Advanced Piezoelectric Materials: Science and Technology [2 ed.] 0081021356, 9780081021354

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ADVANCED PIEZOELECTRIC MATERIALS SECOND EDITION

Related titles Applications of ATILA FEM (ISBN 978-0-85709-065-2) Advanced Piezoelectric Materials (ISBN 978-1-84569-534-7) Handbook of Advanced Dielectric, Piezoelectric and Ferroelectric Materials (ISBN 978-1-84569-186-8)

Woodhead Publishing Series in Electronic and Optical Materials

ADVANCED PIEZOELECTRIC MATERIALS Science and Technology SECOND EDITION Edited by

KENJI UCHINO

An imprint of Elsevier

Woodhead Publishing is an imprint of Elsevier The Officers’ Mess Business Centre, Royston Road, Duxford, CB22 4QH, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States The Boulevard, Langford Lane, Kidlington, OX5 1GB, United Kingdom Copyright © 2017 Elsevier Ltd. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN: 978-0-08-102135-4 (print) ISBN: 978-0-08-101255-0 (online) For information on all Woodhead publications visit our website at https://www.elsevier.com/books-and-journals

Publisher: Matthew Deans Acquisition Editor: Kayla Dos Santos Editorial Project Manager: Ana Claudia Garcia Production Project Manager: Omer Mukthar Cover Designer: Miles Hitchen Typeset by SPi Global, India

Contributors J. Akedo National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Japan Murata Manufacturing Co., Ltd, Nagaokakyo, Japan

A. Ando

Y. Bar-Cohen

Jet Propulsion Lab, Pasadena, CA, United States

V.F. Cardoso

University of Minho, Braga, Portugal

S. Cochran

University of Glasgow, Glasgow, United Kingdom

D.-Y. Jeong

Inha University, Incheon, South Korea

S.D. Johnson

Naval Research Laboratory, Washington, DC, United States

M. Kimura Murata Manufacturing Co., Ltd, Nagaokakyo, Japan N. Korobova National Research University of Electronic Technology (MIET), Moscow, Zelenograd, Russia S. Lanceros-Mendez University of Minho, Braga, Portugal; BCMaterials, Derio, Spain; Ikerbasque, Bilbao, Spain X. Liao

University of Glasgow, Glasgow, United Kingdom National University of Singapore, Singapore, Singapore

L.-C. Lim L. Luo

Shanghai Institute of Ceramics, Shanghai, China

H. Luo Shanghai Institute of Ceramics, Shanghai, China University of California, Los Angeles, CA, United States

C.S. Lynch

D. Maurya Virginia Tech, Blacksburg, VA, United States H. Nagata Tokyo University of Science, Chiba, Japan S. Priya Virginia Tech, Blacksburg, VA, United States University of Minho, Braga, Portugal

C. Ribeiro

J. Ryu Korea Institute of Materials Science (KIMS), Changwon, South Korea Y. Saigusa

River Eletec Corporation, Nirasaki-city, Japan

V.Ya. Shur

Ural Federal University, Ekaterinburg, Russia

T. Takenaka K. Uchino

Tokyo University of Science, Chiba, Japan

The Pennsylvania State University, State College, PA, United States

K. Wasa

Kyoto University, Kyoto, Japan

X. Zhao

Shanghai Institute of Ceramics, Shanghai, China

xi

Preface Piezoelectricity was discovered by Pierre Curie in 1880. There was a wait of about 30 years until World War I for its practical application in underwater detecting sonars. Then after another 30 years, barium titanate (BT) was discovered during World War II, followed by the discovery of PZT, the present key composition, in 1954. At the end of the “polymer boom,” polyvinylidene difluoride was discovered. In the 1970s and 1980s, PMN-based electrostrictive materials ignited actuator applications, followed by the discovery of extraordinarily large electromechanical coupling factors of relaxor-PTs. In parallel, ecological restrictions may terminate the usage of the present Pb-containing piezoceramics in the 2020s. Ten years have passed since the publication of the first edition. During this period, the development trend in piezoelectric devices has gradually changed; there are five key trends for providing future perspectives: “performance to reliability,” “hard to soft,” “macro to nano,” “homo to hetero,” and “single to multifunctional.” This second edition was developed to update the manuscript to be more relevant for future trends. The first, regarding the materials trend, the worldwide toxicity regulation is accelerating the development of Pb-free piezoelectrics for replacing the conventional PZTs. Second, high-powered piezoelectrics with low loss have become a central research topic from the energy-efficiency improvement viewpoint; that is to say. Third, we are facing the revival of the polymer era in the 1980s because of the elastically soft superiority of polymers. Larger, thinner, lighter, and mechanically flexible human interfaces are the current necessities in portable electronic devices, leading to the development of elastically soft displays, electronic circuits, and speakers/microphones. Polymeric and polymer-ceramic composite piezoelectrics are reviving and becoming commercialized. PZN-PT or PMN-PT single crystals became a focus, due to the rubber-like soft piezoceramic strain, 25 years after their discovery. In the MEMS/NEMS area, piezo MEMS is one of the miniaturization targets for integrating the piezo actuators in micro-scale devices, aiming at biomedical applications for maintaining human health. The homo to hetero structure change is also a recent research trend: the stress gradient in terms of space in a dielectric material exhibits piezoelectricequivalent sensing capability (i.e., “flexoelectricity”), while an electric-field gradient in terms of space in a semiconductive piezoelectric can exhibit bimorph-equivalent flextensional deformation (“monomorph”). New functions can be realized by coupling two effects. Magnetoelectric devices

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xiv

PREFACE

(i.e., voltage is generated by applying magnetic field) were developed by laminating magnetostrictive Terfenol-D and piezoelectric PZT materials, and photostriction was demonstrated by coupling photovoltaic and piezoelectric effects in PLZT. In the application area, the global regime for “ecological sustainability” particularly accelerated new developments in ultrasonic disposal technology of hazardous materials, diesel injection valves for air pollution, and piezoelectric renewable energy harvesting systems. The editorial philosophy of this edition does not change: “learning the history and forecasting the future.” This philosophy is based on the following: • There is a new product “you believe” has been tried one generation back. • Once the development fails, a period of one generation (25 years) is required to restart a similar development. • Development starts from the application, then moves back to the fundamental research. In most cases, actual applications pull the development of suitable materials (needs-pull model). • No research will die; it revives after a generation. • Political/legal forces are stronger than technological ones. This book is not intended to be just an omnibus of review papers, each paper primarily including each group’s own research content. Rather, this book is intended to be a comprehensive textbook for graduate students and junior researchers of piezoelectric materials by transferring historical aspects comprehensively and correctly as well as suggesting future directions. Since this is a difficult process, the editor carefully selected authorities in each subarea of piezoelectric materials and asked them to draft their manuscripts according to the editorial philosophy. The editor also asked his graduate students to evaluate the manuscript quality as a graduatelevel textbook, and these comments were provided to the contributors. Thus each draft has been modified and revised several times. Chapter 1 is devoted to an overview of piezoelectric materials history, and each section corresponds to the summaries in the subsequent chapters. Chapter 1 also provides the fundamentals of piezoelectricity and necessary terminologies and equations/formulas, followed by overall applications of piezoelectrics. Part I, Piezoelectric Materials, includes Chapter 2, which discusses PZT-based ceramics; Chapter 3 discusses relaxor ferroelectric ceramics, which are widely used at present; and Chapter 4 focuses on lead-free piezoceramics, which may represent the future and replace Pb-containing materials in the next 10 years. Chapter 5 focuses on quartz and Chapter 6 discusses how lithium niobate/tantalate can be used to treat traditional single crystals; the present status and future prospects in the twenty-first century communication age are also discusses. Chapter 7 provides information on single crystal PZNPT, PMN-PT and discusses superior piezoelectricity—in other words,

PREFACE

xv

high electromechanical coupling factors—and its medical applications. Chapter 8 on electroactive polymers is an exceptional part of this book, reviewing the state-of-the-art challenges and potential applications of electroactive polymers. The reader will learn what differentiates electroactive polymers from the piezoceramics. Chapter 9, which discusses piezoelectric composite materials, introduces special features that are introduced by coupling piezoceramics and polymers, starting from the basic principles of composite designing. Manufacturing techniques are also included in this chapter. Part II, Preparation Methods and Applications, will answer the practical design and fabrication issues related to piezomaterials. Chapter 10 on piezoceramic manufacturing methods covers recent practical manufacturing methods. Chapter 11 describes multilayer technologies, particularly important for manufacturing actuators and transformers. Chapter 12 deals with how to prepare piezoelectric single crystals in general, focusing in particular on PNZ-PT and PMN-PT. In contrast, “thin film” manufacturing technologies are introduced in Chapter 13. Chapter 14 discusses piezoelectric materials development, microfabrication processes, and device fabrication for MEMs technologies. Chapter 15 describes the mechanisms and features of the aerosol deposition process for thick piezoelectric ceramic thin films. Chapter 16 introduces transducer designing and manufacturing technologies. Part III, Application-Oriented Materials Development, includes Chapter 17 on high power piezoelectrics, Chapter 18 on photostrictive actuators, and Chapter 19 on piezoelectric performance under mechanical stress. High power drive generates significant heat generation, while the hysteresis of piezoelectrics is enhanced significantly under high mechanical stress. Methods to prevent this performance degradation and aging are discussed in Part III. A photostrictor, which basically originated from coupling photovoltaic and piezoelectric effects, may be a future material that is useful in the optical communication age. Thanks to the contributing authorities’ sincere efforts, the editor believes that this book covers most of the fundamentals, history, and future trends relating to piezoelectric materials. I hope this book will become a standard textbook on advanced piezoelectric materials in most of the related universities and institutes. K. Uchino The Pennsylvania State University, University Park, PA, United States Micromechatronics, Inc., State College, PA, United States

Acknowledgments I would like to express my sincere appreciation to the following authorities for their cooperation with this project: • Drs. Yukio Sakabe, Akira Ando, and Masahiko Kimura, Murata Manufacturing Co.—PZT-ceramics. • Prof. Tadashi Takenaka, Tokyo University of Science—Pb-free piezoceramics. • Mr. Yasutaka Saigusa, River Eletec—Quartz. • Prof. Vladimir Ya. Shur, Ural State University—Lithium niobate, tantalate. • Profs. Haosu Luo, Laihui Luo, and Xiangyong Zhao, Shanghai Institute of Ceramics—Single crystals. • Dr. Yoseph Bar-Cohen, Jet Propulsion Lab—Electroactive polymers. • Prof. Leong Chew Lim, National University of Singapore—Single crystal preparation. • Prof. Kiyotaka Wasa, Kyoto University—Thin film technologies. • Dr. Jun Akedo, National Institute of Advanced Industrial Science and Technology—Aerosol technique. • Prof. Christopher S. Lynch, University of California LA— Piezoelectricity under stress.

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C H A P T E R

1 The Development of Piezoelectric Materials and the New Perspective K. Uchino The Pennsylvania State University, State College, PA, United States

Abstract Certain materials produce electric charges on their surfaces as a consequence of applying mechanical stress. The induced charges are proportional to the mechanical stress. This is called the direct piezoelectric effect and was discovered in quartz by Pierre and Jacques Curie in 1880. Materials showing this phenomenon also conversely have a geometric strain proportional to an applied electric field. This is the converse piezoelectric effect, discovered by Gabriel Lippmann in 1881. This article first reviews the historical episodes of piezoelectric materials in the sequence of quartz, Rochelle salt, barium titanate, PZT, lithium niobate/tantalate, relaxor ferroelectrics, PVDF, Pb-free piezoelectrics, and composites. Then, the detailed performances are described in the following section, which is the introduction to each chapter included in this book. Third, since piezoelectricity is utilized extensively in the fabrication of various devices such as transducers, sensors, actuators, surface acoustic wave (SAW) devices , frequency control, etc., applications of piezoelectric materials are also introduced briefly in conjunction with materials. The author hopes that the reader can “learn the history aiming at creating new perspective for the future in the piezoelectric materials.” Keywords: Piezoelectric material, Quartz, Rochelle salt, Barium titanate, Lead zirconate titanate, Relaxor ferroelectrics, Pb-free piezoelectrics, Electromechanical coupling factor.

1.1 THE HISTORY OF PIEZOELECTRICS Any material or product has a lifecycle, which is determined by four “external” environmental forces, which can be summarized under the acronym STEP (Social/cultural, Technological, Economic, and Political

Advanced Piezoelectric Materials http://dx.doi.org/10.1016/B978-0-08-102135-4.00001-1

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Copyright © 2017 Elsevier Ltd. All rights reserved.

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1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

forces).1 We will observe first how these forces encouraged/discouraged the development of piezoelectric materials.

1.1.1 The Dawn of Piezoelectrics The Curie brothers (Pierre and Jacques Curie) discovered direct piezoelectric effect in single crystal quartz in 1880. Under pressure, quartz generated electrical charge/voltage from quartz and other materials. The root of the word “piezo” means “pressure” in Greek; hence the original meaning of the word piezoelectricity implied “pressure electricity.” Materials showing this phenomenon also conversely have a geometric strain proportional to an applied electric field. This is the converse piezoelectric effect, discovered by Gabriel Lippmann in 1881. Recognizing the connection between the two phenomena helped Pierre Curie to develop pioneering ideas about the fundamental role of symmetry in the laws of physics. Meanwhile, the Curie brothers put their discovery to practical use by devising the piezoelectric quartz electrometer, which could measure faint electric currents; this helped Pierre’s wife, Marie Curie, 20 years later in her early research. It was at 11:45 pm on Apr. 10, 1912 that the tragedy of the sinking of the Titanic occurred (see Fig. 1.1). As the reader knows well, this was caused by an iceberg hidden in the sea. This would have been prevented if the ultrasonic sonar system had been developed then. Owing to this tragic incident (social force), there was motivation to develop ultrasonic technology development using piezoelectricity.

FIG. 1.1 The sinking of the Titanic was caused by an “iceberg” in the sea.

3

1.1 THE HISTORY OF PIEZOELECTRICS

1.1.2 World War I—Underwater Acoustic Devices With Quartz and Rochelle Salt The outbreak of World War I in 1914 led to real investment to accelerate the development of ultrasonic technology in order to search for German U-Boats under the sea. The strongest forces both in these developments were social and political. Dr. Paul Langevin, a professor at Ecole Sup
erieure de Physique et de Chimie Industrielles de la Ville de Paris (ESPCI Paris Tech), who had many friends including Drs. Albert Einstein, Pierre Curie, Ernest Ratherford, among others, started experiments on ultrasonic signal transmission into the sea, in collaboration with the French Navy. Langevin succeeded in transmitting an ultrasonic pulse into the sea off the coast of southern France in 1917. We can learn most of the practical development approaches from this original transducer design (Fig. 1.2). First, 40 kHz was chosen for the sound wave frequency. Increasing the frequency (shorter wavelength) leads to better monitoring resolution of the objective; however, it also leads to a rapid decrease in the reachable distance. Notice that quartz and Rochelle salt single crystals were the only available piezoelectric materials in the early 20th century. Since the sound velocity in quartz is about 5 km/s, 40 kHz corresponds to the wavelength of 12.5 cm in quartz. If we use a mechanical resonance in the piezoelectric material, a 12.5/2 ¼ 6.25 cm thick quartz single crystal piece is required. However, in that period, it was not possible to produce such large high-quality single crystals.2

Angle dependence of acoustic power

1.0 Center axis

0.5

0.5

Steel

28.7

Quartz pellets were arranged

5.0 28.7 260 mm f

FIG. 1.2 Original design of the Langevin underwater transducer and its acoustic power directivity.

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1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

In order to overcome this dilemma, Langevin invented a new transducer construction; small quartz crystals arranged in a mosaic were sandwiched by two steel plates. Since the sound velocity in steel is in a similar range to quartz, with 6.25 cm in total thickness, he succeeded to set the thickness resonance frequency around 40 kHz. This sandwich structure is called Langevin type and remains popular even today. Notice that quartz is located at the center, which corresponds to the nodal plane of the thickness vibration mode, where the maximum stress/strain (or the minimum displacement) is generated in the resonance mode. Further, in order to provide a sharp directivity for the sound wave, Langevin used a sound radiation surface with a diameter of 26 cm (more than double of the wavelength). The half-maximum-power angle ϕ can be eval
 uated as ϕ ¼ 30  ðλ=2aÞ degree , (1.1) where λ is the wavelength in the transmission medium (not in steel) and a is the radiation surface radius. If we use λ ¼ 1500 (m/s)/40 (kHz) ¼ 3.75 cm, a ¼ 13 cm, we obtain ϕ ¼ 4.3 degree for this original design. He succeeded practically in detecting the U-Boat 3000 m away. Moreover, Langevin also observed many bubbles generated during his experiments, which seems to be the “cavitation” effect that was utilized for ultrasonic cleaning systems some 60 years later. Though the mechanical quality factor is significantly high (i.e., low loss) in quartz, its major problems for this transducer application include its low electromechanical coupling k, resulting in (1) low mechanical underwater transmitting power and receiving capability, and in (2) narrow frequency bandwidth, in addition to the practical fact that only Brazil produced natural quartz crystals at that time. Thus, US researchers used Rochelle salt single crystals, which have a superior electromechanical coupling factor (k is close to 100% at 24°C!) with a simple synthesizing process. Nicholson,3 Anderson, and Cady undertook research on the piezoelectric underwater transducers during World War I. General Electric Laboratory (Moore4) and Brush Company produced large quantities of crystals in the early 1920s. The detailed history on Rochelle salt can be found in Ref. 5. Rochelle salt is sodium potassium tartrate [NaKC4H4O64H2O], and it has two Curie temperatures at 18°C and 24°C with a narrow operating temperature range for exhibiting ferroelectricity; this leads to high electromechanical coupling at 24°C and, however, rather large temperature dependence of the performance. It was used worldwide for underwater transducer applications until barium titanate and lead zirconate titanate (PZT) were discovered. Since this crystal is water-soluble, it is inevitable that it is degraded by humidity. However, the most delicate problem is its weakness to dryness. Thus, no researcher was able to invent the best coating technology for the Rochelle salt devices to achieve the required lifetime. Many efforts to discover alternative piezoelectrics of Rochelle salt with better stability/reliability continued after WWI. Potassium dihydrogen

5

1.1 THE HISTORY OF PIEZOELECTRICS

phosphase (KH2PO4 or KDP) was discovered by Georg Busch in 1935.6 Knowing the ferroelectricity of Rochelle salt, and guessing the origin to be from the hydrogen bonds in the crystal, Busch searched hydrogen bond crystals systematically and found KDP as a new ferroelectric/piezoelectric. Though many piezoelectric materials (such as Rochelle salt, barium titanate, and PVDF) were discovered accidentally through “serendipity,” KDP is an exceptional example of discovery created by the perfectly planned systematic approach. Following KDP, ADP, EDT, and DKT, amongst others, were discovered continuously and examined. However, most of the water-soluble single crystal materials have been forgotten because of the performance and preparation improvements in synthetic quartz and perovskite ceramics (BT, PZT).

1.1.3 World War II—Discovery of Barium Titanate Barium titanate (BaTiO3, BT) ceramics were discovered independently by three countries, the United States, Japan, and Russia, during World War II: Wainer and Salomon7 in 1942, Ogawa8 in 1944, and Vul9 in 1944, respectively. Compact radar system development required compact high capacitance “condensers” (the term “condenser,” rather than “capacitor,” was used at that time). Based on the widely used “Titacon” (titania condenser) composed of TiO2-MgO, researchers doped various oxides to find higher permittivity materials. According to the memorial article authored by Ogawa and Waku,10 they investigated three dopants, CaO, SrO, and BaO, in a wide fraction range. They found a maximum permittivity around the compositions CaTiO3, SrTiO3, and BaTiO3 (all were identified as perovskite structures). In particular, the permittivity, higher than 1000, in BaTiO3 was enormous (10 times higher than that in Titacon) at that time, as illustrated in Fig. 1.3. BaO

1000 800

BaTiO3

600 400 200

TiO2

(

%)

MgO

FIG. 1.3 Permittivity contour map on the MgO-TiO2-BaO system, and the patent coverage composition range (dashed line).10

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1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

It should be pointed out that the original discovery of BaTiO3 was not related with piezoelectric properties. Equally important are the independent discoveries by R. B. Gray at Erie Resister (patent applied for in 1946)11 and by Shepard Roberts at MIT (published in 1947)12 that the electrically poled BT exhibited “piezoelectricity” owing to the domain realignment. At that time, researchers were arguing that the randomly oriented “polycrystalline” sample should not exhibit piezoelectricity, but the secondary effect, “electrostriction.” In this sense, Gray is the “father of piezoceramics,” since he was the first to verify that the polycrystalline BT exhibited piezoelectricity once it was electrically poled. The ease in composition selection and in manufacturability of BT ceramics prompted Mason13 and others to study the transducer applications with these electroceramics. Piezoelectric BT ceramics had a reasonably high coupling coefficient and nonwater solubility, but the bottlenecks were (1) a large temperature coefficient of electromechanical parameters because of the second phase transition (from tetragonal to rhombohedral) around the room temperature or operating temperature, and (2) the aging effect due to the low Curie temperature (phase transition from cubic to tetragonal) around only 120°C. In order to increase the Curie temperature higher than 120°C, and to decrease the second transition temperature below 20°C, various ion replacements such as Pb and Ca were studied. From these trials, a new system PZT was discovered. It is worth noting that the first multilayer capacitor was invented by Sandia Research Laboratory engineers under the Manhattan Project with the coating/pasting method for the switch of the Hiroshima nuclear bomb (Private Communication with Dr. Kikuo Wakino, Murata Mnfg).

1.1.4 Discovery of PZT 1.1.4.1 PZT Following the methodology taken for the BT discovery, the perovskite isomorphic oxides such as PbTiO3, PbZrO3, and SrTiO3 and their solid solutions were intensively studied. In particular, the discovery of “antiferroelectricity” in lead zirconate14 and the determination of the Pb(Zr,Ti)O3 system phase diagram15 by the Japanese group, E. Sawaguchi, G. Shirane, and Y. Takagi, are noteworthy. Fig. 1.4 shows the phase diagram of the Pb(Zr,Ti)O3 solid solution system reported by E. Sawaguchi—which was read and cited worldwide—and triggered the PZT era. A similar discovery history as the barium titanate was repeated for the lead zirconate titanate system. The material was discovered by the Japanese researcher group, but the discovery of its superior piezoelectricity was conducted by a US researcher, Bernard Jaffe, in 1954. Jaffe worked at the National Bureau of Standards at that time. He knew well about the Japanese group’s serial studies on the PZT system, and he focused on the piezoelectric measurement around the MPB (morphotropic phase

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1.1 THE HISTORY OF PIEZOELECTRICS

500

Pa

400

Fb

300 T (°C)

300

°C Pa

250 200

Ab

200

Ab

Fa

Fa 160

Aa

100 100

Aa 0

0

0 PbZrO3 20

PbZrO3

40

1 2 3 4 5 Atomic percent of PbTiO3 60

80

Atomic percent of PbTiO3

100 PbTiO3

FIG. 1.4 Phase diagram for the Pb(Zr,Ti)O3 solid solution system proposed by Sawaguchi.15 We now know another ferroelectric phase below the Fα phase.

boundary) between the tetragonal and rhombohedral phases; he found enormous electromechanical coupling around that composition range.16 His patent had a significant effect on the future development strategies of Japanese electroceramic industries. It is important to remember two important notions for realizing superior piezoelectricity: (1) Pb-included ceramics and (2) MBP compositions. 1.1.4.2 Clevite Corporation As mentioned above, Brush Development Company manufactured Rochelle salt single crystals and their bimorph components for phonograph applications in 1930s, and in the 1940s they commercialized piezoelectric quartz crystals by using a hydrothermal process. There was a big piezoelectric group in Brush, led by Hans Jaffe. However, in 1952 the Clevite Corporation was formed by merging the Cleveland Graphite Bronze Corporation and Brush, and H. Jaffe welcomed B. Jaffe from NBS to Clevite and accelerated the PZT business. Their contribution to developing varieties of PZTs (i.e., hard and soft PZT’s) by doping acceptor (Mn) and donor (Nb) ions is noteworthy. By the way, PZT was the trademark of Clevite, and it had not been used by other companies previously. Also,

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1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

Hans Jaffe and Bernard Jaffe were not related at all. These episodes are described in their famous book, Piezoelectric Ceramics.11 Clevite first concentrated on high quality military and commercial piezoelectric filters. In the mid-1960s, they tried to develop consumer filters for AM radios, especially automobile radios, but this was not commercially viable initially. However, after 1967, they successfully started mass-production of 10.7 MHz ceramic filters for FM automobile radios, and they delivered them to Philco-Ford. Clevite was bought by Gould Inc. in 1969, and it was resold to Vernitron in 1970. These drastic business actions terminated the promising piezoelectric filter program initiated by Clevite. 1.1.4.3 Murata Manufacturing Company The Murata Manufacturing Co., Ltd. was founded by A. Murata in 1944. He learned ceramic technology from his father who was the Chairman of the former Murata Pottery Manufacturing Co. Murata Manufacturing Company began with 10 employees that produced electroceramic components. After World War II, under the guidance of Prof. Tetsuro Tanaka, who was one of the promoters of Barium Titanate Study Committee during WWII, Murata started intensive studies on devices based on barium titanate ceramics. The first products with barium titanate ceramics were 50-kHz Langevin-type underwater transducers for fish-finders in Japan.17 The second products were mechanical filters.18 In 1960, Murata decided to introduce PZT ceramics by paying a royalty to Clevite Corporation. As already mentioned in the previous section, because of the disappearance of Clevite from the filter business, Murata increased the worldwide share in the ceramic filter products market. 1.1.4.4 Ternary System Since the PZT was protected by Clevite’s US patent subsequently, ternary solid solutions based on PZT with another perovskite phase were investigated intensively by Japanese ceramic companies in the 1960s. Examples of these ternary compositions are the following: PZTs in a solid solution with Pb(Mg1/3Nb2/3)O3 (Matsushita-Panasonic), Pb(Zn1/3Nb2/3) O3 (Toshiba), Pb(Mn1/3Sb2/3)O3, Pb(Co1/3Nb2/3)O3, Pb(Mn1/3Nb2/3)O3, Pb(Ni1/3Nb2/3)O3 (NEC), Pb(Sb1/2Sn1/2)O3, Pb(Co1/2W1/2)O3, and Pb (Mg1/2W1/2)O3 (Du Pont), all of which were patented by different companies (almost all composition patents have already expired). The ternary systems with more material-designing flexibility exhibited better performance in general than the binary PZT system, which created advantages for the Japanese manufacturers over Clevite and other US companies.

1.1 THE HISTORY OF PIEZOELECTRICS

9

1.1.5 Lithium Niobate/Tantalate Lithium niobate and tantalate have the same chemical formula, ABO3, as BaTiO3 and Pb(Zr,Ti)O3. However, the crystal structure is not perovskite, but ilmenite. Ferroelectricity in single crystals of LiNbO3 (LN) and LiTaO3 (LT) was discovered in 1949 by two researchers in Bell Telephone Laboratories, Matthias and Remeika.19 Since the Curie temperatures in these materials are high (1140°C and 600°C for LN and LT, respectively), perfect linear characteristics can be observed in electro-optic, piezoelectric, and other effects at room temperature. Though fundamental studies had been conducted, particularly into their electrooptic and piezoelectric properties, commercialization was not accelerated initially because the figure of merit was not very attractive in comparison with perovskite ceramic competitors. [Cb (columbium) was the former name of the chemical element niobium in the 1950s.] Since Toshiba, Japan started mass production of LN single crystals after the 1980s, dramatic production cost reductions were achieved. Murata commercialized filters, SAW filters, by using the SAW mode on the LN single crystal. Recent developments in electro-optic light valves, switches, and photorefractive memories, which are encouraged by optical communication technologies, can be found in Ref. 20.

1.1.6 Relaxor Ferroelectrics—Ceramics and Single Crystals After the discovery of barium titanate and PZT, in parallel to the PZTbased ternary solid solutions, complex perovskite structure materials were intensively synthesized and investigated in the 1950s. In particular, the contributions by the Russian researcher group led by G. A. Smolenskii were enormous. Among them, huge dielectric permittivity was reported in Pb(Mg1/3Nb2/3)O3 (PMN)21 and Pb(Zn1/3Nb2/3)O3 (PZN).22 PMNbased ceramics became major compositions for high dielectric constant k (10,000) capacitors in the 1980s. It is noteworthy to introduce two epoch-making discoveries in the late 1970s and early 1980s, relating to electromechanical couplings in relaxor ferroelectrics: electrostrictive actuator materials and high electromechanical coupling factor k (95%) piezoelectric single crystals. Cross, Jang, Newnham, Nomura, and Uchino23 reported extraordinarily large secondary electromechanical coupling, in other words, electrostrictive effect, with the strain level higher than 0.1% at room temperature, exhibiting negligible hysteresis during rising and falling electric field, in a composition of 0.9 PMN-0.1 PbTiO3 (see Fig. 1.5). Every phenomenon has primary and secondary effects, which are sometimes recognized as linear and quadratic phenomena, respectively. In actuator materials, these correspond to the piezoelectric and electrostrictive effects.

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1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

Electric field in KV/cm−1 −25

−20

−15

−10

−5

+5

(A)

+10 (B)

+15

+20

+25

(A)

−2

−3

Strain S2 × 10−4

−1

−4

FIG. 1.5 Transverse strain in ceramic specimens of 0.9PMN-0.1PT (A) and a typical hard PZT 8 piezoceramic (B) under varying electric fields.23

When the author started actuator research in the the mid-1970s, precise “displacement transducers” (we initially used this terminology) were required in the Space Shuttle program, particularly for “deformable mirrors,” for controlling the optical pathlengths over several wavelengths (1 micron). Conventional piezoelectric PZT ceramics were plagued by hysteresis and aging effects under large electric fields; this was a serious problem for an optical positioner. Electrostriction, which is the secondary electromechanical coupling observed in centrosymmetric crystals, is not affected by hysteresis or aging.20 Piezoelectricity is a primary (linear) effect, where the strain is generated in proportion to the applied electric field, while the electrostriction is a secondary (quadratic) effect, where the strain is in proportion to the square of the electric field (parabolic strain curve). Their response should be much faster than the time required for domain reorientation in piezoelectrics/ferroelectrics. In addition, electric poling is not required. However, at that time, most people believed that the secondary effect would be minor and could not provide a larger contribution than the primary effect. Of course, this may be true in most cases, but the author’s group actually discovered that relaxor ferroelectrics, such as the lead magnesium niobate-based solid solutions, exhibit enormous electrostriction. This discovery, in conjunction with the author’s multilayer actuator invention (1978), accelerated the development of piezoelectric actuators after the 1980s. Dr. S. Nomura’s group was interested in making single crystals of PZT in the 1970s, in order to clarify the crystal orientation dependence of

1.1 THE HISTORY OF PIEZOELECTRICS

11

the piezoelectricity. However, it was difficult to prepare large single crystals around the MPB compositions (52/48). Thus, we focused on the Pb (Zn1/3Nb2/3) O3-PbTiO3 solid solution system, which has a phase diagram similar to the PZT system, but large single crystals are easily prepared. See the MPB between the rhombohedral and tetragonal phases in Fig. 1.6, in comparison with Fig. 1.4.24 Fig. 1.7 shows changes of electromechanical coupling factors with a mole fraction of PT in the Pb(Zn1/3Nb2/3)O3-PbTiO3 solid solution system, reported by Kuwata, Uchino, and Nomura in 1982,25 which was best cited in 1998. Note that the MPB composition, 0.91 PZN-0.09 PT, exhibited the maximum for all parameters, as expected, but the highest values in electromechanical coupling factor k33* and the piezoelectric constant d33* reached 95% and 1600 pC/N. (Superscript * was used because the poling direction was not along the spontaneous direction.) When a young PhD student, J. Kuwata, reported to the author first, even the author could not believe the large numbers. Thus, the author and Dr. Kuwata worked together to re-examine the experiments. When the author saw the antiresonance frequency almost twice of the resonance frequency, the author needed to believe the incredibly high k value. The author still remembers that the first submission of our manuscript was rejected because the referee could not “believe this large value.” The maximum k33 in 1980 was about 72% in PZT-based ceramics. The paper was published after a year-long communication by sending the raw admittance curves, etc. However, the original discovery was not believed or not required for applications until the mid-1990s. Economic recession and aging demographics (average age reached 87 years old) in Japan accelerated medical technologies, and high-k piezoelectric materials have focused on in medical acoustics since the mid1990s. Toshiba started reinvestigation of PZN-PT single crystals, with a FIG. 1.6

Phase diagram for the Pb(Zn1/3Nb2/3) O3-PbTiO3 solid solution system.

Cubic

Transition temperature (°C)

200

Tetragonal 100

0 Rhombohedral

−100 0 PZN

0.1 x

0.2 PT→

1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

l3(´10−4 Cm−2K−1)

12

10

5

:Rhombo.

:Tetr. * d33

dij (´10−10 CN−1)

15 10

* d31 d33

d33

5

−d33 0

* k33

1.0

k33, −k31

k33

0.5

−k31

k33

* −k31

−k31

E* s33

1 E s33

* s33

E s11

E

sij (´10−10 m−2N−1)

0

0

T*

e3 2

E//[111]

E//[001]

T

e3 (´103)

4

0

0 PZN

0.1 x

0.2 PT→

FIG. 1.7 Changes of electromechanical coupling factors with mole faction of PT in the Pb (Zn1/3Nb2/3)O3-PbTiO3 solid solution system.

13

1.1 THE HISTORY OF PIEZOELECTRICS

strong crystal manufacturing background of lithium niobate in the 1980s. These data reported 15 years earlier have been reconfirmed, and improved data were obtained, aiming at medical acoustic applications.26 In parallel, Park and Shrout27 at The Penn State University demonstrated the strains as large as 1.7% induced practically for the PZN-PT solid solution single crystals. There is considerable interest at present in the application of these single crystals, sponsored by the US Navy. The single crystal relaxor ferroelectric is one of the rare examples, where interest has been revived 15 years after the original discovery. It is notable that the highest values are observed for a rhombohedral composition only when the single crystal is poled along the perovskite [0 0 1] axis, not along the [1 1 1] spontaneous polarization axis. Fig. 1.8 illustrates an intuitive principle model in understanding this piezoelectricity enhancement depending on the crystal orientation in perovskite ferroelectrics. The key is the largest electromechanical coupling for the d15 shear mode in perovskite structures (i.e., d15 > d33 > d31), because there is easy rotation of the oxygen octahedron, in comparison with the squeeze deformation of the octahedron. The reader can refer to the theoretical paper (Ref. 28) authored by X. H. Du, U. Belegundu, and K. Uchino, which was also one of the most cited papers in 1998.

[001]

Z

[100]

[010]

X Y

d33

PS

PS

E1

PS

d33eff Strain

E1

E E

d15

PS

E2 E2

FIG. 1.8 The intuitive principle model in understanding the piezoelectricity enhancement depending on the crystal orientation in perovskite ferroelectrics.

14

1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

1.1.7 Polyvinylidene Difluoride In 1969, the piezoelectricity of polyvinylidene difluoride, PVDF, was discovered by Kawai29 at Kureha. The piezoelectric coefficients of poled thin films of the material were reported to be as large as 6–7 pCN1: 10 times larger than that observed in any other polymer. PVDF has a glass transition temperature (Tg) of about 35°C and is typically 50%–60% crystalline. To give the material its piezoelectric properties, it is mechanically stretched to orient the molecular chains and then poled under tension. Unlike other popular piezoelectric materials, such as PZT, PVDF has a negative d33 value. Physically, this means that PVDF will compress instead of expand or vice versa when exposed to the same electric field. PVDF-trifluoroethylene (PVDF-TrFE) copolymer is a wellknown piezoelectric, which has been popularly used in sensor applications such as keyboards. Bharti et al. reported that the field induced strain level can be significantly enhanced up to 5% by using a high-energy electron irradiation onto the PVDF films.30

1.1.8 Pb-Free Piezoelectrics The 21st century is called the “century of environmental management.” We are facing serious global problems such as the accumulation of toxic wastes, the greenhouse effect on Earth, contamination of rivers and seas, and lack of energy sources, oil, natural gas etc. In 2006, the European Community started RoHS (restrictions on the use of certain hazardous substances), which explicitly limits the usage of lead (Pb) in electronic equipment. The net result is that we may need to regulate the usage of lead zirconate titanate (PZT), the most famous piezoelectric ceramic, in the future. Governmental regulation on PZT usage may be introduced in Japan and Europe in the next 10 years. RoHS seems to be a significant threat to piezoelectric companies who have only PZT piezoceramics. However, this also represents an opportunity for companies that are preparing alternative piezoceramics for the piezoelectric device market. Pb (lead)-free piezoceramics started to be developed after 1999. Fig. 1.9 shows statistics of various lead-free piezoelectric ceramics. The share of the papers and patents for bismuth compounds (bismuth layered type and (Bi,Na)TiO3 type) exceeds 61%. This is because bismuth compounds are easily fabricated in comparison with other compounds. Fig. 1.10 shows the current best data reported by Toyota Central Research Lab, where strain curves for oriented and unoriented (K,Na,Li) (Nb,Ta,Sb)O3 ceramics are shown.31 Note that the maximum strain reaches up to 1500  106, which is equivalent to the PZT strain.

Other 6%

Tungsten bronze type compound 13%

Bi-layered type compound 34%

(Na,K)NbO3 type compound 20% (Bi1/2Na1/2)TiO3 type compound 27%

FIG. 1.9 Patent disclosure statistics for lead-free piezoelectric ceramics. (Total number of patents and papers is 102).

Strain (10-6)

2000 Oriented LF4

1500

1000

PZT-D

500 Unoriented LF4 0 0

(A)

500 1000 1500 Electric field (V/mm)

2000

1000 Oriented LF4 Smax /Emax (pm/V)

800 600 Unoriented LF4 400 200 0

(B) FIG. 1.10

0

50

100

150

200

Temperature (°C)

Strain curves for oriented and unoriented (K,Na,Li) (Nb,Ta,Sb)O3 ceramics.31

16

1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

1.1.9 Composites 1.1.9.1 Composite Effects Kitayama and Sugawara,32 Nippon Telegraph and Telephone, reported on piezoceramic:polymer composites at the Japan IEEE Conference in 1972, which would appear to be the first paper of the piezoelectric-based composites. As shown in Fig. 1.11, their paper dealt with the hot-rolled composites made from PZT powder and PVDF, and they reported on the piezoelectric and pyroelectric characteristics. Flexibility similar to PVDF, but higher piezoelectric performance than PVDF, was obtained. Newnham’s33 contribution to establishing the composite connectivity concept, and the summary of sum, combination, and product effects, promoted the systematic studies in piezocomposite field. In certain cases, the average value of the output of a composite exceeds both outputs of Phase 1 and Phase 2. Let us consider two different outputs, Y and Z, for two phases (i.e., Y1, Z1; Y2, Z2). When a figure of merit (FOM) for an effect is provided by the fraction (Y/Z), we may expect an extraordinary effect. Suppose that Y and Z follow the concave and convex type sum effects, respectively, as illustrated in Fig. 1.12; the combination value Y/Z will exhibit a maximum at an intermediate ratio of

FIG. 1.11 The first report on piezoelectric composites by Kitayama and Sugawara in 1972.

17

1.1 THE HISTORY OF PIEZOELECTRICS

Phase 1 : X ® Y1/Z1

X ® (Y/Z)*

Phase 2 : X ® Y2/Z2

Improvement Y1

Y2 Phase 1

Phase 2

Y1/Z1

Y2/Z2

Z1 Z2 Phase 1

Phase 1

Phase 2

Phase 2

FIG. 1.12 Basic concept of the performance improvement in a composite via a combination effect.

phases—that is, the average FOM is higher than either end member FOMs (Y1/Z1 or Y2/Z2). This was called a “combination effect.” Newnham’s group studied various connectivity piezoceramic/polymer composites, which exhibited a combination property of g (the piezoelectric voltage constant); this is provided by d/ε0ε (d: piezoelectric strain constant, and ε: relative permittivity), where d and ε follow the concave and convex type sum effects.

1.1.9.2 Magnetoelectric Composites When Phase 1 exhibits an output Y with an input X, and Phase 2 exhibits an output Z with an input Y, we can expect for a composite that exhibits an output Z with an input X. A completely new function is created for the composite structure, called a “product effect.” Philips developed a magnetoelectric material based on the product effect concept,34 which exhibits electric voltage under the magnetic field application, aiming at a magnetic field sensor. This material was composed of magnetostrictive CoFe2O4 and piezoelectric BaTiO3 mixed and sintered together. Fig. 1.13A shows a micrograph of a transverse section of a unidirectionally solidified rod of the materials with an excess of TiO2. Four finned spinel dendrites CoFe2O4 are observed in a BaTiO3 bulky whitish matrix. Fig. 1.13B shows the magnetic field dependence of the magnetoelectric effect in an arbitrary unit measured at room temperature. When a magnetic field is applied on this composite, cobalt ferrite generates magnetostriction, which is transferred to barium titanate as stress, finally leading to the generation of a charge/voltage via the piezoelectric effect in BaTiO3.

18

1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

DE DH

Hmax

(A)

Hdc

(B)

FIG. 1.13

(A) Micrograph of a transverse section of a unidirectionally solidified rod of mixture of magnetostrictive CoFe2O4 and piezoelectric BaTiO3, with an excess of TiO2. (B) Magnetic field dependence of the magnetoelectric effect in a CoFe2O4: BaTiO3 composite (at room temperature).34

Ryu et al.35 extended the magnetoelectric composite idea into a laminate structure (2–2 composites). We used Terfenol-D and high g soft PZT layers, which are much superior to the performances of cobalt ferrite and BT, respectively. However, due to the difficulty in cofiring of these two materials, we invented the laminated structures. This idea now forms the basis of the magnetoelectric sensor designs in the microelectromechanical systems (MEMS) area. 1.1.9.3 Piezoelectric Dampers An intriguing application of PZT composites is as a passive mechanical damper. Consider a piezoelectric material attached to an object whose vibration is to be damped. When vibration is transmitted to the piezoelectric material, the vibration energy is converted into electrical energy by the piezoelectric effect, and an AC voltage is generated. If a proper resistor is connected, however, the energy converted into electricity is consumed in Joule heating of the resistor, and the amount of energy converted back into mechanical energy is reduced so that the vibration can be rapidly damped. Indicating the series resistance as R, the capacitance of the piezoelectric material as C, and the vibration frequency as f, damping takes place most rapidly when the series resistor is selected in such a manner that the impedance matching condition, R ¼ 1/2πf C, is satisfied.36 Being brittle and hard, ceramics are difficult to assemble directly into a mechanical system. Hence, flexible composites can be useful in practice. When a composite of polymer, piezoceramic powder, and carbon black is fabricated (Fig. 1.14), the electrical conductivity of the composite is greatly changed by the addition of small amounts of carbon black.37 By properly selecting the electrical conductivity of the composite (i.e., electrical impedance matching), the ceramic powder effectively forms a series

1.1 THE HISTORY OF PIEZOELECTRICS

PZT ceramic

Piezoelectricity

FIG. 1.14

Carbon

Conductivity

19

Polymer

Mechanical flexibility

Piezoceramic:polymer: carbon black composite for vibration damping.

circuit with the carbon black, so that the vibration energy is dissipated effectively. The conductivity of the composite changes by more than 10 orders of magnitude around a certain carbon fraction called the “percolation threshold,” where the carbon powder link starts to be generated. This eliminates the use of external resistors. Note that the damper material exhibits a selective damping performance for a certain vibration frequency, depending on the selected resistivity of the composite, which can be derived from the electrical impedance matching between the permittivity and resistivity.

1.1.10 Other Piezoelectric-Related Materials 1.1.10.1 Photostrictive Materials The phtostriction phenomenon was discovered by Dr. P. S. Brody and the author independently, and almost at the same time, in 1981.38,39 In principle, the photostrictive effect arises from a superposition of the “bulk” photovoltaic effect, in other words, generation of large voltage from the irradiation of light, and the converse-piezoelectric effect, in other words, expansion or contraction under the applied voltage.39 In certain ferroelectrics, a constant electromotive force is generated with exposure of light, and a photostrictive strain results from the coupling of this bulk photovoltaic effect with converse piezoelectricity. A bimorph unit has been made from PLZT 3/52/48 ceramic doped with a slight addition of tungsten.40 The remnant polarization of one PLZT layer is parallel to the plate and in the direction opposite to that of the other plate. When a violet light is irradiated to one side of the PLZT bimorph, a photovoltage of 1 kV/mm is generated, causing a bending motion. The tip displacement of a 20 mm bimorph 0.4 mm in thickness was 150 μm, with a response time of 1 s. A photo-driven micro walking device, designed to begin moving by light illumination, has been developed.41 As shown in Fig. 1.15, it is simple

20

1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

FIG. 1.15

Photo-driven walking machine.

in structure, having neither lead wires nor electric circuitry, with two bimorph legs fixed to a plastic board. When the legs are irradiated alternately with light, the device moves like an inchworm with a speed of 100 μm/min. In pursuit of thick film type photostrictive actuators for space structure applications, in collaboration with Jet Propulsion Laboratory, Penn State investigated the optimal range of sample thickness and surface roughness dependence of photostriction. 30-μm thick PLZT films exhibit the maximum photovoltaic phenomenon.42 1.1.10.2 Monomorphs The “monomorph” is defined as a single uniform material that can bend under an electric field. A semiconductive piezoelectric plate can generate this intriguing bending phenomenon, discovered by Uchino’s group.43 When attending a basic conference of the Physical Society of Japan, the author learned about a surface layer generated on a ferroelectric single crystal due to formation of a Schottky barrier. It was not difficult to replace some of the technical terminologies with our words. First polycrystalline piezoelectric samples were used, with reduction processes to expand the Schottky barrier thickness. Uchino’s group succeeded in developing a monolithic bending actuator. A monomorph device has been developed to replace the conventional bimorphs, with simpler structure and manufacturing process. A monomorph plate with 30 mm in length and 0.5 mm in thickness can generate a 200 μm tip displacement, an equal magnitude to that of the conventional bimorphs. The “rainbow” actuator by Aura Ceramics44 is a modification of the above-mentioned semiconductive piezoelectric monomorphs, where half of the piezoelectric plate is reduced so as to make a thick semiconductive electrode to cause a bend.

1.2 PIEZOELECTRIC MATERIALS—PRESENT STATUS

21

1.2 PIEZOELECTRIC MATERIALS—PRESENT STATUS In the following sections, the author provides the reader with the necessary fundamental knowledge on piezoelectricity and the present status of materials.

1.2.1 Piezoelectric Figures of Merit There are five important figures of merit in piezoelectrics: the piezoelectric strain constant d, the piezoelectric voltage constant g, the electromechanical coupling factor k, the mechanical quality factor Qm, and the acoustic impedance Z. 1.2.1.1 Piezoelectric Strain Constant d The magnitude of the induced strain x by an external electric field E is represented by this figure of merit (an important figure of merit for actuator applications): x ¼ dE:

(1.2)

1.2.1.2 Piezoelectric Voltage Constant g The induced electric field E is related to an external stress X through the piezoelectric voltage constant g (an important figure of merit for sensor applications): E ¼ gX:

(1.3)

Taking into account the relation, P ¼ dX, we obtain an important relation between g and d:
 (1.4) g ¼ d=ε0 ε: ε : relative permittivity 1.2.1.3 Electromechanical Coupling Factor k The terms electromechanical coupling factor, energy transmission coefficient, and efficiency are sometimes confused.45 All are related to the conversion rate between electrical energy and mechanical energy, but their definitions are different.46 (a) The electromechanical coupling factor k
 k2 ¼ Stored mechanical energy=Input electrical energy or


 k2 ¼ Stored electrical energy=Input mechanical energy

(1.5)

(1.6)

Let us calculate Eq. (1.5), when an electric field E is applied to a piezoelectric material. See Fig. 1.16A, left. Since the input electrical

22

1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

x Mass E

(1.7)

x

x

E PS

dE

PS

0

E

Piezo-actuator sX

(A)

(B) x Output mechanical energy

P Input electrical energy

dE e0eE+dX dE+sX

E

−dE/s 0

0

X

E

dX X

(C)

sX

(1.9)

(D)

FIG. 1.16

Calculation of the input electrical and output mechanical energy: (A) load mass model for the calculation, (B) electric field versus induced strain curve, (C) stress versus strain curve, and (D) electric field versus polarization curve.

energy is (1/2) ε0εX E2 (εX: permittivity under stress free condition) per unit volume and the stored mechanical energy per unit volume under zero external stress is given by (1/2) x2/sE ¼ (1/2) (dE)2/sE (sE: elastic compliance under short-circuit condition), k2 can be calculated as the following: h i   k2 ¼ ð1=2Þ ðdEÞ2 =sE = ð1=2Þε0 εX E2 (1.7) ¼ d2 =ε0 εX  sE : (b) The energy transmission coefficient λmax Not all the stored energy can be actually used, and the actual work done depends on the mechanical load. With zero mechanical load or a complete clamp (no strain), no output work is done. The energy transmission coefficient is defined by
 λmax ¼ Output mechanical energy=Input electrical energy max or equivalently,

(1.8)

1.2 PIEZOELECTRIC MATERIALS—PRESENT STATUS


 λmax ¼ Output electrical energy=Input mechanical energy max

23 (1.9)

The difference of the above from Eqs. (1.5), (1.6) is “stored” or “spent.” Let us consider the case where an electric field E is applied to a piezoelectric under constant external stress X (10

X

TC (°C)

5

120

transducers. Sm-doped lead titanates exhibit extremely high mechanical coupling anisotropy kt/kp, suitable for medical transducers. Piezopolymer PVDF has small permittivity, leading to a high piezo g constant, in addition to mechanical flexibility, suitable for pressure/stress sensor applications.

1.2 PIEZOELECTRIC MATERIALS—PRESENT STATUS

35

1.2.3.1 Single Crystals Although piezoelectric ceramics are widely used for a large number of applications, single crystal materials retain their utility, being essential for applications such as frequency-stabilized oscillators and surface acoustic devices. The most popular single-crystal piezoelectric materials are quartz, lithium niobate (LiNbO3), and lithium tantalate (LiTaO3). The single crystals are anisotropic, exhibiting different material properties depending on the cut of the materials and the direction of bulk or surface wave propagation. Quartz is a well-known piezoelectric material. α-Quartz belongs to the triclinic crystal system with point group 32 and has a phase transition at 537°C to its β-form, which is not piezoelectric. Quartz has a cut with a zero temperature coefficient. For instance, quartz oscillators, operated in the thickness shear mode of the AT-cut, are used extensively for clock sources in computers, and frequency stabilized ones in TVs and VCRs. On the other hand, an ST-cut quartz substrate with X-propagation has a zero temperature coefficient for SAW, so it is used for SAW devices with highly stabilized frequencies. Another distinguished characteristic of quartz is an extremely high mechanical quality factor, QM > 105. Lithium niobate and lithium tantalate belong to an isomorphous crystal system and are composed of oxygen octahedron. The Curie temperatures of LiNbO3 and LiTaO3 are 1210 and 660°C, respectively. The crystal symmetry of the ferroelectric phase of these single crystals is 3 m, and the polarization direction is along the c-axis. These materials have high electromechanical coupling factors for SAWs. In addition, large single crystals can easily be obtained from their melt using the conventional Czochralski technique. Thus, both materials occupy very important positions in the SAW device application field. Single crystals of Pb(Mg1/3Nb2/3)O3 (PMN), Pb(Zn1/3Nb2/3)O3 (PZN), and their binary systems with PbTiO3 (PMN-PT and PZN-PT) with extremely large electromechanical coupling factors are discussed in the following section. 1.2.3.2 Polycrystalline Materials Barium titanate, BaTiO3, is one of the most thoroughly studied and most widely used ferroelectric materials. Just below the Curie temperature (130°C), the vector of the spontaneous polarization points in the [0 0 1] direction (tetragonal phase), below 5°C it reorients in the [0 1 1] (orthorhombic phase) and below 90°C in the [1 1 1] direction (rhombohedral phase). The dielectric and piezoelectric properties of ferroelectric ceramic BaTiO3 can be affected by its own stoichiometry, microstructure, and by dopants entering onto the A or B site in solid solution. Modified ceramic BaTiO3 with dopants such as Pb or Ca ions have been developed

36

1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

to stabilize the tetragonal phase over a wider temperature range and have been used as commercial piezoelectric materials. After the discovery of PZT, BT’s role in piezoelectric devices ceased, and it is primarily used in capacitors at present. However, in these 10 years, once Pb usage will be strictly regulated, interest in BT based piezoceramics may revive. Piezoelectric Pb(Ti,Zr)O3 solid solutions (PZT) ceramics discovered in the 1950s are widely used nowadays because of their superior piezoelectric properties. The phase diagram for the PZT system (PbZrxTi1xO3) is shown in Fig. 1.20. The crystalline symmetry of this solid-solution system is determined by the Zr content. Lead titanate also has a tetragonal ferroelectric phase of a perovskite structure. With increasing Zr content, x, the tetragonal distortion decreases and at x > 0.52 the structure changes from the tetragonal 4 mm phase to another ferroelectric phase of rhombohedral 3 m symmetry. The line dividing these two phases is called the morphotropic phase boundary (MPB). The boundary composition is considered to have both tetragonal and rhombohedral phases coexisting together. Fig. 1.21 shows the dependence of several piezoelectric d constants on composition near the MPB. The d constants have their highest values near the MPB. This enhancement in piezoelectric effect is attributed to the increased ease of reorientation of the polarization under an applied electric field. Doping the PZT material with donor or acceptor ions changes its properties dramatically. Donor doping with ions such as Nb5+ or Ta5+ provides “soft” PZTs, such as PZT-5, because of the facility of domain motion due to the resulting Pb-vacancies. On the other hand, acceptor doping with Fe3+ or Sc3+ leads to “hard” PZTs, such as PZT-8, because the oxygen vacancies will pin the domain wall motion. PZT in a ternary solid solution with another perovskite phase has been investigated intensively by Japanese ceramic companies. Examples of these ternary compositions are the following: PZTs in a solid solution with Pb(Mg1/3Nb2/3)O3 (Panasonic), Pb(Zn1/3Nb2/3)O3 (Toshiba), Pb (Mn1/3Sb2/3)O3, Pb(Co1/3Nb2/3)O3, Pb(Mn1/3Nb2/3)O3, Pb(Ni1/3Nb2/3) O3 (NEC), Pb(Sb1/2Sn1/2)O3, Pb(Co1/2W1/2)O3, and Pb(Mg1/2W1/2)O3 (Du Pont)—all of which were patented by different companies (almost all composition patents have already expired). Table 1.3 summarizes piezoelectric, dielectric, and elastic properties of typical PZTs: “soft” PZT-5H, semihard PZT-4, and “hard” PZT-8. Note that soft PZTs exhibit high k, high d, and high ε, in comparison with hard PZTs, while QM is quite high in hard PZTs. Thus, soft PZTs should be used for off-resonance applications, while hard PZTs are suitable to the resonance applications. The end member of PZT, lead titanate has a large crystal distortion. PbTiO3 has a tetragonal structure at room temperature with its tetragonality c/a ¼ 1.063. The Curie temperature is 490°C. Densely sintered PbTiO3 ceramics cannot be obtained easily, because they break up into a powder

37

1.2 PIEZOELECTRIC MATERIALS—PRESENT STATUS

500 Cubic

400

a a

Temperature (°C)

a

300 Tetragonal c

PS

100

a

0

0 10 PbTiO3

Rhombohedral

Morphotropic phase boundary

200

20

a

a

a PS a

30

40

50

60

70

80

90

100 PbZrO3

Mole % PbZrO3

FIG. 1.20

Phase diagram of lead zirconate titanate (PZT).

800

dij (´10−12 C/N)

600 d15

400 d33 200 −d31 0 48

50

52

54 Mole % PbZrO3

56

58

60

FIG. 1.21 Dependence of several d constants on composition near the morphotropic phase boundary in the PZT system.

when cooled through the Curie temperature due to the large spontaneous strain. Lead titanate ceramics modified by adding a small amount of additives exhibit a high piezoelectric anisotropy. Either (Pb,Sm)TiO351 or (Pb, Ca)TiO352 exhibits an extremely low planar coupling, that is, a large kt/kp ratio. Here, kt and kp are thickness-extensional and planar electromechanical coupling factors, respectively. Since these transducers can generate

38

1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

TABLE 1.3 Piezoelectric, Dielectric, and Elastic Properties of Typical PZTs Soft PZT-5H

Semi-Hard PZT-4

Hard PZT-8

kp

0.65

0.58

0.51

k31

0.39

0.33

0.30

k33

0.75

0.70

0.64

k15

0.68

0.71

0.55

d31 (1012 m/V)

274

122

97

d33

593

285

225

741

495

330

9.1

10.6

11.0

g33

19.7

24.9

25.4

g15

26.8

38.0

28.9

ε33X/ε0

3400

1300

1000

ε11X/ε0

3130

1475

1290

Dielectric loss (tan δ) (%)

2.00

0.40

0.40

s11E (1012 m2/N)

16.4

12.2

11.5

s12E

4.7

4.1

3.7

s13E

7.2

5.3

4.8

s33E

20.8

15.2

13.5

s44E

43.5

38.5

32.3

Mechanical QM

65

500

1000

Density ρ (103 kg/m3)

7.5

7.5

7.6

Curie temp (°C)

193

325

300

EM coupling factor

Piezoelectric coefficient

d15 3

g31 (10

Vm/N)

Permittivity

Elastic compliance

purely longitudinal waves through kt associated with no transverse waves through k31, clear ultrasonic imaging is expected without a “ghost” caused by the transverse wave. (Pb,Nd)(Ti,Mn,In)O3 ceramics with a zero temperature coefficient of the SAW delay have been developed as superior substrate materials for SAW device applications.53

1.2 PIEZOELECTRIC MATERIALS—PRESENT STATUS

39

1.2.3.3 Relaxor Ferroelectrics Relaxor ferroelectrics can be prepared either in polycrystalline form or as single crystals. They differ from the previously mentioned normal ferroelectrics in that they exhibit a broad phase transition from the paraelectric to ferroelectric state, a strong frequency dependence of the dielectric constant (i.e., dielectric relaxation) and a weak remanent polarization. Lead-based relaxor materials have complex disordered perovskite structures. Relaxor-type electrostrictive materials, such as those from the lead magnesium niobate-lead titanate, Pb(Mg1/3Nb2/3)O3-PbTiO3 (or PMNPT), solid solution are highly suitable for actuator applications. This relaxor ferroelectric also exhibits an induced piezoelectric effect. That is, the electromechanical coupling factor kt varies with the applied DC bias field. As the DC bias field increases, the coupling increases and saturates. Since this behavior is reproducible (no hysteresis), these materials can be applied as ultrasonic transducers that are tunable by the bias field.54 Single-crystal relaxor ferroelectrics with the MPB composition show tremendous promise as ultrasonic transducers and electromechanical actuators. Single crystals of Pb(Mg1/3Nb2/3)O3 (PMN), Pb(Zn1/3Nb2/3) O3 (PZN) and binary systems of these materials combined with PbTiO3 (PMN-PT and PZN-PT) exhibit extremely large electromechanical coupling factors.25,55 Large coupling coefficients and large piezoelectric constants have been found for crystals from the MPBs of these solid solutions. PZN-8%PT single crystals were found to possess a high k33 value of 0.94 for the (0 0 1) perovskite crystal cuts; this is very high compared to the k33 of around 0.70–0.80 for conventional PZT ceramics.

1.2.3.4 Polymers Polyvinylidene difluoride, PVDF or PVF2, is piezoelectric when stretched during fabrication. Thin sheets of the cast polymer are then drawn and stretched in the plane of the sheet, in at least one direction and frequently also in the perpendicular direction, to transform the material to its microscopically polar phase. Crystallization from the melt forms the nonpolar α-phase, which can be converted into the polar β-phase by a uni-axial or bi-axial drawing operation; the resulting dipoles are then reoriented through electric poling (see Fig. 1.22). Large sheets can be manufactured and thermally formed into complex shapes. The copolymerization of vinylidene difluoride with trifluoroethylene (TrFE) results in a random copolymer (PVDF-TrFE) with a stable, polar β-phase. This polymer need not be stretched; it can be poled directly as formed. A thickness-mode

40

1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

[CH2CF2]n Carbon Fluoride Hydrogen

z y x

FIG. 1.22

Structure of polyvinylidene difluoride (PVDF).

coupling coefficient of 0.30 has been reported. Piezoelectric polymers have the following characteristics: (a) small piezoelectric d constants (for actuators) and large g constants (for sensors), due to small permittivity (b) light weight and soft elasticity, leading to good acoustic impedance matching with water or the human body (c) a low mechanical quality factor QM, allowing for a broad resonance band width Such piezoelectric polymers are used for directional microphones and ultrasonic hydrophones. 1.2.3.5 Composites Piezo-composites comprising piezoelectric ceramic and polymer phases are promising materials because of their excellent and readily tailored properties. The geometry for two-phase composites can be classified according to the dimensional connectivity of each phase into 10 structures: 0–0, 0–1, 0–2, 0–3, 1–1, 1–2, 1–3, 2–2, 2–3, and 3–3.33 A 1–3 piezo-composite, such as the PZT-rod:polymer composite, is one of the most promising configurations. The advantages of this composite are high coupling factors, low acoustic impedance, good matching to water or human tissue, mechanical flexibility, broad bandwidth in combination with a low mechanical quality factor, and the possibility of making undiced arrays by structuring the electrodes. The thickness-mode electromechanical coupling of the composite can exceed the kt (0.40–0.50) of the constituent ceramic, approaching almost the value of the rod-mode electromechanical coupling, k33 (0.70–0.80) of that ceramic.56 The electromechanical coupling factor of the composites is much superior to the pure polymer piezoelectrics. Acoustic impedance is the square root of the product of its density and elastic stiffness. The acoustic match to tissue or water (1.5 Mrayls)

1.2 PIEZOELECTRIC MATERIALS—PRESENT STATUS

41

of the typical piezoceramics (20–30 Mrayls) is significantly improved by forming a composite structure, that is, by replacing some of the heavy, stiff ceramic with a light, soft polymer. Piezoelectric composite materials are especially useful for underwater sonar and medical diagnostic ultrasonic transducer applications. Fujifilm unveiled their bendable and foldable 0:3 composites (PZT fine powder was mixed in a polymer film) through a news release; its superior acoustic performance seems to be promising for flat-speaker applications.57

1.2.4 Thin-Films Both zinc oxide (ZnO) and aluminum nitride (AlN) are simple binary compounds with a Wurtzite-type structure, which can be sputterdeposited as a c-axis oriented thin film on a variety of substrates. Since ZnO has reasonable piezoelectric coupling, thin films of this material are widely used in bulk acoustic and SAW devices. The fabrication of highly oriented (along c) ZnO films have been studied and developed extensively. However, the performance of ZnO devices is limited, due to their low piezoelectric coupling (20%–30%). PZT thin films are expected to exhibit higher piezoelectric properties. At present the growth of PZT thin films is being carried out for use in microtransducers and microactuators. 1.2.4.1 Thin Film Preparation Technique Techniques for fabrication of oxide thin films are classified into physical and chemical processes: (a) Physical processes electron beam evaporation RF sputtering, DC sputtering ion beam sputtering ion plating (b) Chemical processes sol-gel method (dipping, spin coating etc.) chemical vapor deposition (CVD) MOCVD liquid phase epitaxy, melting epitaxy, capillary epitaxy, etc. Sputtering has been most commonly used for ferroelectric thin films such as LiNbO3, PLZT, and PbTiO3. Fig. 1.23 shows the principle of a magnetron sputtering apparatus. Heavy Ar plasma ions bombard the cathode (target) and eject its atoms. These atoms are deposited uniformly on the substrate in an evacuated enclosure. Choosing a suitable substrate and deposition condition, single crystal-like epitaxially deposited films can be obtained. The sol-gel technique has also been employed for processing

42

1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

Heater

Ar

Holder Substrate O2

Gas Plasma

Magnetic field

Vacuum pump

Target N S

S N

N S

High f power supply

FIG. 1.23

Principle of a magnetron sputtering apparatus.

PZT films. Applications of thin film ferroelectrics include memories, SAW devices, piezo sensors and micromechatronic or MEMS (micro electromechanical system) devices. As was discussed with regard to Fig. 1.8 in the previous section, (0 0 1) epitaxially oriented PZT rhombohedral composition films are most suitable from the application viewpoint.28 Kalpat et al. demonstrated (0 0 1) and (1 1 1) oriented films on the same Pt-coated Si substrate by changing the rapid thermal annealing profile.58 Fig. 1.24A and B shows the PZT (70/30) films with (0 0 1) and (1 1 1) orientations.

1.2.4.2 MEMS Application The micromachining process used by the author’s group to fabricate the PZT micropump is illustrated in Fig. 1.25. The etching process for the silicon:PZT unit is shown on the left-hand side of the figure and that for the glass plate is shown on the right-hand side. A schematic of the micropump for a blood tester is pictured in Fig. 1.26.58 The blood sample and test chemicals enter the system through the two inlets, shown in Fig. 1.26, are mixed in the central cavity, and finally are passed through the outlet for analysis. The movement of the liquids through the system occurs through the bulk bending of the PZT diaphragm in response to the drive potential provided by the interdigital surface electrodes.

43

1.2 PIEZOELECTRIC MATERIALS—PRESENT STATUS

800 600 400

PZT(111)

PZT(200)

CPS (abritrary units)

Temperature (°C)

PZT(100)

PZT(100) PZT(111)

200 0 0

20

40

60

80

100

Annealing time (s)

(A)

20

25

30

35

40

45

50

2q

(B)

FIG. 1.24 Epitaxially grown rhombohedral (70/30) PZT films with (0 0 1) and (1 1 1) orientations: (A) optimum rapid thermal annealing profiles and (B) X-ray diffraction patterns for films grown according to these profiles.58

Pt/Ti/Silicon on insulator wafer (SOI) Bottom glass plate

PZT thin film sputtering

Masking and wet etching formation of cavity in glass

Top electrode Au/Ti deposition

Top electrode patterning (photolithography and lift-off)

Anodic bonding to silicon wafer

Deep reactive Ion-etching (DRIE) membrane formation

FIG. 1.25

The micromachining process used to fabricate a PZT micropump.58

SiO2/Si

Inlet Glass wafer

Top electrode

PZT

IDTs

Bottom electrode

Inlet Outlet

FIG. 1.26 A schematic diagram of the structure of a PZT micropump.58 Actual size: 4.5 mm  4.5 mm  2 mm.

44

1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

1.2.4.3 Constraints in Thin/Thick Films The thin film structure is inevitably affected by four significant parameters: (1) Size constraints: Similar to a powder sample, there may exist a critical film thickness below which the ferroelectricity would disappear.59 (2) Stress from the substrate: Tensile or compressive stress is generated due to thermal expansion mismatch between the film and the substrate, sometimes leading to a higher coercive field for domain reorientation. Curie temperature is also modified with a rate of 50°C per 1 GPa. We may manipulate the Curie temperature to increase or decrease, theoretically owing to the induced stress. (3) Epitaxial growth: Crystal orientation dependence should be also considered, similar to the case of single crystals. An example can be found in a rombohedral composition PZT, which is supposed to exhibit the maximum performance when the Ps direction is arranged 57 degree cant from the film normal direction (i.e., (0 0 1) crystallographic orientation).28 (4) Preparation constraint: Si substrate requires a low sintering temperature of the PZT film. Typically 800°C for a short period is the maximum for preparing the PZT, which may limit the crystallization of the film, leading to the reduction of the properties. A metal electrode on a Si wafer such as Pt also limits the crystallinity of the PZT film.

1.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS 1.3.1 Pressure Sensors/Accelerometers/Gyroscopes One of the basic applications of piezoelectric ceramics is a gas igniter. The very high voltage generated in a piezoelectric ceramic under applied mechanical stress can cause sparking and ignite the gas. There are two means to apply the mechanical force: either by a rapid, pulsed application or by a more gradual, continuous increase. Piezoelectric ceramics can be employed as stress sensors and acceleration sensors, because of the direct piezoelectric effect. Fig. 1.27 shows a 3D stress sensor designed by Kistler. By combining an appropriate number of quartz crystal plates (extensional and shear types), the multilayer device can detect 3D stresses.60 Fig. 1.28 shows a cylindrical gyroscope commercialized by NEC-Tokin (Japan).61 The cylinder has six divided electrodes, one pair of which is

45

1.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

X Z

+ –

Y

+ – – +

+ –

+ –

+ –

FIG. 1.27

– + + – – + + –

– +

+ –

2

+ –

3

+ –

4

X

– + + –

– + + –

– +

+ –

– +

– +

1

+ –

Z

– + + –

– +

– +

Y

3D stress sensor (by Kistler).60

Vibrator

Lead

Holder

Support

FIG. 1.28

Cylindrical gyroscope (by NEC-Tokin).

used to excite the fundamental bending vibration mode, while the other two pairs are used to detect the acceleration. When the rotational acceleration is applied about the axis of this gyro, the voltage generated on the electrodes is modulated by the Coriolis force. By subtracting the signals between the two sensor electrode pairs, a voltage directly proportional to the acceleration can be obtained.

1.3.2 Piezoelectric Vibrators/Ultrasonic Transducers 1.3.2.1 Piezoelectric Vibrators In the use of mechanical vibration devices such as filters or oscillators, the size and shape of a device are very important, and both the vibrational mode and the ceramic material must be considered. The resonance

46

1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

frequency of the bending mode in a centimeter-size sample that ranges from 100 to 1000 Hz, which is much lower than that of the thickness mode (100 kHz). For these vibrator applications the piezoceramic should have a high mechanical quality factor (QM) rather than a large piezoelectric coefficient d; that is, hard piezoelectric ceramics are preferable. For speakers or buzzers audible by humans, devices with a rather low resonance frequency are used (100 Hz–2 kHz range). Examples are a unimorph consisting of one piezoceramic plate bonded with a metallic shim, a bimorph consisting of two piezoceramic plates bonded together, and a piezoelectric fork consisting of a piezo-device and a metal fork. A piezoelectric buzzer design has merits such as high electric power efficiency, compact size, and long life. A state-of-the-art speaker has only a 0.7 mm ultra-thin thickness and a 0.4 g weight.62 The power consumption is only 1/5–2/3 compared to electromagnetic types. The piezo-speaker has wide frequency range and high sound pressure, and in particular no interference with credit cards (with a magnetic memory strip), which is important nowadays. 1.3.2.2 Ultrasonic Transducers Ultrasonic waves are now used in various fields. The sound source is made from piezoelectric ceramics, as well as magnetostrictive materials. Piezoceramics are generally superior in efficiency and in size to magnetostrictive materials. In particular, hard piezoelectric materials with a high QM are preferable because of high power generation without heat generation. A liquid medium is usually used for sound energy transfer. Ultrasonic washers; ultrasonic microphones; sonars for short-distance remote control, underwater detection, and fish finding; and nondestructive testers are typical applications of piezoelectric materials. Ultrasonic scanning detectors are useful in medical electronics for clinical applications ranging from diagnosis to therapy and surgery. (a) Ultrasonic imaging One of the most important applications is based on the ultrasonic echo field.63,64 Ultrasonic transducers convert electrical energy into a mechanical form when generating an acoustic pulse, and they convert mechanical energy into an electrical signal when detecting its echo. The transmitted waves propagate into a body and echoes are generated which travel back to be received by the same transducer. These echoes vary in intensity according to the type of tissue or body structure, thereby creating images. An ultrasonic image represents the mechanical properties of the tissue, such as density and elasticity. We can recognize anatomical structures in an ultrasonic image since the organ boundaries and fluid-to-tissue interfaces are easily

1.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

47

discerned. The ultrasonic imaging process can also be carried out in real time. This means we can follow rapidly moving structures such as the heart without motion distortion. In addition, ultrasound is one of the safest diagnostic imaging techniques. It does not use ionizing radiation like X-rays and thus is routinely used for fetal and obstetrical imaging. Useful areas for ultrasonic imaging include cardiac structures, the vascular systems, the fetus, and abdominal organs such as the liver and kidneys. In brief, it is possible to see inside the human body without breaking the skin by using a beam of ultrasound. Fig. 1.29 shows the basic ultrasonic transducer geometry. The transducer is mainly composed of three layers: matching layer, piezoelectric ceramic, and backing layer.65 One or more matching layers are used on the surface of the piezoceramic array to increase sound transmissions into tissues. The backing is added to the rear of the transducer in order to dampen the acoustic backwave and to reduce the pulse duration. Piezoelectric materials are used to generate and detect ultrasound. In general, broadband transducers should be used for medical ultrasonic imaging. The broad bandwidth response corresponds to a short pulse length, resulting in better axial resolution. Three factors are important in designing broad bandwidth transducers: acoustic impedance matching, a high electromechanical coupling coefficient of the transducer, and electrical impedance matching. These pulse echo transducers operate based on thickness mode resonance of the piezoelectric thin plate. Further, a low planar mode coupling coefficient, kp, is beneficial for limiting energies being expended in nonproductive lateral mode. A large dielectric constant is necessary to enable a good electrical impedance match to the system, especially with tiny piezoelectric sizes. There are various types of transducers used in ultrasonic imaging. Mechanical sector transducers consist of single, relatively large resonators and can provide images by mechanical scanning such as wobbling. Multiple element array transducers permit discrete elements to be individually accessed by the imaging system and enable electronic focusing in the scanning plane to various adjustable penetration depths through the use of phase delays. Two basic types of array transducers are linear and phased (or sector). A linear array is a collection of elements arranged in one direction, producing a rectangular display (see Fig. 1.30). A curved linear (or convex) array is a modified linear array whose elements are arranged along an arc to permit an enlarged trapezoidal field of view. The elements of these linear type array transducers are excited sequentially group by group with the sweep of the beam in one direction. These linear array transducers are used for radiological and obstetrical examinations. On the other hand, in a

48

1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

Piezoelectric element Backing

Matching layer

Ultrasonic beam

Input pulse

FIG. 1.29

Basic transducer geometry for acoustic imaging applications.

W L

T

(A) Piezoelectric vibrator

Backing

(B) FIG. 1.30 Linear array type ultrasonic probe: (A) vibrator element and (B) structure of an array-type ultrasonic probe.

phased array transducer the acoustic beam is steered by signals that are applied to the elements with delays, creating a sector display. This transducer is useful for cardiology applications where positioning between the ribs is necessary. Figure 1.31 demonstrates the superiority of the PZN-PT single crystal to the PZT ceramic for medical imaging transducer applications,

1.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

49

FIG. 1.31 Ultrasonic imaging with the two PZT ceramic probes (left) and with the PZN-PT single crystal probe (right). Courtesy of Toshiba.

developed by Toshiba Corporation.66 Conventionally, the medical doctor needs to use two different frequency PZT probes, one (2.5 MHz) for checking wider and deeper area and the other (3.75 MHz) for monitoring the specified area with a better resolution. The PZN-PT single crystal (with very high k33 and kt) probe provides two additional merits: (1) wide bandwidth—without changing the probe, the doctor can just switch the drive frequency from 2.5 to 3.75 MHz— and(2) a strong signal; because of the high electromechanical coupling, the receiving signal level is enhanced more than double compared with the PZT probe. (b) Sonochemistry Fundamental research on “sonochemistry” is now very rapidly occurring. With using the “cavitation” effect, toxic materials such as dioxin and trichloroethylene can be easily transformed into innocuous materials at room temperature. Ultrasonic distillation is also possible at room temperature for obtaining highly concentrated Japanese sak
e. Unlike the regular boiling distillation, this new method gives sak
e a much higher alcoholic concentration, while keeping gorgeous taste and fragrance. Fig. 1.32A shows the alcoholic concentration in the base solution and mist. This high-quality sak
e product is now commercially available.68 High power ultrasonic technology is applicable to transdermal drug delivery. The Penn State researchers are working to commercialize a “needle-free” injection system of insulin by using cymbal piezoactuators (see Fig. 1.32B).67

50

1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

Ethanol mol concentration in mist (mol %)

100

Boiling distillation 50

10°C

50

0

(A)

30°C

50°C

100

Ethanol mol concentration in solution (mol %)

(B)

FIG. 1.32

(A) Room temperature distillation with high ultrasonic power and (B) a transdermal insulin drug delivery system using cymbal transducers.67 (A) Courtesy of Matsuura Brewer and (B) Courtesy of Paul Perreault.

1.3.2.3 Resonators/Filters When a piezoelectric body vibrates at its resonant frequency, it absorbs considerably more energy than at other frequencies, resulting in a dramatic decrease in the impedance. This phenomenon enables piezoelectric materials to be used as a wave filter. A filter is required to pass a certain selected frequency band or to block a given band. The bandwidth of a filter fabricated from a piezoelectric material is determined by the square of the coupling coefficient k, that is, it is nearly proportional to k2.


 The background is from the relation k31 2 = 1  k31 2 ¼ π 2 =4 ðΔf =fR Þ, where Δf ¼ fA  fR, and the bandwidth is provided by Δf. Quartz crystals with a very low k value of about 0.1 can pass very narrow frequency bands of approximately 1% of the center resonance frequency. On the other hand, PZT ceramics with a planar coupling coefficient of about 0.5 can easily pass a band of 10% of the center resonance frequency. The sharpness of the passband is dependent on the mechanical quality factor QM of the materials. Quartz also has a very high QM of about 106, which results in a sharp cut-off to the passband and a well-defined oscillation frequency. A simple resonator is a thin disc type, electroded on its plane faces and vibrating radially, for filter applications with a center frequency ranging from 200 kHz to 1 MHz and with a bandwidth of several percent of the center frequency. For a frequency of 455 kHz the disc diameter needs to be about 5.6 mm. However, if the required frequency is higher than 10 MHz, other modes of vibration such as the thickness extensional mode are exploited, because of its smaller size. The

1.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

51

Electrode

Ceramic plate Top

FIG. 1.33

Bottom

Schematic drawing of a trapped-energy filter.

trapped-energy type filters made from PZT ceramics have been widely used in the intermediate frequency range for applications such as the 10.7 MHz FM radio receiver and transmitter. When the trapped-energy phenomena are utilized, the overtone frequencies are suppressed. The plate is partly covered with electrodes of a specific area and thickness. The fundamental frequency of the thickness mode of the ceramic beneath the electrode is less than that of the unelectroded portion, because of the extra inertia of the electrode mass. The lower-frequency wave of the electroded region cannot propagate into the unelectroded region. The higher-frequency overtones, however, can propagate away into the unelectroded region. This is called the trapped-energy principle. Fig. 1.33 shows a schematic drawing of a trapped-energy filter. In this structure the top electrode is split so that coupling between the two parts will only be efficient at resonance. More stable filters suitable for telecommunication systems have been made from single crystals such as quartz or LiTaO3.

1.3.3 SAW Devices A surface acoustic wave (SAW), also called a Rayleigh wave, is essentially a coupling between longitudinal and shear waves. The energy carried by the SAW is confined near the surface. An associated electrostatic wave exists for a SAW on a piezoelectric substrate, which allows electroacoustic coupling via a transducer. The advantages of SAW technology are the following69,70: (1) The wave can be electroacoustically accessed and trapped at the substrate surface and its velocity is approximately 104 times slower than an electromagnetic wave. (2) The SAW wavelength is on the same order of magnitude as line dimensions produced by photolithography and the lengths for both short and long delays are achievable on reasonably sized substrates.

52

1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

There is a very broad range of commercial system applications that include front-end and IF (intermediate frequency) filters, CATV (community antenna television) and VCR (video cassette recorder) components, synthesizers, analyzers, and navigators. In SAW transducers, finger (interdigital) electrodes provide the ability to sample or trap the wave, and the electrode gap gives the relative delay. A SAW filter is composed of a minimum of two transducers. A schematic of a simple SAW bidirectional filter is shown in Fig. 1.34. A bidirectional transducer radiates energy equally from each side of the transducer. Energy that is not associated with the received signal is absorbed to eliminate spurious reflection. Various materials are currently being used for SAW devices. The most popular single-crystal SAW materials are lithium niobate and lithium tantalate. The materials have different properties depending on the cut of the material and the direction of propagation. The fundamental parameters considered when choosing a material for a given device application are SAW velocity, temperature coefficients of delay (TCD), electromechanical coupling factor, and propagation loss. SAWs can be generated and detected by spatially periodic, interdigital electrodes on the plane surface of a piezoelectric plate. A periodic electric field is produced when an RF source is connected to the electrode, thus permitting piezoelectric coupling to a traveling surface wave. If an RF source with a frequency, f, is applied to the electrode having periodicity, d, energy conversion from an electrical to mechanical form will be maximum when f ¼ f0 ¼ vs =d,

(1.38)

where vs is the SAW velocity and f0 is the center frequency of the device. The SAW velocity is an important parameter determining the center frequency. Another important parameter for many applications is temperature sensitivity. For example, the temperature stability of the center

SAW Output

Input

Interdigital electrode Piezoelectric substrate

FIG. 1.34

Fundamental structure of a surface acoustic wave device.

1.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

53

frequency of SAW bandpass filters is a direct function of the temperature coefficient for the velocity and the delay for the material used. The firstorder temperature coefficient of delay is given by ð1=τÞ  ðdτ=dT Þ ¼ ð1=LÞ  ðdL=dT Þ  ð1=vs Þ  ðdvs =dT Þ,

(1.39)

where τ ¼ L/vs is the delay time and L is the SAW propagation length. The surface wave coupling factor, ks 2 , is defined in terms of the change in SAW velocity that occurs when the wave passes across a surface coated with a thin massless conductor, so that the piezoelectric field associated with the wave is effectively short-circuited. The coupling factor, ks 2 , is expressed by ks 2 ¼ 2ðvf  vm Þ=vf ,

(1.40)

where vf is the free surface wave velocity and vm is the velocity on the metallized surface. In actual SAW applications, the value of ks 2 relates to the maximum bandwidth obtainable and the amount of signal loss between input and output, which determines the fractional bandwidth as a function of minimum insertion loss for a given material and filter. Propagation loss is one of the major factors that determines the insertion loss of a device and is caused by wave scattering at crystalline defects and surface irregularities. Materials that show high electromechanical coupling factors combined with small temperature coefficients of delay are generally preferred. The free surface velocity, vf, of the material is a function of the cut angle and propagation direction. The TCD is an indication of the frequency shift expected for a transducer due to a temperature change and is also a function of the cut angle and propagation direction. The substrate is chosen based on the device design specifications that include operating temperature, fractional bandwidth, and insertion loss. Piezoelectric single crystals such as 128 ° Y-X (128 °-rotated-Y-cut and X-propagation)—LiNbO3 and X-112 ° Y (X-cut and 112 °-rotated-Ypropagation)—LiTaO3 have been extensively employed as SAW substrates for applications in VIF filters. A c-axis oriented ZnO thin film deposited on a fused quartz, glass, or sapphire substrate has also been commercialized for SAW devices. Table 1.4 summarizes some important material parameters for these SAW materials. A delay line can be formed from a slice of glass such as PbO or K2Odoped SiO2 glass in which the velocity of sound is nearly independent of temperature. PZT ceramic transducers are soldered on two metallized edges of the slice of glass. The input transducer converts the electrical signal to a shear acoustic wave that travels through the slice. At the output transducer the wave is reconverted into an electrical signal delayed by the length of time taken to travel around the slice. Such delay lines are used in color TV sets to introduce a delay of approximately 64 μs and are also employed in videotape recorders.

54

1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

TABLE 1.4 SAW Material Properties

Single crystal

Ceramici

Thin film

Material

Cut-Propagation direction

k2 (%)

TCD (ppm/C)

V0(m/s)

εr

Quartz

ST-X

0.16

0

3158

4.5

LiNbO3

128 degree Y-X

5.5

74

3960

35

LiTaO3

X112 degree-Y

0.75

1 8

3290

42

Li2B4O7

(1 1 0)–

0.8

0

3467

9.5

PZT-In (Li3/5W2/5)O3

1.0

10

2270

690

(Pb,Nd)(Ti,Mn, In)O3

2.6

50%. Fig.1.45 illustrates the recent inkjet printer produced by Seiko Epson,96 in which PZT thin plates were laminated with vibration, chamber, and communication plates to create a unimorph actuation mechanism. Using the cofiring technique with PZT and ZrO2 elastic parts for manufacturing this, ML chips head (MACH), Epson achieved superior stability in ink chamber vibration

62

1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

FIG. 1.42 Hubble Telescope using three PMN electrostrictive multilayer actuators for optical image correction.

Lag pin Piezoelectric crystals

Torque tube Hub Flexbeam Pitch link Blade

FIG. 1.43

Bearingless rotor flexbeam with attached piezoelectric strips. A slight change in the blade angle provides for enhanced controllability. Head element Platen Paper Ink ribbon Guide Piezoelectric actuator

Wire Wire

Stroke amplifier

Wire guide

(A) FIG. 1.44

(B)

(A) Structure of a dot-matrix printer head (NEC) and (B) a differential-type piezoelectric printer-head element. A sophisticated monolithic hinge lever mechanism amplifies the actuator displacement by 30 times.

63

1.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

MLChips Upper electrode PZT Lower electrode

0.5 mm

Vibration plate Chamber plate Communication plate Ink pass

Adhesive layer Stainless plate

Ink supply hole Ink chamber Nozzle

FIG. 1.45

MACH Ink-jet printer head developed by Seiko Epson.

and for various inks. In addition, more importantly, the manufacturing cost reduced dramatically by adopting this cofiring technique. Toyota developed a Piezo TEMS (Toyota Electronic Modulated Suspension), which is responsive to each protrusion on the road in adjusting the damping condition, and installed it on a Celcio (equivalent to a Lexus, internationally) in 1989.97 In general, as the damping force of a shock absorber in an automobile is increased (i.e., “hard” damper), the controllability and stability of a vehicle are improved. However, comfort is sacrificed because the road roughness is easily transferred to the passengers. The purpose of the electronically controlled shock absorber is to obtain both controllability and comfort simultaneously. Usually the system is set to provide a low damping force (“soft”) so as to improve comfort, and the damping force is changed to a high position according to the road condition and the car speed to improve the controllability. In order to respond to road roughness, a very high response of the sensor and actuator combination is required. Fig. 1.46 shows the structure of the electronically controlled shock absorber. The sensor is composed of 5 layers of 0.5 mm thick PZT disks. The detecting speed of the road roughness is about 2 ms and the resolution of the up-down deviation is 2 mm. The actuator is made of 88 layers of 0.5 mm thick disks. Applying 500 V generates a displacement of about 50 μm, which is magnified by 40 times through a piston and plunger pin combination. This stroke pushes the change valve of the damping force down then opens the bypass oil route, leading to the decrease of the flow resistance (i.e., “soft”). The up-down acceleration and pitching rate were monitored when the vehicle was driven on a rough road. When the TEMS system was used, the

64

1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

FIG. 1.46 Toyota Electronic modulated suspension (TEMS) with a multilayer piezoelectric actuator and a sensor.

up-down acceleration was suppressed to as small as the condition fixed at “soft,” providing comfort. At the same time, the pitching rate was also suppressed to as small as the condition fixed at “hard,” leading to better controllability. In order to increase the diesel engine efficiency, high pressure fuel and quick injection control are required. For this purpose, piezoelectric actuators, specifically ML types, were adopted. The highest reliability of these devices at an elevated temperature (150°C) for a long period (10 years) has been achieved. Common-rail type injection valves have been widely commercialized by Siemens, Bosch, and Denso Corp (Fig. 1.47).98 Fig. 1.48 shows a walking piezomotor with four multilayer actuators developed by Philips.99 Two shorter actuators function as clamps and the longer two provide the movement by an inchworm mechanism. A major drawback of this inchworm design is the mechanical noise created by the on-off drive (audible frequency due to the requirement lower than the mechanical resonance of the system).

1.3.7 Ultrasonic Motors The USM is one of the piezoelectric actuator categories. However, since it has been maturing as an industry already, the author uses a different section for its discussion.

1.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

65

Piezoelectric actuator

Control valve

Displacement amplification unit Injector body Nozzle

FIG. 1.47 Common rail-type diesel injector with a piezoelectric multilayer actuator. Courtesy by Denso Corp.

FIG. 1.48 Walking piezo motor using an inchworm mechanism with four multilayer piezoelectric actuators by Philips.

Electromagnetic motors were invented more than one hundred years ago. While these motors still dominate the industry, a drastic improvement cannot be expected except through new discoveries in magnetic or superconducting materials. Electromagnetic motors smaller than 1 cm exhibit an energy efficiency S (tetragonal) > S (rhombohedral) for their compositions. Table 4.2 summarizes7 the piezoelectric properties of BNBK2:1(x) (x ¼ 0.78, 0.88 and 0.98) including the d* and the S obtained from the results of Fig. 4.17. The d33* defined by the equation, d33 ½pm=V ¼

Strain, S  106 , Ea ½kV=mm

for example, is 188 pm/V with a relatively high Td (206°C) in the tetragonal composition (x ¼ 0.78). Finally, Table 4.3 summarizes the depolarization temperatures, Td, and piezoelectric properties of rhombohedral, MPB, and tetragonal compositions of the BNBK2:1(x) ternary system. TABLE 4.2 Piezoelectric Properties of BNBK2:1(x) (x ¼ 0.78, 0.88 and 0.98) x in BNBK2:1(x)

Td [°C]

k33

d33 [pC/N]

d33* [pm/V] at Ea 5 80 kV/cm

Strain [%] at 80 kV/cm

0.98

Rhombohedral

200

0.42

80

121

0.097

0.88

MPB

113

0.56

181

240

0.183

0.78

Tetragonal

206

0.45

126

188

0.150

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TABLE 4.3 The Depolarization Temperature, Td, and Piezoelectric Properties of Rhombohedral, MPB, and Tetragonal Compositions of BNBK2:1(x) Ternary System Comp. (x)

Rhombohedral

MPB

Tetragonal

0.94

0.90

0.89

0.88

0.84

0.82

0.80

0.78

Td(°C)

185

115

95

113

144

169

182

206

εs

844

1668

1698

1786

1617

1627

1058

879

εT33/ε0

493

756

778

999

1118

1081

993

883

εT11/ε0

652

900

1010

–

–

1078

–

–

k33

0.476

0.543

0.579

0.560

0.455

0.473

0.455

0.452

k31

0.153

0.207

0.222

0.217

0.094

0.098

0.097

0.100

kt

0.443

0.499

0.510

0.501

0.474

0.445

0.450

0.417

kp

0.253

0.340

0.361

0.319

0.156

0.159

0.170

0.162

k15

0.330

0.449

0.459

–

–

0.316

–

–

d33

91.6

142

168

181

140

144

128

126

d31 (pC/N)

28.5

48.0

54.3

59.2

27.7

28.2

26.8

26.3

d15

109

184

212

–

–

139

–

–

4.4 (Bi1/2Na1/2)TiO3 [BNT]-(Bi1/2Li1/2)TiO3 [BLT]-(Bi1/2K1/2)TiO3 [BKT] SYSTEM The BNT presents the low depolarization temperature Td of 185°C, and the MPBs of BNT-based solid solutions show a particularly low Td of approximately 100°C,86–89 even though the MPBs have excellent piezoelectric properties. For example, while the BNT-BKT-BT system shows a high electromechanical coupling factor, k33, of 0.56 and a high piezoelectric constant, d33, of 181 pC/N at the MPB, the Td is as low as 113°C.86 The piezoelectric working temperature range is limited to below the Td because piezoelectric properties disappear at the Td and with higher temperatures. Therefore, it is important to increase the Td of the MPB composition to enable its practical use in piezoelectric applications. Recently, we have investigated the variation in phase transition temperatures, such as the Td, rhombohedral-tetragonal phase transition temperature, TR-T, and the maximum dielectric temperature, Tm, of a BNT-based solid solution to increase the Td of BNT. As a result, we have clarified that the substitution of small amounts of Li1+ and K1+ in the A-site of BNT is possible for increasing the Td to 199 and 209°C, respectively. Moreover, in

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order to cosubstitute Li1+ and K1+ into the A-site of BNT, Td can be increased to 221°C at the rhombohedral composition. To clarify the details of the behavior of phase transition temperatures, the relationship between phase transition temperatures and electrical properties of BNT solid solutions substituted by monovalent (Li+ and K+) ions were investigated in detail. Two solid solutions, (1x)(Bi1/2 Na1/2)TiO3-x(Bi1/2K1/2)TiO3 [BNKT100x] and (1x)(Bi1/2Na1/2)TiO3-x(Bi1/2Li1/2)TiO3 [BNLT100x] ceramics,90 were prepared by the conventional ceramic fabrication process. X-ray powder diffraction patterns of BNKT100x and BNLT100x (x ¼ 0–0.24) indicated a single-phase perovskite structure and a few secondary phases for BNLT28. Therefore, the solubility of Li (x) in the A-site of BNLT100x was limited to 0–0.24 at atmospheric pressure because of its small ionic radius. The lattice constants a and c, rhombohedrality of 90°-α, and tetragonality c/a of BNKT100x show an MPB between rhombohedral and tetragonal phases at x ¼ 0.18–0.2. The 90°-α of BNKT100x was the highest at x ¼ 0.1, and then it decreased with increasing x. In addition, the tetragonality c/a increased with x at x > 0.20. Phase transition temperatures, Td, TR-T and Tm, are summarized in Fig. 4.15. Field-induced strains of BNKT100x under unipolar driving at 0.1 Hz are shown in Fig. 4.16, and the piezoelectric constant, d33, and the normalized strain, d33* (¼Smax/Emax), at 80 kV/cm are summarized in Fig. 4.17. The d33* was higher than the d33, because the d33* includes the domain contribution due to the high applied voltage and the low measuring frequency.91 The highest value was obtained near the MPB composition for BNKT100x. Moreover, the ratios of the d33* to the d33 are larger for the

400

Td, TR–T, Tm [ºC]

Tm 300 TR–T 200 Td 100

0 0.0

0.1

0.2 0.3 Composition, x

0.4

0.5

FIG. 4.15 Phase transition temperatures Td, TR-T and Tm as a function of the content (x) of BKT for BNKT100x ceramics.

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0.25 x = 0.22

BNKT100x 0.20

x = 0.20

Strain [%]

x = 0.30 0.15 x = 0.10 0.10

x = 0.04

0.05 0.1 Hz 0.00

0

20

40 60 Applied field [kV/cm]

80

100

FIG. 4.16 Field-induced strains of BNKT100x (x ¼ 0.04, 0.10, 0.20, 0.22 and 0.30) under unipolar driving at 0.1 Hz.

d33, d33∗ [pC/N or pm/V]

300

d33∗

250 200 d33

150 100 50 0.00

0.05

0.20 0.10 0.15 x in BNKT100x

0.25

0.30

FIG. 4.17 Compositional dependence of the piezoelectric constant d33 and the normalized strain, d33*, for BNKT100x.

tetragonal compositions than for the rhombohedral compositions due to the difference in the domain structures. The typical D-E hysteresis loops of a ferroelectric were obtained at RT for BNKT100x (x ¼ 0, 0.18 and 0.22). The variation of the D-E hysteresis loops for BNKT100x in the temperature range between 80 and 260°C is shown in Fig. 4.18. Double-hysteresis-like loops were observed at approximately the Td to 180°C for BNKT18 and BNKT22. It is considered that a double-hysteresis-like loop is due to the mixture phases because of the existence of the intermediate phase near the MPB. On the other hand,

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–100

(A)

BNKT18 40

40 20

–50

50 –20

50 Hz –40 Applied field [kV/cm]

100

80°C 120°C 160°C 200°C

20

–60 –40 –20

(B)

BNKT22 40

20

–20 –40 Applied field [kV/cm]

40

60

Polarization [μC/cm2]

100°C 170°C 180°C 200°C

Polarization [μC/cm2]

Polarization [μC/cm2]

BNT

80°C 160°C 20 180°C 220°C

–60 –40 –20

(C)

20

40

60

–20 –40 Applied field [kV/cm]

FIG. 4.18 Temperature dependences of D-E hysteresis loops for (A) BNT, (B) BNKT18, and (C) BNKT22.

weak ferroelectric hysteresis loops were observed at 200°C for BNKT18 and 220°C for BNKT22. There is no discussion about ferroelectricity of the middle phase of TR-T-Tm (TR-T > Td) and Td-Tm (TR-T < Td) for BNTbased solid solutions. However, the results of this study indicate that those regions are probably in a very weak ferroelectric state. Recently, an excellent piezoelectric constant d33 (d33 meter value) of 231 pC/N was obtained at the MPB composition of (Bi1/2Na1/2)TiO3(Bi1/2Li1/2)TiO3-(Bi1/2K1/2)TiO3 [BNT-BLT-BKT] ternary systems.92 However, the relationship between Td and d33 has not been clarified. From the effects of Li and K substitution on the Td in the A-site of BNT,90 it is seen that the Td of BNT increases when small amounts of Li and K are substituted. Thus, it is thought that cosubstitution of Li and K is effective in increasing the Td of BNT-based solid solutions. Therefore, this section describes the phase transition temperatures and the relationship between the Td and the d33, and also the piezoelectric properties of the x(Bi1/2Na1/2) TiO3-y(Bi1/2Li1/2)TiO3-z(Bi1/2K1/2)TiO3 (x + y + z ¼ 1) (abbreviated to BNLKT100y-100z) three-component system.93,94 In order to increase the Td, a small amount of Li substitution is probably optimal. In addition, it is important to use the MPB composition to enhance the piezoelectric properties. Thus, BNLKT4-100z and BNLKT8-100z have been studied to clarify the effects of Li and K concentrations. Fig. 4.19 shows the phase relation of the xBNT-yBLT-zBKT system including BNLT100y (BNTBLT) and BNKT100z (BNT-BKT). The ratios of the measured density to the theoretical density of sintered ceramics were all higher than 96%. BNLKT0-100z (z ¼ 0–0.26), BNLKT4100z (z ¼ 0–0.28), and BNLKT8-100z (z ¼ 0–0.28) all showed single phases of the perovskite structure. X-ray powder diffraction patterns displayed coexistence of rhombohedral and tetragonal phases at z ¼ 0.18–0.20 for BNLKT4-100z and at z ¼ 0.18–0.22 for BNLKT8-100z. Therefore, the morphotropic phase boundaries (MPBs) exist in these compositions. The rhombohedrality, 90°-α, and the tetragonality, c/a, of BNLKT4-100z and BNLKT8-100z indicate that the 90°-α of BNLKT4-100z is larger than that of BNLKT8-100z and the 90°-α reached the maximum at z ¼ 0.08 and

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175

(Bi1/2K1/2)TiO3

y = 0.08

y = 0.04 Tetr. MPB

BNLKT100y–100z

BNKT100z Rhomb.

(Bi1/2Li1/2)TiO3

BNLT100y

(Bi1/2Na1/2)TiO3

FIG. 4.19

The phase relation of the (Bi1/2Na1/2)TiO3 [BNT]-(Bi1/2Li1/2)TiO3 [BLT]-(Bi1/2 K1/2)TiO3 [BKT] system.

showed the lowest at the MPB. However, the c/a increased significantly near the MPB composition with increasing z, which tendency is similar to the MPB of PZT.1 Fig. 4.20 shows the variation in the depolarization temperature, Td, as a function of the content (z) of BKT, for BNLKT0-100z, BNLKT4-100z and BNLKT8-100z. In order to determine the Td accurately, it was measured from the temperature dependence of piezoelectric properties using fully poled (33)-mode specimens and a dielectric loss tangent, tan δ, using fully poled specimens.88 The Td of BNLKT4-100z was higher than those of 220 y = 0.04

Td [°C]

200

y=0

180 160 y = 0.08

140 120 0.00

0.05

0.10 0.15 0.20 z in BNLKT100y-100z

0.25

0.30

FIG. 4.20 Depolarization temperature, Td, of BNLKT100y-100z (y ¼ 0, 0.04 and 0.08) as a function of the content (z) of BKT.

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BNLKT0-100z and BNLKT8-100z. On the rhombohedral side (0 < z < 0.16), the Td was the highest (221°C) at z ¼ 0.08. Then, the Td decreased with increasing z and the lowest value of Td was approximately 160°C for y ¼ 0.04 at around the MPB composition of z ¼ 0.16–0.18. On the tetragonal side (0.2 < z < 0.28), the Td increased with increasing z, and that of BNLKT4-28 was 218°C. The Td of BNLKT0-0 (BNT), BNLKT4-0 and BNLKT8-0 were 185, 196, and 170°C, respectively. This result indicates that a small amount of Li substitution is effective in increasing Td of the BNT-based solid solution. In addition, the Td of BNLKT4-100z and BNLKT8-100z showed the maximum at z ¼ 0.08 at the rhombohedral side, which was the same as BNLKT0-100z. Although very few data on an increase in Td have been reported for a rhombohedral composition of BNT-based solid solutions,95 the Td could be increased up to 221°C for BNLKT4-8. Recently, piezoelectric ceramics have attracted much attention for high-powered devices, such as ultrasonic motors and transducers.96–98 These devices were mainly composed of Pb(Zr,Ti)O3 (PZT)-based piezoelectric ceramics with a high mechanical quality factor Qm, which is called hard PZT. However, the resonant vibration of hard PZT becomes unstable at a vibration velocity of approximately 1.0 m/s, resulting in Qm markedly decreasing and vibration velocity not increasing. Moreover, PZT contains a large amount of PbO; therefore, there has been much interest recently in lead-free piezoelectric ceramics as a material for replacing PZT-based ceramics. As materials for lead-free, high-powered applications, SrBi2Nb2O9 and (Sr,Ca)2NaNb5O15 have been reported.99–101 The relationship between the Td and the d33, and also the piezoelectric properties of the BNLKT100y-100z system, indicate that it has the high possibility of the use for high-powered applications. Therefore, in this section, we would like to compare the properties of the rhombohedral and tetragonal sides of MPB composition in the Td vs Qm, and to discuss the optimum composition for high-powered applications. In addition, we clarified the effect of Mn doping on the variations in Td and piezoelectric properties with high-power characteristics of BNLKT100y-100z, including w wt% MnCO3-doped BNLKT100y-100z (abbreviated to BNLKT100y-100zMnw). Fig. 4.21 shows the piezoelectric strain constant, d33, and the mechanical quality factor, Qm(33), in the (33)-mode, of BNLKT4-100z as a function of the content (z) of BKT. The d33 reaches about 180 pC/N at the MPB composition (z ¼ 0.20). On the other hand, the Qm(33) was the highest of approximately 200 at z  0.08 and it decreased to below 90 at z 0.18. Fig. 4.22 shows the relationships between the Td and (A) the d33 and (B) the Qm on the rhombohedral and tetragonal sides. As has already been described, the tetragonal side of the MPB is considered to be an excellent candidate composition for actuator applications with high Td and high d33 compared with the rhombohedral side and the MPB composition. On the I. PIEZOELECTRIC MATERIALS

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250

200 Rhomb.

MPB

Tetr.

d33 [pC/N]

150

120

Qm (33-mode)

200

160

100

80

0.00

0.05

0.20 0.10 0.15 z in BNLKT4-100z

50 0.30

0.25

FIG. 4.21 Piezoelectric strain constant, d33, and the mechanical quality factor, Qm(33), in (33) mode, of BNLKT4-100z as a function of the content (z) of BKT.

200

250

Actuator application Tetr.

140 110 Rhomb.

(A)

160

Rhomb. 150 100

80 50 140

High-power application

200 Qm

d33 [pC/N]

170

180 200 Td [ºC]

220

240

50 140

Tetr. 160

(B)

180 200 Td [ºC]

220

240

FIG. 4.22

Relationship of the depolarization temperature, Td, between (A) the d33 and (B) the Qm(33) for rhombohedral (Rhomb.) and tetragonal (Tetr.) sides.

other hand, it was found that the Qm(33) on the rhombohedral side is higher than those on the tetragonal side and the MPB composition. This indicates that the rhombohedral side is a suitable composition for highpowered applications. MnCO3 was doped into BNLKT4-8 because this seems to be the optimum composition for high-powered applications having both a high Td and a high Qm. BNLKT4-8Mnw (w ¼ 0–0.6) showed high density ratios of more than 97% without any secondary phases. The resistivity, ρ, of these ceramics was higher than the order of 1012 Ω cm. The temperature dependences of the dielectric constant, εs, and the loss tangent, tan δ, of BNLKT4-8Mnw (w ¼ 0–0.6) show that the maximum dielectric constant, εmax, and tan δ decrease with an increasing amount of Mn (w). On the other hand, the dielectric maximum temperature, Tm, was almost constant at approximately 272°C. Fig. 4.23 shows the variations of the k31 and the kp, and the Qm(31) and Qm(p) in the (31) and the planar (p) modes of BNLKT4-8 as a function of the Mn concentration (w). Although the k31 and the kp slightly decreased I. PIEZOELECTRIC MATERIALS

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800

Qm (31) kp

k31 and kp

700

Qm (p)

0.25

600 500

0.20

400

Qm (31 and p)

0.30

0.15 300 k31 200

0.10 0.0

0.5 0.2 0.3 0.4 Mn concentration [wt%]

0.1

0.6

0.7

FIG. 4.23 Coupling factors, k, and mechanical quality factors, Qm, in the (31) and the planar (p) modes as a function of the Mn concentration (w).

with increasing the Mn concentration (w), the Qm(31) and the Qm(p) markedly increased with increasing of w. The Qm(31) and the Qm(p) values were approximately 300 and 400 for BNLKT4-8 (w ¼ 0), and they were 730 and 720 for BNLKT4-8Mn0.6, respectively. On the other hand, the d33 gradually decreased with increasing the Mn concentration (w), and the d33 values of BNLKT4-8 and BNLKT4-8Mn0.6 were 94 and 85 pC/N, respectively. Fig. 4.24A shows the temperature dependence of the k33 for BNLKT48Mnw (w ¼ 0 and 0.6). It is found that the k33 is almost constant up to the Td.

0.6

(A)

0.4 225

(B)

220

0.3

Td [ºC]

Coupling factor, k33

0.5

0.2

Mn0.6

215

Mn0

210 205 200

0.1

0.0

0.2

0.4

0.6

Mn concentration [wt%]

0.0 0

50

150 100 Temperature [ºC]

200

250

FIG. 4.24 (A) Temperature dependence of the coupling factor, k33, for BNLKT4-8Mnw (w ¼ 0 and 0.6) and (B) the Td as a function of w.

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179

Moreover, the Td gradually decreases with increasing the Mn concentration (w), as shown in Fig. 4.24B, with Td ¼ 204°C for BNLKT4-8Mn0.6. The decrease in the Td with increasing the Mn content (w) indicates that the Mn ion is substituted into either the A-site or B-site of BNLKT4-8. According to previous reports, both εmax and Tm decrease with increasing the amount of Mn in BNT and BNT-BT.102,103 In BNLKT4-8Mnw, although the temperature dependence of the dielectric constant showed that the εmax decreased with increasing w, the Tm was almost constant at 272°C.94 Considering the valence state of Mn ions in BNT, the Mn4+ substitution into the B-site probably decrease Tm because the ionic radius of Mn4+ is ˚ , which is similar to that of Al3+. In contrast, the substitution of 0.530 A 2+ Mn and Mn3+ into the A-site or B-site of BNT should increase the Tm of BNT. Therefore, the decay of Td and the lack of variation in Tm indicate that Mn ions exist in BNLKT4-8, in the mixed state of Mn2+ or Mn3+, and in Mn4+. The resistivity was a maximum at w ¼ 0.2, and then it decreased with increasing Mn concentration w. The vaporization of A-site ions such as Bi, Na, and K occurs during sintering. Therefore, the very small amount of Mn probably compensates for the A-site vacancies as a donor, resulting in an increase in resistivity.102,103 In contrast, Mn2+ or Mn3+ in the B-site works as an acceptor; therefore, resistivity decreases at w > 0.2. Generally, acceptor ions associate with oxygen vacancies and cause domain pinning, thereby increasing in Qm.104,105 Therefore, the Qm of BNLKT4-8Mnw increases with increasing w. The high-power characteristics of BNLKT4-8, BNLKT4-8Mn0.6, and PZT-H were evaluated by the high-power characteristic measurement.94,106 The small amplitude Qm(31) values of BNLKT4-8, BNLKT48Mn0.6, and PZT-H are 440, 740, and 1770, respectively. Fig. 4.25 shows 104 6 4

PZT-H Qm (31)

2

BNLKT4-8Mn0.6

103 6 4 2

102 0.0

BNLKT4-8

0.3

0.6 0.9 1.2 Vibration velocity, n0-p [m/s]

FIG. 4.25

1.5

Variations in Qm(31) as a function of the vibration velocity v0-p for BNLKT4-8, BNLKT4-8Mn0.6, and PZT-H.

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the variation in Qm(31) as a function of the vibration velocity v0-p. It is found that the Qm(31) values of BNLKT4-8 and BNLKT4-8Mn0.6 decrease slower than that of PZT-H. Although the small amplitude Qm(31) of PZT-H was twice as high as that of BNLKT4-8Mn0.6, the amplitude of BNLKT48Mn0.6 was larger than that of PZT-H at v0-p > 0.6 m/s. Moreover, the Qm(31) of BNLKT4-8Mn0.6 was higher than 400 even at v0-p ¼ 1.5 m/s. It is considered that the small decay of Qm(31) under a high amplitude vibration for BNLKT4-8 and BNLKT4-8Mn0.6 is attributed to the high coercive field Ec. It is known that the Ec at the rhombohedral composition is larger than that at the MPB and on the tetragonal side for BNT-based solid solutions.86 The BNLKT4-8 has high Ec of 60 kV/cm, which is four times larger than that of PZT-H. Moreover, domain wall motion is suppressed by oxygen vacancies associated with the doping of acceptor ions.96 Therefore, the acceptor-ion-doped rhombohedral composition of BNT-based solid solutions is stable even at vibration velocity higher than PZT-H.

4.5 (Bi1/2K1/2)TiO3 [BKT]-BASED CERAMICS Bismuth potassium titanate, (Bi1/2K1/2)TiO3 [BKT], is a typical lead-free ferroelectric with a perovskite structure of tetragonal symmetry at room temperature. According to the x-ray diffraction (XRD) study by Ivanova et al., BKT has relatively high tetragonality (c/a) of 1.02 at room temperature and exhibits two phase transitions upon heating: tetragonal to pseudocubic at approximately 260°C and pseudocubic to complete cubic at approximately 410°C.36,107 This indicates that BKT has a certain promise as a candidate for lead-free piezoelectrics in a wide working temperature range. However, there are few reports about this material owing to its poor sinterability.108 This problem has restricted extensive activities of researchers investigating the BKT-based solid solution systems. Hiruma et al.109,110 reported the electrical properties of BKT ceramics prepared by the hot-pressing (HP) method. The optimum sintering temperature seems to be 1060–1080°C. Fig. 4.26 shows the temperature dependences of dielectric constants, εs, and dielectric loss tangents, tan δ, for BKT-HP1060°C and BKT-HP1080°C—in the temperature range from room temperature to 600°C, measured at frequencies of 10 kHz, 100 kHz, and 1 MHz. The tan δ curves in Fig. 4.26 show two peaks. Hightemperature peaks show frequency dispersions; therefore, it is thought that these peaks are related to the Tc. On the other hand, low-temperature peaks are almost independent of frequencies; therefore, it is considered to indicate the second phase transition, T2, between tetragonal and pseudocubic symmetries, whose temperatures of BKT-HP1060°C and BKTHP1080°C are about 340 and 315°C, respectively. The Tc of Bi2O3, La2O3

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4.5 (Bi1/2K1/2)TiO3 [BKT]-BASED CERAMICS

FIG. 4.26 Temperature dependences of dielectric constant εs and dielectric loss tangent tan δ for the hot-pressed BKT ceramics sintered at (A) 1060°C and (B) 1080°C.

and MnCO3 doped BKT ceramics showed a tendency to decrease with increasing the content of dopants. Fig. 4.27 shows D-E hysteresis loops of BKT-HP1060°C and BKT-HP1080°C. Well-saturated D-E hysteresis loops with a low leakage current were obtained for all specimens at RT. The Pr and the coercive fields Ec were 22.2 μC/cm2 and 52.5 kV/cm for BKT-HP1080°C, and they were 14.2 μC/cm2 and 47.3 kV/cm for BKT-

Polarization, Pr [μC/cm2]

40 BKT-HP1080°C 20

–200

–100

100 –20

200

BKT-HP1060°C at 50 Hz

–40 Applied field, Ea [kV/cm]

FIG. 4.27

D-E hysteresis loops of the HP-BKT at 1060°C and 1080°C.

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HP1060°C, respectively. The different tendencies seem to be the difference in grain size 0.2 μm for BKT-HP1060°C and 0.4 μm for BKT-HP1080°C. The electromechanical coupling factor, k33, and piezoelectric strain constant, d33, of BKT-HP1080°C ceramic were 0.34 and 82 pC/N, respectively, from the measurement of resonance and antiresonance characteristics. After this work, Tabuchi et al. showed that dense BKT ceramics were obtained through an ordinary sintering procedure using BKT fine powder which that fabricated by the solid-state reaction (without HP) using TiO2 nanopowder as a starting material.111 Also, Hagiwara et al. synthesized BKT powder by using the hydrothermal method, and dense BKT ceramics were fabricated with a single-phase perovskite structure.112,113 Moreover, textured BKT ceramics were prepared by using the reactive templated grain growth (RTGG) method.114 Fig. 4.28 shows SEM micrographs of textured BKT ceramics, showing platelike texture grains. The grain orientation factor (Lotgering factor), F, of the texture BKT ceramic was approximately 82% with a preferable orientation of 100/001 directions. Small signal k33 and d33 were approximately 0.48 and 125 pC/N, respectively, on the textured BKT ceramic with F ¼ 82%. Fig. 4.29 shows E-field-induced strains of the randomly oriented BKT ceramic and the textured ones with F ¼ 0.59 and 0.82. The maximum strain of 0.19% at 80 kV/cm was achieved in the sample with F ¼ 0.82. The normalized piezoelectric strain constants, d33* (pm/V), at 80 kV/cm were 127 and 238 pm/V on the randomly oriented and the textured samples (F ¼ 0.82), respectively. The normalized d33* was greatly improved by the grain orientation. From these investigations, BKT ceramics have high transition temperatures or TC, large remanent polarization (Pr), and superior piezoelectric properties, so they have been attracting increasing attention as lead-free piezoelectric materials for actuator

FIG. 4.28

SEM micrograph of textured BKT ceramic prepared by the reactive templated grain growth (RTGG) method.

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4.6 (Bi1/2K1/2)TiO3 [BKT]-BaTiO3 [BT] SYSTEM

183

FIG. 4.29 Electric field-induced strains of randomly oriented and textured BKT ceramic.

applications with wide working temperature ranges. Recently, Nagata et al. successfully fabricated BKT multilayer actuators by cofiring BKT ceramics with Ag-Pd (7:3) electrodes.115

4.6 (Bi1/2K1/2)TiO3 [BKT]-BaTiO3 [BT] SYSTEM A solid solution system, (1x) (Bi1/2K1/2)TiO3–xBaTiO3 [BKTBT100x],36,116,117 was investigated for evaluating characterizations and electrical properties of this system by using randomly oriented and grain-oriented samples. The compositions near the BKT (x ¼ 0–0.4) were specifically focused on as lead-free piezoelectric ceramics with wide working temperatures. X-ray diffraction patterns of BKT-BT100x ceramics with 0 ≦ x ≦ 1 show a single phase of the perovskite structure with tetragonal symmetry at room temperature. The sintered ceramics of BKT-BT indicated higher relative densities than 95%, even in the compositions of the BKT side as shown in Table 4.6. Fig. 4.30 shows the temperature dependence of electromechanical coupling factor, k33, and the phase, θ, in the impedance-frequency characteristics of the (33)-mode for BKT109 ceramic. This figure indicates that the BKT and BKT-BT ceramics seem to be attractive for higher temperature applications compared with the BT ceramic. Fig. 4.31 shows lattice constants, a and c, and lattice anisotropy, c/a, as a function of the amount (x) of BT in BKT-BT100x ceramics. Both BKT (x ¼ 0) and BT (x ¼ 1) have the same crystal structure of tetragonal symmetry; however, the c/a indicated nonlinear tendency. The c/a shows the maximum (
1.025) at the composition around x ¼ 0.2, which is a very large

I. PIEZOELECTRIC MATERIALS

184 0.35

60

0.30

40 20

0.25

150°C 0

315°C

0.20

–20

0.15

–40

0.10

Phase, q (°)

Coupling factor, k33

4. BI-BASED LEAD-FREE PIEZOELECTRIC CERAMICS

–60 0.05 –80 0.00 0

100

400

200 300 Temperature (°C)

500

FIG. 4.30 Temperature dependence of electromechanical coupling factor, k33, and the phase, θ, in the impedance-frequency characteristics of the (33)-mode for the BKT ceramic.109

1.030 Lattice anisotropy, c/a

c/a 1.025

4.05

1.020

4.00

1.015

3.95 a

1.010

Lattice constants, a and c [Å]

4.10 c

3.90 0.0

0.2

0.4 0.6 x in BKT-BT100x

0.8

1.0

FIG. 4.31 Lattice anisotropy, c/a, and lattice constants, a and c, as a function of the amount (x) of BT in BKT-BT100x ceramics.

value among lead-free piezoelectric materials. This result corresponds almost to what is shown in Buhrer’s report.36 From temperature dependences of the dielectric constant, εr and loss tangent, tan δ, for the BKT-BT100x ceramics, the Curie temperature, Tc, linearly shifted to lower temperatures with increasing the amount of BT content (x), as shown in Fig. 4.32. The Tc of BKT-BT80 (x ¼ 0.8) still shows a higher temperature than 200°C. However, both the εr at RT and at the Tc decrease with increasing x. The T2 in Fig. 4.34 shows the second-phase transition temperature from tetragonal to pseudocubic phases, existing near 270°C in BKT. The T2 of the BKT ceramic was reported by Ivanova.107

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4.6 (Bi1/2K1/2)TiO3 [BKT]-BaTiO3 [BT] SYSTEM

450 Tc

Temperature [ºC]

400

Cubic

350 Pseudo-cubic 300 T2

250

305ºC 200 Tetr. 150 100 0.2

0.0

0.4 0.6 x in BKT-BT 100x

0.8

1.0

FIG. 4.32 Curie temperature, Tc, and secondary phase transition temperature, T2, of BKTBT100x ceramics, as a function of the amount (x) of BT, measured at 1 MHz.

Fig. 4.33 shows temperature dependences of the coupling factor, k33, and the resonance frequency, fr, for BKT-BT40. The k33 (¼0.35) at RT maintained the same value up to around 250°C and then almost disappeared at about 300°C. Also, the temperature dependence of the fr showed the minimum at 305°C. This temperature is not equal to the Tc of BKTBT40. From this result, we determined the depolarization temperature, Td, which corresponds to the secondary phase transition temperature, T2, from the tetragonal to the pseudocubic phases, as shown in

620

BKT-BT40

Coupling factor, k33

k33

600

0.4 580 0.3

560 fr

0.2

540 520 305ºC

0.1

500 0.0

Resonance frequency, fr [kHz]

0.5

480 50

100

150 200 250 Temperature [ºC]

300

350

FIG. 4.33 Temperature dependences of the coupling factor, k33 and the resonance frequency, fr, for the BKT-BT40.

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4. BI-BASED LEAD-FREE PIEZOELECTRIC CERAMICS

Piezoelectric strain constant, d33 (pC/N)

240 BNBK4:1(0.852) BT BNLKT4-100x (Tetr)

200

BNKT30+La2O3

Tetr. 160

MPB

Rhomb.

BKT

120 BNBT-6 80

BNBK2:1(x) BNT 50

100 200 250 150 Depolarization temperature, Td (°C)

300

FIG. 4.34 Relationship between the piezoelectric strain constant, d33, and depolarization temperature, Td, for BT and BNT, and BKT-based ceramics.

Fig. 4.32. The BKT-BT100x ceramics (x ¼ 0–0.4) indicated high Td temperatures around 300°C. Furthermore, grain orientation effects for piezoelectric properties were investigated in BKT-BT100x using a reactive template grain growth (RTGG) method.119 The piezoelectric strain constant, d33, for randomly oriented BKT-BT10, 20 and 30 are 73.4, 69.1, and 67.6 pC/N, respectively. These values are relatively small for the practical use as actuators. So, we tried to prepare the textured samples by the RTGG method to enhance their piezoelectric properties. Textured specimens were prepared using the RTGG method with a matrix and templates of platelike Bi4Ti3O12 (BIT) particles for BKT-BT. Calcination and sintering temperatures were 900–1000°C and 1100–1400°C, respectively. The piezoelectric properties of the textured and nontextured BKT-BT10, 20 and 30 are summarized in Table 4.4. The measured direction of textured specimens is parallel [//] to the tape stacking direction. The d33 in textured specimens were improved as compared with those of nontextured specimens. For example, the d33 in BKT-BT10 was improved from 73.4 to 84.5 pC/N. However, the increment was relatively small because the orientation factor, F, was still low, about 35%. Further systematic studies for improving the F may be necessary as future work. From these results, the BKT-BT system seems to be a superior candidate for lead-free piezoelectric materials at high temperature applications.

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4.7 BiMeO3-BASED MATERIALS

TABLE 4.4 Physical and Piezoelectric Properties for Nonoriented (OF) and Grain-Oriented (RTGG) BKT-BT10, 20 and 30 Prepared by Ordinary Firing (OF) and RTGG Methods119 BKT-BT10

BKT-BT20

BKT-BT30

OF

RTGG

OF

RTGG

OF

RTGG

ρo/ρx (%)

98.5

97.8

99.3

95.4

98.0

94.3

F (%)

–

35

–

72

–

61

k33

0.35

0.37

0.36

0.33

0.38

0.38

602

560

532

501

461

426

8.2

10.5

8.2

10.1

7.8

13.0

d33 (pC/N)

73.4

84.5

69.3

70.7

67.6

83.3

d33* (pm/V)

103

168

116

143

103

134

εT33/ε0 sE33

2

(pm /N)

ρo/ρx, relative density ratio; F, orientation factor; k33, electromechanical coupling factor; εT33, free permittivity; sE33, elastic constant; d33, piezoelectric strain constant; d33*, normalized strain (¼ Smax/Emax).

4.7 BiMeO3-BASED MATERIALS The typical composition of BiMeO3 systems is BiFeO3(BFO), which has a rhombohedral symmetry with large lattice distortion of α ¼ 89.51°120 and a high Curie temperature Tc at 830°C.121 J. Wang et al. firstly reported BFO thin films prepared by a pulse laser deposition (PLD) method, which possess ferromagnetic properties combined with large ferroelectric properties. BFO has attracted quite an amount of attention as a multiferroic material.120 Therefore, the BFO is also considered a good candidates for lead-free piezoelectric materials; however, there are limited reports on detail piezoelectric properties of bulk BFO ceramics because of the large coercive field Ec and large leakage current.122,123 On the other hand, some solid solution systems including BFOs such as BiFeO3-BaTiO3 (BF-BT) and xBiFeO3-(1x)(Bi1/2K1/2)TiO3 (BF-BKT) systems have been investigated; for example, in the BF-BKT composition of x ¼ 0.4, a piezoelectric strain constant d33* measured from the strain behavior was reported to be 250 pC/N124 Focusing on other BiMeO3 systems, various ions such as Mn, Cr, Co, Ni, Al, Sc, and Ga are considered as 3 + valence ions in BiMeO3 systems. BiMnO3,125 BiCoO3,126 and BiCrO3127,128 have been focused on as multiferroic materials as well as BFO. However, these materials require a high pressure of about several GPa to synthesize, so it is difficult for these materials to fabricate for characterizing the physical and electrical properties.120–123 Similar to the above compositions, BiScO3,129 BiAlO3,130 BiGaO3131 are also known as difficult materials in terms of

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obtaining a single-phase perovskite structure synthesized by the conventional solid reaction route under the ambient pressure. BiScO3 has strong anisotropy in the crystal structure, and it is one of the important key materials to increase the Curie temperature Tc of PbTiO3.129,132 However, at present, there is no report about synthesizing pure BiScO3 ceramic and its electrical properties. BiAlO3 and BiGaO3 powders were synthesized under high pressure conditions, and their physical properties have been getting clear.130,131 Furthermore, BiAlO3 ceramic was fabricated under high-pressure conditions and remanent polarization Pr, and piezoelectric strain constants d33 were reported as 9.5 μC/cm2 and 28 pC/N, respectively.126 Physical and electrical properties of BiMeO3-based materials were summarized in Table 4.5. There are few reports about electrical properties due to the difficulty in making dense samples. However, crystal structures and physical properties have been extensively investigated by using their powders with a single perovskite structure. For example, BiCoO3 with tetragonal symmetry was reported to have extraordinary large lattice distortion (c/a ¼ 1.297).126 This is because of the strong hybridization of Bi ions with oxygen ions and the stabilization of the distorted structure by a Bi 6s2 lone pair.130,133 Large lattice distortion leads to large spontaneous polarization Ps, then the quite large Ps can be calculated as shown in Table 4.5.128,130 These Ps values are higher that of PbTiO3 (
75 μC/cm2), so

TABLE 4.5 Physical and Electrical Properties for BiMeO3-Based Materials121–132 Structure

Tc (°C)

εr at RT

Pr (μC/cm2) At RT

d33 (pC/N)

Ref.

Ceramic

Rhomb.


836

65(100 k)

0.1

11.5

123

BiMnO3

Single crystal

Mono.


500

…

520

28

130,132

BiFeO3

BiGaO3 BiAlO3 a

Powder Ceramic

94.2

a

(67 ) a

(152 ) a

9.5(75.6 )

From the first principle calculation.

I. PIEZOELECTRIC MATERIALS

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4.8 SUMMARY

we can understand that BiMeO3-based materials have high potential as excellent ferroelectric and piezoelectric materials.

4.8 SUMMARY The dielectric, ferroelectric, and piezoelectric properties of Bi-based lead-free perovskite-type ceramics were investigated as candidates for lead-free piezoelectric materials to reduce environmental damage during the disposal of piezoelectric waste products. Table 4.6 summarizes electrical and piezoelectric properties of various Bi-based, lead-free ceramics. Piezoelectric strain constants d33 in this table were basically measured by a resonance and antiresonance method (*: d33 from the E-field induced strain, **: d33 from a d33 meter). Please note that it is important to compare these values by measuring from the same method. This is because the d33 from the E-field induced-strain includes much amount of contribution TABLE 4.6 Electrical and Piezoelectric Properties of Various Bi-Based, Lead-Free Ceramics

k33

d33 (pC/N)

(Bi1/2Na1/2)0.94Ba0.06TiO3[BNBT-6]

0.55

125

BNBT-5.5 (TGG) BNBT-5.5 (single crystal)

εT33/ε0

Td, Tm (°C)

Ref.

580

125

52

…

520

a

…

…

53

…

650a

…

…

BNBT-15—0.1% (Bi1/2Na1/2) (Mn1/3Nb2/3)O3

0.41 (kt)

Qm ¼ 477

511

258

0.8 (Bi1/2Na1/2) TiO3-0.2 (Bi1/2K1/2) TiO3 [BNKT-20]

0.418(kt)

46.9(d31)

1030

…

85

0.535

157

884

174

85

BNKT-30 + La2O3 0.2 wt%

0.496

155

1071

219

89

BNBK4:1(0.895)

0.560

191

1141

110

84

BNBK2:1(0.78)

0.452

126

883

206

86

0.97BNT-0.03NaNbO3 [BNTN-3]

0.43

71

–

–

55

(Bi0.51Na0.49)(Sc0.02Ti0.98)O3 [BNST-2]

0.42

75

0.7BNT-0.2BKT-0.1BLT

0.401(kp) 0.505(kt)

56 c

118

431

145

54

216

b

1190

130

92

223

b

…

190

92

a

d33 from strain. d33 from d33 meter. c Tm value. b

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4. BI-BASED LEAD-FREE PIEZOELECTRIC CERAMICS

from non 180° domain wall movement and the d33 meter method has not been standardized yet133. The k33 value reaches 0.55 and the maximum d33 values are about 200 pC/N. Therefore, BNT and BKT-based ferroelectric ceramics are still candidates as lead-free piezoelectric materials. For example, BNT-BT-based thin films with excellent piezoelectric properties have been fabricated by Fujii et al.134 in a Japanese company, and they have tried to put these materials into practical applications such as inkjet printers and angular velocity sensors. Additionally, many BNT-based ceramics have large coercive fields as compared with PZT- or BT-based ceramics, so the mechanical quality factor Qm is stable even under the large amplitude vibration at the resonance frequency. Therefore, BNT-based piezoelectric ceramics are also expected for ultrasonic applications. In fact, Honda Electronics Corporation released ultrasonic cleaners that used a BNT-BT-based system.135 Under this situation, one of the future research trends for BNT-based lead-free ceramics is determining how to totally meet the requirements and specifications for each application—which include not only a piezoelectric constant, but also temperature stability, mechanical strength, stress resistance, breakdown strength, reliability, aging behavior, and so on. Many of these compositions in this table, however, are near to the MPBs, so the depolarization temperatures, Td, are not so high. Fig. 4.34 summarized piezoelectric strain constant, d33, versus depolarization temperature, Td, for BT and BNT, and BKT-based ceramics. As seen in this figure, d33 and Td show a tradeoff relationship with each other. Therefore, it is necessary for actual applications to obtain the value in the upper right corner (high d33 and high Td) of this figure. Future trends in the research and development of BNT-based, lead-free piezoelectric ceramics seem to be focused on textured grain orientations and domain controls including the engineered domain to enhance the piezoelectric activities without the decrease of the Td. Also, the quenching treatment may be a possible way to increase Td without deteriorating the piezoelectric activities. To replace PZT-based systems, more complex solid solutions and doping schemes still need to be explored because these provide an increasing number of degrees of freedom for identifying extraordinary properties. Also, it is important to establish fruitful interactions between the areas of atomistic modeling, synthesis, and characterization of lead-free piezoelectric ceramics while keeping device requirements in mind.

