Piezoelectric and Acoustic Materials for Transducer Applications

This chapter is about the macroscopic theory of ferroelectrics, which is based on the Landau theory of phase transformations. It was first proposed by Landau in the 1930s to study a wide range of complex problems in solid-state phase transformations in general, and ordering phenomena in metallic alloys in particular (Landau and Lifshitz 1980). It was further developed and brought to the realm of ferroelectrics by Devonshire (1949, 1951). It has since then proven to be a very versatile tool in analyzing ferroelectric phenomena, and has become a de facto tool of analysis among ferroelectricians.

At the heart of the Landau theory of phase transformations is the concept of order parameter, which was first proposed in the context of order–disorder transformation involving a change in the crystal symmetry. In such systems, the material of interest transforms from a high-symmetry disordered phase to a low-symmetry ordered phase (de Fontaine 1979; Ziman 1979). The so-called broken symmetry of the crystal due to ordering is represented by an order parameter. Landau has shown that the (Helmholtz) free energy of an order–disorder transformation can be expressed very simply as a Taylor series expansion of the order parameter describing the degree of order (or disorder). Generally, the order parameter can be any variable of the system that appears at the phase transition point. In the case of ferroelectrics, it is the spontaneous polarization. Originally, the Taylor expansion of the order parameter was intended to be limited to temperatures close to the phase transformation temperature, as any mathematical series has a radius of convergence. However, quite oddly, it is a well-established fact that the free energy functional provides a very good approximation even at temperatures far below the transition temperature once higher-order expansion terms are included.

In this chapter, the symmetry aspects of the piezoelectric effect in various materials (single crystals, ceramics, and thin films) are briefly overviewed. First, the third-rank tensor of piezoelectric coefficients defined in the crystallographic reference frame is discussed. On this basis, the orientation dependence of the longitudinal piezoelectric response in ferroelectric single crystals is described. This dependence is especially important for relaxor single crystals, where a giant piezoelectric effect is observed. Then, the effective piezoelectric constants of polydomain crystals, ceramics, and thin films and their dependence on crystal symmetry are discussed. The domain-wall contribution to the piezoelectric properties of ferroelectric ceramics and thin films is also described. Finally, the crystallographic principles of piezomagnetic, magnetoelectric, and multiferroic materials are presented.

Piezoelectricity linearly relates an induced polarization to an applied stress, as shown in (3.1),

Where σ _jk is the applied stress, P _i is the induced polarization, and d _ijk is the piezoelectric charge coefficient. Einstein notation is used, where repeated indices are summed. Because piezoelectricity is a third-rank tensor property, a good starting point to understanding the crystal chemistry of piezoelectric materials is to consider the impact of symmetry on such a property.

Neumann’s law states that the geometrical representation of any physical property contains the symmetry of the point group of the material. As shown in Fig. 3.1, of the 32 crystallographic point groups, only 21 are noncentrosymmetric. Odd-rank tensor properties are symmetry forbidden in centrosymmetric structures, making piezoelectricity a null property for such materials. In the same way, in point group 432, the combination of symmetry elements eliminates piezoelectricity. The remaining 20 point groups are potentially piezoelectric. Of these 20 point groups, ten are polar, that is, they have a vector direction in the material that is not symmetry-related to other directions. Such materials can have a spontaneous polarization, which is typically a function of temperature. Thus, these materials are pyroelectric. Ferroelectric materials are a subset of pyroelectric materials in which the spontaneous polarization can be reoriented between crystallographically-defined directions by a realizable electric field. Thus, all ferroelectric materials are both piezoelectric and pyroelectric.

This chapter discusses properties of lead-based piezoelectric materials, the most versatile and the most widely used piezoelectrics. Majority of these materials were discovered in 1950s and 1960s, and their properties and applications are described in classical textbooks, e.g. (Jaffe et al. 1971; Lines and Glass 1979). After giving essential background, this chapter will focus on recent developments. Lead titanate is discussed first, followed by modified lead titanate compositions. Lead zirconate titanate is then discussed in some details, focusing on mechanisms of hardening and softening and properties at morphotropic phase boundary. The subsequent sections discuss field-induced piezoelectric effect in relaxors, relaxor-ferroelectric ceramics, and crystals. Other lead-based materials and environmental issues are briefly discussed in the closing sections of the chapter.

