Etzold K F "Ferroelectric and Piezoelectric Materials The Electrical Engineering Handbook Ed. Richard C. Dorf Boca raton crc Press llc. 2000
Etzold, K.F. “Ferroelectric and Piezoelectric Materials” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
49 Ferroelectric and Piezoelectric materials 49.1 Introduction 49.2 Mechanical Characteristics Applications. Structure of Ferroelectric and Piezoelectric Materials 49.3 Ferroelectric materials K. EEtzold Electrical Characteristics IBM T. I. Watson Research Center 49.4 Ferroelectric and High Epsilon Thin Films 49.1 Introduction Piezoelectric materials have been used extensively in actuator and ultrasonic receiver applications, while ferroelectric materials have recently received much attention for their potential use in nonvolatile(Nv)memory applications. We will discuss the basic concepts in the use of these materials, highlight their applications, and describe the constraints limiting their uses. This chapter emphasizes properties which need to be understood for the effective use of these materials but are often very difficult to research. Among the properties which are discussed are hysteresis and domains. Ferroelectric and piezoelectric materials derive their properties from a combination of structural and elec trical properties. As the name implies, both types of materials have electric attributes. A large number of materials which are ferroelectric are also piezoelectric. However, the converse is not true. Pyroelectricity closely related to ferroelectric and piezoelectric properties via the symmetry properties of the crystals. Examples of the classes of materials that are technologically important are given in Table 49. 1. It is apparent that many materials exhibit electric phenomena which can be attributed to ferroelectric, piezoelectric, and electret materials. It is also clear that vastly different materials(organic and inorganic)can exhibit ferroelec tricity or piezoelectricity, and many have actually been commercially exploited for these properties As shown in Table 49.1, there are two dominant classes of ferroelectric materials, ceramics and organics. Both classes have important applications of their piezoelectric properties. To exploit the ferroelectric property, ently a large effort has been devoted to producing thin films of PzT (lead [Pb] zirconate titanate)on various lbstrates for silicon-based memory chips for nonvolatile storage. In these devices, data is retained in the absence of external power as positive and negative polarization. Organic materials have not been used for their ferroelectric properties. Liquid crystals in display applications are used for their ability to rotate the plane of polarization of light and not their ferroelectric attribute It should be noted that the prefix ferro refers to the permanent nature of the electric polarization in analog with the magnetization in the magnetic case. It does not imply the presence of iron, even though the root of the word means iron. The root of the word piezo means pressure; hence the original meaning of the word piezoelectric implied"pressure electricity-the generation of electric field from applied pressure. This defini tion ignores the fact that these materials are reversible, allowing the generation of mechanical motion by applying a field. c 2000 by CRC Press LLC
© 2000 by CRC Press LLC 49 Ferroelectric and Piezoelectric Materials 49.1 Introduction 49.2 Mechanical Characteristics Applications • Structure of Ferroelectric and Piezoelectric Materials 49.3 Ferroelectric Materials Electrical Characteristics 49.4 Ferroelectric and High Epsilon Thin Films 49.1 Introduction Piezoelectric materials have been used extensively in actuator and ultrasonic receiver applications, while ferroelectric materials have recently received much attention for their potential use in nonvolatile (NV) memory applications. We will discuss the basic concepts in the use of these materials, highlight their applications, and describe the constraints limiting their uses. This chapter emphasizes properties which need to be understood for the effective use of these materials but are often very difficult to research. Among the properties which are discussed are hysteresis and domains. Ferroelectric and piezoelectric materials derive their properties from a combination of structural and electrical properties. As the name implies, both types of materials have electric attributes. A large number of materials which are ferroelectric are also piezoelectric. However, the converse is not true. Pyroelectricity is closely related to ferroelectric and piezoelectric properties via the symmetry properties of the crystals. Examples of the classes of materials that are technologically important are given in Table 49.1. It is apparent that