Piezoelectricity

Type of physical science: Condensed matter physics

Field of study: Solids

Piezoelectricity is the phenomenon whereby an electric potential is generated in certain crystals, thin films, and composites in response to an applied force. The converse piezoelectric effect is the generation of elastic-mechanical vibrations and acoustic waves in the same materials in response to an applied voltage. Piezoelectricity is the basis of many ultrasonic transducers, surface-acoustic-wave (SAW) signal-processing devices, and other circuits to complement or replace integrated circuits.

Overview

Thermoelectricity, or pyroelectricity, was discovered in crystals around the mid-nineteenth century. When placed in contact with conductors and a heated contact, pyroelectric materials produce a flow of electricity from one to the other. Thermoelectric response depends not only on thermoelectric properties but also on intrinsic directionality within the crystal, which is defined by atomic lattice orientations. Examples of pyroelectric materials include pyrites, tourmaline, hemimorphite, and monoclinic tartaric acid. Since a crystal also expands when heated, similar piezoelectric (from the Greek word piezein, meaning to press or squeeze) effects occur when mechanical pressure is increased along the principal crystal axis. Piezoelectricity was first identified as a well-defined phenomenon by Pierre and Marie Curie in 1880. Piezoelectricity was observed as electrical voltage resulting from application of mechanical or elastic-acoustic pressure to a dielectric crystal, where voltage intensity is directly proportional to applied stress. Conversely, applying a voltage between the crystal faces was shown to produce mechanical distortions in the crystal.

Since the development of atomic and quantum theory as applied to the solid state, the piezoelectric effect is explained by electrical charges moving to opposite crystal sides in response to preferentially applied stress. The source of these electric charges is the crystal lattice common to all piezoelectric materials. The magnitude and ease with which the piezoelectric effect can be developed in crystals depends on the crystal axis's specific orientation with respect to the applied stress. It is necessary that the crystal structure lack a center of symmetry. Of the thirty-two classes of crystals found naturally, twenty-one lack a symmetry center, and all but one of them are piezoelectric to some degree. In a quartz crystal, the best-known piezoelectric material, an applied stress of one newton per meter along the crystal's main axis produces an electric field of approximately 10^-12 coulombs per square meter. Conversely, an applied electric field of 10⁴ volts per meter yields an elastic strain of about 10^-8. Larger piezoelectric strains can be induced by alternating currents with a frequency equal to the crystal's mechanical resonance frequency.

Piezoelectric materials vary widely in their electrical, elastic-acoustic, thermal, and optical properties. Many different materials exhibit piezoelectric properties, including rock quartz, Rochelle salt (potassium sodium tartrate), tourmaline, ammonium dihydrogen phosphate (ADP), and ethylene diamine tartrate (EDT). Since the 1950s, piezoelectric ceramics such as lead zirconate titanate (PZT) and thin polar polymer films such as polyvinyl chloride (PVC) have been used most widely. These and other man-made composites can be tailored for very high piezoelectric response; for example, PZT has an electromechanical conversion efficiency of 98 percent.

Since their early use in underwater sonar transducers and radio tuner crystals, piezoelectric materials have frequently been considered as effective parts of a total electrical circuit. The inductive and capacitative values of the equivalent piezoelectric circuit can be calculated directly from the crystal's base constants, such as length, mass, density, elastic compliance, and dielectric constant. For a piezoelectrical crystal resonating at 10⁵ hertz, typical values for piezoelectric components in the equivalent circuit are an inductance (L) of 10² henrys and a capacitance (C) of 10^-2 picofarads.

These values cannot be achieved using conventional electric coils and capacitors. Piezoelectric filters combining the above properties often are used to replace conventional tuned LC (resonant) circuits in solid-state electronics. The higher quality factor, or Q (50 to 10⁵), realized in piezoelectric crystal resonators is advantageous for obtaining highly stable and sharply defined filter response. Piezo crystal Q is controlled by carefully modifying plate diameter, edge contours, and surface polish.