Alkaline niobates and, more particularly, the sodium potassium niobate solid solution became the topic of much research at the end of the 1990s, because of increased environmental awareness. Prior to this, a lot of work on these materials was carried out in the 1950s and 1960s. The compositions with the highest electromechanical coupling coefficients are those close to the morphotropic phase boundary (MPB) at 52.5% Na, and the most studied composition has been K_0.5Na_0.5NbO₃, subsequently referred to as KNN (Shirane et al. 1954; Egerton and Dillon 1959; Jaeger and Egerton 1962; Jaffe et al. 1971).

Important ferroelectric or antiferroelectric oxide ceramics for dielectric, ferroelectric, piezoelectric, electrostrictive, and/or pyroelectric applications are restricted to perovskite-type, tungsten bronze-type, and bismuth layer-structured compounds. A recent trend in the study on piezoelectric and/or pyroelectric ceramic compounds is the use of lead-free materials. The other trend is the use of grain orientation techniques as the ceramic fabrication methods.

Recently, bismuth layer-structured ferroelectrics (BLSF), which form one of BO6 octahedral ferroelectric groups, have been extensively studied in the form of thin films because they seem to be an excellent candidate for nonvolatile FeRAM applications. For example, SrBi₂Ta₂O₉ shows fatigue-free properties, which are very desirable in such applications.

This chapter covers the main features and material examples of the electric fieldactivated electropolymers used for electromechanical applications. This class of electropolymers is very attractive in performing the energy conversion between the electric and mechanical forms and hence can be utilized as both solid-state electromechanical actuators and motion sensors. These polymers are also attractive for artificial muscles and for energy-harvesting applications. As will be discussed, the electromechanical response in this class of polymers can be linear, as in typical piezoelectric polymers and electrets, or nonlinear, as the electrostrictive polymers and Maxwell stress-induced response.

Most of the piezoelectric polymers under investigation and in commercial use are based on poled ferroelectric (FE) polymers, including poly(vinylidene fluoride) (PVDF) and related copolymers. This chapter will discuss in detail the properties of these FE polymers. In comparisonwith the electromechanical responses in inorganic materials, the electromechanical activity in these polymers is relatively low. To significantly improve the electromechanical properties in these electropolymers, new avenues or approaches have to be explored. From the basic material consideration, these approaches include the strain change accompanied with the molecular conformation change, due to the polar vector reorientation, from the morphology change due to the ordering degree change in the interfacial layer between crystalline and amorphous regions, and from the Maxwell stress effect in soft polymer elastomers. This chapter will discuss the recent advances based on those approaches, which have produced remarkable improvements in terms of the electric field-induced strain level, elastic energy density, and electromechanical conversion efficiency in the electropolymers.

Medical ultrasonic diagnostic apparatus have been used as a noninvasivemethod for diagnosing the human body since the 1970s. Figure 8.1 shows various types of commercialized medical pulse-echo ultrasound probes: (1) cardiac probe, (2) abdomen probe, and (3) high-frequency linear probe for diagnostic applications.

The medical ultrasonic array probe consists of four basic materials: backing, piezoelectric, acoustic matching layers, and acoustic lens. A piezoelectric material such as lead zirconate titanate (PZT) or relaxor single crystals is the only active material used for the transducer, which transmits and receives ultrasound. On the other hand, acoustic matching layers are installed on the transducer in order to raise the transmission efficiency of the ultrasound, because the acoustic impedance (Z), which is expressed as sound velocity (c) × density(ρ), of PZT ceramic and that of human tissue are mismatched otherwise;i.e., Z_PZT = 35×10⁶ kg/m²s vs. Ztissue = 1.55×10⁶ kg/m² s. In general, the ultrasound is re-flected at the boundary with different Z.

Moreover, a convex-shaped acoustic lens is attached on top of the acoustic matching layers to focus the ultrasound beam and to ensure good contact to the human body. Specifically, the acoustic lens is used for focusing of the short axis; the elevation dimension determines the effective slice thickness of the image plane. The ultrasound transmission is attenuated in acoustic matching layers, acoustic lens, and human tissue. The acoustic attenuation (α) of the acoustic lens is very important because it is usually thicker than the matching layers.Moreover, α becomes large with increasing frequency; the α of the acoustic lens has a great effect on the sensitivity of a medical ultrasonic probe as well.