References 1. Sawaguchi E. Ferroelectricity versus antiferroelectricity in the solid solutions of PbZrO3 and PbTiO3. J Phys Soc Jpn 1953;8:615–29. 2. Jaffe B, Roth RS, Marzullo S. Piezoelectric properties of lead zirconate-lead titanate solid-solution ceramics. J Appl Phys 1954;25:809. 3. Jaffe B, Cook WR, Jaffe H. Piezoelectric ceramics. New York: Academic; 1971. p. 142.

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4. Yamamoto T. Ferroelectric properties of the PbZrO3-PbTiO3 system. Jpn J Appl Phys 1996;35(9B):5104–8. 5. Takenaka T. Piezoelectric properties of some lead-free ferroelectric ceramics. Ferroelectrics 1999;230:87–98. 6. Takenaka T, Nagata H. Current status and prospects of lead-free piezoelectric ceramics. J Eur Ceram Soc 2005;25(12):2693–700. 7. Takenaka T, Nagata H, Hiruma Y. Current developments and prospective of lead-free piezoelectric ceramics. Jpn J Appl Phys 2008;47:3787–801. 8. Ro¨del J, Jo W, Seifert KTP, Anton E, Granzow T. Perspective on the development of lead-free piezoceramics. J Am Ceram Soc 2009;92(6):1153–77. 9. Panda PK, Sahoo B. PZT to lead free piezo ceramics: a review. Ferroelectrics 2015;474:128–43. 10. Aksel E, Jones JL. Advances in lead-free piezoelectric materials for sensors and actuators. Sensors 2010;10:1935–54. 11. Leontsev S, Eitel R. Progress in engineering high strain lead-free piezoelectric ceramics. Sci Technol Adv Mater 2010;11:13. 044302. 12. Safari A. Lead-free piezoelectric ceramics and thin films. IEEE Trans Ultrason Ferroelectr Freq Control 2010;57(10). 13. Shimamura K, Takeda H, Kohno T, Fukuda T. Growth and characterization of Lanthanum gallium silicate La3Ga5SiO14 single crystals for piezoelectric applications. J Cryst Growth 1996;163:388–92. 14. Kimura M, Minamikawa T, Ando A, Sakabe Y. Temperature characteristics of (Ba1xSrx)2NaNb5O15 ceramics. Jpn J Appl Phys 1997;36:6051–4. 15. Doshida Y, Kishimoto S, Ishii K, Kishi H, Tamura H, Tomikawa Y, et al. Jpn J Appl Phys 2007;46:4921. 16. Ikegami S, Ueda I. Piezoelectricity in ceramics of ferroelectric bismuth compound with layer structure. Jpn J Appl Phys 1974;13:1572–9. 17. Takenaka T, Sakata K. Grain orientation and electrical properties of hot-forged Bi4Ti3O12 ceramics. Jpn J Appl Phys 1980;19:31–9. 18. Takenaka T, Sakata K. Piezoelectric and pyroelectric properties of calcium-modified and grain-oriented (NaBi)1/2Bi4Ti4O15 ceramics. Ferroelectrics 1989;94:175–81. 19. Takenaka T, Nagata H. Grain orientation and electrical properties of some bismuth layer-structured ferroelectrics for lead-free piezoelectric applications. Ferroelectrics 2006;336:119–36. 20. Ye Z-G. Part VII: Novel processing and new materials, No. 27 “grain orientation and electrical properties of bismuth layer-structure ferroelectrics”. In: Handbook of advanced dielectric, piezoelectric and ferroelectric materials. Cambridge, England: Woodhead Publishing Limited and CRC Press LLC; 2008. p. 818–51. 21. Nanao M, Hirose M, Tsukada T. Piezoelectric properties of Bi3TiNbO9-BaBi2Nb2O9 ceramics. Jpn J Appl Phys 2001;40:5727–30. 22. Ando A, Kimura M, Sakabe Y. Piezoelectric resonance characteristics of SrBi2Nb2O9based ceramics. Jpn J Appl Phys 2003;42:150–6. 23. Von Hippel A, Brechenridge RG, Chesley FG, Tisza L. High dielectric constant ceramics. J Ind Eng Chem 1946;28:1097–109. 24. Robert S. Dielectric and piezoelectric properties of barium titanate. Phys Rev 1947;71:890. 25. von Hippel A. Ferroelectricity, domain structure, and phase transitions of barium titanate. Rev Mod Phys 1950;22:221–37. 26. Matthias BT. New ferroelectric crystals. Phys Rev 1949;75:1771. 27. Mathias BT, Remeika JP. Dielectric properties of sodium and potassium niobates. Phys Rev 1951;82:727. 28. Shirane G, Danner H, Pavlovic A, Pepinsky R. Phase transitions in ferroelectric KNbO3. Phys Rev 1954;93:672–3.

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29. Kurtz SK, Perry TT. A powder technique for the evaluation of nonlinear optical materials. J Appl Phys 1968;39:3798. 30. Uematsu Y, Fukuda T. Nonlinear optical properties of KNbO3 single crystals. Jpn J Appl Phys 1971;10:507. 31. Zgonik M, Schlesser R, Biaggio I, Voit E, Tscherry J, G€ unter P. Materials constants of KNbO3 relevant for electro- and acousto-optics. J Appl Phys 1993;74:1287–97. 32. Reisman A, Holtzberg F, Triebwasser S, Berkenblit M. Preparation of pure potassium metaniobate. J Am Chem Soc 1956;78:719–20. 33. Egerton L, Dillon DM. Piezoelectric and dielectric properties of ceramics in the system potassium-sodium niobate. J Am Ceram Soc 1959;42:438–42. 34. Jaeger RE, Egerton L. Hot pressing of potassium-sodium niobates. J Am Ceram Soc 1962;45:20–213. 35. Smolensky GA, Isupov VA, Agranovskaya AI, Krainic NN. New ferroelectrics of complex composition IV. Sov Phys Solid State 1961;2(11):2651–4. 36. Buhrer CF. Some properties of bismuth perovskites. J Chem Phys 1962;6(3):798–803. 37. Saito Y, Takao H, Tani T, Nonoyama T, Takatori K, Homma T, et al. Lead free piezoceramics. Nature 2004;42:84–7. 38. Takahashi H, Numamoto Y, Tani J, Tsurekawa S. Piezoelectric properties of BaTiO3 ceramics with high performance fabricated by microwave sintering. Jpn J Appl Phys 2006;45:7405–8. 39. Karaki T, Yan K, Miyamoto T, Adachi M. Lead-free piezoelectric ceramics with large dielectric and piezoelectric constants manufactured from BaTiO3 nano-powder. Jpn J Appl Phys 2007;46:L97–8. 40. Liu W, Ren X. Large piezoelectric effect in Pb-free ceramics. Phys Rev Lett 2009;103:257602. 41. Nagata H, Shinya T, Hiruma Y, Takenaka T, Sakaguchi I, Haneda H. Piezoelectric properties of bismuth sodium titanate ceramics. Ceram Trans 2005;167:213–22. 42. Park S-E, Chung S-J. Nonstoichiometry and the long-range cation ordering in crystals of (Bi1/2Na1/2)TiO3. J Am Ceram Soc 1994;77:2641–7. 43. Pronin IP, Syrnikov PP, Isupov VA, Egorov VM, Zaitseva NV, Ioffe AF. Peculiarities of phase transitions in sodium-bismuth titanate. Ferroelectrics 1980;25:395–7. 44. Zvirgzds JA, Kapostis PP, Zvirgzde JV. X-ray study of phase transition in ferroelectric (Bi0.5Na0.5)TiO3. Ferroelectrics 1982;40:75–7. 45. Suchanicz J, Ptak WS. On the phase transition in Na0.5Bi0.5TiO3. Ferroelectr Lett 1990;12:71–8. 46. Tu C, Siny I, Schmidt V. Sequence of dielectric anomalies and high-temperature relaxation behavior in Na1/2Bi1/2TiO3. Phys Rev B 1994;49:11550–9. 47. Vakhruskev SB, Isupov VA, Kvyatkovsky BE, Okuneva NM, Pronin IP, Smolenskii GA, et al. Phase transitions and soft modes in sodium bismuth titanate. Ferroelectrics 1985;63:153–60. 48. Sakata K, Masuda Y. Ferroelectric and antiferroelectric properties of (Bi1/2Na1/2)TiO3SrTiO3 solid solution ceramics. Ferroelectrics 1974;7:347–9. 49. Takenaka T, Sakata K. New piezo- and pyroelectric sensor materials of (BiNa)1/2TiO3based ceramics. Sens Mater 1988;1:123–31. 50. Takenaka T, Sakata K. Dielectric, piezoelectric and pyroelectric properties of (BiNa)1/2 TiO3-based ceramics. Ferroelectrics 1989;95:153–6. 51. Takenaka T, Sakata K, Toda K. Piezoelectric properties of (Bi1/2Na1/2)TiO3-based ceramics. Ferroelectrics 1990;106:375–80. 52. Takenaka T, Maruyama K, Sakata K. (Bi, Na)TiO3-BaTiO3 system for lead-free piezoelectric ceramics. Jpn J Appl Phys 1991;30:2236–9. 53. Yilmaz H, Messing G, Mckinstry ST. J Electroceram 2003;11:207. 54. Nagata H, Takenaka T. Lead-free piezoelectric ceramics of (Bi1/2Na1/2)TiO3-1/2 (Bi2O3 Sc2O3) system. Jpn J Appl Phys 1997;36:6055–7.

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78. Kounga AB, Zhang ST, Jo W, Granzow T, Ro¨del J. Morphotropic phase boundary in (1  x)Bi0.5Na0.5TiO3-xK0.5Na0.5NbO3 lead-free piezoceramics. Appl Phys Lett 2008;92:222902. 79. Zhang J, Pan Z, Guo F, Liu W, Ning H, Chen YB, et al. Semiconductor/relaxor 0–3 type composites without thermal depolarization in Bi0.5Na0.5TiO3-based lead-free piezoceramics. Nat Commun 2015;7615:1–10. 80. Zang J, Jo W, R€ odel J. Quenching-induced circumvention of integrated aging effect of relaxor lead lanthanum zirconate titanate and (Bi1/2Na1/2)TiO3-BaTiO3. Appl Phys Lett 2013;102:032901. 81. Sch€ utz D, Deluca M, Krauss W, Feteira A, Jackson T, Reichmann K. Lone-pair-induced covalency as the cause of temperature- and field-induced instabilities in bismuth sodium titanate. Adv Funct Mater 2012;22:2285–94. 82. Keeble DS, Barney ER, Keen DA, Tucker MG, Kreisel J, Thomas PA. Bifurcated polarization rotation in bismuth-based piezoelectrics. Adv Funct Mater 2013;23:185–90. 83. Moriyoshi C, Takeda S, Kuroiwa Y, Goto M. Off-centering of a Bi ion in cubic phase of (Bi1/2Na1/2)TiO3. Jpn J Appl Phys 2014;53:09PD02. 84. Nagata H, Yoshida M, Makiuchi Y, Takenaka T. Large piezoelectric constant and high Curie temperature of lead-free piezoelectric ceramic ternary system based on bismuth sodium titanate-bismuth potassium titanate-barium titanate near the morphotropic phase boundary. Jpn J Appl Phys 2003;42:7401–3. 85. Yoshii K, Hiruma Y, Nagata H, Takenaka T. Electrical properties and depolarization temperature of (Bi1/2Na1/2)TiO3-(Bi1/2K1/2)TiO3 lead-free piezoelectric ceramics. Jpn J Appl Phys 2006;45:4493–6. 86. Hiruma Y, Makiuchi Y, Aoyagi R, Nagata H, Takenaka T. Lead-free piezoelectric ceramics based on (Bi1/2Na1/2)TiO3-(Bi1/2K1/2)TiO3-BaTiO3 solid solution. Ceram Trans 2005;174:139–46. 87. Hiruma Y, Yoshii K, Aoyagi R, Nagata H, Takenaka T. Piezoelectric properties and depolarization temperatures of (Bi1/2Na1/2)TiO3-(Bi1/2K1/2)TiO3-BaTiO3 lead-free piezoelectric ceramics. Key Eng Mater 2006;320:23–6. 88. Hiruma Y, Nagata H, Takenaka T. Phase transition temperatures and piezoelectric properties of (Bi1/2Na1/2)TiO3-(Bi1/2K1/2)TiO3-BaTiO3 lead-free piezoelectric ceramics. Jpn J Appl Phys 2006;45:7409–12. 89. Hiruma Y, Yoshii K, Nagata H, Takenaka T. Investigation of phase transition temperatures on (Bi1/2Na1/2)TiO3-(Bi1/2K1/2)TiO3 and (Bi1/2Na1/2)TiO3-BaTiO3 leadfree piezoelectric ceramics by electrical measurements. Ferroelectrics 2007;346:114–9. 90. Hiruma Y, Yoshii K, Nagata H, Takenaka T. Phase transition temperature and electrical properties of (Bi1/2Na1/2)TiO3-(Bi1/2A1/2)TiO3 (A ¼ Li and K) lead-free ferroelectric ceramics. J Appl Phys 2008;103:1–7. 91. Tsurumi T, Sasaki T, Kakemoto H, Harigai T, Wada S. Domain contribution to direct and converse piezoelectric effects of PZT ceramics. Jpn J Appl Phys 2004;43:7618. 92. Lin D, Xiao D, Zhu J, Yu P. Piezoelectric and ferroelectric properties of [Bi(Na K Li)]TiO3 lead free piezoelectric ceramics. Appl Phys Lett 2006;88:062901. 93. Hiruma Y, Nagata H, Takenaka T. Phase-transition temperatures and piezoelectric properties of (Bi1/2Na1/2)TiO3-(Bi1/2Li1/2)TiO3-(Bi1/2K1/2)TiO3 lead-free ferroelectric ceramics. IEEE Trans Ultrason Ferroelectr Freq Control 2007;54:2493–9. 94. Hiruma Y, Watanabe T, Nagata H, Takenaka T. Piezoelectric properties of (Bi1/2Na1/2) TiO3-based solid solution for lead-free high-power applications. Jpn J Appl Phys 2008;47:7659–63. 95. Hiruma Y, Watanabe Y, Nagata H, Takenaka T. Phase transition temperatures of divalent and trivalent ions substituted (Bi1/2Na1/2)TiO3 ceramics. Key Eng Mater 2007;350:93–6. 96. Takahashi S, Hirose S. Vibration-level characteristics of lead-zirconate-titanate ceramics. Jpn J Appl Phys 1992;31:3055–7.

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97. Hirose S, Magami N, Takahashi S. Piezoelectric ceramic transformer using piezoelectric lateral effect on input and on output. Jpn J Appl Phys 1996;35:3038–41. 98. Tashiro S, Ikehiro M, Igarashi H. Influence of temperature rise and vibration level on electromechanical properties of high-power piezoelectric ceramics. Jpn J Appl Phys 1997;36:3004. 99. Kawada S, Ogawa H, Kimura M, Shiratsuyu K, Niimi H. High-power piezoelectric vibration characteristics of textured SrBi2Nb2O9 ceramics. Jpn J Appl Phys 2006;45:7455–9. 100. Kawada S, Ogawa H, Kimura M, Shiratsuyu K, Higuchi Y. Relationship between vibration direction and high-power characteristics of -textured SrBi2Nb2O9 ceramics. Jpn J Appl Phys 2007;46:7079–83. 101. Doshida Y, Kishimoto S, Ishii K, Kishi H, Tamura H, Tomikawa Y, et al. Miniature cantilever-type ultrasonic motor using Pb-free multilayer piezoelectric ceramics. Jpn J Appl Phys 2007;46:4921–5. 102. Nagata H, Takenaka T. Effects of substitution on electrical properties of (Bi1/2Na1/2)TiO3based lead-free ferroelectrics. In: Proc. the 12th IEEE international symposium on the applications of ferroelectrics (ISAF XII 2000) (IEEE Catalog No. 00CH37076); 2001. p. 45–51. 103. Zhu M, Liu L, Hou Y, Wang H, Yan H. Microstructure and electrical properties of MnO-doped NBBT lead-free piezoceramics. J Am Ceram Soc 2007;90:120. 104. Gerthsen P, H€ ardtl KH, Schmidt NA. Correlation of mechanical and electrical losses in ferroelectric ceramics. J Appl Phys 1980;51:1131–4. 105. Takahashi S. Effects of impurity doping in lead zirconate-titanate ceramics. Ferroelectrics 1982;41:143–56. 106. Umeda M, Nakamura K, Ueha S. The measurement of high-power characteristics for a piezoelectric transducer based on the electrical transient response. Jpn J Appl Phys 1998;37:5322–5. 107. Ivanova VV, Kapyshev AG, Veenevtsev YN, Zhdanov GS. Dokl Akad Nauk SSSR 1962;26:354. 108. Konig J, Spreitzer M, Jancar B, Surorov D, Samardzija Z, Popovic A. The thermal decomposition of K0.5Bi0.5Tio3 ceramics. J Eur Ceram Soc 2009;29:1695–701. 109. Hiruma Y, Aoyagi R, Nagata H, Takenaka T. Ferroelectric and piezoelectric properties of (Bi1/2K1/2)TiO3 ceramics. J Appl Phys 2005;44:5040–4. 110. Hiruma Y, Nagata H, Takenaka T. Grain-size effect on electrical properties of (Bi1/2K1/2) TiO3 ceramics. Jpn J Appl Phys 2007;46:1081–4. 111. Tabuchi K, Nagata H, Takenaka T. Fabrication and electrical properties of potassium excess and poor (Bi1/2K1/2)TiO3 ceramics. J Ceram Soc Jpn 2013;121:623–6. 112. Hagiwara M, Fujihara S. Fabrication of dense (Bi1/2K1/2)TiO3 ceramics using hydrothermally derived fine powders. J Mater Sci 2015;50:5970–7. 113. Hagiwara M, Fujihara S. Grain size effect on phase transition behavior and electrical properties of (Bi1/2K1/2)TiO3 piezoelectric ceramics. Jpn J Appl Phys 2015;54:10NF10. 114. Nagata H, Saitoh M, Hiruma Y, Takenaka T. Fabrication and piezoelectric properties of textured (Bi1/2K1/2)TiO3 ferroelectric ceramics. Jpn J Appl Phys 2010;49:09MD08. 115. Nagata H, Tabuchi K, Takenaka T. Fabrication and electrical properties of multilayer ceramic actuator using lead-free (Bi1/2K1/2)TiO3. Jpn J Appl Phys 2013;52:09KD05. 116. Takenaka T, Hiruma Y, Nemoto M, Nagata H. Piezoelectric properties of (Bi1/2K1/2)TiO3BaTiO3 ceramics with wide working temperatures. In: Extended abstract of the 17th international symposium on the applications of ferroelectrics (ISAF 2008), PL002; 2008. 117. Hiruma Y, Nagata H, Takenaka T. Dielectric, ferroelectric and piezoelectric properties of barium titanate and bismuth potassium titanate solid-solution ceramics. J Ceram Soc Jpn 2004;112(5):S1125–1128. 118. Tou T, Hamaguti Y, Maida Y, Yamamori H, Takahashi K, Terashima Y. Properties of (Bi0.5Na0.5)TiO3–BaTiO3–(Bi0.5Na0.5)(Mn1/3Nb2/3)O3 lead-free piezoelectric ceramics and its application to ultrasonic cleaner. Jpn J Appl Phys 2009;48:07GM03.

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119. Nemoto M, Hiruma Y, Nagata H, Takenaka T. Fabrication and piezoelectric properties of grain-oriented (Bi1/2K1/2)TiO3-BaTiO3 ceramics. Jpn J Appl Phys 2008;47:3829–32. 120. Wang J, Neaton JB, Zheng H, Nagarajan V, Ogale SB, Liu B, et al. Epitaxial BiFeO3 multiferroic thin film heterostructures. Science 2003;299:1719–22. 121. Kumar MM, Palkar VR. Ferroelectricity in a pure BiFeO3 ceramic. Appl Phys Lett 2000;76 (19):2764–6. 122. Zhang ST, Lu MH, Wu D, Chen YF, Ming NB. Larger polarization and weak ferromagnetism in quenched BiFeO3 ceramics with a distorted rhombohedral crystal structure. Appl Phys Lett 2005;87:262907. 123. Jiang Q-H, Nan C-W, Shen Z-J. Synthesis and properties of multiferroic La-modified BiFeO3 ceramics. J Am Ceram Soc 2006;89(7):2123–7. 124. Matsuo H, Noguchi Y, Miyayama M, Suzuki M, Watanabe A, Sasabe S, et al. Structural and piezoelectric properties of high-density (Bi0.5K0.5)TiO3-BiFeO3 ceramics. J Appl Phys 2010;108:104103. 125. Kimura T, Kawamoto S, Yamada I, Azuma M, Takano M, Tokura Y. Magnetocapacitance effect in multiferroic BiMnO3. Phys Rev B 2003;67 [Article no. 180401(R)-1]. 126. Azuma M, Niitaka S. Japanese Patent 2005-104744. 127. Niitaka S, Azuma M, Takano M, Azuma M, Nishibori E, Sakata M. Crystal structure and dielectric and magnetic properties of BiCrO3 as a ferroelectromagnet. Solid State Ionics 2004;172:557–9. 128. Baettig P, Ederer C, Spaldin NA. First principles study of the multiferroics BiFeO3, Bi2FeCrO6, and BiCrO3: structure, polarization, and magnetic ordering temperature. Phys Rev B 2005;72:213105-1. 129. Inaguma Y, Miyaguchi A, Yoshida M, Katsumata T, Shimojo Y, Wang R, et al. High-pressure synthesis and ferroelectric properties in perovskite-type BiScO3-PbTiO3 solid solution. J Appl Phys 2004;95(1):231. 130. Belik AA, Wuernisha T, Kamiyama T, Mori K, Maie M, Nagai T, et al. High-pressure synthesis, crystal structures, and properties of perovskite-like BiAlO3 and pyroxene-like BiGaO3. Chem Mater 2006;18:133–9. 131. Zylberberg J, Belik AA, Takayama-Muromachi E, Ye Z-G. Draft of proceedings of the 16th IEEE international symposium on the applications of ferroelectrics (IFAF2007) (2007) 28PS-B13; 2007. 132. Eitel RE, Randall CA, Shrout TR, Park SE. Preparation and characterization of high temperature perovskite ferroelectrics in the solid solution (1  x)BiScO3-xPbTiO3. Jpn J Appl Phys 2002;41:2099–104. 133. Hill A, Rabe KM. First-principles investigation of ferromagnetism and ferroelectricity in bismuth manganite. Phys Rev B 1999;59:8759. 134. Stewart M, Battrick W, Cain M. Measuring piezoelectric d33 coefficients using the direct method. Measurement Good Practice Guide No. 44, NPL Report, 2001. 135. Tanaka Y, Harigai T, Adachi H, Fujii E. US Patent, US 8591009 B2.

Further Reading 1. Muramatsu H, Nagata H, Takenaka T. Quenching effects for piezoelectric properties on lead-free (Bi1/2Na1/2)TiO3 ceramics. Jpn J Appl Phys 2016;55:10TB07.

I. PIEZOELECTRIC MATERIALS

C H A P T E R

5 Quartz-Based Piezoelectric Materials Y. Saigusa River Eletec Corporation, Nirasaki-city, Japan

Abstract This chapter examines the piezoelectric characteristics and common applications of quartz crystal. Section 5.1 covers the discovery of quartz crystal piezoelectricity including its structure and its differences from other piezoelectric materials. Section 5.2 compares natural quartz crystal with artificial quartz crystal and explains the methods and specifications for artificial quartz crystal growth. Section 5.3 introduces typically applied quartz crystal plates for vibrators and shows actual cutting angles. These vibrators include the most popular AT-cut thickness shear mode and the tuning fork bending mode, and their characteristics such as frequency and temperature are explained in detail. This section also shows examples of quartz crystal miniaturization using another cutting method developed by River Eletec Corporation. Section 5.4 demonstrates applications and standards for the quartz crystal vibrators and oscillators described throughout the chapter. Keywords: Artificial quartz crystal, Piezoelectricity, Zero temperature coefficient, Thirty-two (32) point groups, Single crystal, Vibration mode, Resonator, Oscillator, Filter.

5.1 PIEZOELECTRICITY OF QUARTZ CRYSTAL 5.1.1 Discovery of Piezoelectricity Today, most electronic instruments use quartz crystal devices. When stress is applied to piezoelectric materials such as quartz crystal, PZT, and LiNbO3, electric polarization is created. This polarization phenomenon was first discovered by the Curie brothers in 1880.

Advanced Piezoelectric Materials http://dx.doi.org/10.1016/B978-0-08-102135-4.00005-9

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Copyright © 2017 Elsevier Ltd. All rights reserved.

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z−axis

R R’ s x

m 0 y−axis

x−axis

x s

FIG. 5.1 The typical external form of natural quartz crystal with its axis.

Fig. 5.1 shows the typical external form of natural quartz crystal and its axis. Fig. 5.2 illustrates its cross section to the z-axis and the cutting angle of the crystal plate. The Curie brothers used a plate that was perpendicular to the x-axis (called the X-cut) for their piezoelectric experiment. They found that when they compressed or pulled on this plate, electric polarization was created in the direction of its thickness; this is called direct piezoelectricity. In opposition to this, they found that when an electric field is added to the X-direction, there is either expansion or contraction in the x or y-axis directions. This phenomenon (called inverse piezoelectricity) was hypothesized by G. Lippmann and later confirmed by the Curie brothers. Professor W.G. Cady was one of the pioneers of the quartz crystal resonator. Cady made the X-plate (called the Langevin vibrator) where the Y dimension is longer than the Z dimension, and he drove it by an alternative electric field shown in Fig. 5.3. He swept the frequency of alternative electric fields and found that there exists a resonant point unique to the dimension of the X-plate.

I. PIEZOELECTRIC MATERIALS

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5.1 PIEZOELECTRICITY OF QUARTZ CRYSTAL

m’

m

m’ Y−plate

m

Z

Y

X−plate pla

Y−

te

m’

m

X

FIG. 5.2

Cross section to the z-axis and cutting angle of crystal plate.

~

Electrode X−plate

FIG. 5.3

X

Z Y

Experimental device by W.G. Cady.

I. PIEZOELECTRIC MATERIALS

Direction of vibration

200

5. QUARTZ-BASED PIEZOELECTRIC MATERIALS

Electrode X−plate

X

Z Y

Direction of vibration

FIG. 5.4 Pierce circuit.

Professor Pierce had first published the quartz crystal oscillation circuit using a vacuum tube. This circuit is shown in Fig. 5.4. This circuit is the most basic quartz crystal oscillation circuit and is called the Pierce circuit. Compared with the previous LC oscillation circuit, the Pierce oscillation circuit provided a much more stable frequency. With the improvements of radio frequency (RF) communication technology, changes in the stable frequency oscillation and temperature adjustments have been required. At one point, the Curie brothers had missed their cutting angle and made a Y-cut vibrator. Its frequency temperature characteristic showed the opposite curve to the X-cut. As a result of the X-cut vibrator and the Y-cut vibrator having an opposite frequency temperature curve, many people tried to find the zero temperature coefficient between these cuts. However, since the vibration mode of the X-cut and the Y-cut is different; there is not necessarily a zero temperature coefficient(s) that exists between these two cutting angles. In 1932, Dr. Koga discovered that there exists a zero temperature coefficient with the plate at 35°150 rotating the Y-plate from the z-axis.1 He named this cutting angle the “R1-cut.” A similar discovery had been made by R. Bechmann and the Bell Laboratory. The Bell Laboratory named this cutting angle the “AT-cut.” After these publications, other rotated Y-cuts had been discovered and named the “BT-cut,” “CT-cut,” and “DT-cut” successively (see Fig. 5.14).2

5.1.2 Symmetry of Quartz Crystal and Its Axis In crystallography, there are 32 point groups and seven crystal systems. Quartz crystal belongs to the three-two point group of the trigonal crystal system. It has one axis of threefold symmetry and three axes of twofold symmetry. As shown in Fig. 5.2, the z-axis (optic axis) is the threefold I. PIEZOELECTRIC MATERIALS

201

5.1 PIEZOELECTRICITY OF QUARTZ CRYSTAL

symmetry axis, and when the crystal is rotated 120/240 degrees around it, the characteristics are the same as the original position.3 The x-axis (electric axis) and y-axis (mechanical axis) are the twofold symmetry axis and each pair of X1-Y1, X2-Y2 and X3-Y3 axes have the same characteristics and relationships to each other (see Fig. 5.5). These properties are used to investigate and determine constants of quartz crystal presented by tensor. When the quartz crystal is cut with a specified angle(s), these constants are transformed to the new axis of coordinates. Fig. 5.6 shows the unit cell of α-quartz. Small black circles show the Si atom and the large white circles show the O atom. Fig. 5.7 shows the arrangement of these Si atoms and O atoms in the α-quartz viewed from the z-axis. Si atoms and O atoms make a spiral structure toward the z-axis. It is easily understood that the electrical center is located at the origin of the Z-Y plane. Fig. 5.8 shows that when there is no stress added to the quartz crystal, the electrical center of the three Si atoms, the electrical center of the three O atoms, and the origin of the X-Y plane coincides with each other. Fig. 5.9 shows that when mechanical pressing stress is added toward the x-axis, the electrical center of the three Si atoms do not coincide with the electrical center of the three O atoms, and polarization toward the x-axis occurs. On the other hand, when pulling stress is added toward the x-axis, the opposite polarization occurs. Furthermore, when electrodes are placed

X1 Y2

Y1

X3

X2

Y3

FIG. 5.5 x-Axis (electric axis) and y-axis (mechanical axis) are the twofold symmetry axis.

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Si atom 0 atom

Z Y

X

FIG. 5.6 Unit cell of α-quartz. −X

Si

0

−

+ 0 0

−

−

0

−

Y + Si

0 − −

+ Si

0

+X

FIG. 5.7 Arrangement of Si atoms and O atoms in the α-quartz viewed from the z-axis.

on both X planes and an AC electric field is added between these electrodes, mechanical vibrating displacement occurs in the direction of X. When the mechanical vibration matches to the frequency and phase of the AC electric field, the resonance of the quartz crystal plate occurs. This behavior, as shown in Fig. 5.9, is called the longitudinal piezoelectricity. I. PIEZOELECTRIC MATERIALS

203

5.1 PIEZOELECTRICITY OF QUARTZ CRYSTAL

−X

Si + 0

−

0

−

Y +

+

Si

Si

− 0

+X

FIG. 5.8

One unit of Si and O atoms in the α-quartz viewed from the z-axis.

−X

−

−

−

−

−

Si

0

A

0

+

−

−

− Y

+

+

−

Si

Si

0

+

+

+

+

+

+

+X

FIG. 5.9

Direct longitudinal piezoelectricity.

I. PIEZOELECTRIC MATERIALS

B

204

5. QUARTZ-BASED PIEZOELECTRIC MATERIALS

−X +

+

+ Si

0

+

+

−

−

0 Y

+

+

Si

Si

−

−

0

−

−

−

+X

FIG. 5.10

Direct perpendicular piezoelectricity.

Fig. 5.10 shows the perpendicular piezoelectricity compared with the longitudinal piezoelectricity explained above. When mechanical stress is applied to the Y direction, polarization occurs toward the X direction. When the AC electric field along the Y direction is applied, vibration occurs to the X direction. Piezoelectricity and inverse piezoelectricity are explained as above. Fig. 5.11 shows that when you apply compress displacement to the x-axis and extensional displacement to the y-axis at the same time, the electric field to the X direction appears. This is called inverse piezoelectricity. Even if these stresses were applied to the Z direction, no polarization would occur.

5.1.3 Differences Among Other Piezoelectric Materials There are many materials that have piezoelectricity aside from quartz crystal. These are classified as single crystals and polycrystals. Generally, single crystals like SiO2, LiNbO3, LiTaO3, and La3Ga5SiO14, etc., have a steady construction of elements so that their characteristics are stable. On the other hand, polycrystals such as Pb(Zr.Ti)O3, BaTiO3, and PbTiO3 have many rates of the elements so they have many characteristics. All these piezoelectric materials have a relationship between their geometrical element arrangements and characteristics. The designer has to choose suitable material(s) when considering their process and purpose.4 I. PIEZOELECTRIC MATERIALS

205

5.1 PIEZOELECTRICITY OF QUARTZ CRYSTAL

−X

+

+

+

+

+

+

A

Si +

0 −

+

0 − Y

−

Si

+

+

−

Si

0

−

−

−

−

−

−

B

+X

FIG. 5.11

Inverse piezoelectricity.

Piezoelectric materials are used when electric energy is changed to mechanical energy or vice versa. It is very important for a device designer to choose the material with characteristic(s) that suit their purpose. Table 5.1 shows the required characteristics for typical piezoelectric devices. The suitable material(s) have to be chosen based on these characteristics. For example, in designing timing devices, the designer has to regard frequency stability as the most important characteristic. The primary factors are the following: • excellent frequency stability • negligible deviation of equivalent circuit constants for aging • stable oscillator. Regarding the first factor, it is possible to get a device that has a zero temperature coefficient by choosing a suitable cut angle such as the AT-cut quartz crystal resonator. Its frequency stability are excellent under a wide range of temperatures compared with other resonators using other materials. Regarding the second factor of having little or no deviation of equivalent circuits, the quartz crystal resonator has excellent aging stability because it is a very stable material from the viewpoint of chemical and I. PIEZOELECTRIC MATERIALS

206 TABLE 5.1 Devices

5. QUARTZ-BASED PIEZOELECTRIC MATERIALS

The Energy Change and Required Characteristics for Typical Piezoelectric

Typical piezoelectric devices Actuator Buzzer

Energy transduction Electrical to mechanical

Ultrasonic cleaner

Requirement Piezoelectric constant, d:

large

Permittivity, ε:

high

Quality factor, Q:

small

Piezoelectric constant, g:

large

Permittivity, ε:

high

Electromechanical coupling factor, k:

large

Quality factor, Q:

large

Frequency-to-temperature coefficient, α:

approximately 0

Change in frequency with time, 4f

small

Electromechanical coupling factor, k:

large

Ultrasonic motor Speaker Acceleration sensor

Mechanical to electrical

Microphone Ignitor Sonar

Electrical to mechanical

Flaw detector Tuning fork vibrator Resonator Oscillator Ceramic filter

Electrical to mechanical to electrical

physical aspects compared with other piezoelectric materials. Generally, polarization is necessary for polycrystals like PZT in order to unidirectionally polarize them by an external electric field. At this point, their piezoelectric characteristics are influenced not only by the polarization condition but also by the microscopic state of the material (grain size, grain boundaries, porosity, etc.). The reliability (aging rate, performance change by temperature, etc.) is also influenced by the polarization condition. Compared with these polycrystalline materials, quartz crystal is one of the single crystal forms, and its composition is extremely stable. Therefore, the piezoelectric device that is made from it shows very stable reliability during aging.

I. PIEZOELECTRIC MATERIALS

5.2 PRODUCTION OF ARTIFICIAL QUARTZ CRYSTAL

207

TABLE 5.2 Various Constants of Piezoelectric Single Crystal and Polycrystal Pb(Zr, Ti)O3 Materials

Specific permittivities ε

Quartz crystal (SiO2)

εT11/ε0 ¼ 4.52,

Piezoelectric constants, d/10212 CN21 d11 ¼ 2.31, d14 ¼ 0.727

εT33/ε0 ¼ 4.68 Lithium niobate

εT11/ε0 ¼ 84

d15 ¼ 68, d22 ¼ 21

(LiNbO3) crystal

εT33/ε0 ¼ 30

d31 ¼ 1, d33 ¼ 6

Lithium tantalate

εT11/ε0 ¼ 51

d15 ¼ 26, d22 ¼ 7

(LiTaO3) crystal

εT33/ε0 ¼ 45

d15 ¼ 68, d33 ¼ 8

Lead zirconate titanate

εT11/ε0 ¼ from 1500 to 1700

d15 ¼ from 500 to 580, d31 ¼ from 170 to 125

(Pb(Zr,Ti)O3) ceramics

εT33/ε0 ¼ from 1300 to 1700

d33 ¼ from 290 to 370

Regarding the final factor, the Q-value of the quartz crystal resonator is so high that the oscillation stability is not particularly influenced by the element characteristics of the electric circuit. This leads to excellent frequency stability of the quartz crystal oscillator. Table 5.2 shows various constants of piezoelectric single and polycrystal (Pb(Zr,Ti)O3). Since the constants of (Pb(Zr,Ti)O3) change with its composition of (Zr,Ti)O3, they may be recognized as typical values. Electromechanical coupling factors of quartz crystal are small, but it has many superior points when compared with other piezoelectric materials as described above. Therefore it is one of the current indispensable materials in frequency control devices.

5.2 PRODUCTION OF ARTIFICIAL QUARTZ CRYSTAL 5.2.1 The Relationship Between Natural and Artificial Quartz Crystal Since its discovery, natural quartz crystal has been valued for its mysterious properties. People would admire it and use it for religious ceremonies and fortune-telling, among other things. More recently, we can see quartz crystal in jewelry and applied in other fine arts. From the standpoint of fascination, natural quartz crystal has much more value when compared with artificial quartz crystal.

I. PIEZOELECTRIC MATERIALS

208

5. QUARTZ-BASED PIEZOELECTRIC MATERIALS

The quartz crystal used for piezoelectric devices requires the following: • • • •

no twin in a crystal the crystal should be either right-hand or left-hand coordinated less inclusion(s) and less dislocation fine production yields.

When comparing natural and artificial quartz crystal under these requirements, artificial quartz crystal has an advantage over natural quartz crystal. Therefore, 100% of piezoelectric devices are made from artificial quartz crystals today. Artificial quartz crystals are produced by the hydrothermal process. They are grown in the autoclave as shown in Fig. 5.12.5 The autoclave

Pressure gauge

Seeds (Quartz bars)

Crystallization zone

Autoclave body

Thermocouple Heaters

Baffle

Dissolution zone Lasca (Quartz supply)

FIG. 5.12

The cross section of the autoclave.

I. PIEZOELECTRIC MATERIALS

5.2 PRODUCTION OF ARTIFICIAL QUARTZ CRYSTAL

209

is divided into two zones by the baffle that controls the convection of the autoclave. The upper zone is the crystal growth zone and the lower zone is the raw material zone. Seed crystals are set in the growth zone and raw quartz called “lasca” is set in the raw material zone. Generally, a Y-bar and/or Z-plate are used for the seeds. Under high pressure and high temperature quartz crystal is soluble in alkaline solutions like Na2CO3 or NaOH, and this alkaline solution is placed in the autoclave. The autoclave is then sealed and heated. Generally, the temperature of the growth zone and the material zone are kept around 300°C and 400°C, respectively. Then the pressure of the autoclave becomes about 400 MPa and convection begins. At this time, the solution quartz convection contributes to quartz crystal growth on the seeds. The growth speed is different for each crystal axis as shown below. Growth speeds : Z > + X > X > Y ¼ approximately 0 The shapes of grown artificial quartz crystals are shown in Fig. 5.13. Compared with natural quartz crystal shown in Fig. 5.1, we can see the difference between them lies not only in their shape but also their axis. Artificial quartz crystal that has been grown is ground into lumbered quartz.

5.2.2 Specifications of Artificial Quartz Crystal The evaluation of artificial quartz crystal quality is specified in IEC 60758. Its leading terms are inclusion density, etch channel (dislocation) density, and infrared absorption constant α. Usually, the inclusions contain an Fe radical, Al radical, etc. Dislocations are evaluated for the quartz crystal element(s)/wafer(s) by etching it with HF, etc. If there is no dislocation, there is no strain, and the energy density of the quartz crystal lattice is uniform. However, if there is any dislocation, the energy density of that point has higher energy compared with other parts of quartz crystal, and it will be selectively etched. We can then find the dislocation as an etch channel. When we present an infrared beam to the quartz crystal, absorption occurs at the specified wavelength. The absorption has a relationship to the Q (quality factor) value of quartz crystal. This technique is used as a nondestructive way to evaluate the quartz crystal quality. Before 1987, the evaluation of quartz crystal had been carried out by making an actual crystal vibrator and measuring its Q value directory. This method can cause a process deviation and can create a small error in calculating the Q value of the quartz crystal. For these reasons, the infrared absorption method is used to evaluate the quality of quartz crystal. This directly measured Q value is used as a reference value today. Tables 5.3–5.5 show the grade of quartz crystal and its required values as specified in JIS C6704.

I. PIEZOELECTRIC MATERIALS

210

5. QUARTZ-BASED PIEZOELECTRIC MATERIALS

Cross−section A−A’

Y-bar Y or Y’

X

Z or Z’

A

A’

X

Seed

Z-bar

Cross−section A−A’

Y or Y’

X

Z or Z’

A

A’

X

Seed

FIG. 5.13

The shapes of grown artificial quartz crystal.

5.3 CUTTING ANGLES AND THEIR VIBRATION MODE 5.3.1 Examples of Typical Cutting Angles and Their Vibration Mode and Characteristics Fig. 5.14 shows some of the cutting angles of quartz crystal vibrators.6,7 There are many kinds of vibration modes on quartz crystal resulting from its symmetry and its piezoelectric characteristics. Among these vibration modes, there are some modes that have first-degree zero temperature coefficient α. These cutting angles have excellent frequency stability against the temperature. The cutting angles shown in Fig. 5.14 are typical cutting angles for quartz crystal vibrators’ applied bulk waves.

I. PIEZOELECTRIC MATERIALS

211

5.3 CUTTING ANGLES AND THEIR VIBRATION MODE

TABLE 5.3 The Grade of Inclusion Density in JIS C6704 Quantity of inclusions according to dimensions (pcs/cm2)

Grade

10–30 μm

30–70 μm

70–100 μm

>100 μm

Ia

2

1

0

0

Ib

3

2

1

1

I

6

4

2

2

II

9

5

4

3

III

12

8

6

4

TABLE 5.4 The Grade of Infrared Absorption Constant a in JIS C6704 Limit for average α α3500

α3585

α3410

Q/106

Aa

0.026

0.015

0.075

3.8

A

0.033

0.024

0.082

3.0

B

0.045

0.050

0.100

2.4

C

0.060

0.069

0.114

1.8

D

0.080

0.100

0.145

1.4

E

0.120

0.160

0.190

1.0

Grade

TABLE 5.5 The Grade of Etch Channel (Dislocation) Density r in JIS C6704 Grade

Maximum etch channel density, ρ/cm2

1

10

2

30

3

100

4

300

5

600

Fig. 5.15 shows examples of quartz crystal vibrators’ frequency temperature characteristics that have a zero temperature coefficient shown in Fig. 5.14.6 Generally, using third-degree Taylor expansion, the frequency deviation of quartz crystal 4f/f is shown by the following equation:

I. PIEZOELECTRIC MATERIALS

212

5. QUARTZ-BASED PIEZOELECTRIC MATERIALS

Z AT−cut (q = 35° 15’) CT−cut (q = 38° )

q

q

Y

DT−cut (q = 49° ) DT−cut (q = 52° 30’)

q

+1° X−cut (q = 1° )

f

f

q q LQ1T−cut (q = 36° , f = 45°) GT−cut (q = 51° , f = 45°)

LQ2T−cut (q = 50° , f = 45°) +X Z

Y

+X

FIG. 5.14

Cutting angles of typical quartz crystal vibrators.

Δf =f ¼ αðt  t0 Þ + βðt  t0 Þ2 + γ ðt  t0 Þ3 , where t0 is the Taylor expansion temperature. The first-degree temperature coefficient α’s of each quartz crystal vibrators shown in Fig. 5.14 become zero at 25°C, and their temperature characteristics are determined by second-degree temperature coefficients β. Table 5.6 also shows the value of second- and third-degree temperature coefficients of quartz crystal vibrators having a zero temperature coefficient α. For example, a +1°. X cut tuning fork quartz crystal vibrator, which is used in time clock bases, has a comparatively large value for the second-degree temperature coefficient β. The temperature coefficient is around 3.5  108/°C2, and its frequency deviation versus temperature curve becomes a quadratic function curve in the operating temperature range shown in Fig. 5.15.

I. PIEZOELECTRIC MATERIALS

213

Frequency change in parts per million, Δf ⁄ f /ppm

5.3 CUTTING ANGLES AND THEIR VIBRATION MODE

−50

−40

−30

−20

50 40 30 20 10 0 −10−10 0 10 20 30 40 50 60 −20 −30 −40 −50 −60 AT cut Thickness shear mode −70 −80 BT cut Thickness shear mode −90 +1° X cut Flexural mode −100 NS-GT cut Length extensional and width −110 extensional coupling vibration mode −120 LQ1T cut Lame mode −130 LQ2T cut Lame mode −140 −150 Temperature in degree centigrade, t /°C

70

80

90

100

FIG. 5.15 Examples of temperature frequency characteristics of quartz crystals vibrators.

For the AT-cut to be used mainly in the MHz frequency range, which vibrates with the thickness shear mode, the value of the second-degree temperature coefficient β is around 0.12  108/°C2, and it could be negligible. Therefore, its frequency deviation versus temperature curve becomes, depending on γ, a cubic function curve also shown in Fig. 5.15.8,9 The quartz crystal vibrator that has the smallest frequency deviation within the operating temperature range is the NS-GT cut vibrator. Among the vibrators shown in Fig. 5.15, only the NS-GT cut vibrator works with coupled vibration mode. Other vibrators work with single vibration modes. Therefore, we can control the inflection point by designing the coupling condition and create the NS-GT quartz crystal vibrator that has an extremely small frequency deviation. Fig. 5.16 shows the typical vibration mode of quartz crystal vibrators that have a zero temperature coefficient. There are other vibration modes, but they have not been applied at present, because of the following: • they do not have zero temperature coefficients • it is difficult to hold the specimen without interference to the vibration part of element. It is known that, with the exception of the thickness shear mode, the other six modes shown in Fig. 5.16 have difficulty in holding the specimen. In order to solve this problem, the vibrating part and holding part are unified into one piece. It is very difficult to place the through holes on the vibrating element shown in Fig. 5.17 using only the machinery process.

I. PIEZOELECTRIC MATERIALS

214

5. QUARTZ-BASED PIEZOELECTRIC MATERIALS

TABLE 5.6 Resonant Frequency Temperature Coefficients of Crystal Resonator With Zero Temperature Coefficient α

β/1028/(°C)2

γ/10210/(°C)3

0

–3.5

+0.37

0

+0.12

+1.0

0

4.0

0.95

0

5.8

+0.21

0

1.8

+0.40

0

0.05 to +0.05

0.03 to +0.03

0

5.8

+0.2

0

1.5

+0.3

0

1.5

+0.41

0

3.2

+0.35

+ 1°X cut Flexural mode (tuning fork) AT cut Thickness shear mode BT cut Thickness shear mode CT cut Contour shear mode DT cut Contour shear mode NS-GT cut Length extensional and width extensional coupling vibration mode LQ1T cut Lame mode LQ2T cut Lame mode TT(X1) cut Torsional mode Z cut Length extensional mode

In this case, photolithography technology is used, with fluoride hydrogen as the etchant of quartz crystals.

5.3.2 Major Cutting Angles (AT-Cut and +1°-X-Cut) and Their Vibration 5.3.2.1 AT-Cut Thickness Shear Mode Quartz Crystal Vibrator Consider the infinite Y-plate (perpendicular to the y-axis), and determine its thickness 2y0, with consistency ρ. Then we can determine the resonant frequency f as below. I. PIEZOELECTRIC MATERIALS

5.3 CUTTING ANGLES AND THEIR VIBRATION MODE

1. Thickness shear mode

215

2. Flexural mode

3. Lame mode

4. Torsional mode

Width-extensional mode (primary vibrational mode)

Length-extensional mode (subvibrational mode)

5. Coupling mode which vibrates in the coupled width-extensional mode and length-extensional mode

6. Length-extensional mode

FIG. 5.16

7. Face shear mode

Typical vibration modes of quartz crystal vibrators.

m f¼ 2ð2y0 Þ

sffiffiffiffiffiffiffi c0 D 66 , ρ

where e226 ε0 S22 E c0 66 ¼ cE66 cos 2 θ + cE44 sin 2 θ + 2cE14 cos θ sin θ   e26 ¼  e11 cos 2 θ + e14 cosθ sinθ 0E c0 D 66 ¼ c 66 +

ε0 S22 ¼ εS11 cos 2 θ + εS33 sin 2 θ I. PIEZOELECTRIC MATERIALS

(5.1)

1. Shape of AT (BT) cut thickness shear mode quartz crystal

2. Shape of +1º X cut flexural mode quartz crystal

3. Shape of LQ1T (LQ2T) cut lame mode quartz crystal

FIG. 5.17

Examples of the shapes of quartz crystal vibrators and their electrodes.

I. PIEZOELECTRIC MATERIALS

5.3 CUTTING ANGLES AND THEIR VIBRATION MODE

217

θ: Y-plate rotated angle around x-axis cE66, cE44, cE14: elastic stiffness (under the static electric field) e11, e14: piezoelectric constants εS11, εS33: dielectric constants m: the constant determined by electrical boundary condition. Therefore, when the angle is rotated θ ¼ 35°150 , the first-order temperature coefficient α becomes zero. This cutting is called the AT-cut, and it has excellent frequency temperature characteristics. It is obvious from Eq. (5.1) that when the cutting angle θ is designed, the resonant frequency is automatically determined by its thickness (2y0), and they are inversely proportional to each other. Eq. (5.1) can be approximately written as c : f¼ 2y0 The frequency of the AT-cut quartz crystal resonator partially depends on the thickness of the electrode. However, this proportional constant c has a value range from 1640 to 1680 MHz μm. From the calculation above, the AT-cut resonator frequency range is practical from several MHz to over 100 MHz with fundamental vibration. 5.3.2.2 +1°-X-Cut Tuning Fork Quartz Crystal Vibrator (Cantilever, Tuning Fork) The resonant frequency of the flexural mode cantilever crystal vibrator with length 2y0 along the y-axis, width 2x0 along the x-axis, and its consistency, ρ, can be written as the following: sffiffiffiffiffiffi m2 2x0 c022 pffiffiffi  , (5.2)  f¼ ρ 2π  2 3 ð2y0 Þ2 where c022 is elastic stiffness and m is the constant of vibration determined by the boundary condition. From Eq. (5.2), it is obvious that resonant frequency is determined by the length and width of the cantilever crystal vibrator. For the fundamental vibration, the value of m will be approximately 1.875. Eq. (5.2) then becomes the following: f ¼c

2x0 ð2y0 Þ2

:

For the +1°-X-cut cantilever crystal vibrator, the value of c (partially depends on mass of electrode) will range between 900 and 950 kHz mm. The actual resonant frequency of the tuning fork crystal vibrator meets the calculated resonant frequency that uses the length of 2y0 when the width of the tuning fork base part is added.

I. PIEZOELECTRIC MATERIALS

218

5. QUARTZ-BASED PIEZOELECTRIC MATERIALS

The quartz crystal vibrator plays a very important part in providing a stable frequency. The relationship between the seven vibrating modes shown in Fig. 5.16 and their frequency is described below. In order to understand this relationship, we have to consider the construction of the quartz crystal vibrator. The vibrating crystal element has to be held in mid-air. Furthermore, the inside of the package sometimes needs to be kept in a vacuum and at other times filled with N2, etc. Therefore, the package has to be designed with hermetic sealing technology. From the examples, the thickness shear mode and flexural mode crystal vibrators described above, it is clear that the frequency range of these vibrators is determined by the package sizes they use. Thus, we have to design the package size for the required frequency and the reliability of the vibrator(s). On the other hand, we can choose a suitable vibration mode for the required frequency.

5.3.3 Other Cutting Angles Developed by River Eletec Corporation Generally, the AT-cut crystal vibrator is applied for the MHz range frequency control and its vibration mode is thickness shear mode. To miniaturize the vibrators, it is also necessary to miniaturize the vibrating crystal elements. Recently, the typical ceramic package sizes for the surface mounting devices (SMD) are 3.2  2.5 mm or smaller. (Note: In 2016, River Eletec Corporation succeeded in developing the world’s smallest package size of 1.2  1.0 mm.) As shown in Section 5.3.2, the resonant frequency of an AT-cut vibrator is determined by its thickness. For example, the thickness of a 4 MHz AT-cut crystal vibrator will be around 0.42 mm, and when we design the 3.2  2.5 mm AT-cut SMD vibrator, we have to achieve a crystal element size of around 2.4  1.7  0.42 mm and put it in the ceramic package. In considering the size of the crystal element, it is very important that the AT-cut vibrator works on the condition that the AT plate is infinite. The closer the element area is to the thickness in its dimension, the more the energy of the thickness shear mode will weaken and other unwanted modes will increase. As a result, the vibrator will not satisfy the required specification(s). The bevel process is used to concentrate the vibrating energy to the central area of the AT-cut element, but we have not seen the AT-cut 4 MHz vibrator with a 3.2  2.5 mm package. 5.3.3.1 Lame Mode Resonator In miniaturizing the quartz crystal vibrators, River Eletec Corporation has created a few MHz quartz crystal vibrators with a 3.2  2.5 mm package by applying Lame mode vibrating. Figs. 5.18 and 5.19 illustrate the

I. PIEZOELECTRIC MATERIALS

5.3 CUTTING ANGLES AND THEIR VIBRATION MODE

FIG. 5.18

The fundamental Lame mode quartz crystal.

FIG. 5.19

Integration of the Lame mode quartz crystal.

219

Lame mode quartz crystal10 vibration form. From Fig. 5.18, we can see that there are four nodal points in the corners of the unit crystal element. From Fig. 5.19 we can see that the Lame mode vibrator can be achieved with integral numbers of the unit element to the length direction. Considering a rectangular Y-plate perpendicular to the y-axis (mechanical axis) and its length to the x-axis 2x0 (¼2z0), length to the z-axis 2z0 (¼2x0), and consistency, ρ, the resonant frequency of this Lame mode vibrator will be the following: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 c011  c013 1 c033  c013 f¼ ¼ , (5.3) ρ ρ 2ð2x0 Þ 2ð2z0 Þ where c011, c013, c033 are elastic stiffness. As shown in Fig. 5.14, the Y-plate, rotated θ ¼ 36° around the x-axis toward the AT-cut direction and again rotated ϕ ¼ 45° in the plate,

I. PIEZOELECTRIC MATERIALS

220

FIG. 5.20

5. QUARTZ-BASED PIEZOELECTRIC MATERIALS

Comparison of two packages, LMX-01 and FCX-01, vibrating the same

frequency.

gives LQ1T-cut and its temperature coefficient α ¼ 0. The cutting of θ ¼ 130° and ϕ ¼ 45° gives a LQ2T-cut, and also its temperature coefficient α will be zero. Comparing second-order temperature coefficient β’s shown in Table 5.6, the frequency temperature characteristic LQ2T-cut is superior to the LQ1T-cut, and its second-order temperature coefficient is 1.7  108/°C2 S. River Eletec Corporation first developed and commercialized the smallest SMD crystal vibrator, called LMX-01, which has a resonant frequency range of 3.5–4.5 MHz in the LQ2T-mode. Fig. 5.20 shows a comparison of previous AT-cut 4 MHz SMD resonators and the LMX-01 4 MHz SMD resonator. The new resonator has an 87% smaller mounting area, is 96% smaller in volume, and is 95% lighter in weight. In spite of this drastic miniaturization, the electric characteristics of LMX-01 compare favorably with previous AT-cut crystal vibrators as shown in Table 5.7, and it is compatible with the larger size AT-cut crystal vibrator FCX-01 (already end of life (EOL)). The shape of crystal element of LMX-01 (LQ2T-cut) is shown in Fig. 5.17 #3, and its dimensions are 2.4  1.6 mm with thickness 70 μm. Its cutting angle is shown in Fig. 5.14. In order to satisfy the temperature-frequency characteristic from 10 to +60°C within +10 to 50 ppm, the cutting angle θ has to be kept 50°  300 . Its vibrating frequency is determined mainly by the width of element 2x0, and is given from Eq. (5.3) as f¼

K , 2x0

where K is the frequency constant and its value is around 3350 MHz μm. At present, only River Eletec Corporation produces and supplies the LMX-01 to the global market. It has very particular applications at this I. PIEZOELECTRIC MATERIALS

5.3 CUTTING ANGLES AND THEIR VIBRATION MODE

221

TABLE 5.7 The Characteristic Compatibility Between 4 MHz LMX-01 and FCX-01 LMX-01 (Lame mode)

FCX-01 (Thickness shear mode)

Series resonant frequency, fr/MHz

4.00

4.00

Equivalent series resistance, R1/Ω

79

76

Shunt capacitance (include case capacitance), C0/pF

1.2

1.4

Motional capacitance, C1/fF

3.5

3.5

Motional inductance, L1/mH

452

450

Quality factor, Q

145,000

149,000

Capacitance ratio (include case capacitance), r

400

400

time and several tens of thousands of pieces are produced each month. (Note: LMX-01 reached its EOL in 2010 and is no longer in production.)

5.3.4 Other New Resonators Developed by River Eletec Corporation Since the publication of the first edition of this book in 2010, River Eletec Corporation has developed two new quartz-crystal resonators. Both have been the world’s first achievements of their kind, and they received immense praise at the IEEE International Frequency Control Symposium (FCS) held in May 2014 in Taiwan. 5.3.4.1 GT-Cut Resonator11 The first is an ultracompact, high-performance quartz-crystal resonator that supports lower MHz bands. This resonator utilizes a GT-cut quartzcrystal and employs a “GT-cut width-extensional mode,” which is the width-extensional mode coupled with the length-extensional mode. The vibration image of this mode is shown in Fig. 5.21. Fig. 5.22 shows the frequency-temperature characteristics of the GT-cut resonator and a widely used AT-cut crystal resonator. As you can see from this, the GT-cut resonator obtains more stability than that of the AT-cut resonator over a wide temperature range. Moreover, the 4.19 MHz GTcut resonator used in this experiment has a significantly miniaturized size, which is 2.5 mm  2.0 mm  0.55 mm, compared with the practicable size of the AT-cut resonator, which is approximately 10 mm  5 mm  3 mm. For example, the image comparison of a 12 MHz GT-cut resonator and an AT-cut resonator of the same frequency is shown in Fig. 5.23. In addition, the equivalent circuit constants (measured value) of the GT-cut I. PIEZOELECTRIC MATERIALS

(A)

Principal vibration (width-extensional vibration)

(B)

Sub-vibration (length-extensional vibration)

FIG. 5.21 GT-cut width-extensional vibration (width-extensional vibration (A) coupled with length-extensional vibration (B)).

Frequency deviation (ppm)

10 8 6

GT measured AT measured

4 2 0 −2 −4 −6 −8 −10 −30 −20 −10

FIG. 5.22

0

10 20 30 40 50 Temperature (°C)

60

70

80

90

Temperature frequency characteristics of the GT-cut.

GT cut quartz crystal unit AT cut quartz crystal unit (1.6 mm × 1.2 mm × 0.33 mm) (2.5 mm × 2.0 mm × 0.6 mm)

FIG. 5.23 Package size comparison of a GT-cut resonator and an AT-cut resonator with the same frequency, 12 MHz. I. PIEZOELECTRIC MATERIALS

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TABLE 5.8 Equivalent Circuit Constants of GT-cut 12 MHz Resonator Fr1(MHz)

R1(Ω)

C1(fF)

L1(mH)

γ1

Q1

C0(pF)

11.9992

98

2.30

76

304

58,000

0.70

resonator are shown in Table 5.8. As you can see from these factors, the GT-cut resonator is quite suitable for low power consumption circuits.

(Thickness direction)

5.3.4.2 Lamb Wave Resonator12 The second is a super-high-performance, high-frequency Lamb wave resonator having the world’s newest cutting angles that River Eletec Corporation has discovered. This Lamb wave resonator had been completed with the frequency of 433 MHz, and it was presented at FCS on 2014. With continuous development since then, River Eletec Corporation also has achieved 920 MHz on this Lamb wave resonator. The vibration image of the Lamb wave resonator is shown in Fig. 5.24. Fig. 5.25 shows the frequency-temperature characteristics of the Lamb wave resonator and a typical ST-cut surface acoustic wave (SAW) resonator. This figure shows that the Lamb wave resonator obtains more stability than that of the SAW resonator over a wide temperature range. In addition, the equivalent circuit constants (representative value) of the Lamb wave resonator are shown in Table 5.9. As you can see from these factors, the Lamb wave resonator is also quite suitable for low power consumption circuits. River Eletec Corporation has been searching for more application fields for these two high-performance quartz-crystal resonators. (0°, 37.85° , 0°)

H/l = 1.20, Hs/l = 0.006, Hb/l = 0

Y’

X (Propagation direction) • Symmetric mode • Electromechanical coupling coefficient K2 = 0.08%

FIG. 5.24

Quartz crystal vibration of the Lamb wave.

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Frequency deviation Δf/f [ppm]

50

(0 º, 37.825 º, 0 º) H/l = 1.20, Hs/l = 0.010, Hb/l = 0.005

25 0 −25 −50 −75

ST-cut SAW Lamb wave

−100 −125 −150 −40

−20

0

20

40

60

80

100

Temperature [ºC]

FIG. 5.25

Temperature frequency characteristics of the Lamb wave resonator.

TABLE 5.9 Equivalent Circuit Constants of Lamb-Wave 433 MHz Resonator Frequency (MHz)

R1 (Ω)

Q

L1 (mH)

C1 (fF)

γ

433

29

11,000

0.12

1.15

3300

5.4 RESONATOR, OSCILLATOR, AND FILTER APPLICATIONS 5.4.1 Mobile Communications 5.4.1.1 Bluetooth Bluetooth is a near-field communication standard established by the Ericsson Corporation. The industry group Bluetooth-SIG works mainly to improve this standard and certify applications of the technology. Bluetooth uses the ISM 2.4 GHz band frequency and uses Gaussian frequency shift keying for communication. The communication distance is around 100 m or less. Bluetooth technology allows wireless communication between electronic devices. The selected profile regulates the flow of information and contains serial, parallel, and IP communication as well as IO devices such as keyboards. The same profile must be used for communication between devices. The Bluetooth standard is now frequently used for IO computer devices and wireless headsets for cellular phones. In many cases Bluetooth has all but replaced the need for infrared communication in these devices.

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Characteristics of bluetooth

• Standards: Bluetooth Version 1.0b/1.0b + CE/ 1.1/1.2/2.0/2.1/3.0/4.0/4.1/4.2. • Uses: Near field wireless communication for electronic devices. • Features: Gaussian frequency shift keying with ISM band. • Velocity: 24 Mbps maximum (Version 3.0). Most devices that use Bluetooth technology integrate the module within the device. This module is driven by the base oscillation of the TCXO/quartz crystal resonator. It is common for cellular phones to use its TCXO for the GSM band processor as the time base. Bluetooth improves these functions and continues to increase its profiles, creating complicated process standards, even with backward compatibility of previous versions. Recently, version 3.0 has been added and it has compatibility with the previous versions. Applying the wireless LAN standard IEEE302.11 PAL (Protocol Adaptation Layer), this version achieves maximum speed of 24 Mbps as an option. After version 4.0, BLE (Bluetooth low energy), which has a much lower power consumption than the previous versions, has been adopted. The latest version is version 4.2, which has the communication speed of 650 kbps with the function of connecting to the internet on its own.

5.4.1.2 Wireless LAN The wireless LAN standard, IEEE802.11, was established in 1997. The 802.11 and the 802.11b standards use the 2.4 GHz frequency band and use the Direct Sequence Spread Spectrum Communication System. Their maximum communication speeds are 2 and 11 Mbps, respectively, and the frequency bandwidth of the channels are arranged partially duplicated to one another. The 802.11a standard uses the 5 GHz frequency band and utilizes the OFDM (orthogonal frequency division multiplexing) applied Direct Sequence Spread Spectrum Communication System with a maximum speed of 54 Mbps. The 802.11 g uses the 2.4 GHz frequency band and also has a maximum speed of 54 Mbps. This speed is achieved by using OFDM to the 802.11b base. The 802.11n uses the frequency band of 2.4 GHz/5 GHz with a maximum speed of 600 Mbps. The 802.11 ac is a new standard, having a maximum communication speed of 6.9 Gbps. This speed is achieved by adopting the frequency band of 5 GHz with channel 160 MHz MU-MIMO. Characteristics of wireless LAN

• Standards: IEEE802.11/11b/11g/11a/11n/11ac. • Uses: Mainly applied for the IP network.

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TABLE 5.10 List of Wireless LAN Standards Standard no.

Frequency band (GHz)

Diffusion/ modulation

Communication velocity (Mbps)

Note

802.11

2.4

FHSS

2.0

Frequency hopping

802.11b

2.4

DSSS

11

Direct diffusion

802.11a

5.0

DSSS + OFDM

54

Applying OFDM

802.11g

2.4

DSSS + OFDM

54

Expanding 11b and applying OFDM

802.11n

5.0/2.4

DSSS + OFDM + MIMO

600

Completed in 2009 and applying MIMO

802.11ac

5.0

MU-MIMO

6900

MU-MIMO

• Features: Spread Spectrum Communication System using ISM band (2.4 GHz/5 GHz). • Velocity: 2 Mbps (802.11) to 6.9 Gbps (802.11ac). Data volume can be increased proportionally to the quantity of antennas, by simultaneously processing the data based on corresponding information. Based on this, communication speed is expected to be faster using the 5 GHz frequency band. A list of the Wireless LAN standards is shown in Table 5.10.

5.4.2 Cellular Phones 5.4.2.1 One-Segment/Full Segment Tuners Digital terrestrial television broadcasting is a digital broadcasting service that uses terrestrial electromagnetic waves. NHK, a leader in digital broadcasting in Japan, developed the ISDB (integrated services digital broadcasting) standard, based on the ISDB-T standard. The frequency range for one channel of analog broadcasting is divided into 13 segments, four of which are used for one channel of standard definition or 12 are used for a channel in high definition. One segment tuners use the one of 13 segments, and full segment tuners use the four or 12 segments described above. In Japan, digital TV sets and recording devices contain the digital tuner required to decode the signal. One-segment tuners are used for smaller displays such as those found in cellular phones and digital media players. Characteristics of one-segment/full segment tuners

• Standard: ISDB-T. • Uses: Transmitting and receiving digital TV broadcasting. I. PIEZOELECTRIC MATERIALS

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5.572 MHz 1

2

3

4

5

6

7

8

9

10

11

12

13

Full segment = 13 segments

1 segment 432 career

FIG. 5.26 Explanation of frequency occupation with “one segment” and “full segment.”

• Features: Effective use of the limited frequency range and highdefinition TV transmission. Quartz crystal vibrators are used for RF receivers and OFDM decoders with the ICs. In most cases, a one-crystal vibrator is used that has a commonly required frequency, and a recently developed IC chip contains both the RF receiver and OFDM decoder. The standards of DVB-H, T-DMB, and Media FLO are applied in Europe and the United States, while CMMB is applied in China, although not in wide use. Brazil is also planning on adopting Japan’s ISDB-T standard for digital terrestrial TV broadcasting. An explanation of frequency occupation with “one segment” and “full segment” is shown in Fig. 5.26.

5.4.2.2 RF Module IEEE802.15.4 (ZIGBEE, ETC.)

The short range RF communication technology based on IEEE802.15.4 uses the ISM band frequency. The frequency range of 2.4 GHz is allowed for this technology in Japan, and there are other cases using frequency ranges of 800–900 MHz. The RF module in compliance with Zigbee specification employs the protocol which the Zigbee alliance certified. This standard settles smaller output power increasing battery life. The Zigbee communication distance is tens of meters and transporting velocity is 250 kbps. To make data relay possible between the clients, not only does the device make direct communication between the two clients but it can also use network topology such as star connection, mesh connection, etc. There are 65,535 nodes available for connections, and it is possible to sense the position and communicate between them. Adding a low-power consumption CPU or sensor will make it possible for individual data correction from a wide area on an autonomous distributed network. I. PIEZOELECTRIC MATERIALS

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Characteristics of the RF module

• Standard: IEEE802.15.4. • Uses: Usually for the near-field wireless communications. • Features: Autonomous distributed networks are available, using the ISM frequency band and low power consumption. • Velocity: maximum 250 kbps. There are other similar RF module devices that have protocols not sanctioned by the Zigbee Alliance. Some of the devices are used to calculate the data of heart beats, velocity, air pressure, GPS, and even some sports goods. UWB (ULTRAWIDE BAND)

UWB is a spread spectrum communication technology using a wide frequency band in the 3–4 GHz range. It is best suited for high capacity, fast communication and features low power consumption and strength to external noises. Its communication distance is around ten meters and the quartz crystal vibrator is used as its RF frequency oscillation. Characteristics of the ultrawide band

• Standard: none (abandoned in 2006). • Uses: Large capacity of data transmitting for very near-field communication. • Feature: Applied spread spectrum communication using ultrawide band microwave, and used for very near-field communication. • Velocity: From 100 to 500 Mbps. In 2006 the ultrawide band standard was abandoned because of various problems and nonconformity. Recently, some of the protocols (transfer-jet, etc.) that were based on UWB have been proposed to make the connections between electronic devices from wired to unwired. This technology has the possibility to popularize the standard if product developers and designers can agree on a common protocol. The serial transfer velocity is from 100 to 500 Mbps, excluding the protocol header. 5.4.2.3 Secure Private Cosm (SPC) Encryption Today, various types of personal information are stored on cellular phones, personal digital assistants (PDAs) and other electronic devices, and there is an increasing demand to keep that personal information protected. Secure private cosm is a protection method that permits the device to work only under certain circumstances and become unusable when outside the designated parameters. An example of this technology could use human skin as the encryption key and only function in the hands of certain users. A quartz crystal vibrator would be used for the

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LOCK

229

OK!

SPC

FIG. 5.27

Image of the SPC action.

communication between the key and the device. An image of this action is shown in Fig. 5.27. 5.4.2.4 Duplexer Duplexers are commonly used in antennas. They contain a diverging circuit and transmitting/receiving filters that select the required frequency from the widely spread electric wave. While the duplexer separates two waves, a triplexer separates three electric waves. The dielectric resonator and/or SAW (surface acoustic wave) resonator and recently the BAW (bulk acoustic wave) resonator are applications. 5.4.2.5 IF (Intermediate Frequency) Filter Cellular phones and other wireless electronic devices such as televisions and radios use a super heterodyne detection system. The electric waves generated in this system are mixed with the aimed/received electric wave, and their differential frequency of wave is picked out. This wave (IF) is handled easily with a suitable electric circuit. In order to resolve the noise(s) of the IF wave, quartz crystal, ceramic, and SAW filters are used. Recently, the filters have been used in the IC, and the use of the IF filter has decreased. 5.4.2.6 Monolithic Crystal Filter (MCF) MCF is a filter that has a combined plural quartz crystal resonator and several pairs of electrodes on a single quartz crystal plate. It does not require the winding coil for designing electric circuits. The characteristics of MCF are limited but it can miniaturize and lighten the filter function. Compared with SAW filters, MCF is preferable for narrow band and high Q filters in lower frequency applications. MCF is used in band pass filters that have nominal frequency layers from very low MHz to some hundreds of MHz, and a bandwidth from tens of KHz to hundreds of KHz—similar

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to RF communication and wired transfer devices. MCF is frequently used in cellular phone applications. 5.4.2.7 Camera Module The camera modules used in cellular phones consist of smaller sized CCD or CMOS optical lenses. These applications require miniaturization and high definition, auto focus functions. High-end cameras contain optical zoom functions that require special circuits for driving the optical lenses and focus adjustment feedback. A quartz crystal vibrator is used to drive the CCD or CMOS camera and is also used for controlling these circuits.

5.4.3 Automotive Applications 5.4.3.1 Navigation (GPS) A GPS (global positioning system) can locate your exact longitude and latitude position on the ground. It calculates and shows your current location using the time difference of the signals from the orbit of 30 satellites that are controlled by the United States Army and other commercial companies. The plane point on the ground is calculated by the information from three of the satellites and the 3-D point is calculated by the information from four of these satellites. Each satellite has an atomic clock and a very precise time is transmitted to earth. The signals from these satellites are transmitted using pulse diffusion communication technology, received by antenna and then the current position can be calculated. This technology requires very accurate time base and TCXO in the receiving circuit. Car navigation systems show route information to your destination using GPS information. It can show the shortest and the most suitable way to get to your destination by using the present point data and destination point data on the map. High-end car navigation systems also include other functions such as audio, TV, DVD player, and an outside CCD camera. Smaller, less expensive portable car navigation systems that can be used between multiple cars and also as a PND (personal navigation device) for other modes of travel are becoming popular. 5.4.3.2 Car Audio/Video System The staple of the car audio system has been the radio receiver. The media have changed and improved throughout the years from cassette players to CD and MD and now other forms of media. Current systems allow not only audio playing, but also TV and DVD viewing. Many of these systems also contain hard disk drives, providing increased storage

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for media and navigation systems as well as digital data through the LCD. A quartz crystal vibrator was used for the original radio analog tuner, but these advanced systems now use plural quartz crystal vibrators. 5.4.3.3 Keyless Entry Keyless entry systems are used to remotely lock, unlock, and start your car’s engine using RF signals. There are two types of keyless entry systems: active and passive. Active systems send a signal to the receiver in the car, and the system disarms. Passive systems transmit the signal and will receive and require a response signal from the key, before the system disarms. The RF modules are used in both the transmitting and receiving circuits and communication between these circuits are coded. Quartz crystal vibrators are used in these RF modules. 5.4.3.4 Laser/Millimeter Wave Radar The next generation of traffic control systems is being developed by many automotive companies throughout the world. These systems will avoid traffic accidents by using laser/millimeter wave radar technology. An applied example of this technology could allow a vehicle to be controlled by markers buried along the road that would receive the reflection of laser or millimeter waves that were being transmitted from the vehicle. The distance between vehicles can also be measured by laser/millimeter wave radar techniques and help prevent collisions. Quartz crystal vibrators are used for the base of these waves and for the information treatment circuit. 5.4.3.5 Body Control Module The body control module (BCM) is the main computer in a vehicle that supervises all of the car’s electronic systems. Modern vehicles use electricity for many systems including starting the engine, fuel control, lighting, and other factors play a critical role in controlling the vehicle. Every electric circuit is required to work under extremely severe conditions and a wide range of temperatures. These systems are required to work reliably for the life of the vehicle.

5.4.4 Other Applications 5.4.4.1 Medical Instruments CAPSULE ENDOSCOPES

Capsule endoscopes are a type of endoscope that are stored and sealed in a 10–30 mm diameter capsule. The patient swallows this capsule and it takes internal pictures of the digestive tract on its way down. This new method reduces the pain for the patient of tradition endoscope

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FIG. 5.28

5. QUARTZ-BASED PIEZOELECTRIC MATERIALS

Capsule endoscope.

procedures. The capsule contains a battery, RF communication circuit, lighting LED, and CCD camera and takes a picture every few seconds, resulting in tens of thousands of pictures during the process. These pictures are immediately transmitted by RF to an external receiver. Other than swallowing the capsule, there is no other action required of the patient. Quartz crystal vibrator/oscillators are used in these endoscopes for driving the CCD camera and RF communication circuit. Capsule endoscopes can take pictures of the small intestine where traditional fiber endoscopes could not reach. Each year, tens of thousands of capsule endoscope procedures are performed in Europe and the United States and they are increasing in frequency. The Ministry of Welfare in Japan permitted the use of the foreign-made capsule endoscopes in 2008 and some medical facilities could introduce this test in the near future. It is expected to enlarge the market for capsule endoscopes. An image of a capsule endoscope is shown in Fig. 5.28. BLOOD SUGAR LEVEL SENSORS

Blood sugar level sensors allow diabetic patients to know when they require an insulin injection. These devices need direct contact (the sensor has to directly contact blood). Indirect contact devices observe the electromagnetic wave through the blood tube. Scientists are developing a device that would combine the indirect contact sensor and insulin injection mechanism. 5.4.4.2 Near-Field Communications Near-field communications (NFC) is an international standard for nearfield RF communication that uses one of the ISM frequency bands around the 13.56 MHz range. NFC consists of two integrated systems called FeliCa and MIFARE. FeliCa was proposed by SONY and is widely supported in Asia. MIFARE was proposed by Philips and has widespread usage in Europe and the United States. NFC is used in the no contact-type IC card, set to replace traditional magnetic cards. CHARACTERISTICS OF NEAR-FIELD COMMUNICATIONS

• Standard: ISO/IEC IS 18092. • Use: Near-field wireless communications between devices. I. PIEZOELECTRIC MATERIALS

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• Feature: Low power consumption and uses 13.56 MHz. • Velocity: 424 kbps max. Many applications are expected to use the NFC compatible standard that requires low capacity data communications between electronic devices.

Acknowledgements I would like to express my sincere gratitude to Dr. Yasuhiko Nakagawa, Honorary Professor at Yamanashi University, Mr. Katsuya Mizumoto, Mr. Yusuke Yamagata, and Mr. Tasuku Kon, River Eletec Corporation R&D, for their many helpful discussions.

References 1. Koga I. Piezoelectricity and high frequency. Ohm-sya; 1938. 2. Sykes RA. Quartz crystal for electrical circuits. In: Heising RA, editor. New York: D. Van Nostrand Company Inc.; 1946. 3. Shinada T. Theory and the facts of quartz crystal. Ohm-sya; 1963. 4. Yanagida H, Nagai M. The science of ceramic. Gihodo; 1993. 5. QIAJ Technical Committee. The explanation of quartz crystal devices and its applications. The Meiden media front; 2007. 6. Kawashima H. The base of quartz crystal resonator. The Ultrasonic Techno serialized report. 7. The ultrasonic handbook editing committee. Ultrasonic Handbook. Japan: Maruzen; 1999. 8. Ariga M. Isothermal elastic constants of quartz crystal and its temperature characteristics. Tokyo Institute of Technology Report A–2; 1956. p. 88–182. 9. Bechmann R, Ballato AD, Lukaszek TJ. Higher-order temperature coefficients of the elastic stiffnesses and compliances of alpha-quartz. Proc IRE 1962;50(8):1812–22. 10. Kawashima H, Matsuyama M. Analyses of double rotated Lame mode piezoelectric resonator with energy method. Inst Electr Inform Commun Eng Pap A 1996;J79-A(6). 11. Yamagata Y, Mizumoto K. A miniature 12 MHz GT cut quartz resonator vibrating in a (m ¼ 3, n ¼ 1) mode. In: IEEE international frequency control symposium technical papers; 2014. p. 85–8. 12. Kon T, Mizumoto K, Saigusa Y. An analysis of frequency temperature characteristics of a lamb wave type quartz acoustic wave device. In: IEEE international frequency control symposium technical papers; 2014. p. 89–94.

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C H A P T E R

6 Nano- and Microdomain Engineering of Lithium Niobate and Lithium Tantalate for Piezoelectric Applications V.Ya. Shur Ural Federal University, Ekaterinburg, Russia

Abstract This chapter discusses the influence of the tailored periodical nano- and microdomain structures on the piezoelectric properties of LiNbO3 and LiTaO3 crystals. The chapter first reviews the main piezoelectric characteristics of LiNbO3 and LiTaO3 crystals and acoustic properties of the crystals with periodic laminar domain structure. The chapter then discusses the physical basis of nano- and microdomain engineering in LiNbO3 and LiTaO3 crystals and the application of the periodically poled LiNbO3 and LiTaO3 for light frequency conversion and generation of the terahertz radiation. Keywords: Light frequency conversion, Tailored periodical domain structure, Generation of acoustic waves, Nanoscale domains, Generation of the terahertz radiation.

6.1 INTRODUCTION Lithium niobate (LiNbO3) and lithium tantalate (LiTaO3) crystals are not encountered in nature and are manmade. The single crystals of LiNbO3 and LiTaO3 were synthesized for the first time in Bell Laboratories and their ferroelectric properties were revealed by Matthias and Remeika.1 Both crystals belong to the ilmenite structure. Ilmenite (FeTiO3) is a mineral named after its locality in the Ilmen Mountains, Southern Urals,

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Russia. It looks like a black crystal with trigonal (rhombohedral) symmetry (space group R3). It is not easy to recognize lithium niobate LiNbO3 in the first paper,1 because it is referred to as lithium columbite, LiCbO3. The element niobium had two names, niobium and columbium, for about a century after its discovery. The name of the element was officially adopted as niobium (Nb) in 1949. Niobium has physical and chemical properties similar to those of tantalum (Ta), and the two are therefore difficult to distinguish. The English chemist Charles Hatchett reported a new element similar to tantalum in 1801 and named it columbium. In 1809, the English chemist William Hyde Wollaston wrongly concluded that tantalum and columbium were identical. The German chemist Heinrich Rose determined in 1846 that tantalum ores contain a second element, which he named niobium. In 1864 and 1865, a series of scientific findings clarified that niobium and columbium were the same element, and for a century both names were used interchangeably. Theoretically the ferroelectricity of LiNbO3 and LiTaO3 was studied by Schweinler2 using the Slater method proposed for BaTiO3. The properties of LiNbO3 and LiTaO3 have been studied systematically after a delay of about 15 years when Ballman,3 Fedulov et al.,4 and Nassau et al.5 independently succeeded in growing large LiNbO3 single crystals using the Czochralski technique. The results of a detailed investigation of their structure and properties were reviewed.6–8 Both LiNbO3 and LiTaO3 are well known for their low acoustic losses and are thus excellent materials for surface acoustic wave (SAW) devices, causing a commercial growth of several tons every year. Nowadays LiNbO3 is widely used in various devices that exploit its superior elastic, piezoelectric, dielectric, acousto-optic, electro-optic, pyroelectric, photoelastic, and photovoltaic properties. LiNbO3 possesses very large electromechanical coupling coefficients, which are several times larger than those in quartz, and it has very low acoustic losses. Because of its Curie temperature of 1142°C, it can be utilized as a high-temperature acoustic transducer, such as an accelerometer for jet aircraft. Acoustic wave delay lines and acousto-optic modulators, deflectors, and filters now routinely employ LiNbO3 for both shear and longitudinal wave generators because of its high efficiency, broad bandwidth capability, low dielectric constant for all orientations, and consistent repeatability. LiNbO3 possesses a number of useful cuts that are now extensively used in transducer applications. Two longitudinal cuts are popular, the z-cut and the 36 degrees rotated y-cut. The shear mode cuts most commonly used are the x-cut and 163 degrees rotated y-cut. LiTaO3 also possesses useful cuts for longitudinal and shear wave mode transducers. The two most popular longitudinal cuts are the z-cut

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and the 47 degrees rotated y-cut, while the x-cut and the 165 degrees rotated y-cut are the most commonly used shear mode cuts. Compared to quartz, LiTaO3 has a much larger electromechanical coupling and a number of zero temperature coefficient cuts of resonant frequency. As a result, it finds application in communications for acoustic resonator filters of broad bandwidth. In recent decades both crystals have become the most important objects of domain engineering. The main target of the domain engineering is the improvement of the important for application characteristics of commercially available ferroelectrics by the manufacturing of stable tailored domain patterns (periodic poling). The creation of a stable periodic domain structure allows the introduction of spatial modulation of the piezoelectric, electro-optic, photorefractive, and nonlinear optical properties, thus upgrading the device performance. The low price of these devices achieved under mass production based on periodic poling by electric field will expand this technology into the wide market. The optimization of the poling process that resulted from the fundamental studies of the domain kinetics is expected to enable the fabrication of submicron-pitch gratings and engineered 1-D and 2-D structures, which could meet the demanding specifications for acoustic and nonlinear optical applications. The ultimate interest is the exploitation of nanoscale domain structures and the precise periodical microscale structures with nanometer accuracy. For example, for achieving high conversion efficiency of laser light the structure has to be precisely reproducible with the period dispersion below 20 nm.

6.2 PIEZOELECTRIC PROPERTIES OF LITHIUM NIOBATE AND LITHIUM TANTALATE LiNbO3 and LiTaO3 are colorless, chemically stable, insoluble in water, and are organic solvents. They are ferroelectric crystals that possess very high melting points and Curie temperatures. Both crystals can be grown by the Czochralski technique—thus large, high-quality single crystals in a number of different growth directions are available. The general properties of LiNbO3 and LiTaO3 not related to the piezoelectric effect are given in Table 6.1. Although sometimes several digits for a value are published, a scatter of more than 10% is found in the literature. Therefore, the values should be regarded as examples for the order of the magnitude of the respective property.13 LiNbO3 and LiTaO3 structures below Curie temperature consist of planar sheets of oxygen atoms in a distorted hexagonal close-packed configuration (see Fig. 6.1). The octahedral interstices formed in this structure are one-third filled by lithium ions, one-third filled by niobium/tantalum

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TABLE 6.1 Main Physical Properties of LiNbO3 and LiTaO3 Property/materials

LiNbO3

LiTaO3

Ref.

Melting point (°C)

1255

1650

9

Mohs hardness


5


5.5

9

Lattice constant aH (pm)

515.0

515.4

10

Lattice constant cH (pm)

1386.4

1378.1

10

Density (g cm )

4.64

7.454

7

Curie temperature (°C)

1140

605

9,11

Spontaneous polarization PS (μC cm2)

71

60

11,12

-1

O2− Nb5+ Li+ Oxygen plane

(A)

(B)

(C)

(D)

(E)

(F)

FIG. 6.1 Structure of LN in paraelectric (A, B) and ferroelectric phases (C–F) with the relative positions of Li ions, Nb ions, and oxygen planes. Reproduced from Kang X, Liang L, Song W, Wang F, Sang Y, Liu H. Formation mechanism and elimination methods for anti-site defects in LiNbO3/LiTaO3 crystals. CrystEngComm 2016;18:8136–46 with permission of The Royal Society of Chemistry.

ions, and one-third vacant. In the paraelectric phase (above phase transition point), the Li atoms lie in an oxygen layer that is c/4 away from the Nb/Ta atom, and the Nb/Ta atoms are centered between oxygen layers. These positions make the paraelectric phase nonpolar6,8 (see Fig. 6.1A). Below the phase transition point, the lithium and niobium ions shift into new positions (see Fig. 6.1B). The charge separation resulting from the ions shifting relative to the oxygen octahedra leads to exhibition of spontaneous polarization. Thus, LiNbO3 and LiTaO3 belong to a broad class of displacement ferroelectrics just like BaTiO3. The structures of LiNbO3 and LiTaO3 at room temperature belong to the rhombohedral (trigonal) space group R3c, with point group 3m. Above

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(0,0,1)

(0,0,1)

(−2/3,−1/3,2/3) (0,1,1)

(1,0,1) (2/3,1/3,5/6) (0,0,1/2)

(1/3,−1/3,2/3)

(1,1,1) (1/3,2/3,2/3)

(−1/3,−2/3,1/3)

(1/3,2/3,2/3) (−1/3,1/3,1/3)

(0,1,1/2)

(1,0,1/2) (2/3,1/3,1/3) (0,0,0)

(1/3,2/3,1/6)

(0,0,0)

(0,1,0)

(1,0,0)

(A)

(2/3,1/3,1/3)

(1,1,1/2)

(1,1,0)

(B)

FIG. 6.2 (A) Hexagonal unit cell of LiNbO3 with positional coordinates of lithium and niobium atoms indicated. (B) Conventional rhombohedral unit cell of LiNbO3 shown with respect to the hexagonal unit cell.

the phase transition temperature both crystals transform to the centrosymmetric space group R3m. The positions of the lithium and niobium ions in both the paraelectric and ferroelectric phases are shown in Figs. 6.2 and 6.3. It is known that the setting of the crystallographic axes for the trigonal symmetry is not unambiguous; thus three types of elementary cells can be chosen, namely, rhombohedral, hexagonal, and orthohexagonal cells (see Figs. 6.2 and 6.3). The former two are considered more convenient for crystallographic aims and structure determination.13 For most applications, the orthohexagonal setting is preferred and the tensor components of properties are given with respect to these axes. In an orthohexagonal setting, all axes are mutually orthogonal. Their directions according to standards of piezoelectric crystals14 are settled in the following way: (1) Z is the threefold axis, (2) the y-axis lies in the mirror plane, and (3) the x-axis is orthogonal to both of them (see Fig. 6.3A). Both Z and Y axes are polar (piezoelectric) and by convention their positive ends correspond to appearance of the negative charge under a uniaxial compression. Additionally, the z-axis is pyroelectric; by convention its positive end corresponds to the appearance of a positive charge on crystal cooling. The x-axis in this setting is nonpolar. The axes’ orientations relative to the crystal boule (grown in the Z direction) are shown in Fig. 6.3B. Moreover, the orientations of the domain walls of the isolated domain for congruent LiNbO3 (CLN) (see Fig. 6.3C) and congruent LiTaO3 (CLT) (see Fig. 6.3D) arising under

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Mirror plane

Mirror plane

m m Mirror plane

m

y x

(B)

y

(C)

x

x y

y

(A)

(D)

x

FIG. 6.3 (A) Standard orientation of the principal axes used to describe tensor physical properties in LiNbO3. Standard orientation of the principle axes relative to (B) crystal boule, (C) hexagonal domain in congruent LiNbO3, and (D) triangular domain in congruent LiTaO3.

“equilibrium switching conditions”15 are presented. Both hexagonal and triangular domain shapes are observed in these crystals during usual slow “quasi-equilibrium” polarization reversal. It must be pointed out that the strict orientations of the domain walls along crystallographic directions are useful for creation of the stripe domain patterns. The variety of domain shapes can be observed in LiNbO3 and LiTaO3 during polarization reversal with ineffective screening of the depolarization field.15–17 Moreover it was shown recently that the shape of isolated domains in LiNbO3 and LiTaO3 changes drastically for polarization reversal at the elevated temperatures.18 A piezoelectric solid exhibits an induced polarization with applied stress. The linear relationship between induced polarization ΔPi so called direct piezoelectric effect, can be written as follows: X ΔPi ¼ dijk σ jk , (6.1) jk

where dijk is the third-rank piezoelectric tensor symmetrical over the two last indexes and σ jk is the second-rank stress tensor. According to standard symmetry considerations the piezoelectric effect in LiNbO3 and LiTaO3 possessing trigonal symmetry (point group 3m) is fully described by four independent piezoelectric coefficients.19 The contracted notation is the following: I. PIEZOELECTRIC MATERIALS

6.2 PIEZOELECTRIC PROPERTIES OF LITHIUM NIOBATE AND LITHIUM TANTALATE



dijk



3 0 0 0 0 d15 2d22 0 5: ¼ 4 d22 d22 0 d15 0 d31 d31 d33 0 0 0

241

2

(6.2)

If we choose strain as the independent variable, then the induced polarization due to the piezoelectric effect would be proportional to strain magnitude: X eijk ujk , (6.3) ΔPi ¼ jk

where eijk is the third-rank tensor symmetric over the two last indexes and ujk is the second-rank strain tensor. Accordingly, there exists a converse piezoelectric effect that linearly couples induced strain Δujk and the applied external electric field Ei. It can be shown that the coefficients relating stress and induced polarization in the direct piezoelectric effect are the same (not taking the sign into account) as the ones relating induced strain and applied electric field in the converse piezoelectric effect. X dijk Ei (6.4) Δujk ¼ i

This equality is easily understood if we carry out the following “thought experiment”: let us apply external compressive force to the piezoelectric slab. If the piezoelectric effect were absent, the work of compressive force would be equal to the potential energy of the elastically deformed sample. Due to piezoelectric effect the charges are induced on the slab surfaces and the electric field is generated in the bulk. It means that the total deformed sample energy increases by the stored energy of the electric field and thus we are to do additional work to compress the piezoelectric; in other words the additional forces resisting compression arise in the sample. These forces are thus the manifestation of the converse piezoelectric effect. It is clear that if the same charges, as in the direct effect, are generated on the slab surfaces by external electric field the sample will stretch out. We can arrive to the same result considering thermodynamics of the piezoelectric material under the action of external field and deformations. Choosing the electric field Ei and strain uij as independent variables, the variation of the free energy of the piezoelectric δF given by the expression20: δF ¼ 

X X X Di δEi  uij δσ ij  dijk δEi σ jk : i

ij

(6.5)

ijk

@F @F and uij ¼  we arrive at the result Using definition Di ¼  @Ei @σ ij stated above. I. PIEZOELECTRIC MATERIALS

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Alternatively, if the sample is clamped and cannot deform, the converse piezoelectric effect reveals itself as the appearance of additional mechanical stress in the sample under application of external an electric field. It is known that temperature behavior of ferroelectrics in most cases is fairly well described within the Ginsburg-Landau-Devonshire theory. According to this theory only effects of the second order (electrostrictive coupling between the polarization and strain/stress) exist in paraelectric proto-phase. This means that in the expansion of free energy only the terms of the type QijklPiPjukl emerge. When structural transition to the ferroelectric phase occurs, the component of polarization along the polar axes Pz “stiffens” and turns into spontaneous polarization PS. Thus the thirdrank piezoelectric constants appear. It is clear that due to their history the sign of these constants is dependent on spontaneous polarization orientation. In antiparallel domains the relative signs of all piezocoefficients are opposite. This property is a very useful one making it possible to induce required spatial variations in stress/strain by tailored domain structure, and it is also the basis of high-resolution domain observation by piezoresponse force microscopy (PFM).21–23 The experimentally obtained values of piezoelectric coefficients for LiNbO3 and LiTaO3 are listed in Table 6.2.7 The measurements of these coefficients present a formidable task.24 One of the experimental methods of obtaining the required data is based on the ultrasonic phase velocity measurements coupled with low-frequency capacitance measurements for dielectric constants.7 TABLE 6.2 Piezoelectric Coefficients for LiNbO3 and LiTaO37 Piezoelectric coefficients/materials

LiNbO3

LiTaO3

d15

69.2

26.4

d22

20.8

7.5

d31

-0.85

-3.0

6.0

5.7

Piezoelectric strain constants—dij (pC/N)

d33 2

Piezoelectric stress constants—eij (C/m ) (at 25°C) e15

3.76

2.72

e22

2.43

1.67

e31

0.23

-0.38

e33

1.33

1.09

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It must be understood that piezoelectric properties are interconnected with elastic and dielectric properties of the investigated material. The acoustic experiments yield simultaneously the values of elastic stiffness coefficients Cijkl and compliance coefficients sijkl (six independent coefficients in crystals with 3m point-group symmetry). 2

C11 C12 6 C12 C11 6   6 C13 C13 Cij ¼ 6 6 C14 C14 6 4 0 0 0 0 2 s11 s12 6 s12 s11 6   6 s13 s13 sij ¼ 6 6 s14 s14 6 4 0 0 0 0

3 C13 C14 0 0 7 C13 C14 0 0 7 7 C33 0 0 0 7 7 0 C44 0 0 7 5 C14 0 0 C44 0 0 C14 ðC11  C12 Þ=2 3 s13 s14 0 0 7 s13 s14 0 0 7 7 s33 0 0 0 7 7 0 s44 0 0 7 5 2s14 0 0 s44 0 0 2s14 2ðs11  s12 Þ

The values of elastic and dielectric constants are listed in Table 6.3. It must be mentioned that the strong piezoelectric effect leads to a large difference between resonance frequencies in LiNbO3 and LiTaO3 predicted within the elastic theory and the ones accounting for piezoelectric effect. This is due to the large contribution of the field produced by the surface charges induced through the piezoelectric effect into the stiffness coefficients.

6.3 THE ADVANTAGES OF SINGLE-CRYSTAL FERROELECTRICS FOR PIEZOELECTRIC APPLICATIONS Most of the commercially available piezoelectric actuators are based on ferroelectric ceramics with random orientation of the grains. Nevertheless, single-crystal actuators possess higher energy density due to the fact that the crystals can be oriented along proper higher-strain crystallographic directions. The LiNbO3 and LiTaO3 crystals used for ultrasonic device applications are commonly poled near Curie temperature into a stable single-domain state. As a result, a uniform, highly consistent piezoelectric transducer crystal with a “frozen” single-domain state is obtained. Recently the strong influence of the domain walls on the piezoelectric and acoustic properties put forward a problem of creation of the periodic domain structures in LiNbO3 and LiTaO3. The production of the tailored I. PIEZOELECTRIC MATERIALS

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TABLE 6.3 Elastic and Dielectric Coefficients for LiNbO3 and LiTaO37 Elastic/dielectric coefficients/materials 11

Elastic stiffness constants—cij (10

LiNbO3

LiTaO3

2

N/m ) (in constant electric field, at 25°C)

c11

2.03

2.298

c12

0.573

0.44

c13

0.752

0.812

c14

0.085

–0.104

c33

2.424

2.798

0.595

0.968

c44 12

Elastic compliance constants—sij (10

2

m /N) (in constant electric field, at 25°C)

s11

5.831

4.93

s12

-1.15

-0.519

s13

-1.452

-1.28

s14

-1.00

0.588

s33

5.026

4.317

s44

17.1

10.46

ε11 (S)

0.392

0.377

ε33 (S)

0.247

0.379

ε11 (T)

0.754

0.474

ε33 (S)

0.254

0.384

Dielectric constants—εij (109 F/m)

domain patterns with desirable geometrical parameters is based on deep understanding of the physical basis of domain engineering. In single crystalline LiNbO3 and LiTaO3 all advantages of domain engineering can be realized. It is possible to achieve an extremely high concentration of the domain walls and to control their orientation along crystallographic directions. The important input of the tailored charged domain walls in dielectric permittivity has been observed in LiNbO3 crystals.25 This is the clear demonstration of the reversible hysteresis-free motion of the domain walls as a whole. Such hysteresis-free motion is very important for piezoelectric devices. The field induced shift of the domain walls depends on the spatial distribution of the screening charges that compensate the depolarization field. The existence of the surface intrinsic nonferroelectric layer (dielectric gap) leads to incomplete screening of the

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depolarization field even in a short-circuited ferroelectric capacitor.25 The retardation of the bulk screening of the residual depolarization field leads to spontaneous backswitching in LiNbO3 and LiTaO3 after an external field switch off, which reconstructs the initial domain pattern (returns the domain walls to initial place). This effect is the most pronounced in LiNbO3 and LiTaO3 due to the extremely low value of bulk conductivity and the record high value of spontaneous polarization. As a result the hysteresis-free motion of the domain walls is observed in the wide range of the applied electric field magnitudes. It looks like the tailored periodic 1-D and 2-D domain structures in congruent LiNbO3 (CLN) and LiTaO3 (CLT) are very stable due to the extremely high value of the coercive field (above 210 kV/cm). It must be noted that the domain patterns of periodically poled LiNbO3 (PPLN) and LiTaO3 (PPLT) are resistant to heating and cooling. The pyroelectric field that appeared during heating/cooling is very high in a singledomain state and almost negligible in PPLN and PPLT with precise domain periodicity.

6.4 THE INFLUENCE OF THE PERIODIC DOMAIN STRUCTURE ON PIEZOELECTRIC AND ACOUSTIC PROPERTIES The idea to optimize the piezoelectric properties of ferroelectrics by creation of the stable tailored domain structures has been advanced more than 40 years ago by Robert Newnham and Eric Cross with coauthors.26 They have written about tailored domain patterns in piezoelectric crystals and have discussed the possibility of modifying the crystal properties by creation “domains which are not to be switched during device operation.” The main discussed area of application has been related to piezoelectric devices. The authors believe that the domain structure should be added to the list of important factors, which can be manipulated in selecting a desired resonance pattern along with boundary conditions and electrode configurations. They have pointed out that arising of the domain walls (twinning) “is generally considered to be a nuisance which detracts from the performance of a piezoelectric oscillator, but this need not be so.” They claimed that “if the domain structure is properly designed, the resonant frequency spectrum can be adjusted to enhance or eliminate certain modes. Normally forbidden modes can be generated in this way, and very high frequency modes become possible.”26 It is necessary to mention the independent development of the alternative branch of the domain engineering dealing with creation of the periodical domain structures in the nonlinear optical ferroelectric crystals for

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achievement of the quasi-phase-matching (QPM) for light frequency conversion, first of all for second harmonic generation (SHG), and optical parametric oscillators (OPO).27 Enhancement of piezoelectric properties in the multidomain state as compared with the single-domain state is due in general to two main factors: contribution from the domain walls that are absent in singledomain crystals and strong orientation dependence. It leads to the ability to control the acoustic characteristics of single crystals. The acoustic properties of the LiNbO3 and LiTaO3 crystals with periodic laminar domain structure named “acoustic superlattices” (ASL) were investigated theoretically and experimentally in the series of works by Zhu et al.28–30 and Zhu and Ming.31 The structures with a period in the range of several micrometers can find useful application in highfrequency bulk-wave acoustic devices. Two types of 1-D periodic laminar structures of 1800 domains were considered: (1) the “in-line system” aligned along optical axes composed of encountering domains (tail-to-tail and head-to-head) and (2) the “cross-field system” aligned at the right angle to optical axes (see Fig. 6.4). As it was discussed already the adjacent domains possess the opposite sign of the piezoelectric tensor. The spatial discontinuity of piezocoefficients at the domain walls plays the role of sound sources under application of the external alternating electric field. Neglecting the domain wall width as compared with the excited sound wavelength, these sources can be treated as delta-like. If constructive

a

b

Z

(A)

a

b

(D) d33

d15 (or –d22) X

Z

(B)

(E) X

Z

(C)

X

(F)

FIG. 6.4 Acoustical superlattices in LiNbO3: (A–C) “in-line system” aligned along optical axes composed of encountering domains, (D–F) “cross-field system” aligned normal to optical axes: (A and D) schematic diagram with arrows indicating the directions of the spontaneous polarization; (C and F) corresponding sound sources; piezoelectric coefficient as a function of (B) z, (E) x.

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interference of the waves emitted by these sources can be achieved, then the acoustic power emitted by the ASL is proportional to the square of the domain number. The promising advantages of ASL lie in the fact that the main resonance frequency determined solely by the period of domain structure is independent on the sample sizes. In single-domain crystal the thickness of the resonator is about acoustic wavelength. Thus the resonators for several hundred MHz have to possess the dimensions that are beyond existing common processing techniques (Fig. 6.5).32 Theoretically main and satellite-like types of resonance are predicted. The main resonance frequency is given by fn ¼ nf0 , where fundamental frev quency is f0 ¼ , a and b are the thicknesses of positive and negative a+b domains respectively, and v is the velocity of excited sound wave. The m satellite-like resonance frequency is fm ¼ fn  f0 , where N is the number 2N of periods and m is the integral number. It must be stressed that for successful application of ASL for production of the acoustic devices several main requirements concerning engineered domain structures must be fulfilled. (1) Regular domain geometry—the planar domain walls must be strictly parallel and the structure period must be held to within sufficient accuracy. (2) Wall shift has to be reversible and parallel in the required range of magnitudes and frequencies of the applied electric field.

Reflection coefficient (dB)

0 −5 −10 −15 −20 −25 −30 −35 100

200

300

400 500 600 700 Frequency (MHz)

800

900 1000

FIG. 6.5 The measured reflection coefficient of an acoustical superlattice in LiNbO3 with the modulation period of 10.3 mm. Reprinted from Wan ZL, Wang Q, Xi YX, Lu YQ, Zhu YY, Ming NB. Fabrication of acoustic superlattice LiNbO3 by pulsed current induction and its application for crossed field ultrasonic excitation. Appl Phys Lett 2000;77:1891, with the permission of AIP Publishing.

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It is clear that the pointed requirements can be met in LiNbO3 and LiTaO3 with the domain walls parallel to the YZ planes. All other orientations are nonequilibrium and can be realized only under special switching conditions.15–18 The piezoresponse of the charged domain walls of encountering domains needs additional consideration. It was shown that the shape of the charged domain walls in LiNbO3 and LiTaO3 that appeared in the crystals with periodical growth striations strongly depends on the cooling rate.33 The bulk pyroelectric field caused by retardation of the bulk screening can drastically change the shape of the charged domain walls during cooling.33 The ability to control the shape of the charged domain walls is an additional factor in engineering of the devices with improved piezoelectric properties. The experimental results of ultrasonic generation and detection in the range of 500–800 MHz using an acoustic superlattice of LiNbO3 crystals were reported.28 Transducers with an insertion loss of nearly 0 dB at 555 MHz and a 5.8% 3 dB bandwidth have been made. The piezoelectric properties of LiNbO3 and LiTaO3 crystals were used recently for visualization of the micro- and nanoscale domain structures. It is possible to reveal the two most popular complimentary methods of high resolution visualization of the domain structures: piezoresponse force microscopy22,34 (Fig. 6.6) and scanning electron microscopy.35,36 Both methods allow the visualization of domains at the surface only. Two optical methods have been developed recently for domain visualization in the bulk: Raman confocal microscopy18,23,37–39 and Cherenkov-type second harmonic generation.40,41

−50 V

−60 V

−70 V

−35 V

−40 V

−45 V

−20 V

−25 V

−30 V

1µm

(A)

(B)

FIG. 6.6 PFM (A) amplitude and (B) phase images of ferroelectric domains in stoichiometric LiNbO3. Reprinted from Rodriguez BJ, Nemanich RJ, Kingon A, Gruverman A, Kalinin SV, Terabe K, et al. Domain growth kinetics in lithium niobate single crystals studied by piezoresponse force microscopy. Appl Phys Lett 2005;86:012906, with the permission of AIP Publishing.

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6.5 NANO- AND MICRODOMAIN ENGINEERING IN LITHIUM NIOBATE AND LITHIUM TANTALATE CRYSTALS LiNbO3 and LiTaO3 possessing remarkable piezoelectric, nonlinear optical, and electro-optic properties have been chosen as the favorable crystals for domain engineering. The merits of congruent LiNbO3 and LiTaO3 for production of precise periodic domain structures are the stability of tailored domain patterns and the strict orientation of 180-degree domain walls in the proper crystallographic directions. The demerits are the problems with periodic poling under application of an external electric field caused by an extremely high coercive field (above 210 kV/cm) and domain widening out of the electrodes.42,43 The first crystals with a periodic domain structure, called the “dielectric superlattice,” were produced by Feng and Ming44,45 by growing doped LiNbO3 crystals by the Czochralski method in periodically variable temperature field conditions, giving rise to the artificially controlled growth striations, which in turn led to the formation of the periodic domain structure. The melt was doped with 0.5% yttrium and the crystal was grown in an asymmetric temperature field, which was realized by intentionally displacing the rotation axis of the growing crystal from the symmetric axis of the temperature field by means of a fine screw to adjust the position of the heater relative to the rotation axis.46 The period of the domain structure was controlled by parameters of crystal growth. It was given by L ¼ vpull + vdec =nrot , where vpull is the pulling rate, vdec is the decreasing rate of free surface of melt in the crucible during crystal growth, and nrot is the rotation rate of the pulling crystal. Even periodic domain structures with varied periods have been obtained by gradual change of the pulling rate. Many other methods were proposed later for the creation of periodic domain structures, such as diffusion, proton exchange, scanning by electron beam, etc.,47 but none of them satisfy the requirements of industrial technology. The most important step in the development of domain engineering in LiNbO3 and LiTaO3 occurred in 1993, when the poling of CLN at room temperature by application of an electric field using the lithographic electrode pattern was realized by Yamada et al.,48 thus opening the way to creating the periodically poled LiNbO3 (PPLN) and LiTaO3 (PPLT) crystals. Several scientific groups—Byer and Fejer from Stanford university,49 Hanna from the University of Southampton,50 and Zhu and Ming from Nanjing University51—have independently developed a technology that allows the creation of high-quality PPLN and PPLT by application of the external electric field to a lithographically produced electrode pattern in 0.5-mm thick wafers.

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It was noted by Byer27 that “the leverage of mass production made possible by lithographic patterning with subsequent domain inversion has led to a rapid transition from nonlinear crystals that cost thousands of dollars to fabricate to nonlinear chips that cost less than one dollar each to fabricate.” Further activities were directed toward improving the electrical poling method, decreasing threshold fields, and addressing optical damage issues. Nevertheless the goal of mass production with low cost is still unachieved. It is believed that the essential progress in domain engineering requires the understanding of the physical mechanisms governing the formation of the domain structure from the micro- to nano scale. The kinetic nature of the engineered domain patterns has been clearly shown in a series of recent papers.15,52–54 We will restrict ourselves to the polarization reversal through arising and growth of the domains with 180-degree walls because LiNbO3 and LiTaO3 belong to the uniaxial ferroelectrics group. The domain evolution during polarization reversal of a single-domain state by application of an external electric field pulse can be divided into the following main stages53–55: (1) “nucleation of new domains,” (2) “forward domain growth,” (3) “sideways domain growth,” (4) “domain merging,” and (5) “spontaneous backswitching” after applied field switch off (see Fig. 6.7). (1) The nucleation of new nanoscale domains is practically impossible to study experimentally. It can be shown only that in the high-quality crystals the domains appeared at the polar surface. This can be attributed to the fact that the intrinsic surface nonferroelectric gap leads to incomplete compensation of the depolarization field in the vicinity of the polar surface (see Fig. 6.7A).52,56 (2) The “forward growth” (domain tip propagation) represents a fast expansion of the formed “nuclei” in the polar direction (see Fig. 6.7B). The residual depolarization fields produced by bound charges result in pronounced optical contrast due to electro-optical effect in LiNbO3 and LiTaO3. (3) The “sideways domain growth” (domain spreading) represents the domain’s expanding perpendicular to the polar direction (see Fig. 6.7C). Usually in LiNbO3 and LiTaO3 the anisotropic sideways domain wall motion results in the formation of regular shaped hexagonal or triangular domains with walls oriented along crystallographic directions (see Fig. 6.3C and D). It was revealed that the domain shape depends crucially on the screening effectiveness.15,18,53 The control of screening ineffectiveness, for example, by increasing of the surface dielectric layer thickness, allows the domain shape to be governed.15,17,57,58

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(A)

(B)

(C)

(D)

251

(E) FIG. 6.7 The main stages of the domain kinetics during polarization reversal in ferroelectrics: (A) "nucleation of new domains," (B) "forward domain growth," (C) "sideways domain growth," (D) "domain merging," (E) "spontaneous backswitching" after applied field switch-off.

(4) The “domain coalescence” (merging) is observed when the switching process is close to completion (see Fig. 6.7D). It is characterized by pronounced deceleration and even stopping of the approaching domain walls due to electrostatic interaction. This effect results in the existence of the residual isolated submicron domains.43 (5) The “spontaneous backswitching” (flip-back) represents full or partial reconstruction of the initial domain pattern after the external electric field switch off. The shrinkage of the arisen domains through the backward wall motion and the nucleation of the domains with the initial orientation of spontaneous polarization are observed (see Fig. 6.7E). The backswitching takes place under the action of the abnormally high field and can be used for creation of self-assembled nanodomain structures.59 All stages of the domain structure evolution can be considered from the unified point of view as a manifestation of the various nucleation processes driving the first-order phase transformations.55,60 Within this approach the coexisting domains with opposite orientation of the

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spontaneous polarization are considered as the volumes of different phases, while the domain walls represent the phase boundaries. The domain kinetics is to be considered as a result of elementary processes of thermally activated generation of one-, two- and three-dimensional nuclei with preferred orientation of the spontaneous polarization. In analogy with the heterogeneous nucleation during first-order phase transformation, the nucleation sites during polarization reversal are situated mostly at imperfections and point defects. The domain growth by wall motion is achieved through 1-D and 2-D nucleation. The elementary one-unit-cell-thick steps are generated at the domain wall by 2-D nucleation. The subsequent kink motion along the wall is a result of 1-D nucleation. The nucleation probability determining the switching rate is governed by electric field averaged over the volume of the order of the nucleus size (“local field” Eloc).52 Eloc is spatially inhomogeneous and can undergo essential changes during polarization reversal. In a ferroelectric capacitor Eloc is the sum of the following: (1) the external field applied by the electrode’s pattern, (2) the depolarization field produced by bound charges, (3) the external screening field originating from the redistribution of the charges at the electrodes, and (4) the bulk screening field governed by various bulk screening processes. The singularities of the external field exist in the surface layer near the boundaries of the electrode patterns used for engineering of PPLN structures due to the fringe effect. Thus new domains appear under the edges and tips of the stripe electrodes. Such field concentration must be accounted for while creating the tailored domain structures.53 The bound charges at the polar surfaces and at the charged walls of the encountering domains (“head to head” or “tail to tail”) are the sources of the depolarization field Edep, which is proportional to the spontaneous polarization PS. Edep usually exceeds by far the experimentally observed threshold fields and leads to fragmentation of the domain structure into narrow domains. The effect of Edep on polarization reversal during manufacturing of PPLN and PPLT is crucial for LiNbO3 and LiTaO3, which possess the highest PS value. Edep is compensated by screening processes. The incomplete screening leads to the partial or full reconstruction of the initial domain state after the external field switch off (spontaneous backswitching). External and bulk screening processes must be distinguished. The fast external screening with characteristic times ranging from nanoseconds to microseconds is achieved through charge redistribution in the electrodes. This process never compensates Edep completely due to existence of the intrinsic dielectric surface layer.52,61 The bulk residual depolarization field Erd remains in the switched areas after complete external screening. Erd is by several orders of magnitude less than Edep and close to experimentally observed threshold field. Thus, the further compensation of Erd by slow bulk

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screening is necessary. That is why retardation of bulk screening plays the key role in the evolution of the domain structure. Three groups of the bulk screening mechanisms are considered: (1) redistribution of the bulk charges,52,61 (2) reorientation of the defect dipoles,62 and (3) injection of carriers from the electrode through the dielectric gap.63 All bulk screening mechanisms are slow with time constants ranging from milliseconds to days and months. According to the above discussed considerations Eloc being the driving force of all nucleation processes is spatially inhomogeneous and time dependent. The application of the short field pulse, for which the bulk screening of the new domain state is ineffective, does not allow modification of the domain pattern. After external field switch off the complete spontaneous backswitching will be observed. The stable tailored domain configuration can be created only if the field pulse duration is enough for effective bulk screening. The slow switching when the redistribution of the bulk screening charges is fast enough to keep pace with changes of the domain structure corresponding to quasi-equilibrium switching. Any retardation of the bulk screening leads to nonequilibrium switching. The domain shape is strongly dependent on the spatial distribution of the nucleation sites at the domain walls. A hexagon domain shape in LiNbO3 with walls oriented along Y directions can usually be obtained if we assume the determined nucleation with inhomogeneous step generation. The nucleation must be realized at polygon domain vertices (Fig. 6.8). The crystal symmetry restricts the kink motion directions, which leads to the experimentally observed step generation at three nonadjacent vertices and kink propagation along three allowed Y directions53 (Fig. 6.8). As a result the domain shape is determined by the ratio between step generation and kink propagation rates. It was shown experimentally that qualitatively different domain shapes can be produced at the same place of a CLN wafer (Fig. 6.9). In this case the hexagon has been produced

A

B

Y

B

A

A

B

FIG. 6.8 Predetermined nucleation: step generation at vertices and step growth along three Y directions.

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Y

2 µm

FIG. 6.9 The domain shapes formed by pulse switching and subsequent spontaneous backswitching in congruent LiNbO3. Switching by single short pulse. Z+ view. Optical images of domains revealed by etching.

during switching, while the triangular domain appears within a freshly switched hexagon during backswitching. The effects of loss of the domain wall shape stability are observed under highly nonequilibrium switching conditions. The loss of stability is caused by self-assembled nucleation and oriented growth of domain rays. The nonequilibrium switching is obtained due to the essential role of the screening retardation effect. It is possible to accelerate the polarization reversal by application of a “super-strong” external field or by increasing the input of the residual depolarization field by deposition of an artificial surface dielectric layer. The last situation is realized during conventional production of the PPLN using a periodical electrode pattern.47–51,64 The area between the stripe electrodes is covered by photoresist, and domain “broadening” out of the electrodes is frequently accompanied by the loss of the regular wall shape.15,53 The formation of the domain shape instabilities (“fingers”) was revealed (Fig. 6.10A).15,53 The backward wall motion after external field switch off (backswitching) is realized frequently through formation and propagation of the quasiregular “dendrite” structures (Fig. 6.10B).53 The recent study reveals the “discrete switching” representing formation of nanoscale domain structures under highly nonequilibrium switching in LiNbO3. The self-assembled structures usually demonstrate quasiregular spatial distribution of the isolated submicron domains. The typical structure produced in congruent LiNbO3 covered by an artificial dielectric layer (photoresist) as a result of backswitching is shown in Fig. 6.11. This domain pattern is stable (frozen-in) and does not undergo any evident changes for years.

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Y

5 µm

(A)

Y

5 µm

(B)

FIG. 6.10 (A) Finger domain structure formed during periodical poling in congruent LiNbO3. (B) Dendrite structure formed during backswitching in MgO:LN. Z + view. Strip electrode oriented along Y direction covers the area between the black lines. Optical images of domains revealed by etching.

Y

1 µm

FIG. 6.11 Stable nanodomain array in congruent LiNbO3 formed as a result of backswitching during periodical poling. Strip electrode oriented along Y direction covers the area between the black lines. Domain patterns revealed by etching and visualized by scanning electron microscopy. Z+ view.

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The backswitching process is always considered as an undesirable one, because it destroys the tailored domain structure, but its detailed study allows us to make it useful. We have proposed an original poling method for creation of short-pitch periodical domain structures in LiNbO3 and LiTaO3, “backswitched poling.”59,64,65 The unique feature of the backswitching process is that the polarization reversal occurs without application of any external electric field. The domain kinetics is activated by an internal source, Erd, existing after an abrupt external field switch off due to retardation of the bulk screening. The process starts with nucleation of chains of the new needle-like nanodomains along the electrode edges at the Z + surface due to the field singularities (Fig. 6.12A). The nanodomains merge and propagate through the wafer forming the lamellar domains (with the initial orientation of Ps) along the electrode edges (see Fig. 6.12B).The backswitch poling allows the overcoming of the undesirable effect of domain broadening leading to the difference between the electrode pattern and the produced periodical domain structure, whereas the domains enlarged during the poling stage shrink by the backward wall motion. The backswitch poling has been applied for 2.6-μm periodic poling of the LiNbO3 and LiTaO3 0.5-mm-thick wafers.54 It has been shown recently that illumination of the polar surface of the congruent LiNbO3 crystal by pulsed ultraviolet laser leads to the formation of the surface domain structure with the depth of a few microns.66 The process of formation of the nanoscale domain structure as a result of pulse infrared laser irradiation has been studied in detail in LiNbO367–69 and LiTaO370 crystals. Three types of domain patterns have been revealed on the Z + surface: (1) “dots,” isolated domain patterns in the narrow region along the boundary of the irradiated area (Fig. 6.13A); (2) “lines,” quasiperiodic nanodomain patterns, consisting of parallel rays inside the irradiated area (Fig. 6.13B); and (3) “fractals,” self-similar domain patterns formed inside the irradiated area as a result of ray

Y

2 µm

2 µm

FIG. 6.12 Formation of the nanodomain rays along the electrode edges during backswitching in congruent LiNbO3. Strip electrode oriented along Y direction covers the area between the black lines. Domain patterns revealed by etching and visualized by scanning electron microscopy. Z + view.

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(A)

5 µm

(B)

5 µm

(C)

257

25 µm

FIG. 6.13 Nanodomain patterns formed in congruent LiNbO3 as a result of pulsed laser irradiation on a Z + face: (A) dots, (B) lines, (C) fractal structure. Optical images of nanodomains revealed by etching.

“reflection” (see Fig. 6.13C). The detailed study of the nanodomain structures by piezoresponse force microscopy demonstrates that all structures represent the chains of isolated nanodomains.67,68 It was considered that the driving force of the polarization reversal is the pyroelectric field appearing during cooling after pulse laser irradiation.54,68,71–73 The “discrete switching” can be attributed to highly nonequilibrium switching conditions caused by ineffective screening of the depolarization field while switching without electrodes when the residual depolarization field is abnormally high.53 The self-assembled formation of the nanoscale domain chains is caused by electrostatic domain-domain interaction,74 which is very strong for ineffective screening. The reflection effect can be understood as a result of suppression of the nucleation in the initial direction due to electrostatic domain-domain interaction. The tailored self-similar nanoscale structures with a typical width about 200–300 nm and depth up to 300–400 μm can be produced by spatially nonuniform illumination (Fig. 6.14). The

FIG. 6.14 Periodical nanodomain structure produced by pulse laser irradiation in congruent LiNbO3.

5 µm

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production of the stable bulk nanodomain patterns with submicron periods can be realized this way.

6.6 APPLICATIONS OF DOMAIN-ENGINEERED LITHIUM NIOBATE AND LITHIUM TANTALATE CRYSTALS FOR LIGHT FREQUENCY CONVERSION Domain engineering in LiNbO3 and LiTaO3 has revolutionized their use in nonlinear optical applications.27,49 The performance of LiNbO3 and LiTaO3 as electro-optic, photorefractive, piezoelectric, and nonlinear optical crystals makes them useful for various applications. It has been shown that LiNbO3 and LiTaO3 with periodic 1-D and 2-D domain structures possessing an efficient quasi-phase-matching open up a wide range of possibilities for bulk and waveguide nonlinear optical devices49,75,76 (Fig. 6.15). Fifteen years after the first electrical poling of bulk LiNbO3 samples,48 research on periodically poled LiNbO3 and LiTaO3 has gained interest worldwide, resulting in production of photonic devices. It is well known that efficient quadratic nonlinear optical interactions require a constant relative phase shift between the interacting light waves. The phase drift that results from the difference in phase velocities due to material dispersion must be compensated by some phase-matching methods.77 For the first 25 years of nonlinear optics, the dominant employed method was birefringent phase-matching (BPM), in which the difference in phase velocity of orthogonally polarized waves was used to compensate the difference caused by dispersion. BPM has been Z X

M Y

G

K M

FIG. 6.15

Two-dimensional (2-D) nonlinear photonic crystal. The 2-D nonlinear periodic domain structure with hexagonal symmetry in LiNbO3. The structure period is 18.05 μm. Reprinted figure with permission from Broderick NGR, Ross GW, Offerhaus HL, Richardson DJ, Hanna DC. Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal. Phys Rev Lett 2000;84(19): 4345–8. Copyright (2016) by the American Physical Society.

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demonstrated by Maker et al.78 and Giordmaine,79 independently. PFM has become very well developed and has shown to be practical in a wide variety of commercial applications. An alternative approach, quasi-phase-matching (QPM), uses a periodic modification of the properties of the nonlinear medium to correct the relative phase at regular intervals without matching phase velocities. Armstrong et al.80 and independently Franken and Ward81 have proposed the original method of phase-matching by reversing the sign of the nonlinear coefficient every coherence length (lc), which is the distance over which an accumulated phase difference between the interacting waves is equal π. This idea has been applied experimentally to an array of ferroelectric domains by Miller,82 who claimed that “the optimum domain array for SHG is one where the crystal consists of sheets of antiparallel domains, each lc thick, with the wall normal parallel to the beam direction.” He has shown that a SHG intensity enhancement is proportional to (1 + 2N), where N is the number of 180-degree properly placed domain walls in an array. While QPM was invented at the same time as BPM, it did not see widespread use due to difficulties in fabricating suitable crystals with the required micron-scale periodical domain structures. The crystals of the LiNbO3 and LiTaO3 family are the first and still the most widely exploited periodically poled ferroelectrics. Both are readily available in three- and four-inch diameter substrates, convenient for lithographic patterning and processing, and they have established waveguide technologies compatible with periodic domain structures. Quasi-phase-matched SHG to wavelengths as short as 386 and 325 nm has been demonstrated in LiNbO3 and LiTaO3.83,84 In the mid-IR, multi-phonon absorption in both materials rises steeply at 4–5 μm, limiting high average power operation to wavelengths longer than 4 μm, though CW interactions out to 6.6 μm, and short-pulse operation (enabling the use of short crystals) to wavelengths as long as 7.25 μm have been demonstrated.85 Efficient frequency conversion has been shown to cover the range from 460 nm to 2.8 microns in device lengths about 4 cm. In MgO-doped LiNbO3 the periods as small as 1.4 microns have been achieved in bulk devices.86 “Fan-out” gratings with the gradual variation of the domain period in the direction perpendicular to the stripes had been used for optical parametric oscillation (OPO) signal and idler wavelength tuning in a wide spectral range.87–89 The large coercive field of these materials has limited conventional poling to 1-mm-thick substrates and imposes a limit to the available aperture for high energy and peak power applications. Efforts to extend this thickness by diffusion bonding90 and pulsed poling91 techniques have increased the usable thickness up to 5 mm.

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6.7 GENERATION OF TERAHERTZ RADIATION IN PERIODICALLY POLED LITHIUM NIOBATE CRYSTAL One of the promising and in-demand applications of PPLN is development of new devices for generation, propagation, and detection of terahertz (THz) bandwidth electromagnetic radiation.92–97 The radiation in the THz region has attracted special attention due to its potential advantages for various applications. THz radiation covers the frequency range from 100 GHz to 30 THz, filling the frequency gap between microwave and infrared bandwidths. The absorption of the photons with THz energies leads to the excitation of bending and stretching vibration modes of molecules. Thus applications of THz technology in medicine, biology, physics, telecommunications, and so on are expected. The possible applications range from quality control of food and global environment monitoring to ultrafast computing.98 For detailed information on achievements and basic principles of THz technology the readers are referred to numerous reviews.99–103 The method of THz wave generation by PPLN is based on the above discussed effect of frequency conversion in nonlinear optical materials.92–97 Frequency conversion is achieved through excitation in the media second-order nonlinear polarization under the action of external “pump” electromagnetic fields. The effect is described by second-order nonlinear susceptibility, which accounts for the presence of three waves: two pump waves and one response wave. Second-order nonlinear susceptibility is third-rank tensor symmetrical over the last two indexes: χ ijk ¼ χ ikj . Regarding its symmetrical properties, they coincide formally with those of piezoelectric tensor dijk. Thus, the components of this tensor also reverse the sign between the neighboring domains. The three waves, which are involved in the nonlinear process, must satisfy the k-vector requirement or the phase-matching condition: k1  k2 ¼ k and for the frequencies ω1, ω2, ω these waves the following equality holds due to conservation of energy ω1  ω2 ¼ ω One of the most popular methods of generating THz radiation based on difference frequency generation (DFG) is capable of producing tunable, highly coherent THz radiation. There were several proposed and realized DFG schemes. The “direct” one was based on the output of the laser oscillating at two wavelengths.104 The drawbacks of this method are due to large absorption loss in LiNbO3 in the THz frequency range.105 The special method of surface-emitting (SE) DFG using PPLN structures, when generated THz radiation propagates perpendicular to the optical beam, was proposed to overcome this difficulty. The PPLN period 2π ¼ k1  k2 , where k1 and k2 are wavenumbers at ΛSE was chosen to be: ΛSE corresponding optical frequencies ω1 and ω2. The modifications of this method using the slant-stripe-type and two-dimensional PPLN crystals were proposed95 (see Figs. 6.16 and 6.17).

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L +d

-d

+d

-d

w 1, w 2

+d

-d

+d

-d

a

w 3 = THz-wave Z Xc k1 - k2 k3

Y

a kL

Yc

X

FIG. 6.16 Schematic illustration of THz generation in slant-stripe-type periodically poled LiNbO3 (upper) and the wave-vector diagram (lower), d—nonlinear optical coefficient. Reprinted from Sasaki Y, Avetisyan Y, Kawase K, Ito H. Terahertz-wave surface-emitted difference frequency generation in slant-stripe-type periodically poled LiNbO3 crystal. Appl Phys Lett 2002;81:3323–5, with the permission of AIP Publishing.

LTHz

Ps

w1, w 2

w 3 = THz-wave LSE

FIG. 6.17 Schematic illustration of THz generation in two-dimensional periodically poled LiNbO3. Reprinted with permission from Sasaki Y, Avetisyan Y, Yokoyama H, Ito H. Surface-emitted terahertz-wave difference-frequency generation in two-dimensional periodically poled lithium niobate. Opt Lett 2005;30:2927–9, with the permission of Optical Society of America.

