A Review on Piezoelectric Energy Harvesting: Materials, Methods, and Circuits

2.1 Fundamentals of Piezoelectricity

Piezoelectricity is the property of certain crystals to generate an electric potential in response to applied mechanical stress. There are two different kinds of phenomena commonly observed which are termed as direct and the converse piezoelectric effects. When the mechanical stress is applied to a piezoelectric material, an electric charge proportional to the applied stress is produced. This refers to the direct piezoelectric effect. Conversely, when electric field is applied to the same material, strain or displacement is produced proportional to the magnitude of electric field. This is called as converse piezoelectric effect. The following two constitutive equations are used to describe the piezoelectric effect:

Here in these two constitutive equations, Di is the electrical displacement, Sj is mechanical strain, σj is mechanical stress, Ei is the electric field, c_ij is the elastic stiffness coefficient, s_ij is the elastic compliance coefficient, and ε_ij is the permittivity. The superscript used in the equation shows the constant parameter used. d_ij and e_ij are piezoelectric coefficients which are third rank tensors.

Piezoelectric ceramics are anisotropic in nature implying that the electromechanical properties exhibit maximum along specific crystallographic direction. The properties are commonly described using two subscripts (reduced order tensor notation) which indicate the direction of the electrical and mechanical parameters. Figure 4 shows the direction indexes of constants in rectangular crystallographic system. The principal properties along X, Y and Z axes are described using 1, 2 and 3 notations, respectively. The shear constants are represented by 4, 5 and 6 respectively. For example, in case of piezoelectric charge constant d₃₁, the first index “3” indicates that electrodes are perpendicular to axis 3 and the second index “1” indicates that the applied stress or induced strain is along direction 1. A superscript index on the electromechanical constant is used to represent the constant condition under which measurements were conducted. For example – in case of compliance, s36E, “E” indicates that the compliance was measured under constant electric field or with electrodes connected together.

Figure 4:

Direction index of electromechanical constants in poled piezoelectric ceramics.

Non-centrosymmetricity is requirement for observing the piezoelectric effect and most of the high performance piezoelectric materials are ferroelectric perovskites as shown in Figure 5. The leading representative of the perovskite piezoelectric ceramics, Pb(Zr,Ti)O₃ (PZT), has many possible variations depending upon the doping and solid solution. As shown in Figure 4(a), PZT unit cell has a symmetric cubic structure above the Curie temperature (paraelectric), however, below that it transforms into asymmetric tetragonal structure (approximately Zr/Ti ratio <1, where Zr + Ti=1) as schematically depicted in Figure 5(b). Thus, PZT unit cell shows spontaneous polarization because of the shift in the position of B-site atom.

Figure 5:

Perovskite PZT unit cell. (a) PZT unit cell in the symmetric cubic state above the Curie temperature. (b) Tetragonally distorted unit cell below the Curie temperature.

Neighboring dipoles formed in the distorted perovskite unit cell align together to form domains. Typically, polycrystalline piezoelectric ceramics have randomly oriented domain distribution as shown in Figure 6(a), thus, overall net polarization of material is negligible. Because of the ferroelectric nature of the material, domains can be permanently aligned by applying strong electric field. This process is called poling (see Figure 6(b)) and is normally performed at an elevated temperature slightly below Curie point to facilitate the domain wall motion. During poling process, most of the domains are aligned along applied electric field direction and neighboring domains exhibit new dimensions through nucleation and growth. After poling process, most of the dipoles retain their alignment imparting the piezoelectric material a remanent polarization (see Figure 6(c)).

Figure 6:

Piezoelectric domains in piezoelectric materials. (a) Randomly oriented domains, (b) Domains during and (c) after poling process.

Besides piezoelectric ceramics, there are piezoelectric polymer materials which have semi-crystalline structure for examples polyvinylidene fluoride (PVDF), polyamides, ParyleneC, liquid crystal polymers, PVDF-TrFE block copolymer etc. The operation principle of these piezoelectric polymers are similar to piezoelectric ceramic materials. The semi-crystalline polymers have microscopic crystals inside matrix which are also polarized and function as dipoles as described Figure 6. The microcrystals are distributed within an amorphous matrix. To obtain effective piezoelectricity in such materials, these small crystals should be reoriented and kept in one orientation through electrical poling or mechanical stretch process. There is another type of piezoelectric material known as voided charged polymer (VCP, sometimes called ferroelectret or piezoelectret) that contains internal gas voids. When the polymer surfaces surrounding the void are charged by electrical poling or X-ray, the space charges are created inside matrix and the VCP behaves like piezoelectric material. These polymers have very high d₃₃ values. However, these piezoelectric polymers have serious life time and ageing problems. The VCP is easily neutralized in extremely moist environment and the surface charge can be rapidly decayed in high temperature.

2.2 Transfer Function for Energy Harvester

The simple vibration energy harvester can be modeled as a second-order, spring-mass system. The characteristics of the energy harvester can be described by damping constant and natural frequency of the system. A cantilever beam structure with piezoelectric plate and proof mass is equivalent to a lumped spring mass system of a vibrating rigid body. Thus, the governing equation of motion of a lumped spring mass system can be written as:

which can be transformed using Laplace transform as following:

where as is the Laplace transform of the acceleration, at, given as:

Therefore, the transfer function of the energy harvester can be expressed as:

where Q=km/b is quality factor of system and ωr is resonance frequency of the energy harvester. The natural frequency of the spring mass system and energy harvester can be given as:

where K and M are the transverse stiffness and effective mass, respectively. The stiffness K can be calculated from loading condition. In case of simple cantilever beam structure, the stiffness can be expressed as:

where E is modulus of elasticity, I is the moment of inertia, and L is the length of beam. The moment of inertia for a rectangular cross-section is I=112bh3, where b and h are the width and thickness of the beam in transverse direction, respectively.

