 V, giving a minor loop, ±10 V, giving an unsaturated polarization, and ±15 V, giving a saturated polarization, as shown in Fig. 5. The values of Pr and Ec at ±5 V in the MFIS device were 0.15 µC/cm2 and 12 kV/cm, respectively. These values were not sufficient. At ±10 V, although the ferroelectric polarization was


211

Fig. 11. The memory retention characteristics of a YMnO3 /Y2 O3 /Si epitaxial structure. The polarizing voltage was (a) ±5 V, (b) ±10 V and (c) ±20 V

unsaturated, a Pr of 0.45 µC/cm2 and an Ec of 55 kV/cm were enough to maintain memory retention. The ferroelectric domains were fully polarized at ±15 V. Figure 11 shows the memory retention characteristics of an epitaxially grown YMnO3 /Y2 O3 /Si capacitor at various bias voltages. The polarizing pulse applied to the capacitor was 100 ms in duration. In Fig. 11(a), the retention time is less than 10 s. The retention time at ±10 V (Fig. 11(b)) with an unsaturated polarization and at ±15 V (Fig. 11(c)) with a saturated polarization was 1 ×103 s and over 1 ×104 s, respectively. These results suggest that a fully polarized domain structure can lead to a long memory retention time.

7 Influence of Leakage Current on the Retention Characteristics of YMnO3 /Y2 O3 /Si Capacitors Although the stability of the polarization in a ferroelectric thin film on a semiconductor is not yet understood clearly, it is obvious that to reduce the depolarization field, increases in the capacitance per unit area of the insulator layer, the coercive electric field of the ferroelectric film and the thickness of the ferroelectric film are required [22, 23, 24, 25, 26, 27]. In device applications, the first two are important because an increase in the thickness results in an increase in the switching voltage. Recently, long retention characteristics of the polarization (> 104 s) have been observed in some samples which were designed taking into account the need for a reduction of the depolarization field [28]. This progress also reveals the relationship between the retention properties and the leakage current of MFIS capacitors. It has been reported that the Schottky current affects the

212


Fig. 12. C–V characteristics of an epitaxial YMnO3 /Y2 O3 /Si capacitor

retention characteristics [22]. Since the retention characteristics depends on the retained charge density in the ferroelectric layer, it is reasonable that the leakage current influences the retention properties. When the space charge is rearranged inside the ferroelectric layer so that the polarization is neutralized, the polarization apparently disappears, although the polarization of the ferroelectric layer is retained. In this section, the influence of the leakage current on the retention properties of YMnO3 /Y2 O3 /Si capacitors is discussed in detail. Figure 12 shows C–V characteristics of an epitaxial YMnO3 /Y2 O3 /Si capacitor. The C–V characteristics show a ferroelectric-type hysteresis with a saturated memory window at ±13 V. Figure 13(a) shows the I–V characteristics of the capacitor. The leakage current density of the as-deposited capacitor below 3 V was below 10−7 A/cm2 . The leakage current of YMnO3 films originates from excess oxygen, as reported in [21]. Therefore, annealing in N2 for 10 min was attempted. As shown in Fig. 13(b), the leakage current density in the low-electric-field region could be decreased to 2 ×10−9 A/cm2 by N2 annealing. In addition, the leakage current density of the capacitor annealed in nitrogen increased after annealing in an oxygen ambient (Figs. 13(c) and (d)). This result corresponds well to the fact that the leakage current of YMnO3 films is attributed to excess oxygen. Figure 14 shows the memory retention characteristics of these YMnO3 /Y2 O3 /Si capacitors with various leakage currents. Although the leakage current changed with annealing, saturation of the memory window was observed in the C–V characteristics. The retention time of the asdeposited capacitor was about 103 s (Fig. 14(a)). A capacitor with a lower leakage current shows a longer retention time. By annealing in a nitrogen ambient, the retention time was prolonged to over 104 s (Fig. 14(b)). As shown in Fig. 14, a change in the leakage current density is obvious in the low-voltage region. In contrast, such a change is not obvious in the high-voltage region.


213

Fig. 13. I–V characteristics of epitaxial Pt/YMnO3 /Y2 O3 /Si capacitors. (a) Asdeposited YMnO3 /Y2 O3 film, (b) N2 -annealed, (c) O2 -annealed (3 min) and (d) O2 -annealed (6 min)

In order to investigate the relationship between the retention properties and the leakage current in detail, the I–V characteristics were analyzed using several leakage current mechanisms [28]. Since the YMnO3 and Y2 O3 layers have different dielectric properties, the electric field applied to the each layer must be different. To estimate each electric field, the dielectric constants of the YMnO3 and Y2 O3 layers were assumed to be 75 and 10, respectively, on the basis of the capacitance measurement. The dielectric constant of YMnO3 was calculated using not the capacitance measured by the LCR meter but the polarization hysteresis loop, because the actual induced charge in a ferroelectric film surface cannot be calculated from the linear component of the dielectric constant. Using the thicknesses of the YMnO3 and Y2 O3 layers (400 and 20 nm, respectively), the ratio of the electric fields applied to the two layers was calculated as 73:27. First, the I–V characteristics of the capacitor were analyzed using the Schottky and Poole–Frenkel (P–F) emission models. Figures 16(i) and (ii) show Schottky plots of the I–V characteristics obtained using an electric field applied to the YMnO3 and the Y2 O3 layer, respectively. Linear relations were obtained at high electric fields. The dielectric constant was calculated from Figs. 16(i) and (ii) using the equation for the Schottky emission Jsh ,

q q/4πεi ε0 √ qΦB 2 + E, (6) ln Jsh /T ∼ − kT kT where εi is the dielectric constant and ΦB is the barrier height. The dielectric constants calculated from Figs. 15(i) and (ii) are 0.2 and 1.6, respectively, and are obviously too low compared with the dielectric constants of YMnO3 and Y2 O3 . This suggests that Schottky emission is not the dominant leakage mechanism. Figures 16(i) and (ii) show P–F plots of the I–V characteristics

