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
FIGURE 49.1 Charge configurations in ferroelectric model materials: (a)uncompensated and( b)compensated dipol and is not permanent, as it is in the ferroelectric materials, electrostrictive materials have essentially no hysteresis. Unlike PZT, electrostrictive materials are not reversible; PZT will change shape on application of a field and generate a field when a strain is induced. Electrostrictive materials only change shape on application of a field and, therefore, cannot be used as receivers. PZT has inherently large hysteresis because of the domain nature Organic electrets have important applications in self-polarized condenser(or capacitor)microphones where the required electric bias field in the gap is generated by the diaphragm material rather than by an external power supply. Structure of ferroelectric and piezoelectric material Ferroelectric materials have, as their basic building block, atomic groups which have an associated electric field, either as a result of their structure or as result of distortion of the charge clouds which make up the groups In the first case, the field arises from an asymmetric placement of the individual ions in the group(these groupings are called unit cells). In the second case, the electronic cloud is moved with respect to the ionic core. If the group is distorted permanently, then a permanent electric field can be associated with each group. we can think of these distorted groups as represented by electric dipoles, defined as two equal but opposite charges which are separated by a small distance. Electric dipoles are similar to magnetic dipoles which have the familiar north and south poles. The external manifestation of a magnetic dipole is a magnetic field and that of an electric dipole an electric field. Figure 49.1(a)represents a hypothetical slab of material in which the dipoles are perfectly arranged In actual materials the atoms are not as uniformly arranged, but, nevertheless, from this model there would be a very strong field emanating from the surface of the crystal. The common observation, however, is that the fields are either absent or weak. This effective charge neutrality arises from the fact that there are free, mobile charges available which can be attracted to the surfaces. The polarity of the mobile charges is opposite to the charge of the free dipole end. The added charges on the two surfaces generate their own field, equal and opposite to he field due to the internal dipoles. Thus the effect of the internal field is canceled and the external field zero, as if no charges were present at all [ Fig. 49.1(b)1 In ferroelectric materials a crystalline asymmetry exists which allows electric dipoles to form. In their absence the dipoles are absent and the internal field disappears. Consider an imaginary horizontal line drawn through the middle of a dipole. We can see readily that the dipole is not symmetric about that line. The asymmetry thus requires that there be no center of inversion when the material is in the ferroelectric state All ferroelectric and piezoelectric materials have phase transitions at which the material changes crystalline symmetry. For example, in PZT there is a change from tetragonal or rhombohedral symmetry to cubic as the temperature is increased. The temperature at which the material changes crystalline phases is called the Curie temperature, Te. For typical PZT compositions the Curie temperature is between 250 and 450.C A consequence of a phase transition is that a rearrangement of the lattice takes place when the material is cooled through the transition. Intuitively we would expect that the entire crystal assumes the same orientation throughout as w hrough the transition By orientation we mean the direction of the preferred axis(say c 2000 by CRC Press LLC
© 2000 by CRC Press LLC and is not permanent, as it is in the ferroelectric materials, electrostrictive materials have essentially no hysteresis. Unlike PZT, electrostrictive materials are not reversible; PZT will change shape on application of a field and generate a field when a strain is induced. Electrostrictive materials only change shape on application of a field and, therefore, cannot be used as receivers. PZT has inherently large hysteresis because of the domain nature of the polarization. Organic electrets have important applications in self-polarized condenser (or capacitor) microphones where the required electric bias field in the gap is generated by the diaphragm material rather than by an external power supply. Structure of Ferroelectric and Piezoelectric Materials Ferroelectric materials have, as their basic building block, atomic groups which have an associated electric field, either as a result of their structure or as result of distortion of the charge clouds which make up the groups. In the first case, the field arises from an asymmetric placement of the individual ions in the group (these groupings are called unit cells). In the second case, the electronic cloud is moved with respect to the ionic core. If the group is distorted permanently, then a permanent electric field can be associated with each group. We can think of these distorted groups as represented by electric dipoles, defined as two equal but opposite charges which are separated by a small distance. Electric dipoles are similar to magnetic dipoles which have the familiar north and south poles. The external manifestation of a magnetic dipole is a magnetic field and that of an electric dipole an electric field. Figure 49.1(a) represents a hypothetical slab of material in which the dipoles are perfectly arranged. In