9.5.1 Modelling and configurations of piezoelectric transducers

If a piezoelectric prism of area A and thickness b is considered and harmonic regime at angular frequency ω is assumed, under the hypothesis that stress and strain do not depend on position along the thickness, the element behaves as mechanically concentrated. Under the mono-dimensional assumption, starting from Eq. [9.1c] and passing to the global variables tensile force F, outward displacement X, voltage V and current I, the equivalent electromechanical lumped-element model of Fig. 9.4 can be derived. The terms k^E and C^S represent mechanical stiffness at constant field and electrical capacitance at constant strain, respectively. This model is quasi static, being valid for frequencies lower than the first resonance of the piezoelectric element. Mechanical and electrical losses are not accounted for in the model. The circuits can be seen as the low-frequency limit of the Mason’s model corresponding to the same force applied at the two faces of the transducer (Mason, 1948).

The ideal DC-responding transformer with turn ratio α:1 represents the linear coupling between the electrical and mechanical domains. The electromechanical coupling factor κ can be derived from the model by reflecting the impedances through the transformer ports, leading to the following expression consistent with Eq. [9.3]:

[9.5]

While the transformer ratio α depends on dimensions, the electromechanical coupling factor κ is only related to specific material properties. Typical nominal values of κ for PZT ceramics range between 0.3 and 0.7.

Different types of piezoelectric transducers can be obtained depending on the configurations in which piezoelectric elements are arranged. Fig. 9.5 summarizes four general cases.

Figure 9.5(a) shows the electromechanical (EM) conversion where the input signal is the electrical (E) stimulus to the piezoelectric element, and the output signal is the mechanical (M) response. In this configuration the piezoelectric element acts as an actuator. Examples of this type are micropositioners, motors, sonic or ultrasonic emitters.

Figure 9.5(b) represents the opposite case, where the input signal is the mechanical stimulus to the piezoelectric element and the output signal is the electrical response; this configuration gives a mechanoelectrical (ME) conversion and the piezoelectric transducer works as a sensor. Examples of this type are vibration pick-ups, sonic or ultrasonic receivers. When power, rather than current or voltage, is taken as the electrical output, the device is intended to perform mechanoelectrical energy conversion, such as in energy harvesting from mechanical vibrations.

Figure 9.5(c) represents a sensor configuration based on an EM–ME open loop conversion. An electrical stimulus to an input piezoelectric element generates a mechanical effect in a medium that is converted back into an electrical response by a second piezoelectric element. The input quantity, i.e. the one to be measured, modulates some property of the mechanical propagation path between the two piezoelectric elements, thus it is transduced into the output signal in the form of a perturbation of the electrical transfer function between stimulus and response. The mechanical propagation path can be external to the transducer or be an integral part of the transducer itself. In the latter case, the transducer sustains the propagation of mechanical elastic vibrations, i.e. acoustic waves, and the sensor can be referred to as an acoustic-wave (AW) sensor (Ballantine et al., 1997). The presence of two separate piezoelectric elements as input and output devices is not strictly required, since a single element can be used as well. In this case, the mechanoacoustic propagation path becomes the piezoelectric element itself.

Figure 9.5(d) extends the concept of acoustic-wave sensors by inserting the configuration of Fig. 9.5(c) as the feedback element of an amplifier, therefore creating an EM–ME closed-loop conversion. If proper gain conditions are satisfied, the system can be made resonating at one of the natural frequencies of the mechanoacoustic propagation path that, in turn, depends on the input measurand quantity. Therefore, the resonant frequency can be conveniently taken as the output signal. The resulting device is called an acoustic-wave resonant sensor (Benes et al., 1995; Hauptmann, 1991). AW resonant sensors offer a number of potential advantages such as high sensitivity, determined only by the mechanical properties of used materials and a response virtually unaffected by piezoelectric coefficients and amplifier gain. Good stability, resolution and high noise immunity are additional benefits, since the signal information is conveyed in the time scale rather than in the analogue amplitude. The ‘quasi digital’ nature of the frequency output facilitates the direct interfacing of resonant sensors to digital systems. Piezoelectric AW and resonant microsensors are comprehensively discussed in V. Ferrari and Lucklum (2008) and references therein.