214


Fig. 14. Memory retention characteristics of epitaxial Pt/YMnO3 /Y2 O3 /Si capacitors. (a) As-deposited YMnO3 /Y2 O3 film, (b) N2 -annealed, (c) O2 -annealed (3 min) and (d) O2 -annealed (6 min). The voltage and time used for memorizing the status were 15 V and 100 ms, respectively

Fig. 15. Schottky plots of the I–V properties obtained using the electric field (i) the YMnO3 , and (ii) the Y2 O3 layer. (a) As-deposited YMnO3 /Y2 O3 film, (b) N2 -annealed, (c) O2 -annealed (3 min) and (d) O2 -annealed (6 min)

obtained using an electric field applied to the YMnO3 and the Y2 O3 layer, respectively. In both plots, although the slopes of the plots at low electric field are negative, linear relations with a positive slope were obtained in the high-electric-field region. From the equation for the P–F emission JPF , q q/πεi ε0 √ qWt + ln (JPF /E) ∼ − E, (7) kT kT where Wt is the barrier height, in the high-electric-field region, the dielectric constants calculated using the electric fields in YMnO3 and Y2 O3 are 1.2 and


215

Fig. 16. P–F plots of the I–V properties obtained using the electric field in (i) the YMnO3 layer and (ii) the Y2 O3 layer. (a) As-deposited YMnO3 /Y2 O3 film, (b) N2 -annealed, (c) O2 -annealed (3 min) and (d) O2 -annealed (6 min)

9.1, respectively. The latter is a reasonable value for the dielectric constant of Y2 O3 . Therefore, this indicates that the dominant leakage current mechanism for the Pt/YMnO3 /Y2 O3 /Si capacitor in the high-electric-field region is P–F emission from the Y2 O3 layer. It should be noted that the effect of annealing on the leakage current is small in the high-electric-field region. It is suggested that the annealing affects the electrical properties of YMnO3 . Since a small voltage (∼ 1 V) is applied to the ferroelectric layer owing to the depolarization field, the leakage current mechanism at low electric field is important in investigating the memory retention mechanism. Figure 17 shows log J vs. log V plots for Pt/YMnO3 /Y2 O3 /Si capacitors. Since the slope of the plot in the low-electric-field region is nearly 1, the leakage current at low electric field can be explained by ohmic conduction [29]. The effect of annealing on the leakage current is clearly observed in the low-electric-field region. From the results for the retention characteristics shown in Fig. 14, it is suggested that the ohmic conductance at low voltage is very much related to the retention properties and that decreasing the ohmic conductance at low voltage should be effective in prolonging the memory retention time. Since it is known that the ohmic conductance at low voltage is caused by charge trapping by defects in the film, we attempted to evaluate the defect density, which affects the memory retention properties. In this study, pseudoisothermal capacitance transient spectroscopy spectra were replotted from the retention characteristics. In the case of a normal isothermal capacitance transient spectroscopy (ICTS) spectrum, an instantaneous change of the capacitance is measured under the inversion condition of an MIS capacitor to detect the emission from the traps existing in a semiconductor. In contrast, a pseudo-ICTS spectrum, which is obtained from the retention characteristics of an MFIS capacitor, is the change of the capacitance over

216


Fig. 17. Plots of log J vs. log V for Pt/YMnO3 /Y2 O3 /Si capacitors. (a) Asdeposited, (b) N2 -annealed, (c) O2 -annealed (3 min) and (d) O2 -annealed (6 min)

Fig. 18. Pseudo-ICTS spectra of (a) Asdeposited, (b) N2 -annealed, (c) O2 -annealed (3 min) and (d) O2 -annealed (6 min) samples

a long time ( 1 s) without an applied bias voltage. In addition, the inversion condition of the MFIS capacitor is maintained not by a bias voltage but by the remanent polarization of the ferroelectric layer. Therefore, the pseudo-ICTS spectrum should reflect the status of the traps in the ferroelectric layer, because there is a relationship between the remanent polarization and the traps. The ICTS signal was derived using the following formula: S (t) = tdC 2 / dt = [qε0 εS NT /2 (Vbi − V ) τ ] [t exp (−t/τ )] ,

(8)

where the S (t) is the ICTS signal; NT and τ are the trap density and the time constant of the carrier emission, respectively. Figure 18 shows pseudo-ICTS spectra of the Pt/YMnO3 /Y2 O3 /Si capacitors. A single peak is observed in each spectrum except for the N2 -annealed sample. It seems that the trap density of the N2 -annealed capacitor is too low to detect a signal in this measurement time. The trap density NT was calculated from the intensity and the value of τ of the peak of the pseudoICTS spectrum. The trap densities of the (a) as-deposited, (c) O2 -annealed


217

(3 min) and (d) O2 -annealed (6 min) samples were of the order of 1015 cm−3 . The trap density of the Pt/YMnO3 /Y2 O3 /Si capacitors decreases as the leakage current at low electric field decreases. From these results, the mechanism for the vanishing of the stored charge in the Pt/YMnO3 /Y2 O3 /Si capacitors can be concluded to be as follows. The traps existing in the YMnO3 layer underlie the mechanism and are also responsible for the relaxation current, which is observed as a leakage current at low electric field. During the memory retention, the remanent polarization of the YMnO3 is neutralized by charge trapping induced by the leakage current. Therefore, the retention time can be prolonged by decreasing the leakage current, which can be done by decreasing the trap density of the YMnO3 layer. Further developments regarding YMnO3 have been reported elsewhere [30, 31, 32].

