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 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 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 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 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, 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 defini- tion 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 ? 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 24 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 LiNbO 3 SAW devices Electrostrictive Ceramic PMN Actuators ? 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 + (e T ) –1 D (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 d 33 , d 13 , and d 15 are nonzero. Also, again by symmetry, d 13 = d 23 and d 15 = d 25 . 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 e 33 — 1300 1700 3400 1000 d 33 10 –2 ?/V 289 374 593 225 d 13 10 –2 ?/V –123 –171 –274 –97 d 15 10 –2 ?/V 496 584 741 330 g 33 10 –3 Vm/N 26.1 24.8 19.7 25.4 k 33 — 70 0.705 0.752 0.64 T Q °C 328 365 193 300 Q — 500 75 65 1000 r g/cm 3 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 ss 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 é ? ê ê ê ê ê ê ê ê ù ? ú ú ú ú ú ú ú ú = é ? ê ê ê ê ê ê ê ê ù ? ú ú ú ú ú ú ú ú é ? ê ê ê ê ê ê ê ê ù ? ú ú ú ú ú ú ú (–) ú + é ? ê ê ê ê ê ê ê ê ù ? ú ú ú ú ú ú ú ú é ? ê ê ê ù ? ú ú ú 00 00 00 00 00 000 13 13 33 15 15 1 2 3 d d d d d E E E ? 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 k 33 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 33 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) s 3 = d 33 E 3 (49.6) or (49.7) where s is the strain, E the electric field, and V the potential; d 33 is the coupling coefficient which connects the two. Thus Dd = d 33 V (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 d 33 is 225 (from Table 49.2). Hence Dd = 225 ? or 2.25 ?/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], 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 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 33 == D ? 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, T Q . 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 49.1Charge configurations in ferroelectric model materials: (a) uncompensated and (b) compensated dipole arrays. ? 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 rhombo- 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 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 (PbZr x Ti (1–x) O 3 ) 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 ABO 3 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 called a morphotropic phase boundary (change 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 temperature. PZT typically is a p-type conductor and niobium will significantly decrease the conductivity because of the electron which Nb 5+ contributes to the lattice. The Nb ion substitutes for the B-site ion Ti 4+ or Zr 4+ . 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- tivity, 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 ? 2000 by CRC Press LLC about 150°C (to lower the coercive field, E c ) 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 C o (and the dielectric loss R d ) 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 o and a dielectric loss (R d ), 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, C o . 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 C o . From the previous definition of k we find (49.9) FIGURE 49.2Domains in PZT, as prepared (a) and poled (b). FIGURE 49.3Equivalent circuit for a piezoelectric resonator. The reduction of the equivalent circuit at low frequencies is shown on the right. k CV CCV C C o o 2 2 2 2 2 1 1== + =+ energy stored mechanically total energy stored electrically / /() ? 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 (C o and R d 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 d 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 C o and R d . 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 C o and R d 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 49.4Sawyer Tower circuit. ? 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 e o is the permittivity of vacuum. Until recently, the dielectric constant, like the polar- ization, 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 49.5Modern hysteresis circuit. An op amp is used to integrate the charge; loss and static capacitance compensation are included. FIGURE 49.6Idealized 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( Y P r )and the coercive field ( Y E c )aredefined. While the loop is idealized, the values given for the polarization and field are realistic for typical PZT materials. C A t o =ee ? 2000 by CRC Press LLC A piezoelectric component often has a very simple geometric shape, especially when it is prepared for measurement purposes. There will be mechanical resonances associated with the major dimensions of a sample piece. The resonance spectrum will be more or less complicated, depending on the shape of a sample piece. If the object has a simple shape, then some of the resonances will be well separated from each other and can be associated with specific vibrations and dimensions (modes). Each of these resonances has an electrical equiv- alent, and inspection of the equivalent circuit shows that there will be a resonance (minimum impedance) and an antiresonance (maximum impedance). Thus an impedance plot can be used to determine the frequencies and also the coupling constants and mechanical parameters for the various modes. 