The phase-matching condition discussed above is the important prerequisite for efficient energy conversion from external pump fields via such second-order processes into a desired spectral range. The physical essence of this condition is a requirement that the phase of induced signal

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wave of quadratic polarization in the given place must interferer constructively with the waves generated at every other point. Only in this case is the energy conversion from the pump fields efficient. This condition is violated due to the wavelength dependence of refractive index.106 At the passage of the optical beam a DC potential difference across the crystal can appear. This effect called optical rectification (also electrooptical rectification (EOR)) was reported for the first time by Bass et al.107 EOR can be easily understood taking into account the retardation of induced polarization. The quadratic polarization induced by an external laser electromagnetic field does not reverse completely when the sign of the field is reversed. EOR is observed only in the low symmetry crystals that provide preferred internal direction. It is clear that LiNbO3 and LiTaO3 just fulfill this condition. If we assume the sinusoidal time variation of the pump field the time average polarization develops in full analogy with arising of dc currents in congenial electronic rectificators.107 The modification of the EOR effect was used for generation of THz radiation. The distinction with “classical” EOR, which leads to arising of DC second-order polarization, is due to the fact that in these experiments the crystal is illuminated by ultrashort (femto- or picosecond) optical pulses. When an intense optical pulse propagates in the crystal with nonzero second-order nonlinear susceptibility χ ijk the time dependence of induced quadratic polarization Pqi (t) is determined by time dependence of the optical pulse intensity jEopt(t)j2. Fourier decomposition of the short pulse contains a broad frequency spectrum, which leads to generation of far infrared radiation as a result of beating between frequency components. The only obstacle for obtaining intense THz radiation while illuminating a single crystal is due to the existing mismatch between group velocities of optical and THz waves. The destructive interference due to the walk off of THz pulses generated in different parts of the crystal occurs. As a result only the regions in the vicinity of front and back surfaces of the crystal contribute to the observed THz radiation. The promising technique for generating narrow-band THz radiation overcoming this problem is based on the EOR of femtosecond pulses in PPLN. When a pump wave is propagating across PPLN the crystal response is periodically modulated as far as adjacent domains have an opposite sign of second-order susceptibility. The period of engineered PPLN is matched to the walk-off length between the optical and THz pulses. In each domain the nonlinear polarization is generated by EOR and contributes a half-cycle to the emitted THz radiation. The frequency of the generated THz radiation is given c , where ld is domain width, nopt and nTHz are refracby f ¼  2ld nopt  nTHz tive indices at optical and THz frequencies respectively.

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It is seen that obtained THz radiation frequency is dependent only on the period of PPLN and respective refractive indices. This means that by engineering proper PPLN structures the THz radiation of desirable wave length can be obtained.

6.8 CONCLUSIONS AND FUTURE TRENDS In the present chapter, we have discussed the influence of the tailored periodic nano- and microdomain structures on the piezoelectric properties of LiNbO3 and LiTaO3 crystals. First, the main piezoelectric characteristics of both crystals have been reviewed. It was pointed out that LiNbO3 and LiTaO3 are two of the most popular commercially produced ferroelectric crystals. It was also indicated that in recent decades both crystals have become the most important objects of domain engineering. The main target of domain engineering is the improvement of the application characteristics of commercially available ferroelectrics by the manufacturing of stable tailored domain patterns (periodic poling). The periodic domain structures introduce the spatial modulation of the piezoelectric, electro-optic, photorefractive, and nonlinear optical properties thus upgrading the device performance. The tailored domain patterns in piezoelectric crystals that are not to be switched during device operation, which allow modification of the piezoelectric properties, were discussed. The domain structure has been included in the list of the factors that can be manipulated in selecting a desired resonance along with boundary conditions and electrode configurations. It was shown that the properly designed domain pattern can be adjusted to enhance or eliminate certain modes and very high frequency modes become possible. It was shown that the spatial discontinuity of piezocoefficients at the domain walls play a role of delta-like sound sources under application of the external alternating electric field. If constructive interference of the waves emitted by these sources can be achieved then the acoustic power emitted by crystal with periodic domain structure will be proportional to the square of the domain number. It was stressed that the main resonance frequency is determined solely by the period of domain structure and is independent on the sample sizes. The independent development of the alternative branch of domain engineering dealing with creation of the periodical domain structures in the nonlinear optical ferroelectric crystals for achievement of the quasiphase-matching for light frequency conversion, first of all for second harmonic generation, has been considered. The application of the periodically poled LiNbO3 and LiTaO3 for light frequency conversion and generation

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of the terahertz radiation has been discussed. The main achievements in this area have been demonstrated. The strong influence of the domain walls on the piezoelectric and acoustic properties put forward a problem of creation of the periodical domain structures in LiNbO3 and LiTaO3. It was stressed that the production of the tailored domain patterns with desirable geometrical parameters is impossible without deep understanding of the physical basis of domain engineering. The unified approach to domain kinetics based on the nucleation mechanism of the polarization reversal allows an understanding of the variety of experimentally observed domain evolution scenarios in LiNbO3 and LiTaO3 crystals. We have proved that the domain kinetics essentially depend upon the effectiveness of the bulk screening. Original scenarios of the domain structure evolution were revealed and discussed within approach accounting for the decisive role of the retardation of the screening process. It has been shown that in LiNbO3 and LiTaO3 the predetermined nucleation effect plays the key role in the domain growth. The formation of the self-assembled nanoscale domain structures has been studied for different nonequilibrium switching conditions: (1) spontaneous backswitching, (2) switching with an artificial surface layer, and (3) switching as a result of pulse laser irradiation. The recent achievements in studying the domain kinetics with nanoscale spatial resolution allow the prediction that the future of the domain engineering lies in the production of the tailored nanodomain structure and the structures possessing the nanoscale period accuracy. The structures can be produced as a result of the local switching of the singledomain using application of the inhomogeneous electric field by a nanoscale electrode pattern, conductive tip of SPM, or electron beam. The periodic nanoscale modification of the surface layer looks very promising. It is proposed that the effective methods are based on formation of selfassembled structures. The piezoresponse of the charged domain walls dividing encountering domains need additional study. It was shown that the cogged shape of the charged domain walls in LiNbO3 and LiTaO3 strongly depend on technological conditions such as the cooling regime. The ability to control the shape of the periodical charged domain walls is the additional factor in engineering of the devices with improved piezoelectric properties. It is clear that the future development of nanoscale engineering requires deep investigation of the polarization kinetics in LiNbO3 and LiTaO3 using modern sophisticated experimental methods with nanoscale resolution, including elaborate modes of SPM and scanning electron microscopy. The development of a reliable technology for domain engineering at the submicron scale would be a major breakthrough, leading to new generation of devices. I. PIEZOELECTRIC MATERIALS

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Acknowledgments The research was made possible by the Russian Scientific Foundation (Grant 14-12-00826). It is a pleasure to acknowledge the many helpful stimulating discussions with A.L. Korzhenevskii and E.L. Rumyantsev throughout the process of preparing this publication.

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41. Sheng Y, Best A, Butt H-J, Krolikowski W, Arie A, Koynov K. Three-dimensional ferro
electric domain visualization by Cerenkov-type second harmonic generation. Opt Express 2010;18(16):16539–45. 42. Shur VYa, Rumyantsev EL, Nikolaeva EV, Shishkin EI, Batchko RG, Fejer MM, et al. Recent achievements in domain engineering in lithium niobate and lithium tantalate. Ferroelectrics 2001;257:191–202. 43. Shur VYa, Akhmatkhanov AR, Baturin IS. Micro- and nano-domain engineering in lithium niobate. Appl Phys Rev 2015;2:1–22. 44. Feng D, Ming NB, Hong JF, Yang YS, Zhu JS, Yang Z, et al. Enhancement of secondharmonic generation in LiNbO3 crystals with periodic laminar ferroelectric domains. Appl Phys Lett 1980;37:607–9. 45. Ming NB, Hong JF, Feng D. The growth striations and ferroelectric domain structures in Czochralski-grown LiNbO3 single crystals. J Mater Sci 1982;17(6):1663–70. 46. Cheng SD, Zhu YY, Lu YL, Ming NB. Growth and transducer properties of an acoustic superlattice with its periods varying gradually. Appl Phys Lett 1995;66:291–2. 47. Rosenman G, Skliar A, Arie A. Ferroelectric domain engineering for quasiphasematched nonlinear optical devices. Ferroelectr Rev 1999;1:263–326. 48. Yamada M, Nada N, Saitoh M, Watanabe K. First-order quasi-phase matched LiNbO3 waveguide periodically poled by applying an external field for efficient blue secondharmonic generation. Appl Phys Lett 1993;62:435–6. 49. Myers LE, Eckardt RC, Fejer MM, Byer RL, Bosenberg WR, Pierce JW. Quasi-phasematched optical parametric oscillators in bulk periodically poled LiNbO3. J Opt Soc Am B 1995;12(11):2102–16. 50. Webj€ orn J, Pruneri V, Russell P St J, Barr JRM, Hanna DC. Quasi-phase-matched blue light generation in bulk lithium niobate, electrically poled via periodic liquid electrodes. Electron Lett 1994;30(11):894–5. 51. Zhu S-N, Zhu Y-Y, Zhang Z-Y, Shu H, Wang H-F, Hong J-F, et al. LiTaO3 crystal periodically poled by applying an external pulsed field. J Appl Phys 1995;77(10):5481–3. 52. Shur VYa. Fast polarization reversal process: evolution of ferroelectric domain structure in thin films. In: Paz de Araujo CA, Scott JF, Taylor GW, editors. Ferroelectric thin films: synthesis and basic properties. New York: Gordon and Breach; 1996. p. 153–92. 53. Shur VYa. Correlated nucleation and self-organized kinetics of ferroelectric domains. In: Schmelzer JWP, editor. Nucleation theory and applications. Weinheim: WILEY-VCH; 2005. p. 178–214. 54. Shur VYa. Nano- and micro-domain engineering in normal and relaxor ferroelectrics. In: Ye ZG, editor. Advanced dielectric, piezoelectric and ferroelectric materials—synthesis, characterization & applications. Cambridge: Woodhead; 2008. p. 622–69. 55. Fatuzzo E, Merz WJ. Ferroelectricity. Amsterdam: North-Holland Publishing Company; 1967. 56. Janovec V. Anti-parallel ferroelectric domain in surface space-charge layers of BaTiO3. Czech J Phys 1959;9:468–80. 57. Shur VYa, Letuchev VV, Rumyantsev EL. Field dependence of the polarization switching parameters and shape of domains in lead germanate. Sov Phys Solid State 1984;26:1521–2. 58. Shur VYa, Letuchev VV, Rumyantsev EL, Ovechkina IV. Triangular domains in lead germanate. Sov Phys Solid State 1985;27:959–60. 59. Shur VYa, Rumyantsev EL, Nikolaeva EV, Shishkin EI, Fursov DV, Batchko RG, et al. Nanoscale backswitched domain patterning in lithium niobate. Appl Phys Lett 2000;76(2):143–5. 60. Miller RC, Weinreich G. Mechanism for the sidewise motion of 180° domain walls in barium titanate. Phys Rev 1960;117:1460–6. 61. Fridkin VM. Ferroelectrics semiconductors. New York/London: Consult. Bureau; 1980. 62. Lambeck PV, Jonker GH. The nature of domain stabilization in ferroelectric perovskites. J Phys Chem Solids 1986;47:453–61.

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63. Tagantsev AK, Stolichnov I, Colla EL, Setter N. Polarization fatigue in ferroelectric films: basic experimental findings, phenomenological scenarios, and microscopic features. J Appl Phys 2001;90:1387–402. 64. Batchko RG, Shur VYa, Fejer MM, Byer RL. Backswitch poling in lithium niobate for high-fidelity domain patterning and efficient blue light generation. Appl Phys Lett 1999;75(12):1673–5. 65. Batchko R, Miller G, Byer R, Shur V, Fejer M. Backswitch poling method for domain patterning of ferroelectric materials, United States Patent No. 6,542,285 B1, April 1; 2003. 66. Valdivia CE, Sones CL, Scott JG, Mailis S, Eason RW, Scrymgeour DA, et al. Nanoscale surface domain formation on the + z face of lithium niobate by pulsed ultraviolet laser illumination. Appl Phys Lett 2005;86. 67. Kuznetsov DK, Shur VYa, Negashev SA, Lobov AI, Pelegov DV, Shishkin EI, et al. Formation of nano-scale domain structures in lithium niobate using high-intensity laser irradiation. Ferroelectrics 2008;373:133–8. 68. Shur VYa, Kuznetsov DK, Lobov AI, Pelegov DV, Pelegova EV, Osipov VV, et al. Selfsimilar surface nanodomain structures induced by laser irradiation in lithium niobate. Phys Solid State 2008;50(4):717–23. 69. Shur VYa, Kuznetsov DK, Mingaliev EA, Yakunina EM, Lobov AI, Ievlev AV. In situ investigation of formation of self-assembled nanodomain structure in lithium niobate after pulse laser irradiation. Appl Phys Lett 2011;99(8):1–3. 70. Shur VYa, Kosobokov MS, Mingaliev EA, Kuznetsov DK, Zelenovskiy PS. Formation of snowflake domains during fast cooling of lithium tantalate crystals. J Appl Phys 2016;119:1–6. 71. Miyazawa S. Ferroelectric domain inversion in Ti-diffused LiNbO3 optical waveguide. J Appl Phys 1979;50:4599–603. 72. Nakamura K, Tourlog A. Single-domain surface layers formed by heat treatment of proton-exchanged multidomain LiTaO3 crystals. Appl Phys Lett 1993;63:2065–6. 73. Zhu Y-Y, Zhu S-N, Hong J-F, Ming N-B. Domain inversion in LiNbO3 by proton exchange and quick heat treatment. Appl Phys Lett 1994;65:558–60. 74. Ievlev AV, Jesse S, Morozovska AN, Strelcov E, Eliseev EA, Pershin YV, et al. Intermittency, quaziperiodicity, and chaos during scanning probe microscopy tip-induced ferroelectric domain switching. Nat Phys 2014;10:59–66. 75. Broderick NGR, Ross GW, Offerhaus HL, Richardson DJ, Hanna DC. Hexagonally poled lithium niobate: a two-dimensional nonlinear photonic crystal. Phys Rev Lett 2000;84:4345–8. 76. Ross GW, Pollnau M, Smith PGR, Clarkson WA, Britton PE, Hanna DC. Generation of high-power blue light in periodically poled LiNbO3. Opt Lett 1998;23:171–3. 77. Hum DS, Fejer MM. Quasi-phasematching. C R Phys 2007;8:180–98. 78. Maker PD, Terhune RW, Nisenoff M, Savage CM. Effects of dispersion and focusing on the production of the optical harmonics. Phys Rev Lett 1962;8(1):21–3. 79. Giordmaine JA. Mixing of light beams in crystals. Phys Rev Lett 1962;8(1):19–20. 80. Armstrong JA, Bloembergen N, Ducuing J, Perhsan PS. Interactions between light waves in a nonlinear dielectric. Phys Rev 1962;127(6):1918–39. 81. Franken PA, Ward JF. Optical harmonics and nonlinear phenomena. Rev Mod Phys 1963;35(1):23–39. 82. Miller RC. Optical harmonic generation in single crystal BaTiO3. Phys Rev 1964;134: A1313–9. 83. Meyn JP, Fejer MM. Tunable ultraviolet radiation by second-harmonic generation in periodically poled lithium tantalate. Opt Lett 1997;22:1214–6. 84. White R, McKinnie I, Butterworth S, Baxter G, Warrington D, Smith P, et al. Tunable single-frequency ultraviolet generation from a continuous-wave Ti: sapphire laser with an intracavity PPLN frequency doubler. Appl Phys B: Lasers Opt 2003;77:547–50.

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85. Watson MA, O’Connor MV, Lloyd PS, Shepherd DP, Hanna DC, Gawith CBE, et al. Extended operation of synchronously pumped optical parametric oscillators to longer idler wavelengths. Opt Lett 2002;27:2106–8. 86. Mizuuchi K, Morikawa A, Sugita T, Yamamoto K. Efficient second-harmonic generation of 340-nm Light in a 1.4-μm periodically poled bulk MgO:LiNbO3. Jpn J Appl Phys 2003;42:L90. 87. Ishigame Y, Suhara T, Nishihara H. LiNbO3 waveguide second-harmonic-generation device phase matched with a fan-out domain-inverted grating. Opt Lett 1991;16:375–7. 88. Terry JAC, Tsiminis G, Dunn MH, Rae CF. Eye-safe broadband output at 1.55 μm through the use of a fan-out grating structure in MgO:PPLN. J Opt A Pure Appl Opt 2007;9:229–34. 89. Xiong B, Ma J-L, Chen R, Wang B-H, Cui Q-J, Zhang L, et al. High-power, highrepetition-rate mid-infrared generation with PE-SRO based on a fan-out periodically poled MgO-doped lithium niobate. Opt Commun 2011;284:1391–4. 90. Nakamura K, Hatanaka T, Ito H. High output energy quasi-phase-matched optical parametric oscillators using diffusion-bonded periodically poled and single domain LiNbO3. Jpn J Appl Phys 2001;40:L337–9. 91. Ishizuki H, Taira T. High-energy quasi-phase-matched optical parametric oscillation in a periodically poled MgO:LiNbO3 device with a 5 mm  5 mm aperture. Opt Lett 2005;30:2918–20. 92. Ding YJ, Kurgin JB. A new scheme for generation of coherent and incoherent submillimeter to THz waves in periodically poled lithium niobate. Opt Commun 1998;148:105–9. 93. Lee Y-S, Meade T, Perlin V, Winful H, Norris TB. Generation of narrow-band teraherz radiation via optical rectification of femtosecond pulses in periodically poled lithium niobate. Appl Phys Lett 2000;76:2505–7. 94. Lee Y-S, Meade T, Norris TB, Galvanauskas A. Tunable narrow-band terahertz generation from periodically poled lithium niobate. Appl Phys Lett 2001;78:3583–5. 95. Sasaki Y, Avetisyan Y, Kawase K, Ito H. Terahertz-wave surface-emitted difference frequency generation in slant-stripe-type periodically poled LiNbO3 crystal. Appl Phys Lett 2002;81:3323–5. 96. Sasaki Y, Suzuki Y, Suizu K, Ito H, Yamaguchi S, Imaeda M. Surface-emitted terahertzwave difference-frequency generation in periodically poled lithium niobate ridge-type waveguide. Jpn J Appl Phys 2006;45:L367–9. 97. Suizu K, Suzuki Y, Sasaki Y, Ito H, Avetisyan Y. Surface-emitted terahertz-wave generation by ridged periodically poled lithium niobate and enhancement by mixing of two terahertz waves. Opt Lett 2006;31(7):957–9. 98. Tonouchi M. Cutting-edge terahertz technology. Nat Photonics 2007;1:97–105. 99. Ferguson B, Zhang X-C. Materials for terahertz science and technology. Nat Mater 2002;1:26–33. 100. Mittleman D. Sensing with terahertz radiation. Berlin: Springer; 2003. 101. Sakai K. Terahertz optoelectronics. Berlin: Springer; 2005. 102. Siegel PH. Terahertz technology in biology and medicine. IEEE Trans Microwave Theory Tech 2004;52:2438–46. 103. Tonouchi M. Terahertz technology. Tokyo: Ohmsha; 2006. 104. Avetisyan Y, Sasaki Y, Ito H. Analysis of THz-wave surface-emitted difference-frequency generation in periodically poled lithium niobate waveguide. Appl Phys B 2001;73:511–4. 105. Shall M, Helm H, Keiding SR. Far infrared properties of electro-optic crystals measured by THz time-domain spectroscopy. Int J Infrared Millimeter Waves 1999;20:595–604. 106. Bakker HJ, Hunsche S, Kurz H. Investigation of anharmonic lattice vibrations with coherent phonon polaritons. Phys Rev B 1994;50:914–20. 107. Bass M, Franken PA, Ward JF, Weinreich G. Optical rectification. Phys Rev Lett 1962;9:446–8.

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Further Reading 1. Sasaki Y, Avetisyan Y, Yokoyama H, Ito H. Surface-emitted terahertz-wave differencefrequency generation in two-dimensional periodically poled lithium niobate. Opt Lett 2005;30:2927–9. 2. Shur VYa, Rumyantsev EL, Pelegov DV, Kozhevnikov VL, Nikolaeva EV, Shishkin EI, et al. Barkhausen jumps during domain wall motion in ferroelectrics. Ferroelectrics 2002;267:347–53. 3. Shur VYa, Zelenovskiy PS. Micro- and nanodomain imaging in uniaxial ferroelectrics: joint application of optical, confocal Raman and piezoelectric force microscopy. J Appl Phys 2014;116(6):1–20. 4. Soergel E. Visualization of ferroelectric domains in bulk single crystals. Appl Phys B 2005;81:729–52.

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C H A P T E R

7 Single Crystal PZN-PT, PMN-PT, PSN-PT, and PIN-PT-Based Piezoelectric Materials L. Luo, X. Zhao, H. Luo Shanghai Institute of Ceramics, Shanghai, China

Abstract This chapter reviews the investigation of several relaxor-PT single crystals with perovskite structure. First, this chapter introduces several milestones during the development of relaxor-PT complex solid solutions, and then discusses the PMN-PT, PZN-PT, PSN-PT and PIN-PT in separate sections, focusing on their growth, phase structure and performance. We then introduce two theoretical models to explain the excellent piezoelectric properties of relaxor-based crystals and the application of relaxor ferroelectric single crystals in piezoelectric actuators and medical transducers. Finally, the challenges and future trends in relaxor-based crystals are discussed. Keywords Relaxor single crystals, Crystal growth, Bridgman method, Flux method, Ferroelectrics, Piezoelectric performance, Dielectric constant.

7.1 INTRODUCTION Novel relaxor ferroelectric single crystals refer to Pb(Mg1/3Nb2/3)O3 (PMN) or Pb(Zn1/3Nb2/3)O3 (PZN) and ferroelectric PbTiO3 (PT), namely (1
x) PMN-xPT and (1
x)PZN-xPT, which are a kind of single crystal of solid solution with perovskite structure. They are solid solutions synthesized with relaxor ferroelectric A(B0 B00 )O3 and normal ferroelectric PT, and their general chemical formulas are written as A(B0 B00 )O3-PbTiO3, in

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which, the A site is usually occupied by Pb; the B0 site is occupied by Mg, Zn, Sc, Ni, etc., and the B00 site is occupied by Nb, Ta or W. It can form lots of ferroelectrics due to the variation of B site element; however, most of the compounds are unable to be applicable at present, with only several kinds of solid solution that can in practice. The crystal growths, performance, structure, and device applications of PZN-PT, PMN-PT, Pb(Sc1/2Nb1/2)PbTiO3 (PSN-PT), Pb(In1/2Nb1/2)-PbTiO3 (PIN-PT), Pb(Yb1/2Nb1/2)PbTiO3 (PYN-PT) have been investigated intensively during the past two decades. Among the family of relaxor ferroelectric single crystals, PZN-PT, PMN-PT PIN-PT and PSN-PT are the most important representatives of relaxor-based perovskite. So this chapter is mainly about these four kinds of crystals in terms of their growth, structure, performance and applications. Intensive research into relaxor ferroelectrics crystals has been carried out, mainly concerning crystal growth, their properties (including piezoelectric, ferroelectric, pyroelectric and optic performance) and microstructures, their applications in transducers and actuators. In this chapter, we will discuss some of the most important results. Following this introduction, Section 7.2 presents the development history of relaxor ferroelectrics. PZN-PT and PMN-PT single crystals posses the largest piezoelectric performance in piezoelectric materials, and they have been commercialized in medical ultrasonic probes. So in Sections 7.3 and 7.4, we discuss in detail some of the results about PZN-PT and PMN-PT, respectively. In Sections 7.5 and 7.6, we present results for PSN-PT and PIN-PT, which can make up for the deficiency of PMN-PT and PZN-PT in temperature stability. Finally, two theoretical models on relaxor crystals, applications of these crystals and a general conclusion are presented.

7.2 THE HISTORY OF RELAXOR FERROELECTRICS In 1959 and 1961, Bokov and Myl’nikova reported the growth of PMN1 and PZN2 crystals from a flux of PbO, and they observed their ferroelectric properties successfully. The dielectric relaxation properties of composite perovskite ferroelectrics A(B0 B00 )O3 were first observed by Smolenskii et al. In 1961, they reported the dielectric relaxation behavior of PMN single crystals.3 In 1967, PMN single crystals were grown by Bonner and Uiter4 using the Kyropoulos method. After that, many scientists grew PZN and PZN-PT single crystals using the flux method.5–8 The growth method of PMN-PT and PZN-PT crystals was mainly using a flux of PbO or B2O3. During this time, the properties of these crystals were difficult to characterize due to the small size of grown crystals. In the following years, no great progress was achieved in the growth of PZN-PT and PMN-PT crystal.

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The research into relaxor ferroelectric single crystals got a large boost in the early 1980s, because of obtaining a large size sample (size of one side not less than 6 mm) to measure its piezoelectric performance, which was achieved by Kuwata, Uchino and Nomura.9,10 They used the flux method to grow PZN-PT with compositions near the morphotropic phase boundary (MPB). The d33 and k33 of 0.91PZN-0.09PT achieved 1500–1570 pC/N and 90%–92%, respectively; however, piezoelectric properties of tetragonal PZN-PT was relatively low (d33 < 800 pC/N, k33 < 85%). At the same time, they also found that the orientation of rhombohedral PZN-PT with optimized d33 was along the direction, not along its spontaneous polarization < 111 > direction. After that, the growth of relaxor ferroelectric single crystals made little further progress during the 1980s, partly because not enough attention was paid to Kuwata et al. study and partly because the growth of these single crystals was too difficult. Towards the end of the 1980s, further studies were carried out on relaxor ferroelectric single crystals. In 1989 and 1990, Shrout et al. from Pennsylvania State University grew PMN-PT crystal by the flux method, and the d33 of the sample reached 1500 pC/N.11 In 1990, Ye et al. grew PMN single crystal using the same method, and the largest size reached 13 mm.12 Yamashita and Saitoh from Toshiba Co. repeated Kuwata et al. study, and got similar results to the original study. In 1994 and 1995, they were granted several patents for ultrasonic probes based on relaxor ferroelectric crystal.13–15 From then on, investigation of growth of the ferroelectric single crystals and their properties became the focus in ferroelectrics. PZN-PT crystals with size larger than 20 mm were grown successfully by Mulvihill et al.16 The size of their crystals met the size requirement for some kinds of ultrasonic probe. At the same time, the piezoelectric performance of the crystals was improved considerably: the d33 and k33 achieved 2500 pC/N and 94%, respectively; it achieved a strain of 1.7% with a hysteresis of 0.6%. Fig. 7.1 presents the high-piezoelectric performance of these kinds of crystals, as reported by Park and Shrout.17 Compared with PZT ceramics, their piezoelectric performance is much superior to that of PZT. A piezoelectric materials expert at Penn State, Eric Cross, described it as “an exciting breakthrough.” The journal sciences reported their investigation.18 These excellent performances make relaxor-based single crystal a promising candidate for the next generation of transducers. In 1997, Kobayashi et al. used improved flux method to grow PZN-PT crystal, and the size of the as-grown crystal reached 43  42  40 mm3, the largest size reported at that time.19 In 1998, Shimanuki et al. used the Bridgman method to grow PZN-PT crystal; the size reached a diameter of 30 mm and a length of 20 mm.20 In 1997, Luo et al. used a modified Bridgman method to grow PMN-PT single crystals successfully directly from their melt, the size reaching dimensions of ϕ40  80 mm3.21,22 The Bridgman method is now widely adapted to make PMN-PT, which are

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0.8

Single crystal PZN-4.5%PT (001)

0.6

Single crystal PZN (001)

Strain (%)

Single crystal PZN-8%PT (001)

Single crystal PMN-24%PT (001)

0.4

0.2 Ceramics, PZT-5H Ceramics, PMN-PT Ceramics, PZT-8 0.0 0

20

40 60 Electric field (kV/cm)

80

100

FIG. 7.1 Strain vs E-field behavior for oriented rhombohedral crystals of PZN-PT and PMN-PT and for various electromechanical ceramics.17

promising candidates for the practical applications of the next generation of high-performance devices.

7.3 PZN-PT CRYSTAL PZN is rhombohedral phase, and PT is tetragonal phase; the structure of (1
x) PZN-xPT crystal depends on the composition x at room temperature. The MPB in (1
x) PZN-xPT occurs near x ¼ 0.09. (1
x)PZN-xPT is rhombohedral if PT content is lower than MPB composition, and it becomes tetragonal phase at PT content larger than MPB composition. At MPB composition, rhombohedral and tetragonal phases coexist in PZN-PT; some ferroelectric experts think that monoclinic and orthorhombic phases also exist at the MPB. Fig. 7.2A shows a simple phase diagram of PZN-PT at low temperature. PZN-PT crystal near MPB is very unstable: on the one hand, the existence of MPB in PZN-PT enables it to possess excellent performance characteristics, such as very high electromechanical coefficient, piezoelectric constant and strain induced by electric field; on

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250

Transition temperature (°C)

Cubic 200

150

Tetragonal

100 Rhombohedral

50

0

0

0.05

(A)

0.10 x

0.15

0.20

3000 2500

1500

MPB

d33(pC/N)

2000

1000

Tetragonal Rhombohedral

500

0

0 5 Pb(Zn1/3Nb2/3)O3

10

15 20 % of PbTiO3

(B) FIG. 7.2 (A) Phase diagram of the (1
x)Pb(Zn1/3Nb2/3)O3-xPbTiO3 solid solution system near MPB,9,10 (B) d33 as a function of crystal composition and orientation for PZN-PT.17

the other hand, the instability of PZN-PT make the crystal very difficult to grow, especially in controlling homogeneity and composition of the crystal.23 The piezoelectric performance of PZN-PT crystal depends not only on its composition, but also on its orientation, as shown in Fig. 7.2B. Rhombohedral PZN-PT crystal near its MPB has the largest d33, reaching 2500 pC/N; furthermore, its optimized orientation for highpiezoelectric performance is along the direction, not along its spontaneous polarization direction < 111 >. In the rhombohedal region,

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d33 increases sharply with PT content when approaching the MPB. PZNPT with 9% PT content has the largest d33, and then d33 decreases sharply in the tetragonal region. Compared with in the rhombohedral phase, d33 is relatively low in the tetragonal phase.

7.3.1 Growth of PZN-PT PZN-PT is not stable at high temperature; it decomposes from perovskite structure to pyrochlore phase. It is not easy to fabricate high-quality and large-size single crystals in a pure phase, a result of the high volatility of lead oxide and instability of PZN-PT at high temperature. Until now, many methods have been used to grow this crystal. At the prophase during the investigation of PZN-PT, scientists mainly used the fluxing method to grow PZN-PT, though the grown crystal is not large enough for application in practice. In terms of synthetic process, PZN-PT crystals were mainly grown by the flux method16,24,25 and by a modified Bridgman technique.20,26,27 The fluxing method is usually unsuitable for the growth of large crystals because of the occurrence of spontaneous nucleation. The as-grown crystals produced by fluxing are liable to contain inclusions of PbO flux and a pyrochlore phase. The Bridgman method allows for the manufacture of crystals with controlled dimension and good reproducibility. The perovskite phase of PZN-PT is not very stable; it decomposes from perovskite phase to pyrochlore phase. The decomposition from perovskite to pyrochlore phase is one of the main reasons that the crystal is difficult to grow. It partially decomposes into a pyrochlore phase above 1148°C and undergoes an incongruent melting at 1226°C.28 PZN-PT single crystals need to be grown in sealed platinum crucibles to suppress the volatilization of PbO and occurrence of spontaneous nucleation. We have developed a modified Bridgman technique to grow 0.91PZN-0.09PT single crystals with 0.69PMN-0.31PT seed crystal oriented along < 111> direction. Fig. 7.3A is a sketch of the furnace used to grow PZN-PT. High-purity raw powders of PbO, ZnO, Nb2O5 and TiO2 are dried before weighing. The mixture of these powders is maintained in the ratios of PZN:PT ¼ 91:9 and PZN-PT:PbO ¼ 45:55 in mole percentage. PbO acts as flux. The raw materials are precalcined by B-site precursor synthesis, which can prevent, to some extent, the formation of the pyrochlore phase.26 B-site precursor synthesis of raw materials can effectively reduce the formation of pyrochlore phase during crystal growth. 0.91PZN-0.09PT crystals are grown in sealed platinum crucibles to prevent the evaporation of PbO during crystal growth. PZN-PT crystals are grown at about 1250°C. It is possible to obtain four 0.91PZN-0.09PT crystal boules simultaneously by this method. Temperature gradient is an important consideration for the Bridgman technique.27 Fig. 7.3B shows the temperature gradient of

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Ceramic crucible Pt crucible MoSi2 resistance Seed crystal Al2O3 powder Thermocouple

Drop-down mechanism

(A) 12 Thermocouple 1 Thermocouple 2

Temperature gradient (°C/mm)

Thermocouple 3 Thermocouple 4 9

6

Growth zone 3 b –150

–100

–50 0 Growth position (mm)

50

(B) FIG. 7.3 (A) Schematic diagram of the modified Bridgman furnace used for the growth of PZN-PT single crystal from flux. (B) Axial temperature gradient profile of the Bridgman furnace for the growth of 0.91PZN-0.09PT single crystals.29

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(A)

2 cm

2 cm

(B)

FIG. 7.4 (A) As-grown 0.91PZN-0.09PT crystal boules grown by a modified flux Bridgman method. (B) Morphology of 0.91PZN-0.09PT crystals grown by a modified flux Bridgman method.29

the Bridgman furnace. The temperature gradient could be dominated at around 30–50°C/cm at the solid-liquid interface by this method, which is ideal for crystal growth. 0.91PZN-0.09PT single crystals with diameter 28 mm and length 30 mm can be obtained, as shown in Fig. 7.4A. The asgrown crystals exhibit dark-brown color on their surface due to a thin coat of PbO flux. After flux removal by boiling acetic acid, the obtained crystals reveal three faces, as shown in Fig. 7.4B.

7.3.2 Properties of PZN-PT Ranjan et al.25 investigated the relation between the Tc and PT content of PZN-PT; Fig. 7.5 indicates a nearly linear function between Tc and PT. If PZN-PT single crystal is heated to a temperature higher than Tc, the tetragonal phase transforms to a cubic phase. The PT content of the PZN-PT can be 190

Tc(°C)

180 170 160 150 140 3

4

5

6 7 Mol% PT

8

FIG. 7.5 Tc of PZN-PT as a function of PT content.25

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10

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T

Dielectric constants e33

20,000

TC

15,000 0.93PZN-0.07PT 10,000

Trt

5000 0.91PZN-0.09PT 0 0

50

100 150 Temperature (°C)

200

250

FIG. 7.6 Temperature dependence of the dielectric constants of poled 0.93PZN-0.07PT and 0.91PZN-0.09PT crystal measured at 1 kHz.30

inferred according to the wafer’s Tc. Fig. 7.6 shows the temperature dependence of the dielectric constants of poled wafers of 0.93PZN-0.07PT and 0.91PZN-0.09PT single crystal. Between 70°C and 100°C, there are two dielectric peaks, which relate to the phase transition temperature Trt, responding to the phase transition from rhombohedral to tetragonal. The existence of Trt makes piezoelectric performances of PZN-PT unstable with temperature, which limits its application in some transducers to some extent. The Trt of 0.93PZN-0.07PT and 0.91PZN-0.09PT single crystal occur at about 110°C and 72°C, respectively. The Trt of 0.93PZN-0.07PT single crystal is about 40°C higher than that of 0.91PZN-0.09PT, while the Tc of 0.93PZN-0.07PT single crystal is about 10°C lower than that of 0.91PZN-0.09PT. Although the piezoelectric performance of 0.93PZN-0.07PT is lower than that of 0.91PZN-0.09PT, the stability of 0.93PZN-0.07PT is higher than that of 0.91PZN-0.09PT, due to its higher Trt.30 So 0.93PZN-0.07PT is more practical in piezoelectric devices. A stable multidomain state and correspondingly high level of piezoelectric activity can be achieved in nonpolar -oriented crystals. A complete set of elastic, piezoelectric and dielectric constants has been reported for 0.955PZN-0.045PT, 0.93PZN-0.07PT and 0.92PZN-0.08PT single crystal systems.31–33 It is helpful to list the complete set of matrix properties for those crystals for both fundamental study and device design purposes; the data is presented in Table 7.1. The elastic constant of the three crystals is very close to each other. Compared with the other two crystals, the 0.955PZN-0.045PT single crystal system represents relatively lower electromechanical capability of this solid solution system, because it is further away from the MPB composition. 0.92PZN-0.08PT single crystal system possesses much better piezoelectric performance than that of 0.955PZN-0.045PT. The electromechanical coupling coefficient k33 of I. PIEZOELECTRIC MATERIALS

280

Density: ρ(kg/mm3) 0.93PZN-0.07PT 8350

0.92PZN-0.08PT 8315

0.955PZN-0.045PT 8310

Elastic stiffness constants: cij (1010 N/m2) PT (%)

cE11

cE12

cE13

cE33

cE44

cE66

cD 11

cD 12

cD 13

cD 33

cD 44

cD 66

7.0

11.30

10.3

10.5

10.91

6.30

7.10

11.37

10.37

10.00

14.00

6.80

7.10

8.0

11.50

10.50

10.90

11.51

6.34

6.50

11.80

10.80

10.00

14.30

6.76

6.50

4.5

11.10

10.20

10.10

10.50

6.40

6.30

11.30

10.40

9.50

13.50

6.70

6.30

212

Elastic compliance constants: (10

2

m /N)

PT (%)

sE11

sE12

sE13

sE33

sE44

sE66

sD 11

sD 12

sD 13

sD 33

sD 44

sD 66

7.0

85.90


14.10


69.0

142

15.9

14.1

56.7


43.3


9.6

20.9

14.7

14.1

8.0

87.0


13.1


70.0

141

15.8

15.4

55.8


44.2


8.2

18.5

14.8

15.4

4.5

82.0


28.5


51.0

108

15.6

15.9

61.5


49.0


9.0

20.6

14.9

15.9

7. SINGLE CRYSTAL-BASED PIEZOELECTRIC MATERIALS

I. PIEZOELECTRIC MATERIALS

TABLE 7.1 Measured and Derived Material Properties of 0.955PZN-0.045PT, 0.93PZN-0.07PT, 0.92PZN-0.08PT Single Crystal Poled Along 31–33

Piezoelectric constants: eiλ (C/m2) diλ (10212 C/N) giλ (1023 V m/N) hiλ (108 V/m) PT (%)

e15

e31

e33

d15

d31

d33

g15

g31

g33

h15

h31

h33

7.0

11.1


2.3

15.1

176


1204

2455

6.6


24.2

49.3

4.5


3.1

20.7

8.0

10.1


5.1

15.4

159


1455

2890

6.2


21.3

42.4

4.2


5.8

17.7

4.5

8.9


3.7

15.0

140


970

2000

5.0


21.0

44

3.4


4.3

17

Dielectric constants: ε(ε0) β(10

24

/ε0)

εS11

εS33

εT11

εT33

βS11

βS33

βT11

βT33

k15

k31

k33

kt

7.0

2779

823

3000

5622

3.60

12.2

3.33

1.78

0.27

0.58

0.92

0.47

8.0

2720

984

2900

7700

3.68

10.2

3.45

1.30

0.25

0.60

0.94

0.45

4.5

3000

1000

3100

5200

3.4

10.0

3.2

1.9

0.23

0.50

0.91

0.50

7.3 PZN-PT CRYSTAL

I. PIEZOELECTRIC MATERIALS

PT (%)

281

282

7. SINGLE CRYSTAL-BASED PIEZOELECTRIC MATERIALS

0.92PZN-0.08PT can reach 0.94. PZN-PT single crystal systems near the MPB composition exhibit strong property fluctuations because of their complex domain structure. Among the domain engineered PZN-PT single crystal systems, the 0.93PZN-0.07PT single crystal system might be the best candidate for device applications since its properties are comparable to that of 0.92PZN-0.08PT and it is much more stable, because it is a little further away from the MPB composition. It has been reported that the properties of 0.92PZN-0.08PT vary greatly33: the measured value of d33 varies from 2000 to 4000 pC/N and the value of ε33T varies from 5000 to 8000, which makes 0.92PZN-0.08PT single crystal unsuitable for many practical device applications. Furthermore, the Trt of 0.93PZN-0.07PT is higher than that of 0.92PZN-0.08PT, which makes 0.93PZN-0.07PT more stable with temperature. The piezoelectric properties of PZN-PT crystal have strong anisotropy. PZN-PT is a complicated solid solution; its properties are sensitive not only to its composition but also to its orientations, as shown in Table 7.2. Although PZN-PT crystals with the same composition are grown from their high-temperature melt, their properties are much different from each other due to different growth techniques and posttreatment processes. Even a different position of one wafer produces different properties due to its complex domain structure and phase structure, so the reported results in the literature are different. To find the optimal orientation for high-piezoelectric performance, Park and Shrout17 have investigated 0.955PZN-0.045PT samples whose orientation deviates from to < 111>. The dice method and result are presented in Fig. 7.7, the results of which are consistent with Table 7.2. Strain saturation becomes more significant as α increases from < 001 > to < 111> direction. At high fields, strain level decreases with increased a; however, crystals oriented close to < 001> (α < 20°) exhibit no saturation and low hysteresis. So the orientation is the optimal direction for high-piezoelectric coefficient. P-E hysteresis loops are measured for < 001>, < 011 > and < 111> oriented crystals at room temperature under electric field level of 10 kV/cm,38 as shown in Fig. 7.8. The data clearly show the ferroelectric state of the PZN-PT and anisotropy in the three orientations. At room temperature, the value of Ps and Pr for the orientation are 35 and 25 μC/cm2, 35 and 30 μC/cm2 for < 110 > orientation, while those for the < 111 > orientation are 35 and 33 mC/cm2, respectively. These results show that in each orientation the room temperature polarization state (Ps) is equivalent along all of the three directions. Furthermore, there are significant differences in the magnitude of the Pr, area of the hysteresis loops and in the coercive field (Ec). The coercive field at room temperature is found to increase from 2.2 kV/cm for the to 4.5 kV/cm for the to 6 kV/cm for the orientations.38

I. PIEZOELECTRIC MATERIALS

TABLE 7.2 The Main Piezoelectric Properties of PZN-PT Crystal With Different Compositions and Orientations23 Direction

k33 (%)

k31 (%)

ε

tan δ (%)

d33 (pC/N)

d31 (pC/N)

Reference

0.91PZN-0.09PT

(001)

95.3

80.8

4600

0.9

2500


1700

Ref.34

(110)

/

59

3512

2.09

530


715

Ref.35

(111)

/

18.9

1606

0.89

190


167

Ref.35

(001)

94

60

5000

1

2500


1250

Ref.17

(110)

/

31

3745

/

580

331

Ref.36

(111)

39

/

1000

1.2

84

/

Ref.17

0.93PZN-0.07PT

(001)

92

58

5622

or < 111 > direction. The furnace is kept at about 1380°C during crystal growth, and the temperature gradient is about 40–100°C at the solid-liquid interface. After the accomplishment of growth, the furnace is cooled down to room temperature at a rate of 25°C/h. Using this method, large sizes over ϕ50  80 mm3 PMN-PT can be grown. Fig. 7.10 shows the as-grown crystals with composition near the MPB. The PMN-PT can be diced into different shapes to be used in different devices. By replacing the flux technique with the Bridgman method, crystal size increases and cost reduces. However, it brings a problem for the PMN-PT crystal: Ti content varies along the boule axis, which results in property

I. PIEZOELECTRIC MATERIALS

287

7.4 PMN-PT CRYSTAL

300 PMN-PT Unploed Poled

Curie temperature (°C)

200

Cubic Tetragonal

100

0 Pseudo cubic (rhombohedral) –100

0

0.1

0.2 0.3 Mole (X) PT

(A) 600

0.4

0.5

Pb(Mg1/3Nb2/3)1–xTixO3

C

T(K)

400

200

T

R

MC

0 0.25

(B)

0.30

0.35 X

0.40

0.45

0.50

FIG. 7.9 (A) Phase diagram of (1
x)PMN-xPT at low temperature.43 (B) Modified phase diagram in (1
x)PMN-xPT around the MPB by Noheda et al.44

variation along the axis. Fig. 7.11 shows Park and Hackenberger’s result, in which the Tc of the boule varies with boule axis.49 By using a combination of zone melting technique with Bridgman method, the Ti distribution can be manipulated to some degree. H.C. Materials Corp. has improved

I. PIEZOELECTRIC MATERIALS

288

FIG. 7.10

7. SINGLE CRYSTAL-BASED PIEZOELECTRIC MATERIALS

The as-grown PMN-PT crystals with composition near the MPB.

35

170 30

160 150

25

140 130 120 0

PT composition

Curie temperature (°C)

180

3.5% Axial composition gradient 10 20 30 40 50 Position from top cone (mm)

20 60

FIG. 7.11 PMN-PT crystals grown by the Bridgman method and PT content along the growth direction.49

the composition uniformity by using a combination of zone melting technique with Bridgman method.50

7.4.2 Dielectric Properties The Curie points of the pure PbTiO3 and pure Pb(Mg1/3Nb2/3)O3 crystals are 490°C and
10°C, respectively. The Tc of the PMN-PT increases with PT content. Segregation will occur during the growth of PMN-PT

I. PIEZOELECTRIC MATERIALS

289

7.4 PMN-PT CRYSTAL

900 800 700

T(K)

600 500 400 300 200 0.0

0.2

0.4

0.6

0.8

1.0

x

FIG. 7.12

The compositional dependence of Tc fitted with one line.51

single crystals, it is necessary to determine the composition of the grown crystal. Zekria et al.51 have investigated the relation between composition and the Tc of PMN-PT crystal. The local compositions of the PMN-PT were determined by electron probe microanalysis. The Curie temperature was measured by an optical method. The compositional dependence of Tc is shown in Fig. 7.12. One line can fit the relation between Tc and PT content51: Tc ¼ 268 + 494x for x < 0:50

7.1

By this relation, we can calculate the PT content (x) by measuring the Tc. The content of PT and the orientation influence the dielectric properties of PMN-PT greatly. Zhao et al.52 have investigated the dielectric behavior of the -oriented unpoled (1
x)PMN-xPT single crystals with different composition. The temperature corresponding to the maximum of the dielectric constant is called the temperature Tm (or Tc). For the rhombohedral PMN-PT crystals, only one dielectric peak is obtained at Tm, indicating a phase transition from the FEr phase to paraelectric cubic phase near the Tm.53,54 For the tetragonal PMN-PT crystal, there is also one dielectric peak at the Tm, indicating a phase transition from the FEt phase to paraelectric cubic phase. (1
x)PMN-xPT crystals with x  0.31 is a dominant relaxor state for the evident frequency dispersion of dielectric constant in the ferroelectric phases.52 However, with the increment of PT, the frequency dispersion behavior is not obvious and could be observed only near Tm.

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290

7. SINGLE CRYSTAL-BASED PIEZOELECTRIC MATERIALS

For the poled rhombohedral PMN-PT near the MPB, its phase transition is very complex. As shown in Fig. 7.13A, upon heating from room temperature along the -direction of 0.70PMN-0.30PT, rhombohedral macrodomain begins to transit to microdomain near Trd at 100°C; then rhombohedral microdomain transitions to tetragonal microdomain near Trt at 105°C.55 Near the temperature Tm at 135°C, ferroelectric tetragonal (FEt) phase transforms to paraelectric cubic phase. Three temperatures (Trd, Trt, Tm) correspond to three discharging current peaks. As presented in Fig. 7.13B, upon heating from room temperature along the direction, two small permittivity peaks can be observed at Tro (89°C) and Tot (100°C), respectively. The first small peak Tro coincides with a phase transition from the FEr to a ferroelectric orthorhombic FEo state, and the second small peak Tot indicates the transition from the FEo to FEt state.56,57 For < 001> poled 0.70PMN-0.30PT crystals shown in Fig. 7.13C, there are also two small permittivity peaks at Trm and Tmt, respectively, a monoclinic ferroelectric FEm phase being a metastable state between the lower temperature FEr phase and the higher temperature FEt phase.42,58 Corresponding to the permittivity versus temperature curve, there are also three discharging current peaks in the discharging current curve. Two broad small permittivity peaks and two broad discharging current peaks indicate three ferroelectric phases (FEr, FEm, and FEt) coexisting in a large temperature range. For the poled < 111> PMN-PT, it transmits to tetragonal ferroelectric phase at about 100°C; for the < 110 > poled PMN-PT, the orthorhombic ferroelectric and tetragonal phase can be easily induced during the heating process; for the < 001> poled PMN-PT, monoclinic and tetragonal phase transition occur, all the phase transitions are mentioned as above. The piezoelectric response can be greatly affected due to phase transition happening. So the practical application of the poled PMN-PT is limited by the first phase transition temperature. Fig. 7.14 presents the composition and orientation dependence of the first structure transformation temperature of the poled PMN-PT. In order to keep high response in a broad temperature range, these < 001> poled crystals with x from 0.28 to 0.30, whose first phase transformation temperature is between 80°C and 100°C and piezoelectric performance is very high, should be some of the preferred materials for practical applications in transducers, sensors, and actuators.

7.4.3 Piezoelectric Properties Piezoelectric coefficients as a function of composition and crystal orientation for PMN-PT are presented in Fig. 7.15. As shown, large piezoelectric coefficients (d33  2500 pC/N) were found for PMN-PT single crystals with the MPB composition (0.7PMN-0.3PT). This is in perfect accord with that reported by Singh and Pandey.59 As shown, crystals poled along the

I. PIEZOELECTRIC MATERIALS

291

7.4 PMN-PT CRYSTAL

50,000 1.6

Tm

1.0

20,000

er

1.2

Trt

30,000

0.8

Trd

0.6 10,000

0.4 0.2

0

Current density (10–3A/m2)

1.4

40,000

0.0 –10,000

0

50

(A)

100

150

200

250

Temperature (°C)

80,000

Tm

70,000

2.4

er

50,000 Tot

40,000

1.6 Tro

30,000 20,000

0.8

10,000

Current density (10–3A/m2)

3.2

60,000

0.0

0 0

50

(B)

100

150

200

250

Temperature (°C) 0.6

Tm

60,000

0.4

40,000

er

30,000

0.3

Trm Tmt

20,000

0.2 10,000 0.1

0 –10,000

0.0 0

(C)

Current density (10–3A/m2)

0.5 50,000

50

100 150 Temperature (°C)

200

FIG. 7.13

250

Temperature and orientation dependence of the dielectric constant and discharging current density for the poled 0.70PMN-0.30PT single crystals: (A) , (B) , and (C) .

I. PIEZOELECTRIC MATERIALS

292

7. SINGLE CRYSTAL-BASED PIEZOELECTRIC MATERIALS

180



Temperature (°C)

160 140 120 100 80 60 40 0.24

0.28

0.32 Composition x

0.36

FIG. 7.14 Composition and orientation dependence of the first structure transformation temperature for the poled (1
x)PMN-xPT crystal.

2500

Rhombohedral

d33 (pC/N)

2000 1500

MPB Tetragonal

1000

500 0 20 22 24 26 Pb(Mg1/3Nb2/3)O3

28

30

32

34

36

38 40 xPbTiO3

FIG. 7.15 Piezoelectric coefficient d33 as a function of composition and orientation dependence for PMN-PT single crystals.

pseudocubic direction exhibit large piezoelectric coefficients and d33 increases with PbTiO3 content for < 001>-oriented rhombohedral crystals. However, piezoelectric coefficients d33 and electromechanical coefficients k33 for -oriented rhombohedral PMN-PT single crystals are only 100 pC/N and 35%. For poled PMN-PT single crystals, piezoelectric coefficient also has a strong dependence on the PT content. As shown in Fig. 7.15, in the rhombohedral region, piezoelectric coefficient d33 has a similar trend to < 001> poled crystals. Two abnormal points (or rather, almost certainly two narrow regions) of the piezoelectric

I. PIEZOELECTRIC MATERIALS

293

7.4 PMN-PT CRYSTAL

0.6 PMN-35% PT

0.4 Strain (%)

PMN-33% PT

PMN-31% PT PMN-29% PT

0.2

PMN-37% PT 0.0

FIG. 7.16

0

3

6

9 12 Electric field (kV/cm)

15

18

Strain versus F-field curve for -oriented PMN-PT crystals.60

constant appear clearly for < 110>-oriented crystals, the piezoelectric coefficients for the composition region 0.30 < x < 0.35 are very low. It can be concluded that the equivalent domain configuration is indispensable for a strong piezoelectric response in ferroelectric perovskite crystals. In the MPB region, orthorhombic phase can be easily induced which leads to low piezoelectric properties. -oriented PMN-PT crystals near the MPB exhibit very highstrain and low hysteresis, as reported by Park and Shrout.17 We also have calculated the strain behavior of PMN-PT as a function of composition and orientation. Fig. 7.16 is an E-field-induced strain as a function of composition for -oriented PMN-PT crystals. Due to the complexity of the domain configuration and phase composition near the MPB in PMN-PT crystals, domain motion and phase transformation can easily be induced by an E-field, which can cause unusually high-strain and large hysteresis. In the rhombohedral ferroelectric phase such as 0.71PMN-0.29PT and 0.69PMN-0.31PT, high-strain values and small hysteresis can be achieved with the engineered domain stability. The -oriented PMN-PT with engineered domain structure is suitable for high-strain actuators due to its high-strain and little hysteresis. Viehland et al.61 have carried out temperature dependent electromechanical investigations of , < 001>, and < 111>-oriented MPB compositions of PMN-PT crystals. Fig. 7.17A reveals that the values of d33 along the and < 011> directions are nearly equivalent over the temperature range of 25–80°C. d33 increases from 1200 to 4000 pC/N sharply with temperature over this temperature range. The results are

I. PIEZOELECTRIC MATERIALS

294

7. SINGLE CRYSTAL-BASED PIEZOELECTRIC MATERIALS

5000



d33 (pC/N)

4000

3000

2000

1000

0 0

(A)

50 100 Temperature (°C)

150

1.0

0.8

k33

0.6

0.4



0.2

0.0 0

(B)

50

100

150

Temperature (°C)

FIG. 7.17 (A) d33 and (B) k33 as a function of temperature for , and oriented PMN-PT crystals.61

consistent with Fig. 7.15, which shows that -oriented PMN-PT with MPB composition also has high d33. Although direction is the spontaneous direction of rhombohedral PMN-PT, the value of d33 for the < 111>-oriented crystal is much lower. The piezoelectric constant increment of , < 011>, and < 111>-oriented PMN-PT with temperature may be due to the phase transition, softening of Young’s modulus and the increased mobility of domain with temperature. Fig. 7.17B shows the longitudinal electromechanical coupling coefficient (k33) as a function of temperature for poled , < 111>, and < 011>orientations. The data reveal that the values of k33 along the and < 011> directions are also

I. PIEZOELECTRIC MATERIALS

7.4 PMN-PT CRYSTAL

295

nearly equivalent over the temperature range from 25 to 80°C, However, it is almost temperature independent, which is different from the behavior of d33. Furthermore, the value for the < 111> orientation is much lower. At room temperature, only a k33 of 0.38 is obtained; however, it increases with temperature reaching 0.8 at 100°C. The properties of PMN-PT crystals are influenced greatly by their orientation, composition, process of growth, postprocessing and so on. So the properties of PMN-PT reported by different researchers are different. Table 7.3 shows the piezoelectric performance of < 001>-oriented PMNPT obtained by different research groups. -poled 0.7PMN-0.3PT crystals exhibit 4 mm symmetry in macroscopic material properties because of stable engineered domain structure. There are a total of 11 independent physical constants describing the elasto-piezo-dielectric matrices for this symmetry. Because of its high-piezoelectric performance, it is necessary to determine the complete set of elastic, piezoelectric, and dielectric constants of these crystals for device design. Peng et al.68 used a resonant method to determine the entire set of constants for these crystals according to the IEEE standard on piezoelectricity. The data are presented in Table 7.4. Wang et al.69 have also determined the complete set of -poled 0.7PMN-0.3PT crystals. Zhang et al.70 used a hybrid method combining the advantages of ultrasonic and resonance techniques to determine the complete set of constants of -oriented 0.67PMN-0.33PT with single domain, which can minimize the propagation of measurement errors and improve the consistency of the complete data set. The complete set of constants of PMN-PT with single domain is very useful to calculate the optimal orientation for piezoelectric, dielectric, and other properties; furthermore, it is helpful in understanding the origin of the excellent performance. Using these data, Damjanovic et al.71 demonstrated that the multidomain configuration contributes relatively little to the piezoelectric response of 0.67PMN-0.33PT single crystals; the dominant contribution to the large piezoelectric response in this composition appears to be intrinsic lattice effects (such as the large shear piezoelectric coefficients).

7.4.4 Solid State Crystal Growth Solid state crystal growth (SSCG) or templated grain growth of PMNPT crystals has been studied for many years due to its comparatively low cost.45,72,73 This technique can convert ceramics with random orientation into single crystal without melting, and its principle is simple: bury an external single crystal seed in fine grain matrix grains; the seed grows by consuming the fine matrix grains without melting the major constituents. SSCG can develop PMN-PT with properties similar to single crystals grown by the melt method using only conventional powder processing

I. PIEZOELECTRIC MATERIALS

296

TABLE 7.3 Properties of PMN-PT Reported by Different Research Groups d31 (pC/N)

εT

k33/k31

Tc (°C)

tan δ

Reference

0.7PMN-0.3PT

2200–2500


900

7500–9000

0.92–0.94

130–140

-oriented relaxor crystal, as presented in Fig. 7.24. Fig. 7.24 schematically presents engineered domain states and their piezoelectric response under high field for rhombohedral crystals oriented and poled along . It can be divided into three steps with the outer field varying from low field to high field. When strain is induced by a low E field along < 001 >, the polar direction of each domain inclines close to the outer E-field direction, which is responding to step A, as shown in Fig. 7.24. In this procedure, it results in an increased rhombohedral lattice distortion and domain reorientation is not necessary during this step. In this step, hysteresis-free or low hysteresis strain behavior for < 001>-oriented rhombohedral crystals No bias, after poling Under bias along 2.0 E d33 –480 pC/N Step A Poling direction Step B

Strain (%)

1.5 Tetragonal 1.0 Step B

Induced tetragonal phase 0.5 Step A E

0.0 0

(A)

(B)

20 40 60 80 100 120 Electric field (kV/cm)

(A) Schematic diagram of domain configurations in -oriented rhombohedral ferroelectric crystals under bias (step A—piezoelectricity, step B—induced rhombohedral to tetragonal phase transition); (B) strain vs E-field behavior for -oriented PZN-8%PT crystal (corresponding to (A)).17

FIG. 7.24

I. PIEZOELECTRIC MATERIALS

308

7. SINGLE CRYSTAL-BASED PIEZOELECTRIC MATERIALS

is observed. During step B, far from saturation, the strain abruptly increases with outer E-field. The observed strain behavior is related to an E-field induced rhombohedral-tetragonal phase transition. Polarization inclination towards finally results in collapse of all polarizations into the < 001 > direction. In step B, larger hysteresis and slope of strain versus E field are observed. In step C, the strain continues to increase with outer E-field, due to lattice extension by E-field. During this step, a much lower piezoelectric performance can be obtained, as shown in Fig. 7.24B where a d33 of only  480 is obtained for 0.92PZN-0.08PT. Wada et al.96 and Park et al. extended97 this model to BaTiO3 single crystal, and proposed engineered domain configuration. This concept includes three main aspects: (a) the E-field-induced strain is hysteresis-free or low hysteresis due to inhibition of movement of domain wall; (b) piezoelectric properties along nonspontaneous polarization direction is higher than along polarization; (c) the macroscopic symmetry of the crystal is changed by the engineered domain configuration; for example, the rhombohedral crystal before step B owns 4 mm symmetry, as shown in Fig. 7.24A. This theory explains many phenomena in relaxor crystals successfully. However, it is difficult to explain why the relaxor crystal exhibits optimal properties near the MPB.

7.7.2 Polarization Rotation and Mesophase In 2000, Fu and Cohen reported a first principles study of the ferroelectric perovskite, BaTiO3, which is similar to relaxor single crystal, but is a simpler system to analyze.98 The result shows that a large piezoelectric response can be driven by polarization rotation induced by an external electric field. They proposed a polarization rotation mechanism, as shown in Fig. 7.25. Fig. 7.25A is the rotation path for polarization from to < 111 > direction, which polarization might take when driven by outer field: one path is along a f g e; the other along a b c d e. Fig. 7.25B shows free energies as a function of field strength for different polarization directions. Fig. 7.25C shows the internal energies ΔU (ΔU ¼ U
Urhom) relative to the rhombohedral phase along the closed path a b c d e g f a. It is easier to rotate through path a f g e than a b c d e due to lower free energy according to their calculations, Furthermore, the piezoelectric constant along path a f g e is closer to experimental results than along path a b c d e. Polarization at a site corresponds to the direction of the rhombohedral phase; c site corresponding to the < 110 > direction of the orthorhombic phase; and the e site corresponding to the < 001 > direction of the tetragonal

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c

e

b

d

a

gf

e

z y

Energies ΔU (meV)

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x

7 6 5 4 3 2 1 0

Free energies (meV)

5

e d

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f

0

g

–10 –4 –8 0

d

5 10 15

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c b

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0 g

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10 15 20 25 Electric field (mV Å–1)

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0.0 0.5 1.0 1.5 2.0 2.5 3.0 Path distance

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FIG. 7.25 Polarization rotation paths from to under applied electric field.98

phase. The monoclinic mesophase will appear when the polarization rotation path is along a f g e; and the orthorhombic mesophase will appear when path a f g e is taken by polarization rotation. The polarization rotation mechanism presents the phase transition induced by the electrical field and the possible path of polarization rotation; the result is consistent with the monoclinic and orthorhombic phase found in relaxor crystal near the MPB. This theory has pushed forward the microstructure and polarization rotation research for relaxor crystals.

7.8 APPLICATION IN PIEZOELECTRIC ACTUATORS AND MEDICAL TRANSDUCERS 7.8.1 Application in Piezoelectric Actuators Piezoelectric actuators are used as critical elements in various electromechanical systems. Relaxor-based rhombohedral PMN-PT and PZN-PT exhibit ultrahigh electric-field-induced strain and low hysteresis,17,60 which is very suitable for piezoelectric actuators. Feng et al. have

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manufactured different size < 001>-oriented PMN-PT actuators.60,99 Actuators based on PZT-SF ceramics with the same size and fabricating process have also been manufactured. Under free-load conditions, 48 μm displacements can be achieved in PMN-PT actuators with electric fields ranging from
1.5 to 10 kV/cm, which is more than twice the displacement of the PZT-SF actuators driven from
10 to 10 kV/cm. Under 4 kg loading, the displacements in PMN-PT actuators are decreased to 42.5 mm. Jiang et al.100 have investigated the relationship between electromechanical coupling coefficient of PMN-PT crystals and the crystal thickness. It is found that the electromechanical coupling coefficient of PMN-PT single crystal thin plates are slightly lower than that of bulk single crystal. Single crystal actuators are then assembled using crystal plates with thickness ranging from 150 to 200 μm. A 5 mm  5 mm  12 mm single crystal actuator exhibits 13.5 μm stroke at room temperature under 150 V, and 6 μm stroke at 77 K under 150 V. Ko et al.92 have proposed a new optical pick-up bimorph actuator for slim and small form factor optical disk drives using PMN-PT. Woody et al.101 have discussed the relative merits and limitations of using PMN-PT actuator material for adaptive structures and a case study is presented for a high bandwidth steering mirror using ultra-high-strain single crystals. KCF technologies have designed a motor based on PMN-PT layer actuator.102 The motor achieves a speed of 330 rpm under free load and a stall torque of 0.11 N.m. If an optimal external load is applied by appropriate motion amplification, the single-crystal stack can deliver five to ten times as much work per cycle compared to a piezoceramic actuator. The power density for the piezocrystal stack reaches over 10,000 W/kg when the drive frequency is in the kHz range. The power density of the piezocrystal stack motor can be over 1000 W/kg, which compares favorably with even the highest-performing electromagnetic actuators. The results of actuators based on relaxor single crystal show that single crystal actuators hold promise for space precise positioning and adaptive structures and cryogenic applications. The major limitation to bringing single crystal multilayer devices to mass production is assembly cost.

7.8.2 Application in Medical Transducers Many company such as Toshiba, GE and Philips have investigated the application of an ultrasonic imaging system based on relaxor-based single crystals PMN-PT or PZN-PT, due to their ultrahigh piezoelectric performance. Theoretically, ultrasound transducer models indicate a dramatic bandwidth increment when using PMN-PT or PZN-PT crystals to replace

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PZT ceramics. The extended transducer bandwidth and sensitivity offer significant performance advantages, particularly in penetration and imaging resolution. Philips has released iE 33 ultrasound systems with pure wave single crystal technology, and have received excellent market acceptance.103 The processing of fabrication of transducers based on relaxor single crystal is similar to that of PZT ceramics, and the difference is the modification of design parameters due to using different piezoelectric materials. It is necessary to modify the size of the materials used in the devices and matching materials and so on. Saitoh et al.104 from Toshiba Corp. have developed a 40-channel phased array ultrasonic probe using 0.91Pb(Zn1/3Nb2/3)O3-0.09PbTiO3 single crystal. The 40-channel phased array ultrasonic probe exhibits greater sensitivity and broader bandwidth than conventional probes. The echo amplitude of the PZN-PT single-crystal probe is 8 and 5 dB higher than that of one- and two-matching-layer PZT probes, respectively. Moreover, the fractional bandwidth of the single-matching-layer PZN-PT probe is broader than that of the two-matching-layer PZT probes. The PZN-PT single crystals provide great increment in the sensitivity and bandwidth of phased array probes. Also they have fabricated a 20 MHz single-element ultrasonic probe using PZN-PT single crystal.105 The bandwidth of the PZN-PT probe is 13–26 MHz, which is 4 MHz broader than that of the conventional PZT probe. Cheng et al. have used PMN-PT to fabricate PMN-PT/epoxy 1–3 composites with different volume fractions of PMN-PT. It was demonstrated that the thickness electromechanical coupling coefficients of the composites could reach as high as 0.8. A 2.4 MHz plane ultrasonic transducer was fabricated using a PMN-PT/epoxy 1–3 composite with 0.37 volume fraction of PMN-PT. It shows a –6 dB bandwidth of 61% and an insertion loss of –14 dB.106 Sung et al.107 have developed multilayer PMN-PT single crystal transducers for medical application. The performance of a multilayer 64-channel 3.5 MHz phased array ultrasonic probe has been investigated. Ritter et al.108 have investigated PZN-PT for potential application in ultrasound transducers. Modeling of 1–3 composites and experimental results have demonstrated that thickness coupling greater than 0.80 could be achieved with a 40%–70% volume fraction of PZN-PT. Ultrasonic transducers fabricated using PZN-PT 1–3 composites achieve experimental bandwidths as high as 141%. Medical transducers based on single crystal were developed more than two decades ago, but commercialization was started only a few years ago. The performance of single crystal medical transducers is much better than that of conventional PZT transducers, and single crystal transducers have increasingly replaced conventional PZT transducers especially in high end medical products, which require high-penetration imaging resolution.

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7.9 CONCLUSION AND FUTURE TRENDS This chapter has discussed four kinds of crystal: PZN-PT, PMN-PT, PSN-PT and PIN-PT, which are typically representative of relaxor-PT crystals. In this chapter, we have introduced a modified Bridgman method to grow PMN-PT and PZN-PT crystal based on the complete investigation of the feasibility of relaxor-PT crystal. PZN-PT is not stable at high temperature; it decomposes from perovskite structure to pyrochlore phase. It is not easy to fabricate high-quality and large-size single crystals in a pure phase; we established a novel method to grow PZN-PT from a flux of PbO with an allomeric PMN-PT as seed crystal. Pure perovskite PZNPT with size over 28 mm in diameter can be obtained. The growth method of PMN-PT crystal is similar to that of PZN-PT, PMN-PT is more stable than PZN-PT at high temperature, and it is less difficult to grow PMN-PT than PZN-PT. The size of as-grown PMN-PT can reach ϕ50  80 mm3, which meets the size requirements for most ultrasonic transducers. Currently, PZN-PT and PMN-PT exhibit the highest piezoelectric performance of all piezoelectric materials. There is a MPB in PMN-PT and PZN-PT, near to which the relaxor crystals exhibit very high-piezoelectric response (d33 > 2000 pC/N, k33 > 0.90, S  1.7%) along the direction, but not along its spontaneous direction < 111>. The Tc of PZN-PT and PMN-PT near the MPB is around 170–190°C and 140–165°C, respectively. The phase structure of PMN-PT and PZN-PT is very complex; FEr, FEt, FEm and FEo exist or coexist in these crystals. Also the complete elastic, piezoelectric, dielectric constants of PZN-PT and PMN-PT are discussed in this chapter for both fundamental research and device design. The Tc of PSN-PT crystal near the MPB is much higher than for PMN-PT and PZN-PT. The melting point of PSN-PT is over 1425°C, which makes this crystal difficult to grow directly from its melt. The size of PSN-PT grown from a flux of PbO-B2O3 is very small, and the composition of the as-grown crystal deviates from the nominal composition. PSN-PT possesses a MPB at compositions of 0.60PSN-0.40PT and 0.575PSN-0.425PT, respectively. The piezoelectric and ferroelectric properties of PSN-PT single crystal near the MPB has still not been investigated fully. The difficulty in growing PSN-PT limits its research. Pure PIN-PT crystal is also very difficult to grow in large sizes. In this chapter, we use a Bridgman method using PMN-PT as seed crystal to grow large size PIN-PT crystal. The piezoelectric properties of the as-grown crystal is comparable with that of PMN-PT and PZN-PT near the MPB, but with a much higher Trt and Tc, which give the PIN-PT crystal good temperature stability. Perovskite oxide piezoelectric materials are of great fundamental and technological importance since the discovery of ferroelectric PZT ceramics. Among them, single crystals PZN-PT and PMN-PT have been

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the focus for recent decades because of their ultrahigh piezoelectric coefficients and electromechanical coupling factors. They are promising materials for the next generation of ultrasonic transducers and high-strain actuators. Now many research studies on piezoelectric devices based on PMN-PT and PZN-PT crystal have been carried out. However, there are still a number of technical challenges to overcome before PMN-PT and PZN-PT can be widely applied in commercial piezoelectric devices. These technical challenges include the facts that PZN-PT and PMN-PT single crystals are difficult to grow in large sizes by flux, and the crystals are very expensive. To minimize this and reduce the cost, the Bridgman method should replace the flux technique. However, due to the compositional gradient associated with Bridgman growth, single crystal properties vary along the growing axis which causes variation of properties from wafer to wafer, and even within one wafer. From an application point of view, the property variations between wafers make the single crystal difficult to use and more expensive. The variation of properties of the crystals in manufacturing is the most serious issue. To solve this problem, crystal growers should use a combination of zone melting technique with the Bridgman technique. Also SSCG techniques to grow PMN-PT crystals or aligned polycrystalline materials is an effective method. Commercial crystal could be realized for PZN-PT or PMN-PT at commercial sources: TRS Ceramics, JFE Mineral Company, Morgan Electro Ceramics, H.C. Materials Corporation, Kawatetsu Mining Co. Ltd. Research Lab., Shanghai Institute of Ceramics, etc. A further technical challenge is that the relatively low elastic stiffness and phase transition temperature make the crystals susceptible to outer mechanical condition and temperature. Their piezoelectric performance degrades in bonded condition or under high-compressive preloads. Also the low Trt limits their application in piezoelectric devices and the temperature range of operation. Low coercive electric field is another disadvantage. To broaden the application field for relaxor crystal, crystal with high-Curie temperature, phase transition and coercive field should be paid much more attention. Large size PSN-PT, PYN-PT, PIN-PT and Bi (Me)O3-PbTiO3 (Me ¼ Sc3+, In3+, Yb3+) binary systems should be grown by an improved method. To reduce the growth difficulty of high-Curie crystal, ternary system complex with PMN such as PMN-PIN-PT, PMN-PSN-PT should also be developed. In summary, relaxor-PT single crystals have a bright future in the next generation of piezoelectric devices.

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71. Damjanovic D, Budimir M, Davis M, Setter N. Monodomain versus polydomain piezoelectric response of 0.67Pb(Mg1/3Nb2/3)O3–0.33PbTiO3 single crystals along nonpolar directions. Appl Phys Lett 2003;83:527. 72. Li T, Scotch AM, Chan H, Harmer M, Park S, Shrout T, et al. Single crystals of Pb(Mg1/3 Nb2/3)O3–35 mol%PbTiO3 from polycrystalline precursors. J Am Ceram Soc 1998;81:244. 73. Messing G, Trolier-McKinstry S, Sabolsky E, Duran C, Kwon S, Brahmaroutu B, et al. Templated grain growth of textured piezoelectric ceramics. Crit Rev Solid State Mater Sci 2004;29:45. 74. Kim M, Fisher J, Kang S. Grain growth control and solid-state crystal growth by Li2O/ PbO addition and dislocation introduction in the PMN–35PT system. J Am Ceram Soc 2006;89:1237–43. 75. http://www.ceracomp.com/. 76. Zhang S, Ru X, Lebrun L, Anderson D, Shrout TR. Piezoelectric materials for high power, high temperature applications. Mater Lett 2005;59:3471–5. 77. Eitel R, Randall CA, Shrout TR, Rehrig P, Hackenberger W, Park S-E. New high temperature morphotropic phase boundary piezoelectrics based on Bi(Me)O3–PbTiO3 ceramics. Jpn J Appl Phys 2001;40:5999–6002. 78. Smolenskii GA, Isupov VA, Agranovskaya AI. New ferroelectrics of complex composi3+ 5+ tion of the type A+2 2 (BI BII )O6. Sov Phys Solid State 1959;1:150–1. 79. Edward FA, Bhalla AS. High strain and low mechanical quality factor piezoelectric Pb [(Sc1/2 Nb1/2) 0.575Ti0.425]O3 ceramics. Mater Lett 1968;35:199–201. 80. Tennery VJ, Huang KW, Novak RE. Ferroelectric and structural properties of the Pb (Sc1/2Nb1/2)1-xTixO3 system. J Am Ceram Soc 1968;51:671–4. 81. Yamashita Y, Harada K. Crystal growth and electrical properties of lead scandium niobate-lead titanate binary single crystals. Jpn J Appl Phys 1997;36:6039–42. 82. Bing YH, Ye Z-G. Effects of chemical compositions on the growth of relaxor ferroelectricPb(Sc1/2Nb1/2)1-xTixO3 single crystals. J Cryst Growth 2003;250:118–25. 83. Rajasekaran SV, Singh AK, Jayavel R. Growth and morphological aspects of Pb[(Sc1/2 Nb1/2)0.58Ti0.42]O3 single crystals by slow-cooling technique. J Cryst Growth 2008;310:1093–8. 84. Guo Y, Xu H, Luo H, Xu G, Yin Z. Growth and electrical properties of Pb(Sc1/2Nb1/2)O3– Pb(Mg1/3Nb2/3)O3–PbTiO3 ternary single crystals by a modified Bridgman technique. J Cryst Growth 2001;226:111–6. 85. Hosono Y, Harada K, Yamashita Y, Dong M, Ye Z-G. Growth, electric and thermal properties of lead scandium niobate-lead magnesium niobate-lead titanate ternary single crystals. Jpn J Appl Phys 2000;39:5589–92. 86. Bing Y-H, Ye Z-G. Growth and characterization of relaxor ferroelectric (1-x)Pb(Sc1/2 Nb1/2)O3–xPbTiO3 single crystals, In: Proceedings of the 13th IEEE international symposium on applications of ferroelectrics; 2002. 87. Kodama U, Osada M, Kumon O, et al. Piezoelectric properties and phase transition of Pb (In1/2Nb1/2)O3–PbTiO3 solid solution ceramics. Am Ceram Soc Bull 1969;48:1122–4. 88. Yasuda N, Ohwa H, Hasegawa D, Hayashi K, Hosono Y, Yamashita Y. Temperature dependence of piezoelectric properties of a high Curie temperature Pb(In1/2Nb1/2) O3-PbTiO3 binary system single crystal near morphotropic phase boundary. Jpn J Appl Phys 2000;39:5586–8. 89. Duan Z, Xu G, Wang X, Yang D. Growth and electrical properties of Pb(In0.5Nb0.5)O3– PbTiO3 crystals by the solution Bridgman method. J Cryst Growth 2004;275:1907–11. 90. Guo Y, Luo H, He T, Yin Z. Peculiar properties of a high Curie temperature Pb(In1/2Nb1/2) O3–PbTiO3 single crystal grown by the modified Bridgman technique. Solid State Commun 2002;123:417–20. 91. Duan Z, Xu G, Wang X, Yang D, Pan X, Wang P. Electrical properties of high Curie temperature (1–x)Pb(In1/2Nb1/2)O3–xPbTiO3 single crystals grown by the solution Bridgman technique. Solid State Commun 2005;134:559–63.

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92. Ko B, Jung J, Lee S. Design of a slim-type optical pick-up actuator using PMN-PT bimorphs. Smart Mater Struct 2006;15:1912–8. 93. Yasuda N, Hidehiro O, Kume M, Yamashita Y. Piezoelectric properties of a high Curie temperature Pb(In1/2Nb1/2)O3–PbTiO3 binary system single crystal near a morphotropic phase boundary. Jpn J Appl Phys 2000;39:L66–8. 94. Guo Y, Luo H, He T, Pan X, Yin Z. Electric-field-induced strain and piezoelectric properties of a high Curie temperature Pb(In1/2Nb1/2)O3–PbTiO3 single crystal. Mater Res Bull 2003;38:857–64. 95. Yasuharu H, Yohachi Y, Kentaro H, Nobory I. Dielectric and piezoelectric properties of Pb [(In1/2Nb1/2)0.24(Mg1/3Nb2/3)0.42Ti0.34]O3 single crystals. Jpn J Appl Phys 2005;44:7037–41. 96. Wada S, Suzuki S, Noma T, et al. Enhanced piezoelectric property of barium titanate single crystals with engineered domain configurations. Jpn J Appl Phys 1999;38:5505–11. 97. Park S-E, Wada S, Cross LE, Shrout TR. Crystallographically engineered BaTiO3 single crystals for high-performance piezoelectrics. J Appl Phys 1999;86:2746–50. 98. Fu H, Cohen RE. Polarization rotation mechanism for ultrahigh electromechanical response in single-crystal piezoelectrics. Nature 2000;403:281–3. 99. Feng Z, Luo H, Yin Z, Guang C, Ling N. High electric-field-induced strain of Pb(Mg1/3Nb2/3) O3–PbTiO3 crystals and their application in multilayer actuators. Appl Phys A 2005;81:1245–8. 100. Jiang X, Rehrig PW, Hackenberger WS, et al. Advanced piezoelectric single crystal based actuators. Proc SPIE 2005;5761:253. 101. Woody S, Smith S, Jiang X, Rehrig P. Performance of single-crystal Pb(Mg1/3Nb2/3)–32% PbTiO3 stacked actuators with application to adaptive structures. Rev Sci Instrum 2005;76:075112. 102. http://www.kcftech.com. 103. Chen J, Panda R. Review: commercialization of piezoelectric single crystals for medical imaging applications, In: Ultrasonics symposium, 2005 IEEE, vol. 1; 2005. p. 235–40. 104. Saitoh S, Kobayashi T, Harada K, Shimanuki S, Yamashita Y. Forty-channel phased array ultrasonic probe using 0.91Pb(Zn1/3Nb2/3)O3–0.09PbTiO3 single crystal. IEEE Trans Ultrason Ferroelectr Freq Control 1999;46:152–7. 105. Saitoh S, Kobayashi T, Harada K, Shimanuki S, Yamashita Y. A 20 MHz single-element ultrasonic probe using 0.91Pb(Zn1/3Nb2/3)O3–0.09PbTiO3 single crystal. IEEE Trans Ultrason Ferroelectr Freq Control 1998;45:1071–6. 106. Cheng K, Chan H, Choy C, Yin Q, Luo H, Yin Z. Single crystal PMN-0.33PT/epoxy 1–3 composites for ultrasonic transducer applications. IEEE Trans Ultrason Ferroelectr Freq Control 2003;50:1177–83. 107. Sung M, Jung H, Lee K. Multilayer PMN-PT single crystal transducer for medical application, In: Ultrasonics symposium, 2004 IEEE, vol. 2; 2004. p. 1021–4. 108. Ritter T, Geng X, Shung K, Lopath K, Park S, Shrout T. Single crystal PZN/PT-polymer composites for ultrasound transducer applications. IEEE Trans Ultrason Ferroelectr Freq Control 2000;47:792–800.

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C H A P T E R

8 Electroactive Polymers as Actuators Y. Bar-Cohen Jet Propulsion Lab, Pasadena, CA, United States

Revised by V.F. Cardoso*,a, C. Ribeiro*,a, S. Lanceros-M
endez*,†,‡ *University of Minho, Braga, Portugal † BCMaterials, Derio, Spain ‡ Ikerbasque, Bilbao, Spain

Abstract Electroactive polymers (EAP) are actuators that most closely emulate biological muscles compared to any other actuators that are human-made; therefore they earned the moniker “artificial muscles.” The materials that were developed in the early days of this field generated limited actuation strain and therefore received relatively little attention. However, over the last years a series of EAP materials has emerged that exhibits a significant shape change in response to electrical stimulation. Their capability allowed the production and demonstration of various exciting and novel mechanisms including robot fish, catheter steering elements, miniature grippers, loudspeakers, fishlike blimps, and dust-wipers. Novel applications such as microfluidic systems and tissue engineering have also emerged. The impressive advances in improving their actuation strain are attracting the attention of many engineers and scientists from many different disciplines. These materials are particularly attractive to biomimetic applications since they can be used to make biologically inspired intelligent robots and other mechanisms. Increasingly, EAP-actuated mechanisms are being engineered with large application potential. This chapter reviews the state of the art, challenges, and potential applications of EAP materials. a

Equal contribution.

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Keywords: EAP, Electroactive polymers, Polymer actuators, Robotics, Artificial muscles, Biomimetics, Biologically inspired technologies, Tissue engineering, Microfluidic.

8.1 INTRODUCTION Polymers are inherently lightweight, easy to process and to mass produce, as well as mechanically flexible, making them highly attractive for numerous applications. In response to stimulation, some polymers sustain change in properties adding significant advantages to their use. For many years, mechanically responsive polymers were known to vary in shape or size when subjected to electric, chemical, pneumatic, optical, or magnetic fields. Electrical excitation is one of the most sought after stimulation methods for causing elastic deformation in polymers. The convenience and practicality of their electrical stimulation and recent response improvements made electroactive polymers (EAPs) the most preferred among the activatable polymers.1 An added benefit of EAP materials is that some of these polymers also exhibit the reverse effect of converting mechanical strain to electrical signals. This makes them useful for sensors and energy harvesting mechanisms. Today, there are many known EAP materials and, according to their activation mechanism, they can be classified into electronic (also known as the fieldactivated) and ionic EAP.1 One of the main applications of EAP materials is their use for biologically inspired applications, a field known as biomimetics.2–5 Being a relatively new material, there is still a need to establish the proper scientific and engineering foundations of the field of EAP to allow turning them into actuators-of-choice. This involves improving the understanding of the basic principles that drive them. Some of the necessary scientific foundations involve having effective computational chemistry models, comprehensive material science, electromechanics analytical tools, and material processing techniques. The development of the foundations requires gaining better understanding of the parameters that control their electro-activation behavior. In order to maximize the actuation capability and operational durability, effective processing techniques are being developed for their fabrication, shaping, and electroding.6,7 Methods of reliably characterizing the response of EAP materials are being developed and efforts are underway to create databases with documented material properties. To bring these materials to the level of application in daily use, products will necessitate finding niches that address critical needs.

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8.2 HISTORICAL REVIEW The first documented study of EAP materials was conducted in 1880 by Roentgen. In his experiment he used a rubber band subjected to an electric field across the fixed end and a mass attached to the free end.8 This experiment was followed by Sacerdote in 1899,9 who formulated the strain response to electric field activation. A subsequent progress milestone was recorded in 1925 by Eguchi,10 who discovered a piezoelectric polymer called electret when carnauba wax, rosin, and beeswax were cooled to solidify while being subjected to a DC bias field. Electrets are insulation materials (mostly polymers) that can hold electric charges after being polarized in an electric field. They generate voltage when subject to stress and also have the reverse behavior of being deformed under an electric field. However, their output strain is generally very low for application as actuators and therefore their use has been limited to sensors.11,12 Only about 40 years later, in 1969, was another breakthrough reported, when Kawai observed a substantial piezoelectric activity in uniaxially drawn and poled poly(vinylidene fluoride) (PVDF or PVF2).13 This breakthrough was preceded by Fukada’s work on piezoelectric biopolymers.14 Subsequent investigations of PVDF and its copolymers have shown that some noncrystalline polymers with very large dielectric relaxations exhibit strong electromechanical activity due to the orientation of molecular dipoles.6,15 In the last decades extensive research and development related to PVDF-based materials have been carried out where, in parallel to the efforts to improve the performance and processing of the materials, they have been successfully applied in many distinct areas such as tissue engineering,4 drug delivery systems,16 energy harvesting and storage,17 microfluidics,18 and, most often, as sensors and actuators.19,20 Further, green chemistry approaches are being developed in order to achieve environmentally friendlier PVDF-based sustainable technologies.21 The success in developing and applying PVDF was followed with an extensive search for other polymer systems that exhibit relevant electroactive response, including piezoelectric biopolymers4,22,23 and composite systems.24–26 With respect to dielectric elastomer EAP materials, they generate strain levels that have even exceeded 100% with a relatively fast response speed (10 V/μm) are required, which may be close to the breakdown level. The required high activation field is the result

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of the relatively low dielectric constant in polymers, which typically is below 10. To address this issue two different approaches are used: • making multilayered structures of thin films that are stacked to reach the required thickness (this is a method that is commonly used in piezoelectric ceramic actuators) • increasing the dielectric constant by forming a composite Since the actuation does not involve diffusion of charge species, these EAP materials respond quickly in the range of milliseconds. Examples of these materials include electrostrictive, electrostatic, piezoelectric, and ferroelectric materials. Generally, the electronic EAP materials can be made to hold the induced displacement while operated under a DC voltage, allowing them to be considered for robotic applications with high efficiency.35 The electronic EAP materials have a greater mechanical energy density and they can be activated in air with no major constraints. The generated displacement in both the electronic and ionic EAP materials can be designed geometrically to bend, stretch, or contract. For example, in the case of linear strain an EAP material bonded to a passive film acts as a bimorph that bends in response to electric stimulation. Generally, the bending that is produced by EAP materials involves low force, and due to their low modulus they generate low moments and torques. 8.3.1.1 Ferroelectric Polymers The property of piezoelectricity is found in noncentrosymmetric materials. The phenomenon is called ferroelectricity when a nonconducting crystal or dielectric material exhibits spontaneous electric polarization that can be reversed by the application of an external electric field. Piezoelectricity was discovered in 1880 by Pierre and Paul-Jacques Curie, who found that a voltage is produced on the surface of the crystal when certain types of crystals such as quartz, tourmaline, and Rochelle salt are compressed along certain axes. The Curie brothers followed this discovery a year later with the observation of the reverse effect that, upon application of an electric voltage, these crystals sustain an elongation. There are also polymers with ferroelectric behavior and the most widely exploited one is PVDF, and its copolymers.6,15 These polymers are partly crystalline, with an inactive amorphous phase, having a Young’s modulus near 1-10 GPa. While, as mentioned earlier, PVDF exhibits piezoelectric behavior with the strain related linearly to the electric field that generates it, the strain response of electrostrictive materials is quadratic with the field.27 This relatively high elastic modulus provides a high mechanical energy density. Generally, PVDF generates strain levels of about 0.1% and a pressure level of about 5 MPa, where under large electric field (200 V/μm) its copolymers can generate a strain that is nearly 2%.1 However, this field level is

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dangerously close to dielectric breakdown, and the dielectric hysteresis is very large. In 1998, Zhang and his coinvestigators introduced defects into the crystalline structure using electron radiation to increase the dielectric constant of the copolymer P(VDF-TrFE).36 The resulting material generates strains as large as 5% and levels of pressure of about 45 MPa under voltages of about 150 V/μm. The drawback to the irradiation is the introduction of many undesirable defects including the formation of crosslinkings and chain scission.37 This issue was addressed by producing terpolymers via molecular design that enhances the degree of conformational changes at the molecular level in the polymer. The resulting terpolymer generates a greater electromechanical response than the high energy electron irradiated copolymer.34 The formation of composites as an approach for increasing the dielectric constant has also been effectively applied. Zhang and his coinvestigators (2004) used an all-organic composite that consists of particulates having a high dielectric constant (K > 10,000).38 For a CuPc-PVDF-based terpolymer composite having an elastic modulus of 750 MPa, the particulates increased the dielectric constant from single digits to the range from 300 to 1000 (at 1 Hz). Further, under a field of 13 V/μm, a strain of 2% and pressure level of 7.5 MPa is generated. Photographs of such a composite ferroelectric EAP in passive and activated states are shown in Fig. 8.1. PZT,39 BaTiO3,40 BCZT,41 CaCu3Ti4O12,42 carbon nanofibers,43 and carbon nanotubes (CNTs)44 are other examples of fillers used to increase the dielectric constant of PVDF-based materials. 8.3.1.2 Dielectric Electroactive Polymers Discovered in the early 1990s,45 these kinds of polymers present low elastic stiffness with high dielectric breakdown strength when they are subjected to an electrostatic field generating a large strain and acting as EAP materials. These materials are known as dielectric elastomer EAP and can be represented by a parallel plate capacitor as shown schematically in Fig. 8.2. To avoid impeding the generated high strain it is necessary to use highly compliant electrodes such as conductive carbon grease. Dielectric elastomers offer good performance in a large range of applications including actuators, sensors, and generators.7 A 1992–93 study by Pelrine and his co-investigators46–48 led to the first observation of the fact that dielectric elastomers sustain large strain (23% in silicone films) when subjected to a high electric field. In their reports they suggested the use of dielectric EAP materials for actuation mechanisms. Independently, in 1994, Zhenyi and his co-investigators reported that they measured a 3% strain in polyurethane when subjected to a 20 V/μm electric field.49 Significant levels of strain started to be observed in the years that followed, where in 1998 a level of strain of 30% was reported being measured in silicone47 . A major milestone in the

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FIG. 8.1 Photographs of a composite ferroelectric EAP in passive (left) and activated states (right). This EAP material was provided to the author courtesy of Qiming Zhang, Penn State University.

Dielectric elastomer + Electrode

– Electrode

FIG. 8.2 Under electroactivation, a dielectric elastomer with compliant electrodes on both surfaces expands laterally and can be made to operate longitudinally.

development was documented in 2000 when using acrylic as an elastomer and preload; Pelrine and his co-investigators reported strains that are much higher than 100%.27 Today, there are many researchers who are using dielectric elastomers as EAP materials, and significant progress has been made towards making practical actuators.34,50,51 Application of an electric field results in a strain that is proportional to the square of the electric field and to the dielectric constant while inversely proportional to the elastic modulus. Practically, to apply the required electric field at the levels of 100 V/μm and above, it is necessary to use thin films. Dielectric elastomer EAP actuators can generate significant levels reaching more than 100% strain. The applied field causes thickness contraction and lateral expansion. To produce linear actuators using dielectric elastomer films, scientists at SRI International rolled two elastomer layers

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FIG. 8.3 A dielectric elastomer EAP-based multifunctional electroelastomer roll (MER) spring roll. Courtesy of Qibing Pei, UCLA, Roy Kornbluh, SRI International, and SPIE; Adapted from Pei Q, et al. Multifunctional electroelastomer rolls and their application for biomimetic walking robots; 2002 and Kornbluh R, et al. Electroelastomers: applications of dielectric elastomer transducers for actuation, generation and smart structures, In: Proceedings of SPIE—The International Society for Optical Engineering; 2002.

with carbon-based electrodes on both sides of one of the layers, forming a cylindrical actuator.50 Further modifications of their actuator design led to the development of the multifunctional electroelastomer roll (MER). In this actuator (Fig. 8.3) highly prestrained dielectric elastomers are rolled around a compression spring.52 By selectively actuating only certain regions of electrodes around the periphery of the actuator, the actuator can be made to bend as well as elongate. The required voltages for the activation of dielectric elastomers are close to the breakdown strength of the material, and a safety factor that lowers the actuator potential is used. Another concern associated with the use of such EAP materials is the required prestraining that over time is released due to creep degrading the actuator performance. A method was developed that has shown promise with regard to eliminating the need for prestrain.53,54 An interpenetrating polymer network (IPN) where tension in the network is balanced by compression was also developed.54 To form an IPN thermally crosslinkable liquid, additives were used including a difunctional acrylate (e.g., HDDA) and a trifunctional acrylate (e.g., TMPTMA). Alternatively, using a folded film structure, a contractile

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Dielectric elastomer Compliant elastomer Dielectric elastomer ΔV

FIG. 8.4 A contractile EAP actuator using a folded film structure. Courtesy of Federico Carpi, University of Pisa, Italy.

FIG. 8.5 Photographs of multilayered dielectric elastomer in passive (left) and activated € states (right). Courtesy of Gabor Kovacs, EMPA Dubendorf, Switzerland.

actuator was produced that does not require prestrain (Fig. 8.4). Also, a method of stacking thousands of thin layers of a dielectric elastomer to form an effective actuator that generates contraction and does not require preload was developed (Fig. 8.5). Using this design, levels of 40% strain were measured using up to a 40-mm diameter and 100-mm long actuator, and it generated as high as 250 N contractile force.55 Further, a dielectric elastomer film that was designed in wavy configuration along the thickness led to a process that is easy to mass produce. Actuators frabricated from this configuration are capable of lifting and pushing levels of kilograms (Fig. 8.6).56

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FIG. 8.6 A dielectric elastomer with wavy shape film made by PolyPower, Danfoss, Denmark, is shown lifting 10 kg (the cylinders).

8.3.1.3 Electrostrictive Graft Elastomers Graft-elastomer EAP is a polymer that exhibits electrostriction behavior when subjected to a large electric field, and it can generate strain levels of about 4% and stress levels of about 24 MPa.38,57 This electronic EAP material offers relatively high electromechanical power density and, compared to the ferroelectric EAP, is relatively easy to process. Grafted-elastomer EAP was developed,57 consisting of two components: a flexible backbone macromolecule and a grafted polymer that can form a crystalline structure (see Fig. 8.7). The grafted crystalline polar phase provides moieties in response to an applied electric field and cross-linking sites for the elastomer system.

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Flexible backbone

Graft polymer

FIG. 8.7 Structure and morphology of the graft elastomer EAP. Courtesy of Ji Su, NASA LaRC, VA.

FIG. 8.8 An electrostrictive grafted elastomer-based bimorph actuator in an unexcited state (left) and in one of the two directions of the excited state (right). Courtesy of Ji Su, NASA LaRC, VA.

A combination of the electrostrictive-grafted elastomer with a piezoelectric poly(vinylidene fluoride-trifluoroethylene) copolymer yields several compositions of a ferroelectric-electrostrictive molecular composite system.58 Such a combination can be operated both as a piezoelectric sensor and electrostrictive actuator.59 Careful selection of the polymer composition allows for the creation and optimization of a molecular composite system with respect to its electrical, mechanical, and electromechanical properties.60 A photographic view of an activated grafted elastomer-based bimorph actuator is shown in Fig. 8.8, where on the left an unexcited state is shown while on the right it is shown in an excited state.

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8.3.2 Ionic EAP Ionic EAP materials consist of two electrodes and an electrolyte, and their mechanism of activation involves transport or diffusion of ions.61 Therefore, a particularity of this type of materials is that they must be operated in a wet state or in solid electrolytes. Examples of these materials include ionomeric polymer-metal composites (IPMC), conductive polymers (CPs), CNTs, and ionic polymer gels (IPG). Their advantages include the large bending under low activation voltage (1–10 V), which is extremely attractive for applications such as microelectromechanical systems and smart materials and systems.62–64 Nonetheless, ionic EAPs feature a relatively low efficiency in the range of 1%, and they have difficulty sustaining constant displacement under activation of a DC voltage (except for CPs). The diffusion or macroscopic motion of ions is responsible for the slow speed of actuation of these materials, which is the range of tens to a fraction of a second. 8.3.2.1 Ionomeric Polymer-Metal Composites (IPMC) IPMC is an ionic EAP that bends in response to an electrical activation (Fig. 8.9) as a result of mobility of cations in its polymer network.61,65,66 A relatively low voltage stimulates the bending of IPMC, where the base polymer provides channels for mobility of positive ions in a fixed network of negative ions on interconnected clusters.67,68 Electrodes on the surface are used to supply the required electrical field and the polarity determines the direction of bending and even a fraction of a volt leads to a response. Two types of base polymers are widely used to produce an IPMC: perfluorosulfonate that is also known as Nafion (DuPont, United States) and perfluorocarboxylate, which is also known as Flemion (Asahi Glass, Japan). An illustration of the principle of activation of a Nafion-based IPMC is shown in Fig. 8.10. In order to electrode the polymer films, metal ions (platinum, gold, etc.) are dispersed throughout the hydrophilic regions of the polymer surface and are subsequently reduced to zerovalence metal atoms.69 The ionic content of IPMC determines its electromechanical response.65 The response of IPMC is relatively slow ( 2800; 10 μF/1206; 300 total layers with 3 μm each) by magic ion (Dy and Ho) doping.

Ni Pb NiTiO3

TiO2 NiO2 Condensed phases (mol ratio)

Condensed phases (mol ratio)

11.4.3.2 Cu-Embedded Cofired PZT ML Actuators The situation is different for Pb-containing ceramics from BT-based ceramics; that is, Cu should be chosen rather than Ni. Fig. 11.19A and B compare thermodynamic calculations for PbTiO3 and (A) Ni and (B) Cu electrodes, based on the Ellingham diagram. When Ni is used as an electrode, 15% of Ni becomes NiO at the sintering temperature of 1000°C (1300 K). In contrast, when Cu is used as an electrode, only 0.2% of Cu becomes Cu2O. This calculation clearly indicates that Cu should be used for the internal electrode of Pb-included PZT-based materials. The reader is requested to try similar thermodynamic calculations on the stability of Ni and Cu for BaTiO3. The results should indicate the suitability of Ni for BT. An innovative fabrication technique has been developed by Morgan Electroceramics, which involves incorporating a copper (Cu) internal electrode in a PZT ML actuator.14 The PZT and Cu electrode materials are cofired. Ordinarily the sintering temperature of PZT is too high to allow for cofiring with a Cu electrode. The sintering temperature of the PZT used in these structures is reduced to 1015°C by adding excess PbO. Special measures are taken to optimize the cofiring process. The oxygen (O2) pressure is precisely regulated by sintering in a nitrogen (N2) atmosphere (1010 atm). The pieces are also fired in a special sintering sand, which is essentially a mixture of the Cu and PZT powders. This helps to inhibit the oxidation of the Cu electrode during firing.

1

0.1

0.01 500

(A)

1000 Temperature (K)

Cu PbTiO3

TiO2 Cu2O

1

0.1

0.01

0.001

1500

500

(B)

1000 1500 Temperature (K)

FIG. 11.19 (A) Thermodynamic calculation on PbTiO3 + Ni: closed volume and (B) thermodynamic calculation on PbTiO3 + Cu: closed volume.

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FIG. 11.20

441

A PZT multilayer actuator with Cu internal electrodes cofired at 1015°C.14

A four-layer PZT actuator (with layer thickness of 25 μm) fabricated by this method is pictured in Fig. 11.20. The Penn State group developed practically two piezoceramic compositions with low sintering temperatures based on a commercially available hard piezoceramic (APC 841). When 1.1wt% ZnO was incorporated with 0.2wt% CuO or 0.2wt% Li2CO3, the sintering temperature of the APC 841-based piezoceramic composition was decreased to 1000°C or below without creating any significant secondary phases. Both piezoceramic compositions showed high-power application potential: a mechanical quality factor (Qm) around 1000, electromechanical coupling factors (kp) between 0.45 and 0.65, and piezoelectric coefficients of 280–300 pC/N. Because Li2CO3-modified APC 841 piezoceramics show lower dielectric loss (tan δ ¼ 0.4%) than that of CuO-modified piezoceramics (tan δ ¼ 1.7%), Li2CO3-modified piezoceramics seem to be more promising for highpowered application potential. The Penn State group developed Cu and pure-Ag embedded ML piezotransformers (Fig. 11.21A), which were sintered at 900°C in a reduced atmosphere with N2, as illustrated in Fig. 11.21A.15 Ring-dot disk ML

UHP N2, pO2=10−6 atm.

Fe3O4 (s)

(A)

Al (s)

PbO (s)

(B)

FIG. 11.21 (A) Experimental setup for sintering Cu-electrode-embedded multilayer transformers in a reduced N2 atmosphere and (B) multilayer cofired transformer with hard PZT and Cu (left) or pure Ag (right) electrode, sintered at 900°C (Penn State trial products).15

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types (OD ¼ 27, Center Dot D ¼ 14 mm) with Cu and Ag/Pd (or Ag/Pt) (as references) revealed the maximum power density (at 20°C temperature rise) 42 and 30 W/cm3, respectively. This big difference comes from the poor electric conductivity of Pd or Pt, compared to Cu or pure Ag. Note that the power density depends not only on the piezoceramic composition, but also on the choice of electrode material in a ML design.

11.4.4 ML Actuators With Ceramic Electrodes Mechanical weakness at the junction between the ceramic and the electrode metal often gives rise to delamination problems. One solution to this problem has been to make a more rigid electrode by mixing the ceramic powder of the composition used for the actuator material with the metal electrode paste. Abe, Uchino, and Nomura examined some of the more popular conducting ceramic materials as electrodes in ML ceramic actuators.16

11.4.4.1 Ceramic Electrodes The most attractive ceramic electrode materials are conducting or semiconducting perovskite oxides because of their compatibility with the crystal structure of the actuator ceramics. Among the conducting ceramics Sr(Fe,Mo)O3, (La,Ca)MnO3, and Ba(Pb,Bi)O3 (which is actually a superconductor) are considered the best, but their conductivity is dramatically reduced when they are sandwiched between the lead-based ceramic layers and sintered. One of the few successful structures utilizing a ceramic conductor is a unimorph device comprising a piezoceramic and a Ba(Pb,Bi)O3 fabricated by hot-pressing. Semiconducting BaTiO3-based ceramics with a positive temperature coefficient of resistivity also appear to be promising alternative electrode materials for these structures. In general, good ceramic electrode materials should possess the following characteristics: (1) high conductivity (2) sintering temperature and shrinkage similar to that of the piezoelectric ceramic (3) good adhesion with the piezoelectric ceramic (4) slow diffusion into the piezoelectric ceramic during sintering The last characteristic is perhaps the most critical and the ultimate success of the structure will depend on a well-defined interface between the electrode and piezoelectric layers.

II. PREPARATION METHODS AND APPLICATIONS

11.4 ELECTRODE MATERIALS

443

11.4.4.2 Barium Titanate-Based ML Actuator Barium titanate (BaTiO3), which is a ferroelectric with a Curie temperature of 130°C, is known to become electrically conductive when polycrystalline samples are doped with rare-earth ions.16,17 The resistivity of some BaTiO3-based ceramics (with 5 mol% SiO2 and 2 mol% Al2O3) is plotted in Fig. 11.22 as a function of La2O3 concentration. We see from these data that relatively small concentrations of La in the range of 0.1 to 0.25 at% lead to a change in the resistivity of more than 10 orders of magnitude. ML actuators consisting of alternating layers of undoped resistive BaTiO3 and the BaTiO3-based semiconducting composition doped with 0.15 at% La have been fabricated by the tape-casting process. The main advantage in using these materials is that atomic diffusion across the interface between layers during the sintering process tends to be suppressed because the layers are compositionally similar, resulting in a well-defined interface between the actuator and electrode layers. Another beneficial feature of this combination is that the sintering temperature and shrinkage of both materials are almost the same, so that no residual stress is present in the sample after sintering. The fabrication of this structure is also somewhat simpler since it requires no binder burnout process, which is a time consuming step required in the fabrication of devices with metal electrodes. A prototype device of this type has been produced with eight 0.5-mm thick actuator layers of 0.5 mm thickness, sandwiched between 0.25-mm thick electrode layers.16 The mechanical strength of ML samples having an overall plate-like shape with their piezoelectric and ceramic electrode layers perpendicular to the plate, as shown in Fig. 11.23A, has been tested by a three-point bend method.16 Data were also collected for samples of this configuration having FIG. 11.22 The resistivity of BaTiO3-based ceramics (with 5 mol% SiO2 and 2 mol% Al2O3) plotted as a function of La2O3 concentration.16,17

Resistivity (W −cm)

1015

1010

105

100

0

0.1 0.2 0.3 0.4 1/2 La2O3 (atm%)

0.5

II. PREPARATION METHODS AND APPLICATIONS

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11. MULTILAYER TECHNOLOGIES FOR PIEZOCERAMIC MATERIALS

P P/2

P/2 h L

sf = −

Nondestruction probability 1 - p (%)

(A)

b

3PL 2bh2

1 10 30

(Reference)

50 70 90 (Pd electrode)

95

BT semiconductor electrode

99 5

(B)

10

15

20

30

50

70

100

Stress s (MN/m ) 2

FIG. 11.23 Three-point bend testing of multilayer actuators: (A) sample configuration and experimental setup and (B) Weibull plots for the ceramic electrode and metal electrode (reference) structures.16

the same piezoelectric ceramic and palladium (Pd) electrode layers as the test specimens, which served as a reference. Weibull plots for both are shown in Fig. 11.23B. The mechanical strength of the ceramic electrode device is observed to be about 50 MN/m2, which is approximately three to four times higher than that observed for the metal electrode actuator. It is also noteworthy that the Weibull coefficient is generally much larger when the ceramics electrodes are used, indicating that the deviation in fracture strength is much smaller. Fracture was observed to occur mainly at the ceramic-electrode interface for the structures with the metal electrodes, while no such tendency was observed for the ceramic electrode device. The electric field-induced strains measured in the prototype ceramic electrode device are shown in Fig. 11.24A. It was determined in the study of this structure that the longitudinal strain induced in the actuator layers was x3 ¼ 5  104 and the transverse strain x1 ¼  1.2  104. II. PREPARATION METHODS AND APPLICATIONS

445

-500

10

2.0

PZT (E = 16 ¥ 105 [V/m])

8

0.65 PMN−0.35 PT (E = 8.4 ¥ 105 [V/m])

6 x3 [¥ 10-4]

Long, Displacement [mm]

11.5 INNOVATIVE ML STRUCTURES

1.0

0

4 2

E = 15 ¥ 105 [V/m] 10 ¥ 105 [V/m]

0 500 Voltage [V]

(A)

10

20

−2 0 [V/m]

30 X3 ¥ 106 [N/m2]

(B)

FIG. 11.24 (A) Displacement curve for a BaTiO3-based multilayer actuator with ceramic electrodes.16 and (B) uniaxial stress dependence of the strain induced in BaTiO3 for several applied electric field strengths. The typical strain responses of PZT and PMN-PT specimens are also shown for comparison.18

The measured strains are 30% and 60% smaller than the predicted values for the longitudinal and transverse strains, respectively. This reduction effect associated with the strain anisotropy can be reduced by decreasing the thickness of the ceramic electrode layers. The uniaxial stress dependence of the strain induced in BaTiO3 for several applied electric field strengths is shown in Fig. 11.24B. The typical strain responses of PZT and PMN-PT specimens are also shown in the figure for comparison.18 The magnitude of the induced strain in BaTiO3 is not as large as that generated in the lead-based materials, but the generative (blocking) stress (32 MPa or 320 kgf/cm2) level is comparable with those of the PZT and PMN-PT samples mainly due to the relatively small elastic compliance [sE33 ¼ 13  1012 (m2/N)] of BaTiO3.

11.5 INNOVATIVE ML STRUCTURES 11.5.1 Super-Long ML Design A ML actuator incorporating a new interdigital internal electrode pattern has been developed by NEC-Tokin.19 In contrast to devices with the conventional interdigital electrode structure, line electrodes are printed for this modified design on the piezoelectric green sheets (i.e., the printing pattern has an interdigital type), which are stacked so that alternate electrode lines are displaced by one-half pitch. This actuator produces displacements normal to the stacking direction (i.e., in-plane of the PZT sheet) through the longitudinal piezoelectric effect. ML actuators up to 74 mm in length have been manufactured, which can generate longitudinal displacements up to 55 μm. Because both the amount of precious electrode metal and the number of lamination can dramatically be reduced, this design seems to be very cost effective. II. PREPARATION METHODS AND APPLICATIONS

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11.5.2 3D Positioning Stage A three-dimensional positioning actuator with a stacked structure has been proposed by PI Ceramic, Germany, in which both longitudinal and shear strains are induced to generate displacements.20 As shown in Fig. 11.25A, this actuator consists of three parts: the top 10-mm long Z-stack generates the displacement along the z direction, while the second and the bottom 10-mm long X and Y stacks provide the x and y displacements through shear deformation, as the principle is illustrated in Fig. 11.25B. The device can produce 10-μm displacements in all three directions (3D) when 500 V is applied to the 1 mm thick layers.

Z-stack (10 layers) (extension)

X-stack (10 layers) (shear)

Y-stack (10 layers) (shear)

(A)

E

Ps

(B) FIG. 11.25

A three-dimensional positioning actuator with a stacked structure proposed by PI Ceramic: (A) a schematic diagram of the structure and (B) an illustration of the shear deformation.20

II. PREPARATION METHODS AND APPLICATIONS

447

11.6 RELIABILITY/LIFETIME OF ML ACTUATORS

11.6 RELIABILITY/LIFETIME OF ML ACTUATORS 11.6.1 Heat Generation in ML Actuators The Penn State group reported on the heat generation from “soft” PZT-based ML piezoelectric ceramic actuators of various sizes under off-resonance (slow) drive.21 The temperature change was monitored in actuators driven by a large electric field 3 kV/mm and at 300 Hz. Fig. 11.26 shows the saturated temperature plotted as a function of Ve/A, where Ve is the effective volume (electroded portion of the actuator, excluding nonactive PZT volume) and A is the surface area. This linear relation is reasonable because the volume Ve generates the heat through the material’s dielectric loss (intensive loss tan δ0 ) and this heat is dissipated (radiation) through the area A. Thus, if you need to suppress the heat, a small Ve/A is preferred, in other words, flat and hollow cylinder shapes are better than cube and solid rod structures, respectively.

11.6.2 Lifetime Test The effect of aging in ML actuators is manifested clearly by the gradual decrease in its resistance with the number of drive electric field cycles. Ceramic aging is an extremely important factor to consider in the design of a reliable actuator device, although there have been relatively few investigations done to better understand and control it. Aging is associated with two types of degradation: (1) depoling and (2) mechanical failure. Creep and zero-point drift in the actuator displacement are caused by depoling of the ceramic. The strain response is also seriously impaired when the device is operated under conditions of very high electric field, elevated temperature, high humidity, and high mechanical stress. Pure silver (Ag) electrode metal

Temperature rise DT (°C)

120 100 80 60 40 20 0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Ve / A (volume mm3/area mm2)

FIG. 11.26 Temperature rise in ML actuators versus Ve/A (under 3 kV/mm, 300 Hz), where Ve is the effective volume and A is the surface area.20

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448

11. MULTILAYER TECHNOLOGIES FOR PIEZOCERAMIC MATERIALS

is believed to migrate/diffuse into piezoelectric ceramics under high DC electric field, leading to decrease in the ceramic resistance. Therefore, AgPd is used (though expensive) to reduce Ag diffusion by adding Pd. According to Nagata,22 the lifetime of a ML piezoelectric actuator operated under a DC bias voltage can be described by the empirical relationship: tDC ¼ AEn exp ðWDC =kT Þ,

(11.2)

where WDC is an activation energy ranging from 0.99 to 1.04 eV. Measuring the lifetime at an elevated temperature (i.e., accelerated test), we can estimate the lifetime at room temperature of its using temperature.

11.6.3 Health Monitoring Various failure detection techniques have been proposed for implementation in smart actuator devices to essentially monitor their own “health.”23 One such “intelligent” actuator system that utilizes acoustic emission (AE) detection is shown in Fig. 11.27. The actuator is controlled by two feedback mechanisms: position feedback, which can compensate for positional drift and hysteresis, and breakdown detection feedback, which can shut down Actuation Feedback (2) Breakdown detection sensor

Piezoelectric actuator

Feedback (1) Strain sensor

Control voltage

Signal (1)

Signal (2) Computer-controlled power supply

FIG. 11.27 An intelligent actuator system with both position and breakdown detection feedback mechanisms.23

II. PREPARATION METHODS AND APPLICATIONS

11.6 RELIABILITY/LIFETIME OF ML ACTUATORS

449

the actuator system safely in the event of an imminent failure. AE from a piezoelectric actuator driven by a cyclic electric field is a good indicator of mechanical failure. The emissions are most pronounced when a crack propagates in the ceramic at the maximum speed. A portion of this smart piezoelectric actuator is therefore dedicated to sensing and responding to AEs. The AE rate in a piezoelectric device can increase by three orders of magnitude just prior to complete failure. During the operation of a typical ML piezoelectric actuator, the AE sensing portion of the device will monitor the emissions and respond to any dramatic increase in the emission rate by initiating a complete shut-down of the system. Another development by the Penn State group on ML device failure self-monitoring is based on a strain gauge type electrode configuration as shown in Fig. 11.28.24 We embedded the strain gauge type electrode every 10 layers, in practice, by replacing the ground full electrodes. Both the electric field-induced strain and the occurrence of cracks in the ceramic can be detected by closely monitoring the resistance of a strain gauge shaped electrode embedded in a ceramic actuator. The resistance of such a smart device is plotted as a function of applied electric field in Fig. 11.29. The field-induced strain of a “healthy” device is represented by the series of curves depicted in Fig. 11.29A. The resistance “butterfly” curve corresponds to the piezoelectric transverse strain change; shrinkage in the gauge length decreases the gauge resistance (i.e., we can monitor the field induced strain). Each curve corresponds to a distinct number of drive cycles. A gradual decrease in resistance after thousands of times of operation may suggest the generation of a microcrack in the ceramic actuator. Microcracks decrease the resistance and increase the leak current, in general. A sudden decrease in the resistance as shown in Fig. 11.29B is a typical symptom of device failure.

TR6847 High voltage supply

FIG. 11.28 Strain gauge configuration of the internal electrode for an intelligent “health monitoring” actuator.24

II. PREPARATION METHODS AND APPLICATIONS

(A) 39.00

Normal

38.50

Resistance (W)

38.00

37.50

37.00

36.50 Abnormal 36.00

35.50 -100

(B)

Current flow at 60V

0

100

200 Voltage (V)

300

400

500

FIG. 11.29 Resistance change with applied electric field for a smart actuator with a strain gauge-type internal electrode for self-monitoring of potential failure: (A) the electric fieldinduced strain response of a “healthy” device and (B) the response of a failing device.24

II. PREPARATION METHODS AND APPLICATIONS

REFERENCES

451

References 1. Yamashita S. Piezoelectric Pile. Jpn J Appl Phys 1981;20(Suppl. 2–24):93. 2. Uchino K, Nomura S, Cross LE, Newnham RE, Jang SJ. J Mater Sci 1981;16:569. 3. Saito Y, Takao H, Tani T, Nonoyama T, Takatori K, Homma T, et al. Lead-free piezoceramics. Nature 2004;432:84–7. 4. Doshida Y, In: Proceedings of 81st Smart Actuators/Sensors Study Committee, JTTAS, Dec. 11, Tokyo; 2009. 5. Takahashi S, Ochi A, Yonezawa M, Yano T, Hamatsuki T, Fukui I. Internal Electrode Piezoelectric Ceramic Actuator. Jpn J Appl Phys 1983;22(Suppl. 2–22):157. 6. Furuta A, Uchino K. Dynamic Observation of Crack Propagation in Piezoelectric Multilayer Actuators. J Am Ceram Soc 1993;76:1615. 7. Furuta A, Uchino K. Ferroelectrics 1994;160:277. 8. Takahashi S. Actuators. In: Shiosaki T, editor. Fabrication and application of piezoelectric materials. CMC Publications; 1984 [chapter 14]. 9. Takahashi S. Sens Technol 1983;3(12):31. 10. Aburatani H, Uchino K, Furuta A, Fuda Y. In: Proceedings of the 9th international symposium on applications of ferroelectrics; 1995. p. 750. 11. Laurent M, B€ odinger H, Steinkopff T, Lubitz K, Schuh C, Wagner S, et al. In: Proceedings of 14th IEEE international symposium on applications of ferroelectrics ´04, IEEE-UFFC-S, Montreal, Canada, August; 2004. p. 23–7. 12. Ohnishi K, Morohashi T. Production of Multilayer Piezoelectric Actuator Using Bonding Method. J Jpn Ceram Soc 1990;98:895. 13. Kishi H. Mater Integr 2006;19(3):47–51. 14. Groen WA, Hennings D, Thomas M. In: Proceedings of 33rd international smart actuator symposium, State College, PA, April; 2001. 15. Ural S, Park S-H, Priya S, Uchino K. In: Proceedings of 10th international conference on new actuators, Bremen, Germany, June 14-16; 2006. p. 23, 556–8. 16. Abe K, Uchino K, Nomura S. Ferroelectrics 1986;68:215. 17. Saburi O. Properties of Semiconductive Barium Titanates. J Phys Soc Jpn 1959;14:1159. 18. Uchino K, Giniewicz JR. Micromechatronics. New York, NY: CRC/Dekker; 2003. 19. Ohashi J, Fuda Y, Ohno T. Jpn J Appl Phys 1993;32:2412. 20. Banne A, Moller F. In: Proceedings of 4th international conference on new actuators, AXON Tech. Consult. GmbH; 1995. p. 128. 21. Zheng J, Takahashi S, Yoshikawa S, Uchino K, de Vries JWC. J Am Ceram Soc 1996;79:3193. 22. Nagata K. In: Proceedings of 49th Solid State Actuator Study Committee, JTTAS, Japan; 1995. 23. Uchino K, Aburatani H. In: Proeedings of 2nd international conference on intelligent materials; 1994. p. 1248. 24. Aburatani H, Uchino K. In: American Ceramic Society annual meeting proceedings, SXIX-37-96, Indianapolis, April; 1996.

II. PREPARATION METHODS AND APPLICATIONS

C H A P T E R

12 Single Crystal Preparation Techniques for Manufacturing Piezoelectric Materials L.-C. Lim National University of Singapore, Singapore, Singapore

Abstract Recent progresses in high-temperature flux growth of relaxor-PT ferroelectric single crystals with PbO-based fluxes are reviewed. The PT content of the grown crystals, and hence the solution, plays a significant role in the growth mechanism and result. For crystals of low PT contents, such as PZN-PT, the solution is composed of simple ions. By engineering the solution isotherms and the growth conditions to promote near-equilibrium layer growth of the crystal, large crystals of relatively uniform compositions can be readily grown by the flux technique with PbO flux. In contrast, for crystals of high PT content for which ionic complexes are present in the solution (such as PMN-PT–PbO solution), careful control of the flux composition to break up such ionic complexes into simpler ones (e.g., with suitable amounts of B2O3) and the growth conditions is essential to promote layer growth of the crystal for a good growth result. In addition to the solution chemistry, typical problems encountered in the flux growth of relaxor-PT single crystals are described and their causes and remedies briefly discussed. Keywords: Relaxor-PT single crystal, PZN-PT, PMN-PT, Flux growth, Flux compositions, Typical growth problems

12.1 INTRODUCTION Due to their excellent dielectric and piezoelectric properties, the growth and property characterization of lead-based relaxor-PT single crystals, notably lead zinc niobate-lead titanate (Pb(Zn1/3Nb2/3)O3-PbTiO3 or PZN-PT) and lead magnesium niobate-lead titanate (Pb(Mg1/3Nb2/3)O3PbTiO3 or PMN-PT) solid solutions, have been pursued aggressively over Advanced Piezoelectric Materials http://dx.doi.org/10.1016/B978-0-08-102135-4.00012-6

453

Copyright © 2010, Wood head publishing Ltd. All rights reserved.

454

12. SINGLE CRYSTAL PREPARATION TECHNIQUES

the past 15 years. These single crystals display much superior dielectric and piezoelectric properties to state-of-the-art lead zirconate titanate (PZT) ceramics. For instance, while [001]-poled PZN-(6%–7%)PT single crystals exhibit k33
0.92 and d33
2800 pC/N, PMN-28%PT single crystals give k33
0.90 and d33
2000 pC/N. 1–8 Very high transverse piezoelectric properties were also reported for [0 1 1]-poled crystals, giving k32
0.92 and d32
(3200–4000) pC/N for PZN-(6%–7%)PT and k32
0.90 and d32
 2200 pC/N for PMN-28%PT single crystals.7–15 Furthermore, these single crystals have relatively high elastic compliances16–21 and hence low sound velocities.22,23 They are thus candidate materials for future high-performance piezoelectric devices. Unlike PZT materials, most lead-based relaxor-PT single crystals can be grown readily using the high-temperature flux techniques from PbObased fluxes. However, there have been many technological hurdles in growing large-size relaxor-PT single crystals for commercial exploitation. This chapter reviews the recent developments in the flux growth of leadbased relaxor-PT single crystals, focusing on the growth of large-size highquality PZN-PT and PMN-PT single crystals. The flux growth of relaxor single crystals was pioneered by Myl’nikova and Bokov24–26 in the late 1950s. They successfully synthesized monocrystals of PbMg1/3Nb2/3O3 (PMN), PbZn1/3Nb2/3O3 (PZN), PbNi1/3Nb2/3O3 (PNiN), PbCo1/3Nb2/3O3 (PCoN), PbMg1/3Ta2/3O3 (PMT), PbNi1/3Ta2/3 O3 (PNiT) and PbCo1/3Ta2/3O3 (PCoT) by the solution growth technique with PbO flux. About a decade later, Nomura et al.27,28 succeeded in growing single crystals of PbZn1/3Nb2/3O3-PbTiO3 (PZN-PT) solid solution over the whole composition range by the same technique. In 1982, Kuwata et al.1 investigated the dielectric and piezoelectric properties of single crystals of PZN-9%PT and reported that samples poled along the [001] crystal axis exhibited anomalously high piezoelectric coefficients and electromechanical factors (d33 ¼ 1500 pC/N and k33 ¼ 0.92). In 1990, Shrout et al.2 successfully synthesized PbMg1/3Nb2/3O3-PbTiO3 (PMN-PT) solid solution single crystals from high temperature solution with PbO-B2O3 fluxes. By the mid 1990s, systematic studies on the growth of PZN-PT and PMN-PT single crystals had been performed by Saitoh et al.,29 Park et al.,30–32 and Kobayashi et al.33,34, respectively. By then, the size of the crystals obtained was sufficiently large to enable detailed property evaluation of the material. In 1997, Park and Shrout3–5 published a series of papers detailing the superior dielectric and piezoelectric properties of single crystals of PZN-PT and PMN-PT of near-morphotropic phase boundary compositions. Their work has created a renewed interest worldwide in growing large-size relaxor-PT single crystals as well as in their applications in high-performance piezoelectric devices such as ultrasound medical imaging probes, sonar for underwater communications and imaging, high-power-density and high-sensitivity sensors and actuators, etc.

II. PREPARATION METHODS AND APPLICATIONS

12.2 FLUX GROWTH OF PZN-PT SINGLE CRYSTALS

455

Tables 12.1–12.3 list the earlier developments in the flux growth of PZN-PT, PMN-PT and other lead-based relaxor-PT single crystals, respectively. Since 1998, the present author has been involved in relaxor crystal growth, focusing on the growth of large-size high-homogeneity PZN-PT and PMN-PT single crystals using the high-temperature flux technique. In what follows, typical flux growth processes for PZN-PT and PMNPT single crystals are presented and discussed. Various commonly encountered problems concerning the subject matter are described.

12.2 FLUX GROWTH OF PZN-PT SINGLE CRYSTALS (I.E., RELAXOR-PT CRYSTALS OF LOW PT CONTENTS) Flux growth is an efficient self-purification process. The use of high purity charge is thus not a necessity in that 99.9% purity starting powders generally suffice. PZN-xPT system has a morphotropic phase boundary at x ¼ 0.09– 0.11.124 Flux growth of PZN-PT single crystals of near morphotropic phase boundary compositions using PbO self-flux has been well documented (see Table 12.1). Other than having a reasonably low viscosity and high solubility for complex oxides, being an end element of the final compound, the use of PbO flux is advantageous in that introduction of foreign ions can be avoided. However, its major drawbacks include its toxicity, volatility above 1100°C and a tendency to corrode platinum above 1300°C. A schematic of the typical setup for high temperature flux growth of lead-based relaxor-PT single crystals is provided in Fig. 12.1A. For the growth of PZN-PT, the starting precursor powders are PbO, ZnO, Nb2O5 and TiO2, all of 99.95% or higher in purity. The component powders, weighed to desired proportions, are first mixed thoroughly for more than 24 h. Depending on the PT content, typical solute-to-flux mole ratio used varies from 0.45:0.55 to 0.50:0.50. After mixing, the charge is loaded directly into the Pt crucible. Then, the Pt crucible is covered with the lid and further placed in a sealed alumina crucible assembly, as shown in Fig. 12.1A. This serves to contain potential PbO loss during the crystal growth run. The assembly is then placed in the crystal growth furnace, which is equipped with a local cooling arrangement to eliminate unwanted nucleation. Various techniques have been used for local point cooling including the use of a thin metal rod,55–59,62 metal wire,60,61 controlled stream of gas flow33,34,36,37,41,47 and their combination.46 The crucible assembly with the charge is heated to high temperatures, typically between 1150°C and 1250°C, and held for a period to melt and homogenize the solution. Then, the assembly is cooled at a controlled rate, typically in the range of 0.5–2.0°C/h, to start the crystal growth

II. PREPARATION METHODS AND APPLICATIONS

456

12. SINGLE CRYSTAL PREPARATION TECHNIQUES

TABLE 12.1 Growth of PZN and PZN-PT Single Crystals With PbO-Based Fluxes Technique

Materials

Activities—approx. largest size of crystals grown

Flux-growth via

PZN and

Bokov and Myl’nikova 25; few mm (edge length)

spontaneous

PZN-PT

Nomura et al. 27,28; 10 mm

nucleation

Saitoh et al. 29

with or

Park et al.

without local

Kobayashi et al.

cooling

Park et al.

arrangement

30–32

; 20 mm 33,34

; 43 mm

35

; 10 mm

Saitoh et al.

36,37

; 40 mm

Zheng et al. 38; 17 mm Gentil et al. 39; few mm 40,41

Kumar et al. Xiao et al.

42

; 30 mm

; 26 mm

Santailler et al. 43,44; 30 mm Lim et al. 6,45; 35 mm Dabkowski et al. 46; 30 mm Benayad et al. 47; 35 mm Babu et al. 48; 15 mm Solution (flux)

PZN-PT

Shimanuki et al.

; ϕ30  20 mm3

49

; ϕ40  20 mm3

Bridgman

Harada et al.

50–52

growth with

Harada et al.

53,54

or without

Matsushita et al.

seed

Xu et al. 56,57; seed; ϕ338  20 mm3 Fang et al.

; ϕ50  12 mm3 ; ϕ75  55 mm3

55

; seed; ϕ28  30 mm3

58

Benayad et al.47; ϕ25  40 mm3 Xu et al. 59; ϕ50  15 mm3 Top-seeded

PZN-PT

Chen and Ye 60; seed; ϕ30  10 mm3

solution

Karaki et al.61; seed; ϕ16  12 mm3

growth

Bertram et al.62; pointed Pt rod; ϕ10  20 mm3

(TSSG)

Ye and Chen63

Flux-growth via

Fe-doped

Priya et al.64

spontaneous

PZN-PT

Zhang et al.65; 24 mm

II. PREPARATION METHODS AND APPLICATIONS

12.2 FLUX GROWTH OF PZN-PT SINGLE CRYSTALS

457

TABLE 12.1 Growth of PZN and PZN-PT Single Crystals With PbO-Based Fluxes—cont’d Technique

Materials

Activities—approx. largest size of crystals grown Sato et al.66

nucleation Mn-doped

Priya et al.67

PZN-PT

Zhang et al.68; 30 mm [(Mn,F)-co-doped] Kobor et al.69,70; few mm

Co-doped

Priya and Uchino71

PZN-PT

TABLE 12.2

Growth of PMN and PMN-PT Single Crystals With PbO-Based Fluxes

Technique

Materials

Activities–approx. largest size of crystals grown

Flux-growth via

PMN and

Myl’nikova and Bokov24,26; few mm

spontaneous

PMN-PT

Afanas’ev et al.72

nucleation with

Setter and Cross73; 3 mm

or without local

Petrovskii et al.74

cooling

Ye et al.75; 13 mm

arrangement

Shrout et al.2; 10 mm Park et al.30; 20 mm Park et al.35; 10 mm Dong and Ye76; 10 mm Jiang et al.77; 4 mm Fan et al.78; 5 mm Lim et al.79,80; 35 mm Kania et al.81; edges and (001) crystal faces, as evident in Fig. 12.2. This is typical of crystal growth from a solution of simple ionic salts,126 suggesting that PZN-PT-PbO solutions must be composed of simple ions. This holds even when the PT content in the solution is near the morphotropic phase boundary compositions, that is about 9–10 mol%PT. With an increased degree of supersaturation in the solution, growth of respective single crystals via nucleation at edges and on {001} faces becomes feasible. Examples of such are shown in Fig. 12.3A and B. The growth remains very much crystallographic in

(A)

(B)

(C)

5 mm

FIG. 12.3 Nucleation of (001) layer growth at (A) edge and (B) (001) face in PZN9%PT. (C) Shows noncrystallographic crystal faces at higher cooling rates.