2.3 Frequency Dependence of Output Power

The vibration displacement of energy harvester can be maximized in resonance. The harvester will convert mechanical to electric energy most effectively when the applied vibration frequency is closer to the fixed natural frequency of the device. As shown in Figure 7, a few percent of mismatched frequency with resonance results in a dramatic decrease of output power. Therefore, tuning or adjusting frequency to an external vibration source is essential in order to improve energy conversion efficiency. From eq. [7], the natural frequency of the energy harvester is closely related to dimension and effective mass. The natural frequency of the energy harvester is usually adjusted by changing the weight of proof mass. However, the bandwidth at resonance frequency is usually narrow and thus needs some additional mechanism to effectively capture ambient vibrations which usually represent a wide spectrum of frequencies or time varying vibration spectra.

Figure 7:

Frequency dependent output power of typical vibration energy harvester. The maximum output power can be achieved at resonance frequency.

2.4 Vibration Kinematics

Vibration is common ambient energy source that can be found in household appliances (refrigerators, microwave ovens, washing machines etc.), large civil structures (buildings, bridges etc.), industrial plant (refineries), automobiles and many other common locations. Table 2 shows some of the common sources of mechanical energy that can be harnessed through piezoelectrics. Table 3 quantifies the vibration energy available in some of these environments (Marin and Priya 2012; Priya 2007).

The general model of a vibration energy harvester is a typical mass-spring-damper system. Maximum power is achieved when the excitation frequency ω is equal to the natural frequency ω_n. Maximum extractable electrical power in terms of mechanical damping ratio ζ_m, electrical damping ratio ζ_e, proof mass m and acceleration A becomes,

Several conclusions can be drawn from the observation of eq. [9] (Xu 2012). The extractable power from the beam is inversely proportional to resonance frequency at a fixed acceleration, A; therefore the energy harvester should be designed at lowest possible frequency to achieve highest power if we do not consider that frequencies of external vibration sources are normally fixed in real applications. The extractable power is also proportional to the square of acceleration (Chandrakasan et al. 1998), which limits the energy available for conversion with low-g vibrations whatever the specific design is chosen. It can also be seen that power is proportional to the proof mass, so a large proof mass is always desirable for energy harvesting. Finally, the term composed of the mechanical and electrical damping ratio implies that the maximum power is achieved when the electrical damping matches the mechanical damping (Dutoit, Wardle, and Kim 2005). When the electrical damping is equal to mechanical damping (ζe=ζm), the maximum electrical power is given as:

where the acceleration amplitude A and proof mass deflection Y are related by the relationship given as:

Equation [10] represents the theoretical maximum of extractable power, which can be dissipated in the electrical load. This is actually a limiting factor for all linear resonator based energy harvesters if the piezoelectric layer’s transformation capacity is not a limiting factor. It has been reported that a nonlinear resonator based energy harvester can circumvent this limit and is able to generate much higher power than the mechanical damping, which will be discussed in the later section. Another parameter of interest in design of thin film harvesters is given by the generalized electromechanical coupling (GEMC) factor, k_G² (Uchino 2009). The GEMC factor is obtained from the equation:

where ω_short and ω_open are the angular resonance frequencies of the associated short and open circuits, respectively. The GEMC represents the power generation performance of the vibration harvesters, and this value can be theoretically derived from the mechanical properties, thickness ratio, and electromechanical coupling factors of piezoelectric thin films (Wang et al. 1999).

2.5 Energy Conversion and Figures of Merit

Piezoelectric energy harvesters can be categorized by the targeted energy sources, such as ambient vibrations, impact or shock stress, fluid flow and human motion. Regardless of the various energy sources, the basic working principle is the same – the environment applies a stress on piezoelectric material and by the direct piezoelectric effect, the input mechanical energy is converted in to electrical energy. Piezoelectric generators produce high voltages and low currents, and require no voltage source to operate. Some believe they are more difficult to be integrated into microsystems (Roundy, Wright, and Rabaey 2003a), but there have been several successful implementations of MEMS scale piezoelectric energy harvesters (see Table 1). In case of the thin films, piezoelectric response is drastically reduced compared to bulk PZT due to clamping effect of the substrate (Lefki and Dormans 1994; Li et al. 2004). Since both longitudinal and transverse piezoelectric components are coupled to each other, thus on application of electric field normal to the films surface, an expansion in longitudinal piezoelectric response and a contraction in transverse piezoelectric response is observed due to clamping effect. The effective piezoelectric coefficient of a thin film on a rigid substrate can be written as (Bono et al. 2009; Krulevitch et al. 1996).

Since the second term in the right hand side of eq. [13] contributes negatively to the effective piezoelectric response, thus effective piezoelectric response is reduced. The electromechanical coupling coefficient (k) is another parameter which is very important especially in resonating structures. The electromechanical coupling coefficient can be given as:

The electromechanical coupling coefficient represents the ratio of the mechanical (electrical) energy converted into the input electrical (mechanical) energy for the piezoelectric material.

