Introducing an extremely high output power and high temperature piezoelectric bimorph energy harvester technology based on the ferroelectric system Bi(Me)O₃-PbTiO₃

Extremely high temperature energy harvesting technologies (>200 °C) are gaining more interest as scientists and engineers appreciate the implications and technological needs of the Internet of Things (IoT).^1–5 There are a large number of industries where elevated service temperatures are required (>200 °C), such as oil-gas, nuclear, space, and hypersonic materials. Although high temperature capable piezoceramic compositions have been demonstrated, there is virtually no discussion on piezoelectric harvesters over broad temperature ranges and any consideration of vibrational energy harvesting at these elevated temperatures. It is this lack of scientific and engineering knowledge that has motivated this study. Boisseau et al. provide a comparative benchmarking of the different energy harvesting sources in various surrounding environments.⁶ We see a dramatic performance range in power densities ranging from about 10 mW/cm³ to 0.001 mW/cm³. It is noteworthy that indoor solar compares well with mechanical vibration output power for low temperatures. However, elevating the operation temperature of vibrational energy harvesters over 150 °C there is a dramatic degradation in performance, as shown in Fig. 1.^6–10 These higher temperatures would eliminate the more controversial polymer triboelectric energy harvesting and so are ignored here. We do, however, conjecture that such temperature ranges require a multitude of factors including optimized high temperature piezoelectric materials that are also designed and integrated to address complex clamping and thermal depolarization stresses.^11–14 

As an approximate material selection criterion for high temperature energy harvesting piezoelectric materials performance, we can consider d₃₃ × g₃₃ as a figure of merit (FoM) as shown in Fig. 2.^15–17 Considering the desired operational limit to be above 200 °C, then from Fig. 2 (1 − x)BiScO₃-xPbTiO₃ (named BSPT hereafter) is a very attractive selection. The BSPT material has a large piezoelectric constant (d₃₃) due to the rhombohedral-tetragonal morphotropic phase boundary (MPB) and a high Curie temperature, T_c, together with a high d₃₃ × g₃₃.^18,19 Various types of structural design have already been considered for piezoelectric energy harvester; these include cymbal structures,²⁰ d₃₁ bimorph structures,¹⁰ and d₃₃ mode barbell structures.⁹ Earlier, Wu et al.¹⁰ proposed a piezoelectric harvester with a d₃₁ mode bimorph type using BSPT ceramic plates. The maximum output power output was around 24 μW at 150 °C (∼0.04 mW/cm³) and then gradually decreased to around 4 μW at 300 °C (∼0.01 mW/cm³). A barbell-shaped piezoelectric energy harvester operating in d₃₃ mode was shown to have a maximum output power around 10.5 μW at 175 °C (∼9 × 10⁻⁴ mW/cm³) and then gradually decreased to around 2.5 μW at 350 °C (∼2 × 10⁻⁴ mW/cm³).⁹ Gao et al.²¹ also reported on a barbell structure with a ternary piezoelectric composition based on Pb(Ni_1/3Nb_2/3)O₃-Pb(Zr,Ti)O₃-Pb(In_1/2Nb_1/2)O₃ with an extremely high d₃₃ of ∼1000 pC/N. In this case, the maximum output power was still only 30 μW at room temperature (∼3 × 10⁻³ mW/cm³). Thus, one must conclude that the piezoelectric energy harvesters not only need high performance materials, but also major consideration given to the design and assembly. In addition, when operating at various temperatures, each of these factors needs to be optimized with respect to temperature. Here, we will demonstrate an ambitious performance of output on the order of milliWatts and operating at temperatures up to 350 °C. The high temperature experimental results of the energy harvester including harvested power, resonance frequency, and optimal load resistance as a function of temperature are herein reported. The details of interest to accomplish such high performance reported here include

1. optimization of the piezoelectric material performance through composition,

2. cantilever shape design, and

3. optimized bonding and minimization of thermal expansion mismatch to limit de-poling.