actual materials the atoms are not as uniformly arranged, but, nevertheless, from this model there would be a very strong field emanating from the surface of the crystal. The common observation, however, is that the fields are either absent or weak. This effective charge neutrality arises from the fact that there are free, mobile charges available which can be attracted to the surfaces. The polarity of the mobile charges is opposite to the charge of the free dipole end. The added charges on the two surfaces generate their own field, equal and opposite to the field due to the internal dipoles. Thus the effect of the internal field is canceled and the external field is zero, as if no charges were present at all [Fig. 49.1(b)]. In ferroelectric materials a crystalline asymmetry exists which allows electric dipoles to form. In their absence the dipoles are absent and the internal field disappears. Consider an imaginary horizontal line drawn through the middle of a dipole. We can see readily that the dipole is not symmetric about that line. The asymmetry thus requires that there be no center of inversion when the material is in the ferroelectric state. All ferroelectric and piezoelectric materials have phase transitions at which the material changes crystalline symmetry. For example, in PZT there is a change from tetragonal or rhombohedral symmetry to cubic as the temperature is increased. The temperature at which the material changes crystalline phases is called the Curie temperature, TQ. For typical PZT compositions the Curie temperature is between 250 and 450°C. A consequence of a phase transition is that a rearrangement of the lattice takes place when the material is cooled through the transition. Intuitively we would expect that the entire crystal assumes the same orientation throughout as we pass through the transition. By orientation we mean the direction of the preferred axis (say FIGURE 49.1 Charge configurations in ferroelectric model materials: (a) uncompensated and (b) compensated dipole arrays
ne tetragonal axis). Experimentally it is found, however, that the material breaks up into smaller regions in which the preferred direction and thus the polarization is uniform. Note that cubic materials have no preferred direction. In tetragonal crystals the polarization points along the c-axis(the longer axis) whereas in rhomb- hedral lattices the polarization is along the body diagonal. The volume in which the preferred axis is pointing in the same direction is called a domain and the border between the regions is called a domain wall. The energy of the multidomain state is slightly lower than the single-domain state and is thus the preferred configuration The direction of the polarization changes by either 90 or 180 as we pass from one uniform region to another. Thus the domains are called 90 and 180 domains. Whether an individual crystallite or grain consists of a single domain depends on the size of the crystallite and external parameters such as strain gradients, impurities, etc. It is also possible that the domain extend beyond the grain boundary and asses two or more grains of the crystal Real materials consist of large numbers of unit cells, and the manifestation of the individual charged groups is n internal and an external electric field when the material is stressed. Internal and external refer to inside and outside of the material. The interaction of an external electric field with a charged group causes a displacement of certain atoms in the group. The macroscopic manifestation of this is a displacement of the surfaces of the material This motion is called the piezoelectric effect, the conversion of an applied field into a corresponding displacement 49.3 Ferroelectric materials PZT (PbZr Tin-sO3 )is an example of a ceramic material which is ferroelectric. We will use PZT as a prototype ystem for many of the ferroelectric attributes to be discussed. The concepts, of course, have general validity The structure of this material is abo where a is lead and b is one or the other atoms ti or Zr. This material consists of many randomly oriented crystallites which vary in size between approximately 10 nm and several microns. The crystalline symmetry of the material is determined by the magnitude of the parameter x. The material changes from rhombohedral to tetragonal symmetry when x>0.48. This transition is almost inde pendent of temperature. The line which divides the two phases is hange of symmetry as a function of composition only). Commercial materials are made with x=0.48, where the d and g sensitivity of the material is maximum. It is clear from Table 49.2 that there are other parameters which can be influenced as well. Doping the material with donors or acceptors often changes the properties dramatically. Thus niobium is important to obtain higher sensitivity and resistivity and to lower the Curie mperature. PZT typically is a p-type conductor and niobium will significantly decrease the conductivity because of the electron which nb+ contributes to the lattice. the nb ion substitutes for the b-site ion ti+ or Zr*. The resistance to depolarization(the hardness of the material)is affected by iron doping Hardness is a definition giving the relative resistance to depolarization. It should not be confused with mechanical hardness. Many other dopants and admixtures have been used, often in very exotic combinations to affect aging, sensi- The designations used in Table 49.2 reflect very few of the many combinations which have been developed. The PzT designation types were originally designed by the U.S. Navy to reflect certain property combinations. These can be obtained with different combinations of compositions and dopants. The examples given in the table are representative of typical PZT materials, but today essentially all applications have their own custom formulation. The name PZT has become generic for the lead zirconate titanates and does not reflect Navy or When PZT ceramic material is prepared, the crystallites and domains are randomly oriented, and therefore the material does not exhibit any piezoelectric behavior[Fig. 49. 