Two piezoelectric modes, d₃₁ or d₃₃, are commonly used in piezoelectric micro devices (Figure 8). The relative directions of the electric field and the strain distinguish them: d₃₁ when the electric field is perpendicular to the input strain, d₃₃ when they are parallel (Bernstein et al. 1999). Conventional MEMS piezoelectric devices/actuators have d₃₁ configuration in which a piezoelectric layer is sandwiched between top and bottom electrodes. For a d₃₁ mode energy harvester, the generated voltage is proportional to the thickness of the piezoelectric layer (t_xx), the effective piezoelectric constant, g31,f (Vm/N), and the applied stress, σxx

For typical values of g31,f and accelerations, the generated voltage becomes too small for the rectifying circuits as the thickness of the piezoelectric layer drops below 1 μm (mostly less than 0.5 μm) in MEMS–scale harvesters. Therefore, d₃₁ mode of a piezoelectric device is often not favorable for energy harvesting applications even though the generated power could be higher. For high permittivity ferroelectric piezoelectrics, the d₃₃ mode can generate higher open circuit voltages by increasing the spacing between the IDT electrodes where polarization wraps from one electrode to the next in alternating directions as shown in Figure 8. Jeon et al. showed that operating piezoelectric elements in d₃₃ mode is more advantageous than in d₃₁ mode for MEMS-scale PZT harvesters (Jeon et al. 2005).

Figure 8:

Two modes of piezoelectric conversion of input mechanical strain depending on the relative direction of the stress σxx (or strain) and the electric field, E. (Credit: Prof. Sang-Gook Kim).

The power trapped in each cycle from eq. [9] is dissipated to structural and aerodynamic damping as well as to electrical energy via piezoelectric effect. To maximize the harvested power, the electrical damping needs to be increased while the structural and aerodynamic damping needs to be minimized. The electrical power generated via d₃₃ mode piezoelectric effect of a unimorph cantilever can be expressed as:

where Vpiezo, Epiezo, s, ωexc, k33, εpiezo, and e33 are the volume of the piezo material, Young’s modulus, strain, excitation frequency, electromechanical coupling coefficient, dielectric permittivity and piezoelectric coefficient. As long as the beam’s stored energy minus the mechanical loss (dissipated via structural and aerodynamic damping), which can be defined as “extractable energy,” is bigger than the “conversion energy” from eq. [17], the maximum harvested energy is determined by the piezoelectric layer’s volume and coupling coefficient. Similar statement can be made for the d₃₁ mode piezoelectric harvesters.

The coupling coefficient described in eq. [18] may only be applied to conditions where the passive elastic layer’s stiffness can be neglected. For most MEMS energy harvesters with unimorph structure where the piezoelectric layer is much thinner compared to the passive elastic layer, eq. [18] may not be accurate. For an MEMS energy harvester, which consists of a thin layer of piezoelectric material and a much thicker passive elastic layer, the coupling factor can be written as (Xu and Kim 2012):

It can be readily seen that only a portion of the input mechanical energy is injected into the piezoelectric layer to be converted into electrical energy, while much of the energy stays in the elastic layer as strain energy and will not be converted. Therefore, the coupling coefficient will be lower than the real intrinsic conversion rate of the piezoelectric material itself.

Figure of merit (FOM) for the piezoelectric materials can be derived by considering the power response of the piezoelectric transducer. Recently, Oliver and Priya have conducted detailed modeling of the piezoelectric cantilever (Bedekar, Oliver, and Priya 2010) and proposed a dimensionless figure of merit (DFOM) for piezoelectric transducer material in energy harvesting application as (Priya 2010):

where k₃₁ is the transversal electromechanical coupling factor, Q_m is the mechanical quality factor, s₁₁^E 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. The DFOM is a product of two FOM’s representing off-resonance and on-resonance conditions.

By comparing DFOMs for the commercial piezoelectric compositions, one could identify the better piezoelectric composition for energy harvesting applications. Defosseux et al. have compared the off-resonance FOM for the PZT and AlN and noticed higher magnitude response for AlN (7.8×10⁻¹¹ m²/C as compared to 4×10⁻¹¹ m²/C) (Defosseux et al. 2012). For PZT, the values were taken to be ε₃₃/ε_o=935, d₃₁=–110×10⁻¹² m/V and tanδ=3.6 % (measured on PZT 53/47 [100]-textured 2 µm thin film (Ledermann et al. 2003)). For AlN, the values were taken to be ε₃₃/ε_o=10, d₃₁=–2.6×10⁻¹² m/V and tanδ=0.1 % (dielectric properties measured at 10 kHz for film with thickness of 2 µm by Martin et al. (2004) and piezoelectric property was reported by Tsubouchi and Mikoshiba for 1 µm thick film (Tsubouchi and Mikoshiba 1985). Considering the fact that AlN processing can be made compatible with CMOS, these results indicate the promise of AlN films towards developing MEMS harvesters.

2.6 Impedance Matching

Likewise the natural frequency matching with an external vibration source, the impedance of the piezoelectric generator should be matched to that of an external circuit in order to maximize the power extraction. Usually, an electrical impedance matching circuit is placed between the piezoelectric generator and external loads such as a rechargeable battery and supercapacitor. Thus, the matching network should be lossless and requires that the input impedance should be matched to the output impedance. Equation [21] shows the electrical input impedance of the energy source generated by the piezoelectric harvester.

where ω is vibration frequency of energy harvester, C0 is capacitance of piezoelectric materials. The impedance matching circuit consists of load resistors in accordance with the impedance of the piezoelectric generator calculated by eq. [21].