9.5.2 Examples of devices and applications

Since the earliest investigations on piezoelectric printed films for buzzers (Fu et al., 1985), loudspeakers (Baudry, 1987) and developments thereof (Morten et al., 1989), piezoelectric films have been attracting a significant research interest for innovative applications in sensors and microsystems (Muralt, 2008b; Tadigadapa and Mateti, 2009).

Even limiting our attention to screen-printed films, the scenario of the investigated techniques and proposed devices is increasingly wide and diverse, with a growing tendency to migrate form traditional TFT substrates, such as alumina and possibly metal, to include silicon MEMS. This often implies deposition techniques and dimensional scales that are different from those of conventional screen printing, which in turn produces a range of ongoing developments and opportunities toward hybrid microfabrication technologies. For this reason, it was chosen to group the following examples according to the operating principles and configurations, as discussed in section 9.5.1, rather than divide them into technology categories, which are continuously evolving and increasingly interrelated.

A first implementation of an accelerometer (Morten et al., 1990) makes use of two piezoelectric films of 5 mm × 5 mm poled along the thickness, mounted back-to-back on the opposite sides of the seismic mass. Therefore the output results in a differential signal and the common-mode effects, such as temperature, are minimized. A flat frequency response between 0.5 and 500 Hz was observed, with a sensitivity of about 2.5 V/g for an acceleration range of ± 4 g and a temperature sensitivity of 3 × 10^− 3 g/°C. The device proposed by Crescini et al. (2001) applies a similar structure. The sensor consists of two PZT layers, with a thickness of 40–50 μm each, screen-printed on the opposite sides of an alumina substrate and connected with opposite polarity to allow for thermal compensation. The sensor works without added seismic mass. A low-noise, large-bandwidth charge amplifier sets the low-frequency limit in the sub-hertz region. Experimental tests demonstrate a d₃₃ coefficient of the PZT layers around 180 pC/N when poled at 3 MV/m, a sensitivity of the device of about 60 mV/g over the bandwidth 0.7 Hz–40 kHz, with a resolution of 0.025% of the full scale (FS).

The piezoelectric accelerometer described in Beeby et al. (2001) is one of the early examples of migration of PZT screen-printed sensors from alumina to micromachined silicon. It consists of a micromachined square seismic mass 2 mm × 2 mm suspended by four silicon 750 μm × 975 μm beams where PZT films are screen-printed. The sensor is equipped with a microprocessor circuit that provides self-validation by driving the piezoelectric elements and reading the resulting output.

Efforts to integrate screen-printed piezoelectric PZT thick-films with silicon technology have recently led to the micromachined high-bandwidth triaxial accelerometer described in Hindrichsen et al. (2010b). The microsensor has a square 1.2 mm × 1.2 mm seismic mass suspended on four 600 μm × 800 μm beams onto which 30 μm thick PZT films are screen-printed (Chapter 10). The tests demonstrate that voltage sensitivity is 0.31 mV/g in the vertical direction, 0.062 mV/g in the horizontal directions and the first mode resonance frequency is 11 kHz.

Pressure sensors based on PZT thick films and their evolution are a significant example of the flexibility of the technology and the capability to transfer different transduction principles into devices. Static pressure cannot be measured with piezoelectric elements, unless they are arranged in resonant sensor configurations as discussed in the examples presented later on in this section. Instead, dynamic pressure, or shock pressure waves, can be directly detected.

An example is the dynamic pressure sensor described in Crescini et al. (2002), which was designed for pressure peaks up to 100 MPa. The sensor consists of a 2 mm thick alumina substrate onto which a screen-printed PZT layer, 3 mm in diameter, is sandwiched between Pt-Au printed electrodes and poled through the thickness. The performance characteristics include a sensitivity of 80–110 pC/MPa, a linearity better than 2% FS in the range between 25 and 60 MPa, and a response time lower than 10 μs.

The use of PZT thick-films in slip sensors for the feedback control of prosthetic hands is illustrated in Cranny et al. (2005). Each stainless-steel fingertip of the hand, configured as a cantilever, is equipped with a sensor made by a poled PZT layer, about 100 μm thick, sandwiched between two gold electrodes overlapping over an area of 8 mm × 8 mm. The results of tests run with small masses dropped onto the surface of an inclined fingertip and allowed to slide over the top electrode indicate the potential of the sensor to detect the moment of first contact between the hand and an object, as well as its ability to detect the onset of slip.

