1. n Ceramic Engineering: Properties, Processing, and Use in Design. d Edition, Revised and Expanded, David W. rich er so^

2. ~ntro~uction to Engineering Materials: Behavior, Properties, and Selection, G.

olidified Alloys: Processes * ~ t ruc t~ res 0 Applications, ed~ed by

inforced Ceramics for Structural Applications, ~ a v j d

5. Thermal Analysis of Ceramics, robe^ F. S~eyer tion and Wear of Ceramics, ed~ed by Said ~ a h a n ~ j r hanical Properties of Metallic Composites, edjfed by S ~ o ~ j r o Ochjaj

8. Chemical Processing of Ceramics, ed~ed by B ~ ~ r a n d 1. Lee and ~ ~ ~ a r d J. A.

9. Handbook of Advanced Materials Testing, ed~ed by ~ i c ~ o / a s P, C ~ e r e ~ j - Pope

s j n o ~ and Paul ~. Chere~ js ino~ I O . Ceramic Processing and Sintering, M. N. R a h ~ ~ a n 11. Composites Engineering Handbook, ~ d ~ e d by P. K. 12. Porosity of Ceramics, Roy W. Rice 13. Intermetallic and Ceramic Coatings, ed~ed by ~afendra B. aho of re and 7: S.

on Techniques: Technological Applications, ed~ed by K. 6.

eering Materials: Impact, Reliabili~, and Control, ed~ed by

International Center for Actuat~rs an^ Trans~ucers ~ I C ~ ~ ~ T ~ e Pennsylvania State ~niversity

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Ferroelectrics can be utilized in various devices such as ~ g h - p e ~ ~ i v i t y dielectrics, pyroelectric sensors, piezoelectric devices, electrooptic devices and PTC components. The industries are producing large amounts of simple devices, e.g. ceramic capacitors, piezoelectric igniters, buzzers and PTC t h e ~ s t o r s continuously. But until now ferroelectric devices have failed to reach co~ercialization in more functional cases. In the light sensor, for example, semiconductive materials are superior to ferroelectrics in response speed and sensitivity. Magnetic devices are much more popular in the memory field, and liquid crystals are typically used for optical displays. Ferroelectric devices often fail to be developed in the cases where competitive materials exist. This is mainly due to a lack of systematic acc~ula t ion of hndamental knowledge of the materials and developmental experiences on the devices.

During my 12-year teaching period on "Ferroelectric Devices," I found that no suitable textbook is available in this particular field, except some professional books like multi-author paper collections. Hence, I decided to write a single-authored textbook based on my lecture notes, including my device development philos~phy. This textbook introduces the theoretical background of ferroelectric devices, practical materials, device designs, drivelcontrol techniques and typical applications, and looks forward to the hture progress in this field. Though the discovery of ferroelectricity i s relatively old, since the device development is really new and interdisciplinary, it is probably impossible to cover all the recent studies in a limited- page book. Therefore, I selected only important and basic ideas to understand how to design and develop the ferroelectric devices, putting a particular focus on thidthick film devices.

Let me introduce the contents. Chapter 1 introduces the overall background, "General view of ferroelectrics," followed by the theoretical background in Chapter 2, "Mat~ematical treatment of ferroelectrics." Chapter 3, "Device designing and fabrication processes," provides practical designing and manufacturing of the devices. Capacitor applications are described in Chapter 4, "High permittivity devices," Chapters 5 and 6 treat thidthick film applications, i.e. "Ferroelectric memory devices" and "Pyroelectric devices," respectively. Chapter 7, "Piezoelectric devices" deals with piezoelectric actuators and ultrasonic motors as well as acoustic transducers and piezoelectric sensors. Optical devices such as light valves, displays, wave guides and bulk photovoltaic devices are described in Chapter 8, "Electrooptic devices." In Chapters 9 and 10, we learn basic concepts of "PTC materials" and

... 111

iv Preface

"Composite materials," and their device applications. Finally in Chapter 11 we discuss "Future of ferroelectric devices," in which the rnarket size is estimated, and the author's strategy for developing bestseller devices is introduced.

This textbook was written for graduate students and industry engineers s ~ d ~ g or working in the fields of electronic materials, optical materials and c o ~ ~ c a t i o n s , precision machinery and robotics. Though this text is designed for a course with thirty 75-~ninute lectures, the reader can learn the content by himselflherself aided by the availability of examples and problems.

Critical review and content corrections on this book are highly appreciated. Send the i ~ f o ~ t i o n directed to Kenji Uchino at 134 Materials Research Laboratory, The Pennsylva~a State University, University Park, PA 16802-4800. Fax: 814-865- 2326, E-mail: KenjiUchino~PSU.EDU

For the reader who needs detailed i n f o ~ t i o n on smart piezoelectric actuators and sensors, "Piezoelectric Actuators and Ultrasonic Motors" (349 pages) authored by K. Uchino, (Kluwer Adademic Publishers 1997) is recomended.

Even though I am the sole author of this book, it nevertheless includes the contributions of many others. I express my gratitude to my ICAT center faculty who have generously given me their advice and help during the writing, particularly to Dr. U m a ~ ~ e l e g ~ d u , who worked out all the problems. Dr. Yulcio Ito (now in Rutgers University) allowed me to use some paragraphs and figures from our coauthored papers. Specific acknowledgement is given to Professor J ape Giniewicz, Indiana Universi~ of Pennsylvania, who reviewed and criticized the entire manuscript and provided linguistic corrections.

Kenj i Uchino

iii

vii

viii

ix

1 2

1.2 Origin of ~pontaneous Polarization 4 1.3 Origin of Field ~nduced Strain 9 1.4 Electrooptic EBect 13 1 .S Example of Ferroelectrics 18 1.6 Applications of Fe~oelectrics 20

L 2.1 Tensor Representation of Physical Properties 23 2 .2 ~heno~enolo~y of Ferroelectricity 38

3.1 Material Resigning 57 3.2 Fa~rication Processes of Ceramics 67 3.3 Device Resigning 73 3.4 Grain Size Effect on Ferroelec~icity 84 3.5 Ferroelectric Domain ~ontributions 89

4.1 Ceramic Capacitors 105 4.2 Chip Capacitors 106 4.3 Hybrid Substrate 108 4.4 Relaxor F e ~ o e l ~ t r i c s 108

119 126

V

.2 T e m p e r a t ~ e ~ n ~ a r e ~ Light Sensors 6.3 Infrared Image Sensors

iezoelectric Vib

10.2 Composite Effects

Contents

131 138 139

145 158 161 174 176 180 197

22 1 222 230 239

243 248 250

255 257 260 269

275 276 279 283

3~~

ion emanent ~ o l ~ z a t i o n yroelectric coefficient

Lorentz factor

elative ~ e ~ i t t i v i t y , dielectric constant

tran§ition t~mPerature)

Strain Spontaneous strain Stress

Electro§tric~ve coefficients mechanical co~pling factor tran§mi§§ion coefficient ive index

lmary electrooptic coefficient Secondary electrooptic coefficient

hase ret~dation

Q. 1. 2. 3. 4. 5 . 6, 7. 8 . 9. 1 Q. 11.

Course Explanation & Prerequisite Knowledge Check General View of Ferroelectrics ~ a ~ e m a t i c a l Treatment of Ferroelectrics Device Designing and Fabrication Processes High ~ e ~ i t t i v i t y Dielectrics Ferroelectric Memory Devices Pyroelectric Devices Piezoelectric Devices Electrooptic Devices PTC Materials Composite Materials Future of Ferroelectric Devices ~ e v i e w l ~ ~ ~

1 Time 4 Times 4 Times 3 Times 2 Times 1 Time 1 Time 7 Times 2 Times 1 Time: 2 Times 1 Time 1 Time

viii

In order to understand ferroelectric devices, some prerequisite knowledge is expected. to solve the following questions without seeing the answers on the next page.

Q1 escribe the definitions of elastic stifness c and c o ~ ~ l i u n c e S, using a stress X - strain x relation.

Q2 Indicate a shear stress on the following square.

Q3 ~escribe the s~~~ v ~ l o c i ~ v in a material with mass density p and elastic

Q4 Calculate the capaci~nce C of a capacitor with area S and electrode gap t

Q5 Calculate the ~ ~ l u r i z a t i o n of a material with dipole density

compliance SE.

filled with a material of relutive ~ e r ~ ~ t t i v i ~ E.

dipole moment qu (Gm).

Weiss temperature To and a Cu~e-Weiss constant C.

velocity in vacuum).

6 escribe the C ~ r i e - ~ e ~ ~ s law of relative pe~i t t ivi ty E, using a C~rie-

Q7 Describe the light velocity in a material with a refractive index n (c: light

Q8 Indicate the work function in the following energy band of a metal.

eve1

In of id0

Q9 There is a voltage supply with an internal impedance 20. Indicate the

Q10 Calculate the induced polarization P under an external stress X in a

ix

external impedance 21 to obtain the maximum output power.

~ i e z o e l e c t ~ c with a piezoelectric constant d.

X

1 2

Prerequisite Knowledge

(Correct rate more th

l

, ~ e ~ o e ~ e c ~ i c s are said to be very

T

riC C

1

2 Chapter 1

Ferroel~trics are utilized in various devices such as h i g h - p e ~ i t t i v i ~ dielectrics, pyroelectric sensors, piezoelectric devices, electrooptic devices, and PTC (positive ~mperat~e coe~c ient o f resistivity) components. owever, ferroelectric devices often fail to be c o ~ e r c i ~ ~ in areas of applicatio competitive materials exist. Light sensors, €or example, typically are manufac~ed from se~conductive materials which are superior to ferroelectrics in response

are typically used for optical displays. One reason for this is due to the lack of systematic and comprehensive com~ilation of knowledge on ferroelectric materials. In this chapter, we will learn ~ n d ~ e n t ~ knowledge on ferroelec~ci~ '

agnetic devices are much more popular for memo^ applicati

lectric materials, the constituent atoms are considered to be ionized and are either positively or negatively charged. In such i

electric field is applied, cations are attracted to the cathode anions to the anode due to eiectros~tic interaction. The electron clouds also deform, causing electric dipoles. This phenomenon is own as electric po~rization of the

electric, and the polarization is expressed ~ u ~ t i ~ t i v e l y as the sum of the electric lpoles per unit volume [C/m2]. Figure 1.1 shows schematically the origin of the

electric polarization. There are three primary con~ibutions: electronic, ionic and ole r e o r i e n ~ ~ o n - ~ ~ ~ t e ~ . The degree to which eac 'sm c o n ~ i b ~ t e s to the overall ~olarization of the material d e ~ n ~ on the ~lectronic polarization can follow alte~ating fields W

ond, higher than visible light wave) and ionic polarization z (109-101~ cyclelsec, microwave region). Thus, you should

relation between the relative pe~ittivity E and the refractive

ti0

=O

l l

+ + : c + l l 4 I)

l f

l l

origins of the electric polarization.

eneral View of Ferroel~~tflcs 3

is valid only when the applied electric field has a higher. ~ermanent dipole reo~en~tion can follow cyclelsec). "his is why fe~oelectric materials with permane for ~ c r o w a v e dielectric materials; their permittivities are typically high at low

signi~cantly with increasing applied electric field frequency.

Compared with air-filled capacitors, dielectric capacitors can store more electric charge due to the dielectric pol~zation as shown in Fig. 1.2. The physical ~uantity

displace , and is related to the electric fi the following expression: comspo * o the stored electric charge t area is called the e l e c ~ * c

Here, ;EO is the vacuum permittivity (= 8 . 8 5 4 ~ 1 0 ' ~ ~ F/m), E is the material's reiiztive p e r ~ i t t i v i ~ (also simply called permittivity or d~electric consta~t, and in general is a tensor property).

Depending on the crystal structure, the centers of the positive and negative charges may not coincide even without the application of an external electric field. Such crystals are said to possess a s p o n ~ n e o ~ p o l a ~ z a ~ o n . When the spon~neous polarization of the dielectric can be reversed by an electric field, it is d e d ferroelectric.

ob: Bound charge

ot: True charge

Charge accumulation in a dielectric capacitor.

mom~nts result from th

(electric c h ~ ~ e 4) relative to the crystal lattice. ~onsider the case in which the ~ o l ~ ~ a t i o n is caused by all the ions being displace^ equally in a lattice.

ugh lattice vibrations at a finite eigen lattice vibrations in a

becomes zero.

t follows that, at any indivi~ual ion site, there exists a local field from , even if there is no external field.

own schematically in Fig. 1.4. It can be shown that:

(c)

ossible eigen lattice vibration modes in a ~erovskite crystal.

6 Chapter l

External Field

Eo

\ \

Dielectric material

of the local field. Eloc is given by loC = EO + X [3(pi*ri)ri - $pi] / &Eo ri5.

i

This local field is the driving force for the ion shift. Here y is called the brentz factor. For an isotropic cubic system, it is known that y = 1. l ) EO is the pe~ittivity of vacuum and is equal to 8 . 8 5 4 ~ 1 0 " ~ ~ F/m. If the ionic ~oZarizabiZi~ of ion A is a, then the dipole moment of the unit cell of this crystal is:

The energy of this dipole moment (dipole-dipole coupling) is

Defining N to be the number of atoms per unit volume:

F u ~ e ~ o r e , when the A ions are displaced from their nonpolar equilibrium positions, the elastic energy also increases. If the displacement is U, and the fm constants k and k', then the increase of the elastic energy per unit volume can be expressed as:

Here, k' (> 0) is the higher-order form constant. It should be noted that in pyroelectrics, k' plays an important role in determining the magnitude of the dipole moment. By rewriting Eq. (1.7) using:

General View of Ferroelectrics 7

where q is the electric charge, and combining with l3q. (1.6), the total energy can be expressed as follows (see Fig. 1.5):

From this, one can see that 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 = 0; the A ions are stable and remain at the -polar e~uilibrium positions. Otherwise, a shift from the equilibrium position = [(2Nay2/9&o2) - oNqIL)]/ [k'/N3q4]) is stable. Spontaneous polarization can occur more easily in perovskite type crystal structure (e.g. barium titanate) due to a higher value of Lorenz factor y (=

than found for other crystal structures. Note also that the polarizability is sensitive to temperat~e, leading to the phase transition. Suppose that the ionic polarizability of ion A, a, increases with decreasing temperature, even if [(W2Nq2) - (Nay2/9q2)] > 0 ~ ~ l e c t r i c ! ) at a high temperature, this value may become negative with decreasing temperature, leading to a ferroelectric phase transition. Considering a first approximation, a linear relation of the a with temperature, the

urie-Weiss law is derived, which will be discussed in detail in Section 2.2( 1).

(a) Dipole interaction (b) Elastic energy )W Welas =: (~2Nq2)P2 + (~/4N3q4)P4

(c) Total energy wtot = wdip + welas

Fig. 1.5 Energy explanation of the origin of spontaneous polarization.

i03 exhibits ionic ~splacemen~ as i l l u s ~ a t ~ in Fig. 1.6 at room culate the magnitude of the spontaneous pol~zation.

= 4.036 A and a = 3.992 A.

C

a

: number of the dipole

S c ~ c u l a ~ by taking e product of the c ~ ~ g e magnitude total dipole moment in a unit cell is c ~ c u ~ a t ~ by summing

dipoles (notice the ~actional contri i. e, l/$ for corner atoms and 1/2 for face-centered atoms);

)(0.061x10-10m~ + 4e(0.12~10-~

e unit cell volume is given

9

v = a2c = (3.992)2(~.036) x m3 (P1 * 1.2)

e spon~neous p o l ~ z a ~ o n is defined as the pol~zation (total dipole moment) unit volume:

lomz9 Cm(64.3 x m3

The e x ~ e r i m e ~ ~ l value of PS is about 0.25 C/m2.

(P1.1.3)

"eZectro~t~ctio~" is used in a gener~ sense to train, and hence ~ ~ u e n ~ y also implies the "converse o~ever , in solid state theory, the converse p i e z ~ l e c ~ c e E i t

'cal coupling effect, that e l ~ ~ o s ~ c t i o n is a sec

material is a mono-

electric field and the anions in the opposite direction, leading to the relative change in the inter-ionic distance. Depending on the direction of the electric field, the soft spring expands or contracts more than the contraction or expansion of the had spring, causing a strain x (a unit cell length change) in propo~on to the electric field E. "his is the converse ~iezoezecEr~c eflect. When expressed as

X = d E , (1 .lo)

the propo~onality constant d is called the piezoelec~c constant.

On the other hand, in Fig.l.7(b), the amounts of extension and contractio~ of the spring are nearly the same, and the distance between the two cations (lattice parameter) remains almost the same, hence, there is no strain. precisely, ions are not connected by such idealized springs (those are cded harmonic springs, in which force (F) = spring constant (k) x displacement (A) holds). In most cases, the springs possess u ~ ~ ~ ~ o ~ i c i ~ (F = k1A - k2A2>, that is, they m somewhat easy to extend but hard to contract. Such subtle ~ e ~ n c e s in the displace~ent causes a change in the lattice parameter, producing a strain which is inde~ndent of the direction of the applied electric field (+E or -E), and hence is an even-function of the electric field. This is called the ezectrosEric~ve efect, and can be expressed as

is the electrostrictive constant.

(a) P I ~ % ~ i ~ c t r i c Strain

( 1 . 1 1 )

E

+ l ,- C

(b) E l ~ t r o s t ~ ~ t i o n

.7 ~icroscopic explanation of the piezostriction and electrostriction.

11

in Fig. 1.7(a) also possesses a s p o n ~ e ~ u s bias dipole moment. The total dipole moment puza~~atiun. When a large reverse bias elec

s p o . ~ ~ e o u s p o l ~ ~ t i o n in a particular polar mother stable crystal state in which

the ions are re (In terms of an u n ~ n n e d single 180" about an axis ~ ~ n ~ c ~ l ~ to

ntial double minima in Fig. 1 .S.) , also causes a remarkable change in

to as~e~ueZec~'cs, as men~oned in Section 1.1. Generally, what is actually observed .as a field-indu~ strain is a com~licated combination of the three basic effects just d e s c r i ~ .

Figure 1.8 shows typical strain curves for a piezoelectric lead zirconate titanate ( strictive lead magnesium niobated (PMN) based c ~ ~ c . ~ )

in PZT becomes distorted md shows large hys~resis field level, which is due to the p o l ~ ~ t i o n reorientation. does not exhibit hysteresis under an electric field cycle.

relation (E2) at a high e field level.

the converse iez~lectric effect above. Then, what is the normal or phenomenon whereby charge (Coulo~b

al stress (force per unit area). Note the same piezoelectric coefficient d is used as used in Eq.( 1. lo), in the relation

P = d X , (1.12)

Ei6ctric field (kV/cm) Electric fieM (kV/cm)

Typical strain curves for a piezoelectric zirconate titanate (W based (a) and an el~~ostrictive lead ma~nesium niobate (P"?) based ceramic (b).

1

ne of the lead zirconate tita~ate ( 590 X C/N with a dielectric con§tant e3 = 3400 and an elastic com~liance s33

) calculate the indu

will in~oduce the tensor ~ u ~ ~ ~ e s ectin~ the su~§cript§ at

x = d E = d

~ n d e r a completely clamp

3 = x3/ s33 = 5.9 x /2Q X m2 = 3.0 x 1Q7 N/m2

3 = P3/ WE = (1.77 X c/m2)/(3400 X 8.854 X

= 5.9 x 105 Vlm I

13

en electric energy is supplied to a piezoelectric sample and some e l e c t r o ~ e c ~ ~ i c a l c o u ~ l ~ ~ ~ ~ a c t o r

ener~y)/(~nput electrical energy). = (1/2)(x2/ S)/( 1/2)( = d2 / S € 0 ~

, hen mechanical energy is suppli

put mechanical energy).

0 x 10-l2 m 2 ~ ) ( 3 4 0 0 x 8.854 x F/m) (P1 -2.10)

(b) is about k2 of the 10 x 105 ~ansd~ction ratio accomp

(1.13)

ion isp placement is ently the r e ~ ~ c ~ v e

14

Generally, the refractive index is treated as a symme~ical s e c o n d - r ~ tensor quantity and is represented geometrically by the optical i ~ i c a t ~ which is described by

(1.14)

where "1, n2 and n3 are the principal refractive indices. th the appli~ation of an electric field, the change in refractive index is given by an expansion expression:

ere n(E) and n(0) (no) are the refractive indices at E and zero rijk is the p r i ~ ~ electrooptic coe~cient ( ~ o c ~ e l s e#e~t) and c ~ ~ c i e n t (Kerr e#&).

ons side ring the paraelectric phase of a perovskite crystal (m3m) as an example, the rr coefficients are represented in the following matrix:

1 1 R12 R12 0 0 0 12 R11 R12 0 0 0

0 0 0 0 0 0 0 0 0

so that the refractive indicatrix under an electric field applied along the z direction is expressed as:

x2 + y2 22 + = 1 . (1.16)

no2( 1 - ( n 0 ~ / 2 ) R l 2 E ~ ~ ) ~ no2( 1 - (no2/2)Rl 1E22)2

The refkactive index change under an external electric field is explained intuitively as en an electric field Ez is applied to a cubic perovskite crystal, the crystal

is elongated along the z-axis and contracted along both ~onse~uently, the material's density or compac~ess will be axis and densified along the x and y axes, leading to a decrease nz and an increase of the indices nx and ny . (Note that the refkactive index is propo~ional to the electron density or ion compactness the polarized light electric field direction which is pe~endicular to the light pr on ~rection.) i

en light is ~ansmitted along the y direction, the phase re~dation rY between the o r ~ i ~ ~ and e ~ r a o r ~ i ~ ~ waves is given by

+ l

15

Optical phase retardation through an electrooptic crystal. Notice the crossed polarizer con~g~at ion .

where d is the electrode gap and L is the optical path length (See Fig. 1.9). Placing the crystal between crossed polarizers m g e d at a 45O angle with respect to the z- axis, the output light intensity is modulated as a function of applied voltage according to:

This is the p~nciple b e ~ n d the operation of a light shutterlvalve, and the voltage required for the first i~tensity maximum (i.e., ry = E ) is an impo~ant ch~acte~stic called the ha~-wave vo~ta~e.

ZT) sample with a r e c ~ g u l ~ shape (optical at 45" with respect to

to the sample with an

dent intensity: IQ) is light intensity IFz) by ne~lectin are listed below:

16

refractive index at E = 0 : no electrooptic Ken coefficients : phase retardation: ry reflectance at the crystal surfac

int

The initial spherical indicatrix will be deformed into an ellipsoidal one under an applied electric field EZ:

x2 + y2 22 + = 1. (P1.3.1)

no2( 1 - ( n 0 ~ / 2 ) R l 2 E ~ ~ ) ~ no2( 1 - (no2/2)Rl 1Ez2)2

The output light intensity is reduced twice, once at the inlet and once again at the outlet crystal surfaces by a factor of (1 - Re)2,

Also you should notice that the incident light (after passing polarizer) has or^^^^ and e x ~ u o r ~ i ~ ~ light componen~ of qual mag~tudes.

In a cubic s ~ c t u r e , the refractive index change under an external electric field along z-axis is expressed by the following two equations:

l/nZ2(Ez) - Uno2 = R1 1Ez2, l/nx2(Ez) - Uno2 =

Taking into account the relation, d(l/n2) = - (2/n3) dn,

(P1.3.2)

(P 1.3.4) (P1.3.5)

11 > 0 and R12 c0 in most cases.

Since the wavelengths of the e x ~ a o r ~ n ~ @oldzed along z-direction) and the or din^ (polarized dong x) waves are described as

(P1.3.6) (P1.3.7)

where is the vacuum wavelengt~ of the incident light, and numbers of waves exist in^ in the crystal with an optical ~ a t h ~ n g t h of L L& and Llhx, respectively, the phase difference between these waves ( ~ e ~ u ~ ~ ~ ~ o ~ rY) is ~ iven by

the linearly polarized light incident on the PLZT in terns of its electric field vector as

(P1.3.9)

the output light fiom the ZT can be described as

in[(2n/?q)) y - cot + (p] , (P1.3.10)

sin[(2n/?q)) y - cot + (p -

at the - 45O orientation, the electric field comp~nent

ex 142 .. eZ 142 = (1 - [sin[@ /ho)y .. cot + (p] - sin[(2 Iho)y - a t + (p -

lntensi~

A ~ ~ l i e d Voltage

ariat ti on in the light intensity of an electrooptic shutter with app voltage.

18 Chapter 1

Thus, the output intensity through the 2nd polarizer is obtained:

I = (112) (1 - Re)2 (Io 12) [( 1 - cosry)2 e (sinr'y)2] 4 1 2 ) IO (1 - cosry) (P1.3.12)

Figure l. 10 shows the output intensity I as a function of applied voltage Vz. The ~ a ~ - w a v e voltage, which is &find as the minimum voltage required to produce the first m ~ i m u m in the transmitted light intensity, is given by

A typical ceramic ferroelectric is barium titanate, which is used here as an example to illustrate some properties of ferroelectrics. As shown in Fig. 1.11, BaTiQ3 has a perovskite crystal structure. In the high temperature paraelectric phase (non - polar phase) there is no spontaneous polarization (the symmetry is Q, - m3m). Below the ans sit ion temperature TC called the Curie t e ~ p e r ~ ~ r e (about 13OoC), spontaneous polarization occurs, and the crystal s ~ c ~ e becomes slightly elongated, that is, tetragonal (C4v - 4mm). Figure 1.12 shows schematically the tem~rature dependence of the spon~neous pol~zation PS and pe~ittivity E. PS decreases with increasing temperature and vanishes at the Curie temperature, while E tends to diverge near Tc. Also, the reciprocal (relative) p e ~ t t i v i t y 1 1 ~ is known to be linear with respect to the temperature over a wide range in the paraelectric phase (so-called Curie- Weiss law),

E = C / ( T - T o ) , (1.19)

where C is the C u r i e - ~ e i s s ~ ~ n s t a n t and TO is the C u r i e - ~ e i s s t e ~ p e r a ~ r e . TO is slightly lower than the exact transition temperature Tc.

It is also known that the spontaneous pol~zation PS and the spontaneous strain xs follow the relationship

and xs decreases almost linearly with increasing temperature. In the case of it exhibits the piezoelectric effect in the ferroelectric phase, while in the p ~ e l ~ t r i c phase, it is non-piezoel~tric and exhibits only the el~trostrictive effect. With d ~ r e a s i n g ~ m p e r a t ~ e from room tempera~e, however, barium titanate undergoes a series of complicated phase transitions. Figure 1.13 illustrates these successive phase ~ansitions.

General View of Ferroelectrics

A

TC : Curie temperature

Crystal structures of BaTi03.

(a) Capacitor

Te~per~ture

(d) Piezoelectric ~ ~ s d u c e r (e) Electrostrictor

(f) Electrooptic device

Temperat~e de~ndence of the spontaneous polarization pe~ittivity in a ferroelectric material. (a) - ( f ) indicate the temperature ranges for each application. In other words, if we can shift such temperature range closer to room temperature, a practical material is obtained.

0

R h o m b o h e ~ ~

" 150 -100 -so 0 50 100 150

Tempe~ture ( 5)

V ~ i o ~ s phase transitions in b ~ i ~ ~ titanate.

1

1.1

1.

22

and x1 = Q I ~ P ~ ~ , and refkactive index changes An3 = - (112) no3gl 1P32 and An 1 = - (112) no3g 1 2 P 3 ~ . ~ x p e ~ m e n ~ values of these are: Q1 1 = 0.090 m 4 C 2 , 4 1 2 = - 0.035 m 4 C 2 ; g 1 1 = 0.136 m 4 C 2 , g12 = - 0.038 m4C2. Co~paring the absolute values between Q and g and the ratios

12 and g1 1412, discuss s i ~ l ~ t i e s in terns of the crystal lattice compac~ess along and pe~endicular to the electric field.

1 ) C. Kittel: In~oduction to Solid State Physics 6th edition, Chap.13, John Wiley

2) . Kinase, U. Ukmura and M. Kikuchi: J. Phys. 3) . Uchino and S. Nomura: Bull. Jpn. Appl. Phy

4) trostrictive Actuators: Materials and Applications, Bull. Amer.

Sons, New York (1986)

omura, L. E. Cross, R. E. Newnham and S. J. Perovskites and Its Transducer Applications, J. Mater. Sci., 16, 569 (1981).

No.4, 647 (1986).

Physicists usually treat a natural p~enomenon using .a simple mathematical form: one is a linear approximation and another is a non-linear expansion theory. Hooke's law, the stress - strain relation and Ohm's law, the voltage - current relation a m two of the most famous linear laws in physics. These linear relations are extended into matrix or tensor relations in linear algebra. On the other hand, the Maclaurin or Taylor series are popularly used to calculate slightly perturbed physical quanti~es around an equilibrium state inclu~ng non-linear effects. In this chapter, we will consider the tensor representation of physical properties (linear relation) pheno~enology of ferr~lectricity (non-linear relation).

Let us fiist consider the tensor for electric conductivity. The conductivity is &fined so as to correlate an applied electric field and the induced current density follows:

Since both the electric field the current density are fiist rank tensor (that is, vector) ~uan~t ies , the conductivity should have a second rank tensor representation (that is, with two suffixes); this is described as

(2.3)

e x e ~ ~ l i f i ~ by ~iezoelectric coe~cients, providin~ a relatio~ ~etween the applie~ field and the induced strain

23

are f~st-rank and second-r& tensors, respectively, the d should have a ~ d - r a n k tensor form represent^ as

Xjk = L= dijk Ei (2.5) i

The d tensor is composed of three layers of the symme~ical matrices.

dl11 dl12 dl1 1st layer (i = 1) dl21 dl22 dl23

131 dl32 d13

2nd layer (i = 2)

3rd layer (i = 3)

211 d212 d21 d221 d222 d223 d231 d232 d23

311 d312 d31 d321 d322 d32 d331 d332 d33

Generally speaking, if two physical properties are represented using tensors of prank and q-rank, the quantity which combines the two properties in a linear relation is also represented by a tensor of (p c 4)-rank.

rys t etry

A physical property me as^^ along two different dir~tions must be equal if these two directions are c ~ s ~ l l o ~ a p ~ c a l l y equivalent. is consideration sometimes reduces the number of i n d e ~ ~ d e n t tensor components representing the above property.