We also benchmark the temperature dependent data of the prototyped energy harvesters, which here is rationalized against finite element models, phenomenological models, and other high-performance piezoelectric harvester publications. The data presented here show the advantage of our design strategy and show that piezoelectric harvesters are highly effective in temperatures up to at least 350 °C where other energy harvesting device performance suffers.

The compositional optimization of BSPT materials was investigated by changing the PT content in the system. The optimal range was investigated by preparing (1 − x)Bi,ScO₃-xPb,TiO₃ [x = 55%, 62%, 63.5%, and 64% (named BSPT64 hereafter)] materials via the mixed oxides method. They were prepared from oxides with a purity of >99% through conventional solid-state synthesis. Oxide compounds of Bi₂O₃, Sc₂O₃, PbO, and TiO₂ (all from High Purity Chemicals, >99%, Japan) were mixed for 24 h in a high-density polyethylene (HDPE) jar with zirconia balls and then dried. The dried powders were calcined at 850 °C for 6 h. After re-milling, the powders were dried, and cold isostatic pressed into discs under a pressure of 280 MPa and then sintered at 1100 °C for 45 min. Structural properties of the specimens were examined by x-ray diffraction (PANalytical Empyrean X-Ray Diffractometer third generation) and scanning electron microscope (FEI Nova NanoSEM 630 SEM). The specimens were poled in silicone oil at 100 °C by applying a DC field of 4.0 kV/mm for 15 min. The piezoelectric and dielectric properties and the k_p value were determined using a d₃₃ meter (PIEZOTEST, PM300) and an LCR meter (HP4980, Hewlett-Packard, USA).

Regarding the bonding process, an in-house metal paste is applied on the ceramics via screen printing with a screen mesh/emulsion of 325/25 μm. After printing, a leveling time at 25 °C for 5–10 min is applied. Drying and firing are carried out at 120 °C for 10–15 min and 500 °C for 30 min. During firing, the device is pressed under a load to improve bonding, which is critical for the success of the vibration tests. The samples are then poled as the same procedures described in Sec. II A. The piezoelectric coupling coefficient is measured by a resonance–antiresonance method with electrochemical impedance sweeps over a frequency range of 20 Hz to 2 MHz on poled plates using a computer-controlled impedance analyzer (Agilent Technologies HP 4194A), based on IEEE standards. The external vibration is applied using a shaker (Lab Works, Inc., ET-136) with a vibration acceleration of 1 g (g = 9.8 m/s²). The output voltage of the harvester is measured using a digital oscilloscope (Tektronix TDS3052). The electric power is calculated at various electric load resistances and external vibration frequencies. A schematic diagram of the measurement system with the load resistance is shown in the supplementary material. Hence, there are many key design aspects to be considered at the device level. We have already discussed the material selection criteria earlier and the importance of T_c and d₃₃ × g₃₃. The interface between the clamped region and the vibrating piezoelectric cantilever must be designed to operate over the functional temperature range. The thermal expansion of the different materials must be minimized to prevent stress buildup in the interface region. Stresses can clamp and depole the piezoelectric such that if the stress increases the point where domains can rearrange and depole the piezoelectric performance is greatly diminished. We also can consider the strain gradients relative to the interface regions, which will be discussed later.^22,23 The electrical circuit must be matched with the electrical impedance of piezoelectric, and so the resistance is often varied to aid in this transfer. This is accomplished by the use of a variable resistor to simulate the impedance matching under the experimental conditions, as is typically the case.^24,25