A field of topical interest where piezoelectric thick films can be used as both sensors and actuators is in piezoelectric micromachined ultrasound transducers (pMUT). A typical requirement is to decrease dimensions of the single transducer to make compact arrays. At the same time, piezoelectric films of comparatively high thickness are necessary to generate and detect sufficient acoustic power. To this purpose, the combination of Si-MEMS technology with piezoelectric thick-films is attractive.

Arrays of pMUTs made by PZT films screen-printed on silicon are reported in Hirsch et al. (2005). As illustrated in Fig. 9.6, the configuration consists of a transducer matrix on top of a micromachined membrane. Since the PZT transducers were intended to operate as thickness-mode resonators instead of as actuators for the eigenfrequencies of the silicon membrane, they were designed so that there is no overlap between the resonance frequencies of PZT elements and membrane, respectively. A multi stage screen-printing process with firing at 950 °C allowed the creation of layers of PZT with a final thickness variable between 30 and 110 μm. In this latter case, a resonance peak at 4.9 MHz has been measured with a quality factor improvement over commercial bulk ceramics.

A two-dimensional pMUT array based on PZT films is described in Wang et al. (2006). The considered films range in thickness between 2 and 50 μm. It is recognised that they occupy a technological region between the processing capabilities of thin film and machining of bulk ceramics. To avoid the high firing temperature usually required for conventional thick-film pastes, a composite thick-film deposition technique is described. The process uses composite slurry consisting of a ceramic powder and an oxide ceramic producing sol. The composite slurry is then deposited using a spin coating process whereby the electroded substrate wafer is coated with the slurry spun at high speed to yield a thick film. The final thermal treatment is at 600 °C, which is lower than the conventional firing temperatures.

In the field of piezoelectric acoustic-wave and resonant sensors, one early example in TFT is the pressure sensor reported in Morten et al. (1992), which, thanks to the resonant principle, allows the measurement of static pressure. The sensor has a two-port resonator configuration based on an alumina circular diaphragm where an annular interdigitated actuator and a central sandwich sensor made by screen-printed PZT films are deposited. The diaphragm is excited in flexural resonance at its third vibration mode by properly applying feedback across the driving and reading PZT elements by means of a phase-locked loop (PLL) electronic circuit forming a pressure-controlled oscillator. The differential pressure applied across the diaphragm deforms it and generates a radial tension. This in turn increases the diaphragm equivalent stiffness, therefore the resonant frequency rises and the sensor is thus able to measure static pressure. The reported sensitivity is around 150 Hz/mmHg at a frequency of 57.8 kHz.

A hydrostatic pressure resonant sensor based on a rectangular alumina beam excited in flexural resonance by two PZT thick-film elements is described in V. Ferrari (2004). The beam was mounted in a dual-in-line (DIL) package supported by the bonding wires in an approximately free-free condition that provided a marked resonance at the fifth flexural mode located at 198 kHz. The hydrostatic pressure of a surrounding gas results in the increase of the beam inertia and the resonant frequency decreases accordingly. A linear behaviour up to 4 bar has been measured, with a sensitivity of around –35 Hz/bar in air. This sensor configuration has an extended measuring range and a high overload capability since no deformable diaphragms are present that may fracture. On the other hand, the sensitivity depends on the particular gas.

An intense activity on the development and applications of PZT printed films has been carried out at Fraunhofer Institute of Ceramics in Dresden (Gebhardt et al. (2004). Here the development of many sensors has also comprised piezoelectric resonant pressure sensors realized in LTCC technology (Partsch et al., 2003).

The Jožef Stefan Institute in Slovenia has also been very active in the development and applications of PZT thick-films. In particular, resonant pressure sensors with diaphragms less than 10 mm × 10 mm in size realized in LTCC technology for different pressure ranges in collaboration with HIPOT-RR are reported in Zarnik et al. (2009).