II. PREPARATION METHODS AND APPLICATIONS

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461

nature until the supersaturation is sufficiently high to promote profuse nucleation and growth on {001} faces. Should this occur, {001} growth faces are gradually replaced with smooth, noncrystallographic crystal faces. An example of such is shown in Fig. 12.3C. Small, newly nucleated PZN-PT single crystals are cubic in shape.39,40 With favourable isotherms in the solution, preferential nucleation at certain < 111> corners is promoted such that the corner nucleation rate outpaces the spreading rate onto adjacent {001} crystal faces. As a result, the small cube-shaped crystals would evolve into various shapes as they grow in size, as shown in Fig. 12.4. With the above knowledge, one may engineer the isotherms in the solution such that upon nucleation in the middle of the Pt crucible bottom, subsequent < 111 > corner nucleation and {001} layer growth of the crystal occur preferentially across the base of the Pt crucible. In other words, for growing large-size relaxor-PT single crystals by the spontaneous nucleation technique, it is imperative that the isotherms in the solution be appropriately engineered such that the sideward growth rate of the crystal outpaces its vertical growth rate into the solution. Since the growing crystal is totally surrounded by the PbO-rich solution, it will grow in a stress-free near-equilibrium condition. A PbO-rich solution environment is important for PZN-PT crystal growth. This is because PZN-PT is unstable at high temperatures even in PbO-rich vapor environments.127–129 The entire crystal growth run may last for one to several weeks. Depending on the crystal composition, slow cooling is stopped after the

(A)

Small arrowhead

Disappearing quadrant

Magnification : 32 ×

(B)

(C)

(D)

FIG. 12.4 Evolution from (A) near-cubic, to (B) star-shaped, (C) arrowhead-shaped, and finally (D) spearhead-shaped crystal as a result of increased growth rate along certain directions promoted by favorable isotherms in the solution.

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30 mm

FIG. 12.5

Pictures of PZN-PT single crystals grown from PbO flux.

growth temperature reaches about 800–1000°C, whereupon the assembly is cooled at a faster rate to room conditions. At the conclusion of the crystal growth run, the crystal is retrieved from the solidified flux by leaching in boiling concentrated nitric acid. Pictures of typical flux-grown PZN-PT single crystals are provided in Fig. 12.5. They measure about 30–35 mm in edge length and up to 20 mm in height, extending to the bottom edge of the Pt crucible. As-grown PZNxPT crystals, x ¼ 0.0450.09, are light brownish-yellow in color. Good quality crystals are translucent when viewed against the light and are relatively clear except for the shadowing effects produced by diffraction of light due to domains and inclined crystal surfaces. Fig. 12.5 further shows that the growth direction of the crystals can be engineered with a certain degree of success by exploiting the fast growth direction with respect to the isotherms in the solution. The compositional uniformity of as-grown PZN-PT crystals was examined by slicing the entire crystal into 0.5 mm thick wafers parallel to the largest (001) growth facet and measuring the distribution of Curie temperature (Tc) over the entire wafer area using the array dot electrode technique.130 The results showed that under optimum growth conditions, a large part (i.e., 80%–90% of the crystal boule) of as-grown PZN-xPT single crystals with x  0.07 exhibit good compositional uniformity with ΔTc   2.5°C, corresponding to Δx   0.005.6,45 The last part is typically higher in PT content. For PZN-xPT single crystals with x  0.07, this part is comparatively small, giving a high crystal yield.

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12.3 FLUX GROWTH OF PMN-PT SINGLE CRYSTALS

12.3 FLUX GROWTH OF PMN-PT SINGLE CRYSTALS (I.E., RELAXOR-PT CRYSTALS OF HIGH PT CONTENTS) PMN-yPT system has a morphotropic phase boundary at y ¼ 0.330.35.131,132 The setup, charge preparation and growth procedure for flux growth of PMN-PT single crystals are similar to those for PZN-PT crystals described in the previous section. To determine the optimum flux composition, the following charge compositions were studied (in mode fraction): 0.4(PMN-yPT)  (0.6  z) PbO-zB2O3, with y ¼ 0.300.32 and z ¼ 0.000.20. Small PMN-PT single crystals (of a few millimetres edge length) can be readily grown from PbO-based fluxes. They generally exhibit clear (001) growth facets, as shown in Fig. 12.2B. However, it may not be as straightforward when growing large PMN-PT single crystals, because the high PT content of the system produces significant complications to the flux growth of this material.79,80 Thus, PbO + B2O3 complex fluxes were used instead. Even so, the growth results depended sensitively on the B2O3 content in the PbO solution, as will be shown below. Fig. 12.6A shows the effect of charge composition on the growth result of PMN-PT single crystals. With nil or insufficient B2O3 in the solution, the starting charge has a high liquidus. In this case, the initially grown crystal falls within the “liquid + (PMN + PT)SS” two-phase field of the flux-free

T

L+ L

L+ PbO

PMNT +L

(B)

PbO+ B2O3

PMNT

PMN

Charge compositions (PMNT)Charge PT

(C)

(A)

FIG. 12.6 (A) A hypothetical phase diagram of the PMN-PT-(PbO + B2O3) system. The vertical sections of PMN-PT single crystals grown with insufficient B2O3 and sufficient B2O3 in PbO-based fluxes are given in (B) and (C), respectively.

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binary relaxor-PT system. When this happens, the initially formed phase is actually a mixture of a crystalline phase of PMN-PT solid solution of lower PT content and a liquid phase of higher PT content. Under limited convection conditions, as in the flux growth of most relaxor-PT crystals, the newly separated liquid phase may become trapped between the solidifying PMN-PT crystallites, leading to the “hollow-crystal” feature shown in Fig. 12.6B. Flux inclusions are thus an expected feature when the liquidus of the precursor powder mixture is high, that is when it falls within the “liquid + (PMN + PT)SS” phase field of the flux-free binary relaxorPT system. The problem of phase-separated flux inclusions, or hollow crystals, can be avoided by increasing the B2O3 in the PbO flux, and hence the starting charge, such that crystal growth takes place predominantly below the solidus of the corresponding binary relaxor-PT system. This is shown schematically in Fig. 12.6A. No phase-separation problem occurs in this case and the grown PMN-PT single crystals are free of flux inclusions and fully dense, as shown in Fig. 12.6C. The amount of B2O3 in PbO flux also affects the growth mechanism of PMN-PT single crystals. Fig. 12.7A and B shows the general morphologies of large-size PMN-PT single crystals (i.e., those 20 mm edge length) grown in the author’s laboratory. Although all crystals exhibit apparent (001) growth facets, those grown with or without sufficient B2O3 in PbO flux have a platelet morphology (Fig. 12.7A). An obvious change from (001) platelet growth to microscopic (001) layer growth is evident even with a few mol% of B2O3 (i.e., about 5 mol%) added to the PbO flux (Fig. 12.7B). Fig. 12.8 shows the change in nucleation mechanism during growth from solution with increasing B2O3 content, revealed by deliberately increasing the cooling rate at the later stage of the crystal growth run.

(A)

(B)

FIG. 12.7 Different (001) growth morphologies in flux-grown PMN-30%PT single crystals: (A) (001) platelet growth in the absence of B2O3 in PbO flux; (B) microscopic (001) layer growth with >5 mol%B2O3 addition to PbO flux.

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(A)

465

(B)

FIG. 12.8 Different nucleation mechanisms revealed by higher cooling rates near the end of the growth runs: (A) cluster nucleation on (001) facets with less-than-optimum amounts of B2O3 in PbO flux: (B) corner and edge nucleation and growth with nearoptimum amounts of B2O3 in PbO flux.

Apparently, with a low B2O3 content in the PbO flux, the (0 0 1) layer growth is initiated via the nucleation and growth of (001)-oriented crystal blocks on the (0 0 1) growth facets (Fig. 12.8A). On the other hand, with sufficient B2O3 addition, (001) layer growth occurs through corner nucleation followed by spreading down the adjacent < 001 > edges and (0 0 1) faces (Fig. 12.8B). The above observations suggest that ionic complexes formed in the high temperature solution of the PMN-PT-PbO(B2O3) system play an important role in the growth of PMN-PT single crystals. Owing to the strong affinity between Ti4+ and O2ions and the substantial amount of PT present in the PMN-yPT system studied (y ¼ 0.280.34), it is likely that Ti4+ and O2ions may form various large ionic complexes or clusters (possibly with some covalent nature) in the solution. The growth of PMN-PT with insufficient B2O3 addition is thus controlled by cluster growth of Ti4+-O2-based complexes, leading to a significant increase in the PT content of successively grown layers as the crystal grows in size. On the other hand, owing to the strong B3+dO2bonds and the valency difference, addition of B2O3 helps modify the nature of the Ti4+-O2-based complexes in the solution. With sufficient B2O3 in the PbO flux, a change from the cluster nucleation on (001) faces (Fig. 12.8A) followed by platelet growth (Fig. 12.7A), to corner and < 001> edge nucleation (Fig. 12.8B) followed by microscopic (001) layer growth (Fig. 12.7B) takes place. Since the corner and edge nucleation mechanisms are favoured in the growth of ionic crystals from solutions of simple ions,126 the addition of B2O3 must have broken up existing Ti4+-O2-based complexes into simpler or smaller ones comprising, possibly, Ti4+, B3+, and O2ions. When this occurs, the diffusivity of the simpler or smaller ionic complexes in

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FIG. 12.9

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Two large PMN-PT single crystals grown from PbO + B2O3 complex fluxes.

the solution is substantially enhanced. This, in turn, would lead to reduced compositional gradients in the grown crystal. Fig. 12.9 shows two large PMN-PT single crystals grown from optimal fluxes of PbO + zB2O3, where z 0.10. The color of as-grown PMN-PT crystals varies from brownish-to-greenish yellow. High quality crystals are translucent when viewed against the light. Unlike PZN-PT single crystals, the surfaces of as-grown PMN-PT crystals often show characteristic domain wall traces criss-crossing one another at right angles (see also Section 12.4.9). Even with successful growth of large-size PMN-PT single crystal, the amount of B2O3 was found to play a significant role in the extent of compositional segregation in the crystal. For instance, measurements of Tc distributions from wafers cut parallel to the largest (001) growth facet from as-grown PMN-PT crystals showed that with less-than-optimum amounts of B2O3 in PbO flux, the variations within wafers were acceptable (i.e., ΔTc   3.0°C) but were too large even between adjacent cuts of wafers (of about 0.5 mm thickness).79,80 On the other hand, the reverse was observed when the amount of B2O3 in the PbO flux is higher than the optimum. For PMN-32%PT single crystals grown with optimum B2O3 in the PbO flux, the initial part of the grown crystal (of 60%–70% of the entire crystal) has a relatively uniform PT content (i.e., with ΔTc   3.0°C typically). The outer part, however, shows a fairly steep increase in PT content. The same observation was made for crystals grown at two different growth rates of 0.8 and 0.2°C/h, respectively.80 Since the composition remains relatively uniform over a large initial portion of the grown crystals which is independent of the growth rate, flux growth of PMN-PT crystals from optimum PbO-B2O3 fluxes is likely to occur under equilibrium or near-equilibrium

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L+ PMNT

T

2

L

L+ PbO

PMNT +L PbO + (B2O3 + δPT)

PMNT 4 PMN

1 Charge composition

3

(PMNT)xtal, of δPT lower than (PMNT)charge

PT

FIG. 12.10 Modified phase diagram and growth path for flux growth of PMN-PT single crystals from PbO-B2O3 based fluxes.

conditions, at least during the initial to intermediate stage of the growth. Furthermore, since the difference between the PT content in the initial charge and the grown crystal is not affected by the growth rate used, it is likely that this difference, i.e., about 2.0 mol%PT, is retained in the solution to maintain the equilibrium of the complex flux formation reaction. This being the case, one can anticipate that the grown crystal always has a lower PT content than the charge, regardless of the initial charge composition and the growth rate. This holds as long as equilibrium is attained for the complex flux reaction. The above hypothesis was confirmed with the successful growths of PMN-28%PT (Tc
125°C) and PMN-30%PT (Tc
135°C) by using starting charges of PMN-30%PT and PMN-32%PT instead. The Tc values of the flux-grown PMN-PT single crystals agree reasonably well with those obtained by Choi et al.131 and Noblanc et al.132 from PMN-PT ceramics of controlled compositions. The above result confirms that the actual fluxes for the growth of PMNPT are indeed complex fluxes of PbO + z(B2O3 + dPT), where d is a function of B2O3 content in the flux. Furthermore, it suggests that with the established complex flux, the growth path is nearly vertical under equilibrium or near-equilibrium growth conditions. This is illustrated schematically in Fig. 12.10. The actual flux should be PbO + z(B2O3 + dPT), because a fixed

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amount of PT, determined by the amount of B2O3 in the flux, is needed to maintain the equilibrium of the complex flux formation reaction in the solution (marked “1” in the figure). The growth path is relatively vertical at sufficiently high growth temperatures under near-equilibrium growth conditions (marked “2”). As a result, the composition of the initial part of the grown crystal is about 2 mol%PT less than that of the initial charge (marked “3”). The growth path deviates from the vertical line at low growth temperatures when the growth becomes kinetics controlled, as indicated by the dashed curve (marked “4”). Our finding has shown that with optimum B2O3 content in the flux, such that the large ionic complexes are broken up into simpler ions, high uniformity PMN-PT single crystals can be grown with PbO-based fluxes when the growth is allowed to proceed in a near-equilibrium manner. However, as the growth temperature reduces, the ratio of B2O3-to-PT in the solution increases appreciably and the B3+-based ionic complexes may reform in the solution. When this happens, the viscosity of the solution would increase considerably. The (001) layer growth may then become kinetics-controlled. As a result, the uniformity in the crystal composition degrades accordingly, leading to an appreciable increase in PT content in the last part of the crystal.

12.4 OTHER COMMONLY ENCOUNTERED PHENOMENA Despite being a convenient means, the flux growth technique via spontaneous nucleation is often plagued with formidable technical problems. Such problems become more pronounced when the technique is used to grow large-size relaxor-PT single crystals for commercial exploitation. The various problems encountered can be grouped into those pertaining to nucleation of crystals and those pertaining to growth of crystals. Multiple nucleation at the cooling point, formation of satellite and parasitic crystals and size-wall nucleation are problems related to the first group (see Fig. 12.1B), while flux inclusions, cracks, solute segregation and fragile domain walls are problems related to the second group. They are briefly described below.

12.4.1 Multiple Nucleation and Satellite Crystals The use of local point cooling arrangement in flux growth does not always guarantee single crystal nucleation and growth. Instead, multiple crystal nucleation at the intended cooling point is common. Even if single nucleation is successful, satellite crystals may nucleate later in the course

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of slow cooling, destroying an otherwise perfect crystal growth run. Under less controlled conditions, the situation could be a lot worse and the end result is many mm-size crystals. The problem of satellite crystal formation has been traced to limited convection in the solution coupled with a high cooling and hence growth rate. Such problems can be eradicated, to a large degree, by improving the point cooling arrangement and lowering the cooling rate used.

12.4.2 Parasitic Crystals Unlike satellite crystals which nucleate at the periphery of the main crystal at the base of the Pt crucible, parasitic crystals nucleate and grow onto the main growing crystal. The cause for the formation of parasitic crystals is the same as that for satellite crystals except that a higher degree of supersaturation is required for their formation. Small parasitic crystals are a common feature when the remaining solution is cooled too quickly after the end of the crystal growth run. Similar to satellite crystals, the formation of parasitic crystals can be suppressed by lowering the cooling rate.

12.4.3 Side-Wall Nucleation In flux growth of relaxor-PT single crystals, profuse spontaneous nucleation often occurs at the Pt crucible wall along the meniscus ring. Although this may not affect the quality of the main crystal growing from the base of the Pt crucible, it deprives the latter of needed solute to feed its growth. Suppression of side-wall nucleation is crucial for the growth of large-size relaxor-PT single crystals by the flux growth technique. This can be achieved by carefully engineering the temperature gradient of the growth setup such that the meniscus region is of higher isotherms than the solution below.

12.4.4 Pyrochlore Crystals Pyrochlore crystals could form in the early stage of the crystal growth run when the starting solution is far from homogenized. They also appear when the crystal growth run is allowed to proceed to a much lower temperature, say, 30 mm edge length), high-homogeneity PZN-PT single crystals can be reproducibly grown by the high-temperature flux technique, by implementing appropriate measures to induce single-point nucleation, applying a slow cooling rate to ensure near-equilibrium growth conditions, and engineering the isotherms in the solution to promote controlled (001) layer growth. Under optimum growth conditions, as-grown PZN-xPT single crystals with x  0.07 exhibit good compositional uniformity with Δx   0.005 over 80%–90% of the crystal boule. Flux growth of PZN-xPT single crystals with x  0.07 thus shows promise for large-scale growth for commercial exploitation. In addition to improved compositional homogeneity, and hence higher crystal yield in terms of larger usable boule, other advantages of the flux growth technique include lower charge cost, reusable Pt crucibles and ease of crystal growth process.

Acknowledgments The author wishes to acknowledge the financial support received from the following organizations over the past six years under which the present research has been made possible: Defense Science and Technology Agency (Singapore), Temasek Defence Science Institute (Singapore), Ministry of Education (Singapore), Maritime and Port Authority (Singapore), National University of Singapore, Office of Naval Research (United States)/ NICOP (United States), and Microfine Materials Technologies Pte. Ltd. (Singapore). The author is also indebted to the staff of the Department of Mechanical Engineering, NUS, and of MMT for the technical support and assistance rendered.

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43. Santailler JL, Ferrand B, Damjanovic D, Couchaud M, Dusserre P, Budimir M, et al. Growth and characterization of piezoelectric PZN-PT 89/11 and PMN-PT 66/34 single crystals for ultrasonic transducers. In: White G, Tsurumi T, editors. Proceedings of the 2002 international symposium of applications of ferroelectrics (ISAF’02). vol. 1. Piscataway, NJ: IEEE; 2002. p. 443–6. 44. Santailler JL, Ferrand B, Couchaud M, Renault A, Dusserre P, Calvat C, et al. Growth of ferroelectric single crystals—application to PZN-PT 91/9 and PMN-PT 66/34, In: Presented at the 15th American conference on crystal growth and epitaxy (ACCGE15), July, 2003, Keystone, CO; 2003. 45. Lim LC, Rajan KK. High-homogeneity high-performance flux-grown Pb(Zn1/3Nb2/3) O3-PbTiO3 single crystals. J Cryst Growth 2004;271:435–44. 46. Dabkowski A, Dabkowdka HA, Greedan JE, Ren W, Mukherjee BK. Growth and properties of single crystals of relaxor PZN-PT materials obtained from high-temperature solution. J Cryst Growth 2004;265:204–13. 47. Benayad A, Kobor D, Lebrun L, Guiffard B, Guyomar D. Characteristics of Pb[(Zn1/3 Nb2/3)0.955Ti0.045]O3 single crystals versus growth method. J Cryst Growth 2004;270:137–44. 48. Babu JB, Madeswaran G, Prakash C, Dhanasekaran R. Growth, structural phase transition and ferroelectric properties of Pb[(Zn1/3Nb2/3)0.91Ti0.09]O3 single crystals. J Cryst Growth 2006;292:399–403. 49. Shimanuki S, Saitoh S, Yamashita Y. Single crystal of the Pb(Zn1/3Nb2/3) O3-PbTiO3 system grown by the vertical Bridgman method and its characterization. Jpn J Appl Phys 1998;37:3382–5. 50. Harada K, Shimanuki S, Kobayashi T, Saitoh S, Yamashita Y. Crystal growth and electrical properties of Pb[(Zn1/3Nb2/3)0.91Ti0.09]O3 single crystals produced by solution Bridgman method. J Am Ceram Soc 1998;81:2785–8. 51. Harada K, Shimanuki S, Kobayshi T, Saitoh S, Yamashita Y. Growth of Pb[(Zn1/3 Nb2/3)0.91Ti0.09]O3 single crystal of ultrasonic transducer for medical application. J Intell Mater Syst Struct 1999;10:493–7. 52. Harada K, Shimanuki S, Kobayashi T, Saitoh S, Yamashita Y. Dielectric and piezoelectric properties of Pb[(Zn1/3Nb2/3)0.91Ti0.09]O3 single crystal grown by solution Bridgman method. Key Eng Mater 1999;157–158:95–102. 53. Harada K, Hosono Y, Kobayashi T, Yamashita Y, Miwa K. Piezoelectric Pb[(Zn1/3 Nb2/3)0.91Ti0.09]O3 single crystals with a diameter of 2 inches by the solution Bridgman method supported on the bottom of a crucible. J Cryst Growth 2001;229:294–8. 54. Harada K, Hosono Y, Kobayashi T, Yamashita Y, Wada S, Tsurumi T. Piezoelectric single crystal Pb[(Zn1/3Nb2/3)0.93Ti0.07]O3 (PZNT 93/7) for ultrasonic transducers. J Cryst Growth 2002;237–239:844–52. 55. Matsushita M, Tachi T, Echizenya K. Growth of 3-in single crystals of Pb[(Zn1/3 Nb2/3)0.91Ti0.09]O3 by the supported solution Bridgman method. J Cryst Growth 2002;237–239:853–7. 56. Xu J, Fan S, Lu B, Tong J, Zhang A. Seeded growth of relaxor ferroelectric single crystals Pb[(Zn1/3Nb2/3)0.91Ti0.09]O3 by the vertical Bridgman method. Jpn J Appl Phys 2002;41:7000–2. 57. Xu J, Tong J, Shi M, Wu A, Fan S. Flux Bridgman growth of Pb[(Zn1/3Nb2/3)0.93Ti0.07]O3 piezocrystals. J Cryst Growth 2003;253:274–9. 58. Fang BJ, Xu HQ, He T-H, Luo HS, Yin Z-W. Growth mechanism and electrical properties of Pb[(Zn1/3Nb2/3)0.91Ti0.09]O3 single crystals by a modified Bridgman method. J Cryst Growth 2002;244:318–26. 59. Xu J, Wu X, Tong J, Shi M, Qian G. Two-step Bridgman growth of 0.91Pb(Zn1/3Nb2/3) O3-0.09PbTiO3 single crystals. J Cryst Growth 2005;280:107–12. 60. Chen W, Ye Z-G. Top-cooling-solution-growth and characterization of piezoelectric 0.955Pb(Zn1/3Nb2/3)O3-0.045PbTiO3 [PZNT] single crystals. J Mater Sci 2001;36:4393–9.

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61. Karaki T, Nakamoto M, Adachi M. Top-seeded solution growth of Pb[(Zn1/3 Nb2/3)0.93Ti0.07]O3 single crystals. Jpn J Appl Phys 2002;41:6997–9. 62. Bertram R, Reck G, Uecker R. Growth and correlation between composition and structure of (1x)Pb(Zn1/3Nb2/3)O3-xPbTiO3 near the morphotropic phase boundary. J Cryst Growth 2003;253:212–20. 63. Ye Z-G, Chen W. Top-seeded solution growth and characterization of PMN-PT and PZN-PT single crystals. In: Presented at the 15th American conference on crystal growth and epitaxy (ACCGE15), July, 2003, Keystone, CO; 2003. 64. Priya S, Uchino K, Viehland D. Fe-substituted 0.92Pb(Zn1/3Nb2/3)O3-0.08PbTiO3 single crystals—a hard piezocrystal. Appl Phys Lett 2002;81:2430–2. 65. Zhang S, Lebrun L, Jeong D-Y, Randall CA, Zhang Q. Growth and characterization of Fe-doped Pb(Zn1/3Nb2/3)O3-PbTiO3 single crystals. J Appl Phys 2003;93:9257–62. 66. Sato Y, Abe S, Fujimura R, Ono H, Oda K, Shimura T, et al. Photorefractive effect and photochromism in the Fe-doped relaxor ferroelectric crystal Pb(Zn1/3Nb2/3)O3-PbTiO3. J Appl Phys 2004;96:4852–5. 67. Priya S, Uchino K, Viehland D. Crystal growth and piezoelectric properties of Mnsubstituted Pb(Zn1/3Nb2/3)O3 single crystal. Jpn J Appl Phys 2001;40:L1044–7. 68. Zhang S, Lebrun L, Randall CA, Shrout TR. Growth and electrical properties of (Mn, F) co-doped 0.92Pb(Zn1/3Nb2/3)O3-0.08PbTiO3 single crystal. J Cryst Growth 2004;267:204–12. 69. Kobor D, Lebrun L, Sebald G, Guyomar D. Characterization of pure and substituted 0.955Pb(Zn1/3Nb2/3)O3-0.045PbTiO3. J Cryst Growth 2005;275:580–8. 70. Kobor D, Guiffard B, Lebrun L, Hajjaji A, Guyomar D. Oxygen vacancies effect on ionic conductivity and relaxation phenomenon in undoped and Mn doped PZN-4.5PT single crystals. J Phys D Appl Phys 2007;40:2920–6. 71. Priya S, Uchino K. High power resonance characteristics and dielectric properties of Cosubstituted 0.92Pb(Zn1/3Nb2/3)O3-0.08PbTiO3 single crystal. Jpn J Appl Phys 2003;42:531–4. 72. Afanas’ev II, Berezhnoi AA, Bushneva TS, Prokof’ev SV. Growing crystals of lead magnoniobate and magnotantalate. J Opt Technol 1977;44:613–5. 73. Setter N, Cross LE. Flux growth of lead scandium tantalite Pb(Sc0.5Ta0.5)O3 and lead magnesium niobate Pb(Mg1/3Nb2/3)O3 single crystals. J Cryst Growth 1980;50:555–6. 74. Petrovskii GT, Bonder IA, Andreev EM, Keroleva N. Formation of single crystals of the perovskite like ferroelectrics PMN. Inorg Mater 1984;20:924–8. 75. Ye Z-G, Tissor P, Schmid H. Pseudo-binary Pb(Mg1/3Nb2/3)O3-PbO phase diagram and crystal growth of Pb(Mg1/3Nb2/3)O3 [PMN]. Mater Res Bull 1990;25:739–48. 76. Dong M, Ye Z-G. High-temperature solution growth and characterization of the piezo-/ ferroelectric (1x)Pb(Mg/3Nb2/3)O3-xPbTiO3 [PMNT] single crystals. J Cryst Growth 2000;209:81–90. 77. Jiang X, Tang F, Wang JT, Chen TP. Growth and properties of PMN-PT single crystals. Physica C 2001;364–365:678–83. 78. Fan H, Zhao L, Tang B, Tian C, Kim H-E. Growth and characterization of PMNT relaxorbased ferroelectric single crystals by flux method. Mater Sci Eng B 2003;99:183–6. 79. Lim LC. Flux growth of large-size high-homogeneity PMN-PT single crystals. In: Presented at the 2003 US Navy Workshop on acoustic transduction materials and devices, 6–8 May, 2003, State College, PA, and at the 15th American conference on crystal growth and epitaxy (ACCGE15), July, 2003, Keystone, CO; 2003. 80. Lim LC, Shanthi M, Rajan KK, Lim CYH. Flux growth of high-homogeneity PMN-PT single crystals and their property characterization. J Cryst Growth 2005;282:330–42. 81. Kania A, Slodczyk A, Ujma Z. Flux growth and characterization of (1-x) PbMg1/3Nb2/3 O3-xPbTiO3 single crystals. J Cryst Growth 2005;29:134–9. 82. Tang Y, Luo L, Jia Y, Luo H, Zhao X, Xu H, et al. Mn-doped 0.71Pb(Mg1/3Nb2/3)O30.29PbTiO3 pyroelectric crystals for uncooled infrared focal plane arrays applications. Appl Phys Lett 2006;89:162906.

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83. Bonner WA, Van Uitert LG. Growth of single crystals of Pb3MgNbO9 by Kyrpoulos technique. Mater Res Bull 1967;2:131–4. 84. Chen W, Ye Z-G. Top seeded solution growth and characterization of piezo/ferroelectric (1 x)Pb(Mg/3Nb2/3)O3-xPbTiO3 single crystals. J Cryst Growth 2001;233:503–11. 85. Hosono Y, Harada K, Yamashita Y, Dong M, Ye Z-G. Growth, electric and thermal properties of lead scandium niobate-lead magnesium niobate-lead titanate ternary single crystals. Jpn J Appl Phys 2000;39:5589–92. 86. Hosono Y, Yamashita Y, Sakamoto H, Ichinose N. Growth of single crystals of highCurie-temperature Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 ternary system near morphotropic phase boundary. Jpn J Appl Phys 2001;40:5664–7. 87. Raevskii IP, Emelyanov SM, Savenko FI, Zakharchenko IN, Bunina OA, Malitskaya MA, et al. Growth and study of single crystals of solid solutions of ferroelectric-relaxor (1x) PbMg1/3Nb2/3O3-(x)PbSc1/2Nb1/2O3 with different degrees of compositional order. Crystallogr Rep 2003;48:461–5. 88. Fesenko EG, Grigor EA, Ya Dantsiger A, Golovko YuI, Dudkina SI. Synthesis and study of PbNb0.5Sc0.5O3 single crystals. Bull Acad Sci USSR 1971;33:2287–9. 89. Smotrakov IJ, Raevskii IP, Malitskaya MA, Zaitsev SM, Popov YuM, Strekneva NA. Preparation and properties of single crystals of Pb2ScNbO6. Inorg Mater 1983;19:105–9. 90. Caranoni C, Lampin P, Siny I, Zheng JG, Li Q. Z.C. Kang and C. Boulesteix Comparative study of the ordering of B-site cations in Pb2ScTaO6 and Pb2ScNbO6 perovskites. Phys Status Solidi A 1992;130:25–37. 91. Wolak J, Hilczer B, Caranoni C, Lampin P, Boulesteix C. Dielectric studies of PSNT single crystals. Ferroelectrics 1994;158:399–404. 92. Lampin P, Menguy N, Caranoni C. Microstructure of PbSc0.5(Nb, Ta)0.5O3—a highly ordered solid-solution of complex perovskite compounds. Philos Mag Lett 1995;72:215–22. 93. Yamashita Y, Shimanuki S. Synthesis of lead scandium niobate-lead titanate pseudo binary system single crystals. Mater Res Bull 1996;31:887–95. 94. Yamashita Y, Harada K. Crystal growth and electrical properties of lead scandium niobate-lead titanate binary single crystals. Jpn J Appl Phys 1997;36:6039–42. 95. Yanagisawa Y, Rendon-Angeles JC, Kanai H, Yamashita Y. Stability and single crystal growth of dielectric materials containing lead under hydrothermal conditions. J Eur Ceram Soc 1999;19:1033–6. 96. Eremkin VV, Smotrakov VG, Gagarina ES, Zaitsev SNM, Shevtsova SI. Growth and study of the crystals of the PbSc1/2Nb1/2O3-PbSc1/2Ta1/2O3 solid solutions. Crystallogr Rep 1999;44:818–20. 97. Raevski IP, Malitskaya MA, Gagarina ES, Smotrakov VG, Eremkin VV. T-x-s phase diagram of compositionally orderable (1x)PbSc1/2NBb1/2O3-xPbSc1/2Ta1/2O3 solid solution. Ferroelectrics 1999;235:221–30. 98. Raevskii IP, Smotrakov VG, Eremkin VV, Gagarina ES, Malitskaya MA. The growth and study of PbSc0.5Nb0.5O3-BaSc0/5Nb0.5O3 solid solution crystals. Ferroelectrics 2000;247:27–36. 99. Bing Y-H, Ye Z-G. Growth and characterization of relaxor ferroelectric (1-x) Pb(Sc1/2 Nb1/2)O3-xPbTiO3 single crystals. In: White G, Tsurumi T, editors. Proceedings of the 2002 international symposium of applications of ferroelectrics (ISAF’02). Piscataway, NJ: IEEE; 2002. p. 447–50. 100. Bing YH, Ye Z-G. Effect of chemical compositions on the growth of relaxor ferroelectric Pb(Sc1/2Nb1/2)1xTixO3 single crystals. J Cryst Growth 2003;250:118–25. 101. Rajasekaran SV, Singh AK, Jayavel R. Growth and morphological aspects of Pb[(Sc1/2 Nb1/2)0.58Ti0.42]O3 single crystals by slow-cooling technique. J Cryst Growth 2008; 310:1093–8.

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102. Grove P. Structural phase transitions and long-range order in ferroelectric perovskite lead indium niobate. J Phys C Solid State Phys 1986;19:111–28. 103. Kania A, Rowinski E. Dielectric properties for differently quenched PbIn0.5Nb0.5O3 crystals. Ferroelectrics 1991;124:265–70. 104. Yasuda N, Ohwa H, Hasegawa D, Hayashi K, Hosono Y, Yamashita Y, et al. Temperature dependence of piezoelectric properties of a high Curie temperature Pb(In1/2Nb1/2) O3-PbTiO3 binary system single crystal near a morphotropic phase boundary. Jpn J Appl Phys 2000;39:5586–8. 00 105. Kania A. Crystallographic and dielectric properties of flux grown PbB0 1/2B1/2O3 (B0 B00 : InNb, InTa, YbNb, YbTa and MgW) single crystals. J Cryst Growth 2008;310:2767–73. 106. Topolov VYu, Gagarina ES, Demidova VV. Domain structure and related phenomena in PbYb0.5Nb0.5O3 crystals. Ferroelectrics 1995;172:373–6. 107. Yasuda N, Ohwa H, Kume M, Hosono Y, Yamashita Y, Ishino S, et al. Crystal growth and dielectric properties of solid solutions of Pb(Yb1/2Nb1/2)O3-PbTiO3 with a high Curie temperature near a morphotropic phase boundary. Jpn J Appl Phys 2001;40:5664–7. 108. Yasuda N, Mori N, Ohwa H, Hosono Y, Yamashita Y, Iwata M, et al. Crystal growth and some properties of lead indium niobate-lead titanate single crystals produced by solution Bridgman method. Jpn J Appl Phys 2002;41:7007–10. 109. Zhang SJ, Rehring PW, Randall CA, Shrout TR. Crystal growth and electrical properties of Pb(Yb1/2Nb1/2)O3-PbTiO3 perovskite single crystals. J Cryst Growth 2002;234:415–20. 110. Ichinose N, Takahashi T, Yokomizo Y. Crystal growth of Pb(Cd1/3Nb2/3)O3 and its dielectric properties. J Phys Soc Jpn 1971;31:1848–50. 111. Brunskill IH, Tissot P, Schmid H. Determination of the phase diagrams, PbO-Pb(Fe1/2 Nb1/2)O3 and PbO-Pb(Mn1/2Nb1/2)O3. Thermochim Acta 1981;49:351–5. 112. Brunskill IH, Boutellier R, Depmeier W, Schmid H. High-temperature solution growth of Pb(Fe0.5Nb0.5)O3 and Pb(Mn0.5Nb0.5)O3 crystals. J Cryst Growth 1982;56:541–6. 113. Galasso F, Darby W. Preparation of single crystals of complex perovskite ferroelectric and semiconducting compounds. Inorg Chem 1965;4:71–3. 114. Kania A. A new perovskite PbIn1/2Ta1/2O3 (PIT). Ferroelectr Lett 1990;11:107–10. 115. Bokov AA, Rayevsky IP, Neprin VV, Smotrakov VG. Investigation of phase transitions in Pb(In0.5Ta0.5)O3 crystals. Ferroelectrics 1991;124:271–3. 116. Gagarina ES, Zaitsev SM, Topolov VY, Demidova VV, Titov SV, Tsikhotskii ES. X-ray diffraction studies of the domain structure in PbYb0.5Ta0.5O3 crystals. Crystallogr Rep 1998;43:415–8. 117. Kania A, Majda A, Miga S, Slodczyk A. Anisotropic dielectric properties of PbYb1/2Ta1/2 O3 single crystals. Physica B 2007;400:42–6. 118. Kania A. Flux growth of PbMg1/3Ta2/3O3 single crystals. J Cryst Growth 2007;300:343–6. 119. Kania A, Leonarska A, Ujma Z. Growth and characterization of (1 x) PbMg1/3Ta2/3 O3-xPbTiO3 single crystals. J Cryst Growth 2008;310:594–8. 120. Sun BN, Boutellier R, Sciau Ph, Burkhardt E, Rodriguez V, Schmid H. High temperature solution growth of perovskite Pb2CoWO6 single crystals. J Cryst Growth 1991;112:71–83. 121. Ye Z-G, Schmid H. Growth from high temperature solution and characterization of Pb (Fe2/3W1/3)O3 singe crystals. J Cryst Growth 1996;167:628–37. 122. Ye ZG, Toda K, Sato M, Kita E, Schmid H. Synthesis, structure and properties of magnetic relaxor ferroelectric Pb(Fe2/3W1/3)O3. J Korean Phys Soc 1998;32:S1028–31. 123. Kania A, Jahfel E, Kugel GE, Roleder K, Hafid M. A Raman investigation of the ordered complex perovskite PbMg0.5W0.5O3. J Phys Condens Matter 1996;8:4441–53. 124. Kuwata J, Uchino K, Nomura S. Phase transitions in the Pb(Zn1/3Nb2/3) O3-PbTiO3 systems. Ferroelectrics 1981;37:579–82. 125. Dong M, Ye Z-G. High-temperature thermodynamic properties and pseudobinary phase diagram of the Pb(Zn1/3Nb2/3)0.91Ti0.09O3-PbO system. Jpn J Appl Phys 2001;40:4604–10.

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126. Van Hook A. Crystallization: Theory and Practice. New York: Reinhold Publishing Corp; 1961. p. 73. 127. Jang HM, Oh SH, Moon JH. Thermodynamic stability and mechanisms of formation and decomposition of perovskite Pb(Zn1/3Nb2/3)O3 prepared by the PbO flux method. J Am Ceram Soc 1992;75:82–5. 128. Wakiya N, Ishizawa N, Shinozaki K, Mizutani N. Thermal stability of Pb(Zn1/3Nb2/3) O3(PZN) and consideration of stabilization conditions of perovskite type compounds. Mater Res Bull 1995;30:1121–31. 129. Lim LC, Liu R, Kumar FJ. Surface breakaway decomposition of perovskite 0.91PZN– 0.09PT during high-temperature annealing. J Am Ceram Soc 2002;85:2817–26. 130. Kumar FJ, Lim LC, Lim SP, Lee KH. Nondestructive evaluation of large-area PZN–8% PT single crystal wafers for medical ultrasound imaging probe applications. IEEE Trans Ultrason Ferroelectr Freq Control 1997;44:1140–7. 131. Choi SW, Shrout TR, Jang SJ, Bhalla AS. Dielectric and pyroelectric properties in the Pb (Mg1/3Nb2/3)O3-PbTiO3 systems. Ferroelectrics 1989;100:29–38. 132. Noblanc O, Gaucher P, Galvarin G. Structural and dielectric studies of Pb(Mg1/3Nb2/3) O3-PbTiO3 ferroelectric solid solutions around the morphotropic boundary. J Appl Phys 1996;79:4291–7. 133. Luo H, Xu G, Xu H, Wang P, Yin Z. Compositional homogeneity and electrical properties of lead magnesium niobate titanate single crystals grown by a modified Bridgman technique. Jpn J Appl Phys 1999;39:5581–5. 134. Karaki T, Adachi M, Hosono Y, Yamashita Y. Distribution of piezoelectric properties in Pb[(Mg1/3Nb2/3)0.7Ti0.3]O3 single crystals. Jpn J Appl Phys 2002;41:L402–4. 135. Zawilski KT, Custodio MCC, DeMattei RC, Lee S-G, Monteiro RG, Odagawa H, et al. Segregation during the vertical Bridgman growth of lead magnesium niobate-lead titanate single crystals. J Cryst Growth 2003;258:353–67. 136. Shanthi M, Chia SM, Lim LC. Overpoling-induced property degradation in Pb(Mg1/3 Nb2/3)O3-PbTiO3 single crystals of near-morphotropic phase boundary compositions. Appl Phys Lett 2005;86:262908.

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C H A P T E R

13 Thin Film Technologies for Manufacturing Piezoelectric Materials K. Wasa Kyoto University, Kyoto, Japan

Abstract Over the past 20 years, research work has been carried out on the thin films of the ferroelectric ceramics including Pb(Zr,Ti)O3 (PZT) in relation to their applications for infrared sensors, micro-electromechanical systems (MEMS), and ferroelectric dynamic random access memory (FEDRAM). This chapter is not intended to be a comprehensive review of these works. In this chapter, principles and technologies of deposition of ferroelectric thin films are described in relation to their application for fabrication of PZT-based MEMS based on the author’s research since 1967. The differences between bulk PZT ceramics and PZT thin films are discussed in relation to their piezoelectric properties. It has been shown that thin film processing is environmentally benign. Keywords: Thin film PZT, Thin film process, PZT thin film actuators, Thin film MEMS.

13.1 INTRODUCTION: BULK AND THIN FILM MATERIALS Since the discovery of bulk ferroelectric perovskite BaTiO3(BT) ceramics in 1943, varieties of perovskite ferroelectric materials such as PbTiO3(PT), binary compound Pb(Zr,Ti)O3(PZT), and ternary compound Pb(Mg,Nb)O3-PT(PMNT) have been developed.1 These ferroelectric functional materials are used in practice mostly in the form of bulk ceramics. Current interest has been paid to thin film dielectric and piezoelectric devices in relation to their application for micro-electromechanical

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systems (MEMS). The minimum thickness of the bulk ceramic materials in production is typically 100–300 μm, while the thickness of thin film materials is typically less than several microns. The thin film materials are not created by thinning bulk materials but by depositing source materials on a substrate. Thin film growth exhibits the following features: • The birth of thin films of all materials created by any deposition technique starts with a random nucleation process followed by nucleation and growth stages. • Nucleation and growth stages are dependent upon various deposition conditions, such as growth temperature, growth rate, and substrate chemistry. • The nucleation stage can be modified significantly by external agencies, such as electron or ion bombardment. • Film microstructure, associated defect structure, and film stress depend on the deposition conditions at the nucleation stage. • The crystal phase and the orientation of the films are governed by the deposition conditions. The basic properties of thin films, such as film composition, crystal phase and orientation, film thickness, and microstructure, are controlled by the deposition conditions. Thin films exhibit unique properties that cannot be observed in bulk materials: • Unique material properties resulting from the depositing process. • Size effects, including quantum size effects, characterized by the thickness, crystalline orientation, and multi-layer aspects. It is expected that thin film piezoelectric materials lower the working voltage of piezoelectric actuators by one order in magnitude. This thin film material process is based on the thin film technology established for a variety of industries, first and foremost, the semiconductor industry. Thin films of ferroelectric perovskite materials have been grown for more than 40 years. Initially thin films of BT were prepared by thermal evaporation in the 1950s.2 In the 1960s, the thin films of PT were deposited by sputtering.3 However, the ferroelectric properties of these thin films were poor and not well characterized. In the past 20 years, a variety of the fabrication process of the perovskite materials has been extensively studied in relation to the development of high Tc superconductors4 and ferroelectric random access memory (FERAM).5 At present, thin films of perovskite materials are widely fabricated by a magnetron sputtering, laser ablation, sol-gel, and/or metal organic chemical vapor deposition (MOCVD). The PZT-based thin films are used in practice for the sensors and high precision actuators including gyro-sensors and printer heads.6

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An excellent review of thin film piezoelectric materials has been published in relation to MEMS applications.7 Ferroelectric ceramics have been studied in the past half century and a large amount of basic material data on them has been accumulated. Novel functional devices including nano-scale engineered connectivity originally proposed by Newnham et al.8 is provided by the combination of the thin film technology and the bulk ceramic technology. It is also noted that environmental restrictions may terminate the usage of the present toxic bulk Pb-based piezo-ceramics in the 2010s. Thin films are environmentally benign materials due to the minimization of the usage of the Pb-based materials.9 The thin films of the Pb-based piezo-ceramics could be used forever, since the thin film device technology could further reduce the toxic Pb consumption10 (p. 1).

13.2 FUNDAMENTALS OF THIN FILM DEPOSITION 13.2.1 Classification of Deposition Process The thin film deposition technologies and the related nanotechnologies are described in several textbooks.11–14 Typical deposition processes for the PZT-based thin films are shown in Table 13.1. Among these deposition processes sputtering, plasma enhanced metal organic chemical vapor deposition (PE-MOCVD), and sol-gel processes are mostly used for the deposition of PZT-based thin films. These deposition processes are defined as follows: TABLE 13.1 Classification

Classification of the Deposition System for PZT-Based Thin Films Deposition system

Source materials

Thermal evaporation, electron beam, crucible MBE

Individual metals, individual oxides, multi-source

Laser ablation

PZT compounds, individual oxides, multi-target

Sputtering

PZT compounds, individual metals, individual oxides, multi-target

CVDb

Low pressure, CVD, MOCVD, PE-MOCVD

Individual halide, metal organic gas

CSDc

MOD, sol-gel deposition

Metal organic gas Metal alkoxide

a

PVD

a b c

Physical vapor deposition. Chemical vapor deposition. Chemical solution deposition.

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• Sputtering deposition. Source materials of sintered PZT disk are sputtered by the impingement of high energy ions in an oxidizing atmosphere. Sputtered source materials are deposited on a heated substrate in an oxidizing atmosphere resulting in the growth of PZT thin films. Multisource materials of Pb, Zr, and Ti metal disks and/or multi-source materials of PbO, ZrO2, and TiO2 sintered disks are also used for the deposition of PZT thin films. • PE-MOCVD. This process is based on a chemical reaction of metalorganic precursors of PZT in the gas phase, which includes Pb, Zr, and Ti metal elements, followed by diffusion of reactants to a heated substrate. The diffused reactants create a chemical reaction on the heated substrate in an oxidizing atmosphere resulting in the growth of PZT thin films. The high energy electrons in plasma enhance the chemical reaction of metal-organic complexes. • Sol-gel deposition. Chemical solutions of PZT precursor complexes are spin-coated on a substrate followed by drying, pyrolysis, and sintering.

13.2.2 Key Deposition Conditions of PZT-Based Thin Films The PZT thin films of perovskite phase are fabricated by two different deposition conditions as shown in Table 13.2. One is deposition at room temperature followed by post-annealing at crystallizing temperature of perovskite phase (mode 1, low temperature process), the other is deposition at crystallizing temperature of perovskite phase (mode 2, high temperature process). The sintering process of the bulk ceramics is also shown in Table 13.2. The low temperature process, mode 1, is similar to the bulk sintering process. The mixing process at the bulk ceramic sintering corresponds to the deposition at room temperature. The post annealing process corresponds to the bulk sintering process. The high temperature process, mode 2, creates the perovskite PZT thin films without the post-annealing. TABLE 13.2 Basic Fabrication Processes for PZT-Based Thin Films Composition

Crystallization

Structure

Ceramics

Mixing

Sintering (800– 1200°C)

Polycrystal

Thin films

Low temp. mode 1

Deposition (non-heated)

Post annealing (700–800°C)a

Polycrystal

Deposition (600– 700°C)

Polycrystal single crystalb

High temp. mode 2 a b

Rapid thermal annealing (RTA). Heteroepitaxial growth on single crystal substrates.

II. PREPARATION METHODS AND APPLICATIONS

13.2 FUNDAMENTALS OF THIN FILM DEPOSITION

485

Many kinds of the deposition conditions of PZT thin films are reported in the literature. The important factors for the deposition of the PZT thin films are control of chemical compositions, control of crystal phase, and control of micro-structure. 13.2.2.1 Control of Chemical Compositions The important factors that influence the chemical compositions are as follows: • Sputtering process: target composition, deposition temperature, and oxygen partial pressure of sputtering atmosphere. • Sol-gel process: chemical compositions of PZT precursors and sintering temperature. • MOCVD process: Ar carrier gas flow ratios of each metal precursor and deposition temperature. 13.2.2.2 Control of Crystal Phase The important factors that influence the crystal phase are deposition temperature and chemical compositions of the deposited thin films. The crystal phase of the deposited perovskite thin films is governed chiefly by the substrate temperature during film growth. PT is a base composition of PZT. Here, the effects of the deposition temperature on the crystal phase of PT thin films are described. The PT is a base material of the PZT. Thin films of the PT were deposited by a planar sputtering system and the crystal phases of the sputtered thin films were studied for various substrate temperature. Sapphire (0001) single crystals were used for the substrates. The XRD analyses show that the sputtered PT thin films at cooled substrates (at liquid nitrogen temperature) comprise amorphous PT phase with Pb crystallites.15 Heating the substrate activates the surface migration of the Pb adatoms on the substrates and the Pb crystallites will transfer into amorphous PT resulting in the formation of Pb crystallite-free amorphous PT thin films. Fig. 13.1 shows XRD patterns of sputtered PT thin films on (0001) sapphire substrates for different substrate temperatures. The sputtered PT thin films at 200°C are amorphous phase and free from the Pb crystallites as shown in the XRD patterns of Fig. 13.1A. Further activation of the surface migration causes the formation of crystalline phase. The sputtered thin films deposited at 500°C show the pyrochlore phase as shown in the XRD patterns of Fig. 13.1B. The PT thin films deposited at 600°C show perovskite PT phase as shown in Fig. 13.1C. The figure shows the sputtered films are epitaxially grown on the (0001) sapphire, and the epitaxial relation is (111) PT/(0001) sapphire. These experiments suggest the epitaxial temperature and the crystallizing temperature of perovskite PT is

II. PREPARATION METHODS AND APPLICATIONS

486 13.

THIN FILM TECHNOLOGIES FOR MANUFACTURING PIEZOELECTRIC MATERIALS

0

10

20

30 2q (°)

40

50

60

10

20

30 2q (°)

40

50

60

(A)

0

PbTiO3 thin film

(222)

(111)

(B)

20

(C)

30

40

50 2q (°)

60

70

80

FIG. 13.1 X-ray diffraction patterns of sputtered PbTiO3 thin films on (0001) sapphire: (A) deposited at 200°C, (B) deposited at 500°C, and (C) deposited at 600°C.

around 600°C and the crystallizing temperature of pyrochlore phase is around 500°C. Fig. 13.2A and B shows the XRD patterns of the sputtered PT amorphous thin films annealed at 480°C and 600°C, respectively. It is seen the PT thin films annealed at the crystallizing temperature of perovskite PT show the perovskite PT structure as expected. Fig. 13.3 shows the temperature variations of crystal phase for the sputtered PT thin films. A

II. PREPARATION METHODS AND APPLICATIONS

487

13.2 FUNDAMENTALS OF THIN FILM DEPOSITION

0

10

20

30 2q (°)

40

50

10

20

30 2q (°)

40

50

(A)

0

(B)

60

60

FIG. 13.2

X-ray diffraction patterns of sputtered PbTiO3 thin films on (0001) sapphire at room temperature: (A) post annealed at 480°C, (B) post annealed at 600°C.

Substrate temperature (°C) 600

500 Pb-crystallites Amorphous

FIG. 13.3

Pyrochlore

Perovskite

Crystalline

Schematic phase diagram of sputter-deposited PbTiO3.

conventional planar magnetron sputtering system was used for the measurement of the crystal phase shown in Fig. 13.3. In the conventional planar magnetron sputtering system, the energy of the sputtered particles was thermallized and the effect of high-energy sputtered particles on the crystallizing temperature was removed. Therefore, the crystallizing temperature of sol-gel and/or MOCVD PZT thin films is possibly similar to the sputtered PZT thin films.

II. PREPARATION METHODS AND APPLICATIONS

488 13.

THIN FILM TECHNOLOGIES FOR MANUFACTURING PIEZOELECTRIC MATERIALS

600

Growth temperature (°C)

(PbTiO3)

500

PbTiO3

Pb2Ti3O7 (PbTiO3)

400 Pb2Ti2O6 PbO 300

0 TiO2

0.5 Pb/(Pb + Ti)

1.0 PbO

FIG. 13.4 Crystal phase of sputtered Pb-Ti-O thin films on (001)MgO substrates showing chemical composition of thin films vs. growth temperature. B 100 kV/cm. The Ec values increase with the decrease of film thickness. If the sputtered PZT thin films comprise a mixed orientation, their compositional dependence of crystal structure and dielectric constant is similar to bulk PZT properties.50 II. PREPARATION METHODS AND APPLICATIONS

506 13.

THIN FILM TECHNOLOGIES FOR MANUFACTURING PIEZOELECTRIC MATERIALS

6

Deflection (µm)

4 2 0 −2 −4 −6 −40

−30

−20

−10

(A)

0

10

20

30

40

10

20

30

40

Voltage (V)

15

Deflection (µm)

10 5 0 −5 −10 −15 −20 −40

(B)

−30

−20

−10

0 Voltage (V)

FIG. 13.18 Tip deflection of the cantilevers: (A) PZT thin films on Pt/MgO, (B) PZT thin films on Pt/Ti/Si.

13.5 PZT-BASED THIN FILMS FOR MICROELECTROMECHANICAL SYSTEMS (MEMS) Thin films of intrinsic PZT are widely used for the fabrication of PZTbased thin film MEMS devices. However, the thin films of the Pb-based ternary perovskite compounds, i.e., Pb(Mg,Nb)O3(PMN) and PT (PMNT), PMN-PZT and/or Pb(Mn,Nb)O3 (PMnN)-PZT, will be much more useful for the fabrication of MEMS devices, since a variety of ferroelectric properties will be realized by the selection of the chemical compositions. In this section, the deposition and the ferroelectric properties of the Pb-based ternary ferroelectric thin films are described in relation to their application for MEMS devices.

II. PREPARATION METHODS AND APPLICATIONS

13.5 PZT-BASED THIN FILMS FOR MICRO-ELECTROMECHANICAL SYSTEMS (MEMS)

507

4.20

Lattice constant [Å]

4.15

4.10

4.05

c/(100) a/(100) c/(111) a/(111) bulk

4.00

3.95 30

40

50 60 x in Pb(ZrxTi1−x)O3

70

STO STO STO STO

80

FIG. 13.19 Lattice constants of PZT thin films as a function of Zr/Ti ratio. ● and  represent the c- and a-lattice constants of PZT thin films grown on (001)Pt/(001)SrTiO3, respectively. ■ and □ represent the c- and a-lattice constants of PZT grown on (111)Pt/(111)SrTiO3, respectively. ♦ and dashed line indicate the bulk data.

13.5.1 PMNT Thin Films The PMNT, (1  x)PMN-xPT, is a solid solution of a relaxor ferroelectric material PMN and a normal ferroelectric material PT and exhibits a very high dielectric permittivity and an exceptionally high coefficient of electromechanical coupling.51 The PMNT shows a morphotropic phase boundary (MPB) at about x ¼ 0.33 for the bulk single crystals. Several deposition processes are reported including a sputtering,52 MOCVD,53 PLD,54 and sol-gel method.55 These PMNT thin films often include the isometric compound of the pyrochlore, Pb2(Mg,Nb)2O7, and include grains and/or interfacial dislocated layers. The structure looks like polycrystalline ceramics with a large porosity and a poor crystal orientation. The reliable deposition process of the single crystal-like PMNT thin films is necessary for the development of the thin film MEMS devices but also for the understanding of the ferroelectric thin films. Among these deposition processes, sputtering is the most promising process for the deposition of the bulk single crystal-like thin films10 (p. 71). The PMNT thin films are directly sputtered from PMNT powder target on (001)SrTiO3 and/or (001)MgO single crystal substrates. The target powder is composed of the mixture of PT, PbO, MgO, Nb2O5, and TiO2 powder. The epitaxial temperature is 500–550°C. The Pb-reduced structure, Pb(Mg1/3,Nb2/3)3O7, is grown at a temperature higher than 600°C. The typical sputtering conditions are shown in Table 13.8. The optimum

II. PREPARATION METHODS AND APPLICATIONS

508 13.

THIN FILM TECHNOLOGIES FOR MANUFACTURING PIEZOELECTRIC MATERIALS

TABLE 13.8 Sputtering Conditions for PMNT Thin Films Sputtering system a

Planar rf-magnetron

Target

Mixed powder: PbO, MgO, Nb2O5, PT

Substratesb

La-0.75 wt% doped(001)ST, (001)MgO

Buffer layer

(110)SRO, (001)PLT

Sputtering gas

0.5 Pa (Ar/O2 ¼ 20/1)

Growth temperature

480–600°C

Sputtering power

1.3 W/cm2

Growth rate

200 nm/h

Film thickness

20–8000 nm

Quenching rate

100°C/min. in air

a b

Typical composition: stoichiometric + 10%PbO. Conductive base electrode: (001)Pt for (001)MgO.

growth temperatures showed a narrow window of 500–550°C. The sputtered thin films were quenched after the deposition in order to suppress the growth of the pyrochlore phase during the cooling down stage. The quenching process is essential for the deposition of high quality thin films with a high reproducibility. Fig. 13.20 shows a typical XRD pattern of the sputtered PMNT thin films on the (001)MgO substrate. The XRD Θ-2Θ pattern showed the sputtered film was highly (001) orientated (Fig. 13.20A). The pole figure of the (110) direction showed a strong fourfold intensity describing three dimensional epitaxy (Fig. 13.20B). The similar epitaxial properties were also observed for the different substrates. The lattice parameters of the sputtered PMNT thin films are shown in Table 13.9. It is noted that the in-plane lattice parameters of the PMNT thin films are almost the same as the bulk lattice values independent of the substrate lattice parameters. The c-axis is slightly prolonged probably due to the inclusion of the high energy particles during the sputtering deposition. The cross-sectional SEM and TEM images in Fig. 13.21 show that the sputtered PMNT thin films exhibit continuous single crystal-like structure without grains and/or interfacial dislocated layer between the PMNT thin films and the substrates. These structural analyses show that the sputtered PMNT thin films comprise bulk-like single crystal structure without inplane stress. The point and/or line defects are found in the interface between the thin films and the substrates. However, the dislocated interfacial layer is absent.56 Typical P-E curves are shown in Fig. 13.22. The Pr increases with the addition of the PT into the PMN similar to the bulk materials. Fig. 13.23

II. PREPARATION METHODS AND APPLICATIONS

002 Pt : 002

13.5 PZT-BASED THIN FILMS FOR MICRO-ELECTROMECHANICAL SYSTEMS (MEMS)

001

4000

101

MgO : 002

011

2000

011

101

(B)

1000 110

Intensity (cps)

3000

509

0 20

(A)

30 2-theta/omega (°)

40

50

FIG. 13.20 Typical XRD patterns of the sputtered PMN-33PT thin films on (001)MgO substrates. Film thickness: 230 nm. TABLE 13.9 Substrates

Lattice Parameters of Sputtered PMNT Thin Films for Different Bulk PMN a 5 0.405 nm

c 5 0.405 nm

Substrates

PMN thin films

(001)MgO

a ¼ 0.405 nm

c ¼ 0.406 nm

(001)Pt/(001)MgO

0.405

0.406

(001)SrTiO3

0.405

0.406

MgO a ¼ 0.420 nm, SrTiO3 a ¼ 0.3905 nm.

shows a typical temperature variation of the dielectric constants of the sputtered PMNT thin films. A broad peak near the phase transition temperature is observed. The figure shows frequency dependence of the dielectric properties similar to the bulk PMNT. The transition temperature is slightly higher than bulk values. The shift of the transition temperature suggests that the sputtered PMNT thin films are almost relaxed according to the XRD analyses; however, the sputtered PMNT thin films are still constrained to substrate.57 The temperature shift decreases with the increase in the film thickness.58 The piezoelectric properties have been evaluated by a deflection of cantilever beam. A typical deflection of the cantilever beams for the sputtered PMNT thin films of different compositions is shown in Fig. 13.24. The cantilever comprises the PMNT thin film capacitor deposited on metallized MgO substrate beam. The length, width, and thickness of the MgO beam are 7–10 mm, 1–3 mm, and 0.3 mm, respectively. The tip displacements show a parabolic change with the applied electric field for PMN thin films,

II. PREPARATION METHODS AND APPLICATIONS

510 13.

THIN FILM TECHNOLOGIES FOR MANUFACTURING PIEZOELECTRIC MATERIALS

Surfae

PMNT thin film Interface (100)SrTiO3

(A)

PMNT thin film

Interface (001)SrTiO3

(B) FIG. 13.21

Cross-sectional SEM and TEM images of (001)PMNT thin films on (001)ST: (A) SEM image. Film thickness: 1170 nm, (B) TEM lattice image with SAD patterns at interface. Film thickness: 300 nm.

PMN (1 µm)

PMN–33PT (0.9 µm) 40 P(µC/cm2)

P(µC/cm2)

20 0

20 0 −20

−20 −40

(A)

−200 −100 0 100 E (kV/cm)

200

−200

(B)

−100

0 100 E (kV/cm)

200

FIG. 13.22 Typical P-E curves for PMNT thin films on (001)MgO substrates: (A) PMN thin films, (B) PMN-33PT thin films. Film thickness: 300 nm.

II. PREPARATION METHODS AND APPLICATIONS

13.5 PZT-BASED THIN FILMS FOR MICRO-ELECTROMECHANICAL SYSTEMS (MEMS)

511

100 kHz

1000

10 kHz 1 kHz

e*

900

800

700

600

0

50

100 150 Temperature (°C)

200

FIG. 13.23 Temperature variations of the dielectric constants for sputtered PMNT thin films. Film thickness: 300 nm.

while the displacements show linear dependence with the electric field for PMN-33PT thin films similar to the bulk PMNT. Their transverse piezoelectric constants, d31, were d31 ¼  73 pC/N for PMN and 104 pC/N for PMN-33PT. The frequency range of the piezoelectric properties evaluated by the cantilever beam is lower than 100–500 kHz. Planar PMNT thin film BAW resonator is useful for the evaluation of GHz piezoelectric properties.59 Fig. 13.25 shows the typical structure of the PMNT thin film BAW resonator for the measurement of the resonant spectrum.60 A typical resonant spectrum for the PMN-33PT thin films of 2.3 μm film thickness is shown in Fig. 13.26. The resonance was observed at about 1.3 GHz indicating the longitudinal phase velocity of 5500–6000 m/s. The multi-reflection mode was superposed on the main spectrum. This mode was caused by the acoustic multi-reflection of a longitudinal standing wave excited in the MgO substrate. The electromechanical coupling kt evaluated by Mason’s equivalent circuit was about 45% at the resonant frequency of 1.3 GHz with εs33 ¼ 500 Qms ¼ 2000, Qmp ¼ 20, where Qms and Qmp are mechanical Q values of the MgO substrate and PMNT thin films. The observed coupling values are almost the same as the single crystal values as expected.61 The structure of the sputtered PMN thin films is almost the same as the bulk PMN except for a small enlargement of the c-axis. A complex composition with a small additive is used for the bulk ceramics piezoelectric materials. The present sputtering process easily achieves the complex composition by using a powder target. Fig. 13.27 shows an example of ferroelectric properties of complex compound PMN-PT-PZ thin films with

II. PREPARATION METHODS AND APPLICATIONS

512 13.

THIN FILM TECHNOLOGIES FOR MANUFACTURING PIEZOELECTRIC MATERIALS

PMN (3 µm) 6

Displacement (µm)

5 4 3 2 1 0 −10

−5

0 E (V/µm)

5

10

(A) PMN–33PT (2.3 µm)

Displacement (µm)

15

10

5

0

−5 −10

−5

0 E (V/µm)

5

10

(B)

FIG. 13.24 Tip deflection of cantilever with applied voltage for PMNT thin film cantilevers. Film thickness: (A) 3.0 μm, PMN thin films; (B) 2.3 μm, PMN-33PT thin films.

Au/Cr:80 µmφ, 30 nmt

Network analyzer

E

PMN–PT

E

(100)MgO (0.3 mm)

FIG. 13.25 Construction of PMNT thin film FBAR for measurement of resonant properties.

II. PREPARATION METHODS AND APPLICATIONS

13.5 PZT-BASED THIN FILMS FOR MICRO-ELECTROMECHANICAL SYSTEMS (MEMS)

513

−10 −15

1st

|Y| (dB)

−20 −25 −30 −35 −40 −45 2

4 6 Frequency (GHz)

8

10

−15

|Y| (dB)

−20

−25

−30

−35 1.0

1.5 Frequency (GHz)

2.0

FIG. 13.26 Typical resonant spectrum of PMN-33PT thin film FBAR. Film thickness: 2.3 μm.

addition of Sr.62 The PMN-PT-PZ ceramic composition was developed by Ouchi.16 Excellent ferroelectric P-E curves with a large Pr was observed. In the bulk ceramics, the addition of the Sr increases the dielectric constant. In the present sputtered PMN-PZT films, the addition of the Sr also increases the dielectric constants similar to the bulk ceramics. These experiments suggest that the sputtering with the quenching is useful for the deposition of Pb-based ferroelectric perovskite thin films. The selection of the chemical composition with a variety of the small additive will achieve the well designed ferroelectric thin films including dielectric properties, piezoelectric properties, and mechanical properties for the fabrication piezoelectric thin film devices. The traditional material design for the perovskite ferroelectric ceramics including doping effects is applicable for the material design of the perovskite ferroelectric thin films. II. PREPARATION METHODS AND APPLICATIONS

514 13.

THIN FILM TECHNOLOGIES FOR MANUFACTURING PIEZOELECTRIC MATERIALS

50 40 30

P (μC/cm2)

20 10

−150

−100

0

−50

0

50

100

150

−10 −20 −30 −40 −50 E (kV/cm)

FIG. 13.27 P-E hysteresis curve of Sr-doped PMN-PT-PZ thin films on SRO/Pt/(001) MgO. Film thickness: 1.9 μm.

13.5.2 PMnN-PZT Thin Films Based on the understanding of the deposition mechanism of PMNT thin films by using the sputtering process, the thin films of the ternary compounds PMnN-PZT were deposited using the sputtering process and their ferroelectric properties were evaluated. The PMnN-PZT ternary ceramics comprise PZT with a donor additive Nb and an acceptor additive Mn. However, it is known that the ternary ceramics show hard ferroelectric response.63 The single crystal PMnNPZT thin films are provided by the sputtering deposition similar to the deposition of PMNT thin films. The target powder was composed of the mixture of PT, PZT, PbO, Nb2O5, MnO2, ZrO2, and TiO2.64 Fig. 13.28 shows a typical P-E hysteresis curve for the single c-domain/single crystal thin films of 0.06PMnN–0.94PZT(45/55).65 The hysteresis curve shows typical hard ferroelectric properties of the square shaped loops with high Ec and large Pr values (2Ec ffi 230 kV/cm and Pr ffi 60 μC/cm2). The PMnNPZT thin films showed the dielectric anomaly at Tc ¼ 560°C as shown in Fig. 13.29. The Tc was higher than the bulk PMnN-PZT ceramic value. The observed relative dielectric constants were 150–200 with tan δ ¼ 0.01–0.02 at 1 kHz. The dielectric constants were much lower than the bulk non-doped intrinsic PZT ceramics (bulk ceramic values ffi 700). The transverse piezoelectric coefficients of the (001)PMnN-PZT thin films epitaxiallly grown on (001)MgO were e31f ¼  10.8 C/m2, d31 ¼  83  1012 m/V, respectively. The observed transverse piezoelectric II. PREPARATION METHODS AND APPLICATIONS

13.5 PZT-BASED THIN FILMS FOR MICRO-ELECTROMECHANICAL SYSTEMS (MEMS)

515

µC/cm2

100 80 60 40 20

−200

0

−100

0

100

200

−20 kV/cm

−40 −60 −80

FIG. 13.28 Typical P-E hysteresis curve for the single c-domain/single crystal thin films of 0.06 PMN-0.94PZT(45/55). Film thickness: 1.9 μm.

Relative dielectric constant e r

12000 10000

8000

6000 Cooling 4000 Heating 2000 0 0

100

200

300 400 Temperature (°C)

500

600

FIG. 13.29 Temperature variations of dielectric constant for the single c-domain/single crystal thin films of 0.06PMnN–0.9PZT(45/55). Film thickness: 1.9 μm.

II. PREPARATION METHODS AND APPLICATIONS

516 13.

THIN FILM TECHNOLOGIES FOR MANUFACTURING PIEZOELECTRIC MATERIALS

200

0.8

(1 − x) PMnN − xPZT kt

Qm

kt 0.7

150

0.6

Qm

3.9 GHz

0.4

100 0

5

10 x (%)

FIG. 13.30

Typical variations of the Qm and the coupling factor kt for the different amounts of PMnN doping to PZT.

constants were almost the same as the bulk PZT ceramic values at the MPB compositions. The doping effects of the PMnN into the PZT on the piezoelectric constants were not large. However, it is known that the bulk PMnN-PZT ceramics show that the doping of the PMnN into the intrinsic PZT remarkably enhances the mechanical quality factor Qm. In order to confirm the effect of the PMnN doping on the Qm, the PMnN thin film FBAR structure was fabricated and their Qm values were evaluated. Fig. 13.30 shows typical variations of the Qm and the coupling factor kt for the different amounts of PMnN doping. In the figure it is seen that the Qm and the kt for the intrinsic PZT thin films are 100% and 70%, respectively. The Qm values increase with the doping of the PMnN to the PZT. The kt decreases with the doping of PMnN. However, the decrease of the kt is around 10% for the doping of PMnN of 10%, while the Qm increases almost two times. Therefore, the doping is effective for the improvement of Qm for intrinsic PZT thin films. Typical thin films of PMnN-PZT, 0.1PMnN–0.9PZT(55/45), 300 nm in film thickness showed fs ¼ 3.373 GHz and fp ¼ 3.870 GHz. Taking the observed fp and fs values, the keff ¼ 0.487 and the kt ¼ 0.689. From the phase properties, Qm ¼ 185. Thin films of intrinsic PZT (48/52) showed fs ¼ 3724 MHz and fp ¼ 4451 MHz. Their keff ¼ 0.547 and kt ¼ 0.726. The Qm was 114. So, it is found that the doping of the PMnN into the PZT does not remarkably affect the kt values. The kt of the intrinsic PZT thin films was slightly higher than the PMnN-doped PZT thin films. The doping increases the Qm almost two times in magnitude.66

II. PREPARATION METHODS AND APPLICATIONS

517

13.6 PZT-BASED THIN FILM MICRO-ELECTROMECHANICAL SYSTEMS (MEMS)

13.6 PZT-BASED THIN FILM MICROELECTROMECHANICAL SYSTEMS (MEMS) 13.6.1 PZT-Based Thin Film Piezoelectric Actuators Several types of actuators are proposed for fabrication of MEMS as shown in Fig. 13.31. Among these actuators the piezoelectric actuators show low voltage operation and fast response. Thin films of PZT-based piezoelectric materials are useful for the fabrication of the piezoelectric actuators. A basic construction of PZT-based thin film piezoelectric actuators is shown in Fig. 13.32. Thin film piezoelectric actuators comprise piezoelectric thin films deposited on a substrate such as a Si wafer. Since a displacement of the thin film longitudinal actuators is small, the cantilever and/or diaphragm type actuators are used in practice. From Eqs. (13.5) and (13.6), the deflection of the cantilevers δ and the resonance frequency f0 are given by the following relations:   δ ¼ 3ðL=hs Þ2 s11,s =sE11,p V, (13.8) ¼ 3ðL=hs Þ2 ðs11, s Þ  e31 V,

(13.9)

 1=2 f0 ¼ 0:161 hs =L2 ðρs11,s Þ ,

(13.10)

where V denotes the applied voltage between top and bottom electrodes, L, hs, s11s, ρ are, length, thickness, elastic compliance, and density of cantilever substrates, respectively. A blocking force F is given by the following relation: F ¼ ð1=s11s Þwðhs Þ3 δ=4L3 ,

Electrostatic

ε 0S V2 F(x) = 1 2 (d – x)2

Magnetic

22

F =n I 2x0

µ0A µ L gµ + 0 m µ

(13.11)

Thermal

Piezoelectric

F = a · ΔT · E

T3 = E · d33 · V t V T1 = E · d31 · L t

Easy microfabrication Fast response

Conventional and traditional actuators Remote operation

Large force Simple structure

Fast response Low voltage Large force

Small force (high voltage)

Microfabrication Generation of heat

Cross talk Slow response

Thin film growth Microfabrication

FIG. 13.31

Classifications of micro-actuators.

II. PREPARATION METHODS AND APPLICATIONS

518 13.

THIN FILM TECHNOLOGIES FOR MANUFACTURING PIEZOELECTRIC MATERIALS

Electrodes

Unimorph cantilevers

V(w)

PZT thin films Substrate beam Electrodes Diaphragm

V(w)

PZT thin films Vibration disc

FIG. 13.32

Constructions of thin film piezoelectric actuators.

where w denotes the width of cantilevers.67,68 The deflection of the thin film cantilevers is governed by the combination of piezoelectric properties of PZT thin films and the dimension and the elastic properties of the substrate beam. The resonant frequency is determined by the dimension and the elastic constants of the substrate beam. The resonant frequency and the vibration modes of the thin film diaphragms are also governed by the dimension and the elastic properties of the substrates. The resonant frequency of the diaphragms is expressed by the relation:

1=2 f0 ¼ 0:932t=D2 ðE=ρÞ 1  σ 2 , (13.12) where D, t, E, ρ, and σ denote the diameter, thickness, density, Young’s modulus, and Poisson’s ratios of the substrate materials.69 For the PZT thin film cantilevers deposited on the Si beam, taking L ¼ 10 mm, hs ¼ 0.3 mm, s11s ¼ 5.95  1012 m2/N (Si), *e31 ¼  5 C/m2, ρ ¼ 2.33 g/cm3, the deflection δ becomes δ ¼ 1 μm at the applied voltage V ¼ 10 V and the resonant frequency f0 becomes f0 ¼ 4.1 kHz. Table 13.10 shows the deflection properties of the PZT-based piezoelectric thin film cantilevers for different substrate materials. The piezoelectric properties are governed by the domain structure and/or orientation of the PZT thin films. The PMnN-PZT thin films with Si substrates show the maximum deflections probably due to their domain motions.70 The tip displacements of these thin film unimorph cantilevers are almost the same as those of the bulk PZT-based ceramic bimorph cantilevers, if we compare the tip displacements of thin film cantilevers with the ceramic bimorph cantilevers under the same dimension. A suitable selection of substrates could further improve their piezoelectric properties.71,72

II. PREPARATION METHODS AND APPLICATIONS

II. PREPARATION METHODS AND APPLICATIONS

PZT composition

Substrates

Displacements δa (μm)

Piezoelectric e31,f (C/ m2)

Constants d31(pC/ N)

Deposition method

(001)PZT (52/48)

MgO

1.13

11.3

91.3

Sputter

Wasa et al.65

(111)PZT (53/47)

Si

1.33

10.1

107.2

Sputter

Kanno et al.24

(111) PZT(53/47)

Si

2.13

16.5

172

Sol-gel

Xiong et al.38

(001)PMnN-PZT

MgO

1.03

10.1

83.1

Sputter

Zhang et al.64

(111)PMnN-PZT

Si

1.95

14.9

158

Sputter

Zhang et al.70

(001)/(101)PZT (53/47)

Ti

0.5

5.6

47.7

Sputter

Kanda et al.71

Reference

δ*1: Tip displacement for thin film cantilevers, δ ¼ 3d31(L/hs)2V at V ¼ 10 V, L ¼ 10 mm, and hs ¼ 0.3 mm. Bulk PZT ceramic bimorph cantilever: δ ¼ 3d31(L/2t)2V, δ ¼ 0.75 μm for PZT (52/48) at V ¼ 10 V, L ¼ 10 mm, 2t ¼ 0.3 mm, and d31 ¼ 93  1012 C/N; δ ¼ 2.2 μm for PZT-5H at V ¼ 10 V, L ¼ 10 mm, 2t ¼ 0.3 mm, and d31 ¼ 274  1012C/N.

13.6 PZT-BASED THIN FILM MICRO-ELECTROMECHANICAL SYSTEMS (MEMS)

TABLE 13.10 Piezoelectric Properties of PZT-Based Thin Film Unimorph Cantilevers

519

520 13.

THIN FILM TECHNOLOGIES FOR MANUFACTURING PIEZOELECTRIC MATERIALS

FIG. 13.33

Photograph of PZT thin film cantilever on Si beam.

Fig. 13.33 shows a photograph of a typical PZT-based thin film cantilever fabricated on a Si beam. Fig. 13.34 shows the construction of the PZT-based thin film cantilevers without the substrate.73 The length of the cantilevers is 100–500 μm. The thickness of the PZT thin films is 2–5 μm. Since the wavelength of the fundamental transverse oscillation mode λ is 4L, and the longitudinal elastic wave velocity vs for the piezoelectric thin films is given by the relation: vs ¼ f0 λ, and the resonant frequency fn are expressed by
1=2 ð2n + 1Þf0 ¼ ð1=4LÞ 1=ρsE11 n ¼ 0,1, 2,3:

(13.13)

(13.14)

Fig. 13.35 shows typical resonant properties of the (001)PZT (53/47) thin film resonators. The resonant frequency is three orders of magnitude higher than the PZT-based thin films with Si cantilever beam. From the measurements of resonant properties, the sE11 values and vs for PZT thin films are estimated. The vs and sE11 values for the PZT thin films are 3520 m/s and 10.8  1012 m2/N, respectively. These values are the same as the bulk PZT values. This suggests that the elastic constants of the bulk PZT could be used for the design of the PZT-based thin film actuators.

13.6.2 Some Examples of the PZT-Based Piezoelectric Thin Film MEMS and Related Devices Several kinds of thin film MEMS and MEMS sensors are fabricated using the piezoelectric thin film actuators. The PZT thin film cantilever beams and diaphragms are used for the fabrication of the optical MEMS, II. PREPARATION METHODS AND APPLICATIONS

13.6 PZT-BASED THIN FILM MICRO-ELECTROMECHANICAL SYSTEMS (MEMS)

µm 500 400 300 200 100

50 µm

100–500 µm

PZT ~3 µm Pt ~100 nm Substrate

FIG. 13.34

Photographs of PZT thin film cantilevers without substrate Si beam.

1.5 f

f0

3

-3

Admittance (1 ¥ 10 /Ω)

f2 f1

1.0

0.5

0 0

FIG. 13.35

4.0

8.0 12.0 Frequency (MHz)

16.0

Typical resonant properties of the PZT thin film microcantilevers.

II. PREPARATION METHODS AND APPLICATIONS

521

522 13.

THIN FILM TECHNOLOGIES FOR MANUFACTURING PIEZOELECTRIC MATERIALS

TABLE 13.11

Summary of Thin Film Piezoelectric MEMS Devices

MEMS devices

Typical devices

Constructions

Optical MEMS

Micro-mirror Scanner Display Deformable mirrors

Laser beam Mirror

PZT thin film cantilevers Micro-optical scanner RF MEMS

Microwave switches Antennas Resonators Varactors Phase shifters (FBAR)

Power MEMS

Cantilever beam

Contact

Micro-strip line

Piezoelectric generators (Micro fuel cells) (Micro-gas turbine)

IDT Proof mass PZT 74 ZrO2 Membrane Si Micro-power generators

Micro-fluid devices

Bio-MEMS μ-TAS Micro-chemical reactors

MEMS sensors

Gyro-sensors Force sensors Pressure sensors IR sensors Gas sensors

Deflection

PZT thin film diaphragm PZT thin films Polyimide

Micro-pump for micro-fluid devices69

RF-MEMS, power MEMS, bio-MEMS, and/or MEMS sensors. Table 13.11 shows a summary of the piezoelectric thin film MEMS and thin film MEMS sensors. The optical MEMS devices are useful for fabrication of the optical switch, 1D or 2D optical scanners, and the display system. The deformable mirrors are useful in medical applications.75 The RFMEMS devices are useful for a mobile communication system due to the small power consumption with low voltage operations.76,77 The GHz PZT piezoelectric thin film resonators, FBAR (film bulk acoustic resonators), are also promising devices in the near future. The power MEMS comprises the micro-fuel cells and/or micro-power generators by using the piezoelectric effect.74 In the micro-fuel cells, the PZT thin film pumps will be applicable. The piezoelectric micro-power generators have been

II. PREPARATION METHODS AND APPLICATIONS

13.6 PZT-BASED THIN FILM MICRO-ELECTROMECHANICAL SYSTEMS (MEMS)

(A)

523

(B) Si

150 µm

FIG. 13.36

Construction of PZT thin film angular rate sensor.

developed for energy harvesting from the environment. Most of all, mechanical vibration is a potential power source. The micro-power will be used in wireless applications. In the micro-fluid devices, the cantilever and/or the diaphragm type pump is used for the operation of micro-fluid devices. Bio-MEMS devices comprise a micro-fluid device.78 The thin film pump is a key device for the stable operation of micro-fluid devices. Among these thin film MEMS devices, some of them, such as a gyrosensor and an inkjet printer head, are used in practice. In this section, the construction and operations of the gyro-sensors, the inkjet printer head, and the GHz-FBAR are described. 13.6.2.1 Gyro-Sensors The PZT thin films deposited on (111)Pt/Ti/Si substrates are used in practice for fabrication of a tuning fork type angular rate sensor in a car navigation system.6 A construction of the tuning fork type angular rate sensors is shown in Fig. 13.36. The tuning fork-type angular rate sensor, when an angular rate is applied to its vibrating tuning fork element, detects the Coriolis force exerted perpendicularly to its direction of vibration. The PZT thin films play two roles: generation of the tuning fork vibration and detection of the Coriolis force. The Si tuning forks with high aspect ratio were fabricated by Si deep etching. Table 13.12 shows the operating properties of the Si tuning fork type angular rate sensor. 13.6.2.2 Inkjet Printers The other example of piezoelectric PZT thin film MEMS used in practice is an inkjet printer head (see Fig. 13.37). The inkjet head consists of PZT thin film actuators, pressure chambers, ink canals and nozzle plates with water-repellent films. Each inkjet head has 400 nozzles and 400 pressure chambers. Typical operating properties of the inkjet head are shown in Table 13.13.6 II. PREPARATION METHODS AND APPLICATIONS

TABLE 13.12 Sensors

Operating Properties of Si Tuning Fork Type Thin Film Angular Rate

Operating temperature range

40 to +85°C

Power supply voltage range

5  0.25°C

Sensitivity

25 mV(°/S)

Frequency response (7 kHz)

>7 dB

Output voltage range

0.3–4.7 V

Output noise

1010 drops/nozzle

13.6.2.3 FBAR The thin film bulk acoustic wave resonator (FBAR) is currently of interest for key micro-devices in a GHz range for a mobile communication system.79 The bulk acoustic resonators use a longitudinal oscillation excited in the piezoelectric disc. The resonant frequency f0 is basically expressed by f0 ¼ vs/2d, where vs and d denote the phase velocity of longitudinal elastic wave and thickness of the piezoelectric disc. Conventional piezoelectric thin films are ZnO and AlN.80 Their phase velocities are vs ¼ 6400 m/s for ZnO and vs ¼ 11,000 m/s for AlN. Assume d ¼ 100 nm, f0 ¼ 3.2 GHz for ZnO and f0 ¼ 5.5 GHz for AlN. Although the mechanical quality factor Qm is high, the coupling coefficient kt is not sufficient for fabrication of wide band filters. PZT thin films have been tried in making the FBAR, since the kt of PZT ceramics is higher than ZnO and AlN. However, the Qm of PZT thin films is too small for fabrication of the FBAR. For fabrication of PZT-based FBAR, the ternary PZT-based thin films, PMnN-PZT thin films, will be useful. Fig. 13.38 shows a typical construction of the PMnN-PZT thin film FBAR.65 The FBAR comprises the high Qm thin films of the PMnN-PZT. The 0.3 mm thick (001)MgO substrates were used for

Al SiO2 PMN-PZT SRO Pt

MgO

FIG. 13.38

Construction of PMnN-PZT thin film for FBAR. II. PREPARATION METHODS AND APPLICATIONS

THIN FILM TECHNOLOGIES FOR MANUFACTURING PIEZOELECTRIC MATERIALS

60

1.5

50

1

40

0.5

30

0

20

−0.5

10

−1

0 3.5

3.7

3.9 4.1 Frequency (GHz)

4.3

−1.5 4.5

3.7

3.9 4.1 Frequency (GHz)

4.3

4.5

(A)

Phase j (rad)

Impedance Z (db)

526 13.

50 0

Q

−50 −100 −150 −200 3.5

(B) FIG. 13.39

Typical impedance properties of PMnN-PZT thin film FBAR.

fabrication of the FBAR structure. The FBAR structure comprised the PMnN-PZT thin films, 280 to 320 nm thick, SRO/Pt base conductive electrodes, and Al top electrodes. The thickness of the SRO, Pt, and Al electrodes were typically 50 nm, 60 nm, and 100 nm, respectively. The surface roughness of the PMnN-PZT thin films was 3 to 4 nm. The size of the Al top electrodes was 50 μm  50 μm. The outside of the Al electrode was covered by a layer of SiO2 100 nm thick. The back side of the MgO substrate was removed by chemical etching.66 The effective coupling factor keff was evaluated by the relation keff ¼ [(f2p  f2s /f2p]1/2, where fp and fs denote the parallel and the series resonant frequency, respectively. The kt was evaluated by the relation k2t ¼ (π/8)2 (k2eff)/(1  k2eff). The Qm was obtained by the phase change of the impedance at the anti-resonant frequency fp using the relation Qm ¼ 1/2ω(dϕ/ dω). These impedance properties were evaluated by a network analyzer. Their typical impedance properties are shown in Fig. 13.39 for the PMnNII. PREPARATION METHODS AND APPLICATIONS

527

13.7 CONCLUSIONS

TABLE 13.14

Figure of Merits of PZT-Based Thin Films for FBAR

Deposition

Composition

Freq. (GHz)

kt2 (%)

Qm

kt2 × Qm

Sputter

(111)PZT(58/42)

2

9

220

19.8a

MOCVD

(111)PZT(30/70)

2.1

22

30

6.6a

Sputter

(001)PZT(45/55)

3.9

52

110

57b

Sputter

0.1PMnN–PZT(55/45)

3.9

49

185

90.6b

a b

Muralt et al.81 Wasa et al.65

PZT thin film FBAR. From these impedance measurements, the doping effects of PMnN on kt and Qm were clarified. Table 13.14 provides a summary of the kt and Qm of the present sputtered thin films in comparison with reported values. The doping of PMnN into PZT increases the Qm. The sputtered PMnN-PZT thin films show the highest kt. The doping does not affect the kt. The high values of figure of merit, k2t  Qm, are observed. This suggests that the PMnN-PZT thin films have a potential to alternate with AlN piezoelectric thin film which is widely studied for making FBAR.81 Since the PMnN-PZT thin films show high kt, the PMnN-PZT thin films will be very useful for making wide band planar filters. From the impedance analyses of the PMnN-PZT thin film FBAR using BVD model, the capacitance of C0 is found to be 6.5 pF, which shows the relative dielectric constant of PMnN-PZT thin films is 88 at 4 GHz. The dielectric constants are by one order of magnitude smaller than bulk values. The small dielectric constant is useful for the operation of the GHz-FBAR. The high Curie temperature of 580°C observed in the PMnN-PZT thin films is also essential for the stable operation of the planar thin film filters. One of the reasons why high kt and high Qm values are observed in present sputtered thin films is their in-plane relaxed structure. The relaxed structure was achieved by the sputtering deposition followed by the quenching after the deposition. The second reason is the doping of the PMnN into the intrinsic PZT. The small doping of the PMnN, similar to the bulk ceramics, improves the Qm. The excess addition of the PMnN induces the growth of the pyrochlore phase resulting in the decrease in kt. Further improvement of composition will further increase the Qm.82

13.7 CONCLUSIONS This chapter describes the fundamentals of the thin film process of the PZT-based ferroelectric materials. The PZT-based ferroelectric thin films have been studied over the past 20 years. Production of these thin films has only just started, but environmental restrictions may terminate the II. PREPARATION METHODS AND APPLICATIONS

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usage of Pb-based bulk piezo-ceramics in the near future. Several processes are proposed for production of the Pb-based piezoelectric thin films. It should be remembered that each fabrication process has its own advantages and disadvantages. The sol-gel process is simple and the sol-gel–derived PZT thin films exhibit a high coupling value. However, their mechanical quality factor Qm is low. The piezoelectric properties of MOCVD-derived PZT thin films are similar to the sol-gel derived ones. The PZT-based piezoelectric thin films with high Qm and high coupling are obtained by the sputtering process. A suitable selection of deposition process is essential for the production of PZT-based ferroelectric thin film devices. We should also create an environmentally benign production system for PZT-based ferroelectric ceramics. In order to achieve this the key factors will be pollution prevention, waste minimization, and energy saving. Thin film material processing essentially meets these requirements. The PZT materials include toxic lead elements. However, the amount of lead in thin film PZT actuators is less than 0.3% of bulk PZT actuators, if we consider the thickness of PZT is 1 μm for thin film actuators and 300 μm for bulk actuators. The amount of lead in thin film actuators will be further reduced in multilayer and/or nano-composites. Therefore, it would still be possible to use PZT-based piezoelectric materials in the form of thin films.

Acknowledgments The author thanks R.E. Newnham, L.E. Cross, K. Uchino, S. Trolier-McKinstry, and T. Yamamoto for their helpful discussions, and H. Adachi, K. Nakamura, I. Kanno, T. Matsushima, and T. Matsunaga for their measurements of PZT-based thin films.

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74. Jeon YB, Sood R, Jeong J-H, Kim S-G. MEMS power generator with transverse mode thin film PZT. Sensors Actuators A 2005;122:16–22. 75. Kanno I, Kunisawa T, Suzuki T, Kotera H. Development of deformable mirror composed of piezoelectric thin films for adaptive optics. IEEE J Sel Top Quantum Electron 2007;13:155. 76. Kanno I, Endo H, Kotera H. Low-voltage actuation of RF-MEMS switching using piezoelectric PZT thin films. In: Reich H, editor. Micro system technologies 2003. Berlin: SpringerVerlag; 2003. p. 529–31. 77. Rebeiz GM, Muldavin JB, Tan G-L. MEMS switch library. In: Rebeiz GM, editor. RF MEMS – theory design, and technology. New York: Wiley; 2003. p. 151. 78. Zahn JD. Micropump applications in bio-MEMS. In: Wang W, Soper SA, editors. BioMEMS-technologies and applications. Boca Raton, FL: CRC Press; 2007. p. 151. 79. Lakin KM. Thin film resonators and filters, In: Proc. 1999 IEEE Ultrason. Symp., Lake Tahoe; 1999. p. 895–907. 80. Lobl HP, Klee M, Milsom R, Dekker R, Metzmacher C, Brand W, Lok P. Materials for bulk acoustic wave (BAW) resonators and filters. J Eur Ceram Soc 2001;21:2633–40. 81. Muralt P, Antifakos J, Cantoni M, Lane R, Martin F. Is there a better material for thin film BAW applications than AlN. Proc IEEE Ultrasonic Symp 2005;1:315–20. 82. Hwang SM, Yoo JH, Hwang LH, Hong JI, Ryu SR, Lee SI, Lee MS. Proc. of 13th IEEE ISAF; 2002. p. 367–70.

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C H A P T E R

14 Piezoelectric MEMS Technologies N. Korobova National Research University of Electronic Technology (MIET), Moscow, Zelenograd, Russia

Abstract This chapter will start by providing a general introduction on the working principle, material systems, and configuration of MEMS, followed by an overview of state-ofthe-art piezoelectric MEMS. As an introduction to the detailed presentations that follow, this chapter will give a qualitative overview of the key technologies and principles in the field, with some historical background. Topics will include mechanics and machine elements, electromechanical conversion, as well as microfabrication and system implementations. We will present the recent research works on modern piezoelectric MEMS, in which we will discuss the following: (1) MEMS design, (2) material development for piezoelectric MEMS, (3) microfabrication processes; (4) design optimization in terms of piezoelectric system configuration, and (5) process integration and device fabrication. Finally, we will examine key application areas for MEMS and how these are being assisted or enabled, or may be in the future, by developments in the field. Keywords Micro electromechanical systems, Microfabrication, Design, Device, Film, Sensing element, Actuator, Sensor.

14.1 INTRODUCTION With advancements in technology, the power demand of individual devices has drastically decreased. Therefore energy scavenging by converting vibration energy into useful output electrical power is looked upon as a promising solution. Mechanical vibrations are more popular compared to other available ubiquitous ambient energy sources. There availability is almost everywhere in the environment and easily converted

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into usable electrical power. In short, the micro electromechanical systems (MEMS) are processor-like microelectronics, but with ultrafine mechanical moving components, integrated into a single system with electronics. From a strictly scientific basis, the MEMS is a mechanical structure and it is created in a limited volume of a solid body or on its surface in the form of complex microsystems submillimeters in size. It is ordered composition of material with a specified structure and geometry, in which a static and dynamic combination enables the realization of processes generation, energy conversion, and transfer to the tight integration with the perception, processing, translation, and information storage in the programmed operations and actions in the required operating conditions with a predominantly functional, energetic, time and reliable indicators. Although this is a long and seemingly complicated definition, it is the most complete one I was able to find in the specialized literature on MEMS systems. MEMS is the technology used to create microminiature electronic mechanical devices. The MEMS pressure sensor is a MEMS sensing device that can detect and measure external stimuli such as pressure. It can respond to the measured pressure by having some mechanical movements, for example rotation of the motor, to compensate for the pressure change. The materials used to fabricate the MEMS pressure sensor are in micro-sized.1 On the other hand, the demands of the MEMS pressure sensor are growing with the vast development in various engineering fields. These include biomedical applications, automotive industry, control systems, and weather forecasts.2–4 In recent years, the study of MEMS has shown significant opportunities for microsensors and microactuators based on various physical mechanisms such as piezoresistive, capacitive, piezoelectric, magnetic, and electrostatic.1–5 Compared to other MEMS technologies, piezoelectric MEMS offers many advantages.5 Those devices utilizing the piezoelectric effect to convert mechanical strain into electricity are called transducers, which can be used in sensing applications, such as sensors, microphones, strain gages, etc., while those devices utilizing the inverse piezoelectric effect to generate a dimension change by adding an electric field are called actuators. They are used in actuation applications, such as positioning control devices, frequency selective devices, etc. Many works have been presented on the MEMS pressure sensors that have been developed in the 1970s.6 For example, accelerometers that have been manufactured for over 40 years utilize the phenomenon of piezoelectricity. They generate an electric charge signal proportional to vibration acceleration. The active element of accelerometers consists of a specially developed ceramic material with excellent piezoelectric properties. Piezoelectric accelerometers are widely accepted as the best choice for measuring absolute vibration. Compared to the other types of sensors, piezoelectric accelerometers have important advantages: extremely wide

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dynamic range; low output noise, suitable for shock measurement as well as for almost imperceptible vibration; excellent linearity over their dynamic range; wide frequency range; compact yet highly sensitive; no moving parts, no wear; self-generating, o external power required; great variety of models is available for nearly any purpose; and the acceleration signal can be integrated to provide velocity and displacement. Piezoelectric thin-film materials belong to the broad category of electronic ceramics, and they find applications in electronic and electromechanical devices ranging from tunable radio-frequency capacitors to ultrasound transducers. The importance of these materials has motivated a new generation of materials synthesis processes, leading to the creation of thin films and superlattices with impressive control over the composition, symmetry, and resulting functionality. In turn, improved processing has led to smaller devices, with sizes far less than 1 μm, faster operating frequencies, and improved performance and new capabilities for devices.7 Due to further miniaturization and technological development the MEMS device has evolved into a nano electromechanical system (NEMS) device.8 NEMS is defined as a technology used to create nanominiature electronic mechanical devices.9,10 The NEMS pressure sensor is fabricated by using a nanosized wire and a nanosized sensing element. Furthermore, the pressure sensor with NEMS technology has slowly gained much popularity in many applications. This is more advantageous than the MEMS technology, especially in terms of performance and cost. Thus, the NEMS pressure sensor is estimated to have better performance and lower cost as well as low power consumption.11 Also much of the MEMS devices has been taken from Refs. 3,5.

14.2 MEMS APPLICATIONS Vibration and shock are present in all areas of our daily lives. They may be generated and transmitted by motors, turbines, machine tools, bridges, towers, and even by the human body. While some vibrations are desirable, others may be disturbing or even destructive. Consequently, there is often a need to understand the causes of vibrations and to develop methods to measure and prevent them. The sensor can serve as a link between vibrating structures and electronic measurement equipment.12 Nowadays, the MEMS pressure sensor plays an essential role in many fields of application such as automotive applications and biomedical applications to monitor and measure the external pressure. In automotive applications, the MEMS pressure sensor is integrated into the automotive system to ensure the safety of the driver and passengers; some examples are a tire pressure monitoring system, diesel particulate filter, and brake

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booster. On the other hand, the MEMS pressure sensor is also used in biomedical applications. This includes the blood pressure monitoring system, respiratory monitoring system, kidney dialysis regulation system, and others.3,5 Piezoelectric thin films present a great interest for microsystems thanks to their reversible effect.13 Fig. 14.1 illustrates some types of MEMS sensor applications. Combining micromachined silicon membranes with piezoelectric thin films has resulted in novel microdevices such as (Fig. 14.2) motors,14 accelerometers,15–17 pressure sensors,1 (Fig. 14.3) micro pumps,18 actuators,19–21 and acoustic resonators.22 MEMS accelerometers have been integrated alongside gyroscopes for inertial guidance systems and instrument positioning systems. MEMS-based accelerometers have

FIG. 14.1

(A)

Types of MEMS sensors.

(B)

FIG. 14.2 (A) Micromotor with piezoelectric elements and drive sprocket (8 mm). It was set up in the UMR University laboratory; (B) hexapod system using six piezoelectric SQUIGGLE micromotors.23

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PZT component Diaphragm

Pump chamber Inlet flap 1000 µm Outlet flap 6000 µm

FIG. 14.3

Sketch of micropump cross section. Alternating voltage causes the PZT component to expand and contract along the horizontal direction. This induces a bending stress on the diaphragm, which in turn pumps the fluid through the chamber.1

undergone a large market increase recently because they are being incorporated into many personal electronic devices. Smartphones, personal digital assistants, and cameras are utilizing this technology to handle, for example, switching between landscape and portrait modes as devices are turned on their sides. Laptops are using MEMS-based accelerometers to detect shock-type events, protecting against hard disk crashes in the event of an unexpected drop. As you can see, there is a wide variety of specialized devices that can perceive changes in the environment and re-encode (transduser or convert) received information in optic or electrical signals; and rarely re-encode into mechanical motion of some elements in MEMS structures. Fundamental design today is available as a launch point for further development and customization; for example, the M3-HEX-1.8 is the world’s smallest 6 degree-of-freedom (DOF) motion system with an integral controller. It was developed in 2016 as part of a project funded by the National Eye Institute of the NIH to create a “clinically-compatible, handheld micromanipulator for hand tremor cancellation in microsurgical systems.” The system uses a hexapod configuration23 based on parallel kinematic principles to move a single platform in X, Y, Z, θx, θy , and θz. The design uses rigid struts with moving pivots to minimize the system diameter while maximizing the lateral force and stability of the platform. This tiny hexapod is just one example of how New Scale Technologies together with Carnegie Mellon University can create innovative and highly competitive products in less time. It was estimated that more than 10 billion MEMS chips were integrated into mobile phones in 2010 and that the global MEMS market will exceed $20 billion by 2017. Most of the MEMS devices and figures have been referred to Ref. 23.

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14.3 MEMS FABRICATION Many different types of pressure sensors have been implemented today. They can be classified according to their applications, such as high pressure and low pressure; type of measurements, such as absolute pressure and differential pressure; or their sensing element, such as piezoresistive, piezoelectric, or capacitive.3,5 The electronics are fabricated using integrated circuit (IC) processing sequences such as complementary metal-oxide semiconductor (CMOS) or bipolar CMOS (BiCMOS) processes.24 Today, in the almost twenty years of micromechanics’ existence in many academic laboratories (MIT Microsystems Technology Laboratories; Case Western Reserve University MEMS Labs; Southern California’s Information Sciences Institute MEMS Lab; University of Wisconsin-Madison MEMS Lab; Sandia National Laboratories; NASA Labs; DARPA MEMS Labs; UCLA MEMS Labs; Stanford University) and commercial companies (IBM, TRW, BF Goodrich, Rockwell, Standard Microsystems Corporation (SMC), Motorola, Delco, Honeywell, Allied Signals, Analog Devices, etc.), probably several hundred various technologies and design methods of MEMS systems have been created25 (Fig. 14.4). I will discuss only a few of them. EFAB (Electrochemical FABrication) technology. This is new technology based on the galvanic deposition of metals on an insulating surface and the subsequent dissolving of the insulating material. This allows the creation of a three-dimensional difficult intertwined mechanical microstructure.26 EFAB was developed by two research institutions— Information Sciences Institute (ISI) and University of Southern California—with funding from the military agency DARPA. As the EFAB developers say, unlike the traditional methods, EFAB technology allows

Chemicals Temperature

MEMS sensors

Sound Pressure

Analog signal processing

Digital signal processing

Analog signal processing

MEMS actuators

Mechanics

Light

Display Electrical power Other devices

Optical or electrical communication

FIG. 14.4

MEMS integration scheme with analog-to-digital CMOS systems.25

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you to create three-dimensional microstructure with a huge number of independent 5-micron layers, up to 1000. Besides, it does not require ultrapure rooms, it is fully automated, and it has fewer manufacturing steps. The time it takes to create each layer is only a few minutes, in contrast to other methods, where construction for a single layer may take several days. LIGA technology. In the early eighties at the German Nuclear Research Center in Karlsruhe (Karlsruhe Nuclear Research Center) the first technology with three-dimensional structures, LIGA, was developed. It was a few millimeters in height with very flat rectangular faces, and the cross-section of the MEMS parts was only 5–7 μm to 300–500, with high-energy radiation, precision casting polymers for a given form, and galvanic metal deposition on micro-surfaces . LIGA is an abbreviation of the German words LItographie (lithography), Galvanoformung (electroplating), and Abformung (pressing). The essence of the method consists of using radiation that was obtained using an elementary particles accelerator (synchrotron), instead of using simple x-ray radiation from the x-ray lamp. Synchrotron x-rays are very powerful, and they have an ultradivergence electromagnetic beam (no more 0,006°), in other words, and actually formed parallel beam, hence the very smooth vertical wall in MEMS structures. The depth of such x-radiation penetration in a polymeric material can reach a few millimeters, which is a large amount. Micro parts obtained by this method are very bulky and lack planarity. In short, the steps of the LIGA-technology are the following. (1) Deposit PMMA (polymethylmethacrylate) plastic film with thickness (
100 μm); (2) synchrotron X-rays pass through a given mask form,27 i.e., with the topological pattern of future detail. Since a chromium-plated mask itself does not transmit radiation, x-rays fall on the plastic only on the profile drawing; the drawing is then destroyed and formed in the recessed detail shape. A thin metal layer, such as nickel, is then applied. After the whole polymer is chemically removed, exposing the threedimensional shape of the metal parts, this subsequently will serve as a mold. Different molten polymers are filled in such a mold. Polymers are recovered after cooling and are polished by a very fine abrasive. The result is an MEMS item, such as a gear or toothed reversible balk. SUMMIT Technology (Sandia Ultraplanar Multilevel MEMS Technology) is based on the creation of four polycrystalline silicon mechanical structures where the first fixed layer (Silicon substrate) forms a mechanical and electrical foundation for the other three moving layers. The most perfect material for MEMS machines to date is a polycrystalline silicon (polysilicon, Poly-0, 1, 2, 3). Its mechanical properties are excellent: it is stronger than steel by more than 100 times, and it is more flexible and has less wear. Its production is fully compatible with modern IC-chip technology; moreover, it is used in the manufacture of the transistor

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FIG. 14.5

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MEMS fabrication.

element processor electrodes (Fig. 14.5). Conveyor production of MEMS systems is possible in high volumes and very low-cost production. Due to this, the polysilicon is widely used worldwide when creating micromachines. The mechanical structures of the MEMS systems are created using thin film techniques of photolithography and chemical etching. Eleven complex three-dimensional masks—the same amount as in the simpler CMOS IC process—are formed by repeating the procedures from layer to layer as with polycrystalline silicon structures and with the insulating layers SiO2- (Oxide-1,2,3). Further, SiO2 is chemically removed by etching, exposing outward the mechanical structure of polycrystalline silicon. The more layers in a planar micromachine, the more difficult it is, and the more tasks and functions it may perform. For example, freely rotating gears are manufactured in two mechanical layers lying on one core substrate. The more difficult arranged electrostatic engine has been made on three layers. SUMMiT-V Technology (Sandia Ultraplanar Multilevel MEMS Technology for five levels) already uses five layers, one of which forms a fixed platform. By using this technology it is possible to create the following: (1) more advanced micromachines with one or more mobile platforms, (2) taller machines that are up to 12 microns in height, (3) and machines that are more rigid and mechanically strong. The extra weight of moving parts can be used to achieve higher capacity drives. Current accelerometers are often MEMS, and they are usually very basic in design, consisting of a cantilevered beam with some type of deflection sensing circuit. Under the influence of acceleration the beam deflects from its nominal position and the deflection is measured using optical, capacitive, or piezoelectric techniques. MEMS represents the integration of micromechanical and electrical components with actuation and sensing elements onto a common substrate using microfabrication technology.28 Microaccelerometers are now in large-volume production, cost a few dollars, incorporate many functions, including self-testing, and have been shown to be extremely reliable for many years. This impressive level of

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FIG. 14.6

541

Operating principle of MEMS accelerometer.

performance has been achieved by resolving many obstacles in areas of device fabrication, interface and readout circuitry, assembly and packaging, and testing.12 The piezoelectric principle requires no external energy, and only alternating acceleration can be measured (Fig. 14.6). This type of accelerometer is not capable of a true DC response, e.g., gravitation acceleration. The high impedance sensor output needs to be converted into a low impedance signal first. For processing the sensor signal a variety of equipment can be used, such as (1) time domain equipment, e.g., RMS and peak value meters; (2) frequency analyzers; (3) recorders; and (4) PC instrumentation. However, the capability of such equipment would be wasted without an accurate sensor signal. In many cases the accelerometer is the most critical link in the measurement chain. To obtain precise vibration signals some basic knowledge about piezoelectric accelerometers is required. The active (or sensing) element of the accelerometer is a piezoelectric material. One side of the piezoelectric material is connected to a rigid post at the sensor base. A seismic mass is attached to the other side. When the accelerometer is subjected to vibration a force is generated which acts on the piezoelectric element. This force is equal to the product of the acceleration and the seismic mass. Due to the piezoelectric effect a charge output proportional to the applied force is generated. Since the seismic mass is constant the charge output signal is proportional to the acceleration of the mass.12 Over a wide frequency range both sensor base and seismic mass have the same acceleration magnitude hence the sensor measures the acceleration of the test object.29 The piezoelectric element

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FIG. 14.7 Three-dimensional model of sensing element: (A) for transducer linear acceleration; (B) tethered proof mass structure.31

is connected to the sensor output via a pair of electrodes (Fig. 14.7). To reduce the effects of secondary and torsional bending modes, another design incorporating four serpentine tethers was considered, Fig. 14.7B. This configuration allows for the addition of a proof mass to further lower the structure’s natural frequency. Some accelerometers feature an integrated electronic circuit that converts the high impedance charge output into a low impedance voltage signal. A piezoelectric accelerometer can be regarded as a mechanical lowpass with a resonance peak. Its equivalent circuit is a charge source in parallel to an inner capacitor. Within the useful operating frequency range the sensitivity is independent of frequency.30 The low frequency response mainly depends on the chosen preamplifier, and often it can be adjusted. With voltage amplifiers the low frequency limit is a function of the RC time constant formed by accelerometer, cable, and amplifier input capacitance together with the amplifier input resistance. The upper frequency limit depends on the resonance frequency of the accelerometer. In order to have a wider operating frequency range the resonance frequency has to be increased. This is usually achieved by reducing the seismic mass. However, the lower the seismic mass, the lower the sensitivity. Therefore, accelerometers with a high resonance frequency are usually less sensitive (e.g., shock accelerometers). Bulk micromachining of piezoelectric materials is of considerable interest since it allows for the direct integration of sensors and actuators into a monolithic structure.31 A fabrication process is developed allowing for both front and back side contact for electrical measurements. The effects of thin film stresses on the frequency response of piezoelectric membranes are investigated using experimental, analytical, and computational techniques. Results indicate that thin film stresses in silicon dioxide (SiO2) and Si3N4 can shift the natural frequencies of sensor membranes by as much as 20%.

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Optimization of sensor membranes is conducted using available numerical methods, particularly finite element analysis (FEA). Coupled electromechanical measurements of fabricated membranes are conducted and experimental results are compared with numerical and analytical solutions.31 Additionally, the optimized and often superior properties of bulk materials can be directly harnessed for these applications. Using multiple front and backside masks, ICP-RIE etches at various depths can produce stair-stepped structures from bulk piezoelectric substrates. Mask metallization provides ground and power electrodes that activate and/or measure the charge developed in specific areas of the structure to enable truly revolutionary MEMS devices.32 In the devices using additive process very often many researchers begin typical surface micromachining processes with the sequential deposition of passive, active, and electrode layers in the desired order. The piezoelectric device stack is patterned using a wet or dry micromachining processes. Finally the exposed sacrificial layer is etched to release the freestanding piezoelectric sensor structure.33 In the integrative process, precision micromachined piezoelectric (silicon) structures are integrated onto a silicon (piezoelectric) substrate.34 However, the success of this technique is predicated upon the availability of low temperature (preferably 30:1 for PZT etching. PZT is typically etched in fluorine or chlorine plasma. Using SF6 and Ar several groups have reported high aspect ratio etching of PZT.35 Much information about MEMS fabrication have been taken from Refs.12,35

14.4 PECULIARITIES OF PIEZOELECTRIC MEMS TECHNOLOGIES As you can see from Fig. 14.3 there are essentially three approaches to realizing piezoelectric MEMS devices: (1) deposition of piezoelectric thin films on silicon substrates with appropriate insulating and conducting layers followed by surface or silicon bulk micromachining to realize the micromachined transducers (additive approach); (2) direct bulk micromachining of single crystal or polycrystalline piezoelectrics and piezoceramics that are thereafter appropriately electroded to realize micromachined transducers (subtractive approach); and (3) integrating micromachined structures in silicon or piezoelectrics via bonding techniques onto bulk piezoelectric or silicon substrates (integrative approach).35 The most successful piezoelectric MEMS devices, at present, are the commercially available aluminum nitride-based film bulk acoustic resonators (FBAR) from Agilent Technologies.40 Another commercially available piezoelectric MEMS sensor is the family of quartz gyroscopes from the Systron Donner division of BEI Technologies.41

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Piezoelectric materials have attractive electromechanical properties for realizing micromachined sensors and actuators. Piezoelectric actuation is a bidirectional, linear, and reliable mechanism that does not exhibit failure modes associated with charge storage. The inherently large forces associated with piezoelectric actuation when coupled with micron scale structures enable submicrosecond mechanical response times at low bias voltages (5 –15 V) while consuming only microwatts of power.4 Piezoelectric materials can be available in bulk42 or thin film43 forms for transducer applications. These materials in either form can be integrated using appropriate micromachining techniques into micromechanical structures to realize the required transducers. Typically piezoelectric materials in the form of thin films from 100 nm to several tens of microns in thickness with piezoelectric properties approaching those of the corresponding bulk materials are desired. Properties of thin-film piezoelectric materials depend upon stoichiometry, film morphology, film density, impurities, and defects. In order to obtain a large response to mechanical deformations, piezoelectric films have to be grown with a textured structure with a high degree of alignment of the piezoelectric (poling) axis. Piezoelectric thin films can be deposited by several techniques such as sputtering, chemical solution methods, screen printing, and atomic layer deposition techniques.4 Reviews of the history of piezoelectric materials and properties in bulk form are available in numerous books.44–46 Comprehensive piezoelectric thin-film materials and devices reviews, which have seen much progress in the past 10 years, are also available to the interested reader.4,35,38,42,47 Table 14.1 summarizes some of the commonly used piezoelectric materials in MEMS applications.35 Piezoelectric thin films of materials such as lead zirconate titanate (PZT) have piezoelectric coefficients an order of magnitude higher than those shown by AlN and ZnO and enable a substantial reduction in the required drive voltages. The introduction of PZT into the MEMS fabrication process is difficult because PZT is not a CMOS-compatible material, and all wafer handling must take place in dedicated areas.48 Other piezoelectric materials, such as aluminum nitride (AlN), are TABLE 14.1 Comparison of the Mechanical and Electromechanical Properties of Quartz, Zinc Oxide, Aluminum Nitride, and PZT Materials35 Property

Units

α-Quartz (AT-cut)

Density

g/cm3

2.65

3.26

5.68

7.5–7.6

kt2

%

kp2 ¼ 8.8–14

6.5

9

7–15

1.05

1.0

e31, f

C/m

e11 ¼ 0.173

d33, f

pm/V

d11 ¼ 4.6 to 2.3

2

AlN

3.9

ZnO

5.9

PZT (thin film, 1–3 μm)

8 to 12 60–130

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5 Bonding pads

4

SiO2 Ti/Pt/Ti PZT

Bottom electrode Top electrode 3 2 1

Pt/Ti SiO2

PZT elements

Si

1.0 µm 0.2 µm 3.0 µm 0.2 µm 0.3 µm 3.9 µm

Proof mass 0.1 g

3

2 Supporting base 1

Supporting beam

FIG. 14.8 Schematic drawing of the energy harvester cantilever with a large proof mass to gain in low resonant frequency.54

CMOS-compatible and can be used to overcome these limitations.49 However, these materials have limited coupling coefficients between the electrical and mechanical domains, particularly for bending-induced strains. Current macro-based low frequency vibration sensors tend to be bulky, difficult to use in confined spaces, or outfitted on a mechanical component. The desire to miniaturize low frequency vibration sensors is driven by reducing weight and limited space requirements in mechanical equipment.50–52 These requirements push current research into the micro and nano scale for vibration sensing.53 Up to now one of the difficulties in the modeling and design is the presence of uncertain characteristics of thin film materials. The Young’s moduli of MEMS materials vary a lot based on different conditions. These values were found from publications, but they are not yet verified. The yield strengths of the materials are also hard to measure, especially for the PZT film (Fig. 14.8).54 This yield stress value of the PZT film is actually the property of a bulk PZT material. The real value of the yield stress of PZT thin film should be much lower. Based on the above reasons, the calculation of safety factor will not be accurate. But it can help to estimate the safety factor change from design to design.54

14.4.1 Lead Zirconate Titanate Films for MEMS Among the variety of available piezoelectric materials, the most popularly used material is lead zirconate titanate (PZT) due to its superior piezoelectricity.44 There are several available methods to grow PZT II. PREPARATION METHODS AND APPLICATIONS

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thin film, such as chemical solution deposition (CSD), which includes solgel,17,44,48,55, and metal-organic decomposition,56,57 RF/DC magnetron sputtering,58 metal-organic chemical vapor deposition (MOCVD), ion beam sputtering, pulsed laser deposition (PLD),59 and the electrophoretic deposition method.60,61 Among them, sol-gel is the most popular one mainly because of the low cost. Let’s summarize the characteristics of some film preparation methods: 1. Chemical Solution Deposition (CSD): sol-gel, metal-organic decomposition Deposit amorphous thin films at low substrate temperature, followed by post-annealing; low cost. 2. RF/DC Magnetron Sputtering: Deposit amorphous thin films at low substrate temperature, followed by post-annealing or deposit at high substrate temperature with in-situ crystallization. The sputtering was selected for mass production technology of perovskite oxide thin films owing to the following factors: good compatibility with conventional Si LSI processes; superb controllability of film quality (e.g., film composition), which enabled relatively easy thin film deposition; better possibilities of obtaining uniform surfaces in large diameter substrates (e.g., 6—8 in.); sputtering was plasma processing, which was promising for deposition and heat treatment at low temperature; feasibility of high speed deposition; used the same deposition method as electrodes (Pt, Ir, Ru, etc.), which will facilitate in-situ integration; and there are present difficulties and a lack of future potentialities in other technologies. 3. Metal-organic chemical vapor deposition (MOCVD): This is a deposit at a high substrate temperature with in-situ crystallization, and it is suited for integrated circuit (IC) production. MOCVD is a more complicated deposition process because it requires a cold-walled deposition chamber integrated with a liquid delivery system, a showerhead, a heater, and a specifically designed vaporizer. This deposition technique also tends to yield high surface roughness, causing degradation in the quality of the piezoelectric film. 4. Ion beam sputtering: This is a deposit at a high substrate temperature with in-situ crystallization. 5. Pulsed laser deposition (PLD): This is a deposit at a high substrate temperature with in-situ crystallization. PLD is popular because it easily allows for the reproduction of the chemical makeup of piezoelectric thin films, which means the coupling coefficients and electrical characteristics are well known and easily repeatable. However, it creates concerns similar to those of cosputtering in that it contaminates the fabrication facility, and it can also require the development of the ceramic target using a solid state reaction technique in which a conventional sintering process can be used. This is

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difficult because these types of processes are generally not available in conventional fabrication facilities.59 For piezoelectric MEMS applications, the formation of a perovskite structure is very important in the PZT thin film fabrication. Nucleation and growth of perovskite requires a precise stoichiometry, or formation of competing phases with fluorite and pyrochlore structures may be kinetically favored over the perovskite phase. At a low temperature, the fluorite phase is caused by O2 deficiency; at a high temperature, the pyrochlore phase is caused by heavy Pb loss due to high diffusitivity and volatility of Pb/PbO when the temperature is above 500°C. Activation energy for nucleation of perovskite is larger than for its growth (4.4 vs. 1.1 eV per unit cell), and it increases with Zr content.59,62 High-quality PZT films cannot be grown directly on silicon, and buffer layers are needed to prevent interdiffusion and oxidation reactions. For most applications, the PZT film has to be grown on an electrode, such as metal Pt, and metal oxide RuO2, SrRuO3, and (La,Sr)CoO3. Adhesion layers are used at the interface between SiO2 or Si3N4 and the bottom electrode. A proper adhesion layer can significantly reduce the PZT film stress, and it can affect PZT film properties. Possible adhesion layer materials: TiN, TiO2, Ti, Ta, Cr, ZrO2, Zr, Ru, etc.63–65 Besides the perovskite structure, the other important parameter affecting the property of PZT thin film is the residual stress. In thin film studies, only biaxial or in-plan stress will be considered. Compressive stress increases the switching polarization and coercive filed; tensile stress decreases the switching polarization and coercive filed. Tensile stress stabilizes domains oriented parallel to the plane of the layers; compressive stress favors polarization alignment perpendicular to the layer. The stretch or contract of PZT thin film lattice constant to match the lattice constant of substrate generates misfit strain, and it leads to lattice distortion, dislocation formation, piezoelastic domain wall generation, and motion. The elastic properties of PZT thin film can also be affected by the film composition and domain mobility. By the formation process, there are two types of residual stress: intrinsic and extrinsic stresses. Intrinsic stress is generated in film deposition and caused by film microstructure and lattice defects. Compressive stress is generally generated by ion bombardment. Extrinsic stress is caused by changes in volume or lattice parameter in film, densification, crystallization, and phase transformation during heat treatment. However, the most important residual stress in PZT thin film at room temperature is the thermal stress. It is caused by different thermal expansion coefficients of the substrate and PZT. Low Zr content exhibits compressive stress, and high Zr exhibits tension stress because the thermal expansion coefficient of film decreases with an increasing Zr/(Ti + Zr) ratio and the sign changes at about 0.25. The substrates and deposition techniques therefore have a significant influence on the

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TABLE 14.2 Dependence of the Residual Stress of PZT Thin Film on the Substrate Conditions67

Substrate

Deposition technology

Film thickness (nm)

Pt(150 nm)/Ti(15 nm)/ SiO2(400 nm)/Si

CSD

400

1200

Pt(70 nm)/Ti(4 nm)/SiO2/Si

CSD , annealed 3-layer

220

113

(100)Si

CSD, single layer CSD, >5 layer

82 –

200 20

Pt(100 nm)/Ti(50 nm)/ SiO2(20 nm)/Si

CSD, 3 layers CSD, 10 layers

104 405

228 515

Pt(170 nm)/Ta(20 nm)/ SiO2(700 nm)/Si

CSD

500

175

Sapphire

Electron beam evaporation and furnace annealing

300

30

Pt(100 nm)/Ti(50 nm)/ SiO2(500 nm)/SiNx(100 nm)membrane

Reactive sputtering, rapid temperature annealing

1000–2000

380

(111)Pt(40 nm) /TiO2(100 nm)/ SiO2(500 nm)/Si

Reactive sputtering and furnace annealing

750–1000

200

(111)Pt(40 nm)/TiO2(100 nm) / SiO2(500 nm)/Si

In-situ crystallization during reactive sputtering

750–1000

80–110

Pt(60 nm)/ZrO2(20 nm)/ SiO2(500 nm)/Si

In-situ crystallization during reactive sputtering

700–1200

170 to 300

(111)Pt(50 nm)/TiO2(50 nm)/ Si3N4(500 nm)/SiO2(200 nm)/Si

In-situ crystallization during reactive sputtering

1000

850  200

(100)Pt(100 nm)/(100)MgO

MOCVD

–

600–1600

Stress (MPa)

properties of PZT thin films.31,66 Table 14.2 lists the dependence of the residual stress of PZT thin film on the substrate and deposition techniques.67 From the literature survey we found that PZT/Pt/Ti/SiO2/Si is the most widely applied sequence.25,35,67 Oxygen migrates along the grain boundaries through the platinum film and reacts with the Ti. Titanium diffuses and reacts with oxygen and serves as nucleation centers for PZT and facilitates the formation of nucleation sites for perovskite PZT films and improved the adhesion between Pt and SiO2.68 There are two ways to improve the Ti out-diffusion: thicker Ti and thinner Pt, but (100) orientation decreases. It also decreases with the preparation temperature of the Pt/Ti layers; thermal treatment in O2 causes rapid oxidation of Ti and migration

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of Ti into the Pt layer.67 However, excess Ti diffusion not only gives rise to hillocks leading to a short circuit between top and bottom electrodes. It also decreases the total capacitance of PZT due to the low dielectric constant interfacial layer. Hillocks are generated by the volume expansion of the Pt layer due to oxidation of diffused Ti. Hillocks relieve the compressive stress of the Pt films, but size and hillock density leads to an electrical “short” of the PZT capacitors.31 There are several ways to control the Ti diffusion. In this the author proposed that a denser Pt film can control Ti diffusion.66 As the deposition temperature of Pt increases and the deposition rate decreases, the film becomes dense so that Ti out diffusion and film deformation are suppressed. Besides, preannealing Pt/Ti in the Ar atmosphere and decreasing O2 partial pressure during oxygen annealing will also control the Ti diffusion. A multilayer MEMS-scale piezoelectric cantilever power harvesting device is proposed based on PZT thin film, as shown in Fig. 14.9 PZT is deposited by one of the chemical solution deposition (CSD) methods, sol-gel. Although post annealing is required for this amorphous sol-gel PZT thin film and the fabrication process is complex, the cost of this method is very low. Buffer layer Ti is used to grow high-quality PZT films on silicon wafer to prevent interdiffusion and oxidation reactions. For this energy harvesting application, the PZT thin film has to been grown on an electrode. Platinum is used as the top and bottom electrodes because of its high conductivity, high melting point, and high stability in air at high temperature. Silicon dioxide was used to compensate for the internal stress. An adhesion Ti layer is used at the interface between SiO2 and the bottom electrode because a proper adhesion layer can significantly improve the adhesion, reduce the PZT film stress, and affect PZT film properties. A Pt/PZT/Pt/Ti/SiO2/Si sequence is applied to the MEMS-scale piezoelectric cantilever power harvesting device. Silicon is used as the proof mass, and the supporting layer to improve the mechanical strength of the beam.67 In the works64,69 PZT d33 mode cantilevers were fabricated using surface micromachining techniques. Low-stress silicon nitride (SixNy)

Pt (120 nm) PZT (1 µm)

Si (20 µm) Si (~500 µm)

Ti (10 nm) SiO2 (500 nm)

FIG. 14.9 Schematic diagram of the side view of an MEMS piezoelectric power harvesting device.67

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PZT ZrO2 SixNy Si

(A)

(B) FIG. 14.10 (B) surface.69

SEM of PZT deposited on ZrO2/SixNy/Si substrate: (A) cross section and

was used as the support layer. High-quality PZT films cannot be deposited directly on SixNy, so a buffer layer is needed to prevent reaction and interdiffusion (Fig. 14.10). ZrO2 has been shown to be a good buffer layer between PZT and a thermally oxidized silicon substrate. Thus, ZrO2 thin films were also explored as a buffer layer between the PZT and the low stress SixNy. Because the properties of PZT depend on the substrate, the structure and piezoelectric behavior of the PZT deposited on the multilayer ZrO2/SixNy/Si substrate were characterized by ZrO2 films. These films were deposited by a sol-gel method onto low stress silicon nitride SixNy coated silicon substrates. The PZT has the perovskite structure, with approximately random orientation, and an average grain size of about 3 μm. Good piezoelectric behavior, with a remanent polarization of 26 μC/cm2, is also observed in the PZT film. d33 mode cantilevers with a width of 100 μm, and lengths from 80 to 280 μm have been successfully fabricated using surface micromachining. The resonance frequencies of

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the cantilevers with lengths from 130 to 280 μm have been measured in the 6.1–28.6 kHz range, which agree with the simulations for T-shaped cantilevers. A tip displacement of 30 μm has been measured in the cantilever with length of 280 μm. The study of the displacement versus the magnitude and frequency of the applied field is in progress. The largest displacement is expected at an AC field with the cantilever’s resonance frequency. Also we want to note that Pt, Ir, and other rare metal electrodes and the PZT piezoelectric thin films that compose piezoelectric elements react poorly with halogen gases and their halides have low vapor pressures. For these reasons, such materials are called “hard-to-etch materials.” The following technical moments are important for dry etching of the PZT piezoelectric thin films for MEMS productions: (1) etching selectivity to resist mask and the bottom rare metal electrode; (2) adhesion of conductive deposit to the pattern sidewalls and damage to PZT; (3) plasma stability during continuous processing; (4) uniformity of etching rate within the wafer. For the first case a piezoelectric element film consists of PZT with a thickness of several micrometers and the rare metal electrodes with a thickness of about 100 nm. Generally, the bottom electrode is left after the PZT etching. Therefore, a low etching rate for the bottom electrode, the high etching selectivity, is important as a PZT etching condition. In the second case materials are hard to etch and their etching products easily adhere to the pattern sidewalls, and this results in leaks between the top and bottom electrodes. What is worse, the pattern sidewalls are exposed to reactive gas plasma during etching, and they tend to experience the release of lead and oxygen, and other damage. In the third case adhesion of etching products to chamber walls, especially the RF introduction window that generates plasma, causes instabilities of plasma and deteriorates the etching rate and the shape reproducibility. Avoiding of adhesion of etching products to chamber walls is important for mass production. For the fourth case as in the case of (1), to stop the thick PZT at the thin bottom electrode after etching, the uniformity of the etching rate within wafer is important.38 However, poor stability and loss of polarization with continuous usage are the major issues with PZT. Their piezoelectric properties are also strongly affected by operating temperatures and due to brittleness they cannot be deformed mechanically for long duration. A four-mask process was used to fabricate the PZT cantilever, as shown in Fig. 14.11. The fabrication process began with a 100-mm low-cost bare silicon wafer. SiO2 was grown on both sides of the silicon wafer by the wet O2 method. Interlayer Ti and electrode Pt were deposited one after another by magnetron sputtering. PZT was deposited layer-by-layer using the solgel method to reach a thickness of 1 μm. The top electrode was patterned by the first mask and obtained by liftoff process after Pt deposition on a layer of patterned photo resist (PR). The bottom electrode together with

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(A)

(B)

(C)

(D)

(E) Si

SiO2

Ti

Pt

PZT

PR

FIG. 14.11 Fabrication flow chart: (A) multilayer deposition; (B) top electrode patterning by liftoff (mask 1); (C) bottom electrode opening via RIE (mask 2); (D) cantilever patterning by RIE (mask 3); (E) proof mass patterning and cantilever release via backside RIE (mask 4).67

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the cantilever structure were patterned by the second mask and etched by inductively coupled plasma (ICP) reactive ion etching (RIE) to create a bare window for easy access during wire bonding. The cantilever structure without the bottom electrode was then patterned by the third mask and etched by RIE. The back side proof mass was finally patterned by the fourth mask and the cantilever structure was finally released after back side Si RIE.67 Thus, we can conclude that piezoelectric materials such as lead zirconate titanate (PZT) have potential applications in a wide range of miniaturized devices, including RF components (e.g., fixed capacitors, varactors, and resonators), piezoelectric sensors, and actuators. However, the high processing temperatures required to produce dense and fully crystallized piezoelectric layers can make integration of these materials into such devices challenging. For example, thin film processing methods typically involve annealing temperatures in the range 500–700°C.70 This precludes fully monolithic fabrication on low-temperature (e.g., polymer) substrates that are of increasing interest in consumer electronics. Even with traditional substrate materials such as silicon the design possibilities are reduced because the piezoelectric film has to be deposited at an early stage before other materials are introduced. These compatibility issues are even more severe for thick films produced by tape-casting or screen printing, where sintering temperatures in the range 800–1000°C are typical. The difficulties associated with fully monolithic integration can be avoided by forming the piezoelectric film on a high-temperature growth substrate and then transferring it to a second “target” substrate where the rest of the device fabrication will take place. This kind of transfer can be achieved by bonding the film to the target substrate and then removing the growth substrate by some combination of mechanical grinding and chemical etching. However, this approach is laborious and wasteful of the growth substrate material. Another possibility is to use a growth substrate with a thin sacrificial layer, for example a metal oxide, that can be selectively etched away to release the film. A third option, which avoids the use of any wet chemicals during release, is to use laser transfer processing (LTP), also referred to as laser liftoff (LLO). Here the film is released from the growth substrate by a pulse of laser radiation incident through the substrate. The laser wavelength is typically ultraviolet (UV), and it is chosen such that the substrate is highly transmissive while the film to be transferred is strongly absorbing. The incident laser energy is absorbed in a thin layer of the film adjacent to the interface with the growth substrate, causing delamination to occur. The delamination process is generally attributed at least partly to ablative decomposition of the film, although in principle it could result purely from thermally induced shear stresses at the interface.70 A number of surface micromachined actuators utilizing PZT films have been reported.25,31,35,59,66,67 Furthermore, the recently available single II. PREPARATION METHODS AND APPLICATIONS

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crystal relaxor ferroelectric materials such as lead magnesium niobatelead titanate (PMN-PT) offer even higher performance figures in comparison to conventional piezoceramics.71 The ultrasound transducers of which center frequencies are lower than 10 MHz are commonly used in low-frequency photoacoustic (PA) imaging systems. However, the improvement of their sensitivity is still needed to detect weak PA signals. A circular array transducer was constructed by using 120 needle hydrophones made of piezoelectric single crystal lead magnesium niobate-lead zirconate titanate (PMN-PZT).71 The needle hydrophone was designed to have high sensitivity and wide bandwidth through the Krimtholz-Leedom-Matthaei (KLM) simulation of receiving impulse response. The sensitivity of the fabricated PMN-PZT hydrophone was compared with a commercial poly(vinylidene fluoride) (PVDF) needle hydrophone. The usefulness of the circular array transducer was demonstrated by applying it to a PA system for obtaining images.71–74 Based on their high piezoelectric response, lead zirconate titanate (PZT) thin films are natural candidates for microsensors and microactuators; however, the piezoelectric properties of bulk ceramics can be optimized by the addition of dopants.75 Only a few papers have been published regarding Nb-doped PZT in thin film form.58,76,77 Sol-gel thin PNZT films were prepared by spin coating the Pb1.1Nb0.04Zr0.2Ti0.8O3 solution onto platinized silicon substrates at 3000 rpm for 30 s. The substrates used were (100) Si wafers with a 150 nm thick (111)-Pt bottom electrode. The effect of processing on the ferroelectric and piezoelectric properties of sol-gel grown Pb1.1Nb0.04Zr0.2Ti0.8O3 (PNZT) thin films was investigated in Ref. 76. The effective d31 piezoelectric coefficient of as-grown films was measured using piezoelectrically actuated cantilevers. The results indicate that films annealed after each layer possess a significant internal field, leading to high piezoelectric coefficients in the as-grown PNZT films. But the films annealed in the final step possess a very small internal field and, consequently, small piezoelectric response. This is due to the strong internal field, which poles the sample almost completely. External electric fields cause ions in the piezoelectric sample to align, a process called “poling.” So, when a field with an upper negative electrode is applied, the poling field was antiparallel to the internal field and the piezoelectric coefficient showed large changes. The piezoelectric coefficient decreased at first, since the poling field was switching the orientation of the domains, decreasing the polarization. The piezoelectric coefficient began increasing when the applied field was strong enough to increase the polarization in the opposite direction relative to the initial one. Takamichi Fujii et al.58 developed a method of forming PZT films with Nb dopant (12%) on silicon substrates with a high piezoelectric coefficient using RFsputtering. Across the 6-inch wafer plane the film exhibited excellent structure and composition. Authors confirmed that the film requires no polarization process because

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it is prepolarized immediately after its deposition. They used an Si substrate with a (100) orientation, and they formed PNZT film with their original RF magnetron sputtering equipment that allows 6-inch film formation. First, a 20-nm Ti adhesion layer was formed on the Si substrate by sputtering. Then, a 150-nm lower Ir electrode was deposited. On that substrate PNZT film was formed by sputtering using a Pb1.1(Zr0.46Ti0.42Nb0.12) O3 target. The ratio of Zr to Ti in the target was set 52:48, which is the same as that of the morphotropic phase boundary (MPB). That composition achieves the highest piezoelectric constant and electromechanical coupling coefficient; therefore, it is suitable for actuators. Using a deposition temperature between 450 and 550°C, authors succeeded in the formation of stable PNZT film with piezoelectric constants, d31 and e31,f of 250 pm/V and 25.1 C/m2 respectively. It proves that the performance of the film is much higher than conventional genuine PZT materials. Zinc oxide (ZnO) is another important piezoelectric material that is popularly used as one of the pollution-free piezoelectric material and is free from limitations found with PZT.78 ZnO is highly tensile and may undergo huge mechanical deformations for a long duration without the effect of temperature variation. Therefore it has received increased attention for various MEMS device applications.79–81 Due to the unique combinations of electrical, optical, and piezoelectric properties of ZnO, it has great potential for applications in solar cells, photo detectors, and light emitting diodes (LEDs), also it can be easily integrated with other processes and materials. However piezoelectricity of ZnO is generally smaller than that of PZT,80 but it has the additional advantage of flexibility in processing. ZnO thin films can be deposited at room temperature and a variety of acidic etchants are also available.81 ZnO is an n-type semiconductor with a wide direct band of 3.3 eV (at room temperature), good electron transporting properties, and solution-based processability at low work function. It has a hexagonal quartzite structure and large excitation binding energy of 60 meV, which makes ZnO a potential material to realize the next generation of MEMS and UV semiconductors.82 Fabrication and characterization of ZnO piezoelectric microcantilevers by the simple and inexpensive wet etching method has been discussed. Most importantly, it was demonstrated as a simple cost effective platform for the development of vibration-based energy scavengers. Multiferroic/ZnO composite microcantilever energy harvesters are also under investigation with a change in dimensions and design to increase and store the generated energy from vibrations. The obtained values of Young modulus and hardness are 208  4 GPa and 4.84  0.1 GPa, respectively. The transverse piezoelectric constant d31 of the ZnO film calculated data obtained from LDV is -3.32 pC/N. Peihong Wang et al.83 reported about ZnO energy harvesters that were fabricated by using MEMS micromachining. The natural frequencies of the fabricated ZnO energy harvesters were simulated and tested.