many materials exhibit electric phenomena which can be attributed to ferroelectric, piezoelectric, and electret materials. It is also clear that vastly different materials (organic and inorganic) can exhibit ferroelectricity or piezoelectricity, and many have actually been commercially exploited for these properties. As shown in Table 49.1, there are two dominant classes of ferroelectric materials, ceramics and organics. Both classes have important applications of their piezoelectric properties. To exploit the ferroelectric property, recently a large effort has been devoted to producing thin films of PZT (lead [Pb] zirconate titanate) on various substrates for silicon-based memory chips for nonvolatile storage. In these devices, data is retained in the absence of external power as positive and negative polarization. Organic materials have not been used for their ferroelectric properties. Liquid crystals in display applications are used for their ability to rotate the plane of polarization of light and not their ferroelectric attribute. It should be noted that the prefix ferro refers to the permanent nature of the electric polarization in analogy with the magnetization in the magnetic case. It does not imply the presence of iron, even though the root of the word means iron. The root of the word piezo means pressure; hence the original meaning of the word piezoelectric implied “pressure electricity”—the generation of electric field from applied pressure. This definition ignores the fact that these materials are reversible, allowing the generation of mechanical motion by applying a field. K. F. Etzold IBM T. J. Watson Research Center
TABLE 4 lectric Piezoelectric, and Electrostrictive materials Type Material Class Example Applications Electret Electret Organic Fluorine based Ferroelectric No known Ferroelectric PZT thin film Organic PVF2 PLZT Single cry LiNbO Electrostrictive Ceramic PMN 49.2 Mechanical characteristics Materials are acted on by forces(stresses)and the resulting deformations are called strains. An example of a strain due to a force to the material is the change of dimension parallel and perpendicular to the applied force. It is useful to introduce the coordinate system and the numbering conventions which are used when discussing these materials. Subscripts 1, 2, and 3 refer to the x, y, and z directions, respectively. Displacements have single indices associated with their direction. If the material has a preferred axis, such as the poling direction in PZT, the axis is designated the z or 3 axis Stresses and strains require double indices such as xx or xy. To make the notation less cluttered and confusing, contracted notation has been defined. The following mnemonic rule is used to reduce the double index to a single index 165 This rule can be thought of as a matrix with the diagonal elements having repeated indices in the expected order, then continuing the count in a counterclockwise direction. Note that xy yx, etc so that subscript 6 applies equally to xy and yx. Any mechanical object is governed by the well-known relationship between stress and strain, S=ST (49.1) where S is the strain(relative elongation), T is the stress(force per unit area), and s contains the coefficients <s nnecting the two. All quantities are tensors; S and T are second rank, and s is fourth rank. Note, however, that usually contracted notation is used so that the full complement of subscripts is not visible PZT converts electrical fields into mechanical displacements and vice versa. The connection between the two is via the d and g coefficients. The d coefficients give the displacement when a field is applied(transmitter), while the g coefficients give the field across the device when a stress is applied (receiver ). The electrical effects are added to the basic Eq (49.1)such that s=st +dE (49.2) where E is the electric field and d is the tensor which contains the coupling coefficients. The latter parameters are reported in Table 49.2 for representative materials. One can write the matrix equation [Eq (49.2)1 c 2000 by CRC Press LLC
