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Abstract—The growing class of ferroelectric sensors covers a broad spectrum of devices based on piezoelectric, electrostrictive, pyroelectric, dielectric, and ...
IEEE SENSORS JOURNAL, VOL. 1, NO. 3, OCTOBER 2001

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Ferroelectric Sensors Dragan Damjanovic, Paul Muralt, and Nava Setter

Abstract—The growing class of ferroelectric sensors covers a broad spectrum of devices based on piezoelectric, electrostrictive, pyroelectric, dielectric, and conduction phenomena. It finds applications in as diverse and wide areas as industrial production, automotive and aerospace applications, communications, health care, and environmental monitoring. In this brief review, we first introduce the physical phenomena underlying the major types of ferroelectric sensors and the materials used. Then, the principal types sensors are described: infrared sensors, pressure sensors, force and motion sensors, flow sensors, hydrophones, ultrasonic transducers for medical imaging and material testing, and a variety of devices based on the exponential temperature dependence of resistivity. Emphasis is placed on recent advances and emerging technologies, such as thin-film array devices and novel single crystal sensors. Index Terms—Ferroelectric, piezoelectric, pyroelectric, thermistor, transducer.

I. INTRODUCTION

F

ERROELECTRICS, being also pyroelectrics (thermoelectric transducers) and piezoelectric (electromechanical transducers), find applications in a wide range of sensors and transducers. Ferroelectric sensors are used to measure force, pressure, flow and motion, temperature, and IR radiation. Imaging using ferroelectric transducers include ultrasonic medical imaging, underwater transducers, devices for nondestructive evaluation, and testing and thermal imaging systems. The sensor materials include bulk ceramics, multi-layer ceramics, single crystals, polymers, and ceramic-polymer composites. In recent years, a number of ferroelectric thin-film sensors have been developed and are entering the market. An important advantage of the thin-film devices is the relative ease of fabrication of arrays. Another direction that lately has gained interest are thick film devices that provide advantages in highfrequency applications. New relaxor-ferroelectric crystals show an extremely high piezoelectric energy conversion efficiency, which is of interest, in particular, for medical imaging applications. Applications at high temperatures impose more stringent demands on the stability of the piezoelectric response and new materials are developed to meet these requirements. This brief review aims to give a general picture of the state of the art in the field of ferroelectric sensors. To make the review self-contained, we start with a summary of ferroelectric physics and ferroelectric materials. Following this, sensors are described in the following order: pyroelectric detectors, piezoelectric sen-

sors, resistive sensors based on the ferroelectric phenomenon, and finally, capacitive sensors. The review encompasses, in a very brief way, most of the important ferroelectric sensors. References are indicated for further details. II. DEFINITIONS OF FERROELECTRICITY, PYROELECTRICITY, AND PIEZOELECTRICITY Ferroelectric materials possess spontaneous electric polarwhose orientation can be switched by a sufficiently ization strong external electric field. The polarization switching indicates that there are at least two equilibrium orientations of in absence of an external field [1]. The switching property distinguishes ferroelectrics from pyroelectric materials (such ZnO and AlN), which also possess spontaneous polarization, but which cannot be reoriented by practically achievable electric fields. Spontaneous polarization is a function of temperature (see Section IV). If the temperature of a pyroelectric material is , a charge will appear on its surface. This effect changed by is called the pyroelectric effect. Presence of the spontaneous electrical polarization indicates a basic asymmetry of the ferroelectric and pyroelectric materials. Only materials that possess a unique polar axis may show spontaneous polarization and pyroelectric or ferroelectric effect. Presence of a unique polar axis means that these materials lack a center of symmetry. With exception of materials which belong to point group 43, all noncentrosymmetric crystals, such as quartz, can be polarized (exhibit surface charge) by mechanical stress. The linear relationship between the stress and the surface charge density is called the direct piezoelectric effect. In addition to the direct effect, the piezoelectric materials exhibit a converse effect, which describes the linear mechanical deformation of the material that is induced by an external electric field, . Ferroelectric materials are, thus, a subclass of pyroelectric materials, which, in turn, are a subclass of piezoelectric materials. Classification of materials according to their symmetry can be found in several classical textbooks [2], [3]. In a summary, ferroelectric materials will develop surface (pyroeleccharge when subjected to temperature change tric effect), electrical field (dielectric polarization), and stress (piezoelectric effect). The combined effect can be written in tensor form as (1) where

Manuscript received September 27, 2000; revised August 7, 2001. The associate editor coordinating the review of this paper and approving it for publication was Dr. Thaddeus A. Roppel. The authors are with the Ceramics Laboratory, Materials Department EPFL, Swiss Federal Institute of Technology, Lausanne, Switzerland (e-mail: [email protected]; [email protected]; [email protected]). Publisher Item Identifier S 1530-437X(01)09472-6.

pyroelectric coefficient; dielectric permittivity; the converse piezoelectric coefficient. Alternatively, ferroelectric materials exhibit mechanical deformation or strain by changing their temperature (thermal expansion), applying an external force (Hooke’s law), or electric

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field (converse piezoelectric effect). These effects can be written as

nations of independent variables give six remaining isothermal piezoelectric constitutive equations [4]

(2) where is the thermal expansion coefficient and the elastic compliance of the ferroelectric. In (1) and (2), and the superscripts indicate independent variables, which are held constant in order to obtain response from a single effect. Due to the symmetry of material, certain elements of the tensors coefficients may be zero or related to eachother. Following well-known Voigt relations for mechanical properties, it is possible to express piezoelectric coefficients in reduced notations and write relations (1) and (2) in the matrix form [2]. The quadratic and higher-order terms may be added to (1) defines and (2). For example, and are electrostrictive coelectrostrictive effect, where efficients. The majority of sensor applications of ferroelectric materials as sensors are based on effects described by (1). Relations (1) and (2) imply that different effects can couple, and that response of piezoelectric and, therefore, ferroelectric materials depends on measurement conditions. For example, when stress is applied on a ferroelectric sample, the charge will be produced through the direct piezoelectric effect. If the temperature of the sample is not constant while the stress is applied, additional charge will be produced through the pyroelectric effect. The two charges, one coming from the signal (stress) and the other from the thermal noise will interfere. As will be discussed later, this coupling of the properties is of outmost importance when designing measurements and devices based on ferroelectric materials. Because of the piezoelectric coupling between the electrical and elastic fields, the values of the dielectric permittivity and elastic compliance (or stiffness) measured under different experimental conditions will not be the same. We can demonstrate this on an example of the dielectric permittivity measured on a clamped sample [conditions of a constant (zero) strain]. For simplicity, we omit tensor indices. If electric field is ap) conditions and plied on a sample under isothermal ( ), (2) gives . the sample is clamped ( Replacing now this stress into expression (1) for the surface where charge density, one obtains is called the clamped (zero is strain) dielectric constant. The combination known as the electromechanical coupling coefficient. It can be measured under shown similarly that the elastic compliance open circuit conditions (zero or constant ) and compliance , measured under short circuit conditions (zero or constant ), are [4]. related by In some ferroelectrics, may be as large as 0.7–0.9 [5], leading to as much as 50–80% difference between the free (zero stress) and clamped (zero strain) dielectric constant and elastic compliance measured under short circuit and open circuit conditions. For samples with a simple geometry, the coupling coefficient may be related to the mechanical-to-electrical energy conversion [4]. ) chosen in (1) and The set of independent variables ( (2) was arbitrary. Other thermodynamic potentials and combi-