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The test results were shown that two energy harvesters with different designs had almost the same natural frequency. The effects of series connection and parallel connection of two ZnO elements on the load voltage and power were also analyzed. The ZnO thin film microcantilever energy scavenger route opens the possibility of innovative research and may be the future replacement for traditional bulky batteries in sensing applications.84 Electroactive polymers are emerging in the fields of actuators and microsensors because their good dielectric and mechanical properties make them suitable for such applications.85 Martinez and Artemev86 try to analyze the possibility of a pressure sensor design. The authors consider a relatively simple C-shaped piezoelectric element embedded into a cubic shaped polymer matrix. It was important to note that this study focuses on the piezoelectric element of the pressure sensor that can then be incorporated into the different sensor designs employed to augment the voltage output of the sensing elements. PVDF (CH2–CF2)n is a piezoelectric material having a solid structure with approximately 50%–65% crystallinity.87 The morphology consists of crystallites dispersed within amorphous regions. During the manufacturing process the PVDF sheet is stretched to cause a chain packaging of the molecules into the piezoelectric crystalline phase. These dipole moments are randomly oriented and result in a zero net polarization. In the polarization stage the polymer is exposed to a high electric field. The dipoles are oriented in the direction of the field and a net polarization is formed. Finally, the film is metalized to provide electrodes. The change in film thickness due to an external force compressing the film generates a charge and thus a voltage appears at the electrodes. The piezoelectric coefficient dij is related to the electric field produced by a mechanical stress; the first suffix i ¼ 1, 2, 3 refers to the electrical axis and the second, j ¼ 1, 2,……, 6, refers to the mechanical axis. The dij is a third-rank tensor conventionally expressed in terms of a 3 x 6 matrix; however, crystal symmetry reduces the number of independent piezoelectric coefficients. The model presented in this study87 predicts the sensor operation of a sensor constructed from piezoelectric PVDF material. L. Persano et al.88 introduce a large area of flexible piezoelectric material that consists of sheets of electrospun fibers of the polymer poly[(vinylidenefluoride-co-trifluoroethylene]. The flow and mechanical conditions associated with the spinning process yield free-standing, three-dimensional architectures of aligned arrangements of such fibers, in which the polymer chains adopt strongly preferential orientations. The resulting material offers exceptional piezoelectric characteristics, to enable ultrahigh sensitivity for measuring pressure, even at exceptionally small values (0.1 Pa). Quantitative analysis provides detailed insights into the pressure sensing mechanisms, and it establishes engineering design rules. The potential applications range may be from self-powered micromechanical elements, to self-balancing robots and sensitive impact detectors.

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Yongqiang Qiu et al.89 reported about bulk piezoelectric transducers that use the thickness-mode motion of a plate of piezoelectric ceramic such as PZT or single-crystal PMN-PT. This PMUT was based on the flexural motion of a thin membrane coupled with a thin piezoelectric film, such as PVDF. In comparison with bulk piezoelectric ultrasound transducers, PMUT can offer advantages such as increased bandwidth, flexible geometries, natural acoustic impedance match with water, reduced voltage requirements, mixing of different resonant frequencies, and potential for integration with supporting electronic circuits especially for miniaturized high frequency applications. A flexible PMUT capable of wrapping around a human finger and producing fairly good images was developed by a group from Tsinghua University. Much of the content has been taken from the Refs.67,69.

14.5 PIEZOELECTRIC MEMS FOR SEMICONDUCTOR TESTING It has been established that packaging, assembly, and testing can account for between 50%–75% of the total cost of the solution with testing accounting from between 25% and 35% based upon the device and its intended application. Many MEMS suppliers consider testing to be a major product differentiator in the market. Efforts are underway to help the MEMS industry better understand the issues of MEMS testing and to develop testing standards for MEMS.

14.5.1 How to Test the Piezoelectric Films? The structure of the as-deposited piezoelectric films can be determined using the x-ray diffraction (XRD) method. (XRD) is a nondestructive and efficient technique used to characterize unknown crystalline materials and orientations. X-rays are reflected from evenly spaced planes of the crystalline material, producing a diffraction pattern of spots called reflections.66,67 Advances in x-ray scattering characterization technology now allow piezoelectric thin-film materials to be studied in new and promising regimes of thinner layers, higher electric fields, shorter times, and greater crystallographic complexity. Understanding the atomic origins of piezoelectricity, particularly at nanosecond time scales, has proved challenging, but new techniques based on x-ray scattering address this void. X-ray diffractometry techniques provide direct insight into the piezoelectricity of ceramics and epitaxial oxides.90–92 Also, scanning electron microscopy (SEM) can be used to investigate the grain size and

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shape of the piezoelectric film after fabrication. SEM scans the surface of a sample with a high-energy beam of electrons in a raster scanning mode. The beam of electrons interacts with the sample producing a signal that contains information about the sample’s surface topography.66 SEM can also be used for failure analysis to monitor crack propagation and initiation as well as capturing defects and impurities in samples. Auger electron spectroscopy (AES) and x-Ray photoelectron spectroscopy (XPS) are well-established techniques to reveal the elemental composition of the outermost atomic layers of a sample. The two techniques are largely complementary. XPS is rather more sensitive and gives more information about the chemistry, while AES is faster and has a higher spatial resolution. Combined with the successive removal of material by inert gas ion sputtering, both techniques are widely used for in-depth profiling through layer stacks to detect, e.g., interfacial contamination and interlayer migration. Due to their inherent sensibility to the chemical states of the detected species AES and XPS are indispensable tools for the corroboration of reaction zones. Wavelength-dispersive x-Ray fluorescence spectroscopy (XRF) is a nondestructive analytical technique used to identify and determine the concentrations of the elements in solids and liquids. The composition of piezoelectric films has been measured by XRF. The thinness, faster operating timescales, and novel structural degrees of freedom available in epitaxial piezoelectric thin films pose difficult challenges for characterization using conventional experimental methods. Researchers have developed a series of powerful, now standard, characterization techniques based on measuring the displacement of the surface of the thin film using piezoelectric force microscopy or interferometry. Alternatively, the stress imparted by the piezoelectric material can be quantified using the curvature of the substrate or a cantilever. Another approach is to use focused ion-beam milling or selective etching to create a bridge structure or cantilever into the film by removing a section of the underlying substrate and to observe the distortion of the shape of this structure. These approaches have proved to be phenomenally successful, but they face important limits, particularly regarding time resolution and the precision with which the relationship between atomic scale effects and the overall electromechanical distortion of the sample can be determined. Ellipsometry uses the reflection of linearly polarized light to measure the film thickness of thin films.93 An ellipsometer measures the phase difference between the parallel and perpendicular component before and after reflection, and the intensity ratio between the perpendicular and parallel component after reflection. These two parameters can then be used to calculate thickness and index of refraction of the thin film with a proper model (e.g., Cauchy model). The model can also handle multilayer systems or multicomponent layers. Porous films with many voids have

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to be considered as a two component. The advantage with ellipsometry is the possibility to measure both the index of refraction and the film thickness without anything else other than a mathematic model of the surface reflection. Due to the relatively large surface needed for this method (5  15 mm), ellipsometry is used only for nonpatterned samples.66,67 Sheet resistance measurements were performed after sputtering and heat treatment of thin metallic films in order to determine crystallization, oxidation, or interdiffusion. The sheet resistance Rs is defined as the resistance per unit area of a film with a constant thickness t. The most common method for measuring the resistivity r of a film is the four-point probe method. In this method a constant current is passed between two outer probes, and the voltage drop across the middle probes is measured.66 By properly selecting the probes, probe separations, and current, the voltmeter reading can directly give the sheet resistance Rs. The piezoelectric property, such as hysteresis loop of piezoelectric film was characterized, for example, by a TF analyzer 2000 measurement system (axiACCT systems),67 or the high field piezoelectric hysteresis properties can be characterized using a ferroelectric test system (Radiant Technology, Albuquerque, NM) with an amplifier. An impedance analyzer can be used to measure the fundamental resonance frequency, and a Zygo interferometer can be used to determine tip deflection. A remanent polarization can be obtained from the loop, which is close to the value for piezoelectric films deposited on metal bottom electrodes for d31 actuation. Thorough this test, the quality of the piezoelectric film and the top electrode of a device can be easily estimated since we have already a large amount of data about the piezoelectric properties of the piezoelectric film. If there is a signal of short circuit, it is likely the device is bad. If there is a signal of open circuit, the connection of wires should be examined. The resonant frequency of device was characterized by the impedance analyzer, for example (Agilent Technologies, 4294A).67 Usually, resonant frequency is the one of the main targets of the investigation. The electromechanical resonances of the released cantilevers can be investigated by measuring the impedance of the piezoelectric actuator as a function of frequency. For example, CoventorWare can be used to simulate the resonance frequency results. To observe the bending, the cantilevers can be put in the SEM chamber and an external DC voltage V is applied. The magnitudes of the bending displacement can be measured using the Zygo interferometer. Usually, the displacement increases with beam length.69 Typically, the actuators entail a cantilever beam consisting of a thin structural material supporting a piezoelectric film sandwiched between top and bottom electrodes as shown as an example in Fig. 14.12. The in-plane strain x1 in the PZT, induced by an external electric field E3 normal to the plane, is expressed by the converse piezoelectric

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X1

X1

Top electrode Bottom electrode

PZT

P3

V

E3

Support

(A) IDT electrode V X3

X3 PZT Buffer layer

P3

E3

Support

(B) FIG. 14.12 Schematic diagram of cantilever actuated by (A) d31 mode and (B) d33 mode for microswitches (they are not drawn to scale).69

effect: x1 ¼ d31E3, where d31 is the transverse piezoelectric coefficient, typically a negative number. When a voltage is applied to the top and bottom electrodes, the PZT film contracts laterally for E3 parallel to the remanent polarization (Pr) of PZT, which makes the beam bend up. PZT expands laterally with E3 antiparallel with Pr, bending the beam down. However, the polarization state changes when E3 is large compared to the coercive field of PZT. The large E3 repoles the PZT, again making E3 parallel with Pr, which makes the beam bend up again. Thus, this kind of cantilever can produce large upward bending displacements, actuated by the piezoelectric d31 effect of the PZT. When an interdigitated (IDT) electrode is deposited on the top of PZT as shown in Fig. 14.12B, both the applied electric field and the polarization are largely in the plane of the PZT film. The induced in-plane strain x3 resulting from an in-plane electrical field E3 is also expressed by the converse piezoelectric effect: x3 ¼ d33E3, where d33 is the longitudinal piezoelectric coefficient of PZT, typically a positive number. The transverse piezoelectric strain is converted into cantilever bending, so the beam is actuated by the piezoelectric d33 effect of the PZT. It is well known that the magnitude of the d33 coefficient of PZT is about twice the d31 coefficient, thus cantilever beams actuated by the d33 effect are expected to produce substantial deflections. Fig. 14.12B also shows that d33 mode cantilevers are primarily downward-moving cantilevers since

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the PZT film expands in-plane when E3 is applied parallel to Pr; again note that the magnitude of E3 is limited by the coercive field value when applied antiparallel to Pr.69 Due to the complexity of MEMS device and fabrication, the simplified model could show large deviation. Therefore, the model or even the parameters used in the model should be optimized by comparing the experimental results and the calculation. The output behavior of device was characterized again by the experimental setup, and it was measured by varying resistance loads, vibration frequency, and vibration acceleration. By varying the resistance loads at certain acceleration, the optimal resistance can be found. By varying the vibration frequency at certain acceleration, the resonant frequency at the vibration acceleration can be found.67 One of the common tools for the electrical characterization of piezoelectric materials is the hysteresis loop test.93 Hysteresis effects in ferromagnetic materials are well documented, where external magnetic fields are applied to a sample and magnetic flux densities are measured. Very similar behaviors are observed during hysteresis loop testing of piezoelectric materials (Fig. 14.13). External electric fields cause ions in the piezoelectric sample to align, a process called “poling.” As with its ferromagnetic analog, piezoelectrics exhibit saturation polarization values Ps as well as remnant polarization Pr values when the field is reduced to zero. The coercive electric field value, EC, is defined when the polarization is zero but the field is nonzero. The area contained within the bounds of the hysteresis curves is directly proportional to the electrical work required to polarize the piezoelectric material. The ideal shape of this curve would be wide in the middle, with little difference between the remnant and saturation

P b c

Pr

d Ec

a

Ec

E

e

FIG. 14.13

Polarization vs. electric field hysteresis loops for a piezoelectric material.

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values for polarization. This would ensure that all of the work occurs between the remnant polarization values, which are where these types of devices are intended to be used. Because there is very little change in polarization once the device reaches its remnant state the amount of work that can be extracted from the device beyond that point diminishes even with large increases in power supplied via the electric field. Another common tool is the relative dielectric constant (er) vs. the voltage (V) test, which allows for the determination of relative dielectric constants. er -V curves exhibit a “butterfly behavior” with the maximum relative dielectric constants near the coercive electric field value. At these peak relative dielectric constants, the charge storage capacity is maximized. The shape of this curve is indicative of hysteretic behavior also as the changing electric field modifies the orientation of the dipoles thus changing the capacitance in the structure. The peaks of the er-V curve correspond to large polarization changes where the ferroelectric domain is switching from one orientation to another. The “butterfly” curve has peaks at voltages that correspond to the coercive field strength of the film. At higher voltages the relative dielectric constant decreases. The need to provide rigorous, high throughput and low-cost testing is paramount in the battle for market share. There is a great deal of test equipment for MEMS, MEMS test cells for example. This modular equipment, combining pick-and-place handling, testing, and physical stimulus for functional test and calibration (including test at temperature), is now enriched by additional stimulus units, while enhanced handling performance provides greater throughput and accuracy. The range of testable devices now includes inertial MEMS, pressure sensors, MEMS microphones, UV sensors, etc. Applying physical stimuli to MEMS devices during testing guarantees the correct calibration of the devices, and it keeps all the tolerances and parameter spreads related to frontend and backend manufacturing processes under control. Parameters like zero-g level and sensitivity are fundamental for the final customer application and need to be guaranteed by proper calibration during testing on automated test equipment (ATE). The cost of test results is greatly reduced, thanks to the high throughput, the lower investment, the short application development time, and the rapid accommodation of different applications. Automotive, aerospace, telecommunications, security, aviation, marine, medical, and entertainment are just some of the areas in which testing systems are used daily. Their reliability, their unmatched productivity, and adaptability have become essential tools in a technological market in which the competition is getting tighter. Much of the content and figures have been taken from the papers (Refs. 67,69).

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14.6 NEW BROAD BENEFIT OF PIEZOELECTRIC MEMS Mainly driven by the automotive industry, piezoelectric MEMS have been the subject of extensive research and development over the past few years. The performance of piezoelectric MEMS has drastically improved over a rather short period. Much effort is also under way for large-volume production of piezoelectric MEMS. Production cost, performance, and reliability are the key factors in commercializing piezoelectric sensors. Precision micromachining, robust vacuum packaging, and high-performance interface circuit and electronic tuning techniques are required to reduce the production cost to a level that is acceptable for the large-volume market. By shrinking the capacitive gaps to nanometer levels, bias and control voltages will also shift down to CMOS acceptable levels. Future high-performance tactical- and inertial-grade sensors will make use of dynamic electronic tuning of the structure to compensate for temperature and long-term drift effects of the sensor.35 Further progress is also anticipated in the development of integrated multiaxis devices on a single chip, for example, six-degree-of-freedom, fingernail-sized inertial measurement unit (IMU) with integrated signalprocessing and control circuitry.94 From a technology point of view MEMS us not limited to silicon-based technologies, and it integrates polymer-based technologies, printing technologies (e.g., for printed antennas, printed sensors, displays, or batteries), different nanotechnologies, and even embroidering technologies for sensors as well. Piezoelectric thin-film materials belong to the broad category of electronic ceramics, and they find applications in electronic and electromechanical devices ranging from tunable radio-frequency capacitors to ultrasound transducers. The importance of these materials has motivated a new generation of materials synthesis processes, leading to the creation of thin films and super lattices with impressive control over the composition, symmetry, and resulting functionality. In turn, improved processing has led to smaller devices, with sizes far less than 1 μm, faster operating frequencies, and improved performance and new capabilities for devices. Important work continues to build on these advances to create materials that are lead-free and that incorporate other fundamental sources of new functionality. In general, all-silicon, mixed-mode (bulk/film) fabrication technologies, combined with high-aspect-ratio deep dry-etching techniques, can provide features that are required for future high-performance piezoelectric MEMS. Formation of nanometer capacitive gaps through sacrificial layer etching, high-aspect-ratio, and thin structures with high quality factor and uniform material properties, along with chip-level vacuum packaging, will help improve the performance by orders of magnitude. Further

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miniaturization of the MEMS sensor into an NEMS device offers better performance and lower manufacturing cost. The NEMS sensor consumes less energy than the MEMS technology. With these advantages, the NEMS sensor has increasingly attracted attention in recent years. In spite of advances in piezoelectric material deposition, processing, patterning, and integration methods, at present only a limited number of piezoelectric devices have been successfully commercialized and several fabrication-related challenges still remain. For example, chemical solution methods offer attractive low-cost methods for the deposition of uniform films of piezoelectrics; however, the success of these methods is still predicated upon the use of appropriate layers for proper nucleation and film growth. As a consequence the sensor structure often consists of multi-layered material stacks and requires extensive device-specific development efforts. Further understanding of thin-film piezoelectric materials is also required to reduce and control material and sensor drift and aging characteristics. Optimization of the residual stress in individual layers to result in an overall stress compensated sensor structure continues to pose a significant challenge. Development of deposition techniques resulting in thin films with properties approaching those of bulk materials is another area of significant challenge. Chemistries and etching characteristics of most piezoelectric materials still remain slow, and further improvements are still desired. Micromachined piezoelectric devices offer significant opportunities in terms of sensing and actuation at the micron scale. Recent work on micromachined, high-frequency, and bulk acoustic wave quartz resonators has allowed for detailed investigation of atomically thin layers of viscoelastic materials in fluid ambient. Real-time investigation of such phenomenon can be the basis of next generation biosensors. Micromachined ultrasonic transducers (MUTs) arrays are another area where piezoelectric thin films are finding increasing use. Piezoelectric micromachined transducer arrays mounted at the tip catheter can be used for two- and three-dimensional ultrasound imaging of the vascular system. In the area of inertial systems, piezoelectric devices are expected to dominate the markets especially for tactical and inertial grade devices. In summary, as piezoelectric materials technology, fabrication processes, and modeling/design tool sets improve, the next generations of micromachined piezoelectric sensors have the potential of operating at or near the fundamental thermal fluctuation limits. Since 2008, the MEMS consumer inertial accelerometer has become “a must-have” in new-generation game consoles, smart phones, and several other consumer user-interface applications, such as remote controls. In the years ahead, the MEMS sensors will become part of our daily lives in many other applications. MEMS technology has become mature, and new products like gyroscopes and inertial modules are arriving on the

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market. Integrating different sensors in one package, miniaturization, and performance improvements are the new challenges. Very soon it will be possible to integrate a complex-structure device—one that can sense not only acceleration, but also speed, pressure, magnetic field, and more— in the footprint-area of today’s MEMS accelerometer. The success of these new products will depend on improved performance of handler platforms capable of guaranteeing throughput, flexibility, and increased accuracy. This means equipment that will be able to generate different stimuli—electric, magnetic, pressure, temperature, acoustics and their combinations. A single testing platform capable of executing all these tasks will represent a new turnkey solution that will contribute to the decrease of the final product cost, catalyzing MEMS penetration in the consumer market. Finally, miniaturization is the other trend that will drive the market in the second decade of MEMS consumerization. Smaller packages will fit into a much greater number of applications across many different fields, where dimensions currently are the limiting factor. MEMS testing equipment must be capable of handling very small devices without inducing mechanical stress or issues on the silicon. Experience from traditional semiconductor fields is a good starting point for identifying a solution to this new challenge in the MEMS world. A good testing platform that guarantees a high level of flexibility regarding different stimuli and is capable of handling ever smaller packages is the key to success in the exploding MEMS arena.95 Much of the content has been taken from Refs.35,95

14.7 CONCLUSIONS Low frequency vibration sensing is being used increasingly to monitor the health of machinery and civil structures, enabling “need-based” maintenance scheduling and reduced operating costs. Passive sensors are of particular interest because they don’t require input energy to monitor vibration. Modern vibration sensors are often micro electromechanical systems, and they are usually very basic in design consisting of a cantilevered beam with some type of deflection sensing circuit. Under the influence of acceleration the beam deflects from its nominal position, and its deflection is measured using optical, capacitive, or piezoelectric techniques. MEMS sensors tend to exhibit very large stiffness to mass ratios, making them best suited to high frequency vibration sensing. Sensors utilizing the piezoelectric effect can achieve direct energy conversion from the mechanical domain (strain) to the electrical domain (charge) via piezoelectric coupling coefficients. Thin-film piezoelectric materials offer a number of advantages in microelectromechanical systems, due to the large motions that can be

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generated often with low hysteresis, the high available energy densities, as well as high sensitivity sensors with wide dynamic ranges, and low power requirements. For ten years or more, thin-film process technologies for piezoelectric application of advanced semiconductor and electronics usage have been developed and completed the piezoelectric thin-film solutions (sputtering, MOCVD, and etching) that became the de facto standard. These technologies will support a wide variety of convenient energy-saving devices such as MEMS production (actuators, gyro meters, tunable devices, and so on). Among piezoelectric films, the majority of the MEMS sensors and actuators developed have utilized lead zirconate titanate (PZT) films as the transducer. Randomly oriented PZT films show piezoelectric e 31, f coefficients of about 7 C/m2 at the morphotropic phase boundary. In PZT films, orientation, composition, grain size, defect chemistry, and mechanical boundary conditions all impact the observed piezoelectric coefficients. The highest achievable piezoelectric responses can be observed in {001} oriented rhombohedrally distorted perovskites. To maximize the electrical output, PZT is an excellent piezoelectric material due to its high coupling coefficients. However, the introduction of PZT into standard MEMS processes is problematic because lead is considered a contaminant in most silicon-based fabrication facilities. Additional complications with stresses and delamination in thin film stacks have hindered the development of robust fabrication processes for these devices. Optimization of sensor membranes is usually conducted using available numerical methods, particularly finite element analysis (FEA). A robust integrated piezoelectric material fabrication process was developed that can be used for future works in this field. This process includes a reliable adhesion layer that can be used when deep wet etching of silicon is required. Integration of substrate materials other than silicon and its compounds into micromachined transducers is a rapidly emerging area of MEMS research technology. For example, future innovations and improvements in inertial sensors for navigation, high-frequency crystal oscillators and filters for wireless applications, microactuators for RF applications, chip-scale chemical analysis systems, and countless other applications can be significantly impacted by the successful miniaturization and integration of piezoelectric materials and subsystems onto silicon or other substrates. Piezoelectric materials are high energy-density materials that scale favorably upon miniaturization. By taking advantage of many of the developed technologies for piezoelectric, MEMS has been able to enhance their performance by a factor of 10 every two years since 1991, and there is every indication that this trend will continue for at least the next few years. It is clear that piezoelectric MEMS will be capable of

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providing the internal market performance at orders of magnitude less cost. In the next decade, much effort will be expended to advance precision micromachining further, to develop low-noise and low-drift interface circuitry, and provide reliable low-cost packaging for the development of even higher performance, lower cost, and lower power piezoelectric MEMS for many emerging and currently unknown applications.

Acknowledgments The author owes a great debt of gratitude to Professor Sergey Timoshenkov at the National Research University of Electronic Technology (MIET), Russia, for his help with providing new scientific results and piezoelectric MEMS that have been used in this chapter. The author would like to thank all colleagues for useful suggestions given during the preparation of this chapter, and all those who contributed their device illustrations and photographs shown in this chapter. The field of piezoelectric MEMS has seen tremendous developments over the last decade, and it is not possible to include all relevant references to all the subjects that are discussed. To give coherent coverage to such a broad field, the author has discussed and referenced works which that are most familiar with in greater detail.

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72. Ivan I, Agnus J, Lambert P. PMN-PT (lead magnesium niobate-lead titanate) piezoelectric material micromachining by excimer laser ablation and dry etching (DRIE). Sens Actuat A: Phys 2012; Ivan A, Rakotondrabe M, Agnus J, Bourquin R, Chaillet N, Lutz P, et al. Comparative material study between PZT ceramic and newer crystalline PMN-PT and PZN-PT materials for composite bimorph actuators. Rev Adv Mat Sci 2010;24(2):1–9. 73. Xu T-B, Tolliver L, Jiang X, Su J. A single crystal lead magnesium niobate-lead titanate multilayer-stacked cryogenic flex tensional actuator. Appl Phys Lett 2013;102:042906. 74. Carneiro Cardoso da Costa G, Wu L, Navrotsky A. Synthesis and thermochemistry of relaxor ferroelectrics in the lead magnesium niobate–lead titanate (PMN–PT) solid solutions series. J Mater Chem 2011;21:1837–45. 75. Colin M, Mortier Q, Basrour S, Bencheikh N. Compact and low-frequency vibration energy scavenger using the longitudinal excitation of a piezoelectric bar. J Phys Conf Ser 2013;476:012135. IOP Science. 76. Nistorica C, Zhang J, Padmini P, Kotru S, Pandey RK. Integrated PNZT structures for MEMS gyroscope. Integr Ferroelectr 2004;63:49–54. 77. Haccart T, Cattan E, Remiens D. Evaluation of Niobium effects on the longitudinal coefficients of Pb(Zr, Ti)O3 thin films. Appl Phys Lett 2000;76:3292–4. 78. Yang K, Li Z, Chen D. Design and fabrication of a novel T-shaped piezoelectric ZnO cantilever sensor. Active Passive Electron Comp 2012;2012:7. 79. Cao Z, Zhang J, Kuwano H. Design and characterization of miniature piezoelectric generators with low resonant frequency. Sensors Actuators A 2012;179:178–84. 80. Panda PK. Review: environmental friendly lead-free piezoelectric materials. J Mater Sci 2009;44(19):5049–62. 81. Prashanthi K, Naresh M, Seena V, Thundat T, Ramgopal Rao V. A novel photoplastic piezoelectric nanocomposite for MEMS applications. J Microelectromech Syst 2012;21 (2):259–61. 82. Xu T, Wu GY, Hang GBZ, Hao YL. Sens Actuat A: Phys 2003;104:61–7. 83. Wang P, Hejun D. ZnO thin film piezoelectric MEMS vibration energy harvesters with two piezoelectric elements for higher output performance. Rev Sci Instrum 2015;86 (075002). 84. Bhatia D, Sharma H, Meena RS, Palkar VR. A novel ZnO piezoelectric microcantilever energy scavenger: fabrication and characterization. Sens Biosensing Res 2016;http://dx. doi.org/10.1016/j.sbsr.2016.05.008. 85. Kachroudi A, Basrour S, Rufer L, Sylvestre A, Jomni F, Dielectric properties modelling of cellular structures with PDMS for micro-sensor applications. Smart Mater Struct 24(12): 125013. 86. Martinez M, Artemev A. A novel approach to a piezoelectric sensing element. J Sens 2010;5. 87. Pande AS, Kushare BE, Pathak AK. A new PZT (lead zirconate titanate) piezoelectric transducer performances analysis. Int J Res Stud Sci Eng Technol 2014;1(6):1–7. 88. Persano L, Dagdeviren C, Su Y, Zhang Y, Girardo S, Pisignano D, et al. High performance piezoelectric devices based on aligned arrays of nanofibers of poly(vinylidenefluorideco-trifluoroethylene). Nat Commun 2013;1633:4. 89. Qiu Y, et al. Piezoelectric micromachined ultrasound transducer (PMUT) arrays for integrated sensing, actuation and imaging. Sensors 2015;15(4):8020. 90. Evans PG, Sichel-Tissot RJ. In situ X-ray characterization of piezoelectric ceramic thin films. Amer Ceram Soc Bull 2013;92(1):18–23. 91. Wooldridge J, Ryding S, Brown S, Burnett TL, Cain MG, Cernik R, et al. Simultaneous measurement of X-ray diffraction and ferroelectric polarization data as a function of applied electric field and frequency. J Synchrotron Rad 2012;19:710. 92. Jo JY, Chen P, Sichel RJ, Baek S-H, Smith RT, Balke N, Kalinin SV, et al. Structural consequences of ferroelectric nanolithography. Nano Lett 2011;11(3080).

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93. Damjanovic D, Bertotti G. Hysteresis in piezoelectric and ferroelectric materials. In: Mayergoyz I, editor. The science of hysteresis, vol. 3. Elsevier; 2005. [Chapter 4]. 94. Piazza G, Felmetsger V, Muralt P, Olsson III RH, Ruby R. Piezoelectric aluminum nitride films for microelectromechanical systems. MRS Bull 2012;37:1051–61. 95. Cortese MF, Avenia G. The increasing penetration of MEMS into consumer applications presents continuous challenges to device testing, STMicroelectronics, 2010. http://www. electronicproducts.com.

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C H A P T E R

15 Aerosol Deposition (AD) and Its Applications for Piezoelectric Devices J. Akedo*, J. Ryu† *National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Japan † Korea Institute of Materials Science (KIMS), Changwon, South Korea

J. Ryu*, D.-Y. Jeong†, S.D. Johnson‡, and J. Akedo§ *Korea Institute of Materials Science (KIMS), Changwon, South Korea † Inha University, Incheon, South Korea ‡ Naval Research Laboratory, Washington, DC, United States § National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Japan

Abstract Technological innovations in manufacturing processes are critical for devices that require high-quality thick piezoelectric ceramic films. However, ceramic films synthesized by conventional methods usually suffer from mechanical failures, poor adhesion, reliability, and rough interfaces. Furthermore, with traditional piezoelectric thin film methods, such as sputtering, sol-gel, pulsed laser, and etc., it is difficult to synthesize piezoelectric films with complex material compositions and with multiple dopants in a short deposition time and over a large surface area, in general. The aerosol deposition (AD) process is a unique approach for depositing thick piezoelectric ceramic films to overcome these technological hurdles. In this process, (sub)-micron ceramic particles fluidized by gas flow are accelerated in a low-vacuum environment at velocities of up to 100–300 m/s to be impacted on the desired substrates. The impact results in a thick, dense, uniform, and homogeneous polycrystalline ceramic film formed at room temperature without the need for any additional heating to solidify the resulting film. The process is extremely cost-effective and requires comparatively simple equipment installation that is integratable with modern industrial fabrication facilities. This technique is particularly useful for fabricating piezoelectric thick films

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for microactuators, sensors, and energy-harvesting devices. This chapter describes the mechanisms and features of the AD process, followed by applications of AD for fabricating piezoelectric materials and devices. Keywords: Aerosol deposition, RTIC, Consolidation, Ceramic powder, Piezoelectric, Ferroelectric, MEMS, Actuator, Transducer.

15.1 INTRODUCTION High-quality ceramics generally require sintering temperatures higher than 1000°C, which makes it difficult for integration into monolithic structures containing low melting temperature components or substrates such as metal, glass, or plastic. This incompatibility is a major obstacle for emerging electroceramic and optical components fabrication. In this regard, development of innovative new manufacturing processes is of critical importance in the near future for producing high performance functional devices that utilize thin/thick films and at the same time reduce the device fabrication cost. Fig. 15.1 highlights the application spectrum of piezoelectric films with desired thickness. Piezoelectric films with a thickness range of 1–100 μm have been used in devices such as microfluidics, micropumps, accelerometers, acoustic sensors, infrared detectors, and energy harvesters. For these applications, dense crack-free piezoelectric films are required. However, synthesis of films fulfilling these requirements is challenging, since these dense thick films are more susceptible to cracks due to thermal stresses caused by differences between the thermal expansion coefficients of the film and substrate.

FIG. 15.1

Application areas of piezoelectric materials with varying thickness.1

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Thickness of piezoelectric layer

Layer deposition technologies: 10 mm 1 mm 100 μm 10 μm 1 μm 100 nm

Bulk ceramics actuators Micro-actuators Micro sensors memory devises

Bulk machining (grinding, polishing, bonding) Aerosol Screen deposition printing method Sol-gel

10 nm 1 nm

Super lattice devices

Sputtering MO-CVD laser ablation

MBE

1 μm 10 μm100 μm 1 mm 10 mm Distance between patterning lines

FIG. 15.2

Fabrication method for PZT film in various thickness ranges.

As Fig. 15.1 demonstrates, the film thickness is a major factor in tuning a device for a target application. If a film is too thin, it may generate too small of a displacement/force; on the other hand, a film that is too thick may require too high of a driving voltage. The window of utility for piezoelectric or electrostrictive materials that achieve the needed displacement/force and high-speed response are found to be a thickness that exceeds 1 μm, but this is thinner than bulk ceramics.2–4 However, thick films prepared by conventional methods usually exhibit cracks and may easily be peeled from the substrates, have difficulty in producing stoichiometrically complex materials, and require time-consuming and costly fabrication processing, which is prohibitive for industrial mass-production. Fig. 15.2 summarizes the conventional methods used to fabricate leadzirconate-titanate [Pb(Zrx,Ti1
x)O3: PZT] piezoelectric films on a substrate along with example device applications of these films. There are many reports on the fabrication of PZT films in thicknesses ranging from 0.08 to 5 μm prepared using thin film processes, such as sol-gel,4–6 sputtering,7,8 metalorganic chemical vapor deposition (MO-CVD),9 pulse laser ablation,10 electron beam evaporation,11 and ion-beam deposition.12 In these methods, dense PZT films can be formed and oriented on a Pt/Ti/SiO2/Si substrate. However, fabrication of PZT films with a thickness of over 1–3 μm with these methods is time consuming and requires careful consideration of the process parameters to avoid degredation of film quality during long deposition cycles and time. In addition, these processes require high temperature, making integration into current semiconductor processing difficult. Hydrothermal synthesis13,14 has the advantage of operating at a low process temperature at around 150°C and without the need for a poling procedure. The drawback is that the

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surface roughness and the density of the films are quite poor. PZT thick films can also be fabricated by conventional screen-printing methods15,16; however, the resulting thick films have a low density and the need for long firing times at over 800°C can damage the delicate PZT/Pt/Si structures. An improved screen-printing method involving a low-temperature sintering using a high-resistance electrode has been reported,17 but the piezoelectric properties of films produced by this method were not reported. The other popular ways to fabricate a piezoelectric device are with a thin ceramic plate, mechanically ground bulk piezoelectric ceramics, or single crystals adhered to a Si membrane. It is difficult to ensure an adequate mechanical adhesion and electromechanical coupling between the substrate and thin plate, and it is also difficult to assemble complex structures. Thus, it can be concluded that, by conventional methods, fine patterning of thick (over 1 μm) PZT films on Si-based substrates is still difficult. To reduce cost and fabrication time and avoid damage to existing circuitry on the substrate, it is very important to develop a film deposition process with a high-speed deposition rate, low process temperature, and fine patterning capabilities. Until now, a number of studies have been aimed at reducing the sintering temperature, for the purpose of reducing energy consumption, and implementing innovative functional components for integration with metal, polymer, or glass materials. Several film deposition methods based on the principle of particle collisions have also been investigated. For example, the cold spaying method (CSM) for metallic materials has attracted much attention. However, CSM is suitable only for ductile metal and has not been successful for deposition of brittle ceramic materials. For hard and brittle ceramic materials, a new deposition technique called aerosol deposition (AD) is being explored by researchers.13–21 AD is based on the collision and adhesion of fine ceramic particles with a substrate to form a dense polycrystalline film. This technique that has attracted much attention as a promising coating method for ceramic integration, because the ceramic film can be grown at room temperature and onto almost on any substrate material. To achieve film formation, (sub) micrometer-sized ceramic powder is mixed with a carrier gas to form a fluidized aerosol flow. The aerosolized powder is ejected through a micro-orifice nozzle, whereupon it gains sufficient kinetic energy, impacts, fractures, and adheres to the substrate located in the low-vacuum deposition chamber. Using this method, ceramic films such as PZT, (K,Na) NbO3, α-Al2O3, TiO2, Y2O3, ZrO2, AlN, MgB2, Hexa-ferrite, and YIG,20 among others, can be formed with nanocrystalline structure, high transparency, high hardness, and high breakdown voltage. Since the powder remains in the solid phase during the entire process, there is no significant stoichiometric or structural change in the film compared with the powder and the resulting film displays many of the same characteristics as the

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15.2 AEROSOL DEPOSITION AND GRANULE SPRAY IN VACUUM (GSV) PROCESS 60

P.R. China (> 10 mm

Fracture and separation of particles Porous films with insufficient quality

Fracture of particles Abrasive blasting of substrate or surface No film formation

Stage 1

Formation of an anchor layer / interface Deformation of soft substrates Distinct layer with high adhesion, density and nanocrystallinity

Stage 2

Film formation and growth by RTIC Consolidation by hammering of subsequent particles

(B) FIG. 15.9 (A) Illustration of possible particle-substrate interactions based on the speed and kinetic energy of the ceramic particles. Anchor layer formation can take place at intermediate energies. (B) The RTIC process, with distinction between stage 1 (anchor layer formation) and stage 2 (film buildup), during which particle hammering and fracturing takes place.21

by fracturing and plastic deformation and therefore adhere to the substrate or the already deposited film. The reported empirical particle ranges are convenient for most materials, but they still are dependent on material properties like hardness, fracture toughness, and density. Larger particles (≫ 10 μm) obtain kinetic energies that are too high, leading to an abrasive blasting of the substrate/film (similar to sand-blasting). These particles are likely to fracture too, but without plastic deformation. Even if a feedstock powder contains appropriate sized particles, agglomeration can still disturb the deposition. Agglomerates absorb a part of the kinetic energy and affect the momentum transfer between particle and surface while impacting, and by that they impede the densification process. Films then tend to be porous, with decreased strength and adhesion. The AD process can be separated into two stages (Fig. 15.8B): the creation of an anchor film (1) and subsequent film buildup (2). Stage (1) includes an initial plastic deformation of the substrate surface by first impacting particles. This is associated with an increase of the roughness (especially for

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softer substrate materials like metal and glass). Mechanical entanglement might also play a more important role in the buildup stage.40 Film growth in stage (2) takes place by RTIC of subsequent particles. According to several recent reports on the AD and particle deformation, it is clear that high rate impacts during AD is the first step in understanding the mechanisms. Akedo41 suggested that the following questions about AD remain unanswered: Does the creation of clean and active particle surfaces make bonding possible at low temperature? Is there a chemical reaction during impact? Nao et al. have recently published one of the few papers with direct evidence of chemical bonding between anchoring Al2O3 particles and the copper substrate, because electron energy-loss spectra (EELS) from the interface suggested the presence of ionic and covalent bonding between Cu (substrate) and O2-(Al2O3).42 There is much evidence that the anchor layer is critical to film adhesion and stability.43 Substrate properties, of course, influence the deposition and determine the dominant bonding mechanism, especially in the first stage. It has been demonstrated how substrate hardness affects AD film properties.44 Ductile and/or lowmelting substrates can be expected to give strong film anchoring by local interface deformation and perhaps melting. High hardness substrates can be expected to lead to efficient particle size reduction and dense consolidation as the film grows in thickness, but higher velocity particles might be required to form an adherent anchor layer initially. The initial substrate roughness plays an important role. It is reported that an increased surface roughness prevents the deposition of particles, especially when the depth of the surface valleys is greater than the particle size.45 Maki et al. showed a strong reduction of the deposition rate above a deposition angle of 30 degrees (angle between the aerosol jet axis and the substrate normal.).46 This can help to explain the negative effects of substrate roughness, and the nonconformal nature of AD coatings.

15.4 FABRICATION OF FERROELECTRIC AND PIEZOELECTRIC THICK FILMS BY AD 15.4.1 Thick Film Fabrication With traditional deposition processes, such as sol-gel, sputtering, or chemical vapor deposition, films thinner than 1 μm can be easily fabricated, but it is difficult to make films thicker than 10 μm due to the low deposition rate (about 1 μm/h) and high interfacial stress. Screen-printing is a well-known process capable of generating thick films at a very high production rate. However, this process suffers some shortcomings such as applicable substrate materials, low sintered density, high sintering temperature (typically over 800°C), weak adhesion strength between the film and substrate, and a quite porous microstructure with large pores. II. PREPARATION METHODS AND APPLICATIONS

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A process capable of forming dense films with a thickness in the range of 1–100 μm is urgently required to satisfy the needs of various applications. The AD process can overcome these limitations. However, to fabricate high-quality thick films by AD, stress control in the film is critical. The ceramic films deposited by the AD process retain a high compressive stress that is induced during the deposition due to the high-energy impact of the particles onto a substrate.47–49 The phenomenon is similar to that of sputtered film in which compressive stress is generated by the bombardment of energetic particles.50 The residual stress can be categorized by an intrinsic or extrinsic stress: the former is often called a growth stress and is related to the deposition method or growth process, whereas the latter originates from environmental factors.51 Thermal stress is an extrinsic residual stress produced by the difference in the thermal expansion coefficients of the film and substrate. The residual compressive stress within the film due to the AD process is an intrinsic stress. Generally, the total intrinsic stress stored in the film increases with increasing film thickness. Therefore, a thick film is likely to be detached from the substrate by high intrinsic stress and extrinsic thermal stress during post annealing of the film. This delamination effect can often be observed in the PZT-based films with thickness above 20 μm after post-deposition annealing.52 There are several ways to relieve the intrinsic residual stress and avoid delamination in AD thick films. One way is to relieve the intrinsic residual stress by introducing fine pores within the film as proposed by Hahn et al., who successfully fabricated crack-free PZT films thicker than 20 μm by AD with subsequent annealing.49 PZT powders containing organic species were used for AD PZT films. By using the powers with organic species the residual stress was dramatically reduced from 250 MPa compressive stress to 46 MPa tensile stress. The stress relaxation in the PZT film was attributed to the evaporation of organics during the annealing process. Thanks to this stress relaxation, thick films over 100 μm-thick were successfully deposited onto Si-based substrate as shown in Fig. 15.10. A similar, but simpler, approach was carried out by Han et al. In this work, a mixture of PZT and polymer powders were deposited at the same time. They report that by simply mixing PZT powders and polymer PVDF, PZT films over 180 μm thick were fabricated. These films showed minimal interfacial residual stress (Fig. 15.11).53 This innovative fabrication process for stress control can maximize actuating/sensing/transducing properties of piezoelectric thick films, as well as related devices.54

15.4.2 Thick Film Fine Patterning When fabricating practical devices, patterning ceramic thick films with a well-controlled feature size is a critical issues to be considered. It is reported that AD thick film patterning can be achieved by using a mask II. PREPARATION METHODS AND APPLICATIONS

(A)

(B)

20 μm

PZT film

Pt/Ti/SiO2/Si substrate

10 μm

(C)

500 nm

(D)

100 μm

20 μm

500 nm

FIG. 15.10 FE-SEM micrographs of PZT thick films deposited from powder with small contents of organic residue after annealing at 700°C: cross sections of films with thicknesses of (A) 20 μm and (C) 100 μm; surface microstructures of films with thicknesses of (B) 20 μm and (D) 100 μm.49

(B)

(A)

1 μm

20 μm

Si substrate 3 μm

Si substrate

20 μm

(D)

(C)

180 μm

100 μm

40 μm

Si substrate

80 μm

FIG. 15.11 Fracture-sectional scanning electron micrographs of 700°C annealed AD-PZT films on silicon substrate with thicknesses of (A) 1 μm, (B) 20 μm, (C) 100 μm, and (D) 180 μm.53 II. PREPARATION METHODS AND APPLICATIONS

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deposition method.55,56 In this procedure, a particle jet is impacted onto the substrate through a defined pattern or “shadow” mask with width openings of at least 50 μm. The presence of a physical mask may alter the particle jet flow, so careful consideration of the aerosol jet flow in the deposition chamber and through the mask orifices must be made. If the pressure in the deposition chamber is not sufficiently low, the particle jet is scattered by the edge of the openings in the mask and the resulting mask pattern is not preserved on the substrate. The effect of the ceramic particles sprayed onto a substrate changes from deposition to erosion,56 depending on the particle diameter, velocity, and angle of incidence of the particle jet to the substrate. These factors also influence the film density and surface roughness. Fig. 15.12 shows a thick, patterned PZT film deposited under optimum deposition conditions onto Si, Stainless steel, and Pt/Si substrates.57 A ceramic microstructure with a 50-μm line width and aspect ratio (line height/line width) greater than 1 can be patterned by

FIG. 15.12 Schematic and micrographs of the patterned thick AD ceramic film using the mask deposition method.57

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PZT film t~4 μm

25 μm

Si wafer

FIG. 15.13 Fine patterning of PZT thick films deposited by GSV using liftoff process with photoresist.

controlling the substrate heating temperature and starting particle properties. The AD process is useful for making piezoelectric films more than 10-μm thick, for applications such as ultrasonic devices. However, pattern widths less than 50 μm were difficult to obtain using this method. Recently, the production of ceramic fine patterns using AD and the liftoff technique was tried. The hardness and thickness of the photoresist (PR) film must be chosen carefully so that erosion of the patterned PR film does not occur and that the patterned PR film is sufficiently thick so as to maintain the designed pattern. Typically PR with high hardness and strong adhesion strength such as SU-8 epoxy based PR is more suitable to maintain PR patterns under high kinetic particle beam collision. A minimum pattern width of less than 10 μm for 5-μm thick PZT and α-Al2O3 films was obtained, as shown in Fig. 15.13,58 and further device fabrications by this method are ongoing.

15.5 ELECTRICAL PROPERTIES OF PIEZOELECTRIC THICK FILMS BY AD 15.5.1 High Breakdown Voltage of AD Thick Films Fundamentally, the AD process is based on the shock loading consolidation of solid state particles, known as RTIC, and the resulting microstructures of the AD films are completely different from those of the films made by other thin/thick film fabrication methods. The features of AD are dense film formation, room temperature growth, and the ability to retain the same material composition and crystal structure as the starting powder. AD films generally have high electrical insulation and electrical breakdown characteristics that exceed that of the bulk material. This high electrical insulation is due to many grain boundaries from the nanosized grains. For example, the electrical breakdown of α-Al2O3 and Y2O3 exceeded 3 MV/cm and for PZT it was found to exceed 500 kV/cm.18,59,60

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The volume resistivity, the dielectric constant, and the dielectric loss of α-Al2O3 thick films formed by the AD process were 1.5  1015 Ω cm, 9.8 at 1 kHz and 0.2%, respectively.60 Those values are almost the same as those of the bulk materials. Such electrical characteristics can be useful for developing devices such as electrostatic chucks61 and electrical insulation films with a good thermal conductivity for high-power electric devices.

15.5.2 Ferroelectric and Piezoelectric Properties of AD Thick Films In ferroelectric and piezoelectric thick films, such high insulating and electrical breakdown characteristics are desired for high performance and low loss devices. Typically PZT films deposited by AD exhibit polarization switching at a high external field over 1 MV/cm, as shown in Fig. 15.14A. The remanent polarization (Pr) and coercive field (Ec) were 13 μC/cm2 and 300 kV/cm, respectively. These results indicate that asdeposited AD-PZT films have very high electrical resistance and breakdown voltage due to the high density film structure. These films also have spontaneous polarizations in spite of the structural defects introduced by the reduction of the crystallite size. It should be noted that these properties are unacceptable for practical applications, but they can be improved to acceptable standards by post-annealing in air at temperatures ranging from 500 to 700°C for 10 min to 1 h (depending on film thickness, composition, and substrate material). As a result of this, post-deposition treatment grain growth of fine crystals and defect recovery in the AD films were observed, which dramatically improved the ferroelectric properties. The grain size of AD-PZT films after annealing was 80–120 nm. Fig. 15.14B Pr, μC/cm2

Polarization, μC/cm2

1

60

2

–20 3

40

4 –10 20

–1000

–600

600

1000 E, kV/cm

–400

–10

–20

–200

200 400 Electrical field, kV/cm –20 1 180 ms 2 260 ms 3 350 ms –40 4 540 ms –60

(A)

(B)

FIG. 15.14 P-E hysteresis loops of as deposited 5-μm thick PZT films by AD (A), and after post annealing at 600°C (B) with a variety of particle impact velocities.28

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Piezoelectric constant (–d31, pm/V)

140 Poling: 40 kV/cm, at 250°C, for 20 min 120 100 80 60 40

Without poling

20 0

0.01

0.1

10 100 1 Driving frequency (Hz)

1000

10,000

FIG. 15.15 Frequency dependence of the piezoelectric coefficient (
d31) of the unimorph cantilever sample. □, PZT on the Si cantilever; , PZT on stainless steel. Applied electrical field was 40 kV/cm. The resonance frequency of the sample was 80 kHz.62

shows the P-E hysteresis loops of 5-μm thick PZT thin films annealed at 600°C for 15 min with a variety of particle impact velocities. The best values of Pr and Ec were 36 μC/cm2 and 89 kV/cm, respectively and were achieved using a He carrier gas for an estimated particle impact velocity of 150 m/s. The breakdown electric field of a 5-μm thick film after annealing was about 600 kV/cm, and it was more than 1 MV/cm for a 2-μm thick PZT thin film. According to the conventional understanding of shock loading consolidation, the defect density and residual strain of asdeposited PZT thin films might be increased by increasing the impact force during the deposition. Even after the annealing procedure that reduced defects, the influence of the particle impact velocity remained.28 The piezoelectric constant (d31) of the postannealed films formed at 600°C in Fig. 15.15 was
100 pm/V62, which is comparable to the value of the specimen obtained with a conventional thin film growth method. Moreover, the electrical breakdown (80 GPa) of the AD films exceeded those obtained with conventional thick film formation technologies.

15.5.3 Property Enhancement by Stress Modulation Due to the mismatch in the coefficient of thermal expansion (CTE) between the film and substrate, tensile or compressive stress is generated in the thick film during the cooling process after post-annealing,47,48 as shown in Fig. 15.16.63 The magnitude of the stresses influences the crystal

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10

Strong compressive stress

Sapphire

PZT

Sapphire

Weak compressive stress

60 40 20

–40

–300 –200 –100 0

Si

Weak tensile stress

100 200 300

Electric Field (kV cm–1)

60 40 20 0

2.3 × d33,Sieff

–20 –40 –60 –300 –200 –100 0

100 200 300

Electric Field (kV cm–1)

5

Si

2.5 × d33,Sieff

0 –20

–60

Polarization (mC cm–2)

YSZ

Polarization (mC cm–2)

Coefficient of thermal expansion (⫻10–6 °C–1)

YSZ

Polarization (mC cm–2)

PZT thick film

60 40 20

d33,Sieff

0 –20 –40 –60 –300 –200 –100 0

100 200 300

Electric Field (kV cm–1)

0

After annealing

Domain behavior

Piezoelectric constant

FIG. 15.16 Schematic diagram of high piezoelectric performance in PZT thick films grown on various substrates; their stresses were controlled by the thermal expansion mismatch between substrates and PZT films.63

structure and domain alignment of thick films and affects ferroelectric and piezoelectric properties of the thick film. KIMS researchers investigated ferroelectric and piezoelectric properties of polycrystalline PZT thick films with a thickness of 10 μm on Si, sapphire, and single crystal yttria stabilized zirconia (YSZ) substrates and analyzed the in-plane stress effects on the electrical properties. The stress conditions in these films were simply controlled by the CTE mismatch between the PZT films and substrates. The results showed that the films deposited on the YSZ and sapphire substrates bear an in-plane compressive stress and have superior dielectric, ferroelectric (90%), and piezoelectric (>200%) properties over that of the Si wafer, which showed a weak tensile stress. Among these three substrates, YSZ showed superior properties of all the PZT films tested. These results confirm that in-plane compressive stresses within the films are beneficial to the piezoelectrical properties desired in the film, due to the formation of c-domains parallel to the thickness direction. Furthermore, these results were found to be consistent with the theory that domain alignment is facilitated by compressive stress. These polycrystalline thick films show great promise for industrial electronics applications due to the desirable properties and low-cost fabrication process as compared to epitaxial and textured thin film; this work suggests a new possibility that the properties of a polycrystalline thick film can be adjusted by simply choosing substrates with different CTEs.63

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15.5.4 Laser Annealing for AD Films Conventional thermal treatments of AD thick films using a furnace or by rapid thermal annealing processing are acceptable for most applications. However, special thermal treatment is necessary for specific applications, where temperature-sensitive materials are incorporated into the film or device structure—for example, metal substrate-based MEMS devices. In such a case, calcination is needed to improve the piezoelectric property of the AD-PZT film, but consideration must be made to reduce the damage to the substrate. For such applications, laser annealing was introduced by AIST researchers in Japan. A CO2 laser (CL) was used for heat treatment of AD thick films without damaging the metal substrate by adjusting the laser power density.64 It is well known that most ceramics can absorb infrared radiation very well. Because this is the wavelength range covered by CLs, they are ideally suited to be used to heat treat and sinter ceramic films.65–68 The AIST researchers investigated the electrical property enhancement of PZT thick films deposited by AD on stainless steel (SS) sheets and subsequently annealed using CL radiation.64 The surface brilliance of the SS sheets was not influenced by thermal heating by CL, and the temperature of the reverse side of the film (i.e., the SS sheet) in Fig. 15.17 was measured to be 150°C or less during the annealing process. The remanent polarization, coercive field value, and the dielectric constant are 34 μC/cm2, 25 kV/cm, and 1500–1800, respectively of the laser annealed film. Recently, in order to improve the piezoelectric properties and reduce thermal damage to the substrate, a fiber laser (FL) with

60

Laser irradiated film

Polarization [uC/cm2]

40 5 min

–250

Electric furnance annealed film

20

–150

0 –50

As-deposited film 50

150

250 Pr = 34 μC/cm2 Ec = 25 kV/cm2

–20 –40

600ºC 5 min

ε = 1500~1800 tand = 2~5%

–60

5 min

Electric field [kV/cm]

FIG. 15.17 (A) Dielectric properties and (B) ferroelectric hysteresis loops of 10 μm-thick AD-PZT films directly deposited on an SS substrate and annealed using a fiber laser at 600°C (FL-annealed PZT/SS), and those annealed using an electric furnace at 600°C (EF-annealed PZT/SS).64

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CW laser (560 nm) Effective beam size ~50 μm PZT film on Metglas

PZT film

Metglas

~ 4 μm

3 μm

scanning X-Y linear stage

(A)

(B)

FIG. 15.18

(A) Schematic of laser annealing of deposited PZT film on Metglas. (B) Optical and cross-sectional SEM images of laser annealed PZT.25

laser spot size of 50 mm was also introduced for the annealing procedure.69 The results show that FL annealing can effectively improve the grain growth of PZT/SS by suppressing thermal damage to the SS substrate. In 2015 and 2016, researchers at KIMS in Korea and Virginia Tech also succeed in laser annealing PZT thick films on a magnetostrictive amorphous metal substrate (Metglas) by continuous wave (CW) visible laser source (wavelength 560 nm) for 2-2 structured magnetoelectric (ME) composites as shown in Figs. 15.18 and 15.19.24,25 The longer wavelength laser utilized in this work is able to anneal the entire thick PZT film layer without any deteriorative effects, such as chemical reaction and/or atomic diffusion at the interface, or crystallization of the amorphous Metglas substrates as shown in Fig. 15.19. As a result, a colossal off-resonance ME voltage coefficient that is two orders of magnitude larger than previously reported output from PZT/Metglas film composites was achieved. The combination of AD/GSV (in this work, GSV was used) and laser annealing proves to be a promising solution to alleviate the difficulty involved in the fabrication of PZT/metal film-composites. This processing approach appears to have high feasibility for fabricating ME thin/thick film composites, and it can be extended to other devices that employ piezoelectric film on low thermal budget substrates.

15.6 LEAD-FREE PIEZOELECTRIC THICK FILMS BY AD High performance lead-free piezoelectric ceramics are not easy to fabricate in thin/thick film forms using conventional film growth processes due to the volatile nature of the elements involved, such as K, Na, Bi, etc.70–73 These volatile elements are not stable at high processing temperatures and can negatively affect the density, crystal structure, II. PREPARATION METHODS AND APPLICATIONS

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100 nm

100 nm

100

Atomic percentage

Atomic percentage

100 80 Si Ti Fe Zr Pb

60 ∼10 nm

40 20 0

80 Si Ti Fe Zr Pb

60 ∼10 nm

40 20 0

0

25

50

75

Distance (nm)

100

125

0

25

50

75

100

125

Distance (nm)

FIG. 15.19

(A and B) Cross-sectional TEM images and (C and D) corresponding EDS line scanning analysis of the as-deposited and laser annealed PZT/Metglas, respectively.25

and electrical properties of the resulting film. Since AD is a room temperature deposition process and thermal treatment can be conducted at relatively low temperature, it may offer a solution to the difficultly in fabricating temperature-sensitive piezoelectric films. To demonstrate this concept, one of the well-known lead-free piezoelectric materials, (K0.44Na0.52Li0.04)(Nb0.86Ta0.10Sb0.04)O3 (LF4) thick films, were successfully grown directly on glass, SS, and Pt/Ti/ZrO2 substrates at room temperature by AD by researchers at AIST.70 The results indicate that moisture elimination by preheating the starting powders and postannealing the AD films plays an important role in realizing good dielectric properties of LF4 films for practical applications in lead-free piezoelectric ceramics. Fig. 15.20 shows P-E hysteresis loops for LF4 thick films deposited on YSZ substrates at various post-annealing temperatures. The Pr and Ec of 4–5 μm thick LF4 films were increased by increasing the annealing temperature. The highest values reached were 5 μC/cm2 and 42.4 kV/cm, respectively, at 1000°C. The P-E hysteresis loop for the LF4 bulk material is shown in the inset of Fig. 15.20. The bulk LF4 was sintered in air at 1100°C for 5 h and shows a Pr value of 3.6 μC/cm2, which is about three times higher than that of the film (1.3 μC/cm2) in the same electrical field (90 kV/cm). It is thought that the Pr values are related to the grain size in films, annealing temperature, and holding time. Another good candidate for lead-free piezoelectric material applications is based on (Bi0.5Na0.5)TiO3 (BNT). Although BNT shows promise as a II. PREPARATION METHODS AND APPLICATIONS

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15.6 LEAD-FREE PIEZOELECTRIC THICK FILMS BY AD

LF4 bulk (sintering at 1100ºC, 5 h) Pr = 3.6 (μC/cm2) Ec = 11.5 kV/cm

LF4 bulk 2 10 P, μC/cm

Polarization, P (μC/cm2) 30

0 –100

At room temperature At 10 Hz

5

0

–50 –5

50

100

1000ºC

20

Ea, kV/cm

600ºC 10

–10

as-depo. 0 –400

–200

0 –10

200

400

Applied field, Ea (kV/cm)

–20

–30

FIG. 15.20 P-E hysteresis loops for as-deposited LF4 thick films and films deposited at various annealing temperatures. The inset shows P-E hysteresis loops for LF4 bulk sintered in air at 1100°C for 5 h.70

potential lead-free piezoelectric material because of its large remanent polarization,74,75 this value is decreased by a large leakage current density and lattice defects in BNT.76 In fabricating BNT dense ceramics by a solidphase reaction, BNT should be sintered at a high temperature (at around 1200°C), which induces Bi vaporization. The AIST team in Japan obtained dense 25-μm thick BNT ceramic films by AD and compared the resulting films with the same composition ceramic counterparts. For BNT bulk ceramics, Nagata and Takenaka fabricated them by solid-phase reaction using high-purity materials and reported a Pr of 33.7 μC/cm2 and Ec of 57.9 kV.77 The resulting AD films of the same composition were annealed at 1000°C to avoid the bismuth vaporization, which creates lattice defects and oxygen vacancies. The resulting films showed electrical properties (Pr of 27 μC/cm2 and Ec of 40 kV/cm), comparable to those of bulk ceramic counterparts. Additionally, the KIMS researchers in Korea presented several papers about the improvement of lead-free piezoelectric AD films based on the KNN material system.71–73,78–80 They also reported that the AD process was found to be very effective for the formation of dense lead-free piezoelectric KNN films. The higher density and slight crystal distortion were suggested as being the main reasons for the improved properties as shown in Fig. 15.21.71,73 Results show that a 20-μm thick KNN-BaTiO3 film had a piezoelectric constant d33 that was 100 pm/V, which is comparable to that of the PZT-based film.79 II. PREPARATION METHODS AND APPLICATIONS

40 Polarization (μC/cm2)

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60

(B)

(A)

(C)

20 0 As-Deposited Annealed 300°C

–20

Annealed 500°C Annealed 600°C Annealed 700°C Annealed 800°C Annealed 900°C

–40

KIMM

SEI

5.0kV

X5.000

1μm

WD 9.2mm

KIMM

SEI

5.0kV

X2.000

10μm

WD 9.2mm

–60 –800 –600 –400 –200

0

200

400

600

800

Electric field (KV/cm)

Typical microstructure of KNN-based (A) sintered ceramics (density 95%), (B) AD film, and (C) polarization properties of KNN lead-free thick film fabricated by AD.71,73

FIG. 15.21

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601

15.7 DEVICE APPLICATIONS 15.7.1 Piezoelectric Films for Bending Mode Microactuator81 Piezoelectric-type actuators as compared with electromagnetic ones have some advantages such as low cost, small size, low energy consumptions, and the possibility of a realizing a multiarray arrangement of actuators. The typical schematic of a unimorph actuator is shown in Fig. 15.22. The displacement of unimorph actuator is described as δ¼

3 l2 2xyð1 + xÞ d31 V, 2 t2p 1 + 4xy + 6x2 y + 4x3 y + x4 y2

(15.1)

where, l, tp, and ts are described in Fig. 15.22; x ¼ ts/tp and y ¼ Ys/Yp (Ys and Yp are the Young’s modulus of the substrate and piezoelectric, respectively.); and d31 is a piezoelectric constant. From Eq. (15.1), the cantilever structured actuator design includes many parameters, such as the piezoelectric constant of the piezoelectric layer, length, and thickness of each layer, which must be considered for large displacement. From the electrical consideration, the maximum driving voltage mainly determines the thickness of the piezoelectric layer. If an external driving voltage to the microactuator is determined and a piezoelectric layer is fabricated from the bulk material, the two factors restricting the minimum thickness of piezoelectric layer are (a) the slicing and grinding process from bulk piezoelectric (it is difficult to fabricate piezoelectric layer thinner than 30 μm) and (b) breakdown electrical voltage of the piezoelectric. Thus, in a conventional design of an actuator, the thickness of the piezoelectric layer is determined first. After that the nonpiezoelectric layer thickness is optimized from the point of view of maximum displacement (for example see Ref. 83). Fig. 15.23 shows a plot of how the displacement of a cantilever microactuator depends on the thickness of piezoelectric films based on Eq. (15.1) and experimental data. Since the AD process can easily generate films at various thicknesses, the AD process can provide more flexibility in design for microactuators compared to the conventional design process. In addition, production cost of PZT films (under 10 μm thickness) using the AD process also is expected to be cheaper than that of PZT films over 30 μm in thickness.

15.7.2 Si-MEMS Optical Microscanner84 High-speed resonance optical scanners have many applications in bar-code readers, laser displays, laser printers, and they are the key components for various optical sensors. Consumer display devices make up an enormous market and require high-performance horizontal

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V Electrodes

Piezoelectric layer

tp

Nonpiezoelectric layer

ts d1

(A) V

Electrodes Piezoelectric layer

Nonpiezoelectric layer

tp

ts

d2

(B) FIG. 15.22 Schematic of a unimorph actuator. (A) The thickness of the piezoelectric layer is equal to that of the nonpiezoelectric layer (tp ¼ ts); (B) The thickness of the piezoelectric layer is smaller than that of the nonpiezoelectric layer (tp < ts). For the PZT/stainless steel actuator, if applied voltage (V) in both (A) and (B) is the same, the displacement in (B) is more (δ2 > δ1).82

scanners with high frequencies (exceeding 20 kHz), large scan-angles of over 20 degrees, and large mirror sizes (>1 mm-in diameter) to achieve good display quality.85–88 MEMS technology has been used to realize optical scanners with special requirements for compact size, low power consumption, and high scanning speed.86–89 The AD process has been applied to generate such a high-performance optical microscanner with a scanning speed at a resonance frequency over

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15.7 DEVICE APPLICATIONS

Electrical field if applying 10 V (kV/cm) 10 5 2.5

100

1

50

Displacement (μm)

New area of actuators’ design using ADM

1 25

Conventional area of actuators’ design, using bulk PZT or screen printing PZT

2

0

20

40 60 80 Thickness of piezoelectric layer (μm)

100

FIG. 15.23 Displacement (δ) of PZT/stainless steel (SUS-304) cantilever for various thicknesses of the PZT layer. Calculations were made with Eq. (15.1): 1—applying 10 V, DC; 2—applying DC electrical field of 2 kV/cm for each thickness of PZT layer; calculations were performed for d31 of the PZT layer of
80 pm/V. The Young’s modules of PZT and stainless steel (Ys, Yp) are 80 and 169 GPa, respectively.5 The length of the cantilever is 10 mm, and the thickness of the stainless steel (ts) is 50 μm.82

30 kHz and a scan angle (peak-to-peak value) over 30 degrees in an atmospheric environment. The AD of piezoelectric materials at a high deposition rate was realized onto a scanner structure fabricated by Si-micromachining, as shown in Fig. 15.24.66,83 This optical scanner has a high scanning speed and is expected to be a key component for various types of sensors for the next generation of projection display devices.

15.7.3 Metal-Based Optical Microscanner89 Current state-of-the-art MEMS technology is hindered by complicated processing, which slows production and creates expensive devices. This effect is amplified as consumer demand continues to grow, outpacing the supply capability of industry. In addition, Si-based optical microscanners are made from silicon that can be easily broken due to mechanical shock or high stress concentration near the mirror. An attractive alternative is to use a much more robust metal substrate in place of the silicon in

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FIG. 15.24 Optical microscanner driven with PZT thick film deposited on an Si-MEMS structure by AD. Scanning speed: over 30 kHz, Scanning angle: over 30 degrees.83

the optical microscanner devices. The advantages are a reduction of the device cost and an improvement of the ambient durability by changing brittle silicon to ductile stainless steel. At the same time, stainless steel and silicon have approximately the same Young’s modulus (Y) value, about of 200 GPa, and the densities of the materials (ρ), 7.81 g/cm3 for steel and 2.33 g/cm3 for silicon, make the ratio of (Y/ρ) 1/2 that determines the mechanical resonance for this material different only by factor of 2. Such a difference in resonance characteristics can be accommodated by appropriate device design. Thus, silicon can be replaced by stainless steel in MEMS structures. Fig. 15.25A shows a schematic and an optical image of a metal-based optical microscanner. An optical mirror was attached using two narrow torsion hinges from both sides at the center of gravity of the mirror (symmetrical mirror structure). The other sides of these hinges were connected to the scanner frame and one edge of the scanner frame was clamped and fixed with a heavy block. A piezoelectric film was directly deposited on the stainless steel scanner frame beside the mirror. The d31 actuation mode of the piezoelectric film bends the scanner frame and induces a vibrational Lamb wave in the scanner frame. The metal scanner structure is designed so that the Lamb waves are two

II. PREPARATION METHODS AND APPLICATIONS

15.7 DEVICE APPLICATIONS

605

FIG. 15.25 (A) Novel design of a 1-D optical microscanner based on metal structure and Lamb wave resonation for raster scanning laser displays. (B) Frequency properties of an optical microscanner driven by a PZT thick film at a driving voltage of 60 V (peak-to-peak).90

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dimensionally guided and concentrated toward the narrow torsion hinges holding the mirror. The waves change with the torsion vibrations of the mirror caused by the vertical difference in the direction between progressing waves and the torsion hinge. The torsional vibration vertically scans the mirror axis. Fig. 15.25B shows frequency properties of the optical microscanner (mirror size: 1 mm  0.25 mm, hinge width and length: 0.1 and 1.35 mm, respectively) driven by a PZT thick film at a driving voltage of 60 V (peak-to-peak). A large optical scanning angle (41 degrees) was achieved at a high resonance frequency (28.24 kHz) in ambient air using the prototype scanner device.90 The torsional resonance frequency of our metal-based optical microscanner showed no hysteresis because of the symmetrical standing mirror. Moreover, the image of the scanned laser beam exhibited no beam distortion. The quality factor of the metal-based scanner was estimated to be 330. This is lower than that of a Si-MEMS scanner (600) [824]. This low quality factor is effective in reducing the temperature dependence of the scanner operation, since the quality factor of the optical scanner was dominated by the mechanical dumping factor of the scanner frame, electrical dumping factor of the PZT films, and the aerodynamic dumping of the scanning mirror motion under ambient atmosphere conditions.

15.7.4 Optical Modulator91 A PZT-based magneto-optic spatial light modulators (PZT-MOSLM) prototype has been fabricated by incorporating a piezoelectric thick film into magneto-optic materials.91 In PZT-MOSLMs, the high switching speed results from the fact that the pixel switching is achieved by switching the direction of magnetization, up or down within 1 ns. The novel PZT-MOSLM is driven by an electric field instead of a magnetic field and was first achieved by using the piezoelectric effect of AD-PZT thick films, which reduces the anisotropic energy of the structured garnet film. The pixels could be easily switched in the presence of a small external bias field. As a result, the power consumption of such a PZT-MOSLM was drastically reduced to be 10 times smaller than that of a conventional current driven device. Successful pixel switching at 20 MHz has already been achieved with an 8 V drive voltage.

15.7.5 Ultrasonic Motor Tube typed ultrasonic micromotors, shown in Fig. 15.26, were fabricated as a prototype for an AD ultrasonic micromotor process.92 In this device, a 10 μm PZT thick film was deposited on a stainless steel tube having a 2 mm

II. PREPARATION METHODS AND APPLICATIONS

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15.7 DEVICE APPLICATIONS

SUS tube t = 200 μm PZT thick layer (10 μm)

10 mm Au-electrode

F 2.0 mm

V • sinwt

V •coswt

FIG. 15.26 Tube-typed ultrasonic motor driven with PZT thick film deposited on an SUS tube by the AD method.

diameter by utilizing the AD processing capability of deposition onto curved surfaces. The rotation speed of this ultrasonic motor ranged between 1200 and 1500 rpm with a 7–15 V drive voltage.

15.7.6 Flexible Energy Harvester26 Flexible piezoelectric energy harvesters, called nanogenerators (NGs), have been studied by many research groups because they can harvest electrical power from ambient mechanical and vibrational energy such as structure/motor vibration, gentle airflow, and even tiny biomechanical movements of muscles and organs.1,26 The KIMS and KAIST researchers demonstrated a high-performance flexible piezoelectric energy harvester enabled by an AD-based PZT thick film on a plastic substrate to develop a self-powered wireless sensor-node system as shown in Fig. 15.27.26 A crystalline AD PZT film annealed at 900°C with a thickness of 7 μm on a rigid sapphire substrate was successfully transferred onto a flexible substrate by an inorganic-based laser liftoff (ILLO) without any structural damage or degradation of its properties. This flexible PZT harvesting device can generate an open-circuit voltage of 200 V and a short-circuit current of 35 μA by biomechanical bending/unbending motions (Fig. 15.28). The high-output performance of the AD PZT harvester is comparable with the performance of a previous flexible single-crystal piezoelectric harvester, which is attributed to the high-temperature

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15. AD & ITS APPLICATIONS FOR PIEZOELECTRIC DEVICES

(ii) ILLO transfer

(i) AD PZT Sap

phir e Su

(iii) Self-powered wireless sensor node PET

b.

. Sub

IDEs 11010...

High-speed aerosol deposition

Laser

PZT

Cold Hot 26 °C

Sapphir e Sub.

Nozzle

T Film

PZ

PET

Rectifying & storage

Sub.

(A)

or ens r p. s mitte Temtrans &

1 mm

5 mm

(B)

10 mm

2 cm

(C)

FIG. 15.27 (A) Schematic illustration of the device-fabrication process and self-powered WSN using a flexible AD PZT energy harvester enabled by ILLO. (B) A cross-sectional SEM image of the AD PZT thick film on a PET substrate. The inset shows a top-view SEM image of the flexible PZT thick film. (C) An optical image of the flexible PZT harvester bent by tweezers. The inset shows a top-view OM image of metal IDEs on the PZT.26

grain growth of AD films. The harvested electricity was used to directly light up 208 blue LEDs and charge a supercapacitor. Finally, a self-powered wireless temperature sensor node was built by integrating the AD PZT energy harvester, rectifying/storage elements, a temperature-sensing processor, and a wireless radiofrequency (RF) transmitter. During the rectifying and storing stage, the alternating current (AC) output of the flexible harvester was converted into a direct current (DC) signal to charge a 1 mF capacitor up to 4.3 V within about 45 min. The stored self-powered energy was used to operate the temperature sensor and then successfully transmit the RF data 18 times to a transceiver.

15.8 SUMMARY In this chapter, the basic deposition mechanism, general aspects of aerosol deposition process, fundamental electrical properties of the ferroelectric and piezoelectric film by the process, and its potential

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609

15.8 SUMMARY

90

15

0 −30 −60 −90

0

5 0

Unbending

Current (µA)

10

Bending

30

Unbending

Voltage (V)

Bending

60

−5

5

10 15 Time (s)

(A)

20

25

−10

0

5

(B)

10 15 Time (s)

20

25

90

Voltage (V)

60 30

~115,000 Cycles

0 −30 −60 −90

(C)

0

5

10

15 Hours (h)

20

25

30

FIG. 15.28 (A) The open-circuit voltage and (B) short-circuit current values from the flexible PZT energy harvester fabricated by AD and ILLO during periodic bending and unbending motions. (C) The result of a bending durability test over around 115,000 cycles to verify the mechanical stability of the flexible harvester.19,26

applications for various piezoelectric devices were introduced. Compared to conventional thin/thick ceramic processes, the AD process features unique processing capabilities, such as (i) high deposition rate, (ii) low processing temperature, (iii) dense film formation at a low temperature, and (iv) a primary material composition and crystal structure that is retained in the deposited films due to the RTIC process. This chapter can be summarized as below: 1. Dense consolidation of ceramic particles at room temperature (RTIC phenomenon) was obtained using the AD process. 2. Reduction of the crystallite size was observed and nanocrystalline ceramic layers were formed by the AD process. 3. The densification mechanism of the AD layer was explained by a 2-stage process, in other words, stage 1 (anchor layer formation) and stage 2 (film buildup), during which particle hammering and fracturing takes place. 4. The AD process is applicable to fabricate complex piezoelectric materials such as PNN-PZT and lead-free KNN, BNT system.

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5. The AD process has great potential for integration of functional ceramic materials and application to micro-devices. 6. For uniform and large-area film deposition, granule spray in vacuum process (GSV) is introduced. 7. AD/GSV can deposit ceramic thick films more than 100 μm thick, and it is possible to enhance piezoelectric device performance. To date, the bonding mechanism between the fine particles themselves and between the substrate and the fine particles has not been clarified, though we described some potential mechanisms expected. We need more studies on the bonding mechanism of ceramic particles in the AD method. There are many potential applications of AD piezoelectric films, but real practical devices are not widely available in the market. The authors believe that it is the right time to increase the effort to develop the AD process for real device applications. For that realization, more reliable control and understanding of the processing parameters, particle feedstocks, and devices production yield need to be carefully investigated.

References 1. Priya S, Ryu J, Park C-S, Oliver J, Choi J-J, Park D-S. Piezoelectric and magnetoelectric thick films for fabricating power source in wireless sensor nodes. Sensors 2009;9 (8):6362–84. 2. Sayer M, Sreenivas K. Ceramic thin films: fabrication and applications. Science 1990;247:1056–60. 3. Abothu IR, Ito Y, Poosanaas P, Kalpat S, Komarneni S, Uchino K. Sol-gel processing of piezoelectric thin films. Ferroelectrics 1999;232:191–5. 4. Chen HD, Udayakumar KR, Gaskey CJ, Cross LE, Bernstein JJ, Niles LC. Fabrication and electrical properties of lead zirconate titanate thick films. J Am Ceram Soc 1996;79:2189–92. 5. Luginbuhl P, Racine G-A, Lerch P, Romanowicz B, Brooks KG, de Rooij NF, et al. Piezoelectric cantilever beams actuated by PZT sol-gel thin film. Sens Actuators A 1996;54:530–5. 6. Annapureddy V, Choi J-J, Kim J-W, Hahn B-D, Ahn C-W, Park D-S, et al. Dependence of ferroelectric properties of modified spin-coating derived PZT thick films on crystalline orientation. J Korean Phys Soc 2016;68(1):1390–4. 7. Watanabe S, Fujiu T, Fujii T. Effect of poling on piezoelectric properties of lead zirconate titanate thin films formed by sputtering. Appl Phys Lett 1995;66:1481–3. 8. Sakata M, Wakabayashi S, Ikeda M, Goto H, Takeuchi M, Yada T. Pb-based ferroelectric thin film actuator for optical applications. J Microsyst Technol 1995;2:26–31. 9. Sakashita Y, Ono T, Segawa H, Tominaga K, Okada M. Preparation and electrical properties of MOCVD-deposited PZT thin films. J Appl Phys 1991;69:8352–7. 10. Kidoh H, Ogawa T, Morimoto A, Shimizu T. Ferroelectric properties of lead-zirconatetitanate films prepared by laser ablation. Appl Phys Lett 1991;58(25):2910–2. 11. Oikawa M, Toda K. Preparation of Pb(Zr,Ti)O3 thin films by an electron beam evaporation technique. Appl Phys Lett 1976;29(8):491–2. 12. Castellano RN, Feinstein LG. Ion-beam deposition of thin films of ferroelectric lead zirconate titanate (PZT). J Appl Phys 1979;50(6):4406–11.

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33. Holmquist TJ, Johnson GR, Grady DE, Lopatin CM, Hertel ES. High strain rate properties and constitutive modeling of glass. In: Proceedings of 15th international symposium on ballistics, TB31, Jerusalem, Israel, May 21–24; 1995. p. 237–44. 34. Anderson CE, Johnson GR, Holmquist TJ. Ballistic experiments and computations of confined 99.5% Al2O3 ceramic tiles. In: Proceedings of 15th international symposium on ballistics, G6, Jerusalem, Israel, May 21–24; 1995. p. 65–72. 35. Hirai H, Kondo K. Shock-compacted Si3N4 nanocrystalline ceramics: mechanisms of consolidation and of transition from α- to β-form. J Am Ceram Soc 1994;77:487–92. 36. Petrovic JJ, Olinger BW, Roof RB. Explosive shock loading on alpha-Si3N4 powder. J Mater Sci 1985;20:391–8. 37. Papyrin A. Cold spray technology. Adv Mater Process 2001;159:49–51. 38. Li C-J, Li W-Y, Liao H. Examination of the critical velocity for deposition of particles in cold spraying. J Therm Spray Technol 2006;15:212–22. 39. Lee D-W, Kim H-J, Kim Y-H, Yun Y-H, Nam, S-M. Growth process of a-Al2O3 ceramic films on metal substrates fabricated at room temperature by aerosol deposition. J Am Ceram Soc 2011;94:3131–8. 40. Kliemann J-O, Gutzmann H, Gartner F, Hubner H, Borchers C, Klassen T. Formation of cold-sprayed ceramic titanium dioxide layers on metal surfaces. J Therm Spray Technol 2011;20:292–8. 41. Akedo J. Room temperature impact consolidation (RTIC) of fine ceramic powder by aerosol deposition method and applications to microdevices. J Therm Spray Technol 2008;17:181–98. 42. Naoe K, Nishiki M, Sato K. Microstructure and electron energy-loss spectroscopy analysis of interface between cu substrate and Al2O3 film formed by aerosol deposition method. J Therm Spray Technol 2014;23:1333–8. 43. Exner J, Hahn M, Schubert M, Hanft D, Fuierer P, Moos R. Powder requirements for aerosol deposition of alumina films. Adv Powder Technol 2015;26:1143–51. 44. Lee D-W, Kim H-J, Kim Y-N, Jeon M-S, Nam S-M. Substrate hardness dependency on properties of Al2O3 thick films grown by aerosol deposition. Surf Coat Technol 2012;209:160–8. 45. Kim J, Lee JI, Park DS. Enhancement of interface anchoring and densification of Y2O3 coating by metal substrate manipulation in aerosol deposition process. In: Park ES, editor. J Appl Phys 2015;117:014903. 46. Maki T, Sugimoto S, Kagotani T, Inomata K, Akedo J, Ishikawa T, et al. Influence of deposition angle on the magnetic properties of Sm-Fe-N films fabricated by aerosol deposition method. J Alloys Compd 2006;408–412:1409–12. 47. Ryu J, Hahn G, Song TK, Welsh A, Trolier-McKinstry S, Choi H, et al. Upshift of phase transition temperature in nanostructured PbTiO3 thick films for high temperature applications. ACS Appl Mater Interface 2014;6:11980–7. 48. Lee J, lee S, Choi M-G, Ryu J, Lee J-P, Lim Y-S, et al. Stress modulation and ferroelectric properties of nano-grained PbTiO3 thick films fabricated by aerosol-deposition. J Am Ceram Soc 2014;97(12):3872–6. 49. Hahn B-D, Kim K-H, Park D-S, Choi J-J, Ryu J, Yoon W-H, et al. Fabrication of lead zirconate titanate thick films using a powder containing organic residue. Jpn J Appl Phys I 2008;47(7):5545–52. 50. Morito K, Suzuki T. Effect of internal residual stress on the dielectric properties and microstructure of sputter-deposited polycrystalline (Ba,Sr)TiO3 thin films. J Appl Phys 2005;97:104107. 51. Lappalainen J, Frantti J, Hiltunen J, Lantto V, Kakihara M. Stress and film thickness effects on the optical properties of ferroelectric Pb(ZrxTi1
x)O3 films. Ferroelectrics 2006;335:149–58. 52. Choi J-J, Hahn B-D, Ryu J, Yoon W-H, Park D-S. Effects of Pb(Zn1/3Nb2/3)O3 addition and post annealing temperature on the electrical properties of Pb(ZrxTi1
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53. Han G, Ryu J, Yoon W-H, Choi J-J, Hahn B-D, Park D-S. Effect of film thickness on the piezoelectric properties of lead zirconate titanate thick films fabricated by aerosol-deposition. J Am Ceram Soc 2011;94(5):1509–13. 54. Choi J-J, Hahn B-D, Ryu J, Yoon W-H, Lee B-K, Park D-S. Preparation and characterization of piezoelectric ceramic-polymer composite thick films by aerosol-deposition for sensor application. Sens Actuators A: Phys 2009;153:89–95. 55. Ryu J, Priya S, Park C-S, Kim K-Y, Choi J-J, Hahn B-D, et al. Enhanced domain contribution to ferroelectric properties in free-standing thick films. J Appl Phys 2009;106 (2):024108. 56. Lebedev M, Akedo J. Patterning properties of lead zirconate titanate (PZT) thick films made by aerosol deposition. IEE J Trans Sens Micromach 2000;20-E(12):600–1. 57. Akedo J. Study on rapid micro-structuring using jet-molding: present status and structuring subjects toward HARMST. Microsyst Technol 2000;6(11):205–9. 58. Akedo J, Park J-H, Tsuda H. Aerosol deposition – film formation, fine patterning of piezoelectric materials and its applications. J Electroceram 2009;22:319–26. 59. Iwasawa J, Nishimizu R, Tokita M, Kiyohara M, Uematsu K. Dense yttrium oxide film prepared by aerosol deposition process at room temperature. J Ceram Soc Jpn 2006;114 (3):272–6. [in Japanese]. 60. Nam S-M, Momotani M, Mori N, Kakemoto H, Wada S, Akedo J, et al. Microstrip band pass filter of GHz region employing aerosol-deposited alumina thick films. Integr Ferroelectr 2004;66:301–10. 61. Akedo J. Aerosol deposition for coating of transparent and high resistive ceramic layer. Metal AGNE Gijutsu Center 2005;75(3):16–23. [in Japanese]. 62. Akedo J, Lebedev M. Piezoelectric properties and poling effect of Pb(Zr,Ti)O3 thick films prepared for microactuators by aerosol deposition. Appl Phys Lett 2000;77(11):1710–2. 63. Han G, Ryu J, Yoon W-H, Choi J-J, Hahn B-D, Kim J-W, et al. Stress-controlled Pb (Zr0.52Ti0.48)O3 thick films by thermal expansion mismatch between substrate and Pb (Zr0.52Ti0.48)O3 film. J Appl Phys 2011;110(12):124101. 64. Baba S, Akedo J. Damage-free and short annealing of Pb(Zr,Ti)O3 thick films directly deposited on stainless steel sheet by aerosol deposition with CO2 laser radiation. J Am Ceram Soc 2005;88(6):1407–10. 65. Chou C-F, Pan H-C, Chou C-C. Electrical properties and microstructures of PbZrTiO3 thin films prepared by laser annealing techniques. Jpn J Appl Phys 2002;41 (11B):6679–81. 66. Pan H-C, Chou C-C, Tsai H-L. Low-temperature processing of sol-gel derived La0.5Sr0.5MnO3 buffer electrode and PbZr0.52Ti0.48O3 films using CO2 laser annealing. Appl Phys Lett 2003;83(15):3156–8. 67. Knite M, Mezinskis G, Shebanovs L, Pedaja I, Sternbergs A. CO2 laser-induced structure changes in lead zirconate titanate Pb(Zr0.58,Ti0.42)O3 sol–gel films. Appl Surf Sci 2003;208–209:378–81. 68. Sugihara S. Sintering of piezoelectric ceramics with CO2 laser. Jpn J Appl Phys 1992;31 (9B):3037–40. 69. Baba S, Akedo J. Fiber laser annealing of nanocrystalline PZT thick film prepared by Aerosol deposition. Appl Surf Sci 2009;255(24):9791–5. 70. Oh S-W, Akedo J, Park J-H, Kawakami Y. Fabrication and evaluation of lead-free piezoelectric ceramic LF4 thick film deposited by aerosol deposition method. Jpn J Appl Phys 2006;45(9B):7465–70. 71. Ryu J, Choi J-J, Hahn B-D, Park D-S, Yoon W-H, Kim K-H. Fabrication and ferroelectric properties of highly dense lead-free piezoelectric (K0.5Na0.5)NbO3 thick films by aerosol deposition. Appl Phys Lett 2007;90:152901–3. 72. Han G, Ahn C-W, Ryu J, Yoon W-H, Choi J-J, Hahn B-D, et al. Effect of tetragonal perovskite phase addition on the electrical properties of KNN thick films fabricated by aerosol deposition. Mater Lett 2011;65:2762–4.

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73. Ryu J, Choi J-J, Hahn B-D, Park D-S, Yoon W-H. Ferroelectric and piezoelectric properties of 0.948(K0.5Na0.5)NbO3-0.052LiSbO3 lead-free piezoelectric thick film by aerosol deposition. Appl Phys Lett 2008;92:12905. 74. Takenaka T, Maruyama K, Sakata K. (Bi1/2Na1/2)TiO3-BaTiO3 system for lead-free piezoelectric ceramics. Jpn J Appl Phys 1991;30(9B):2236–9. 75. Smolenskii GA, Isupov VA, Agranovskaya AI, Krainik NN. New ferroelectrics of complex composition IV. Sov Phys Solid State 1961;2:2651. 76. Park SE, Chung S-J, Kim I-T, Hong KS. Nonstoichiometry and the long-range cation ordering in crystals of (Na1/2Bi1/2) TiO3. J Am Ceram Soc 1994;77(10):2641–7. 77. Nagata H, Takenaka T. Effects of substitution on electrical properties of (Bi1/2Na1/2)TiO3based lead-free ferroelectrics. In: Proc. 2001 12th IEEE Int. Symp. Applications of Ferroelectrics, 1 and 2, 45; 2001. 78. Lau ST, Li X, Zhou QF, Shung KK, Ryu J, Park D-S. Aerosol-deposited deposited KNN-LSO lead-free piezoelectric thick film for high frequency transducer applications. Sens Actuators A: Phys 2010;163:226–30. 79. Han G, Priya S, Ryu J, Yoon W-H, Choi J-J, Hahn B-D, et al. Hardening behavior of Mnmodified KNN-BT thick films fabricated by aerosol deposition. Mater Lett 2011;65:278–81. 80. Han G, Ryu J, Ahn C-W, Yoon W-H, Choi J-J, Hahn B-D, et al. High piezoelectric properties of KNN-based thick films with abnormal grain growth. J Am Ceram Soc 2012;95(5):1489–92. 81. Smits JG, Choi W. The constituent equations of piezoelectric heterogeneous bimorphs. IEEE Trans Ultrason Ferroelectr Freq Control 1991;38:256–70. 82. Lebedev M, Akedo J. What thickness of piezoelectric layer with high breakdown voltage is required for microactuator? Jpn J Appl Phys 2002;41(5B):3344–7. 83. Asai N, Matsuda R, Watanabe M, Takayama H, Yamada S, Mase A, et al. A novel high resolution optical scanner actuated by aerosol deposited PZT films. In: Proc. of MEMS 2003, Kyoto, Japan; 2003. p. 247–50. 84. Bayer M. Retinal scanning display—a novel HMD approach to army aviation: head and helmet-mounted displays VII. Proc SPIE 2002;4711:4557. 85. Dickensheets D, KiNo G. Microfabricated biaxial electrostatic torsional scanning mirror. Proc SPIE 1997;3009:141–50. 86. Yamada K, Kuriyama T. A novel asymmetric silicon micro-mirror for optical beam scanning display. Proc MEMS 1998;98:110–5. 87. Filhol F, Divoux C, Divoux C, Zinck C, Delaye M-T. Resonant micro-mirror excited by a thin-film piezoelectric actuator for fast optical beam scanning. Sensors Actuators A 2005;123–124:483–9. 88. Conant R, Nee J, Lau K, Mulle R. A flat high frequency scanning micromirror. In: Solidstate sensor and actuator workshop, Hilton Head, South Carolina, June 2000; 2000. p. 6–9. 89. Akedo J, Lebedev M, Sato H, Park JH. High-speed optical microscanner driven with resonation of lamb waves using Pb(Zr,Ti)O3 thick films formed by aerosol deposition. Jpn J Appl Phys 2005;44(9B):7072–7. 90. Park J-H, Akedo J, Sato H. High-speed metal-based optical microscanners using stainlesssteel substrate and piezoelectric thick films prepared by aerosol deposition method. Sensors Actuators A 2007;135(1):86–91. 91. Takagi H, Mizoguchi M, Park JH, Nishimura K, Uchida H, Lebedev M, et al. PZT-driven micromagnetic optical devices. Mater Res Soc Symp Proc 2004;785:D6.10.1–6. 92. Nanotech2007. NEDO project on “Nanostructure Forming for Advanced Ceramic Integration Technology in Japan: Nanotechnology Program”, pamphlet, 2/21; 2007.

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C H A P T E R

16 Manufacturing Technologies for Piezoelectric Transducers K. Uchino The Pennsylvania State University, State College, PA, United States

Abstract This chapter deals with piezoelectric transducers, pulse drive actuators, and ultrasonic transducers. We discuss the designing and manufacturing technologies from three viewpoints: (1) electromechanical performance in piezoelectric materials, (2) mechanical displacement amplification and clamping mechanisms, and (3) mechanical/ acoustic energy transfer to media. Off-resonance pulse drive actuators require high soft piezoelectric PZT, while resonant sound sources are made from hard PZT materials with a high QM, because of their higher power generation without heat generation. Compressive bias stress is occasionally applied on a piezoelectric transducer along its elongation direction. A liquid medium is usually used for sound energy transfer, where the acoustic/mechanical impedance matching is to be considered on the transducer interface. We also discuss the problems relating with the complex poling process and its resulting mechanical fracture in piezoelectric transformers. Keywords: Soft and hard PZT, Pulse drive actuator, Bolt-clamped Langevin transducer, Cymbal, Transducer array, Underwater acoustics, Acoustic imaging, Piezoelectric transformer.

16.1 INTRODUCTION Ultrasonic waves are conventionally used in various fields. The sound source is made from piezoelectric ceramics, as well as magnetostrictive materials. Piezoceramics are generally superior in efficiency and in size to magnetostrictive materials. In particular, hard piezoelectric materials with a high QM are preferable because of high-power generation without heat generation. A liquid medium is usually used for sound energy transfer. Typical applications include ultrasonic cleaners, ultrasonic

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hydrophones, and sonars for short-distance remote control, underwater detection, fish finders, and nondestructive testers. Ultrasonic scanning detectors are useful in medical devices for clinical applications ranging from diagnosis to therapy and surgery. Impulse drive motors have been utilized widely in dot-matrix traditionally and inkjet printers, and diesel injection valves recently. Because of a sudden sharp extension of a multilayer piezo-actuator, the overshoot generates severe tensile stress around the center of the actuator. Thus, certain compressive DC bias stress is applied on the actuator to extend the lifetime. This chapter reviews how to design and manufacture the transducers with a particular focus on material choice, impulse actuators, Langevin/cymbal transducers, mechanical displacement amplification mechanisms, and piezoelectric transformers. Most of the content and figures have been referred to previously in Refs. 1–3

16.2 TRANSDUCER MATERIALS Piezoelectric/electrostrictive actuators are classified into two categories, based on the type of driving voltage applied to the device and the nature of the strain induced by the voltage (Fig. 16.1): (1) rigid displacement devices for which the strain is induced unidirectionally along the direction of the applied DC field and (2) resonating displacement devices for which the alternating strain is excited by an AC field at the mechanical resonance frequency (for example, ultrasonic underwater transducers, ultrasonic motors, and transformers). The first can be further divided into E Servo drive Rigid Strain

E

Eb

Em

Feedback

t Pulse

x

Eb x

E ON

On/off drive t E Resonant Strain

AC drive

Em E

Sine t

FIG. 16.1

OFF x

E

Servo displacement transducer Electrostrictive material (hysteresis-free) Pulse drive motor Soft piezoelectric material (low permittivity) Ultrasonic motor Hard piezoelectric material (High Q)

Classification of piezoelectric/electrostrictive actuators and usable materials.

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16.3 TRANSDUCER DESIGNS

617

two types: servo displacement transducers (positioners) controlled by a feedback system through a position-detection signal and pulse drive motors operated in a simple on/off switching mode, exemplified by inkjet printers and injection valves. The material requirements for these classes of devices are somewhat different, and certain compounds are better suited to particular applications. The ultrasonic motor, for instance, requires a very hard piezoelectric with a high mechanical quality factor QM in order to suppress heat generation (low loss). Note that the resonating displacement is amplified by a factor of QM, in comparison with the off-resonance strain/ displacement (i.e., dE
L). The servo displacement transducer suffers most from strain hysteresis and, therefore, a PMN electrostrictor is used for this purpose. The pulse drive motor requires a low permittivity material aiming at quick response with a certain power supply (a high-power supply is expensive from the practical device-application viewpoint) rather than a small hysteresis. Thus, soft PZT piezoelectrics with low permittivity are preferred rather than the high-permittivity PMN for this application.

16.3 TRANSDUCER DESIGNS 16.3.1 Pulse Drive Actuator Pulse drive techniques for ceramic actuators are very important for improving the response of the device.4,5 Fig. 16.2 shows transient vibrations of a bimorph excited after a pseudostep voltage is applied. The rise time is varied around the resonance period (n is the time scale with a unit of T0/2, where T0 stands for the resonance period). It is concluded that the overshoot and ringing of the tip displacement are completely suppressed when the rise time is precisely adjusted to the resonance period of the piezo-device (i.e., for n ¼ 2).4 It is worth noting that this rise time adjustment is a unique vibration damping technique that does not lead to energy loss. A flight actuator was developed using a pulse-drive piezoelectric element and a steel ball. A 5-μm rapid displacement induced in a multilayer actuator can hit a 2-mm ϕ steel ball up to 20 mm in height. A dot-matrix printer head has been developed using a flight actuator as shown in Fig. 16.3.6 By changing the drive voltage pulse width, the movement of the armature was easily controlled to realize no vibrational ringing or double hitting. A compressive DC stress bias is recommended to apply on the multilayer actuator in practice in order to protect the actuator from collapsing at its center due to large tensile stress from the overshoot. Sharp pulse voltage induces a 100% displacement overshoot, rather than 50% overshoot observed for a pseudostep voltage in Fig. 16.2.1,3 A dot matrix printer is the first widely commercialized product using piezoelectric actuators in the 1980s. Each character formed by such a II. PREPARATION METHODS AND APPLICATIONS

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n=1 Tip displacement

Electric field

(A) n=2 Tip displacement Electric field 10 ms

(B) n=3 Tip displacement Electric field

(C) FIG. 16.2 Transient vibration of a bimorph excited after a pseudostep voltage applied. Here, n is a time scale with a unit of 1/2 of the resonance period (i.e., 2n ¼ the resonance period).

Ink ribbon Armature Steel plate Wire

Piezoelectric actuator

Spring Platen Paper 10 mm Base

FIG. 16.3

Dot-matrix printer head using a flight actuator mechanism.

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printer was originally composed of a 24  24 dot matrix. A printing ribbon is subsequently impacted by a multiwire array. A sketch of the printer head appears in Fig. 16.4A.7 The printing element is composed of a multilayer piezoelectric device, in which 100 thin ceramic sheets 100 μm in thickness were stacked, together with a sophisticated magnification mechanism (Fig. 16.4B). The magnification unit is based on a monolithic hinge lever with a magnification of 30, resulting in an amplified displacement of 0.5 mm and energy transfer efficiency greater than 50%. The DC compressive bias stress on the piezoelectric actuator was adjusted by this hinge lever stroke amplifier frame. Fig. 16.5 illustrates the inkjet printer produced by Seiko Epson,8 in which PZT thin plates were laminated with three plates (vibration, Head element Platen Paper Ink ribbon Guide Piezoelectric actuator Wire Wire

Stroke amplifier

Wire guide

(A)

(B)

FIG. 16.4 (A) Structure of a dot-matrix printer head (NEC), and (B) a differential-type piezoelectric printer-head element. A sophisticated monolithic hinge lever mechanism amplifies the actuator displacement by 30 times.

FIG. 16.5

MACH inkjet printer head developed by Seiko Epson.8

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chamber, and communication) to create a unimorph actuation mechanism. Using the cofiring technique with PZT and ZrO2 elastic parts for manufacturing this ML chips head (MACH), Epson achieved superior stability in the ink chamber vibration and for various inks. In addition, more importantly, the manufacturing cost reduced dramatically by adopting this cofiring technique. Note again that the drive voltage should be a pseudo-step type (Fig. 16.2) to minimize undesired vibration ringing, which degrades the ink droplet control significantly. Toyota developed a Piezo TEMS (Toyota Electronic Modulated Suspension), which is responsive to each protrusion on the road in adjusting the damping condition, and installed it on a Celcio (equivalent to Lexus, internationally) in 1989.9 In general, as the damping force of a shock absorber in an automobile is increased (i.e., hard damper), the controllability and stability of a vehicle are improved. However, comfort is sacrificed because the road roughness is easily transferred to the passengers. The purpose of the electronically controlled shock absorber is to obtain both controllability and comfort simultaneously. Usually the system is set to provide a low damping force (soft) so as to improve comfort, and the damping force is changed to a high position according to the road condition and the car speed to improve the controllability. In order to respond to a road protrusion, a very high response of the sensor and actuator combination is required. Fig. 16.6A shows the structure of the electronically controlled shock absorber.9 The sensor is composed of five layers of 0.5-mm thick PZT disks. The detecting speed of the road roughness is about 2 msec and the resolution of the up-down deviation is 2 mm. The actuator is made of 88 layers of 0.5-mm thick disks. Applying 500 V generates a

1s Automatic control Up-down acceleration

0.1 m/s2

Pitching rate

2° /s

Fixed at hard damping Up-down acceleration Pitching rate

Fixed at soft damping Up-down acceleration Pitching rate

(A)

(B)

FIG. 16.6 (A) Toyota Electronic modulated suspension (TEMS) with a multilayer piezoelectric actuator and a sensor. (B) Function of the TEMS adaptive suspension system. Note that both up-down acceleration and pitching rate are minimized under the TEMS system.9

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displacement of about 50 μm, which is magnified by 40 times through a piston and plunger pin combination. This stroke pushes the change valve of the damping force down, then opens the bypass oil route, leading to the decrease of the flow resistance (i.e., soft). Fig. 16.6B illustrates the operation of the suspension system. The up-down acceleration and pitching rate were monitored when the vehicle was driven on a rough road. When the TEMS system was used (top figure), the up-down acceleration was suppressed to as small as the condition fixed at “soft,” providing comfort. At the same time, the pitching rate was also suppressed to as small as the condition fixed at “hard,” leading to better controllability. In order to increase the diesel engine efficiency, high pressure fuel and quick injection control are required. Fig. 16.7 shows an example of a diesel fuel injection timing chart. In this one cycle (typically 60 Hz), the multiple injections should be realized in a very sharp shape. For this purpose, piezoelectric actuators, specifically ML types, were adopted. The highest reliability of these devices at an elevated temperature (150°C) for a long period (10 years) has been achieved. Common-rail type injection valves have been widely commercialized by Siemens, Bosch, and Denso Corp (Fig. 16.7B).10 The specifications of the Siemens multilayer actuators are summarized: • Displacement: 50 μm/length 50 mm (Strain level: 0.14% at 2 kV/mm (d33 ¼ 700 pm/V)) • Temperature stability of displacement: 5% for—40 to 150°C • Curie temperature higher than 335°C • Life time: more than 109 cycles (Under a severe drive condition: switching time ¼ 50 μs; electric field ¼ 2 kV/mm)

Piezoelectric actuator Main Pilot

Pre

Control valve After

Post Displacement amplification unit Injector body

Injection interval

(A)

Nozzle

(B)

FIG. 16.7 (A) Diesel fuel injection timing chart in one cycle (about 60 Hz cycle). (B) Common-rail type diesel injector with a piezoelectric multilayer actuator.10 Courtesy of Denso Corp.

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FIG. 16.8

Walking piezo motor using an inchworm mechanism with four multilayer piezoelectric actuators by Philips.11

• DC bias stress on the ML actuator: 900 N/7  7 mm2 (18 MPa  a half of the blocking stress of the actuator) is applied via the actuator metal capsule. Fig. 16.8 shows a walking piezo motor with four multilayer actuators developed by Philips.11 Two shorter actuators function as clamps on the rail and the longer two provide the movement by an inchworm mechanism. A major drawback of this inchworm design is the mechanical noise created by the on-off drive (audible frequency due to the requirement being lower than the mechanical resonance of the system).

16.3.2 Langevin Transducer P. Langenvin succeeded in transmitting ultrasonic pulse into the southern sea in France in 1917 during World War I. We can learn most of the practical development approaches from this original transducer design (Fig. 16.9). First, 40 kHz was chosen for the sound wave frequency. Taking the sound velocity of water v ¼ 1500 m/s, and v ¼ f
λ (where f is frequency and λ is its wavelength), λ is calculated as 37 mm, which corresponds roughly to the resolution. Increasing the frequency (shorter wavelength) leads to the better monitoring resolution of the objective; however, it also leads to a rapid decrease in the reachable distance. Notice that quartz single crystals were the only available piezoelectric material in the early twentieth century (water soluble Rochelle salt was another possible crystal at that time). Since the sound velocity in quartz is about 5 km/s, 40 kHz

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16.3 TRANSDUCER DESIGNS

Angle dependence of acoustic power

1.0 Center axis

0.5

0.5

Steel

28.7 5.0

Quartz pellets were arranged

28.7 260 mm f

FIG. 16.9 Original design of the Langevin underwater transducer and its acoustic power directivity.

corresponds to the wavelength of 12.5 cm in quartz. If we use a mechanical resonance (k33 type) in the piezoelectric material, a 12.5/2 ¼ 6.25 cm thick quartz single crystal piece is required. However, in that period, it was not possible to produce such a large single crystals. In order to overcome this dilemma, Langevin invented a new transducer construction; small quartz crystals arranged in a mosaic were sandwiched by two steel plates. Since the sound velocity in steel is in a similar range to quartz, taking 6.25 cm in the total thickness, he succeeded in setting the thickness resonance frequency to around 40 kHz. This sandwich structure is called Langevin type, which remains in common use today. Notice that quartz is located at the center, which corresponds to the nodal plane of the thickness vibration mode, where the maximum stress/strain (or the minimum displacement) is generated. If the piezoelectric element is installed at the antinode point, large displacement may collapse the ceramic. Further, in order to provide a sharp directivity for the sound wave, Langevin used a sound radiation surface with a diameter of 26 cm (more than double of the wavelength). Since the half-maximum-power angle φ can be evaluated as
 φ ¼ 30  ðλ=2aÞ degree , (16.1) where λ is the wavelength in the transmission medium water (not in steel) and a is the radiation surface radius, if we use λ ¼ 1500 (m/s)/40 (kHz) ¼ 3.75 cm, a ¼ 13 cm, we obtain φ ¼ 4.3° for this original design (see Fig. 16.9).

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FIG. 16.10

Bolt-clamped Langevin transducer. Courtesy of Honda Electronics, Japan.

Langevin and the French Navy succeeded practically in detecting an enemy German U-Boat 3000 m away. He also observed many bubbles generated during his experiments, which seems to be the cavitation effect. This cavitation effect is widely used at present in ultrasonic cleaning apparatuses. Fig. 16.10 shows a present bolt-clamped Langevin transducer for cleaner applications, commercialized by Honda Electronics, Japan. Because piezoelectric ceramics is mechanically combined (compressive DC bias stress via a center bolt), the transducer is very durable, free from damage even under high amplitude vibrations. Furthermore, it is possible for stable operation with high electroacoustic conversion efficiency and less heat generation and dissipation through steel.

16.3.3 Cymbal Transducer 16.3.3.1 Single Cymbal A composite actuator structure called the “moonie” has been developed to amplify the pressure sensitivity and the small displacements induced in a piezoelectric ceramic.12 The moonie has characteristics

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625

16.3 TRANSDUCER DESIGNS

PZT

Metal endcap

(A) FIG. 16.11

(B)

(C)

Flextensional structures: (A) the moonie, (B) the cymbal, and (C) cymbal

appearance.

intermediate between the conventional multilayer and bimorph actuators; it exhibits a displacement an order of magnitude larger (100 μm) than the multilayer, and it has a much larger generative force (10 kgf) with a quicker response (100 μs) than the bimorph. This device consists of a thin multilayer ceramic element and two metal plates with a narrow moonshaped cavity bonded together as shown in Fig. 16.11A. A moonie with dimensions 5 mm  5 mm  2.5 mm can generate a 20-μm displacement under an applied voltage of 60 V, which is eight times as large as the generative displacement of a multilayer of similar dimensions.12 A displacement twice that of the moonie can be obtained with the cymbal design pictured in Fig. 16.11B and C. The generative displacement of this device is quite uniform, showing negligible variation for points extending out from the center of the endcap.13 Another advantage the cymbal has over the moonie is its relatively simple fabrication. The endcaps for this device are made in a single-step punching process that is both simpler and more reproducible than the process involved in making the endcaps for the moonie structure. A cymbal is a sort of displacement amplifier, and it also fits well with water because of its relatively low acoustic impedance. Compared to the Langevin type, the cymbal has very thin profile, is lightweight, and is easy to assemble into an array. Figs. 16.12 and 16.13 compare the ATILA simulation and the experimental result in terms of transmitting voltage response (TVR) as functions of beam directivity and operating frequency, respectively. Note first that a single cymbal under water works as an almost-uniform monopole sound source. The TVR response is relatively flat, from 20 to 60 kHz. 16.3.3.2 Cymbal Array A 3  3 cymbal array shown in Fig. 16.14A was developed for underwater sonar application at Penn State, and it was analyzed by ATILA simulation and experimentally measured.14 The resonance frequency of the unit cymbal was 17 kHz. When all the cymbals are identical and driven at 17 kHz under water, the displacements of the center, edge, and corner cymbals are calculated as

II. PREPARATION METHODS AND APPLICATIONS

FIG. 16.12 Beam patterns of a single cymbal under different conditions. The cymbal symmetric axis is along the horizontal axis.

140 Experimental ATILA

TVR (dB re 1 uPa/V @1m)

130

120

110

100

90

80

0

10

20

30

40

50

60

70

80

Frequency (kHz)

FIG. 16.13

Comparison of the ATILA simulation and the experimental result in terms of transmitting voltage response (TVR) as a function of frequency.

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16.3 TRANSDUCER DESIGNS

(A)

(B) (A) A 3  3 cymbal array and (B) ATILA simulation model of the cymbal

FIG. 16.14 array.14

100 edge transducer center transducer corner transducer single element

150

edge transducer center transducer corner transducer

80 Displacement (nm)

Displacement (nm)

200

100

50

60

40

20

0

(A)

5

10

15 20 Frequency (kHz)

25

30

0

(B)

0

5

10

15 20 Frequency (kHz)

25

30

FIG. 16.15 (A) The displacements of the center, edge, and corner identical cymbals in a 3  3 array driven at 17 kHz under water. Note that the center cymbal generates a significant magnitude. (B) The displacements of the center, edge, and corner identical cymbals in a 3  3 array driven at 17 kHz under water. Three slightly deviated cymbals are arrayed in this structure (center 17 kHz, edge 16 kHz and corner 18 kHz).14

shown in Fig. 16.15A. The definitions of the center, edge, and corner transducers are illustrated in Fig. 16.14B. Interestingly, the center cymbal excites a significant magnitude, while the corner cymbal does not generate a displacement. Thus, experimentally, the center cymbal collapse was observed occasionally during operation. This peculiar nonuniform distribution of the displacement is originated from the mutual interaction of these three (center, edge, and corner) cymbals through a water medium. This problem can be solved by slightly modifying the cymbal performance; that is, when the resonance frequencies of the center, edge, and corner cymbals are adjusted to 17, 16, and 18 kHz, respectively, as shown in Fig. 16.15B, rather uniform displacements are obtained for these cymbal transducers. In conclusion, the significant interaction originated from the totally identical cymbal transducer choice, and this may not be observed in

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16. MANUFACTURING TECHNOLOGIES FOR PIEZOELECTRIC TRANSDUCERS

FIG. 16.16 Measured and calculated (point source model) beam patterns of the 3  3 array. The cymbal array plane vector is along the horizontal axis.

practice, due to a slight deviation of the transducer performance of each cymbal. A slight deviation of the performance helps with decoupling the mutual interaction between these cymbals through a water medium. Fig. 16.16 shows the measured and calculated (point source model) beam patterns of the 3  3 cymbal array. Unlike the situation of a single cymbal, the array increased the sound beam directivity dramatically with changing the drive frequency. In general, the multiple cymbal array provides the following benefits: (1) Transmitting voltage response (TVR) increases with the number of cymbals (2) Beam maneuverability is improved; 15 kHz is used for wide-angle surveillance, and 60 kHz can be used for narrow-angle detailed surveillance. The audible range for humans differs individually. The audible frequency ranges from 20 Hz to 20 kHz, whereas the audible intensity level ranges from 1012 to 1 W/m2 (this differs depending on the frequency). This minimum audible sound power level (1012 W/m2) is often taken as the intensity standard, 0 dB, which corresponds to the sound pressure 2  105 Pa (or 0.0002 m bar). In contrast, the transmitting voltage ratio (TVR) of a transducer is defined by the sound pressure in water in dB with the standard of 1 μ Pa, when the transducer is driven under 1 Vrms and the pressure sensor is set 1 m from the transducer. 16.3.3.3 Double PZT Layer Cymbal The cymbals discussed so far are basically composed of a single PZT plate, so they basically generate a “monopolar” pressure distribution mode; that is, the forward and backward pressure waves have the same sign. If we use double-layer PZT disks, the transducer performance can be modified significantly. Fig. 16.17 summarizes three typical pressure modes expected from the double-PZT cymbal transducer: monopole,

II. PREPARATION METHODS AND APPLICATIONS

16.3 TRANSDUCER DESIGNS

629

FIG. 16.17 (A) Monopole, (B) dipole, and (C) cardioid mode TVR generation by changing the operation scheme on the double PZT layer cymbal transducer.

dipole, and cardioid, computer-simulated with ATILA software code (Micromechatronics Inc., PA). The detailed simulation process can be found in Ref.2 When we drive two PZT plates in phase, a radial vibration mode is primarily excited on the PZT, which generates a simple breathing mode on two endcaps, leading to a three dimensionally uniform sound pressure propagation, called monopole mode (Fig. 16.17A). In contrast, when we drive two PZT plates out of phase (φ ¼ π), a bending mode (similar to a bimorph speaker) is excited on the PZT element, which generates out-of-phase, updown flextensional vibration on the two endcaps. You can expect a dumbbell-shaped pressure distribution with an opposite sign between the forward and backward directions, called dipole mode (Fig. 16.17B). Most of the transducers transmit the sound energy to both forward and backward directions, but the backward energy should be absorbed in general in order to prevent creating “ghost” images. Therefore, backing materials are usually adopted, as we discuss in Section 16.5. However, without using a backing material, we can completely cancel the backward propagation theoretically. In principle, you can imagine that the backward pressure can be canceled by adding the monopolar and dipolar configurations,

II. PREPARATION METHODS AND APPLICATIONS

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16. MANUFACTURING TECHNOLOGIES FOR PIEZOELECTRIC TRANSDUCERS

P P

FIG. 16.18

Vf

Polyurethane

Vb

Double PZT layer cymbal structure.

because the signs of pressures are opposite each other. More precisely, the front PZT disk drive voltage Vf and back disk voltage Vb (see Fig. 16.17C) should be chosen as Vb 1  R , ¼ Vf 1 + R

(16.2)

TVRm , meaning the TVR ratio between the monopole and TVRd dipole modes are at the same targeted drive frequency. Fig. 16.18 shows a double PZT layer cymbal transducer manufactured at The Pennsylvania State University, and Fig. 16.19 shows the measured beam pattern of (a) monopolar mode (Vf ¼ Vb, φ ¼ 0), (b) dipolar mode (Vf ¼ Vb, φ ¼ π), and (c) cardioid pattern under driving voltages calculated according to the equation, Vf ¼ 100 V, Vb ¼ 13 V, φ ¼ 50°, and (d) under voltages adjusted to Vf ¼ 100 V, Vb ¼ 28 V, and φ ¼ 55°. We can achieve no-backward wave transmission without using the backing layer in the doublelayer PZT cymbal transducers. where R ¼

16.4 ACOUSTIC LENS AND HORN 16.4.1 Acoustic Lens A dolphin is one of the best animal examples to explain ideal acoustic transducer systems. Dolphins and whales do not have vocal chords, but a breathing hole on the head, as shown in Fig. 16.20. By breathing strongly

II. PREPARATION METHODS AND APPLICATIONS

631

16.4 ACOUSTIC LENS AND HORN

30

0 0

330

30

−10 300

60

300

−20

−20

−30

270

120

240

150

180

−30

90

270

120

210

240

150

(A)

180

210

(B) 30

0 0

330

30 300

300 −20

−30

270

120

240

150

180

330

60

−20 90

0 0 −10

−10 60

(C)

330

−10

60

90

0 0

−30

90

270

120

240

150

210

180

210

(D)

FIG. 16.19 Measured beam pattern of (A) monopolar mode (Vf ¼ Vb, φ ¼ 0), (B) dipolar mode (Vf ¼ Vb, φ ¼ π), and (C) cardioid pattern under driving voltages calculated according to the equation, Vf ¼ 100 V, Vb ¼ 13 V, φ ¼ 50°, and (D) under voltages adjusted to Vf ¼ 100 V, Vb ¼ 28 V, and φ ¼ 55°.

through this hole, a dolphin can generate sound like a human whistle. Though this breathing hole is a point sound source, because of additional physical structures, the sound beam can be focused quite sharply toward the front direction (Fig. 16.20 bottom). The cranium shape seems to be a parabola antenna, which reflects the radial propagating sound into a rather parallel frontward beam. Further, a “melon” made of soft tissuelike paraffin (with a sound velocity lower than water) behaves like a convex acoustic lens, and it gives the sound beam a sharper focus. It is notable that if we use a glass lens with a sound velocity higher than water, a convex-shaped acoustic lens diverges the sound beam (like an optical concave lens). This is the initial sound transmitting process.

II. PREPARATION METHODS AND APPLICATIONS

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16. MANUFACTURING TECHNOLOGIES FOR PIEZOELECTRIC TRANSDUCERS

FIG. 16.20 Dolphin head: mesh portion ¼ bone, hatch portion ¼ soft tissue, white portion ¼ air, black portion ¼ ear. The top figure exhibits the biological names, and the bottom illustrates the acoustic beam radiation situation.

In order to receive the returned sound signal reflected from some object, if the strong original transmitting signal transfers directly to the receiving organ (ear), a serious blackout problem occurs. In order to overcome this problem, the dolphin has an acoustic impedance mismatch layer (air), which behaves like a double-glazed window for shutting out the noise. The dolphin’s receiver is its bottom jaws, through which the sound is transferred to the ear. Notice that the highly sensitive ear is isolated from the cranium bones to protect it from the direct sound penetration. This

II. PREPARATION METHODS AND APPLICATIONS

633

16.4 ACOUSTIC LENS AND HORN

situation is rather different from the human ear, which is connected directly to the bones (in fact, we have a headset that uses direct bone transmission of sound for a hearing aid.). Since the dolphin has completely separated right and left jaws, the two ears can detect the right and left sound signals independently, like a 3-D stereo system.

16.4.2 Acoustic Horn The original steel portion of the Langevin transducer can be modified with a horn concept to increase the displacement amplitude. For a resonance mode, the most popular displacement amplification mechanism is a horn. Fig. 16.21 illustrates some of the horn configurations. The axial displacement is increased roughly in inverse proportion to the crosssection area of the vibrator. These three samples exhibit the following features: (a) Exponential taper: highest efficiency, but costly in manufacturing. (b) Straight taper: cheaper in manufacturing, with a reasonable efficiency. (c) Step type: Cheapest, but some mechanical energy is bounced back. By tapering the steel tip portion (exponential taper) as shown in Fig. 16.22, we can significantly amplify the displacement level, which can be utilized for ultrasonic cutters and cavitation instruments. Fig. 16.23 shows another commercialized ultrasonic cutter with a Langevin-type transducer. Note the step-type horn at the tip.

(A)

(B)

(C)

FIG. 16.21 Three example configurations of the horn: (A) Exponential taper; (B) straight taper; (C) step-type.

FIG. 16.22

Langevin transducer with a horn. Courtesy of Honda Electronics, Japan.

II. PREPARATION METHODS AND APPLICATIONS

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16. MANUFACTURING TECHNOLOGIES FOR PIEZOELECTRIC TRANSDUCERS

FIG. 16.23 Ultrasonic cutter with a Langevin-type transducer and a step-type horn at the tip. Courtesy of Honda Electronics, Japan.

Reflection type

Transmission type

FIG. 16.24

Classification of mechanical scan acoustic microscopes (SAM).

When we use a concave radiation surface for a high-frequency wave (GHz) at the tip of the horn, as illustrated in Fig. 16.24, we can focus the acoustic beam into the 0.1 mm range, which can be used as an acoustic microscope. There are two acoustic microscope types: reflection and transmission microscopes. This acoustic microscope is helpful for detecting a cancerous tissue portion that has a harder elasticity than a normal portion of tissue in a patient.

16.5 ACOUSTIC IMPEDANCE MATCHING If we increase the driving frequency of the fish-finder (50 kHz) by 70 times, that is, 3.5 MHz, we can increase the resolution by 70 times (less than 0.5 mm), and this can be used to detect the infant situation in the human body. However, the practical situation is not so easy. Since the piezoelectric ceramic (such as PZT) has very large acoustic impedance pffiffiffiffiffi (defined by pc, where ρ is density and c is elastic stiffness of PZT) in comparison with the human body (like water), most ultrasonic sound power is

II. PREPARATION METHODS AND APPLICATIONS

16.5 ACOUSTIC IMPEDANCE MATCHING

635

Water/human body

2nd matching layer 1st matching layer Piezo ceramic Backing

FIG. 16.25

Acoustic impedance close to the human body Intermediate acoustic impedance

Reduce the Ghost

Acoustic transducer design for medical imaging applications.

reflected at the interface between PZT and water/human tissue, and the transmitted sound power is very low. In order to transmit the sound energy effectively, we need to suitably design the acoustic impedance matching layer. When the acoustic impedances of PZT and water are Z1 and Z2, respectively, the ffi recommended matching impedance of the pffiffiffiffiffiffiffiffiffiffi matching layer is Z1 Z2 (i.e., geometrical average). As shown in Fig. 16.25, we sometimes use multiple matching layers. Also like a dolphin, the backing layer is used for reducing the ghost effect. Soft rubber and cork (used for wine bottle stoppers) are popularly used as a backing material. One of the most important medical diagnostic applications is based on ultrasonic echo field.15,16 Ultrasonic transducers convert electrical energy into mechanical form when generating an acoustic pulse, and they convert mechanical energy into an electrical signal when detecting its echo. The transmitted waves propagate into a body and echoes are generated, which travel back to be received by the same transducer. These echoes vary in intensity according to the type of tissue or body structure, thereby creating images. An ultrasonic image represents the mechanical properties of the tissue, such as density and elasticity. We can recognize anatomical structures in an ultrasonic image since the organ boundaries and fluid-to-tissue interfaces are easily discerned. The ultrasonic imaging process can also be performed in real time. This means we can follow rapidly moving structures such as the heart without motion distortion. In addition, ultrasound is one of the safest diagnostic imaging techniques. It does not use ionizing radiation like x-rays and thus is routinely used for fetal and obstetrical imaging. Useful areas for ultrasonic imaging include cardiac structures, the vascular systems, the fetus, and abdominal organs such as the liver and kidneys. In brief, it is possible to see inside the human body without breaking the skin by using a beam of ultrasound.