© 2000 by CRC Press LLC 49.2 Mechanical Characteristics Materials are acted on by forces (stresses) and the resulting deformations are called strains. An example of a strain due to a force to the material is the change of dimension parallel and perpendicular to the applied force. It is useful to introduce the coordinate system and the numbering conventions which are used when discussing these materials. Subscripts 1, 2, and 3 refer to the x, y, and z directions, respectively. Displacements have single indices associated with their direction. If the material has a preferred axis, such as the poling direction in PZT, the axis is designated the z or 3 axis. Stresses and strains require double indices such as xx or xy. To make the notation less cluttered and confusing, contracted notation has been defined. The following mnemonic rule is used to reduce the double index to a single index: 165 xx xy xz 2 4 yy yz 3 zz This rule can be thought of as a matrix with the diagonal elements having repeated indices in the expected order, then continuing the count in a counterclockwise direction. Note that xy = yx, etc. so that subscript 6 applies equally to xy and yx. Any mechanical object is governed by the well-known relationship between stress and strain, S = sT (49.1) where S is the strain (relative elongation), T is the stress (force per unit area), and s contains the coefficients connecting the two. All quantities are tensors; S and T are second rank, and s is fourth rank. Note, however, that usually contracted notation is used so that the full complement of subscripts is not visible. PZT converts electrical fields into mechanical displacements and vice versa. The connection between the two is via the d and g coefficients. The d coefficients give the displacement when a field is applied (transmitter), while the g coefficients give the field across the device when a stress is applied (receiver). The electrical effects are added to the basic Eq. (49.1) such that S = sT + dE (49.2) where E is the electric field and d is the tensor which contains the coupling coefficients. The latter parameters are reported in Table 49.2 for representative materials. One can write the matrix equation [Eq. (49.2)], TABLE 49.1 Ferroelectric, Piezoelectric, and Electrostrictive Materials Type Material Class Example Applications Electret Organic Waxes No recent Electret Organic Fluorine based Microphones Ferroelectric Organic PVF2 No known Ferroelectric Organic Liquid crystals Displays Ferroelectric Ceramic PZT thin film NV-memory Piezoelectric Organic PVF2 Transducer Piezoelectric Ceramic PZT Transducer Piezoelectric Ceramic PLZT Optical Piezoelectric Single crystal Quartz Freq. control Piezoelectric Single crystal LiNbO3 SAW devices Electrostrictive Ceramic PMN Actuators
TABLE 49.2 Properties of Well-Known PZT Formulations(Based on the Original Navy Designations and Now Used by Commercial Vendor Vern PZT5A PZT5H PZT8 1700 6444 A 330 10-3Vm/N 0.705 0.752 Application High signal Medium signal Receiver Highest signal 00d1 0 E1 00d3 (49.3) S 2(S1-S12)T」[00 Note that T and E are shown as column vectors for typographical reasons; they are in fact row vectors. This equation shows explicitly the stress-strain relation and the effect of the electromechanical conversion A similar equation applies when the material is used as a receiver -gT+(εr) (494) where T is the transpose and d the electric displacement. For all materials the matrices are not fully populated Whether a coefficient is nonzero depends on the symmetry. For PZT, a ceramic which is given a preferred direction by the poling operation( the z-axis), only d33, d13, and dis are nonzero. Also, again by symmetry, di3 =d and dis= dy Applications Historically the material which was used earliest for its piezoelectric properties was single-crystal quartz. Crude sonar devices were built by Langevin using quartz transducers, but the most important application was, and still is, frequency control. Crystal oscillators are today at the heart of every clock that does not derive its frequency reference from the ac power line. They are also used in every color television set and personal computer. In these applications at least one(or more)quartz crystal"controls frequency or time. This explains the label quartz"which appears on many clocks and watches. The use of quartz resonators for frequency control relies on another unique property. Not only is the material piezoelectric(which allows one to excite mechanical vibrations), but the material has also a very high mechanical"Q "or quality factor(Q>100,000). The actual value depends on the mounting details, whether the crystal is in a vacuum, and other details. Compare this value to a Q for PZT between 75 and 1000. The Q factor is a measure of the rate of decay and thus the mechanical losses of an excitation with no external drive. A high Q leads to a very sharp resonance and thus tight frequency control. For frequency control it has been possible to find orientations of cuts of quartz which reduce the influence of temperature on the vibration frequency. c 2000 by CRC Press LLC