(3) where , and

piezoelectric coefficients; elastic compliance; inverse dielectric permittivity. The tensor indices are omitted for simplicity. Equation (4) defines relationships between different piezoelectric coefficients

(4) Which equations will be used in a given problem depends on the boundary conditions. Most ferroelectric materials undergo a structural phase transition from a high-temperature nonferroelectric (or paraelectric) phase into a low temperature ferroelectric phase, Fig. 1. The symmetry of the ferroelectric phase is always lower than the symmetry of the paraelectric phase. The temperature of the ferroelectric-paraelectric phase transition is called the Curie point, . Above the Curie point, the dielectric permittivity falls off with temperature according to the Curie-Weiss law, (5) (5) ) is the Curie-Weiss where is the Curie constant, the dielectric permittivity of the vacuum. temperature, and The transition into a ferroelectric phase usually leads to strong anomalies in the dielectric, elastic, thermal, and other properties of the material [1], and is accompanied with changes in the dimensions of the crystal unit cell. The associated strain is called the spontaneous strain . It represents the relative difference in the dimensions of the ferroelectric and paraelectric unit cells. The spontaneous strain is related to the spontaneous polarization via electrostrictive coefficients. Some changes that can occur in a ferroelectric material, which transforms from a paraelectric cubic into a ferroelectric tetragonal phase, are illustrated in Fig. 1. The spontaneous polarization in a ferroelectric crystal (or a grain in a ferroelectric film or ceramic) is usually not uniformly aligned throughout the whole crystal along the same direction. The regions that have the same direction of the polar-

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Fig. 1. Dielectric anomaly, spontaneous strain, and polarization in a ferroelectric ceramic that transforms from cubic to tetragonal phase.

ization are called ferroelectric domains. The domains are separated by domain walls in which the polarization orientation changes from one direction to another. Ferroelectric domains form to minimize the electrostatic energy of depolarizing fields and the elastic energy associated with mechanical constraints to which the ferroelectric material is subjected as it is cooled through paraelectric-ferroelectric phase transition [1]. Domain walls that differ in orientation of the spontaneous polarization vector are called ferroelectric domain walls and those that differ in the orientation of spontaneous strain tensor are called ferroelastic domain walls. The types of domain walls that can occur in a ferroelectric crystal depend on the symmetry of the crystal. Ferroelectric domain walls are much narrower than domain walls in ferromagnetic materials. Observations with transmission electron microscopy show that ferroelastic domain walls in ferroelectric thin films are on the order of one to ten nanometers [1]. External fields (temperature, mechanical, or electrical) may move domain walls by, e.g., bending or moving them into a new position. The domain wall displacement may, through rather complex mechanisms, contribute to the dielectric, elastic and piezoelectric properties of the ferroelectrics [6]. This contribution, which is often nonlinear, hysteretic, and frequency dependent, may be very large and comparable to the response of the crystal lattice even at relatively weak fields. The domain wall contributions may be controlled by suitable compositional modifications of the ferroelectric. The resulting materials are called “hard” when domain wall displacement is reduced or “soft” when it is enhanced. If the external field is sufficiently large, most of or all domains may switch in directions dictated by the field. The available directions of polarization are determined by the crystallographic properties of the material. Ideally, a single-domain or mono-domain state can be reached in single crystals. Once the crystal is switched, the field reversal will lead to nucleation, growth, and propagation of new domains with the opposite sense of polarization. If the field is cycled, ferroelectric hysteresis is observed, Fig. 2. The hysteresis is characterized by its coercive field , , and maximal (also called saturated) polarization. remnant The coercive field depends not only on the coercive fields of individual domains, but also on fields necessary to nucleate and grow new domains. Strain versus electric field loops (so-called “butterfly” loops) are results of the combined effect of the piezoelectric effect and polarization switching [6].

Fig. 2. The ferroelectric hysteresis in a ferroelectric-thin film. The field cycling switches the polarization orientation. The ferroelectric will remain polarized (P or P state) even if the external field is removed. Single-domain state can be reached only in single crystals but not in ceramics, where many domains remain even at very large fields.

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III. FERROELECTRIC MATERIALS-STRUCTURES COMPOSITIONS

AND

Most ferroelectric sensors are made of oxides: lead zirconate O , abbreviated PZT], is widely used in titanate [Pb(Zr Ti piezoelectric sensors. PZT and lithium tantalate (LiTaO abbreviated LT) are commonly used in pyroelectric sensors and barium titanate (BaTiO ) is used in thermistors. The crystalline structure of these materials is the perovskite structure (described below) or a derivative of perovskites for LT. In recent years, there has been growing interest in sensors for high temperature applications. In this case, the materials have another crystalline structure, which is also related to the perovskite. For the past five years, the so-called relaxor-ferroelectrics has been attracting much attention. These materials show excellent coupling coefficient (exceeding 90% in some materials) in specific crystalline orientation, and, therefore, have to be used in a monocrystalline form. Another development is the trend to avoid lead (Pb) containing materials when possible, therefore lead-free ferroelectrics are sought. At present, however, the lead containing perovskites such as PZT are, by far, the best performing in a large range of sensors. Below, essential materials and related are described. For more details the reader is referred to [7], [8]. A. Ferroelectricity in Materials With Perovskite Structure Perovskite-oxides have the structural formula ABO in which A is a large cation, such as Ba or Pb , and B is a medium size cation, such as Ti or Zr . These cations are located in cages that are formed by the network of the oxygen anions (Fig. 3). A large number of cations have sizes that can fit into the oxygen cages. This is the reason for the abundance of perovskites, natural (minerals), and synthetic ones. Ferroelectric perovskites are a sub-group in the perovkite family. They are cubic at high temperatures and below the Curie temperature, characteristic to each material, they become non cubic (tetragonal, rhombohedral, etc.) and polar. In the cubic phase, the cations are located at the centers of the oxygen cages, while in the non cubic phases,

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(a)

Ti Zr or Na for Pb , results in oxygen vacanies that stabilize the domain walls. The PZT becomes less responsive, but more stable, the dielectric constant is lower (and so are the dielectric losses), and coercive field increases. PZT ceramics with dopants of lower valence (acceptors) are therefore called “hard” PZT and are useful for underwater applications and also for high power and high voltage applications (Table I). Dopants with a higher valence than the substituted cations (donors), e.g., Zr or La for Pb , increase concentration Nb for Ti of lead vacancies, enhancing the mobility of domain walls. They have an opposite effect: permittivity and piezoelectric coefficient are enhanced while elastic stiffness, coercive field and mechanical are reduced. The material is electrically and mechanically “softer”. It is used for medical transducers and for sensitive pressure sensors. PZT ceramics for pyroelectric applications are rich in titanium. The compositions rich in titanium (e.g., ) have a high pyroelectric zirconium titanium coefficient and low permittivity, giving good pyroelectric figure of merit. In addition, their coercive field is high, reducing risk of depolarization during use and making this composition useful also in the form of thin film. C. Relaxors and Relaxor Ferroelectrics

(b) Fig. 3.