An early device relying on the acoustic-wave principle based on piezoelectric thick films was described in White and Ko (1993). A plate-wave sensor structure was realized on a rectangular alumina substrate using two screen-printed PZT elements with interdigitated electrodes working as emitter and receiver, respectively, of acoustic waves along the substrate. The sensor is configured as a two-port delay line that, equipped with an electronic amplifier, behaves as an oscillator. A constant force applied in the centre of the substrate generates a strain, which in turn produces a decrease in the frequency. A frequency decrement of around 40 Hz for a load of 100 g was reported at a resonant frequency of 8 MHz.

Similarly, acoustic waves launched and detected by two pairs of PZT thick films with interdigitated electrodes have been exploited to measure flow in a pipe as described in De Cicco et al. (1994b). The piezoelectric devices were realized on alumina substrates attached to the outside surface of a metal pipe where liquid flows. Flexural plate waves are generated by the PZT films through the substrates, and guided into the pipe. The wave patterns propagate in opposite directions, while their velocities result to be affected by the liquid flow in the pipe. Two different flow-meter designs have been studied, operating in the megahertz region and below 100 kHz, respectively. Both designs were provided with an oscillator, which synchronously drives the two guides at the same frequency. The change in phase difference between the piezoelectric signals induced in the two receivers, due to the change of the flow velocity, is taken as the sensor output. A flow sensitivity in water of 17 × 10^− 2 deg/(mm/s) was measured for the second design over the range between 0 and 750 mm/s.

For the measurement of static force, Fig. 9.7 illustrates a PZT-on-steel resonant tuning fork sensor (Crescini et al., 1996). On a steel beam, a dielectric insulation layer was screen printed followed by three PZT thick films with associate electrodes. The two elements at the beam-ends connected in parallel work as a driver, and the central element as a sensor in a two-port configuration which, arranged in a feedback loop with an electronic amplifier, allows to excite the beam in flexural resonance. When the beam is clamped at both ends, an axial traction force increases the equivalent stiffness, therefore the resonant frequency rises. The relationship between frequency and applied force is linear for small forces. The beam was mounted on a clamped-free aluminium frame to transform an applied vertical force into beam strain. A sensitivity of 1.1 Hz/N at the resonant frequency of 35 kHz was measured, with a linear range reaching 800 N.

PZT thick-films allow the development of variable-mass AW sensors or, more generally, AW sensors responsive to an applied acoustic load (V. Ferrari and Lucklum, 2008). Variable-mass, also called gravimetric, AW sensors work as resonant microbalances. By functionalizing the surface with a sorption coating they can be used for chemical sensing.

PZT thick films were first used for gravimetric sensing in diaphragm and cantilever resonator sensors with polymeric coatings for the detection of humidity in air (Morten et al., 1993; V. Ferrari et al., 1996). A significant increase in mass sensitivity was later obtained by using the PZT thick-film resonator itself as the microbalance, leading to a device named resonant piezo-layer (RPL) sensor (V. Ferrari et al., 1997). As shown in Fig. 9.8(a), the structure of a thick-film RPL sensor is made by the superposition of a nonpiezoelectric substrate, specifically alumina, a bottom electrode layer, a PZT layer poled through its thickness and a top electrode layer. The PZT film is acoustically coupled to the substrate, leading to a thickness-expansion composite resonator, which can be used as a bulk acoustic wave sensor responsive to an acoustic surface load. Typical dimensions are 5 mm for the electrode diameter, and 250, 10 and 90 μm for the thickness of the substrate, electrodes and PZT, respectively. This results in a resonant frequency of around 7 MHz, while higher values can be achieved for thinner devices. A surface mass load on the top electrode determines a frequency decrement with a sensitivity higher than 500 Hz/μg at 7 MHz (V. Ferrari et al., 2001).

A multisensor array of RPLs on the same substrate is shown in Fig. 9.8(b). The array also integrates a resistive heater driven in the constant-temperature mode, to minimize the thermal drift of the sensor resonant frequencies that can typically be as high as 500–1000 Hz/°C.