© 2000 by CRC Press LLC (49.3) Note that T and E are shown as column vectors for typographical reasons; they are in fact row vectors. This equation shows explicitly the stress-strain relation and the effect of the electromechanical conversion. A similar equation applies when the material is used as a receiver: E = –gT + (eT)–1D (49.4) where T is the transpose and D the electric displacement. For all materials the matrices are not fully populated. Whether a coefficient is nonzero depends on the symmetry. For PZT, a ceramic which is given a preferred direction by the poling operation (the z-axis), only d33, d13, and d15 are nonzero. Also, again by symmetry, d13 = d23 and d15 = d25. Applications Historically the material which was used earliest for its piezoelectric properties was single-crystal quartz. Crude sonar devices were built by Langevin using quartz transducers, but the most important application was, and still is, frequency control. Crystal oscillators are today at the heart of every clock that does not derive its frequency reference from the ac power line. They are also used in every color television set and personal computer. In these applications at least one (or more) “quartz crystal” controls frequency or time. This explains the label “quartz” which appears on many clocks and watches. The use of quartz resonators for frequency control relies on another unique property. Not only is the material piezoelectric (which allows one to excite mechanical vibrations), but the material has also a very high mechanical “Q” or quality factor (Q >100,000). The actual value depends on the mounting details, whether the crystal is in a vacuum, and other details. Compare this value to a Q for PZT between 75 and 1000. The Q factor is a measure of the rate of decay and thus the mechanical losses of an excitation with no external drive. A high Q leads to a very sharp resonance and thus tight frequency control. For frequency control it has been possible to find orientations of cuts of quartz which reduce the influence of temperature on the vibration frequency. TABLE 49.2 Properties of Well-Known PZT Formulations (Based on the Original Navy Designations and Now Used by Commercial Vendor Vernitron) Units PZT4 PZT5A PZT5H PZT8 e33 — 1300 1700 3400 1000 d33 10–2 Å/V 289 374 593 225 d13 10–2 Å/V –123 –171 –274 –97 d15 10–2 Å/V 496 584 741 330 g33 10–3 Vm/N 26.1 24.8 19.7 25.4 k33 — 70 0.705 0.752 0.64 TQ °C 328 365 193 300 Q — 500 75 65 1000 r g/cm3 7.5 7.75 7.5 7.6 Application — High signal Medium signal Receiver Highest signal S S S S S S sss sss sss s s s s T T T T T T 1 2 3 4 5 6 11 12 13 12 11 13 13 13 33 44 44 11 12 1 2 3 4 5 6 0 0 2 È Î Í Í Í Í Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ = È Î Í Í Í Í Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ È Î Í Í Í Í Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ ˙ ˙ ˙ (–) ˙ + È Î Í Í Í Í Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ È Î Í Í Í ˘ ˚ ˙ ˙ ˙ 0 0 0 0 0 0 0 0 0 0 000 13 13 33 15 15 1 2 3 d d d d d E E E
high efficiency(electric energy to mechanical energy coupling factor k)and can generate higham Q A Ceramic materials of the PZT family have also found increasingly important applications. The piezo but not the ferroelectric property of these materials is made use of in transducer applications. PZT has a very -amplitude ultrasonic waves in water or solids. The coupling factor is defined by energy stored mechanica (49.5) total energy stored electri Typical values of k33 are 0.7 for PZT 4 and 0.09 for quartz, showing that PZT is a much more efficient transducer material than quartz. Note that the energy is a scalar; the subscripts are assigned by finding the energy conversion coefficient for a specific vibrational mode and field direction and selecting the subscripts accordingly. Thus k, refers to the coupling factor for a longitudinal mode driven by a longitudinal field. Probably the most important applications of PzT today are based on ultrasonic echo ranging Sonar uses the conversion of electrical signals to mechanical displacement as well as the reverse transducer property, which is to generate electrical signals in response to a stress wave. Medical diagnostic ultrasound and nondestructive testing systems devices rely on the same properties. Actuators have also been built but a major obstacle is the small displacement which can conveniently be generated. Even then, the required voltages are typically hundreds of volts and the displacements are only a few hundred angstroms. For PZt the strain in the z-direction due to an applied field in the z-direction is (no stress, T=0) d33E3 (496) (49.7) where s is the strain, E the electric field, and V the potential; d33 is the coupling coefficient which connects the △d=d3V (49.8) field is parallel to the displacement. Let the applied voltage be 100V and let us use PZt8 for which d33 is 225 (from Table 49.2). Hence Ad= 225 A or 2. 