The perovskite structure of BaTiO : (a) the cubic phase (at 120 C), and (b) schematic illustration of dipole switching upon . application of

T >

E > Ec

they are shifted off the center, in a specific crystallographic direction, in a way that leads to creation of dipoles that are oriented in parallel throughout the ferroelectric domain. The direction of the displacement of the cations in reference to the oxygens can be switched with electric field in a way that, upon removal of the field, the dipole stays in the new orientation. This is the basic characteristic of ferroelectric mateials. The non-cubic lattice is distorted relative to the cubic one; Due to the dimensional changes that are coupled to the ferroelectric transition in perovskites, these materials are also ferroelastic, so stress above a critical value can cause domain reorientation. B. Lead Zirconate Titanate (PZT) Because of its high piezoelectric constants, PZT is the most widely used ferroelectric ceramic in sensor applications. PZT is a solid solution (alloy) of lead titanate and lead zirconate. Fig. 4(a) shows the various phases of PZT as a function of composition and temperature. At the morphotropic phase boundary (zirconium/titanium ratio of 53/47 at room temperature), an abrupt transition occurs between the rhombohedral zirconium-rich phase and the tetragonal titanium-rich phase. PZT of the morphotropic boundary composition shows the constants, dielectric constant, and highest piezoelectric electromechanical coupling factors. This is the composition most frequently used for piezoelectric sensors. ) of the PZT The substitution of a small fraction ( cations by other cations modifies the properties. This is used to produce PZT that is optimized for different applications. replacing Doping by cations of lower valence, e.g., Fe

A large number of lead-containing perovskites, called relaxors, show anomalous charcteristics typified by a strong frequency dispersion of the permittivity. Examples are lead magnesium niobate (PbMg Nb O or PMN) and lead zinc niobate (PbZn Nb O or PZN). They are believed to consist of weakly-interacting mesoscopical ferroelectric regions, rather than the usual coherent ferroelectric domains. This feature leads to many useful properties: a) very high permittivity over a wide temperature range, b) large electrostrictive strain, and c) strong piezoelectric, pyroelectric, and electrooptic response under a dc bias field. Recently, much interest is focused on solid solutions of relaxors and normal ferroelectrics, called relaxor ferroelectrics, such as PMN-PbTiO and PZN-PbTiO . In the ceramic form, these materials are similar in performance to soft PZT, while the permittivity is higher (Table I). In direction, the single crystal form, in the pseudocubic PZT-PT, which is rhombohedric at room temperature, has an exceptionally high coupling coefficient, reaching 0.94! D. Layer Perovskites A large number of ferroelectrics crystallize in the so-called layer perovskite phases. These phases are made of layers of perovskites separated by other layers, such as bismuth oxide. Many ferroelectric layer perovskites have a high , making them interesting for high temperature piezoelectric applications. In addition, many of them are lead free. A prototype material is the bismuth titanate (Bi Ti O ). E. Lithium-Niobate and Lithium-Tantalate Lithium-niobate (LN) and lithium-tantalate (LT) are uni-axial ferroelectrics, having trigonal structure, with spontaneous polarization arising from asymmetrical displacement of lithium relative to the other ions. These materials have s of 1210 C and

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(a) Fig. 4.

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(b)

PZT ceramics: (a) the sub-solidous phase diagram and (b) the room temperature piezoelectric d coefficients near the morphotropic boundary (after [7]). TABLE I PHYSICAL PROPERTIES OF IMPORTANT FERROELECTRIC MATERIALS FOR SENSOR APPLICATIONS

620 C, respectivel, and are produced commercially in single crystal form since many years. Both are intensively used for surface acoustic wave devices (e.g., high frequency filters), while LT is used for pyroelectric detection due to its large pyroelectric coefficient and low permittivity. F. Ferroelectric Polymers Ferroelectricity is found in polymers too [9]. Polyvinylidenfluoride [PVDF, CH CF ] is used for sensor applications that can benefit from large sensor area. The ferroelectric polymers have low piezoelectric coefficients and, because of the low permmittivity, a high coefficients. The piezoelectric polymers are light and, therefore, have good acoustic impedance matching to water and to organic and biological matter. G. Dimensional and Microstructural Aspects of Ferroelectric Materials Ferroelectric sensors utilize a wide range of material forms: crystals, bulk ceramics, thick layers, and thin films. Noteworthy among new compositions with improved performance is the

class of relaxor-ferroelectrics. A number of novel ferroelectric sensors utilize thin and thick films. Bulk ferroelectric ceramics for room temperature, piezoelectric, and pyroelectric sensors, are widely available. New compositions with higher permittivity are available now. These are useful for size reduction of individual elements of ultrasonic probes (see Table I). Due to their higher cost, single crystals are used only when providing substantial advantages. Wafers of LiTaO single crystals are used in pyroelectric sensors due to the superior performance and low cost of manufacturing. LiNbO is the dominant piezoelectric substrate for surface acoustic devices, for similar reasons. Efforts for production of large and defect-free single crystals of the ferroelectric-relaxor PZN-PT are underway world-wide, as this material has an outstanding piezoelectric coupling coefficient, which is attractive for medical transducer applications. Multi-layered ceramics are used in actuators for reduction of the operating voltage, or in sensors for enhancing piezoelectric charge output. They are based on the longitudinal mode ( ). For an equivalent over-all thickness, an actuator made of multi -layers will need V volts to attain the same strain as the bulk

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actuator. A further way to enhance response or excursion is to use bending structures exploiting the transverse piezoelectric coefficient ( ). Various geometries are used: bimorph beams, disk benders, and heteromorphs. Examples are rainbow structures [10] and thick film disc benders [11]. Silicon micromachining and thin-film technologies developed during the past decade offer new possibilities to combine piezoelectric and pyroelectric materials with mechanical and – m) for ferroelectric thermal functionality. Thin films ( sensors are prepared mainly in two ways: sputtering and chemical solution deposition (CSD) [12]. The first method is of particular interest for pyroelectric sensors, since the films are self-poled due to the growth conditions [13]. An advantage of CSD is the low cost of equipment needed for preparation of the films. In general, ferroelectric thin films are processed at temperatures higher than 600 C in oxygen. Special care is taken to avoid diffusion of lead into the silicon substrate and of oxygen into metallic substrates [14]. Silicon micromachining is performed after the deposition of ferroelectric films and their electrodes [15], [16]. For some developing applications (e.g., high frequency medical transducers), thicker films are needed. The conventional way of preparation is by the screen printing process, which is convenient for films of 10–100 m thickness. The processing C) and not suitable for silicon or temperature is high ( metallic substrates. Efforts in direction of processing temperature reduction are done using hydrothermal growth [17] and CSD films loaded with powders [18]. H. Poling of Ferroelectric Materials After the manufacturing, ferroelectric materials usually do not possess piezoelectric or pyroelectric properties, since the ferroelectric domains are randomly oriented. The poling process consists of the application of a dc electric field to align the domains. A remanent polarization persists after the removal of the field and the material is piezoelectrically and pyroelectrically active. Poling is usually done at elevated temperatures (below ) using fields larger than the coercive field. During use of ferroelectric materials, care should be taken to avoid depolarization under high temperatures, electric fields, or stresses. IV. PYROELECTRIC APPLICATIONS A. Phenomenon and Materials Pyroelectricity provides one of the best performing principles for the detection of temperature changes [21], [22]. Bulk crystals, ceramics, as well as polymers [9] have, therefore, been used since many years in thermal infrared detectors. They were and still are applied for contact-less temperature measurement, security detectors (intruder alarms), and human presence sensors. With respect to semiconductor detectors, thermal detectors are competitive in the important wavelength interval of 8 to 12 m. Their special attraction lies in the fact that they do not need cooling [23]. The advent of silicon micromachining techniques enabled the cost-effective fabrication of one and two-dimensional (2–D) arrays. A very effective thermal isolation is achieved by fabricating the pyroelectric element on a thin ( m) micromachined ceramic membrane (Fig. 4.1). One-di-