49.4 Ferroelectric and High Epsilon Thin Films While PZT and other ferroelectric (FE) bulk materials have had major commercial importance, thin films prepared from these materials have only recently been the focus of significant research efforts. In this section the material properties and process issues will be discussed. Because of the potentially large payoff, major efforts have been directed at developing the technologies for depositing thin films of ferroelectric and non-ferroelectric but high epsilon (high dielectric constant) thin films. A recent trend has been the ever increasing density of dynamic random access memory (DRAM). The storage capacitor in these devices is becoming a major limiting factor because the dielectric has to be very thin in order to achieve the desired capacitance values to yield, in turn, a sufficient signal for the storage cell. It is often also desirable to have nonvolatile operation (no data loss on power loss). These two desires have, probably more than anything else, driven the development of high epsilon and FE thin films. Of course, these are not the only applications of FE films. Table 49.3 lists the applications of FE (nonvolatile, NV) and high epsilon films (volatile) and highlights which of the properties are important for their use. It is seen that the memory application is very demanding. Satisfying all these requirements simultaneously has produced significant challenges in the manufacture of these films. Perhaps the least understood and to some extent still unsolved problem is that of fatigue. In nonvolatile memory applications the polarization represents the memory state of the material (up o bit 1; down o bit 0). In use the device can be switched at the clock rate, say 100 MHz. Thus for a lifetime of 5 years the material must withstand .10 16 polarization reversals or large field reversals. Typical materials for ferroelectric applica- tions are PZTs with the ratio of zirconium to titanium adjusted to yield the maximum dielectric constant and polarization. This maximum will be near the morphotropic phase boundary for PZT. Small quantities of other materials can be added, such as lanthanum or niobium to modify optical or switching characteristics. The Sol-Gel method discussed below is particularly suitable for incorporating these additives. Devices made from materials at the current state of the art loose a significant portion of their polarization after 10 10 to 10 12 cycles, rendering them useless for their intended memory use because of the associated signal loss. This is a topic of intensive investigation and only one proprietary material has emerged which might be suitable for memory use (Symetric Corporation). High epsilon nonferroelectric materials are of great interest for DRAM applica- tions. As an example, major efforts are extant to produce thin films of mixtures of barium and strontium titanate (BST). Dielectric constants of 600 and above have been achieved (compared to 4–6 for silicon oxides and nitrides). In applications for FE films, significant opportunities also exist for electro-optical modulators for fiber-optic devices and light valves for displays. Another large scale application is actuators and sensors. For the latter the TABLE 49.3Material Properties and Applications Areas Ferroelectric Epsilon Polarization Coercive Field Leakage Aging Electro- Optical Electro- Mechanical NV RAM X X X X X DRAM X X X Actuator X X Display X X X X Optical Modulator X X X X ? 2000 by CRC Press LLC electro-mechanical conversion property is used and large values of d 33 (the conversion coefficient) are desirable. However, economically the importance of all other applications are, and probably will be in the foreseeable future, less significant than that of memory devices. Integration of ferroelectric or nonferroelectric materials with silicon devices and substrates has proved to be very challenging. Contacts and control of the crystallinity and crystal size and the stack structure of the capacitor device are the principal issues. In both volatile and nonvolatile memory cells the dielectric material tends to interact with the silicon substrate. Thus an appropriate barrier layer must be incorporated while at the same time obtaining a suitable substrate on which to grow the dielectric films. A typical device structure starts with an oxide layer (SiO x ) on the silicon substrate followed by a thin titanium layer which prevents diffusion of the final substrate layer, platinum (the actual growth substrate). Significant differences have been observed in the quality of the films depending on the nature of the substrate. The quality can be described by intrinsic parameters such as the crystallinity (i.e., the degree to which