Piezoelectricity is a bulk property of crystals, since a piezocrystal surface yields the strongest discontinuity of field strength and voltage. Surface generation, however, produces the strongest source of high-frequency sonic and ultrasonic acoustic sound waves in response to alternating current voltage. "Ultrasonic" refers to elastic-acoustic waves having oscillation frequencies higher than the nominal limit of human hearing, set by convention at twenty kilohertz, although piezocrystals generate both lower and much higher acoustic frequencies.

As first developed by Paul Langevin in 1915, the active element of a basic piezoelectric transducer is a thin plate fabricated from smaller slices of a piezocrystal and metal and cut to thicknesses calculated to yield sharp output resonances at specific frequencies. For plate sizes and thicknesses in the ten-millimeter and one-millimeter regimes, respectively, ultrasonic waves in the megahertz band result. In specific applications requiring narrow-band acoustic signals—acoustic pulses comprising a narrow spectral bandwidth of frequencies—multiple plate-resonance transducers are often employed. For broadband pulse applications, however, specially shaped multiple-element resonators must be used.

Flat crystal ultrasonic transducers yield high-amplitude fields in the immediate vicinity of the crystal plate; thus, for a given pressure amplitude at the transducer surface, larger surface areas yield higher-pressure amplitudes near the focus. When geometrical focusing by curved piezocrystal faces is not possible, another method to increase ultrasonic transducer surface areas is to use the resonance between the crystal face and a surrounding fluid-filled flask. When this system is driven at a resonance frequency, large-amplitude oscillations occur at the flask wall. As the flask continues to oscillate, the resulting acoustic wave field is focused at the flask's center. One advantage of such resonant transducer systems for ultrasonic microscopy and high-resolution sound imaging techniques is their high quality factor.

The basic properties of a wide array of piezoelectric delay-line transducers, filters, resonators, and signal processors can be understood in terms of the fundamental types of seismic-acoustic waves propagating along, in, and away from a piezocrystal. In addition to several types of elastic-acoustic waves, there are two additional coupled or hybrid waves, each having both electromagnetic and elastic-acoustic wave fields associated with them. In most piezoelectric applications, elastic-acoustic wave fields are primary. The energy flow of guided waves such as Rayleigh, Stoneley, Scholte, or Lamb waves is directed along the piezomaterial's surface. Every such waveguide is theoretically capable of supporting an infinite number of guided waves, called waveguide modes, each with different frequency-dependent propagation velocities, or dispersion.

Wave dispersion refers to the tendency of a wave packet to spread out (disperse) with time. Analysis of the governing Helmholtz wave equation shows that Rayleigh-Love wave dispersion in piezoelectric materials is proportional to the product of plate thickness and wave frequency. Normal or trapped modes such as Lamb waves can be represented as the total wave field resulting from superposition of all modes supported by the waveguide. For surface waves such as Rayleigh waves, there is a finite frequency below which no surface waves can propagate. P, S, and flexural waves have frequencies determined primarily by the waveguide's minimum lateral dimensions. The behavior of the above waves is the same as in underwater, atmospheric, and solid-earth seismic-acoustics, but on a higher frequency and smaller wavelength scale.

Surface-acoustic-wave (SAW) devices typically are composed of a piezoelectric or elastic substrate, onto which special thin films are plated. Applying a voltage across such equispaced surface electrodes will excite propagating Rayleigh waves. The above unit is known as an interdigital transducer, one of the basic building blocks of more complex piezoelectric SAW devices. Placing an interdigital transducer between two suitably spaced electrodes results in a low-loss surface-wave resonator. Interdigital transducers are employed extensively for Rayleigh wave generation at frequencies from 10 to 2,500 megahertz. Below 10 megahertz, it is usually advantageous to use bulk-wave transducers.