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Index

band diagram, 200, 201 C–V curve, 203 capacitance–voltage curve, 203 defect density, 215 depolarization field, 210 endurance characteristics, 205 energy band diagram, 200, 201 EOT, 208 epitaxial film, 204 epitaxial Y2 O3 , 206 equivalent oxide thickness, 208 FeRAM, 199 ferroelectric-gate FET, 199 flat-band voltage, 207–209 forming gas, annealing in, 208 high-frequency C–V curves, 203 ICTS, 215 imprint phenomenon in hysteresis, 205 interface state density, 200 interfacial polarization, 209 isothermal capacitance transient spectroscopy, 215 leakage current, 200 memory retention, 209 memory window, 203

metal–ferroelectric–insulator– semiconductor structure, see MFIS structure MFIS structure, 199 MFIS-FET, 200 Miller’s formula, 200 ohmic conduction, 215 oxygen deficiency, 207 P –E hysteresis loop, 200, 203–206, 209 PLD, 204 Poole–Frenkel emission, see asoFrenkel– Poole current213 potential distribution, 200, 201 pulsed-laser-deposition, 204 pulsed C–V measurement, 209 rapid thermal annealing, 207 remanent polarization, 199, 216 RHEED, 204 RTA, 207 Schottky emission, 213 space charge, 200, 205, 209, 212 two-step growth process, 208 Y 2 O3 epitaxial, 206 Y2 O3 , 200 YMnO3 , 200 YMnO3 /Y2 O3 /Si capacitor, 208

Improvement of Memory Retention in Metal–Ferroelectric–Insulator–Semiconductor (MFIS) Structures Masanori Okuyama and Minoru Noda Department of Systems Innovation, Graduate School of Engineering Science, Osaka University, Machikaneyamacho 1-3, Toyonaka, Osaka 560-8531, Japan {okuyama,noda}@ee.es.osaka-u.ac.jp Abstract. A simple model has been derived to investigate the retention characteristics of an MFIS structure by considering the effects of currents through the insulator and ferroelectric layers. Simulated curves for the hold time dependence of the capacitance can reproduce experimental curves. Band diagram simulations for the MFIS structure have indicated that the retention characteristics can be severely degraded if the currents through the insulator and ferroelectric layers exceed certain values. A slow absorption current in the ferroelectric layer is also considered to degrade the retention. It is concluded from comparison of the experimental data with the simulation that the most serious origin of the retention characteristics can be attributed to the Schottky current through the metal–ferroelectric junction. In order to decrease the charge injected from the top metal electrode into the ferroelectric layer, the physical model for the MFIS structure has been modified and extended to an MIFIS structure. The calculation indicates that insertion of an ultrathin insulator film between the top metal electrode and the ferroelectric layer can be very effective in providing a longer retention time than that of the original MFIS structure. In order to increase the initially stored charge in the MFIS structure and reduce the depolarization field, substitution of a high-k film for the insulator layer in the MFIS structure has been investigated. The calculation indicates that a high-k insulator layer with εi = 30 is expected to extend the MFIS retention time substantially. The effects of O2 annealing on SBT thin films have been studied experimentally. The O2 annealing improved the polarization retention characteristics of Pt/SBT/Pt capacitors, and decreased the current density of the Schottky contribution by an increase of the barrier height in the Pt/SBT/Pt capacitor. Consequently, the O2 annealing is effective in improving the capacitance retention characteristics of MFIS structures. Moreover, an MFIS structure using an SBT film treated by RTA shows a very long memory retention time of 105 s, which can be extrapolated to 1 year. In order to clarify the reason why O2 annealing suppresses the current, UVPYS analysis has been carried out on SBT films before and after O2 annealing. We obtained the result that the barrier height for holes at the metal–ferroelectric junction is enhanced by the O2 annealing and the Schottky current is suppressed.

M. Okuyama, Y. Ishibashi (Eds.): Ferroelectric Thin Films, Topics Appl. Phys. 98, 219–241 (2005) © Springer-Verlag Berlin Heidelberg 2005

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Masanori Okuyama and Minoru Noda

1 Introduction Recently, much attention has been paid to metal–ferroelectric–insulator– semiconductor (MFIS) junctions as a promising gate stack structure for practical use in field-effect-transistor (FET)-type nonvolatile memories. The MFIS-FET shows superior features, such as a good scaling-down rule and nondestructive readout operation. However, many MFIS structures have the drawback that memory retention is short, although a few ferroelectric-gate FET memories have shown fairly long retention times [1, 2]. It is considered that the short retention time can be attributed to several origins, such as polarization relaxation caused by an intrinsic depolarization field, and polarization shielding by mobile charges. The intrinsic depolarization field is produced even in the hold state of zero bias voltage, by voltages induced in the insulator and semiconductor corresponding to the residual polarization of the ferroelectric layer, and has a direction opposite to the polarization and reduces the memory effect. Among the origins of the retention degradation, charge injection into the interface between the insulator and ferroelectric layers is one of the most plausible reasons for polarization shielding, and so the capacitance retention of MFIS structures has mainly been studied by considering charge injection into the ferroelectric layer from the metal electrode side and semiconductor side. It has been found from various experimental results that the memory retention can be elongated very much by oxygen annealing of the MFIS structure. Moreover, a long retention time of more than 105 s has been realized by rapid thermal annealing. This improvement means that this charge injection is suppressed by the oxygen annealing, which might affect electronic properties such as the barrier heights of the junctions and the Fermi levels of the ferroelectric and insulator layers, and the surface roughness of the films and the composition of the ferroelectric film. So, the electronic structure of the ferroelectric film is very important and has been studied by ultraviolet photoyield spectroscopy (UV-PYS). The barrier height at the metal–ferroelectric junction is increased by oxygen annealing, and long retention has been achieved.