By the use of proper sorption coatings, the achieved mass sensitivity was suitable for gravimetric chemical sensing (M. Ferrari et al., 2004; V. Ferrari et al., 2000). To further increase the mass sensitivity, it is desirable to reduce the sensor dimensions. As a significant example, silicon microcantilever resonators based on PZT thick films are described in Park et al. (2006). The thicknesses of the PZT and the silicon cantilever are approximately 22 μm and 12.3 μm, respectively. The reported estimated mass sensitivity for a 400 μm × 380 μm cantilever is nearly 32 kHz/μg at a resonant frequency of about 150 kHz.

A field of application of significant interest for piezoelectric materials is energy harvesting from mechanical sources, predominantly vibrations, to generate electrical supply for low-power sensor nodes (Kim et al., 2009). In this context, thick-film devices could provide solutions at an intermediate dimensional scale, which is conveniently lower than bulk devices yet retaining a sufficient volume to collect enough mechanical energy, as opposed to fully miniaturized devices whose power output inherently reduces due to decreasing size. A recent review of the potential of thick-films in the field of energy harvesting is given in Priya et al. (2009).

An energy harvester from vibrations based on PZT thick films on metal substrate is reported in M. Ferrari et al. (2010b). Vibration harvesters typically are linear mass-spring-damper systems working at resonance. Therefore, they are narrow-band devices whose conversion effectiveness falls if the frequency varies across a comparatively wide range. A different approach is here proposed based on nonlinear converters that exploit stochastic resonance to extract energy from broadband excitation.

As shown in Fig. 9.9(a), the converter consists of a piezoelectric film on an elastic beam coupled to permanent magnets to create a bistable system. Under proper conditions, the system bounces between two stable states in response to random excitation, which significantly improves energy harvesting from wide-spectrum vibrations. Nonlinear converters were realized by screen-printing low-curing-temperature PZT films on steel cantilevers equipped with magnets. Experimental tests were performed by measuring both the beam deflection and the output voltage under excitation by random vibrations at varying degrees of nonlinearity added to the system. Typical plots of the beam displacement and corresponding output voltage are shown in Fig. 9.9(b). The obtained results demonstrate an increase of up to 88% in the rms output voltage at parity of mechanical excitation when the system is made bistable.

The same principle can be implemented in a simplified single-magnet configuration that exploits the ferromagnetic properties of the elastic beam over which PZT thick films are screen printed (M. Ferrari et al., 2011).

9.6.1 Basic theory and relationships of the pyroelectric effect

Pyroelectricity implies that the polarization P of a material is a function of temperature T. To avoid possible confusion with stress, in the present section temperature will be indicated with the symbol Θ.

In polar materials, P includes a spontaneous polarization P_S in addition to the field-induced polarization P(E). In the scalar notation, the dielectric displacement D is therefore:

[9.6]

Assuming constant E, the derivative of D with respect to temperature Θ is:

[9.7]

The quantity p_G is called the generalized pyroelectric coefficient of the material (Damjanovic, 1998). It can be observed that p_G is made by two contributions: the first one, p = ∂P_S/∂Θ, is the so-called true pyroelectric coefficient, while the second contribution represents the induced pyroelectric effect. Sensors exploiting the induced pyroelectric effect are said to operate in the dielectric bolometer mode. They do not require poling and are not limited to work below the Curie temperature of the material, but need an applied electric field (Muralt, 2001).

The pyroelectric coefficients are affected by the mechanical boundary conditions, i.e. whether the material is considered in clamped (constant strain S) or free (constant stress T) conditions (Liu and Long, 1978). Under constant strain, the so-called primary pyroelectric effect occurs. When the material is free to undergo thermal expansion, i.e. at constant stress, an additional contribution results from the piezoelectrically induced charge. This second phenomenon is sometimes called the secondary pyroelectric effect (Muralt, 2001).

The expressions of p_G in the two cases can be derived by coupling Eq. [9.6] with the corresponding piezoelectric equations under either constant T or S, i.e. Eq. [9.1a] or Eq. [9.1c], respectively. This results in:

[9.8]

where α is the linear coefficient of thermal expansion and e is the piezoelectric constant. In the case of films on a substrate, the partially-clamped boundary conditions and the given materials determine the effective value of e, and thereof the relative importance of the primary and secondary pyroelectric effects (Damjanovic, 1998; Muralt, 2001).