2(a)]. The random nature of the displacements for the individual crystallites causes the net displacement to average to zero when an external field is applied The tetragonal axis has three equivalent directions 90 apart and the material can be poled by reorienting the polarization of the domains into a direction nearest the applied field. When a sufficiently high field is applied, ome but not all of the domains will be rotated toward the electric field through the allowed angle 90 or 180o If the field is raised further, eventually all domains will be oriented as close as possible to the direction of the field. Note however, that the polarization will not point exactly in the direction of the field Fig 49.2(b).At nis point, no further domain motion is possible and the material is saturated. As the field is reduced, the majority of domains retain the orientation they had with the field on leaving the material in an oriented state which now has a net polarization. Poling is accomplished for commercial PZT by raising the temperature to c 2000 by CRC Press LLC
© 2000 by CRC Press LLC the tetragonal axis). Experimentally it is found, however, that the material breaks up into smaller regions in which the preferred direction and thus the polarization is uniform. Note that cubic materials have no preferred direction. In tetragonal crystals the polarization points along the c-axis (the longer axis) whereas in rhombohedral lattices the polarization is along the body diagonal. The volume in which the preferred axis is pointing in the same direction is called a domain and the border between the regions is called a domain wall. The energy of the multidomain state is slightly lower than the single-domain state and is thus the preferred configuration. The direction of the polarization changes by either 90° or 180° as we pass from one uniform region to another. Thus the domains are called 90° and 180° domains. Whether an individual crystallite or grain consists of a single domain depends on the size of the crystallite and external parameters such as strain gradients, impurities, etc. It is also possible that the domain extend beyond the grain boundary and encompasses two or more grains of the crystal. Real materials consist of large numbers of unit cells, and the manifestation of the individual charged groups is an internal and an external electric field when the material is stressed. Internal and external refer to inside and outside of the material. The interaction of an external electric field with a charged group causes a displacement of certain atoms in the group. The macroscopic manifestation of this is a displacement of the surfaces of the material. This motion is called the piezoelectric effect, the conversion of an applied field into a corresponding displacement. 49.3 Ferroelectric Materials PZT (PbZrxTi(1–x)O3) is an example of a ceramic material which is ferroelectric. We will use PZT as a prototype system for many of the ferroelectric attributes to be discussed. The concepts, of course, have general validity. The structure of this material is ABO3 where A is lead and B is one or the other atoms, Ti or Zr. This material consists of many randomly oriented crystallites which vary in size between approximately 10 nm and several microns. The crystalline symmetry of the material is determined by the magnitude of the parameter x. The material changes from rhombohedral to tetragonal symmetry when x > 0.48. This transition is almost independent of temperature. The line which divides the two phases is called a morphotropic phase boundary (change of symmetry as a function of composition only). Commercial materials are made with x ª 0.48, where the d and g sensitivity of the material is maximum. It is clear from Table 49.2 that there are other parameters which can be influenced as well. Doping the material with donors or acceptors often changes the properties dramatically. Thus niobium is important to obtain higher sensitivity and resistivity and to lower the Curie temperature. PZT typically is a p-type conductor and niobium will significantly decrease the conductivity because of the electron which Nb5+ contributes to the lattice. The Nb ion substitutes for the B-site ion Ti 4+ or Zr4+. The resistance to depolarization (the hardness of the material) is affected by iron doping. Hardness is a definition giving the relative resistance to depolarization. It should not be confused with mechanical hardness. Many other dopants and admixtures have been used, often in very exotic combinations to affect aging, sensitivity, etc. The designations used in Table 49.2 reflect very few of the many combinations which have been developed. The PZT designation types were originally designed by the U.S. Navy to reflect certain property combinations. These can be obtained with different combinations of compositions and dopants. The examples given in the table are representative of typical PZT materials, but today essentially all applications have their own custom formulation. The name PZT has become generic for the lead zirconate titanates and does not reflect Navy or proprietary designations. When PZT ceramic material is prepared, the crystallites