2 Theoretical Analysis of Memory Retention in MFIS Structures 2.1 Capacitance Retention Characteristics Figure 1 shows an example of the capacitance aging of an MFIS structure. A SrBi2 Ta2 O9 (SBT) thin film was used as the ferroelectric layer and was prepared by pulsed laser deposition (PLD), as SBT films have attracted much interest as one of the best candidates for ferroelectric nonvolatile memories because of their fatigue-free properties and adequate remanent polarization [3]. The band profiles are also illustrated, neglecting some realistic properties

Improvement of Memory Retention

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Fig. 1. An example of capacitance retention and simplified band profiles for an MFIS structure

such as the internal field at zero bias voltage and the space charge. These profiles can be classified into three typical hold states. The ‘off’ state is obtained just after a short positive pulse of bias has been applied to the gate electrode. The ‘on’ state is obtained just after a negative pulse of bias has been applied. After the structure has been held at a certain voltage for a sufficient time, the retained data is lost, as seen in the ‘aged’ state of the capacitance vs. hold time characteristic. In the aged state, the polarization in the ferroelectric layer cannot control the Si surface potential. This noncontrollability is attributed to phenomena such as attenuated polarization of the ferroelectric layer, and polarization shielding by mobile charges consisting of electrons, holes and ions under the influence of the depolarization field. We can suggest four plausible origins of the degradation of the retention characteristics from consideration of various phenomena: (1) insufficient polarization; (2) polarization relaxation of the ferroelectric; (3) ion drift; and (4) leakage current, which stores interface charge, shielding the polarization. Possibility (1) can be avoided by application of a sufficiently large voltage to the MFIS structure, whereby the ferroelectric is polarized fully. For possibility (2), we must ask whether the switched polarization can be relaxed thermally under the influence of the depolarization field. The remanent polarization of an annealed SBT film is not degraded very much, as shown in Sect. 4, and so relaxation is not a serious origin of the retention problem. For possibility (3), ion drift is estimated to have a short response time of several tens of seconds, as reported in our previous work [4], and so relates little to the long-term retention. Therefore, possibilities (1)–(3) are assumed to be negligible in this work. Charge injection from the top metal electrode and the semiconductor into the interface between the insulator and the ferroelectric layer has been studied as one of the significant origins of the retention degradation of MFIS structures. In this section, we describe inves-

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tigations of effect of currents through the ferroelectric and insulator layers on the retention characteristics of MFIS structures [5, 6, 7, 8, 9, 10, 11, 12, 13, 14]. 2.2 Theoretical Studies of Band Profile and Retention Degradation of MFIS Capacitors 2.2.1 Construction of MFIS Model and Analysis Method Retention degradation of an MFIS capacitor has been simulated by obtaining its band diagram. Several simultaneous equations were solved numerically for a sequence of time steps until convergence was obtained in the field distribution [15]. It was assumed that the currents through the ferroelectric and insulator layers were dependent only on the fields applied to those layers. Some basic equations in the one-dimensional case can be written as dQinj = Jf (Ef , t) − Ji (Ei ) : current continuity equation, dt −Pd − Qinj − Qsi : Gauss’s law for the ferroelectric layer, Ef = 0 f −Qsi Ei = : Gauss’s law for the insulator layer 0 i

(2)

Ef df + Ei di + Vsi + Vfb = Vg ,

(4)

(1)

(3)

and

where Ef and Ei are the electric fields in the ferroelectric and insulator layers, respectively; t is the time; Jf (Ef , t) is the current density through the ferroelectric layer under the influence of Ef at t; Ji (Ei ) is the current density in the insulator layer under the influence of Ei ; Pd is the ferroelectric polarization; ε0 is the dielectric constant of free space; and εf and εi are the relative dielectric constants of the ferroelectric and insulator layers, respectively. Qinj is the charge density injected between the ferroelectric and the insulator layers, and QSi is the charge density on the surface of the silicon substrate; df and di are the thicknesses of the ferroelectric and the insulator layers, respectively. VSi is the surface potential of the silicon substrate, Vfb is the flat-band voltage for the MFIS structure and Vg is the voltage applied to the gate metal. Jf (Ef , t) has been assumed to be Jf (Ef , t) = Jf (Ef , 0) t−β .

(5)

β = 0.52 was obtained experimentally, as shown in Fig. 2(a) [15], by using a real capacitor consisting of Al/SBT/Pt at a constant field of Ef = 50 kV/cm, where the SBT thin film was prepared by pulsed laser deposition (PLD) with a stoichiometric SBT target. Jf (Ef , 0) is the sum of two components, as shown in Fig. 2(b) [15]:


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Fig. 2. Current densities obtained experimentally in an Al/SBT/Pt capacitor. Dependence of current density on (a) hold time and (b) electric field f f Jf (Ef , 0) = JSk + JF–N ,

(6)

f f where JSk and JF–N denote the Schottky emission current density, dominant at lower fields, and the Fowler–Nordheim emission current density, dominant at higher fields, respectively. Ji (Ei ) has also been assumed to be given by i i + JF–N , Ji (Ei ) = JSk

(7)

i which is mainly composed of the Schottky (JSk ) and the Fowler–Nordheim i f i f i , JF–N and JF−N are well (JF–N ) emissions, in addition to Jf (Ef , 0). JSk , JSk known to be dependent on the voltage applied to the ferroelectric (Vf ) and the voltage applied to the insulator (Vi ) layer, and on the Schottky barrier height (φB ) as follows [16]: a Vf,i − qφB f,i 2 (8) JSk ∝ T exp kT

and f,i JF–N

∝

2 Vf,i exp

−b (qφB )3/2 Vf,i

,

(9)

where q is the elementary charge; a and b are constants independent of Vf , Vi and φB ; T is the absolute temperature; and k is the Boltzmann constant. In this study, Pd has been assumed to be described by Miller’s equations [17] as follows: Pd− (Ef ) = −Pd+ (−Ef ) and Pd+ (Ef ) = Ps tanh

(Ef − Ec ) 2δ

(10) ,

(11)

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where −1 1 + Pr /Ps δ = Ec log . 1 − Pr /Ps

(12)