Limiting our attention to the true pyroelectric effect expressed by the coefficient p, if electrodes are placed normal to P in a material where temperature Θ is assumed to be uniform and they are wired in a circuit, a time variation of Θ induces a current I_P in the circuit, as shown in Fig. 9.10(a).

The electrical output can be related to the radiant energy input by means of the thermoelectrical equivalent model of Fig. 9.10 (b), where R_T, R_P and C_T, C_P represent the thermal and electrical resistances and capacitances, respectively. Assuming an incoming radiant power W harmonic at the angular frequency ω, the voltage and current responsivities are respectively defined as (Whatmore, 1986):

[9.9a]

[9.9b]

The dynamic properties of a pyroelectric sensor can be analysed by considering the frequency responses of voltage and current responsivities, and including the effect of the input preamplifier. To first order, a thermal and an electrical corner frequencies are present, respectively given by ω_T = 1/R_TC_T and ω_E = 1/R_PC_P. The relative positions of ω_T and ω_E depend on the material and geometrical parameters. For bulk materials generally ω_E > ω_T, whereas the opposite holds for thin films. The use of a transimpedance amplifier, due to its virtually zero input impedance, allows the tailoring of the electrical time constant by means of the external feedback components R_F and C_F, irrespective of R_P and C_P.

The simplified model of Fig. 9.10 becomes inadequate when the sensor has a multilayered structure and, therefore, the thermal profile along the thickness across the different materials is increasingly important (Samoilov and Yoon, 1998).

9.6.2 Examples of devices and applications

The reported pyroelectric coefficient p for PZT thick-films is typically between 1.2 and 1.5 × 10^− 4Cm^− 2 K^− 1, depending on paste composition and poling parameters, while it is around 3.8 × 10^− 4Cm^− 2 K^− 1 for PZT ceramics (Baudry and Delmas, 1991; De Cicco et al., 1999).

Densification promoted by the application of isostatic pressure before firing has been proposed to increase p (Lucat et al., 1997). Even though the pyroelectric coefficient of thick films is low, their reduced dielectric permittivity favourably determines a voltage responsivity that can be similar or higher than for bulk ceramics.

Pyroelectric sensors using PZT or modified-PZT screen-printed thick films have been reported as single-element detectors (De Cicco et al., 1999; Leppävuori et al., 1995; Lozinski et al., 1997), as well as in multisensor arrays (Baudry and Delmas, 1991; Lozinski et al., 1998).

In early works, measurements have been carried out mainly with relatively high-power light sources, such as lamps and lasers. For example, thick films of lead lanthanum zirconate titanate (PLZT) were used to fabricate a linear array that was tested under a flash lamp excitation (Lozinski et al., 1998). A pyroelectric detector made by a PZT thick film with buried electrodes was tested in response to an infrared (IR) chopped source with a peak power of 5.5 mW (De Cicco et al., 1999).

Multi-element thick-film pyroelectric sensors were also proposed for wide spectral range radiation detection (from IR to ultraviolet (UV)), and laser beam alignment and profiling. An array of 3 × 3 pixels (Capineri et al., 1998) and a four-quadrant detector (Capineri et al., 2004) made by PZT thick films on alumina intended for laser spot localization have been developed. The latter device is shown in Fig. 9.11 where the separation of the four quadrants obtained by sawing is visible.

More recently, it has been demonstrated that the pyroelectric signals from PZT thick films can be detected even under excitation by low-power light sources, such as a light-emitting diode (LED) in the visible. If the LED is driven in amplitude modulation and the corresponding pyroelectric current is detected by synchronous demodulation, a DC signal is obtained which depends on the fraction of the LED light intensity impinging on the pyroelectric film. Interferences from thermal and light background are rejected. The maximum responsivity is typically obtained for a modulation frequency in the region around 100 Hz. The typical pyroelectric signal corresponds to peak temperature variations in the PZT film between 50 and 100 mK.