and domains are randomly oriented, and therefore the material does not exhibit any piezoelectric behavior [Fig. 49.2(a)]. The random nature of the displacements for the individual crystallites causes the net displacement to average to zero when an external field is applied. The tetragonal axis has three equivalent directions 90° apart and the material can be poled by reorienting the polarization of the domains into a direction nearest the applied field. When a sufficiently high field is applied, some but not all of the domains will be rotated toward the electric field through the allowed angle 90° or 180°. If the field is raised further, eventually all domains will be oriented as close as possible to the direction of the field. Note however, that the polarization will not point exactly in the direction of the field [Fig. 49.2(b)]. At this point, no further domain motion is possible and the material is saturated. As the field is reduced, the majority of domains retain the orientation they had with the field on leaving the material in an oriented state which now has a net polarization. Poling is accomplished for commercial PZT by raising the temperature to
a)P=0 (b)P=P≤0.86P FIGURE 49.2 Domains in PZT, as prepared(a)and poled(b) ElectricalMechanical FIGURE 49.3 Equivalent circuit for a piezoelectric resonator. The reduction of the equivalent circuit at low frequencies is about 150C( to lower the coercive field, E)and applying a field of about 30-60 kV/cm for several minutes. The temperature is then lowered but it is not necessary to keep the field on during cooling because the domains will not spontaneously rerandomize Electrical Characteristics Before considering the dielectric properties, we will consider the equivalent circuit for a slab of ferroelectric material. In Fig. 49.3 the circuit shows a mechanical(acoustic) component and the static or clamped capacity Co(and the dielectric loss R,) which are connected in parallel. The acoustic components are due to their motional or mechanical equivalents, the compliance(capacity, C)and the mass(inductance, L). There will be mechanical losses, which are indicated in the mechanical branch by R. The electrical branch has the clamped capacity C, and a dielectric loss(R,), distinct from the mechanical losses. This configuration will have a resonance which is usually assumed to correspond to the mechanical thickness mode but can represent other modes as well. This simple model does not show the many other modes a slab(or rod )of material will have Thus transverse, plate, and flexural modes are present. Each can be represented by its own combination of L, C, and R. The presence of a large number of modes often causes difficulties in characterizing the material since some parameters must be measured either away from the resonances or from clean, nonoverlapping resonances For instance, the clamped capacity(or clamped dielectric constant)of a material is measured at high frequencies where there are usually a large number of modes present. For an accurate measurement these must be avoided and often a low-frequency measurement is made in which the material is physically clamped to prevent motion This yields the static, nonmechanical capacity, Co. The circuit can be approximated at low frequencies by ignoring the inductor and redefining R and C. Thus, the coupling constant can be extracted from the value of Cand Co From the previous definition of k we find K=energy stored mechanically= CV12=I+1(49.9) total energy stored electrically (C+C)V/2 Co c 2000 by CRC Press LLC
© 2000 by CRC Press LLC about 150°C (to lower the coercive field, Ec) and applying a field of about 30–60 kV/cm for several minutes. The temperature is then lowered but it is not necessary to keep the field on during cooling because the domains will not spontaneously rerandomize. Electrical Characteristics Before considering the dielectric properties, we will consider the equivalent circuit for a slab of ferroelectric material. In Fig. 49.3 the circuit shows a mechanical (acoustic) component and the static or clamped capacity Co (and the dielectric loss Rd) which are connected in parallel. The acoustic components are due to their motional or mechanical equivalents, the compliance (capacity, C) and the mass (inductance, L). There will be mechanical losses, which are indicated in the mechanical branch by R. The electrical branch has the clamped capacity Co and a dielectric loss (Rd ), distinct from the mechanical losses. This configuration will have a resonance which is usually assumed to correspond to the mechanical thickness mode but can represent other modes as well. This simple model does not show the many other modes a slab (or rod) of material will have. Thus transverse, plate, and flexural modes are present. Each can be represented by its own combination of L, C, and R. The presence of a large number of modes often causes difficulties in characterizing the material since some parameters must be measured either away from the resonances or from clean, nonoverlapping resonances. For instance, the clamped capacity (or clamped dielectric constant) of a material is measured at high frequencies where there are usually a large number of modes present. For an accurate measurement these must be avoided and often a low-frequency measurement is made in which the material is physically clamped to prevent motion. This yields the static, nonmechanical capacity, Co. The circuit can be approximated at low frequencies by ignoring the inductor and redefining R and C. Thus, the coupling constant can be extracted from the value of C and Co. From the previous definition of k we find (49.9) FIGURE 49.2 Domains in PZT, as prepared (a) and poled (b). FIGURE 49.3 Equivalent circuit for a piezoelectric resonator. The reduction of the equivalent circuit at low frequencies is shown on the right. k CV C C V C C o o 2 2 2 2 2 1 = = 1 + = + energy stored mechanically total energy stored electrically / ( ) /