In (10), the plus sign refers to the branch of the polarization for a positivegoing field, and the minus sign refers to a negative-going field. Pr is the remanent polarization, Ps is the spontaneous polarization and Ec is the coercive field. After the potential distribution of the MFIS structure for the initial ferroelectric polarization had been obtained, calculations were carried out iteratively using (1)–(12). Time-dependent electrical characteristics of MFIS structures were numerically obtained by repeating a sequence of the calculations described above with a time increment. In this study, df = 400 nm, di = 10 nm, Vfb = 0 V, εf = 50, εi = 3.9 and T = 300 K were used. A p-type silicon substrate with a uniform doping concentration of Na = 1015 cm−3 , a value of the spontaneous polarization of Ps = 1.2 µC/cm2 , a remanent polarization of Pr = 1.0 µC/cm2 and a coercive field of Ec = 50 kV/cm were assumed. 2.2.2 Calculated Band Diagrams The MFIS structure was held at zero gate voltage after it had been used as a memory cell by applying +10 V or −10 V during a write cycle. The assumed current through the ferroelectric layer in the MFIS structure was as large as about 2 ×10−9 A/cm2 at a field of 10 kV/cm with a time dependence of t−0.52 . The assumed current though the insulator layer was about 2 ×10−15 A/cm2 at a field of 1 MV/cm, which is supported by studies on a good SiO2 thin film [18]. The degradation process modeled in this study was characterized by the time dependences of several basic parameters, as indicated in Fig. 3 [14]. In the initial state at t = 0, the ferroelectric layer in the MFIS structure has a remanent polarization, obtained at zero voltage in the defined hysteresis loop. When the MFIS structure is aged, the absolute values of Ef decrease, as shown in Fig. 3(a), and this results in a decrease of the injected currents Jf (Fig. 3(b)). The final state of the MFIS structure shows almost zero electric field in all of the ferroelectric, insulator and semiconductor layers. The time dependence of the total capacitance of the MFIS structure has been calculated using the calculated band profile. The calculated time dependences of the capacitance and of the band diagram for Vg = 0 V after writing data at Vg = ±10 V are shown in Fig. 4. In the figure, (a) represents a fully written state, (b) represents an intermediate state, described as a case of depletion, and (c) represents an equilibrium state, described as an aged state. These diagrams indicate that charge injected from the top metal electrode into the ferroelectric layer in the MFIS structure (Qinj ) plays the main role in reducing VSi and Ei by becoming gathered into the valley of the potential.


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Fig. 3. Calculated time dependences of basic parameters in the MFIS structure with memory states written at a gate voltage of Vg = 10 V and −10 V. Hold time dependences of (a) the electric field in the ferroelectric layer, and (b) the current density through the ferroelectric layer

This means that reduction of Qinj is an effective way to increase the retention time. The value of Qinj can be reduced by decreasing Ji (Ei ) and Jf (Ef , t). 2.3 Effects of Currents Through the Ferroelectric and Insulator Layers on Retention Characteristics of MFIS Structures The effects of Ji (Ei ) and Jf (Ef , t) on the retention characteristics of an MFIS were investigated. The effects of εi and the ferroelectric absorption current density on Ji (Ei ) and Jf (Ef , t) were also investigated. The retention time was defined as the time when the capacitance change of the written MFIS structure becomes half of the initial value. 2.3.1 Effects of Schottky Current Through Insulator Layer The Ji (Ei ) dependence of the retention time was investigated for an MFIS structure with all the other parameters being fixed. The Schottky emission i ) contributes mainly to Ji (Ei ) because Ei is less than current in (7) (JSk 1 MV/cm for Vg = ±10 V. Ji (Ei ) is increased to AJi0 (Ei ), in which Ji0 (Ei ) is the insulator current used in the analysis in Sect. 2 and is much smaller than Jf (Ef , t) [15]. Time-dependent capacitances for various values of A have been calculated and are shown in Fig. 5. The retention time for A > 104 decreases rapidly as A increases, while the currents for A < 104 exhibit an almost constant maximum retention time of 5 ×103 s. This result implies that if Ji (Ei ) is less than some given value for A ≈ 104 it does not significantly affect the retention time; however, when Ji (Ei ) becomes larger than that value, the retention characteristics are seriously degraded. If A ≈ 106 is assumed, as indicated by the leakage current through an SiO2 layer grown by pyrogenic oxidation at 750 ◦ C [19], the retention characteristics for the MFIS system can be expected to be much worse than those discussed in this study.

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Fig. 4. Capacitance retention characteristics and band diagrams for an MFIS consisting of an SBT/SiO2 /pSi heterostructure: (a) inversion state, (b) depletion state and (c) aged state

Fig. 5. Capacitance retention for various values of the proportionality factor of Ji (Ei ), A

2.3.2 Effects of Schottky Current Through Ferroelectric Layer The Jf (Eve , 0) dependence of the retention time was investigated with all the f ) contributes other parameters being fixed. The Schottky current in (6) (JSk mainly to the current in the ferroelectric Jf (Eve , 0), because the absolute field applied to the ferroelectric layer is less than 40 kV/cm for the value of Vg = ±10 V used in this study. A proportionality parameter B was defined


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Fig. 6. Capacitance retention for various values of proportionality factor of Jf (Ef , 0), B

Fig. 7. Capacitance retention for various values of β

to describe how much current through the ferroelectric layer was observed, such that Jf (Eve , 0) = BJf0 (Eve , 0). Jf0 (Eve , 0) was obtained experimentally and used in the analysis described in Sect. 2 [15]. When B = 1, which means Jf (Eve = 35 kV/cm, 0) ≈ 10−8 A/cm2 , the time dependence of the capacitance for the modeled MFIS structure shows good agreement with the experimental results for the Al/SBT/SiO2 /Si capacitor. Figure 6 shows that the retention time for B > 10−3 decreases rapidly with an increase of B, while the current for B < 10−3 corresponds to almost the maximum, constant retention time of 3 ×108 s. This result implies that a value of Jf (Eve , 0) less than some given value (corresponding to B ≈ 10−3 ) does not significantly affect the retention time; however, if Jf (Eve , 0) becomes larger than that value, seriously degraded retention characteristics are observed. 2.3.3 Effects of Absorption Current in Ferroelectric Layer The time dependence of the current through the ferroelectric layer in the MFIS structure was also studied. The absorption current Jf (t) decays exponentially with time, as shown in (5). Retention characteristics for various values of β are shown in Fig. 7. A large β gives remarkably long retention times, even when the initial current at t = 0 is constant. The results mean that the total charge, which is the integral of the current, is the essential origin of the retention degradation of the MFIS structure assumed here.