Fig. 5. Schematic cross section through a simple macromachined IR detector with housing and optical window acting as a IR passband filter.

mensional (1–D) arrays allow for an improvement of security and human presence detectors (used for instance in air conditioning [24]), but stimulate also some new applications such as low-cost infrared gas spectrometry [25]. 2-D arrays are fast enough to produce real-time thermal images at frame rates of 30 to 50 HZ. Essential problem of 2-d arrays is the readout. However, major advancements have been achieved. Surface micromachining techniques combined with thin-film deposition of pyroelectric thin films allowed the realization of 2-d arrays in a monolithic way directly on the readout chip [26]. Pyroelectricity is based on a pronounced temperature dependence of the electric displacement field in a ferroelectric material. In ferroelectrics, the displacement field is practically identical to the polarization . The basic structure of a pyroelectric element is a planar capacitor as shown in Fig. 5. The charge density on the electrodes is the electric displacement field perpendicular to the electrode faces. Giving the index 3 to this direction, the pyroelectric coefficient p is . In absence of an electric field , written as equals simply the average remanent polarization projected ). A poling process (or polar growth onto the 3-direction ( of thin films) in an electric field has to provide a large as possible remanent polarization along this direction. Subjected to a , a charge density temperature change (6) appears on the electrodes of a parallel plate capacitor. The first , the true term is called the true pyroelectric effect and pyroelectric coefficient. According to the Landau-Devonshire theory of second and ideal first order phase transitions, the proholds, being the spontaneous polarizaportionality tion. This relation is quite well confirmed by experiments [1]. . The second term arises from the first order correction for Pyroelectricity arising due to this second term is called induced pyroelectricity. There are two modes of operation for pyroelectric IR detectors. The first one works without external electric field at a temperature much below the para-to-ferroelectric has previously been maxiphase transition. The polarization mized by hot poling at an elevated electric field, assuring a good time stability of at the application temperature around room temperature. The second mode exploits the peaking of near the

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phase transition. A dc electric field needs to be applied to obtain a nonzero average polarization. One speaks of induced pyroelectric currents or sometimes of dielectric bolometer mode, since the field dependence of can be considered as a dielectric property. The applied field has not only the effect of eliminating 180 domains, it broadens and shifts (first order transition only) the phase transition to higher temperatures. This leads to a reduction of the signal. There is, thus, an optimal dc field (a few MV/m) and temperature (see Fig. 6) at which the response is peaking. The temperature of such a device needs to be stabilized. The advantage of the first method is the simplicity of operation conditions: no dc field and no temperature stabilization are needed. The second method allows much higher induced pyroelectric currents (see Table II). Pyroelectric currents are proportional to the time derivative of the temperature and, in case of IR detectors, thus, to the changes of IR radiation. In order to assess stationary IR sources as well, a chopper is used to modulate the IR radiation. Signals thus exhibit a well-defined angular chopping frequency . The smallest detectable temperature change is limited to either the temperature fluctuation of the detector system [28], the electronics, or the intrinsic noise current of the pyroelectric element, given here for a thin film

(a)

(7) where leakage conductivity of the pyroelectric thin film (in bulk detectors: the parallel resistor); angular frequency; loss tangent; frequency bandwidth; surface; thickness of the element. between The cross over frequency resistor-type noise and dielectric noise amounts to typically 0.1–10 Hz. At typical modulation frequencies of 30 Hz, the dielectric noise is thus dominating. The figure of merit of the dielectric and pyroelectric materials parameters for an optimal detectivity can thus formulated as

(b) Fig. 6. (a) Theoretical behavior of the pyroelectric coefficient as a function of temperature and for various electric fields, as derived from the Landau-Devonshire model [1] for an ideal first-order ferroelectric-to-parelectric phase transition. The behavior near the phase transition in absence of an external field is purely theoretical, since the average polarization decays to zero by thermal fluctuations and (b) experimental curves for Pb(Sc Ta )O (from [27]).

(8) Data of some representative ferroelectrics are given in Table II. A major issue in thin-film pyroelectric materials is the optimization of the polarization component perpendicular to the electrode planes (3-direction). Many of the good pyroelectric materials (such the PbTiO derived compounds) exhibit a tetragonal symmetry, the -axis being larger than the identical and -axis. A (100)-oriented grain of the para-electric high temperature phase will split up into a mixture of (001), (100), and (010) domains. Only the (001)-domains with the polar -axis perpendicular to the film plane will contribute to the pyroelectric effect. The creation of the 90 domains cannot easily be suppressed, as they balance the thermal misfit strains with the substrate. Substrates with large thermal expansion coefficients leading to in-plane compressive stresses upon cooling down (such as MgO) yield higher volume fractions of (001) domains

than the ones with small thermal expansion coefficients (such as silicon) [31]–[34]. For this reason, MgO, which can be micromachined as well, was considered as an alternative solution to silicon for the production linear arrays [24]. B. Pyroelectric Infrared Detectors The response of a thermal detector depends very much on the thermal properties of the detector elements. A large as possible temperature increase must be achieved for a given infrared power absorbed by the detector. This means that the heat caof the element and the heat conductivity to the pacity support and the housing must be as small as possible. This is conveniently achieved by silicon micromachining techniques allowing the fabrication of very thin membranes of thermally inand SiO . Thermal time consulating materials such as Si

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TABLE II REPRESENTATIVE DATA ON THIN FILM PYROELECTRIC MATERIALS

stants of 30 to 100 ms are typically achieved [35]. This means that, at modulation frequencies of 30 Hz, the heat capacity is essential and that the heat conductivity effects are small enough to be neglected. Thin-film detectors are very advanta. With geous in this regime since the heat capacity scales as inclusion of the dielectric noise (6), a scaling behavior for the is obtained. Two major solutions have been detectivity of elaborated for achieving high IR absorption coefficients of the detector. The first one utilizes black absorbing layers. These are usually porous metal films such as black platinum or black gold. The second method uses semitransparent top electrodes (of e.g., thick pyroelectric layers. This leads to an entrapNiCr) on ment and final absorption of radiation. The first method achieves larger absorption coefficients (90%), compared to the second one (60%); however, the total thickness and, thus, heat capacity is increased. Today’s IR imaging devices achieve noise-equivalent temperature differences (NETD) that are below 0.1 K, meaning that a black body target object (whose IR light covers one pixel at least) with a temperature difference of less than 0.1 K with respect to the background can still be detected. Best reported values are as low as 70 mK. C. Device Examples Bulk, micromachined, linear arrays needing no vacuum and no cooling are attractive IR sensors for a variety of applications. The linear array shown in Fig. 7 has been developed for an infrared spectroscopy gas sensor [36]. IR-light source, optics, focal plane array and readout electronics are integrated in one housing. The light source is a filament. The heater current is modulated to obtain a modulation of the signal. Each element of the array receives a certain wavelength section, as defined by a grating. In this way a complete absorption spectrum can be sampled in parallel operation in an interval inside the 4 to 12 m range. The pyroelectric material was a sol-gel deposited (111)-oriented PZT15/85 thin film. A detectivity of cmHz W was calculated from measured , , and . In the case of 2-D arrays, hybrid fabrication and micromachining techniques compete at the moment. The hybrid approach is based on reticulation of ceramic wafers that are polished down in thickness and joined with the read out chip. Quite complex hybrid focal plane arrays with 384 288 and 328 245 pixels were presented by GEC-Marconi and Texas Instruments [38], [39]. They work either with pyroelectric PZT ceramic or with field-induced pyroelectricity (dielectric

Fig. 7. Top view on 50-element array with 200 m period obtained with bulk micromachining, membrane size 2 11 mm. The black platinum absorbers, the Cr-Au contact lines, the membrane layers between the elements and the SiO layer for reduction of parasitic capacitance are well visible (from [36], [37]).

