Ferroelectrics E-Book

Ashim Kumar Bain

• Herausgeber: Wiley-VCH Verlag GmbH & Co. KGaA
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 644

Veröffentlichungsjahr: 2017

Beschreibung

Combining both fundamental principles and real-life applications in a single volume, this book discusses the latest research results in ferroelectrics, including many new ferroelectric materials for the latest technologies, such as capacitors, transducers and memories.
The first two chapters introduce dielectrics and microscopic materials properties, while the following chapter discusses pyroelectricity and piezoelectricity. The larger part of the text is devoted to ferroelectricity and ferroelectric ceramics, with not only their fundamentals but also applications discussed. The book concludes with a look at the future for laser printed materials and applications.
With over 600 references to recent publications on piezoelectric and ferroelectric materials, this is an invaluable reference for physicists, materials scientists and engineers.

Leseprobe

Table of Contents

Cover

Title Page

Copyright

Chapter 1: Dielectric Properties of Materials

1.1 Energy Band in Crystals

1.2 Conductor, Insulator, and Semiconductor

1.3 Fermi–Dirac Distribution Function

1.4 Dielectrics

Chapter 2: Microscopic Properties of Materials

2.1 Phonon

2.2 Phase Transition

References

Chapter 3: Pyroelectricity and Piezoelectricity

3.1 Introduction

3.2 Pyroelectricity

3.3 Piezoelectricity

3.4 Applications of Piezoelectric Materials

References

Chapter 4: Ferroelectricity

4.1 Introduction

4.2 Ferroelectrics

4.3 Classification of Ferroelectric Materials

References

Chapter 5: Ferroelectric Ceramics: Devices and Applications

5.1 Introduction

5.2 Capacitors

5.3 Explosive-to-Electrical Transducers (EETs)

5.4 Composites

5.5 Thin Films

5.6 Alternative Memories Based on Ferroelectric Materials

5.7 Nanoscale Ferroelectrics

5.8 Electro-optic Devices

5.9 Photoelastic Devices

5.10 Photorefractive Devices

References

Index

End User License Agreement

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Guide

Cover

Table of Contents

Begin Reading

List of Illustrations

Chapter 1: Dielectric Properties of Materials

Figure 1.1 Variation of (a) potential in the field of a nucleus with distance and (b) potential energy of an electron with its distance from the nucleus.

Figure 1.2 Potential energy variation of an electron with distance between two identical nuclei.

Figure 1.3 Potential energy of an electron along a row of atoms in a crystal.

Figure 1.4 Splitting of energy levels of isolated atoms into energy bands as these atoms are brought close together to produce a crystal.

Figure 1.5 Energy band structure of (a) a conductor, (b) an insulator, and (c) a semiconductor.

Figure 1.6 Plot of

f

(

E

) against

E

/

E

F

for

T

= 300 and 2000 K.

Figure 1.7 Schematic diagram showing the position of the Fermi level in (a) an insulator, (b) a semiconductor, and (c) a conductor.

Figure 1.8 Polarization processes: (a) electronic polarization, (b) ionic polarization, (c) orientational polarization, and (d) space charge polarization.

Figure 1.9 Frequency dependence of polarization dispersion.

Figure 1.10 The depolarization field

E

1

is opposite to

P

. The fictitious surface charges are indicated: the field of these charges is

E

1

within the ellipsoid.

Figure 1.11 (a) The procedure for computing the local field. (b) The procedure for calculating

E

2

, the field due to the polarization charge on the surface of the Lorentz sphere.

Figure 1.12 Phase diagram of current and voltage in a capacitor with a dielectric material.

Figure 1.13 Electric field pierces a cube with edge

dx

in an insulated portion.

Figure 1.14 (a) Band structure before dielectric breakdown, and (b) band structure after dielectric breakdown.

Chapter 2: Microscopic Properties of Materials

Figure 2.1 A one-dimensional linear chain. The atoms are shown in their equally spaced equilibrium conditions in the top row and with a periodic distortion below. The bottom Figure plots the displacements

u

n

as arrows, and the curve shows how this is a sine wave of period 6

a

in this case.

Figure 2.2 Dispersion relation between frequency and wave vector for a one-dimensional monatomic chain.

Figure 2.3 Diatomic chain. (Reproduced with permission of PB Littlewood and Premi Chandra.)

Figure 2.4 Dispersion of the optical and acoustic phonon branches in a diatomic chain and a schematic picture of the atomic displacements in the optical mode at

q

= 0.

Figure 2.5 Pattern of atomic displacements for an acoustic and an optical phonon of the same wave vector.

Figure 2.6 Representation of a simple model of phase transition in one-dimensional array of atoms.

Figure 2.7 Sequence showing the ordering of atoms for the model of Figure 2.6 when the potential barrier between the two wells is much higher than the interaction between neighboring atoms.

Figure 2.8 Sequence showing the ordering of atoms for the model of Figure 2.6 when the forces between atoms are much larger than the forces due to local potential.

Figure 2.9 Free energy

F

as a function of order parameter

P

above and below the temperature

T

0

.

Figure 2.10 Order parameter

P

s

as a function of temperature in the vicinity of the temperature

T

0

.

Figure 2.11 First-order phase transition. (a) Free energy as a function of the polarization at

T

>

T

c

,

T

=

T

c

, and

T

=

T

o

<

T

c

. (b) Spontaneous polarization

P

s

(

T

) as a function of temperature and (c) susceptibility χ.

Figure 2.12 Order parameter

P

s

as a function of temperature in the vicinity of the phase transition temperature

T

c

.

Figure 2.13 Examples of phase transition in perovskites. Showing the displacive phase transitions involving displacements of cations or rotations of octahedra. The Figure for BaTiO

3

shows the eight sites for the Ti

4+

cations in the cubic phase [6–8].

Figure 2.14 The schematic arrangements of two types of atoms A and B [16].

Figure 2.15 Ordered alloy crystal structures of Fe

3

Al and Cu

3

Au [16].

Figure 2.16 Ordered dipoles. (a) Parallel, (b) antiparallel, and (c) half of the dipoles are antiparallel.

Chapter 3: Pyroelectricity and Piezoelectricity

Figure 3.1 Piezoelectric gas lighter [20].

Figure 3.2 Ultrasound transducer [21]. (Reproduced with permission of Wiley.)

Figure 3.3 Schematic of piezoelectric actuator [22].

Figure 3.4 Schematic of stack actuator [23]. (Reproduced with permission of Lotte J. Beck, http://www.noliac.com/.)

Figure 3.5 Schematic of stripe actuator [24]. (Reproduced with permission of Dr. Ivan Poupyrev, http://www.ivanpoupyrev.com/projects/tactile.php.)

Figure 3.6 (a) Longitudinal mode piezoelectric element and (b) transverse mode piezoelectric element [25].

Figure 3.7 Rosen piezoelectric transformer [26–28].

Figure 3.9 Radial vibration mode piezoelectric transformer [30].

Figure 3.8 Thickness vibration piezoelectric transformer [29].

Figure 3.10 Schematic of piezoelectric accelerometer (a) before acceleration and (b) after acceleration [31]. (https://en.wikipedia.org/wiki/Piezoelectric_accelerometer. Used under CC:BY:SA 3.0 http://creativecommons.org/licenses/by-sa/3.0/.)