The x-ray diffraction peaks represent a typical single perovskite phase and show the detailed spontaneous stress for the (100), (111), and (200) peaks, with a close inspection of the peak shape being consistent with a compositional transition from a tetragonal to rhombohedral ferroelectric phase, all shown in the supplementary material. The corresponding microstructure is given from the BS-PT systems sintered at 1100 °C for 45 min. The materials show high densities and large grain sizes in the compositions of interest around the morphotropic phase boundary. The bulk density and the relative density of BSPT64 are about 7.5 g/cm³ and 96.8%, respectively. In addition, the mean sizes of grains were calculated via the grain size distribution. BSPT64 showed a mean size around 11 μm. Figure 3 shows the important variation of the piezoelectric voltage constant g₃₃ and figure of merit d₃₃ × g₃₃ (FoM) variations with the composition in the regions of 0.55 ≤ x ≤ 0.645, indicating a marked sensitivity to the FoM at x ≈ 0.64 at room temperature. FoM is a useful index demonstrating the performance of energy harvesting material. Particularly, materials with higher FoM offer higher power output suitable for energy harvesting devices.^26–28 We therefore concentrated on the temperature dependence of the BSPT64 materials and investigated the relative permittivity or dielectric constant and coupling coefficient dependence. For the temperatures above 448 °C, the resonance in the impedance is lost owing to the depolarization of the poled ferroelectric material. The dielectric loss increased from 1 kHz to 10 kHz at temperatures above 250 °C. Dielectric constant vs temperature measurements of unpoled BSPT64 show no frequency dispersion of permittivity and there is no detectable variation of T_c with frequency.^22,29 The dielectric constant and loss are 1470 and 0.0215, respectively. Therefore, it is apparent that BSPT64 is a candidate for demonstration of high temperature bimorph materials. The quality of piezoelectric properties is summarized for this system with our processing techniques in Table I. We note that Wu et al.^9,10 have also considered the same material as a good candidate for energy harvesting in both the unimorph and bimorph configurations. This work is very interesting but unfortunately lacks the high piezoelectric energy harvesting power densities. The reported maximum output powers of d₃₁ and d₃₃ mode BSPT-based energy harvesters are around 23 and 10.5 μW, respectively.^9,10 Although BSPT materials processed by Wu et al. are of high performance with properties similar to those reported by Eitel et al.,^22,29–35 as noted in Table I, there are significant performance differences relative to our findings presented below. This is related to the deleterious effects of high temperatures impacting the mechanical/electrical interface, and the design will be discussed in Secs. III B and III D.

To address the optimization of the energy harvester, we modeled the system with the finite element method (COMSOL Multiphysics, COMSOL Inc., Sweden) to simulate at the fundamental vibration mode of the harvester structure: with a fundamental bending mode. We focused on different contributions to potential inefficiencies of the electromechanical coupling in design and assembly. With respect to the basic shape of the device (Fig. 4), we show the evolution of the top profile from a simple near rectangle cantilever (left device) to an hourglass profile (right device) and the impact on the calculated voltage output. The best profile is a hybrid (middle device) between the near parallel and hourglass design. The high performance and higher output are a consequence of the uniformity of strain into the center of cantilever, enabling higher generation of charge over the whole length of the cantilever.

Next, we considered the electrical contacts and the adhesion of the bimorph structure. Typically, the literature notes the use of either mechanical bolts or high temperature epoxies. These solutions are unreliable and ineffective at high temperatures. To solve this, our device uses a silver paste to contact the electrode and metal structures to the unpoled piezoelectrics. Figures 5(a)–5(e) show the top view, side view, detail descriptions, explosion drawing, and test setup of the final design, respectively. The silver bonding layer is relatively thin, in the range of 30–50 μm. Its effect on the actuator performance is negligible as desired.

The thermal expansion from the metal has also implications in high temperature stability and stress driven depoling of the piezoceramic. We therefore selected Invar, a metal that has a sufficiently lower linear coefficient of thermal expansion (α = 0.9 × 10⁻⁶ °C⁻¹ at 200 °C). Internal thermal stresses are also developed after cooling down to room temperature due to a thermal expansion coefficient mismatch between the Invar metal layers and the piezoelectric layers. The selection of Invar has minimized the mismatch issue relative to other candidate metals. If the thermal expansion is too high relative to the piezoelectric material, the stresses will depole the piezoelectric polarity through disordering the aligned domain structures and thereby reduce performance.