A composite, consisting of two or more materials, was developed, wherein optimum acoustic properties were obtained by the judicious choice of its constituents. Specifically, unidirectional carbon-fiber composite materials have a high acoustic impedance and a light weight. Therefore, it is possible to formulate a composite with broad-range acoustic impedance. By the approach described in this chapter, the applications utilizing such carbon-fiber composite in medical transducers are possible. In what follows, the acoustic properties of the carbon-fiber composite materials are presented and a method of fabricating the composite materials to form backing layers will be elaborated on. The characteristics of a prototype transducer, which uses this new composite, will be discussed.

The number one technique for medical imaging and non-destructive evaluation (NDE) is ultrasound. This is due to its non-ionizing character, low cost and to the fact that images and measurements contain data linked to several physical and structural parameters of the explored media.

The overall performance of an ultrasonic system is mainly determined by the transducer characteristics. Consequently, each application having its specific requirements, very different transducers need to be designed. Furthermore, the measurement techniques and imaging modalities are in constant evolution, requiring higher performance and versatility of the transducers. Not only must frequency bandwidth and sensitivity be increased, but transducers must also be able to operate in various modes such as pulse-echo (classical A, B or C modes), burst (Doppler or other velocity measurements) or harmonic reception (non-linear acoustics). Innovations such as ultrasound stimulated elastography and combination of different techniques such as ultrasound and MRI or ultrasound therapy and imaging are only possible if specific transducers are developed.

An electroacoustic transducer is a device that converts acoustic energy (sound) into electrical energy (voltage or current) or vice versa. When the transducer is used to generate sound, it is called a projector, transmitter, or source. When it is used to detect sound, it is called a receiver. Furthermore, when the receiver is employed underwater, it is referred to as a hydrophone. An underwater sonar system consists of projectors, hydrophones, and associated electronics such as amplifiers and data acquisition systems. This chapter, however, will only cover the description and operational principles of the projector and hydrophone components. More specifically, the chapter will focus on piezoelectric ceramic-based transducer designs intended for underwater use that operate in the frequency band spanning from 1 kHz to 1MHz. This span covers weapons sonar (1–100kHz) and imaging sonar (100kHz to 1MHz) applications.

Electromechanical transducers, first used in sonar systems, convert electrical energy into mechanical energy, thanks to the piezoelectric effect, then to acoustic energy, with the generation and the radiation of an acoustic wave in a fluid. To design new transducers and to understand their physical behaviour, several physical mechanisms have to be described (piezoelectric-elastic-fluid-structure coupling-acoustic radiation). To solve such problems, analytical and semi-analytical approaches often rely upon simplifying hypotheses, in terms of geometry of the transducers, behaviour of the piezoelectric part of the device, radiation condition or frequency range of interest. Among these approaches, the equivalent electrical scheme (Beranek 1954) is based on a classical lumped constant representation with masses and springs, and the transfer matrix (Neppiras 1973) uses plane wave approximations.With the help of analytical expressions, these approaches become operational tools, leading to the realization of numerous transducers.

This chapter considers the status of piezoelectric fiber composite fabrication. The description is focused on three topics, the preparation of sol—gel-derived PZT fiber/polymer composites as the first exciting development phase of piezoelectric fiber composites, the soft-mold method with high achievement potential for preparing designed composites and understanding the structure—property relationships, and finally the preparation of powder suspension-derived PZT fiber/polymer composites as the technologically advanced and commercialized process. The use of piezoceramic fibers allows for the fabrication of high-quality fiber composites, covering performance data that cannot be achieved by the conventional dice and fill technique.

Piezoelectric functionally graded materials (FGMs) are attractive alternatives to homogenous-single phase materials for actuator applications because of their reduced internal mechanical stresses and lower production costs. Furthermore, such FGM structures have increased band width if used as an ultrasonic transducer. One of the most effective ways to prepare piezoelectric and dielectric gradients based creating a gradient in chemical composition by powder processing prior to sintering. The sharp chemical interfaces between the green layers disappear because of diffusion during sintering. The chemical gradient is then transformed into a gradient in the piezoelectric properties by a poling process after sintering. Several models have been developed for the description of poling of layered systems, which is a formidable challenge. The ferroelectric properties, such as spontaneous polarization and coercive field strength, also depend on the local chemical composition. This causes an inhomogeneous electric field distribution, which is usually not stable in time because of conductive currents and space charges.