Figure 3.11 The cross section of a piezoelectric accelerometer [31]. (https://en.wikipedia.org/wiki/Piezoelectric_accelerometer. Used under CC:BY:SA 3.0 http://creativecommons.org/licenses/by-sa/3.0/.)

Figure 3.12 Piezoelectric microphone [32].

Figure 3.13 Schematic of a valveless micropump; (a) top view and (b) side view. (Nayana [36] 2012, Reproduced with permission of Dr. Premila Manohar, MSRIT, Bangalore.)

Figure 3.14 Flat-walled diffusers. (Nayana [36] 2012, Reproduced with permission of Dr. Premila Manohar, MSRIT, Bangalore.)

Figure 3.15 Piezoelectric diaphragm [39].

Figure 3.16 Diaphragm operation [39].

Figure 3.17 Illustration of different support methods [39].

Figure 3.18 Cavity measurements for Helmholtz's formula [39].

Figure 3.19 Layers and working principle of a silicon solar cell [40]. (Used under creative commons license – CC:BY:SA 3.0 https://creativecommons.org/licenses/by/3.0/.)

Figure 3.20 Schematic and energy band diagram of (a) a general nanowire piezoelectric solar cell fabricated using a p–n junction structure. Schematics and energy band diagram of the piezoelectric solar cells under (b) compressive strain and (c) tensile strain, where the polarity and magnitude of the piezopotential can effectively tune/control the carrier generation, separation, and transport characteristics. The color code represents the distribution of the piezopotential at the n-type semiconductor nanowires. (Zhang [47], 2012. Reproduced with permission of Royal Society of Chemistry.)

Figure 3.21 Rectangular cantilever beam energy generator (

d

31

mode generator).

S

is strain,

V

is voltage,

M

is mass, and

z

is vertical displacement. (Roundy [50], 2004. Reproduced with permission of Institute of Physics.)

Figure 3.22 General diagram of generator-based vibration energy harvesting using piezoelectric materials. (Minazara [53]. Reproduced with permission of SATIE(CNRS UMR 8029), PRES UNIVERSUD.)

Figure 3.23 The working principle of nanogenerator where an individual nanowire is subjected to the force exerted perpendicular to the growing direction of nanowire [54]. (https://en.wikipedia.org/wiki/Nanogenerator Used under CC:BY:SA 3.0 http://creativecommons.org/licenses/by-sa/3.0/.)

Figure 3.24 The working principle of nanogenerator where an individual nanowire is subjected to the force exerted parallel to the growing direction of nanowire [54]. (https://en.wikipedia.org/wiki/NanogeneratorUsed under CC:BY:SA 3.0 http://creativecommons.org/licenses/by-sa/3.0/.)

Figure 3.25 Schematic view of typical vertical nanowire integrated nanogenerator, (a) with full contact and (b) with partial contact. Note that the grating on the counter electrode is important in the latter case [54]. (https://en.wikipedia.org/wiki/NanogeneratorUsed under CC:BY:SA 3.0 http://creativecommons.org/licenses/by-sa/3.0/.)

Figure 3.26 Schematic view of typical lateral nanowire integrated nanogenerator [54]. (https://en.wikipedia.org/wiki/NanogeneratorUsed under CC:BY:SA 3.0 http://creativecommons.org/licenses/by-sa/3.0/.)

Figure 3.27 Schematic view of typical nanocomposite electrical generator [59]. (https://en.wikipedia.org/wiki/ Nanogenerator Used under CC:BY:SA 3.0 http://creativecommons.org/licenses/by-sa/3.0/.)

Figure 3.28 (a) Piezoelectric motor of William and Brown and (b) the structure of motor core [67].

Figure 3.29 CAD drawing of the miniature ultrasonic piezo motor [74].

Figure 3.30

E

(3,1) modes in a rectangular piezoelectric plate (a) deformation, (b) length oscillation velocity distribution, and (c) height oscillation velocity distribution (FEM simulation) [74].

Figure 3.31 (a) Linear SQUIGGLE motor measures only 1.55 mm × 1.55 mm × 6 mm and (b) SQUIGGLE motor – a vibrating nut turns a screw. (Henderson [75, 76]. Reproduced with permission of New Scale technologies.)

Figure 3.32 SQUIGGLE motor vibration mode shape (called

Hula Hoop wobble

or

orbiting

). (Henderson [75, 76]. Reproduced with permission of New Scale technologies.)

Figure 3.33 Schematic of quartz crystal microbalance [78]. (Reproduced with permission of KSV Instruments Ltd.)

Figure 3.34 Simplified crystal oscillator circuit [79]. (www.electronics-tutorials.ws Reproduced with permission of Electronic Tutorials.)

Chapter 4: Ferroelectricity

Figure 4.1 A polarization versus electric field (

P–E

) hysteresis loop for a typical ferroelectric crystal.

Figure 4.2 Schematic potential well.

Figure 4.3 Plots of spontaneous polarization versus temperature. (a) First-order transition and (b) second-order transition.

Figure 4.4 Ideal domain configuration in a single crystal of cubic ferroelectric material where the coupling to strain is negligible. On the right is the configuration adopted when strain effects are important.

Figure 4.5 Optical micrograph of 90° domains in the single crystal of BaTiO

3

. (Reproduced with permission of American Physical Society.)

Figure 4.6 Asymmetry of the

P–E

hysteresis loop. The ferroelectric hysteresis loop and corresponding footage of the TEM images recorded at various stages of polarization switching (light grey line for positive and dark grey line for negative switching) after poling (black line) to the

P

[001]

polarization. (Lee 2013 [96]. Reproduced with permission of Elsevier.)

Figure 4.7 (a) Series of TEM images and schematic drawing illustrates the domain nucleation at the PZT/Ni interface followed by forward-limited switching and (b) sideways growth-limited switching. (Lee 2013 [96]. Reproduced with permission of Elsevier.)

Figure 4.8 Cubic ABO

3

perovskite-type unit cell and three-dimensional network of corner sharing of O

2−

ions. (Xu 1991 [103]. Reproduced with permission of Elsevier.)

Figure 4.9 Structure of cubic BaTiO

3

. (Ref. [105]).

Figure 4.10 Crystallographic changes of BaTiO

3

. (Kingery 1976 [106]. Reproduced with permission of Wiley.)

Figure 4.11 Dielectric constants of BaTiO

3

as a function of temperature. (Kingery 1976 [106]. Reproduced with permission of Wiley.)

Figure 4.12 Frequency dependence of relative dielectric constant in pure BaTiO

3

. (Benlahrache 2006 [118]. Reproduced with permission of Elsevier.)

Figure 4.13 Multilayer BaTiO

3

ceramic capacitor [121].

Figure 4.14 Positive temperature coefficient BaTiO

3

thermistor [124].

Figure 4.15 (a) Scheme of the as-developed NG. (b) SEM image of the BaTiO

3

nanotubes/PDMS composite. (c) TEM image of the synthesized BaTiO

3

nanotubes. (d) HRTEM image of the synthesized BaTiO

3

nanotubes. (e) Raman spectrum of the synthesized BaTiO

3

nanotubes. (Lin 2012 [74]. Reproduced with permission of American Physical Society.)