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636

16. MANUFACTURING TECHNOLOGIES FOR PIEZOELECTRIC TRANSDUCERS

Backing

Piezoelectric element Matching layer

Ultrasonic beam Input pulse

FIG. 16.26

Basic transducer geometry for acoustic imaging applications.

Fig. 16.26 shows the basic ultrasonic transducer geometry. The transducer is mainly composed of a matching layer, piezoelectric element, and a backing layer.17 One or more matching layers are used to increase the sound transmission into tissues. The backing layer is added to the rear of the transducer in order to damp the acoustic backwave and to reduce the pulse duration. Piezoelectric materials are used to generate and detect ultrasound. In general, broadband transducers should be used for medical ultrasonic imaging. The broad bandwidth response corresponds to a short pulse length, resulting in better axial resolution. Three factors are important in designing broad bandwidth transducers; acoustic impedance matching, a high electromechanical coupling coefficient of the transducer, and electrical impedance matching. These pulse echo transducers operate based on the thickness mode resonance of the piezoelectric thin plate. Further, a low planar mode coupling coefficient, kp, is beneficial for limiting energies being expended in the nonproductive lateral mode. A large dielectric constant is necessary to enable a good electrical impedance match to the system, especially with tiny piezoelectric sizes. There are various types of transducers used in ultrasonic imaging. Mechanical sector transducers consist of single, relatively large resonators and can provide images by mechanical scanning such as wobbling. Multiple element array transducers permit discrete elements to be individually accessed by the imaging system and enable electronic focusing in the scanning plane to various adjustable penetration depths through the use of phase delays. Two basic types of array transducers are linear and phased (or sector). A linear array is a collection of elements arranged in one direction, producing a rectangular display (see Fig. 16.27). A curved linear (or convex) array is a modified linear array whose elements are arranged along an arc to permit an enlarged trapezoidal field of view (see Fig. 16.28). The elements of these linear-type array transducers are

II. PREPARATION METHODS AND APPLICATIONS

637

16.5 ACOUSTIC IMPEDANCE MATCHING

W L

T

(A)

Vibrator element Piezoelectric vibrator

Backing

(B) Structure of an array-type ultrasonic probe FIG. 16.27

Linear array-type ultrasonic probe.

FIG. 16.28 Curved linear (or convex) array whose elements are arranged along an arc to permit an enlarged trapezoidal field of view. Courtesy of Honda Electronics, Japan.

excited sequentially group by group with the sweep of the beam in one direction. These linear array transducers are used for radiological and obstetrical examinations. On the other hand, in a phased array transducer the acoustic beam is steered by signals that are applied to the elements with delays, creating a sector display. This transducer is useful for cardiology applications where positioning between the ribs is necessary.

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16. MANUFACTURING TECHNOLOGIES FOR PIEZOELECTRIC TRANSDUCERS

FIG. 16.29 Ultrasonic imaging with the two PZT ceramic probes (left) and with the PZNPT single crystal probe (right). Courtesy of Toshiba.

Fig. 16.29 demonstrates the superiority of the Pb(Zn1/3Nb2/3)O3-PbTiO3 (PZN-PT) single crystal to the PZT ceramic for the medical imaging transducer application, developed by Toshiba Corporation.18 Conventionally, the medical doctor needs to use two different frequency PZT probes— one is 2.5 MHz for checking a wider and deeper area, and the other is 3.75 MHz for monitoring the specified area with a better resolution. The PZN-PT single crystal (with very high k33 and kt) probe provides two additional merits: (1) wide bandwidth—without changing the probe, the doctor can just switch the drive frequency from 2.5 to 3.75 MHz—and (2) strong signal; because of the high electromechanical coupling, the receiving signal level is more than two times greater than the PZT probe.

16.6 SONOCHEMISTRY Fundamental research on sonochemistry is now rapidly increasing. With using the “cavitation” effect, toxic materials such as dioxin and trichloroethylene can be easily transformed into innocuous materials even at room temperature. Ultrasonic distillation is also possible at room temperature for obtaining highly concentrated Japanese sake. Unlike the regular boiling distillation, this new method gives sake a much higher alcoholic concentration while keeping its gorgeous taste and fragrance. Fig. 16.30A shows the alcoholic concentration in the base solution and mist. Note that the higher alcoholic concentration is obtained from a low concentration solution at the lower ambient temperature. Fig. 16.30B shows an arrayed Langevin transducer system for the sake distillation application. This high-quality sake product is now commercially available.19 High-powered ultrasonic transducers can also be used in transdermal drug delivery. Desktop types have been commercialized as shown in Fig. 16.31A from Honda Electronics, Japan. Penn State researchers worked

II. PREPARATION METHODS AND APPLICATIONS

Ethanol mol concentration in mist [mol.%]

16.7 PIEZOELECTRIC TRANSFORMERS

639

100

Boiling distillation 50

(A)

10°C

30°C

50°C

0 100 50 Ethanol mol concentration in solution [mol.%]

(B)

FIG. 16.30 (A) Low temperature distillation with high-powered ultrasonic and (B) arrayed Langevin transducer system for the sake distillation application. (A) Courtesy of Matsuura Brewer, Japan. (B) Courtesy of Honda Electronics, Japan.

(A)

(B)

FIG. 16.31 (A) Desktop sonicator for drug delivery and (B) portable transdermal insulin drug delivery system that uses cymbal transducers. (A) Courtesy of Honda Electronics, Japan. (B) Cited from Popular Mechanics.

on a needle-free injection system of insulin by using cymbal piezoactuators in a portable fashion (see Fig. 16.31B).20

16.7 PIEZOELECTRIC TRANSFORMERS When input and output terminals are fabricated on a piezo-device and input/output voltage is changed through the vibration energy transfer, the device is called a piezoelectric transformer. Piezoelectric transformers were used in color TVs in the early 1970s, because of their compact size in comparison with the conventional electromagnetic coil-type transformers.

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However, since serious problems were found initially in the mechanical strength (collapse occurred at the nodal point!) and in heat generation, its commercialization was unfortunately stopped at that time. Because laptop computers with a liquid crystal display require a very thin, transformer with no electromagnetic noise, to start the glow of a fluorescent back-lamp, the development “renaissance” began after the 1990s. The previous problems (mechanical strength and heat generation) have been almost overcome by the new high-powered PZT materials development over the past 20 years.

16.7.1 Rosen-Type Transformer Since the original piezotransformer was proposed by C. A. Rosen,21 there have been a variety of such transformers investigated. Fig. 16.32 shows a fundamental structure where two differently-poled parts coexist in one piezoelectric plate. A standing wave with a half wavelength equal to the sample length is excited, a quarter wavelength existing on both the input (L1) and output (L2) parts. The voltage rise ratio r (step-up ratio) is given for the unloaded condition by the following:  pffiffiffiffiffiffiffiffiffiffi    E E r ¼ 4=π 2 k31 k33 QM ðL2 = tÞ 2 s33 =s11 =ð1 + pffiffiffiffiffiffiffiffiffiffi (16.3) sD =sE Þ 33

11

The r ratio is increased by (L2/t), where t is the thickness. The main reason for the mechanical fracture in the fundamental Rosen type transformer can be understood by the superposition of the following two stresses (see Fig. 16.32): (1) Residual stress between the input and output parts during the poling process: the input PZT part extends along the thickness direction, while the output PZT part shrinks along the thickness direction. (2) Dynamic stress during operation: when we use the fundamental (half-wavelength) resonance k31 mode, the stress and strain are concentrated around the center part of the PZT plate. NEC proposed a multilayer-type transformer (Fig. 16.33) in order to increase the voltage step-up ratio by a factor of the layer number.22 Usage L1 Low voltage input

FIG. 16.32

L2 w t

High voltage output

Piezoelectric transformer proposed by Rosen.21

II. PREPARATION METHODS AND APPLICATIONS

16.7 PIEZOELECTRIC TRANSFORMERS

FIG. 16.33

641

Multilayer-type transformer by NEC.22

of the third-order longitudinal mode is another idea to distribute the stress concentration. Let us consider how to assemble a piezoelectric transformer on a circuit board in practice, by using an example adopted for a commercial laptop. A piezotransformer (second resonance mode usage) is held on a circuit board as shown in the photo (Fig. 16.34A). You can find initially that two ring materials are surrounded on the transformer and the bottom of these two rings are adhered on the board; also, electric leads are taken from the PZT plate ends.

(A)

(B) FIG. 16.34

(A) Configuration of a backlight inverter with a modified Rosen-type piezoelectric transformer, and (B) polarization direction and displacement distribution contour for the second resonance mode.

II. PREPARATION METHODS AND APPLICATIONS

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16. MANUFACTURING TECHNOLOGIES FOR PIEZOELECTRIC TRANSDUCERS

What kind of material should be chosen for the rings? Where should the rings be placed? What kind of lead wire (metal species, size, etc.) should be used? The lead wires in this backlight inverter product are connected on both edges of the PZT rectangular plate. Where should the lead wire be installed in principle? Fig. 16.34B shows the configuration of this piezoelectric transformer and the second resonance mode for your reference. Note that a piezotransformer (2nd resonance mode usage) has two nodal lines: one is 1/4 of the full length from the left edge, and the other 1/4 from the right edge, as shown in Fig. 16.34B. The nodal line does not displace, but the maximum strain and stress are concentrated. (a) Two rings should be made of a soft material such as silicone rubber (or equivalent polymer), because the mechanical impedance mismatch with PZT is essential in order to prevent dissipation of the vibration energy. This is basically “acoustic floating.” (b) The rings should be placed around the nodal lines, because clamping at the nodal point shows the minimum disturbance of the resonating vibration, which prevents suppressing the vibration displacement. (c) Electric lead wire—electrical viewpoint: Because the electric impedance of the transformer at the resonance point is very small, the resistance of the lead wire should be also minimized. The wire material should have high conductivity, leading to Cu or Ag for the material. In terms of size, thick and short lead wire is better from the conductance viewpoint. Mechanical viewpoint: However, because the mass and rigidity of the lead wire also dramatically affect the vibration mode, we should minimize the wire thickness and maximize the length. Thus, we need to compromise the thickness and length. The wire installation position should be around the nodal lines to prevent mechanical disturbance. The practical assembly in Fig. 16.34B was merely requested from the client due to their circuit board designing restriction (not our intention!).

16.7.2 Step-Down Transformer The application trend is currently shifting from high-voltage backlight inverters to high-powered transformers aiming at power supplies such as AC/DC and DC/DC step-down adapters. Penn State University invented a ring-dot-type multilayer transformer as shown in Fig. 16.35B, which utilizes a planar kp vibration mode. Using our own high-powered piezoceramics (low temperature sinterable), the ML ring-dot transformer could generate high power density up to 30–35 W/cm3. Unlike a Rosen stepup design, the ring-dot type does not need a large size ratio (L2/t) or

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643

REFERENCES Output dia. t Input diameter

A

B B

A

(A)

(B)

FIG. 16.35

(A) Configuration of a multilayer ring-dot type piezoelectric transformer, and (B) a credit card-sized AC/DC adapter with a piezotransformer for a laptop power supply (35 W level).

complicated poling process. According to a required step-down ratio, we can design the optimized ratio between the input and output electrode areas using ATILA FEM software code. A credit card-sized adapter (110 Vrms ! 15 Vdc) shown in Fig. 16.35B was developed in collaboration with Nihon Ceratec, Japan for laptop computers.23 Compare the size difference from the present electromagnetic transformer adapter shown in the top in Fig. 16.35B.

Acknowledgments The author greatly owes Dr. Nagaya Okada at Honda Electronics, Japan a debt of gratitude for his assistance in permitting Honda’s products to be used in this article. Also, some content and figures can be found in my textbooks (Refs. 1–3) published by CRC Press, New York, NY.

References 1. Uchino K, Giniewics JR. Micromechatronics. New York, NY: CRC Press; 2003. 2. Uchino K. FEM and micromechatronics with ATILA software. New York, NY: CRC Press; 2008. 3. Uchino K. Ferroelectric devices. 2nd ed. New York, NY: CRC Press; 2009. 4. Sugiyama S, Uchino K. In: Proc. Int’l. Symp. Appl. Ferroelectrics ’86, IEEE; 1986. p. 637. 5. Kusakabe C, Tomikawa Y, Takano T. IEEE Trans UFFC 1990;37(6):551. 6. Ota T, Uchikawa T, Mizutani T. Jpn J Appl Phys 1985;24(Suppl. 24-3):193. 7. Yano T, Sato E, Fukui I, Hori S. In: Proc. Int’l Symp. Soc. Information Display; 1989. p. 180. 8. Kurashima N. In: Proc. Machine Tech. Inst. Seminar, MITI, Tsukuba, Japan; 1999. 9. Yokoya Y. Electr Ceram 1991;22(111):55. 10. Fujii A. In: Proc. JTTAS Meeting on Dec. 2, Tokyo; 2005. 11. Koster MP. In: Proc. 4th Int’l Conf. New Actuators, Germany; 1994. p. 144. 12. Goto H, Imanaka K, Uchino K. Ultrason Technol 1992;5:48. 13. Dogan A. Ph.D. Thesis, Penn State University; 1994. 14. Zhang J, Hughes WJ, Bouchilloux P, Meyer Jr RJ, Uchino K, Newnham RE. A class V flextensional transducer: the cymbal. Ultrasonics 1999;37:387–93.

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15. Auld BA. Acoustic fields and waves in solids. 2nd ed. Melbourne: Robert E. Krieger; 1990. 16. Kino GS. Acoustic waves: device imaging and analog signal processing. Englewood Cliffs, NJ: Prentice-Hall; 1987. 17. Desilets CS, Fraser JD, Kino GS. IEEE Trans Sonics Ultrason 1978;SU-25:115. 18. Saitoh S, Takeuchi T, Kobayashi T, Harada K, Shimanuki S, Yamashita Y. An Improved Phased Array Ultrasonic Probe Using 0.91Pb(Zn1/3Nb2/3)03-0.09PbTi03 Single Crystal. Jpn J Appl Phys 1999;38(5B):3380–4. 19. http://www.shumurie.co.jp. 20. Popular Mechanics, 2003;180(3):20. 21. Rosen CA. In: Proc. Electronic Component Symp; 1957. p. 205. 22. Kawashima S, Ohnishi O, Hakamata H, Tagami S, Fukuoka A, Inoue T, et al. In: Proc. IEEE Int’l Ustrasonic Symp. ’94, France; 1994. 23. Ezaki T, Manuspiya S, Moses P, Uchino K, Vazquez Carazo A. J Mater Technol 2004;19(2):79–83.

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C H A P T E R

17 High-Power Piezoelectrics and Loss Mechanisms K. Uchino The Pennsylvania State University, State College, PA, United States

Abstract Heat generation is one of the significant problems in piezoelectrics for high power density applications. In this chapter, we review first the loss phenomenology in piezoelectrics first, including three losses—dielectric, elastic and piezoelectric losses— followed by the equivalent circuit approach with these three losses. Third, heat generation analysis is discussed in piezoelectric materials for pseudo-DC and AC drive conditions. Heat generation at off-resonance is attributed mainly to intensive dielectric loss tan δʹ, while the heat generation at resonance is mainly originated from the intensive elastic loss tan ϕʹ. Fourth, various experimental techniques (high power characterization system, HiPoCS) are introduced to measure dielectric, elastic, and piezoelectric losses separately, including admittance/ impedance spectrum analysis and burst/transient response method. Mechanical quality factors (QA at resonance and QB at antiresonance) are primarily measured as a function of vibration velocity. Fifth, based on the results received by HiPoCS, new driving schemes (antiresonance drive, etc.) are proposed in order to minimize the losses and maximize the transducer efficiency. Sixth, loss mechanisms are discussed from the materials science viewpoint, particularly from the domain dynamics models. Then, practical high-powered “hard” Pb(Zr,Ti)O3 (PZT)-based materials are described, which exhibit vibration velocities close to 1 m/s (rms), leading to the power density capability 10 times that of the commercially available hard PZTs. We propose an internal bias field model to explain the low loss and high power origin of these materials. Finally, we also introduce the polarization angle dependence of losses (sample geometry), and DC bias electric field dependence of losses (sample driving technique) for the high-powered applications. Keywords: High power piezoelectrics, Heat generation, Loss mechanism, Mechanical quality factor, Vibration velocity, Hard PZT, Resonance/antiresonance, Admittance spectrum analysis, Burst mode drive.

Advanced Piezoelectric Materials http://dx.doi.org/10.1016/B978-0-08-102135-4.00017-5

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Copyright © 2017 Elsevier Ltd. All rights reserved.

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17.1 INTRODUCTION With accelerating the commercialization of piezoelectric actuators and transducers for portable equipment applications, we identified the bottleneck of the piezoelectric devices; that is, significant heat generation limits the maximum power density. The current maximum handling energy of a well-known hard Pb(Zr,Ti)O3 (PZT) is only around 10 W/cm3. We desire 100 W/cm3 or higher power density for further miniaturization of devices (such as piezo MEMS actuators) without losing efficiency. Thus, the main research focus seems to be shifting from the “real parameters” such as larger polarization and displacement, to the “imaginary parameters” such as polarization/displacement hysteresis, heat generation, and mechanical quality factor, which are originated from three loss factors (dielectric, elastic, and piezoelectric losses). Reducing hysteresis and heat generation and increasing the mechanical quality factor to amplify the resonance displacement are the primary targets. However, since the resonance displacement is provided by a product of the mechanical quality factor Qm and the real parameter (piezoelectric constant d), and the Qm value is usually reduced with increasing d in the piezoceramics, the target of the material development is highly complicated. Loss and hysteresis in piezoelectrics exhibit both merits and demerits in general. For positioning actuator applications, hysteresis in the fieldinduced strain causes a serious problem, and for resonance actuation such as ultrasonic motors, loss generates significant heat in the piezoelectric materials. Further, in consideration of the resonant strain amplified in proportion to a mechanical quality factor, low (intensive) mechanical loss materials are preferred for ultrasonic motors. In contrast, for force sensors and acoustic transducers, a low mechanical quality factor Qm (which corresponds to high mechanical loss) is essential to widen a frequency range for receiving signals. In summary, this chapter focuses on high-powered actuator developments, not on sensor applications. Historically, K. H. Haerdtl wrote a review article on electrical and mechanical losses in ferroelectric ceramics in the early 1980s.1 Losses are considered to consist of four portions: (1) domain wall motion; (2) fundamental lattice portion, which should also occur in domain-free monocrystals; (3) microstructure contribution, which occurs typically in polycrystalline samples; and (4) conductivity portion in highly ohmic samples. However, in the typical piezoelectric ceramic case, the loss due to the domain wall motion exceeds the other three contributions significantly. Haerdtl reported interesting experimental results on the linear relationship between dielectric (tan δ) and elastic (tan ϕ) losses (i.e., tan ϕ/ tan δ ¼ 0.32) in piezoceramics, Pb0.9La0.1(Zr0.5Ti0.5)1xMexO3, where Me

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represents the dopant ions Mn, Fe, or Al and x varies between 0 and 0.09. However, he measured the mechanical losses on poled ceramic samples, while the electrical losses on unpoled samples, in other words, in a different polarization state, which leads to an ambiguity in the discussion. Losses vary dramatically depending on the polarization direction, which is discussed in Section 17.7.2.1. Not many systematic studies of the loss mechanisms in piezoelectrics have been reported, particularly in high electric field and high power density ranges. Although part of the formulas of this manuscript was described by T. Ikeda in his textbook,2 the piezoelectric losses, which have been found in our investigations to play an important role, were neglected then. Equivalent circuit analysis is a simple method to consider the electrical behavior, taking losses into account.3–11 The Mason’s equivalent circuit was derived from the piezoelectric constitutive and motion equations; therefore, the electromechanical conversion process is clearly described. Though there exist three fundamental losses in the piezoelectric materials (dielectric, elastic, and piezoelectric losses), equivalent circuits so far reported included the mechanical/elastic loss factor (and dielectric loss, occasionally) on the basis of Mason’s model.12–14 D. Damjanovic proposed an equivalent circuit to present the influence of the piezoelectric loss,15 while the coupled loss formulas are insufficient to measure the losses in piezoelectric materials. The major problem is found even in the present IEEE Standard on Piezoelectricity, ANSI/IEEE Std. 176-1987.16 This Standard does not include the terminology “piezoelectric loss,” nor does it discuss the difference between mechanical quality factors QA (at resonance) and QB (at antiresonance); that is, both are exactly the same, against many of the practical experimental results and reports.17,18 Being motivated by various engineers’ requests, we elucidates the comprehensive researches on piezoelectric losses in this chapter. We first review the loss phenomenology in piezoelectrics, including three losses (dielectric, elastic and piezoelectric losses), followed by the equivalent circuit approach with these three losses. Clear ideas are provided on the difference between resonance and antiresonance modes, and how to define the mechanical quality factors. Third, heat generation analysis is discussed in piezoelectric materials for pseudo-DC and AC resonance drive conditions. Heat generation at off-resonance is attributed mainly to intensive dielectric loss tan δʹ, while the heat generation at resonance is mainly originated from the intensive elastic loss tan ϕʹ. Fourth, various experimental techniques (high power characterization system, HiPoCS) are introduced to measure dielectric, elastic, and piezoelectric losses separately, including admittance/impedance spectrum analysis and the burst/transient response method. Mechanical quality factors (QA at

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resonance and QB at antiresonance) are primarily measured as a function of vibration velocity. Fifth, based on the results received by HiPoCS, new driving schemes (antiresonance drive, etc.) are proposed in order to minimize the losses and maximize the transducer efficiency. Sixth, loss mechanisms are discussed from the materials science viewpoint, in particular, from the domain dynamics models. Then, practical high-power hard Pb(Zr,Ti)O3 (PZT)-based materials are described, which exhibit vibration velocities close to 1 m/s (rms), leading to the power density capability 10 times that of the commercially available hard PZTs. We propose an internal bias field model to explain the origin of low loss and high power in these materials. Finally, we also introduce the polarization angle dependence of losses (sample geometry), and DC bias electric field dependence of losses (sample driving technique) for the high-powered applications. “Intensive” and “extensive” losses are introduced in our discussion, in relation with intensive and extensive parameters in the phenomenology. Suppose a certain volume of material first, and imagine cutting it half. The extensive parameter (the material’s internal parameter such as displacement/strain x and total dipole moment/electric displacement D) depends on the volume of the material (i.e., it becomes a half), while the intensive parameter (externally controllable parameter such as force/stress X and electric field E) is independent on the volume of the material. These are not related with the intrinsic and extrinsic losses that were introduced to explain the loss contribution from the monodomain single crystal state and from the others.19 In this manuscript, our discussion in piezoelectrics is focused primarily on the extrinsic losses, particularly losses originated from domain dynamics. However, physical parameters of their performance such as permittivity and elastic compliance still differ in piezoelectric materials, depending on the boundary conditions—mechanically free or clamped, and electrically short-circuit or open-circuit. These are distinguished as intensive or extensive parameters and their associated losses.

17.2 PHENOMENOLOGICAL APPROACH TO LOSSES IN PIEZOELECTRICS 17.2.1 Piezoelectric Constitutive Equations 17.2.1.1 Intensive Losses Since the detailed mathematical treatment has been described in a previous paper,20 we summarize the essential results in this section. We start from the following two piezoelectric constitutive equations:

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651

x ¼ sE X + dE,

(17.1)

D ¼ dX + εX ε0 E,

(17.2)

where x is strain, X is stress, D is the electric displacement, and E is the electric field. Eqs. (17.1), (17.2) are expressed in terms of intensive (i.e., externally controllable) physical parameters X and E. The elastic compliance sE, the dielectric constant εX, and the piezoelectric constant d are temperature-dependent in general. Note that the piezoelectric constitutive equations cannot yield a delay time-related loss, in general, without taking into account irreversible thermodynamic equations or dissipation functions. However, the “dissipation functions” are mathematically equivalent to the introduction of “complex physical constants” into the phenomenological equations, if the loss is small and can be treated as a perturbation (dissipation factor tangent ≪ 0.1, in practice). Therefore, we will introduce complex parameters εX*, sE*, and d*, using *, in order to consider the small hysteresis losses in dielectric, elastic, and piezoelectric constants: εX* ¼ εX ð1  jtan δ0 Þ,

(17.3)

sE* ¼ sE ð1  jtan ϕ0 Þ,

(17.4)

d* ¼ dð1  jtan θ0 Þ:

(17.5)

θʹ is the phase delay of the strain under an applied electric field, or the phase delay of the electric displacement under an applied stress. Both delay phases should be exactly the same if we introduce the same complex piezoelectric constant d* into Eqs. (17.1), (17.2). δʹ is the phase delay of the electric displacement to an applied electric field under a constant stress (e.g., zero stress) condition, and ϕʹ is the phase delay of the strain to an applied stress under a constant electric field (e.g., short-circuit) condition. We will consider these phase delays as “intensive” losses. Figs. 17.1A–D correspond to the model hysteresis curves for practical experiments: D vs. E curve under a stress-free condition, x vs. X under a short-circuit condition, x vs. E under a stress-free condition, and D vs. X under a short-circuit condition for measuring current, respectively. Note that these measurements are easily conducted in practice. The average slope of the D-E hysteresis curve in Fig. 17.1A corresponds to the permittivity εXε0, where the superscript stands for X ¼ constant (occasionally zero). Thus, tan δʹ is called the intensive dielectric loss tangent. The situation of sE is similar; the slope of the x-X relation is the elastic compliance under E ¼ constant condition. Since the areas on the D-E and x-X domains exhibit directly the electrical and mechanical energies, respectively (see Fig. 17.1A and B), the stored energies (during a quarter cycle) and hysteresis losses (during a full

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D0

x0 Ue

we

Um

wm

E0

(A)

X0

(B) x0

D0

E0

(C)

X0

(D)

FIG. 17.1

(A) D vs. E (stress free), (B) x vs. X (short-circuit), (C) x vs. E (stress free), and (D) D vs. X (short-circuit) curves with a slight hysteresis in each relation.

electric or stress cycle) for pure dielectric and elastic energies can be calculated as follows: Ue ¼ ð1=2ÞεX ε0 E20 ,

(17.6)

we ¼ πεX ε0 E20 tan δ0 ,

(17.7)

Um ¼ ð1=2ÞsE X02 ,

(17.8)

wm ¼ πsE X02 tan ϕ0 :

(17.9)

The dissipation factors, tan δʹ and tan ϕʹ, can be experimentally obtained by measuring the dotted hysteresis area and the stored energy area; that is, (1/2π)(we/Ue) and (1/2π)(wm/Um), respectively. Note that the factor (2π) comes from integral per cycle. The electromechanical hysteresis loss calculations, however, are more complicated, because the areas on the x-E and P-X domains do not directly provide energy. The areas on these domains can be calculated as follows, depending on the measuring methods; when measuring the induced strain under an electric field, the electromechanical conversion energy can be calculated by converting E to stress X:  ð ð ð   E0   1 EdE ¼ ð1=2Þ d2 =sE E20 , (17.10) Uem ¼ xdX ¼ E xdx ¼ d2 = sE s 0

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653

where x ¼ dE was used. Then, using Eqs. (17.4), (17.5), and from the imaginary part, we obtain the loss during a full cycle as   wem ¼ π d2 = sE E20 ð2 tan θ0  tan ϕ0 Þ: (17.11) Note that the area ratio in the strain vs. electric field measurement should provide the combination of piezoelectric loss tan θʹ and elastic loss tan ϕʹ (not tan θʹ directly!). When we measure the induced charge under stress, the stored energy Ume and the hysteresis loss wme during a quarter and a full stress cycle, respectively, are obtained similarly as ð   Ume ¼ PdE ¼ ð1=2Þ d2 =ε0 εX X02 ,

(17.12)

  wme ¼ π d2 =ε0 εX X02 ð2 tan θ0  tan δ0 Þ:

(17.13)

Now, the area ratio in the charge vs. stress measurement provides the combination of piezoelectric loss tan θʹ and dielectric loss tan δʹ. Hence, from the measurements of D vs. E and x vs. X, we obtain tan δʹ and tan ϕʹ, respectively, and either the piezoelectric (D vs. X) or converse piezoelectric measurement (x vs. E) provides tan θʹ through a numerical subtraction. The above equations provide a traditional loss measuring technique on piezoelectric actuators at a pseudo-DC condition, an example of which is introduced in Section 17.5. 17.2.1.2 Extensive Losses So far, we have discussed the intensive dielectric, mechanical, and piezoelectric losses (with prime notation) in terms of intensive parameters X and E. In order to consider physical meanings of the losses in the material (e.g., domain dynamics), we will introduce the extensive losses20 in terms of extensive parameters x and D. In practice, intensive losses are easily measurable, but extensive losses are not in the pseudo-DC measurement; they are obtainable from the intensive losses by using the K-matrix, which is introduced later. The extensive losses are essential when we consider a physical microscopic or semimacroscopic model. When we start from the piezoelectric equations in terms of extensive physical parameters x and D, X ¼ cD x  hD,

(17.14)

E ¼ hx + κ x κ 0 D,

(17.15)

where cD is the elastic stiffness under D ¼ constant condition (i.e., electrically open-circuit), κ x is the inverse dielectric constant under x ¼ constant

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condition (i.e., mechanically clamped), and h is the inverse piezoelectric constant d. We introduce the extensive dielectric, elastic, and piezoelectric losses as κx* ¼ κ x ð1 + jtan δÞ,

(17.16)

cD* ¼ cD ð1 + jtan ϕÞ,

(17.17)

h* ¼ hð1 + jtan θÞ:

(17.18)

The sign “+” in front of the imaginary “j” is taken by a general induction principle—that is, “polarization induced after electric field application” and so on. It is notable that the permittivity under a constant strain (e.g., zero strain or completely clamped) condition, εx*, and the elastic compliance under a constant electric displacement (e.g., open-circuit) condition, sD*, can be provided as an inverse value of κ x* and cD*, respectively, in this simplest 1-dimensional expression. Thus, using exactly the same losses in Eqs. (17.16), (17.17), εx* ¼ εx ð1  jtan δÞ,

(17.19)

s ¼ s ð1  jtan ϕÞ, (17.20) where we will consider these phase delays again as extensive losses. Care should been taken in the case of a general 3-D expression, where this part must be translated as inverse matrix components of κ x* and cD* tensors. Here, we consider the physical property difference between the boundary conditions: E constant and D constant, or X constant and x constant in a simplest 1-D model. When an electric field is applied on a piezoelectric sample as illustrated in the top part of Fig. 17.2, this state will be equivalent to the superposition of the following two steps: first, the sample is completely clamped and the field E0 is applied (pure electrical energy (1/2)εxε0E20 is input); second, keeping the field at E0, the mechanical constraint is released (additional mechanical energy (1/2)(d2/sE)E20 is necessary). The total energy should correspond to the total input electrical energy (1/2)εXε0E20 under the stress-free condition (left figure). That is,   ð1=2ÞεX ε0 E20 ¼ ð1=2Þεx ε0 E20 + ð1=2Þ d2 =sE E20 : A similar energy calculation can be obtained from the bottom part of Fig. 17.2, leading to the following equations: D*

D

  εx =εX ¼ 1  k2 ,   sD =sE ¼ 1  k2 ,

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(17.21) (17.22)

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Total input electrical energy = (1/2) e0e X E02

Stored electrical energy = (1/2) e0e X E02

− − − − − − −

−

−

−

Stored mechanical energy = (1/2) (d 2/sE) E02

−

= +

+ + + + + +

Total input mechanical energy = (1/2) sE X02

Strain x = dE0

+ +

+

+

Mechanically clamped

Electrically short-circuited

Stored mechanical energy = (1/2) sD X02

Stored electrical energy = (1/2) (d2/e 0e X)X02 +

+

+

+

Current

=

Inverse Field

+ −

Electrically short-circuited

Electrically open-circuited

−

−

−

Polarization

P = dX0 Inverse field

E = dX0 /e0e X FIG. 17.2

where

Conceptual figure for explaining the relation between εX and εx, sE, and sD.

  κ X =κ x ¼ 1  k2 ,   cE =cD ¼ 1  k2 ,

(17.23)

    k 2 ¼ d 2 = s E ε 0 ε X ¼ h2 = c D κ x κ 0 :

(17.25)

(17.24)

This k is called the electromechanical coupling factor, which is defined as a real number in this manuscript. In order to obtain the relationships between the intensive and extensive  losses, the following three equations are essential [note k2 ¼ h2 = cD κ x κ0 ]:    1 , (17.26) ε0 ε X ¼ κ x κ 0 1  h2 = c D κ x κ 0    1 , sE ¼ cD 1  h2 = cD κx κ 0

(17.27)

     1 d ¼ h2 = cD κx κ0 h 1  h2 = cD κx κ0 :

(17.28)

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Replacing the parameters in Eqs. (17.26)–(17.28) by the complex parameters in Eqs. (17.3)–(17.5), (17.16)–(17.18), we obtain the relationships between the intensive and extensive losses:      (17.29) tan δ0 ¼ 1= 1  k2 tan δ + k2 ð tan ϕ  2tan θÞ ,       tan ϕ0 ¼ 1= 1  k2 tan ϕ + k2 ð tan δ  2tan θÞ , (17.30)       0 2 2 tan θ ¼ 1= 1  k tan δ + tan ϕ  1 + k tan θ , (17.31) where k is the electromechanical coupling factor, defined by Eq. (17.25) and shown here as a real number. It is important that the intensive dielectric, elastic, and piezoelectric losses (with prime) are mutually correlated with the extensive dielectric, elastic, and piezoelectric losses (nonprime) through the electromechanical coupling k2, and that the denominator (1  k2) comes basically from the ratios, εx/εX ¼ (1  k2) and sD/sE ¼ (1  k2). This real part reflects the dissipation factor when the imaginary part is divided by the real part. Knowing the relationships between the intensive and extensive physical parameters, and the electromechanical coupling factor k, the intensive (prime) and extensive (nonprime) loss factors have the following relationship: 2 3 2 3 tan δ tan δ0 4 tan ϕ0 5 ¼ ½K4 tan ϕ 5, (17.32) tan θ tan θ0 2 3 2 2k2 1 4 12 k d2 h2 2 5 , k2 ¼  : ¼ ½K ¼ (17.33) k 1 2k sE ðεT ε0 Þ cD βS =ε0 1  k2 2 1 1 1  k The matrix [K] is proven to be “invertible,” in other words,K2 ¼ I, or K ¼ K1, where I is the identity matrix. Hence the conversion relationship between the intensive (prime) and extensive (nonprime) exhibits full symmetry. We emphasize again that the extensive losses are more important for considering the physical micro/macroscopic models, and they can be obtained mathematically from a set of intensive losses, which can be obtained more easily from the experiments (in particular, pseudo-DC measurement). In the case of a 3-D expression, a PZT polycrystalline ceramic (∞ mm) holds 10 tensor components, as given below [note s66 ¼ 2(s11  s12) in the ∞ symmetry]: 2    3 s11 s12 s13 0 0 0 6 s12 s11 s13 0 0 0 7 2 3 2  3 6    7 ε11 0 0 0 0 0 0 d15 0 6 s13 s13 s33 0 0 0 7 6 7 4 0 0 0 d15 0 0 5, 4 0 ε11 0 5, 6 0 0 0 s 0 0 7 , 44 6 7 d31 d31 d33 0 0 0 0 0 ε33 4 0 0 0 0 s 0 5 44 0 0 0 0 0 s66 (17.34) III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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657

where * means a complex parameter, leading to 20 loss tensor components, taking into account both intensive and extensive losses. However, only 10 components are independent, because of the relationship between the intensive and extensive losses given by Eqs. (17.32), (17.33).

17.2.2 Resonance and Antiresonance So far, we have considered the loss measurement with a quasistatic or a pseudo-DC mode. We consider in this section a piezoelectric resonance method for measuring three losses separately. Let us derive the necessary formulas for the longitudinal mechanical vibration of a piezoceramic plate through the transverse piezoelectric effect (d31) as shown in Fig. 17.3, which is consistently used in this article in derivation examples. Length L ≫ width w ≫ thickness b is adopted. Assuming that the polarization is in the z-direction and the x-y planes are the planes of the electrodes, the extensional vibration in the x direction is represented by the following dynamic equation:   (17.35) ρ @ 2 u=@t2 ¼ F ¼ ð@X11 =@xÞ + ð@X12 =@yÞ + ð@X13 =@zÞ, where u is the displacement in the x direction of a small volume element in the ceramic plate. The relationship between the stress, the electric field (only Ez exists, because Ex and Ey should be zero due to the surface electrode), and the induced strain is described by the following set of equations (see Eq. (17.34) for PZT): x1 ¼ sE11 X1 + sE12 X2 + sE13 X3 + d31 Ez x2 ¼ sE12 X1 + sE11 X2 + sE13 X3 + d31 Ez x3 ¼ sE13 X1 + sE13 X2 + sE33 X3 + d33 Ez

(17.36)

x4 ¼ sE44 X4 x5 ¼ sE44 X5   x6 ¼ 2 sE11  sE12 X6

Let us consider the mechanical resonance intuitively first. When a frequency-sweeping AC electric field (i.e., constant voltage condition) is z

y

w b 0

Pz

L

x

FIG. 17.3 A rectangular piezoceramic plate (L ≫ w ≫ b) for a longitudinal mode through the transverse piezoelectric effect (d31).

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

applied to this piezoelectric plate, length, width, and thickness extensional resonance vibrations are successively excited. Suppose a typical PZT plate with dimensions 100 mm  10 mm  1 mm; these resonance frequencies correspond roughly to 10 kHz, 100 kHz, and 1 MHz, respectively. If we consider here only the fundamental length extensional modes for this configuration (neglecting higher order harmonics), when the frequency of the applied field is well below 10 kHz, the induced displacement follows the AC field cycle, and the displacement magnitude is given by d31E3L (no significant phase lag). As we approach to the fundamental resonance frequency, a delay in the length displacement with respect to the applied field begins to develop, and the amplitude of the displacement becomes enhanced. At the exact resonance frequency, the phase difference will be 90°, and displacement magnification will reach (8/π 2)Qm  d31E3L (a detailed derivation process is in Section 17.3). Then, above 10 kHz, the length displacement no longer follows the applied field (phase lag approaches 180°) and the amplitude of the displacement is significantly reduced. 17.2.2.1 Dynamic Equations for the k31 Mode21 When a very long, thin plate is driven by Ez in the vicinity of this fundamental resonance, X2 and X3 may be set to be equal to zero throughout the plate. Since shear stress will not be generated by the applied electric field Ez, only the following single equation (first equation of Eq. 17.36) applies:   X1 ¼ x1 =sE11  d31 =sE11 Ez : (17.37) Substituting Eq. (17.37) into Eq. (17.35), and assuming that x1 ¼ @u/@x (strain definition along the x axis) and @Ez/@x ¼ 0 (since each electrode is maintained at the same potentials), we obtain the following dynamic equation:     1 ρ @ 2 u=@t2 ¼ ð@X11 =@xÞ ¼ E ð@x1 =@xÞ  d31 = sE11 ð@Ez =@xÞ s11 (17.38)  1  ¼ E @ 2 u=@x2 : s11 Assuming Ez ¼ Ez ejωt, u ¼ u ejωt (i.e., no phase lag, no loss) and the sound velocity v in the piezoceramic given by qffiffiffiffiffiffiffiffiffi (17.39) v ¼ 1= ρ sE11 , we obtain

  ω2 u ¼ v2 @ 2 u=@x2 :

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

(17.40)

17.2 PHENOMENOLOGICAL APPROACH TO LOSSES IN PIEZOELECTRICS

659

Thus, the general solution is described as ω ω u ¼ A sin ðωx=vÞ + B cos ðωx=vÞ, and x1 ¼ A cos ðωx=vÞ  Bsin ðωx=vÞ: v v Taking into account the boundary conditions, X1 ¼ 0 at x ¼ 0 and L (due to the mechanically-free condition at the plate end), A and B can be determined. Then, the following solutions are obtained: ðstrainÞ @u=@x ¼ x1 ¼ d31 Ez ½ sin ωðL  xÞ=v + sin ðωx=vÞ= sin ðωL=vÞ, (17.41) ðL ðtotal displacementÞ ΔL ¼ x1 dx ¼ d31 Ez Lð2v=ωLÞtan ðωL=2vÞ: (17.42) 0

17.2.2.2 Admittance/Impedance Calculation for the k31 Mode When the specimen is utilized as an electrical component such as a filter or a vibrator, the electrical admittance [(induced current/applied voltage) ratio] plays an important role. The essential electric displacement constitutive equation is D3 ¼ d31 X1 + ε33 X ε0 E3 :

(17.43)

Since the current flow into the specimen is described by the surface charge increment, @D3/@t (note that D3 is position dependent, though @E3/@x ¼ 0), the total current is given by i ¼ jωw

ðL

D3 dx ¼ jωw

ðL

0

¼ jωw

ðL



 d31 X1 + ε33 X ε0 Ez dx

0







d31 x1 =s11  d31 =s11 E

E



 Ez + ε33 X ε0 Ez dx:

(17.44)

0

Using Eq. (17.41), the admittance for the mechanically free sample is calculated as follows: ð1=ZÞ ¼ ði=V Þ ¼ ði=Ez bÞ  1 3 2 0 ωðL  2xÞ ðL cos C 6 2 E  B  X  2 E  7 2v 7 B   C ¼ ðjωwL=Ez bÞ 6 A Ez + ε33 ε0  d31 =s11 Ez 5dx 4 d31 =s11 @ ωL 0 cos 2v  2  LC E ¼ ðjωwL=bÞε0 εLC ½1 + d =ε ε s ð tan ðωL=2vÞ=ðωL=2vÞ, 33 31 0 33 11

(17.45) where w is the width, L is the length, t is the thickness of the rectangular piezo-sample, and V is the applied voltage. εLC 33 is the permittivity in a longitudinally clamped sample, which is given by

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

 2  X E εLC (17.46) 33 ¼ ε33  d31 =ε0 s11     2 E X X 2 2 Eq. (17.46) is equivalent to εx1 33 ¼ ε33 1  k31 , since k31 ¼ d31 = s11 ε0 ε33 : However, this is not a three dimensionally clamped permittivity. Accordingly, Eq. (17.45) can be understood as follows: the first term (jωwL/t) ε0εLC 33 is called “damped” capacitance, which is directly proportional to   ω, while the second term, ðjωwL=tÞ d231 =sE11 ð tan ðωL=2vÞ=ðωL=2vÞ, is called “motional” capacitance, which originates from the resonator’s size (length) change via the mechanical vibration and is strongly dependent on ω like tan(ωL/2v). When ω is small, (tan(ωL/2v)/(ωL/2v) ! 1, then the motional   2 current becomes ðjωwL=tÞ d231 =sE11 or ðjωwL=tÞ εX 33 k31 . The total input energy will split into the motional (mechanical) energy k231 and the damped   (electrostatic) energy 1  k231 . However, as ω approaches to the resonance frequency, motional admittance/capacitance increases dramatically like tan(ωL/2v), which we can understand the accumulation/amplification of energy with respect to “time.” Fig. 17.4 shows an example admittance magnitude and phase spectra for a rectangular piezoceramic plate for a fundamental longitudinal mode (k31) through the transverse piezoelectric effect (d31), on the basis of Eq. (17.45) (and Eq. 17.58 with losses). Note that the shown data include losses, and the 3 dB down method to obtain mechanical quality factors Qm is also inserted in advance.

Admittance magnitude (S)

10–1

10–2

90°

90° 3 dB down

10–3

10–4

10–5

10–6

Admittance phase –90°

w 1 wm w 2 86

87

88 Frequency (kHz)

wn 89

90

91

FIG. 17.4 Admittance magnitude and admittance phase spectra for a rectangular piezoceramic plate for a fundamental longitudinal mode (k31) through the transverse piezoelectric effect (d31).

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17.2 PHENOMENOLOGICAL APPROACH TO LOSSES IN PIEZOELECTRICS

661

The piezoelectric resonance is achieved where the admittance becomes infinite or the impedance is zero (by neglecting the loss). The resonance frequency fR is calculated from Eq. (17.46) (tan ðωL=2vÞ ¼ ∞ by putting ωL/2v ¼ π/2), and the fundamental frequency is given by  qffiffiffiffiffiffiffiffi (17.47) fR ¼ ωR =2π ¼ v=2L ¼ 1= 2L ρsE11 : This resonance mode corresponds to the fundamental standing wave with the velocity v on a rod with length L (i.e., v/2L). On the other hand, the antiresonance state is generated for zero admittance or infinite impedance:   E 2 2 (17.48) ðωA L=2vÞ cot ðωA L=2vÞ ¼ d231 =ε0 εLC 33 s11 ¼ k31 = 1  k31 : The final transformation is provided by the following definition: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (17.49) k31 ¼ d31 = sE11  ε33 X ε0 : 17.2.2.3 Strain Distribution on the k31 Plate The position dependence of strain x1 is transformed to the following expression from Eq. (17.41):  cos ½ωðL  2xÞ=2v : (17.50) x1 ðxÞ ¼ d31 EZ cos ðωL=2vÞ The strain distribution is basically sinusoidal with the maximum at the center of plate (x ¼ L/2) (see the numerator). When ω is close to ωR, (ωRL/2v) ¼ π/2, leading to the denominator cos(ωRL/2v) ! 0. Significant strain magnification is obtained. It is worth noting that the stress X1 is zero at the plate ends (x ¼ 0 and L), but the strain x1 is not zero; it is equal to d31EZ. 17.2.2.4 Resonance/Antiresonance Modes22 The resonance and antiresonance states are both mechanical resonance states with amplified strain/displacement states, but they are very different from the driving viewpoints. The mode difference is described by the following intuitive model. In a hypothetically high electromechanical coupling material with k almost equal to 1, the resonance or antiresonance states appear for tan(ωL/2v) ¼ ∞ or 0 [i.e., ωL/2v ¼ (m  1/2)π or mπ (m: integer)], respectively, by neglecting the damped capacitance. The strain amplitude x1 distribution for each state (calculated using Eq. 17.50) is illustrated in Fig. 17.5. In the resonance state, large strain amplitudes and large capacitance changes (called motional capacitance) are induced, and under a constant applied voltage the current can easily flow into the device (i.e., admittance Y is infinite). In contrast, at the antiresonance, the strain induced in the device compensates completely (i.e., a half extends and a half

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

Resonance

Antiresonance

m=1

Low coupling

High coupling m=1

m=2

m=2

FIG. 17.5 Strain distribution in the resonance and antiresonance states. Longitudinal vibration through the transverse piezoelectric effect (d31) in a rectangular plate.22

shrinks in Fig. 17.5 Right), resulting in no motional capacitance change, and the current cannot flow easily into the sample (i.e., Y is zero). In other words, both plate ends become the nodal line, leading to no total displacement change (the antinode lines inside the sample displace largely at the antiresonance mode). Thus, for a high k material the first antiresonance frequency fA should be twice as large as the first resonance frequency fR.22 In a typical case like a PZT, where k31 ¼ 0.3, the antiresonance state varies from the previously-mentioned double-fR mode and becomes closer to the resonance mode (Top-center in Fig. 17.5). The low-coupling material exhibits an antiresonance mode where the capacitance change due to the size change (motional capacitance) is significantly compensated by the current required to charge up the static capacitance (called damped capacitance). Thus, the antiresonance frequency fA will approach the resonance frequency fR, and the plate ends are not the nodal lines anymore; they vibrate largely. Only the difference between the drive schemes for the resonance or antiresonance modes appears as “low voltage/high current” or “high voltage/low current,” due to the admittance/impedance difference. As you can imagine, the displacement amplification does not appear when you sweep the frequency under a constant drive voltage condition, of course. 17.2.2.5 Dynamic Equations for the k33 Mode21 Let us consider additionally the longitudinal vibration k33 mode in comparison with the k31 mode. When the resonator is long in the z direction and the electrodes are deposited on each end of the rod, as shown in Table 17.1 and Fig. 17.8, the following conditions are satisfied: X1 ¼ X2 ¼ X4 ¼ X5 ¼ X6 ¼ 0 and X3 6¼ 0:

(17.51)

Thus, the constitutive equations are X3 ¼ ðx3  d33 Ez Þ=sE33 ,

(17.52)

D3 ¼ ε0 εX 33 Ez + d33 X3 ,

(17.53)

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17.2 PHENOMENOLOGICAL APPROACH TO LOSSES IN PIEZOELECTRICS

TABLE 17.1 The Characteristics of Various Piezoelectric Resonators With Different Shapes and Sizes Factor

Boundary conditions

a

k31

T1 6¼ 0, T2 ¼ T3 ¼ 0 S1 6¼ 0, S2 6¼ 0, S3 6¼ 0

d31 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sE11 ε0 εT33

b

k33

T1 ¼ T2 ¼ 0, T3 6¼ 0 S1 ¼ S2 6¼ 0, S3 6¼ 0

d33 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sE33 ε0 εT33

c

kp

T1 ¼T2 6¼ 0, T3 ¼ 0 S1 ¼ S2 6¼ 0, S3 6¼ 0

k31

d

Kt

T1 ¼ T2 6¼ 0, T3 6¼ 0 S1 ¼ S2 ¼ 0, S3 6¼ 0

h33

e

k24 ¼ k15

Resonator shape

T1 ¼ T2 ¼ T3 ¼ 0, T5 6¼ 0 S1 ¼ S2 ¼ S3 6¼ 0, S5 ¼ 0

Definition

rffiffiffiffiffiffiffiffiffiffi 1 1σ sffiffiffiffiffiffiffiffiffiffi ε0 εS33 sD 33

d15 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E s55 ε0 εT11

for this configuration. Assuming a local displacement u in the z direction, the dynamic equation is given by the following:  @2u 1 @2u @Ez : (17.54)  d ρ 2¼ E 33 @z @t s33 @z2 The electrical condition for the longitudinal vibration is not @Ez/@z ¼ 0, but rather @Dz/@z ¼ 0. From Eq. (17.53)           @EZ @EZ d33 @ 2 u @EZ d33 @ 2 u X 2 + ε0 εX ε 1  k  d : ¼ 0, ε ¼  33 0 33 33 33 @z2 @z @z @z sE33 sE33 @z2 (17.55) Thus,

  @2u 1 @2u  D  ¼ D 2 s33 ¼ 1  k333 sE33 : (17.56) 2 @t s33 @z qffiffiffiffiffiffiffiffi Compared with Eq. (17.39) (v ¼ 1= ρsE11 ) in the surface electroded (E-constant) sample along the vibration qffiffiffiffiffiffiffiffi direction, a nonelectroded k33 (D-constant) sample exhibits v ¼ 1= ρsD 33 , which is faster (elastically stiffened) than that in the E constant condition. In comparison with the resonance/antriresonance strain distribution status in the k31 mode in Fig. 17.5, Fig. 17.6 illustrates the strain distribution status in the k33 mode. ρ

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

Resonance — Strain

Antiresonance — Strain

Low coupling

(A)

fR = vE / 2L; vE = 1/

FA / FR → 2.0

rsE11

Antiresonance — Strain

Resonance — Strain

High coupling

(B)

High coupling

Low coupling

FA / FR → ∞

fA = vD / 2L; vD = 1/

rsD33

FIG. 17.6

Strain distribution in the resonance and antiresonance states. Longitudinal vibration through the transverse d31 (A) and longitudinal d33 (B) piezoeffect in a rectangular plate.

Because k31 and k33 modes possess E-constant and D-constant constraints, respectively, in k31, the resonance frequency is directly related with vE11 or sE11, while in k33, the antiresonance frequency is directly related with vD 33 or D , c . The antiresonance in k and the resonance in k are subsidiary, sD 33 33 31 33 originated from the electromechanical coupling factors. It is also worth noting that with increasing the k value toward 1, the ratio fA/fR approaches 2 in k31, while it can reach ∞ in k33, and the strain distribution becomes almost flat or uniform in k33, though the stress distributes sinusoidally with zero at the plate ends. 17.2.2.6 Boundary Condition: E-Constant vs. D-Constant Both dielectric permittivity ε and elastic compliance s exhibit significant difference in terms of the electromechanical coupling factor k under different boundary conditions—mechanical stress-free or clamped; electric short-circuit or open-circuit—as described in Eqs. (17.21), (17.22). We also discussed the k31 mode vibrator with E-constant sE11 and k33 mode with D-constant sD 33 for analyzing the dynamic equations. We consider here the relation between these status differences. The key principle is from Gauss’ law (static electromagnetic Maxwell relation) is the following: divD ¼ ρ; or divE ¼

1 ðρ  divPÞ: ε0

(17.57)

If free charges, ρ, exist div E can be equal to zero by compensating P with ρ, leading to the E-constant with respect to space/coordinate. In contrast, if no charges,   div D ¼ 0 (D-constant), by generating “reverse P . Fig. 17.7 visualizes the boundary condition electric field” E ¼  ε0

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17.2 PHENOMENOLOGICAL APPROACH TO LOSSES IN PIEZOELECTRICS

E constant: k31 mode (electrode) +

+

+

–

–

–

–

–

–

+

+

+

+

+

–

–

–

E

P

X

(A)

–

–

–

+

+

+

+

D constant: k31 mode (no electrode)

P

E X

(B)

D constant: k33 mode (no electrode; electrode on edge)

P E X

(C) FIG. 17.7

Boundary conditions: E-constant vs. D-constant under dynamic waves.

models for E-constant and D-constant conditions under dynamic waves. A mechanical/sound wave generates polarization modulation in a piezoelectric plate, as D ¼ dX. When the surface is electroded in k31 mode (Fig. 17.7A), charges can easily be supplied through the electrodes, as illustrated. Thus, E-constant  (zero  in the short-circuit between the top @EZ ¼ 0, is derived. When the surface does and bottom electrodes), or @x not have an electrode, no charge is   supplied (Fig. 17.7B), and the reverse @DZ field is induced to maintain ¼ 0, leading to a D-constant condition. @x In the case of k33 mode (Fig. 17.7C), though the edges are electroded, there is no electrode along the wave propagation z axis. Thus, no charge is available to compensate the polarization modulation along the z direction, and the sound velocity along the polarization direction should be a D-constant sound velocity with sD 33. 17.2.2.7 Loss and Mechanical Quality Factor in k31 Mode21 (a) Resonance QA: Now, we introduce the complex parameters into the admittance formula Eq. (17.45) around the resonance frequency22:   E*     X 0 E 0  0 εX* 3 ¼ ε3 1  j tan δ33 , s11 ¼ s11 1  jtan ϕ11 , and d31 ¼ d31 1  j tan θ31 :

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

Y ¼Yd + Ym ¼ jωCd ð1  jtan δ33 Þ       (17.58) 2 E ½ð1  j 2tan θ031  tan ϕ011 ½ð tan ωL=2vE + jωCd K31 11 = ωL=2v11 ,

where C0 ¼ ðwL=tÞε0 εX 33 , ðfree electrostatic capacitance, real numberÞ   Cd ¼ 1  k231 C0 ðdamped=clamped capacitance, real numberÞ 2 ¼ K31

k231 1  k231

(17.59) (17.60) (17.61)

Note that the loss for the first term (“damped/clamped” conductance) is represented by the extensive dielectric loss tan δ, not by the intensive loss tan δʹ. Remember that     tan δ ¼ 1= 1  k231 tan δ0 + k231 ð tan ϕ0  2 tanθ0 Þ . Taking into account   1 tan ϕ011 E E , (17.62) v11 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ffi ¼ v11 1 + j 2 ρsE11 1  jtan ϕ011 we further calculate 1/[tan(ωL/2v*)] with an expansion-series approximation around the A-type resonance frequency (ωAL/2v) ¼π/2, taking into account that the resonance state is defined in this case for the minimum impedance point. Using new frequency parameters, ΩA ¼ ωA L=2vE11 ¼ π=2, ΔΩA ¼ Ω  π=2 ð≪1Þ, and

π  1 π π ¼ cot + ΔΩA  j tan ϕ011 ¼ ΔΩA  j tan ϕ011 , tan Ω* 2 4 4

(17.63) (17.64)

the motional admittance Ym is approximated around the first resonance frequency ωA by        2 Ym ¼ j 8=π 2 ωA Cd K31 1  j 2 tan θ031  tan ϕ011 = ð4=π ÞΔΩA  jtan ϕ011 : (17.65) The maximum Ym is obtained at ΔΩA ¼ 0:       2 2 0 1 Ymax ¼ 8=π 2 ωA C0 k231 QA : (17.66) m ¼ 8=π ωA Cd K31 tan ϕ11   1 can The mechanical quality factor for A-type resonance QA ¼ tanϕ011 be proved as follows: QA is defined by QA ¼ ωA/2Δω, where2Δω is a pffiffiffi pffiffiffi full width of the 3 dB down (i.e., 1= 2, because 20log 10 1= 2 ¼ 3:01) pffiffiffi at ω ¼ ωA. Since jYj ¼ jYjmax = 2 can be of the maximum value Ymax m obtained when the “conductance ¼ susceptance”, ΔΩA ¼ ðπ=4Þtan ϕ011 ,  1 QA ¼ ΩA =2ΔΩA ¼ ðπ=2Þ=2ðπ=4Þtan ϕ011 ¼ tan ϕ011 : (17.67)

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

17.2 PHENOMENOLOGICAL APPROACH TO LOSSES IN PIEZOELECTRICS

667

Similarly, the maximum displacement umax is obtained at ΔΩ ¼ 0:   umax ¼ 8=π 2 d31 EZ LQA : (17.68) The maximum displacement at the resonance frequency is (8/π 2)QA times larger than that at a nonresonance frequency, d31 EZ L. (b) Antiresonance QB: On the other hand, the antiresonance corresponds to the minimum admittance.23 Since the expansion series of tan Ω is convergent in this case, we can apply the following expansion:   Ωtan ϕ011 Ω tan ϕ011 ¼ tan Ω  j : (17.69) tan ðΩ*Þ ¼ tan Ω  j 2 2cos 2 Ω The admittance expression, Eq. (17.45), can be simplified as follows:   E 0 2 2 tan ωl=2v11 Y ¼ 1  k31 + k31 : (17.70) ωl=2vE11 Introducing losses for the parameters leads to    Y0 ¼1  k31 2 1  j 2 tan θ031  tan δ033  tan ϕ011    tan Ω* + k231 1  j 2 tan θ031  tan δ033  tan ϕ011 : Ω*

(17.71)

We separate Yʹ into conductance G (real part) and susceptance B (imaginary part) as Y0 ¼ G + jB G ¼ 1  k231 + k231 

tan Ω : Ω

  tan Ω  2tan θ031  tan δ033  tan ϕ011 B¼ Ω   k231 1 tan Ω   tan ϕ011 : 2 cos 2 Ω Ω

(17.72)

k231  k231

(17.73)

Using new parameters, Ω ¼ ΩB + ΔΩB ,

(17.74)

the antiresonance frequency Ωb should satisfy 1  k231 + k231

tan ΩB ¼ 0: ΩB

(17.75)

Similar to ΔΩA for the resonance, ΔΩB is also a small number and the first order approximation can be utilized.   tan Ω tan ΩB 1 1 tan ΩB ΔΩB : ¼ +  (17.76) ΩB ΩB Ω ΩB cos 2 ΩB

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

Neglecting the high-order term that has two or more small factors (loss factor or ΔB),   k231 1 tan ΩB G¼ ΔΩB :  (17.77) ΩB cos 2 ΩB ΩB     k2 1 tan ΩB B ¼ 2tan θ031  tan δ033  tan ϕ011  31 tan ϕ011 : (17.78)  2 cos 2 ΩB ΩB Consequently, the minimum absolute value of admittance can be achieved when ΔΩB is 0. The antiresonance frequency ΩB is determined by Eq. (17.73). In order to find the 3 dB-up point, let G ¼ B:   k231 1 tan ΩB ΔΩB  ΩB cos 2 ΩB ΩB   (17.79)   k2 1 tan ΩB 0 tan ϕ ¼ 2 tan θ031  tan δ033  tan ϕ011  31  : 11 2 cos 2 ΩB ΩB Further, the antiresonance quality factor is given by QB,31 ¼

ΩB : 2jΔΩB j

(17.80)

Thus, Eq. (17.77) can be represented as   k231 1 tan ΩB  2QB,31 cos 2 ΩB ΩB   (17.81)   k231 1 tan ΩB 0 0 0 0 tan ϕ11 :  ¼  2tan θ31  tan δ33  tan ϕ11 + 2 cos 2 ΩB ΩB

Considering Eq. (17.67), we can obtain the result as    1 1 2  1 tan ΩB 0 0 0 : ¼  2tan θ31  tan δ33  tan ϕ11 =  ΩB QB,31 QA,31 k231 cos 2 ΩB (17.82) Taking into account the following relation,  2 1  k231 Ω2B + k231 1 tan ΩB  ¼ , ΩB cos 2 ΩB k431

(17.83)

the equation of the antiresonance quality factor is given by 1 QB,31

¼

1 QA,31





2

1 1+ k31 k31



2

 2 tan θ031  tan δ033  tan ϕ011 :

Ω2B

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

(17.84)

17.2 PHENOMENOLOGICAL APPROACH TO LOSSES IN PIEZOELECTRICS

k31 plate

669

Electrode

Electrode

b

P

z y

w

l

l

x

k33 bar

P

kp or kt mode disk plate

b

z y x

r=a b

w

Electrode

P

t

Thichness shear mode

Length shear mode

P Electrode

t

P

12

w

L

3

3

FIG. 17.8

w

12

L

Sketches of the sample geometries for five required vibration modes.

17.2.2.8 Loss and Mechanical Quality Factor in Other Modes To obtain the loss factor matrix, five vibration modes need to be characterized in PZTs, as shown in Fig. 17.8 and Table 17.1. The methodology is based on the equations of quality factors QA (resonance) and QB (antiresonance) in various modes with regard to loss factors and other properties.23,24 We measure QA and QB for each mode by using the 3 dB-up/down method in the impedance/admittance spectra (See Fig. 17.4). In addition to some derivations based on fundamental relations of the material properties, all 20 loss factors can be obtained for piezoelectric ceramics. We derived the relationships between mechanical quality factors QA (resonance) and QB (antiresonance) in all five required modes in Table 17.1. The results are summarized below:

(a) k31 mode: 1 tan ϕ011 1 1 ¼ + QB, 31 QA, 31 QA, 31 ¼

 1+

2 1 k31 k31



2

tan δ033 + tanϕ011  2 tanθ031



Ω2B, 31

0 0 0 , tan ϕ11 , tan θ31 : intensive loss factors for εT33, sE11, d31; ΩB,31: [tan δ33 antiresonance frequency]

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

ΩA, 31 ¼

 qffiffiffiffiffiffiffiffiffi ωa l π E ωb l tan ΩB ¼ ¼ 1= ρ sE11 , ΩB, 31 ¼ E , 1  k231 + k231 ¼ 0: v ΩB 2vE11 2 11 2v11

(b) kt mode: Q B, t ¼

1 tan ϕ33

1 1 2 ¼ + ð tan δ33 + tanϕ33  2 tanθ33 Þ QA, t QB, t k2t  1 + Ω2A =k2t [ΩA,33: resonance frequency parameter]  qffiffiffiffiffiffiffiffiffiffiffiffi ωb l π 2 ¼ 1= ρ =cD ΩB, t ¼ D ¼ vD 33 , ΩA ¼ kt tanΩA : 2v33 2 33 (c) k33 mode: QB, 33 ¼

 1  k233 1    tan ϕ33 tan ϕ033  k233 2 tan θ033  tan δ033

  1 1 2 ¼ + 2tan θ033  tanδ033  tan ϕ033 QA, 33 QB, 33 k233  1 + Ω2A =k233 " # 1 2 ð tan δ33 + tanϕ33  2 tanθ33 Þ  + QB, 33 k233  1 + ΩA 2 =k233  qffiffiffiffiffiffiffiffiffi ωb l π 2 ΩB, 31 ¼ D ¼ vD ¼ 1= ρ sD 33 , ΩA ¼ k33 tanΩA : 2v33 2 33 (d) k15 mode (constant E—length shear mode): QEA, 15 ¼

1 tanϕ055

1 1 ¼  QEB, 15 QEA, 15



2

2



2 tan θ015  tan δ011  tan ϕ055



1 Ω2B  k15 k15 qffiffiffiffiffiffiffiffi ωb L ωb L tan ΩB ΩB ¼ E ¼ E ρsE55 , 1  k15 2 + k15 2 ¼ 0: ΩB 2v55 2v55 1+

(e) k15 mode (constant D—thickness shear mode): QD B, 15 ¼

1 tanϕ55

1 1 2 ¼ D + 2 ð tan δ11 + tanϕ55  2tan θ15 Þ QD Q k  1 + ΩA 2 =k15 2 15 B, 15 A, 15 rffiffiffiffiffiffi ωa t ωa t ρ , ΩA ¼ k15 2 tan ΩA : ΩA ¼ D ¼ 2 2v55 cD 55

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17.3 EQUIVALENT CIRCUIT WITH LOSSES

671

Note again that because k31 and k33/kt modes possess E-constant and D-constant constraints, respectively, in k31, the resonance frequency is qffiffiffiffiffiffiffiffi vE directly related with vE11 or sE11 as fA ¼ 11 ¼ 1=2L ρsE11 ; while in k33/kt, 2L D D the antiresonance frequency is directly related with vD 33 or s33 , c33 as ffiffiffiffiffiffiffiffi q ffiffiffiffiffiffiffiffiffiffi ffi q vD ρ=cD fB ¼ 33 ¼ 1=2L ρsD 33 or 1/2b 33 . It is important to distinguish k33 2L (X1 ¼ X2 ¼ 0, x1 ¼ x2 6¼ 0) from kt (X1 ¼ X2 6¼ 0, x1 ¼ x2 ¼ 0) from the boundary conditions. The argument is valid only when the length of a rod k33 is D not very long (cD 33  1=s33 ). The antiresonance in k31 and the resonance in k33/kt are subsidiary, originating from the electromechanical coupling factors. We can also derive the relation for the electromechanical coupling factor losses from Eqs. (17.32), (17.33): ð2 tan θ0  tan δ0  tan ϕ0 Þ ¼ ð2 tan θ  tan δ  tan ϕÞ:

(17.85)

When the side is not clamped (x1 ¼ x2 6¼ 0) in the k33 mode, 1-D Eq. (17.85) is not completely true. Thus, “” is used in the above for roughly translating the intensive losses into the extensive losses. It is important to discuss the assumption in the IEEE Standard: QA ¼ QB. This situation occurs only when ð2tan θ0  tan δ0  tanϕ0 Þ ¼ 0, or tan θ0 ¼ ð tanδ0 + tanϕ0 Þ=2. The IEEE Standard discusses only when the piezoelectric loss is equal to the average value of the dielectric and elastic losses, which exhibits a serious contradiction to the PZT experimental results QA < QB, as introduced in Section 17.7. As we can realize in Fig. 17.4 from the peak sharpness, the PZT’s exhibit QA (resonance) < QB (antiresonance), irrelevant to the vibration mode (Fig. 17.4 is an example of the k31). This concludes that (tan δʹ33 + tan ϕʹ11  2tan θʹ31) < 0, or (tan δʹ33 + tan ϕʹ11)/2 < tan θʹ31 for k31, and (tan δ33 + tan ϕ33  2tan θ33) > 0, or (tan δ33 + tan ϕ33)/2 > tan θ33 for kt. It is worth noting that the intensive piezoelectric loss is larger than the average of the dielectric and elastic intensive losses in Pb-contained piezoceramics. We introduce in Section 17.7 that in Pb-free piezoelectric ceramics, the piezoelectric loss contribution is not significant, and (tan δʹ33 + tan ϕʹ11)/2 > tan θʹ31, which may suggest different loss mechanisms in different piezoceramics.

17.3 EQUIVALENT CIRCUIT WITH LOSSES 17.3.1 Equivalency Between Mechanical and Electrical Systems The dynamic equation for a mechanical system composed of a mass, a spring, and a damper illustrated in Table 17.2 Left is expressed by

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

TABLE 17.2 Equivalency Between a Mechanical and an Electrical System, Composed of M, c, z; L, C, and R

C

z M

F(t)

Mechanical

Electrical (F – V)

Force F(t) Velocity v / ú

Voltage V(t) Current I Charge q Inductance L Capacitance C Resistance R

Displacement u Mass M Spring Compliance 1/c Damping z

L V(t)

C R

  M d2 u=dt2 + ζ ðdu=dtÞ + cu ¼ FðtÞ, or ðt Mðdv=dtÞ + ζv + c v dt ¼ FðtÞ,

(17.86)

0

where u is the displacement of a mass M, v is the velocity (¼ du/dt), c is a spring constant, ζ is a damping constant of a dashpot, and F is the external force. On the other hand, the dynamic equation for an electrical circuit composed of an inductance L, a capacitance C, and a resistance R illustrated in Table 17.2 Right is expressed by   L d2 Q=dt2 + RðdQ=dtÞ + ð1=CÞ Q ¼ V ðtÞ, or ðt (17.87) LðdI=dtÞ + RI + ð1=CÞ Idt ¼ V ðtÞ, 0

where Q is charge, I is the current (¼ dQ/dt), and V is the external voltage. Taking into account the equation similarity, the engineer introduces equivalent circuit; that is, consider a mechanical system with using an equivalent electrical circuit, which is intuitively simpler for an electrical engineer. In contrast, consider an electrical circuit using an equivalent mechanical system, which is intuitively simpler for a mechanical engineer. Equivalency between these two systems is summarized in Table 17.2.

17.3.2 Equivalent Circuit (Loss-Free) of the k31 Mode The equivalent circuit (EC) is a widely used tool that can greatly simplify the process of design and analysis of the piezoelectric devices, in which the circuit, in a standard form,25 can only graphically characterize the mechanical loss by applying a resistor (and dielectric loss sometimes). Damjanovic therefore introduced an additional branch into the standard circuit, which is used to present the influence of the piezoelectric loss.15 However, concise and decoupled formulas of losses have not been derived

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

673

17.3 EQUIVALENT CIRCUIT WITH LOSSES

yet, which can be used for the measurements of losses in piezoelectric material as a user-friendly method. We consider first the equivalent circuit (loss-free) for the k31 mode shown in Fig. 17.3. We start from the admittance equation, already discussed:   E ½1 + d231 =ε0 εLC Y ¼ ð jωwL=bÞε0 εLC 33 33 s11 ð tan ðωL=2vÞ=ðωL=2vÞ, qffiffiffiffiffiffiffiffi (17.45) v ¼ 1= ρsE11 : By splitting Y into the damped admittance Yd and the motional part Ym, Yd ¼ ðjωwL=bÞε0 εLC 33 ,  2 E Ym ¼ ðj2vw=bÞ d31 =s11 ð tan ðωL=2vÞ:

(17.88) (17.89)

The damped branch can be represented by a capacitor with capacitance (wL/b) ε0εLC 33 (Cd in Fig. 17.9). For the motional branch (mechanical   vibration), since 1=Ym ¼ jðb=2vwÞ sE11 =d231 ð cot ðωL=2vÞ is close to zero around the resonance frequency ωAL/2v ¼ nπ/2 (n ¼ 1, 3, 5, …), taking Taylor expansion series around the resonance ωA,n we get   1=Ym  jðb=2vwÞ sE11 =d231 ðΔωL=2vÞ, (17.90) where Δω ¼ ω  ωA,n. Now we convert the mass contribution to L and elastic compliance to C, and we create Ln and Cn series-connections as shown in Fig. 17.9. The impedance of this LC circuit around the resonance ωA is provided by   1=Yn ¼ jωLn + 1=jωCn  j Ln + 1=ωA, n 2 Cn Δω: (17.91) Since the resonance is realized when Ln ¼ 1=ω2A, n Cn , by comparing Eqs. (17.90), (17.91), we can obtain the following two equations which express the L, C by the transducer physical parameters:     2 (17.92) Ln ¼ bLsE11 =4v2 wd231 =2 ¼ ðρ=8ÞðLb=wÞ sE2 11 =d31   Cn ¼ 1=ω2r Ln ¼ ðL=nπvÞ2 ð8=ρÞðw=LbÞ d231 =sE2 11 (17.93)    E ¼ 8=n2 π 2 ðLw=bÞ d231 =sE2 11 s11 ,

Yf

FIG. 17.9

L1

L3

Ln

C1

C3

Cn

Cd

Equivalent circuit for the k31 mode (loss-free).

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

qffiffiffiffiffiffiffiffi ωA, n ¼ nπ=L ρsE11 :

(17.94)

harmonics have the Note initially that Ln is a constant, irrelevant to n (allX same mass-related L). The total motional capacitance Cn is calculated " # n  X 1 π2 : as follows, using the important relation ¼ 2 8 ð2m  1Þ X

C ¼ n n

X 1  8 Lwd2  Lwd2  31 31 ¼ ¼ k231 C0 : n n2 π 2 b b sE11 sE11

(17.95)

Therefore, we can understand that the total capacitance C0 ¼ (wL/b)   2 ε 0ε X 33 is split into the damped capacitance Cd ¼ 1  k31 C0 and the total motional capacitance k231C0, which is reasonable from the energy conservation viewpoint.

17.3.3 Equivalent Circuit (With Losses) of the k31 Mode We start from Hamilton’s principle, a powerful tool for “mechanics” problem solving, which can transform a physical system model to variational problem solving. We integrate loss factors directly into the Hamilton’s principle for a piezoelectric k31 plate (Fig. 17.3).26 By skipping the detailed derivation process, we obtain the following admittance expression, equivalent to Eq. (17.58): " 2 #! " 2 #! 00 d*31 d*31 lw lw X0 X  ε0 ε33  Re  ε ε + Im + ω  Y* ¼jω  0 33 b b sE* sE* 11 11 "

+ jω 

+ jω 

8lw  Re bπ 2

2 #

d*31 sE* 11

8lw  jIm bπ 2

"

π2 l2 ρsE* 11  π2  ω2 l2 ρsE* 11

2 d*31 sE* 11

#!

(17.96)

π2 l2 ρsE* 11 :  π2 2 ω l2 ρsE* 11

Among the above four terms in Eq. (17.96), the first and second terms correspond to the damped capacitance and its dielectric loss (i.e., the extensive dielectric loss (tan ϕ)), respectively, while the third and fourth terms correspond to the motional capacitance and the losses combining with intensive elastic and piezoelectric losses.

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

17.3 EQUIVALENT CIRCUIT WITH LOSSES

FIG. 17.10

675

Equivalent circuit for the k31 mode (IEEE).

LA Cd

CA RA

17.3.3.1 Equivalent Circuit in IEEE Standard Fig. 17.10 shows an IEEE Standard equivalent circuit with only one elastic loss (tan ϕʹ). In addition to Eqs. (17.92)–(17.94), the circuit analysis provides the following R and Q (electrical quality factor, which corresponds to the mechanical quality factor in the piezoplate): pffiffiffiffiffiffiffiffiffiffiffiffiffiffi (17.97) Q ¼ LA =CA =RA : PSpice is a popular circuit analysis software for automatically maximizing the performance of circuits. EMA is distributing a free download of OrCAD Capture, this schematic design solution. The reader can access the download at the following website: http://www.orcad.com/products/ orcad-lite-overview?gclid¼COaXitWJp9ECFcxKDQodCGMB0w. Fig. 17.11 shows the PSpice simulation process of the IEEE type k31 mode. (a) shows an equivalent circuit for the k31 mode. L, C, and R values were calculated for PZT4 with 40  6  1 mm3, and (b) plots the simulation results on the currents under 1 Vac, that is, admittance magnitude and phase spectra. IPRINT1 (current measurement), IPRINT2, and IPRINT3 are the measure of the total admittance (□ line), motional admittance ( line), and damped admittance (▽ line), respectively. First, the damped admittance shows a slight increase with the frequency (jωCd) with +90° phase in a full frequency range. Second, the motional admittance shows a peak at the resonance frequency, where the phase changes from +90° (i.e., capacitive) to –90° (i.e., inductive). In other words, the phase is exactly zero at the resonance. The admittance magnitude decreases above the resonance frequency with a rate of –40 dB down in a Bode plot. Third, by adding the above two, the total admittance is obtained. The admittance magnitude shows two peaks, maximum and minimum, which correspond to the resonance and antiresonance points, respectively. You can find that the peak sharpness (i.e., the mechanical quality factor) is the same for both peaks, because only one loss is included in the equivalent circuit. The antiresonance frequency is obtained at the intersect of the damped and motional

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

(A) 100 mA

10 mA

100 uA

SEL>> 10 uA I (PRINT1)

I (PRINT2)

I (PRINT3)

100d

0d

–100d 34 kHz P (I(PRINT1))

(B)

36 kHz P (I(PRINT2))

38 kHz P (I(PRINT3))

40 kHz

42 kHz

44 kHz

46 kHz

Frequency

FIG. 17.11

PSpice simulation of the IEEE type k31 mode. (A) Equivalent circuit for the k31 mode. L, C, and R values were calculated for PZT4 with 40  6  1 mm3. (B) Simulation results on admittance magnitude and phase spectra.

admittance curves. Because of the phase difference between the damped (+90°) and motional (–90°) admittance, the phase is exactly zero at the antiresonance, and it changes to +90° above the antiresonance frequency. Remember that the phase is –90° (i.e., inductive) at a frequency between the resonance and antiresonance frequencies. III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

677

17.3 EQUIVALENT CIRCUIT WITH LOSSES

17.3.3.2 Equivalent Circuit With Three Losses Damjanovic15 introduced a motional branch to describe the third term in Eq. (17.96), which contains a motional resistor, a motional capacitor, and a motional inductor. Meanwhile, an additional branch is also injected into the classical circuit25 to pictorially express the last term in Eq. (17.96) to present the influence of the piezoelectric loss, where the new resistance, capacitance, and inductance are all proportional to corresponding motional elements with the proportionality constant being " 2 #, " 2 # d*31 d*31 Re . jIm sE* sE* 11 11 Shi et al. proposed a more concise equivalent circuit (EC) shown in Fig. 17.12A with three losses.26 Compared with the IEEE Standard EC with only one elastic loss or the Damjanovic’s EC with a full set of L, C, R, only one additional electrical element G0m is introduced into the classical circuit.26 The new coupling conductance can reflect the coupling effect between the elastic and the piezoelectric loss. The new EC also can be mathematically expressed as follows: 100

Rm

+ Vin

Cd

G ′m

Gd Cm

–

60

50

40

0

20

–50

Lm

0 20

(A)

20.2 20.4 20.6 20.8

(B)

0.2 0.15 0.1 0.05 0 20

(C)

res.

21

–100 21.2 21.4

Frequency [kHz]

2500

tan(q ′) tan(f ′) tan(d ′)

Mechanical quality factor Qm

0.25 Intensive loss factors [%]

Admittance Phase

Phase [Degree]

i = dq/dt

Admittance [mS]

80

21 Frequency [kHz]

Calculation Measurement

2000 1500 1000 500 0 20

antires. 21.5

(D)

res.

21

antires. 21.5

Frequency [kHz]

FIG. 17.12

(A) New equivalent circuit proposed with three intensive loss factors: (B) admittance spectrum to be used in the simulation, (C) frequency spectra of intensive loss factors (i.e., dielectric, elastic and piezoelectric losses) obtained from the admittance spectrum (B) fitting, and (D) the calculated mechanical quality factor Qm as a function frequency around the resonance and antiresonance frequencies.

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

Y* ¼ Gd + jωCd + 

G0m + jωCm   0 2 1 + Gm =Gm  ω Lm Cm + j ωCm =Gm

+ ωLm G0m

 : (17.98)

The parameters of the new EC can therefore be obtained by comparing Eq. (17.96) with Eq. (17.98) as new expressions of three “intensive” loss factors: tan ϕ0 ¼ ωCm =Gm ,

(17.99a)

tan θ0 ¼ tan ðϕ0  β0 Þ,

(17.99b)

Gd , (17.99c) ωCd sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi   ωCm ωCm 2 0 + 1 denotes the disparity where the phase delay tan β ¼ 0  Gm G0 m between the piezoelectric and elastic components. The value of β generally holds negative or approaches to zero (when G0m ! 0), which implies that the piezoelectric loss is persistently larger or equal to the elastic component. The significance of the piezoelectric loss has been therefore verified in theory from the equivalent circuit viewpoint. Using the experimental data in Fig. 17.12B, almost frequency independent circuit parameters as Cd ¼ 3:2nF, Cm ¼ 0:29 nF, Lm ¼ 210 mH, and Gd ¼ 0 (extensive dielectric loss tan ϕ is small) can be obtained along with the frequency dependent parameters (Gm and G0m ). By manipulating Eqs. (17.99a)–(17.99c), we determined intensive dielectric, elastic, and piezoelectric losses as a function of frequency, as shown in Fig. 17.12C. The mechanical quality factor, Qm, is always applied to evaluate the effect of losses. When arriving at a steady state, it can be expressed by the following: tan δ0 ¼ k231 tan ð2θ0  ϕ0 Þ +

Qm ¼ 2π 

energy stored=cycle : energy lost=cycle

(17.100)

The denominator is supposed to compensate the dissipation, wloss; ð π      wloss dV ¼ v3 q3 cos φ, where the phase difference between that is, 2 V h π πi current and input voltage, φ, ranges within  , . Meanwhile, the reac2 2 tive portion of the input energy returns to the amplifier and is neither used nor dissipated. Furthermore, the maximum stored and kinetic energies also get equilibrium in an electric cycle. With definitions of energy items and appropriate substitutions, Qm can be calculated as follows:27 Qm ¼

ω2a  ω2r cos φ

ω2    2   2  : ω2  ω*r ω2  ω*a 

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

(17.101)

17.3 EQUIVALENT CIRCUIT WITH LOSSES

679

As ω2 approaches to ω2r or ω2a , the phase difference will approach zero. Therefore, for low k231 materials, with substituting Eq. (17.101), mechanical quality factors at the resonance and antiresonance frequencies can be calculated as rffiffiffiffiffiffiffi 1 1 Lm ¼ , (17.102) QA ¼ tan ϕ0 Rm Cm QB ¼

1 : 2 8K 0 0 0 0 31 tan ϕ + 2 ½ tan ϕ + tan δ  2 tan θ  π

(17.103)

Eqs. (17.102), (17.103) obtained from a new equivalent circuit are basically the same as we derived analytically in Eqs. (17.67), (17.84). Hence, the calculation of Qm at these special frequencies has been verified by the wellaccepted conclusion. Eq. (17.101) also infers an advanced calculation method of Qm for a wide bandwidth. Fig. 17.12D shows the frequency spectrum of the mechanical quality factor Qm calculated from Eq. (17.101). You can clearly find that (1) the QB at antiresonance is larger than QA at resonance, and (2) the maximum Qm (i.e., the highest efficiency) can be obtained at a frequency between the resonance and antiresonance frequencies. This frequency can theoretically be obtained by taking the first derivative of Eq. (17.101) in terms of ω to be equal to zero, which suggests the best operating frequency of the transducer to realize the maximum efficiency; this will be discussed in Section 17.6. 17.3.3.3 4-Terminal Equivalent Circuit (EC) Though the new two-terminal EC is useful for the basic no-load piezoelectric samples, we need to extend it to four- and six-terminal EC models in this proposal in order to consider the load effect for practical transducer/actuator applications. Uchino proposed a new 4-terminal equivalent circuit for a k31 mode plate, including elastic, dielectric, and piezoelectric losses (Fig. 17.13A), which can handle symmetrical external mechanical losses. The 4-terminal EC includes an ideal transformer with a voltage stepup ratio Φ to connect the electric (damped capacitance) and the mechanical (motional capacitance) branches, where Φ ¼ 2wd31 =sE11 , which is called the “force factor.” New capacitance l and c1 are related with L1 and C1 in the 2-terminal EC given in Eqs. (17.92), (17.93): l ¼ Φ2 L; c1 ¼ C1 =Φ2 :

(17.104)

Regarding the three losses, as shown in Fig. 17.13A in a PZT plate, in Rd, addition to the IEEE standard “elastic” loss r1 and  “dielectric” loss  we introduce the coupling loss in the force factor Φ ¼ 2wd31 =sE11 rcpl as proportional to (tan ϕʹ  tan θʹ), which can be either positive or negative, depending on the tan θʹ magnitude. Fig. 17.13B shows the PSpice software

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

680

17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

Im

I

Icpl

Id V1

Cd

rcpl l

I1

r1

C1

I2

I2+Icpl V2

fV1 = V2 I1 = fI2

Rd Ideal 1:φ

(A) 100 mA

10 mA

1.0 mA

100 uA

+100 kΩ 10 uA

+1,000,000 kΩ −100 kΩ

1.0 uA 38 kHz

(B)

39 kHz I(PRINT1)

40 kHz

41kHz Frequency

42 kHz

43 kHz

44 kHz

FIG. 17.13 4-Terminal (two port) equivalent circuit for a k31 plate, including elastic, dielectric, and piezoelectric losses. r1, Rd, and rcpl correspond to these three losses. PSpice simulation of the IEEE-type k31 mode. (A) Equivalent circuit for the k31 mode. L, C, and R values were calculated for PZT4 with 40  6  1 mm3. (B) Simulation results on admittance magnitude and phase spectra.

simulation results for three values of rcpl. (1) The resonance QA does not change with changing rcpl. (2) When rcpl ¼ 100 kΩ (i.e., tan θʹ  0), QA > QB. (3) When rcpl ¼ 1 GΩ (i.e., tan ϕʹ  tan θʹ  0), QA ¼ QB. (4) When rcpl ¼ –100 kΩ (i.e., tan ϕʹ  tan θʹ < 0), QA < QB. Dong et al. constructed a 6-terminal equivalent circuit with three losses, which can handle asymmetric external loads for a k31 mode plate28 and a Langevin transducer by integrating the head and tail mass loads.29 Section 17.6 discusses this issue in detail.

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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17.4 HEAT GENERATION IN PIEZOELECTRICS

Electrode

l

– Cd

V(t)

P

Cd z

x

(A) FIG. 17.14

C1 R1

b

y

L

w

(B)

(A) k33 mode piezoceramic rod. (B) Equivalent circuit for the k33 mode.

17.3.4 Equivalent Circuit of the k33 Mode Remember that the k33 mode is governed by the sound velocity vD, not by vE, and that the antiresonance is the primary mechanical resonance given by f ¼ vD/2 L, and the resonance is the subsidiary mode originated from the electromechanical coupling factor k33. Therefore, its equivalent circuit includes negative capacitance –Cd (exactly the same absolute value of the damped capacitance in the electric branch) in the motional branch, as shown in Fig. 17.14. The closed-circuit impedance (corresponding to the antiresonance mode) should be the minimum, and the pure mechanical resonance status; the damped capacitance should be compensated by this negative capacitance –Cd, while at the resonance, the open-circuit impedance should be the maximum, and the effective motional capacitance in   1 1 , which provides + the motional branch is provided by 1= C1 Cd     E E 2 sD 33 ¼ s33 1  k33 , rather than s33 (i.e., origin of C1). In comparison with Eqs. (17.92), (17.93), (17.97) in the k31 mode, the EC components, L, C, and R can be denoted as follows:    E  2 Cn ¼ 8=n2 π 2 ðwb=LÞ d233 =sE2 33 s33 1  k33    2 (17.105) Ln ¼ ðρ=8Þ L3 =wb sE2 33 =d33 R1 ¼ ðL1 =C1 Þ1=2 =Q:

17.4 HEAT GENERATION IN PIEZOELECTRICS Heat generation in various types of PZT-based actuators has been studied under a large electric field applied (1 kV/mm or higher) at an off-resonance frequency and under a relatively small electric field applied (100 V/mm) at a resonance frequency.

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

17.4.1 Heat Generation at Off-Resonance Zheng et al. reported the heat generation at an off-resonance frequency from various sizes of multilayer-type piezoelectric ceramic (soft PZT) actuators.30 The temperature change with time in the actuators was monitored when driven at 3 kV/mm (high electric field) and 300 Hz (low frequency) (Fig. 17.15A), and Fig. 17.15B plots the saturated temperature as a function of Ve/A, where Ve is the effective volume (electrode overlapped part) and A is the surface area. Suppose that the temperature was uniformly generated in a bulk sample (no significant stress distribution). This linear relation is reasonable because the volume Ve generates the heat and this heat is dissipated through the area A. Thus, if we need to suppress the temperature rise, a small Ve/A design is preferred. 150 Actuator temperature (∞C)

5×5×20 mm

7×7×2 mm

100

17×3.5×1 mm 4.5×3.5×2 mm

50 31×9×0.3 mm

0

0

200

(A)

400 Driving time (s)

600

800

120 100

DT (∞C)

80 60 40 20 0

(B)

0

0.1

0.2

0.3 0.4 ve / A (mm)

0.5

0.6

0.7

FIG. 17.15 (A) Device temperature change with driving time for ML actuators of various sizes. (B) Temperature rise at off-resonance versus Ve/A in various size soft PZT ML actuators, where Ve A are the effective volume and A the surface area.

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

17.4 HEAT GENERATION IN PIEZOELECTRICS

683

17.4.1.1 Thermal Analysis According to the law of energy conservation, the amount of heat stored in the piezoelectric—which is just the difference between the rate at which heat is generated, qg, and that at which the heat is dissipated, qd—can be expressed as qg  qd ¼ VρCðdT=dtÞ, (17.106) where it is assumed a uniform temperature distribution exists throughout the sample and V is the total volume, ρ is the mass density, and C is the specific heat of the specimen. The heat generation in the piezoelectric is attributed to losses. Thus, the rate of heat generation, qg, can be expressed as qg ¼ wfVe ,

(17.107)

where w is the loss per driving cycle per unit volume, f is the driving frequency, and Ve is the effective volume of active ceramic (no-electrode parts are omitted). According to the measurement conditions (offresonance, no significant stress in the sample), this w corresponds to the dielectric hysteresis loss (i.e., P-E hysteresis), we, which is expressed in Eq. (17.7) in terms of the intensive dielectric loss tan δʹ as w ¼ we ¼ πεX ε0 E20 tan δ0 : If we neglect the transfer of heat through conduction, the rate of heat dissipation (qd) from the sample is the sum of the rates of heat flow by radiation (qr) and by convection (qc):   qd ¼ qr + qc ¼ eAσ T 4  To 4 + hc AðT  To Þ, (17.108) where e is the emissivity of the sample, A is the sample surface area, σ is the Stefan-Boltzmann constant, To is the initial sample temperature, and hc is the average convective heat transfer coefficient. Thus, Eq. (17.106) can be written in the following form: wfVe  AkðTÞðT  To Þ ¼ VρCðdT=dtÞ, where the quantity

  kðTÞ ¼ σe T2 + To 2 ðT + To Þ + hc

(17.109)

(17.110)

is the overall “heat transfer coefficient.” If we assume that k(T) is relatively insensitive to temperature change (if the temperature rise is not large), solving Eq. (17.109) for the rise in temperature of the piezoelectric sample yields

 (17.111) T  To ¼ ½wfVe =kðT ÞA 1  et=τ , where the time constant τ is expressed as τ ¼ ρCV=kðT ÞA:

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

(17.112)

684

17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

40

k(T) (W/m2 K)

k(T) (W/m2 K)

40 30 20 10 0

0

0.5

1

1.5

2

2.5

E (kV/mm)

(A)

3

30 20 10

3.5

0

1.0 kV/mm 1.5 kV/mm 2.0 kV/mm

0

0.5

1

1.5

2

2.5

f (kHz)

(B)

FIG. 17.16

Overall heat transfer coefficient, k(T), plotted as a function of applied electric field (A) and of frequency (B) for a PZT ML actuator with the dimensions of 7  7  2 mm3 driven at 400 Hz.

As t ! ∞, the maximum temperature rise in the sample becomes ΔT ¼ wfVe =kðT ÞA,

(17.113)

while, as t ! 0, the initial rate of temperature rise is given by dT=dt ¼ ðwT fVe =ρCV Þ ¼ ΔT=τ,

(17.114)

where wT can be regarded under these conditions as a measure of the total loss of the piezoelectric. The dependences of k(T) on applied electric field and frequency are shown in Fig. 17.16A and B, respectively. Note that k(T) is almost constant, as long as the driving voltage or frequency is not very high (E < 1 kv/mm, f < 0.3 kHz). The total loss, wT, as calculated from Eq. (17.114) is given for three multilayer specimens in Table 17.3. The experimentally determined P-E hysteresis losses measured under stressfree conditions (Eq. 17.7) are also listed in the table for comparison. It is seen that the extrinsic P-E hysteresis loss agrees well with the calculated total loss associated with the heat generated in the driven piezoelectric.30,31

17.4.2 Heat Generation Under Resonance Conditions Tashiro et al. observed the heat generation in a rectangular piezoelectric plate during a resonating drive.32 Even though the electric field is not large, considerable heat is generated due to the large induced strain/stress TABLE 17.3 Loss and Overall Heat Transfer Coefficient for PZT Multilayer Samples (E ¼ 3 kV/mm, f ¼ 300 Hz)30 Actuator

4.5 × 3.5 × 2.0 mm3

7.0 × 7.0 × 2.0 mm3

17 × 3.5 × 1.0 mm3

wT (kJ/m3) ¼ (ρCV/fVe) (dT/dt)t!0

19.2

19.9

19.7

P-E hysteresis loss (kJ/m3)

18.5

17.8

17.4

38.4

39.2

34.1

2

k(T) (W/m K)

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

17.4 HEAT GENERATION IN PIEZOELECTRICS

685

(A)

(B) FIG. 17.17

Temperature variations in a PZT-based plate sample observed with a pyroelectric infrared camera. The specimens are driven at two different resonance frequencies: (A) the first resonance mode (28.9 kHz) and (B) the second resonance mode (89.7 kHz).

at the resonance. The maximum heat generation was observed in the nodal regions for the resonance vibration, which correspond to the locations where the maximum strains/stresses are generated. The ICAT at the Penn State University also worked on the heat generation comprehensively in rectangular piezoelectric k31 plates when driven at the resonance.31 The arrows indicate the highest temperature areas. The temperature distribution profile in a PZT-based plate sample was observed with a pyroelectric infrared camera, as shown in Fig. 17.17, where the temperature variations are shown in the sample driven at the first (28.9 kHz) (A) and second resonance (89.7 kHz) (B) modes, respectively. The highest temperature (bright spot) is evident at the nodal areas for the specimen in Fig. 17.17A and B. This observation supports that the heat generated in a resonating sample is associated with the intensive elastic loss, tan ϕʹ. As we discussed in Section 17.2, the resonance and antiresonance are both mechanical resonances with the impedance equal to zero, and QB at antiresonance is higher than QA at resonance in PZT. Fig. 17.18A and B shows temperature variations in a PZT-based plate specimen driven at the antiresoance (A) and resonance frequency (B) under the same vibration velocity (i.e., the same output mechanical energy), which clearly exhibit a lower temperature rise in antiresonance than the resonance drive. Numerical profiles of the temperature distribution for the A- and B-type resonance modes are shown in Fig. 17.18C, which seems to be sinusoidal curves. Extending the heat flow equation Eq. (17.108) for a uniform temperature profile, we need to define the coordinate-dependent energy generation profile at the resonance mode.33 Because the strain/stress distribution is almost sinusoidal, we suppose volumetric heat generation is provided by III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

686

17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

(A)

(B) 90

A-type Resonance

80

100

Temperature [C]

90 80

B-type Resonance

70

70 60

60 50

50

40 30 0 550

(C)

40

500 450 Vibr atio 400 n ve locit y [m m

100 200 300

/s]

300

400

m]

m 01 –

n itio

[1

30

s Po

FIG. 17.18 Temperature variations in a PZT-based plate sample observed with a pyroelectric infrared camera. The specimens are driven at the antiresonance (A) and resonance frequency (B). (C) Numerical temperature profile for the A- and B-type resonance modes. III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

17.4 HEAT GENERATION IN PIEZOELECTRICS

uG ðxÞ ¼ uG cos 2

πx : L

687 (17.115)

The mechanical quality factor, Qm, is defined as the ratio of elastic energy of an oscillator to the power being dissipated by elastic mechanisms Qm ¼ 2πfr

Ue , Pd

(17.116)

where Ue is the maximum stored mechanical energy and Pd is the dissipated power, measured in this experiment by heat generation measurements through temperature, under a supposition that Pd ¼ electrically spent energy.34 Because the compliance of a piezoelectric material has nonlinearity, the maximum kinetic energy is used to define the stored energy term. For a longitudinally vibrating rod, the kinetic energy as a function of displacement, ux, is   ð 1 L=2 @ux 2 Ue ¼ A ρ dx: (17.117) @t 2 L=2 Using the geometry of Fig. 17.3 and assuming sinusoidal forcing at a frequency near the fundamental resonance, the spatial vibration can be described as

πx pffiffiffi ux ðx, tÞ ¼ VRMS 2 sin sin ð2πf tÞ: (17.118) L The maximum kinetic energy can be calculated as ð

πx2 pffiffiffi 1 L=2 L 2 A ρ VRMS 2 sin dx ¼ VRMS ρA : Ue ¼ 2 L=2 L 2

(17.119)

The dissipated power due to convection and radiation is equal to the heat generation at steady state, so Pd can be expressed as ð L=2

πx 1 Pd ¼ A uG cos 2 (17.120) dx ¼ uG AL: L 2 L=2 Thus, substituting these expressions into Eq. (17.116), the quality factor in terms of heat generation and RMS vibration velocity can be formed: Qm ¼ 2πfr 

2 ρVRMS : uG

(17.121)

Note that the quality factor does not depend explicitly on geometrical terms, as is expected if the mode of vibration is known. We see that if the vibration velocity is increased, the heat generation must also increase. Although this derivation is specific to longitudinal vibration of a rod at fundamental resonance, it can easily be extended to higher modes of vibration and also other structures such as disks. This can be accomplished by

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

Qm measured by temperature analysis 610 605 600 595 590

Qm

585 580 575 570 565 560 555 550 545 20090

20120

20150

20180

20210

Frequency (Hz)

FIG. 17.19

Change in Qm with frequency (fr  20.006 kHz).33

altering the shape of the heat generation distribution and the vibration velocity distribution and then reinvoking the definition of the mechanical quality factor. Shekhani et al. measured the temperature distribution on a PZT sample with the resonance frequency at 20.04 kHz at room temperature with Qm ¼ 507 with a 3 dB down method on an admittance spectrum. The sample was excited under the vibration velocity of 400 mm/s for 30 s, which corresponds to the heat dissipation of 11.6 W/m2. Fig. 17.19 shows the Qm obtained at three frequencies above the resonance frequency. An increase of Qm with increasing the frequency is obvious.

17.5 HIGH-POWER PIEZOELECTRIC CHARACTERIZATION SYSTEM (HiPoCS) There are various methods for characterizing loss factors and high power characterizations in the piezoelectric materials, in addition to the thermal analysis method introduced in Section 17.4.2: pseudostatic, admittance spectrum, and transient/burst mode methods. The admittance/impedance spectrum method is further classified into (1) constant voltage, (2) constant current, and (3) constant vibration velocity methods. Piezoelectric resonance can be excited by either electrical or mechanical driving, as shown in Fig. 17.20. In the k31 mode, as long as the surface is III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

17.5 HIGH-POWER PIEZOELECTRIC CHARACTERIZATION SYSTEM (HiPoCS)

Resonance

[Short] V E

Electrical excitation

Antiresonance

Ps

(A) [Short]

V E = 1/ psE 11

689

V

E

[Open] V E (B)

N/A

Ps

[Open] V E Resonance (C)

V = VE

Ps

[No electrode] Resonance V = VE 4 f = (vE/2L)(1+( 2 )k231) p Mechanical excitation

VD

Resonance V D = V E(1-k231)-1/2

FIG. 17.20

Resonance and antiresonance mode excitation under electrical or mechanical driving methods.

electroded, the sound velocity is vE originated from sE11, while if there is no electrode, they are vD and sD 11. A short-circuit condition realizes the resonance and an open-circuit condition with a full electrode provides the antiresonance mode. In order to measure the D-constant parameters (sD 11 and its extensive elastic loss tan ϕ) directly, we need to use a nonelectrode sample under mechanical driving methods.

17.5.1 Loss Measuring Technique I—Pseudostatic Method We can determine intensive dissipation factors, tan δʹ, tan ϕʹ, and tan θʹ, separately from (a) D vs. E (stress free), (b) x vs. X (short-circuit), (c) x vs. E (stress free), and (d) D vs. X (short-circuit) curves (see Fig. 17.1). Using a stress applying jig shown in Fig. 17.21, Zheng et al. measured the x vs. X and D vs. X relationships. Fig. 17.22 summarizes intensive loss factors, tan δʹ, tan ϕʹ, and tan θʹ as a function of electric field or compressive stress, measured for a soft PZT-based multilayer actuator. Refer to Eqs. (17.11) and (17.13) for the calculation. Note first that the piezoelectric loss tan θʹ is not negligibly small as believed by the previous researchers, but it is rather large, comparable to the dielectric and elastic losses; tan θʹ (¼0.08) > (1/2)[tan δʹ (¼0.06) + tan ϕʹ (¼0.08)]. This relationship is discussed again in Section 17.5.2. Then, using Eqs. (17.32), (17.33), we calculated the extensive losses as shown in Fig. 17.23. Note again that the magnitude of the piezoelectric loss tan θ is comparable to the dielectric and elastic losses, and it increases gradually with the field or stress; now tan θ (¼0.05) < (1/2)[tan δ (¼0.05) + tan ϕ (¼0.07)]. Also it is noteworthy that the extensive dielectric loss tan δ III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

690

17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

Load cell

Stainless steel Alumina Actuator Strain gauge

Strain gauge Alumina

Centering apparatus

Stainless steel Basement

FIG. 17.21

Stress applying jig construction for a multilayer piezoelectric sample.

0.15

0.15 300 Hz, 25°C

0.1 tan d¢

tan f¢

0.1

0.05

0.05

0

0 0

(A)

0.5 1 1.5 2 2.5 Electric field (kV/mm)

0

3

(B)

5

10

15

20

25

Compressive stress (MPa)

Electric field (kV/mm) 0.15

0.5

0.6

0.7

0.8

0.9

tan q¢

0.1

0.05 x-E p-X

(C)

0 14 16 18 20 22 24 26 28 30 Compressive stress (MPa)

FIG. 17.22 Intensive loss factors, tan δʹ (A), tan ϕʹ (B), and tan θʹ (C) as a function of electric field or compressive stress, measured for a soft PZT actuator.

increases significantly with an increase of the intensive parameter, in other words, the applied electric field, while the extensive elastic loss tan ϕ is rather insensitive to the intensive parameter, in other words, the applied compressive stress. When similar measurements are conducted under constrained conditions—that is, D vs. E under a completely clamped state, and III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

17.5 HIGH-POWER PIEZOELECTRIC CHARACTERIZATION SYSTEM (HiPoCS)

0.15

0.1

0.1

tan d

tan f

0.15

691

0.05 0 0.4

(A)

0.05

0.5

0.6 0.7 0.8 0.9 Electric field (kV/mm)

0.15

0.5

0 15

1

(B)

20 25 30 Compressive stress (MPa)

Electric field (kV/mm) 0.6 0.7 0.8 0.9

tan q

0.1

0.05

(C)

0 14 16 18 20 22 24 26 28 30 Compressive stress (MPa)

Extensive loss factors, tan δ (A), tan ϕ (B), and tan θ (C) as a function of electric field or compressive stress, measured for a soft PZT actuator.

FIG. 17.23

x vs. X under an open-circuit state, respectively—we can expect smaller hysteresis; this means extensive losses, tan δ and tan ϕ, theoretically. However, they are rather difficult in practice because of the migrating charge compensation on the specimen surface.

17.5.2 Loss Measuring Technique II—Admittance/Impedance Spectrum Method 17.5.2.1 Resonance Under Constant Voltage Drive Because the then commercially available impedance analyzer did not generate high voltage/current for measuring the high-powered piezoelectric performance, Uchino (as an NF Corporation Deputy Director) commercialized the frequency response analyzer (500 V, 20 A, 1 MHz maximum) from NF Corporation, Japan.34a Uchino reported the existence of the critical threshold voltage and the maximum vibration velocity for a piezoelectric, above which the piezoelectric drastically increases the heat generation and becomes a ceramic heater.34 Though this measurement technique is simple yet sophisticated, there have been problems in heat generation in the sample around the resonance range, further in

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

significant distortion of the admittance frequency spectrum when the sample is driven by a constant voltage, due to the nonlinear behavior of elastic compliance at high vibration amplitude.34a Fig. 17.24A exemplifies the problem, where the admittance spectrum is skewed with a jump around the maximum admittance point. Thus, we cannot determine the resonance frequency or the mechanical quality factor precisely from these

80 70 2.1 V/mm

Admittance (mS)

60 4.2 V/mm 50 6.3 V/mm 40

8.4 V/mm

30 20 10 0 20.0

20.3

20.5

(A)

20.8

21.0

21.3

21.5

21.8

22.0

Frequency (kHz)

80 100 mA 70

Admittance (mS)

200 mA 60 300 mA 50

400 mA

40

500 mA

30 20 10 0 20.40

(B)

20.45

20.50

20.55

20.60

20.65

20.70

20.75

20.80

Frequency (kHz)

FIG. 17.24

Experimentally obtained admittance frequency spectra under (A) constant voltage and (B) constant current condition. Note the skew-distorted spectrum with a jump under a constant voltage condition. (Data taken by Michael R. Thibeault, Penn State University.)

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

17.5 HIGH-POWER PIEZOELECTRIC CHARACTERIZATION SYSTEM (HiPoCS)

693

skewed spectra. Thus, HiPoCS this version did not have a capability to measure the piezoelectric loss. This high voltage/current power supply is still a key device in the present HiPoCS (I). 17.5.2.2 Resonance Under Constant Current Drive In order to escape from the problem with a constant voltage measurement, we proposed a constant current measurement technique.31 Since the vibration amplitude is primarily proportional to the driving current (not the voltage) at the resonance, a constant current condition guarantees almost constant vibration amplitude through the resonance frequency region, escaping the spectrum distortion due to the elastic nonlinearity. As demonstrated in Fig. 17.24B, the spectra exhibit symmetric curves, from which we can determine the resonance frequency and the mechanical quality factor QA precisely. Although the traditional constant voltage measurement was improved by using a constant current measurement method, the constant current technique (HiPoCS (II)) is still limited to the vicinity of the resonance. In order to identify a full set of high-powered electromechanical coupling parameters and the loss factors of a piezoelectric, both resonance and antiresonance vibration performance (in particular, QA and QB) should be precisely measured simultaneously. Basically, QA can be determined by the constant current method around the resonance (A-type), while QB should be determined by the constant voltage method around the antiresonance (B-type). The mechanical quality factor Qm (or the inverse value, loss factor tanpϕʹ) ffiffiffi is obtained from Qm ¼ ωA/2Δω, where 2Δω is a full width of the 1= 2 (i.e., 3 dB down) of the maximum admittance value at ωA. HiPoCS (II) improved the capability for measuring the mechanical quality factor Qm at the resonance region, but it did not provide information on the piezoelectric loss tan θʹ easily because we need to switch the measuring systems between constant-current and constant-voltage types. We reported the degradation mechanism of the mechanical quality factor Qm with increasing electric field and vibration velocity.31 Fig. 17.25 shows the vibration velocity dependence of the mechanical quality factors QA and QB, and corresponding temperature rise for A (resonance) and B (antiresonance) type resonances of a longitudinally vibrating PZT ceramic transducer through the transverse piezoelectric effect d31 (the sample size is inserted).35 Qm is almost constant for a small electric field/vibration velocity, but above a certain vibration level Qm degrades drastically, where temperature rise starts to be observed.35 In order to evaluate the mechanical vibration level, we introduced the vibration velocity at the rectangular plate tip, rather than the vibration displacement, because the displacement is a function of size, while the velocity is not. The maximum vibration velocity is defined at the velocity where a 20°C temperature rise at the nodal point from room temperature occurs. Note that even if we

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

694

17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

QB

40

QA

1500

30

7 1000

20

2 43 Test sample A-type

500

0 0.01

0.02

Temperature rise 0.05 0.1 0.2 Vibration velocity V0 (m/s)

10

Temperature rise DT (°C)

Mechanical Qm

2000

B-type 0.5

1

0

FIG. 17.25 Vibration velocity dependence of the mechanical quality factors QA and QB, and corresponding temperature rise for A- (resonance) and B (antiresonance)-type resonances of a longitudinally vibrating PZT ceramic transducer through the transverse piezoelectric effect d31 (the sample size is inserted).31

further increase the driving voltage/field, additional energy will convert to merely heat (i.e., PZT becomes a ceramic heater!) without increasing the vibration amplitude. Thus, the reader can understand that the maximum vibration velocity is a sort of material constant that ranks the high-power performance. Note that most of the commercially available hard PZTs exhibit the maximum vibration velocity around 0.3 m/s, which corresponds to roughly 5 W/cm3 (i.e., 1 cm3 PZT can generate maximum 5 W mechanical energy). When we compare the change trends in QA and QB, QB is higher than QA in all vibration levels (This is true in PZTs). This is the same result as already discussed for a small vibration level in Fig. 17.4. Accordingly, the heat generation in the B-type (antiresonance) mode is superior to the Atype (resonance) mode under the same vibration velocity level (in other words, the maximum vibration velocity is higher for QB than for QA). Fig. 17.26B depicts an important notion on heat generation from the piezoelectric material, where the damped and motional resistances, Rd and Rm, in the equivalent electrical circuit of a PZT sample (Fig. 17.26A) are separately plotted as a function of vibration velocity.31 Note that Rm, which we speculate to be mainly related to the extensive mechanical loss (90° domain wall motion), is insensitive to the vibration velocity, while Rd, related to the extensive dielectric loss (180° domain wall motion), increases significantly around a certain critical vibration velocity. Thus, the resonance loss at a small vibration velocity is mainly determined by the extensive mechanical loss that provides a high mechanical quality factor Qm, and with increasing vibration velocity, the extensive dielectric

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

17.5 HIGH-POWER PIEZOELECTRIC CHARACTERIZATION SYSTEM (HiPoCS)

Rd

LA Cd

Rd Rm and RA (W)

100

RA (directly measured) = Rd + Rm

30 Rm = wALA/QB 10

CA

Rd = tand /wACd 3.0

Rm

0.03

(A)

695

(B)

0.1

0.3

1.0

Vibration velocity v0 (m/s)

FIG. 17.26

(A) Equivalent circuit of a piezoelectric sample for the resonance under high power drive. (B) Vibration velocity dependence of the resistances Rd and Rm in the equivalent electric circuit for a longitudinally vibrating PZT ceramic plate through the transverse piezoelectric effect d31.35

loss contribution significantly increases. This is consistent with the discussion made in Fig. 17.23. After variable Rd exceeds Rm, we started to observe heat generation. We did not include the piezoelectric loss in the equivalent circuit previously. An updated discussion will be required in this argument. 17.5.2.3 Resonance/Antiresonace Under Constant Vibration Velocity Zhuang and Uchino derived an expansion-series approximation of the mechanical quality factors at both resonance and antiresonance modes, as introduced in Section 17.2.2, and they finally obtained a useful UchinoZhuang formula:23,24 the mechanical quality factor QB is obtained as 1 1 2 ¼ + ð tan δ0 + tan ϕ0  2tan θ0 Þ:  2 QB QA 1 1+ Ωb 2 k31 k31 The key is that the values QA and QB can be different, and if we precisely measure the both values, the information on the piezoelectric loss tan θʹ can be obtained. Thus, we proposed a simple, easy, and user friendly method to determine the piezoelectric loss factor tan θʹ in the k31 mode through admittance/impedance spectrum analysis.

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

696

17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

PC LabViewTM Algorithm

Amplitude Frequency

Data Port

Log/Monitor/Act

IEEE 1394

Voltage

GPIB

Current Vibration Vel.

Constant

Input E Power

Function Generator HP 33120A

Current Probe Tektronix TCPA305

Power Amplifier

Voltage Probe Tektronix TCPA305

RS232 USB

..00101001010110...

Control Parameters

Dig. Oscilloscope Tektronix TDS3014B

NF 4010 (Res) Trek 350A (A.Res) Polytec Vibrometer (Left)

Polytec Vibrometer (Right)

Nod

al Te m Hiok peratur e i344 5

Dig. Oscilloscope Tektronix TDS3014B

Thermal Image Acquirement FLIR S45 (w/ 200μm lens)

FIG. 17.27

Setup of HiPoCS Version III.

In order to identify both mechanical quality factors QA and QB precisely for adopting the above mentioned user friendly methodology, both resonance and antiresonance vibration performance should be measured simultaneously. Basically, QA can be determined by the constant current method around the resonance (A-type), while QB should be determined by the constant voltage method around the antiresonance (B-type). Thus, we developed HiPoCS Version III shown in Fig. 17.27, which is capable of measuring the impedance/admittance curves by keeping the following various conditions: (1) constant voltage, (2) constant current, (3) constant vibration velocity of a piezoelectric sample, and (4) constant input power. In addition, the system is equipped with an infrared image sensor to monitor the heat generation distributed in the test sample. We demonstrated the usefulness of the new system in a rectangular piezoelectric plate in the whole frequency range including the resonance and antiresonance frequencies. Fig. 17.28 shows an interface display of HiPoCS Ver. III, demonstrating a rectangular k31 plate measurement under a constant vibration velocity condition. In order to keep the vibration velocity constant (i.e., stored/ converted mechanical energy is constant), the current is almost constant and the voltage is minimized at the resonance, while the voltage is almost constant and the current is minimized at the antiresonance frequency. The apparent power is shown in the top of Fig. 17.28, and more detailed results

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

17.5 HIGH-POWER PIEZOELECTRIC CHARACTERIZATION SYSTEM (HiPoCS)

697

FIG. 17.28

Voltage and current change with frequency under the constant vibration velocity condition.36

Input power (W)

10 1 0.1 0.01 0.001 54,500

55,500

56,500

57,500

58,500

Frequency (Hz) 300 mm/s

200 mm/s

100 mm/s

50 mm/s

FIG. 17.29 Frequency spectra of power under constant vibration velocity, conducted across the resonance and antiresonance frequencies.

are shown in Fig. 17.29, which clearly indicates that the antiresonance operation requires less power than the resonance mode for generating the same vibration velocity, or stored mechanical energy. We can conclude that the PZT transducer should be operated at the antiresonace frequency, rather than the resonance mode, if we consider the energy efficiency.

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

698

17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

17.5.2.4 Real Electric Power Method Because the conventional admittance spectrum method can provide the mechanical quality factors only at two frequency points (i.e., resonance QA and antiresonance QB), we had a dilemma for knowing the Qm at any frequency. A unique methodology for characterizing the quality factor in piezoelectric materials has been developed in the ICAT by utilizing real electrical power measurements (including the phase lag), or example, P ¼ V  I  cos φ, rather than the apparent power V  I.34 The relation between mechanical quality factor and real electrical power and mechanical vibration is based on two concepts: (1) at equilibrium the power input is the power lost, and (2) the stored mechanical energy can be predicted using the known vibration mode shape. We can derive the following equation from these concepts, which allows the calculation of the mechanical quality factor at any frequency from the real electrical power (Pd) and tip RMS vibration velocity (VRMS) measurements for a longitudinally vibrating piezoelectric resonator (kt, k33, k31): 1 2 ρVRMS : Qm, l ¼ 2πf 2 P d =ð L w t Þ

(17.122)

Note here that this is only valid when the vibration mode do not change significantly around the resonance and antiresonance frequency range; that is, the electromechanical coupling factor k31 is not very large. The change in mechanical quality factor was calculated for a PZT (APC 841) ceramic plate (k31) under a constant vibration condition of 100 mm/s RMS tip vibration velocity (i.e., stored mechanical energy constant). The experimental key in the HiPoCS Ver. III usage is to determine the phase difference φ precisely to obtain the cos(φ) value. The required power and 0.014

Power (W)

0.012

fA

fB

1800

0.01

1500

0.008

1200 Qm

0.006 0.004 20,000

900

20,400

20,800

21,200

Mechanical quality factor

2100 Power

600

Frequency (Hz)

FIG. 17.30

Mechanical quality factor measured using real electrical power (including the phase lag) for a hard PZT APC 851 k31 plate.

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

699

17.5 HIGH-POWER PIEZOELECTRIC CHARACTERIZATION SYSTEM (HiPoCS)

mechanical quality factor Qm are shown in Fig. 17.30. The quality factor obtained at the resonance is within 2% agreement with results from the impedance spectrum method (3 dB-down bandwidth). This technique reveals the behavior of the mechanical quality factor at any frequency between the resonance and the antiresonance frequencies, and very interestingly the mechanical quality factor reaches a maximum value between the resonance and the antiresonance frequency, the point of which may suggest the optimum condition for the transducer operation merely from an efficiency viewpoint, and also for understanding the behavior of piezoelectric material properties under high-power excitation. 17.5.2.5 Determination Methods of the Mechanical Quality Factor Let us discuss the precise determination method of the mechanical quality factor. The admittance spectrum on the k31 mode and its admittance circle are shown in Fig. 17.31A and B, respectively. Fig. 17.31C is a magnified vision around the antiresonance frequency.

Admittance magnitude (S)

10−1

w1′(quadrantal)

jB 10−2

90°

w1(3 dB)

90°

3 db down

wm

10−3 10

p/4 1/2R1

−4

jw0Cd 10−5 10

(A)

w increase

−6

Admittance phase w1 wm w 2

86

wR = w 0 wR′

wn wA

−90°

87 88 89 Frequency (kHz)

90

G w2(3 dB) w2′(quadrantal)

wn

91

(B) p/4

jB

jw0Cd

w4

wn

1 √2

(C)

p/4

w3

p/4 G

w 2′(quadrantal)

FIG. 17.31 (A) Admittance spectrum on the k31 mode. (B) Admittance circle. (C) Admittance circle magnified around the antiresonance.

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

(a) Resonance/Antiresonance frequencies: The resonance frequency is defined by ωR, the rightmost on the motional admittance circle, while the antiresonance frequency is defined by ωA, the intersect between the admittance circle and the susceptance B ¼ 0. Popularly used maximum and minimum frequencies of the admittance magnitude, ωm and ωn, are not exactly the resonance and antiresonance frequency. Note ωm < ωR ¼ ω0 < ωA < ωn . (b) QA Determination: • 3 dB down method around ωm  1  QA ¼ ðω2  ω1 Þ=ωm (17.123) • Quadrantal frequency method around ωR  1 0  0  QA ¼ ω2  ω01 =ωR

(17.124)

Note ω1(3 dB) < ωʹ1(quadrantal) < ω2(3 dB) < ωʹ2(quadrantal). The 1 difference between (Q1 m ) and (Qm )ʹ can be estimated as  1   1 0 QA = QA ¼ 1 + 1=2M2 , (17.125) where M ¼ jYmj/jYdj ¼ 1/R1ωRCd ¼ QAK and K ¼ C1/Cd (1/K: Capacitance ratio). When we consider Qm  1000, the deviation of Qm values among these ways is less than 1 ppm (negligibly small). (c) QB Determination: See Fig. 17.31C • 3 dB up method around ωn  1  QB ¼ ðω4  ω3 Þ=ωn : (17.126)

17.5.3 Loss Measuring Technique III—Transient/Burst Drive Method 17.5.3.1 Pulse Drive Method The pulse drive method is a simple method for measuring high voltage piezoelectric characteristics, developed in the ICAT/Penn State in the early 1990s. By applying a step electric field to a piezoelectric sample, the transient vibration displacement corresponding to the desired mode (extensional, bending, etc.) is measured under a short-circuit condition. See Fig. 17.32. The resonance period, stabilized displacement, and damping constant are obtained experimentally, from which the elastic compliance, piezoelectric constant, mechanical quality factor, and electromechanical coupling factor can be calculated. Using a rectangular piezoelectric ceramic plate (length: L; width: w; and thickness: b; poled along the thickness. Fig. 17.3), we explain how to determine the electromechanical

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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17.5 HIGH-POWER PIEZOELECTRIC CHARACTERIZATION SYSTEM (HiPoCS)

Applied voltage (V)

Displacement (μm) Time Resonance period

FIG. 17.32

Pulse drive technique for measuring the electromechanical parameters.

coupling parameters k31, d31 and Qm. The density ρ, permittivity εX 33, and size (L, w, b) of the ceramic plate must be known prior to the experiments. 1. From the stabilized displacement, we obtain the piezoelectric coefficient d31: Ds ¼ d31 EL

(17.127)

2. From the ringing period, we obtain the elastic compliance sE11:  1=2 : (17.128) T0 ¼ 2L=v ¼ 2L ρsE11 3. From the damping constant τ, which is determined by the time interval to decrease the displacement amplitude by 1/e, we obtain the mechanical quality factor Qm: Qm ¼ ð1=2Þω0 τ,

(17.129)

where the resonance angular frequency ω0 ¼ 2π/T0. 4. From the piezoelectric coefficient d31, elastic compliance sE11, and permittivity ε3, we obtain the electromechanical coupling factor k31:  1=2 k31 ¼ d31 = ε0 ε3 sE11 :

(17.130)

On the other hand, the antiresonance Qm can be obtained as follows: By removing a large electric field suddenly from a piezoelectric sample, and keeping the open-circuit, the transient vibration displacement corresponding to the antiresonance mode. Although the experimental accuracy of the pulse drive method is not very high, the simple setup is attractive especially for its low cost. Moreover, unlike the resonance/antiresonance method, this technique requires only one voltage pulse during the measurement; this does not generate heat (i.e., temperature effect can be eliminated). Therefore, the electric field dependence of piezoelectricity can be measured.

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

17.5.3.2 Burst Mode Method Because an equilibrium HiPoCS characterization (continuous method, admittance/impedance spectrum measurement) of high-powered piezoelectrics conventionally used is inevitably associated with the temperature rise around the resonance and antiresonance modes, pure vibration amplitude dependence of the Qm cannot be discussed by removing the temperature influence. In order to eliminate the temperature rise effect, the burst method can be chosen. In this method, the internally generated heat is close to none, and observations would be a direct function of the ambient temperature on piezoelectric properties. The pulse drive method was introduced by Uchino in the early 1990s, but it was reported systematically by Umeda et al. for determining the equivalent circuit parameters of a piezoelectric transducer.37 It was thereafter adapted to measure the properties of piezoelectric ceramic samples.38,39 We introduce a short-circuit or an open-circuit system that functions immediately after the resonance burst drive (only for 1 ms) without generating significant heat, which generates the ring-down of vibration amplitude for the resonance and antiresonance mode, respectively. Fig. 17.33 illustrates the results for the short- and open-circuit.40 In the short circuit, the current and vibration velocity are proportional and their decay rate provides the mechanical quality factor QA (resonance). While in the open-circuit condition, the voltage and end displacement are proportional, and their decay rate give the QB (antiresonance). Note that the jump from the resonance to antiresonance frequency is observed on

FIG. 17.33 Vibration ring-down characteristics for the short- (Left) and open-circuit condition (Right). Note the sudden change of the ringing frequency for the open circuit.

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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703

Fig. 17.33 Right owing to a sudden electrical open-circuit, from the initial resonance excitation. Regarding the modification of HiPoCS Ver. III, short-circuit and open-circuit relays should be integrated. With the new blocking circuit added to our burst method characterization with the HiPoCS, we can monitor the mechanical quality factor change also in the antiresonance. We derive the force factor (A31) and voltage factor (B31) comprehensively— first in terms of material properties and sample geometry from the constitutive equations for the k31 piezoelectric sample.40 The force factor is the relationship between current and vibration velocity in resonance, and it is related to the piezoelectric stress coefficient. The force factor analysis for the k31 has been presented previously by Takahashi,38 but its explicit derivation has not. The voltage factor (B31) is the relationship between open circuit voltage and displacement in antiresonance, related with the converse piezoelectric coefficient (h31), which has not been applied nor analyzed in bulk piezoceramics in the antiresonance condition so far. The k31 mode sample geometry is Fig. 17.3. The derivations assume a rectangular plate with a ≪ b ≪ L, fully electroded, and poled along the thickness. Another assumption is that most of the vibration occurs in the length direction, traditionally corresponding to the x direction (x ¼ 0 is at the plate center). In general, the mode shape of a piezoelectric resonator with stress-free boundary conditions—undergoing vibration in 1-D, with losses, and having finite displacement—can be described as uðx, tÞ ¼ u0 f ðxÞ sin ωt,

(17.131)

where f(x) is a function symmetric about the origin normalized to the displacement at the ends of the piezoelectric resonator, where f(0) ¼ 0. Then, according to the fundamental theorem of calculus in terms of strain ð@u=@xÞ, we obtain ð L=2 @u dx ¼ uðL=2, tÞ  uðL=2, tÞ ¼ 2u0 sinωt: (17.132) L=2 @x The constitutive equation describing the electric displacement of a piezoelectric k31 resonator is given by Eq. (17.133) using the piezoelectric constant e31 and longitudinally-clamped permittivity εx331 ε0 : D3 ðtÞ ¼ e31

@u x1 + ε33 ε0 E3 ðtÞ: @x

(17.133)

For the electrical boundary condition of zero electric potential case (short circuit), the external field is equal to zero. Therefore, @u @2u . Now, the current can be written as D3 ðtÞ ¼ e31 , and D_ 3 ¼ e31 @x @x@t ð L=2 ð D_ 3 dx, andi0 ¼ 2e31 u0 bωA ¼ 2e31 bv0 : (17.134) iðtÞ ¼ D_ 3 dAe ¼ b Ae

L=2

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The last transformation uses vibration velocity v0 at the plate edge (x ¼ L/2), given ωu0 ¼v0 for sinusoidal time varying displacement. Thus, the force factor (A31), defined as the ratio between short circuit current and edge vibration velocity, can then be written as A31 ¼

i0 d31 ¼ 2e31 b ¼ 2b E : v0 s11

(17.135)

• For open circuit conditions, D3 ¼ 0, so the constitutive equation described in Eq. (17.133) can be written as E3 ðx, tÞ ¼ 

e31 @u : x1 ε33 ε0 @x

(17.136)

Assuming the variation of strain in thickness is negligible, the electric field across the thickness is uniform. Therefore, the E3(x,t) ¼ –V(t)/a. Integrating across the length of the resonator, ð ð L=2 ð L=2 e31 L=2 @u dx: E3 ðx, tÞ dx ¼  V ðtÞ=a dx ¼ x1 ε33 ε0 L=2 @x L=2 L=2 This equation can be rewritten using Eq. (17.132), assuming free natural vibration at the antiresonance frequency in open circuit conditions, LV0 e31 2ae31 ¼ x1 2u0 , and V0 ¼ x1 u0 : a ε33 ε0 Lε33 ε0 Thus, the voltage factor (B31), the ratio between open circuit voltage and displacement, can be written as B31 ¼

V0 2a e31 2a g31 2a ¼ ¼ ¼ h31 : u0 L εx331 ε0 L sD L 11

(17.137)

By applying the burst mode at resonance (short circuit) or antiresonance (open circuit) conditions, the force factor (A31) or the voltage factor (B31) can directly be obtained from the ratio between short circuit current and edge vibration velocity, or from the ratio between open circuit voltage and displacement. The mechanical quality factors (or elastic loss factors) and the real properties of the material can also be measured. For a damped linear system oscillating at its natural frequency, the quality factor can be described using the relative rate of decay of vibration amplitude. In general, Q¼

2πf   : v1 =ðt2  t1 Þ 2 ln v2

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

(17.138)

17.5 HIGH-POWER PIEZOELECTRIC CHARACTERIZATION SYSTEM (HiPoCS)

705

This equation is valid for both resonance and antiresonance modes. At resonance, the current is proportional to the vibration velocity; therefore its decay can be used. Similarly, the voltage decay can be used at antiresonance to determine the quality factor at antiresonance, which is supported by the above formula derivation. The first resonance frequency in the k31 resonator corresponds to the sE11 according to the following equation: sE11 ¼

1 ð2L fA Þ2 ρ

:

(17.139)

By utilizing the measurement of the force factor, the piezoelectric charge coefficient can be computed as d31 ¼ A31 sE11 =2b:

(17.140)

A more common approach to calculate this coefficient, frequently used in electrical resonance spectroscopy, is as follows: The off-resonance permittivity and resonance elastic compliance can be used to separate the piezoelectric charge coefficient from the coupling coefficient measured from the relative frequency difference between resonance and antireso 2   k31 π ωA π ωA , which can be expressed mathemat¼  =tan nance 2 ωR 2 ωR 1  k231 ically as follows: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (17.141) d31 ¼ k31 sE11 εX 33 ε0 : However, this approach assumes that the εX 33 does not change in resonance conditions. The calculation of d31 using the force factor does not make this assumption, so it is expected to be more accurate. By using a piezoelectric stress coefficient (e31) calculated at resonance (from the force factor) and the converse piezoelectric constant (h31) calculated at antiresonance, the longitudinally clamped permittivity εx33 can be calculated in resonance/antiresonance conditions directly. Then, εX 33 can be calculated using the k231. Permittivity has never been obtained directly in resonance conditions according to the author’s knowledge. Takahashi et al. reported permittivity in resonance conditions,38 but it is assumed that only the motional capacitance changes and the clamped capacitance in resonance does not change.   e31 A31 a 2 x (17.142) ¼ ε0 ε X 33 1  k31 ¼ ε0 ε33 ¼ h31 B31 Lb The experimental results are shown in Figs. 17.34 and 17.35.40 Regarding resonance characterization, the current and vibration data were used to calculate the force factor and the piezoelectric stress constant. Using the resonance frequency, the compliance was calculated; hence the

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

706

17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS Approximate strain (μm/m RMS) 0

20

40

60

80

100

Approximate strain (μm/m RMS) 120

0

1.4×10−10

80

100

0.325 0.3 42k

1.4×10−11

fA, fB (Hz)

E s11 [m2/N] = 2.19E-12 × v + 1.29E-11

1.35×10−11

fB

40k

fA

38k 1.3×10−11 10.6

0.1275

10

0.12

9.8

0.1175 0

0.1

0.2

0.3

0.4

0.5

h31 (V/μm)

10.2

(A)

1000

0.125

e31[N/Vm] = 1.76 × v + 9.66

50

h31[V/μm] = −57.9 × v + 979.0

980

49

960

48

940

0.6

0

(B)

Edge vibration velocity (m/s RMS)

0.1

0.2

0.3

B31 (V/μm)

10.4

A31 (N/V)

e31 (N/Vm)

60

0.35

1.3×10−10

9.6

40

k31 = 0.0634 × v + 0.328

d31[m/V] = 4.58E-11 × v + 1.22E-10

1.2×10−10 sE11 (m2/N)

20

0.375

k31

d31 (m/V)

1.5×10−10

47 0.5

0.4

Edge vibration velocity (m/s RMS)

FIG. 17.34

(A) Resonance characterization (force factor) of Soft PZT, PIC 184 k31 and (B) antiresonance analysis (voltage factor) and electromechanical coupling factor.42

Approximate strain (μm/m RMS) 10 100

Approximate strain (μm/m RMS) 1600

0

25

Catalog Value

X e33 PIC 184 X11 PIC 184 e33 X PIC 144 e33 X11 PIC 144 e33

1500

1000 Relative permittivity

Quality factor

PIC 144 Catalog Value

100

QA PIC 144 QB PIC 144 QA PIC 184 QB PIC 184

125

1400

1300 e33X PIC 184 @ 10kHz

1200

1100

PIC 184

e33X PIC 144 @10kHz

1000

50 0.1

(A)

Edge vibration velocity (m/s RMS)

1

0

(B)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Edge vibration velocity (m/s RMS)

FIG. 17.35 (A) Change in quality factors and (B) change in dielectric permittivity with vibration velocity for PIC 144 (Hard PZT) and PIC 184 (Soft PZT).40

piezoelectric charge coefficient could be calculated as well. The resonance characterization for soft PZT, PIC 184 is shown in Fig. 17.34A, where the properties (e31, sE11, d31) change linearly with vibration velocity. By utilizing the displacement and open circuit voltage at antiresonance, the voltage factor (B31) and the converse piezoelectric coefficient (h31) were calculated (see Fig. 17.34B). The coupling factor can also be calculated using the relative difference between the resonance and antiresonance

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

17.5 HIGH-POWER PIEZOELECTRIC CHARACTERIZATION SYSTEM (HiPoCS)

707

frequencies. The coupling factor increases with the vibration velocity; h31 decreases with increasing vibration velocity, contrary to the behavior of the other properties. That being said, it has a much smaller dependence on vibration velocity than the other properties, namely those determined at resonance. Using the decay of vibration at resonance and antiresonance, the quality factors were calculated. Each data point used amplitude data from two vibration measurements. Therefore the scale was readjusted as an average of the vibration velocity. Fig. 17.35A shows the results; a log-log plot was used in order to more easily distinguish and compare the trends between the two compositions. PIC 144 (Hard PZT) shows stable characteristics of the quality factor, until about 150 mm/s RMS, after which a sharp degradation in the quality factors occurred. PIC 184 (soft), however, showed an immediate decrease in its quality factors. QB was larger than QA for both the materials. Traditional methods cannot measure the permittivity under resonance conditions. This is because the large vibration does not allow the dielectric response to exhibit a unique and distinct feature that can be characterized in order to compute the permittivity. This is also true for the dielectric loss. Therefore, researchers have used one of the two approaches to estimate the permittivity in high-power conditions. The first approach is to assume the permittivity measured at off-resonance applies to resonance conditions. This approach is problematic because the stress conditions and the frequency are different at resonance and therefore the property is expected to change, similar to other properties. The other approach is to assume a perturbation of the off-resonance frequency using the variation in the motional capacitance, which is proportional to d231/sE11. Using the force factor and the voltage factor, the permittivity under constant strain (1 dimensionally constrained) εx331 can be calculated directly (Eq. 17.142). Using the coupling factor k31, εX 33 can be calculated. The permittivity vs. vibration velocity can be seen in Fig. 17.35B. The offresonance permittivity measured for the samples is in good agreement with the low vibration velocity permittivity measured through the burst technique. The off-resonance permittivity is represented as a star symbol. The clamped and free permittivity are both changing with increasing vibration velocity. The permittivity of PIC 184 is larger than that of PIC 144, and this is expected because PIC 184 is a soft PZT with larger offresonance permittivity. From the low vibration state to the high one, the permittivity of both compositions increase. However, the increase in PIC 184 is larger, demonstrating that its properties have a larger dependence on vibration conditions. Unlike the expectation, the result shown in this study demonstrates that a majority of the change seen in the free permittivity can actually be attributed to the clamped permittivity change.