In this chapter, different types of composition gradients for bending actuators are described. Combinations of hard and soft piezoelectric ceramics and electrostrictive and electroconductive materials are presented. The theoretical results are compared with experimental data for lead-free systems based on barium titanate.

Robocasting is a solid freeform fabrication (SFF) technique based on the direct writing of highly concentrated colloidal gels. Similar to other SFF techniques, robocast-ing offers facile assembly of complex three-dimensional geometries and a broad pallet of ceramic, metallic, and polymeric materials from which to design devices. Here, robocasting is used to assemble lead zirconate titanate (PZT) skeletons for direct use or to create epoxy-filled composites suitable for hydrostatic piezoelectric sensors. PZT composites labeled by connectivity (3—3, 3—2, 3—1) are demonstrated. For such composites, the piezoelectric hydrostatic figure of merit (d ^h g ^h) increases by up to 60-fold compared with bulk PZT. Ultimately, SFF allows for rapid iteration, prototyping of designs, and assembly of unique PZT skeletons. Sandia is a multipro-gram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-ACO4 — 94AL85000.

Micropositioning is required in many industrial segments as well as in everyday life. It is often utilized, without being recognized, in applications such as cars, cameras, or even when looking at internet pictures from space taken by telescopes. In such applications, small but accurate movements can significantly improve the performance and usability of the device. For scientific and engineering purposes micropositioning is widely used in research and production facilities such as AFM (atomic force microscope), SEM (scanning electron microscope), FIB (focused ion beam), micromanipulators (e.g., cell manipulators), active vibration dampers, and assembling and production devices, for example, in electronics and semiconductor manufacturing (Hubbard et al. 2006). Demand for wider and more efficient utilization of micropositioning is growing due to trends toward miniaturization in electronics as well as its wider exploitation in application fields.

There are several different materials and actuation schemes upon which micropositioning systems can be based. If especially small size, low forces, and high frequency are required for the system, electrostatic actuators are a good option. However, they are able to produce only a limited range of displacement with high voltage unless a comb structure instead of the basic capacitor plate configuration is employed. For low-voltage applications, thermal as well as magnetic actuators are widely used. Thermal actuators are usually comparable in size to electrostatic actuators but suffer also from a limited range of motion that usually has to be amplified mechanically. In contrast, magnetic and magnetostrictive actuators provide relatively large displacement but require the use of coils to generate the magnetic field and therefore can be bulky and expensive. Additionally, these approaches rely on actuation by current and therefore consume power while holding a static position.

In this chapter, the general properties and requirements of piezoelectric micropositioners, their control and sensor techniques, and some commercial applications are discussed.

Piezoelectric actuators are getting immiscible parts of many important electromechanical and smart systems. Smart systems consist mainly of sensors, actuators, and signal processing units. Actuators are the responding units of many smart systems including those for active vibration and noise control, valve, shutter, focal lens, and many others. Increased demand for actuators with high displacement, high generative force, and quick response time has led to a search for new actuator materials and new designs. In this chapter, first, piezoelectric actuators were compared with magnetically active and thermally active actuators. Second, piezoelectric actuators and their design, especially traditional piezoelectric transducers with newly designed flextensional transducers were compared. Finally, application-related issues have been reviewed.

Self-powered nodes can be developed by harvesting wasted mechanical vibration energy available in the environment. Piezoelectric converters have been found to be most suitable for transforming mechanical energy into electric energy where the charge generation is directly related to the extent to which the element is deformed. This chapter provides the strategy for the selection of the piezoelectric transducer depending upon the frequency and amplitude of the mechanical stress. The figure of merit for the material selection was found to be directly proportional to product (d · g), where d is the piezoelectric strain constant and g is the piezoelectric voltage constant. The criterion for maximization of the product (d · g) was found to be given as \(|d|\ =\ \varepsilon^n\), where n is the material constant which is fixed by the magnitude of the piezoelectric and dielectric constants. Results are reported on various devices utilizing piezoelectric bimorph transducers.