2

bolometer) of (Ba,Sr)TiO (BST) or Pb(Sc Ta O . The version of Texas Instruments (now a product of Raytheon) operates with BST at a stabilized temperature near the ferroelectric critical temperature around 20 C. It is still called an uncooled imaging device, because the necessary heater/Peltier element combination consumes much less power than is required for the standard cooled devices. The starting point of fabrication is a ceramic BST wafer. After reticulation by laser or ion milling processes, bonding to a polymer foil, polishing down, electrode and absorber layer deposition, the so-obtained BST array is bonded to a readout IC via a mesa structure (see Fig. 8). The absorber layer is a transparent organic layer, sandwiched between a semitransparent metal layer and the common electrode. The mesa structure is grown on the readout IC. The latter is either a charge-coupled device (CCD) or exhibits amplifiers and sample-and-holds for each pixel, combined with a multiplexed reading for the output. Such devices achieve a NETD of less than 0.2 K. The micromachining techniques target to fabricate the pyroelectric pixels directly on the readout chip in a post-processing line. This is achieved by means of so-called surface micromachining techniques that are based on sacrificial layers which are removed after growth and patterning of the pyroelectric capacitors. The latter are fixed in place by vertical conductive studs that connect directly to amplifier and multiplexer circuits. Fig. 9 shows a top view of the micromachined pixels. The deposition

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Fig. 8. Two-dimensional array bolometer based on thick film BST bonded to the readout chip by a mesa structure [39]. The pixel thickness (BST) amounts to 10 to 18 m, the pitch is 48.5 m.

temperature for the pyroelectric thin films has to be low enough in order to avoid damage to the aluminum lines on the readout chip. Surface micromachined sensors need vacuum isolation to avoid heat conduction through air, since the distance between thermal element and readout chip is too small. V. PIEZOELECTRIC APPLICATIONS In its most common mode of sensor operation, which is based on constitutive relations (1) and (3), the piezoelectric materials are used to sense and measure force, pressure, vibration, or acceleration [20], [41]. For example, the pressure applied on a piezoelectric material can be determined using relation or [(1) or (3)]. Both the range of applications and modes of operation of piezoelectrics are, however, much wider. The present trends include application in sensor-actuator structures for active control or in so-called “smart” systems where piezoelectrics can serve as both sensors and actuators, ultrasonic imaging in the 40–100 MHz range, operation at high temperatures and under high pressures and use of resonance mode of operation for sensing purposes. Selected applications and merits of ferroelectric materials are discussed below. A. High Temperature Applications There are a number of sensor applications that require oper– C) including pressure ation at high temperatures ( measurements in engine combustion chamber to optimize ignition timing, in turbines, injection molding, and during deep drilling. Many other applications are expected to arise, related, for example, to the noise and vibration monitoring and control, especially in connection with the rapidly growing aerospace transportation systems. The piezoelectric and capacitive ferroelectric pressure sensors are good candidates for many of these applications. There are several requirements that must be rigorously respected when considering ferroelectrics for high temperature applications. The ferroelectrics must possess the Curie temperature well above the maximum operating temperature of the device. There are several reasons for this. The dielectric elastic and piezoelectric properties of ferroelectrics exhibit anomalies as the transition temperature is approached and this must be avoided to insure stable device operation. The devices based on ceramic piezoelectrics may easily depolarize under combined conditions of high temperature and pressure. For many high precision applications, the sensor response must exhibit a low temperature coefficient over hundreds of degrees. The thermal energy facilitates displacement of domain walls, leading to the large power dissipation and hysteretic behavior

Fig. 9. Surface micromachined 2-D IR array based on pyroelectric PLZT thin films [40].

especially close to the transition temperature. The temperature variation will produce pyroelectric charges which, as outlined in Section II, may interfere with the piezoelectric effect. In addition, many ferroelectrics become conducting at high temperatures, leading to the charge drifts and partial loss of the signal. For this reason, the lower frequency limit of sensor operation is significantly increased at high temperatures. The conductivity problem is aggravated during operation in atmosphere with a low oxygen content, where many oxygen-containing ferroelectrics may rapidly loose oxygen and become semiconducting. For all above reasons, nonferroelectric piezoelectrics langasite, La Ga SiO and AlN, are strong candidates for the high temperature piezoelectric applications. Nevertheless, due to the high piezoelectric sensitivity, the high transition temperature in certain families and possibility to tailor properties of ceramic piezoelectrics, the ferroelectrics are attractive materials for high temperature applications. C) and Except for lead-metaniobate, PbNb O ,( C , both of which may suffer from the LiNbO conductivity problems at high temperatures, none of the widely used ferroelectric materials (barium titanate, PZT, potassium niobate, KNbO ) has high enough transition temperature. Recently, several more exotic families of ferroelectrics have been investigated for high-temperature applications. The most attractive are Bi Ti O -based layer structure oxides with up to 940 C and Sr Nb O family with transition temperature up to 1500 C. Significant progress has been made in development and property tuning of Bi Ti O -based ceramic sensors, which are now commercially available, with operation temperature up to 550 C [19]. The thermal (pyroelectric) noise in ferroelectric pressure sensors may be reduced or completely avoided by using sensors in shear-mode, which does not contain component of the polarization. The disadvantage of this mode of operation is that samples