Monolithic piezocrystal filters have all their elements on a single piece of material. These in addition to interdigital transducers can be used to make ultrasonic bulk-wave delay lines, which are of considerable value for real-time information storage in pulse decoding and processing radar and other signals. Ultrasonic delay lines exploit the fact that ultrasonic wave group velocities in piezoelectric materials drop when propagating in thin strips or wires whose thickness or diameter approaches the sonic wavelength. This decrease in group velocity transfers a short amplitude-modulated pulse onto a long frequency-modulated pulse, which is then sent to an output amplifier. In such delay lines, piezoelectric plates with alternating thick and thin sections are employed, each having a different dispersion relation. At the resonant frequencies of the thicker plate region, no elastic-acoustic energy can propagate into the thinner plate region, allowing these trapped-energy resonators to yield very high amplitudes or quality factors.

To enhance the inherent piezoelectric effect, engineers have learned to control the number, intensity, amplitude, and directionality of bulk and surface waves by combining special thin films, gratings, and electrode designs with crystals of complementary geometries. By doing so, engineers build up strong ultrasonic fields much greater than those produced by the piezoelectric effect of a single crystal. The reason for this enhancement is the fact that the total intensity of ultrasonic piezoelectric radiators is limited primarily by crystal mechanical strength and impedance. Both quantities can be improved by employing so-called biomorphic crystals, comprising two crystals with cuts of different orientation that are bonded together such that the voltage applied to the electrodes causes the crystals to deform in opposite directions.

Applications

A piezoelectric resonator is about 10^-5 times the size of a standard electronic component. Because quartz resonators vary by only a few parts per million, even over wide temperature variations and time spans of more than twenty years, they are frequently used in crystal clocks. Biomorphic crystals are used in microphonic and other transducers.

Due to the sensitivity and longevity of piezoelectric SAW sensors, they have been used for detection and measurement of both chemical and physical parameters in industrial and laboratory settings. SAW sensors have been developed to measure temperature, mechanical acceleration, force and pressure, direct-current and alternating-current voltages, electromagnetic field strengths, and gas concentration. Since elastic-acoustic energy in piezoelectric materials normally is confined to a thin near-surface region, resulting wave propagation is highly sensitive to comparatively small perturbations in any of the above variables, which can notably alter propagation characteristics in SAW and related devices.

These sensors can obtain accurate and reliable readouts simply by monitoring the delay line's oscillator frequency, particularly when configured as SAW delay lines to measure changes in ultrasonic wave travel time, attenuation, and phase velocity. SAW chemical and gas sensors make up a central delay line of SAW interdigital transducers on a piezoelectric substrate coated with a thin, chemically absorbent film. When the film absorbs even small gas quantities, notable changes occur in its physical-chemical properties, which in turn alter elastic-acoustic wave propagation. When gas flow ceases, desorption occurs and SAW physical properties soon return to their original values. Delay-line-based SAW sensors are accurate as long as the net acoustic time delay is sufficiently small compared to the smallest periods of the phenomena being measured.

Ultrasonic transducers for biomedical and nondestructive evaluation have been created from the polymer polvinylidene fluoride (PVDF). PVDF has very broad bandwidths, since the piezoelectric constants have a gradient within the substrate in this material. Such broadband ultrasonic wave transducers offer many advantages for enhancing acoustic detection and imaging microscale flaws in thin samples of engineering materials. A further advantage of PVDF transducers is the similarity of their low acoustic impedance to that of water, making them ideal for submerged C-scan imaging.

In 1983, a new type of piezoelectric SAW filter was developed, called the surface-skimming bulk wave (SSBW) device. This device employs multiple reflections of surface waves of P and S types between a diffraction grating mirror etched onto the crystal surface. SSBW devices offer higher operation speeds and reduced sensitivity to effects of surface-layer contaminants. Since about 1968, there have been major efforts devoted to combining piezoelectric SAW devices with a number of other independent sensor types, such as thermoelectric, thermoelastic, and acoustic-optic devices. Some of the earliest acoustic-optic applications of piezoelectricity were direct and magnified visualization of ultrasonic sound fields, where in many cases there exist one-to-one relations between propagation vectors of diffracted laser light and those of the ultrasonic waves in question. Acoustic-optic interactions were also applied to ultrasonic Rayleigh surface waves to design improved micro-sized signal processors.