Let us again take electric conductivity as an example of a s ~ o n ~ - r ~ tensor. If the in an (x,y,z) coordinate system is described in an (x',y',z') system as

J', J and J' are related using a unitary m a t r i ~ ~ as follows:

e electric field is ~ ~ s € o ~ e d in the same way:

at~~~atical T r ~ a t ~ ~ ~ t of

or

Then, we can c~culate the co~esponding a' tensor defined by

(2.10)

012 012 0 1 all a21 a31 21 a22 023 a12 a22 a32 a31 032 03 a13 a23 a33

# A unit^ matrix without an i m a g i n ~ part has the following relation:

31 a32 a3 13 a23 a33

For c e n ~ o - s y ~ e ~ , the ~ a n s f o ~ a t i o n matrix is written as

0 0 -1 Q Q -1

and for rotation about a principal axis,

26

or

Chapter 2

0'" - - aikajl akl (2.12) U

When the crystal has a 2-fold axis along the zLaxis, the electric conductivity should have the same tensor form in terms of the ans sf or mat ion:

0 - 1 0

From the condition

0 0 1

0 0 -1 0 0 1

0 0 -1 0 0 1

(2.13)

the following equivalencies can be derived:

031 = 013 = G32 = 023 = 0 1 1 9 0229 0 3 3 0 (2.14)

012 = 021

It is very impo~ant to note that most physic^ c o n s t ~ t s a s y ~ e t r i c tensor form. [The proof involves t h e r m o d y n ~ c ~ considerations beyond the sco

tric tensor, the ~ a n s f o ~ a t i o ~ due to a

(2.15)

~ t ~ e r n ~ t i c ~ ~ Tre~trnent of Ferro~lectrics 27

W e n the crystal has a 4-fold axis along z-axis, for example, the t r a n s f o ~ a ~ o n matrix is given by

1 0 0 0 0 1

Conside~ng the tensor s y m m e ~ with m and n such that dl23 = dl32 and d213 = d231 (each matrix of the ith layer of the d tensor is symmetrical), we can obtain:

dl 11 = d222 = d l 12 = dl21 = d211= d221= d212 = dl22 = d33 1 = d3 13 = d l 33 = d332 = d323 = d233 = d312 = d321= 0

d333 = 0 d311 =d322 d113=d131=d223=d232 dl23 =dl32 = -d213 = -d231

Then we get the d tensor as follows:

1st lay 0 dl 3 0 dl2

131 dl23 0

2nd la er 0 0

-dl23 dl31 0

3rd layer 311 0 0

d311 0 0 d33

(2.16)

(2.17)

A. general ~ d - r a ~ tensor has 33 = 27 inde~ndent components. Since dijk is s y m m e ~ i c ~ in j and k some of the coefficients can be eliminated, leaving 18 independent dijk coefficients; this facilitates the use of matrix notation.

28

the num~er of suffixes as , for instance, d21 =

by a single suffix 1 to 6 in matrix notation, as follows:

S of these new symbols the may (2.6) is rewritten as:

e last two suffixes in the tensor notation c o ~ e s ~ o n d to ~ o ~ ~ o n e n t s ; eref fore, for consistency, we make ~otation for the s ~ ~ n com~onents.

i (i =: I, 2, 3; j = 1, 2, ..., 6)

or

electrics

(2.2 1)

onents, the (1/2)s are ~ n n e c e s s ~ .

1 6 (2.22) 5

The marix notation has vantage of compactness over makes it easy to displ c ~ ~ c i e n ~ on a plane di remem~~red that in sp ir form, the dij's do not of a second-rank tensor. An example of a piezoelectric matrix for the point group 4 is written as

Q 0 Q Q 15 -dl4 0 (2.23)

d31 d31 d33 0 0 0

theoretical ~ e a ~ e n t of the pheno~enon of ' strain xkl is expressed in terms of the electric

(2.24)

ere, diH and giM are called the piezo ectric coef~cients, and ijkl the electrostrictive coe st-rank and tensors, respectively, d and -rank tensors, respectively.

Using a similar reduction of the notation for the elec~ostrictive c ~ f ~ ~ i e n ~ we get the following equatio~ ~o~esponding to Eq. (2.24):

30 hapter

11 21

M14 M24

Tables 2.1 and 2.2 summarize the matrices d and for all c r y s ~ l o ~ a p ~ c point groups.1)

Suppose that a shear stress is applied to a square crystal and the crystal is deformed as illus~ated in Fig. 2.1. Calculate the induced strain x5 ( = 2x3 1).

F

F

. 2.1 Shear stress and strain c o n ~ ~ u r a ~ o n .

Since x5 = 2x31 = tan 8 = 8 and 1' = IC /l80 rad., x5 = 0.017.

at~~matica~ Tr~atm0nt of F0rro0~~~cs 31

T ~ c ~ i c wit p u p 1

. .

. . . . .

3

(~ontinued) ~iezoelec~c coef~cient m

. . . .

* . . .

Electro~t~ctive coe~ficie~t X. *

b t

. .

. .

. .

34 Chapter 2

continue^) Electrostrictive coefficient m a ~ x . *

. I * .

. . I ) . .

Point group 23, m3 Point group 43m, 432, m 3 ~ . . . * I .

. I .

a t ~ e ~ ~ t i c a l Treat~ent of Ferroelectrics 35

For a cube-sha~d specimen, tensile sass X and compressive stress - simultaneously along the (1 0 1) and (1 0 1) axes, respectively (Fig. 2.2). When we take the p~me-coordinates as illustrated in Fig. 2.2, the stress tensor is represented as

0 0 0

Using the transformation matrix A

calculate Ax-A"~, and verify that the above-stress is equivalent to a pure shear stress in the original (non-prime) coordinates.

Application of a pair of stresses X and .. X to a cube of material

Solution

Using 8 = - 45O, we can obtain the transformed stress r~presen~tion:

A.x.A-~= 0 0 X 0 0 0 (P2.2. l) X 0 0

$

The off-diagonal components X13 and X31 have the same magnitude X, and represent a pure shear stress. Note that a shear stress is equivalent to a combination of

3

extensional and con~action~ stresses. an extensio~al stress a an ntly s i ~ i l ~ diagonal e

ng, without the co~trac~on along the 3' d ~ e c ~ o n ,

0 0 0 0 dl5 0 0 0 0 0

d3 l 31 d33 0 0

is t r a ~ s ~ o ~ e d into

0 0 0 0 0 0 0 15 0 dl5 0 0

0 0

ate exhibits a cubic crystal symne does not show ~ie~oel~trici ty . Ho

is induced under an a ~ ~ l i e d electric field. The relation

1 2 0 0 0

1 2 0 0 0 1 1 0 0 0

0 0 0 0 0 0 0

0 0 0 0

alculate the induced S n under an electric fie1

§olution

38 Chapter 2

The distortion is illustrated in Fig. 2.3(b). The strain x indud along an arbitrary direction is given by

x = I: X" I* I* 1J 1 J (P2.4.3) where li is a direction cosine with respect to the i axis. "herefore, the strain induced along the [ 1 1 l] direction, ~~111111 , is given by

X[I 1 l]// = Z; xij (1/43)(1/43) = [X 1 + x2 + x3 + 2 ( ~ 4 2 + x512 + xd2)]/? = (M11 2M12 + M441 E[111I2/3* (P2.4.4)

On the other hand, the strain induced perpendicular to the [ 1 1 l ] direction, x[ 1 1 1 U, is calculated in a similar fashion as

Figure 2.1 l(b) shows the distortion schematically. It is important to note that the volume~c strain (AVfV) given by

X[lll]// + 2 X[lll]l= (M11 + 2M12) E[111I2 (P2.4.6)

is independent of the applied field direction.

( 1) ~ a n ~ a u Theory of the Phase Transition

A t h e r m o d y n ~ c ~ theory explaining the behavior of a ferroelectric crystal can be obtained by considering the form of the expansion of the free energy as a ~nct ion of the polarization P. We assume that the Landau frwj energy F in one dimension is represented formally as:

F(P,T) = (112)a P2 + (114)p P4. + ( 1 16 )~ P6 + (2.26)

The coefficients a, p, y depend, in general, on the temperature. Note that the series does not contain terms in odd powers of P because the fiee energy of the crystal will not change with polarization reversal (P m-> -P). The phenomenological fo~ulation should be applied for the whole temperature range over which the material is in the paraelectric and ferroelectric states.

~at~ematical Treatment of Ferroelectrics 39

The equilibrium polarization in an electric field E satisfies the condition:

(2.27)

To obtain the ferroelectric state, the coescient of the term must be negative for the polarized state to be stable, while in the paraelectric state it must be positive passing through zero at some temperature To (Curie-Weiss temperature):

cx = (T - TO)/@ C (2.28)

where C is taken as a positive constant called the Curie-Weiss constant and To is equal to or lower than the actual transition temperature Tc (Curie tempera~e). The temperature dependence of a is related on a microscopic level to the temperature dependence of the ionic polarizability coupled with thermal expansion and other effects of a n h ~ o n i c lattice interactions. Refer to the discussion in Section 1.2.

When p is positive, y is often neglected because nothing special is by this term. The polarization for zero applied field is obtained from m. (2.27) as

[(T - To)/&() C] PS + p Ps3 = 0 (2.29)

so that either PS = 0 or Ps2 = (To - T)/p EO C.

For T > To, the unique solution PS = 0 is obtained. For T C To the minimum of the Landau free energy is obtained at:

PS L= ZJ(T0 - T)/(p Q C). (2.30)

The phase transition occurs at Tc = To and the polarization goes continuously to zero at this temperature; this is called a second-order tra~si~ion.

The relative permittivity E is calculated as:

) = &()(a + 3p P2) (2.3 1)

Then,

(2.32)

Figure 2.4(a) shows the variations of PS and E with temperature. It is notable that the permittivity becomes infinite at the transition temperature. Triglycine sulphate is an example of a ferroelectric exhibiting the second-order transition.

40

P e ~ t t i v i t ~ E

Tc Te~perature (Curie Temp.)

(a)

Pe~ittivity E

' c Te~~eratur~ (Curie Temp.)

0)

hase transitions in a ferroelectric: (a) second-order and (b) first-order.

First-order ~ a n s i ~ o n

p is negative in Eq. (2.26) and y is ositive, the transition becomes first . The equilib~um condition for E = . (2.33) leads to either PS = 0 or Eiq.

(2.34).

(2.34)

e transition temperat~e Tc is obtained from the condi~on that the the paraelectric and ferroelectric phases are equal: i.e., F = 0, or:

- TO)/&O C] + (112) p (2.35)

fore:

TC = To + (3/16)(p2 Q C1 y) (~ .36)

ote that the Curie temperature TC is lightly higher than the C te~perature To, and that a discrete jump of appears at Tc. Also, the p exhibits a finite maximum at TC for a ~ ~ s t - o r ~ ~ t r ~ ~ s i t i o ~ [Fig. 2.4(b) tana ate is an example of a ferroelectric that undergoes a ~rst-order phase ~ansi t io~.

es are plotted for the second- and firs res in Fig. 2.5. In the case of p > 0,

shows a maximum and a discon~nuity of the

41

Free Energy

P

Free energy curves plotted €or the second- (a) and first-order (b) phase ans sit ions at various temperatures.

Veri@ the difference between the Curie and C ~ i e - ~ e i s s tempera~res as expressed by:

TC = TQ + (3/16)(p2 EO

€or a €iist-order phase ~ ~ s i ~ o n , where the Landau free energy is expanded as

a = (T - TQ)/EQ C.

The potential ~ i n i m a are o b t ~ n e

(P2.5.1)

There are generally three minima including P = 0 (F = 0).

At the Curie temperature, the free energy at the non-zero pol~zation must be to zero (F = 0). Thus we o b t ~ n another condition:

F = (112)~~ P2 + (1/4)p + (1/6)y P6 = 0 .

42 Chapter 2

Equations (P25 1) and (P2.5.2) are reduced for non-zero polarizations to

a + p p 2 + y P 4 = 0 , (P2.5.3)

a + (1/2) p P2 + (113) y $= 0 g (P2.5.4)

. (P2.5.3) is valid for all temperatures below Tc, but Q. (P2.5.4) is only valid at T = Tc. Eliminating the P terms from these two equations, we obtain

TC = To + (3/16)(p2 C/ y) , (P2.5.6)

~ e n o m e n o ~ o ~ y of E~ectrostrictio

In a ferroelectric whose prototype phase (high temperat~e paraelectric phase) is centrosy~etric and non-piezoelectric, the pi ectric coupling term and only the electrostrictive coupling term is introduced. electrostriction in ferroelectrics were formulated in the 1950s by Devonshire2) and

aye3) Let us assume that the elastic Gibbs energy should be expanded in a one- dimensional form:

X, (a = (T - TO)/EO C ) (2.37)

, X, T are the polarization, stress and temperat~e, respectively, and S and are called the elastic compliance and the electrostrictive coefficient, respectively. This leads to Eqs. (2.38) and (2.39).

(2.38)

X - (aGl/aX) = SX + Q (2.39)

en the external stress is zero, the following equations are derived:

E = a P + p P 3 + y P 5

l / E O & = a + 3 p P 2 + 5 y P 4 X = QP2

(2.40) (2.41) (2.42)

~a the~a t i c a~ Treat~ent of Ferroelectrics 43

If the external electric field is equal to zero (E = 0), two different states are derived;

P = 0 and P2= (4 p2- 4ay - p)/2y.

(i) Paraelectric phase: PS = 0 or P = Q E E (under small E)

Permittivity: E = C/(T - To) (Curie-Weiss law) (2.43)

Electrostriction: x = Q &02e2E2 (2.44)

The previously mentioned electrostrictive coefficient M in Eq. (2.24) is related to the electrostrictive Q coefficient through

M = Q &02e2 (2.45)

(ii) Ferroelectric phase: Ps2= (d p2- 4ay - p)/2y or P = PS + EO& E (under small E)

X = Q(Ps + EO E E)2 = QPs2 + 2 EO E QPsE + Q &02e2E2 (2.46)

where we define the spontaneous strain xs and the piezoelectric constant d as:

Spontaneous strain: xs = QPs2 (2.47)

Piezoelectric constant: d = 2 EO E QPs (2.48)

We see by Eq. (2.48) that piezoelectricity is equivalent to the electrostrictive phenomenon biased by the spontaneous polarization. The temperature dependences of the spontaneous strain and the piezoelectric constant are plotted in Fig. 2.6.

When a hydrostatic pressure p (X = - p) is applied, the inverse permittivity is changed in proportion to p:

I/EO E = a + 3 p p2 + 5 y Pc + 2 ~ p (Ferroelectric state) a + 2Qp = (T - To + 2Q~Cp)/(&oC) (Paraelectric state) (2.49)

Therefore, the pressure dependence of the Curie-Weiss temperature To or the transition temperature Tc is derived as follows:

In general, the ferroelectric Curie temperature is deaeaxd with increasing hydros~tic pressure (i.e. Q h 0).

44

Temperat~e dependence of the spontaneous strain and the pie~oel~tr ic constant.

arium titanate has d33 = 320 x CN, (= €3) = 800 and 33 = 0.1 1 m4c-2 at room te~perature. Estimate the spontaneous pol~zat ion

Let us use the relation:

(P2.6.1)

S = d33Q EO €3 Q33 = 320~10-~~[CN]/{2 x 8 . 8 ~ 4 ~ 1 0 - l ~ [ = 0.21 [c/mZ]

In the case of a second-order phase transition, the elastic Gibbs energy is expanded in a one-di~ensional form as follows:

G1 (P,X,T) = (1/2)a P2 + (1/4)p - (112)s x2 * Q P2 x , (P2.7.1)

where only the coefficient a is dependent on temperature, a = (T - To)/&oC. Obtain the dielectric constant, spont~eous pol~ization, spontaneous strain and piezoelectric constant as a function of te~perature.

4

bee ch~acte~stic e~ua~ons:

et tin^ E = 0 i~itially , we ob n the follow in^ two stable states: Ps2 = 0 or

~ael~ctr ic phase -- T > To --

(P2.7.9)

iezoel~tric cons~nt is obtained as

o far we have discuss the electric field ~ d u c ~ strains, i.e. piezoelec~c strain rse ~ ~ e ~ ~ ~ ~ e c t ~ c ~ ~ e c t * x = d . Let us consider here the CO

46

A( 1k0 E) = 2QX (2.52)

This is the co~verse elecFrost~c~ve e+ecF. The converse ~:lectrostrictive effect, the stress ~ ~ n ~ n ~ of the pe~ittivity, i in stress sensor^.^) A b i m o ~ h s ~ c t u r e which subtracts the static capac of two electric provide superior stress sensitivity and tem~rature s ~ b i l i ~ . The c of the top and bottom plates have opposite signs for uniaxial S

ure change. The response to about 1

in the low p i e z ~ l e c ~ c s will be discuss^ in Section 7.2 of apter er ?.

Several expressions for the electrostrictive coe~cient have been given so far. From the data obtained by independent experimen~ methods such as

1) electric ~ e l d - i n d u c ~ strain in the p~aelectric phase, eous pol~zation and s p o n ~ n ~ ~ u s strain (x-ray

3) d c o n s ~ t s &om the ~eld-induced strain in the ferroelectric phase

4) ~ressure dependence of ~ e ~ i t ~ v i ~ in the paraelectric phase,

~ ~ c t i o n ) in the ferroelectric phase,

or fkom piezoelectric resonance,

T r\ (U

U \ "E

l x lo-2 N n

0 \ "E W

1

- X50 - 100 50 0 50 100

~ e r n ~ r a ~ r e ("c) .7 Temperature dependence of the electrostrictive con st^^ Q33 and

athe~atical Tr~at~ent of Ferroelectrics 47

nearly equal values of Q were obtained. Figure 2.7 shows the temperature dependence of the electrostrictive coefflcients Q33 and Q31 for the complex perovskite ~ b ( ~ g i / 3 ~ b 2 / 3 ) 0 3 , whose Curie tempera~re is near O * C ~ ) It is seen that there is no significant anomaly in the electrostrictive coefiicient Q through the tem range in which the paraelectric to ferroelectric phase transition occurs piezoelectricity a p ~ a r s . Q is almost temperature inde~ndent.

(1) ~ntife~roe~ectrics

The previous sections dealt with the case in which the directions of the spontaneous dipoles are parallel to each other in a crystal (polar crystal). There are cases in which antiparallel orientation lowers the dipole-dipole interaction energy. Such crystals are called anti-polar crystals. Figure 2.8 shows the orientation of the spontaneo~s electric dipoles in an anti-polar state in comparison with a non-polar and a polar state. In an anti-polar crystal, where the ikee energy of an antipolar state does not differ appreciatively from that of a polar state, the application of an external electric field or mechanical stress may cause a transition of the dipole orientation to a parallel state. Such crystals are called u ~ ? ~ e ~ ~ o e ~ e c ? ~ c ~ .

Figure 2.9 shows the relationship between (applied electric field) and in paraelectric, ferroelectric and antiferroelectric phases. In a paraelectric E relation is linear; in a ferroelectric phase there appears a hys

ans sit ion of the spontaneous polarization between the positive negative directions; in an anti ase, at low electric field, the induced polarization is propo~onal t crystal becomes ferroelectric pol~zat ion shows hysteresis removal of the electric field, the crystal returns to its anti-polar state, and hence, no spontaneous polarization can be observed as a whole. This is called a double ~ ~ ~ ~ e ~ e ~ ~ ~ curve.

stripe type checker board typ

Schematic ~angement of the spontaneous dipoles in non-polar, polar and antipolar materials.

48

Polarization

(a) Paraelectric

(b) Ferroelectric ' (c) Antiferroelectric

Polarization

field

Polarization vs. electric field hysteresis curves in paraelectric, ferro- electric and antiferroelectric materials.

We will discuss here the introduction of electros ctive coupling in energy expression for ~tife~oelec~ics.6,7) e simplest model for ~ t i f e ~ ~ l ~ t r i c s is the "one-dimensional two-sublattice model." It treats the coordinat~ as one- ~mensional, and a superlattice (twice the unit lattice) is formed from two neighbor in^ sublattices each having a sublattice polarization Pa and Q,. The state Pa = Pb represents the ferroelectric phase, while Pa = - Pb, the antiferroelectric phase. For the electrostrictive effect, ignoring the coupling between the two sublattices, the strains from the two sublattices are QPa2 and QPb2, respectively (assuming equal electrostrictive constants Q for both sublattices). The total strain of the crystal becomes

(2.53)

owever, since ~tiferroelec~city originates from the coupling between the s~blattices, it is appropriate to consider the sublattice coupli~g also for the

at~emati~al Tr~atm~~t of 49

electrostrictive effect. The coupling term for the elec~ostriction the following form:

in which hy~ostatic pressure p is employed, and XT is the i s o t h e ~ a l compressibility, Qh and are the electrostrictive constants. Introducing the transfo~ations PF = (Pa Pb)/2 and PA = (Pa - Pb)/2 leads to the followin expression:

The dielectric and elastic ~ua t ions of state follow as

( l + ~ ) p + p P F 2 + 3 p P A 2 + y + l@' PF2PA2 + 5" PA4] (2.56)

Hence, the induced volume change in the paraelectric phase can be related to the induced ferroelectric pol~zation by the following formula:

Below the phase ans sit ion temperature (this temperature for antife~~lectrics is called ~eeZ ~ e ~ ~ e r ~ ~ ~ r e ) the spontaneous volume strain and the s p o n ~ e o u s antiferr~lectric pol~zation are related as

(2.60)

Even if the perovskite cystal shows Qh 0, the spontaneous volume strain can positive or negative depending on the value of > l), that is, if the inter-sublattice coupling is s~onger than the coupling, a volume contraction is observed at the Nee1 point. This is quite different from f e ~ ~ l ~ t r i c s , which always show a volume expansion at the C t. Figure 2.10 illustrates the spontaneous strai~s in a crystal scheme tic all^ 0. en Pa and Pb are in the parallel con~~uration (ferroelectric phase), the acts to increase the strain

50 Chapter 2

xs, when they are in the anti-par~lel config~ation (antife~oelctric phase), the a- term acts to decrease the strain.

This phenomenological theory explains well the experimental results for the ~tiferroelectric perovskite crystal PbZr03 and others.8) Figure 2.1 1 shows the strain in the antiferroelectric ceramic Pbo,ggNbo,o2[(Zro,6sno.4)o.g4Tio.o6]0.g8o3 as a function of an applied electric field91 The large change in the strain associated with the field-induced transition from the mtiferrwlectric to ferroelectric phase can be estimated to be

Here, we assume that the magnitudes of Pa and pb do not change drastically through the phase transition.

(a) Ferroelectric Arran~e~ent X = Q (I +Q) (Pa + Pb)2/4

x =QPa2

Intuitive e~planation of the sublattice coupling with respect to electros~ction (for S 2 > 0).

at~e~atical Treat~ent of Ferroelectrics 51

Antiferroelectric phase I (kV /m)

1 Field induced strain in a P b ( ~ , S n ) ~ 3 based ant i fe~oelec~c.

1. Tensor representation: when two physical properties are represented using tensors of p-rank and q-rank, the quanti~ which combines the two properties in a linear relation is also represented by a tensor of (p + 9)-rank.

2. A physical property measured along two diffe~nt directions must be equal if these two directions are c~s~lographically equivalent. This consideration reduces the number of the independent tensor components representing the above property.

3. Shear strain: x5 = 2 x31 = 2 Qb, taken as positive for smaller angle.

4. Phenomenology : (M) > Q --> second-order phase transition

e Q --> first-order phase ~ n s i t i o n

x = Q PS2 + 2 Q &Q& PS E + Q Y ) & 2 2 E 2 spontaneous strain piezos~ction electros~ction

constant is insensi

7 . In ~ t i f e ~ o e l e c ~ c s , consid~ratio~ of ~ublat~ce the stable sublattice ~olariza~on con

jump in strain associate^ i n d ~ c ~ by an external el

'1 e room tem~erature form of ~u~~ belon

at the ~ i e z o ~ l e c ~ c m

1 1 -dl1 0 0 0 0 0

at the ~ i e z ~ l ~ t r i c tensor must be in ~ o u n ~ the %axis a d for a 1~0'rotation transformation matrices are

0 - 1 0

.3 2.3 0 - 0 0 ' 0 0 0 0 0

3

int

t

212

31 33 1

54 Chapter

Next, a 120° rotation is considered such that a1 1 = -112, a12 = 1/3/2, a21 = .. 1/3/2, a22 = -112, a33 = 1 :

Continuing the c~culations for d123, d212, d23 1, d312, d331, we can obtain all the necessary e~uations for deriving the final matrix form.

2.2 In the case of a first-order phase transition, the h d a u free energy is expanded as in Example Problem 2.5. Calculate the inverse pe~ittivity in the vicinity of the Curie tem~rature, and verify that the slope ( (l/e)/ilT) just below Tc is 8 times larger than the slope just above Tc.

In a fmt-order phase transition, PS satisfies the following ~uat ion in the temperature range of T < Tc:

a + p PS2 + yPs4 = 0 .

The pe~ittivity is given by

l/&O& = a + 3 g PS2 + 5 y PS4 .

Thus,

l / € ( ) € = a + 3 p PS2 + 5 (- a - 3 p = - 4 a - 2 P P s 2

Since a = (T .. To)/&o C, Ps2 = (4 p2- 4ay - p)/2y and

(T - to)/^ C = (3/16)(p2/ y) - (Tc - T)kO

a t ~ ~ ~ a t i c ~ ~ Tre~t~ent of Ferroe~ectrics 55

we can obtain

l/€()& = - 4 a - 2 p PS2

= - 4 [(3/16)(p2/ y) - (Tc - Cl

Considering (Tc - T) <c 1, obtain the appro~imation of this equation.

J. F. Nye: Physical Properties of Crystals, Oxford University Press, London, p.123, p.140 (1972) A. F. Devonshire: Adv. Phys. 3, 85 (1954) H. F. Kay: Rep. Prog. Phys. 43, 230 (1955) K, Uchino, S. Nomura, L. E. Cross, S. J. Jang and R. E. Newnham: Jpn. J. Appl. Phys. 20, L367 (1 981); K. Uchino, S. Nomura, L. E. Cross, S. J. Jang and R. E. Newham: Jpn. J, Appl. Phys. L367 (1981); K. Uchino: Roc. Study Committee on Barium Titanate, J. Kuwata, K. Uchino and S, Nomura: Jpn. J. Appl. Phys, 1 C. Kittel: Phys. Rev. 82, 729 (1951) K. Uchino: Solid State Phys. 17, 3’71 (1982) K. chino, L. E. Cross, . E. Newnham and S. Nomura: J. Appl. Phys, (1981) K. Uchino: Jpn. J. Appl. Phys, , Suppl. 24-2, 460 (1985)

le communication S such as cordles§, poaable, e popular worldwi you know what kind of

components are used in a cellular phone?

~ e r ~ i c ~apacitor§ icrowave Oscillators

~ e r ~ c Filters

After the material design such as solid solution compositions and dopants, we nee consider material fabrication processes. The fabrication of f e ~ ~ l e c t r i c devices generally involves S: preparation of the ceramic powders and sintering of the shaped s ~ c t u r e s . chemical prepara~on methods .are uti ceramic powders i ensure reproducibi~ty of the the devices. Popular device designs include multilayers films. Some necessary basic knowledge such as particle size effect and domain con~ibution to fe~oelec~icity will also be discussed in this chapter.

utilized for piezoelectric applications. Their piezoelectric coefficients are s u ~ ~ in the international data book:

ellwege et al.: Landolt - ornstein, Group 111, Vol. 1 1, Sp~nger- Verlag, N.U. (1979).

Figure 3.1 shows the composition dependence of the permittivity and the electro- mechanical coupling factor kp for the E T system.')

If we do not have this sort of comprehensive experimental data, how can we estimate the values for the solid solutions? In general, physical properties of a solid solution

- x) A - x B, can be estimated by a pheno~~nolo~ical S elastic energy of a solid solution is assumed to be a linear bs elastic energy of each component:

,T) = (1/2)[( 1 - X)aA + X 3 P2 + (1/4)[(1 - x ) g ~ + xp + (1/6)[(1 - x ) y ~ + x ' y ~ ] P6 - (1/2)[( 1 - X)SA f XSEj] x2 - [(l - X)QA f X

57

solution provides reasonable fmt-order e s ~ a t e s of e spontaneous pol~zation and strain, ~ ~ i t t i v i t y , pie2 C e l ~ , c ~ o m ~ h ~ i c a l coupling. Abe et al. reported a good example of theo~tical fitting to ~ x p e ~ m e n ~ results for the solid solution P b ~ Z n i ~ N b ~ 3 ) 0 3 - P b T i 0 3 . ~ ) F i ~ ~ e s 3.2- 3.5 show these fittings calculated on the basis of the data presented in Table 3. l .

0 0 20 40 GO 80 100 P b ~ r O ~

PbTiOa 100 80 60 40 20 0 Compos i ti on [mol %)

coupling factor kp in the PZT system.

~ ~ f ~ c i e n t s for ans sit ion tempe """" """

~ ~ n s t a n t s """""""

130 4.7

10.3 6.8 2.4 -0.86 1.6 4.058

nd Fa~~cation Proc

l 00

0

200

l001

0

- 100 " 100 0 0.1 0.2 0 0. l PZN X - PT PZN X-"

(a 1 (b)

; (a) calculated and (b) e x ~ e ~ m e n

4.3

4.2.

4 .l

4.0

3.9

3'80 0.2 0 4 0.6 0.8 1.0

- 4.3

Q: 4.2

S m LLJ f -

Q Q=

3 4.0 U V

t- Q J

3 4.t

Fz 3.9

3.8

PT X PZN PT X

( 0 )

rnbo. fr. c

b ~ ~ m titanate in

3.6(a)J.

~ ~ f i c i ~ n c y is i n ~ o ~ ~ c e

ov e

stal ~ e ~ c i e n c i ~ s in

el helps us to

sTio.25) Q3 .(soft piezoe i ~ u ~ ~ t r ~ i n xmm, and thk

Ax at half of the m ~ i m u m electric field (1 hyste~sis is calcula~d fkom the s t r ~ n devia~on

10

9

8

opant effect on the field-induced strain. ~ i m u m s ~ a i n and hysteresis ceramics, (a) ~ e ~ n i ~ o n of the rn~imu~

strain and the degree of hysteresis, and (b) dopant effect on actuator p ~ ~ e t e r s .

63

On the c o n t r ~ , the ~ c e p t o r - ~ ~ ions with a small valence +l .. +3 suppress the hysteresis and the coercive field. Although acc in designing ~tuator ceramics used for positioner is very n e c ~ s ~ for making "hard" piezocerami

p~icularly suitable for ultrasonic motor applications. These dopant at~ibuted to the ~ o ~ a i n pinning eflect,

The coercive electric field of a ferroelectric material, which is defined as a field for reorienting the pol~zation direction, is affiected by dopants. Explain the dopant effects on the "soft" and "hard" characte~s~cs of piezoelectric ceramics.

First, the "soft" and "hard" characteristics are a reflection of the coercive field E(-, in other words, the stability of the domain walls. The "hard" piezoelectric is defined for

EC 3 1 k~/mm, while the "soft" one is for EC cc 1 kWmm.

Consider the transient state of a 180° domain reversal, which reveals a domain W front with a head-to-head polar~zation config~ation. From Gauss's law,

(p: charge density) (P3.1.1)

the domain wall front is very unstable in a highly insulating materi~, leading to quick ~isap~arance of this domain wall, i. e. a low coercive field. However, if the material has movable charges, the head- polarization configura~on is stabilized, l e ~ i n g to a high coercive field.

xt, let us consider the movable charges due to the c~stal lo~aphic deficiencies. cceptor ions, such as Fe3+, introduce oxygen deficiencies and in the case of donor

b5+, Pb deficiency is intr~uced. Thus, the acceptor doping causes through the easy reorien~tion of deficiency- relate^ dipoles, leading to

"hard' ch~acte~stics. On contrary, the donor doping is not very effective for domain pinning, since the ion can not easily hop to an djacent A-site vacancy due to the close oxygen surroundings.

oreover, it is notewo~hy that lead-con~ning ceramics such as type se~conductors due to Pb evaporation during sintering. doping provides rather "soft" ~haracteristics to the piezoceramics, since donor doping can compensate the original acceptor type deficiencies. Donor- exhibit large piezoelectric d constants, but also a large aging effect due to depoling.

ince the meas~ement t ~ h n i ~ u e to dete ~ a c t e ~ s ~ c s at high v i ~ r a ~ o n levels was not e s~~ l i shed previous

vi~ration levels with a constant c u ~ e n t circuit.6)

40

30

20

10

0 0.01 0.02 0.05 0.1 0.

nin

0

ration velocity v for

100

v i ~ r a ~ o n velocity for un

Figure 3.10 shows mechanical Q versus mole fraction of 29 (x) at effective vibration velocities v S and 0.5 m/s for ~b(29xTi1-x)~3 doped with 2.1 at.% of ~e3+ .8 ) me In m e c h ~ c a l Q with increase in vibration level is ~ n i m u m around the rhombohedral-tetragonal ~ o ~ ~ o t r o ~ i c

words, the worst material at a small vibration lev ation level, and data obtained from an conventional

not relevant to high power materials.