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need to be machined into special shapes or sometimes poled along large thickness, the latter being very difficult in materials with high coercive field, such as bismuth titanate. An interesting alternative to the piezoelectric high temperature sensors are capacitive sensors (see Section VII). Since they operate at high frequencies and their operation is not limited to the ferroelectric phase, the conductivity, charge drifts, pyroelectric interference, and depolarization associated with the ferroelectric materials are no longer an issue. For an operation over a large temperature range, however, strong temperature dependence of the permittivity in the vicinity of the ferroelectric phase transitions would limit interest to those ferroelectric material with transition temperature far away from the operating temperature range. Another way to reduce the conductivity, pyroelectric, and charge drift effects is to use pressure sensitivity of the piezoelectric resonance characteristics. B. Non-destructive Testing, Medical Imaging, and Underwater Applications The dual nature of the piezoelectric effect (converse and direct effect) is used in a large number of applications, including nondestructive testing (NDT), acoustical microspcopy [42], medical ultrasonic imaging [5], [43], [44] and diagnosis, flow measurements in industry and medicine using Doppler effect [45], and underwater acoustics [46]. The operation principle of these very different applications is the following: an acoustic wave is generated by a piezoelectric transducer (emitter), the wave is reflected by an objected and then analyzed by a piezoelectric receiver. The emitter uses the converse piezoelectric effect to generate acoustic waves and the receiver, which is often the same transducer as the emitter, uses the direct effect to transform the reflected acoustical signal into electrical signal or image on the screen [47]. The operating principle is illustrated in Fig. 10 for the Doppler method. Transducers can be piezoelectric crystals, ceramics, or polymers. To illustrate some of the issues relevant for the design of piezoelectric transducers, we take the example of medical ultrasonic imaging. The emitter usually operates at the resonance frequency, with the dimension of the transducer being equal to the one-half of the acoustic wavelength. The operation under resonance conditions limits the bandwidth so that different transducers need to be used for each frequency range. To examine small objects or features (mm size or below), the frequency needs to be high, typically 20 MHz or higher. At such frequencies, the attenuation of the ultrasonic waves is also very high so that only a thin layer can be examined. The high frequency operation is thus applicable to ophthalmology and dermatology, whereas obstetrical, abdominal, and cardiological applications require lower frequencies, on order of 1–5 MHz. The resonance frequency is inversely proportional to the active dimension of the oscillator. The small size of piezoelectric elements for the high frequency applications (tens to hundreds of m) requires high quality of transducer material [48]. Presently, the most widely-used transducer material are PZT ceramics, which for the upper frequency range (tens of MHz) must possess nearly perfect density and small grains. These two requirements are important for both improved acoustical properties and more efficient device fabrication [49]. For very high frequencies (up to

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Fig. 10. Principle of operation of the Doppler probe. An acoustic pulse is emitted by the probe and reflected by the moving blood. The reflected signal is picked up by the probe and analyzed. The blood velocity v is defined by the frequency shift f between the incoming and reflected signal, the sound velocity c, the frequency f of the incoming pulse, and the angle between the transducer and the direction of the blood velocity.

1

80–100 MHz), the thick film and tape casting technologies will probably play an important role as they may allow fabrication of a large number of small transducers with a reduced number of steps. Alternative technologies with silicon micromachining and piezoelectric membranes are currently investigated, as well [50]. For many of these applications, the most important transducer parameter is the coupling coefficient (see Section II) i.e., the efficiency of the electro-mechanical conversion [47]. In array transducers (Fig. 11), individual elements have either form of thick rods (thickness width) or thick, narrow bars. The couand for the bars ( pling coefficient for the rods is clamped in one dimension). The potentially significant advancement has been recently made by developing new single crystal materials such as PZN-PT and PMN-PT (Section III) with [51]. Due to the large coupling coefficient, the effective bandwidth of transducers made of these materials is increased and overall properties better than those of similar probes fabricated with conventional PZT ceramics [5], [43], [44]. Recently, a phased-array transducer using PZN-PT (Fig. 11) has been reported to operate equally well at two distinct frequencies (3.7 MHz and 2.5 MHz), effectively replacing two different PZT probes [5]. Once the present problems with economical production of the large-size single crystals of PMN-PT and PZN-PT are solved, these materials could be potentially very attractive for fabrication of array transducers. ( , and are The large acoustical impedance the density and sound velocity in the material) of solid ferroelectrics is much higher than that of human body, which, in MRayl turn, is close to that of water. For example, for PZT, compared to 4 MRayl for PDF and 1.5 MRayl for water [46]. The impedance mismatch leads to significant reflection of the acoustical signal at the transducer-human body interface, slow pulse-rise time, and prolonged signal ring-down that reduces the resolution [52], [53]. To improve the acoustical impedance matching, additional acoustical layers must be added at the back and front (load side) of the transducer. Alternatively,

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Fig. 11. Geometry of the piezoelectric elements used for array transducers. The long, narrow bars are used for 2-D arrays and rods for 1-D arrays. Each shape has a different coupling coefficient. Shaded areas indicate positions of electrodes. On the right, is the drawing of a 128-channel phased array probe for echocardiography with a center frequency 3.7 MHz using 0.91PZN-0.09PT single crystals. (After [5]).

the impedance matching can be improved by using piezoelectric polymers, such as PVDF, which are soft and possess a low density (thus low ), and have additional advantage of mechanical (high bandwidth) flexibility, low mechanical quality factor and the fact that thin layers can be easily fabricated. One disadvantage of PVDF is the low coupling coefficient (Table I, [20]). The compromise is found in polymer-ceramic [54], [55] composites, which exhibit the coupling coefficient comparable to that of ceramics, lower than in ceramics, reduced transverse coupling (cross-talk) between array elements and mechanical flexibility. The polymer phase is not piezoelectric and, by adjusting the connectivity of the two phases and the properties of the polymer phase [52], the possibility to tune the properties of the composite are significantly increased. Other parameters, such as dielectric permittivity, also play a decisive role in choosing the transducer material. The low permittivity materials, such as polymers, have the disadvantage of the high electrical impedance, which may make difficult the electrical matching of the transducer with the rest of the electrical circuit [47]. In addition, the high dielectric loss of polymers is undesired in the receiver mode because it reduces the signal-to-noise ratio. Besides ultrasonic imaging, the piezoelectric ceramics and polymers are used widely in medicine, from pressure sensors in orthopedics to noninvasive detection of the blood vessels diseases. The latter application uses Doppler effect to detect changes in the blood flow associated with the blood vessels stenosis (see Fig. 12). [45]. Many of the issues discussed above for the medical imaging transducers are also relevant for the underwater sensing (hydrophones) and generation of acoustic waves underwater [46], [56]. One important difference is the operation frequency that is in or below the kilohertz range for the underwater applications, the higher frequencies being strongly attenuated in water. The wave length at low frequencies is larger than the size of the sensor so that the effective pressure is hydrostatic. The relevant material coefficients besides the coupling factor are the hydrostatic piezoelectric coefficients and . The applications include the study of marine life, detection of oil deposits, ship navigation, fish location, shock-wave sensors, detection of seismic waves, and many military applications. Recently, low cost piezoelectric hydrophones have been developed for recreational and educational purposes,

Fig. 12. The Doppler signal velocity as a function of time for a blood vessel without and with stenosis. The spectral broadening on the right indicates a wide range of velocities and presence of stenosis. The Doppler method allows rapid and noninvasive testing and diagnosis.

for example, for listening of sounds emitted by whales and dolphins. C. Resonant Sensors Thesensorspresentedabovehaveincommonthatthemeasured quantity is transformed into a voltage or current. Piezoelectrics offer a further possibility, namely to transform the measured quantity into a frequency. This is done by means of resonating structures that are sensitive to changes of the resonating mass, boundary forces, or temperature. Piezoelectric excitation is, at the same, time applied to keep the structure vibrating at one of its resonance frequencies and to get a feedback response on amplitude and phase. The influence of the measurand changes the vibration frequency, which is tracked by a special electric circuitry (see [57] for a review). Frequency and also time can be measured in a very precise manner. Resonant sensors are, thus, potentially very sensitive. In addition, a frequency can directly be transformed to a digital output and is not sensitive to analog levels of the circuitry. High quality factors and not too large coupling coefficients are obvious conditions for resonators with a precisely defined resonance frequency. A typical example, and probably most often used sensor of this type, is an AT-cut quartz disk in which a standing shear bulk

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Fig. 13.