Many such hybrid sensors exploit interferometric behavior of laser beams caused by small changes in Rayleigh wave path lengths that arise from thermal, electromagnetic, and other environmental influences. In the hybrid sensor technique of thermoacoustic microscopy, modulated laser light is absorbed by a piezoelectric surface, and the resulting thermal diffusion in the material creates local mechanical expansions, in turn generating surface waves radiating outward from the absorption point. Spatial resolutions of 10^-14 meters have been achieved and are frequently used to ensure the quality of integrated circuits and SAW devices.

SAW devices have also been used in touchscreen technology. The touchscreens use piezoelectric transducers that convert electric signals into ultrasonic waves moving beneath a glass overlay. When the glass is touched, it disturbs the ultrasonic waves, allowing the device to register the position of the finger or stylus.

Piezoelectric ceramics, or piezoceramics, such as PZT and barium titanate, are synthetic ceramics with a crystalline structure. These ceramics can be used to create a number of different components that serve as electromechanical transducers. Piezoceramic materials are typically classified as either hard or soft, depending on their degree of ferroelectricity. Soft piezoceramics are easier to polarize and exhibit greater permittivity and dielectric dissipation, making them less stable and thus better suited for sensor rather than power applications. Hard piezoceramics typically exhibit opposite characteristics from soft piezoceramics and are thus ideal for applications with high mechanical loads and voltages.

Piezoelectricity has several medical applications as well. One such application is piezoelectric surgery, or piezosurgery, in which low-frequency ultrasonic vibrations are used to cut through bone and other hard tissue without damaging the surrounding soft tissue. Piezoelectricity has also played roles in fertility treatments, where it can be used to activate oocytes as a supplement to in vitro fertilization, and in cloning, where it is a common method of nuclear transfer.

Context

Until World War I, piezoelectricity remained a theoretical curiosity for a few atomic and chemical physicists. After Langevin's work on the first piezoelectric transducer, piezoelectricity was rapidly considered for wider transduction and related applications. In World War II, piezoelectric crystals were used as contact electrical detonators in aerial bombing, as well as in improved active sonar units for detecting submarines and bathymetry. Between the wars, in piezoelectric phonograph styli, mechanical vibrations of the needle in a record groove were converted into electrical impulses, which were amplified into sound. After the 1950s, most efforts in piezoelectrics were focused on SAW devices for radar, spread-spectrum, and space-navigation applications. A special baseline requirement for piezoelectric materials science is to ensure that relations between elastic and acoustic fields are as high and as linear as possible.

Because an ideal sensor should be highly and predictably sensitive to the specific parameter(s) being measured (and minimally or nonsensitive to other parameters), research in piezomaterials examines not only new material geometries and sizes but also novel combinations of crystals and films to achieve less distorted wave field outputs. A variety of studies examine relations between the properties of piezoelectric materials and the resulting propagation characteristics of Rayleigh, shear, Lamb, flexural, and other ultrasonic waves. Such studies attempt to find optimal crystal cuts, propagation directions, and velocities for given applications. In many of the more complexly configured hybrid piezoelectric media, whose geometries and elastic-electric properties vary in both length and thickness directions, it is also necessary to consider the effects of a slab's finite length and width and the inevitable minor cracks, voids, and inclusions.

Four specific electromechanically vital characteristics of piezoelectric resonators that are of continuing importance in fabricating better SAW devices are intermode coupling, unwanted mode suppression, control of temperature dependence of desired modes, and the complexity and cost of manufacturing plates and films with suitable behavior and tolerances for the above properties. These conditions limit the design of piezoelectric resonators to only a few basic crystal orientations and specific wave types.