Figure 3.1 1 h i g h l i ~ h ~ the key material ated factors ~fecting heat piezoelec~c material. The resistances and Rm in the e ~ ~ i v ~ Z e ~

separately plotted as a function of vibration velocity?) Note ted to the mechanical loss, is insensitive to the average vibration velocity, while , related to the dielectric loss, changes signi~cantly around a certain critical

vibration velocity. Thus, the resonance loss at a small vibration velocity is m ~ n l y d e ~ ~ n ~ by the intrinsic mechanic^ loss, and with incre~ing vibration velocity, the i n ~ n s i c dielectric loss con~bution signi~cantly increases. We can conclude that heat generation is caused primarily by dielec~c loss (i.e., P-E

fer to Chapter 7, Section 7.3 (2) for the e~uivalent circuit.

1 00

30

10

3.0

RA (directly me~sured) =&+Flm

tan

0.03 0.1 0.3 1 .o Vibration Velocity v0 ( d s )

~ibration velocity ~ ~ n d ~ n ~ of the resistances equivalent electric circuit for a piezoelectric component.

~si~nin~ and Fa~~cation

F e ~ o e l e c ~ c devices are typically f a b ~ c a ~ from polyc~s~l l ine ceramics. This involves two steps; preparation of the ceramic powders and sintering of the sh s ~ c t ~ e s .

re

article size dis~bution and compositional u n i f o ~ i t y are the key factors to be control in the raw powder in order to realize reproducibi~ty of the

acte~stics, The usual method is the o x i ~ e - ~ ~ i ~ g t e c ~ ~ i ~ u e , in chemical composition is made by firing raw oxide crushing them into fine powders. Since the oxide-mi~ng

results in dif~culties in achieving microscopic compositional u n i f o ~ chemical methods ( c ~ ~ r e c ~ i t a ~ o ~ , a l ~ x i ~ ) have been employed more recently in

ceramic devices. In this section, processes for f a b ~ c a ~ n g lead zirconate titan~te (PZT) and lead magnesium niobate

ceramics are reviewed.10)

k t us consider the preparation of Pb(~xTil-x)03 powders. The raw powders PbQ, 21-02 and Ti02 are weighed in an a p p r o p ~ a ~ proportion, mixed, and calcined at around 800 - 9 0 0 " ~ for 1 - 2 hours, Then the sample is crushed and milled into fine powders. The drawbacks here are that the milling process does not efficiently give particles of size less than 1 pm, and that the contamination of the sample by milling mdia is unavoidable.

in principle from qui-molar quantities of raw powders of BaO and 7302. In general, BaCO3 powder is en^ instead of BaQ, because high purity BaO is expensive and chemically less reactive.

A similar calcination prmess starting from PbQ, MgO, m205 and Ti02 can be used for Pb[(Mg1/3Nb2/3)1-xTix]03. . However, this simple process generates a second phase ~ y r o c ~ l o r e ) in addition to the perovskite phase. To suppress this second phase several mol 9'0 excess PbO doped in the final sintering stage is effective.l l) Swartz, et al. reported a unique method taking account of the chemical reaction process.12) They demons~ated that the perfect perovskite phase can be obtained by the reaction starting from coZu~~i t e ~ g m 2 0 6 and PbO:

For PMN-PT, MgO, Nb2Q5 and Ti02 are mixed and fired at 1000°C initially. Then PbO is added to the columbite, and the sample is calcined at 800 - 900°C. Several mol % excess MgO is particularly effective in obtaining the perfect perovskite phase.

+

70 Chapter 3

) inter in^ Process

After being shaped into a desired shape, the agglomerated powder body is fired at a high temperature (less than the melting temperature). Accelerated ~ f ~ s i o n of the constituent atoms on the fine particle surfaces due to the surface energy (surface tension) promotes crystal bonding at the contict interface between the two adjacent particles and provides sufficient mechanical strength to the ceramic without signi~cant distortion from the inital molded shape. This firing process is called " ~ i ~ ~ e r i ~ g , " which primarily e l i~na tes pores and increases the ceramic density (see Fig. 3.12). Notice that the physical properties of the sintered body on the property of each fine crystalline particle, but also on the the pores. An example is found in the mechanical strength: mechanical fracture in c e r ~ c bodies occ~ionally occurs at the grain b o u n ~ ( i ~ ~ e r g ~ ~ ~ ~ ~ ~ r type). On the contrary, when the crystal itself has a strong cleavage character, the p o l y c r y s ~ ~ n e material shows higher mechanical strength.

During sintering, the grains grow and the grain shape also changes s i g n i ~ c ~ t l y . However, it is well recognized that the raw powder ch~acte~stics strongly affect the manufact~ng conditions and the final product characteristics. In general, the sintering is accelerated with decreasing particle size of the raw powder (i.e., with increased specific surface area), because the driving force of sintering is related to the surface energy of the particles. Moreover, for fine powders, the necessary diffision length of the atoms for sintering becomes shorter, which accelerates pore diffusion. "his results in high density ceramics.

Diffusion

Molded Body Sintered Body

. 3.12 Schematic diagram of sintering process.

esigning and Fa~~cation Processes 71

wth in the PLZT ceramics 9/65/35 ceramics sintered for (a) 1 hour and (b) 16 hours.

es on grain growth. ~ e f e ~ n ~ 16) is rex ing relationship between the grain size and the sinte~ng

In the case of n ~ ~ l gruin growt~, p = 2, and for ~~~1 grain growth, p = 3. Figure 3.13 shows the microphotographs of a PLZT 9/65/35 surface sintered at 1200°C for 1 and 16 hours, s ~ i n g from the oxalic acid ethanol method.17) Figure 3.14 shows a good linear relation between the sintering period and the square of the grain size.

n

0 4 8 12 16 20 Sintering time (hrj

LZT as a function of sinte~ng time.

at.%) is very e f f ~ ~ v e in s u ~ ~ r e s s i n ~

+ and Nb5+ make a e the A-site and the la e

a~count the charge neu~ality of

+l *( l-x) +3*x +2.( 1-y) +5y = +6

2 x + 3 y = 3 ( O < X < l , 1 / 3 < y < 1)).

rial 73

piezoelectric/elec~ostrictive devices. h y ~ o t h e ~ ~ synthesis ently, N ~ ~ ~ a et al.

m a thin plate of LiNb03 crystal, i to ~ n c ~ o n like

Although this device is agile the displacement curve ~ i t h o ~ t such as scannin~ tunneling mi inves~gated inte~sively for so

1s more than l cm3 can be easily grown by a simple

a special crystal direc~on,20,21)

esigns in this section, including single dis multilayers, composites and thi~thick films.

Single disk devices are nd these days because of low e~ciency in still impo~ant for the laboratory

expe~ments.

constant of a barium titagate based isk sample. However, it was

sample ceramic and the coated electrodes over most S, because of lack of skill in fabrication. Estimate

and two air gap capacitors CO we denote the capacitor area, e total capacitance is

74

1lC = ~/(EOE Sld) + 2 4 ~ 0 Sl6) = (1ko S)((~/E + 2 S) (P3.3.1)

Since the apparent dielectric constant was calculated from

C/(w Sld) = 500,(P3.3.2)

The following relation is obtained:

(l/&) + (2 6ld) = 1 6 0 0 . (P3.3.3)

Substitutin~ d = loB3 m, 6 = 0.5 x m, we obtain the real d ie lec~c constant of E = 1000.

above mistake is occasionally found when alcohol is U polishing, and it is not dried completely on a hot p1

should be careful not to make a air gap (even sub~cron!) d ~ n g the electroding process.

To achieve a low driving voltage, ~ n i a t u r i z a t i ~ ~ and hybridi~ation of the devices, ectric ceramic multilayer structures have been investigated intensively for

capacitor, actuator and electrooptic applications. y words for the fbture trend will be "finer" and "hybridization," Layers thinner than 10 pm, which is currently used in mul~layer capacitors, will also be introduced in actuator devices instead of the present 100 pm thick sheets. Non-un i fo~ con~~ra t ions or he~ro-struc~res of the materials, layer thickness or the electrode p a t t e ~ will be adopted for practical devices.

are two techniques for making mu1 ceramic devices: d and the ~ p e - c ~ t i ~ g eth hod. The

for multilayer capacitor fabrication, and requires e sophisticated techniques, but is suitable for mass-production of more than 10 thousand pieces per month.

As shown in Fig. 3.15, a multilayer structure is composed of alternate f e ~ ~ l e c ~ c ceramic and internal electrode layers fab~cated by c o ~ ~ n g . An electrodes composes a unit ~splacement element, which is connected in parallel by the external electrode up to hundreds of layers, Figure 3.16 shows a flow manufacturing process of the multilayer ceramic actuators. Green sheets in two steps: slip prep~ation of the ceramic powder and a doctor blade slip is made by mixing the ceramic powder with soZvent, d e ~ o c c ~ ~ ~ t , ~ i ~ e r and ~ Z ~ t i c i z ~ r . The slip is cast into a film under a special straight blade, a " ~ c ~ r ~ Z ~ e , ' ' whose distance above the carrier determines the film thickness. After drying, the film, called a green sheet, has the elastic flexibility of sy~thetic l ~ a ~ e r . Tbe volume fiaction of the ceramic in the polymer matrix at this point is about 50%.

and ~ a ~ ~ c a t i o ~ Processes 75

The green sheet is then cut into an approp~ate size, and internal electrodes are printed using silver, paladium or plati~um ink. Several tens to 100s such layers are then l ~ n a t e d , and pressed using a hot press. M e r cutting into small chips, the bodies are sintered at around 1200'C in a hrnace, taking special care to c binder evaporation at 500°C sintered chips are then polished, externally

, lead wires are attached, and finally the chips are coated with a water-proof spray.

Polarization direction Internal electrode

Structure of a multilayer actuator.

(Binder mixing, Vacuu~~zation)

(~nching) (ElFtrode pnnting)

( ~ ~ n a ~ o n , Press, Cutting)

IE Binder evaporation, Sin!ering) xternal electrode pnntlng)

Fig. 3.16 Fabrication process for a multilayer ceramic

External "electrode

actuator.

76

s~lacement m a ~ n i ~ c a t i o ~ can be e ~ i e ~ o e l e c ~ i c . Verify this u s i ~ ~ si ~ i e z o e l ~ ~ c and elec~os~ctive cases, res~ectively .

and n to be the total

= L x = L d E = L

S case the ~enerative dis num~er of layers n (more effe

V 0 0.1 .7

M

T e m ~ r a ~ r e rise versus Ve/A (3 k effective volume ene era tin^ the heat and A is the su

77

lastic shim n e z o c e r ~ i c plate

There have been many reports on equations describing the tip ~ s p l a ~ m e n t and the resonance frequency. Summaries are provided here. Figure 3.19 illustrates two bimorph designs without shims. Two poled piezoceramic plates with tl2 in thickness (i.e., t is the total thickness) and L in length are bonded with their polarization directions opposite to each other (a) or parallel to each other (b). According to the con~guration, the tip displacement 6 under a voltage V is provided as follows when one end is clamped ( c ~ ~ ~ l e v e r condition):

e Two types of piezoelectric bimorphs: (a) the anti-parallel polarization type and (b) the parallel polarization type.

6 = (312) d31 (L2/ t2) V, (3.3a)

Notice that this difference comes from the electrode gap di~erence: t in (a) and 112 in (b). For both cases the ~ n d ~ e n ~ resonance ~ ~ u e n c y is d e ~ ~ n e d by the total thickness t as?3)

f = 0.161 (tl L2) (p ~ 1 1 ~ ) - ~ ’ ~ . (3.4)

As can be ~ t i c i p a ~ , the b i m o ~ ~ drive is inevi~bly ~ c o ~ p ~ e d by a r o ~ t i o n ~ motion. To obtain a perfect parallel motion a special m~hanism must be employed. Figure 3.20 shows such a bimorph sbwture. A complex bimorph proposed by Ampex has divided electrodes electrically connected oppositely at the tip and bottom (suppo~ing part) parts so as to com~nsate the canting angle at the bottom by the opposite bend at the tip.24) The bimorph also included a sensor function: the sensor electrode can detect the voltage generated in proportion to the magnitude of bend.

aterial and Device e s i ~ n ~ n ~ and Fabrication Processes 79

ig. 3.20 B i m o ~ h s ~ c t u r e for a perfectly pardlel motion with a position sensing feedback function.

Using a PZT based ceramic with a piezoelectric constant of d31= - 300 pC/N, design a no-shim bimorph with a total length of 30 mm (5 mm is used for cantilever clamping) which can produce a tip displacement of 40 pm with 20 V applied. Calculate the response S of this bimorph. Here, the density and the elastic compliance of the ceramic are p = 7.9 g/cmf and S 1 1E = 16 x 10-12 m2/N, respectively.

Considering a certain low applied voltage, type (b) in Fig. 3.14 is to type (a) in order to obtain a large displacement. Substituting L of Eq. (3.3b) with 25 mm, we get the piezoelectric plate thickness:

= (25 x m) 4 (3) (300 x Cm) (20 V) /(40 X 10-6 m) = 530 pm. (P3.5.1)

After cutting the ceramic into plates of 265 p m in thickness, 30 mm in length and 4 - 6 mm in width, the two plates are bonded together after electroding and electrical poling. The width of the bimorph is usually chosen as w/L c 115 so as not to suppress the magnitude of bending.

The response time is estimated by the resonance period. From Eq. (3.4)

f = 0.161 (t / L2) (p SI lE)-ll2 = 0.161 [ 5 3 0 ~ 1 0 - ~ ~ ( 2 5 x l O - ~ m)2] I ( 7 . 9 ~ 1 0 ~ k~m3)(16x10-12 m2/N)

(P3.5.2)

us, roughly 2.6 msec.

80

en a p i e z o c e r ~ c can be f a b ~ ~ a t e d . ~ ~ ) style is given by

plate is bonded to a metallic shim, a "he tip deflection 6 of the unimo

Here E is the electric field applied to the piezoelectric ceramic, d31, the piezoelectric constant, L, the length of this unimo~h, Yc or m, Young's modulus for the ceramic or the metal, k or tm is the th i c~ess of eac material. In addition, to mfers to the distance between the s t r Q i ~ - ~ e e ~ e ~ t r ~ Z ~ Z Q ~ e and the ~ n d i n g S represented as

Q = [tc tm2(3 tc + 4 tm) Ym + k4Yc] I [ 6 tm(tc + tm) Ym]. (P3.6.2)

Sup~ose Yc = Ym, calculate the optimi condition of ( t ~ / ~ ) to maximize the deflection 6 for the following conditions:

(a) for a fixed ceramic thickness k, (b) for a fixed total thickness k + tm.

Setting YC = Ym, the equations become:

Substituting to in Eq. (3.6.3) with Eq. (P3.6.4),

6= (d31 E)L23tmtc/(tm+tc)3.

men, the function f(tm) = tm tc I (tm + ~3 must be m zed for a fixed ceramic t ~ c ~ n e s s tc (a) or for a fixed total thickness tc + tm = ttot.

(a) df(tm)/dtm = (tc - 2 tm) tc I (tm + tc)4 = 0 (P3.6.6)

Thus, the metal plate thickness should be adjusted to tm = k I 2. to = k I 2

0th the metal and ceramic plate thickness should be adjusted to tm = tc = ttot I =2*

to = ttot I 3.

I 1

A composite actuator s ~ c t u r e called the " ~ o o ~ i e " has been devel sure sensitivity and the small ~splacements induced in a piezo

ediate characte~stics ~ t w ~ n the conventi ators; it exhibits an order of magni~de larger disp

ltilayer, and much l genera~ve force (10 kgf) w than the b i m o ~ h . S device consists of a thin

WO metal plates with a narrow moon-shaped cavity bonded [Fig. 3.21(a)]. The moonie with a size of 5mm x Srnm x 2.5mm can g~nerate a 20

~splacement of a multilayer o ( ~ ~ ~ ~ ~ 2 type) as shown in Also the generative di of the position from the center of the end c bal to the moonie is its easy f a b ~ c a ~ o ~ process. ne-step punch in^ can make endcaps from a metal plate.

splacement under 60 which is 8 times as large as the

oonie (a) and a modified oonie (Cymbal) (6).

piezoel~tric ceramic bodies are al composites can be fabricated, W

sensitivity by keeping the act~ation ~nct ion. Figure. 3.22(a) shows such a 1 - 3 composite device, where PZT in a polymer in a two dim~nsional array.

The simplest composite from a fab~cation vie~point is a 0 - 3 connectivity type, which is made by dispersing piezoelectric ceramic powders u n i f o ~ l y in a polymer matrix [Fig. 3.22(b)]. The fa~~cat ion processes are classified into a m ~ l t i n ~ and a rolling meth0d2~) Figure 3.23 shows the flowchart for the fab~cation processes. The powders are mixed with molten polymer in the first method, while the ~ w ~ e r s are rolled into a polymer using a hot-roller in the second method. The fab~cation processes for 1 - 3 composites are introduced in Chapter 10, Section 10.3.

82

2 PZT: polymer composites: (a) 1 - 3 connectivity and (b) 0 - 3 connectivity.

(Ball milling) I

(Film casting)

(Rolling) I

(C~endenn~)

Piezoelectric component

Fabrication process for PZT: polymer composites.

c ~ ~ u e s for fab~cation of oxide thin films are classified into physical chemical processes:

aterial and Oevice ~esigning and Fa~~cation Processes 83

Electron beam evaporation RI? sputte~ng, DC sputtering Ion beam sputte~ng Ion plating

Sol-gel method (dipping, spin coating etc.) (b) Chemical Processes

mica1 vapor deposition (CVD) CVD

Liquid phase epitaxy, melting epitaxy, capillary epitaxy etc.

Sputte~ng has been most commonly used for ferroeketric thin films such as LiNb03, I?LZT,~O) and PbTi03,31) Figure 3.24 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. The sol-gel technique has also been employed for processing EZT films.32) ~pplications of thin film ferroelectrics include memories, surface acoustic wave devices, piezosensors and mi~o-mechatronic devices.

. "

Principle of a magne~on sputtering apparatus,

"he thin film structure is inevitably affected by two significant parameters:

(1) Stress from the substrate -- Tensile or compressive stress is generated due to thermal expansion mismatch between the film and the substrate, leading to sometimes a higher coercive field for domain reorientation.

as follows: wi

Etectric field (kV/mrn) I -1.5 -1.0 -0.5 i

200

T

0 0 50 100

o Temp fdl

0 1 2 3 4 5 Grain size ( f l m )

size dependence of the pe

D= 2.

D=1.1

.k A ~ l i ~ d field (ktrlcrn)

Grain size de~endence of the i n d ~ c e ~ s ~ ~ n in

esigning and Fa~~cation Processes 7

R e g ~ n g the much smaller particle size range, Uchino et al. previously a number of info~at ive experimen~. Figure 3.29 shows the tetragonality (c/a) change witb particle size in pure BaTiO3 at room The cia value decreases drastically below 0.2 pm and becomes 1 (i. e.

of the cla ratio ous particle size powders. This demons~ate between the critical particle size md the Curie temperature, which deweases with decreasing particle size.

Z ~ ~ ~ i c Z e size. Figure 3.30 shows the ~ m p e ~ t u r e

Sin le c stat

Particle size ( urn)

b

t e m ~ ~ t ~ e .

Temperature ("C 1

cri size, c y for skites,

ao.g~ro, 1 Ti03 95 0, 19 1.2 57 B a ~ O 3 125 0.12 1.8 54

Bag, g5Pb0.15TiOg 180 0.08 2.9 58 0.032 6.2 50

Ti03 500 0.02 10 so

e

1) ~ o m ~ n reo~ent~tion~ in each rain, ~lyc~stalline state (a c o ~ ~ l e ~ of r a n ~ o ~ l y oriented tiny c ~ s t a l ~ ~ .

Figure 3.33 shows domain reorient~~on observed in ar inde~ndently of ea&

mono-domain state can not achieved.

90

"3

l

~ ~ a i n in a piezoelec

(1) (2)

ornain reorientation in

Fi

~chernatic de~iction of the s ~ a i n change in a ~ e ~ ~ l e c ~ c ~ s ~ i a t e d with the ~ o l ~ z a t i o n reo~entation.

0 3 exhibits a r h o ~ b o

[l 1 l] - [ l li] = [002],

[ l l l ] - [lK] = [022].

us, the angle bet~een two of the non- 1 80° 1s is ca lc~la te~ as follows:

1) 2)/(200), (022)/(0~2)* (002)/(220) (002)*(200) = 0

.l

ction in~icate§ a with cla = 1.01.

on a m o n o ~ o m ~ n si

eter of

(3.10)

94 hapter

~ ~ = § s [ I c o s ~ ~ ~ v / I ~ v - ~ / ~ ] = S S ( C O S ~ (3.1 1)

S model, in which the microscopic regions with s p o n ~ e o u s strain change only their o~entations, accompanied by no volume change, provides CT = 0.5 and

x1 = x2 = .. x312 (3.12)

owever, there is a serious discrepancy with e x p e ~ m e n ~ data.

Next, in order to find the trend for the change in induced strain with an applied electric field, the relations~p between 8 and E3 has to be known. Uchida et al. analyzed this problem by introducing a characteristic angle 890 for non-180° domain reorientations; in tetragonal crystals, 90° reorien~tion and in rhomb 71° and 109O reorientations occur. But in onkr to simplify the explanation, all reorientations are being represented by the former. Suppose a 90° domain rotation occurs in a small region dv in a ceramic, and as a result, the orientation of 6r becomes 0. These authors assumed that there exists a characte~stic angle 890, such

0, a 90° rotation of the small region can occur, ccur, and the region remains in its intial state.

co~esponds to a certain E3, by in ng-Eq. (3.1 1) over a go is satisfied, the induced S x1 and x2 can be o as a ~ n c t i o n of go. Figure 3.36 shows the relationship between 890 and

3.37(a) shows the measured values of i n d u d strain in r h o m b o ~ ~ a l PZT ceramics. ~ o m p ~ n g the two 090 and E3 figures reveals the relationship between 090 and E3 [Fig.3.37(b)]. It is apparent that pronounced hysteresis also appears in the versus E3 curve.

~ u ~ e ~ o r e , by finding the polarization P3 and the field-induced strain x3 (or xi) as a function of the electric field E3, it is possible to estimate the volume in which a 180° reversal or a 90° rotation o c c d . This is because the 180° domain reversal does not contribute to the induced strain, only the 90° rotation does, whereas the 180° domain reversal con~butes mainly to the pol~zation. It is shown sc~ematically in Fig. 3.38 that with the application of an reversal occurs rapidly whereas the 90° rotation occurs slowly?2) It is notable that

G in the figure, there remains some polarization while the induced strain is zero the pol~zations from the 180° and 900 reo~entations cancel each other

ecome zero, but the strain is not at its minimum, Cknerally in such a case, a the induced strain x3 versus pol~zation P3 shows large hysteresis (Fig. 3.39).43)

owever, for materials whose polarization is do~nated by non- 180° domain rotations, the hysteresis in the x versus P plot shoul y be observed. Such is the case for the low t e m ~ r a ~ e phase of Pb(Mg113 03 which is shown in Fig. 3,4O(b).44)

Q. 5

95

'- 1/31, where 690 is a c~tical tio on and (cos2 8 - 113) is pro

X

L. 120 f4 l

U B

Q _.

Electric field E3 k V / ~ 1 (a) (b)

7 Tr~sverse strain x1 versus field in ~b(~o.57Tio,43)~3 (a) and the calculated 690 - E3 relation (b). The m e ~ ~ e m e n t was done at 30042.

J I

&nce of the domain volume (b). Notice the ~eviation of

betw~en 180° and 90°.

x3 x 10 2

3

x

-1 -0.5 0 0.5 1

PS C / m 2 ) -0.2 -0.1 0 0.1 0.2

O f

98 hapter 3

Principal strain, spontaneous polarization, reoriented volume fraction and coercive field in tetragonal and rhomboh~al PLZT ceramics.

specimen

25/50/50 25/52/48 5/50/50 5/52/48 5/54/46

25/58/42 251601~

6/65/35 5.25/60/40

Principal strain Ss (%)

2.4 2.2 2.16 1.96 1.68

0,732 0.74 0.65

0.6 1

Spontaneous polarization (pUcm2)

71 72 65 64.5 65

56.5 58.5 45 49

~ ~ e n t e d volume fraction (%)

22 28 18 23 30

86.5 78.5 85 85

Coercive field Ec (kVIcm)

18 14.7 16.3 14.8 11.7

8.2 7.6 5.6 5.7

Calculated & (kV/cm)

17.8 18.8 13 13.7 13

7 5.4 5.9 4.8

The crystal o~entation of the dielectric c o n s ~ t €3 and piezoeleetric gonal PZT are schematically ill in Fig. 3.4 1. Let us ented polycrystalline sample. the change in the €3

and d33 before and a k r poling.

1 L

Crystal orientation d e ~ n ~ n c i e s of the dielectric and piezoelectric constants of a tetragonal PZT.

Before poling, because of a u n i f o ~ crystalline dis~ibution, the dielectric constant should have an i n ~ ~ ~ a t e value ~ t w ~ n Emin and Emax, and the piezoelec~c constant should be zero.

~ l e c ~ c poling orients the pol~zation along the z-axis, thus, the pe~ittivity approaches E ~ , leading to a decrease in pe~ittivity after poling. ,On the con^^, the piezoelectric c o n s ~ t should increase monotonically with increasing poling field, finally exhibiting a saturation of d33 above a certain poling field (close to the coercive field).

1, Doping effects on fe~oel~tricity in PZT: Acceptor ---> domain p i ~ i n ~ ---> "hard" piezoelectric Donor ---> Pb deficiency com~nsation ---> "soft" piezoelectric

aration of ceramic powders: o x i d e - ~ x i n ~ technique co~r~ipitation alkoxide hydrolysis

3. Device designs: Single disk

ultilayer ~ n i m o ~ ~ i m o ~ h ~oonie/cymbal Flexible composite Thin/thick film

4. omp par is on between multilayers and bimorphs: 1. The multilayer type does not exhibit large displacements, but has advanta~es

in generative force, response speed, life time and elec~om~hanical coupling

2. The bimorph type exhibits large displace men^, but shows disadvantag~ in k33

generative force, response , life time and the e l e c ~ o m ~ h ~ c coupling bff.

5. Tip displacement in a b i m o ~ h under a one-end clamp condition (cantilever):

6 = (312) d3 1 ( ~ 2 / t2) V or 6 = 3 d31 (L2/ t2) V

(according to the structure)

amen~l ~esonance fre

ial ceases to be ~ e ~ o e l e ~ t ~ ~ (i.e.

7.

.. to12

or

3.

102

q + q q + q q + q q

(a) 0 4

-3a -2a -a 0 . a +2a +3a

l- dimension^ finite chain of two kinds of ions +q and -4.

3.5 Barium titanate exhibits a tetragonal crystal symmetry at room t e m ~ r a ~ e and the distortion firom the cubic structure is not very large (cla = 1.01). Calculate all the possible angles between the two non-180' domain walls.

3.6 In calculating Eqs. (3.10) and (3.1 l), the volume element dv is given by Chr = 2nr2 d r sine de. Using this dv, calculate dv, cos0 dv and cos2@ dv, when the polarization is uniformly ~ s ~ i b u t e d with respect to e.

9)

B. Jaffe, W. R. Cook and H. Jaffe: Piezoelectric Ceramics, p.142, Academic Press, NY (1971). K. Uchino and S, Nomura: Jpn. J. Appl, Phys. It K. Abe, 0. Furukawa and H. Inagawa: Ferroelectrics 87,55 (1988). A. Hagimura and K. Uchino: Ferroelectrics, 93, 373 (1989). K. Uchino, H, Negishi and T. Hirose: Jpn. J. Appl, Phys., 28, Suppl. 28-2, 47 (1989). S. Hirose, Y. Yamayoshi, M. Taga and H. Shimizu: Jpn. J. Appl. Phys., 30,

S. Takahashi and S. Hirose: Jpn. J. Appl. Phys., 32, Pt. l , No.SB, 2422 (1993). K. Uchino, J. Zheng, A. Joshi, Y. H. Chen, S. Yoshikawa, S. Hirose, S. Takahashi and J. W. C. de Vries: J. Electroceramics, 2, 33 (1998). S. Hirose, N. Aoyagi, Y. Tomikawa, S. T~ahashi and K. Uchino: Proc. Ultrasonics Int'l. '95, Minburgh, p.184 (1995).

Suppl. 30-1, 1117 (1991).

evice ~ e s i ~ n i n ~ and F~~rication Processes 103

Kato: Fine Ceramics Technology, Vo1.3 Fabrication Technology of Ceramic Powder and Its Future, p.166, Industry Research Center, Japan (1983). M, Lejeune and J. P. Boilot: Ferroelectrics 54, 191 (1984). S. L. SW-, T. R. Shrout, W. A. Schulze and L. E. Cross: J. Amer. Ceram, Soc. 67, 311 (1984). Tanada, Yamam~a, Shirasaki: Abstract 22nd Jpn. Ceram. Soc. Fundamental Div. 3B5, p.81 (1984). Ozaki: Electronic Ceramics 13, Summer, p.26 (1982). Kakegawa, Mohri, Imai, Shirasaki and Tekahashi: Abstract 21st Jpn. Ceram. Soc. Fundamental Div. 2C6, p.100 (1983). H. Abe: ~ec~stuZZizution, Mater. Sci. Series 2, ,Kyoritsu Pub., Tokyo (1969). K. Uchino and T. Takasu: Inspec. 10, 29 (1986). A. Yamaji, Y. Enomoto, E. Kinoshita and T. Tanaka: Proc, 1st Mtg. Ferroelectric Mater. &c Appl. p.269, Kyoto (1977). K, Nakamura, H. Ando and H. Shimizu: Jpn. J. Appl. Phys. 26, Supp1.26-2, 198 (1987). J. Kuwata, K. Uchino and S. Nomura: Ferroelectrics 37, 579 (1981). J. Kuwata, K. Uchino and S. Nomura: Jpn. J. Appl. Phys. 21(9), 1298 (1982). J. Zheng, S. Takahashi, S. Yoshikawa, K. Uchino and J. W. C. de Vries: J, Amer. Ceram. Soc. 79, 3193 (1996). K, Nagai and T. Konno Edit.: Electromechanical Vibrators and Their Applications, Corona Pub. (1 974). K. Uchino: Piezoelectric Actuators and Ultrasonic Motors, Kluwer Academic Publishers, MA, p.241 (1997). K, Abe, K. Uchino and S. Nomura: Jpn. J. Appl, Phys. 21, L408 (1982). Y. Sugawara, K. Onitsuka, S. Yoshikawa, Q. C. Xu, R. E. Newnham and K. Uchino: J. Amer. Ceram. Soc. 75, 996 (1992). H, Goto, K. Imanaka and K. Uchino: Ultrasonic Techno 5,48 (1992). A. Dogan: Ph. D. Thesis, Penn State University (1994). Kitayama: Ceramics 14, 209 (1979). M. Ishida et al.: Appl. Phys. Lett. 31, 433 (1977). M. Okuyama et al.: Ferroelectrics 33, 235 (1981). S. K. Dey and R. Zuleeg: Ferroelectrics 10 A. Yamaji, Y. Enomoto, K. Kinoshita Ferroelectric Mater. 8t Appl., Kyoto, p.269 (1977). K. Uchino and T. Takasu: Inspec. 10, 29 (1986). . Uchino, E. Sadanaga and T. Hirose: J. Amer. Ceram, Soc. 72, 1555 (1989).