2.7 Challenges of Piezoelectric MEMS Energy Harvesters

Many piezoelectric MEMS energy harvesters have been developed and some of them are shown in Table 1. Their form factors are all different, and can only be compared with the power density which can be defined as the ratio of generated power over the active material volume (volume power density, μW/mm³) or over the active material area (area power density, μW/mm²). But, harvesters with high resonant frequency or that requires high acceleration ambient vibration need to be penalized considering the low frequency – low g characteristics of ambient vibrations. In order to generate a comparative figure, normalization was done with respect to both area and volume of harvesters, natural frequency and input acceleration.

Based upon eq. [16], the maximum extractable output power is proportional to (1/frequency) and (acceleration²) (Chandrakasan et al. 1998). From eq. [17], the converted electrical power is proportional to the excitation frequency. Thus, some researchers have taken into account both frequency and acceleration variation, by normalizing the power with frequency or acceleration (Chandrakasan et al. 1998). We propose a simple metric for the normalization as Power / (frequency×acceleration²×area or volume) and refer to it as “areal or volumetric normalized power density” in this paper. Accordingly, a device generating higher power at lower frequency, acceleration and with area/volume will have higher normalized power density. For comparison, we utilized most common units used in literature to describe the physical quantities – Hz for frequency, mm² for area, and g² for acceleration. Table 1 is based on best estimates and data available in literature. Only the active piezoelectric area or volume is used to compute normalized areal power density (NAPD) and normalized volumetric power density (NVPD) depending upon the data availability in literature for MEMS devices developed using thin film deposition and lithography techniques.

For NAPD, harvester area (cantilever, non-linear beam, diaphragm, S-shape beam, corrugated beam, zig-zag beam etc.) is calculated based on the data in the literature. We understand that energy harvested and transformed to electrical power is proportional to volume of piezoelectric material and hence volume may also be taken into account instead of area. For example, Hajati’s non-linear beam energy harvester (Hajati and Kim 2011) showed 1–3 orders higher NVPD than that of any reported devices, but has a relatively low NAPD since it has very thin PZT (0.25 μm) over large area (120 mm). For battery-less operation of various wireless sensor nodes in real world applications, it will be ideal to harvest about 100 μW continuous power at the size of a quarter dollar coin (diameter=24.26 mm, total thickness=1.75 mm) at 100 Hz or lower ambient vibrations with less than 1 g acceleration. This requirement can be converted to a NVPD (assuming one 0.5 μm thick piezoelectric layer in the device)=4.3 μW/(mm³·Hz·g²). Most reported devices show orders of magnitude smaller normalized power density than this (See Table 1), even if we can increase the desired output power as increasing thickness of piezoelectric layer. One of the direct solutions to address this challenge is to improve the electro-mechanical coupling coefficient of the piezoelectric thin films. Another approach is to seek new resonating beam structure designs from which more energy can be extracted at lower frequency and acceleration.

Another metric commonly used in literature is normalized figure of merit, which takes into account bandwidth. Bandwidth is also an important characteristic and should be accounted for determining the performance of piezoelectric harvesters under unpredictable or uncontrollable spectra of ambient vibrations. Most piezoelectric energy harvesters have been designed based on a linear resonator, e. g. a cantilever with a proof mass. The extractable power of an energy harvester based on a linear resonator is proportional to the gain (quality factor, Q=f_r/Δf where f_r is resonance frequency, Δf is full width at half maximum) of the resonator, which is inversely proportional to the bandwidth. If the center frequency of a beam is off about 2 % from the input frequency, the amplitude of the beam bending drops to about 50 % of the resonance peak. If it is off 5 %, then there is no resonance to amplify the strain on the piezoelectric material. Accordingly, there is a trade-off between the output power and the bandwidth. Since we cannot control the frequency of ambient vibrations, an energy harvester with a narrow bandwidth (of most linear resonators) is impractical in most real applications. Several approaches have been adopted to circumvent this gain-bandwidth dilemma. For example, the natural frequency of resonating beams can be tuned by changing the axial tension of a beam through non-contact mechanisms such as magnetic attractive and repulsive forces. Beam dimensions and proof mass have also been tuned mechanically to widen the bandwidth. (Al-Ashtari et al. 2012; Mansour, Arafa, and Megahed 2010). However, frequency tuning inevitably consumes power, the tuning efficiency is low and the tuning range is limited. Multiple beams of different lengths have also been utilized to address this challenge, which may not be practical in terms of size and cost. Simpler and less costly methods have been sought that can provide both the wide bandwidth and high power density as required for practical MEMS-scale devices.