Figure 4.16 Nanogenerator fabrication and energy harvesting from mechanical deformation. (a) (i–iii) Schematics of the fabrication process for a nanogenerator device. (iv) Photograph of the final nanogenerator and (v) SEM micrograph of well-entangled BTO nanocrystal clusters in the PDMS matrix. (b) The measured (i) short-circuit current and (ii) open-circuit voltage signals of the virus-templated nanogenerator device in both forward and reverse connections. (c) The mechanism of energy harvesting from the nanogenerator device. (Jeong 2013 [75]. Reproduced with permission of American Chemical Society.)

Figure 4.17 Structure of SrTiO

3

at room temperature.

Figure 4.18 The BST unit cell in ferroelectric phase. (Johnson 1965 [144]. Reproduced with permission of American institute of Physics.)

Figure 4.19 Temperature dependence of dielectric constant of Ba

0.7

Sr

0.3

TiO

3

ceramic and thin films. (Shaw 1999 [145]. Reproduced with permission of American Institute of Physics.)

Figure 4.20 Assembled band-pass filter [150].

Figure 4.21 Structure of PbTiO

3

above and below the phase transition temperature.

Figure 4.22 The PZT phase diagram. (Jaffe 1971 [152]. Reproduced with permission of Elsevier.)

Figure 4.23 The effect of composition on the dielectric constant and electromechanical coupling factor

k

p

in PZT ceramics [180].

Figure 4.24 Schematic diagram of cantilever actuator in (a)

d

31

mode and (b)

d

33

mode (they are not drawn to scale). (Zhang 2003 [188]. Reproduced with permission of Elsevier.)

Figure 4.25 (a) Schematic view of the PZT nanofiber generator. (b) Scanning electron microscopy (SEM) image of the PZT nanofiber mat across the interdigitated electrodes. (c) Cross-sectional SEM image of the PZT nanofibers in the PDMS matrix. (d) Cross-sectional view of the poled PZT nanofiber in the generator. (e) Schematic view explaining the power output mechanism of the PZT nanofibers working in the longitudinal mode. The color presents the stress level in PDMS due to the application of pressure on the top surface. (Chen 2010 [79]. Reproduced with permission of American Chemical Society.)

Figure 4.26 Fabrication process and structure characterization of the NG. (a–c) Experiment setup for fabricating the high-output NG using the regionally orientated electrospinning nanofibers. (d) Field emission scanning electron microscope (SEM) image of the regionally oriented electrospinning PZT nanofibers. (e) Top-view SEM images of the fabricated VANA. (f–h) Optical photographs of VANA under different deformations that show its flexibility and robustness. (Gu 2013 [82]. Reproduced with permission of American Chemical Society.)

Figure 4.27 Room-temperature phase diagram of the PLZT system. The regions in the diagram are, a tetragonal ferroelectric phase (

F

T

); a rhombohedral ferroelectric phase (

F

R

); a cubic relaxor ferroelectric phase (

F

C

); an orthorhombic antiferroelectric phase (

A

O

), and a cubic paraelectric phase (

P

C

). (Haertling 1987 [190]. Reproduced with permission of Taylor and Francis.)

Figure 4.28 Dielectric constant of PLZT as a function of temperature. (Haertling 1987 [190]. Reproduced with permission of Taylor and Francis.)

Figure 4.29 Representative hysteresis loops obtained for different ferroelectric compositions (a)

F

T

, (b)

F

R

, (c)

F

C

, and (d)

A

O

regions of the PLZT phase diagram. (Haertling 1987 [190]. Reproduced with permission of Taylor and Francis.)

Figure 4.30 Fluorescent lamp supplier PLZT-based disk-type piezoelectric transformer. (Kozielski 2001 [206]. Reproduced with permission of University of Silesia.)

Figure 4.31 Variation of the dielectric properties of PMN with temperature. (Moulson 1990 [207]. Reproduced with permission of Wiley.)

Figure 4.32 Phase diagram of the PMN-PT solid solution system. (Zhao 1995 [214]. Reproduced with permission of Japanese Journal of Applied Physics.)

Figure 4.33 Dielectric constant and dielectric loss of PMN-PT as a function of temperature [215]. (Reproduced with permission of Boston Applied Technologies.)

Figure 4.34 Stacked FA (a) the 2D diagram of the stacked FA, (b) the 3D diagram of the stacked FA, and (c) a picture of the prototyped stacked FA. (Xu 2013 [216]. Reproduced with permission of American Institute of Physics.)

Figure 4.35 Fabrication process for the PMN-PT nanowire-based nanocomposite and device. (a) Photos of the PMN-PT nanowires, PDMS, and final device, as well as schematics of the electrodes and device. (b) SEM image of the cross section of the PMN-PT nanocomposite. (c) SEM image of an individual hierarchical PMN-PT nanowire structure embedded in PDMS. (Xu 2013 [93]. Reproduced with permission of American Chemical Society.)

Figure 4.36 The rhombohedral structure of KNbO

3

. Five coordination shells are around central Nb atom. Different shades of gray indicate inequivalent O

(1)

and K

(2)

sites relative to central Nb. (Frenkel 1998 [219]. Reproduced with permission of American Institute of Physics.)

Figure 4.37 Sequence of symmetry changes as KNbO

3

is cooled. The black arrow denotes the direction of spontaneous polarization (displacement of Nb). (Jundt [221]. Reproduced with permission of Jundt.)

Figure 4.38 Schematic phase diagram near KNbO

3

. (Kimura 2006 [237]. Reproduced with Elsevier.)

Figure 4.39 (a) Schematic diagram and (b) cross-sectional SEM image of the KNbO

3

–PDMS composite nanogenerator. In the insets of (a) and (b), we show a photograph of the flexible device and the enlarged SEM image of KNbO

3

nanorods (white spots) inside PDMS (black background). Piezoelectric/ferroelectric domains (c) before and (d) after electric poling. The light grey and white arrows indicate the direction of electric polarization and the directional component along the applied electric field (

E

), respectively. (e) Piezoelectric potential after the compressive strain

F

(

t

). The (+) and (−) indicate the sign of accumulated charges at each end of the nanorod. (Jung 2012 [91]. Reproduced with permission of Institute of Physics Publishing.)

Figure 4.40 Schematic crystal structures of cubic and orthorhombic NaNbO

3

. (Sakowski-Cowley 1969 [239]. Reproduced with permission of IUCR.)

Figure 4.41 Frequency dependence of real (ϵ′) and imaginary (ϵ″) part of dielectric permittivity of NaNbO

3

crystals. (Konieczny 1998 [250]. Reproduced with permission of Institute of Condensed matter Physics.)

Figure 4.42 (a) Photograph of obtained NaNbO

3

nanowires after one time reaction. (b) Piezoelectric device scheme. Yellow, blue, and light blue layers correspond to the Au/Cr-coated Kapton film, NaNbO

3

–PDMS composite, and PS film, respectively. We show the photograph of a flexible NG device (inset). (c) Top-view optical microscope (left) and cross-sectional SEM (right) image of the device. (d) Schematics of the piezoelectric power generation mechanism. Top: alignment of dipoles after poling. Individual nanowire has ferroelectric (piezoelectric) domains with different electric dipoles. Each dipole (light grey arrow) has a component parallel to the electric field (light grey arrow). Bottom: accumulation of free carriers in electrodes after compressive strain. (Jung 2011 [90]. Reproduced with permission of American Chemical Society.)