T. Yamakawa and K. Uchino: Proc. Int'l. Symp. Appl. Ferroelectrics '90, p.610 (1991). K. Saegusa et al.: Amer. Ceram. Soc., 91th Ann. Mtg. (1989). G. A.. Samara: Ferroelectrics, 2, 277 (1971). K. Uchino, E, Sadanaga, K. Oonishi and H. Yamam~a: Ceramic Trans. Ceramic Dielectrics, 107 ( 1990). N. Uchida and T. Ikeda: Jpn. J. Appl. Phys. 6, 1079 (1967). N. Uchida: Rev. Elect. Commun. Lab. 16, 4 N. Uchida and T. Ikeda: Jpn. J. Appl. Phys. N. A. Schmidt: Ferroelectrics 31 , 105 (1981). J. Kuwata, K. Uchino and S. Nomura: Jpn. J. Appl. Phys. l P. Gerthsen and G, Kmger: Ferroelectrics 11,489 (1976).

hould dis~nguish the device te~inology: monomo~h, unimo~h, bimo ultimo~h. All are bending devices, however, the d e ~ n i ~ o n s are:

- single actuator c e r ~ ~ plate single actuator plate Br; an elastic shim

b i m o ~ h .. double ac~ator plates bonded together with or without an elastic shim

h - multiple actuator plates bonded together with or without multiple elastic shims

e major application of ferro CS is for capacitors, utilizing their high con st^^ around the Curie

two classes of c itors: one is for thermal compensation of rcuits, using a Ti dl and the other is a high permittivity

low-dielec~ic constan

1 ~ , ~ 0 .

Figure 4.1 s ~ ~ ~ z e s the v ~ o u s capacitor types, highlighting their sizes ranges.1) ~ e r ~ i c c a p ~ i t o ~ with a single p opular, while multilayer ceramic capacitors parallel plate type. Se~conductor capacitors e x ~ b i t l

capacitance using very thi tric layers in a se~conductor based ceramic (see Chapter 9, Section 9.3). ip capacitors are ul~a-small capacitors for high frequency applications.

basic s p ~ i ~ c a ~ o n s re

(a) Small size, large capacitance arge dielectric constant are des

th a high dielectric constant are sometimes tric dispersion, which must be

account for prac~cal applications. (c) Te

mate~dls to stabilize the temp

105

106 hapter 4

Satellite Commun.

Automobile Commun. mTv mTv FM Radio

AM Radio

lultilayer :eramic lapacitor

led- onductor lapacitor

Various capacitor types classified according to their sizes and operating frequency ranges.

Calculate the wavelength in air (E = 1) and in a dielectric material with E = 30 for electromagnetic wave at 10 GHz.

_.

Taking account of c = 3.0 x lo8 m/s in air and v t: c / de in the dielectric,

- = 3 x /d30 [m] = 5.5 [mm]

~ ~ Z ? i ~ e r structures have been developed as part of capacitor m ~ u f a c the inte~ation of electrical circuit components. Figure 4.2 schematically shows a multilayer capacitor chip. "hin sheets made by the tape casting tec~ique, starting from a slurry of the dielectric powder and organic solvents, are coated with Ag-Pd, Ag, or cheaper Ni or Cu paste is used to form the electrodes, then several tens of sheets are stacked together and sintered. Finally, external electrodes, used to connect the chip with the circuit, are painted on. See Chapter 3, Section 3.3(2) for the details of the manufact~ing process.

107

The layer thickness of multilayer capacitors has been d u d remarkably, with thickness currently on the order of 7 - 10 pm. "he electrostatic capacitance of a multilayer capacitor is given by the following formula:

where E is the relative permittivity of the dielectric material, n the number of layers, S the electrode area, and L the total thickness of the capaciator. Note that the c a p a c i ~ c e increases in propo~on to the square of the number of layers, when the total size is fixed. Table 4.1 s u ~ ~ z e s specifications for several multilayer capacitors.2) The conventional capacitor of 10 with a 30 pm layer thickness has a volume of 70 mm3. B y decreasing the layer thickness down to 10 pm, the device volume can be reduced to 7.7 mm3. Note that by reducing the layer thickness by h , the total volume is reduced by a factor of ( to sustain the same capacitance.

Total thickness L

ctric field direction " Internal electrode

Structure of a multilayer capacitor.

.l ~imensions of the multilayer ceramic capacitors.

layers n

"- ~..~.. .

Capacitance Dimensions Volume Relative Green Sheet at Room (-1 (mm3) Volume Thickness Temp. (PI?) L W T (W)

Present 1 2.0 1.3 0.8 2.1 (100) 10 Ceram. Cap. 10 3.2 1.6 1.5 7.7' 1 0 0 10

Conventional 1 3.3 1.7 1.2 6.7 (319) 25 Ceram. Cap. 10 7.0 4.2 2.4 70.0 909 30

Tantalum 1 3.2 1.6 1.6 8.2 (390) --- Electrolytic Cap. 10 4.7 2.6 2.1 25.7 334 "..

-~.

S @

C

6 C

6 C

6 C

6 C

e l ~ o r fe~roelectrics such as been utiliz~ for very comp ~ e r o v § ~ t e § have been investi

h ivi ct ri

ir very high ~ e ~ i t ~ v i ~ , and - in§ensi~ve c h ~ a c t ~ ~ § t i c s (i.e.,

a1 f ~ ~ o e l e c ~ c ~ e r o v s ~ t e S

ions.

110

act reason why the phase an sit ion is & h e in the relaxor ferroelectrics has been clarified, We i c c o m p o s i ~ ~ n f l u c ~ a ~ o n " which is one of the most widely models for the relaxor

Fi ure 4.5 shows a comput~r simulati

has reported the sh electron mi~roscopy.8) The high resolution image in Fig. 4. ordered islands in the range of 2 - 5 nm, each of which may hav tr~sition temperature.

v)

0.3 0.4 0.50.6 0.7 Fraction of 0

e000 .eo. 0.0. ...e .OO.

000 0 eo 0 .

.00.

v0.0 eo00 000. e eo0 .eo.

M

oeoo

0000 * e00 00 .0 0 .00 o.00 v.. e

IO. e e to. eo

100. e 0. eo

'O . . .

100 0. l.00. ~ 0 0 0 0 1.0.0 100.0 tee00 ) .OO . t00.0 ~ o * o e l00.0 POOO. PO... )O...

..oe

).a00

toeoa.e*s roe e00 0..

e 0 0 0 eooe

l.000000.

l.0.0.... 10..00..0 ~ O . O . . O O O lOOO..OO. ~ 0 0 . 0 . 0 . 0 k..00. e00 lO.OO0O.O kO.O.O..O tO.O.OO.. teoveoooa ~ . 0 0 . 0 0 0 0 ~ 0 . 0 . 0 0 . 0 lO.OO..O. ) .O . r000. rooooeooe 1.000....

a a 0

20

0.3 0.4 0.5 0.6 0.7 Fraction of 0

l. 0

B. 0.3 0.4 0.5 0.6 0.7 Fraction of 0

IO

om~uter simulation uctua~on - type crystal calcul of ionic

zig region size: 4 x 4).

h P e ~ i ~ i v i ~ ~ieiectrics 111

High resolution e l e c ~ o n - ~ c r o s c o ~ image of a Pb single crystal (1 10). Note ion-ordered islands in the range of 2 - 5 nm.

In the case of the pe~itt ivity, for example, by rimpos posing the Curie- with a ~ ~ e ~ n t Curie tem~era~re , we obtain a rather which provides more stable temperature change. Thus, some is specified rather than the "~ur i e point." The pe~i t t ivi ty of

relaxor f e ~ ~ l e c ~ c s in the p ~ a e l e c ~ c region obeys the following quadra~c relation:

rather t ~ a n the n o ~ a l law

ve the tem~erature c~fficient of pe d i ~ ~ s e d phase sitio ion, the followi~

112

provement of the t e r n ~ e ~ t ~ e ~ o e ~ c i e n t of ~ ~ i t ~ v i t in

type9 tQ

45, (4) 450, (5) 1s

h 113

(a) S ~ ~ a ~ i .. type relaxor

(b) ~ ~ ~ o e l ~ t ~ ~ relaxor

0 ulti-potential-well model for (a) the ~ k ~ a v i - t y fe~oelectric relaxors: Note the difference in the coo~rative ~heno~enon.

near O°C shifts towards higher

perovs~te cell due to the di

pol~zation appears.

Consider an order-disorder ty electric with an ion d in a double-mini~um potential with a relatively lo a (Pig. 4.9). Under a quasi-dc field, the ion follo tric field alte~atin between the positive negative potentials. wever, with increasing drive e ~ h i b i ~ a delay with is an intuitive explanation for the d

(1) sing a mathematical represen~tion, derive the ion rela~on for a ~ono~spersive case:

E(@) = eS f (1 + j WT)

(2) Also discuss how the above dispersion obeys the so-called n (i.e., the real and i ~ a ~ i n ~ parts of pe~itt ivity trace a half ci X pe~itt ivity plane).

114 Chapter 4

F

Ion in a double-minimum potential.

When an external electric field E is applied, the local field F in the crystal is described by

F = E + y P . (P4.2.2)

The transition probability for an ion from the - to the + in Fig. 4.9, a+, and the opposite transition probability a,, are expressed as

a+ = r exp[- (AU - p)/k'I'l , (P4.2.3)

a.. = r exp[- (AU + pF)/k'I'I . (P4.2.4)

ere, AU is the barrier height between the two potential minima, p the dipole moment, and r is a constant.

we in~oduce the numb~r of + (or -) e total dipole number is given by

volume) is re~resented as

e ~ e ~ n d e n c e will be expres

Then,

115

(P4.2.8)

N+ = (112) (N + P/p), (P4.2.9)

(P4.2.10)

Suppose that the external electric field E = Eo ,jot is small and that the p o l ~ ~ ~ o n is given by

P = P s + & o & E o e j o t , (P4.2.11)

From Eq.(P4.2.$),

Consequently, we obtain

E(O) = Es / (1 + j 0%) , ( P 4 2 13)

where

TO = 1 I2r exp(- AUkT) (P4.2.15)

The subsc~pt S stands for a static value (o = 0), and in the paraelectric phase

Es =Z C / (T - Tc). (P4.2.16)

11

Cole-Cole plot for a ~ouble-minim~m

.2.13) can be r e ~ ~ t t e ~ as

€(~) = €'(~) + j €"(~) ,

ivi

6 lo' 0.3

S IO' 0.24

4 410'

.z 3 IO' 8 c. B 0.12 8 2 10'

0.18

1 10' 0.06

0 0

20 40 60 80 100 120 140 160 I

118

3. ~haracte~stics of relaxor ferroelectrics: (a) high pe~ittivity

(c) dielectric relaxation re - insensitive ch~acte~stics (i.e., diffuse phase tr~sition)

ielectric rel~ation in some relaxor ferroelec CS is a ~ b u t e d to the .presence of ~ c r ~ o m ~ n s . Once macrodom~ns are induced by an external electric field, the dielectric dispe~ion disap~ars and the loss becomes very small.

4.1 A multilayer capacitor (50 layers) is made fiom a 10 dielectric mate~al E = 3000. ~ s s u m i n ~ a 90% ratio area over the chip surface area, calculate the chip area to obtain a total capaci~nce of 10 p.

4.2 e relaxation time is ~stributed, the pe~ittivity dispersion follovvs as

&(~) = &S / (1 + (j ~~) iscuss the Cole-Cole plot change in c o m ~ ~ s o n with the

3)

Murata Catalog: Miracle Stones. K. Utsumi: Private communication at 4th U -Japan Seminar on Dielectrics h

~e~oelectricity, ~ijmegen (1995).

Recently, very large scale semiconductor memories using ferroelectric films have been investigat~ y. Since the conventional Si micromachining technology coupled with silicon oxide or nitride, and metal, i s limited in its ability to produce fine-scale capacitors, u~ l i za~on of ferroelectiics with high ~ e ~ i t t i v i t y or polarization hysteresis has been considered as a possible solution to the problem.

There are voZutiZe and ~n-voZatiZe ~ e ~ o ~ devices in erasable semicond memories. ~~A~ m Access memo^), which is widely because of its high in ty, is a volatile memory. Data stored i memory are lost when the electric power is shut off. On the contrary, non-volatile memories include a circuit-latch mu1 s ~ a c e - ~ o t e n ~ a l control both types, in general, h

Figure 5.1 shows the ~ n d ~ e n ~ S a capacitor; a Si02 film capacitor is connected to the source of a 5.2 shows the structure of the chosen by x-y ~ ~ e s s i n g ; that i electrodes simultaneously, thus (~e~or iz ing) , Since the ~ c u m u l a t ~ charge leaks, the capacitor must be repeatedly (re~es~ing).

ord Line

. capacitor.

119

p-type Si

e structure of a D

The el~c~on-hole pair genera~on around the radia~on changes the ~ o u n t of charge on memo^ (SOJ? error). In order retain memo^, the c ~ a c i ~ ~ of the memo^ capacitor must be higher than 30 (remem~r f = 10-15).

E x p l ~ n the genera~on process of the ~ e p l e ~ o n and inversion layers in a p-type Si) using a simple energy b voltage is applied on the metal. the hole and electron concentra~on

band model. For simplicity, you can use th close to zero.

~ o n d u c ~ o n band

Fermi le vel EF EF

I " Valence band

etal Oxide 0 Se~conductor (p-type)

Energy band model for a

E3

(c) Inversion State

p-type s e ~ i c o n ~ ~ t o r

E3 E2

Inversion layer

Let us consider an n-channel enhancement mode MOS as illustrated in Fig. 5.5. A positive gate voltage induces the electron inversion layer, which then connects the n-type source and the n-type drain regions. Discuss the drain current behavior as a function of the drain/source voltage.1)

p-type se~conductor

with a p-type se~conductor ( n - c h ~ e l

ositive gate voltage induces the electron inversion layer, which then connects the n-type source and drain regions. The source terminal is the source of carriers that flow through the channel to the drain terminal. In such an n-channel electrons travel from the source to the drain so that the c o n v e n ~ o n ~ c ~ e n from the drain to the source.

hich is analogo~s to a an insulating coat (the

be, where the water (the

n that the flat band

. Since for small E

S increase^ to the point where is equal to zero (~recisely sp version charge d e n s i ~ is shown in Fig. 5.6(b). A

123

conduc~ce at the drain becomes zero. The slope of the ID versus E omes zero.

en EDS becomes larger than the above value (Ea), the point in the channel at which the inve~ion charge is just zero shifts toward the source t

trons enter the channel at the source, travel and then, at the pinch-off point the electrons

ion (~eple~on layer) where they are swept by the E-field to the contact. If we assume that the c

m I Gate

l / I I I

71nversioi layer I

Electron flow (n chmel) (a) Drain voltage EDS a Gate voltage

" Inversion lay Electron flow

rain voltage EDS = Gate voltage EG

1 Gate

(c) Drain voltage EDS > Gate voltage

-channel with the dsource voltage for an n-ch~nel

r ~ ~ ~ o u r c ~ Volta

vers

1 0k~z 300

I

0

a ferroelectric thin film with a large pol~zation-electric field hysteresis is acitor in the structure pictured in Fig. atile memo a voltage is applied to the gate and the the “on” state, a

the drain generates a drain current nt on the r e m ~ e n t pol~zation state.

Let us assume a P-E hysteresis loop of the f e r r ~ l e c ~ c film as i l l u s ~ a ~ in Fig. pol~zation state is on A. the current flows according contrary, when the pol~zation state is on C! first, the current

increases ~ ~ a t i c a l l y because the spontaneous pol~zation reversal is associated. Figure 5.10 shows the current responses to a series of pulses (two positive pulses ~ o l l o w ~ by two negative pulses) on a PZT film with 20 x 20 ~ m 2 electrodes.~

en a positive pulse is applied just after the negative pulses, a large c ~ e n t Iposi is , which includes the pol~zation reversal. However, the second positive

pulse generates only a small current Iup. Thus, the observed c ~ e n t ~ o u n t for a positive pulse can indicate the initial p o l ~ z a ~ o n state; that is, an on or off state, or 1 or 0 state. In this memory device, after reading the initial state by applying the positive voltage, the minimum pol~zation state becomes A for all the times; that is, the reading process is destructive. , in order to retain the memory state, a wri~ng process similar to the case of is required every time.

on a ferroelectric film at every reading process in , as discussed above, the pol~zation hysteresis

ch~cteristic degrades with increasing cycles. This is c ‘ ~ ~ t ~ g ~ ~ , ” which is the most serious problem of a ferroelectric film to overcome for non-volatile memory applications. From a practical point of view, a lifetime (that is, the time until the ~ o l ~ ~ a t i o n de~adation is observed) of more than 10l5 cycles is requ~ed.

Polarization versus electric field curve for a ferroelectric film.

127

o a series of pulses (two positive pulses follo film with 20 x 20 pm2 electrodes.

The possible origins for the fatigue are related to the generation of oxygen vacancies and the diffusion o uch effort has been made to remedy this proble proposed ideas can

( l ) improvement of the film fabrication process, (2) search for new materials, (3) improvement of electrode materials.

ecent new thin film mate~als include ~ e r - s ~ c ~ r @ ~ @ ~ e Z e c ? ~ c s . material patented by Symme~x, which has a basic compo ws superior an~-fatigue prope~ies. F i g ~ e 5.1 1 shows

for rew~ting the remanent pol~zation in Y1 and the remanent pol~zation does not change signific Y1 even after testing for 1012 cycles, an improvement as is CO wed to the lifetime of lo7 cycles for

New electrode materials RuO2 and Ir have been found to exhibit improvement in fatigue in c o m p ~ s o n with the convention^ Pt electrode. F u ~ e ~ o r e , new drive modes such as a combination of the D M operation during the switch-on sta the memo^ mode during the switch-off stage have been proposed,

1

tin

0

wi

1.

130

3. ~inimum memory capacitance is about 30 P. (f = .

4. is an inversion current type of reading device.

FSET is a channel surface potential control type of FET.

5.1 S ~ e y i n the recent literature, discuss and s u m ~ ~ z e the studies on ferroelectric thin films from the following viewpoin~.

(1) List the papers (minimum 5) which report on epi~xially grown PZT films. (2) Tabulate the experimen~lly obtained physical parameters of the PZT films and compare with the data for bulk ceramics. (3) Discuss the above deviation briefly with reference to the papers' results and conclusions. (4) Discuss the crystal orienta~on the PZT films by referring to the

ate: theoretic^ E x p ~ ~ t i o n for Thin Jpn. J. Appl. Phys., V01.36 [9A], 55$0-55$7, 1997).

5.2 We learned in Chap. 4 that lead magnesium exhibit ve high dielectric c o n s ~ n ~ , If we c

N, is it applicable to the Discuss the fe~ibility of this

operation frequency of the ~crocomputer.

1) D, A. Neamen: Semiconductor Physics and evices, 2nd Edit., Irwin,

2) Okuyama: Ferroelectric emory, Bull. Ceram. Soc. Jpn.,

3) Yam~ichi, T. Sakuma,

4) . S~aemori, S. Ohno, H. Ito, T. Nishimura, T.

5) Mihara, H, ~atanabe, C. A. Pas de Araujo, J. Cuchi~o, M. Scott and L. D,

6) H. Fujii, T. Ohtsuki, Y. Uemoto and K. Shimada: Jpn. Appl. Phys.,

7) Matsui, H. Nakano, M. Okuyama, T. Nakagawa and Y, Yamakawa: Proc, 2nd

(1 997).

(1 995).

, 2193 (1991).

and T. Namba: Nikkei Micro

cMillan: Roc. 4th Int. Symp. on Integrated Ferroelectrics, Monterey, US,

Phys. Electronics, No.456, AP 942235, p.32 (1994).

tg. Ferroelectric Mater. and Appl,, Kyoto, p239 (1979).

~yroezectric eflect in certain materials was n=co a long time ago, and such materials were referred as "electric stones." It was observed when such a stone was thrown in the fire, and it to gene^^ electric charges and a ' f c ~ c ~ n g f f sound. This is basically due to the t e m ~ r a ~ e dependence of the spon~neous pol~zation of a polar material.

ct

Practical applications of the pyroelectric effect in temperat~e sensors and light detectors have been promoted, enabling some commercial marketing of ferroelectric ceramics.

The merits of ~yrosensors as compared to se~conducting inbed-sensor materi are summari~d as follows:

a) wide range of response frequency, b) use at room temperature, c) quick response in comparison with other temperature sensors, d) high quality (optical-grade homogeneity, etc.) materials for the pyrosens~rs are

unnecess~.

The principle on which the pyroelectric effect is based concerns the c ~ ~ g e generation associated with the spontaneous ~ l ~ i z a t i o n change with t e m ~ r a ~ e :

j = - aPs/a t = - (~Ps/aT)(~T/a t) = p(aT/a t). (6.1)

Here p (= laPS/aTl) is denoted as the ~ y r o e Z e c t ~ c c o e ~ c i e ~ t . The phenomenon is illustrated schematically in Fig. 6.1. Two typical electrode ~ ~ g e m e n t s for pyro- sensors are illustrated in Fig. 6.2: (a) face electrodes with the polarization direction parallel to the i irradiation, and (b) edge electrodes with the polarization direction ~ ~ n d i c u l a r to the irradiation. The former type has higher efficiency, but requires a s o p ~ s t i c a t ~ fabrication process for applying uniform transparent electrodes for the inflared light.

131

13

S

in i. e., chop Qf bY

134 Chapter 6

where q is the transmitt~ce of the incident radiation, A a detecting area, y a coefficient co~espon~ng to the loss of heat per unit area of the detector to its s~oundings due to its increase in temperature, and

where p is the density of the pyro-material, cp the specific heat and h is the thickness of the detector [refer to Fig. 6.2(a)].

The ~ ~ r r e n t r e s p u n s i ~ i ~ , ri, is defined by

ri = (IWA) (dq/dt) .

Since the charge generated by a temperature rise AT is given as

q = p A A T ,

using Eq. (6.2), we obtain:

ri = qp UOA ( 9 ~ 2 + ~02~2)-1/2 .

Introducing a thermal time constant

we obtain finally

When ozy) >> 1, ri = qp / p cp h. In order to increase ri, neglecting the size or surface effect, the value (p / p cp) should be increased.

Figure 6.4 shows an amplifier circuit for measuring a pyroelectric voltage signal. The resistance R is relatively high and is inserted to remove the charge after it is thermally induced on the pyroelectric (Cy)). The transistor must have a ~ g h impedance (e.g., €ET).

Amplifier for a pyroelectric infrared detector.

Pyro@~ectric Devices 135

The voltage responsivity for such an amplifier is expressed as:

rv = (l/ WA) (dV/dt) = ri lzl (6.9)

where z is the impedance of the detector-amplifier combination. Assuming RLCC R,

(6.10)

where TIE, = R (CD + CA), and CD and CA are the capacitances of the detector the amplifier. Therefore, Eq. (6.9) may be written as

(6.1 1)

At a high frequency (>> l / z ~ , ME), we obtain

r V = q p / p c ~ & A o 9 (6.12)

assuming that CE) > CA. In order to increase rv9 neglecting again size or surface effects, the value (p / p cp E) should increase. Note that rv differs from ri by a factor of (l/e). The rv decreases with fiquency at high frequencies, but that is relatively independent of frequency between ~ / T D (0.1 - 10 Hz) and l/w (0.01 Hz)2) Thus, in practice, the i ~ a ~ a t i o n chopping frequency is chosen just between UTI) and l/%.

The pyroelectric sensor is a device for transducing optic~thermal energy to electrical energy, and its efficiency or figure of merit is evaluated in several ways; for example, in terms of p, p/cp or p/(cpe).

Figures of merit for pyroelectric materials.

Figure of Merit Application

P’Cp low impedance amplifier P/(CpE) high impedance amplifier p’tcpae) thermal imaging device (vidicon)

p/cp(e tan6)lI2 high impedance amplifier when the pyroelectric element is the main noise source

p: pyroelectric coefficient; cp: specific heat; E: relative permittivity a: thermal diffusivity

oom-temperat~e prop some "figures of merit" for their

ateri

30 19

1

rature ~ e p e ~ ~ e ~ c e of f i ~ ~ e § of m e ~ t for a

om, we can calc~late

138

P 1 Cp& 800

600

400

200

n

300

200

100

18 20 22 24 "0 5 10 ias Field (k:V/cm)

(a) cb)

Figure of merit (p/c~&) change with temperature (a) and bias field (b) for ~.67Sr0.33TiO3-based ce as the

voltage. (a) Note that the bias charac s i g n i ~ c ~ t l y . (b) Maximum black b

ST at a chopper fr~uency of 40

Cushion ring I Silicon window

A polymer-based (PVDF) pyroelectric infrared sensor.

139

infrared ray (input),

-type pyroelectric temperature sensor.

Figure 6.6 shows a typical s t ruct~e for mer p ~ ~ l ~ t r i c in practical usage, a pyrosensor requires an i light (thermal ray the electrical signal can be detected only at the ~ ~ s i e n t stage of light illumination or shut off. An elec~omagnetic motor is conventionally used as a light-chop mechanism, but recently a piez~lectric b i m o ~ h chopper has been developed by ~ u w ~ o et al.$) which allows for miniatu~zation of the pyrosensors (Fig. 6.7).

In Fig. 6.8 the visualization of a thermal-dis~bution image is exemplified by a pyro-vidicon tube.7) The light emitted from an object is filtered with a g e ~ a n i u m lens producing an infrared beam which is focused onto the pyroelectric target ~ o u g h an optical chopper. The ~ m ~ r a t u r e distribution of the object is represented on the target as a voltage dist~bution. This is monitored from the back surface of the target by elec~on-beam scannin~ using a conventional TV tube.

One of the ~ s ~ v ~ ~ g ~ of the p~o-vidicon is the degradation of the image over a long period of usage due to thermal diffusion on the target. et al. proposed a s e ~ e n t e d target design to solve the d i ~ s i o n problem.8) Figure 6.9 shows the microscopic structure of a D-TGS [deuterated triglycine sulphate, ( ~ D 2 ~ ~ 2 ~ O O ~ ) 3 ~ 2 S O 4 ~ target, and Fig. 6.10 is an example of a picture taken in darkness.

h0

cit l

~ ~ c t ~ r ~ of a ~yro-vi~ico~ tu

142 hapter

erits of pyrosensors ~ m p ~ to other sensor materials such as s e ~ c o n d u c t o ~ :

a) wide r uency, b) use at c) quick response in c o m p ~ s o n wi temperature sensors, d) high quality (optical-g mogeneity, etc.) materi

p~osensors is unnece

. Figures of merit for p y r o e l ~ ~ c materials:

Figure of Merit Application

P/Cp P/(CpE)

pl(cpaa t h e ~ a l aging device (vi~con) p/cP(s tan~)1/2 ~ g h i m ~ ~ c e ~ p l i f i e r when the pyroelec~c

element is the main noise source

coefficient; cp: speci~c heat; E: relative ~ e ~ t t i v i t y ; a: thermal diffusivity

ck film s ~ c t ~ e is essential for quick re nsivity, and a l i~ht -chop~r m~hanism (e.g., p i ezoe l~~ ic b imo~hs ) is the to mi~aturization.

6.1 as sum in^ the ~ ~ t - o r d e r phase an sit ion for the free energy, calculate the te~perature dependence of the figures of merit for a pyroelectric detector: p, plcP and p/cp E.

6.2 There is a PLZT (6/80/20) ceramic disk with 1 cm2 in thickness electrically poled along the thickness with When the sample is illuminated 0.1 second, calculate the followi

~ ~ s p ~ e n t electrode, and (c) the o ~ n - c i r c ~ t voltage gene rat^.

143

Assume that all the light energy is absorbed by the sample, and that no heat loss nor electric loss is taken into account. Refer to Table 6.2 for the necessary data.

Total heat energy: 10 (m~/cm2) x 1 (cm2) x 0.1 (S) = 1 (mJ) Sample volume v: 1 (cm21 x 0.01 (cm) = 0.01 (cm31 Temperature rise AT: 1 (mJ) / [2.57 (J/cm3K) x 0.01 (cm3)] = 0.039 (K)

6.3 Consider thee materials: sharp phase transition, diffuse phase an sit ion successive phase transition materials (a, b and c in the figure) with spontaneous polari on vs. temperature relations as illustrated in the following figures. cuss the merits and demerits of each fiom a pyro- detector application viewpoint with respect to the following: (1) the m a g ~ ~ d e of p, (2) the relative pe~itt ivity, (3) temperature stability (4) aging.

I (a) Sharp phase transition

: (b) Diffuse phase tr~sition

(c) Successive phase transition

1) erbert: ~ e ~ o e l e c t ~ c T r ~ d ~ e r s d Sensors, p.267, Gordon & New York (1982).

2) Its Use in In~a~ed

3) : ~rinciples and Applic~tion~ Towcester, NN12 7JN,

Press, Oxford (1977).

144

~ e ~ a i n materials electric charges on their surfaces as a cons

~iez~lectricity is extensively utilized in the fabrica~on of various devices sue t r ~ s d u c e ~ , actuators, surface acoustic ~ a v e devices, ~ ~ u ~ n c y control and so on.

used, and various potenti

There are five ~mpo~ant figures of merit in p i e z ~ ~ ~ ~ c s : constant g, the elwtromec , and the acoustic impedan

e magnitude of the induced strain x by an external electric field E is repres Y this figure of merit (an i m p o ~ n t figure of merit for actuator applications):

c field E is related to an e x t e ~ a l stress voltage cons~nt g (an impo~ant figure of merit for sensor applications):

145

146 Chapter 7

T&ng into account the relation, P = d X, we obtain an impo~ant relation between g and d

g = d / EOE (E : pe~ittivity) (7.3)

Obtain the relations~p between the piezoelectric d and g constants, which indicates the strain per unit electric field and the electric field per unit stress.

From the f u n d ~ e n ~ piezoelectric equations:

(P7.1.1)

(P% 1.2)

the actuator figure of merit d (external X = 0) is given by Eq. ( the sensor figure of merit g (external E = 0) is given by E q . (P3.4.2): P = d X. The polarization P induced in a material with eo&x results in an electric field of

E=P/€()EX = (d X) / €()ex. ( W * 1.3)

ng into account E = g X,

g = d / E ~ E ~ . (P7.1.4)

e terms, e l e c ~ o m ~ h ~ c a l coupling factor, e ef~ciency are sometimes C O ~ ~ S ~ . ~ ) ~ 1 1 electrical energy and mech~ical energy, but

= (Stored mechanical energy / I ut electrical energy) ("7.4) or

electrical e n e r ~ /

147

Let us calculate Eq. (7.4), when an electric field E is applied to a piezoelectric material. Since the input electrical energy is (112) EO& E2 per unit volume and the stored mechanical energy per unit volume under zero external stress is given by (1/2) x2 1 S = (112) (d E)2 / S, k2 can be calculated as

k2 = [(1/2) (d E)2 1 S] / [(1/2) E2] = d2 1 EOE*S.