Optional FE Device Polarization (Y) FIGURE 49.4 Sawyer Tower circuit. It requires charge to rotate or flip a domain. Thus, there is charge flow associated with the rearrangement of the polarization in the ferroelectric material. If a bipolar, repetitive signal is applied to a ferroelectric material, its hysteresis loop is traced out and the charge in the circuit can be measured using the Sawyer Tower circuit ( Fig. 49.4). In some cases the drive signal to the material is not repetitive and only a single cycle is used. In that case the starting point and the end point do not have the same polarization value and the hysteresis curve will not close on itself The charge flow through the sample is due to the rearrangement of the polarization vectors in the domains (the polarization) and contributions from the static capacity and losses(Co and R, in Fig. 49.3). The charge is integrated by the measuring capacitor which is in series with the sample. The measuring capacitor is sufficiently large to avoid a significant voltage loss. The polarization is plotted on a X-Y scope or plotter against the applied voltage and therefore the applied field. Ferroelectric and piezoelectric materials are lossy. This will distort the shape of the hysteresis loop and can even lead to incorrect identification of materials as ferroelectric when they merely have nonlinear conduction characteristics. A resistive component(from R, in Fig. 49.3)will introduce a phase shift in the polarization signal. Thus the display has an elliptical component, which looks like the beginnings of the opening of a hysteresis loop. However, if the horizontal signal has the same phase shift, the influence of this lossy component is eliminated, because it is in effect subtracted. Obtaining the exact match is the function of the optional phase ifter, and in the original circuits a bridge was constructed which had a second measuring capacitor in the comparison arm(identical to the one in series with the sample). The phase was then matched with adjustable high-voltage components which match Co and This design is inconvenient to implement and modern Sawyer Tower circuits have the capability to shift the reference phase either electronically or digitally to compensate for the loss and static components. a contem porary version, which has compensation and no voltage loss across the integrating capacitor, is shown in Fig. 49.5. The op-amp integrator provides a virtual ground at the input, reducing the voltage loss to negligible values. The output from this circuit is the sum of the polarization and the capacitive and loss components These contributions can be canceled using a purely real (resistive)and a purely imaginary(capacitive, 90 phaseshift) compensation component proportional to the drive across the sample. Both need to be scaled magnitude adjustments)to match them to the device being measured and then have to be subtracted(adding negatively) from the output of the op amp. The remainder is the polarization. The hysteresis for typical ferroelectrics is frequency dependent and traditionally the reported values of the polarization are measured at 50 or 60 Hz. The improved version of the Sawyer Tower( Fig. 49.6)circuit allows us to cancel Co and R, and the losses, thus determining the active component. This is important in the development of materials for ferroelectric memory applications. It is far easier to judge the squareness of the loop when the inactive components are canceled. Also, by calibrating the"magnitude controls"the value of the inactive components can be read off directly. In typical measurements the resonance is far above the frequencies used, so ignoring the inductance in the equivalent circuit is justified c 2000 by CRC Press LLC
© 2000 by CRC Press LLC It requires charge to rotate or flip a domain. Thus, there is charge flow associated with the rearrangement of the polarization in the ferroelectric material. If a bipolar,repetitive signal is applied to a ferroelectric material, its hysteresis loop is traced out and the charge in the circuit can be measured using the Sawyer Tower circuit (Fig. 49.4). In some cases the drive signal to the material is not repetitive and only a single cycle is used. In that case the starting point and the end point do not have the same polarization value and the hysteresis curve will not close on itself. The charge flow through the sample is due to the rearrangement of the polarization vectors in the domains (the polarization) and contributions from the static capacity and losses (Co and Rd in Fig. 49.3). The charge is integrated by the measuring capacitor which is in series with the sample. The measuring capacitor is sufficiently large to avoid a significant voltage loss. The polarization is plotted on a X-Y scope or plotter against the applied voltage and therefore the applied field. Ferroelectric and piezoelectric materials are lossy. This will distort the shape of the hysteresis loop and can even lead to incorrect identification of materials as ferroelectric when they merely have nonlinear conduction characteristics. A resistive component (from Rd in Fig. 49.3) will introduce a phase shift in the polarization signal. Thus the display has an elliptical component, which looks like the beginnings of the opening of a hysteresis loop. However, if the horizontal signal has the same