Figure 4.43 Schematic diagram shows a projection of the tungsten bronze structure on the (001) plane. The orthorhombic and tetragonal cells are shown by solid and dotted lines, respectively. (Xu 1991 [103]. Reproduced with permission of Elsevier (North Holland publisher).)

Figure 4.44 The crystal structure of SrBi

2

Ta

2

O

9

. (Jain 2000 [299]. Reproduced with permission with Elsevier.)

Figure 4.45 Stereoscopic view (to be viewed with crossed eyes) of the LiNbO

3

crystal structure. Light gray: oxygen; small dark spheres: lithium; larger dark spheres: niobium. Oxygen octahedrons and triangles are indicated by sticks. (Xue 2000 [326]. Reproduced with permission of Elsevier.)

Figure 4.46 Schematic of a simple SAW band-pass filter. (D.H. Jundt [221].)

Figure 4.47 An apodized electrode pattern for interdigital transducer. (D.H. Jundt [221].)

Figure 4.48 TGS structure in paraelectric and ferroelectric phases. (Choudhury 2004 [336]. Reproduced with permission of Springer.)

Figure 4.49 Schematic representation of (a) AFE phase of ADP, (b) hypothetical FE phase in ADP, and (c) FE phase of KDP [338]. The structures are shown from a top (

z

-axis) view. Acid H-bonds are shown by dotted lines, while in case (a) short and long NH⋯O bonds are represented by short-dashed and long-dashed lines, respectively. Fractional

z-

coordinates of the phosphate units are also indicated in (a). (http://www.intechopen.com/books/ferroelectrics-characterization-and-modeling/ab-initio-studies-of-h-bonded-systems-the-cases-of-ferroelectric-kh2po4-and-antiferroelectric-nh4h2p. Used under CC BY-NC-SA 3.0 license: https://creativecommons.org/licenses/by-nc-sa/3.0/.)

Figure 4.50 Schematic lateral view of the atomic motions (solid arrows) happening upon off-centering of the H-atoms that correspond to the FE mode pattern in KDP [338]. Also shown are the concomitant electronic charge redistributions (dotted curved arrows) and the percentages of the total charge redistributed between different orbitals and atoms. (http://www.intechopen.com/books/ferroelectrics-characterization-and-modeling/ab-initio-studies-of-h-bonded-systems-the-cases-of-ferroelectric-kh2po4-and-antiferroelectric-nh4h2p. Used under CC BY-NC-SA 3.0 license: https://creativecommons.org/licenses/by-nc-sa/3.0/.)

Figure 4.51 Molecular structure of ferroelectric polymer (a) PVDF and (b) P(VDF-TrFE) [358]. (Reproduced with Institute of Electronics Engineers of Korea.)

Figure 4.52 The employment of topographic patterned bottom electrode (a) Scheme of P(VDF-TrFE) capacitor with etched Al. (b) Top view of an etched Al electrode from a tapping mode atomic force microscopy [372]. (Reproduced with Institute of Electronics Engineers of Korea.)

Figure 4.53 Schematic of EMFi transducer with diameter 2

R

. (Kressmann 2001 [379]. Reproduced with permission of American Institute of Physics.)

Figure 4.54 (a) Motions of the unimorph when the applied electrical field is increasing from 0 up to 60 V µm

−1

. The electric field is equal to 0 V µm

−1

for the upper view on the left side. Then the views from the left to the right. (b) From the left to the right and from the top to the bottom, the motions of the unimorph are displayed when the applied electrical field is increasing to a maximum value of 50 V µm

−1

and decreasing to 0 V µm

−1

. (Xia 2006 [380]. Reproduced with permission of Elsevier.)

Figure 4.55 (a) Schematic drawing of the microfluidic pump using P(VDF-TrFE) as the active polymer material. The planar pump operation is based on the rectifying action realized using the two nozzle/diffuser structures. (b) Cross-sectional view of the nozzle–diffuser pump along the line

A–A

shown in (a). The unimorph structure has electrode only in the pump chamber area with two 20 µm thick PVDF active layers bonded onto a 40 µm thick inactive layer. (c) 3D view of the rectangular nozzle/diffuser elements with labels of the various parameters characterizing the nozzle/diffuser structures after. (Xia 2006 [380]. Reproduced with permission of Elsevier.)

Figure 4.56 Scheme of the liquid-filled varifocal lens [381].

Figure 4.57 Characterization of PVDF thin film NGs. (a) Schematic setup for characterizing PVDF thin film NGs for harvesting mechanical energy from surface oscillations. The mesoporous PVDF thin-film weight system can be simplified as a free vibration system with damping, as shown in the inset. (b) The voltage output of a PVDF thin film NG (fabricated from a 50% ZnO mass fraction mixture) generated during one cycle of surface oscillation. The top and bottom curves were collected under forward and reverse connections, respectively. (c) The output voltage and (d) the output current of the PVDF NG under continuous surface oscillation. Insets show the output curve features during one cycle of surface oscillation. (Mao 2014 [390]. Reproduced with permission of Wiley.)

Figure 4.58 Cross-sectionlview of the embedded film capacitor and its advantages [406–408].

Figure 4.59 Manifestation of polarization in (a) an ordered ferroelectric crystal, (b) a dipolar electret, and (c) a space-charge electret. (Reproduced with permission of IEEE.)

Figure 4.60 Small electret microphone [438]. (https://en.wikipedia.org/wiki/Electret_microphone. Used under CC:BY:SA 3.0 https://creativecommons.org/licenses/by-sa/3.0/ license.)

Figure 4.61 Schematic illustration of an ideal case of the ME coupling in the composite multiferroics, that is, there is a magnetic response to an electric field (

M–E

hysteresis response) and vice versa; the modification of polarization by magnetic field (

P–H

behavior).

Figure 4.62 Schematics of a multiferroic 4-bit memory spin valve involving a non-ME FM-FE LBMO tunneling barrier, a LSMO fixed magnetization layer, and an Au sink electrode. Four different currents 1, 2, 3, and 4 are due to independently field-switchable TMR and TER values. (Gajek 2007 [469]. Reproduced with Nature Publishing Group.)

Figure 4.63 Schematics of the electric control of the easy axis of CoFe magnetization via multiferroic domain switching of BiFeO

3

. (Chu 2008 [473]. Reproduced with permission of Nature Publishing group.)

Figure 4.64 Counterclockwise spin spiral of TbMnO

3

promoting an upward directed electric polarization by forced oxygen displacements. (Kimura 2008 [475]. Reproduced with permission of Institute of Physics.)

Figure 4.65 (a) Backscattering emission image obtained by SEM for the PZT-PZN-NZF composite sintered at 1200 °C for 2 h with different NZF ball-milling times. (b) Magnetoelectric properties (dE/dH) of PZT-PZN-NZF composite sintered at 1200 °C for 2 h. (Ryu 2011 [495]. Reproduced with permission of The Japan Society of Applied Physics.) (c) ME voltage coefficient as a function of applied dc magnetic bias field for the composites (1 −

x

)PZT–

x

NCCF. (Ramanna 2009 [494]. Reproduced with permission of Elsevier.)

Figure 4.66 (a) Schematic illustration and the typical micrograph of the fractured surface of the laminated TPT composites. TFD denotes Terfenol-d. (b) The ME sensitivity α

E

values measured at resonance frequency (

f

r

) for the laminated composites as a function of the bias magnetic field at the measuring angle θ = 90°. In the legend 1, 2, 3, 4, 5 correspond to 1/7, 2/7, 3/7, 4/7, 5/7 (

t

p

/L

) ratio, respectively, for various TPT laminated samples. (Lin 2005 [503]. Reproduced with permission of American Institute of Physics.)