(b) m e energy trans~ission &oe~&i~nt

Not all the stored energy can be actually used, and the actual work done on the mechanical load. ~ i t h zero mechanical load or a complete clamp (no strain) m output work is done.

&ax = (~utput mech~ical energy 1 Input electrical energy)max (7.7)

&ax = ( ~ u ~ u t electrical energy / Input mechanical (7.8) or

Let us consider the case where an electric field E is applied to a piezoelectric under constant external stress X (< 0, because a compressive stress is necessary to work to the outside). As shown in Fig. 7.1, the output work can be calculated as

while the input electrical energy is given by

~ E d P = ( ~ & E + d X ) E . (7.10)

to choose a proper load to maximize the energy tr~smission c~fficient. From the maximum c o n ~ ~ o n of

(7.1 1)

we can obtain

&ax = [(Ilk) - II( lk2) .. 1 12

= [(llk) + II( lnC2) - 1 1-2. (7.12)

blem 7.1). Notice that

k2/4 h ~ ~ x c k212 (7.13)

value. For a small k, hmax = k2/4, and for a large k, hmax = lc212.

~ h i c h is close to the v theoretic~ly.

ical ener~y) I ( ~ o n s ~ r n elec~ical ener~y) (7.1 or

y ~a~srnission coe

150

h = - ( S y2 + d y) / (d y + Q&).

e maximum h can be obtained when y satisfies

Wdy = [- (2sy +d)(dy +W) + (sy2 +dy) dl / (dy +w)~ = 0.

en yo2 + 2(&0e/d) yo + ( & ~ d s ) = 0,

~ ~ ~ t e r 7

(P7.2.3)

(P7.2.4)

yo = (Qe/d)(- 1 + dl - k2). (P7.2.5)

ere, k2 = d2 I S EO&. y putting y = yo into h(y), we can get the m ~ i m u m value of h:

= [d y0(21k2 - 1) + EOE] / (d yo + Q&)

= [(- 1 + dl - k2)(21k2 - 1) + 11 / [(- 1 + dl - k2) + l]

= [(llk) - d(l/k2) - 1 12.

e m e c ~ a ~ c a l quality factor, e e l ~ ~ o m ~ h ~ i c a l resonance spectrum.

e resonance kquency 009 the defined with respect to the full width at ~ m / d 2 [2do] as :

M = 00 / 2do. (7.17)

echanical loss (tan S,). de of the resonant S

litude at an off-reson~ce f'requency (d E L, L: length of the s ~ p l e ) is ~ ~ ~ f i e d by a factor propo~ional to QM at the ~ s o n ~ c ~ ikquency. For a long vibration r e c ~ ~ u l ~ plate t ~ o u g h d3 l , the maximum ~s~lacement is

151

The acoustic is a p ~ e ~ r used for evaluating the acoustic en transfer between two materials. It is de~ned, in general, by

2 2 = ~ressure/volume velocity). (7.18)

In a solid material,

=G, (7.19)

where p is the density and c is the elastic stiffness of the material.

~iscussions, there m h e kinds of impedances; specific acoustic

acoustic or mechan matching of mech from one other? E

conceptually.

e m ~ h a n i c ~ work one by one mater i~ on the e a~plied force F an

Fi~ure 7.2 shows a ~ o n c e p t u ~ c ~ o o n illustrating two extreme cases. If the materi

echanical impedance m a t c ~ n

F=O

"0

is section summ~zes the current status of piezoelec c mate~als: s i n ~ l e - c ~ s ~ l materia~s, piezocer~ics, piezopolymers, piezocomposi and ~ i e z o ~ l m s , Table 7.1

~ ~ ~ e t e r s of some of the p i e z ~ l e c ~ c m a t e ~ ~ s . 8 )

roperties of representati~e piezoel~

d33 ( P C N 2.3 190 289 593 6 33 33 ( 1 0 ' 3 V ~ ) 57.8 12.6 26.1 19.7 42 380

0.50 0.30 0.03

5 1700 1300 3400 175 6 105 500 65 9 3 - 10

120 328 193 355

rial p rope~es depending on the cut of the materials and e wave propagation.

z is a ~ e l l - ~ o ~ n

Lithium niobate and lithium tantalate belong to an isomorph0 are composed of oxygen ~ t ~ ~ r o n . The Curie t e m ~ r a t ~ e s of are 1210 and 660°~, respectively. The crystal s y ~ e ~ of the these single crystals is 3m and the pol~zation direction is

m ~ h a n i c ~ co~pling c ~ ~ c i e n ~ for surface acoustic wave.

3 is one of the most

d o ~ a n ~ entering onto with dopants such as phase over a wider temper

0 3 solid sol~tions [ r p i e z ~ l ~ ~ c prop

lution system is d e ~ ~ n ~ by the Zr content,

154 Chapter 7

~tragonal ferrmlec phase of perovskite s ~ c t ~ e , th increasing a content, x, the tetragonal distortion decmses and at x > OS2 the s ~ c t ~ e changes from the tetragonal 4mm phase to another ferrmlec~c phase of r h o m ~ h ~ a l The line dividing these two phases is called the ~ o ~ ~ t r o ~ i c phase boundary composition is considered to have both tetragonal and rhom coexisting together. Figure 7.4 shows the dependence of S cons tan^ on compo~ition near the mo~hotropic phase boundary. have their highest values near the mo~hotropic phase boundary. This e~ancement in piezoelectric effect is attributed to the increased ease of r ~ ~ e n ~ t i o n of the pol~zation under an applied electric field.

~ o p i n ~ the PZT material wi donor or acceptor ions changes its p r o ~ ~ e s ~ ~ a t i c ~ l y . Donor doping w ions such as Nb or Ta5" provides soft P like PZT-5, because of the facility of domain motion due to the resulting Pb- vacancies. On the other hand, acceptor doping with Fe or Sc leads to PZTs, such as PZT-8, because the oxy~en vacancies will pin domain wall ~ o t i o n .

5.t

3" 3.t

efer to ~hapter 3, Section 3.1(3).

Subse~uently, PZT in ternary solid solution with another perov investigat~ intensiv m ositions are: PZTs in

* solution with

hich are patented by different companies.

500

400

300

00

100

n

I I *

" 10 20 30 3 3

zirconate titanate (

155

800

600 A

N _.I 2 400 W X

“cl :S

48 50 52 54 56 58 60

ependence ,of several d c o n s ~ n ~ on composition ne the m o ~ h o ~ o p i c phase bound^ in the PZT system.

e end member of PZT, tanate has a large crystal dis onal s ~ c t u r e at ro erature with its te~agonality

. ~ensely sinter^ P b T i ~ 3 c e r ~ c s cannot be o b ~ n

31°) exhibits an extremely low ere, kt and kp are ~ c ~ e s s - tors, respectively. Since these transducers can generate

purely longitu~inal waves ~ o u ~ h kt ~ s ~ i a t ~ with no tran k3 1, clear ul~asonic imaging is e wave. ( a zero ~ m ~ r a ~ e c acoustic S supe~or substrate device applica~ons.

Relaxor ferroelectrics can be either in polycrystalline form or as single crystals. They differ from the ly mentioned normal ferroelectrics in th exhibit a broad phase ~ a n s i ~ o n from the p~electric to ferroelectric state, a fr~uency de~ndence of the dielectric cons~nt (i.e., dielectric relaxation) and a remanent pol~i~at ion. relaxor materials have complex perovskite s~c tures .

solid solutions.

Y

158 fer 7

One of the very basic applications of piezoelectric ceramics is a gas igniter. The very high voltage generated in a piezoelectric ceramic under applied mechanical stress can cause s ~ ~ ~ n g and ignite the gas (Fig. 7.6). There are two means to apply the mechanical force, either by a rapid, pulsed applica~on or by a more al, continuous increase.

From the expe~mental data shown in Fig. 7.6(b), can you estimate the length L of the ~ i e z o c e r ~ c rod in Fig. 7,6(a)?

If you know the relations~p between the length L and the mech~ical resonance uency fr: fr a: 1 I L, and that 10 mm roughly corresponds to 1 0 0 can estimate the rod length, From the output voltage ringing,

od is roughly e s ~ m a ~ d to be 30 pec, or a resonance ~equency of leading to a length L = 30 mm.

~iezoelectric ceramics can be employed as stress sensors and acceleration sensors, because of the direct ~ ~ e z o e Z e c t ~ c effect. Figure '7.7 shows a 3-D stress sensor

stler. By combining an approp~ate number of quartz crystal plates (extensional and shear types), the multilayer device can detect ~ e - ~ m e n s i o n a l stresses.17)

output voltage @ W

(a) Gas igniter and (b) output voltage.

~oeiectric Devices 159

Z

1 Y

stre§§ sensor (by ~ § t l e r ) .

c ceramic disk ie

oltage of the piem- sensor.

= Do sin cut provides the acceleration

iezo-disk is given by

8sS

ezoeiectric disk

0 sin at Base

Basic s ~ c t ~ r e of an accelerometer.

160

U

rical ~ y r o s c o ~ e (by

ctric

€3

e

162 Chapter 7

ese m called the ~iezoeZect~c e ~ ~ ~ i o ~ ~ . The number of inde~ndent parameters for the lowest s y ~ e ~ trigonal crystal are 21 for Si*E, 18 for h i and 6 for h

e number of independent parameters incre~ing crystallo~ap~c symme~. Conce~ing the polycrys oled axis is usually denoted as the z-axis and the ceramic is to this z-axis (Curie group C,, (mm)). The number of no in this case is 10

(S 1 l', S 1 zE, S 1 3E, ~33'~ q4E, d3 1 , d3 , Section 2.1.

Next let us in&

S. (7.20) and (7.21) are applicable :

e S and E terms represent purely m e c h ~ c a l and electrical energies (U UEE), respectively, and the d term denotes the energy ~ d u ~ &om el mechanical energy or vice versa through the piezoelectric effect. k is defined by :

(7.23)

k value varies with the vibrational mode (even in same ceramic sample), can have a positive or negative value (see Table 7.2).

Note that this definition is equivalent to the defini~on provided in Section 7.1( 1):

k2 = (Stored mechanical energy I Input electrical energy)

k2 = (Stored electrical energy I Input mechanical energy). or

163

le 7.2 Several shapes of the p i e z o e l ~ ~ i c resonator and their e l ~ ~ o r n ~ h ~ c coupling factors.

kr

Elastic bundarv. conditions

x1= x2+ 0 x3* 0

X I # Q= 0 , t3+0

Resonator shaw I Mnition

Thick mode I I

Width mode I !/ ' -

a1 length tension mode (// E) : nsion mode of the circul

Y

fol~owin~ ~ y n ~ c e ~ ~ a ~ o n :

1 volume element in

166

2

X

0

Longitudinal vibration through the transverse piezoelectric effect (d31) in a rectangular plate.

Introducing Eq. (7.26) into Q. (7.24), and allowing for XI= U/ x and E,/ x=O to the equal potential on each electrode), leads to a harmonic vibration equation:

- 0 2 p S1 p U = a2u/ax2 . (7.27)

Here, o is the angular frequency of the drive field, and p is the density. ~ubstituting a general solution u=~l(x)eiO~+u,(x)e-j~~ into Eq. (7.26), and with the boundary condition X1 = 0 at x = 0 and L (sample length), the following solution can be obtained:

adax = x1 = d31Ez [sino(L-x)/v + sin(ox/v) /sin(0Wv) . (7.28)

Here, v is the sound velocity in the piezoceramic which is given by

v = l / . l p s 1 1 E . ("729)

W e n the specimen is utilized as an electrical component such as a filter or a vibrator, the electrical impedance [(applied v o l ~ g ~ ~ d u ~ current) ratio] plays an important role. The current flow into the'specimen is described by the surface charge increment, aD3/a t, and the total current is given by :

L L i = j a w D3 dx = j a w [(E# - d312/sllE)Ez + (d31/sllE)xl] dx .

0 0 (7.30)

Using Q. (7.28), the a d ~ t ~ c e for the mechanically free sample is calculated to be:

( l a ) = (inr) = (rnzt) = 00wWt) E33Lc[1 + (d312/ ~ 3 3 L c s l lE)(tan(0~/2v) / (m~/2v>l ,

(7.3 1)

where W is the width, L the length, t the thickness of the sample, and V the applied voltage. E33LC is the ~ ~ t t i v i t y in a l o n g i ~ ~ n a l l y clamped sample, which is given by

Piezoelectric Devices 167

(7.32)

The piezoelectric resonance is achieved where the admittance becomes infinite or the impedance is zero. The resonance frequency fR is calculated from Q. (7.31), and the ~ n ~ e n t a l frequency is given by

fR = v/2L = 1/(2L+ S1 1E . (7.33)

On the other hand, the antiresonance state is generated for zero admittance or infinite ce:

The final transfo~ation is provided by the definition,

(7.35)

The resonance and antiresonance states are described by the following int~tive model. In a high electromechanic~ coupling material with k almost equal to 1, the resonance or antiresonance states appear for t a n ( a ~ 2 v ) = - or 0 [i. e., aL/2v = (m-l/2) or m (m: integer)], respectively. The strain amplitude x1 dis~bution for each state [calculated using Eq. (7.28)] is illustrated in Fig. 7.13. In the resonance state, large strain amplitudes and large capacitance changes (called ~ o ~ j o n ~ Z c ~ i ~ e ) a m induced, and the current can easily flow into the device. On the other hand, at an~esonance, the strain induced in the device compensates completely, resulting in no capacitance change, and the current cannot flow easily into the sample. Thus, for a high k material the first antiresonance frequency fA should be twice as large as the first resonance frequency k.

Resonan~e

m = 1

Antiresonance Lrtw coupling High coupling

e 7.113 Strain generation in the resonant or antiresonant state.

168

h a typical case, where k31 = 0.3, the an mentioned mode and becomes closer to material exhibits c h ~ g e is c o m ~ n s a t ~ c

a ~ ~ r o a c ~ the resonance frequency fR.

e general processes for calculating the e l ~ ~ o m e c h ~ i c ~ P s11E, and ~ 3 3 ~ ) are described below:

e sound velocity v in the specimen is o ~ ~ n ~ from the resonance (refer to Fig. 7.14), using density p, the elastic com echanical coupling factor k31 is c

coupling piezoelectric materials, the following a~proximate eq~ation is available:

"

k312 f (1 - k3I2) = (~2f4) (Af f (7.36)

Figure 7.14 shows observed im~edance curves for a typical k mate~al (PZT 5 = 0.70) and a high k mate~al (PZ~-PT single crystal, k33 = 0.90). Note

and ~ t ~ ~ s o n a n c e

(7.37) (7.38)

co~esponds to the mech~ical loss.

In con~ast, the equiv ent circuit for the ~ ~ ~ s o n ~ c e state of shown in Fig. 7.15 (b), which has high i m ~ e ~ ~ c e .

P P

I

~ ~ i v a l e n t circuit of a vice for (a) the reson~ce and (b) the an~resonance states.

170

Elastic vibrator \

Piezoceramic

Chapter 7

U U

Piezoelectric buzzer.

In the use of m e c h ~ c a l vibration devices such as filters or oscillators, the size shape of a device are very impo~ant, and both the vibrational mode and the w r m c material must be considered. The reson f the bending mode in a centimeter-size sample ranges &om 100 to much lower than that of the thickness mode (100 kHz). For th ator applications the p i e z ~ e ~ c should have a high mechanical quality fac ) rather than a large piezoelectric coe~lcient d; that is, hard piezoelectric

For speakers or buzzers, audible by humans, devices with a rather low ~sonance ~ ~ u e n c y are used (kHz range). Examples are a b i m o ~ h consisting of two piezo- ceramic plates bonded together, and a piezoelectric fork consisting of a piezo-device and a metal fork. A. piezoelectric buzzer is shown in Fig. 7.16, which has merits such as high electric power efficiency, compact size and long life.

Ultrasonic waves are now used in various fields. The sound source is made &om piezoelectric ceramics as well as magnetostictive materials. P i e z ~ e r ~ c s m generally superior in efficiency and in size to magnetostrictive materials. p ~ c u l a r , M piezoelectric materials with a high QM are preferable. A liquid m e d i ~ is usually used for sound energy transfer. Ultrasonic washers, ultrasonic microphones for short-distance remote control and unde~ater detection, such as sonar and fish finding, and nondes~ctive testing are typical applications. Ultrasonic scannin~ detectors are useful in medical electronics for clinical applications ranging from diagnosis to therapy and surgery.

One of the most important applications is based on ultrasonic echo field.20y21) Ultrasonic transducers convert electrical energy into mechanical form when generating an acoustic pulse and convert m ~ h ~ c ~ energy into an electrical signal when detecting its echo. The transmitted waves propagate into a body and echoes generated which travel back to be received by the same ~nsducer . These echoes vary in intensity accor~ng to the type of tissue or body s~cture, there~y creati~g images. An ultrasonic image represents the mechanical properties of the tissue, such as

171

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 done 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 liver and kidney. In brief, it is possible to see inside the human body without breaking the skin by using a beam of ultrasound.

Figure 7.17 shows the basic ultrasoni~ t r ~ d u c e r geometry. The ~ ~ u c e r is mainly composed of matc~ng, piezoelectric material and backing layers.22) One or more matching layers are used to increase sound tr~smissions into tissues. The backing 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 detect ultrasound. In eneral, broadband transducers should be used for medical ultrasonic imaging. The broad band wid^ response corresponds to a short pulse length, resulting in better axial resolution. Three factors are important in designing broad band wid^ transducers; acoustic impedance matching, a high e l ~ t r o m e c h ~ c a l 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,

ig. 7.17 Basic transducer geometry for acoustic imaging applications.

(a) Vi~rator ~ I ~ r n ~ ~ t

ay type ultrasonic

are various types of tran

dis~ete elements to be in& ic focus in^ in the S the use of phase del

(or sector). A lin lrectlon, pro~ucin~ a rec

is a modified linear

so S

iezoelectric body vibrates at its resonant absorbs consid an at other ~ ~ u e n c i ~ result in^

iezoelectric m a t e ~ ~ s

173

~ e ~ ~ e ~ c y band or to blo ~ i e ~ o e l ~ ~ c mate~al is

e about 5.6 mm. m ~ e s of vi~ratio fits smaller size.

174 Chapter 7

A swji3ce a c o u s ~ ~ wave (SAW), also called a ~ a y l e i g ~ wave, is essentially a coupling between longitudinal and shear waves. The energy carried by the SA^ is confined near the surface. An associated electsostatic wave exists for a SAW on a

* oelectric substrate, which allows electroacoustic coupling via a transducer. ages of SA^ technology are:23,24)

(1) The wave can be electroacoustically surface and its velocity is approxi electromagnetic wave.

SA^ wavelength is on the same order of magnitude as line dimensions produced by photolitho~aphy the lengths for both short and long delays are achievable on reasonably si

There is a very broad range of commercial system applications which include front- end and IF ( I n ~ ~ e d i a t e Frequency) filters, CATV (Community Antenna Television) and VCR (Video Cassette Recorder) components, synthesizers, analyzers navigators. In SA^ transducers, finger (i~Eer~igiEa~ electrodes provide the ability to sample or tap the wave and the electrode gap gives the relative delay. A SA^ filter is composed of a minimum of two transducers. A schematic of a simple SAW bi- ~ r e c t i o n ~ filter is shown in Fig. 7.20. A bi-directional transducer radiates energy equally from each side of the transducer. Energy which is not associated with the received signal is absorbed to eliminate spurious reflection.

Various materials are curren single-cry st^ SA^ material materials have different prop direction of propagation. The material for a given device applications are SAW velocity, temperature c ~ f f l c i e n ~ of delay (TCD), electromechanic~ coupling .factor and propaga~on loss. Surface acoustic waves can be generated and ~~~ by spatially periodic, in~rdigial

S on the plane surface of a piez~lectric plate. A periodic electric field is when an RF source is connected to the electrode, thus p e ~ i t t i n g

piezoelectric coupling to a traveling surface wave. If an source with a Wuency, f, is applied to the electrode having periodicity, d, energy conversion from an electrical to mechanical form will be m ~ i m u m when

(7.39)

where vs is the ~A~ velocity and fo is the center frequency of the device. The SAW velocity is an important parameter d e ~ ~ n i n g the center i m p o ~ t parameter for many applications is t e m ~ r a ~ e sensitivity. For example, the tempera~re stability of the center frequency of SAW bandpass filters is a direct function of the tempera~re coefficient for the velocity and the delay for the materi~ used. The first-order temperature c~fficient of delay is given by:

iezoe~ectric Devices 175

r-" " l

I "l

~ u n d ~ e n t a l structure of a surface acoustic wave device.

where z = L / vs is the elay time and L is the S propagation length. The s d a c e wave coupling factor, ks2 , is defined in terms of the change in SA^ velocity which occurs when the wave passes across a surface coated with a thin massless conductor, so that the piezoelec~c field associated with the wave is effectively short-circui The coupling factor, ks2 , is expressed by :

2 S = 2 ( v f - v m ) / v f

e wave velocity and vm the velocity plications, the value of ks2 relates

bandwidth obt~nable and the ~ o u n t of signal loss between input

(7.41)

on the metdliz to the ma~imum and output, which

~ e t e ~ n e s the ~ a c t i o ~ a l band wid^ as a f~nction of mini mu^ insertion -loss for a given material and filter. Propagation loss is one of the major factors that d e t e ~ i n e s

insertion loss.

marizes some impo~ant

SA^ material properties.

ark S T - X 0.16 0 3158 4.5

Li NW3 12wY - X 5. -74

Li TQ -18

Li2B49 (110)-<001> 0.8 0

1 .o 10

26 c l

0. -15 8.5

1 .o 5

A delay line can be forrned from a slice of glass such as Pb glass in which the velocity of sound is nearly inde~ndent ceramic transducers are soldered on two metalli input transducer converts the electrical signal to a shear wave which travels through the slice. At the output transducer the wave is signal delayed by the length of time taken to travel arou are used in color W sets to introduce a delay of ap

loyed in videotape recorders.

input and output terminals are f a b n c a ~ on a e is changed through the vibration energy tr

~ ~ e z o e l e c t ~ c t r a n s f o ~ e r . Piezoelectric transforrners of their com act size in c o m p ~ s o n with the convention^ electroma~netic coil-

(collapse the nodal point!) and in heat ~enera~on, the development approach e as that used for fabricating ceramic actuators. Recent lap-top computers with a liquid crystal display require a very thin, no electromagnetic-noise transforrner to start the glow of a ~uorescent b a c k - l ~ p . is application has recently accelerated the development of the piezo-transformer.

t r ~ S f 0 ~ erious problems were found initially in the m~hanical stre

177

i e z o e l e c ~ c ~ a n s f o ~ e r proposed by

* the original p i e ~ o - ~ ~ s f o ~ e r was proposed by C. A. variety of such transfo~ers investi~ate~. Figure 7.21

where two ~ e r e n ~ y - p o l e d parts coexist in one s~nding wave wi a w a v e l e n ~ to the sample 1 wavelength existing on both the in~ut (L1) and output ratio r ( ~ t e ~ - ~ ~ r ~ t i ~ ) is ~iven for the unloaded condi~on by :

(7.42)

e r ratio is incre~ed with an increase of (L2 I t), where t is the

e ~ ~ s f o ~ e r (Fig. 7.22) in to i n ~ e ~ e the voltage rise r ~ ~ o . z 6 ) Usage of the third order l~ngitudinal mode is another idea to ist tribute the stress concentration.

ultilayer type transfo~er by

178 Chapter 7

Using Mason's equivalent circuits for two length expander bars, surface and end electrded, as shown in Fig. 7.23, calculate the e q ~ v ~ e n t circuit for a Rosen type transfo~er.

A complete equivalent circuit for a length expander bar (top and bottom swfkce with electric field ~ ~ n ~ c u l a r to the direction of wave propagation is

provided in Fig. 7.23 (a), where

22i =: /sinh (@L,/ vbE), (P7.7.1)

i l:N l"

I

2

V

I

* ent c i rcui~ for len

179

The ch~ctenstic mechanical impedance 20 and the clamped capacitance CO provided by:

~ i = p w t v b ' = w t ( p / s l l E 112 , (P7.7.3)

In a similar fashion, the necessary parameters for a length expander bar electroded) with electric field parellel to ~rection of wave propagation are given by:

(P7.7.6) (P7.7.7)

(P7.7.8)

0=pWtVb~=Wt(p/s33 D ) 112 , coo = wt &33T (1 - k332)/ L,

(P7.7.9) (€37.7.10)

NO = wt d33 / L ~ 3 3 ~ = ( w a ) (&33T/~33D)1/2 k33. (P7.7.11)

ircuits for (a) one-end five length expander bar (surhce length expander bar (end electmded), and (c) the Rosen

n one end of the piezoelectric element is free

a lication as s must be replaced by (L/2)

voltage ratio for an ope^-circuit condition c

L2) = n / L2 (p /S33

ng into account the relation:

S

182 ter 7’

Piezostrictof BST

-20-10 0 10 20

~iectrostric~or PMN-PT

-15-10 -5 0 5 IO 15 Electric field (kV/cm) Electric field (kV/cm) Electric field (kV/cm)

(a) (b)

Phase-change material PNZST PNZST

-30 -20 -10 0 10 20 30 -30 -20 -10 0 10 20 30 Electric field (kV/cm) Electric field (kV/cm)

in ctive

18

MOVING P I E C E

L E A F S P R I N G

C O N T

La~hing relay using a shape memo^ ceramic unimo h. ires a 4 ms pulse voltage, not a continuous voltage, which es a 150 pm

unimo~h tip displacement.

Two of the most popular actuator designs are the mu1tilayers3’) and bimo~hs (S

es of low driving voltage (1 force (10oO N), and hi

e l ~ t r o m e c h ~ c a l coupling. But the dis~lacement, on the order of 10 pm, is n suf~cient for some applications. This contrasts with the characte~stics of the b i m o ~ h which consists of multiple p i e z ~ l e c ~ c tic plates bonded together to gene^^ a large ~ n d i n g displacement of sev pm, but has relatively low response time (1 ms) and genera~ve force (1

l 100 thin p i e z ~ l e c ~ c / e l ~ t r o s ~ c t i v e

U Single Plate

I Multilayer

! L

l ./ i i i

'm

Moonie

/ Typical designs for c e r ~ i c actuators: mul~layer, moonie and bimo

Z-stack (1 0 layers) (extension)

X-stack (1 0 layers) (shear)

Y-stack (1 0 layers) (shear)

ing ~ u l t i l a ~ e r actuat

electric field d i r e c ~ o ~ .

instance, requires a very hard p i e z o e l ~ ~ c with a hig , to suppress heat genera~on. Driving the motor at rather than at resonance, is also an i n ~ g u

on the p i e ~ ~ e r ~ c and the power s u p p l ~ ~ 2 ) "h suffers most from strain hysteres this purpose. The pulse drive m quick response with a certain ow

ap~lication.

X

b

~lassification of piezoelect~c/elec~os~ctive actuators.

186

displaceme

Etectric field n - t

(a)

ent vibration of a bi scale with a unit of half of t

Ink ribbon

187

actuators are very impo~ant for improving the 7.30 shows ~ansient vibrations o applied. The rise time is varied with a unit of To12, where To stands for that the overshoot and ringing o

~splacement is completely suppress^ when the rise time is precisely adj -device (i.e., for n = 21.43) A flight ac~ator

ent a d a steel ball. A 5 pm an hit a 2 mm steel ball up to 20 m

using a flight actuator as se width, the movement of

to realize no vibrational ringing or double hit~ng,

~ o n s i ~ e r the longitudin m e c h a ~ c ~ vibration in a iezw b, width W and length L (bc<

d y n ~ i c equation:

n the following d y n ~ i c e ~ u a ~ o n :

seud~step voltage, as demons 7.30.

7,8.3), using the Laplace z(t) as U(s,x) and

18

S1 p S 2 U(s,x) = ~2U(S,X)/~X2'

is ~ s u m e s the ~ o ~ l o w i n ~ initial conditions:

u(t=O,x) = 0, ~u(t=O,x)/~t = 0.

superi~posin~ the d3 1

onse to a pseudo-s

orn= 1,

0 c t c Liv

For n = 2,

Thus,

0 c t c Liv u(t,L) = (d31E0v2i4L) [t2 - 2 (t - L/v)~] L < t < 2Liv

) [t2 - 2 (t - L/v)2 + (t - 2Llv)2] 2Liv c t

190

0 T 2T

Transient displacement for a ~seudo-step voltage.

does not exhibit ringing [see Fig. 7.32(b)]. en the applied field E* includes the term (I + e-suv), the e~pansion series t e ~ i ~ t e s in finite t e ~ s , l e ~ i n ~ to a co~plete s~ppression of v ibra t io~ l ~ng ing .

For n = 3, U(s,L) is again expanded as an infinite series:

Figure 7.32(c) shows the displacement change with time. Note again that all the curves are composed of parabolic curves and that the height of the overshoot is 116 of

191

S found in a space truss S

i ~ f o ~ a t i o n p r ~ e s s i n g (F

L~gh~eighted f3erel Tilt mirror retainers

Tie bar Pin flexures PMN actuators flexures

N elec~ostrictive actuato~ for optical image c o ~ ~ c t i o n .

B ~ ~ i n g l e s s rotor tric strips. A slight the blade angle provi

1

Video head A (R

thickness are stacked, together with a sophisticated magni~cation mechanism [Fig. 7.37(b)], The magni~cation unit is based on a monolithic hinge lever with a magni~cation of 30, resulting in an ~ p l i ~ e d displacement of 0.5 mm and an energy transfer e~ciency greater than 50%.

iezoelectric c ~ e r a shutter is currently the largest p r ~ u c ~ o n item (Fig. 7.38). A e of p i e z ~ l ~ ~ c b i m o ~ h can open and close the shutter in a ~ l l i - s ~ o n d

ough a mechanical wing rnechani~m.~~)

~ ~ c t u r e of a printer ), and a ~ f f e r e n t i ~ - element (b). A sophis monolithic hinge actuator displacement by 30 times,

3 Closed state Open state

era shutter mechanism using a piezoelectric b i m o ~ h actuator.

19

a P S (Toyota Electronic Modulated Suspension), w ach on the road in adjusting the d ~ p i n g condition,

i n s ~ l e d it on a "Celcio ( ~ ~ ~ a l e n t to Lexus, internationally)" in 1989.56) In general, as the d ~ p i n g force of a shock absorber in an auto ' * *

ntrollabili~ and s ~ b i l i ~ of a vehicle because the road roughness is e

se of the electro~cally controlled shoc

force ("soft") so as to improve c o m f o ~ simul~neously, Usually the S stem is set to

response of the sensor and actuator combination is required.

Figure 7.39 shows the structure of the electronicall controlled shock absorber. sensor is composed of 5 layers of 0.5 mm thick disks. The det~ting the road roughness is about 2 msec and the resol of the u~down devi mm. "%e actuator is made of 88 layers of O S mm thick disks. ~pplying 5~ V generates a displacement of about 50 hich is magnified by 40 times through a piston and plunger pin combination. stroke pushes the chang of the d ~ p i n g force down, then opens the bypass oil route, leading to the of the flow resistance (i.e., "soft").