3.1 Grain Textured and Epitaxial Piezoelectric Films

Bulk PZT ceramics have plethora of dielectric and piezoelectric properties which can be controlled using doping (Funakubo et al. 2012). Lead based relaxor-lead titanate compounds so called relaxor ferroelectrics include Pb(Zn_1/3Nb_2/3)O₃-PbTiO₃(PZN–PT), Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃(PMN–PT) and Pb(Y_1/2Nb_1/2)O₃-PbTiO₃(PYN–PT), exhibit large electromechanical coupling coefficients which makes these materials more attractive option for micro-actuator and micro-sensor applications. For device miniaturization it is important to grow films using these materials. PZT thin films are deposited with variety of methods such as sputtering, chemical solution deposition (i. e. sol-gel), MOCVD and laser ablation processes. Since piezoelectric properties of these materials are strongly dependent on film quality and growth orientation, thus, the control of growth orientation is highly desired with (001) texturing (Trolier-McKinstry and Muralt 2004). Additionally, the composition of the piezoelectric material plays a crucial role in deciding the piezoelectric properties of films. For example, in case of PZT thin films, composition near the morphotropic phase boundary (MPB) is commonly preferred due to its high piezoelectric response (Jaffe 1971). From application point of view, it is very important to integrate these oxides on Si substrates which could pave the way for efficient fabrication of devices. However, the growth of oxide films on Si substrate is still a complicated process due to technical difficulties such as inter-diffusion, large lattice mismatch, and thermal expansion mismatch (Chopra et al. 2013). Tremendous efforts have been made to integrate the oxide films on Si substrate with control of crystal orientation.

The most simple and direct solution towards enhancing the output power at the fixed size of a device is to increase the piezoelectric and electromechanical coupling coefficient. Grain texturing has been shown to be an effective method for improving the magnitude of physical constants in piezoelectrics by achieving a domain-engineered state. In the vicinity of morphotropic phase boundary, a rhombohedral composition oriented along <100> direction is known to exhibit optimum magnitude of electromechanical coefficients (Du et al. 1998). Park and Shrout attributed this high electromechanical performance to domain engineered state achieved through polarization rotation from <111> to <100> (Park and Shrout 1997). Thus, texturing is desired in PZT but poses several challenges in synthesis.

An important characteristic in driving the texture of complex oxides on Si substrates is proper texturing of the electrode layers. Most commonly, Pt electrodes are employed for many applications and achieving highly (111) textured Pt films on Si requires proper control of the adhesion layer, typically TiO₂. Recent efforts have identified the importance of surface roughness of the underlying passive elastic layers (commonly SiO₂), residual oxygen content during the Ti sputtering process, sputter temperature, Ti thickness, and high temperature oxidation of the Ti into textured TiO₂ as critical parameters enabling a nearly pure (111) textured Pt layer with a FWHM ranging from 1.5 to 2.5 degrees (Potrepka et al. 2011). Combining a highly textured Pt electrode with proper seed layer can be used to achieve (001) texture (Sanchez et al. 2013).

In addressing the optimization of synthesis conditions, Temperature-Time-Transformation (TTT) diagrams have been proposed to document texture evolution during thermal treatment of PZT thin films on platinized silicon substrates (Varghese et al. 2011). By varying the annealing/pyrolysis temperature and time, extensive exploration of the sol-gel thermal budget operating space yielded the TTT diagram as shown in Figure 9(a)–(c). It can be seen that films with pyrolysis at 300 °C for 3 min were textured in (100) direction until >750 °C annealing temperature, after which they start showing random orientation. On the other hand, the films pyrolyzed at lower temperature and for shorter times are textured in (100) direction for a narrow threshold annealing temperature range. Ternary diagram [Figure 9(d)] illustrates the frequency of each textured orientation obtained for each pyrolysis binned as per the ranges in annealing temperature and time. Thus, one is able to quantify the operating regime for achieving specific texture orientation. These diagrams are also invoked to understand the texturing mechanism (Chen and Chen 1994) and can be further expanded to include other piezoelectric materials system (Zhou, Apo, and Priya 2013a).

Figure 9:

Temperature-time-transformation diagrams of PZT-sol-gel thin films pyrolyzed at (a) no pyrolysis; (b) 250 °C, 1.5 min; (c) 300 °C, 3 min; and (d) the ternary plot of all the data. (Varghese et al. 2011).

Several studies in literature have been conducted on tuning the piezoelectric properties through interfacial stress. Recent results by Han et al. have shown ~90 % enhancement of ferroelectric and piezoelectric properties in MPB composition PZT thick films by tailoring the magnitude of residual stress by choosing substrates with different coefficient of thermal expansion. The results from this study are summarized in Table 4 (Brennecka et al. 2004; Han et al. 2011a; Tuttle et al. 1992; Yokoyama et al. 2002). The direct piezoelectric constant (d_{33, eff}, pC/N) was measured by d₃₃ meter and the effective piezoelectric constant (d_{33, eff}, pm/V) was obtained by measuring variation in displacement with applied electric field using laser interferometer. The difference between these two coefficients is attributed to the substrate clamping effect. The electrical properties showed that the films on Yttria stabilized Zirconia (YSZ) substrates with highest in-plane compressive stress had the best piezoelectric properties while that on Si wafer with tensile in-plane compressive stress showed lower properties. The enhanced piezoelectric properties were attributed to the reason that c-domain parallel to the thickness were easy to form under in-plane compressive stress. This technique is quite appealing as it can be easily implemented in the fabrication of MEMS components.