Figure 4.67 Schematics of an ME composite consisting of two magnetostrictive FeBSiC layers and a piezoelectric periodically poled PZT piezofiber layer intercalated by Kapton films [512].

Figure 4.68 (a) Schematic configuration of P(VDF-HFP)/Metglas laminate. The polymer film was smaller in area than the Metglas and placed at the central area, optimizing the magnetic flux effect. (b) ME coefficient of hot-pressed P(VDF-HFP)/Metglas laminates as a function of DC magnetic field for conventional poling. The ME coefficient versus DC magnetic field for cyclic poling (

E

p

= 225 V m

−1

for extruded film) is also shown. (Lu 2011 [506]. Reproduced with permission of Applied Physics Letters.)

Figure 4.69 Schematic crystal structures of (a) BiFeO

3

with rhombohedral

R

3

c

symmetry, (b) BiMnO

3

with monoclinic

C

2/

c

symmetry, and (c) YMnO

3

with hexagonal

P

6

3

cm

. (Roy 2012 [515]. Hindawi Publishing Corporation.)

Figure 4.70 Schematic view of a MERAM cell based on ME Cr

2

O

3

(0001) controlling the magnetization of the Pt/Co/Pt trilayer FM1 via voltages ±

V

0

and constant magnetic stray field

H

0

of NdFeB thick film FM2.

R

± is the corresponding giant (or tunneling) magnetoresistance along FM1/NM(Cu or MgO)/FM2 [549, 550].

Figure 4.71 Schematic design of the proposed eight-logic memory cell. MF indicates multiferroic and FM represents ferromagnetic layers. (Yang 2009 [554]. Reproduced with permission of Institute of Physics.)

Chapter 5: Ferroelectric Ceramics: Devices and Applications

Figure 5.1 Applications of bulk and film ceramic electronic materials.

Figure 5.2 Variety of ferroelectric ceramics used in piezoelectric and electrostrictive applications, such as sonar, accelerometers, actuators, and sensors.

Figure 5.3 Examples of PZT, PLZT, and PMN piezoelectric and electrostrictive devices (starting at upper right and going clockwise): Motorola tweeter, triangle gas-grill lighter, Motorola bimorph, Murata intermediate-frequency resonators, Morgan Matroc ultrasonic cleaner ceramics, Aura RAINBOW ceramics, Itek PMN actuator, ferroelectric film memory, Kodak PLZT E/O device, RAINBOW mouse toy actuator, Moonie actuators, Radio Shack buzzer, and unimorphs.

Figure 5.4 Phase diagram of the PZT and PLZT solid-solution systems.

Figure 5.5 Partial image of the 100 × 100 thermopiezoelectric cantilever array (LG Electronics).

Figure 5.6 Process flow for the fabrication of suspended membranes.

Figure 5.7 Performance of two-section π filter based on AlN SMR. The measured S12 scattering parameters in (a) give insertion loss of 7 dB with bandwidth of 200 MHz for central frequency of 7.9 GHz. (b) The resonance of a single resonator (30 µm

2

) gave coupling coefficient of 5.9% and

Q

factor of 460.

Figure 5.8 (a) Parallel-plate and (b) coplanar-plate ferroelectric varactors.

Figure 5.9 (a) Schematic diagrams of 1T1C and (b) 2T2C FRAM bit cells.

Figure 5.10 Scanning electron microscope cross-sectional image of a 1T1C COFO FRAM cell for 256 kbyte memory manufactured on a 0.35 µm three-level Al CMOS process.

Figure 5.11 Scanning electron microscope cross-sectional image of several 1T1C COP FRAM cells for a 4 Mbyte memory manufactured on a 0.13 µm five-level Cu CMOS process.

Figure 5.12 Sketch of the simplified band structure of a ferroelectric tunnel junction. The unit cell represents the ferroelectric (BaTiO

3

) tunnel barrier. The two possible polarization states (related to the position of the Ti atom) are labeled by (1) and (2).

E

F

is the Fermi energy, χ is the electron affinity of the ferroelectric,

t

is the barrier thickness, and φ

1

and φ

2

are the barrier heights at the bottom and top electrodes, respectively.

Figure 5.13 Possible effects on the tunneling current due to the ferroelectric nature of the tunnel barrier. (a) The strain versus voltage curve (butterfly curve) may modify the thickness of the barrier and therefore the band structure; (b) the local position of the oxygen atoms and the Ti atoms may lead to a modified work function of the adjacent metal in dependency of the polarization (only one interface is shown); and (c) screening effects due to incomplete screening of the bound charge by free carriers result in a finite depolarization field. Consequently the contact potential will be modified.

Figure 5.14 Charge distribution at the two MF interfaces of an FTJ (a). The potential is shown in (b), and the solid and dotted lines show how the potential changes when the polarization points to the right and left, respectively. In (c) the two possible

I–V

curves including the resistive switching events are shown. The left

I–V

curve is for a symmetric interface case (i.e., a potential as shown in (b)), whereas the right

I–V

shows an asymmetric case. The dotted circles highlight the fundamental difference between both curves.

Figure 5.15 (a) Experiment of a piezoresponse system (SFM) to detect the deformation of the cantilever in

x-

,

y-

, and

z-

directions, a feedback loop, and an AC reference generator. (b) Example of small dots and the domain radius versus pulse duration width.

Figure 5.16 (a) Schematic circuit diagram of In

2

O

3

nanowire FeFET and (b) characteristics of PZT-gated In

2

O

3

NW transistor. The PZT-gated In

2

O

3

NW transistor with

V

DS

= −0.1 V shows pronounced hysteresis. “1” and “0” denote two states at

V

G

= 0 V for the memory operation.

Figure 5.17 ZnO NW FeFET device. (a) Schematics of the device configuration. (b) SEM image of a single device. (c) Corresponding band diagram showing the gate effect. (d) Idealized field-effect model of the ZnO NW FeFET device at “off” and “on” states, without considering surface and interface trap charges.

Figure 5.18 Schematic views of ZnO NW FET and polarization model for FE NPs surrounding a NW. (a) A schematic view of a top-gate FET-based nonvolatile memory device. For a top-gate ZnO NW FET where a ZnO NW is incorporated with FE NPs, cross-linked poly(4-vinylphenol) (c-PVP) was used as a gate dielectric. (b,c) The schematic views of a simplified polarization model for FE NPs surrounding an NW.

Figure 5.19 Hysteresis behaviors of top-gate NW FET and the switching characteristics. (a) Hysteresis behaviors of a top-gate NW FET as a function of the sweep range of gate voltages. Compared with the hysteretic behavior of a back-gate FET with a clockwise hysteresis loop, devices with the top-gate structure show a counterclockwise hysteresis loop, confirming that the origin of such hysteretic behaviors is due to the polarization of FEs. Arrows indicate gate voltage sweep directions. (b) Switching characteristics of a device with a top-gate structure measured with

V

DS

= 0.1 V and

V

G

= 0 V, clearly showing that a FeFET functions as a 2-bit memory with four different conductance states defined as 00, 01, 10, and 11 after the application of gate voltage pulses of −25, +12, +15, and +25 V, respectively.