Figure 7.40 illust~ates the o acceleration and pi~hing rate were m

to as small as the conditi , the pitching rate was also ed to as small as the condition

"hard," leading to better controllability.

Pi-lectric sensor

Piemelectric multilayer actuator

Piston

Damping change V d W

. 7.39 ~lectronic modulated suspension by Toyota.

1

U~-down Acceleration

S

etic or s ~ ~ e r c o n d ~ c ~ n ~ mate~als.

cQns~ctiQn of

time.

of an ~ l ~ a s o n i c motor.

198

.Horn 1

7.43 Ultrasonic motor by Barth.

In the 1980s, with increasing chip pattern density, the se~conductor industry began to demand much more precise and sophisticated positioners which would not generate magnetic field noise. This urgent need the development of ul~asonic motors. Another advantage of ultrasonic motors over conventional el~~omagnetic motors with expensive copper coils is the improved av~lability of piezoelectric ceramics at reasonable cost. Japanese m ~ u f ~ ~ r e r s m currently pr~ucing piezoelectric buzzers at about 30 .. 40 cents per unit.

Let us summarize the merits and demerits of the ultr~onic motor:

1. Low speed and high torque . -- Direct drive 2. Quick response, wide velocity range, hard brake and no backlash

-- Excellent con~ollability -- Fine position resolution 3. High power I weight ratio and high efficiency 4. Quiet drive 5 . Compact size and light weight 6. Simple structure and easy pr~uction process 7. Negligible effect from external magnetic or radioactive fields,

and also no generation of these fields

8. Necessity for a high frequency power supply 9. Less durability due to frictional drive 10. Drooping torque vs. speed characteristics

199

) ~lassification an les of Ultrasonic

From a customer's point of view, there are rotary and linear type motors. If we categorize them according to the vibrator shape, there are rod type, n-shaped, ring (square) and cylinder types. Two categories are being investigated for ultrasonic motors from a vibration characteristic viewpoint: a standing-wave type and a propagating-wave type. Refresh your memory on the wave formulas. The standing wave is expressed by

us(x,t) = A COS kx COS a t , (7.43)

while the propagatin wave is expressed as

Up(X,t) A COS (kx - at). (7.44)

Using a trigonometric relation, Eq. (7.44) can be transformed as

up(x,t) = A COS kx * COS a t + A COS (kx - M2)* COS (a t - ~ / 2 ) . (7.45)

This leads to an impo~ant result, a propagating wave can be generated by superimposing two standing waves whose phases M e r by 90 de- both in time and in space. This principle is necessary to generate a propagating wave on a limited volumelsize substance, because only standing waves can be excited stably in a solid m e ~ u m of finite size.

The standing-wave type is sometimes m f e d to as a vibratory-coupler type or a "woodpecker" type, where a vibratory piece is connected to a piezoelectric driver the tip portion generates a flat-elliptical movement. Figure 7.44 shows a simple model proposed by T. Sashida6l) A vibratory piece is attached to a rotor or a slider with a slight cant angle 8. Take the x-y coordinate so that the x axis is normal to the rotor face. When a vibration displacement,

ux = uo sin (a t + a) (7.46)

is excited at the piezoelectric vibrator, the vibratory piece generates bending because of restriction by the rotor, so that the tip moves along the rotor face between A --> B, and freely between B --> A. If the vibratory piece and the piezo-vibrator are tuned properly, they form a resonating structure, and if the bending deformation is sufficiently small compared with the length, the tip locus during the free vibration --> A) is represented by

x = uo sin (a t + a), y = u1 sin (a t + p), (7.47)

which is an elliptical locus. Therefore, only the duration A --> B provides a uni~rectional force to the rotor through fiction, and, therefore, an intermittent

I W' 'S. \ l l l

l

ller

Al horn

ler ~ l ~ a s o n i c motor (a) and the motion of the torsional

202

r 1

\ ca

"~indmill" motor with a dis~-shaped torsional coupler.

A com~act ultrasonic roto^ motor, as tiny as 3 mm in eter er, has been devel at the Pennsylv~nia State University. As shown in Fig. 7.47, the stator cons a p i e z ~ l e c ~ c ring and two concav~/convex metal e n d c ~ s with "windmill" slots bonded together, so as to n e ~ t e a coupling of the u ~ - d o ~ n and torslona vibration^.^^) Since the number of components is process is much simplified, the f a b ~ c ~ ~ n price is disposable design becomes feasible. When driven revolution of 600 rpm and a m ~ i m u m t o r ~ u e of 1 eter er motor.

a p i e ~ o e l ~ ~ c ceramic cylinder for a torsional vibrator (Fig. 7.48).64) Using an interdigital type electrode with a 4 5 O cant angle on the cylinder surface, torsion vibration was ch is applicable for a simple ultrasonic motor.

Ceramic J w-Cylinder

(a)

Piezoelectric cylinder torsional vibrator (a) and its electrode pattern (b).

203

BOLT Two-vibration-mode coupled type motor.

Ueha proposed a two-vibration-mode coupled type (Fig. 7.49), that is, a torsional Langevin vibrator was combined with three multilayer actuators to generate larger longitudinal and transverse surface displacements of the stator, as well as to control their phase differen~e6~) The phase change can change the rotation direction.

Uchino invented a m h near motor.66) This linear motor is multilayer piezoelectric r and fork-shaped metallic legs as sho Since there is a slight difference in the mechanical resonance fiquency between two legs, the phase Merence between the bending vibrations of both legs can controlled by changing the drive fkquency, The walking slider moves in a way similar to a horse using its fore and hind legs when trotting. A test motor, 20 x 20 x 5 mm3 in dimension, exhibits a m ~ i m u m speed of 20 c d s and a maximum thrust of 0.2 kgf with a maximum efficiency of 20%, when driven at 98lcHz at 6V (actual power = 0.7 W). Figure 7.51 shows the characteristics of the linear motor. "his motor has been employed in a precision X-Y stage.

Tomikawa's rectangular plate motor is also intr ig~ing6~) As shown in Fig. 7.52, a combination of the two modes of vibration forms an elliptical displacement. The

chosen were the 1st longitudinal mode (L1 mode) and the 8th bending whose resonance frequencies were almost the same. By applying voltages

with a phase difference of 90 degrees to the L-mode and B-mode drive electrodes,

elliptical ~ o t i o n in the same directi

To Oscillator I

I ? I i

O T

114 T

214 T

314 T

1 T

linear ultrasonic motor. (a) cons egree phase ~ f f e ~ n ~ of two le

v > ). t-

V

f

10 -

0

0 50 1OQ LOAD m (g f )

m

P

otor characteristics of the shape^ motor.

20

........

~ ~ h i d a and Ueha et al. linear motor as i l l u s ~ a t ~ in ed at both ends of a steel

s-sec~on. Ass

206

Horn( l: 4 )

Piezo brato or

20 4

Linear motor using a bending vibratio~.

V = (E I / p A) d ~ , (7.50)

(7.5 1)

Using the bending vibration, the wavelength h can be easily chosen as short as several mm to satisfy a stable surface contact with the slider section area A or the moment of inertia I of the ~ansmission 7.53, h = 26.8 mm.

slider, the c o n ~ c t face of which is CO ssion rod with an app~op~ate force. The tran by the vibration source position on the rod, distance from the free end of the rod to the PO

into account the wave phase, the vibration co~esponding to one wavelen th h (i.e., 26.8 mm)

slider, made of a steel c l ~ p e r 60 m~ i waves, was driven at a speed of 20 cm/s w problem with this type of motor is found in its lo the whole rod ~ u s t be excited even when only a output. Thus, ring type motors were invented by

be utilized, because the lengths of the stator arr

When we deform the rod discussed in the previous section to make a ring by conn~ting the two ends topologic~ly, we can make a rotary type motor using a bending vibration. Two types of "ring" motor designs are possible: (a) the bending mode type and (b) the extensional mode t~pe .7~) Al thou~h the principle is similar to the linear type, more sop~sticated structures are employed with respect to the ceramic poling and the mech~ical support mech~ism.

a vibration source drives one positian of a closed ring (circular or co~espondin~ to the resonance of this ring, only a standing

wave is excited, because the vibration propagates in two directions s y ~ e ~ c a l l y from the vibration source and in~~erence occurs. When multiple vibration sources are installed on the ring, displacements can be obtained by superi~posing all the waves (two waves from each vibration source). Using the superimposition principle, we can generate a ~ropagating wave in the closed ring with the profile of the original s t ~ d i n g wave.

Assuming a vibra~on source of A cos cot at the point 8 = Q of the elastic ring, the n- th mode s~nding wave can be expressed by

u(0,t) = A cos ne cos a t , (7.52)

and the traveling wave by

(7.53)

Since the traveling wave can be expressed as a superimposition of two waves as

cos cot + A cos (ne - 2) cos (at - W2), (7.54)

nce is m ~ n ~ n e ~ in S ace

208

ighty percent of the exchange lenses in anon's I'

been replaced by the ul~asoni nic motors done in the Uni

modi~cations of Sashida's type.

U i

U

Vibration source positions for g~n~rating a propa~ating wave in a rin Elastic nng

Slider

Rotor

/ Rotor

Felt

Stator structure of Sashida's motor.

209

into 16 pos~~vely and negati ions so as to generate a 9th

pe was c o m ~ s ~ of a brass ring 2.5 mm in thickness,

c e r ~ i c ring of 0.5 mm in thic~ness with di

shows S~hida's motor characteristics.

ng" motor for a camera automa~c ins~lling the ring motor compactly in the lens fiame. It is stator elastic ring has many ich can ma~nify the displacement and improve the S lens position can be S

with a screw mechanism. The advan~ges of this motor over the conv~ntional e l ~ ~ o m a ~ n e ~ c motor are:

1. Silent drive due to the ul~asonic ~equency drive and no gear mech * , more su i~ble for video as with microphones).

n motor design and no tion mec~anism such as

r v0 sin ot

v0 cos ot "

E Ground "

f =44 kHz

Torque ( gf - cm > otor characteristics of Sashida's motor.

A general problem encountered for these traveling wave type motors is the support of the stator. In the case of a s t a n ~ n ~ wave motor, the points or lines %11p:

generally supported; this causes minimum effects on the resonance vibration. A traveling wave, however, does not have such steady nodal points or lines. Tlt.us, special considerations are necessary. In Fig. 7.55, the stator is basically s u p p o ~ very gently along the axial dimtion on felt so as not to suppress the bending vibration. It is important to note that the stop pins which latch onto the stator teeth only provide high rigidity against the rotation.

atsushita Blectric proposed a nodal line support method using a higher vibration mode [see Fig. 7.57(b)].73) Figure 7.57(a) shows the stator structure, where a wide ring is supported at the nodal circular line and "teeth" the maximum ~ p l i t u d e circle to get larger revolution,

Seiko I n s ~ m e n ~ miniaturized the ultrasonic motor to dimensions as tiny as 10 mm in diameter using basically the same ~ ~ n c i p l e . ~ ~ ) Figure 7.58 shows the cons~ct ion of one of these small motors with a 10 mm diameter and a 4.5 mm thickness. A driving voltage of 3 V and a current of 60 mA produces 6~ rev/min (no-load) with a torque of 0.1 mN*m. AlliedSignal devel ultrasonic motors similar to Shinsei's, which are utilized as m ~ h a n i c ~ switches for laun~hin missiles.75)

VI

( OUTPUT POSl T ION , ~ O ~ A L POS I T ION

0 I S P L A ~ ~ ~ ~ N T D I STR I BUT I ON IN RADIAL DIR~CTION

(a) T o o t h - s h a ~ stator and (b) a higher nodal line for ~xing.

zoelectric Devices 21 1

OTOR,

' ~ ~ P P O R T P FOR !SIXTO

ruction of Seiko's motor.

21

SlON

r7

inn in^" type motor by To

V

Analo~y l

V

214

most suita~le method for achieving o~timum

ver the whole vi~ration

be ~ ~ l i ~ ~ for driving the u l ~ ~ o n i c motor.

000

1500

1000

0 500

0 0.01 0.02 0.05 0.1 0. 0.5 l

40

30 - kc. 20

._.

10

0

~ i ~ r a t i o ~ veloci of the q u ~ i ~ factor ) reson~ces of a PZT

215

1. Piezoelectric figures of merit: (a) p~ezoelectric strain c o n s ~ t d -- x = d E (b) piezoelectric voltage constant g -- E = g X (c) e l ~ t r o m e c h ~ c ~ coupling factor k

k2 = (stored m ~ h ~ i c ~ energy I input electrical energy) = d2 / E O € - S

(d) mechanical quality factor -- Qm = ~ 2 A ~

2. Piezoelectric equations:

k. ( i j = 1,2 ,..., 6 ; m,k = 1,224

re son^^ and an~esonance modes are both m ~ h ~ c a l ~ s o n ~ c e s . ttance maximum and minimum correspond to resonance

~ ~ e s o n ~ c e , respectively.

4. Cl~si f ica~on of ceramic actuators:

~is~lacement ve Technique Actuator Category aterials

gid e Servo displacement ~ ~ s d u c e r E l e c ~ o s ~ c t o r ~ s p l ~ m e n t

Pulse drive motor oft p i e z ~ l e c ~ c

~ ~ ~ o n i c motor

demerits of the u l ~ ~ o n i c motors:

216

ow to generate a traveling wave on an elastic ring: n-th mode standing wave: u(8,t) = A cos n8 cos cot n-th mode ~ a v e l i n ~ w

A propagating wave whose phases differ b

7.1 Calculate the electromechanic~ couplin~ factor vibrator for the follow in^ vibration mode:

(a) Length extension mode (b) Shear mode on the p1

(a) A multilayer ac~ator is

217

verify that the follow in^ approxim couplin~ piezoelectric material:

k3l2 /(1 - k312) = (7t2/4) (6f l fR). (6f = fA - (b) Using a pulse drive technique, the ~ansient displacement was as a function of time, and the displacement curve was obtai how to determine the k3 1 d3 1 and Qpvl values from the data.

ve method is an alte~ative method c~aracte~stics. By apply in^ a step electric field to a

piezoelectric sample, the ~ansient vibra~on correspondi mode (extentional, ~ n d i n g etc.) is measured. The s t a b i l i ~ displacement and damping constant are obtain from which the elastic compliance9 piezoelectric c o n s ~ t ,

Applied Voltage CV)

7. a r ec t an~u l~ p i e~~ lec t r i c plate and the ~ ~ s v e r ~ ~ctuator (pinball machine).

n e ~ a ~ v e pulse (- Eo) is appli xed rigidly at one end, verify

218 Chapter 7

7.5

7.

7.7

other end is given by 2ld3111Egv (v: sound velocity of the ceramic), and is independent of the length.

(b) Suppose that this velocity is ~ o u g h a small steel ball (mass: M) without loss. Calculate the m ~ i m ~ height of the steel ball, when the ball is hit exactly vertically.

From the strain distribution xl(x) for a low e l ~ ~ m ~ h ~ c a l coupling material pictured in Fig. 7.13, draw the ~splacement dis~bution u(x) for both the resonance and an~esonance states, and discuss the nce between the two states.

For the equivalent circuit of a piezoelectric ~ s d u ~ r at the an~sonance state [Fig. 7.15(b)], derive the relations of L and C to intrinsic physical parameters such as p, d, sE and the dimensions of the transducer.

general principle for un imo~h s ~ c ~ e .

mode u(8,t) = A cos (28 - c o n ~ g ~ a t i o n s to be applied t mode of vibration. (There wil

Jaffe: ~iez~electric C ~ r ~ ~ i c s , London: A ~ a d e ~ c Press

11 14 (1982).

I990 ~ l t r a s ~ n i c s ~ y ~ ~ o s i u ~ , 697 (1990).

219

V?. A. Smith: Proc. 1989 IEEE ~ l t r ~ o n i c Symposiu~, 755 (1989).

Newham: Jpn. J. Appl. tee on Barium titan at^,

XXX~-171-1067 (1983). . A. Auld: Aco~t i c ~ i e l ~ and Waves in Solids,' 2nd ed., elb bourne:

* Imaging and Analog Signal Processing, (1987). no: IEEE ~rans. Sonics ~ltrason., SU-25,

C. Campbell: S ~ ~ ~ e Acoustic Wave Devices and ~ ~ i r Signal Processing Applications, San Diego, Calif, Academic Press (1989).

atthews: Su~ace Wave ~ilters, New York: Wiley Interscience (1977).

r ~ r ~ c i s i o n ~ o s i ~ o n ~ o n t ~ ~ l , Edit. iltl Chief

23(3), 187 (1980). . Uchino: Ceramic Data ook '88 (Chap.:Ceramic Actuators), Inst. Indust~al ~ufacturing Tech., Tokyo (1988).

, U. To~ikawa and T. Takano: ( 1 990).

45) 7' . Ota, T. ~ ~ h i k a w a and T. ~izutani: Jpn. J. Appl. Phys., (1 985).

22 1

222 hapter

Electric field

on-linear polarizability of fenoelec various electrooptic and optical par^

, problems still r e m ~ n in prep crystals and, hence, manufact~ing c

e polycrystalline micros ctrooptic effect if it is si

fenoelec~cs are of special inte extraordin~ly large app~en material is in its so-called p electrooptic properties fenoelec~cs.

seful fe~oelectric electrooptic material tra~tionally come from the Ti)O3 system; they generally have sparency in a wavelength

ge extending from the visible to infraredy and exhibit optical anisotropy with an applied electric voltage. Figure 8.2 shows the phase d i a ~ ~ of the ~ b l - x L a x ) ( ~ l - y T i y ) l - ~ 4 ~ 3 system, on which is indicated the electrooptic effects m a ~ f e s t ~ for various phase regions. Notice that the valence of lanthanum ion (3-t) in the a-site (2-t) generates the vacancy of the b-site.

e PLZT solid solution exhibits both the Pockels ( p ~ ~ ) and c effects, depending on the c ition. Some e x ~ p l e s of typical An es are shown in Fig. 8.3. electrooptic coefficien

uch larger than the values ntional crystals SUC

(SBN) (see Table 8.1)¶ which means that the voltage electrooptic shutter is much less for the PLZT.

PbZrO, [mol *h] PbZrO,

223

PbTi

FE,Tat

10

20

30

elation ~ e t w ~ n PLZT compostion and s ~ c t u r e and e lec~oop~c application.

-20 -10 0 10 2( Electric field

E [kVlcm]

-20 -10 0 10 2c Electric field E [kVlcm]

Pol~ization P and b i ~ ~ n ~ e n c e An as a ~nction of electric field E for

Pockels (1st) and materials.

aterial

~mary electrooptic 0.52 coefficient

PLZT 8/65/35 ( ~ ~ = 3 ~ m ) 6.12

KTa0.65~b0.35~3 5.30 Secondary electrooptic 9/65/35 ( ~ ~ = 2 ~ m ) 9.1 2 coef~cient PL2X 10/65/35 ( ~ ~ = 2 ~ m ) 1.07

El > \ P ."-A-A-

1. 7km -0-0-

R COEFFICIENT D COEFFICIENT

BY C. H. H e a r t

1

-

I i n o

1 1.0 2.0 3.0 4 . 0 5 . 0

\

Grain s i z e [ p m l rain size de~enden~e of the electroo~tic coe~~cients,

3 x 1.1 x 10-16 x 1 x 10-3)

226

5

~ ~ n g e n c e vs. electric field response of

possible phenomeno1ogic.al analysis of this peculiar phenomenon is based on the model that the crystal is composed of coexisting ferroelectric and paraelectric phase^.^) Suppose that the volume fraction of the paraelectric phase x(") is given by an cumulated ~aussian distribution with 'respect to temperature, the b ~ ~ n g e n c e An is estimated by the summation of the linear and quadratic electrooptic effects4)

An = [ 1 - x(T)] n3(r33 - r13) E/2 + x(T) n3 (8.3)

where n is the refractive index, and r and R represent the el coefficien~, respectively. Even if the e x ~ ~ m e n ~ l phenomenologically, the actual situation may not be so si as x(T) is also a function of the applied electric field E.

noth her more realistic desc~ption is found in terns of a m mechanism. 3 has very small spindle-l ~ b i g u o u s b p e ~ n ~ c u l ~ to the ex field greater than 0.5 kWmm 1s applied, the domain walls within a certain region of the sample moves together, ' such that micro-domains respond to the appli

perative manner (See Fig. 8.6).5) It is n o t e w o ~ y that the stripe p and bright domains (correspon~ng to up and down p o l ~ ~ t i o n s ) will not

y domain reversal, and that each domain area changes zero net pol~zation at zero field. The relaxor cry

poled easily when an electric field is a p p l i ~ around the ~ a n s i t i ~ n te eratur depoled c o ~ l e t e l y without any remanent p o l ~ ~ a t i o n . “apparent” secondary nodinear effects such as electros phenomena, which occur without any hysteresis.

Domain reversal mechanism in Pb(Zn 1/3Nb2/3)03.

2

~ o ~ p o s i t i o n x

e n = 2.49 of

0.08 0.10 0.12 0. I 4 0.16 T i F r a c t i o n x

tive in~ex as a f ~ n c ~ Q n of cQm~Qsition x for ( 1 - x) 1/3

C o m p o s i t i o n ( x 1

230

The data indicate that the 0.88Pb(Mg1/3Nb2/3)03-0.12PbTiO3 has the potential to be a better electrooptic ceramic than PLZT with high m~hanical toughness. ~ g h e r optical transmit~ce must be achieved, however, by optimi~ing the fabrication process.

One of the earliest applications is Ferpic (Ferroelectric Picture er no^ Device). Figure 8.10 shows the principle of the Ferpic?) Initally, a PLZT 7/65/35 ceramic plate is uniformly DC-poled laterally [see Fig. 8.10(a)]. Then, storage is achieved by switching domains at points corresponding to the image's high-intensity regions. To switch domains, a high-contr~t transparency is placed in front of the Ferpic a d illuminated [Fig. 8.10 (b)], creating low-impedance regions in the photoconduc~ve film. The writing voltage supply will then cause switching in these regions only.

Viewin~reading the memorized image is accomplished by passing polarized light ~ o ~ g h the Ferpic and an analyzer as shown in Fig. 8.10(c). ana ly~r are parallel, the regions with remnant polarization normal to the plate produce a bright image, and the other regions produce a dark image.

Sandia National Laboratories designed PLZT goggles for the U.S. Air Force to provide thermal and ashb blindness protection for aircraft personneL8) The goggle is basically a transverse-mode shutter using an i n t e r ~ g i ~ l surface elec con~guration similar to that shown in Fig. 8.1 1

PLZT eye glasses for stereo TV (see Fig. 8.11) have been fkbricated using the light shutter principleg) The lenses consist of a pair of optically isotropic PLZT (9/65/35) discs sandwiched between two crossed polarizers. en zero voltage is present between the electrodes, light will not be t r a n s ~ ~ e d . The transmitted light intensity increases with increasing applied voltage, and reaches a m ~ i m u m when a phase difference on) of 180° is i n d u d in the PLZT disc (at the half-wave voltage).

Stereo TV images of an object are taken by two video cameras co~esponding to the two eyes and the signal from each camera is mixed alternately to make a frame. for the right and left eyes. When viewing, the right and left PLZT shutters are triggered synchronously to each image frame, resulting in a stereo image.

Electroo~tic Devices 23 1

VER

POLA~IZER FERPIC ANALYZER ( c)

~rinciple of Ferpic: (a) initial DC poling, (b) writing process using a ~hotocon~uctive film, (c) reading process using a pair of parallel polarhers.

2

left

A stereo TV system using a pair of P

current require men^ for high defin been proposed. One of the promisi

one-dimensi*nallO) or two- dimension^ utilizing two-dimensional PL pment of a simple mass

n

cal display: (a) a m a ~ x se

e l ~ ~ ~ e c o n ~ ~ u r a ~ o n of a (lox 10) device in the figure rep re sen^ one inn

e l ~ ~ ~ ~ s . Figure 8,14(b) shows a picture of an actual display. ayer thickness is about 0.35 mm.

234 Chapter 8

I i

Fabrication process for the two-dimensional PLZT optical display.

The driving circuit for the display is shown schematically in Fig. 8,16(a). terminals of the device are addressed as shown in Fig. 8.16(b), the image appearing in Fig. 8.16(c) (letter "F) is generated on the screenel

235

Picture Vertical Electrode External l , Electrode

T

1 d

m front View Side Vi ew

chema~c e l ~ ~ ~ e con~guration of a (lox 10) matrix PL e. (b) Top view photograph of a PLZT light valve array with external electrodes.

rightness on a screen vs. applied voltage for red, green or blue light. Note that the half-wave voltage differs for these three lights.

23

H-l H-2 H-3 H-4 H-§ H-6 H-7 W-8 W-9

1 ms

W-l 0

v-3 V 4 . .

V-§ V-6 v-7

v-l .2.8.9.10

1

CTO

~ r o s s t a l ~ test system. light through a slit focused on the s~reen is r n ~ ~ ~ .

1

~ f f e ~ n t i n ~ ~ t combinations: (a) v

238 Chapt

~ r o s s ~ l k was monitored on the 2-D display using the setup shown in Fig. 8.1'7 with monoc~omatic light?) The test was made by keeping one vertical t e ~ i n a l

h o ~ z o n ~ t e ~ i n a l s (continuous plate- ugh el~trodes) simultaneously. There three different cr~sstuZ~ patterns: vertical, h o ~ z o n ~ and oblique types; that is, light leakage observed at vertically, ho~zontally and obliquely adjacent pixels. The results are shown in Fig. 8.18(a)-(c) for three ~ f f e ~ n t input c and bottom of figures in a pixel indicate the li ht inten the ON and OFF state, respectively vertical and horizon~l crosstal~ i intensity, respectively, which does the other hand, oblique type cros & ~ n ~ n g on the applied voltage and the n u m ~ r of continuous e l ~ t r ~ e s

(=P el=@&) on (i.e., Ground) and applying high v01

' address) (called combination type c onfig~ations is necessary to eliminate

In Fig. 8.15, the first maximum in the ligh tensity is obtained at voltages for red, green and blue light; 160 V for 150 V for green and 1 blue.

(1) Explain the reason physically.

osing that the ~ ~ c t i v e index n (= 2.49) and the e l ~ ~ o o p t i c c - R12) (3.6 x [m2N2]) does not change significantly for e

calculate the wavelength of these thee lights.

e half wave voltage is calculated from

r , = ( m " o E3 (R11 - 3 2 = n . (P8.2.1)

(1) Since the half wave voltage is provided by Eq. (P8.2.1), accor~ng to the illumination light wavelength, the required voltage differs: for shorter wavelengths, a smaller electric field is required.

(2) Taking into account the electrode gap of 0.4 mm, E3 = 3.55, 3.33 and 2.89 x , respectively, and a pat~ength L given by (1 .O - 0.1)

mm (note that the surface depth 0.1 mm is an inactive layer):

239

h = 2.4g3 x ( 3 . 5 5 ~ 1 0 ~ ) ~ (3.6 x 10m16) (0.9 x low3) = 630 [nm] (for red),

h = 555 [nm] (for green),

h = 418 [nm] (for blue). (P8.2.3)

Light waveguides can be f a b r i c a ~ by deposit in^ a ~ g h - r e ~ t i v e index layer on a substrate. The principle of the wave~ide is shown schematically in Fig. 8.19. 2, Like an optical fiber, the light tends to bend toward high ~fractive-index side, so that the light should be confined in the narrow high refractive-index layer fabricated on the

LiNbO3 single crystals are commonly used. Figures 8.~O(a) and 8.20(b) are typical planar and ridge type electrooptic waveguides. 3, The fabrication of a planar type is easy, but the nonunifo~ dis~bution of the applied electric field is a problem. On the other hand, as you can imagine, the ridge type *

sophistic~ted manufacturin~ technology, but the device function is close to t The transmitted light intensity is easily m ~ u l a ~ by applying a relatively low voltage. Phase modulation by 1 * hieved by applying a voltage of 0.3. V with power consumption of S

240

rod

C

Electrooptic waveguides: (a) plan~-type and (b) ridge-type. 12)

l . Relaxor ferroelectrics are widely applicable for el~trooptic light valve/display applications. "he superior ch~ac~ris t ics of these materials are athribu p ~ m ~ i l y to the easy poling of the f e ~ ~ l e c ~ c micro"dom~ns.

2. A new electrooptic cerarnic 0.88Pb( g 1 2 P ~ T i ~ 3 with high mech~ical toughness is one of the ~romising new mate~als for fori lifetime display applications.

3. A new type of PLZT two-dimensional light valve, fabric by a tape casting technique, is one excellent example of a design well-suit~d to mass-produc~on at a low ~an~facturing cost.

4. Light waveguides can be f a b r i c ~ ~ d by depositing a high re a subs~ate such as LiNb03.

8.1 Let us consider a PLZT thin film (l plate with the follow in^ for lateral electric field an

ht

iscuss the merits md d e m e ~ ~ of the above two elec config~ations.

~onsider the ~ire~ingence and the S electric el^.

e l e c ~ o o p ~ c coef~cient matrix for this sy

242 Chapter

"he electrooptic coefficient matrix is given as

E K. Tokiwa and K. Uchino: Ferroelectrics 94,87 (1989). K. Uchino and T. Takasu: Inspec. 10, 29 (1986). F. Kojima, J. Kuwata and S. Nomura: Proc, 1st. Mtg. on Ferroelectric Mater. h Appl. (Kyoto) p.155 (1977).

wata, K. Uchino and S. Nomura: Ferroelectrics 2 iie and K. Uchino: Proc. IEEE Ultrasonic Sympl

K. Uchino: Ceramics International 21, 309 (1995). L. M. Levinson edit.: Electronic Ceramics, Marcel Dekker (New York), Chap.7, p.371 (1988). J. T. Cutchen: Roc, 49th Annual Sci. Mtg. Aerospace Medical Assoc., New Orleans, May (1978). A. Kumada, K. Kitta, K. Kat0 and T. Komata: Proc. Ferroelectric Mater. h Appl., 2, p.205 (1977). K, Murano: Ceramic Transactions 1 ~ater ia ls , p.283 (1990). K. Uchino, K, Tokiwa, J. Giniewicz, Y, Murai and K. ~ h m ~ a : Ceramic Transactions 14 EZectro-Qptics and onl linear Optic ~ a t e r ~ a l s ; p.297 (1990). M. E. Lines and A. M. Glass: Principles and Applications of Ferroelectrics and Related Materials, p. 604, Clarendon Press, Oxford (1977). I. P. Kaminov: Trans, IEEE; M. T. T. 23, 57 (1975).

aTi03) is doped with lanthanum at levels less than 0.3 S semi conduct in^ with a resistivity i

resistivity is drastically increased, t e r n ~ ~ t ~ e around the Curie point.

was discovered in 1954, and is referred to as the PTC or P ~ C ~ c o e ~ c ~ e ~ t of ~esistivi~~ e~ect. Since then it has been investigated intensively by

9.1 shows the impact of various dopants on the resisti eramic as a function of tempera~re.

100 M

10 M

1M CI.

F

1- e t 1 0 0 k v

cz

*# 10 k U

l k

l00

10

l -

I -

..,

~

Mn 0.127

100 200 300 Temperature (“C)

esistivity as a function of temperaturc for several doped BaTi03 PTC c e ~ c s . ~ o p a n t concen~ations are indicated near each curve.