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

A method for determining the piezoelectric loss is summarized for a piezoelectric k31 mode plate sample here23 (refer to a review paper, Ref. 40 for other modes): (1) Obtain tan δʹ from an impedance analyzer or a capacitance meter at a frequency away from the resonance or antiresonance range; (2) Obtain the following parameters experimentally from an admittance/ impedance spectrum around the resonance (A-type) and antiresonance (B-type) range (3 dB bandwidth method), or the burst mode: ωa, ωb, QA, QB, and the normalized frequency Ωb ¼ ωbl/2v; (3) Obtain tan ϕʹ from the inverse value of QA (quality factor at the resonance) in the k31 mode; (4) Calculate the electromechanical coupling factor k from the ωa and ωb with  k2 π ωb π ðωb  ωa Þ ; tan the IEEE Standard equation in the k31 mode: 31 2 ¼ 2ωa 1  k31 2 ωa (5) Finally obtain tan θʹ by the following equation in the k31 mode:  "  2 # tan δ0 + tanϕ0 1 1 1 1 0 + 1+   k31 Ω2b : tan θ ¼ 2 4 QA QB k31

17.5.4 Loss Measuring Technique—Sample Electrode Configuration In order to obtain the material’s extensive and intensive losses, we need to use various sample configurations. Using a k31 plate sample, we can measure sE11 and tan ϕ0 11 ; while in a k33 rod sample, we can measure sD 33 and tan ϕ33. However, we cannot measure extensive tan ϕ11 or intensive tan ϕ0 33 experimentally, but we evaluate by using k31 or k33 values. Though tan ϕ11 or tan ϕ0 33 can be evaluated with the [K] matrix in Eq. (17.33) theoretically, the experimental errors expand dramatically. Thus, Majzoubi et al. proposed a new mechanical-excitation methodology (similar to a composite-bar structure) rather than a conventional electrical excitation, to measure extensive tan ϕ11 directly in the k31 plate, and to examine its self-consistency with past indirect methods.41 For this purpose, rectangular piezoelectric plates with various electrode patterns—including full electrode (FE), partial electrode with short and open circuits between sided electrodes (PE-Short, and PE-Open), and nonelectrode (NE) patterns—are designed and prepared. Their schematic views are shown in Fig. 17.36A. The measurements for the admittance spectrum of these samples (Hard PZT, PIC 144) are summarized in Fig. 17.36B. The FE sample behaves as a typical rectangular PZT k31 plate. For the NE piezoelectric, it has pure D-constant performance (just has a small

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

17.5 HIGH-POWER PIEZOELECTRIC CHARACTERIZATION SYSTEM (HiPoCS)

FE PE-short PE-open NE

V

V

V

P

P G

G

(a)

G

G

Full electrode (FE)

(b)

Partial electrode – short circuit (PE-Short)

V

V

P

P

G

G

(c) Partial electrode – open circuit (PE-Open)

(A)

Admittance (log(*10-5)S)

10,000 V

(d)

709

1000 100 10 1 0.1

Non-electrode – poled (NE)

40

(B)

41 42 Frequency (kHz)

43

FIG. 17.36 (A) Schematic view of different electrode patterns on a rectangular PZT plate. (B) Impedance spectrum of FE, PE-Short, PE-Open, and NE samples.42

portion electrode for excitation), and its losses would mostly correspond to the extensive ones, which we could measure directly for the first time (refer to Fig. 17.20). Higher resonance and antiresonance frequency is observed, in comparison to FE sample, because vD > vE. PE-Short corresponds to the pure E-constant situation, and the resonance mode. As shown in Fig. 17.36B, the resonance frequency of this sample is almost the same as the FE one, and the antiresonance frequency occurs in much lower frequency. In contrast, the antiresonance frequency of PE-Open is in the same range as FE sample, and the resonance frequency occurs in much higher frequency. This case attributed to the antiresonance mode. Since we consider the k31 mode and also there is no voltage distribution on the surface, the mechanical resonance would happen between the pure D and E constant situations, which are actually the NE and PE-Short cases. The coupling factor of PIC 144 derived from resonance and antiresonance frequencies of the FE sample is k31 ¼ 0.31, which is comparable with   2 E the one derived from the equation of sD 11 ¼ s11 1  k31 . In aforementioned E equation, sD 11 and s11 are calculated from the antiresonance frequency of D  the NE sample s11 ¼ 1:06  1011 m2 =N , and resonance frequency is cal culated from the resonance frequency of the PE-Short sample sE11 ¼ 1:17  1011 m2 =NÞ. The coupling factor can be calculated 0.32 for this case. This good agreement of these k31 values verifies the feasibility of our sample configuration for measuring the piezoelectric performances under various electric boundary conditions. The mechanical quality factors for both resonance and antiresonance modes, measured from the impedance curve, are shown in Table 17.4.42 We observe that QA and QB differs significantly in the FE sample, but the difference is much less in the partial electrodes, as expected. The PE-Open and NE samples have higher mechanical quality factors (lower mechanical losses), in comparison to the short circuit one.

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

TABLE 17.4 Resonance and Antiresonance Frequencies and Mechanical Quality Factors42 FE

PE  short

PE  open

NE

fr

[kHz]

40.69

40.64

[41.93]

[42.43]

far

[kHz]

42.31

[40.97]

42.29

42.85

QA

–

1390 28

1350 27

[1720]

[1690]

QB

–

1650 33

[1360]

1700 34

1770 35

Regarding the loss factors, initially from the FE sample data on QA and QB, we determined the intensive losses as follows: tan δ033 ¼ 2:3  103 , tan ϕ011 ¼ 7:194  104 , tan θ031 ¼ 2:2  103 : Using the [K]-matrix, we obtained the extensive losses: tan δ33 ¼ 2:1  103 , tan ϕ11 ¼ 5:76  104 , tan θ31 ¼ 6:65  103 : On the other hand, the extensive losses were directly measured from the QB on the NE sample as tan ϕ11 ¼ 5:92  104 . The slight difference in obtained values between the FE and NE methods, most likely originated both from neglecting the 10% electrode and also from error propagation in indirect calculations.

17.6 DRIVE SCHEMES OF PIEZOELECTRIC TRANSDUCERS Most of commercially available power supplies are designed to drive resistive actuators/transducers such as electromagnetic motors. However, the piezoelectric devices change admittance characteristics from “capacitive” (pseudo-DC), “resistive” (at resonance frequency) and “inductive” (between the resonance and antiresonance frequencies), depending on the operating frequencies. Accordingly, we need to develop a suitable power supply to match the impedance to the actuators.

17.6.1 Off-Resonance (Pseudo-DC) Drive It is known that when we drive a piezoelectric actuator at an offresonance (or pseudo-DC) frequency by linear or switching power supplies, it is 98–94% inefficient, that is, only 2%–6% of energy can be used because of the electrical impedance mismatch. Historically, when NEC Corporation developed a dot-matrix printer with piezoelectric multilayer actuators (capacitance C) in the 1980s; they integrated an inductive coil

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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17.6 DRIVE SCHEMES OF PIEZOELECTRIC TRANSDUCERS

Transmission loss (dB)

80 Concrete 120 mm

60

Glass 10 mm

40

Iron plate 0.7 mm PVDF with circuit

20

PVDF without circuit

0

(A)

(B)

102

2

3

4 5 6 7 89

2

103 Frequency (Hz)

3

4 5 6 789

104

FIG. 17.37

(A) Curved PVDF acoustic noise barrier. (B) Acoustic transmission loss spectrum with the negative capacitance circuit or without the circuit.

(inductance L) at the interface between the piezocomponent and resistive power supply, so that C and L resonate at the printer operating frequency of 1 kHz (much lower than the mechanical resonance frequency 100 kHz). This energy catch ball between C and L helped significantly with trapping the energy locally without dissipation. In a word, when dealing with capacitive piezoelectric actuators, the important consideration is not “apparent power,” but actual “energy flow”! However, because inductor L is usually the bulkiest component in size and weight in drive power electronics (also some electromagnetic noise), a negative capacitance (–Cp) is now popularly used. One example can be found in the noise barrier developed by Kobayashi Riken [Private communication] (Fig. 17.37). Large area PVDF films were used to cover the walls separating residential areas from a busy highway. In order to eliminate acoustic traffic noise around the highway, the acoustic noise is detected by a piezoelectric microphone first, then the signal is fed back to piezoelectric PVDF film speakers to generate a conjugate acoustic wave (i.e., “antinoise”), which effectively cancels the noise signal. Using a negative capacitance circuit, the acoustic transmission loss was remarkably improved by 20 dB in a low-frequency (off-resonance) range, in comparison with the data obtained without this circuit (Fig. 17.37B). The lowfrequency traffic noise less than 1 kHz is the primary annoyance for the human.

17.6.2 Resonance Drive Commercial power supplies with a resistive output impedance can be used for driving resonant-type transducers and ultrasonic motors. Like the Frequency Response Analyzer (500 V, 20 A, 1 MHz maximum) by NF Corporation, a power supply capable of switching the output impedance from the regular 50 Ω to the lowest 0.1 Ω is highly recommended,

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

Rf

INV a(cw)

b(ccw) Cg

(A)

Ultrasonic motor

Cd

(B)

FIG. 17.38 Ultrasonic motor driven by its own oscillation with electric elements. (A) Schematic diagram. (B) Actual circuit developed for driving a metal-tube motor.

because the resonance impedance of a ML actuator is very low, around 1 Ω. The antiresonance mode is a mechanical resonance, similar to the resonance mode with the same resistive characteristic. The difference is only the driving scheme; low voltage and high current are for the resonance, while high voltage and low current are for the antiresonance drive. As Fig. 17.28 clearly demonstrated in PZTs, the antiresonance mode exhibits higher Qm and lower effective mechanical loss than the resonance mode. Therefore, the antiresonance drive is superior to the resonance operation in general, as long as the energy consumption and efficiency are concerned. Since the transducer characteristics at the resonance and antiresonance are both resistive, the power supply design is basically the same. In order to further miniaturize a drive circuit for ultrasonic motors in camera modules (such as smart phones), a self-oscillation drive system has been developed. Fig. 17.38 shows an ultrasonic motor driven by its own oscillation with electric elements. (A) Schematic diagram. (B) Actual circuit developed for driving a metal-tube motor. The drive system has been miniaturized already into a sesame seed size for the smart phone camera module applications (such as Galaxy 6S, Samsung Electronics, Korea).

17.6.3 Inductive Actuator Drive Piezoelectric transducers are conventionally driven at their resonance frequency, where they show resistive characteristics. However, the resonance frequency does not take advantage of the loss reduction mechanism that occurs between the resonance and antiresonance frequency. The resonance drive leads to more heat generation and lower efficiency. An innovative driving scheme of a Langevin piezoelectric transducer under its inductive frequency range was proposed by Dong et al.,29 which takes

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

713

17.6 DRIVE SCHEMES OF PIEZOELECTRIC TRANSDUCERS 10

Actual input power (W) Apparent power (VA)

1 Lf

Ce

Lt1

Ccir R

V 0.1

fR

fOPT

C1e

Lt2

fA VG

Cd

L

R′c

0.01

(A)

C

39

40

41 42 Frequency (kHz)

43

44

(B)

FIG. 17.39 (A) Actual input power and apparent power of the Langevin transducer under constant vibration velocity (30 mm/s) drive. (B) Class E inverter with impedance converter.

advantage of the maximum efficiency frequency between the resonance and antiresonance. In this approach, first, a constant vibration velocity measurement system is used to find the optimum driving frequency, which is defined as the point where the real input electric power is the lowest for a given output mechanical vibration level (Fig. 17.39A). The transducer has an inductive behavior at the optimum frequency. Next in this approach an equivalent circuit of the transducer based on the Butterworth-Van Dyke (BVD) model is established, whose parameters are used to design Class E inverter driving circuits (Fig. 17.39B). Using MATLAB, two Class E inverters are designed to drive the transducer at the resonance frequency (resistive) and transducer at the optimum frequency (inductive). The optimum driving frequency of this Langevin piezoelectric transducer was fopt ¼ 41.27 kHz , which is between resonance frequency and antiresonance frequency. The impedance at this frequency is Zopt ¼ 144.2 + j2065 (Ω), which is mostly an inductive load. According to the analysis of the Class E inverter, Re should be the resistive load; therefore, a capacitor Ccir is connected in series with this Langevin piezoelectric transducer (BVD equivalent circuit is on the right-side of Fig. 17.39B) to accomplish a resistive load Re0 , and the value of Ccir can be calculated by the impedance of optimum frequency: Ccir ¼

1  , ωopt  img Zopt

(17.143)

where ωopt is the optimum driving frequency and ωopt ¼ 2πfopt, and img(Zopt) is the imaginary part of Zopt. The total impedance Re0 of the Langevin transducer and capacitor Ccir is 143 Ω. An impedance converter circuit is applied to change the impedance of Re0 to be the same as Re,42 while the driving frequency set to the experimental determined optimum frequency of 41.27 kHz. The topology of the impedance converter circuit and class E inverter is shown in Fig. 17.39B. The required power for the optimum frequency driving method is reduced by 39% compared with

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

the resonance frequency driving method according to the experiments. Also, temperature rise was smaller in the optimum frequency driving method. Therefore, it is recommended to drive the Langevin transducer at such frequency, which occurs in the inductive region of the transducer. This optimum driving method can be applied to other piezoelectric transducers and actuators such as ultrasonic motors.

17.7 LOSS MECHANISMS IN PIEZOELECTRICS So far, we have focused on the phenomenological discussions of losses. In this section, we consider microscopic or crystallographic origins of loss mechanisms in piezoelectrics from the materials science viewpoint. Losses are considered to consist of four portions: (1) domain wall motion; (2) fundamental lattice portion, which should also occur in domain-free monocrystals; (3) microstructure portion, which occurs typically in polycrystalline samples; and (4) conductivity portion in highly ohmic samples. However, in the typical piezoelectric ceramic case, the loss due to the domain wall motion exceeds the other three contributions significantly.

17.7.1 Microscopic Origins of Extensive Losses We have discussed so far the macroscopic phenomenology of losses in piezoelectrics. We discuss here the relationship of the loss phenomenology with the microscopic origins. To make the situation the simplest, we consider here only the domain wall motion-related losses. Taking into account the fact that the polarization change is primarily attributed to 180° domain wall motion, while the strain is attributed to 90° (or non-180°) domain wall motion, we suppose that the extensive dielectric and mechanical losses are originated from 180° and 90° domain wall motions, respectively, as illustrated in Fig. 17.40. The dielectric loss comes from the hysteresis during the 180° polarization reversal under E, while the elastic loss comes from the hysteresis during the 90° polarization reorientation under X. Regarding the piezoelectric loss, we presume that it originates from Gauss’ Law, div (D) ¼ σ (charge). As illustrated in Fig. 17.40, when we apply a tensile stress on the piezoelectric crystal, the vertically elongated cells will transform into horizontally elongated cells, so that the 90° domain wall will move rightward. However, this “ferroelastic” domain wall will not generate charges because the rightward and leftward polarizations may compensate each other. Without having migrating charges σ in this crystal, div (D) ¼ 0, leading to the polarization alignment “head-to-tail,” rather than “head-to-head” or “tail-to-tail.” After the “ferroelastic” transformation, this polarization alignment will need an

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17.7 LOSS MECHANISMS IN PIEZOELECTRICS

Electric field

Stress

Polarization Stress

Dielectric tan d

Strain

Electric field Mechanical tan f Strain

Polarization

Piezoelectric tan q

FIG. 17.40 Polarization reversal/reorientation model for explaining “extensive” dielectric, elastic, and piezoelectric losses.

additional time lag, which we define the piezoelectric loss. Superposing the ferroelastic domain alignment and polarization alignment (via Gauss’ Law) can generate actual charge under stress application. In this model, the intensive (observable) piezoelectric loss is explained by the 90° polarization reorientation under E, which can be realized by superimposing the 90° polarization reorientation under X and the 180° polarization reversal under E. This is the primary reason why we cannot measure the piezoelectric loss independent from the elastic or dielectric losses experimentally. If we adopt the Uchida-Ikeda polarization reversal/reorientation model,42a,43 we can explain the loss change with an intensive parameter (externally controllable parameter). By finding the polarization P and the field-induced strain x as a function of the electric field E, it is possible to estimate the volume in which 180° reversal or 90° rotation occurred. This is because the 180° domain reversal does not contribute to the induced strain, only the 90° rotation does, whereas the 180° domain reversal contributes mainly to the polarization. The volume change of the domains with external electric field is shown schematically in Fig. 17.41. It can be seen that with the application of an electric field the 180° reversal occurs rapidly at a certain electric field, whereas the 90° rotation occurs gradually from a low field. It is notable that at G in the figure, there remains some polarization while the induced strain is zero; at H the polarizations from the 180° and 90° reorientations cancel each other and become zero, but the strain is not at its minimum. Due to a sudden change in the 180° reversal above a certain electric field, we can expect a sudden increase in the polarization hysteresis and in the dielectric loss [this may reflect to the

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

180° Reversal volume change

Electric field K

J

I H

G (F,A) B

C

D

E

90° Reorientation volume change

FIG. 17.41

Polarization reversal/reorientation model for explaining the loss change with

electric field.

extensive dielectric loss measurement in Fig. 17.23A]; while the slope of 90° reorientation is almost constant, we can expect a constant extensive elastic loss with changing the external parameter, E or X [extensive elastic loss in Fig. 17.23B]. This dramatic increase in 180° domain wall motion (i.e., the extensive dielectric loss) seems to be the origin of the apparent Qm degradation and heat generation above the maximum vibration velocity, which was already discussed in Fig. 17.26.

17.7.2 Loss Anisotropy—Crystal Orientation Dependence of Losses 17.7.2.1 Loss Anisotropy in PZT Zhuang et al. determined all 20 loss dissipation factors for a PZT ceramic using the ICAT HiPoCS admittance spectrum method introduced in the characterization Section 17.2.2.24 Table 17.5 summarizes all elastic, dielectric, and piezoelectric losses determined on a soft PZT, APC 850 (APC International, State College, PA). Note the following general conclusions: (1) The antiresonance QB is always larger than the resonance QA in PZTs: This is a significant contradiction with the IEEE Standard assumption, leading to the necessity of the “Standard” revision. (2) The intensive (prime) losses are larger than the corresponding extensive (nonprime) losses: This is understood by the boundary condition difference between “intensive” and “extensive”—that is, free or clamped/constrained conditions. (3) The intensive piezoelectric losses are significantly larger than the intensive dielectric or elastic losses in PZTs. That is,

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17.7 LOSS MECHANISMS IN PIEZOELECTRICS

TABLE 17.5

The Loss Factors of APC 850 With Experimental Uncertainties 0 tan ϕ11

0 tan ϕ12

0 tan ϕ13

0 tan ϕ33

0 tan ϕ55

Result

0.01096

0.0095

0.01507

0.01325

0.0233

Uncertainty

0.00007

0.0003

0.00034

0.00033

0.0022

Relative

0.6%

3.2%

2.2%

2.5%

9.6%

tan ϕ11

tan ϕ12

tan ϕ13

tan ϕ33

tan ϕ55

Result

0.0105

0.0104

0.0076

0.00433

0.0149

Uncertainty

0.0018

0.0028

0.0013

0.00008

0.0003

Relative

17%

28%

2.1%

tan

0 δ33

tan

17%

1.7%

0 δ11

tan δ33

tan δ11

Result

0.0143

0.0176

0.0058

0.0092

Uncertainty

0.0002

0.0004

0.0011

0.0023

Relative

1.4%

2.3%

20%

25%

tan

0 θ31

tan

0 θ33

tan

0 θ15

tan θ31

tan θ33

tan θ15

Result

0.0184

0.0178

0.0296

0.0133

0.0004

0.0024

Uncertainty

0.0006

0.0004

0.0026

0.0081

0.0004

0.0013

Relative

3.2%

2.1%

8.8%

61%

100%

57%

tan θ0 > ð tan δ0 + tan ϕ0 Þ=2. This is not true for Pb-free piezoelectrics, as discussed later. (4) There is apparent loss anisotropy in dielectric, elastic, and piezoelectric losses, indicating the anisotropy in domain wall mobility in the crystal. Further specific conclusions include the following: (5) tan δ33 < tan δ11: Polarization seems to be more stable along the X spontaneous polarization, similar to the permittivity trend (εX 33 < ε11 ). (6) tan ϕ33 < tan ϕ11: Elastic compliance also seems to be more stable along the spontaneous polarization. (7) tan θ33 < tan θ31: Piezoelectric constant also seems to be more stable along the spontaneous polarization. Choi et al. explored the loss anisotropy in piezoelectric PZT ceramics.44 To observe polarization angle dependence of losses, two different models for k31 and k33 mode vibration were prepared as shown in Fig. 17.42. The samples were prepared by PI Ceramics GmbH with cutting and

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

k15 mode

k33 mode 0°

90º 75°

15°

P

30°

Y X

k31 mode

FIG. 17.42

45°

45°

Z

Electrode

30°

60°

60°

15°

75°

0°

90° k15 mode

PZT sample configurations with various polarization direction.

re-electroding followed by conventional ceramic processing. The polarization angle is defined by the angle of the polarization measured from the electric field direction (i.e., 0°: PS jjE; 90°: PS ?E). With similar elastic compliance and the same length, the fundamental longitudinal resonance of both models occurs around 100 kHz, while the shear vibration occurs around 1 MHz. Three different compositions of 1% Nb-doped PZT are prepared for the tetragonal, rhombohedral, and morphotropic phase boundary (MPB) structures. In our previous paper,45 we reported an effective d33 constant enhancement in a rhombohedral soft PZT composition around a 45° cut angle. However, interestingly we did not observe the peak in d33 value in this composition, but we observed it in the d31 in Rhombohedral composition.44 The intensive and extensive losses for k31 and k33 vibration modes are derived from the off-resonance capacitance and quality factors from resonance and antiresonance frequencies using a [K] matrix (i.e., relationship for intensive/extensive loss conversion). Larger dielectric loss is observed with a higher polarization angle, regardless of the crystal structure. However, the capacitance showed a different tendency by compositions, indicating the tetragonal structure would have smaller capacitance when depoled, while the rhombohedral structure would have larger capacitance by depoling. The elastic compliance and mechanical loss exhibit complicated behavior by the poling angle, though the elastic loss tangent change is less significant than other two losses. The real and imaginary part seems to have a linear tendency, though the further improvement of measuring accuracy is necessary to discuss in detail (Fig. 17.43).

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17.7 LOSS MECHANISMS IN PIEZOELECTRICS Composition 1. Tetragonal

2. MPB

Composition 3. Rhombohedral

15.0 12.5

12 10 8 0.60

k33

k31

3. Rhombohedral

x e33

2 sD 33 (μm /N)

700 17.5

0.30 0.24 0.18

0.40 0.20

d33 (pC/N)

d31 (pC/N)

2. MPB

1200 800 400

1050

2 sE 11 (μm /N)

e x33

1400

1. Tetragonal

140 105 70 0

30 60 90

(A)

0

30 60 90 0 Angle Effective k31 vibration

120 80 0

30 60 90

(B)

30

60

30 60 90 0 Angle Effective k33 vibration

90 0

30

60

90

FIG. 17.43

Polarization direction dependence of dielectric constant, elastic compliance, electromechanical coupling factor, and piezoelectric d constant.44

The piezoelectric constant and coupling factor gradually decrease with increasing polarization angle where the degradation of piezoelectricity can be explained by depoling. The quality factor at resonance becomes closer to the one at antiresonance with increased canted angle, where the relative magnitude changes between the piezoelectric loss and other losses. As depicted in Fig. 17.44, the change of intensive and extensive piezoelectric loss seems to be in much larger scale than the loss tangent change of dielectric or mechanical behavior overall. There remain two problems to be solved in the successive studies: (1) both increase and decrease tendencies appear only in the piezoelectric losses. (2) in particular, negative extensive piezoelectric losses are observed. 17.7.2.2 PMN-PT Single Crystal Extensive studies have been made on the different characteristics between ferroelectric single crystals and polycrystalline PZT. Pb(Mg1/3 Nb2/3)O3 (PMN)-PbTiO3 (PT) single crystals, for example, have significant loss anisotropy and doping dependence, as shown in Figs. 17.45 and 17.46.46 Fig. 17.45A shows the maximum vibration velocities (defined by 20°C temperature rise) of single crystals and ceramics (k31 mode). The performance of single crystals is not as good as high-powered hard PZT, but it is better than soft PZTs. Mechanical quality factors and electromechanical coupling factors for the k31 vibration mode are plotted for various orientations of single crystals in Fig. 17.45B. You may find significant crystallographic orientation dependence of mechanical losses, as well as the real parameter k31 change. In addition, PMN-PT single crystals have been utilized in highpowered applications and have showed significant advantages compared

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

Composition 1. Tetragonal

2. MPB

3. Rhombohedral tan j′11 tan q′31

int. loss

0.06

Ext. loss

tan d′33

0.09

0.03

tan d33

0.00

tan j11 tan q 31

0.03

–0.03 0

30

60

(A)

90 0

30 60 90 0 Angle Effective k31 vibration

30

60

90

Composition 1. Tetragonal

2. MPB

3. Rhombohedral

int. loss

tan d′33 0.06 0.00

tan j′33 tan q′33

Ext. loss

–0.06 0.06

tan d33

0.00 –0.06

tan j33 tan q 33 0

(B)

30

60

90 0

30 60 90 0 Angle Effective k33 vibration

30

60

90

FIG. 17.44

Polarization angle dependence of intensive and extensive dielectric, elastic, and piezoelectric losses.

with hard PZTs. The maximum power densities (defined by 20°C temperature rise) of different high-powered piezoelectric transformers are shown in Table 17.6.47,48 In recent years, the Generation III Pb(In1/3Nb2/3)O3 (PIN) -PMN-PT single crystals have been developed, which have higher coercivity and Curie temperature than PMN-PT.49 Moreover, the highpower characteristics were measured in the ICAT, Penn State University, as shown in Fig. 17.46. High-power characteristics for the k31 mode 0.67PMN-0.33PT and 0.23PIN-0.5PMN-0.27PT samples with different crystal orientations were tested in terms of the maximum vibration (defined by 20°C temperature rise). According to the results, irrelevant to the composition, the Type B orientation ([011] plate with [100] length

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0.7 ‘Hard’ ceramic

Vibration velocity (m/s)

0.6 0.5 0.4 0.3 0.2

‘Soft’ ceramic

0.1

N

85 PC

ft’ A

T So

-P

T M

n-

PM

N

0

1] [0 1

1] [0 0

1] -P

T PM n-

In -

PM

N

-P N

-P

T

[0 1

1] [0 0

1] [0 1 T PM

N

-P In -

M

(A)

PM

H

ar

PM

d’

N

-P

AP

T

C

[0 0

84

1]

1

0

350

1 0.8

250 0.6

200

K31

Quality factor

300

150

0.4

QA Qm k31

100 50

0

(B)

N -P

[0

PM

-P T

PM N

PM

N

-P T

[0

01 ]

11 ]L T [1 [0 00 11 ] ] In L[ 0 In PM -1 -P 0] N M -P N T In PT [0 -P 01 [0 M 11 ] N -P ]L T [ 10 [0 0] 11 ]L M n [0 M -P -1 nM 0] PM N -P N M T P n[0 PM T [0 01 1 ] N 1] -P L[ T 10 [0 0] 11 ]L [0 -1 0]

0

0.2

FIG. 17.45 (A) Maximum vibration velocities of single crystals and ceramics (k31 mode). (B) Mechanical quality factors and electromechanical coupling factors for the k31 vibration mode.

direction) for the k31 vibration mode has the best high power performance   among the three. The type C orientation ([011] plate with 011 length direction) exhibited the second best performance, and the Type A orientation ([100] plate with [001] length direction) seems to show high losses. The ternary composition PIN-PMN-PT is better than the binary PMN-PT III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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Maximum vibration velocity (mm/s)

700

[100] [001] [010]

600

PMN-PT PIN-PMN-PT

500

(A)

400 [011]

300 [100]

[011]

200

(B)

100 0

[011]

A [011]

[100]

C

B Crystal orientation type

(C) FIG. 17.46

High-power characteristics for k31 mode 0.67PMN-0.33PT and 0.23PIN0.5PMN-0.27PT samples with different crystal orientations.

TABLE 17.6 Maximum Power Densities and Efficiencies, Mechanical Quality Factors, and Electromechanical Coupling Coefficients for Each Material (evaluated as a transformer)

Sample

Material

1

APC 841 hard PZT ceramic

2

PMN-PT L[100] w[010] t[001]   PMN-PT L 011 w[100] t[011]

3 4 5 6

Mn-PMN-PT L[100] w[010] t[001]   Mn-PMN-PT L[100] w 011 t[011]   Mn-PMN-PT L 011 w[100] t[011]

Maximum power density (W/cm3)

Maximum efficiency

Qm

k31

7.7

0.66

1100

0.30

1.1

0.33

150

0.40

11.8

0.86

150

0.88

5.2

0.88

250

0.50

30.1

0.96

320

0.6113

38.1

0.93

220

0.83

in the sense of quality factor, maximum vibration velocity, and heat generation. In contrast, crystal orientation dependence of the mechanical quality factor and dielectric loss of PMN-0.30PT crystals were reported by Zhang et al. on the k33 mode.50 According to the results in Table 17.7, for the rhombohedral relaxor-PT crystals, the lowest loss factor was found to be along their respective polar directions, with mechanical Qm values being >1000. Of particular significance is that both high electromechanical coupling ( 0.9) and large mechanical Qm 600) were achieved in [011] poled crystals. Further studies are requested for analyzing the crystal symmetry and polarization orientation dependence of the loss mechanisms. III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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TABLE 17.7 Mechanical Quality Factor and Dielectric Loss of PMN-0.30PT Crystals for Various Orientations Domain engineering

εr

tan δ

k33

d33 (pC/N)

SE33 (pm2/N)

[001]

4R

5200

0.004

0.90

1500

60.0

120

[011]

2R

4400

0.002

0.90

1050

35.9

600

[111]

1R

810

0.002

0.42

90

6.5

1130

Material PMN-0.30PT

Qm

17.7.3 Composition Dependence of Piezoelectric Losses 17.7.3.1 PZT-Based Ceramics “High power” in this article stands for “high power density” in mechanical output energy converted from the maximum input electrical energy under the drive condition with 20°C temperature rise. For an offresonance drive condition, the figure of merit of piezoactuators is given by the piezoelectric d constant (ΔL ¼ dEL). Heat generation can be evaluated by the intensive dielectric loss tan δʹ (i.e., P-E hysteresis). In contrast, for a resonance drive condition, the figure of merit is primarily the vibration velocity v0, which is roughly proportional to Qm dE. Qm can be considered as an amplification factor of the vibration amplitude and velocity. Heat generation is originated from the intensive elastic loss tan ϕʹ (inverse value of Qm). The mechanical power density can be evaluated by the square of the maximum vibration velocity (v20), which is a sort of material’s constant. Remember that there exists the maximum mechanical energy density, above which level does the piezoelectric material become a mere ceramic heater. High vibration velocity piezomaterials are suitable for actuator applications such as ultrasonic motors. Our primary target for the high-power density materials is set around v0 ¼ 0.8 m/s or 40 W/cm3 (of course higher is the better in the future), in comparison with the commercially available v0 ¼ 0.3 m/s or 5 W/cm3. Further, when we consider transformers and transducers, where both transmitting and receiving functions are required, the figure of merit will be the product of v0k (k: electromechanical coupling factor). Let us discuss high vibration velocity materials based on PZTs first. Fig. 17.47 shows the mechanical Qm versus basic composition x at two effective (RMS value) vibration velocities v0 ¼ 0.05 m/s and 0.5 m/s for Pb (ZrxTi1x)O3 doped with 2.1 at.% of Fe.50 The decrease in mechanical Qm with an increase of vibration level is minimum around the rhombohedral-tetragonal MPB (52/48). In other words, the smallest Qm material under a small vibration level becomes the highest Qm material under a large vibration level, which is very suggestive. The data obtained by a conventional impedance analyzer with a small voltage/power do not provide any information relevant to high power characteristics. The reader III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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2000

Vibration velocity v0 = 0.05 m/s v0 = 0.5 m/s

1000

600

400

200

0.48

0.50

0.52

0.54

0.56

Mechanical quality factor Qm

Mechanical quality factor Qm

Pb(ZrXTi1−X)O3 + 2.1 at% Fe

0.58

Mole fraction of Zr (x)

FIG. 17.47

Mechanical Qm versus basic composition x at two effective vibration velocities v0 ¼ 0.05 m/s and 0.5 m/s for Pb(ZrxTi1x)O3 doped with 2.1 at.% of Fe.

should notice that most of the materials with Qm > 1200 in a company catalog are degraded dramatically at an elevated power measurement. This is the major reason why our ICAT/Penn State group has been putting significant efforts on the HiPoCS system developments over the past 30 years. The conventional piezoceramics have the limitation in the maximum vibration velocity (vmax), since the additional input electrical energy is converted into heat, rather than into mechanical energy. The typical rms value of vmax for commercially available materials, defined by the temperature rise of 20°C from room temperature, is around 0.3 m/s for rectangular samples operating in the k31 mode (like a Rosen-type transformer).35 Pb(Mn,Sb)O3 (PMS)-lead zirconate tatanate (PZT) ceramics with the vmax of 0.62 m/s are currently used for NEC transformers.51 By doping the PMS-PZT or Pb(Mn,Nb)O3-PZT with rare-earth ions such as Yb, Eu, and Ce, we further developed high-power piezoelectrics, which can operate with vmax up to 1.0 m/s.52,53 Compared with commercially available piezoelectrics, 10 times (square of 3.3 times of v0) higher input electrical energy and output mechanical energy can be expected from these new materials without generating a significant temperature increase, which corresponds to 50 W/cm2. Fig. 17.48 shows the dependence of the maximum vibration velocity v0 (20°C temperature rise) on the atomic % of the rare-earth ion, Yb, Eu, or Ce in the Pb(Mn,Sb)O3 (PMS)—PZT-based ceramics. Enhancement in the v0 value is significant by the addition of a small amount of the rare-earth ion.54 The high-power

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17.7 LOSS MECHANISMS IN PIEZOELECTRICS

Maximum vibration velocity (m/s)

1.1 1.0 Yb

0.9

Eu

0.8 0.7

Ce 0.6 0.5 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Doping concentration (atom ratio)

FIG. 17.48 Dependence of the maximum vibration velocity v0 (20°C temperature rise) on the atomic % of rare-earth ion, Yb, Eu, or Ce in the Pb(Mn,Sb)O3 (PMS)—PZT based ceramics.52

performance improvement by doping will be discussed in Section 17.7.4 from the mechanism’s viewpoint. 17.7.3.2 Pb-Free Piezoelectrics The twenty-first century is called the “century of environmental management.” In 2006, the European community started RoHS (restrictions on the use of certain Hazardous Substances), which explicitly limits the usage of lead (Pb) in electronic equipment. Basically, we may need to regulate the usage of lead zirconate titanate (PZT), the most famous piezoelectric ceramic, in consumer products. The Japanese and European communities may experience governmental regulations on PZT usage in the next 5 years. Pb (lead)-free piezoceramics were beginning to be developed after 1999, and they are classified into three types: (Bi,Na)TiO3 (BNT),55 (Na,K)NbO3 (NKN),56 and tungsten bronze (TB).57 NKN systems exhibit the highest performance because of the MPB usage and, in particular, in structured ceramic manufacturing with flaky powders. TB types are another alternative choice for resonance applications, because of a high Curie temperature and low loss. A sophisticated preparation technology for fabricating oriented ceramics was developed with a multilayer configuration—that is, preparation under strong magnetic field.57 Though there is a lot of research related with lead-free piezoelectric materials, there is little research on high-power characterization of the lead-free piezoelectric materials. The ICAT’s study enlightened the high power characteristics of Pb-free piezoelectric ceramic compared to hard lead-zirconate-titanate (PZT). Though the RoHS regulation is the trigger

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of the Pb-free piezoelectric development, if we find superior performance in Pb-free piezoelectrics, this new material category may contribute significantly to industrial and military applications. High power characteristics were investigated with our high power piezoelectric characterization system (HiPoCS).58,59 Tested samples were prepared in collaboration with Toyota R&D, Honda Electronics, Korea University, and Rutgers University, including the following: (1) NKN—(Na0.5K0.5)(Nb0.97Sb0.03)O3 prepared with 1.5 mol% CuO addition. (2) BNT-BT-BNMN—0.82(Bi0.5Na0.5)TiO3-0.15BaTiO3-0.03(Bi0.5Na0.5) (Mn1/3Nb2/3)O3. (3) BNKLT—0.88(Bi0.5Na0.5)TiO3–0.08(Bi0.5K0.5)TiO3–0.04(Bi0.5Li0.5)TiO3 with Mn-doped and -undoped. Fig. 17.49 shows the high-power results for a disk sample. The mechanical quality factors at resonance (QA) and at antiresonance (QB) do not decrease with increasing vibration level [mechanical energy density  1 2 ] in Pb-free piezoelectrics, in comparison with the PZT trend. ρv 2 rms It is worth noting that the vibration velocity (vrms) reaches 0.8 m/s in all three Pb-free compositions, but a low mass density can easilygenerate  1 2 ρv large vibration velocity. Therefore, mechanical energy density 2 rms should be used in order to compare the performance superiority in terms of the maximum vibration level of the materials. The maximum mechanical energy density defined with a 20°C increase of the temperature on the nodal point in NKN and BNT-BT-BNMN is superior, when compared to hard-PZTs with their sharp decrease in QA with the increasing vibration level. At antiresonance, the high-power behavior trend for this material did not change. The mechanical quality factor at the antiresonance (QB) also remained constant up to the maximum vibration level. Regarding the figure of merit (actual vibration level, Qm  kp) change with the vibration level, the PZT shows better performance in the low power vibration range, because of the higher kp value in PZT. However, in the high power range (>1000 J/m3), only Pb-free piezoelectrics can practically be adopted. The QA and QB values in Pb-free piezoelectrics are almost the same up to maximum vibration velocity, vmax. This trend is also distinctly different from the hard PZT, where QB is always greater than QA, experimentally (depending on the piezoelectric loss). Comparison of mechanical quality factors at resonance (QA) and antiresonance (QB) provides an aspect to the material losses [i.e., dielectric (tan δʹ), mechanical (tan ϕʹ), and piezoelectric (tan θʹ)] behavior for each different composition. Both soft and hard PZTs result in QB > QA, as we already discussed. While, regarding the Pb-free piezoelectrics, hard Bi-perovskite ceramics

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17.7 LOSS MECHANISMS IN PIEZOELECTRICS

200 ΔTA (°C)

Mechanical quality factor (QA)

2000

35 30 25 20 15 10 5 0 2

20

200

NKN-Cu BNT-BT-BNMN BNKLT-Mn BNKLT Hard-PZT

2000

Mechanical energy density (J/m3)

20

2

20

(A)

2000

200 3

Mechanical energy density (J/m )

30 25

200

ΔTB (°C)

Mechanical quality factor (QB)

2000

20 15

NKN-Cu BNT-BT-BNMN BNKLT-Mn BNKLT Hard-PZT

10 5 0 2

20

200

2000

Mechanical energy density (J/m3)

20

(B)

2

20

200

2000 3

Mechanical energy density (J/m )

FIG. 17.49

Temperature rise and mechanical quality factors for (A) resonance (ΔTA and QA) and (B) antiresonance (ΔTB and QB) as functions of mechanical energy density (umech ρv2rms) for lead-free and hard-PZT piezoelectric ceramics.

(i.e., BNT-BKT-BLT-Mn and BNT-BT-BNMN) seem to be minimally influenced by the piezoelectric loss (tan θʹ) when excited at high vibration levels since they showed the QA > QB relationship. Cu-doped NKN ceramics seem to be more impacted (QA ffi QB for NKN-Cu) by the piezoelectric loss (tan θʹ). Softer BNT-BKT-BLT ceramics seem to be influenced the most (QB > QA for BNT-BKT-BLT) similar to the hard PZT (QB > QA for hard-PZT) at high power levels. We present here rough but intuitive domain reorientation atomic models for explaining the difference of the piezoelectric loss contribution

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0.47Å 0.061 A Ti4+

O2−

Ba2+

0.30 Å Ti

Ti4+

O2−

Ba2+ 0.12 A

c

c

a

a Pb

PbTiO3 FIG. 17.50

0.036 A

BaTiO3

Crystal structures of PbTiO3 and BaTiO3.

among Pb-based and Pb-free piezoceramics. Fig. 17.50 shows the crystal structure of PbTiO3 and BaTiO3. The spontaneous polarization is primarily contributed by perovskite A-ion (Pb) shift in PbTiO3, while the B-ion (Ti) shift is the largest contribution in BaTiO3, due to anisotropic large ionic polarizability of Pb2+ ion (Ba2+ has a spherical and closed electron shell). If we illustrate 90° domain wall models for both A-ion shift and B-ion shift spontaneous polarization materials, Fig. 17.51 may be obtained.

“Head-to-Head”

“Head-to-Head”

(A)

A-ion shift model

(B)

B-ion shift model

FIG. 17.51 Domain reorientation atomic models for explaining the piezoelectric loss. (A) A-ion shift model and (B) B-ion shift model.

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17.7 LOSS MECHANISMS IN PIEZOELECTRICS

As we discussed in Fig. 17.40, the piezoelectric loss may be originated from Gauss’ Law, div (D) ¼ σ (charge). That means the piezoelectric loss is a measure of the polarization alignment easiness from the head-to-head or tail-to-tail to the head-to-tail. In the perovskite A-ion model piezoelectric, large size A-ions need to move largely with distorting the crystal frame during this reorientation process, which seems to require higher energy, leading to a large piezoelectric loss tan θ. In the B-ion model piezoelectric, the small-sized B-ion can easily move in a relatively large “rattling” space in a solid frame created by A-ions. This explains the large piezoelectric loss factor contribution in PZT and the small contribution in Pb-free piezoelectrics.

17.7.4 Doping Effect on Piezoelectric Losses 17.7.4.1 Hard and Soft PZTs Small amounts of dopants sometimes dramatically change the dielectric and electromechanical properties of ceramics. Donor doping tends to facilitate domain wall motion, leading to enhanced piezoelectric charge coefficients, d, and electromechanical coupling factors, k, producing what is referred to as a soft piezoelectric. Acceptor doping, on the other hand, tends to pin domain walls and impeding their motion, leading to an enhanced mechanical quality factor, Qm, producing what is called a hard piezoelectric. Table 17.8 summarizes the advantages and disadvantages of soft and hard piezoelectrics and compares their characteristics with an electrostrictive material, Pb(Mg1/3Nb2/3)O3 (PMN). The electrostrictive ceramic is commonly used for positioning devices where hysteresis-free performance is a primary concern. However, due to their high permittivity, the electrostrictive devices are generally used only for applications that require slower response times. On the other hand, the soft piezoelectric materials with their relatively low permittivity and high piezoelectric charge coefficients, d, can be used TABLE 17.8 Advantages (+) and Disadvantages () of Soft and Hard Piezoelectrics, Compared With the Features of an Electrostrictive Material, Pb(Mg1/3Nb2/3)O3 (PMN) Off-Resonance Applications

Resonance Applications

Low (DC Bias)

High displacement+ No hysteresis+

Broad bandwidth+

High+

Low

High displacement+

Heat generation

Low

High+

Low strain

High AC displacement+

Material

d

k

Qm

PMN

High+ (DC Bias)

High+ (DC Bias)

Soft PZT-5H

High+

Hard PZT-8

Low

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for applications requiring a quick response time, such as pulse-driven devices like inkjet printers. Soft piezoelectrics generate a significant amount of heat when driven at resonance, however, due to their small mechanical quality factor, Qm. Thus, for ultrasonic motor applications, hard piezoelectrics with a larger mechanical quality factor are preferred despite the slight sacrifices incurred with respect to their smaller piezoelectric strain coefficients, d, and the electromechanical coupling factors, k. Let us consider the crystallographic defects produced on the perovskite lattice due to doping. Acceptor ions, such as Fe3+, lead to the formation of oxygen deficiencies (□) in the PZT lattice (from charge neutrality), and the resulting defect structure is described by the following:    Pb Zry Ti1yx Fex O3x=2 □x=2 Acceptor doping allows for the easy reorientation of deficiency-related dipoles. These dipoles are composed of an Fe3+ ion (effectively the negative charge because it is situated in the 4 + Ti site) and an oxygen vacancy (effectively the positive charge). The oxygen deficiencies are produced at a high temperature (> 1000°C) during sintering, but the oxygen ions are still able to migrate at temperatures well below the Curie temperature (even at room temperature), because the oxygen and its associated vacancy are ˚ apart and the oxygen can readily move into the vacant site, only 2.8 A as depicted in Fig. 17.52A. In the case of donor dopant ions, such as Nb5+, a Pb deficiency is produced and the resulting defect structure is designated by the following:    Pb1x=2 □x=2 Zry Ti1yx Nbx O3 : Donor doping is not very effective in generating movable dipoles, since the Pb ion cannot easily move to an adjacent A-site vacancy due to the proximity of the surrounding oxygen ions as depicted in Fig. 17.52B. Soft characteristics are, therefore, observed for donor-doped materials. Another factor that should be considered here is that lead-based perovskites, such as PZT, tend to be p-type semiconductors due to the evaporation of lead during sintering and are thus already hardened to some extent A vacancy

O vacancy

Easy to move

Prohibited

3+

(A) FIG. 17.52

5+

(B) Lattice vacancies in PZT containing (A) acceptor and (B) donor dopants.

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P

+ −

−

E

+

+

+ −

− +

+ −

P

+ − + Ebias −

+ −

+ −

P

E

(A)

+ −

Ebias

(B)

+ −

+ −

+ −

+ −

P

E

E

(C)

FIG. 17.53

Impurity dipole alignment possibility and the expected P vs. E hysteresis curves: (A) random alignment, (B) unidirectionally fixed alignment, and (C) unidirectionally reversible alignment.

by the lead vacancies that are produced. Hence, donor-doping will compensate the p-type, then they exhibit large piezoelectric charge coefficients, d, but they will also exhibit pronounced aging due to their soft characteristics. There are three types of the impurity dipole (originated from a pair of the acceptor ion and oxygen vacancy) alignment possibilities as schematically visualized in Fig. 17.53: (a) random alignment, (b) unidirectionally fixed alignment, and (c) unidirectionally reversible alignment. Accordingly, the expected polarization versus electric hysteresis curve will be (a) high coercive field P-E loop in comparison with that of the original undoped ferroelectric, (b) DC bias field P-E loop, and (c) double hysteresis loop. 17.7.4.2 Dipole Random Alignment The soft and hard characteristics are reflected in the coercive field Ec, or more precisely in the stability of the domain walls. A piezoelectric is classified as hard if it has a coercive field greater than 1 kV/mm, and it is classified as soft, if the coercive field is less than 1 kV/mm. Consider the transient state of a 180° domain reversal that occurs at a domain wall associated with a configuration of head-to-head polar domains. We know from Gauss’ law that: div D ¼ ρ,

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(17.144)

732

17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

− Ps

Ps

− Ps

Ps

Stable

Easy to move

(A)

E

(B)

E

FIG. 17.54 Stability of 180° domain wall motion in: (A) an insulating material and (B) a material with free charges.

where D is the electric displacement and ρ is the charge density. The domain wall is very unstable in a highly insulating material and therefore readily reoriented and the coercive field for such a material is found to be low. However, this head-to-head configuration is stabilized in a more conductive (some movable charges) material; thus a higher coercive field is required for polarization reversal and the associated domain wall movement to occur. These two cases are illustrated schematically in Fig. 17.54. As we explained above, the free charges associated with defect structures are present in a doped PZT material. The presence of acceptor dopants, such as Fe3+, in the perovskite structure is found to produce oxygen deficiencies, while donor dopants, such as Nb5+, produce A-site deficiencies. Only the acceptor doping generates movable dipoles, which correspond to ρ and can stabilize the domain walls. These simple defect models help us to understand and explain various changes in the properties of a perovskite ferroelectric of this type that occur with doping. The effect of donor doping in PZT on the field-induced strain response of the material was examined for the soft piezoelectric composition (Pb0.73Ba0.27)(Zr0.75Ti0.25)O3.60 The parameters maximum strain, xmax, and the degree of hysteresis, Δx/xmax, are defined in terms of the hysteresis response depicted in Fig. 17.55A. The maximum strain, xmax, is induced under the maximum applied electric field. The degree of hysteresis, Δx/xmax, is just the ratio of the strain induced by half the maximum applied electric field to the maximum strain, xmax. The effect of acceptor and donor dopants (2 at.% concentration) on the induced strain and degree of hysteresis is shown in Fig. 17.55B. It is seen that materials incorporating high valence donor-type ions on the B-site (such as Ta5+, Nb5+, W6+) exhibit excellent characteristics as positioning actuators, namely, enhanced induced strains and reduced hysteresis. On the other hand, the low valence acceptor-type ions (+1, +2, +3) tend to suppress the strain and increase the hysteresis and the coercive field. Although acceptor-type dopants are not desirable when designing actuator ceramics for positioner applications, acceptor doping is important in producing

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10

2

xmax

3 Dx

Strain (× 10−4)

4

Emax Emax/2

1 0

(A)

0.5 Electric field

Maximum strain (1 kV/mm) xmax (× 10−4)

9

5

+1~+3 8 Th 7 Y 6 W

5

Undoped

Group B

Mg

Group C

3 2

Yb Er

Pr La

1

Na Zn

Cr B

Fe 0

(B)

Ta Nb

4

0

1.0

+4~+6 Rare earth

Group A

25 50 Hysteresis Δx/xmax (%)

FIG. 17.55

Maximum strain and hysteresis in Pb0.73Ba0.27(Zr0.75Ti0.25)O3-based ceramics: (A) hysteresis curve showing the parameters needed for defining the maximum strain, xmax, and the degree of hysteresis, Δx/xmax and (B) the dopant effect on actuator parameters.60

hard piezoelectric ceramics, which are preferred for ultrasonic motor applications. In this case, the acceptor dopant acts to pin domain walls, resulting in the high mechanical quality factor characteristic of a hard piezoelectric. Let us now consider high-power piezoelectric ceramics for ultrasonic (AC drive) applications. When the ceramic is driven at a high vibration rate (that is, under a relatively large AC electric field) heat will be generated in the material resulting in significant degradation of its piezoelectric properties. A high-power device such as an ultrasonic motor therefore requires a very hard piezoelectric with a high mechanical quality factor, Qm, to reduce the amount of heat generated. The temperature rise (at the nodal point, i.e., plate center) in undoped, Nb-doped, and Fe-doped PZT k31 plate samples is plotted as a function of vibration velocity (rms value measured at the plate end) in Fig. 17.56.31 A significant reduction in the generation of heat is apparent for the Fe-doped (acceptor-doped) ceramic. Commercially available hard PZT ceramic plates tend to generate the maximum vibration velocity around 0.3 m/s (rms) when operated in a k31 mode. Even when operated under the higher applied electric field strengths, the vibration velocity will not increase for these devices; the additional energy is just converted into heat.

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Temperature rise DT (°C)

60 Undoped Pb(Zr0.54 Ti0.46)O3 0.5 wt% Nb-doped 40 0.5 wt% Fe-doped

20

0 0.01

0.1 0.05 Vibration velocity v0 (m/s)

0.5

1.0

FIG. 17.56 Temperature rise, ΔT, plotted as a function of effective vibration velocity, v0, for undoped, Nb-doped, and Fe-doped PZT samples.31

Higher maximum vibration velocities have been realized in PZT-based materials modified by dopants that effectively reduce the amount of heat generated in the material and thus allow for the higher rates of vibration. NEC, Japan developed multilayer piezoelectric transformers with the (1  z)Pb(ZrxTi1x)O3-(z)Pb(Mn1/3Sb2/3)O3 composition.61 The maximum vibration velocity of 0.62 m/s occurs at the x ¼ 0.47, z ¼ 0.05 composition and is accompanied by a 40°C temperature rise from room temperature. The incorporation of additional rare-earth dopants to this optimum base composition results in an increase in the maximum vibration velocity to 0.9 m/s at 20°C temperature rise, already introduced in Fig. 17.48.52 This increased vibration rate represents a threefold enhancement over what is typically achieved by commercially produced hard PZT devices and corresponds to an increase in the vibration energy density by an order of magnitude with minimal heat generated in the device. The mechanism of this stable high power performance is explained in the next section.

17.7.4.3 Unidirectionally Fixed Dipole Alignment Hard PZT is usually used for high-power piezoelectric applications, because of its high coercive field, in other words, the stability of the domain walls. Acceptor ions, such as Fe3+, introduce oxygen deficiencies in the PZT crystal (in the case of donor ions, such as Nb5+, Pb deficiency is introduced). Thus, in the conventional model, the acceptor doping causes “domain wall pinning” through the easy reorientation of deficiency-related dipoles, leading to hard characteristics (domain wall pinning model [Ref. 23]). ICAT/Penn State University explored the origin of our high power piezoelectric ceramics, and they found that the “internal bias field model” seems to be better for explaining our material’s characteristics. III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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2000 1800 1600

PZT-PSM-Yb PZT-PSM Hard PZT Soft PZT

1400 Qm

1200 1000 800 600 400 200 0 10

100 Time (min)

1000

FIG. 17.57

Change in the mechanical Qm with time lapse (minute) just after the electric poling, measured for various commercial soft and hard PZTs, PSM-PZT, and PSM-PZT doped with Yb.62

High mechanical Qm is essential in order to obtain a high-power material with a large maximum vibration velocity. Fig. 17.57 exhibits suggestive results in the mechanical Qm increase with a time lapse (minute) after the electric poling, measured for various commercial soft and hard PZTs, PSM-PZT, and PSM-PZT doped with Yb.54,62 It is worth noting that the Qm values for commercial hard PZT and our high-power piezoelectrics were almost the same, slightly higher than soft PZTs, and around 200–300 immediately after the poling. After a couple of hours passed, the Qm values increased more than 1000 for the hard materials, while no change was observed in the soft material. The increasing slope is the maximum for the Yb-doped PSM-PZT. We also found a contradiction that this gradual increase (in a couple of hours) in the Qm cannot be explained by the abovementioned domain wall pinning model, in which it is hypothesized that the oxygen-deficit-related dipole should move rather quickly on a millisecond scale. Fig. 17.58 shows the polarization vs. electric field hysteresis curves measured for the Yb-doped Pb(Mn,Sb)O3—PZT sample immediately after poling (fresh), 48 h after, and a week after (aged).63,64 Remarkable aging effects could be observed: (a) in the decrease in the magnitude of the remnant polarization and (b) in the positive internal bias electric field growth (i.e., the hysteresis curve shift leftwards with respect to the external electric field axis). The phenomenon (a) can be explained by the local domain wall pinning effect, but the large internal bias (close to 1 kV/mm) growth (b) seems to be the origin of the high-power characteristics. Suppose that III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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0.3

Polarization (C/m2)

0.2 0.1 0.0 −0.1 PZT-PSM-Yb Fresh PZT-PSM-Yb 48 hr PZT-PSM-Yb Aged

−0.2 −0.3 −40

−30

−20

−10 0 10 20 Electric field (kV/cm)

30

40

FIG. 17.58 Polarization vs. electric field hysteresis curves measured for the Yb-doped Pb(Mn,Sb)O3-PZT sample just after poling (fresh), 48 hours after, and a week after (aged).

the vertical axis in Fig. 17.41 (Uchida-Ikeda domain reorientation model) shifts rightwards (according to 1 kV/mm positive internal bias field): the larger negative electric field is required for realizing the 180° polarization reversal, leading to the resistance enhancement against generating the hysteresis or heat with increasing the applied AC voltage. Finally, let us propose the origin of this “internal bias field” growth. Based on the presence of the oxygen deficiencies and the relatively slow (a couple of hours) growth rate, we assume here the oxygen deficiency diffusion model, which is illustrated in Fig. 17.59.63,64 Under the electric poling process, the defect dipole Pdefect (a pair of acceptor ion and oxygen

Diffusion

Pdefect

PS Pdefect Acceptor

EB

FIG. 17.59 Oxygen deficiency diffusion model for explaining the internal bias electric field growth.63,64

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deficiency) will be arranged parallel to the external electric field. After removing the field, the oxygen diffusion occurs, which can be estimated in a scale of hour at room temperature. Taking into account slightly different atomic distances between the A and B ions in the perovskite crystal in a ferroelectric (asymmetric) phase, the oxygen diffusion probability will be slightly higher for the downward, as shown in the figure schematically, leading to the increase in the defect dipole with time. This may be the origin of the internal bias electric field. You can easily understand that the dipole alignment is unidirectionally fixed along the polarization direction. 17.7.4.4 Unidirectionally Reversible Dipole Alignment Tan and Viehland reported a double hysteresis in K-doped PZT ceramics (PKZT).65 Fig. 17.60A shows a P-E hysteresis curved observed in an aged sample of 4 at.% doped Pb(Zr0.65T0.35)O3. Probably due to

FIG. 17.60

(A) Room temperature P-E hysteresis curve observed in an aged 4 at.% doped Pb(Zr0.65T0.35)O3. (B) The P-E hysteresis at 350°C.65

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the unidirectionally (along the spontaneous polarization direction) switchable impurity dipole, though the hysteresis curve is symmetry (no internal DC bias field), the polarization is pinched around E ¼ 0. However, with increasing the temperature, this pinching curve was released to the normal high coercive field hysteresis. 150°C is reported to be the temperature near which mobile defects begin to move to be a random alignment.

17.7.5 Grain Size Effect on Hysteresis and Losses To understand the grain size dependence of the piezoelectric properties, we must consider two size regions: the μm range in which a multiple domain state becomes a mono-domain state and the sub-μm range in which the ferroelectricity becomes destabilized. We will primarily discuss the former region in this manuscript. Fig. 17.61A shows the transverse field-induced strains of 0.8 at.% Dy-doped fine grain ceramic BaTiO3 (grain diameter around 1.5 μm) and of the undoped coarse grain ceramic (50 μm), as reported by Yamaji et al.66 As the grains become finer, under the same electric field, the absolute value of the strain decreases and the hysteresis becomes smaller. This is explained by the increase in the coercive field for 90° domain rotation with decreasing grain size. The grain boundaries (with many dislocations on the grain boundary) “pin” the domain walls and do not allow them to move easily. Also the decrease of grain size seems to make the phase transition of the crystal much more −4 1 × 10

Electric field (kV/mm) –1.5

–1.0

–0.5

0.5

1.0

1.5

0.8 at.% Dy doped BaTiO3 ceramic Longitudinal strain x3 (× 10−4)

20

–2

–3

(A)

Transverse strain x1

–1

Undoped BaTiO3 ceramic

−15

(B)

−7.5

Grain size D = 4.5 μm D = 2.4

16

12

D = 1.1

8

4

15 0 7.5 Applied field (kV/cm)

FIG. 17.61

(A) Electric field-induced strain curves in Dy-doped and undoped BaTiO3 ceramic samples.66 (B) Grain size dependence of the induced strain in PLZT ceramics.67

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diffuse. Although the effective value of d33 decreases in the Dy-doped sample, the temperature dependence is remarkably improved for practical applications. It should be noted that Yamaji’s experiment cannot separate the effect due to intrinsic grain size from that due to dopants. Uchino and Takasu studied the effects of grain size on PLZT.67 We obtained PLZT (9/65/35) powders by coprecipitation. Various grain sizes were prepared by hot-pressing and by changing sintering periods, without using any dopants. PLZT (9/65/35) shows significant dielectric relaxation (frequency dependence of the permittivity) below the Curie point of about 80°C, and the dielectric constant tends to be higher at lower frequency. We prepared various grain size samples in the range of 1–5 μm. For a grain size larger than 1.7 μm, the dielectric constant decreases with the decreasing grain size. Below 1.7 μm, the dielectric constant increases rapidly. Fig. 17.61B shows the dependence of the longitudinal fieldinduced strain on the grain size. As the grain size becomes smaller, the maximum strain decreases monotonically. However, when the grain size becomes less than 1.7 μm, the hysteresis is reduced. This behavior can be explained as follows: with decreasing grain size, (anti)ferroelectric (ferroelastic) domain walls become difficult to form in the grain, and the domain reorientation contribution to the strain becomes smaller (multidomain monodomain transition model). The critical size is about 1.7 μm. However, note that the domain size is not constant, but it is dependent on the grain size; also, in general the domain size decreases with decreasing grain size. Sakaki et al. studied the grain size effect on high-power performance, from a practical device application viewpoint.68 The vibration velocity versus the temperature rise was investigated for various grain size soft Nb-doped PZTs from 0.9 to 3 μm. For two different grain sizes, 0.9 and 3.0 μm indicate that a higher maximum velocity of about 0.40 m/s is observed for the 0.9 μm-grain ceramic than that of the 3.0 μm-grain ceramic (0.30 m/s). Furthermore, the temperature rise for the fine grain ceramic is observed to be about 40% lower than the coarse grain ceramic near the maximum vibration velocity (0.30 m/s). This trend has suggested that a higher vibration velocity and lower heat generation can be achieved by reducing the grain size, which has been confirmed by investigating the heat generation phenomenon as a function of the grain size at various vibration velocities, and the observed trend is shown in Fig. 17.62. A linear trend in heat generation can been found with grain size. In addition, the slope of heat generation is found to increase with an increment of the vibration velocity. This in turn suggested effective control over heat generation with the lowering grain size of ceramic. It is known that an Nb-doped PZT with a molecular formula (Pb1-y/2□y/2) (ZrxTi1xyNby)O3 is free of oxygen vacancies; hence, the movable space charge or impurity dipole may not be observed in this material. Thus, it is apparent that the increment of the mechanical quality factor (Qm) with

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

Temperature rise (°C)

80

60

Vibration velocity 0.30 m/s

40 0.25 m/s 20

0.20 m/s 0.10 m/s

0 0.5

1.0

1.5 2.0 2.5 Grain size (μm)

3.0

3.5

FIG. 17.62 Grain size dependence of the temperature rise of the specimen for various vibration velocities. Note that the heat generation is suppressed with reducing the grain size.68

reducing the grain size is not caused by the space charge effect of oxygen vacancies. Instead, it is caused by the grain size effect. The origin of such an effect is speculated due to the following reasons: (1) The change in the configuration of the domain structure. (2) The pinning effect by the grain boundaries with reduction in the grain size (i.e., grain boundaries contribute as additional pining points).

17.7.6 Extended Rayleigh Law Approach The introduction of the complex parameters into dielectric permittivity, elastic compliance, and piezoelectric constant, as described in Eqs. (17.3), (17.4), (17.5), merely means a slight time lag of the extensive parameters D or x from the intensive E or X, with no particular insight into domain reorientations. The introduction of “j” generates the flat elliptical shape hysteresis automatically with a rounded curve at the maximum (or minimum) electric field or stress range, which shows a discrepancy from the actual hysteresis curve with a sharp kink at the end points (see Fig. 17.1). We will construct domain-dynamics models to explain high-power piezoelectric performances. Ferromagnetic materials have domains of uniform spin/dipole orientation and behave similarly to ferroelectric materials under application of an external magnetic field. Under external fields, the domain in ferromagnetic materials can switch polarity. These materials also have intrinsic and extrinsic contributions to their properties. Based on principles of domain wall motion under an external field, the change in material properties

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741

due to reorientation of domain walls with increasing amplitude driving yields the relationship known as the Rayleigh law. Originally derived for ferromagnetic materials, researchers have applied its premises to ferroelectric materials under external stresses and electrical fields with success.69,70 17.7.6.1 Conventional Rayleigh Law The Rayleigh law has become a successful analysis tool to describe the change of material properties in ferroelectric materials with driving amplitude. However, its application has solely been toward off-resonance measurements, mostly at low power. The work at ICAT/Penn State University developed the Rayleigh law into a tool to analyze-high power resonance properties of piezoelectric materials.71 Preliminary analysis on 0 the elastic properties (sE11 and tan ϕ11) has been done on the k31 mode plate, taking into account both reversible and irreversible domain wall motions, to introduce Rayliegh coefficent αX accordingly. In order to apply the Rayleigh law to resonance measurements, a new derivation must be performed to account for the energy distribution in resonating k31 plate samples. The derivation is summarized here. First, the elastic energy of a resonating sample (k31) with length L is derived as 1 π 2 ðu0, 1 : displacement at the endÞ (17.145) ue ¼ E u0,1 L 4s11 Then the energy lost due to elastic losses is defined according to the loss tangent and stored energy: we ¼ 2πue tan ϕ011 :

(17.146)

Next, the Rayleigh law is defined in terms of RMS stress, due to the stress variation in the sample: sE11 ¼ sE11,i + αX X1,RMS ,   @u1  E αX  2 X1,RMS  X12 , ¼ s11,i + αX X1,RMS X1,RMS @x1 2

(17.147) (17.148)

@u1 ) curve is com@x1 posed of two parabolic curves with sharp kinks at the maximum stress points, closer to the actually observed loop. Integrating the area in the parabolic hysteresis defined by the Rayleigh law (Fig. 17.63), the energy lost according to αX is   αx π 3 we ¼ pffiffiffi u0, 1 E : (17.149) Ls11 3 2

where αX is the Rayleigh coefficient. Note that the strain (

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

742

17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

Xmax

a x(X ) = (SEinit + axXmax)Xmax ± —x (X 2max − X 2) 2

x

0

E x(x) = (Sinit + axXmax)X

−Xmax –Xmax

0

Xmax

X

FIG. 17.63

Rayleigh law for elastic response of a ferroelectric material.

Combining these equations, the relationship between the Rayliegh coefficent αX and the elastic loss tangent is derived:  2 2αx 1 0 tan ϕ11 ¼ pffiffiffi u0, 1 E : (17.150) s11 3L 2 Using this formulation it is possible to verify the relationship between the Rayliegh coefficent αX and the loss tangent, thus verifying the applicability of the Rayleigh law. 17.7.6.2 Application of Hyperbolic Rayleigh Law The hyperbolic Rayleigh law introduces nonlinearity in the Rayleigh law formulation based on a domain wall dynamics perspective. This model was introduced by Borderon,72 but here it is extended toward elastic measurement in high-power conditions. Additionally, the significance of the model’s parameters is elucidated by the work of ICAT (see Fig. 17.35, Sample PIC 144). The hyperbolic Rayleigh law introduces nonlinearity in the pre-threshold stress region; this is essential to describe the behavior seen in the hard PZT material. The previous representation of the Rayleigh law is only true for a larger stress level than the threshold stress Xth. If the stress is lower than this, domain wall vibrations will provide the majority of the extrinsic response. Thus, the elastic compliance remains relatively constant as a function of applied stress. The threshold stress Xth is a measure of the degree of pinning in the material; this stress does not show a clearly defined feature, where sometimes only the linear and the high field region can be realized under electric fields that are experimentally considered. Without the hyperbolic Rayleigh law, the threshold level is usually determined by inspection, which may lead to a large error in its reported value, and therefore a large error in analysis of microstructure properties. This threshold stress level may be related with the

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

743

17.7 LOSS MECHANISMS IN PIEZOELECTRICS 1.3 × 10−11 Hyperbolic Rayliegh law

SE = srl + (SEr –rev)2 + (axX )2 E

S E

=S

rl

+a

E

X

x

E

S (0) = Srl + Sr –rev

SE = SrlE + SrE–rev

Elastic compliance, SE11 (m2/N)

Elat. comp. S E

1.25 × 10−11 1.2 × 10−11 1.15 × 0−11 1.1 × 10−11 1.05 × 10−11

E Srl

(A)

Xth = SrE–rev/ax

10−11 0 Stress X

(B)

X1,th

5M

10 M

15 M

20 M 25 M

RMS stress, X1,RMS (Pa)

FIG. 17.64

(A) Hyperbolic Rayleigh law—illustrated parameter relationships; (B) Hyperbolic fitting to change in elastic compliance with stress in hard PZT.

threshold vibration velocity in Fig. 17.35, below which the Qm value is rather constant and above which the Qm starts dramatic reduction. The hyperbolic is schematically represented in Fig. 17.64A. In large stress conditions, the threshold stress is passed and the traditional Rayleigh law can be applied. However, at low stress levels, apparent nonlinearity exists that cannot be modeled by the Rayleigh law, thus the hyperbolic Rayleigh law is introduced. Fig. 17.64B shows the change in elastic compliance with effective applied RMS stress for a hard PZT material. From the calculation of the threshold stress from the hyperbolic Rayleigh parameters, the threshold stress is larger than the largest stress level measured. The meaning of this is that hard PZT can practically only be driven in its pre-threshold region (i.e., reversible domain wall motion). This explains the discrepancies found by previous researchers in applying the Rayleigh law to nonlinear behavior below the threshold field.

17.7.7 DC Bias Field Effect on High-Power Characteristics Regarding the bias electric field effect, our previous reports62,64 clarified the stabilization mechanism of the high-power performance in hard Pb(Zr,Ti)O3 (PZT)-based ceramics in terms of the internal bias field, as discussed in Figs. 17.57 and 17.58. This section mainly focuses on the dependence of properties of the PZT k31-type plates under different vibration velocity conditions as a function of external DC bias field, by comparing the results among hard and soft PZTs. The goal is to clarify the DC bias field dependence of three losses (dielectric, elastic, and piezoelectric losses), which are primarily caused by semimicroscopic domain dynamics. Though Wang et al. reported on the “effect of the DC bias field on the complex materials coefficients of piezoelectric resonators,” they did not identify three losses separately.73 III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

TABLE 17.9 Change in Material Properties With Applied Positive DC Bias Field, in Comparison With Vibration Velocity74 Vibration velocity (per 0.l m/s)

Electric field (per 100 V/mm at 0.01 m/s)

Electric field (per 100 V/mm at 0.03 m/s)

% Change in material properties

Hard PZT

Soft PZT

Hard PZT

Soft PZT

Hard PZT

Soft PZT

Dielectric constant (εt33)

+2.9%

+5%

0.8%

1.7%

–

–

0 tan δ33

–

–

0.4%

1.5%

–

–

Elastic compliance (sE11)

+3%

+5%

0.7%

1.7%

1.7%

2.3%

0 tan φ11

+75%

(+) 0% & 75%

1.1%

2.4%

3.5%

4.2%

Piezoelectric constant (d31)

+2.7%

+5.1%

1%

1.5%

–

–

0 tan θ31

+70%

+20%

1.9%

3.1%

–

–

Electromechanical coupling factor (k31)

+3.5%

+5.3%

Change within error limits

Change within error limits

–

–

We provided the dependency of dielectric, elastic, and piezoelectric coefficients (real parameters and imaginary losses) on the vibration velocity and DC bias field comprehensibly.74 Note that as we drive the piezoelectric ceramic at a high vibration velocity, we are introducing AC stress in the material. Table 17.9 summarizes the material’s coefficients change with the vibration velocity and DC electric field. Using a burst mode, our results excluded any temperature rise during the measurements. It has been found that with the k31 mode vibration velocity increase, the dielectric constant, elastic compliance, piezoelectric coefficient, and their corresponding losses increase for both the hard and soft PZTs. However, the change is more pronounced in the soft PZT as compared to the hard PZT. In contrast, the influence of a DC bias field depends strongly on the direction of the field with respect to the original poling field. A positive DC bias electric field results in a decrease in the dielectric constant, elastic compliance, piezoelectric coefficient and their corresponding losses, whereas a negative DC bias field has the opposite effect. The decrease rate of these physical parameters under small vibration level is enhanced under large vibration level, as shown in the third column in Table 17.9. This situation can be visualized in the 3-D plot in Fig. 17.65, showing the dependence of elastic loss tan ϕʹ on the externally applied DC bias field and the vibration velocity at the k31 sample length edge in the III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

745

17.8 HIGH-POWER PIEZOELECTRICS FOR PRACTICAL APPLICATIONS

8

1.8

7

1.6

6 tanf′(¥10-2)

tanf′(¥10-3)

1.4 1.2

5 4

1.0

3

0.8

2

-200 -100

C D

C

D

-200 -100

0 0

0

c)

m/se

ity (m

eloc

nv ratio

30

0

20

0

(B)

0

10

0

300

15

200 50

0

(mm

25

100

) m /m V (k

0

s ia B

30 /sec)

0

0 ity

eloc

nv ratio

Vib

0

20

15

50

300

10

(A)

200 0

) m /m

V

(k

100

25

s ia

B

0

Vib

FIG. 17.65

3-D plot showing the variation of elastic loss for PZTs as a function of DC Bias field and vibration velocity for (A) hard PZT and (B) soft PZT.

hard (PIC 144) and soft (PIC 255) PZT. In comparison with a relatively smooth plane contour for the soft PZT, a clear bend on the contour plane is observed for the hard PZT. We can find the intensive elastic loss tan ϕʹ shows two different trends under vibration velocity and DC bias field: there is an increase with the vibration velocity (domain wall destabilization) and a decrease with a positive DC bias field (domain wall stabilization). Roughly speaking, the vibration velocity of 100 mm/s (+3% and 5% change in sE11 for the hard and soft PZT’s) exhibits the almost equivalent “opposite” change rate (–1.7%  2 and –2.3%  2 change in sE11 for the hard and soft PZTs) of a 200 V/m DC electric field. Another noteworthy point is the two-step mechanisms observed in Fig. 17.65A in the hard PZT: a bend of the slope can be observed in the elastic loss tan ϕʹ on the vibration velocity change, while a bend of the slope in the dielectric constant εX 33 and dielectric loss tan δʹ is observed on the DC bias field change. This may suggest a sort of threshold value in terms of mechanical stress or electrical field in the hard PZT for stabilizing/destabilizing the domain wall motions. This may suggest a sort of domain stabilization threshold, and the detailed analysis is required.

17.8 HIGH-POWER PIEZOELECTRICS FOR PRACTICAL APPLICATIONS 17.8.1 Low Temperature Sinterable “Hard” PZT Though we have developed “high power density” piezoelectric ceramics, multilayer structure and/or cofiring are the keys to developing actual high power components from the device design viewpoint. III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

However, the present Ag-Pd electrode structure includes two problems: (1) Pd is expensive and (2) although Ag migration during sintering and under electric field applied can be suppressed by Pd, the electrode conductance is significantly decreased with Pd content. The latter is the major problem in designing multilayer ultrasonic motors and transformers, because the electrode loss appears to be large, leading to heat generation and low efficiency. In order to solve the problems, a pure Cu or pure Ag electrode is a key. But the multilayer samples need to be sintered at a relatively low temperature (900°C or lower) in a reduced atmosphere, when utilizing Cu embedded electrodes. Thus, low temperature sintering of hard-type PZT’s is a necessary technology to be developed. Unlike soft PZTs, most of the conventional dopants to decrease the sintering temperature have not been used, because these dopants also degrade the Qm value significantly. Based on our high-power piezoelectric ceramics, the Sb, Li, and Mn-substituted 0.8Pb(Zr0.5Ti0.5)O3-0.16Pb(Zn1/3Nb2/3)O3-0.04Pb(Ni1/3 Nb2/3)O3, we further modified them by adding CuO and Bi2O3 in order to lower the sintering temperature of the ceramics.75,76 Table 17.10 summarizes piezoelectric properties of semihard piezoelectric ceramics based on Pb(Zn1/3Nb2/3)O3-Pb(Ni1/3Nb2/3)O3-Pb(Zr0.5Ti0.5)O3, sinterable at 900°C. Under a sintering condition of 900°C for 2 h, the properties were as follows: kp ¼ 0.56, Qm (31-mode) ¼ 1023, d33 ¼ 294 pC/N, ε33/εo ¼ 1326 and tan δ ¼ 0.59%, when CuO and Bi2O3 were added 0.5 wt.% each. The maximum vibration velocity of this composition was 0.41 m/s. Fig. 17.66 shows the maximum vibration velocity versus applied field change with various amounts of CuO. Note that with increasing CuO content (0.4 wt.% or higher) only 6–8 Vrms/mm is required for obtaining the v0 ¼ 0.48 m/s. The composition 0.8Pb(ZrdTi1d)O3-0.2Pb[(1  c){(1  b) (Zn0.8 Ni0.2)1/3 (Nb1aSba)2/3  b (Li1/4(Nb1a Sba)3/4)}  c (Mn1/3 (Nb1aSba)2/3)]O3 (a ¼ 0.1, b ¼ 0.3, c ¼ 0.3 and d ¼ 0.5) showed the value of kp ¼ 0.56, Qm ¼ 1951 (planar mode), d33 ¼ 239 pC/N, εT3 =ε0 ¼ 739 and the maximum vibration velocity ¼ 0.6 m/s at 31-mode. By adjusting the Zr/Ti ratio, compromised properties of kp ¼ 0.57, Qm ¼ 1502 (planar mode), d33 ¼ 330 pC/N, εT3 =ε0 ¼ 1653 and the maximum 31-mode vibration velocity ¼ 0.58 m/s were obtained when Zr/Ti ¼ 0.48/0.52 (refer to Table 17.10). These compositions are suitable for piezoelectric transformers and transducers.

17.8.2 High-Power Piezoelectric Transformers Using the above low-temperature-sinterable hard PZT, ICAT/ Penn State developed Cu and pure-Ag embedded multilayer piezotransformers (Fig. 17.67B), which were sintered at 900°C in a reduced atmosphere

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

εT33/ε0

d33

kp

k31

Tc (°C)

v0 (m/s)

1815

739

239

0.56

0.3

285.6

0.6

1502

1404

1653

330

0.573

0.33

289.58

0.58

1282

–

1326

294

0.56

–

–

0.41

Composition

Sintering condition

Qm (planar)

Qm (31-mode)

HP-HT-6-2

1200/2 h

1951

HP-HT-12-4

1200/2 h

HP-LT-17-3

900/2 h

HT, high temperature sintering; LT, low temperature sintering. HP-HT-6-2: Pb(Zr,Ti)-Pb(Zn,Ni)Nb with Sb, Li and Mn substitution. HP-HT-12-4: Further modification on the HP-HT-6-2. HP-LT-17-3: Low temperature sintering of the HP-HT-12-4 with CuO and Bi2O3.

17.8 HIGH-POWER PIEZOELECTRICS FOR PRACTICAL APPLICATIONS

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

TABLE 17.10 Piezoelectric Properties of Semihard Piezoelectric Ceramics Based on Pb(Zn1/3Nb2/3)O3-Pb(Ni1/3Nb2/3)O3-Pb(Zr0.5Ti0.5)O3

747

748

17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

0.7

Vibration velocity (m/s)

0.6 0.5 0.4

0.1 wt.% CuO 0.2 wt.% CuO

0.3

0.3 wt.% CuO 0.4 wt.% CuO

0.2

0.5 wt.% CuO 0.6 wt.% CuO

0.1 0.0 0

5

10

15

20

25

30

35

40

Applied field (V/mm, RMS value)

FIG. 17.66

Vibration velocity variation with applied field in 0.8Pb(Zr,Ti)O3-0.2Pb[0.7{0.7 (Zn,Ni)1/3  (Nb, Sb)2/3 0.3Li1/4(Nb,Sb)3/4}  0.3Mn1/3(Nb,Sb)2/3]O3 for various x wt.% of CuO added to the ceramic.

UHP N2, pO2 = 10–6 atm.

Fe3O4 (s)

(A)

Al (s)

PbO (s)

(B)

FIG. 17.67 (A) Experimental setup for sintering Cu-electrode-embedded multilayer transformers in a reduced N2 atmosphere. (B) Multilayer cofired transformer with hard PZT and Cu (left) or pure Ag (right) electrode, sintered at 900°C [Penn State trial products].77

with N2, as illustrated in Fig. 17.67A.77 Ring-dot disk multilayer types (OD ¼ 27, Center Dot D ¼ 14 mm) with Cu and Ag/Pd (or Ag/Pt) (as references) revealed the maximum power density (at 20°C temperature rise) 42 and 30 W/cm3, respectively. This big difference comes from the poor electric conductivity of Pd or Pt, compared to Cu or pure Ag. Note that the power density depends not only on the piezoceramic composition, but also on the electrode species. ICAT and the Center of Dielectric and Piezoelectric Studies at Penn State, together with Solid State Ceramics, Inc., PA, recently developed various Ag/Pd cofired multilayer piezotransformers using a similar lowtemperature-sinterable hard PZT. Ring-dot disk step-down multilayer III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

17.9 SUMMARY AND CONCLUSIONS

749

types (OD ¼ 19, Center Dot D ¼ 8 mm) cofired at 900°C revealed a power density of 30, 45, and 60 W/cm3 at a temperature rise of 20°C, 40°C, and 80°C, respectively. This design was further tested with Cu cofiring in a reduced atmosphere firing furnace by completely avoiding oxidation of Cu. Initial measurements showed that Cu cofired transformers possess about 40% reduction in resistance in identical designs. Since high-power applications are typically driven at high currents because of high admittance at the resonance, the difference in the electrode resistance can become critical due to simple Joule heating in the electrodes. Hence, by incorporating Cu cofiring this effect can be significantly reduced, and improved performance can be observed as well as reduction in overall manufacturing cost.

17.9 SUMMARY AND CONCLUSIONS (1) There are three loss origins in piezoelectrics: the dielectric, elastic, and piezoelectric losses. The 180° and non-180° domain wall motions contribute primarily to the extensive dielectric and elastic losses, respectively. The piezoelectric loss is related with Gauss’ Law (div D ¼ ρ)—that is, the motive force from the head-to-head or tail-to-tail to the head-to-tail domain configuration. (2) We introduced three loss measurement techniques for separately measuring dielectric, elastic, and piezoelectric losses: quasi-DC, resonance drive, and pulse/burst drive methods. (3) Heat generation occurs in the sample uniformly under an off-resonance mainly due to the intensive dielectric loss, while heat is generated primarily at the vibration nodal points via the intensive elastic loss under a resonance. In both cases, the loss increase is originated from the extensive dielectric loss change with electric field and/or stress. (4) In a hard piezoelectric PZT, the mechanical quality factor QB for the antiresonance (B-type) mode is higher than QA for the resonance (A-type) mode. QA < QB indicates that intensive piezoelectric loss tan θʹ is larger than the average of the elastic tan ϕʹ and dielectric tan δʹ. Since the maximum vibration velocity is also higher for the antiresonance mode than for the resonance mode, we proposed the antiresonance usage for the motor and transducer applications. (5) After determining the mechanical quality factor Qm between the resonance and antiresonance frequencies using the precise real electric power method, the maximum Qm was discovered at a frequency between the resonance and antiresonance points. We thus proposed an inductive drive method for realizing the maximum efficiency in piezoelectric transducers/motors.

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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17. HIGH-POWER PIEZOELECTRICS AND LOSS MECHANISMS

(6) Pb-free piezoelectric perovskites exhibit QA > QB or QA  QB, which suggests that the contribution of the intensive piezoelectric loss tan θʹ is not large in Pb-free piezoelectrics. (7) Actuator materials: Doping rare-earth ions into PZT-Pb(Mn,X)O3 (X ¼ Sb, Nb) ceramics increases the maximum vibration velocity up to 1 m/s, which corresponds to energy density one order of magnitude higher than conventionally commercialized piezoceramics. To obtain high power density/high vibration velocity materials, domain wall immobility/stabilization via the positive internal bias field seems to be essential, rather than the local domain wall pinning effect. (8) Transducer materials: The Sb, Li, and Mn-substituted 0.8Pb(Zr0.48Ti0.52) O3-0.16Pb(Zn1/3Nb2/3)O3-0.04Pb(Ni1/3Nb2/3)O3 ceramics showed the value of kp ¼ 0.57, Qm ¼ 1502 (planar mode), d33 ¼ 330 pC/N, εT3 =ε0 ¼ 1653 and the maximum vibration velocity ¼ 0.58 m/s at k31-mode. Low-temperature sinterable hard piezoelectrics were also synthesized based on the Sb, Li, and Mn-substituted ceramics of 0.8Pb(Zr0.5Ti0.5)O3-0.16Pb(Zn1/3Nb2/3)O3-0.04Pb(Ni1/3Nb2/3)O3, by adding CuO and Bi2O3, giving rise to kp ¼ 0.56, Qm (31-mode) ¼ 1023, d33 ¼ 294 pC/N, ε33/ε0 ¼ 1326 and tan δ ¼ 0.59%, and vibration velocity 0.41 m/s. (9) Cu and Ag embedded ring-dot disk multilayer piezotransformers were manufactured under a low temperature sintering process (900°C for 2 h) in a reduced N2 atmosphere. Cu and Ag/Pd (or Ag/Pt) (as references) revealed the maximum power density (at 20°C temperature rise) 42 and 30 W/cm3, respectively. This big difference comes from the poor electric conductivity of Pd or Pt, compared to Cu or pure Ag. In order to achieve the high power density multilayer transducers/motors, we need to consider not only the piezoceramic composition, but also the internal electrode species.

Acknowledgments This research was supported by the Office of Naval Research Code 332 during from 1991 to 2020 without any intermission through the grants N00014-96-1-1173, N00014-99-1-0754, N00014-08-1-0912, N00014-12-1-1044, and N00014-17-1-2088.

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30. Zheng J, Takahashi S, Yoshikawa S, Uchino K, de Vries JWC. Heat generation in multilayer piezoelectric actuators. J Am Ceram Soc 1996;79:3193–8. 31. Uchino K, Zheng J, Joshi A, Chen YH, Yoshikawa S, Hirose S, et al. High power characterization of piezoelectric materials. J Electroceram 1998;2:33–40. 32. Tashiro S, Ikehiro M, Igarashi H. Influence of Temperature Rise and Vibration Level on Electromechanical Properties of High-Power Piezoelectric Ceramics. Jpn J Appl Phys 1997;36:3004–9. 33. Shekhani HN, Uchino K. Characterization of mechanical loss in piezoelectric materials using temperature and vibration measurements. J Am Ceram Soc 2014;97(9):2810–4. 34. Shekhani HN, Uchino K. Evaluation of the mechanical quality factor under high power conditions in piezoelectric ceramics from electrical power. J Euro Ceram Soc 2014;35(2):541–4. 34a. Uchino K, Negishi H, Hirose T. Drive voltage dependence of electromechanical resonance in PLZT piezoelectric ceramics. Jpn J Appl Phys 1989;28(28-2):47–9. [Proceeding of the FMA-7, Kyoto]. 35. Hirose S, Aoyagi M, Tomikawa Y, Takahashi S, Uchino K. High-power characteristics at antiresonance frequency of piezoelectric transducers, In: Proc Ultrasonics Int’l ‘95, Edinburgh; 1995. p. 184–7. 36. Ural SO, Tuncdemir S, Zhuang Y, Uchino K. Development of a High Power Piezoelectric Characterization System (HiPoCS) and its application for resonance/antiresonance mode characterization. Jpn J Appl Phys 2009;48:056509. 37. Umeda M, Nakamura K, Ueha S. Effects of a Series Capacitor on the Energy Consumption in Piezoelectric Transducers at High Vibration Amplitude Level. Jpn J Appl Phys 1999;38:3327–30. 38. Takahashi S, Sasaki Y, Umeda M, Nakamura K, Ueha S. Characteristics of piezoelectric ceramics at high vibration levels. MRS Proc 1999;604:15. 39. Umeda M, Nakamura K, Ueha S. Effects of vibration stress and temperature on the characteristics of piezoelectric ceramics under high vibration amplitude levels measured by electrical transient responses. Jpn J Appl Phys 1999;38:5581. 40. Shekhani H, Scholehwar T, Hennig E, Uchino K. Characterization of piezoelectric ceramics using the burst/transient method with resonance and antiresonance analysis. J Am Ceram Soc 2016;1–10. http://dx.doi.org/10.1111/jace.14580. 41. Uchino K, Zhuang Y, Ural SO. Loss determination methodology for a piezoelectric ceramic: new phenomenological theory and experimental proposals. J Adv Dielectr 2011;1(1):17–31. 42. Majzoubi M, Shekhani HN, Bansal A, Hennig E, Scholehwar T, Uchino K. Advanced methodology for measuring the extensive elastic compliance and mechanical loss directly in k31 mode piezoelectric ceramic plates. J Appl Phys 2016;120(22), http://dx.doi.org/ 10.1063/1.4971340. 42a. Uchida N, Ikeda T. Electrostriction in Perovskite-Type Ferroelectric Ceramics. Jpn J Appl Phys 1967;6:1079. 43. Kazimierczuk MK, Bui XT. Class-E amplifier with an inductive impedance inverter[J]. IEEE Trans Ind Electron 1990;37(2):160–6. 44. Choi M, Uchino K, Hennig E, Scholehwar T. Polarization orientation dependence of piezoelectric losses in soft lead zirconate-titanate ceramics. J Electroceram 2017, http://dx. doi.org/10.1007/s10832-017-0085-y. 45. Du XH, Wang QM, Belegundu U, Uchino K. Piezoelectric property enhancement in polycrystalline lead zirconate titanate by changing cutting angle. J Ceram Soc Jpn 1999;107(2): 190–1. 46. Rajapurkar A, Ural SO, Zhuang Y, Lee H-Y, Amin A, Uchino K. Jpn J Appl Phys 2010;49:071502. 47. Zhuang Y, Ural SO, Gosain R, Tuncdemir S, Amin A, Uchino K. High Power Piezoelectric Transformers with Pb(Mg1/3Nb2/3)03-PbTiO3 Single Crystals. Appl Phys Express 2009;2:121402.

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48. Uchino K, Zhuang Y, Ural S, Amin A. High power single crystal piezoelectric transformer. US Patent; 2011. 49. Sun P, Zhou Q, Zhu B, Wu D, Hu C, Cannata JM, Tian J, Han P, Wang G, Shung KK. IEEE Trans Ultrason Ferroelect Freq Control 2009;56(12). 50. Zhang S, Sherlock N, Meyer Jr. R, Shrout T. Appl Phys Lett 2009;94:162906. 51. Takahashi S, Hirose S. Vibration-Level Characteristics for Iron-Doped Lead-ZirconateTitanate Ceramic. Jpn J Appl Phys 1993;32:2422–5. 52. Ryu J, Kim HW, Uchino K, Lee J. Effect of Yb addition on the sintering behavior and high power piezoelectric properties of Pb(Zr, Ti)O3-Pb(Mn, Nb)O3. Jpn J Appl Phys 2003;42(3): 1307–10. 53. Gao Y, Uchino K, Viehland D. Rare earth metal doping effects on the piezoelectic and polarization properties of Pb(Zr, Ti)O3-Pb(Sb, Mn)O3 ceramics. J Appl Phys 2002;92: 2094–9. 54. Gao Y, Uchino K. Development of high power piezoelectrics with enhanced vibration velocity. J Mater Tech 2004;19(2):90–8. 55. Tou T, Hamaguthi Y, Maida Y, Yamamori H, Takahashi K, Terashima Y. Properties of (Bi0.5Na0.5)Ti03-BaTi03-(Bi0.5Na0.5)(Mn1/3Nb2/3)03 Lead-Free Piezoelectric Ceramics and Its Application to Ultrasonic Cleaner. Jpn J Appl Phys 2009;48:07GM03. 56. Saito Y. Measurement System for Electric Field-Induced Strain by Use of Displacement Magnification Technique. Jpn J Appl Phys 1996;35:5168–73. 57. Doshida Y. Proc 81st smart actuators/sensors study committee, JTTAS, Tokyo; 2009. 58. Gurdal EA, Ural SO, Park HY, Nahm S, Uchino K. High power characterization of (Na0.5K0.5)NbO3 based lead-free piezoelectric ceramics. Sensors Actuat A Phys 2013;200:44. 59. Hejazi M, Taghaddos E, Gurdal E, Uchino K, Safari A. High power performance of manganese-doped BNT-based Pb-free piezoelectric ceramics. J Am Ceram Soc 2014;97 (10):3192–6. 60. Hagimura A, Uchino K. Ferroelectrics 1989;93:373. 61. Takahashi S, Sasaki Y, Hirose S, Uchino K. In: Proc Mater Res Soc Symp. 360:; 1995. p. 305. 62. Gao Y, Uchino K, Viehland D. Time dependence of the mechanical quality factor in ‘hard’ lead zirconate titanate ceramics: development of an internal dipolar field and high power origin. Jpn J Appl Phys 2006;45(12):9119–24. 63. Gao Y, Uchino K, Viehland D. Domain wall release in ‘hard’ piezoelectrics under continuous large amplitude AC excitation. J Appl Phys 2007;101(11):114110. 64. Gao Y, Uchino K, Viehland D. Effects of thermal and electrical history on ‘hard’ piezoelectrics: a comparison of internal dipolar fields and external DC bias. J Appl Phys 2007;101(5):054109. 65. Tan Q, Viehland D. Philosophical magazine; 1997. 66. Yamaji A, Enomoto Y, Kinoshita E, Tanaka T. In: Proc 1st Mtg Ferroelectr Mater Appl, Kyoto; 1977. p. 269. 67. Uchino K, Takasu T. Inspection 1986;10:29. 68. Sakaki C, Newarkar BL, Komarneni S, Uchino K. Grain size dependence of high power piezoelectric characteristics in Nb doped lead zirconate titanate oxide ceramics. Jpn J Appl Phys 2001;40:6907–10. 69. Damjanovic D. Stress and frequency dependence of the direct piezoelectric effect in ferroelectric ceramics. J Appl Phys 1997;82:1788–97. 70. Hall DA. Review nonlinearity in piezoelectric ceramics. J Mater Sci 2001;36:4575. 71. Shekhani HN. Characterization of the high power properties of piezoelectric ceramics using the burst method: methodology, analysis, and experimental approach, PhD Thesis. The Pennsylvania State University; 2016. 72. Borderon C, Renoud R, Ragheb M, Gundel H. Description of the low field nonlinear dielectric properties of ferroelectric and multiferroic materials. Appl Phys Lett 2011; 98:112903.

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73. Wang QM, Zhang T, Chen Q, Du XH. Effect of DC bias field on the complex materials coefficients of piezoelectric resonators. Sensors Actuat A Phys 2003;109(1–2):149–55. 74. Bansal A. Bias electric field dependence of high power characteristics in PZT piezoelectric ceramics, MS Thesis. The Pennsylvania State University; 2017. 75. Park S-H, Ural S, Ahn C-W, Nahm S, Uchino K. Piezoelectric properties of the Sb-, Li- and Mn-substituted Pb(ZrxTi1x)O3-Pb(Zn1/3Nb2/3)O3-Pb(Ni1/3Nb2/3)O3 ceramics for high power applications. Jpn J Appl Phys 2006;45:2667–73. 76. Park S-H, Kim Y-D, Harris J, Tuncdemir S, Eitel R, Baker A, Randall C, Uchino K. Low temperature co-fired ceramic (LTCC) compatible ultrasonic motors, In: Proc 10th Int’l conf new actuators, Bremen, Germany, June 14–16, B7.3; 2006. p. 432–5. 77. Ural S, Park S-H, Priya S, Uchino K. High power piezoelectric transformers with cofired copper electrodes—part I, In: Proc 10th Int’l conf new actuators, Bremen, Germany, June 14–16, P23; 2006. p. 556–8.

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C H A P T E R

18 Photostrictive Actuators Based on Piezoelectrics K. Uchino The Pennsylvania State University, State College, PA, United States

Abstract Photostrictive materials, exhibiting light-induced strains, are of interest for future generation wireless remote control photoactuators, microactuators, and microsensor applications. The photostrictive effect arises from a superposition of the “bulk” photovoltaic effect. In other words, this arises from the generation of large voltage from the irradiation of light, and the converse piezoelectric effect, expansion or contraction under the voltage applied. (Pb,La)(Zr,Ti)O3 (PLZT) ceramics doped with WO3 exhibit large photostriction under uniform illumination of near-ultraviolet light. Using a bimorph configuration, a photo-driven relay and a micro walking device have been demonstrated. However, for the fabrication of these devices, higher response speed must be achieved. This chapter first reviews the theoretical background for the photostrictive effect, then it discusses enhanced performance through composition modification, and it also discusses sample preparation techniques (thickness and surface characteristics of the sample). Future applications of photostrictive actuators are briefly described. Keywords: Photovoltaic effect, Piezoelectricity, Photostriction, Actuator, Surface characteristics, PLZT ceramics.

18.1 INTRODUCTION 18.1.1 Prologue to the Discovery Uchino made a breakthrough that could lead to “photophones”— devices without electrical connections that convert light energy directly into sound. Perhaps this discovery will help commercialize optical telephone networks. It also could allow robots to respond directly to light—again, without a need for wire connectors.

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Uchino’s group had been working on ceramic actuators—a kind of transducer that converts electrical energy to mechanical energy—at the Tokyo Institute of Technology, Japan, when the trigger for the lightcontrolled actuator was initiated. In 1980 when I was an active young assistant professor, one of my friends, a precision-machine expert, and I were drinking together at a Karaoke bar in Tokyo—an important information exchange activity after 5 o’clock. We were organizing a sort of “study committee on micromechanisms” such as millimeter-size walking robots. He explained that as electrically controlled walking mechanisms become very small (on the order of a millimeter), they don’t walk smoothly because the frictional force drops drastically and the weight of the electric lead becomes more significant. Fig. 18.1 visualizes the moving principle change with insect size. The key factor is a ratio, (surface area)/(volume or weight), to change the moving fashion; It starts with the example of a cockroach that walks with six legs; a mm-sized flea needs to jump with two legs because the friction force at the contact points is too small to move horizontally. Then, a much smaller (sub-mm) paramecium uses the surface cilia; finally, an amoeba moves or swims with pure surface tension force. Thus, the weight of the lead wires to provide the energy becomes more significant with reducing the microrobot size. My friend asked me, “What if you, an expert on actuators, could produce a remote-controlled actuator? One that would bypass the electrical lead?” “Remote control” equals control by radio waves, light waves, sound, or magnetic field. Light-controlled actuators require the light energy to be transduced twice: first from light energy to electrical energy and second from electrical energy to mechanical energy. These are “photovoltaic”

Cockroach

Flea

6-Leg walk

2-Leg jump

Surface Microfluidic or tension

mm

100 μm

cm

Paramecium

Ameba

Surface area Ratio ; Remove the Lead Wire Volume or weight FIG. 18.1 Moving principle change with the insect size. The key factor is a ratio (surface area)/(volume or weight) to change the moving fashion.

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and “piezoelectric” effects. A solar cell is a well-known photovoltaic device, but it does not generate sufficient voltage to drive a piezoelectric device. The key to success is to adopt a high-impedance photovoltaic effect (“anomalous” or “bulk” photovoltaic effect), which is totally different from the p-n junction-based solar cell. So my friend’s actuator needed another way to achieve a photovoltaic effect. I must have had a bit too much drink that night since I promised I would make such a machine for him. In an academic meeting, about six months after my promise, a Russian physicist reported that a single crystal of lithium niobate produced a high electromotive force (10 kV/mm) under purple light. His discovery excited me. Could this material make the power supply for the piezoelectric actuator? Could it directly produce a mechanical force under purple light? I returned to the lab and placed a small lithium niobate plate onto a plate of piezoelectric lead zirconate titanate. Then, I turned on the purple light and watched for the piezoelectric effect (mechanical deformation). But it was too slow, taking an hour for the voltage to become high enough to make a discernable shape change. Then the idea hit me: what about making a single material that could be used for the sensor and the actuator? Could I place the photovoltaic and piezoelectric effects in a single crystal? After much trial and error, I came up with a tungstate-doped material made of lead lanthanum zirconate titanate (PLZT) that responded well to purple light. It has a large piezoelectric effect and has properties that would make it relatively easy to fabricate. Remembering the promise to my friend, I fabricated a simple “lightdriven micro walking machine,” with two biplate legs attached to a plastic board, as introduced later in this chapter. When light alternately irradiated each leg, the legs bent one at a time, and the machine moved like an inchworm. It moved without electric leads or circuits! That was in 1987, seven years after my promise.

18.1.2 Background of Photostriction The continuing thrust towards greater miniaturization and integration of microrobotics and microelectronics has resulted in significant work towards the development of piezoelectric actuators. One of the bottlenecks of the piezo-actuator is the need for an electric lead wire, which is too heavy for a miniaturized self-propelling robot less than 1 cm3. The important reason is a drastic reduction of the propelling friction force due to the increase in specific area; that is, surface area/volume or weight ratio. The small contact area of the legs cannot generate horizontal propelling force.

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Photostrictive actuators, which directly convert the photonic energy to mechanical motion, have drawn significant attention for their potential usage in microactuation and microsensing applications. Optical actuators are also anticipated to be used as the driving component in optically controlled electromagnetic noise-free systems. The photostrictive effect will also be used in fabricating a photophonic device, where light is transformed directly into sound from the mechanical vibration induced by intermittent illumination at a human-audible frequency. The photostrictive effect has been studied mainly in ferroelectric polycrystalline materials for potential commercial applications. Lanthanummodified lead zirconate titanate (PLZT) ceramic is one of the most promising photostrictive materials due to its relatively high piezoelectric coefficient and ease of fabrication. However, previous studies have shown that for commercial applications, improvements in photovoltaic efficiency and response speed of the PLZT ceramics are still essential. The improvement in photostrictive properties requires consideration of several parameters, such as material parameters, processing condition and microstructure, and sample configuration and performance testing conditions. This chapter first reviews theoretical background of the photostrictive effect, before going on to discuss enhanced performance through the composition modification, sample preparation technique (thickness and surface characteristics of the sample). Future applications of photostrictive materials are briefly described.

18.2 PHOTOVOLTAIC EFFECT The photostriction phenomenon was discovered by Dr. P.S. Brody and the author independently almost at the same time in 1981.1 In principle, the photostrictive effect arises from a superposition of the “bulk” photovoltaic effect, in other words, generation of a large voltage from the irradiation of light, and the converse piezoelectric effect, in other words, expansion or contraction under the voltage applied.2 The photostrictive phenomenon has been observed in certain ferroelectric/piezoelectric materials. By doping suitable ionic species, the photovoltaic effect is introduced in the material. The figure of merit (FOM) for photostriction magnitude is generally expressed as the product of photovoltage (electric field), Eph, and the piezoelectric constant, d33, while the FOM for response speed is determined by the photocurrent (current density), Iph, as d33Iph/C (C: capacitance of the photostrictive device). Therefore, for application purposes, enhancement and/or optimization of photostrictive properties require consideration of both the terms in the figure of merit; that is, photovoltaic voltage and current (or “power”), as well as its piezoelectric d constant. Currently, PLZT ceramics have gained considerable attention

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due to their excellent photovoltaic properties, high d33, and ease of fabrication. We will review the background of photovoltaic effect first in this section.

18.2.1 Experimental Phenomena of the Bulk Photovoltatic Effect 18.2.1.1 Bulk Photovoltaic Effect When a noncentrosymmetric piezoelectric material (with some dopants) is illuminated with uniform light having a wavelength corresponding to the absorption edge of the material, a steady photovoltage/ photocurrent is generated.3 The distinction between the photovoltaic effect and pyroelectric effect (i.e., voltage/charge generation due to the temperature change) may not be obvious. Fig. 18.2 demonstrates the difference, where illumination responses of photovoltaic current are plotted under two different external resistances in 1.5 mol% MnO2-doped 0.895PbTiO3-0.105La(Zn2/3Nb1/3)O3 ceramic.4 (Uchino’s group developed this ceramic first, aiming at a high anisotropic piezoelectric material for medical acoustic imaging applications.) Mercury lamp illumination on this ceramic sample slightly increased the sample temperature, leading to the initial voltage peak (up to 8 mV through 10 MΩ resistor) for a couple of tens of seconds. However, note that the output voltage is stabilized around 4 mV after the temperature stability was obtained. The magnitude of the 8

Hg Lamp Vout R

Output voltage (mV)

6 R = 10 MΩ

p

4

Current source I0 = 0.4 nA

2 1.82 MΩ 0 100

200 Time (sec)

–2 Light on

Light off

–4

FIG. 18.2 Illumination responses of photovoltaic current for 1.5 mol% MnO2-doped 0.895 PbTiO3-0.105 La(Zn2/3Nb1/3)O3 ceramic.

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steady current is independent of the externally connected resistance. When the illumination was shut off, the negative pyrocurrent was observed due to a slight temperature decrease again for a period of tens of seconds. But, the output voltage became completely zero after the saturation, which verified that there was no junction (piezoelectric ceramic-metal electrode) effect. The reader can now clearly understand the difference between the photovoltaic and pyroelectric effects from this demonstration. Note that we can eliminate the pyroelectric effect when we use an IR blocking filter for cutting the longer wavelength light intensity (see Fig. 18.3). In some materials, the photovoltage generated is greater than the bandgap energy, and it can be of the order of several kV/cm. This phenomenon, thus referred to as the bulk or anomalous photovoltaic effect (APV), seems to be totally different from the corresponding phenomenon in the p-n junction of semiconductors (e.g., solar battery).5,6 The APV effect is observed primarily in the direction of the spontaneous polarization (PS) in the ferroelectric material, and the generated photovoltage is proportional to the sample length along the PS direction. The origin of photovoltaic effect is not yet clear, even though several models have been proposed on the mechanism of photovoltaic effect. Two of the suggested models (current source model and voltage source model) will be discussed in Section 18.2.2. The key features of the APV effect to be remembered are summarized as follows:

volt amp ohm

Electrometer (Keithley 617)

Sensor

Sample

High Bandpass IR pressure blocking filter Displacement mercury filter (248–390 sensor lamp nm) (>700 nm)

FIG. 18.3

Millitron displacement meter

Oscilloscope

Experimental setup for measuring photovoltaic and photostrictive effects.5

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(1) This effect is observed in a uniform single crystal or polycrystalline ceramic having noncentrosymmetry crystallographically, and is entirely different in nature from the p-n junction effect observed in semiconductors. (2) A steady photo voltage/current is generated under uniform illumination. (3) The magnitude of the induced voltage is greater than the band gap of the crystal. (Typical band gap for a perovskite oxide is around 3.3 eV.) 18.2.1.2 Experimental Setup Prior to the detailed discussion, the measuring setup is described here (Fig. 18.3). PLZT ceramic samples are cut into the standard sizes of 5
5 mm2 and polished to 1-mm thickness. The samples are poled along the length (5 mm) under a field of 2 kV/mm at 120°C for 10 min. The ceramic preparation methods will be described in Sections 18.2.3 and 18.3.3. Radiation from a high-pressure mercury lamp (Ushio Electric USH-500D) is passed through infrared-cut optical filters in order to minimize the thermal/pyroelectric effect. The light with the wavelength peak around 366 nm, where the maximum photovoltaic effect of PLZT is obtained, is then applied to the sample. A xenon lamp is alternatively used to measure the wavelength dependence of the photovoltaic effect. The light source is monochromated by a monochromator to 6 nm HWHM. The photovoltaic voltage under illumination generally reaches several kV/cm, and the current is on the order of nA. The induced current is recorded as a function of the applied voltage over a range 100 to 100 V, by means of a high-input impedance electrometer (Keithley 617). The photovoltaic voltage and current are determined from the intercepts of the horizontal and the vertical axes, respectively. An example measurement is shown in Fig. 18.4. The photovoltage (typically kV) is estimated by Current (nA) Photocurrent

3 2

Conductivity

1 Voltage (v) –50

0

50

100

Photovoltage

FIG. 18.4

Photocurrent measured as a function of applied voltage under illumination.6

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the linear extrapolation method. Photostriction is directly measured by a differential transformer (pseudo-DC measurement) or an eddy current displacement senor (dynamic measurement).

18.2.2 Physical Models for the Bulk Photovoltaic Effect Two models proposed previously by Uchino’s group were the current source model and the voltage source model. 18.2.2.1 Current Source Model Taking into account the necessity of both doping and crystal asymmetry, we proposed a current source model, as illustrated in Fig. 18.5, which is based on the electron energy band model for (Pb,La)(Zr,Ti)O3 (PLZT).7,8 The energy band is basically generated by the hybridized orbit of p-orbit of oxygen and d-orbit of Ti/Zr. The donor impurity levels induced in accordance with La doping (or other dopants) are present slightly above the valence band. This deep donor level position was estimated by the peak performance of photo current around λ ¼ 380 nm. The transition from these levels with an asymmetric potential due to the crystallographic anisotropy may provide the “preferred” momentum to the electron when excited by light illumination. Electromotive force is generated when electrons excited by light move in a certain direction of the ferroelectric/piezoelectric crystal, which may arise along the spontaneous polarization PS direction. The asymmetric crystal exhibiting a photovoltaic response is also piezoelectric in principle, and therefore, a photostriction effect is expected as a coupling of the bulk photovoltaic voltage (Eph) with the piezoelectric strain constant (d). Asymmetric potential at the local donor site primarily originates from the same as the ionic potential asymmetry in a ferroelectric ionic crystal. Conduction band

Light illumination

3.26 eV

Eg = 3.3 eV

380 nm

Valence band

FIG. 18.5 Energy band gap model of excited electron transition from deep donor-impurity level in PLZT.7

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Let us review it quickly here.9 Defining N to be the number of atoms per unit volume in a crystal, dipole coupling energy Wdip can be calculated as follows:
 Wdip ¼ Nwdip ¼  Nαγ 2 =9ε0 2 P2 , (18.1) where P is polarization, α is the ionic polarizability, γ is the Lorentz factor, and ε0 is the permittivity of the vacuum. On the other hand, when ions are displaced from their nonpolar equilibrium positions, the elastic energy also increases. If the displacement is u and the force constants k and k0 , then the increase of the elastic energy per unit volume can be expressed as follows:   Welas ¼ N ðk=2Þu2 + ðk0 =4Þu4 : (18.2) Here, k0 (>0) is the higher-order force constant. It should be noted that in pyroelectrics, k0 plays an important role in determining the magnitude of the dipole moment. Using P ¼ Nqu (q: the electric charge), the total energy can be expressed as follows: Wtot ¼ Wdip + Welas 

   ¼ k=2Nq2  Nαγ 2 =9ε0 2 P2 + k0 =4N 3 q4 P4

(18.3)

From this, if the coefficient of the harmonic term of the elastic energy is equal to or greater than the coefficient of the dipole-dipole coupling, then P ¼ 0; the ions are stable and remain at the nonpolar equilibrium positions symmetric). the equilibrium position
(i.e., 
Otherwise,
 a shift from  P2 ¼ 2Nαγ 2 =9ε0 2  k=Nq2 = k0 =N 3 q4 is stable, which is called “spontaneous polarization.” When the ions are situated on the spontaneous position (one of the double minima of energy), taking Taylor expansion of Eq. (18.3) around PS, you can derive the potential asymmetry of Wtot. Taking into account the potential skew, and the electric field induction parallel to the spontaneous polarization under the light illumination, we can expect the extensive deformation in the photostrictive materials along the polarization direction. The photocurrent Jph varies in proportion to the illumination intensity I: Jph ¼ καI,

(18.4)

where α denotes the absorption coefficient and κ is a Glass constant (named according to Glass’s contribution to the APV effect).10 On the other hand, the photovoltage Eph shows saturation caused by a large photoconductive effect, represented by Eph ¼ καI=ðσ d + βI Þ,

(18.5)

where σ d is the dark conductivity and β is a constant relating to the photoconductivity.

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3

Photovoltaic current (μA/W)

0.895PT-0.105LZN

2

PLZT 3/52/48

1

0 300

400 Wavelength (nm)

500

FIG. 18.6 Wavelength dependence of photovoltaic current in 0.895PT-0.105LZN and PLZT (3/52/48).8

This model is validated: (1) The photovoltaic current is constant in Fig. 18.2, regardless of the externally connected resistance. (2) The photocurrent Jph is strongly dependent on the wavelength under constant intensity of illumination, suggesting a sort of band gap, as is shown in Fig. 18.6. A sharp peak is observed at 384 or 372 nm near the absorption edge for 0.895PT-0.105LZN or PLZT (3/52/48), respectively. The donor level seems to be rather deep, close to the valence band level. (3) The linear relationship of the photocurrent with light intensity (Eq. 18.4) is experimentally verified in Fig. 18.7, where photo-induced short-circuit current Jph (a) and the open-circuit electric field Eph (b) are plotted as a function of illumination intensity I for pure and MnO2-doped 0.895PT-0.105LZN.4 18.2.2.2 Voltage Source Model In this model, the photovoltaic properties are attributed to the photocarriers and internal electric fields generated by near-UV illumination. The optical nonlinearity of the second order, which is popularly

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Undoped 3 1 2 0.5

0

Mn-doped

0

(A)

2 4 6 8 Light intensity (×102W/m2)

Jph (×10–5 A/m2)

Photocurrent Jph (x10–4 A/m2)

4 1.5

1

0 10

Photovoltage Eph (x105 V/m)

1 0.8 0.6 0.4 Undoped

0.2 0

(B)

Mn-doped

0

2 4 6 8 Light intensity (×102W/m2)

10

FIG. 18.7 Short-circuit current Jph (A) and open-circuit electric field Eph (B) as a function of illumination intensity I for pure and MnO2-doped 0.895PT-0.105LZN.8

introduced in ferroelectrics, is proposed as the origin of photo-induced dc field generation.11 The expression for the polarization of dielectrics, considering the nonlinear effect up to the second order, is given by the following12:   P ¼ εo χ 1 Eop + χ 2 E2op , (18.6) where ε0 is the permittivity of the vacuum, χ 1 is the linear susceptibility, χ 2 is the nonlinear susceptibility of the second order, and Eop is the electric field of the illumination beam at an optical frequency (THz). In dielectrics, the value of the local electric field is different from the value of the external electric field. For simplicity, the local field in dielectrics has been approximated using the Lorentz relation for a ferroelectric material as Ref. 13:

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18. PHOTOSTRICTIVE ACTUATORS BASED ON PIEZOELECTRICS

Elocal ¼ E +

γP , 3εo

(18.7)

where E is the external electric field and γ is the Lorentz factor. When an alternating electric field at an optical frequency is applied (i.e., light illumination), the average of the local electric field Elocal is not zero, but it can be calculated as follows: 1 Elocal ¼ γχ 2 E2op : 6

(18.8)

It must be noted that Eq. (18.8) has been derived for a coherent propagation of the light wave at a single frequency. However, the condition of coherent illumination may not be satisfied in our experimental conditions, where a mercury lamp is used as a light source. The nonlinear effect will be affected by the degree of coherence. Therefore, considering the depression of nonlinear effect due to the incoherency, the expression for the effective dc field induced by an incoherent light source may be modified as follows:  β Elocal ¼ c1 γχ 2 E2op , (18.9) where c1 is a constant and β is a parameter expressing the depression effect. The value of parameter β is expected to lie between 0 and 1. Replacing the variable E2op with the intensity (Iop),12 the following expression for the average induced (dc) field due to the incoherent light can be obtained:
β (18.10) Edc ¼ Elocal ¼ c2 γχ 2 Iop , where c2 is a constant and Edc is the effective dc field for photo-induced carriers. Note that the induced field, Edc, is proportional to the nonlinear susceptibility as well as the Lorentz factor, γ. The photoconductivity can be obtained as a function of light intensity, Iop: rffiffiffiffiffiffi Iop , (18.11) σ op ¼ c3 qμ R where q is the charge of the photocarrier, μ is the carrier mobility, R is the recombination rate of the carrier, and c3 is a constant. Since the photocurrent is provided by
the product  of the photoconductivity and the photoinduced dc field Jph ¼ σ op Edc , we finally obtain rffiffiffiffi 1
β + 12 Jph ¼ c4 qμγχ 2 , (18.12) Iop R where c4 is another constant. Eqs. (18.11) and (18.12) provide a correlation for the photovoltaic response of ferroelectrics on the basis of optical nonlinearity.

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

767

18.2 PHOTOVOLTAIC EFFECT

Photoconductivity (10–12 ohm–1)

: Experimental data

0.1

0.54 : Fitted by s op = 0.34 (lop)

Photovoltage (V/cm)

1.0 1

: :

0.1

10 1 Light intensity (mW/cm2)

Experimental data Fitted by Eph = 0.66 (lop)0.50

1 10 Light intensity (mW/cm2)

(B)

1

: Experimental data

0.1

0.96 : Fitted by J ph = 0.26 (lop)

1 10 Light intensity (mW/cm2)

(C)

Photocurrent (nA/cm)

(A) Photocurrent (nA/cm)

1

1

0.1 : Experimental : Fitted

0.01 1

data by Jph = 0.016 (lop)1.3

10 Light intensity (mW/cm2)

100

(D)

FIG. 18.8 Dependence of (A) photoconductivity, (B) photovoltage, and (C) photocurrent on illumination intensity in a PLZT 3/52/48 sample 1 mm in thickness; (D) the result for a sample 140 μm in thickness.11

The model validation and analysis are made by the light intensity dependence of photovoltaic properties. The experiments were made on PLZT 3/52/48 samples with 1 mm and 140 μm in thickness. Fig. 18.8A shows the plot of photoconductivity (σ op) as a function of light intensity (Iop). The exponent relating the photoconductivity and the light intensity was calculated to be 0.54. This is in good agreement with the value of 0.5 derived for the recombination process of the carriers (Eq. 18.11). Note the difference from Eq. (18.5), where we assume the photoconductivity directly in proportion to the intensity (see Fig. 18.7). Fig. 18.8B shows the experimental results of the open-circuit photovoltage (Eph) as a function of light intensity. The photovoltage was found to be proportional to the square root of the light intensity, leading to β ¼ 0.5 (Eq. 18.10). Fig. 18.8C shows the results of a short-circuit photocurrent (Jph) as a function of Iph. The parameter β based on Eq. (18.12) was calculated to be 0.46, which is very close to the above β value. The depression in the β value can be attributed to the incoherent illumination of the mercury lamp. Note again that Jph is almost directly proportional to Iph, in accordance with Eq. (18.4) (Fig. 18.7).

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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18. PHOTOSTRICTIVE ACTUATORS BASED ON PIEZOELECTRICS

Investigation was further made in terms of the illumination coherency. Since a partial coherence of light can be achieved in a very small area, an increase in the β value is expected in thinner photovoltaic samples. The photocurrent measured as a function of light intensity in a very thin (140 μm) PLZT sample (Fig. 18.8D) resulted in the parameter β (Eq. 18.12) being 0.80, which is higher than the β value of 0.46 in the thicker sample (1 mm thickness). These results suggest that the parameter β increases with a decrease in the thickness of photovoltaic sample, due to higher coherency of illumination in thinner samples. This suggests that an enhancement in the photovoltaic properties may be achieved in a very thin sample or by using coherent illumination. As suggested already, we cannot conclude at present which of the two models (current source or voltage source) better fits for the experiments. 18.2.2.3 Effect of Light Polarization Direction Determining the effect of the light polarization direction on the photovoltaic phenomenon also helps with understanding the mechanism.14 Fig. 18.9 shows the measuring system of the dependence of photovoltaic effect on light polarization direction (a), and the photovoltaic voltage and current as a function of the rotation angle measured for the PLZT (3/52/ 48) polycrystalline sample (b). The rotation angle θ was taken from the vertical spontaneous polarization direction. Even in a polycrystalline sample, both the photovoltaic voltage and current provide the maximum at θ ¼ 0 and 180 degrees and the minimum at θ ¼ 90 degrees; this also indicates that the contributing electron orbit may be the p-d hybridized orbit mentioned above (i.e., the perovskite Zr/Ti-O direction). This experiment is also important when the photostriction is employed to “photophones,” where the sample is illuminated with the polarized light traveling through an optical fiber.

18.2.3 PLZT Composition Research Since the FOM of the photostriction is evaluated by the product of the photovoltaic voltage and the piezoelectric constant, in other words, dEph, Pb(Zr,Ti)O3 (PZT)-based ceramics are the focus primarily because of their excellent piezoelectric properties—high d values. Lanthanum-doped PZT (PLZT) is one such material, with La3+ donor doping in the perovskite A-site, which is also well known as a transparent ceramic (good sinterability) applicable to electro-optic devices. PLZT (x/y/z) samples were prepared in accordance with the following composition formula:
 Pb1x Lax Zry Tiz 1x=4 O3 ðy + z ¼ 1Þ:

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

769

18.2 PHOTOVOLTAIC EFFECT

Polarization direction

θ Ps

Photovoltaic sample

Polarizer

Mercury lamp

Lens

Photovoltage change (V/V0)

Photocurrent change (J/J0)

(A)

1.1

1.05

1 0

(B)

45 90 135 Polarizer rotation angle (deg)

180

FIG. 18.9

(A) Measuring system of the dependence of the photovoltaic effect on light polarization direction. (B) Photovoltaic voltage and current as a function of the rotation angle.14

As discussed in Fig. 18.13 in the details, the piezoelectric d coefficient exhibits the maximum around the morphotropic phase boundary (MPB) between the tetragonal and rhombohedral phases, so our composition search was also focused around the MPB compositions. Fig. 18.10 shows the photocurrent Jph for various PLZT compositions with tetragonal and rhombohedral phases, plotted as a function of their remanent polarization Pr. (1) Significantly large photocurrent is observed for the tetragonal composition PLZT (3/52/48).15 This is the major reason why many data in this paper were taken for this composition. The details will be discussed in Section 18.3.2.

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

770

18. PHOTOSTRICTIVE ACTUATORS BASED ON PIEZOELECTRICS

3/52/48

Photovoltaic current (nA)

PLZT (x/y/1–y) 0.6

Tetragonal Rhombohedral

2/50/50 4/56/44

0.4 3/60/40

7/62/38 8/58/42 9/60/40 0

4/58/42

5/55/45

0.2

6/56/44 25

4/60/40 4/66/34

30 40 35 Remanent polarization (×10–2 C/m2)

45

FIG. 18.10 Interrelation of photovoltaic current with remanent polarization in the PLZT family.15

(2) The relation Jph ∝ Pr first proposed by Brody16,17 appears valid for the PLZT system. Further, it is worth noting that the Pr value capable of producing a certain magnitude of Jph is generally larger in the rhombohedral symmetry group than in the tetragonal group. The average remanent polarization exhibiting the same magnitude of photocurrent differs by 1.7 times between the tetragonal and pffiffiffi rhombohedral phases, which is nearly equal to 3, the inverse of the direction cosine of the [1 1 1] axis in the perovskite structure. This suggests again the photo-induced electron excitation is related to the perovskite (0 0 1) axis-oriented orbit, in other words, the hybridized orbit of the p-orbit of oxygen and the d-orbit of Ti/Zr.18

18.2.4 Dopant Research The photovoltaic effect is caused by small amount of a dopant in a ferroelectric/piezoelectric crystal, as we discussed in Section 18.2.1. La3+ seems to be the primary dopant in Pb(Zr,Ti)O3. Additional impurity doping on PLZT also affects the photovoltaic response significantly. Fig. 18.11 shows the photovoltaic response for various dopants with the same concentration of 1 at.% into the base PLZT (3/52/48) under an illumination intensity of 4 mW/cm2 at 366 nm.7 The dashed line in Fig. 18.11 represents the constant power (half of the product of maximum photo-induced voltage and photocurrent) curve corresponding to the nondoped PLZT (3/52/ 48). Photovoltaic power is enhanced by donor doping onto the perovskite B-site (Nb5+, Ta5+, W6+). In contrast, impurity ions substituting at the A-site

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

771

18.2 PHOTOVOLTAIC EFFECT

5.0

Photocurrent (nA/cm)

POWER-CONST.