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2.3.4 Discussion of Current Reduction From a comparison of Figs. 5 and 6, it can be seen that a reduction of Jf (Eve , 0) improves the retention characteristics more than a reduction of Ji (Ei ) does. It is also preferable that the current through the ferroelectric decreases rapidly with time. Therefore, it is desired that the current through the ferroelectric should be made as small as possible.

3 Advanced Structures to Improve Retention Time In order to enhance the memory retention time, some improvements to reduce the current through the metal–ferroelectric junction have been proposed and simulated. 3.1 Enhancement of Barrier Height The most plausible cause of memory retention degradation is the current through the ferroelectric layer, which is attributed to Schottky conduction and changes drastically with the barrier height of Schottky junction. In an MFIS structure, metals with a large work function are generally considered to contribute to increasing the barrier height for electrons and decreasing it for holes injected from the top metal electrode into the ferroelectric layer. Since Jf (Eve , 0) is considered to depend exponentially on the effective φB , as described in (8), even a slight increase of φB (∆φB ) can result in a large decrease of Jf (Eve , 0). If the Schottky current through the ferroelectric layer is multiplied by a factor of 10−2 (Fig. 8(a)), then the modeled MFIS structure shows a retention time of about 108 s (Fig. 8(b)), which corresponds to a increase of 0.12 eV in the effective φB of the ferroelectric layer (Fig. 8(c)) [15]. Experimentally, however, optimizing the work function of the top metal electrode is not realistic, because pinning of the surface Fermi level in the ferroelectric layer can make the barrier height less dependent on the work function of the metal [20]. 3.2 Insertion of Ultrathin Insulator Layer Between Metal and Ferroelectric Layers Insertion of an ultrathin insulator layer between the top metal electrode and the ferroelectric layer is expected to be effective in decreasing Jf (Eve , 0); this forms an MIFIS structure. The retention characteristics of the MIFIS structure (Fig. 9(a)) have been simulated by using a physical model similar to that for the MFIS structure. Calculated retention characteristics of the MIFIS structure are given in Fig. 9(b). The structures exhibit remarkably better retention characteristics than the original MFIS structure. The insulator between the metal and the ferroelectric layers should be very thin, so as to


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Fig. 8. Calculated effects of decreasing the current through the ferroelectric layer in an MFIS structure. (a) Field dependence of the current through the ferroelectric layer, and (b) hold time dependence of the capacitance retention for the initial barrier height in the ferroelectric (∆φB = 0) and an increased barrier height (∆φB = 0.12 eV). (c) Band diagram for the increased ferroelectric barrier height in the MFIS structure

Fig. 9. (a) Band diagram of MIFIS structure. (b) Calculated capacitance retention of the MIFIS structure for various thicknesses of the inserted insulator layer: di0 = 0.1, 0.5, 1.0 and 5.0 nm

enhance the voltage applied to the ferroelectric layer in the write operation. The current through the insulator layer on the silicon substrate was assumed to correspond to A = 1 as given in Fig. 5, and the current through the ferroelectric layer was assumed to correspond to B = 1 as given in Fig. 6. It was assumed that the thickness di0 of the additional SiO2 thin layer was 0.1, 0.5, 1.0 or 5.0 nm, and the current through the insulator layer was assumed to be due to the Schottky, Fowler–Nordheim and direct tunneling conduction. The direct tunneling current, Jt through an additional thin insulator layer was assumed to be given by the following equation [21]:

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Fig. 10. (a) Capacitance retention characteristics of MFIS structures for various insulator dielectric constants i up to i = 30. (b) Dependence of the ferroelectric polarization on the applied gate voltage in the MFIS structures

2di0 √ Jt = αEi di0 exp − ϕm , h ¯

(13)

where h ¯ is Planck’s constant, ϕ is the work function difference for the M– I system and m is the carrier mass. The parameter α was determined to make Ji for di0 = 0.1 nm comparable to the current through the ferroelectric layer, which is about 10−7 A/cm2 . In this calculation, ϕ = 3.2 eV for the system Al/SiO2 , and the free-electron mass were used. When di0 = 1.0 nm, the calculation indicates that the retention time will be over 10 years, as shown in Fig. 9(b). 3.3 High-k Insulator Layer Instead of SiO2 Film Using a high-k insulator is expected to increase the reverse polarization in an MFIS structure and reduce the depolarization field. High-k dielectrics have been studied intensively for application in gate oxide layers in MOS transistors with a small effective oxide thickness (EOT) and a small tunneling current. Some dielectric constants εi that have been reported are 20–25 for HfO2 , 27 for 3.3 nm La2 O3 (0.48 nm EOT), 8.5 for 2.1 nm Al2 O3 (0.96 nm EOT) [22] and 31 for 12 nm Pr2 O3 (1.4 nm EOT) [23]. Retention characteristics for various values of εi up to 30 have been simulated (Fig. 10(a)). As εi increases, the ratio of the share of the voltage in the ferroelectric layer to the total Vg becomes larger and so the retention time becomes long. The initial capacitance difference between the curves for positive and negative Vg becomes larger because the initial capacitance difference has been increased by making the ferroelectric hysteresis loop large (Fig. 10(b)). The retention curves for negative Vg extend to longer hold times before convergence occurs than do those for positive Vg , as shown in Fig. 10(a).