243

244

esistivi~ vs, t isovalent su~stitution

d o ~ ~ t s t y ~ i c ~ l y have a highe ions such as La, §m, Ce or Cd) or the T host s ~ c t u r e . Since the t e m ~ r a ~ e closely related with the Curie ~oint,

Pb (resistivity curve

ec

is ex to e

to

.3.

246

-e Conduction band

Ns Fermi level

Grain 't/oundary

Energy-level diagram near a grain bound^ of aTiO3.

In order to explain the PTC or PTC phenomenon, the most acceptable model is illustrated in Fig. 9.4, which was initially prop the

(m-type) ceramic particles an er (Schottky barrier) is ge ven

by the following equation:

.Q, = e ~ s 2 / 2 & 0 & ~ d , (9.1,)

where Nd is the concen~ation of donor atoms

at the p e ~ i t t i ~ i ~ E obeys th

& = C / ( T - T o ) ,

above Tc, and that the low resistance at T c is thus accoun the ~ o t e n t i ~ barrier due to the increase in p e ~ t t i v i ~ as

elow TC the pe~itt ivity falls, but t ~ e spontaneo controls the electron concen~ation to

lectronic properties in ceramics are strongly grain bound^. Suppose that a grain bou grains possesses acceptor impurities, and that

dis~bution model represented in Fig. 9.5: er is generated as shown

(x) = e (0 < 1x1 < L) =O (1x1 > L) ,

following ¶uestions:

C h ~ g e density distribution near the grain ~ u n d ~ ~ t w ~ n n-ty semiconductive grains.

escribe the potential @(x) by using the donor density , the p e ~ i ~ i v i t y EOE and electronic charge e. S that the change in

occurs within a re

(b) Describe the barrier t ~ ~ k n e s s L by the donor density surface acceptor density Ns.

(c) In se~conductive aTi03, the p e ~ t t i v i t y is s i g n i ~ c ~ t l y above Curie te~perature (= 13OOC). xplain the resistivity c h ~ g e by ons side ring barrier height - e $0.

(a) Poisson's e~uation is given by

I &o€ (0 c 1x1 c L) (P9.1.2)

Taking into account

a general solution @(x) = - ( s~lution:

8

(b) ~ o n s i d e ~ n ~ charge n e u ~ a l i ~ a ~ o n 9 we obtain

arrier height - e $0 is represent^

E = C/ (T - TO),

height increases in propo~on to sistivity is l to exp(-$ e $0 / kT), it increases (m' exp(l -

n we consider the s i ~ a ~ o n below

detection but also

ications for these

e r ~ c heaters" have also been widely commerc ttles and hair dryers. Figure 9.6 neyco~b air heater for and a u t o ~ o ~ v e chokes manufac

2

honeycomb air heater for a hair dryer (photo cou~esy of

The resistivity vs. te re ch~ctenstic of a barium shown in Fig. 9.7. ng into account heat generatio discuss the c ~ e n t vs. voltage relationship under * a ro con~ition qualitatively.

I

esistivity vs. t~m~erature ch~actens~c of a barium ita an ate^ PT

250

AX VOLTAGE

~ u ~ e n t vs. voltage relationship for a ~ ~ i ~ m titanate

e ini~al stage, the cu~en~-voltage rela~on obeys Ohm's law (that is, p is almost

aterials

P

25 1

el of the grain ~ o u n d ~ layer capacitor.

L capacitor is cornpos of rnany cubic core-shell units of a grain size n of ~ e l e c ~ c constant ( kin thickness, half of the

chess), calculate the apparent diel constant &app of this corn has an electrode area S and an electrode gap d, and zero

. 9.10, let us divide the sample into two regions:

(W G2: is ) of a capacitor with an

l d

, I ' 1

61 c2 (6onductor included) (€S)

~ ~ e n t dielbctric cons

9.1 nt vs. voltage re1 stors,

.2

1) eywang: J. Amer. Ceram. Soc. 2) E, Andrich: Electr. Appl. 26, 123 (1965-66). 3) E, Newnham: "St~cture-~rope~y elations in Electronic Ceramics," J .

4) urata Mfg. Comp. Catalog, "Misterious Stones." aterials Education, Vo1.6-5.

Piezocomposites c o m ~ s e d of a

I polymer-matrix composite is osite are high coupling factors,

match in^ to water or human tissue, mechanical on with a low mecha~cal quality factor

ve ceramic and a agnetoelectric effect

magnetic field.

Newnham et al. i n ~ ~ u c e d the conce t of " ~ ~ ~ ~ e c ~ ~ v ~ ~ ' ' for classifyi PZT:polymer composite s~ctures.1 conside~ng a two-phase connectivity of each phase is identi ., if a phase is self-connected in all x, and z directions, it is called "3"; if a phase is self-connected only in z direction, it is called "1". A diphasic composite is identified with this notation with two numbers m-n, where m stands for the connectivity of an active phase (such as PZT) and n for an inactive phase (such as a polymer). In general, there are 10 types of phasic composites: 0-0, 1-0, 2-0, ..., 3-12, 3-3, as illus~ated in Fig. 10.1

A 0-0 composite, for example, is depicted as two ~ t e ~ a t i n g hatched and ~ ~ h e d cubes, while a 1-0 composite has Phase 1 connected along the z direction. A 1-3 composite has a structure in which E T rods (1-dimensionally connected) are arranged in a 3-dimensionally connected polymer matrix, and in a 3-1 composite, a honeycomb-shaped PZT contains the 1-dimensionally connected polymer phase. 2-2 indicates a s ~ c ~ r e in which ceramic and olymer sheets are S and a 3-3 is compos^ of a jun frame e m ~ d d e d i polymer.

255

2 r l

- 0 " 0 2,- 0 3-0

1 " 1 2-1 3 " 1 2-2

tify the connectivity of

ha

1

S

volume fraction of Phase 2 for a case of Y1 Y2. The v ~ a t i o n may exhibit a con~ave or a convex shape, but the averaged value in a ~ o m p o s i ~ dues nut U1 nor is it less than U2. This effect is called a ’ ’ ~ ~ ~ eflec?.’’

example is a fishing rod, i.e., a light-wei~h~tough material, where carbon are mixed in a polymer matrix ~~~n 3-1 and 3-0). The densi~ of a com should be an average value with respect to volume fraction, if no chemical reaction occurs at the interface between the carbon fibers and the polymer, following the linear trend depicted in Table lO.l(a). A dramatic enh in the mechanical strength of the rod is achieved by adding carbon fibers in orien~tion, i.e., along a rod (showing a convex relation as depicted in Table

nother interesting example is an WC- in epoxy with a relatively high pac ~ 2 ~ 3 exhibits a semiconductor-m

ith i n c r e ~ i n ~ temperat~e. A al expansion for ep for the ceramic, 1 le and the s ~ c t ~ e

effect observed in a ~ 2 ~ 3 : e p o x y c o m ~ o s i t e . ~ )

alue of the output, Y ut refers to an

p ~ e t e r s U and 2. Suppose that Y and 2 follow convex and concave type sum

effects, respectively, as illustrated in Table 10.1 (b), the combination value Y E will exhibit a maximum at an inte~ediate ratio of phases. This is called a ' ' co~~ina t ion eflect."

Certain piezoelectric cer~c:polymer composites exhibit a combination property of g (the ~iezoezectric voltage c o ~ t a n t ) which is provided by dk (d piezoel~tric strain constant, and E: pe~ittivity). The details of these materials will be next section.

When Phase 1 exhibits an output Y with an input X, and Phase 2 exhibits an output 2, with an input Y, we can expect for the composite an output 2, with an input X. A completely new function is ma for the composite structure, c eflect."

a ~ g n e t o e z e c t ~ c ~ t e ~ a Z based on this concept.2) "his mate^^ magnetostrictive CoFe2O4 and piezoelectric BaTi03 mixed

sintered together. Figure 10.3 shows a micrograph of a transverse section of a uni- directionally solidified rod of the materials with an excess of Ti02 (1.5 wt.%). Four finned spinel dendrites are observed in cells (x 100). Figure 10.4 shows the magnetic

nce of the magnetoelectric effkct in an arbitrary unit meas~ed at room n a magnetic field is applied on this composite, cobalt ferrite

generates magnetostriction, which is ~ s f e ~ to barium titanate as stress, finally leading to the ene era ti on of a ch~ge/voltage via the piezoelectric effect in BaTi03.

~icrograph of a transverse section of a uni-directionally Solidified rut3 of m i x t ~ e of ma~netostrictive CoFe2O4 and piezoelectric BaTiO3, with an excess of Ti02 (1 .S wt.%).2)

2

sive s e n s ~ ~ s for

S

onse of

constant const~t P c33 E3 d33 833

(103k~~-3) (GPa) (10"2CN") (10-3,~~1)(10-3~~~1)

3 - 1 3 - 3

3 - 0

"

7:9 81. 2000

3.0 19 00 ZT:,~ilicone 3.3 3 40

00

120

40

13

i

73 , ,

4

3 110

250 ,

90 52

20

20

7 280

1

0

85 140 30

90

80

262

1

A l - 3 composite of I?ZT rods and polymer, top and bottom planes are rigid electrodes.

d33* = ld33.

Similarly,

(10.1)

where h is the volume fraction of phase 1 (piezoelectric). On an external stress is applied to the composite, the elastically S

will support most of the load, and the effective stress is drastically enhanced inversely propo~onal to the volume fraction. Thus, larger induced electric fields larger g* cons^^ are expected:

(10.3)

Figwe 10.6 shows the p i e z o e l ~ ~ c coefficients for a I?ZT-Spu~s epoxy composite with 1-3 connectivity, measured with a Berlincom d33 meter. A

for this composite, the measured d33* values are

n, but are only about 75% of the d33 value of the PZT SO1A ceramic. This discrepancy may be due to incomplete poling of the rods, A linear relation between the p e ~ i t ~ v i t y and the volume fraction lV is almost satisfied, resulting in a dramatic increase in 833" with decreasing fraction of PZT. "he piezoelectric

* for the 1-3 composite m listed in Table 10.2, together with those of a e composite with 3-3 connectivity. In conclusion, for the composites,

the piezoelectric g coeffkient can be enhanced by two orders of mag~tude with decreasing volume fraction of E T , while the d coefficient remains constant.

263

"he advantages of this composite are high coupling factors, low acoustic * ce, good matching to water or human tissue, mechanical flexibility, broad bandwidth in combination with a low mechanical, quality factor and the poaibility of making undid arrays by simply patterning the electrodes. ?he ~ c ~ e s s - m o d e e l e c ~ ~ e c h ~ c a l coupling of the composite can ex& the kt (0.40-3.50) of the constituent ceramic, approaching almost the value of the rod-mode e l e c t r o m ~ h ~ c a l coupling, k33 (0.70-0.80) of that c e r ~ c . 6 ) The acoustic match to tissue or water

when they are inco~orated in forming a composite structure, that is, by replacing the dense, stiff ceramic with a low density, soft polymer, Piezo composite materials are especially useful for underwater sonar and medical di ultrasonic transducer applications.

ayls) of the typical piezoceramics (20-30 Mrayls) is significantly improv

Although the PZT composites are very useful for acoustic ~ s d u c ~ applications, care must be taken when using them in actuator applications, Under an applied DC field, the field induced strain exhibits large hysteresis and creep due to the viscoelastic property of the polymer matrix. More serious problems are found when they m driven under a high field, related to the generation of heat. The heat generated by f e ~ ~ l e c ~ c hysteresis in the piezoceramic cannot be dissipated easily due to the very low thermal conductivi~ of the polymer matrix, which results in rapid de~adation of pie~oelectricity.

4001

2000

P m volume fraction ( %)

Volume fraction dependence of the permittivity E and the p i e z o e l ~ ~ c constants d33 and g33 in a 1 - 3 P~:polymer composite.

4

(b) eff~tive p i e z ~ l ~ ~ c d33* c ~ ~ c i e n t , 8 (c) e f f ~ ~ v e p i e z o e l ~ c ~ c v o l ~ ~ e c ~ f ~ c i e n t

3, x3, S33 ~ h i c h are e stress, the strain, and the elastic complia~

odes are common and E3 is c

3 = l&3eo E3 + 2V 2&3so = &3*&0 E3.

fore,

PZT (Phase 1)

Qolym6r (Phase 2)

(a) P ~ ~ l e l C o ~ e c t i v i ~ (b) Series Connectivity

iphasic composites in S.

Phases 1 and 2 are inde~ndently free:

(P10.2.3) (P10.2.~)

e strain x3 must be c the ave~ge strain x3* is given by the follo~ing e~uation:

1 v (1x3 - x3*) l Is33 = 2 v (x3* - 2x3) l2s33. (P10.2.~)

x3* = [(lV 2s33 ld33 + 2 1 V s33 2d33)/(1V %33 + 2V ls33)] E3, (P10.2.6)

iezmlectric c o n s ~ t is

33* = (1V 2s33 Id33 + 2 v Is33 2d33) 4333) EO ( h l&3 + 2V 2&3)]. (P10.2.8)

1

266

L

t , I

0 20 40 60 80 1

Relative pe~itt ivity plotted as a function of volume fkac~on of PZT p0wder:polyureth~e ~ b ~ r compos

cube model, sphere model, parallel and series

d33* = 'd33 [a3(a + (l-a)n)]/[a + (l-a)n(l&3~&33)] / [( 1 - a ) ~ ( a + ( 1-a)n) + a31 (10.5)

d3 1 * = Id3 1 [a2(a + (l-a)n)]/[a + (1-a)n( l € 3 ~ & 3 3 ) ~ * a/[ 1 .. a (a + (1 -a)n)1'2 + a31

e volume fraction of ase 1 is given by

1~ = a34a + ( 1-a)n) . (10.7)

e case n = 1 co~sponds to the cu S model, and a general case 0 < n 1 co~esponds to a con~guration more den n. F i ~ ~ e 10.10 shows the ~ ~ p e r i m e n ~ l l y d e ~ ~ n ~ p e ~ i t t i v i * (= d33* c 2 d31*) coef~cient for PbTiO3: chloropr~ne rubb ~eoretical c ~ e s ~ )

en the volume fkaction of PbTiO3 (l be less than 1 (that IS, the rubber thickness ~ o u n d a Pb thinner along the z direction and thicker along the x and y action, n ap s 1 (that is, the dimensions). n ~ g ~ a t i o n chang w ~ c h typically involves rolling and calendering.

Phase 1

267

(b)

a

(l-a)n 1 -a)m

(l-a)l a

* Unit cell con~guration for a Q-3 composite according to m ~ ~ e d cubes model.

3-3 composites were first fabricated by the replamine method. A negative replica of a natural coral structure with 3-3 connectivity was made of wax. replica of the negative structure was by i n ~ ~ u c i n g a PZT slurry into the

the negative template, drying, burning out the wax, and finally ceramic.lO) In oder to make highly porous PZT skeletons, the

astic Spheres) method was proposed, where PZT powders mixed in a binder solution, and the mixture is '

orted an alternative method, that involves piling up thin in a 3-dimensionally connected array. 12)

3-1 and 3-2 composites can be fabricated by drilling holes in a PZT block, back~lled with epoxy. In addition to this drilling method, an extrusion method also been used to f a b ~ c a ~ a PZT honeycomb. The 3-1 and 3-2 composites show large dh and gh values. 13) As shown in Fig. 10.11, there are two types of c o n f i ~ r a ~ o n s c o ~ o n l y applied to these composites: parallel [P] and series [S]. general, S types exhibit larger dh and gh values than P types do.

500

0 0.2 0.4 0.6 0.8 I 1 .

volume fraction I V !. a J

n E l O O L

volume fraction 'V (b)

(10.8)

270

PZ" ceramic Carbon Polymer

Piezoelectricity Conductivity flexibili~

on black composite for vl~ration

P V D F PLZT C B W e i g h i n g

I I I I I

composites. Fabrica~on process of c F

27 1

Being brittle and hard, ceramics are difficult to assemble directly into a mechanical ence, ~exible composites can be useful in practice. When a composite of

polymer, piez~eramic powder and carbon black is faixicated (Fig. 10.12), the electrical conductivity of the composite is greatly changed by &I: addition of small ~ o u n ~ of carbon black.16) Figure 10.13 illustrates the fabrication process. By properly selecting the electrical conductivity of the composite, the ceramic powder effectively forms a series circuit with the carbon black, so that the vibrational energy is dissipated. The conductivity changes by more than 10 orders of magni~de around a certain carbon fraction called the percolation threshold, where the carbon powder link start to be generated. This eli~inates the use of external resistors.

Figure 10.14 shows the relation between the damping time constant and the volume p e r ~ n ~ g e of carbon black in the PL2T:P~~F and ~ Z T : ~ ~ ~ F composites. A volume percentage of about 7% carbon black exhibited the minimum damping time constant, and therefore, the most rapid vibrational damping. Note that the PLZT with a higher elec~omechanical coupling k shows a larger dip (more effective) in the ping time constant curve.

ime c stant vs. volume erc cent age of carbon bl minim~m t~me constant (quic

2'12

1. Composite effects: (1) sum effect, (2) combination effect, (3) product effect.

(b) good acoustic impedance matc~ng with water and human tissue. (c) mechanical flexibility

l

3. 1-3 composites: The effective piezoelectric c o e ~ c i e n ~ ' d * and

where lV is the volume fraction of Phase 1 (piezoelectric).

4. The principle of mechanical d ~ p i n g : (1) Vibration is trans mi^^ to the piezoelec~ic material. (2) Vibrational energy is converted into electrical energy (AC voltage) the piezoelectric effect. (3) If a proper resistor is connected, the energy con

anical energy is

(5) Damping takes place a manner that the impedance 'matc~n

10.1 Two kinds of piezoelectric materials, 1 and 2, poled along the 3-axis compose a composite in a series c o n ~ ~ r a t i o n as shown in Fig. 10.7 (b). m e volume Eraction is f~ : 2~ (Iv + 2~ = 1). bottom electrodes are rigid enough to prevent su ~ansverse ~ i e z ~ l e ~ ~ c coupling between has small, calculate the following physical p r o p e ~ e

. ,

(a) effective dielectric constant &3*, (b) effective piezoelectric d33* coe~cient, (c) effective piezoelectric voltage coefficient 833".

Use the p a r ~ e t e ~ 3, E3, X3, x3, s33 which are displacement, the electric field, )the striss, the strain, compliance, res~t ively .

1 I * b I " ,

ops from the " r n ~ f i ~ cubes model," which ic ~is~ibution 'of cubes with res d in Pig. 10.9 (1 = m = 1, 'n j ~ , 1

j/[a2&33 + (1-a)n.1&331 +*[I. - az(a + ( l - ~ ) n ) ~ 2 ~ 3 3

4

3 1 * = 1 [a2(a + (~-i)n)l/[a + (l-a)n(l&33/2&3~)1 9 a/[l- a (a + (1-a)n)llz + a31 . P

10.3 composites as shown below as prim^ p ~ ~ l e c t r i c cwffici

ce in thermal expansion cwfficien~ S this secondary pyroelectric effect

rwlectkic effect is anticipat~ in a com osite

p~allel and series connections.

~ s s u m e that the top and bottom electtodes are rigid enough to prevent surface ben~ng, and that the transve~e stress between ne~ligibly small, The volume fraction is l V : 2U ( lV + ex~ansion coef~cient, the stress, the strain, and the elastic compliance, r e s ~ c t i ~ e l y .

a r ~ e t e r s T, OCT, 3, x3, s33 which are

d Electrode

(b) Series ~onne~tivity

ctures for p y r o ~ ~ ~ t r i c materials.

9)

R. E. Newnham et al.: Mater. Res. Bull. 13, 525 (1978). K. Uchino: Solid State Phys. 21, 27 (1986). K. Uchino, S. Nomura and R. E. Newnham: Sensor Technology 2, 81 (1982). K. A. Klicker, J. V. Biggers and R. E. ~ e w n h ~ : J. Amer. Cerm. Soc. (1981) Materials Systems Inc. catalog (1994) W. A. Smith: Proc. IEEE Ultrasonic Symp. "'89, p.755 (1989). L. A. Pauer: IEEE Int'l Convention Record, 1-5 (1973). H. Banno: Proc. 6th Int'l Meetin €7-6, Kobe, 1985), Jpn.

H. Banno and T. Tsunooka: Technology Soc., p.328 (1987). D. P. Skinner, R. E. Newnham and L. E. Cross (1 978). T. R. Shrout, W. A. Schulze and J. V. Biggers, (1 979). M. Miyashita et al.: Ferroelectrics 27, 397 (1980). A. Safari, R. E. Newnham, L. E, Cross and W. A. S (1982). K. Uchino and T. Ishii: J. Ceram. Soc. Jpn, ACX Company catalogue: Passive Damping Y. Suzuki, K. Uchino, W. Gouda, M. Sumita, R. E. new^^ and A. R a ~ a c h a n ~ a n : J. Ceram. Soc. Jpn., Int'l Edition

J. Appl. Phys. 24, Suppl. 24-2,

have studied the ~ n d ~ e n ~ s and applications of ferroelectrics, including

high pe~itt ivity dielectrics, ferroelectric memories, pyroelectric devices, piezoelectric devices, electrooptic devices, PTC materials, and composite materials.

viewpoint of commercialization, capacitor dielectrics dominate at present, followed by $ezoelectric vibrators such as Gzzers and speakers. Among the other classes of devices, sales are relatively low,

?&'hat will be the next ~romising market for ferroelectric devices? As we have seen, ferroelectrics can be utilized for various applications, but have failed to

ialized in most cases. In the case of the light sensor, for semiconductive materials are superior to ferroelectrics in response sensitivity. Magnetic devices are popular for memory applications,

ed for optical displays. High p e ~ i ~ i v i ~ dielectric thin film can survive in S, but commercialization of ferroelectric memory ( u n c e ~ n because of the variability of the coercive field of the material. Ferroelectric devices may fail to be developed when c o m ~ ~ t i v e materials already exist. Therefore, we see again, ferroelectrics an: strong only in the fields where no other replacement material exists.

In the author's opinion, the following will be promising areas in the very near future:

(1) Electromechanical devices (piezoelectric actuators, ultrasonic motors), (2) Thin film hybrid sensors (pyro-, pressure, acceleration sensors), and (3) Electrooptic devices (light wave-guides, thin film hybrid displays).

Of course, this is not meant to discount the other areas of potential development. owever, it is anticipated that these other fields of application will q u i r e a higher

inves~ent in time, money and expertise and a much longer development period than the areas identi~ed as the most promising.

in the future. / *

1.2

U . 0.2

arket share of f e ~ ~ l ~ ~ c devices by Japanese m

278 hapter 11

machi~ng-relat~ ~cromotors. European deve~opmen~ are a littl the unit^ States, and they seem to have been searching for a applications. The device sizes at the trial manufact~ng stage range m generally around 10 cm.

e markets in the United States are limited to military and defense applications, it is dif~cult to estimate the sales ~ o u n t . Among the current needs of the Navy smart submarine skins, ~ y ~ o p h o n e actuators, prop ise cancellation deviws; and of the .Air Force: smart aircraft skins; while the quires helicopter rotor twis~ng, aeroservoelastic control and cabin noiseheat vibration cancellation devices.

In Japan, piezoelectric camera shutters olta C ~ e r a ) and auto S in cameras (Canon), dot-m rinters (NEC) and p a - ng c o ~ e r c i ~ i z ~ and m ~ s - p r ~ u c ~ on the order of tens

Piezoelectric ink jet p~nters (Epson) and piezoelectric etc.) are incre~ing th ber of

disclosed ushita , Brother I n d u s ~ , T

S u m m ~ of ceramic actuator develop men^ c o m p ~ n g the United

~ilitary-oriented product

Vibration suppressor

~ P ~ C A ~ O ~ Space structure ilitary vehicle

Up-sizing (30 cm)

S ~urleigh AlliedSignal

ass-consumer product

~icro-motor Positioner

Office equipment Camera Precision machine Automobile own-sizin~

(1 cm)

Tokin C o ~ o r a t i o ~

Canon Seiko Inst~ments

Lab-equipment product cro-motor sitioner

Vibration suppressor

Lab stage/stepper Airplane ~utomobile

ydraulic system ~nterme~iat~ size

(10 cm)

Philips Siemens Hoechst CeramTec Ferropem

hysik Inst~mente

uture of Ferroelectric Devices 279

The annual sales of ceramic actuator units, catnera-related devices and u l ~ a s o ~ c motors in 2005 in Japan are estimated to reach $500 million, $300 million and $150 million, respectively4) The total sales may become equivalent to those of the capacitor industry. If these are installed in final actuator-related products, sales projected to reach $10 billion. Thus, a bright future is anticipated in many fields of application.

The potential and range of application for ferroelectric materials have ~ghlighted in the previous section. owever, there still remain various problems to resolve before their full commercial potential can be realized. Of particular concern are the issues of reliability and durability. Let us consider the reliability issue with respect to materials, device designs, and drive/control techniques.

e reproducibili~ of the dielectric and ferroelectric characteristics of a *

epends strongly on grain size, ~ o r ~ s i ~ and i ~ ~ ~ ~ i ~ ont tent. I n c ~ ~ i n g size enhances the magnitude of the f i e l d - ~ d u ~ polarization and strain, but some of the characteristics such ture tou~hness. The grain size should optimized for each application. e, fine powders made from wet c h e ~ c a l processes such as co-precipi~tion and sol-gel will be required.

Porosity must be el i~nated completely from the sintered ceramic, when it is for electrooptic devices. On the other hand, porosity does not aRect the ~iezoelectric strain behavior s igni~ , even when it is more than 94%. The tip deflection of a unimo~h made from based material does not change for porosities less than

ng, donor- or acceptor-~pe, produces r e m a r ~ b l e c h ~ g e s in Since donor doping provides "soft" characteristics, the S

exhibits larger strains and less hysteresis when driven under a high electric kWmm). On the other hand, acceptor dopi S "hard'' characteristics, le to a very small hystere~c loss and a large m a small AC electric field (that is, ultrasoni

ystematic stu~ies on the high electric field and stress evices are also eager1 awaited, as well as the compositio

strength.

aging effect is very o~ant , not many investiga~ons have ing effect arises o factors: depoling and ~ e s ~ c t i o n .

as a multilayer piezoelectric actuat obeys an empirical rule+)

(11.1)

DC is a sort of activation energy and n is a characteristic p ~ ~ e t e r .

popular silver electrodes have a serious problem of ~grat ion under a high electric field and high h u ~ d i t y in actuator, electroop~c and m ~ m o ~ applications.

be overcome with the use of a silv~-palla~um alloy (or more ce i n e ~ ~ n s i ~ e ceramic actuators, 'we need to introd~ce Cu or

h requires a sinte~ng tempera~e as e sintered at low t e m ~ r a ~ e have

veloped for actuators.

trode layer is another ~roblem for multilayer types as we1 o e ~ ~ c e adhesion, composite electrode m a t e ~ ~ s of a metal colloid, ceramic electrodes, a d electrode configurations with via-

ppress the internal stress concentration which initiates

lifetime is extended with decreasing layer ~ i c ~ e s s has not yet been clarified.

Lif~time prediction or health monito~ng systems using failure detection ~ ~ q u e s are also i m p o ~ ~ t for some devices7) Figure 11.3 shows such an "intelli~ent"

e actuator is controlled

utilized as an AE sensor.

28 1

~ctuation Feedback (2) Breakdown d ~ t e ~ i o ~

I Strain sensor

Control voltage 0

0 U U U 0 U

0 0 o n D O n u a n 0 0

Co~puter-controlled ower supply

~ntelligent actuator system with both position detection feedback mech~sms.

e Strain gauge conf ig~a~on of the intern^ electrode for an intelligent actuator.

A special internal electrode con~guration with a strain gauge config~ation has proposed to increase the reliability of multil~yer piezoelectric actuators.*) in Fig. 1 1.4, strain gauge configured electrode patterns are inserted at every ten

282 hapter 11

internal layer of a multilayer actuator. In an electric field cycle n o ~ a l l y applied to the device, the resistance change corresponds to the transverse p iezoe lec~~ strain induced in the device. However, if crack or d e l ~ n a t i o n occurs in the actuator, an abno~al ly large resistance change is monitored. Thus, this electrode con~guration can be used for both feedback detectors (1) and (2) shown in Fig. 1 1.3.

Ferroelec~ic devices generally have quick responses. owever, when a sharp pulse or step-like voltage is applied to a device, an unstable output ringing tends to occur just after the voltage is applied. This occurs even in capacitors and electrooptic devices, where it is sometimes called " s c r e ~ n g " because of the sound it some~mes generates. It is caused by a piezoelectrically or electrostrictively induced mechanical re son an^.

In addition to the unstable output, pulse driving the ferroelectric generates very large tensile stresses in the device, sometimes large enough to initiate cracks. In such cases, a compressive bias stress should be applied to the device with c l ~ p i n g mechanisms such as a helical spring or a plate spring.

is occasionally obse~ed, p ating electric ~ e l d , that

iezoelectric a lications such as piezoelectric t r a n s f o ~ e ~ and ultrasonic motors. e is due to the imbalance ~ t w ~ n heat generation, basically hysteresis loss, and heat dissipation, d e t e ~ n e d by the device size

(i.e., surface area).9) It is necessary to select a suitable duty ratio for the so as to produce a tempera~re rise no greater than 40°C

As far as high power ultrasonic transducers and motors are conce~ed , o~e ra~on in the an~esonance mode has been proposed.l0) Ultrasonic motors have conventionally

operated in the resonance mode, at the so-called "reso l'

ver, the mechanical re son^^ state at the "an~esonance~' higher Q and lower heat genera~on than observed for

onance," where admi ving, in contrast to high

This means that a conven~onal in ultrasonic device.

ture research and development should focus

uture of Ferroelectric 283

cont~ning lead. Pb-free single crystals, such as BaTiO3 and K(Ta,~)O3, will studied vigorously in the near future, p ~ c u l a r l y in the fields of medical automobile applications.

Safety systems, which can both monitor the fatigue or symptom of failure of materialsldevices and stop the equipment safely without causing serious problems,,

. A str~n-gauge internal electrode config~ation for multilayer piezoelectric actuators is a good example of a future safety system.

en closely involved with 60 ferroelectric devices for more than 25 years. During these developments, the author has been a professor, a vice presi an R&D center deputy director or a s~nding auditor at several universities and private comp~ies both in Japan and the United States.

In this last section, the author wishes to describe his personal philosophy on ow to ~ e v e Z o ~ ~estseller devices, especially in the area of smart materials and s~c tu res .

is sort of "how-to" is, the author believes, much more i m p o ~ ~ t to younger researchers than practical knowledge about devices.

r. AGO Morita, former president of S O W ~ o ~ o r a t i o n , , responded to a ~uestion from a journalist concerning the lack of creativity on the parts of Japanese hers by saying "Japanese researchers are good at chasing and imitating the original idea for commercialization, but they in general lack creativity." Mr. Morita suggested that

ould be thee types of creativity with respect to Research & Development at : T h e U.S. people are focusing only on tec~nological creat iv i~. But the

people must understand there are two more creativities; ~ r o ~ ~ c t ~ ~ n n ~ ~ g creat iv i~ ~ r ~ e t i n ~ c r e a t i v ~ ~ , which are equally i m p o ~ n t for commercial success."

atsushita Panasonic's famous color TV technology (black color resolution), for example, has indeed been transferred even though the idea c Philips, they could suppo~ng technolo~ies. shita, on the other han the idea after an intensiv -year development on it. reader (you!) to decide which company is at a her level with respect to

ever, apparent that only sushita obt~ned a large

Table 1 1.2 s u m m ~ z e s the three impo~ant types of creativity to be implemen~d

following sections. gy,, each of which will be described in her detail in

284 r l

S of crea~vity in research and development.

oduct Planning ~ r e a ~ v i t y - Speci~ca~on itivity, size, power^ n

(3 arke~ng ~rea~vi ty .. ~ d v e ~ s e m e n t

(a) hoose your ~ u s t o ~ e r s , (b) arrow your focus, md (c) ominate your market.

will consider the details of this concept accordin

by solving the following example

Met" (a personal hygiene system, for cle ) is a big hit in Japan, t in the United States.