Epitaxial PZT thin films with c-axis orientation are excellent materials for MEMS energy harvesters (Kanno et al. 1997; Morimoto et al. 2010). However, epitaxial substrates, such as MgO and SrTiO₃, are usually not suitable for unimorph cantilevers because of their brittleness and difficulty of microfabrication. One of the solutions is transferring the epitaxial PZT films on flexible cantilevers. Qi et al. transferred epitaxial PZT thin films deposited on MgO substrates to PDMS substrates and have evaluated performance of stretchable piezoelectric energy harvester (Qi et al. 2011). Morimoto et al. have developed high efficiency piezoelectric energy harvesters using c-axis oriented PZT thin films by radio-frequency (rf)-sputtering, which were transferred onto stainless steel (Morimoto et al. 2010). The fabrication process from this study is shown in Figure 10. The c-axis oriented PZT thin films were grown on (100) MgO single crystals with an epitaxial (001) Pt bottom electrodes. Reciprocal lattice space maps before and after transfer process clearly showed spotty diffractions of the (204) PZT, indicating that the transfer process did not degrade the crystal structure of the epitaxial PZT film. After the PZT film was bonded to 50-μm-thick stainless steel sheets with epoxy resin, the MgO substrate was etched out in phosphoric acid. The photograph of the stainless steel cantilever beam covered with the epitaxial PZT is shown in Figure 10. The relative dielectric constant ε_r of the transferred films on stainless steel was as low as 166, while the piezoelectric coefficients e_31,f of the transferred PZT films was around −6 C/m². The thickness and length of stainless steel cantilever was 50 μm and 18.5 mm respectively. Because of the thin dimension of the metal cantilever, the first resonance was found to occur at 126 Hz. Averaged output voltage and calculated value are plotted in Figure 11 (acceleration: 5 m/s²). The maximum output electric power of 5.3 μW was obtained across a load resistance of 50 kΩ. In this measurement, GEMC, k_G² was calculated to be 1.3×10⁻² which is much larger than polycrystalline PZT thin films on Si substrates. This result is attributed to large electromechanical coupling coefficient k₃₁ of epitaxial PZT thin films. The output power increases monotonically with the acceleration, reaching 244 μW at 50 m/s². The flexible metal cantilever enables considerable reduction of the resonant frequency and offers enhanced toughness compared with brittle Si-based cantilevers.

Figure 10:

Fabrication process flow and photograph of transferred epitaxial PZT thin films on stainless steel cantilever (Morimoto et al. 2010).

Figure 11:

Output voltage and generated power of transferred epitaxial PZT thin films as a function of load resistance (Morimoto et al. 2010).

Recently, direct deposition of PZT thin films on Nickel foil for MEMS energy harvesters have been successfully demonstrated by Yeo and Trolier-McKinstry (2014). (001) oriented PZT thin films were grown by sol-gel process on Ni substrate. HfO₂ and (001) oriented LaNiO₃ films were used as a passivation layer to suppress the substrate oxidation and buffer layer to subsequently grow (001) oriented film, respectively. Surface and cross-sectional microstructure images of PZT films on Ni are shown in Figure 12(a) and (b). The PZT film have columnar structure and there was no evidence of cracks or delamination among layers as shown in Figure 12(b). The permittivity and loss tangents of (001) oriented PZT films on Ni are near 780 and 0.04 at 1 kHz. The PZT film on Ni foil displayed a well-saturated hysteresis loop with a large remanent polarization of ~36 μC/cm², while the (100) oriented PZT on Si substrate showed much lower remanent polarization as plotted in Figure 13. In addition, this PZT film on Ni had a large transverse piezoelectric constant e_31,f of –10.6 C/m². This PZT film directly grown on metal substrate is favorable for a low resonance frequency and robust MEMS energy harvester.

Figure 12:

(a) Surface and (b) cross-sectional SEM images of PZT films deposited on LNO (100 nm)/HfO₂ (30 nm)/Ni foil after PbO-precursor cover coat (Yeo and Trolier-McKinstry 2014).

Figure 13 :

P-E hysteresis curves of (001) oriented PZT (52/48) films on Ni and silicon substrates respectively (Yeo and Trolier-McKinstry 2014).

Epitaxial growth of ferroelectric thin films on silicon suffers minimal leakage and optical scattering which results in a drastic improvement of electrical properties when compared to polycrystalline films. Thus epitaxial integration of ferroelectric films such as PZT, PST (PbSc_0.5Ta_0.5O₃) on Si substrate is highly desirable for the development of next generation devices. However, direct integration of PZT on Si using Pulsed laser deposition (PLD) still remains a challenging task due to inter-diffusion, structural and chemical incompatibilities, and thermal and lattice mismatch issues. These issues can be addressed using buffer layers such as SrTiO₃ and yttria-stabilized zirconia (YSZ)/CeO₂ (Chopra et al. 2013; Du et al. 1998). These buffer layers act as diffusion barrier as well as help in bridging the lattice mismatch between film and substrate. PLD is one of the preferred methods for fast deposition of high quality films. Zirconium (Zr) is one of the few metals which has a higher affinity towards O₂ than Si. This makes YSZ inert to Si and prevents oxidation of Si during deposition in O₂ atmosphere. CeO₂ is another buffer layer which is employed in combination with YSZ to reduce the lattice mismatch further. Successful integration of functional oxides on Si substrate has been reported in literature (Chopra et al. 2013, Chopra, Alexe, and Hesse 2015a; Gardeniers, Smith, and Cobianu 1995). (001)-oriented growth of oxides is achieved by fabricating Si (100)/YSZ/CeO₂/LaNiO₃ structures (Chopra et al. 2013). The orientation of the films can be switched from (001) to (110) just by replacing the heterostructure with Si (100)/YSZ/SrRuO_3. LaNiO₃ and SrRuO₃ both act as a bottom electrode in their respective heterostructures, which are necessary for the electrical measurements. The XRD measurements performed on such heterostructures reveal a (001) and (110)-oriented growth as shown in Figure 14.