non- crystalline phases are present). The uniformity of the orientation of the crystallites also seems to play a role in determining the electrical properties of the films. In the extreme case of perfect alignment of the crystallites of the film with the substrate and the formation of large single crystal areas, an epitaxial film is obtained. These films tend to have the best electrical properties. In addition to amorphous material, other crystalline but nonferroelectric phases can be present. An example is the pyrochlore phase in PZT. These phases often form incidentally to the growth process of the desired film and usually degrade one or more of the desired properties of the film (for instance the dielectric constant). The pyrochlore and other oxide materials can accumulate between the Pt electrode and the desired PZT or BST layer. The interface layer is then electrically in series with the desired dielectric layer and degrades its properties. The apparent reduction of the dielectric constant which is often observed in these films as the thickness is reduced can be attributed to the presence of these low dielectric constant layers. There are many growth methods for these films. Table 49.4 lists the most important techniques along with some of the critical parameters. Wet methods use metal organic compounds in liquid form. In the Sol-Gel process the liquid is spun onto the substrate. The wafer is then heated, typically to a lower, intermediate temperature (around 300°C). This spin-on and heat process is repeated until the desired thickness is reached. At this temperature only an amorphous film forms. The wafer is then heated to between 500 and 700°C usually in oxygen and the actual crystal growth takes place. Instead of simple long term heating (order of hours), rapid thermal annealing (RTA) is often used. In this process the sample is only briefly exposed to the elevated temperature, usually by a scanning infrared beam. It is in the transition between the low decomposition temperature and the firing temperature that the pyrochlore tends to form. At the higher temperatures the more volatile components have a tendency to evaporate, thus producing a chemically unbalanced compound which also has a great propensity to form one or more of the pyrochlore phases. In the case of PZT, 5 to 10% excess lead is usually incorporated which helps to form the desired perovskite material and compensates for the loss. In preparing Sol-Gel films it is generally easy to prepare the compatible liquid compounds of the major constituents and the dopants. The composition is then readily adjusted by appropriately changing the ratio of the constituents. Very fine quality films have been prepared by this method, including epitaxial films. The current semiconductor technology is tending toward dry processing. Thus, in spite of the advantages of the Sol-Gel method, other methods using physical vapor deposition (PVD) are being investigated. These methods use energetic beams or plasma to move the constituent materials from the target to the heated substrate. TABLE 49.4Deposition Methods for PZT and Perovskites Process Type Rate nm/min Substrate Temperature Anneal Temperature Target/Source Wet Sol-Gel 100 nm/coat RT 450–750 Metal organic Wet MOD 300 nm/coat RT 500–750 Metal organic Dry RF sputter .5–5 RT–700 500–700 Metals and oxides Dry Magnetron sputter 5–30 RT–700 500–700 Metals and oxides Dry Ion beam sputter 2–10 RT–700 500–700 Metals and oxides Dry Laser sputter 5–100 RT–700 500–700 Oxide Dry MOCVD 5–100 400–800 500–700 MO vapor and carrier gas ? 2000 by CRC Press LLC The compound then forms in situ on the heated wafer (.500°C). Even then, however, a subsequent anneal is often required. With PVD methods it is much more difficult to change the composition since now the oxide or metal ratios of the target have to be changed or dopants have to be added. This involves the fabrication of a new target for each composition ratio. MOCVD is an exception here; the ratio is adjusted by regulating the carrier gas flow. However, the equipment is very expensive and the substrate temperatures tend to be high (up to 800°, uncomfortably high for semiconductor device processing). The laser sputtering method is very attractive and it has produced very fine films. The disadvantage is that the films are defined by the plume which forms when the laser beam is directed at the source. This produces only small areas of good films and scanning methods need to be developed to cover full size silicon wafers. Debris is also a significant issue in laser deposition. However, it is a convenient method to produce films quickly and with a small investment. In the long run MOCVD or Sol-Gel will probably evolve as the method of choice for realistic DRAM devices with state of the art densities. Defining Terms A-site: Many ferroelectric materials are oxides with a chemical formula ABO 3 . The A-site is the crystalline location of the A atom. B-site: Analogous to the definition of the A-site. Coercive field: When a ferroelectric material is cycled through the hysteresis loop the coercive field is the electric field