Figure 5.20 Schematic illustration of nanotetrapod transistor and images of CdS nanotetrapod and the fabricated device. (a) Schematic illustration of a nanotetrapod transistor with a 300 nm thick ferroelectric dielectric under testing with scanning tunneling microscope (STM) tips. The source (S) and drain (D) electrodes are the patterned Pt layer. (b) Typical TEM image of the multiarmed CdS nanotetrapod used in this study. (c) The enlarged micrograph of a single CdS nanotetrapod. (d) SEM image of a single CdS nanotetrapod device. (e)

In situ

SEM image of two STM tips (shown in white) probing on a testing device.

Figure 5.21

I–V

G

transfer characteristics [146]. Typical

I–V

G

transfer characteristic was measured at (a) 300, (b) 140, (c) 80, and (d) 8.5 K (with

V

DS

= 2 V for (a) to (c);

V

DS

= 50 mV for (d)). In (a), a counterclockwise hysteresis loop occurs at room temperature due to a charge-store effect. In (b), at 80 K, a clockwise hysteresis loop is opened, indicating a nonvolatile memory operation. In (c), a competition between the ferroelectric effect and the charge storage effect essentially closes the memory window at 140 K. In (d), at 8.5 K, a ferroelectric-modulated SET behavior is observed. The two circles represent a bistable (“on” and “off”) state. The sharp increase at a gate voltage of −6 V is due to the leakage current.

Figure 5.22 Schematic sketch and TEM images of the CNT FeFET and the

I

D

–

V

G

transfer characteristics. (a) Schematic sketch of the fabricated CNT FeFET. (b) Structural characterization of BaTiO

3

thin films deposited on STON substrates by TEM, indicating the coherent epitaxial growth of the BaTiO

3

thin film with respect to the STON substrate. (c) Typical

I

D

–

V

G

transfer characteristics of the CNT FeFET made up of SWCNT with 600 nm in length. The arrows indicate a clockwise hysteresis loop.

Figure 5.23 Transfer characteristics of the device and calculated electric field mappings around the SWCNT channel. (a) Transfer characteristics of the FeFET memory unit with a 300 nm SWCNT as conducting channel. (b,c) Calculated electric field mappings around the SWCNT channel at 1 and 0.1 V gate voltages, respectively. The red dashed line in the scale bar indicates the measured coercive electric field of the ferroelectric film.

Figure 5.24 Scheme of the fabrication of the two top-gate FeFETs assembled on a single nanotube. (a) A CNT FET fortuitously composed of an individual nanotube. (b) Coating of amorphous ferroelectric at room temperature onto the top of CNT FET by using PLD. (c) After annealing, double-top electrodes (G1 and G2) made up of Pt were patterned in series onto the deposited ferroelectric films. (d) SEM image of the double top-gate CNT FeFET memory. (e) The schematic sequential chart for G1/G2 and the programming of the two top-gate CNT FeFET memory.

Figure 5.25 Schematic diagram and AFM image of a finished memory device. (a) Sample geometry of a finished memory device. (b) AFM image of the memory device. The contrast comes from the slightly different crystallization of PVDF-TrFE on SiO

2

, graphene, and Au electrodes, respectively.

Figure 5.26 Electrical switch characteristics of the fabricated device. (a) Resistance hysteresis loop. The black curve represents the experimentally measured

D

of the PVDF-TrFE thin film with similar thickness. Inset (a) The electric displacement continuity equation at ferroelectric–graphene interface. Inset (b): a polarized PVDF-TrFE molecule. The fluorine(F-), carbon(C) and hydrogen(H+) atoms are represented. (b) Electric hysteresis loop.

R

is used as a function of

V

TG

for the graphene–ferroelectric sample. From the linear part of this curve at high voltage, the charge carrier mobility is estimated to be 700 cm

2

V

−1

s

−1

, taking

k

PVDF

= 10. (c) Switching from 0 to 0 state in graphene–ferroelectric memory by a full loop sweep of

V

TG

(±85 V). (d) Switching from 1 to 1 state by an asymmetrical loop sweep of

V

TG

from (85 to −34 V). (e) Switching from 0 to 1 state. (f) Switching from 1 to 0 state.

Figure 5.27 Integrated nanogenerator schematic with vertically aligned ZnO nanowires on a gold-coated flat surface. Both electrodes are separated by a PMMA layer. A platinum-coated flat electrode is placed on top of the nanowires. The SEM image of the nanowire array immersed in PMMA with its tips exposed greatly improved the robustness of the structure and the corresponding voltage of the system generated due to exposure to mechanical forces.

Figure 5.28 Integration of laterally aligned nanowires. Schematic, voltage generated, current generated, and SEM image (clockwise).

Figure 5.29 Phase shift ϕ with respect to applied voltage

V

.

Figure 5.30 (a) Transverse and (b) longitudinal modulators.

Figure 5.31 An integrated optical phase modulator.

Figure 5.32 An integrated optical intensity modulator (or optical switch). A Mach–Zehnder interferometer and an electro-optic phase modulator are implemented using optical waveguides fabricated from a material such as LiNbO

3

.

Figure 5.33 Schematic representation of the ridge waveguide modulator structure.

Figure 5.34 The geometry of the

c

-axis optical modulator for optical switching device.

Figure 5.35 Schematic of KTN crystal waveguide based electro-optic phase modulator.

Figure 5.36 Typical configuration of an electro-optic deflector. (a) EOD based on refraction at the interface(s) of an optical prism.

Figure 5.37 (a) Space-charge-controlled high-speed KTN deflector and (b) structure of wavelength swept light sources [198].

Figure 5.38 (a) A schematic design of TFL and (b) a fiber-version four-stage TLF with driving circuit.

Figure 5.39 (a) TLF responses when three stages were powered and (b) transmission spectra of a TFPF.

Figure 5.40 Measured outputs of a composite TFPF with different applied voltages.

Figure 5.41 Configuration of a

Q

-switched DPSS laser.

Figure 5.42 Pulse width and repetition rate of a

Q

-switch made from an opto-ceramic PMN-PT.

Figure 5.43 Schematic of the VOA construction and an Eclipse™ VOA device.

Figure 5.44 Optical modulation of a VOA at 1 MHz.

Figure 5.45 Schematics of a polarization controller design and an Acrobat™ polarization controller.

Figure 5.46 A screen print of the measurement of a PC.

Figure 5.47 Schematic of a sinusoidal filter and an Equinox™ VGTF.

Figure 5.48 Measured results of a 24 nm sine filter.

Figure 5.49 Equinox™ DGFF.

Figure 5.50 Fitting of a DGFF consists of five sine filters and a VOA.

Figure 5.51 The configuration of the measurement system.

Figure 5.52 The structure of the sensor: (a) top view and (b) cross-sectional view.

Figure 5.53 The structure of the sensors: (a) two electrodes connected with vertical dipole antennas design; (b) horizontal dipole antennas combined with electrodes design; and (c) mono- shield electrode design.

Figure 5.54 Mono-shielding electrode: optimized as a grid type. (a) Schematic of the sensor and (b) micrograph of the fabricated electrode [226].

Figure 5.55 (a) Schematic of CI-based IOES and (b) sensor after encapsulation.

Figure 5.56 The CPI-based IOES with dipole antenna and electrode [229]. (a) Schematic of the sensor and (b) fabricated sensor with dimensions of 5 × 1.2 × 0.5 cm

3

.