Figure 14:

Out of plane XRD patterns obtained from the PST films deposited on (a) LNO/CeO₂/YSZ/Si, (b) SRO/YSZ/Si (Chopra, Alexe, and Hesse 2015a).

The in-plane XRD scans confirm that both the discussed structures are epitaxial, however LNO and subsequent layers in the (001)-oriented heterostructure were found to be rotated in plane by 45 degrees with respect to the underlying YSZ and CeO₂ layers as shown in Figure 15(a). This kind of in-plane rotation is facilitated due to good arrangement in the lattice parameters of both CeO₂ (a=0.541 nm) and LNO (a_pc=0.386 nm) which resulted in an in-plane rotation for the top ferroelectric layer too.

Figure 15:

(a) In-plane φ-scan for PST on LNO/CeO₂/YSZ/Si showing LNO and PST has 45 ^o in-plane rotation with respect to CeO₂/YSZ/Si. (b) A schematic showing the 45 ^o rotation (Chopra et al. 2013, Chopra, Alexe, and Hesse 2015a).

Recently successful integration of PZT films on glass substrates using 2D nanosheets has been demonstrated (Chopra et al. 2015b; Jumpertz et al. 2014). The biggest advantage of using nanosheets is reduction in growth temperature. Crystalline growth of YSZ, CeO₂ and SrTiO₃ buffer layers is achieved at very high temperature of 750 °C which is not suitable for substrates like glass. Thus, low temperature growth of buffer layers was achieved by replacing the oxide buffer layers with nanosheets which grow at room temperature. The nanosheets were transferred to the substrates using langmuir-blodgett deposition process. The orientation control of PZT films was achieved using Ca₂Nb₃O₁₀ (CNO) and Ti_0.87O₂ (TO) nanosheets. A (001)-oriented growth of LNO films was achieved using CNO nanosheets due to the exact lattice match between CNO nanosheets (lattice parameter=a=3.86 Å) and LNO (lattice parameter=a=3.86 Å) which further promoted a (001)-oriented growth of subsequent PZT thin films. On the other hand, TO-nanosheets which are known to have a lepidocrocite-type structure with a lattice parameter of a=3.76 Å and b=2.97 Å promotes (110)-oriented growth of both LNO and subsequent layer of PZT as shown in Figure 16(a). However, all the films deposited were polycrystalline due to random in-plane distribution of nanosheets. Growth of nanosheets with single orientation in in-plane direction is the next challenge in the field which is being addressed to achieve a complete epitaxial growth of subsequent layers. Fatigue and piezoelectric measurements demonstrated on nanosheet buffered PZT films showed stable and good piezoelectric properties which are essential for the stable operation of the next generation devices. A comparison of the piezoelectric response of PZT films on nanosheets and Pt is shown below in Figure 16(b).

Figure 16:

(a) Out of plane (θ–2θ) scans and (b) Longitudinal piezoelectric response of the PZT films deposited on Pt, Ti_0.87O₂ and Ca₂Nb₃O₁₀ buffer layers coated on glass substrate (Bayraktar et al. 2014).

It is well-known that relaxor ferroelectric single crystals, such as PMN-PT and PZN-PT, show about 10 times larger piezoelectric coefficient than that of conventional PZT ceramics (Kuwata, Uchino, and Nomura 1982; Park and Shrout 1997). Recently, Baek et al. successfully grew epitaxial PMN-PT thin films on SrTiO₃–buffered miscut Si substrate by off-axis sputtering. The piezoelectric coefficient e_31,f in their work was reported to be –27 C/m², which is the highest value reported (Baek et al. 2011). Using these films, they fabricated a unimorph micro-cantilever and confirmed the excellent inverse piezoelectric performance. Because of the large electromechanical coupling coefficient k₃₁ (or figure of merit: e²_31,f/ε_r) of PMN-PT epitaxial thin films, this system is quite promising towards improving the performance of current MEMS energy harvesters.

3.2 Lead-Free Piezoelectric Films

For powering medical implants and human use of energy harvesters, lead-free piezoelectric material is desirable. Potassium sodium niobate (K_xNa_1–xNbO₃) abbreviated as KNN, is considered as a most promising lead-free piezoelectric material owing to its higher Curie temperature and higher ferroelectric orthorhombic – ferroelectric tetragonal transition temperature (Ahn et al. 2008a). The piezoelectric properties of KNN based compositions are directly correlated to the fraction of orthorhombic (O) and tetragonal (T) phase as shown in Figure 17(a). One of the strategies for achieving higher piezoelectric response has been to modulate the composition such that O/T transition lies close to room temperature (Ahn et al. 2008b). Another strategy adopted for designing lead-free compositions is based upon the trend between atomic weight ratio of A to B sites (R_w=W_a/W_b) and longitudinal piezoelectric constant d₃₃ as shown in Figure 17(b) (Ahn et al. 2009). It can be observed that 1/R_w for KNN ceramics (for Na/K ratio of 0.5) is similar to R_w for PZT ceramics at MPB composition and both of these materials exhibit high piezoelectric response. Piezoelectric compositions show large response when R_W for A-site heavy perovskites and 1/R_W for B-site heavy perovskites is higher than 2.0.

Figure 17:

(a) Variation of longitudinal piezoelectric coefficient with O–T transition temperature in KNN system, and (b) Variation of longitudinal piezoelectric coefficient as a function of weight ratio in bulk perovskites (Ahn et al. 2008b).