Interdigital electrodes (IDT) for sending and receiving a Rayleigh (SAW), Love, or Lamb wave.

wave is excited. The wave reacts sensitively to mass loading of the surface. Such quartz balances are used in thin-film thickness monitors and biomedical sensors. The latter exploit the mass increase of a surface layer due to enzymatic or antibody reactions. Ferroelectric materials are not much suited for precisely this type of resonant sensors, as they exhibit less good -factors and higher coupling coefficients, yielding broader resonance peaks. They neither exhibit the excellent temperature stability of quartz. However, there are a variety of other devices with standing and travelling waves that are suitable for the application of ferroelectric materials. They can be grouped into two major categories. The first category consists of sensors with propagating waves including surface acoustic wave (SAW) sensors, flexural plate wave (FPW) or Lamb wave sensors, and Love wave sensors. The second category is based on standing (bulk) waves in micromachined structures. Such resonant microsensors are conceptually the same as quartz resonators (beams, forks, plates, etc). However, they consist mainly of silicon or related materials (thermal oxide and nitride). Actuation and strain detection are performed by means of a piezoelectric thin film or by means of electrostatic interaction.

high wave velocities (meaning larger than the sound velocity in the liquid), as occurring in SAW and Love devices, shear waves are the best suited for applications in liquids [58]. In contrast to Lamb and SAW waves, asymmetric Lamb waves can be generated with sound velocities much lower than the sound of water [60]. The transverse nature of this wave can even be used to drag the liquid (or particles) in a small interface layer [61]–[63]. Common to all the wave sensors is the type of transducer needed to couple electrical energy into the piezoelectric material and to detect the wave. This is an interdigital electrode [64], [65] also called interdigital transducer (IDT) (see Fig. 13). Gas sensors with SAW resonators are commercially available. In most cases, -cut quartz is used, for instance, for an electronic nose based on fast gas chromatography [66]. Higher temperature drifts hinder the application of ferroelectric materials. It has been shown [67], however, that a Love-wave device LiTaO crystals with small thermal drifts is obtained on when the wave guide layer is made of SiO . Lamb wave devices for liquid or particle transport need mechanical powers as large as possible. In this case, best performance should be achieved with PZT thin films. Fig. 14 shows a stationary Lamb wave in a micromachined membrane containing a PZT thin film.

D. Sensors Based on Propagating Waves In order to be surface sensitive, wave sensors are based on waves confined in a thin layer of material. One possibility is surface acoustic waves (SAW) that do not radiate into the bulk of the material, but are constraint to run in a layer of about 1 wavelength thickness adjacent to the surface. Such devices are readily available as they are produced in huge quantities for mobile telecommunications, where they are used for signal filtering. Major materials in use for this purpose are the piezoelectric materials quartz, LiNbO , and LiTaO . A second possibility are Love waves. In this case, a shear wave is confined to a top layer (wave guide layer) deposited onto a substrate with larger acoustic velocity than the wave guide layer [56], [58]. A sensitive solution was found with an inelastic polymer layer on top of a quartz crystal [59]. A further possibility is to excite waves in a thin membrane called flexural plate waves or Lamb waves. A piezoelectric thin film is included in the membrane structure. The principle of sensor operation is basically the same for all of them. There is, firstly, the mass loading effect that can be used. Material that agglomerates or condenses on the surface enhances the mass to be moved by the wave and thus reduces the wave velocity or the attenuation. In liquids, there is also an interaction between the wave and the liquid (viscous coupling) that needs to be considered. Dipolar or ionic nature of the liquid may also produce acousto-electric effects. Generally, one prefers waves that do not radiate into the liquid. In case of

E. Resonant Microsensors The principle is schematically shown in Fig. 15. A micromachined silicon bridge is coated with a piezoelectric thin film such as ZnO, AlN, or PZT. Two separate electrodes on sites with maximum deflections (the two ends in this case) are used to excite a deflection wave (electrode 1) and to detect the response (electrode 2). The latter is amplified and used to drive the first electrode. In this way, a standing wave is excited at resonance. The silicon part of the resonant structure can be chosen to be several times thicker than the piezoelectric film. In this way, one takes profit of the good quality factor of silicon ( factors of up to 600000 have been demonstrated with silicon structures [68]). The coupling coefficient is reduced in this way. However, it can be still higher than in quartz. If there is a pulling force acting on the two ends of the bridge, or a pressure difference between the two sides (of a membrane), the bridge is stretched and the resonance frequency goes up. In this way, it is possible to measure static forces as well [69], [70], which, otherwise, is not possible with piezoelectrics. The quality factor is very much reduced by the power transmitted by vibration and acoustic emission into the carrier of the resonating structure. For this reason, moments and shear forces on the clamped ends have to be reduced. Fork and triple beam structures are suitable solutions [68]. is, as well, reduced by air and water [71], [72]. Vacuum packaging is, therefore, often

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Fig. 14. Lamb wave in PZT/Pt/Si Nomarsky light microscope [62].

N

membrane (mm

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2 mm), as seen by

Fig. 15. Schematic cross section through of a resonant microsensor having the shape of a bridge or a membrane.

required to achieve enough high -values. A force sensor based on a ZnO coated triple-beam resonator has been demonstrated with a sensitivity of 10 kHz/N [73]. F. Motion and Vibration Sensors The sensing of vibration, pressure waves, and other mechanical impacts are one of the standard applications of piezoelectric materials. In recent years, the need for motion sensors has been rapidly increasing for automotive applications, robotics, and navigation systems. Simple accelerometer structures are, for instance, obtained with bimorph or heteromorph beams loaded with a seismic mass at the free end. More challenging are gyros (angular speed sensors). These consist of oscillating structures moving in a defined plane in absence of any rotational motion. The Coriolis forces of an angular motion move the structure out of this plane, thus distorting the oscillating structure. Piezoelectricity can be used to activate the oscillation as well as to detect the distortion. Several solutions have been proposed. The oscillating body can be a PZT cylinder, a fork [74], a PZT triangular prism [75], a membrane [76], a PZT disk [77], or even a surface acoustic wave [78]. Fig. 16 shows the working principle of the triangular prism. All of the three facets are covered with electrodes. One is used to excite the oscillation. The output is the difference of the piezoelectric currents induced in the other two electrodes. At rest, the output is zero. Under rotation, the prism bends more to one than to the other side, yielding a nonzero output current. VI. PTC EFFECT The PTC effect illustrates very well the richness of very different phenomena useful for sensor applications, which are associated with the ferroelectricity. The abbreviation PTC