Nb5+

4.0

W6+ K1+

3.0

Al3+ Mg2+

2.0

Bi3+

Ta5+ Y3+

Sn4+ Si4+

1.0

Undoped

Na1+ Ba2+

ACCEPTOR A-site ACCEPTOR B-site

Fe3+

DONOR A-site DONOR B-site

0

0.5 1.0 1.5 Photo-induced voltage (kV/cm)

2.0

FIG. 18.11 Photovoltaic response of PLZT (3/52/48) for various impurity dopants (illumination intensity: 4 mW/cm2).7

and/or acceptor ions substituting at the B-site, whose ionic valences are small (+1 to +4), degrade the effect on the performance. Fig. 18.12 shows the photovoltaic response plotted as a function of at.% of the WO3 doping concentration.6 Note that the maximum power is obtained at 0.4 at.% of the dopant, due to a significant enhancement in the current density. It is worth noting that the maximum photovoltaic performance was observed at

Photocurrent (nA/cm) Energy (μW/cm2)

Tip displacement (×10 μm)

Photocurrent

15

Voltage

10

Displacement

Energy

5

Photoinduced voltage (×101kV/cm)

20

0 0.0

0.2 0.4 0.6 0.8 Concentration of WO3 doping (atm%)

1.0

FIG. 18.12 Photovoltaic current, voltage, power, and tip displacement of a bimorph specimen as a function of dopant concentration in WO3-doped PLZT (3/52/48).6

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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18. PHOTOSTRICTIVE ACTUATORS BASED ON PIEZOELECTRICS

0.9 at.% of the Ta2O5 dopant, leading to the conclusion that a half amount of W6+ (two electrons) doping exhibits an equivalent photovoltaic enhancement in comparison with the amount of Ta5+ (one electron) dopant.

18.3 PHOTOSTRICTIVE EFFECT 18.3.1 Figures of Merit The figures of merit for photostriction are derived here. The photostriction is induced as a function of time, t, as

t xph ¼ d33 Eph 1  exp , (18.13) RC where xph is the photo-induced strain, d33 is the piezoelectric constant of the material, Eph is the maximum photovoltage, Iph is the photocurrent, t is the time, and R and C are resistance and capacitance of the material, respectively. (1) For t ≪ 1, we obtain

xph ¼ d33 Eph

t : RC

(18.14)

Thus, the

figure of merit for response speed should be provided by 1 : d33 Eph RC Eph , this figure of merit is Taking account of the relation Iph ¼ R d33 Iph d33 Iph transformed to . Or it can be given by (ε: permittivity). C ε (2) On the other hand, for t ≫ 1, the saturated strain is provided by the following: xph ¼ d33 Eph :

(18.15)

Thus, the figure of merit for the magnitude of strain is defined by d33Eph. In order to obtain a high photo-induced strain, materials with high d33 and Eph are needed. On the other hand, for high response speed such as photophonic applications, materials with high d33, Iph and low dielectric constant ε are required.

18.3.2 Materials Considerations We reconsider the optimum compositions in the PLZT system from the photostrictive actuator’s viewpoint. Figs. 18.13A, B, and C show contour maps of photovoltaic voltage, Eph, photocurrent, Iph, and piezoelectric

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

lph = photocurrent (nA/cm) y/1–y y/1–y at.% PT at.% PT at.% PZ 58/42 56/44 54/46 52/48 50/50 48/52 46/54 44/56 58/42 56/44 54/46 52/48 50/50 48/5246/5444/56 0 0 Rhombohedral Tetragonal Rhombohedral Tetragonal

at.% PT at.% PZ

58/42 56/44 54/46 52/48 50/50 48/52 46/54 44/56 Rhombohedral Tetragonal

1 338 443

2

450

3

749

1054

4

961

901

5 252 144 2435 1025 6

(A) FIG. 18.13

267

697 658

at.% La

at.% La

1

864 1002 298 397

951

916

126

2

0.44

0.85 1.31 1.16

3

0.72

1.19 1.18 2.05

4

1.11

1.19

1.45 2.81 0.71 0.90

5 0.36 0.21 0.68

0.44

0.83 1.01

6

(B)

d33 (×10–12 m/V)

1 2 at. % La

0

y/1–y

468

317 210 187

3

392

372

242 197

4

422

366

272

160 199 145

5 287 457 468

338

272

228

0.16 6

435

18.3 PHOTOSTRICTIVE EFFECT

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

Eph = photovoltage (V/cm) at.% PZ

(C)

Contour maps of (A) photovoltaic voltage Eph, (B) photocurrent Iph, and (C) piezoelectric constant d33 in the PLZT (x/y/1  y) system.

773

774

18. PHOTOSTRICTIVE ACTUATORS BASED ON PIEZOELECTRICS

constant, d33, on the PLZT (x/y/1  y) phase diagram, respectively.19 The morphotropic phase boundary (MPB) appears between the rhombohedral and tetragonal phases around 52%–56% of Zr concentration y. As is well known, the piezoelectric coefficient exhibits the maximum along the MPB. The photovoltaic effect is also excited around the MPB. However, precisely speaking, the photovoltage was found to be a maximum at PLZT 5/54/46, while the maximum photocurrent was found at PLZT 4/48/ 52. In Figs. 18.13A and B, the solid circles indicate the location of PLZT 3/52/48, which had been reported earlier to exhibit the maximum photovoltage and current. In the finer measurement, the maximum photovoltage and current have been found at different compositions of the PLZT system, both still being in the tetragonal phase. In conclusion, the FOM d33Eph shows a maximum for PLZT 5/54/46, while the maximum of the FOM d33Iph/C is for PLZT 4/48/52. A similar composition study was reported by Nonaka et al.20

18.3.3 Ceramic Preparation Method Effect 18.3.3.1 Processing Method Fabrication and processing methods have been reported to profoundly influence the photovoltaic properties and strain responses of PLZT ceramics.18,21,22 This effect comes through the influence of processing methods on the microstructure, and other physical properties such as density, porosity, and chemical composition. Ceramic materials with high density, low porosity, better homogeneity, and a good control of stoichiometry are desired for enhanced photovoltaic and photostrictive properties. Coprecipitation and sol-gel techniques are two of the chemical routes that have the inherent advantage in producing high density homogeneous ceramics with a greater control of stoichiometry. Therefore, processes to fabricate photostrictive ceramics via chemical routes with suitable nonoxide precursors are attractive. PLZT ceramics prepared by sol-gel and coprecipitated techniques exhibit better photovoltaic and photostrictive properties as compared to the oxide mixing process.21,22 Ceramics prepared by the solid state reaction have compositional variation and inhomogeneous distribution of impurities whereas the ceramics prepared by chemical synthesis exhibited high purity with good chemical homogeneity at the nanometer scale. 18.3.3.2 Grain Size Effect Even when the composition is fixed, the photostriction still depends strongly on the sintering condition, or in particular, grain size.18,23 Fig. 18.14 shows the dependence of the photostrictive characteristics on the grain size. As is well known, the piezoelectric coefficient d33 gradually

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

775

300

90

200

60

100

30

16

12 400 0.8 350 0.4

Light intensity (40W/m2) 0

0

1

2

3

4

0

0

Grain size (μm)

FIG. 18.14

300

Light intensity (40W/m2) 0

d33 (pm/V)

120

Strain (×10–4)

400

Photocurrent (nA/m)

Photovoltage (kV/m)

18.3 PHOTOSTRICTIVE EFFECT

1

2

3

4

Grain size (μm)

Grain size dependence of photostrictive characteristics in PLZT (3/52/48).18

decreases as the grain size decreases down to a 1 μm range. On the other hand, photovoltage increases dramatically with a decrease in grain size, and the photocurrent seems to exhibit the maximum at around 1 μm. Thus, the photostriction exhibits a dramatic increase similar to the photovoltage change. The smaller grain sample is preferable, if it is sintered to a high density. 18.3.3.3 Surface/Geometry Dependence Since the photostrictive effect is excited by the absorption of illumination in the surface layer of ceramics, it is apparent that the surface geometry of the photostrictive material will have a strong bearing on the generation of photocurrent and photovoltage. Using a sample thickness closer to the penetration depth will ensure that the entire film will be active and efficiently utilized. We also discussed on the light coherency for the “thin” sample in Fig. 18.8. Therefore, investigation of photovoltaic response as a function of sample thickness is desired in determining the optimal thickness range with maximum photovoltaic effect. In addition, studying the effect of surface roughness will provide an insight on the absorption dependence of photostriction. In order to determine the optimum sample thickness, the dependence of the photovoltaic effect on sample thickness of PLZT (3/52/48) ceramics doped with 0.5 at.% WO3 was examined.24 The photovoltaic response was found to increase with a decrease in sample thickness in PLZT ceramics (see Fig. 18.15). A model was proposed in Fig. 18.16 to explain and quantify the observed influence of sample thickness on photovoltaic response,24 where the absorption coefficient is assumed to be independent of light intensity and the photocurrent density is taken to be proportional to light intensity. The sample is assumed to comprise thin slices along the sample thickness direction of the sample. Fig. 18.15 shows the plot between the normalized photocurrent (im) and sample thickness calculated for the external

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

776

18. PHOTOSTRICTIVE ACTUATORS BASED ON PIEZOELECTRICS

12 Proposed model Normalized photocurrent (nA/cm)

10 Experimental results 8

6

4

2

0

0

200

400

600

800

1000

Sample thickness (μm)

FIG. 18.15 Comparison of measured and computed normalized photocurrent with photovoltaic coefficient (im/k) in 0.5 at.% WO3-doped PLZT (3/52/48).

resistance (Rm ¼ 200 TΩ). The computed result shows good agreement with the experimental data (□ is for the measured photocurrent, and ▮ is for the computed results from the proposed model). With increasing in sample thickness, im increases, reaches a maximum, and subsequently it decreases with the sample thickness. The decrease in im can mainly be attributed to the dark conductivity (σ d). The optimum thickness (for the present set of samples) that yields maximum photocurrent is found at 33 μm, which is close to the light (366 nm) penetration depth of the PLZT (absorption coefficient α of PLZT (3/52/48) ¼ 0.0252 μm1 at 366 nm; the inverse of α ¼ 39 μm). The relatively low value of optimum thickness implies that the lower sample thickness will be expected to give better photovoltaic response. The effect of surface roughness on photovoltaic and photostrictive properties was also examined in the PLZT sample, with a different surface roughness obtained by polishing different surface finishes. The surface roughness was measured by a profilometer (Tencor, Alpha-Step 200), and the average surface roughness was determined using the graphical center line method. The variation of photovoltaic current with surface roughness is plotted in Fig. 18.17.11 The photocurrent increases exponentially with decreasing surface roughness. This is due to the fact that with an increase in surface roughness, the penetration depth of the illumination decreases, while contributions from multiple reflections increase. A model based on the effect of multireflection has been proposed for two different shapes, a sine profile and a “V” profile roughness. In both these shapes,

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

Thickness Length w l

Illumination

ii represented by

Width

Ri

dt

im

i1

R1

i2

R2

...n... in

Rm

Rn

im

io – im io

Ro

io

Ro

Rm

FIG. 18.16 Model to compute the dependence of photocurrent on sample thickness. The sample was modeled as laminated thin slices along the thickness direction and the corresponding circuit diagrams are also shown.

2.5

Normalized photocurrent (nA/cm)

Proposed Sine and V profiles 2

Experimental results

1.5

1

0.5

Sine profile V profile

0

0

0.5

1

1.5

2

2.5

3

3.5

4

Surface roughness (μm)

FIG. 18.17 Variation of photocurrent with surface roughness in 0.5 at.% WO3-doped PLZT. Comparison with the normalized computed photocurrent for the two surface profiles is also made. III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

778

18. PHOTOSTRICTIVE ACTUATORS BASED ON PIEZOELECTRICS

half of the up-down amplitude was taken as a roughness (r) and the cyclic distance period as a roughness pitch (g). The normalized photo-currents (im) computed for the above two surface profiles are plotted also in Fig. 18.17 as a function of surface roughness. A distance pitch (wavelength) of roughness at 1 μm gave the best fit of the experimental results, which is close to the size of the grain of this PLZT sample. In conclusion, the optimum profile of the photostrictive PLZT actuator is a film shape with the thickness around 30 μm and the surface roughness less than 0.2 μm.

18.4 PHOTOSTRICTIVE DEVICE APPLICATIONS In this section, we introduce the possible applications of photostriction to photo-driven relay, a micro walking machine, a photophone, and the micro propelling robot, which are designed to function as a result of light irradiation, having neither lead wires nor electric circuits. See Ref. 25 for details of applications of photostrictive devices.

18.4.1 Displacement Amplification Mechanism Since the maximum strain level of the photostriction is only 0.01% (one order of magnitude smaller than the electrically induced piezostriction, and this corresponds to 1 μm displacement from a 10-mm sample), we need to consider a sophisticated amplification mechanism of the displacement. We employed a bimorph structure, which is analogous to a bimetal consisting of two metallic plates with different thermal expansion coefficients bonded together to generate a bending deformation according to a temperature change. Two PLZT plates were pasted back to back, but they were placed in opposite polarization, then they were connected on the edges electrically, as shown in Fig. 18.18.7 A purple light (366 mn) was shone to one side, which generated a photovoltaic voltage of 7 kV across the length (along the polarization direction). This caused the PLZT plate on that side to expand by nearly 0.01% of its length, while the plate on the other (unlit) side contracted due to the piezoelectric effect through the photovoltage. Since the two plates were bonded together, the whole device bent away from the light. Fig. 18.19 demonstrates the tip deflection of the bimorph device made from WO3 0.5 at.% doped PLZT under a dual beam control (illumination intensity: 10 mW/cm2). For this 20-mm long and 0.35-mm thick biplate, the displacement at the edge was 150 μm, and the response speed was a couple of seconds.

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

779

18.4 PHOTOSTRICTIVE DEVICE APPLICATIONS

To contract

20 mm Ps

To expand

Irradiation of light

Electrode

m

5m

0.4 mm

FIG. 18.18

Structure of the photo-driven bimorph and its driving principle.

150

Displacement (μm)

100 50 0

5

10

15

25

30

–50 –100 BIMORPH

DUMMY

BIMORPH

–150 Time (sec)

FIG. 18.19 Tip deflection of the bimorph device made from WO3 0.5 at.% doped PLZT under a dual beam control (illumination intensity: 10 mW/cm2).7

18.4.2 Photo-Driven Relay A photo-drive relay was constructed using a PLZT phtostrictive bimorph as a driver that consists of two ceramic plates bonded together with their polarization directions opposing each other (Fig. 18.20).7 A dummy PLZT plate was positioned adjacent to the bimorph to cancel the photovoltaic voltage generated on the bimorph. Utilizing a dual beam method, switching was controlled by alternately irradiating the bimorph and the dummy. Using this dual beam method, the time delay of the bimorph that ordinarily occurs in the off process due to a low dark

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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18. PHOTOSTRICTIVE ACTUATORS BASED ON PIEZOELECTRICS

PLZT dummy Moving piece

Ps

Operating direction

Leaf spring

Contact PLZT bimorph Ps

Beam 2 Dual beam method

Beam 1 Base

FIG. 18.20

Structure of the photo-driven relay.7

conductivity could be avoided. 150 μm displacement was transferred to a snap action switch, with which on/off switching was possible. The on/ off response of the photo-driven relay was demonstrated with a typical delay time of 1–2 seconds.

18.4.3 Micro Walking Machine A photo-driven micro walking machine (well-known as Uchino’s Walker) was also developed using the photostrictive bimorphs.26 It was simple in structure, having only two PLZT bimorph legs (5 mm
20 mm
0.35 mm) fixed to a plastic board, as shown in Fig. 18.21. When the two legs were irradiated with purple light alternately, the device moved like an inchworm. The photostrictive bimorph as a whole bent by 150 μm as if it averted the radiation of light. The inchworm built on a trial basis exhibited rather slow walking speed (several tens μm/min), since slip occurred between the contacting surface of its leg and the floor. The walking speed can be increased to approximately 1 mm/min by providing some contrivances such as the use of a foothold having microgrooves fitted to the steps of the legs.

18.4.4 Photophone The technology to transmit voice data (i.e., a phone call) at the speed of light through lasers and fiber optics has been advancing rapidly. However, the end of the line—interface speaker—limits the technology, since optical phone signals currently must be converted from light energy to III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

18.4 PHOTOSTRICTIVE DEVICE APPLICATIONS

781

FIG. 18.21 Photo-driven micro walking machine made of two photostrictive bimorphs. Alternating irradiation provides a walking motion.26

mechanical sound via electrical energy. The photostriction may provide new photoacoustic devices. Photomechanical resonance of a PLZT ceramic bimorph has been successfully induced using chopped near-ultraviolet irradiation, having neither electric lead wires nor electric circuits.27 A thin cover glass was attached on the photostrictive bimorph structure to decrease the resonance frequency so as to easily observe the photo-induced resonance. A dual-beam method was used to irradiate the two sides of the bimorph alternately with an optical chopper, intermittently with a 180 degrees phase difference. The mechanical resonance was then monitored by changing the chopper frequency. Fig. 18.22 shows the tip displacement of the thin-plate-attached sample as a function of chopper frequency. Photo-induced mechanical resonance was successfully observed. The resonance frequency was about 75 Hz with a mechanical quality factor Qm of about 30. The maximum tip displacement of this photostrictive sample was about 5 μm at the resonance point. Though the sound level is low, the experiment suggests the promise of photostrictive PLZT bimorphs as photoacoustic components, or photophones, for the next optical communication age.

18.4.5 Micro Propelling Robot A new application of highly efficient, photostrictive PLZT films on flexible substrates has been conceived for usage in the new class of small vehicles for future space missions.28 A micro propelling robot can be designed III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

782

18. PHOTOSTRICTIVE ACTUATORS BASED ON PIEZOELECTRICS

6

Displacement (μm)

5

4

3

2

1

0 50

60

70 80 Frequency (Hz)

90

100

FIG. 18.22 Tip deflection of the bimorph device made from WO3 0.5 at.% doped PLZT under a dual beam control (illumination intensity: 10 mW/cm2).

into arch-shaped photoactuating composite films (unimorph type) with a triangular top (Fig. 18.23). In order to maximize the photostrictive properties of the sample, the sample thickness was determined to be 30 μm. This device is driven at resonance mode under an intermittent illumination. Photoactuating films may be fabricated from PLZT solutions and coated on one side of a suitable flexible substrate that will then be designed to have a curvature of 1 cm1. A slight difference in length/width between the right and left legs is designed in order to provide a slight difference between their resonance frequencies. This facilitates in controlling the device in both clockwise and counterclockwise rotations (i.e., right and left steering). A light chopper operating at a frequency close to resonance can be used to illuminate the device, in order to maximize the vibration of the bimorph that will then provide the capability to turn by applying different resonance frequencies to the two legs.

18.5 CONCLUSIONS Photostrictive actuators can be driven only by the irradiation of light, so they will be suitable for use in actuators, to which lead wires can hardly be connected because of their ultrasmall size or the conditions in which they are employed, such as an ultrahigh vacuum or outer space. The photostrictive bimorphs will also be applicable to photophones. Note also their remote control capability without being interfered by electromagnetic

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18.5 CONCLUSIONS

1. Initial stage Polarization direction PLZT film flexible substrate

Transparent electrode

50 μm 30 μm Nail

Nail

2. Illumination on Illumination

30 μm 50 μm

PLZT film flexible substrate Move

Nail

Moving direction 3. Illumination off

Polarization direction

PLZT film flexible substrate

Transparent electrode

50 μm 30 μm Move

Nail

(A)

A B

(B) FIG. 18.23 (A) Schematic diagram of an arch-shaped photoactuating film device, and (B) its triangular top shape.

noise. Fig. 18.24 summarizes the improvement in response speed of photostrictive bulk ceramics and it lists device improvements by year and key technological developments. Compared to the speed of 1 hour at the point of discovery in PZT, two-orders-of-magnitude improvement (up to 10 seconds) has been achieved in materials, and even photo-induced resonance has been realized in devices. The new principle actuators will have a considerable effect on the future of micromechatronics.

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80 Discovery in PZT 84 PLZT 3/52/48 Sol-gel Grain size control Donor doping

Device Year

88 Bulk ceramic

92

Doping concentration device designing (resonance usage)

96

PLZT 4/48/52 00 104

100 102 Responsivity (sec)

10–2

FIG. 18.24

Response speed improvement of the photostrictive bulk ceramic and device improvements listed by year and key technology development.

References 1. Brody PS. Optomechanical bimorph actuator. Ferroelectrics 1983;50:27. 2. Uchino K, Aizawa M. Photostrictive actuators using PLZT ceramics. Jpn J Appl Phys Suppl 1985;24:139–41. 3. Fridkin VM. Photoferroelectrics. In: Cardona M, Fulde P, Queisse H-J, editors. Solid-state sciences 9. New York: Springer-Verlag; 1979. p. 85–113. 4. Uchino K, Miyazawa Y, Nomura S. High-voltage photovoltaic effect in PbTiO3-based ceramics. Jpn J Appl Phys 1982;21(12):1671–4. 5. Uchino K. New applications of photostriction. Innov Mater Res 1996;1(1):11–22. 6. Chu SY, Uchino K. Impurity doping effect on photostriction in PLZT ceramics. Adv Perform Mater 1994;1:129–43. 7. Tanimura M, Uchino K. Effect of impurity doping on photo-strictive in ferroelectrics. Sens Mater 1988;1:47–56. 8. Uchino K, Aizawa M, Nomura S. Photostrictive effect in (Pb, La)(Zr, Ti)O3. Ferroelectrics 1985;64:199. 9. Uchino K. Ferroelectric devices. 2nd ed. Boca Raton, FL: CRC Press; 2010. 10. Glass AM, von der Linde D, Negran TJ. Appl Phys Lett 1974;25:233. 11. Poosanaas P, Tonooka K, Uchino K. Photostrictive actuators. Mechatronics 2000;10:467–87. 12. Hecht E. In: Zajac A, editor. Optics. 2nd ed. Massachusetts: Addison-Wesley Publishing; 1987. p. 44, 81–104, 610–6. 13. Kittel C. Introduction to solid states physics. 7th ed. New York: John Wiley & Sons, Inc; 1996. p. 388. 14. Chu SY, Ye J, Uchino K. Photovoltaic effect for the linearly polarized light in (Pb,La)(Zr, Ti)O3 ceramics. Smart Mater Struct 1994;3:114–7. 15. Uchino K, Miyazawa Y, Nomura S. Photovoltaic effect in ferroelectric ceramics and its applications. Jpn J Appl Phys 1983;22:102.

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16. Brody PS. Large polarization-dependent photovoltages in ceramic BaTiO3 + 5 wt.% CaTiO3. Solid State Commun 1973;12:673. 17. Brody PS. High voltage photovoltaic effect in barium titanate and lead titanate-lead zirconate ceramics. J Solid State Chem 1975;12:193. 18. Sada T, Inoue M, Uchino K. Photostriction in PLZT ceramics. J Ceram Soc Jpn Int Ed 1987;95:499–504. 19. Poosanaas P, Uchino K. Photostrictive effect in lanthanum-modified lead zirconate titanate ceramics near the morphotropic phase boundary. Mater Chem Phys 1999;61:31–41. 20. Nonaka K, Akiyama M, Takase A, Baba T, Yamamoto K, Ito H. Nonstoichiometry effects and their additivity on anomalous photovoltaic efficiency in lead lanthanum zirconate titanate ceramics. Jpn J Appl Phys 1995;34:5380–3. 21. Poosanaas P, Dogan A, Prasadarao AV, Komarneni S, Uchino K. Effect of ceramic processing methods on photostrictive ceramics. Adv Perform Mater 1999;6:57–69. 22. Poosanaas P, Dogan A, Prasadarao AV, Komarneni S, Uchino K. Photostriction of sol-gel processed PLZT ceramics. J Electroceram 1997;1:105–11. 23. Sada T, Inoue M, Uchino K. Photostrictive effect in PLZT ceramics. J Ceram Soc Jpn 1987;5:545–50. 24. Poosanaas P, Dogan A, Thakoor S, Uchino K. Influence of sample thickness on the performance of photostrictive ceramics. J Appl Phys 1998;84(3):1508–12. 25. Uchino K. New applications of photostrictive ferroics. Mater Res Innov 1997;1:163–8. 26. Uchino K. Micro walking machine using piezoelectric actuators. J Rob Mechatronics 1989;124:44–7. 27. Chu SY, Uchino K. In: Proc. 9th Int’l. Symp. Appl. Ferroelectrics, State College, PA; 1995. p. 743. 28. Thakoor S, Morookian JM, Cutts JA. The role of piezoceramics microactuation for advanced mobility. In: Conf. Proc. 10th IEEE Int’l. Symp. on Appl. Ferroelectrics. 1; 1996. p. 205–11.

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C H A P T E R

19 The Performance of Piezoelectric Materials Under Stress C.S. Lynch University of California, Los Angeles, CA, United States

Revised by X. Liao, S. Cochran University of Glasgow, Glasgow, United Kingdom

Abstract The performance variation of piezoelectric materials under large stress fields is discussed in this chapter. The variation relates microscopically to polarization reorientation and phase transitions and manifests macroscopically in changes in bulk material properties. The ferroelectric phase with the perovskite structure and the phase diagram with polarization reorientation are first described. A model is introduced to explain the phase transition with an energy function on polarization based on stabilization as the fundamental driving force. Then stress effects are described theoretically in relation to multidomains for piezocrystal and piezoceramics. Quasistatic and resonance techniques are described for experimental characterization of material property variation under uniaxial compressive pressure, with results presented for both piezocrystal and piezoceramics. Keywords: Ferroelectric, Piezoelectric, Piezocrystal, Ceramics, Phase diagram, Stress, Domains, Grains, Domain engineering, Phase transitions.

19.1 INTRODUCTION Piezoelectric materials are widely used in active and passive transducers based on bulk and thick and thin film devices utilizing the direct and inverse piezoelectric effects. In active transducers, the piezoelectric material is used for actuation to generate an acoustic field or a

Advanced Piezoelectric Materials http://dx.doi.org/10.1016/B978-0-08-102135-4.00019-9

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displacement or pressure. In passive transducers, the material is used as a sensor to detect acoustic pressure with high sensitivity.1–3 In both cases, however, the performance of the transducers may be unstable or inconsistent because of degradation of the piezoelectric material. In active transduction, the piezoelectric material may be subject to a high electrical drive field to generate high acoustic power output, depending upon which high dynamic stress is generated within the transducer and the temperature may increase because of loss effects. In passive applications, under extreme conditions, the piezoelectric materials may also suffer from temperature rises induced by heat conduction from the environment and from high stress levels in deep-sea applications and from preloading during transducer assembly. Temperature, T, pressure, P (also called stress, σ), and electric field, E, can act in isolation or combine to take effect, and they can be involved actively in high field operation or can cause significant deterioration of piezoelectric material performance under extreme conditions.4–10 The single factor of pressure, which is the subject of principal interest in this chapter, can be realized as a dynamic parameter under high drive conditions or as a static parameter under preloading or environmental pressure, with associated fatigue, degradation, and even failure in relation to the functional performance of the material.11–20 In the past two decades, increasing interest has been placed on relaxorbased single crystals that demonstrate both ultrahigh piezoelectric response and higher electromechanical coupling coefficients than conventional piezoceramics. The high piezoelectric performance and new vibrational modes with special crystal cuts, such as the k36 mode, provide the potential to design a new generation of ultrasonic transducers with higher sensitivity and wider bandwidth.21–27 However, piezocrystals are more sensitive to mechanical stress and more susceptible to mechanical failure than polycrystalline piezoceramics, considering that the strength of piezoceramics is enhanced by their formation from random distributions of multiple grains. This situation leads to the need to characterize the newly generated piezocrystals to understand performance variation with stress. Such characterization not only benefits understanding of the materials but may also aid the inclusion of material property changes in finite element analysis (FEA) for new transducer design. Performance degradation of piezoelectric materials under stress can be expressed as variation of material properties and figures of merit (FOMs). It comes from both intrinsic contributions relating to the distortion of the unit cell and extrinsic contributions relating to domain wall motion for both piezoceramics and piezocrystals.28 In terms of intrinsic contributions, degradation fundamentally relates to polarization reorientation and crystal phase transitions. Under high stress, the energy density profile of the ferroelectric crystal changes and the unit cell of the crystal phase

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correspondingly changes its crystal structure by spatial rearrangement of the ions, with the polarization rotating until it stabilizes at the lowest energy in the energy density profile.29,30 Extrinsic contributions are more complicated, with high-level domain wall motion generally corresponding with large piezoelectric coefficients. When a high stress is applied, defects are more easily initiated with effects such as dislocations, pinning, and hardening in the crystal. Additionally, the random spatial distribution of grains in ceramics complicates the analysis further. The remainder of this chapter begins with a description of the ferroelectric phase, including the perovskite structure and the phase diagram with polarization reorientation. Examples of the unit cell are provided for tetragonal, orthorhombic, rhombohedral, and orthorhombic phases, followed by phase diagrams with an explanation of polarization reorientation of a unit cell in the tetragonal phase. Next, the driving forces for polarization reorientation are introduced, with an energy function that combines mechanical and dielectric work, based on which the phase transition under stress and electric field for the tetragonal phase is explained in terms of polarization. Stress effects in multidomains are described theoretically for relaxor-based single crystals and ceramics, with emphasis on the needs of experimental characterization. The chapter is completed with descriptions of two uniaxial experimental arrangements for characterization and demonstrations of the variations in material properties and FOMs for piezocrystals and piezoceramics.

19.2 THE UNIT CELL AND FERROELECTRICITY Crystal structure, material properties, and functional performance are three highly correlated factors for crystalline materials. Based on the fundamental crystal unit cell structure, crystalline ferroelectrics can be categorized into four basic types: (1) the tungsten-bronze group, (2) the perovskite group, (3) the pyrochlore octahedral group, and (4) the layer structure group.31 Among these, the perovskite group is the most important because of its wide use in applications, with compositions such as BaTiO3, Pb[ZrxTi1
x]O3 (PZT), (x)Pb(Zn1/3Nb2/3)-(1
x)PbTiO3 (PZNPT), and (x)Pb(In1/2Nb1/2)O3-(y)Pb(Mg1/3Nb2/3)O3-(1
x
y)PbTiO3 (PIN-PMN-PT). The perovskite structure is conventionally expressed as ABO3, with the cubic phase of PZT shown as an example in Fig. 19.1. In this structure, the Ti4+ or Zr4+ ion sits at the center of the unit cell, the O2
ions sit at the center of each face of the unit cell, and the Pb2+ ions sit at each corner. In each unit cell, the single Ti4+ or Zr4+ ion contributes +4 charge; the six O2
ions contribute
6 charge, with each O2
ion shared at the face of two unit cells

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19. THE PERFORMANCE OF PIEZOELECTRIC MATERIALS UNDER STRESS

A: Pb2+ B: Ti4+/Zr4+ O3: O2– ABO3 perovskite structure

FIG. 19.1 The unit cell of the cubic phase of Pb[ZrxTi1
x]O3 with a Ti4+ or Zr4+ ion at the center of the unit cell, an O2
ion at the center of each face of the unit cell, and a Pb2+ ion at each corner.

[001]

[011]

[111]

Tetragonal

Orthorhombic

Rhombohedral

FIG. 19.2

The shapes and polarization directions of the unit cells for the ferroelectric tetragonal phase, orthorhombic phase, and rhombohedral phase.

and the eight Pb2+ ions contribute +2 charge with each lead ion shared at the corner of eight unit cells. In total, the charges sum to zero; in the cubic phase, the unit cell exhibits overall neutral charge with the positive and negative charge centers overlaid spatially. Besides the neutral cubic phase, three other phases commonly exist in ferroelectric materials according to the shape and polarization of the unit cell, as shown in Fig. 19.2: tetragonal, orthorhombic, and rhombohedral. Here, Miller indices are used to describe the crystallographic directions. In the tetragonal phase, the positive and negative charge centers shift in opposition in the h001i direction and the crystal lattice deforms into a square cuboid, leading to both elongation strain and spatial polarization in the h00 1i direction. For the orthorhombic and rhombohedral phases, similar shifts and deformations happen in the h011i and h111i directions

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19.2 THE UNIT CELL AND FERROELECTRICITY

T MA R

MC MB

O

Monoclinic

MA

MB

MC

FIG. 19.3

The transitional phase paths between tetragonal, orthorhombic, and rhombohedral phases, and the unit cells of the three monoclinic phases: MA, MB, and MC.

respectively, with the crystal lattices deformed into cuboid and trigonal trapezohedrons. Under specific conditions, the ferroelectric material adaptively stabilizes its crystal structure to sit at the phase corresponding to a stable, low energy level. If external conditions change, the crystal structure changes correspondingly, driven towards another relatively lower energy level. If the change is sufficient, a phase transition may take place between different ferroelectric phases. Transitions between the tetragonal, orthorhombic, and rhombohedral phases can be direct or indirect through three types of monoclinic phase: MA, MB, and MC, as shown in Fig. 19.3. The MA phase exists on the transitional path between tetragonal and rhombohedral, MB on the transitional path between rhombohedral and orthorhombic, and MC on the transitional path between orthorhombic and tetragonal.32 Driving conditions for phase transition can involve T, P, E, and compositional change during crystal growth. Evaluation of the effects of such conditions provides insight into the intraphase property variation and performance stability across phase transitions. Conventionally, the phase diagram is used for quality control in crystal growth and also for optimization of composition to obtain higher piezoelectric coefficients, and it is expressed in terms of composition and T. As shown for PZT and relaxorbased single crystal in Fig. 19.4, above the Curie temperature, TC, the material is in the cubic phase and does not demonstrate piezoelectricity.

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19. THE PERFORMANCE OF PIEZOELECTRIC MATERIALS UNDER STRESS

500

Temperature (ºC)

Temperature (ºC)

Cubic

Cubic

400 300 200

Rhombohedral

Tetragonal

Tetragonal

100 Rhombohedral

0

0 20 PbZrO3

40

60

80 100 PbTiO3

PZT

FIG. 19.4

Orthorhombic

Relaxor

PT

Relaxor-PT single crystal

The phase diagram of lead zirconate titanate and relaxor-based single crystal.

However, below TC, the crystalline unit cell is piezoelectric, evolving into nonsymmetric structures with positive and negative centers shifted from the balanced and overlaid position, resulting in a dipole moment vector, p; this is given by the following: p ¼ Qd,

(19.1)

where Q is the scalar charge and d is the equivalent distance vector between the positive and negative charge centers, pointing from negative to positive. The spontaneous polarization vector Ps forms with p, and it is expressed as the polarization density, given by the dipole moment per unit volume ΔV: Ps ¼ Δp=ΔV:

(19.2)

For ferroelectric materials, the spontaneous polarization is reversed when a suitably strong electric field is applied in the opposite direction. In this process, the polarization reorientation depends not only on the present external electric field but also on the previous polarization state, displaying hysteresis. Meanwhile, the strain demonstrates a butterfly loop, as shown in Fig. 19.5. The polarization versus electric field (P-E) and strain versus electric field (S-E) curves can be used directly to examine the polarization dynamics and also, by using the slope of the respective curves, to characterize the dielectric permittivity and the piezoelectric coefficients. The polarization reorientation dynamics can be explained in a cycle with seven critical states (a–g) in the tetragonal phase example shown in Fig. 19.6, which also corresponds to Fig. 19.5. In the initial state, a,

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19.2 THE UNIT CELL AND FERROELECTRICITY

b

a

d

g EC

–EC

e

b

Strain

Polarization

c

f e

c a

f

g

d Electrical field

Electrical field

FIG. 19.5 Ferroelectric hysteresis of polarization versus electrical field (P-E) curve (left), and butterfly loop of strain versus electrical field (S-E) curve (right).

E

E a

b

c

d E E

E e

f

g

h

FIG. 19.6

Polarization reorientation during reversal in an external electrical field (see text for explanation of sequence a ! b ! … ! g ! b …).

the positive and negative charge centers are overlaid in the neutral cubic phase. From state a to b, increasing positive E is applied, the positive and negative ions in the unit cell are further separated, and both polarization and strain increase. In state b, the polarization forms upward and saturates. From b to c, E decreases from a positive value to zero, but the overall polarization is maintained because of the remanent polarization and strain. From c to d, E becomes negative and the polarization is further reduced by shortening the positive and negative charge distances in the unit cell. In state d, the coercive field, E ¼
EC, is reached when the polarization starts to reverse and the strain reaches a minimum. From d to e, the reversed negative electric field further increases, with the reverse

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TABLE 19.1 Polarization Reorientation Dynamics of Tetragonal Phase in P-E Curve Ferroelectric Hysteresis and S-E Butterfly Loop State

Polarization reorientation dynamics

a

Cubic phase

a!b

Polarization saturates and strain reaches maximum

b!c

Remanent polarization and strain are retained

c!d

Polarization and strain decrease

d!e

After E <
EC, polarization reverses to negative and strain starts to increase

e!f

After saturation, polarization and strain decrease to remanent levels

f!g

Polarization and strain further decrease

g!b

After E > EC, polarization reverses to positive and strain starts to increase

polarization increasing negatively until it saturates in state e. From e to f, the negative value of E approaches zero and the magnitude of the polarization and strain reduce to remanent levels. From f to g, E is reversed from negative to positive and the polarization and strain both decrease as the cubic phase approaches. In the final transition from g back to b, with E exceeding the coercive field EC, both polarization and strain increase again until saturation. The dynamic cycle is then completed, as summarized in Table 19.1.

19.3 DRIVING FORCES FOR POLARIZATION REORIENTATION Polarization reorientation affects the performance of the crystalline material in a specific crystal phase and may even lead to a phase transition if certain thresholds are exceeded. These thresholds include T, P, and E and composition. The effect of compositional change can be explained theoretically with molecular dynamics and modeled and studied with first principle methods.33 The effects of T relate to the thermodynamics of the crystal lattice. These two factors are well represented in the phase diagram for quality control in manufacturing. In practical use, piezoelectric materials are subject to external mechanical (P) and electrical (E) conditions: in sensors, P is detected with an electrical signal output based on the direct piezoelectric effect; in actuators, electrical drive is input to generate mechanical work as an output based on the inverse piezoelectric effect. In many transducers, both the direct and inverse piezoelectric effects are utilized. Performance degradation and phase

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transitions in piezoelectric material are possible under the application of high values of P and E. The effects of these two factors can be explained from the perspective of energy dissipation or work done during a phase transition. Considering both P and E applied, the total external work, wT, per unit volume is mathematically expressed as a sum of the mechanical work, wM, and the electrical work, wE, both per unit volume: wT ¼ wM + wE :

(19.3)

When mechanical work is done on a volume of material, the elastic energy, WM, is simply related to the applied force, F, and the deformation distance, x, through the integration: Z (19.4) W M ¼ F  dx: When a small fractional volume is considered, F can be normalized as the second-order stress tensor, σ, across the surface to which the tensor is applied and the deformation distance, x, can be normalized as another second order tensor, ε, representing strain, relative to the original dimension, so that the mechanical work per unit volume is given as Z (19.5) wM ¼ σ  dε: Similarly, the electrical work, WE, amounts to moving a positive charge, Q, against a potential gradient, φ, and is given by the following: Z E (19.6) W ¼ φ  dQ: When considering the charge distribution in a small region, Q can be normalized as the surface charge density or electric displacement, D, for a given surface area. Additionally, φ can be normalized as the electrical field, E, with distance, so that, in analogy with mechanical work, the electrical work per unit volume is given as the following: Z E (19.7) w ¼ E  dD: Combining Eqs. (19.3), (19.5), and (19.7), wT per unit volume can be found from Eq. (19.8): Z Z (19.8) wT ¼ wM + wE ¼ σ  dε + E  dD:

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19. THE PERFORMANCE OF PIEZOELECTRIC MATERIALS UNDER STRESS

When σ and E are constant, wT can be simplified as the following: Z Z wT ¼ wM + wE ¼ σ  dε + E  dD: (19.9) Now considering a phase transition from phase α to phase β for a piezoelectric material, the energy difference— in other words, work to be done, wTðα!βÞ —can be obtained from the following:     wTðα!βÞ ¼ σ  ε β
ε α + E  Dβ
Dα : (19.10) Assuming that the piezoelectric material behaves linearly in both phases, α and β, ε and D can be expressed according to the constitutive equations as the following: ε ¼ sE  σ + d  E + ε0 D ¼ κσ  E + d  σ + D0

(19.11)

where sE is the fourth order tensor representing elastic compliance at constant E, d is the third-order piezoelectric coefficient tensor, κ σ is the second-order tensor of dielectric permittivity under constant stress, and ε 0 and D0 are the spontaneous strain and spontaneous electric displacement respectively. When ε β , ε α , Dβ , and Dα in Eq. (19.10) are replaced by the expressions in Eq. (19.11), wTðα!βÞ can be expanded explicitly:       sEβ
sEα  σ + dβ
dα  E + ε0β
ε0α wTðα!βÞ ¼ σ        +E  κ σβ
κ σα  E + dβ
dα  σ + D0β
D0α :

(19.12)

This energy difference represents the energy barrier criterion for the transition from any crystal phase, α, to another crystal phase, β. If the total applied work exceeds this barrier criterion, it initiates the phase transition in the crystal structure, with corresponding changes in material properties and functional performance. To further simplify the analysis, the polarization reorientation mechanism can be expressed with an energy function that represents a linear superposition of several contributions with the single major variable, polarization, P:       (19.13) Fðε, PÞ ¼ fL ðPi Þ + fG Pi, j + fels εij + felest εij , Pk + fdip ðPi Þ,

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19.3 DRIVING FORCES FOR POLARIZATION REORIENTATION

where the total energy function F(ε, P) has five components: Landau energy, fL(Pi), Ginzburg energy, fG(Pi, j), elastic energy, fels(εij), electrostrictive energy, felest(εij, Pk), and long-range dipole-dipole interaction, fdip(Pi). Considering analysis with a two-dimensional model, the Landau energy, fL(Pi), with the polarization along the z-axis, Pz ¼ 0, can be expressed as follows:       fL ðPi Þ ¼ α1 P2x + P2y + α11 P4x + P4y + α12 P2x  P2y ,

(19.14)

where Px and Py represent the polarizations along the x and y axes respectively, and α1, α11, and α12 are weighted coefficients. α1 is positive for the paraelectric cubic crystal phase, and it is negative for the nonparaelectric (ferroelectric) crystal phase. Taking the tetragonal phase as an example of a nonparaelectric phase, energy surfaces for both phases are plotted in Fig. 19.7. The Landau energy plot of the paraelectric phase displays a convex surface with respect to the positive axis as a function of polarization along the x and y axes. An imaginary free ball placed on this surface will finally stabilize at a minimum of this energy surface. Each minimum corresponds to a stable polarization point in equilibrium, in other words, unaffected by external factors. For the paraelectric phase, the minimum is at the origin, which indicates the stable point is neutral, without polarization in the x- or y-axis. In comparison, for the tetragonal phase, the free ball may rest at any one of the four equal minima according to prior thermodynamic disturbance, with polarization established randomly in one of the four possible directions corresponding to the positive and negative x and y axes. Landau free energy of paraelectric phase

Landau free energy of tetragonal phase

0.6 fL of tetragonal Phase

fL of paraelectric Phase

10 8 6 4 2 0 –15 –10

–5

0

5 Py

10

15

20

10

0 Px

–10

–20

0.4 0.2 0 –0.2 –0.4 –0.6 –15 –10

–5

0

5 Py

10

15

20

10

0

–10

–20

Px

FIG. 19.7 Landau energy for paraelectric phase without polarization (left) and tetragonal phase with four possible polarization directions (right).

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19. THE PERFORMANCE OF PIEZOELECTRIC MATERIALS UNDER STRESS Landau + compresssive energy of tetragonal phase

Landau + electric energy of tetragonal phase

1

3

fL + felectric

fL + fcompressive

2 0.5 0

1 0 –1

–0.5 –2 –1 –15 –10

–5

0

5 Py

10

15 20

10

0

–10

–20

–3 –15 –10

Px

–5

0

5 Py

10

15 20

10

0

–10

–20

Px

FIG. 19.8 Energy surface plot for Landau energy with compressive energy (left) and for the Landau energy with electric energy (right).

Now if a uniaxial  compressive stress  is applied along the y-axis, the elastic energy, fels εij ¼ fcompressive εij , Pi , superimposed on the Landau energy fL(Pi), is given by the following:      1 1  (19.15) fels εij ¼ fcompressive εij , Pi ¼ σ ij εij ¼ σ ij Q11  P2y + Q12  P2x , 2 2 where Qij is the electrostrictive coefficient relating polarization with strain. On the energy surface superimposing fL(Pi) and fels(εij) in Fig. 19.8, there are four possible nonequivalent minima, the two in the x-direction (Py ¼ 0) being deeper and more stable than the two in the y-direction (Px ¼ 0). Thus, if a compressive stress is applied along the y-axis of a piezoelectric material in the tetragonal phase, the polarization will tend to stabilize and rotate towards the x-axis, explaining the 90 degree switching of the unit cell under uniaxial stress from the perspective of energy. Similarly, when an electric field is applied along the y-axis, the Landau energy, fL(Pi), has an electrical energy term superimposed upon it, where felectric(Pi) is given by the following: felectric ðPi Þ ¼ Ey  Py :

(19.16)

For the energy surface superimposing fL(Pi) and felectric(Pi), also shown in Fig. 19.8, the surface is tilted compared with the normal tetragonal phase, with only one stable minimum with positive Py. This means that if spontaneous polarization aligns in the negative y-direction, when positive electrical field is applied the polarization reverses into the positive y-direction, which energetically explains the 180 degree switching of the unit cell under electrical field. Analysis using energy surfaces or profiles, explained here with examples of the paraelectric and tetragonal phases with additional external conditions, provides theoretical insights into how practical conditions drive polarization reorientations and phase transitions, which generally work

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in a manner that minimizes the total energy of the crystal structure and adaptively stabilizes it to maintain the equilibrium in dynamics.

19.4 DOMAINS UNDER STRESS In current applications, two types of piezoelectric material are in wide use: polycrystalline piezoelectric ceramics and relaxor-based single crystals. The use of piezoelectric ceramics started with the discovery of BaTiO3 in the early 1940s, motivated by use in capacitors, with subsequent development in the 1950s for ultrasonic applications. Now, piezoelectric ceramics have a huge range of applications, including high-powered ultrasonic transducers, high precision actuators, high sensitivity sensors, and microscale microelectromechanical systems (MEMS) devices for use in industry, consumer markets, scientific research, and healthcare. Since the 1990s, relaxor-based piezoelectric single crystals have gained increasing attention, mainly because of their ultrahigh piezoelectric properties and excellent electromechanical coupling coefficients, which enhance actuation performance and detection sensitivity and also help to reduce the complexity of driving systems significantly. Considering the uniformity of piezocrystals in their crystal lattice arrangement, it is useful first to examine the single crystal’s piezoelectric behavior to better understand both polycrystalline ceramics and single crystals. Ferroelectric single crystal, after growth, exhibits spontaneous polarization in the h001i direction in the tetragonal phase, in the h101i direction in the orthorhombic phase, and in the h11 1i direction in the rhombohedral phase. As shown in Fig. 19.9, for the tetragonal phase there are six directions equivalent to the h001i direction, labeled “6T”; for the orthorhombic phase there are twelve directions equivalent to the h101i direction, labeled “12O”; and for the rhombohedral phase, there are eight directions equivalent to the h111i direction, labeled “8R.” When the poling direction aligns with the direction of spontaneous polarization, single domains form in the single crystal, labeled “1T,” “1O,” and “1R” for the tetragonal, orthorhombic, and rhombohedral phases respectively, with only one domain variant favored by the poling field. To optimize the piezoelectric properties, multidomains can be formed by poling with a sufficiently large electric field in directions other than the spontaneous polarization direction; in Fig. 19.9, these are labeled “2T” and “3T” for the tetragonal phase, “4O” and “3O” for the orthorhombic phase, and “4R” and “2R” for the rhombohedral phase. In multidomain single crystals, the macroscopic polarization comes from multiple domain variants, with easier tilting of polarization in each domain for larger piezoelectric properties. Table 19.2 compares the distinctive characteristics

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[0 0 1]C

[1 0 1]C

[1 1 1]C

90º

6T

1T

90º

2T

3T

90º 60º

12O

4O

1O

3O

2R

1R

109º

71º

8R

4R

FIG. 19.9 Single domains for tetragonal, orthorhombic, and rhombohedral phases, with possible multidomain polarization in domain engineering.

TABLE 19.2 Characteristics of Single-Domain and Multidomain Piezoelectric Single Crystals Single domain

Domain engineering

Multidomain

dijk

!

dijk0 "

Qm

!

Qm0 #

k33 & k31 modes

!

k15 & k36 modes

of single-domain and multidomain single crystals. Generally, because of the easy polarization rotation and domain wall motion in multidomain crystals, the piezoelectric coefficients, dijk, increase and the mechanical quality factor, Qm, decreases. Meanwhile, the poling direction varies from the direction of spontaneous polarization, and this leads to special crystal cuts to optimize vibration modes, including k15 and k36, for piezoelectric functionality. In the k36 mode, a piezoelectric plate vibrates with face shear motion, as shown in Fig. 19.10. The k36 mode is the only shear mode for which the polarization direction aligns with the direction of the driving electric field, which may help in practice to maintain the polarization by repolarization under active high field drive. Optimization of the

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19.4 DOMAINS UNDER STRESS

d36* (pC/N)

[1 0 0] 20 90 1500

y position

20

Original Measured Fitted

Phase: 10 degree

120

q: rotation angle 30

150

15

500 180

10 5 0

60

1000

0

330

210 240

0

5

10 15 x position

[0 -1 1]

300 270

20

Poling direction [0 1 1]

FIG. 19.10

Experimental measurement of face shear motion from laser vibrometry (left) and orientation dependence of piezoelectric coefficient d36* (right).

Z’’Z’’’

Z Z’ Coordinates XYZ R(j) Y ’’’

X

X’X’’

FIG. 19.11

X ’’’

Y

Coordinates X⬘Y⬘Z⬘

y q

j

Rotate j about Z axis

Y ’’

R(q)

Rotate q about X⬘ axis Coordinates X⬙Y⬙Z⬙

Y’

R(y)

Rotate y about Z⬙ axis Coordinates X⵮Y⵮Z⵮

Coordinate system rotations for tensor rotation transformations.

piezoelectric coefficient, d36*, depends on the polarization direction and on two other piezoelectric coefficients, d32 and d31, based on the rotation angle θ: d∗36 ¼ ðd32
d31 Þ  sin ð2θÞ:

(19.17)

The material properties of multidomain piezocrystal (permittivity ε*ij, piezoelectric coefficient d*ijk, elastic compliance s*ijkl) gained from domain engineering optimization can be derived from the properties of single domain piezocrystal (permittivity εij, piezoelectric coefficient dijk, elastic compliance sijkl) by tensor rotation, neglecting the 10%–20% extrinsic contribution from domain wall motion. The tensor rotation operation comprises three steps in rotating the coordinate system, as shown in Fig. 19.11: (1) rotate φ about the Z-axis, (2) rotate θ about the X0 -axis, and (3) rotate ψ about the Z00 -axis. With these three rotations, the coordinate system transforms from XYZ to X0 Y0 Z0 , X00 Y00 Z00 and finally X000 Y000 Z000 with Euler angles (φ, θ, ψ), and the three rotation operations correspond to III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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19. THE PERFORMANCE OF PIEZOELECTRIC MATERIALS UNDER STRESS

s33

R

O

s33

FIG. 19.12 Polarization rotation and phase transition of [0 0 1] poled multidomain sample from rhombohedral (R, left) to orthorhombic (O, right) under uniaxial stress in the h0 0 1i plane.

three mathematical rotation matrices R(φ), R(θ), and R(ψ). Thus, the transformation of the second-order tensor, εij, third-order tensor, dijk, and fourth order tensor, sijkl, is given by the following: R ¼ Rðψ Þ  RðθÞ  RðϕÞ,

(19.18)

ε*ij ¼ rim  rjn  εmn , d*ijk ¼ rim  rjn  rko  dmno , s*ijkl ¼ rim  rjn  rko  rlp smnop , where rij are the coefficients in the combined rotation matrix, R. These tensor rotation equations provide a way to search for the optimal desired material property in a specific vibration mode, suitable for both theoretical analysis and practical use with specific crystal cuts after growth. Domain-engineered multidomain relaxor-based piezoelectric single crystals provide the benefits of higher piezoelectric coupling and new functional vibration modes. At the same time, the multidomain structure may reduce stability under practical conditions. As shown in Fig. 19.12, when a uniaxial stress is applied in the h001i plane, with a piezoelectric sample in a multidomain rhombohedral phase poled in the h001i direction, a phase transition to the orthorhombic phase can be induced under compressive stress. In comparison, if the stress is applied in the h011i plane as shown in Fig. 19.13, there will be only partial conversion of rhombohedral domains to the tetragonal phase, with the rhombohedral domains in the h011i plane intact. This is because the applied stress points perpendicularly to the polarization vectors in the h011i plane, which does not affect the dipole within the crystal unit cell. The difference in behavior depending on the application of stress in different directions demonstrates possible stability enhancement of multidomain single crystals by adopting III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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19.4 DOMAINS UNDER STRESS

s11

s11

R

R&T

FIG. 19.13

Polarization rotation and partial phase transition of [001] poled multidomain sample from rhombohedral (R, left) to rhombohedral and tetragonal (R & T, right) under uniaxial stress in the h011i plane.

Polycrystalline ceramic sample

Grain

Grain

Porosity 180 domain walls

FIG. 19.14

90 domain walls

Structure hierarchy of polycrystalline ceramics.

different arrangements in use but also leads to the need to characterize the material in different vibration modes.34,35 Macroscopically, polycrystalline piezoelectric ceramics are composed of many grains and the grains are separated by boundaries or defective porosity, as show in Fig. 19.14. Every grain in the ceramic sample can be considered as a tiny single crystal. In each grain there exists a single domain or multidomains. In the tetragonal phase, 180 degree domain walls separate 180 degree domains parallel to polarization direction, and 90 degree domain walls separate 90 degree domains that are oriented at 45 degree to the polarization. For both piezoelectric ceramics and single crystals, dipole defects, doping-induced oxygen vacancies, and domain wall intersects are supposed to stabilize and pin the domain wall motion, with an overall piezoelectric “hardening” effect. Considering the effect of a uniaxial stress on piezoelectric ceramics in an underwater Tonpilz transducer as shown in Fig. 19.15, when the pressure plus preload is applied to the top, wet surface of the transducer III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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19. THE PERFORMANCE OF PIEZOELECTRIC MATERIALS UNDER STRESS

s33

s33

s33 Underwater Tonpilz transducer

Volume averaging effect

FIG. 19.15

Volume averaging effect of stress on piezoelectric ceramics in an underwater Tonpilz transducer.

underwater in the deep ocean, the aggregate effect on piezoelectric ceramics corresponds to volume averaging of the effects on each single crystal plus the effects on the grain boundaries.

19.5 OBSERVATION OF EFFECTS OF STRESS The domain engineering configuration in piezoelectric single crystal, the volume averaging effect in piezoelectric ceramics, and the stress application directions combine to magnify the performance instability and also make theoretical analysis for performance prediction more difficult. To evaluate the performance of piezoelectric materials under uniaxial or hydrostatic stress, some FOMs, variations of key material properties, or even the full elastoelectric matrix may need to be characterized under different stress levels for entry into analytical equations or numerical FEA. Such characterization forms a vital link between theoretical understanding of piezoelectric behavior under stress and the exploitation of these materials in practical use. To characterize the performance variation of piezoelectric material under uniaxial stress, two configurations can be used: quasistatic and resonant. In the quasistatic configuration shown in Fig. 19.16, the piezoelectric material under test (PZ-MUT) is placed between two fixtures, underneath which a calibration element (Cal. element) or force sensor is aligned vertically with a vibration motor on a stable base. The principle is similar to the quasistatic Berlincourt method, with a standard piezoelectric sample used as Cal. element. The vibration motor generates vertical vibration in a low frequency range, 1–10 kHz. The charge output, Q, the reaction force, F, and the voltage, V, and current, I, can be measured from

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19.5 OBSERVATION OF EFFECTS OF STRESS

805

s

Fixture

Amplifier

Q, F, V, I, A PZ-MUT

C

A1

C’

A2

Fixture

Q’, F’, V’, A’,

Cal. element/ force sensor

dij eij tan d

Vibration motor Base

FIG. 19.16 Quasistatic setup for characterization of the performance variation of piezoelectric material under stress.

PZ-MUT with reference to its cross-sectional area, A. For Cal. element with a cross-sectional area, A0 , the measurements can be made to determine the charge output, Q0 , the force, F0 , and the voltage, V0 . All these physical parameters are digitized after amplification with shunt capacitors C and C0 . Three key properties can then be characterized with Eq. (19.19): piezoelectric coefficient, dij, free dielectric permittivity, εij, and dielectric loss, tan δ: dij ¼

Q=A Q CV ¼ ¼ , F=A F F

(19.19)

dij CV=F V ¼ ¼ , d0ij C0 V 0 =F0 V 0 Z¼

V ¼ jZjejθ I

tan δ ¼
cot θ: In these equations, dij0 is the piezoelectric coefficient of the Cal. element, F ¼ F0 is the uniaxial force, C is selected to be the same as C0 for convenience, and the impedance magnitude, jZj, in the low frequency range can be converted into an equivalent low frequency capacitance relating the dielectric permittivity, εij, with the sample’s dimensions. In the resonant configuration shown in Fig. 19.17, PZ-MUT is placed between two fixtures, and the electric outputs, V and I, are measured directly by a commercial electrical impedance analyzer. Following this, the impedance spectra of PZ-MUT are measured at different stress levels.

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19. THE PERFORMANCE OF PIEZOELECTRIC MATERIALS UNDER STRESS

s

Fixture

Electric output

Impedance analyser fs, fp Qm, kij, tan d

PZ-MUT Fixture

sij, dij, eij

s

FIG. 19.17

Resonance setup for characterization of the performance variation of piezoelectric material under applied stress.

The serial and parallel resonance frequencies, fs and fp, can be obtained and the electromechanical coupling coefficient, kij, can be calculated from them. By utilizing the impedance magnitude peak profile and the impedance phase, Qm and tan δ can be obtained.36–38 Based on the IEEE Standard on Piezoelectricity, combined with impedance spectroscopy, variations in elastic compliance, sij, piezoelectric coefficient, dij, and the permittivity, εij, can also be derived.39 The resonant configuration allows more parameters and material properties to be characterized than the quasistatic setup. However, it depends on clear identification of the resonance and antiresonance peaks in impedance spectra. When a PZT-4 ring sample is tested between brass fixtures as shown in Fig. 19.18, it is found that the curve of impedance magnitude degrades so seriously as pressure is increased from 0 to 20 MPa that it is impossible to identify resonance peaks in the magnitude plot. The reason for the distortion of the impedance spectra is explained by the model shown in Fig. 19.19. Under stress, the acoustic impedances of PZ-MUT and the fixture are Z1 and Z2 respectively. With PZ-MUT connected to the impedance analyzer, the necessary electrical excitation is converted to mechanical (acoustic) energy, which leaks from PZ-MUT into the fixtures via transmission coefficients T1 and T2, and reflects backwards from the fixtures to PZ-MUT via reflection coefficients R1 and R2. These coefficients, R and T, are defined by the following:   Z2
Z1 2 4Z2 Z1 , T¼ : (19.20) R¼ Z2 + Z1 ðZ2 + Z1 Þ2 Eq. (19.20) indicates that most energy is transmitted, with T  1 and R  0, when the acoustic impedances at the contact interface are similar. In contrast most energy is retained, with R  1 and T  0, when the two acoustic impedances are significantly different.

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807

19.5 OBSERVATION OF EFFECTS OF STRESS Brass fixture

Impedance magnitude (Ohms)

1.0E+06

0 MPa 1.0E+05 5 MPa 1.0E+04 10 MPa 1.0E+03 15 MPa 1.0E+02 20 MPa 1.0E+01 0.0E+00

2.0E+05

4.0E+05

6.0E+05

8.0E+05

1.0E+06

Frequency (Hz) Brass fixture

1.0E+05 Impedance magnitude (Ohms)

s

Brass PZT-4 Ring Brass

0 MPa 5 MPa

1.0E+04

10 MPa 1.0E+03

15 MPa 20 MPa

1.0E+02 2.0E+05 2.5E+05 3.0E+05

s

3.5E+05 4.0E+05 4.5E+05

5.0E+05

Frequency (Hz)

FIG. 19.18

Resonance setup with a PZT-4 ring sample and its impedance spectra measured under pressure with brass fixtures from 0 to 20 MPa.

s

s T1

Fixture: Z2

Fixture Modelling

PZ-MUT: Z1

PZ-MUT Fixture

s

FIG. 19.19

R1

Fixture: Z2

R2 T2

s

Acoustic leakage model in the stress application setup.

By examining the acoustic impedance, Zac, of common materials listed in Table 19.3, it is clear that PZT-4 and brass are similar, so that most energy leaks into the brass and little is retained in PZ-MUT to form the mechanical standing waves needed for clear resonance in impedance spectra. To eliminate the leakage, a material with significantly different acoustic impedance must be selected for the fixture so as to appropriately

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19. THE PERFORMANCE OF PIEZOELECTRIC MATERIALS UNDER STRESS

TABLE 19.3 Acoustic Impedance Zac of Some Common Materials Material

Density (kg/m3)

Speed of sound (m/s)

Acoustic impedance Zac (MRayl)

Air

1.3

330

0.0004

Water

1000

1500

1.5

PZT-4

7500

4600

34.5

Brass

8640

4700

40.6

Stainless steel

7890

5790

45.7

Epofix

1130

2630

2.97

Nylon

1150

2600

2.99

PTFE

2200

1400

3.08

Acrylic

1190

2750

3.27

represent the material property variation with an accurate measurement of the electrical impedance. This material must also withstand the applied stress, up to at least P  60 MPa. A high pressure microbubble-filled epoxy fixture is one solution, based on the significantly lower acoustic impedances of both air and epoxy than PZT-4. As shown in Fig. 19.20, the impedance spectra of PZT-4 are measured with clearer resonance peaks, because of the diminished acoustic leakage. By utilizing the resonant configuration, the property variations of piezoelectric single crystal with stress can be illustrated, based on two PZ-MUTs: 5 mm  5 mm  0.5 mm thickness-extensional (TE) mode samples of PIN-PMN-PT and Mn-doped PIN-PMN-PT (Mn:PIN-PMN-PT) respectively. Clear impedance spectra from each PZ-MUT are first measured under uniaxial pressure in the range 0–60 MPa. Then the IEEE standard method is used to obtain the relative permittivity under constant stress, εr33S; the piezoelectric stress coefficient, e33; the elastic stiffness constant in the open circuit condition, c33D; the TE mode electromechanical coupling coefficient, kt; the mechanical quality factor at resonant frequency, Qr; and the dielectric loss in the clamped condition, tan δ33, using Eq. (19.21): εr33 S ¼ t  C=ðA  ε0 Þ, sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  ffi π  fs π fp
fs kt ¼  tan  , 2  fp fp 2 c33 D ¼ 4  ρ  t2  fp2 ,

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

(19.21)

809

Impedance magnitude (ohms)

19.5 OBSERVATION OF EFFECTS OF STRESS

1.0E+06

Microbubble-filled epoxy fixture—encapsulated

1.0E+05 1.0E+04 1.0E+03 1.0E+02 1.0E+01 0.0E+00 2.0E+05

4.0E+05

6.0E+05

8.0E+05 1.0E+06

0 MPa 5 MPa 10 MPa 15 MPa 20 MPa 25 MPa 30 MPa 35 MPa 40 MPa 45 MPa 50 MPa 55 MPa 60 MPa

Frequency (Hz)

Microbubble filled epoxy

PZT-4 Ring

Epoxy s

Impedance magnitude (Ohms)

s 1.0E+05

Microbubble-filleld epoxy fixture—encapsulated

1.0E+04

1.0E+03

1.0E+02 2.0E+05 2.5E+05 3.0E+05 3.5E+05 4.0E+05 4.5E+05 5.0E+05

0 MPa 5 MPa 10 MPa 15 MPa 20 MPa 25 MPa 30 MPa 35 MPa 40 MPa 45 MPa 50 MPa 55 MPa 60 MPa

Frequency (Hz)

FIG. 19.20

Resonance setup with a PZT-4 ring sample and its impedance spectra measured under pressure in the range of 0–60 MPa, with encapsulated microbubble-filled epoxy fixtures.

e33 D ¼ kt 

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ε33 S  c33 D ,

f0 , jf2
f1 j R Z  cos θ , tan δ33 ¼ ¼ X Z  sin θ Qr ¼

where t is the thickness of the PZ-MUTs, C is the capacitance measured at 2 fp, A is the lateral surface area, ε0 is the permittivity of free space, fs is the equivalent circuit series resonance frequency measured at minimum electrical impedance magnitude, and fp is the equivalent circuit parallel resonance frequency measured at peak electrical impedance magnitude; ρ is the density of the PZ-MUT; ε33S is the permittivity under constant stress; f0 is the central frequency and j f2
f1j is the 3 dB bandwidth at resonance; Z is the impedance with phase angle θ off resonance in the clamped condition, and corresponding resistance is R and reactance is X. These property variations are shown in Fig. 19.21. The results demonstrate that εr33S increases generally with pressure for both PIN-PMN-PT and Mn:PIN-PMN-PT. The values of e33, c33D, and kt first decrease from 0 to 20 MPa, remain stable to 40 MPa, and fall again to the maximum pressure. The transitional region, 20–40 MPa, is considered to be related

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

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19. THE PERFORMANCE OF PIEZOELECTRIC MATERIALS UNDER STRESS

20

1600

16

e33 (C/m2)

er33 s

1200 800

12 8 Mn:PIN-PMN-PT

400

4

Mn:PIN-PMN-PT

PIN-PMN-PT

PIN-PMN-PT

0 0

10

20 30 40 50 Pressure (Mpa)

0 0

60

10

20 30 40 50 Pressure (Mpa)

60

0.6

1.8E+11

0.5

c33D (N/m2)

1.6E+11 0.4

kt

1.4E+11

0.3 0.2

1.2E+11

Mn:PIN-PMN -PT

PIN-PMN-PT

PIN-PMN-PT

1E+11 0

10

20 30 40 Pressure (MPa)

50

0

60

700

0.12

600

0.10

500

0

10

20 30 40 Pressure (MPa)

50

60

0.08

400

tan d33

Qr

Mn:PIN-PMN-PT

0.1

0.06

300

0.04

200

Mn:PIN-PMN-PT Mn:PIN-PMN-PT

0.02

100 PIN-PMN-PT

0 0

10

20 30 40 Pressure (Mpa)

50

60

0.00

PIN-PMN-PT

0

10

20 30 40 Pressure (MPa)

50

60

FIG. 19.21

Property variations of piezoelectric single crystal TE samples of PIN-PMN-PT and Mn:PIN-PMN-PT under stress in the range of 0–60 MPa.

to a phase transition from rhombohedral to orthorhombic. Qr follows the same pattern. For PIN-PMN-PT, tan δ33 increases up to P ¼ 10 MPa, then it decreases in the range 20–30 MPa and stabilizes afterwards from 30 to 60 MPa. Mn:PIN-PMN-PT exhibits a more stable response for tan δ33. This observation of behavior under stress provides important indications of functional performance of the piezoelectric crystals in transducers deep underwater and with preloading, and it can also be related to the theoretical understanding of the basic properties of the piezocrystals. III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

19.5 OBSERVATION OF EFFECTS OF STRESS

811

Polycrystalline piezoelectric ceramics, PZT-4 and PZT-8, representative of piezoelectrically hard materials in common use for high-power applications—and PZT-5A and PZT-5H, piezoelectrically soft materials for low power and sensing applications—were systematically examined by Krueger40,41 to determine variations in permittivity, dielectric loss, and piezoelectric constant with compressive stress both parallel and perpendicular to the polarization axis. With the parallel arrangement, permittivity, ε33T, and dielectric loss increased, and the piezoelectric constant, d33, decreased when the stress was increased up an equivalent of 138 MPa. With the perpendicular arrangement over the same range of stress, ε33T and piezoelectric constant, d31, decreased, while tan δ and d32 increased. In this process, a phase transition was identified at a stress level equivalent to 34 MPa. To overcome such variations, heat treatment and stress stabilization were checked, with the stabilizing effect from heat treatment observed as permanent and the effect from stress stabilization as nonpermanent.42 Property variation of polycrystalline ceramics is difficult to analyze and hard to predict, because of the presence of multiple grains, with each polarized individually. To simplify this, piezoelectric ceramics can be modeled as a collection of noninteracting grains with each oriented individually relative to the global coordinate system. The overall piezoelectric response can be calculated as the volume average of all the individual grains. The orientation of each grain can be described by introducing a local coordinate system with a rotation matrix, which relates to three Euler angles, φ, θ, and ψ. Random generation of Euler angles for each grain generates a texture, rather than a random grain orientation. Combining the volume averaging and stress effects, the averaged properties of piezoelectric ceramics with n grains under stress can be expressed as follows: Z n X 1 ð nÞ εij ¼ f1  εij dv ¼ f1 ðnÞ εij , (19.22) v v a¼1 1 dijk ¼ v sijkl ¼

1 v

Z f2  dijk dv ¼

n X

v

a¼1

Z f3  sijkl dv ¼ v

ðnÞ

f2 ðnÞ dijk ,

n X

ðnÞ

f3 ðnÞ sijkl ,

a¼1

where the volume averaging is expressed as integration and summation, and f1, f2 and f3 represent the stress-induced variation functions for permittivity, piezoelectric strain constant, and elastic compliance respectively. This analysis neglects grain boundary effects but intergranular interactions can be incorporated in Eq. (19.22), as additional items relating to stress level, adding to the complexity of performance analysis and functional prediction of piezoelectric ceramics.

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19.6 CONCLUSIONS AND FUTURE TRENDS Large stress fields degrade microscopic crystal structure and lead to phase transitions by polarization orientation for both polycrystalline piezoelectric ceramics and relaxor-based piezoelectric single crystals. The effects are manifest macroscopically as variations in material properties and degradation of FOMs in functional piezoelectric performance. Thorough investigation for deeper understanding of the fundamental mechanisms and the effect in transduction is of vital importance for both new compositions in material design and transducer design with careful directional arrangements for stress and polarization. This will help stabilize performance in applications including deep-sea sonar transducers, preloaded Langevin transducers for many industrial applications, and ultrasonic thin film devices. It will also be useful to gain better control of stress-induced phase-transition-based ultrasonic devices for large piezoelectric outputs.43 In this chapter, two characterization configurations representing quasistatic and resonant measurements have been introduced to apply uniaxial static pressure, based on the Berlincourt method and the IEEE standard method respectively. To further investigate the stress effects on immersion transducers with pressure compensation, it will also be necessary to perform characterization under hydrostatic conditions. Additionally, piezoelectric materials are subject not only to static pressure but also high dynamic stress by driving fields in applications. In future work, characterization with full material properties, loss parameters, and performance FOMs especially for new compositions of piezoelectric single crystals is expected to be performed with cyclic test under preloading, when the PZ-MUT experiences a few cycles of stress loading. This will also occur with fatigue testing under high drive, when the PZ-MUT experiences large numbers of stress cycles. Engineering methods to enhance mechanical strength, including heat treatment and surface finishing, also need further investigation. The fundamental polarization mechanism that has been discussed is expected to be further utilized in material engineering, so as to design more stable and potentially higher performing piezocrystal configurations for applications requiring specific vibration modes. The identified variations of material property and FOMs should also be integrated in FEA software packages to allow virtual prototyping to include stress effects, providing better prediction of transduction performance than is presently possible. It is clear that, although considerable efforts have been made to better understand piezoelectric material under stress and to measure macroscopic material property variation with stress, further research on materials and methodology is necessary.

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

REFERENCES

813

References 1. Zhang S, Li F. High performance ferroelectric relaxor-PbTiO3 single crystals: status and perspective. J Appl Phys 2012;111(3):031301. 2. Zhang S, et al. Advantages and challenges of relaxor-PbTiO3 ferroelectric crystals for electroacoustic transducers—a review. Prog Mater Sci 2015;68:1–66. 3. Zhang S, et al. Relaxor-PbTiO(3) single crystals for various applications. IEEE Trans Ultrason Ferroelectr Freq Control 2013;60(8):1572–80. 4. Xiaochun L, et al. Functional characterization of piezocrystals monitored under high power driving conditions. In: Ultrasonics symposium (IUS), 2015 IEEE international; 2015. 5. Liao X, et al. Functional piezocrystal characterization under varying conditions. Materials 2015;8(12):5456. 6. Qiu Z, et al. Characterization of piezocrystals for practical configurations with temperature- and pressure-dependent electrical impedance spectroscopy. IEEE Trans Ultrason Ferroelectr Freq Control 2011;58(9):1793–803. 7. Gallagher JA, Lynch CS. Combining experiments and modeling to characterize field driven phase transformations in relaxor ferroelectric single crystals. Acta Mater 2015;89:41–9. 8. Webber KG, Zuo R, Lynch CS. Ceramic and single-crystal (1
x)PMN–xPT constitutive behavior under combined stress and electric field loading. Acta Mater 2008;56(6):1219–27. 9. Zhang S, et al. Piezoelectric property of relaxor-PbTiO3 crystals under uniaxial transverse stress. Appl Phys Lett 2013;102(17):172902. 10. Zhang S, et al. Field stability of piezoelectric shear properties in PIN-PMN-PT crystals under large drive field. IEEE Trans Ultrason Ferroelectr Freq Control 2011;58(2):274–80. 11. Meeks SW, Timme RW. Effects of one-dimensional stress on piezoelectric ceramics. J Appl Phys 1975;46(10):4334–8. 12. Krueger HHA, Berlincourt D. Effects of high static stress on the piezoelectric properties of transducer materials. J Acoust Soc Am 1961;33(10):1339–44. 13. Cain MG, S M, G MG. Degradation of piezoelectric materials. Teddingtong, UK: NPL; 1999. p. 1-39. 14. Finkel P, et al. Study of phase transitions in ternary lead indium niobate-lead magnesium niobate-lead titanate relaxor ferroelectric morphotropic single crystals. Appl Phys Lett 2010;97(12):122903. 15. Lynch CS. The effect of uniaxial stress on the electro-mechanical response of 8/65/35 PLZT. Acta Mater 1996;44(10):4137–48. 16. Pohanka RC, et al. Fracture, fractography and internal stress of BaTiO3 ceramics. Ferroelectrics 1976;10(1):231–5. 17. Cook RF, et al. Fracture of ferroelectric ceramics. Ferroelectrics 1983;50(1):267–72. 18. Weitzing H, et al. Cyclic fatigue due to electric loading in ferroelectric ceramics. J Eur Ceram Soc 1999;19(6–7):1333–7. 19. dos Santos e Lucato SL, et al. Electrically driven cracks in piezoelectric ceramics: experiments and fracture mechanics analysis. J Mech Phys Solids 2002;50(11):2333–53. 20. Westram I, et al. Mechanism of electric fatigue crack growth in lead zirconate titanate. Acta Mater 2007;55(1):301–12. 21. Tian J, Han P. Growth and characterization on PMN-PT-based single crystals. Crystals 2014;4(3):331. 22. Sun E, Cao W. Relaxor-based ferroelectric single crystals: growth, domain engineering, characterization and applications. Prog Mater Sci 2014;65:124–210. 23. Zhang S, et al. Face shear piezoelectric properties of relaxor-PbTiO(3) single crystals. Appl Phys Lett 2011;98(18):182903. 24. Mitsuyoshi M, Yoshihito T, Yosuke I. Development of large-diameter single-crystal PMN-PT with high energy conversion efficiency. JFE Technical Report, Oct. 2005.06. p. 46–53.

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25. Huo X, et al. Elastic, dielectric and piezoelectric characterization of single domain PINPMN-PT: Mn crystals. J Appl Phys 2012;112(12):124113. 26. Jiang X, Kim J, Kim K. Relaxor-PT single crystal piezoelectric sensors. Crystals 2014;4 (3):351. 27. Park S-E, Shrout TR. Ultrahigh strain and piezoelectric behavior in relaxor based ferroelectric single crystals. J Appl Phys 1997;82(4):1804–11. 28. Randall CA, et al. Intrinsic and extrinsic size effects in fine-grained morphotropic-phaseboundary lead zirconate titanate ceramics. J Am Ceram Soc 1998;81(3):677–88. 29. Oates WS, et al. Phase field modeling of domain structures in ferroelectric materials. In: Proc SPIE 5387 Smart Structures and Materials 2004;314. http://dx.doi.org/ 10.1117/12.539902. 30. Wang J, et al. Phase-field simulations of ferroelectric/ferroelastic polarization switching. Acta Mater 2004;52(3):749–64. 31. Haertling GH. Ferroelectric ceramics: history and technology. J Am Ceram Soc 1999; 82(4):797–818. 32. Cox DE, et al. Universal phase diagram for high-piezoelectric perovskite systems. Appl Phys Lett 2001;79(3):400–2. 33. de Jong M, et al. A database to enable discovery and design of piezoelectric materials. Sci Data 2015;2:150053. 34. McLaughlin EA, Liu T, Lynch CS. Relaxor ferroelectric PMN-32%PT crystals under stress and electric field loading: I-32 mode measurements. Acta Mater 2004;52(13):3849–57. 35. McLaughlin EA, Liu T, Lynch CS. Relaxor ferroelectric PMN-32%PT crystals under stress, electric field and temperature loading: II-33-mode measurements. Acta Mater 2005;53(14):4001–8. 36. Uchino K, Hirose S. Loss mechanisms in piezoelectrics: how to measure different losses separately. IEEE Trans Ultrason Ferroelectr Freq Control 2001;48(1):307–21. 37. Yuan Z, Seyit OU, Kenji U. Loss factor characterization methodology for piezoelectric ceramics. IOP Conf Ser: Mater Sci Eng 2011;18(9):092027. 38. Liu G, et al. Losses in ferroelectric materials. Mater Sci Eng: R: Rep 2015;89:1–48. 39. 176-1987—IEEE Standard on Piezoelectricity. Available online: http://ieeexplore.ieee. org/xpl/articleDetails.jsp?arnumber¼26560&contentType¼Standards ANSI/IEEE Std 176-1987, 1988. p. 0_1. 40. Krueger HHA. Stress sensitivity of piezoelectric ceramics: Part 1. Sensitivity to compressive stress parallel to the polar axis. J Acoust Soc Am 1967;42(3):636–45. 41. Krueger HHA. Stress sensitivity of piezoelectric ceramics: Part 3. Sensitivity to compressive stress perpendicular to the polar axis. J Acoust Soc Am 1968;43(3):583–91. 42. Krueger HHA. Stress sensitivity of piezoelectric ceramics: Part 2. Heat treatment. J Acoust Soc Am 1968;43(3):576–82. 43. Finkel P, et al. Simultaneous stress and field control of sustainable switching of ferroelectric phases. Sci Rep 2015;5:13770.

III. APPLICATION ORIENTED MATERIALS DEVELOPMENT

Index Note: Page numbers followed by f indicate figures, and t indicate tables.

A

Accelerometers, 536–537, 540–542, 541f, 566–567 Acceptor doping, 104–106, 391–392, 391f Acoustic emission (AE) detection, 448–449, 448f Acoustic horn, 633–634, 633–634f Acoustic impedance, 807–808, 808t matching, 47, 634–638, 635f, 637f Acoustic lens, 630–633, 632f Acoustic microscope, 634 Acoustic resonators, 536–537 Acoustic transducer systems, 630–631 Active systems, 231 Active transducers, 787–788 Actuators, 56–64, 517–520, 536–537, 616–617, 616f actuator designs, 58–59 classifications of, 517, 517f constructions of thin film, 517, 518f drive/control techniques, 59–61 electrodes, 438 pulse drive motors, 61–64 servo displacement transducers, 61 single crystal piezoelectric materials, application, 309–310 thin film unimorph cantilevers, 518–520, 519t, 520–521f AD. See Aerosol deposition (AD) Additive process, 543 Admittance spectrum, k31 mode, 699f Aerosol deposition (AD), 119–120, 409, 410f cold spaying method, 578 densification mechanism of ceramic films, 586–588 device applications, 601–608 electrical properties of piezoelectric thick films, 592–597 fabrication of PZT films, 577–578, 577f ferroelectric and piezoelectric thick films, fabrication of, 588–592 film thickness, 576–577, 576f

and granule spray in vacuum process, 579–582 for hard and brittle ceramic materials, 578–579 lead-free piezoelectric thick films, 597–600 particle impact velocity, 583–585, 585f research groups, 579 Ag metal, 116 Alkoxide hydrolysis, 396–397, 397t α-Al2O3 film, microstructure of, 582–583, 584f Aluminum nitride (AlN), 544–547 Amorphous ferroelectrics, 413–414 Anomalous photovoltaic effect (APV), 760 Anti-ferroelectricity, 6 Anti-resonance frequency, 424, 657–671, 688–689, 708–709 Anti-resonance quality factor, 667–668 APV. See Anomalous photovoltaic effect (APV) Argon ion milling, 544 Array transducers, 636–637 Artificial muscles. See Electroactive polymers (EAPs) Artificial quartz crystal relationship between natural and, 207–209, 208f specifications of, 209, 211t AT-cut crystal vibrator, 218 AT-cut quartz crystal resonator, 205, 218 frequency of, 217 Q-value of, 207 AT-Cut Thickness Shear Mode Quartz Crystal Vibrator, 214–217 ATILA software code, 625, 626–627f, 628–629, 642–643 Atomic force microscopy (AFM), 489–490 Auger electron spectroscopy (AES), 560 Autoclave, 208–209, 208f Automated test equipment (ATE), 564 Automotive applications, 230–231

815

816 B

INDEX

Backswitch poling, 256 Barium titanate (BT) BaTiO3, 4–6, 35–36, 156–157 based chip, 439–440 based ML actuator, 443–445, 443f Base-metal internal electrode, 439–442, 439f BCM. See Body control module (BCM) Bead mill, 119 Bending mode microactuator, 601 Bevel process, 218 BiAlO3 ceramics, 187–188 Bi-based lead-free piezoelectric ceramics BiMeO3-based materials, 187–189, 188t bismuth potassium titanate, 180–183, 181–182f bismuth sodium titanate, 158–166, 159f, 164f, 166t BKT-BT system, 183–186, 184–185f, 187t BNT-BKT-BT system, 166–170, 167–169f, 170–171t BNT-BLT-BKT system, 171–180, 172–173f, 175f, 177–179f BiMeO3-based materials, 187–189, 188t Bimorphs, 406, 406f definition, 404, 405f types, 405, 405f Biomimetics, 320 Bipolar CMOS (BiCMOS) processes, 538 Birefringence vs. electric field, 151f Birefringent phase-matching (BPM), 258–259 Bismuth layer-structured ferroelectrics (BLSF) ceramics, 157 Bismuth potassium titanate (BKT) (Bi1/2K1/2)TiO3, 180–183, 181–182f Bismuth sodium titanate(BNT) (Bi1/2Na1/2) TiO3, 158–166, 159f, 164f, 166t BKT-BT system, 183–186, 184–185f, 187t Blackout problem, 632–633 BLE. See Bluetooth low energy (BLE) Blood sugar level sensors, 232 BLSF. See Bismuth layer-structured ferroelectrics (BLSF) Bluetooth, 224–225 Bluetooth low energy (BLE), 225 Bluetooth-SIG, 224 BNT-based solid solutions, 166–172, 174 BNT-BKT-BT system, 166–170, 167–169f, 170–171t BNT-BLT-BKT system, 171–180, 172–173f, 175f, 177–179f

Body control module (BCM), 231 Bolt-clamped Langevin transducer, 624, 624f BPM. See Birefringent phase-matching (BPM) Braille reading interface, 335–336 Brazil, 227 Bridgman method, 276, 286–288, 288f, 305–306 Broad frequency spectrum, 262 BT-based ceramics, 156–157 Buildup approach, 119 Bulk and thin film materials, 481–483, 546 perovskite ferroelectric materials, 481–483 thin film growth, features, 481–482 thin films, basic properties, 482 Bulk photovoltaic effect experimental phenomena of, 759–762, 759–761f physical models for, 762–768 Bulk pyroelectric field, 248 Bulk screening mechanisms, 253 “Butterfly behavior”, 564 Butterfly curve, 103–104 Butterworth–Van Dyke (BVD) model, 712–714

C

Calcination, 394–395 Calibration element (Cal. element), 804–805 Camera modules, 230 Cantilevers, 562–563, 562f Capsule endoscopes, 231–232, 232f Car audio system, 230–231 Carbon nanotubes (CNTs), 333–334 Car navigation systems, 230 Cauchy model, 560–561 Cavitation effect, 4, 638 Cellular phones, 226–230 camera modules, 230 duplexer, 229 intermediate frequence filter, 229 monolithic crystal filter, 229–230 one-segment/full segment tuners, 226–227, 227f RF module, 227–228 secure private cosm encryption, 228–229, 229f Ceramic powders alkoxide hydrolysis, 396–397 coprecipitation, 396 orientation, principle of, 428–429 preparation process, 394–395, 395f solid state reaction, 394–395

INDEX

Ceramics, 788–789, 799, 803–804, 804f, 811–812 electrodes, 442 fabrication processes, 394–401 films, densification mechanism of, 586–588 multilayer technology, 116 preparation method effect, 774–778 Chemical powder synthesis, 119 Chemical solution deposition (CSD), 548, 551 Chemical solution methods, 566 Chemical wet etching, 544 Chip pattern density, 66–67 Clevite Corporation, 8 Coefficient of thermal expansion (CTE), 594–595 CO2 emission, 119 Cofiring technique, 403, 619–620 CO2 laser (CL), 596–597 Cold spaying method (CSM), 578 Cole-Cole dispersion, 145 Combination effect, 16–17 Complementary metal-oxide semiconductor (CMOS), 538 Complex perovskite compounds, 106–107 for PZT ternary system, 107t Composite-bar structure, 708 Composite effects, 355–358 combination effects, 357 product effects, 357–358 sum effects, 355–356 Composites, 16–19, 407–408 composite effects, 16–17 fabrication process, 408, 408f magnetoelectric composites, 17–18 melting and rolling method, 408, 408f piezoelectric dampers, 18–19 polymer matrix, 407–408, 408f Compositional segregation, 471 Compressive stress, 549–551 Conductivity portion, losses, 648–649 Conductivity window, 356 Conventional bimorph bending actuators, 86–87 Conventional experimental methods, 560 Converse piezo-electric effect, 2, 32–33 Coprecipitation technique, 396, 774 direct precipitation method, 396 Core-shell model, 419 Coriolis force, 44–45 Corner cymbal, 625–628

817

Coupling factor, 52–53, 709, 719 Covalent bonding, 98–99 CoventorWare, 561–562 Cracks, 471 Critical exponent in relaxor ferroelectrics, 141–145, 142–144f, 142t Critical particle size, 416–418, 418f Cross-field system, 246–247 Crystalline ferroelectrics, 789 Crystal structures of relaxor ferroelectrics, 130–132, 131f technology of, 122 Crystal symmetry, 253–254 Cu-embedded cofired PZT ML actuators, 440–442, 440–441f Cu inner electrode, 122 Curie temperature (Tm), 36–38, 134, 288–289, 301–302, 386–388, 387–388f Curie–Weiss law, 128, 133–134 Current source model, 762–764, 762f, 764f Cut-and-bond method, 402, 424–425 Cutting angles AT-cut thickness shear mode quartz crystal vibrator, 214–217 characteristics of, 210–214, 212f, 214t, 215f +1°-X-cut tuning fork quartz crystal vibrator, 217–218 Cymbal array, 625–628, 627–628f Cymbal energy harvesting process, 379t Cymbal piezoelectric transducer, 79 Cymbal structure, 58–59 Cymbal transducer, 624–630 cymbal array, 625–628, 627–628f PZT layer cymbal, 628–630, 629–630f single cymbal, 624–625, 625–626f Czochralski technique, 236, 249, 400

D

Damped capacitance, 33, 660, 662 Damped permittivity, 31 Data volume, 226 DC bias field effect, high-power characteristics, 743–745 stress, 616–619, 622, 624 Debye dispersion relation, 137–139 Debye model, 137–139 Degree of hysteresis, 732–733 D-E hysteresis curve, 651 Delay line, 53

818

INDEX

Depolarization temperature, 161–172, 175–176, 185–186, 190 Deposition mechanism classification of, 483–484 consolidation of ceramic powders, 582–583 film characterizations, 489–493 PZT-based thin films, 484–489, 493–497 Device designing, 402–413 DFG. See Difference frequency generation (DFG) Dielectric coefficients for lithium niobate (LiNbO3), 244t Dielectric constants, 278–279 Dielectric elastomer actuators, 85 Dielectric elastomer film, 326–327 Dielectric properties, of relaxor ferroelectrics, 132f, 133–148 dielectric relaxation, 137–140, 137f diffuse phase transition, 134–136, 135–136f fractal analysis of, 140–148 origin of giant permittivity, 133–134, 133f Dielectric relaxation, 39, 130, 137–140, 137f, 739 Dielectric superlattice, 249 Difference frequency generation (DFG), 260 Diffuse phase transition, 134–136, 135–136f Digital terrestrial television broadcasting, 226–227 Diphasic composites, 354, 363f Dipole mode, 629 Direct perpendicular piezoelectricity, 204f Direct piezoelectric effect, 2, 44 Direct Sequence Spread Spectrum Communication System, 225–226 Discovery of piezoelectricity, 197–200, 198–200f Discrete switching, 254, 256–257 Disordered perovskite, 131, 133–134 Displacement amplification mechanism, 778, 779f Displacement transducers, 10 Dissipation factor tangent, 650–653 Dissipation functions, 650–651 Domain coalescence, 251 Domain engineering configuration, 800f, 801–802, 804 Domain kinetics, 252, 256 Domains, 803 rotation, 104–106 shape, 253–254

under stress, 799–804 structure, 263 types of, 256–257 wall motion, losses, 648–649 wall pinning model, 390–391, 390f Donor-doped PZT, 106 Donor doping, 36, 104–106, 391 Dopant effects, 388–394 crystallographic deficiencies, 390–392 domain wall stability, 389–390 field-induced strains, 391–392, 392f high-power characteristics, 393–394 soft and hard properties, 388–389, 389f, 390t Dopant research, 770–772, 771f Doping effect, 399, 729–738 dipole random alignment, 731–734 hard and soft PZTs, 729–731 unidirectionally fixed dipole alignment, 734–737 unidirectionally reversible dipole alignment, 737–738 Dot-matrix printer, 616–619, 618–619f Duplexer, 229 Dynamic stress, 640

E

EFAB (Electrochemical FABrication) technology, 538–539 Efficiency, 24 802.11a standards, 225–226 802.11b standards, 225–226 Elastic coefficients for lithium tantalate (LiTaO3), 244t Elastomer actuators, 85 Electrets, 321 Electrical admittance, 30–31 Electrical excitation, 320 Electrical impedance matching, 47, 378, 380 Electrical properties for BiMeO3-Based Materials, 188–189, 188t Electrical-to-mechanical conversion, 114–116 Electric dipoles, 104–106 Electric energy, 370 Electric field, 102–103, 133–134 birefringence vs., 151f induced AE, fractal analysis of, 145–148, 145f, 147f Electroactive polymers (EAPs), 320, 558 applications, 335–340 armwrestling challenge, 341–342

INDEX

biomimetic robotics, 338–339 challenges, 342–344 groups, 322 historical review, 321–322 lab-on-a-chip systems, 336–337 medical applications, 335–336 planetary applications, 340 potential developments, 342–344 state-of-the-art indicator, 341–342 tissue engineering, 337–338 trends, 342–344 Electrode materials, 438–445 Electromagnetic radiation, 260 Electromechanical coupling, 380 coefficient, 47, 278–282, 293–295 factors, 39–41, 304–305, 386, 386f, 655–656, 719 losses, 671 Electromotive force, 762 Electron energy band model, 485 Electronic EAP, 320, 322–329 dielectric electroactive polymers, 324–327 electrostrictive graft elastomers, 328–329 ferroelectric polymers, 323–324 Electronic tuning techniques, 565 Electro-optic effect, 150–152, 151f Electrostatic domain-domain interaction, 257–258 Electrostriction, 9–10 actuators, 616–617, 616f polymers, 85 in relaxor ferroelectrics, 148–150, 149–150f Ellipsometry, 560–561 Elliptical shape hysteresis, 740 ELV. See End-of-Life Vehicles (ELV) End-of-Life Vehicles (ELV), 156 Energy transmission coefficient, 22–24 Equivalent circuit in IEEE Standard, 675–676 of k33 mode, 681 with losses, of k31 mode, 674–680 loss-free, of k31 mode, 672–674 mechanical and electrical systems, equivalency, 671–672 4-terminal equivalent circuit, 679–680 with three losses, 677–679 Equivalent circuit analysis, 649 Ericsson Corporation, 224 Extended Rayleigh law approach, 740–743 conventional Rayleigh law, 741–742 hyperbolic Rayleigh law application, 742–743

819

Extensive loss factors, 689–691, 691f Extrinsic contributions, 788–789

F

Fabrication process, 408, 553–555, 554f, 565–566, 588–592 and processing method, 774 thick film fabrication, 588–589 thick film fine patterning, 589–592 FEA. See Finite element analysis (FEA) FeliCa, 232 Ferroelectric ceramics, 483 Ferroelectric domains, 102–103, 109–110 Ferroelectric hysteresis loops, 596–597, 596f Ferroelectricity, 9, 323–324, 789–794 3-D particle size effect, 416–419, 417–419f, 420t grain size effect, 413–419, 415–417f Ferroelectric PE hysteresis curve, 102–103 Ferroelectric properties, 158, 187 Ferroelectric random access memory (FERAM), 482–483 Ferroelectric relaxor, 137–139, 152 Ferroelectric single crystal, 799 Ferromagnetics, 413–414 Fiber laser (FL), 596–597 Field-activated EAP. See Electronic EAP Figures of merit (FOMs), 16–17, 21–25, 111, 758–759, 768, 772–774, 788–789, 812 acoustic impedance (Z), 25 electromechanical coupling factor (k), 21–24 mechanical quality factor (QM), 25 piezoelectric strain constant (d), 21 piezoelectric voltage constant (g), 21 Film bulk acoustic resonators (FBAR), 525–527, 545 construction of PMnN-PZT thin film, 525–526, 525f impedance properties, 526–527, 526f sputtered thin films, 526–527, 527t Film manufacturing techniques, 409, 410f Filter application, 224–233 Fine powder, 119 Finite element analysis (FEA), 568, 788, 812 Finite-element method (FEM), 584–585 Flexible energy harvester, 607–608 Flexoelectricity, 86 Flextension/hinge lever amplification mechanisms, 406–407, 406f

820

INDEX

Flux inclusions/trappings, 470, 470f FOMs. See Figures of merit (FOMs) Force factor, 679, 703–708 Forward growth domain, 250 Fractal dimension, 147–148, 152 dielectric properties of relaxor ferroelectrics, 140–148 of electric field-induced strain, 146 Frequency conversion, 260 Full segment tuners, 226–227, 227f Fundamental lattice portion, losses, 648–649

G

Gauss’s law, 389–390, 390f Gedanken experiment, 241 Ghost images, 629–630 Giant permittivity origin of, 133–134, 133f Gibbs energy, 386–388 Ginsburg–Landau–Devonshire theory, 242 Glass’s contribution, 763 Global positioning system (GPS), 230 GPS. See global positioning system (GPS) Grains, 788–789, 803, 811 Grain size effect, 774–775, 775f hysteresis and losses, 738–740 Granule spray in vacuum (GSV) process AD system configuration, 580–581 agglomeration, 581–582 ceramic particles, 579 deposition conditions, 580–582, 580t Greenhouse effect, 14 GT-cut resonator, 221–223, 222f, 223t GT-cut width-extensional mode, 221 Gyro-sensors, 523, 523f, 524t

H

Half-maximum-power angle, 4 Hard PZT, 106, 617 “Hard-to-etch materials”, 553 Heat generation at off-resonance, 682–684 in piezoelectrics, 681–688 rate of, 683 under resonance conditions, 684–688 thermal analysis, 683–684 Heat transfer coefficient, 683–684 High-end cameras, 230 High-power characteristics, 179–180 High-powered ultrasonic transducers, 638–639

High power piezoelectric characterization system (HiPoCS), 688–710, 726 loss measuring technique, sample electrode configuration, 708–710 loss measuring technique I, pseudostatic method, 689–691 loss measuring technique II, admittance/ impedance spectrum method, 691–700 loss measuring technique III, transient/ burst drive method, 700–708 High-power piezoelectrics high-power piezoelectric transformers, 746–749 low temperature sinterable hard PZT, 745–746 for practical applications, 745–749 High-pressure mercury lamp, 761 Hot isostatic pressing, 119 Hubble Telescope, 151f Hydrolic reaction, 396–397 Hydrostatic FOM, 111–112 Hydrostatic pressure model, 419 Hydrothermal process, 119, 208–209, 577–578 Hysteresis-free motion, 244–245

I

IEEE802.11, 225–226 IEEE802.15.4 (ZIGBEE, ETC.), 227–228 IEEE International Frequency Control Symposium (FCS), 221 IEEE standard method, 805–806, 808–809, 812 IF filter. See Intermediate frequency (IF) filter Imaginary parameters, 648 Impedance matching condition, 18, 369–370 Impulse drive motors, 616 Inkjet printers, 523–524, 524f, 525t In-line system, 246–247 Innovative ML structures, 445–446 3D positioning stage, 446, 446f super-long ML design, 445 Inorganic-based laser liftoff (ILLO), 607–608 Integrated circuit (IC) processing sequences, 538 Integrated services digital broadcasting (ISDB), 226–227 Integrative process, 543 Intensive dielectric loss, 683 Intensive dissipation factors, 689 Intensive losses, 650, 678, 689, 690f Interdigital surface electrodes, 42 Interdigital-type electrode, 430–433

INDEX

multilayer structure, 430–433, 432f piezoelectric actuators, 433, 433f Interdigitated (IDT) electrode, 562–563 Intermediate frequency (IF) filter, 229 Internal bias model, 391 Internal electrode design, 430–438 interdigital-type electrode, 430–433 plate-through internal electrode, 433–434 slit-insert design/interdigital with float electrode, 434 Intrinsic contributions, 788–789 Intuitive crystallographic model, 133 Inverse matrix components, 654 Inverse piezoelectricity, 198, 204, 205f Ion beam sputtering, 548 Ion-disordered crystals, 136 Ionic EAP, 320, 330–335 carbon nanotubes, 333–334 conductive polymers, 331–333 ionic polymer gels, 334–335 ionomeric polymer-metal composite, 330–331 Ionic polymer gels (IPG), 334–335 Ionomeric polymer-metal composite (IPMC), 330–331, 338–339 Ion rattling model, 149–150 Irreversible domain wall motions, 741 ISDB. See Integrated services digital broadcasting (ISDB) ISM band frequency, 227–228

J

Johnson–Holmquist material model, 584–585

K

Ka˜nzig region, 134 Keyless entry, 231 King of piezoelectric materials, 95–97 KNN-based ceramics, 157 KNN material system, 599, 600f Krimtholz-Leedom-Matthaei (KLM), 555–556

L

Lamb-Wave 433 MHz Resonator equivalent circuit constants of, 224t Lamb wave resonator, 223, 223–224f, 224t temperature frequency characteristics of, 224f Lame mode quartz crystal, 219f integration of, 219f Lame mode resonator, 218–221, 219–220f, 221t

821

Landau energy, 796–798, 797–798f Langevin transducer, 622–624, 623–624f, 712–714 Langevin type, 4, 623 Langevin vibrator, 198 Large strain ceramics, 85 Lasca, 208–209 Laser ablation, 482–483 Laser liftoff (LLO), 555 Laser transfer processing (LTP), 555 Laser wave radar, 231 Layer-thickness effect, 435–437, 436–437f Lead (Pb)-free piezoelectrics, 14–15 patent disclosure statistics for, 15f P-E hysteresis loops, 598, 599f Lead lanthanum zirconate titanate (PLZT), 758, 761, 768–774 Lead magnesium niobatelead titanate (PMN-PT), 555–556 Lead titanate, 36–38 Lead zirconate titanate (PZT), 4, 6–7, 36, 546–547, 555–557, 568 Clevite Corporation, 7–8 compositional modifications, 101–109, 102t, 103f, 107t, 108f crystalline structure and phase relations of, 97–101, 98f, 100f discovery of, 6–8 low-temperature sintering, 119–121, 121f micropump, 43f Murata Manufacturing Company, 8 phase diagram of, 37f PZT-based ceramics, 109–114, 110–113f, 115t shaping approach, 114–118, 117–118f in ternary solid solution, 36 ternary system, 8 LIGA technology, 539 Light-controlled actuators, 756–757 Light polarization direction effect of, 768, 769f Linear array transducers, 636–637 Lithium niobate (LiNbO3), 9, 35 acoustic properties of, 245–248, 246–248f generation of terahertz radiation in, 260–263, 261f for light frequency conversion, domain-engineered applications of, 258–259, 258f nano-and microdomain engineering in, 249–258, 251f, 253f

822

INDEX

Lithium niobate (LiNbO3) (Continued) piezoelectric properties of, 237–243, 238–239f, 238t, 242t single-crystal ferroelectrics for, 243–245 Lithium tantalate (LiTaO3), 9, 35 acoustic properties of, 245–248, 246–248f generation of terahertz radiation in, 260–263, 261f for light frequency conversion, domain-engineered applications of, 258–259, 258f nano-and microdomain engineering in, 249–258, 251f, 253f piezoelectric properties of, 237–243, 238–239f, 238t, 242t single-crystal ferroelectrics for, 243–245 Longitudinal piezoelectricity, 201–202, 203f Lorentz relation, 765–766 Loss anisotropy PMN-PT single crystal, 719–722 in PZT, 716–719 Loss measuring technique II, admittance/ impedance spectrum method, 691–700 mechanical quality factor, determination methods of, 699–700 real electric power method, 698–699 resonance/antiresonace, constant vibration velocity, 695–697 resonance/antiresonance frequencies, 699–700 resonance, constant current drive, 693–695 resonance, constant voltage drive, 691–693 Loss measuring technique III, transient/ burst drive method, 700–708 burst mode method, 702–708 pulse drive method, 700–701 Loss mechanisms DC bias field effect, high-power characteristics, 743–745 extended Rayleigh law approach, 740–743 extensive losses, microscopic origins, 714–716 grain size effect, hysteresis and losses, 738–740 loss anisotropy, crystal orientation, 716–722 in piezoelectrics, 714–745

M

Macro fiber composite (MFC), 80, 375–378 Magnetoelectric (ME) composites, 17–18, 597, 597–598f Magnetoelectric effect, 87–88 Magnetoelectric material, 357–358 Magnetoelectric sensors, 380–381 Magnetostrictive materials, 615–616 Magnetron sputtering, 482–483 apparatus principle, 42f Mask deposition method, 589–592, 591f Mask metallization, 543 Material designing, 385–394 Maximum strain, 732–733 Maximum vibration velocity, 693–694, 725f MCF. See Monolithic crystal filter (MCF) Mechanical-electrical energy transduction, 378 Mechanical energy density, 726 Mechanical impedance matching, 378 Mechanical impedance mismatch, 379 Mechanical-mechanical energy transfer, 378 Mechanical power density, 723 Mechanical pulverizing method, 119 Mechanical quality factor (Qm), 4, 35, 157, 176, 189–190, 649–650, 678–679, 687, 693–695, 698–699, 719 3 dB down method, 700 3 dB up method, 700 determination methods of, 699–700 quadrantal frequency method, 700 resonance/antiresonance frequencies, 700 Mechanical sector transducers, 47–48 Mechanical-to-electrical conversion, 114–116 Medical instruments applications, 231–232 Medical transducers single crystal piezoelectric materials, application, 310–311 MEMS application, 410–411, 411f Metal-based optical microscanner, 603–606, 605f Metal-organic chemical vapor deposition (MOCVD), 482–483, 548 chemical compositions, 485 plasma-enhanced, 496, 496f Sol-Gel processes, 496–497 Metglas substrates, 597, 598f M3-HEX-1.8, 537 Microaccelerometers, 540–541 Micro-and nanoscale domain structures, 248

INDEX

Micro electromechanical system (MEMS), 85, 481–482 benefits, 565–567 fabrication, 506, 538–545, 540f mechanical and electromechanical properties, 546, 546t mechanical vibrations, 533–534 MEMS and MEMS sensors, 520–523, 522t peculiarities of piezoelectric MEMS technologies, 545–559 PMNT thin films, 507–513 pressure sensors, 534–536 PZT-based thin films, 506–527 for semiconductor testing, 559–564 sensor applications, 535–537 yield stress value, 547 Microfabrication technology, 540–541 Micromachined piezoelectric devices, 566 Micromachined transducers, 568–569 Micromachined ultrasonic transducers (MUTs) arrays, 566 Micro-Macro domain change, 139–140, 140f Micromass sensor, 54–55 biosensor, 54 viscosity sensor, 55 Micro propelling robot, 781–782, 783f Micro pumps, 536–537, 537f Microscopic composition fluctuation model, 134 Microstructure, 122 portion, losses, 648–649 Micro walking machine, 780, 781f Microwave sintering, 119 MIFARE, 232 Millimeter wave radar, 231 Ministry of Welfare, 232 ML actuators, 442–445, 447–449 barium titanate, 443–445 ceramic electrodes, 442 health monitoring, 448–449 heat generation, 447, 447f lifetime test, 447–448 MLCC. See Multilayer ceramic capacitor (MLCC) ML manufacturing processes, 424–430 advantages and disadvantages, 424 cut-and-bond method, 424–425 modern micromechatronic systems, 424 tape-casting method, 425–426 Mobile communications, 224–226

823

Modern micromechatronic systems, 424 Modern vibration, 567 Monoclinic phase, 791 Monolithic crystal filter (MCF), 229–230 Monolithic hinge lever, 61, 617–619 Monomorphs, 20, 86 definition of, 20 Monopolar pressure distribution, 628–629 Monopole mode, 629 Moonie composite actuator structure, 624–625 Moonie or cymbal, 407 structure, 58–59, 407, 407f Morphotropic phase boundary (MPB), 36, 96, 130, 166, 507, 556–557, 769–770, 772–774 Motional admittance, 665–667 Motional capacitance, 32–33, 660–662, 674 Motors, 536–537, 536f MPB272. See Morphotropic phase boundary (MPB) Multidomain-monodomain transition model, 414–415, 739 Multidomain single crystals, 799–801 Multifunctional electroelastomer roll (MER), 325–326 Multilayer ceramic capacitor (MLCC), 116 Multilayer technologies, 402–404, 403f, 423–452 Multiple element array transducers, 47–48 Multiple nucleation and satellite crystals, 468–469 Multi-potential-well model, 139f Multiwalled CNTs, 334 Murata Manufacturing Company, 8

N

Nanodomain structures, 256–257 Nano electromechanical system (NEMS), 85, 535 Nanogenerators (NGs), 607–608 Nanoscale domain structures, 250, 254, 256–257, 264 “Nano technology”, 413–414 NASA, 150 Navigation (GPS), 230 Near-field communications (NFC), 232–233 Neutral cubic phase, 790–791 Neutron diffraction experiments, 161–163 New Ferroelectric Crystals, 156–157 NFC. See Near-field communications (NFC)

824

INDEX

Noncentrosymmetric piezoelectric material, 759–760 Nonparaelectric phase, 797 Nucleation, 549 of new nanoscale domains, 250

O

O atoms, 201–202 OFDM. See Orthogonal frequency division multiplexing (OFDM) Off-resonance permittivity, 707–708 One-crystal vibrator, 227 One-segment toners, 226–227, 227f Open-circuit voltage, 607–608, 609f OPO. See Optical parametric oscillation (OPO) Optical actuators, 758 Optical modulator, 606 Optical parametric oscillation (OPO), 259 Optical rectification, 262 Orthogonal frequency division multiplexing (OFDM), 225–226 Orthorhombic phases, 789–791, 790f, 799–802, 800f, 802f, 809–810 Oscillator application, 224–233 Oxide-mixing technique, 394 Oxide thin film fabrication chemical processes, 41 physical processes, 41 Oxygen deficiency diffusion model, 736f Oxygen octahedron, 98 Oxygen vacancies, 104–106, 160–161

P

Paraelectric phase, 797 Parasitic crystals, 469 3-D Particle size effect, 416–419 3-D Particle size effect, 416–419, 417–419f, 420t Passive systems, 231 Passive transducers, 787–788 Pb crystallites, 485, 527–528 Pb-Free Piezoelectrics, 426–429, 428f P-E hysteresis curve, 104–106, 282, 737–738 Percolation threshold, 113–114, 372–373 Permittivity, 365–366, 367f pressure dependence of, 143 temperature dependence of, 128f, 137f, 141 Perovskite barium titanate (BaTiO3), 98–99 Perovskites, 166 ABO3 structure, 98f crystals, 300f

oxide piezoelectric materials, 312–313 structure, 789–790 thin films, 485 type crystalline structure, 96 Phase boundary, 96 Phased array transducer, 636–637 Phase diagram, 789, 791–792, 792f, 794–795 Phase transitions, 788–789, 791–792, 794–796, 798–799, 802, 802–803f, 809–812 Phenomenological theory, 386 Photoacoustic (PA) imaging systems, 555–556 Photoconductivity, 766–767, 767f Photo-driven micro walking device, 19–20, 20f Photo-driven relay, 779–780, 780f Photophones devices, 755, 780–781, 782f Photoresist (PR) film, 589–592 Photostriction, 88, 757–758 Photostrictive actuators, 88, 758 Photostrictive bulk ceramic, 784f Photostrictive device applications, 778–782 Photostrictive effect, 772–778, 773f Photostrictive materials, 19–20 Photovoltaic effect, 756–772 Physical properties for BiMeO3-Based Materials, 188–189, 188t PIC 184, 707–708 Pierce circuit, 200f Pierce oscillation circuit, 200 Piezoceramics, 615–616 Piezocrystal, 801–802, 812 Piezoelectric coefficient, 385–386, 389t Piezoelectric composite dampers, 369–375 Piezoelectric composite energy harvesting, 375–380 cymbal energy harvesting, 378–380 macro fiber composites, 375–378 Piezoelectric composite materials composite dampers, 368–380 composite effects, 355–358 connectivity concept, 354 energy harvesters, 368–380 magnetoelectric sensors, 380–381 PZT, 359–368 Piezoelectric constant, 719 Piezoelectric constitutive equations, 650–657 extensive losses, 653–657 intensive losses, 650–653 Piezoelectric dampers, 18–19

INDEX

Piezoelectric devices, 44–81 accelerometers, 44–45 gyroscopes, 44–45 micromass sensor, 54–55 piezoelectric actuators, 56–64 piezoelectric energy harvesting, 77–81 piezoelectric transformers, 55–56 piezoelectric vibrators, 45–46 pressure sensors, 44–45 SAW devices, 51–54 ultrasonic motors, 64–77 ultrasonic transducers, 46–49 Piezoelectric effect, 756–757 Piezoelectric energy harvesting, 77–81 high energy harvesting, 79–80 low-energy harvesting, 80–81 piezoelectric passive damping, 77–79 Piezoelectric films, 559–564 Piezoelectricity, 10 Piezoelectricity of quartz crystal and axis, symmetry of, 200–204, 201–204f differences of, 204–207, 206–207t discovery of, 197–200, 198–200f Piezoelectric losses composition dependence, 723–729 doping effect on, 729–738 Pb-free piezoelectrics, 725–729 PZT-based ceramics, 723–725 Piezoelectric materials, 21–44 composites, 40–41 figures of merit, 21–25 overview of, 33–41 piezoelectric properties of, 34t piezoelectric resonance, 25–33 polycrystalline materials, 35–38 polymers, 39–40 relaxor ferroelectrics, 39 resonators/filters, 50–51 single crystals, 35 thin-films, 41–44 Piezoelectric material under test (PZ-MUT), 804–806, 808–809, 812 Piezoelectric passive damping, 77–79, 354 electrical-electrical energy transfer, 79 mechanical-electrical energy transduction, 79 mechanical-mechanical energy transfer, 78 Piezoelectric properties, 489–493 direct or inverse, 489–491, 492f displacement of cantilever, 492–493 grain orientation effects for, 186 of KN single crystals, 156–157

825

measurement frequency, 493 transverse piezoelectric coefficient, 493 Piezoelectric resonance, 25–33, 657–671, 688–689 admittance/impedance, k31 mode, 659–661 boundary condition, E-constant vs. D-constant, 664–665 characteristics of, 663t dynamic equations, k31 mode, 658–659 dynamic equations, k33 mode, 662–664 electromechanical coupling factor (k), 26–27 longitudinal vibration mode, 27–33 loss and mechanical quality factor, k31 mode, 665–668 loss and mechanical quality factor, other vibration modes, 669–671 piezoelectric constitutive equations, 25–26 strain distribution, k31 plate, 661 Piezoelectrics, 81–88 biodegradable polymer, 83 dawn of, 2 elastomer actuators, 85 electrostrictive polymers, 85 heat generation in, 681–688 history of, 1–20 large strain ceramics, 85 loss and hysteresis in, 648 losses in, 83 loss mechanisms in, 714–745 low-loss piezoelectrics, 83–84 magnetoelectric effect, 87–88 Pb-free piezoelectrics, 82 photostriction, 88 1:3 PZT composites, 85 reliability, performance, 82–84 World War I and, 3–5 World War II and, 5–6 Piezoelectric strain constants, 189–190 Piezoelectric stress coefficient, 705 Piezoelectric transducers acoustic impedance matching, 634–638 acoustic lens and horn, 630–634 designs, 617–630 drive schemes of, 710–714 inductive actuator drive, 712–714 materials, 616–617 off-resonance (pseudo-DC) drive, 710–711 resonance drive, 711–712 sonochemistry, 638–639 Piezoelectric transformers, 55–56, 639–643 definition of, 639–640

826

INDEX

Piezoelectric transformers (Continued) rosen-type transformer, 640–642 step-down transformer, 642–643 Piezoelectric vibrators, 45–46 Piezoelectric voltage constant, 357 Piezoresistors, 543–544 Piezo TEMS, 620 PIN-PT crystal, 303–306 modified Bridgman technique, 303–304 piezoelectric performance of, 305–306 segregation, 304 Plasma enhanced metal organic chemical vapor deposition (PE-MOCVD), 483–484, 496, 496f Plate-through internal electrode, 433–434, 434f PLD method. See Pulse laser deposition method PMN-based relaxor ferroelectrics, 130 PMN electrostrictor, 617 PMnN-PZT thin films, 514–516 sputtering process, 514 PMN-PT crystal, 286–298 crystal growth, 286–288 dielectric properties, 288–290 modified phase diagram, 286, 287f phase diagram, 286–288 phase transition, 289 piezoelectric properties, 290–295 polarization-electric field measurements, 285f solid state crystal growth, 295–298 strain behavior of, 293 PMN-PT single crystals, flux growth ionic complexes, 465, 473 nucleation mechanism, 464–466, 465f optimum flux composition, 463 PbO+B2O3 complex fluxes, 463–464, 466–468, 466–467f PMNT thin films, 507–513 measurement of resonant spectrum, 511, 512–513f morphotropic phase boundary, 507 P-E curves, 508–509, 510f, 513–514, 514f SEM and TEM images, 508, 510f sputtering conditions, 507–511, 508–509t, 511–512f transverse piezoelectric coefficients, 514–516, 516f XRD pattern, 508, 509f PMUT, 559 Polarization, 102–103

vs. electric field hysteresis loops, 563–564, 563f Polarization-electric (P-E) field hysteresis loops, 302–303 Polarization reorientation driving forces for, 794–799 Poling process, 563–564 optimization of, 237 Polycrystalline piezoelectric ceramics, 811 thermal expansion in, 150f Polyvinylidene difluoride (PVDF), 14, 39–40 glass transition temperature (Tg), 14 needle hydrophone, 555–556 structure of, 40f Polyvinylidene difluoride-trifluoroethylene (PVDF-TrFE), 85 Portable car navigation systems, 230 Positive internal bias electric field, 735–736 Potassium dihydrogen phosphase, 4–5 Precision micromachining, 565 Pressure dependence of permittivity, 143 Pressure electricity, 2 Printing pattern of electrode, 434–435, 435f Product effect, 17 PSN-PT crystal, 298–303 flux method, 301 growth of, 300–301 properties of, 301–303 PSpice software, 675 Pt inclusions, 471 PT-rich surface layer and fragile domain walls, 472, 472f Pulsed laser deposition (PLD), 548 Pulse drive actuator, 617–622, 618–622f motor, 616–617 Pulse laser deposition (PLD) method, 187 Pure-silver ML actuators, 438–439 PVDF (CH2–CF2)n, 558 Pyrochlore crystals, 469–470 Pyrochlore phase, 276 PZ-MUT. See Piezoelectric material under test (PZ-MUT) PZN-PT crystal, 274–285 growth of, 276–278 properties of, 278–285 PZN-PT single crystals, flux growth, 455–462 array dot electrode technique, 462 crystal growth rate, 455–460 high-temperature flux technique, 473

INDEX

lead-based relaxor-PT single crystals, 455, 459f nucleation, 460–461, 460f PbO self-flux, 455, 461–462, 462f PZT-based ceramics, 95–97 PZT-based ferroelectric materials and single crystal substrates, 490t PZT-based magneto-optic spatial light modulators (PZT-MOSLM), 606 PZT-based thin films bulk sintering process, 484 chemical compositions, 485 chemical structures, 496, 497f crystal phase, 485–489 deposition processes, 483t, 493–497 dielectric and piezoelectric properties, 498–505 fabrication processes, 484, 484t film structure, 489 MEMS and MEMS sensors, 520–527 microstructure, 489 piezoelectric actuators, 517–520 piezoelectric properties, 489–493 sol-gel–derived polycrystalline, 498, 500f structural properties, 498, 500f using MOCVD, 496–497, 498t PZT composites, 85 PZT layer cymbal, 628–630, 629–630f PZT-polymer composites, 359–368 advanced, 366–368 0-3 composites, theoretical models for, 364–366 piezoelectric composite materials, 359–361 principle of, 361–364 PZT ternary systems, 106–107, 120–121 complex perovskite compounds for, 107t PZT thick films, 119–120

Q

QPM. See Quasi-phase-matching (QPM) Quadratic law, 128 Quadratic polarization, 262 Quartz, 3–5, 35, 54 Quartz-based piezoelectric materials automotive applications of, 230–231 cellular phones applications of, 226–230 cutting angles and vibration mode, 210–223 medical instruments applications of, 231–233

827

mobile communications applications of, 224–226 piezoelectricity of quartz crystal, 197–207 production of artificial quartz crystal, 207–209 Quartz crystal resonator GT-cut resonator, 221–223 lamb wave resonator, 223, 223–224f, 224t lame mode resonator, 218–221, 219–220f, 221t Quartz crystals, 544–545 Quartz crystal vibrators AT-cut thickness shear mode quartz crystal vibrator, 214–217 +1°-X-cut tuning fork quartz crystal vibrator, 214–217 Quasi-equilibrium, 239–240 Quasi-phase-matching (QPM), 259 Quasistatic configuration, 804–805, 805f

R

Radial vibration mode, 629 Radio frequency (RF) sputtering, 543–544 Rattling ion model, 133 Rayleigh law, 740–741 Rayleigh wave. See Surface acoustic wave Reactive-templated grain growth (RTGG), 401 Rechargeable battery impedance, 380 Reciprocal permittivity dependence of, 129f logarithmic plots of, 144f Relaxor-based crystals engineered domain configuration, 307–308 mesophase, 308–309 polarization rotation mechanism, 308–309 theoretical models for, 306–309 Relaxor ferroelectrics, 9–13, 129–130 critical exponent in, 141–145 crystal structures of, 130–132, 131f Curie–Weiss law in, 128 dielectric properties of, 133–148 electro-optic effect, 150–152, 151f electrostriction in, 148–150, 149–150f history of, 272–274 PMN-based relaxor ferroelectrics, 130 Remanent polarization, 102–103 Remanent strain, 103–104

828

INDEX

Remote-controlled actuator, 756–757 Replamine method, 366–367 Residual stress, 549–551, 550t, 589, 640 Resistive shunt method, 77–78 Resonance, 708–709 Resonance configuration, 805–806, 806f Resonating displacement devices, 616–617 Resonator application, 224–233 Restriction of Hazardous Substances (RoHS), 156 Reversible domain wall motions, 741 RF/DC magnetron sputtering, 548 RF frequency oscillation, 228 RF modules, 227–228, 231 Rhombohedral phases, 789–791, 790f, 799–803, 800f, 802f, 809–810 Rigid displacement device, 616–617 River Eletec Corporation, 218–221 cutting angles developed by, 218–221 new Resonators developed by, 221–223 Robust vacuum packaging, 565 Rochelle salt, 3–5 RoHS. See Restriction of Hazardous Substances (RoHS) Room temperature impact consolidation (RTIC), 582–583, 583f, 608–610 Rosen-type transformer, 640–642, 640–641f

S

Sake distillation application, 638 Sapphire (0001) single crystals, 485–486, 486f Sashida motor, 73 SAW. See Surface acoustic wave (SAW) Scanning electron microscopy (SEM), 559–560 Schottky barrier, 20 Screening processes, 252–253 Screen printing, 555 Screen-printing methods, 577–578, 588–589 SE. See Surface-emitting (SE) Second harmonic generation (SHG), 156–157 Second-order nonlinear susceptibility, 260 Secure Private Cosm (SPC) encryption, 228–229, 229f Seed crystals, 208–209 Segment tuners, 226–227 Self-assembled structures, 254 SEM micrographs, 113f Servo displacement transducers, 616–617 Shaping approach, 114–118, 117–118f Sheet resistance measurements, 561 SHG. See Second harmonic generation (SHG) Si atoms, 201–202

Si-based substrate, 589, 590f Side-wall nucleation, 469 Sideways Domain Growth, 250 Silicon-based technologies, 565 Si-MEMS optical microscanner, 601–603 Si-micromachining, 602–603, 604f Single crystal growth, 204, 400 PZN-PT, PMN-PT, PZT, 400, 401f Quartz, LN, LT, 400 Single crystal preparation techniques, 453–480 lead-based relaxor-PT single crystals, 453–454 PZN-PT and PMN-PT, growth of, 454–455, 456–459t Single disks, 402 Single-domain crystal, 247 Single-walled CNTs, 334 Sintering process, 397–400, 398–399f low-temperature, 119–121, 121f temperature, 160 Skanavi-type dielectric relaxation, 137–139, 138–139f Slater method, 236 Slit-insert design/interdigital with float electrode, 434 Smart pill, 335–336 Smooth impact drive mechanism (SIDM), 74–77 Sodium potassium tartrate. See Rochelle salt Soft PZT, 106 Soft PZT piezoelectrics, 617 Sol-gel processes, 396–397, 482–484, 552–553 chemical compositions, 485 deposition, 484 MOCVD, 498–503 for PZT-based thin films, 497, 499t, 499f synthesis, 119 wet process, 497–501, 501f Zr/Ti ratios, 501, 502f, 503–505, 507f Sol-gel technique, 774 Solid solutions, 95–97 Solid state crystal growth (SSCG), 295–298 Solid-state displacement transducers, 57 Solid state reaction, 394–395 Solid-state single crystal growth (SSCG), 400 Sonochemistry, 638–639, 639f Sound transmitting process, 630–631 Spacer grid, 99 Space Shuttle program, 150 Spark plasma sintering, 119 SPC encryption. See Secure Private Cosm (SPC) encryption

INDEX

Spontaneous backswitching, 251 Spontaneous polarization, 763 Sputter-deposited PbTiO3, 486–489, 486–488f Sputtering system, 41–42, 493–496 chemical compositions, 485 cycloid motion of electrons, 495 deflections of cantilevers, 503–504, 506f deposition, 484 multi-target sputtering system, 495–496, 495f P-E hysteresis curves, 503–504, 505f PZT thin films, 503–505 rf-magnetron diode sputtering system, 493–495, 494f structure of, 493–494, 495f Step-down transformer, 642–643, 643f Stoichiometric specimens, 120–121 Strain gauge type electrode configuration, 449, 449–450f Stress compressive, 549–551 DC bias, 616–619, 622, 624 domains under, 799–804 dynamic, 640 observation effects of, 804–811 residual, 549–551, 550t tensile, 549–551 SUMMIT Technology, 539–540 SUMMiT-V Technology, 540 Super heterodyne detection system, 229 Surface acoustic wave (SAW), 236 advantages of, 51–52 devices, 51–54 lithium niobate, 52–53 lithium tantalate, 52–53 material properties, 54t velocity, 52–53 Surface-emitting (SE), 260 Surface micromachining techniques, 551–553, 552f Switch shunt, 80

T

Tailored domain patterns, 263 Tailored periodical domain structure, 245 Tape-casting method, 402, 425–426, 555 green sheet, 426 manufacturing process, 426, 427f multilayer actuator, structure of, 426, 426f

829

Tc superconductors, 482–483 TCXO/quartz crystal resonator, 225 Temperature dependence of permittivity, 128f, 137f, 141 of spontaneous polarization, 129f Temperature gradient, 276–278 Templated grain growth (TGG), 400–401, 402f Template ML preparation, 429–430, 430–431f, 431t TEMS system. See Toyota Electronic Modulated Suspension (TEMS) system Tensile stress, 549–551 Terahertz radiation, 260 in LiNbO3 and LiTaO3, 260–263, 261f Terfenol-D, 380 4-Terminal equivalent circuit, 679–680 6-Terminal equivalent circuit, 680 Tetragonal phase PZT, 96 Tetragonal phases, 789–794, 790f, 794t, 797–803, 797f, 800f, 803f Textured ML actuators, 426–430 Pb-Free Piezoelectrics, 426–429 Template ML preparation, 429–430 TF analyzer 2000 measurement system (axiACCT systems), 561–562 Thermal anodic bonding process, 543–544 Thick films, 409–413 aerosol deposition, 409 constraints, 411–413 constraints in, 44 domain texture creation model, 413, 413f epitaxial growth, 44 fabrication, 588–589 ferroelectric and piezoelectric properties, 593–594, 593–594f film manufacturing techniques, 409 fine patterning, 589–592, 592f high breakdown voltage, 592–593 laser annealing, 596–597 MEMS application, 410–411 multilayer PZT actuators, 412, 412–413f preparation constraint, 44 property enhancement by stress modulation, 594–595 size constraints, 44 stress from substrate, 44 Thin-films aerosol deposition, 409 bulk and thin film materials, 481–483 constraints in, 44

830

INDEX

Thin-films (Continued) epitaxial growth, 44 evaluation methods, 489, 491t fundamentals, 483–493 MEMS application, 42–43 microelectromechanical systems (MEMS), 506–527 preparation constraint, 44 preparation technique, 41–42 process technologies, 568 PZT-based thin films, 493–505 size constraints, 44 stress from substrate, 44 3-D printing technology, 113–114 Three-point bend method, 443–444, 444f THz radiation, 260 Titacon, 5 Tonpilz transducer, 803–804, 804f Torsion coupler, 69 Torsion Langevin vibrator, 70 Toyota Electronic Modulated Suspension (TEMS) system, 620–621 Traffic control systems, 231 Transducers, 534 Transmission efficiency, 72 Transmission electron microscope (TEM) images, 582–583 Transmitting voltage ratio (TVR), 625, 626f, 628–630 Transverse piezoelectric effect, 27 Trapped-energy filter, 50–51 Trapped-energy principle, 50–51 TVR. See Transmitting voltage ratio (TVR)

USM classification and principles of, 67–68 demerits, 67 merits, 66 propagating wave-type motors, 68, 71–74 smooth impact drive mechanism, 74–77 standing wave-type motors, 67–70 UWB. See Ultrawide band (UWB)

U

X

Uchino-Zhuang formula, 695 Ultrasonic echo field, 635 Ultrasonic motors, 64–77, 393, 606–607, 607f Ultrasonic scanning detectors, 615–616 Ultrasonic transducers, 46–49, 311 geometry, 636 sonochemistry, 49 ultrasonic imaging, 46 Ultrasonic waves, 615–616 Ultrawide band (UWB), 228 Underwater acoustic devices, 3–5 Uniaxial compressive stress, 798, 803–805, 808–809, 812 Unimorphs, 404–406 actuator, 601, 602f definition, 404, 405f types, 405, 405f Unit cell, 789–794, 790–793f, 794t

V

Vacuum tube, 200 Vertical crack, 437–438, 437f Vibration mode of quartz crystal vibrators, 213, 215f Vibration velocity, 393–394, 393f Video system, 230–231 Voltage factor, 703–704, 707–708 Voltage rise ratio, 55–56 Voltage source model, 764–768, 767f

W

Waste from Electrical and Electronic Equipment (WEEE), 156 WEEE. See Waste from Electrical and Electronic Equipment (WEEE) Weibull coefficient, 443–444 Weibull plots, 443–444 Wet jet mill, 119 Wireless LAN, 225–226, 226t Wireless sensor-node system, 607–608, 608f Wobbling, 636–637 Wolframite phase oxide, 303–304

+1°-X-cut tuning fork quartz crystal vibrator, 217–218 Xenon lamp, 761 X-ray diffraction (XRD) method, 559–560 X-Ray fluorescence spectroscopy (XRF), 560 X-Ray photoelectron spectroscopy (XPS), 560

Y

Young’s modulus (Y) value, 603–604

Z

Zero temperature coefficient, 200, 205, 212 Zigbee communication, 227–228 Zinc oxide (ZnO), 544–545, 557–558 Zygo interferometer, 561–562