The power output was measured with the outer electrodes and the middle electrodes, connected by the electrical load (R_L) and varying between 10 and 1000 kΩ, because the piezoceramic layers are polarized in the same directions. By measuring the V_L(RMS) voltage drop across R_L, the output power could then be calculated according to the equation²¹ 

The optimal resistive load will vary mainly due to the changes in the mechanical property, device geometry, and thickness. The optimal resistive load of the device is calculated from Eq. (2), where f and C are frequency and capacitance, respectively. The optimal load is inversely proportional to the intrinsic static capacitance of the piezoelectric transducer,²⁵ 

Energy harvesting tests at room temperature were carried out at constant acceleration (1 g) and sweeping the vibration input frequency around the resonance. Each frequency sweep is repeated for a set of resistors in order to experimentally confirm the optimal load that provides the maximum power output, resonance frequency (f_r), optimum resistance (R_opt), and maximum output power (W_max).

Mechanical vibrations have typically broadband spectra and range between 1 and 250 Hz. The resonance frequency of a cantilever device can be reduced to lower frequencies by increasing the mass at the tip of the beam. The experimental dependence of the hybrid bimorph cantilevers is shown in Fig. 6(a), the masses are varied between 0.8 g and 30 g, and the resonance frequency can be reduced between 69 and 650 Hz. As a simple harmonic oscillator, we expect this relationship to scale as frequency–mass^−0.5; the basic trends are upheld in Fig. 6(b). Power density (PD) and normalized power density (NPD) are frequently used to compare energy harvesters.^5,30 The power density (PD) shows the power per volume, and the NPD is defined as the power density per acceleration squared. Detailed data including power, frequency, active area, active volume, loading mass, area-metric, and NPD are shown in Table II. There is also an increase in the maximum extractable power in a cantilever device. The effective volume of the power generator was almost equal to that of cantilever, so the generated average power density was estimated to be 5.64 mW/g² cm³. When a load mass of 30 g is used, as shown in Table II, the output power density was five times larger and reaches a high output of 29.77 mW/g² cm³.

The performance of the harvesters prototyped here is 100 times better output than all previous studies, such as with d₃₁ bimorphs¹⁰ and two d₃₃ mode barbell structures^9,21 that respectively show 7.5, 4.5, and 30 μW. This promising output performance obviously breaks the previous perception that piezoceramic energy harvesters typically perform with output powers at the μW level. This means that the piezoelectric material needs a high electromechanical d₃₃ × g₃₃ figure of merit, but for the high output performance of the energy harvester to push beyond the μWatt to mWatt performance requires attention of the bonding and interfaces. The hybrid design enhances interface adhesion between ceramic/metal by using a homogeneous silver bond. This provides a more efficient mechanical energy transmission than the pre-tightened clamping bimorph and barbell structures.^9,10,21 In careful design that considers the mismatch of ceramic/metal, the thermal expansion and the associated transient stresses in the bimorphs can be minimized and therefore not drive the de-poling and irreversible changes to the piezoelectric properties until the higher temperatures near T_c are approached.

Most vibration-based power generators can be approximated by the simple model describing the generator attaching to a vibrating source, the damped spring, and mass combination. The piezoelectric materials act as the springs, developing a voltage difference when strained. Maximum extractable electrical power is given by^6,31