Figure 5.57 Single-crystal photoelastic modulator (SCPEM) made up of a 3 m crystal.

Figure 5.58 Course of amplitude (top) and phase (bottom) of current and deformation at one typical resonance of a piezoelectric element against normalized frequency.

Figure 5.60 Voltage course on the crystal (1), current signal of the crystal (2), measured transmission for the pumping light (dark grey) and estimated transmission for the laser light (light grey ) (3), and optical output of the laser (4).

Figure 5.59 Setup of a fiber laser with SCPEM

Q

-switch. Two photo detectors are used simultaneously in order to detect both the transmittance of the SCPEM and the output pulses of the laser.

Figure 5.61 (a) Arrangement for recording light-induced waveguide structures. (b) Simplified electric field (dashed light grey) and refractive index (solid dark grey) distribution in a photorefractive crystal during the formation of the waveguides.

Figure 5.62 (A) CCD images of the output face of a 6.8 mm long SPS crystal without (a) and with (b) a photoinduced waveguide. (B) Buildup times τ

b

of the light-induced waveguide as a function of the controlling light intensity.

Figure 5.63 Schematic diagram of the fabricating technique for array of 3D-WGs. BP-Fresnel's biprism, LN-LiNbO

3

crystal. Insets 1 and 2 show the intensity patterns propagating along the

x-

and −

x-

axis, respectively. Inset 3 depicts the index variations in the waveguide array; (a,b) for Λ

1

= Λ

2

, θ = 45°; (c) for Λ

1

= Λ

2

, θ = 20°; and (d) for Λ

1

= 2Λ

2

, θ

=

45°.

Figure 5.64 Experimental setup for fabricating an array of rectangular waveguides in LiNbO

3

:Fe. DPL, diode pumped solid-state laser; T, telescope; BP, Fresnel's biprism;

I

total

, total intensity for illuminating the crystal.

Figure 5.65 Experimental results for fabricating an array of rectangular waveguide. (a,b) The intensity patterns for the first and second exposures, respectively; (c) the near-field pattern of the waveguide array; (d) 2D index map of the waveguide array; (e,f) the holograms, which are used for index profile measurement, before and after waveguide fabrication respectively; (g) the index profiles along the horizontal and the vertical arrows in (d), top for vertical, bottom for horizontal; and (h) 3D display of the 2D index distribution of the waveguide array.

Figure 5.66 Experimental setup for guiding tests of the waveguide array. T, telescope; LN, LiNbO

3

:Fe crystals; CCD, charge-coupled device camera.

Figure 5.67 Experimental results for guiding tests of the waveguide array. (a,b) Light intensity patterns without and with guidance, respectively, and (c) light intensity profiles along the white lines in (a) and (b), dashed line for (a), solid line for (b).

Figure 5.68 Schematic top view of the experimental setup. The recording beams are directed to the crystal from the top by means of a 45° inclined mirror, as can be better seen by the view from direction

A

shown in the inset.

Figure 5.69 Grating configuration and angle convention used in this work. Top view at the

bc

-plane of the KNbO

3

crystal, where all

k

-vectors are lying in this plane. The angles are internal to the crystal. If

K

is changed by Δ

K

by tuning the grating,

k

R

has to change by Δ

k

R

in order that the Bragg condition is still fulfilled.

Figure 5.70 Bragg wavelength as function of the frequency applied to the acousto-optic deflector and of the corresponding grating mismatch Δ

K

for the central wavelength.

Figure 5.71 Wavelength selectivity scan for three different grating vectors separated by 0.4 nm (50 GHz). The three peaks are obtained using three different frequencies applied to the acousto-optic deflector mutually separated by 13.4 MHz, corresponding to a grating mismatch of Δ

K

= 40 cm

−1

. The solid lines are guides to the eye.

Figure 5.72 Measured diffraction signal as a function of the grating spacing at fixed readout wavelength λ

R

= 1550 nm. To determine the tuning times of the optical filter, the diffraction signal was recorded while tuning the grating from point

A

to point

B

and vice versa. The solid line is a guide to the eye.

Figure 5.73 (a) Time development of the diffraction efficiency for tuning-in and tuning-out for

I

R

= 3.9 mW cm

−2

. (b) Tuning time of the holographic reflection grating as a function of the average total recording intensity at the crystal surface.

Figure 5.74 Schematic diagram of the experimental setup. BS represents a beam splitter,

I

0

is the input power,

I

t

is the power of the transmitted beam,

I

pc

is the output power of the phase-conjugate beam, θ

0

is the incident angle outside the crystal, and θ

i

and θ

f

are propagation angles of the incident beam and fanning beam relative to the

x-

axis, respectively, inside the crystal.

Figure 5.75 Temporal evolutions of the transmitted power

I

t

and of the output phase-conjugate power

I

pc

under no applied electric field. The input power

I

0

is turned on at

t

= 0.

Figure 5.76 (a,b) Temporal evolution of the transmitted power

I

t

with an AC-square-form external voltage applied to the crystal after the system reaches the steady state. Panel (c) is the elongation of (b) along the time axis.

Figure 5.77 Temporal evolution of the output phase-conjugate power

I

pc

with an AC square-form external voltage applied to the crystal after the system reaches its steady state.

Figure 5.78 (a)

I

t

(

V

)/

I

t

(0) and (b)

I

pc

(

V

)/

I

pc

(0) as a function of the applied voltage

V

for incident angle θ

0

= 30° (lines with filled rhombuses), θ

0

= 2.5° (lines with unfilled squares), and θ

0

= −30° (lines with filled triangles).

Figure 5.79 Real-time holographic interferometry with photorefractive BSO crystals setup, where the light source is an argon laser (λ = 514.5 nm); M1, M2, M3, M4 are mirrors; BS1, BS2, BS3 are beam splitters; SF1, SF2 are spatial filters; L1, L2 are lens; O1, O2 are objectives; Po1, Po2 are polarizers; PZL/M is piezoelectric translator + mirror; PD is photodetector; BSO is photorefractive crystal; and CCD is the camera for capture of images [323].

Figure 5.80 Holographic interferograms of a mirror static: (a) θ = 0, (b) θ = π/2, (c) θ = π, and (d) θ = 3π/2. Phase map: (e) wrapped and (f) unwrapped [323].

Figure 5.81 Holographic interferograms of a mirror slopping: (a) θ = 0, (b) θ = π/2, (c) θ = π, and (d) θ = 3π/2. Phase map: (e) wrapped and (f) unwrapped [323].

Figure 5.82 Image of PZO and the connected mirror.

Figure 5.83 Schematic of the photorefractive interferometer based on the two-wave mixing in a BSO crystal.

Figure 5.84 Frequency response of the BSO photorefractive crystal at a laser intensity of 0.1 W cm

−2

.

Figure 5.85 Comparison of the sensitivity of a photorefractive (a) and Michelson interferometer (b) on a mirror surface at 20 kHz.