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4 Experimental Improvement of Retention Time by O2 Annealing In the previous section, it was proposed that the current through the ferroelectric could be reduced by some improvements such as barrier height enhancement, insulator insertion and a high-k insulator layer. The insertion of MgO and SiO2 films as insulators and the use of a high-k insulator PrOx film have been tried [13, 24], but a significant improvement was not obtained. The barrier height enhancement by annealing the ferroelectric film in an O2 atmosphere has been successful in elongating the retention time through reduction of the current [25, 26]. So, in this section, annealing and its effect on the retention are described [6, 8, 9, 12, 13, 26]. 4.1 Effect of O2 Annealing on Physical Properties of SBT Thin Films on (111) Pt/Ti/SiO2 /Si Substrates SBT thin films on (111) Pt/Ti/SiO2 /Si were annealed in a 1 atm O2 atmosphere at 600 ◦ C for 20 minutes. From XRD analysis, it was found that the preferential (115) peak intensity of the O2 -annealed SBT thin film was much enhanced, although the crystalline orientation was almost the same as that of the as-deposited film [26]. Therefore, it is considered that the O2 annealing improved the ferroelectricity of the Bi-layered SBT. AFM images of SBT film surfaces have also been studied before and after annealing [26]. The asdeposited SBT showed some large hillocks on a flat, fine surface (Fig. 11(a)), while the surface of the annealed SBT was dense, with grains (Fig. 11(b)) but not with large hillocks. The O2 annealing enlarged the SBT grain sizes on the flat terrace and removed the hillocks, which implies that the surface roughness of the SBT, which enhances the current, was improved by the O2 -annealing treatment. 4.2 Polarization Retention Characteristics of Pt/SBT/Pt Capacitors The polarization retention characteristics of Pt/SBT/Pt capacitors were analyzed [26] by applying a pulsed triangular voltage to measure the C–V characteristics of an MFIS capacitor held under a DC bias. The definition of the retained-polarization ratio is the ratio of the remanent polarization after a hold time to the maximum remanent polarization immediately after the device had been polarized. As shown in Fig. 12(a), a capacitor consisting of as-deposited SBT/Pt/Ti/SiO2/Si with a top Pt electrode showed a polarization retention degradation which was severely affected by the hold DC bias voltage. On the other hand, a capacitor consisting of O2 -annealed SBT/Pt/Ti/SiO2/Si with a top Pt electrode showed much more retained polarization, which was independent of the hold DC bias voltage (Fig. 12(b)).

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Fig. 11. AFM images of (a) as-deposited and (b) O2 -annealed SBT thin films [26]

Fig. 12. Polarization retention characteristics of (a) as-deposited and (b) O2 annealed SBT thin films [26]

The polarization retention characteristics were improved by the O2 annealing, possibly because the annealing improved the crystallinity of the SBT. 4.3 Current Conduction in SBT Films The current density through as-deposited and O2 -annealed SBT thin films were studied by using Pt/SBT/Pt diodes [26]. As shown in Fig. 13(a), O2 annealing succeeded in decreasing the current density through the SBT thin film. The current density through the as-deposited and the O2 -annealed SBT film was analyzed into two contributions, from the Schottky and the Frenkel– Poole conduction. The Schottky current JSk was obtained from (8) and the Frenkel–Poole current was expressed as ⎫

⎧ ⎨ −q φB − qEf /πεf ⎬ JFP ∼ E exp . (14) ⎭ ⎩ kT As shown in Fig. 13(b), both the Schottky and the Frenkel–Poole conduction are decreased by the O2 annealing. The Schottky conduction has a larger


233

Fig. 13. (a) Current density through as-deposited and O2 -annealed SBT thin films. (b) The current densities in (a), analyzed into combinations of Schottky and Frenkel–Poole conduction [26]

Fig. 14. Capacitance retention characteristics of two MFIS structures, consisting of as-deposited SBT/SiON/Si with Al electrodes and O2 -annealed SBT/SiON/Si with Pt electrodes

value than the Frenkel–Poole conduction, similarly to what was found in Sect. 2.2, and consists of carrier transport brought about by thermionic emission across the metal–ferroelectric interface, whereas the Frenkel–Poole conduction is brought about by field-enhanced thermal excitation of trapped carriers into the band. Therefore, the decreased contributions from both the Schottky and the Frenkel–Poole conduction to the current density shown in Fig. 13(b) imply that the O2 annealing has increased the barrier height of the ferroelectric layer and decreased the trap density in the ferroelectric layer. 4.4 Retention Improvement of MFIS Structures by O2 Annealing The capacitance retention characteristics of two MFIS structures consisting of an as-deposited SBT/SiON/Si structure with Al electrodes and an O2 -

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Fig. 15. Flowchart of effects of O2 annealing on retention characteristics of MFIS structures using ferroelectric PLD-SBT thin films

annealed SBT/SiON/Si structure with Pt electrodes were studied, as shown in Fig. 14 [26]. Hold DC bias voltages were applied to compensate the flatband shifts shown in the capacitance retention characteristics of the two MFIS structures, which are considered to be caused by the work function differences between the metal and the SBT film and by fixed charge distributions in the ferroelectric and insulator layers. The O2 -annealed SBT/SiON/Si structure with Pt electrodes showed much more retained capacitance than did the asdeposited SBT/SiON/Si structure with Al electrodes. This result indicates that O2 annealing can be expected to improve the capacitance retention characteristics of MFIS structures. The mechanisms of the retention improvement of MFIS structures by O2 annealing have been considered, as shown in the flowchart in Fig. 15. The O2 annealing improves the crystallinity of the PLD-SBT and decreases the Schottky conduction in the PLD-SBT. The Frenkel–Poole and absorption currents through the PLD-SBT are believed to be decreased by decreasing the trap density. The polarization retention characteristics are also improved. As a result, we believe that an improvement in the retention of an MFIS structure can be achieved by O2 annealing [25, 26]. 4.5 More Improvement by Rapid Thermal Annealing It is expected that rapid thermal annealing (RTA) for a short time at a high temperature will improve the crystallinity and thus the ferroelectricity in a film without sacrificing the excellent interface properties of the MFIS structure. From the viewpoint of ultra-LSI (ULSI) processes, it is adequate to anneal the ferroelectric layer in an MFIS gate stack simultaneously forming