stands for the positive temperature coefficient of the resistivity. The effect is closely related to the ferroelectric phase transition and thus presents a critical phenomenon. It may appear in many materials, but the best known one is in donor-doped BaTiO [79]. As seen in Fig. 18, the resistivity of the donor-doped barium titanate increases sharply with increasing temperature near the ferroelectric phase transition and, outside of this narrow region, decreases with the increasing temperature as expected for a semiconducting material. The physical origin of the effect is extremely complex. The grain core is semiconducting but is surrounded by an insulating grain-boundary region depleted of charge carriers. This depleted region forms a Schottky barrier at the grain boundaries. The resulting barrier height for an electron moving across the grain boundary is inversely proportional to the dielectric permittivity [80]. Thus, at temperatures above , where the permittivity is low, the ceramic has a high is approached on resistivity (region I in Fig. 17). As the cooling, the permittivity increases according to the Curie-Weiss law (5) and the barrier decreases leading to the sharp decrease in the resistivity (region II). The resistivity does not increase (region III, Fig. 17) where as the sample is cooled below permittivity now decreases (see Fig. 1). The reason for this is that the charge that appears at the grain boundaries due to the onset of the ferroelectric polarization will partially cancel the effect of the depletion layer and will reduce the barrier in some places, thus forming the low resistivity path through the sample. The nature of the semiconducting properties of the grain core is associated with the ionized trivalent (e.g., Sm) or pentavalent (e.g., Nb) cations replacing Ba or Ti, respectively. The reasons for the high concentration of the deep acceptors states in the grain boundary region are complex. The electrical properties of the grain boundary layer depend on oxygen and cation vacancy diffusion rates, sintering atmosphere, quenching rate, and other preparation parameters. The fact that the effect is observed only in ceramics is an advantage because ceramics properties can be easily tailored. Thus, even though the effect is closely linked to can be adjusted by appropriate the critical temperature, the modifications. For example, (Sr,Pb,Ba,Re) TiO , where Re is a rare earth cation, can exhibit the PTC effect anywhere between and 450 C [79]. The PTC effect can be used in one of its three major types of operation. The resistance/temperature characteristics are used in thermal switching, to protect overheating of devices, in thermal sensors and for heaters. The sensitive semiconductor devices and quartz crystals for frequency control can be kept at a constant temperature using PTC heaters. A PTC heater will selfregulate and keep a constant temperature within a few degrees even if the ambient temperature changes by a hunfrom the dred degrees [80]. The current/time characteristics are used for transient current generators, degaussors, and delay circuits. The voltage/current characteristics (Fig. 18) are dependent on the power dissipated from the surface of the PTC element. This is the basis of operation of liquid, level sensors and flow meters. If the PTC sensor is immersed in the liquid or if the liquid velocity changes, the power dissipation rate will change affecting, thus, the current-voltage characteristics of the sensor. On the same principle works the sensor for detecting the onset of icing on helicopter blades, [20], [80].

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Fig. 16.

Triangular prism gyro made of PZT ceramics (from [75]).

Fig. 17. The temperature dependence of the resistivity for a BaTiO -based PTC resistor. The indicated regions are explained in the text. Note the logarithmic scale for resistivity.

VII. CAPACITIVE SENSORS Capacitive pressure sensors are based on the pressure dependence of the dielectric permittivity. In a centrosymmetric material and under conditions of constant polarization, the pressure dependence of the permittivity is related to the electrostrictive . [81] The fercoefficient by roelectric materials are good candidates for these applications, as they have large permittivity, but the disadvantage is that rearrangement of domain walls leads to a time dependence of the response [81]. Since the presence of the spontaneous polarization is not required for the operation, material can be used in the paraelectric phase, where overall losses are smaller, providing that the transition temperature is far outside of the operating range so that the temperature coefficient of the permittivity is small. The sensitivity of the effect is much lower than in the piezoelectric effect. In contrast to the devices based on the piezoelectric effect, the capacitive sensors can be used for measurements of the static pressure and exhibit less problems at high temperatures (Section V-A).

Fig. 18. Voltage-current characteristic typical for a PTC resistor in thermal equilibrium (solid line). When the external conditions for the rate of heat dissipation change, the temperature of the PTC element changes only slightly, but the V-I curve shifts significantly (broken line). If the voltage is kept constant, the current changes as a function of the heat dissipation rate (After [80]).

VIII. CONCLUSION Ferroelectric materials are very versatile and offer a wide spectrum of possible sensor applications. Current trends go in the direction of miniaturization, increase of resolution and precision, applications under extreme conditions, new processing methods, and improved materials. REFERENCES [1] M. E. Lines and A. M. Glass, Principles and Applications of Ferroelectrics and Related Materials. Oxford, U.K.: Clarendon, 1979. [2] J. F. Nye, Physical Properties of Crystals. Oxford, U.K.: Oxford University, 1985. [3] Y. I. Sirotin and M. P. Shaskolskaya, Fundamentals of Crystal Physics. Moscow, USSR: Mir, 1982. [4] D. A. Berlincourt, D. R. Curran, and H. Jaffe, “Piezoelectric and piezomagnetic materials and their function in transducers,” in Physical Acoustics-Principles and Methods, W. P. Mason, Ed. New York: Academic, 1964, pt. Part A, vol. I.

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Dragan Damjanovic was born in Sarajevo, Yugoslavia, in 1957. He received the diploma in physics from the University of Sarajevo in 1980. He attended Pennsylvania State University (PSU), University Park, PA, where he received the Ph.D. degree in ceramics science in 1987 for his work on piezoelectric anisotropy in lead titanate-based ferroelectrics. After working briefly on high temperature superconductors at Materials Research Center, Energoinvest Corporation, Sarajevo, he returned in 1988 to Materials Research Laboratory (MRL) of PSU. At MRL, he worked on dielectric, piezoelectric, and ferroelectric properties of ferroelectric and relaxor ceramics, biological polymers, ceramic-polymer composties, and on pyro-optic imagers, He joined the Ceramics Laboratory, Materials Department, at the Swiss Federal Institute of Technology (EPFL) Lausanne, Switzerland, in 1991. His current research interests include investigations of the mechanisms that contribute to the piezoelectric hysteresis and nonlineraity, applications of piezoelectric materials under extreme conditions (low frequency, high temperature, high pressure, reducing conditions), ferroelectric materials for medical applications, piezoelectric sensors and actuators for vibration and noise control, properties of relaxor-ferroelectric thin films, thick films, single crystals, and ceramics and properties of nonlead based ferroelectrics.

Paul Muralt was born in Zurich, Switzerland, in 1954. He received the diploma in experiemental physics in 1978 from the Swiss Federal Institute of Technology (ETH), Zurich, where he received the Ph.D. thesis in the field of commensurate-incommensurate phase transitions in 1984. In 1984 and 1985, he held a post-doctoral position at the IBM research Laboratory, Zurich. He poineered the application of scanning tunneling microscopy to surface potential imaging. After a stay at the Free University of Berlin, Berlin, Germany, he joined the Ceramics Laboratory headed by Prof. N. Setter at the Materials Department, Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland, as Senior Researcher. His interests are the growth of ferroelectric and other polar thin films, property-microstructure relationships, the integration of ferroelctric thin films into memeory devices and of piezoelectric and pyroelectric thin films into microelectro-mechanical systems.

Nava Setter received the Ph.D. degree in solid-state science from Pennsylvania State University (PSU), University Park, in 1980. She has worked in the area of ferroelectric ceramics and single crystals, microwave dielectrics, and ferrites at PSU, at the University of Geneva, Geneva, Switzerland, and at the MoD R&D Laboratories, Haifa, Israel. Since 1989, she has been Professor of materials science and engineering and Head of the Ceramics Laboratory, Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland. Her current scientific interests are in piezoelectric and related bulk ceramics/crystals and ceramic thin and thick films for sensors, actuators, and capacitors.