phase shift, the influence of this lossy component is eliminated, because it is in effect subtracted. Obtaining the exact match is the function of the optional phase shifter, and in the original circuits a bridge was constructed which had a second measuring capacitor in the comparison arm (identical to the one in series with the sample). The phase was then matched with adjustable high-voltage components which match Co and Rd. This design is inconvenient to implement and modern Sawyer Tower circuits have the capability to shift the reference phase either electronically or digitally to compensate for the loss and static components. A contemporary version, which has compensation and no voltage loss across the integrating capacitor, is shown in Fig. 49.5. The op-amp integrator provides a virtual ground at the input, reducing the voltage loss to negligible values. The output from this circuit is the sum of the polarization and the capacitive and loss components. These contributions can be canceled using a purely real (resistive) and a purely imaginary (capacitive, 90° phaseshift) compensation component proportional to the drive across the sample. Both need to be scaled (magnitude adjustments) to match them to the device being measured and then have to be subtracted (adding negatively) from the output of the op amp. The remainder is the polarization. The hysteresis for typical ferroelectrics is frequency dependent and traditionally the reported values of the polarization are measured at 50 or 60 Hz. The improved version of the Sawyer Tower (Fig. 49.6) circuit allows us to cancel Co and Rd and the losses, thus determining the active component. This is important in the development of materials for ferroelectric memory applications. It is far easier to judge the squareness of the loop when the inactive components are canceled. Also, by calibrating the “magnitude controls” the value of the inactive components can be read off directly. In typical measurements the resonance is far above the frequencies used, so ignoring the inductance in the equivalent circuit is justified. FIGURE 49.4 Sawyer Tower circuit
FE Device P+Cap +Loss Polarization aseshift 0 deg FIGURE 49.5 Modern hysteresis circuit. An op amp is used to integrate the charge; loss and static capacitance compensation cluded Remanent (E2 300-200-10 200300 FIGURE 49.6 Idealized hysteresis curve for typical PZT materials. Many PZT materials display m the origin and ive asymmetries with respect to the origin. The curve shows how the remanent polarization the coercive field (Dare defined. While the loop is idealized, the values given for the polarization and field are realistic for typical PZT The measurement of the dielectric constant and the losses is usually very straightforward. a slab with a circular or other well-defined cross section is prepared, electrodes are applied, and the capacity and loss are measured(usually as a function of frequency). The dielectric constant is found from C=8￡ (49.10) where A is the area of the device and t the thickness. In this definition(also used in Table 49. 2)E is the relative dielectric constant and e, is the permittivity of vacuum. Until recently, the dielectric constant, like the polar ion, was measured at 50 or 60 Hz(typical powerline frequencies). Today the dielectric parameters are typically specified at 1 kHz, which is possible because impedance analyzers with high-frequency capability are readily available. To avoid low-frequency anomalies, even higher frequencies such as 1 MHz are often selected. This is especially the case when evaluating PZT thin films. Low frequency anomalies are not included in the equivalent circuit(Fig. 49.3)and are due to interface layers. These layers will cause both the resistive and reactive components to rise at low frequencies producing readings which are not representative of the dielectric properties c 2000 by CRC Press LLC
© 2000 by CRC Press LLC The measurement of the dielectric constant and the losses is usually very straightforward. A slab with a circular or other well-defined cross section is prepared, electrodes are applied, and the capacity and loss are measured (usually as a function of frequency). The dielectric constant is found from (49.10) where A is the area of the device and t the thickness. In this definition (also used in Table 49.2) e is the relative dielectric constant and eo is the permittivity of vacuum. Until recently, the dielectric constant, like the polarization, was measured at 50 or 60 Hz (typical powerline frequencies). Today the dielectric parameters are typically specified at 1 kHz, which is possible because impedance analyzers with high-frequency capability are readily available. To avoid low-frequency anomalies, even higher frequencies such as 1 MHz are often selected. This is especially the case when evaluating PZT thin films. Low frequency anomalies are not included in the equivalent circuit (Fig. 49.3) and are due to interface layers. These layers will cause both the resistive and reactive components to rise at low frequencies producing readings which are not representative of the dielectric properties. FIGURE 49.5 Modern hysteresis circuit.An op amp is used to integrate the charge; loss and static capacitance compensation are included. FIGURE 49.6 Idealized hysteresis curve for typical PZT materials. Many PZT materials display offsets from the origin and have asymmetries with respect to the origin. The curve shows how the remanent polarization (PY r) and the coercive field (EY c) are defined. While the loop is idealized, the values given for the polarization and field are realistic for typical PZT materials. C A t = o e e