value at which the polarization is zero. A material has a negative and a positive coercive field and these are usually, but not always, equal in magnitude to each other. Crystalline phase: In crystalline materials the constituent atoms are arranged in regular geometric ways; for instance in the cubic phase the atoms occupy the corners of a cube (edge dimensions ?2–15 ? for typical oxides). Curie temperature: The temperature at which a material spontaneously changes its crystalline phase or symmetry. Ferroelectric materials are often cubic above the Curie temperature and tetragonal or rhom- bohedral below. Domain: Domains are portions of a material in which the polarization is uniform in magnitude and direction. A domain can be smaller, larger, or equal in size to a crystalline grain. Electret: A material which is similar to ferroelectrics but charges are macroscopically separated and thus are not structural. In some cases the net charge in the electrets is not zero, for instance when an implantation process was used to embed the charge. Electrostriction: The change in size of a nonpolarized, dielectric material when it is placed in an electric field. Ferroelectric: A material with permanent charge dipoles which arise from asymmetries in the crystal struc- ture. The electric field due to these dipoles can be observed external to the material when certain conditions are satisfied (ordered material and no charge on the surfaces). Hysteresis: When the electric field is raised across a ferroelectric material the polarization lags behind. When the field is cycled across the material the hysteresis loop is traced out by the polarization. Morphotropic phase boundary (MPB): Materials which have a MPB assume a different crystalline phase depending on the composition of the material. The MPB is sharp (a few percent in composition) and separates the phases of a material. It is approximately independent of temperature in PZT. Piezoelectric: A material which exhibits an external electric field when a stress is applied to the material and a charge flow proportional to the strain is observed when a closed circuit is attached to electrodes on the surface of the material. PLZT: A PZT material with a lanthanum doping or admixture (up to approximately 15% concentration). The lanthanum occupies the A-site. PMN: Generic name for electrostrictive materials of the lead (Pb) magnesium niobate family. Polarization: The polarization is the amount of charge associated with the dipolar or free charge in a ferroelectric or an electret, respectively. For dipoles the direction of the polarization is the direction of the dipole. The polarization is equal to the external charge which must be supplied to the material to produce a polarized state from a random state (twice that amount is necessary to reverse the polarization). The statement is rigorously true if all movable charges in the material are reoriented (i.e., saturation can be achieved). ? 2000 by CRC Press LLC PVF2: An organic polymer which can be ferroelectric. The name is an abbreviation for polyvinyledene diflu- oride. PZT: Generic name for piezoelectric materials of the lead (Pb) zirconate titanate family. Remanent polarization: The residual or remanent polarization of a material after an applied field is reduced to zero. If the material was saturated, the remanent value is usually referred to as the polarization, although even at smaller fields a (smaller) polarization remains. Related Topics 47.2 SAW Material Properties ? 48.3 Piezoelectric Excitation ? 58.4 Material Properties Conducive for Smart Material Applications References J. C. Burfoot and G. W. Taylor, Polar Dielectrics and Their Applications, Berkeley: University of California Press, 1979. H. Diamant, K. Drenck, and R. Pepinsky, Rev. Sci. Instrum., vol. 28, p. 30, 1957. T. Hueter and R. Bolt, Sonics, New York: John Wiley and Sons, 1954. B. Jaffe, W. Cook, and H. Jaffe, Piezoelectric Ceramics, London: Academic Press, 1971. M. E. Lines and A. M. Glass, Principles and Applications of Ferroelectric Materials, Oxford: Clarendon Press, 1977. R. A. Roy and K. F. Etzold, “Ferroelectric film synthesis, past and present: a select review,” Mater. Res. Soc. Symp. Proc., vol. 200, p. 141, 1990. C. B. Sawyer and C. H. Tower, Phys. Rev., vol. 35, p. 269, 1930. Z. Surowiak, J. Brodacki, and H. Zajosz, Rev. Sci. Instrum., vol. 49, p. 1351, 1978. Further Information IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control (UFFC). IEEE Proceedings of International Symposium on the Application of Ferroelectrics (ISAF) (these symposia are held at irregular intervals). Materials Research Society, Symposium Proceedings, vols. 191, 200, and 243 (this society holds symposia on ferroelectric materials at irregular intervals). K.-H. Hellwege, Ed., Landolt-Bornstein: Numerical Data and Functional Relationships in Science and Technology, New Series, Gruppe III, vols. 11 and 18, Berlin: Springer-Verlag, 1979 and 1984 (these volumes have elastic and other data on piezoelectric materials). American Institute of Physics Handbook, 3rd ed., New York: McGraw-Hill, 1972. ? 2000 by CRC Press LLC