25 A/V, a small displacement indeed. We also note that Eq (49.6)is a special case of Eq (49.2)with the stress equal to zero. This is the situation when an actuator is used in a force-free environment, for example, as a mirror driver. This arrangement results in the n displacement. Any forces which tend to oppose the free motion of the PZT will subtract from the available displacement with the reduction given by the normal stress-strain relation, Eq (49.1) It is possible to obtain larger displacements with mechanisms which exhibit mechanical gain, such laminated strips(similar to bimetallic strips). The motion then is typically up to about 1 millimeter but at a cost of a reduced available force. An example of such an application is the video head translating device provide tracking in VCRs There is another class of ceramic materials which recently has become important. PMN (lead [Pb],magne sium niobate), typically doped with =10% lead titanate)is an electrostrictive material which has seen appli cations where the absence of hysteresis is important. For example, deformable mirrors require repositioning of the reflecting surface to a defined location regardless of whether the old position was above or below the Electrostrictive materials exhibit a strain which is quadratic as a function of the applied field. Producing a displacement requires an internal polarization. Because the latter polarization is induced by the applied field c 2000 by CRC Press LLC
© 2000 by CRC Press LLC Ceramic materials of the PZT family have also found increasingly important applications. The piezoelectric but not the ferroelectric property of these materials is made use of in transducer applications. PZT has a very high efficiency (electric energy to mechanical energy coupling factor k) and can generate high-amplitude ultrasonic waves in water or solids. The coupling factor is defined by (49.5) Typical values of k33 are 0.7 for PZT 4 and 0.09 for quartz, showing that PZT is a much more efficient transducer material than quartz. Note that the energy is a scalar; the subscripts are assigned by finding the energy conversion coefficient for a specific vibrational mode and field direction and selecting the subscripts accordingly. Thus k33 refers to the coupling factor for a longitudinal mode driven by a longitudinal field. Probably the most important applications of PZT today are based on ultrasonic echo ranging. Sonar uses the conversion of electrical signals to mechanical displacement as well as the reverse transducer property, which is to generate electrical signals in response to a stress wave. Medical diagnostic ultrasound and nondestructive testing systems devices rely on the same properties. Actuators have also been built but a major obstacle is the small displacement which can conveniently be generated. Even then, the required voltages are typically hundreds of volts and the displacements are only a few hundred angstroms. For PZT the strain in the z-direction due to an applied field in the z-direction is (no stress, T = 0) s3 = d33E3 (49.6) or (49.7) where s is the strain, E the electric field, and V the potential; d33 is the coupling coefficient which connects the two. Thus Dd = d33V (49.8) Note that this expression is independent of the thickness d of the material but this is true only when the applied field is parallel to the displacement. Let the applied voltage be 100 V and let us use PZT8 for which d33 is 225 (from Table 49.2). Hence Dd = 225 Å or 2.25 Å/V, a small displacement indeed. We also note that Eq. (49.6) is a special case of Eq. (49.2) with the stress equal to zero. This is the situation when an actuator is used in a force-free environment, for example, as a mirror driver. This arrangement results in the maximum displacement. Any forces which tend to oppose the free motion of the PZT will subtract from the available displacement with the reduction given by the normal stress-strain relation, Eq. (49.1). It is possible to obtain larger displacements with mechanisms which exhibit mechanical gain, such as laminated strips (similar to bimetallic strips). The motion then is typically up to about 1 millimeter but at a cost of a reduced available force. An example of such an application is the video head translating device to provide tracking in VCRs. There is another class of ceramic materials which recently has become important. PMN (lead [Pb], magnesium niobate), typically doped with ª10% lead titanate) is an electrostrictive material which has seen applications where the absence of hysteresis is important. For example, deformable mirrors require repositioning of the reflecting surface to a defined location regardless of whether the old position was above or below the original position. Electrostrictive materials exhibit a strain which is quadratic as a function of the applied field. Producing a displacement requires an internal polarization. Because the latter polarization is induced by the applied field k 2 = energy stored mechanically total energy stored electrically s d d d V d 3 = = 33 D