Piezocomposite ultrasonic transducers for high-frequency wire bonding of semiconductor packages are developed to alleviate the strong mode coupling and high mechanical quality factor intrinsic in piezoceramic transducers by using ring-shaped lead zirconate titanate (PZT)/epoxy 1–3 piezocomposites as the driving elements. In this chapter, the background and challenges involved in the state-of-the-art high- frequency wire-bonding process are described. The fabrication, resonance characteristics, and material properties of the piezocomposite rings having high PZT volume fractions in excess of 0.8 and with a small epoxy width of 77μm are reported. The structure, electrical characteristics, vibrational characteristics, and wire-bonding performance of a 136-kHz piezocomposite transducer are presented, together with those of a PZT piezoceramic transducer of similar structure. With the guide of a finite-element modal analysis, the nature of most experimental resonance modes in the two transducers is identified. The low lateral coupling of the piezocomposite rings effectively suppresses the nonaxial and many other spurious resonances in the piezocomposite transducer, retaining only the axial-mode resonances. Because of the effect of epoxy damping, the piezocomposite transducer exhibits a 2.4-times reduction in mechanical quality factor to a desired low value of 296. The process study confirms the value of the piezocomposite transducer in commercial wire bonders for enabling high-frequency wire-bonding technology.

MEMS technology emerged in early 1990s by leveraging many of the materials and processes from the IC industry, and thus it was mainly based on the silicon technology.As the field has grown over the years, concepts of more complex devices have been proposed and demonstrated, many based on new, functional materials with new fabrication processes, which allow creation of systems consuming less power, with faster and more reliable response, and capable of incorporating more complex functions.

Ultrasonic imaging is one of the most important and still growing diagnostic tools today. Ultrasound is more appealing as a clinical imaging modality compared with such modalities as magnetic resonance imaging (MRI), nuclear imaging, and x-ray computed tomography (CT) in that it is more cost-effective, noninvasive, capable of real-time operation, and portable while providing images of comparable quality and resolution. State-of-the-art ultrasonic scanners offer real-time gray scale images of anatomical detail with millimeter spatial resolution, which are superimposed on a map of Doppler blood flow, displaying the information in color thereby (Shung 2006). Clinical applications of these devices are still expanding, and the operating frequencies of these devices seem to inch higher and higher. High-frequency (HF) imaging (higher than 20MHz) yields improved spatial resolution at the expense of a shallower depth of penetration. There are a number of clinical problems that may benefit from high-frequency ultrasonic imaging (Lockwood et al. 1996). Intravascular imaging with probes mounted on catheter tips at frequencies higher than 20MHz with the highest frequency being 60MHz has been used to characterize atherosclerotic plaque and to guide stent placement and angioplasty procedures (Saijo and van der Steen 2003). Endoscopic imaging with probes mounted on the tip of an endoscope or a catheter at frequencies from 10 to 20MHz has been proven clinically beneficial in diagnosing esophageal, gastrointestinal, and urinary lesions (Liu and Goldberg 1995). Medical efficacy of ultrasonic imaging of anterior segments of the eye at frequencies higher than 50MHz in diagnosing glaucoma and ocular tumors and in assisting refractive surgery has been demonstrated (Pavlin and Foster 1995). The availability of a noninvasive imaging tool for dermatological applications could reduce the number of biopsies that are associated with patient discomfort and could better demarcate tumor involvement. An additional benefit is that the results are known immediately or shortly after the examination unlike biopsy where a substantial time lag is likely to occur between the examination time and the report of histological analysis. Small-animal imaging is another frontier of HF ultrasound. Small-animal imaging is of intense interest recently because of the utilization of small animals in drug and gene therapy research.MicroMR, microCT, and microPET have all been developed to meet this need. Ultrasound thus far has only played a very limited role.

In this chapter the basic principles, the fabrication process, and some modeling approaches of the novel micromachined ultrasonic transducers (MUTs) are described. These transducers utilize the flextensional vibration of an array of micromembranes. They are usually called cMUT (capacitive MUT) or pMUT (piezoelectric MUT) depending on the actuation principle, electrostatic or piezoelectric. For water coupling applications, both these kinds of transducers offer a better matching to the load compared with the typical piezoelectric transducers and therefore they have a larger intrinsic bandwidth. Here emphasis is given to the cMUTs because they have shown good electroacoustic characteristics, which parallel, or even exceed, those of conventional piezoelectric transducers. Good echographic images of internal organs of the human body have been obtained demonstrating the possibilities of this technology to be utilized in commercial 1D and 2D probes for medical applications. At present pMUTs are in a very early stage of development and the potential advantages over the cMUTs are still to be demonstrated.