235

Fig. 16. (a) Retention curves of capacitance of MFIS structures formed using SBT films treated by RTA. (b) Extrapolated retention characteristics of MFIS structures annealed at 1000 ◦ C for 30 s

the source–drain high-density dopant regions of shallow junctions in MOSFETs, by RTA at around 1000 ◦C for 10 s. The initial heating rate was about 50 ◦ C/s from room temperature to 800 ◦ C, and then about 10 ◦ C/s from 800 ◦C to 1050 ◦C. Several MFIS samples were annealed at 600 ◦ C to 1000 ◦C in an O2 atmosphere for 30 s and 1 min. Figure 16(a) shows the retention characteristics for annealing conditions of 900 ◦ C for 30 s, 900 ◦C for 1 min and 1000 ◦C for 30 s. The MFIS sample annealed at 1000 ◦C for 30 s shows a large difference between the on and off capacitances even after 1 ×105 s (i.e., 1 d). In Fig. 16(b), the extrapolated retention time is estimated to be 3.3 ×107 s (i.e., 1 year). It is especially important to note that the case of 1000 ◦ C for 30 s showed a very long retention time, even though the initial on/off capacitance ratio was small compared with the cases of annealing at 900 ◦C, with a memory window of about 0.5 V. It is suggested in this case that the crystallinity of the ferroelectric dominates the retention capability, rather than the insulator–Si interface conduction.

5 Photoyield Spectroscopic Studies on SBT Thin Films 5.1 Principle of Photoyield Spectroscopy of SBT Films As investigated in Sect. 4, an O2 -annealing treatment is an effective way to reduce leakage currents through SBT films deposited by pulsed laser deposition and to improve the retention characteristics. In this section, we describe the effects of O2 annealing on the electronic properties of the SBT film, studied by the photoemission spectroscopy technique of photoyield ultraviolet spectroscopy (UV-PYS). UV-PYS gives information about the total number of photoelectrons which are excited from all the occupied states and Fermi levels, as shown in Fig. 17. Our UV-PYS system gives very precise data, with

236


Fig. 17. Relation between UV-PYS spectra and energy states

a resolution of about ±0.05 eV. X-ray photoelectron spectroscopy (XPS) also gives precise information about electronic characteristics such as the valence bands and core levels in SBT films, but its spectral resolution depends on the spectral width of the X-ray source and is much worse than that of UV-PYS. These features indicate that UV-PYS is preferable for estimating the starting point of a photoemission spectrum, such as a Fermi level. UV-PYS spectra for an SBT film before and after an O2 -annealing treatment were studied. If the SBT was an ideal insulator, the threshold energy for photoemission from the valence band would be about 7.7 eV [27], which is larger than the value obtained in the present work. Instead, the photoemission from the SBT surface, as shown in Fig. 18, seems to have a threshold energy which is much closer to the SBT work function of 5.4 eV. This result indicates that the threshold energy detected by UV-PYS is the excitation energy from the Fermi level to the vacuum level, because the maximum energy of the occupied states is indicated by the band tail in the valence band, and can be considered to be the Fermi level. 5.2 Effects of O2 Annealing on SBT Thin Films Studied by UV-PYS The UV-PYS spectra obtained for the SBT film before and after O2 -annealing treatment were analyzed. The photoemission yield from the SBT, Y , is described by the following equation, which has the form of an indirect-opticalexcitation equation [28]: 5/2

Y ∼ (¯ hω − Eth )

,

(15)

where h ¯ ω is the excitation photon energy and Eth is the photoemission threshold energy. Figure 18 shows Y 2/5 vs. photon energy. The experimental data can be fitted well with straight lines. The as-deposited SBT film exhibits a Fermi energy of 5.90 eV, while the O2 -annealed film exhibits a value of 5.56 eV. These results indicate that the O2 -annealing treatment has increased the Fermi level of the film surface by 0.34 eV.


237

Fig. 18. UV-PYS spectra of PLDSBT thin films before and after O2 annealing

Fig. 19. Band diagrams considered for the PLD-SBT surface before and after O2 annealing

If an electron affinity of 3.5 eV is assumed for the SBT [27], the energy difference between the Fermi level and the conduction band minimum can be considered to be the barrier height for electrons of the metal–ferroelectric interface, and is estimated to be 2.40 eV for the as-deposited film and 2.06 eV for the O2 -annealed film, as shown in Fig. 19. On the other hand, the hole barrier height is estimated to be 1.80 eV for the as-deposited film and 2.14 eV for the O2 -annealed film if a band gap of 4.2 eV is assumed [27]. The Fermi-level differences discussed above suggest that the as-deposited SBT film shows ptype thermionic conduction, with its Fermi level of 0.30 eV being lower than the intrinsic value obtained after O2 annealing; however, the film shows much less conduction when the Fermi level is close to the intrinsic level. This idea qualitatively supports the experimental studies on the effects of O2 annealing described in Sect. 4, where the O2 annealing was considered to decrease the Schottky current through the SBT film and successfully improved the memory retention characteristics of the MFIS structure.

238


Acknowledgement The authors would like to thank Dr. Mitsue Takahashi for helping with the work.

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Index

absorption current, 225, 234

MFIS structure, 220

band diagram, 222, 224 barrier height, 220, 223, 228

oxygen annealing, 220

depolarization field, 219–221 energy band diagram, 222, 224 ferroelectric-gate FET, 220 Frenkel–Poole current, see asoPoole– Frenkel emission232 high-k insulator, 230, 231 memory retention, 219, 220, 228, 237 metal–ferroelectric–insulator– semiconductor structure, see MFIS structure

polarization relaxation, 220, 221 polarization retention, 219, 234 PrOx , 231 pulsed laser deposition, 235 rapid thermal annealing, 234 RTA, 234 SBT, 220 Schottky current, 226, 228 SiON, 233 ultraviolet photoyield spectroscopy, 220 UV-PYS, 220

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