where m is the mass, ζ_e is the electrical damping ratio, A is the acceleration factor, ζ_m is the mechanical damping ratio, and ω is the natural angular frequency. Therefore, the extractable power from the cantilever beam is linearly and inversely proportional to the resonance frequency for a fixed acceleration. The output power maxima are achieved when the driving frequency is equal to the resonant frequency. Therefore, a suggested vibration power generator should be designed to match a resonant frequency with the frequency of the vibration source. Moreover, two important design considerations are suggested from Eq. (3). First, the power will be maximized when mechanical damping is zero. Second, the mass should be maximized because the power is proportional to the loading mass. Any increase in loading mass also reduces the resonant frequency because they are in inversely proportional. However, increased loading mass creates higher stress on the base and bonding areas of the cantilever and thus poses a risk for critical device failure; therefore, design should consider the maximum stress on cantilever structure as a function of loading mass and targeted peak acceleration. In Fig. 6(b), the linear relation between loading mass and resonance frequency is in good agreement with Eq. (3). This simply means the energy harvester should be designed for the lowest possible frequency to achieve the highest power.

Figure 7(a) shows the output power, V_rms, and I_rms at matching load resistance. Likewise, there is also a corresponding stability in the natural frequency between 25 and 350 °C with a load resistance of 68 kΩ. This provides a maximum power output of 0.6–1.05 mW across this broad temperature range. As shown, output V_rms, I_rms, and power obviously demonstrated a similar tendency, increasing monotonously with the elevated temperature from 25 to 250 °C and then experienced a systematic falloff. It is also worth noting that the output V_rms is over 4 V and I_rms of over 70 μA in a wide range of elevated temperatures up to 300 °C. The experimental maximum output power is about 1.05 mW at 250 °C. This power should give the prospect of being able to power microdevices in electric systems.

Therefore, we have produced one of the highest performance energy devices over the broadest temperature ranges ever reported in vibrational energy harvesting. We can see this more clearly when plotting the NPD data of earlier studies with respect to temperature, as shown in Fig. 7(b). Note there is a scaling of the data on the ordinate latitude or Y axis of the graph to accommodate the orders of magnitude differences. Furthermore, Table III benchmarks the overall performance of several important piezoelectric energy harvesting reports relative to this study. Table III gives the material type, physical characteristics, power output, and NPD as a function of temperature from 25 to 350 °C. As shown in the general vibration model, the power output is proportional to the square of the acceleration magnitude when operating at resonance. Therefore, it is adopted to compare NPD by the output power per the square of the acceleration times unit volume shown in Fig. 7(b) and Table III. The volume is only of the transducer and does not include clamping fixture and electric circuit board.^31–33 The harvester could still operate even at temperatures above 250 °C, but it had a systematic falloff of the high performance values with the power densities of 8.7, 5.4, and 1.4 mW/g² cm³ at 250, 300, and 350 °C, respectively. It should be noted that these performance numbers are still high compared to the room temperature operation. Moreover, the influence of mass loading on the power was discussed in Table II, manifesting an approximately fivefold enhancement between 0.8 g and 30 g mass. Therefore, when the load mass of 30 g is used, the output power densities are measured to be 43.5, 27, and 7 mW/g² cm³ at 250, 300, and 350 °C. We can see that this investigation in terms of power densities is comparable and often superior to the best in class, and unequalled at elevated temperatures.

The piezoelectric energy harvester not only shows higher output power but also achieves the peak output power at a higher temperature (250 °C), which is significantly higher than earlier reports of BSPT-based on the d₃₁ mode, which was reported to peak at 125 °C, and also the d₃₃ mode that peaked at 175 °C.^9,10 The peak performance of the piezoelectric harvester introduced here at a temperature of ∼250 °C is not associated with extrinsic factors such as the thermal stress and depoling. This is inferred through the observations that the performance is reversible in this temperature range. Therefore, we consider the peak temperature is related to the temperature dependences of critical electromechanical parameters that control piezoelectric energy harvesters.