Principal terms

ACOUSTIC IMPEDANCE: in solids, the product of material density and compressional velocity; measures one material's degree of resistance or admittance to elastic-acoustic waves propagating from another material

BULK ACOUSTIC WAVE: any elastic-acoustic wave traveling through the bulk of a piezoelectric material

COMPRESSIONAL WAVE: an oscillation traveling in a solid or fluid medium, characterized by changes in volume and by particle motion parallel to the direction of propagation; also known as a P wave, pressure wave, dilatational wave, or longitudinal wave

ELASTICITY: the property whereby a solid changes its shape or size in response to applied forces and recovers its original form when the forces are removed

FILTER: any device or algorithm that separates data or signal components according to specified quantitative criteria

FLEXURAL WAVE: an elastic wave comprising a bending mode in a plate or strip

PERMITTIVITY: a key electromagnetic parameter characterizing the ease with which a material conducts electricity

RAYLEIGH WAVE: an S wave propagating on the surface of a solid, exponentially decaying in amplitude away from the surface

RESONATOR: an electric or mechanical device exhibiting amplitude resonance at a given frequency; often used in detection hardware for sensors

SHEAR WAVE: an oscillation that causes an element of an elastic medium to change shape without changing volume; also known as S wave, transverse wave, or irrotational wave

Bibliography

Auld, Bertram A. Acoustic Fields and Waves in Solids. New York: Wiley, 1973. Print. A classic intermediate-level text, treating all aspects of theory and fabrication of ultrasonic transducers and SAW devices from piezoelectric materials. Numerous historical and current references. Reviews the effects of particular crystal cuts on seismic-acoustic wave-propagation behaviors.

Bhagavantam, S. Crystal Symmetry and Physical Properties. New York: Academic, 1966. Print. A standard reference on solid-state physical and material properties for all naturally occurring piezoelectric crystals. Discusses the atomic- and molecular-level physics of piezoelectric charge generation in response to applied stress.

Bottom, Virgil E. Introduction to Quartz Crystal Unit Design. New York: Van Nostrand, 1982. Print. Contains much valuable information on piezoelectric and pyroelectric properties of quartz. Emphasizes the trend toward technology transfer between semiconductor SAW efforts and their potential for hybridization.

Cady, Walter G. Piezoelectricity. New York: McGraw, 1946. Print. Perhaps the best introduction to the history, principles, and applications of piezoelectricity. Many valuable historical references and illustrations. Includes important material on natural and synthetic obstacles to fabricating optimal single- and multicrystal devices. Somewhat dated.

Jaffe, Bernard, William R. Cook, and Hans Jaffe. Piezoelectric Ceramics. New York: Academic, 1971. Print. The best general reference on this man-made piezoelectric material from the perspective of fabrication engineering. Contains details on the historical development of piezoceramics. The circumstances where ceramics significantly surpass natural quartz crystals are also discussed. Intermediate technical level.

Mason, Warren P. Electromechanical Transducers and Wave Filters. New York: Van Nostrand, 1948. Print.

Mason, Warren P. Piezoelectric Crystals and Their Application to Ultrasonics. New York: Van Nostrand, 1950. Print. Both of these monographs by Mason are classical references for the macro- and microscopic physics, early history, and engineering of piezoelectric transducers and the first SAW-type devices. Mason contributed historically pioneering theoretical and laboratory work in developing pure and uniform crystals.

Pavlíková, G., et al. "Piezosurgery in Oral and Maxillofacial Surgery." International Journal of Oral and Maxillofacial Surgery 40.5 (2011): 451–57. Print.

Piezoelectric Ceramics: Principles and Applications. 2nd ed. Mackeyville: APC, 2011. Print.

Qin, Qing-Hua. Advanced Mechanics of Piezoelectricity. Beijing: Higher Educ., 2013. Print.

Redwood, Martin. Mechanical Waveguides. New York: Pergamon, 1960. Print. Prepares the reader for more advanced theoretical and applications monographs. Very readable, with many illustrations of two- and three-dimensional waveguides. Slightly dated.

Rosenbaum, Joel F. Bulk Acoustic Wave Theory and Devices. Boston: Artech, 1988. Print. Devoted to the theory, construction, and applications of piezoelectric bulk wave transducers and SAW devices. Very extensive coverage.

Tiersten, H. F. Linear Piezoelectric Plate Vibrations. New York: Plenum, 1969. Print. A comprehensive introduction to the mathematics of modeling piezoelectric bulk and wave motions in the linear regime, with some information on nonlinear behaviors. Carefully connects bulk and surface wave vibrations to those in mechanical, earth, and ocean waveguides in general.

Thermal Properties of Solids