28

Japanese toilet ~ a ~ i l i t y hygiene sys te~ such as

both bath shower an

to leu^ the culture

286

NG OK ~ua~~ty

"All check for military use" - us

Difference between basic m~s"consumer products.

hapter 11

Pr~uction

NG OK NG Quality "No check for mass-~roductionn

- Japan

trends in quality control for military use

t us consider as a good example Toshiba light bulbs, Toshiba is one of the largest n Japan. The light bulbs typically have an a v e ~ g e lifetime of quality control curve has a standard deviation of A 10% ( 1 8 ~ - production lots happen to be of a little better qualit lifetime

of 2400hr, what will happen? A company executive might mention ba of the division. For this kind of mature i n d u s ~ ~ field, the total number is almost saturated, and this 10% longer lifetime translates directly to a 10% in annual income. Therefore, "too high quality" must be strictly e l i~na ted for mass- consumer products.

Of course, Toshiba has the technological capability to extend the bulb's lifetime. the reader has a chance to visit Japan to look for light bulbs, 2400 hr-lifetime bulbs can be fo~nd in shops. The reader should not be su~rised, however, to find the price exactly 10% higher than the usual 2~ hr bulbs.

A final comment: sometimes, even a famous Jqanese consumer-pr~uct company may con~bute to ~ l i ~ / g o v e ~ m e n t a l applications such as the NASA Space Shuttle program. The main reason for this is to obtain a ce~ficate of high ~u~~ for that com~any's product, leading to a very effwtive adve~sement although the development effort will not bring significant profit directly.

~ a t c h the ~enerul Social ~ r e ~ s

~ a r ~ e t also exhibits trends, which reflect cultural ch~acteristics, and, hence, may gradually or drastically change with time. ~e consider here changes in the Japanese market trends, which must be fully understood before an industry can expand its market in Japan. A s u m m ~ is shown in Table 1 1.3. Japanese people use "four Chinese character words" to express these trends, as shown at the bottom of Table 11.3.12)

287

1.3 Japanese market trends over time.

____". .

1960s eavier Thicker Longer Larger

1980s ~ighter nner

Shorter Smaller

Tas te~l Creative

-- Ship m a n u f a c ~ n g -- Steel industry -- ~uilding cons~ction -- Power plant (dam)

-- Printer, Camera -- TV, Computer -- ~ i n t i n g time, Communication period

b a n " , Air conditioner

-- ell- own brand apparel -- T.V. game -- Cellular phone (private commun.) -- " C u l ~ e " center,

the was a university student, the most popular d e p ~ e n t s in my sity etallurgy (for manu el plates and ships) and

engineering (for build in^ power p1 pr~ucing the bigger owever, once into 1980s, most se i n ~ u s ~ e s became

ith electronics or CO and sought the miniaturization of ezoelectric actuators, ltrasonic motors have been utiliz

to realize the hest st degree of fab~cation a c c ~ ~ y .

In the 2 ~ 0 s , the "beau~ful," "amusi "tasteful," and "cre by in ten do, which video game system Nintendo used to be a the be~inning of the 1970s, when most of the Japanese chasing the U.S. technologies in semiconductor devices, a major se~conductor company had a large number of failure ranked %bit chips (the Jap that time had suc l!), Since most of the basic functions

ase them at a very low price, prototype Game Boy did not

technologies, but utilized the cheap 8-bit chips with vvell-know key to this big hit was its ability to fit a social trend, "amusement," and to f i ~ l y attract the kids' attention.

fter choosing a suitable customer, we will start to n ~ o w our development focus. e follow in^ s u m m ~ z e s a proced~e for n ~ o w i n

ssible application fields.

ossible applicatio~s, find the sim ocess with the follow in^ E x ~ p l e

on in which we can most easily utilize

nts for the life~me of office continuous opera~on for more an 3 months or 101

~ m a ~ i n e how many pictu

ly use a scoring sheet to identify the development t ~ g ~ t . A sample of ow to score 1s shown in Table 11.4. ~ o m p ~ e the total scores, and select the hi~her

2

c o r i ~ ~ table for ~ e ~ i c e s ,

0 1 2 0 1 2

erit 1 2 0 1 1 2 0 1

0 1 1 1

6) ~ e s i ~ n 7) ~ro~uction ~uantity 8) maintenance service

0 x1 2 Q x1 2 x0 1 2

Q x1 2 x0 1 2

Q x1 2 0 x1 2 Q x1

x0 1 2 x0 1 0 1 x2

Q 1 x2 Q 1 x2

0 x1 2 Q 1 x2 0 x1 2

6 10

290

Mer identi~ing the target, we develop the products ~ c o r ~ g to the follo~ing technology and product planning creativity considerations, At the same time, we need to consider a suitable adve~sement and price range.

g or selecting a suitable ~~~~ for a de device is very i m ~ o ~ n t . the author d e v e l o ~ C O " multilayer ac they we= i~itially named

"dis~lacement transducers." Of course, this is not a bad name &om a physics point of view, however, it was not attractive to the customers. The name "positioner" was also used in the mechanics fields.

After discussing this with colleagues at rporation, the t e ~ n o l o g y "piez~lectric ac~ator" was selected, half of w ~ c h is f ~ l i ~ to electricians ("piezoel~~c") , and the remaini

an interdisciplin~ field.

m the a p p r ~ p ~ t e price

e profit ratio for a p ~ i c u l ~ sales price on the i n ~ u s ~ category: have rela~vely high profitability such as 10% in electronic

, as comp~ed with 3 - 4% for chemical industries. ns, we can estimate the maximum raw mate~als'

cost, labor costs, etc. Refer to the rough price calculation presented in Table 11 .S.

en the reader's company is th in~ng about s ~ n g a will need to consider if a tape-casting system really or usually recommends the ins~llation of a ~ p e - c ~ t i nt exceeds 1 million pieces per year. O t h e ~ i s e ~ the conven~onal c u t - ~ d - ~ n d

~ ~ t h o d should be employed by hiring several manufacturing a s s i s ~ t s .

com~any considers p ~ c h ~ i n g a price. A typical one-task robot c

S$) is enough to hire one worker in some c o u ~ ~ ~ s such g line having ten workers c o ~ e s ~ o n ~ to a

robot. So, an alternative so asing a robot is to start a facto^ in one of these countri~s.

uture of Ferroe~ectric Devices 29 1

Price calculation sample.

~ o ~ e r c i a l price 100 (must be comparable to equivalent things)

anufac~er's price 25 - 50 (varies depen~ng on the circulation route)

Raw materials 10 8t Labor cost 10 8t Profit 5

ec

There are two ~fferent approaches in exercising technology creativity: to find a new ~nctional effect or material and to achieve a high performance or figure of merit. These are typically called "research" and "development," respectively.

New ~ n c t i o n

~ e ~ e ~ ~ ~ i ~ is often an i m p o ~ n t factor in discovering a new function in a material. A ood exam le can be found in piezoelectric 01 mer, PVDF, which

Another example th cting ceramic discover^

~e are told that every researcher has "3 lucky chances" in hisher life to discover new things (a ~aditional Japanese proverb). owever most o le do not even reco these chances and lose their chances. Only the can really find the new phenomenon. A Japane a person who develops a ~ d e l y - c o ~ e ~ i ~ ~ product has the chance to bec general manager; a person who develops two products for the company is gu to be a vice resident; and a person who contributes more than three can be prom to president. From this illus~ation the reader can understand how d i ~ c u l t it is to develop an actual bestseller product.

The personality and aptitude of the researcher arc, of course,. also important factors here. Why don't you try the following Example Problem 11.4 to assess your ability to experience s e ~ n ~ p i ~ ?

292

First, familiarize yourself with the contents of this page as much as possible in one minute.

Test picture. (Note that this article was randomly cited from an academic journal.)

293

Second, answer True or False for the following sentences:

S article is printed on p.15 of an academic journal.

wears a dotted-design tie.

Solution

ENTS:

our Score Aptitude

4 You can be a good engineer. ou fit to a ~anager/sales engineer.

a bandon your dream to be an engineer.

erson who aims to be an engineer tries to remember the written content first. If answer questions (1) and (2) correctly, you must recognize your^

* * n is also expected, because it belongs directly may not remember his tie, to which you see it only when you try to."

he author usually asks unconventional questions of a job inte~iewee to our

any stairs a couple of minutes ago.

seen a p ~ e s ~ a n traffic signal just before entering the company U remember an illus~ation of a walking man lit up in blue? Is

he w a l ~ n g toward the left or toward the right?

e second question, most of the interviewees recognize the illus~ation, but the ers to the w ~ ~ n g direction M e r remarkably, When the answer is "I don't mber," we usually suggest he r e t u ~ home. Even when the answer is corre

"left," if the answer is given as a guess and the correct answer probability is 5076, may be hired for a management position. Only when the correct answer arises from a confident memory, will we hire him as a ~ r o ~ e ~ s i o n a l engineer.

294

If you missed the above three chances, what should you do? Quit research? The following example is dedicated to the unlucky reader, who, like the author, missed those lucky chances. We can still research using a more systematic way, for example, by using our int~ition. The author is malcing use of (1) secondary effects and (2) scientific analogy.

(1) As is well known, any phenomenon has primary and secondary effects, which a m sometimes recognized as linear and quadratic phenomena, respectively. In electrooptic devices, the Pockels and Kerr effects correspond to the primary Secondary effects, as you leaned in this textbook, In actuator materials, these correspond to the piezoelectric and electrostrictive effects.

en the author started actuator research in the middle of the 197Os, precise "displacement transducers" (we used this terminology initially) were required in a Space Shuttle program, in particular for " d e f o ~ b l e mirrors," for controlling the optical pathlengths over several wavelengths. Conventional p i e z ~ l e c ~ c PZT ceramics were plagued by hysteresis and aging effects under large electric fields; this was a serious problem for an optical positioner. Electros~ction, which is the secondary electromech~cal coupling observed in a c e n t r o - s y ~ e ~ c crystal, is not affkcted by hysteresis or aging. The response should be much faster than the time required for domain reorientation in piezoelectric~ferr~lectrics. In addition, electric poling is not required.

owever, at that time, most of the people believed that the secondary effect would be a minor effect, 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 found that telaxor ferroelectrics, such as the lead magnesium n i o b a ~ - b ~ e d solid solutions exhibit enormous electrostrictions.

(2) roba ably most of the readers are familiar with shape memory alloys, which can revert rather quickly back to their initial shape when subjected to the heat of a cigarette lighter. The basic principle is a "stress or ~ m p e ~ ~ - i n d u c ~ ' phase ~ ~ s f o ~ a t i o n from the austenite to martensite phase. The author tried to consider an analogous case among the ferroelectrics. Yes, we have an ttelec~c-field indud' phase transition from an antiferroelectric to ferroelectric phase. This type of phase transition should be much quicker in response and more energy efficient theoretically. After this speculation, we started to investigate lead zirconate based a n t i f e r r ~ l ~ ~ c s intensively, and discovered the "shape memory effect" in ceramic actuator materials.

The concept of composite effects is very useful, p ~ c u l a r l y for systematically improving the properties and figure of merits. As we learned in Chapter 10, a combination effect can provide an improved figure of merit g (= &E) in piezoelectric P2T:polymer composites.

Future of Ferroe~ectric Devices 295

Product effects are more attractive. Philips' m a g n e t ~ l e c ~ c material is a g example, which can be employed as a simple magnetic field monitor. The authork photos~ctive materials were also discovered along a similar line of reasoning. "he following anecdote cited from R&D Innovator13) will be of interest.

I've 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.

Where did I come up with the idea for this light conversion? Not with the sunlight shining through my office window, and not outside feeling the warmth of the sun, but in a dimly lit Karaoke bar.

I've been working on ceramic actuators -- a kind of transducer that converts electrical energy to mechanical energy -- at the Tokyo Institute of Technology when the trigger for "the light-controlled actuator" was initiated. In 1980, one of my friends, a precision- machine expert, and I were drinking together at a Karaoke bar, where many Japanese go to enjoy drinks and our own singing. We call this activity our "after-5-o'clock meeting." My friend studied ~cromechanisms 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 work smoothly because the frictional force drops drastically and the weight of the electric lead becomes more significant.

After a few drinks, it becomes easier to play "what if?" games. That's when he asked, "What if you, an expert on actuators, could produce a remote-controlled actuator? One that would bypass the electrical lead?" To many people, "remote control" equals control by radio waves, light waves, or sound. Light-controlled actuators require that light energy be transduced twice: first from light energy to electrical energy, and second from electrical energy to mechanical energy. These are "photovoltaic" and "piezoelectric" effects.

A solar cell is a well-known photovoltaic device, but it doesn't generate sufficient voltage to drive a piezoelectric device. So my friend's actuator needed another way to achieve a photovoltaic effect, Along with the drinking and singing, we enjoyed these intellectual challenges. I must have had a bit too much that night since I promised I'd make such a machine for him. But I had no idea how to do it!

While my work is applied research, I usually come home from scientific meetings about basic research with all kinds of ideas. At one of these meetings, about six months after my promise, a Russian physicist reported that a single crystal of lithium niobate produced a high electomotive force (10 kVlmm) under purple light. His talk got me excited. 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 defo~ation). But it was too slow, taking an hour for the voltage to get high enough to make a discernable shape change.

296 ter

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 ~ y m m e t ~ c crystal? After lots of trial and error, I came up with a tungstate-doped material made of lead lanthanum zirconate titanate that responded well to purple light. It has a large piezoelectric effect and has properties that would make it relatively easy to fabricate.

make a device out of this material, I pasted two plates back to back, but: placed them in opposite polarization, then connected the edges. I shined a purple light to one side, which generated a photovoltaic voltage of 7 kV across the length. This caused the

plate on that side to expand by nearly 0.1% of its length, while the other (unlit) side contracted due to the piezoelectric effect thr~ugh the photovol whole device from the light. For this 20 mm long, 0.4 mm thick displace~ent was 150 pm, and the response speed was l second. This fast and significant response was pretty exciting.

emembe~ng the promise to my friend, I fabricated a simple "light-driven micro wal~ing machine?" with two bi-plate legs attached to a plastic board. hen light alternately i~adiated each leg, the legs bent one at a time, and the machine ~ o v e d like an inchworm. t moved without electric leads or circuits! That was in 1987, seven years after my

promise.

busy with my "toy"; but not too busy to attend "after-5-o'clock ~ e e t i n ~ s " in Tokyo's -club area. In 1989, at my favorite Karaoke bar,

end who worked for a telephone company. e a photo-acoustic device -- perhaps as a solu

fiber communication.

e technology to t r ~ s ~ t voice data -- a pho light throu~h lasers and fiber optics has been advancing rapidly. -- the ear speaker -- l i ~ t s the technology, since optical phone signal conve~ed from light energy to mech~ical movement via electrical energy.

optical communication.

ell, what's my message for you, dear reader? To find a noisy not necessary; but what is necessary is listening to others outside your particular research area: for instance, basic researchers or people with specific, applied objectives.

scovering "monomo milar to the above.

ciety of Japan, the author lectric single crystal due to the

t to replace some of the

was used first, and som esses were b ~ e r thickness. finally in

developing a monoli actuator. The It

developed by Aura C of the monomo~h modifications, althou~h fabrication process is their original work.

the author usually suggests to a person in the p r ~ u c t planning division in a any is to r e e x ~ n e 10- d research. If the social nee& still exist,

because the related patents expired Or will expire soon, there likely be a good business o ost impo~antly, find out the reasons for

ability to overcome them. * .

tors: strong social p

technology to provi

nologies is also inn rtant in ~nding "seeds" for p attelle's predic~on attelle reports regularly on top ten for 2 ~ ~ , is listed: 14)

an genome mapping. Genetic-based personal identification and diagnostics will lead to preventive treatments of disease and cures for specific cancers.

2. Super m a t e ~ ~ s . Computer-based design and m ~ u f a c t u ~ n ~ of new materials at the molecular level will mean new, h i ~ h - p e r f o ~ ~ c e materials for use in transportation, computers, energy, and communications.

3. Compact, long-lasting, highly portable energy sources, including fuel cells and batte~es, will power electronic devices of the future, such as portable personal computers.

298 Chapter 11

4.

5.

6.

17.

8 .

9.

Digital, high-definition TV. A major bre~through for American television manufacturers -- and a major source of revenue -- that will lead to better advanced computer modeling and imaging.

Electronics mi~atu~zation for personal use. Interactive, wireless data centers in a pocket-size unit will provide users with a fax machine, telephone, and computer that contains a hard drive capable of storing ail the volumes found in their local library.

Cost-effective "smart systems" will integrate power, sensors, and controls. These systems will even~aily control the m~ufac~r ing process from beginning to end.

Anti-aging products -- that rely on genetic information to slow the aging process -- will include aging creams that really work.

Medical treatments that will use highly accurate sensors to locate problems, and ~g-delivery systems that will precisely target parts of the body, such as chemotherapy targeted specifically to cancer cells to duce the side effects of nausea and hair loss,

Hyb~d-fuel vehicles. Smart vehicles, equipped to operate on a variety of fuels, will be able to select the most appropriate one based on driving conditions.

10, "Edutainment." ~ucational games and computerized simulations will meet the sophisticated tastes of computer-literate s~dents.

Note that there is a very high possibility of using ferroelectric devices, e s p ~ i ~ l y in the areas, 2, 3, 4, 5, 6, 8 and 9.

F u ~ e r down-sizing of actuators will be such as blood test kits and surgical c Systems ( ~ E ~ S ) have currently been developing rapi force itself is, in general, too weak to move something with s u ~ c i e n t mechanic^ ef~ciency. ~ i e ~ o e l ~ ~ c thin films compatible with silicon technology will be much more focused upon micro-el~~omechanic~ sys~ms. An ul~asonic rotary motor as tiny as 2 mm in diameter, fabricated on a silicon membrane, is a good e x ~ p l e (see Fig. 1 1.7). 15) Even this prototype motor can generate a torque thee to four of magnitude higher than an equivalent size silicon motor.

As the size of min ia t~e robots/actuators decreases, the weight of the electric wire conn~ting the power supply becomes s i ~ n i ~ c a n t , and remote con definitely be required for sub-~llimeter devices. The photo-~ven ac~ator in the previous section is a promising andi id ate for micro-robots.

effoelectfic Devices

c

299

electrode e

.7 ~ ~ a s o n i c rotary motor as tiny as 2 mm in diameter fabricated on a silicon membrane.

to consider a suitable research and development pace so as to introduce new and products not too early, but not too late either. 'I'hree years prior to the

co~ercialization is a good target for the ferroelectric device field. The company changed their development pace from 5 to 3 years several yews ago, c o ~ e r c i a ~ ~ d the "Taurus" successfully.

Some engineers believe that lowering the drive voltage of a piezoelectric actuator is owever, this is not really true for portable equipment if one considers the

available battery voltages. Does the reader know the available battery voltages? The answers are 1.5, 3,6, 12,24 (automobile applications) and 250 V.

the author collaborated with COPAL to develop piezoelectric camera shutters a bimorph structure, we initally used conventionally commercialized bimorphs

driven at around 100 V. But, when we tried to c o m m e r c i ~ i ~ it, we recognized that we needed an additional 100 V power supply, which would cost more than a couple of dollars. Thus, we needed to change the birnorph design, by thic so that it could be driven by 250 V (this voltage is generated in a power supply conventionally used for a stroboscopic lamp).

The reader needs to collect the necessary i n f o ~ a ~ o n on the specifications:

*sensitivity *size *lifetime *available power supply

3

consi~ering glass cosmetic bottles in the s ~ i t c ~ e .

~ e ~ e n c e in ~ e v e l o ~ ~ e n t conc es

301

of componen~ in the system, and ~ m i n g fx e actuator is a ve ood e x ~ p l e

desig~de ems is illustrated in Fig. 11.8, using case of ul a ~ropaga~ng-wave type motor with piezo-ac~ators and two PO me groups moved to a more complex

motor with 4 piezo- group took the opposite approach, simpli~cation, and de pe with a single actuator element.

* evelopme~t conce ~sonlc motors.

302 hapter 11

l Applications of ferroelectrics -- (l) high p e ~ t t i v i t y dielectrics, (2) ferroelectric memo~es, (3) pyroelectric devices, (4) piezoelectric devices, (5) electrooptic devices, (6) C materials, and (7) composite materials.

. Resent market shares of ferroelectric devices -- US $2 ( l ) capacitors (2) piezoelectric devices (3) t h e ~ s t o r s

3. Reliability issues of ferroelectric devices:

a. Reliability of ceramics -- repr~ucibility of ceramics, temperat~e characteris~cs, electric field and stress de~ndence of properties, agin

electrode materials, electrode designs, layer thickness dependence, failure detection techniques

pulse drive method, heat generation mechanism, high power technique

b. Reliabili~ of devices --

c. Drive techniques --

4. Bestseller devices --

t plannin~, and mar~eting creativities

choose your customers, narrow your focus and dominate your maket.

c. T ~ ~ n o l o g i c a l creativity serendipity, analogy, product effect

d. Product planning creativity seeds and needs, developing speed, specifications

5 . Directions of smart systems -- a. Adding components for higher ~nction b. Reducing components €or ~iniaturization an

Future of Ferroelectric Devices 303

9, Ceram. Soc. Jpn., December issue (1984). J. Ceram, Soc. Jpn., December issue (1990). K. Uchino: Piezoele~tric Actuators and ~ l t r ~ o n i ~ Motors, Iuuwer Academic Publishers, MA (1996). K. Uchino: Proc. 9th Int'l. Symp. Appl. Ferroelectrics, p.319 (1995). K. Abe, K. Uchino and S. Nomura: Jpn. J. Appl, Phys., 21, U08 (1982). K. Nagata: Proc. 49th Solid State Actuator Study Committee, J"AS (1995). K. Uchino and H. Aburatani: Proc. 2nd Int'l Conf, Intelligent Materials, p. 1248 (1994). . A b u r a t ~ and K. Uchino: Amer. Ceram. Soc. Annual Mtg. Proc., S ~ 1 ~ - 3 7 - 9 6 ,

ndianapolis, April (1996). J. Zheng, S. T ~ ~ a s h i , S. Yoshikawa, K. Uchino and J. W. C. de Vries: J. Amer, Ceram. Soc. 79, 3193 (1996). N. Kanbe, M. Aoyagi, S. Hirose and Y. Tomikawa: J. Acoust. Soc. Jpn. (E), 235 (1993). M. Treacy and F. Wiersema: ~iscipline of Market Leaders, Addison-Wesley Publishing, MA (1996). E'. Hiroshima: P ' in the ~eeling Consumer Era (1996).

on J. Brill 8z Associates (1995).

R. A. Brooks, D. J. ~o- mechanic^ Systems,

This Page Intentionally Left Blank

abnormal grain growth, 71 absence of hysteresis, 62 acoustic impedance, 15 1

photostrictive ---, 295 accelerometer, 158, 159 acceptor, 61 aging, 279 alkoxide, 67, 68 anharmonici ty, 10 antife~oelectrics, 47 barium titanate (BT), 7, 8, 18, 67, 84,

92, 243 bimorph, 77, 184 birefringence, 221

grain boundary layer ---, 250 ceramic ---, 105

camera shutter, 194 cantilever, 78 I

ceramic capacitor, 105 ceramic electrode material, 280 chip capacitor, 106 coercive field, 90, 97 cofiring, 74 Cole-Cole relation, l 13 columbite, 67 combination effect, 258

--- effect, 257 --- material, 255 piezoelectric ---, 157, 255

connectivity, 8 1 , 255 converse electrostrictive effect, 160 converse piezoelectric effect, 1 , 10 coprecipitation, 67, 68 Coriolis force, 160 creep, 279 critical particle size, 87 crosstalk, 238 Curie temperature, 18 Curie-Weiss constant, 18 Curie-Weiss law, 18 Curie-Weiss temperature, l 8 cut-and-bond method, 74

cymbal, 81, 183 damped capacitance, 168 ~ a m ~ e r , 269

mechanical ---, 269 damping effect, 269 Debye dispersion, 1 13 deformable mirror, 19 1 degree of hysteresis, 62 depletion state, 121 depoling, 64, 279 ~ielectric, IO --- material, 2, 105 --- constant, 3, 105

--- relaxation, 84, 1 12, 1 16 diffuse phase transition, l10 digital displacement transducer, 182 dipole reorientation-related

polarization, 2 direct piezoelectric effect, 158 direction cosine, 38 doctor blade, 74 domain pinning effect, 63 domain reorientation, $9 donor, 61 doping effect, 61 dot-matrix printer head, 194 double hysteresis curve, 48 DRAM, 119 drain, 123 D-TGS, 139 efficiency, 149 e~ectric

--- loss, 116

--- displacement, 3 --- polarization, 2 --- poling, $9 --- -al impedance, 166 electrocaloric effect, 1 electromechanical coupling factor, 13,

electronic polarization, 2 electronic modulated suspension, 195 electrQQ~tic, 13, 221

--- effect, 13, 221 --- device, 221 bulk --- devices, 223

146, 162

305

306 Index

electrostriction, 9, 46, 185 --- -tive effect, 10 converse --- -tive effect, 46, 160

elliptical locus, 199 energy transmission coefficient, 147 equivalent electric circuit, 66, 169 Ferpic, 230 ~erroelectric, 1

ferroelectricity, 2 9 47 anti-

--- DRAM, 124 FEiT, 119 filter, 172 first-order transition, 40 float electrode, 280 €%AM, 126 friction material, 197 frictional coating, 197 gate, 123 grain growth, 71

abnormal ---, 71 grain boundary layer capacitor, 250 green sheet, 74 gyroscope, 158 "hard" piezoelectric, 63 half-wave voltage, 15, 18, 221 heat generation, 64 high permittivity capacitor, 105 hubble space telescope, 191 hybrid substrate, 108 hydrostatic pressure model, 88

ysteresi~, 11, 48 degree of ---, 62 double --- curve, 47

impedance matching, 269 inchworm, 196 infrared image sensor, 139 infrared light sensor, 138 intelligent material, 1 interdigital electrode, 74 internal electrode, 74 inversion state, 121 ionic crystal, 2 ionic polarization, 2 ' ic polarizability, 6

zig region, l 10 err e€fect, 14, 221, 224

Landau theory, 38 Laplace transform, 187 lattice vibration, 5 lead zirconate (E), SO, 182

lead zirconate titanate ( E T ) , 57, 153, 181

lifetime, 279 light valve, 233 lithium niobate, 73, 175, 239 local field, 5 longitudinally clamped permittivity,

166 Lorentz factor, 6 Madelung energy, 101 magnetoelectric material, 259 maximum Geld-induced strain, 62 maximum strain, 62 mechanical damper, 269 mechanical impedance, 15 1 mechanical quality factor, 150 memory device, 119

volatile ---, 1 19 non-volatile ---, 119

MFSFEiT, 128 micro domain, 116 microscopic composition fluctuation,

monolithic hinge lever mechanism, 194 monomorph, 100, 104 moonie, 81, 183 mo~hotropic phase boundary, 66 MOSFET, 119 multidomain - monodomain transition

model, 84 multilayer, 74, 183 noise cancellation, 269 non-volatile memory, 126 normal grain growth, 71 ordinary wave, 14, 16

overshoot, 187 oxide-mixing technique, 67 P-E hysteresis, 47 n-shaped linear motor, 203

110

extra-ordinary ---, 14, 16

pe~anent dipole, 3

relative ---, 3 vacuum ---, 3

erovskite 18

--- of electrostriction, 42 --- of antiferroelect~cs, 48

Index 307

photoconductive film, 230 photostrictive actuator, 295 photostrictive effect, 295 photovoltaic effecct, 295 ~iezoelectrjc, 145

--- actuator, 180 --- devices, 145 --- figure of merit, 145 --- strain constant, 145 --- voltage constant, 145 --- material, 152 "hard" ---, 63, 185

--- equation, 161 --- resonance, 161 converse --- effect, 10 direct --- effect, 158 high power ---, 64

piezoelectric transformer, 176 plate-through design, 280 PLZT, 15, 57, 84, 181, 222, 296 PMN, 1 1 , 46, 67, 156, 181, 228 point group, 4 Poisson's equation, 247 Poisson's ratio, 90 Pockels effect, 14, 224

olariz~tion, 2 electonic ---, 2 ionic ---, 2 dipole reorientation-related ---, 2 spontateous ---, 3, 4

polarization reversal, 1 l positioner, 185 pressure sensor, 158 principal strain, 93 product effect, 259 propagating wave type motor, 200 FT, 57

''Soft" ---, 63, 185

--- phenomenon, 243 --- thermister, 248

pulse drive method, 187 pulse width modulation (PWM), 214 pulse-drive motor, 185, 193 PVDF, 138, 156

pyroelectricity, 4 --- coefficient, 13 l --- devices, 13 1 --- figure of merit, 135 --- material, 1

--- responsivity, 133 --- sensor, 131

PZN, 1 17, 225 PZT, 1 1 , 57, 67, 153, 181 P2T:polymer composite, 260 rattling ion model, 109 refractive index, 221 relative permittivity, 3 relaxor ferroelectrics, 108, 155 reliability of device, 279 resonance frequency, 167 reson~ce/antiresonance method, 168 r~sonance mode, 16?

resonating displacement device, 185 resonator, 172 retardation, 16 rigid displacement device, 185 safety system, 282 Schottky barrier, 246 second-order transition, 39 servo displacement transducer, l 85, 19 1 shape memory effect, 182 shear stress, 30 shim, 77 sintering, 70 Skanavi-type relaxation, 1 13 smartness, l , 300 smart material, 1, 300 soft error, 120 soft phonon mode, 5 "soft" piezoelectric, 63 sol-gel method, 68 spontaneous polarization, 3, 4, 18 spontaneous strain, 18 sputtering, 83 standing wave type motor, 199 step-up ratio, 177 stereo TV , 230 strain, 9

anti- ---, 167

electric field induced ---, 9 m~imum ---, 62 principal ---, 93, 97

strontium titanate, 125 sum effect, 257 surface tension, 88 surface acoustic wave, 174 tape-casting method, 74 ten so^, 23

reduction of ---, 27 thinlthick film, 82, 157 torsional coupler, 201

308 Index

tr~sfomation matrix, 35 transformer, 176 trapped-energy filter, 173 trivial material, 1 two-dimensional display, 232 ~ c h i d a - I k ~ a model, 93

propagating wave type ---, 199, 205 standing wave type ---, 199, 201 "surfing" type ---, 200, 205 "woodpecker" type ---, 199, 201

ultrasonic transducer, 16 1 , 170 unhamonicity, 10 unimorph, 77 unitary matrix, 24 VCR head tracking actuator, 192 vibration mode, 165 vibration velocity, 66 vibratory-coupler type, 199 volatile memory, 1 19 wave guide, 239 "~oodpecker" type, 199 zero point drift, 280