List of Tables

Chapter 4: Ferroelectricity

Table 4.1 NoTable events in the history of ferroelectricity

Chapter 5: Ferroelectric Ceramics: Devices and Applications

Table 5.1 Piezoelectric and electrostrictive applications for ferroelectric ceramics [1]

Table 5.3 Comparison of 1T1C FRAM capacity, architecture, and critical parameters produced at the 0.5, 0.35, and 0.13 µm technology nodes [43]

Table 5.4 Comparison of performance of different nanogenerators

Table 5.5 Summary of the VOA performance [199]

Table 5.6 Key parameters of polarization controllers [199]

Ferroelectrics

Principles and Applications

Ashim Kumar Bain

Prem Chand

Authors

Prof. Ashim Kumar BainUniversity of BirminghamElectronic, Electrical & Systems EngineeringB15 2TT EdgbastonUnited Kingdom

Prof. Prem ChandIndian Institute of Technology KanpurDepartment of Physics208016 KanpurIndia

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Chapter 1Dielectric Properties of Materials

1.1 Energy Band in Crystals

In crystallography, a crystal structure is a unique arrangement of atoms, ions, or molecules in a crystalline solid. It describes a highly ordered structure, occurring due to the intrinsic nature of its constituents to form symmetric patterns. The crystal lattice can be thought of as an array of “small boxes” infinitely repeating in all three spatial directions. Such a unit cell is the smallest unit of volume that contains all of the structural and symmetry information to build up the macroscopic structure of the lattice by translation. The crystal structure and symmetry play a role in determining many of its physical properties, such as electronic band structure and optical transparency.

To discuss the behavior of electrons in a crystal, we consider an isolated atom of the crystal. If Z is the atomic number, the atomic nucleus has a positive charge Ze. At a distance r from the nucleus, the electrostatic potential due to the nuclear charge is (in SI units)

1.1

where ϵ0 is the permittivity of free space. Since an electron carries a negative charge, the potential energy of an electron at a distance r from the nucleus is

1.2

V(r) is positive, while Ep(r) is negative. Both V(r) and Ep(r) are zero at an infinite distance from the nucleus. Figure 1.1a,b shows the variation of V(r) and Ep(r), respectively, with r.

Figure 1.1 Variation of (a) potential in the field of a nucleus with distance and (b) potential energy of an electron with its distance from the nucleus.

We now consider two identical atoms placed close together. The net potential energy of an electron is obtained as the sum of the potential energies due to the two individual nuclei. In the region between the two nuclei, the net potential energy is clearly smaller than the potential energy for an isolated nucleus (Figure 1.2).

Figure 1.2 Potential energy variation of an electron with distance between two identical nuclei.

The potential energy along a line through a row of equispaced atomic nuclei, as in a crystal, is diagrammatically shown in Figure 1.3. The potential energy between the nuclei is found to consist of a series of humps. At the boundary AB of the solid, the potential energy increases and approaches zero at infinity, there being no atoms on the other side of the boundary to bring the curve down.

Figure 1.3 Potential energy of an electron along a row of atoms in a crystal.

The total energy of an electron in an atom, kinetic plus potential, is negative and has discrete values. These discrete energy levels in an isolated atom are shown by horizontal lines in Figure 1.4a. When a number of atoms are brought close together to form a crystal, each atom will exert an electric force on its neighbors. As a result of this interatomic coupling, the crystal forms a single electronic system obeying Pauli's exclusion principle. Therefore, each energy level of the isolated atom splits into as many energy levels as there are atoms in the crystal, so that Pauli's exclusion principle is satisfied. The separation between the split-off energy levels is very small. A large number of discrete and closely spaced energy levels form an energy band. Energy bands are represented schematically by the shaded regions in Figure 1.4b.

Figure 1.4 Splitting of energy levels of isolated atoms into energy bands as these atoms are brought close together to produce a crystal.

The width of an energy band is determined by the parent energy level of the isolated atom and the atomic spacing in the crystal. The lower energy levels are not greatly affected by the interaction among the neighboring atoms and hence form narrow bands. The higher energy levels are greatly affected by the interatomic interactions and produce wide bands. The interatomic spacing, although fixed for a given crystal, is different for different crystals. The width of an energy band thus depends on the type of the crystal and is larger for a crystal with a small interatomic spacing. The width of a band is independent of the number of atoms in the crystal, but the number of energy levels in a band is equal to the number of atoms in the solid. Consequently, as the number of atoms in the crystal increases, the separation between the energy levels in a band decreases. As the crystal contains a large number of atoms (≈1029 m−3), the spacing between the discrete levels in a band is so small that the band can be treated as continuous.

The lower energy bands are normally completely filled by the electrons since the electrons always tend to occupy the lowest available energy states. The higher energy bands may be completely empty or may be partly filled by the electrons. Pauli's exclusion principle restricts the number of electrons that a band can accommodate. A partly filled band appears when a partly filled energy level produces an energy band or when a totally filled band and a totally empty band overlap.

As the allowed energy levels of a single atom expand into energy bands in a crystal, the electrons in a crystal cannot have energies in the region between two successive bands. In other words, the energy bands are separated by gaps of forbidden energy.

The average energy of the electrons in the highest occupied band is usually much less than the zero level marked in Figure 1.4b. The rise of the potential energy near the surface of the crystal, as shown in Figure 1.4b, serves as a barrier, preventing the electrons from escaping from the crystal. If sufficient energy is imparted to the electrons by external means, they can overcome the surface potential energy barrier and come out of the crystal surface.

1.2 Conductor, Insulator, and Semiconductor

On the basis of the band structure, crystals can be classified into conductors, insulators, and semiconductors.

1.2.1 Conductors

A crystalline solid is called a metal if the uppermost energy band is partly filled or the uppermost filled band and the next unoccupied band overlap in energy as shown in Figure 1.5a. Here, the electrons in the uppermost band find neighboring vacant states to move in and thus behave as free particles. In the presence of an applied electric field, these electrons gain energy from the field and produce an electric current, so that a metal is a good conductor of electricity. The partly filled band is called the conduction band. The electrons in the conduction band are known as free electrons or conduction electrons.

Figure 1.5 Energy band structure of (a) a conductor, (b) an insulator, and (c) a semiconductor.

1.2.2 Insulators

In some crystalline solids, the forbidden energy gap between the uppermost filled band, called the valence band, and the lowermost empty band, called the conduction band, is very large. In such solids, at ordinary temperatures, only a few electrons can acquire enough thermal energy to move from the valence band into the conduction band. Such solids are known as insulators. Since only a few free electrons are available in the conduction band, an insulator is a bad conductor of electricity. Diamond having a forbidden gap of 6 eV is a good example of an insulator. The energy band structure of an insulator is schematically shown in Figure 1.5b.

1.2.3 Semiconductors

A material for which the width of the forbidden energy gap between the valence and the conduction band is relatively small (∼1 eV) is referred to as a semiconductor. Germanium and silicon having forbidden gaps of 0.78 and 1.2 eV, respectively, at 0 K are typical semiconductors. As the forbidden gap is not very wide, some of the valence electrons acquire enough thermal energy to go into the conduction band. These electrons then become free and can move about under the action of an applied electric field. The absence of an electron in the valence band is referred to as a hole. The holes also serve as carriers of electricity. The electrical conductivity of a semiconductor is less than that of a metal but greater than that of an insulator. The band diagram of a semiconductor is given in Figure 1.5c.

1.3 Fermi–Dirac Distribution Function

The free electrons are assumed to move in a field-free or equipotential space. Due to their thermal energy, the free electrons move about at random just like gas particles. Hence these electrons are said to form an electron gas. Owing to the large number of free electrons (∼1023 cm