Normally, the temperature effects on elastic stiffness coefficients can be negligible.³⁶ Moreover, there are a number of reports that consider the temperature effects on −d₃₁, d₃₃, −g₃₁, and g₃₃ of BSPT as a function of temperature from 50 to 450 °C.^34–36 Both −d₃₁ and d₃₃ coefficients increase as a function of elevated temperature from 50 to 400 °C, followed by a fast decrease to zero at around 450 °C, which is the depoling and loss of spontaneous polarization temperature which is not completely reversible. The d₃₁ values at 50 °C and 300 °C are 125 and 250 (pC/N), and for d₃₃, these are 450 and 850 (pC/N), respectively. In contrast, both −g₃₁ and g₃₃ coefficients decrease as a function of elevated temperatures from 50 to 400 °C as the permittivity increases; again, g₃₁ and g₃₃ decrease to zero at around 450 °C.

Alternatively, we can rationalize the high temperature performance with a dimensionless figure of merit (FOM) by considering the power response of the piezoelectric transducer material in an energy harvesting application as⁶ 

where k₃₁ is the transversal electromechanical coupling factor, Q_m is the mechanical quality factor (inverse of the Q_m represents the mechanical loss), $s11E$ is the elastic compliance at the constant field condition, d₃₁ is the transversal piezoelectric strain constant, g₃₁ is the transversal piezoelectric voltage constant, and tanδ is the loss factor. DFOM is a more precise figure of merit for the piezoelectric transducer material in an energy harvesting application. It not only considers the properties of energy harvesting material but also the dynamic performance of device design. Therefore, it is a product of two FoMs representing off-resonance and on-resonance conditions.^6,37,38 We note that the measured tanδ in our processed BSPT samples starts to rise from around 250 °C and systematically increases until reaches the maximum at T_c of 450 °C. This would in turn reduce the DFOM and limit power output from the piezoelectric materials assuming no non-linear thermal mismatch depoling that was assumed to be minimal, as the response from the energy harvester was found to be reversible at temperatures in and around 250 °C. Therefore, based on Eq. (4), the controlling factors from the BSPT material are the temperature dependence of tanδ and dielectric constant, which in turn limit the power output at high temperature over 250 °C.

In this paper, we have demonstrated high performance piezoelectric energy harvesting. This has been considered from materials selection and design, the integration and interfacial considerations that lower performance through mechanical clamping, and thermal stresses under high temperature performance. Optimal power output was designed through both with COMSOL finite element analysis software and phenomenological vibrational modes, and qualitative considerations of the overall system. The piezoelectric materials are selected around the high temperature morphotropic phase boundary piezoelectric ceramic systems based on the family Bi(Me)O₃-PbTiO₃. The power densities are measured under optimal power conditions, and the tuning resistance and natural frequency are found to be remarkably stable over a broad temperature range, provided that the thermal stresses are considered in the device design. The overall performance is benchmarked across other notable piezoelectric harvesters and alternative technologies. The maximum output power of 1.05 mW was obtained with an impedance-matched load resistance of 68 kΩ at 250 °C. The generated power densities of 8.7, 5.4, and 1.4 mW/g² cm³ at 250, 300, and 350 °C, respectively, are much larger than that of conventional piezoelectric harvesters. Practical power generation from the ambient vibration may be possible because resonance frequencies can be reduced from 580 to 69 Hz by using the proof mass from 0.8 to 30 g, improving output power density from 5.64 to 29.77 mW/g² cm³, which has about a five times enhancement. As we have shown carefully prototyped designs with milliWatt output performance levels under resonance conditions, we believe that this paper points to a very promising strategy for intermediate level vibrational harvesters and sensors applicable for high temperature up to 300 °C.

See the supplementary material for the x-ray powder diffraction data, depolarization of the poled sample, the permittivity, and dielectric loss temperature variation for BSPT64 in the high temperature regions.

This work combined efforts that were conducted under work supported by the National Science Foundation, as part of the CDP under Grant Nos. IIP-1841453 and 1841466 and under the NASA STTR program (No. NNX16CS16C).

The data that support the findings of this study are available within the article [and its supplementary material].