Based on this principle, pyroelectric contactless displacement sensors were proposed. As shown in Fig. 9.12, a pyroelectric film coupled to a LED can work respectively as the reference element and the movable light-spot cursor of a contactless linear displacement sensor (V. Ferrari et al., 2002). The sensor consists of a planar multi layer structure on alumina substrate where a rectangular film of PZT is enclosed between two PdAg electrode layers at the top and bottom. Each layer is in turn composed of a pair of triangular split electrodes (left, L, and right, R). The resulting four electrodes are combined in reverse-parallel with respect to the common poling direction, so that the pyroelectric signals from the R and L subsections subtract in a push-pull configuration producing a differential current. The LED spot position along the sensor length is converted into a suitably linear DC output by means of amplitude modulation of the LED and synchronous demodulation of the pyroelectric differential current. The readout method, combined with the differential configuration of the sensor, provides rejection of vibrations and microphonics caused by the piezoelectric response of PZT, as well as of external thermal and light sources. With a LED driving current of 33 mA at the stand-off distance of 3 mm, the measured sensitivity was 120 mV/mm over the range ± 10 mm, with a resolution better than 1.5 × 10^− 3 of the span.

An extension of the same principle was proposed for biaxial position measurements by means of the pyroelectric sensor array shown in Fig. 9.13 (V. Ferrari et al., 2003). The sensor array is made by 8 × 8 pixels of PZT screen printed on an alumina substrate. The electrodes are configured as eight columns and eight rows evenly spaced, whose respective crossings form the 64 pixels of the array. As shown in Fig. 9.14(a), with an amplitude-modulated LED placed in front of the array and movable in the XY plane parallel to the array surface, the array and the LED respectively work as the reference element and the contactless cursor of a biaxial position sensor. A tailored readout and processing technique based on weighted amplification of the column and row pyroelectric signals produces a continuous and linear dependence of the output voltages on the XY position of the LED cursor. The measured sensitivity was 1 V/mm over the range ± 3.5 mm, with nonlinearity within ± 1% of the span. The resolution threshold was 4 μm, which is much better than the pixel pitch. Fig. 9.14(b) shows the results of biaxial measurements along the worst-case squared test path with side of 7 mm, i.e. on the borders of the linearity region. A good reconstruction of the LED trajectory can be observed.

Thick-film pyroelectric sensors for contactless displacement measurement offer low cost at large sensing areas when compared with semiconductor position-sensitive detectors. On the other hand, due to their limited frequency response with standard film and substrate thickness, they have been investigated for quasi-static applications so far.

Recently, the pyroelectric effect in PZT thick-films has started to be investigated for energy harvesting and possible use in generators for ultralow-power sensor modules. In Cuadras et al. (2010), PZT thick-films and commercial polyvinylidene fluoride (PVDF) elements were subject to thermal transients measuring currents and charges in the order of 10^− 7 A and 10^− 5 C, respectively, for temperature fluctuations from 300 to 360 K in a time period of the order of 100 s. Heating–cooling cycles were also investigated in order to accumulate energy. The pyroelectric current was rectified and the generated charge stored in a 1 μF capacitor up to an energy of 0.5 mJ.

In Dalola et al. (2010) sinusoidal temperature fluctuations were applied to screen-printed PZT films on alumina substrate. The charge extracted from the pyroelectric converter was stored into a capacitor using different rectifying circuits. The results of Fig. 9.15, where full-wave and voltage-doubler rectifiers are compared, show that after a few dozen heating–cooling cycles with a temperature rate of 1.8 °C/s, voltages in the order of 5 V and more are reached on a 10 μF capacitor in either case. The corresponding harvested energy can be compatible with use in autonomous sensors working in low duty cycle intermittent mode.

• Energy Harvesting Network

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• IEEE Instrumentation and Measurement Society (IMS)

    Society dedicated to research concerning the theory, methodology and practice of measurement, and in the design, development and evaluation of instrumentation and associated measurement systems: http://www.ieee-ims.org.

• IEEE Sensors Council

    Council dedicated to research on the theory, design, fabrication, manufacturing and application of devices for sensing and transducing physical, chemical, and biological phenomena, with emphasis on the electronics, physics and reliability aspects of sensors and integrated sensor-actuators: http://www.ieee-sensors.org.

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• International Microelectronics and Packaging Society (IMAPS)

    Society dedicated to the advancement and growth of microelectronics and electronics packaging technologies through professional education: http://www.imaps.org/default.asp.

• Piezo Institute

    Consortium of academic and industrial researchers dedicated to the field of piezoelectric materials and devices: http://www.piezoinstitute.com

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