The fabrication process of these lead-free piezoelectric materials in thin-film form is still under development, and it is expected that these materials will be utilized in the design of MEMS energy harvesters in the near future (Zhou et al. (2013b)). Recently, Shibata et al. reported that KNN thin films deposited by RF magnetron sputtering showed large transverse piezoelectric properties comparable to those of PZT thin films (Shibata et al. 2011). Kanno et al. have compared the energy harvesting performance of KNN thin films with PZT thin films by using simple unimorph Si-cantilevers (Kanno et al. 2012). The piezoelectric coefficient of both KNN and PZT films showed almost the same value of e_31,f=−10 C/m² (Kanno et al. 2012). The relative dielectric constants of the KNN and PZT films were 744 and 872, respectively. Figure 11 shows the average output power P=V²/(2R) as a function of load for energy harvesters made of KNN and PZT unimorph cantilevers. Measurements were performed at the resonance frequency of each cantilever (KNN: 1.0 kHz, PZT: 0.89 kHz; acceleration 10 m/s²). Peak output power for the KNN and PZT films was 1.1 µW at 1.7 kΩ and 1.0 µW at 1.2 kΩ, respectively. Because KNN and PZT thin films have almost same dielectric and piezoelectric properties, the KNN film performs comparably to the PZT film with respect to power generation. GEMC k_G² of KNN and PZT energy harvesters was around 0.6 ~ 1.7×10⁻³ as determined by fitting the calculated value of eq. [12] to experimental results.

3.3 Aluminum Nitride (AlN) – A MEMS Compatible Piezoelectric Film

AlN is a piezoelectric material with wurtzite structure. The properties of AlN based films are highly process dependent. Aluminum nitride has a band gap of 6.2 eV with lattice parameter of a=13.112 Ǻ and c=4.982 Ǻ. It is a potential candidate for UV light emission and SAW devices due to large acoustic wave (SAW) velocity (Duffy et al. 1973). AlN films have been deposited using chemical vapor deposition (CVD) (Chubachi, Sato, and Kojima 1984), plasma assisted CVD (Zhang et al. 1993), metalorganic CVD (Saxler et al. 1994), reactive DC-magnetron sputtering (Meng, Heremans, and Cheng 1991), plasma assisted molecular beam epitaxy (MBE) (Stevens et al. 1994), laser-induced chemical vapor deposition (Li and Tansley 1990), and pulsed laser deposition (Norton, Kotula, and Carter 1991). Most of these techniques required a high processing temperature (1,000 °C) to obtain the best crystal quality and texture in the deposited thin films. However, high quality growth at low temperature is desired to ensure the compatibility with IC technology. In this regards, different process techniques have been developed (Aita 1982; Shiosaki et al. 1980; Takeda, Mori, and Takahashi 1981). In addition to (0001)–orientation, it is also observed that tuning of the ion energy and flux of the bombarding ions (Ar⁺, N²⁺) is equally important (Dubois, and Muralt 2001). AlN films have a much higher phase velocity and chemical stability in comparison to the ZnO films. However, AlN has lower piezoelectric coupling and it is difficult to control the growth of AlN films.

Recently, significant progress has been made towards incorporating the AlN films in energy harvesting applications. Schaijk et al. have demonstrated the performance of micomachined AlN cantilevers and shown that device with dimension of 3×1.3 mm was able to provide 10 µW at the resonance frequency of 1,155 Hz under 8 g acceleration (Van Schaijk et al. 2008). Under practical acceleration values of 1 g or lower, the power generated was smaller than 1 µW. Heidrich et al. have investigated the energy generation from [001] textured AlN cantilevers and corrugated membranes for bio-implants. The growth was conducted on Si (001) substrates, which resulted in tensile (<+300 MPa) and compressive strains (>–100 MPa) depending upon the deposition parameters. In the non-resonant condition of 70 Hz, for a 3×4 corrugated membrane array (radius of individual membrane=400 µm) the peak power of 10 µW was measured across 10 kΩ with a bias of 1 V and acceleration of 0.01 g (Heidrich et al. 2011). Yen et al. conducted detailed experimentation and modeling of the corrugated AIN cantilever structures. At a resonance frequency of 853 Hz, a cantilever with a width of 2,400 µm, length of 500 µm, and a 2 µm thick piezoelectric layer was able to provide 0.17 µW under an acceleration of 1 g using a tip mass of dimension 2,400×500×680 µm (Ting-Ta et al. 2011). Andosca et al. also demonstrated a AlN thin film based MEMS energy harvester with high power density. The energy harvester with a width of 6.0 µm, length of 7.8 µm, a 2 µm thick AlN film and a proof mass of 28.9 mg was able to generate 119 µW power under 1 g acceleration at a resonance frequency of 56.6 Hz (Andosca et al. 2012).

A simulation study in this area has been conducted by Stoppel et al., who computed the effect of thickness on power generation (Stoppel et al. 2011). It was pointed out that since the Young’s modulus of AIN (345 GPa) is about 4× that of PZT, the thickness of AIN for maximum power output is about 3× smaller than that of PZT. For a cantilever with 2 µm thick AIN operating at resonance frequency of 105.6 Hz under acceleration of 1 m/s², output power of 0.8 µW was measured across 21 MΩ load. Based upon the experimental data available in literature, the normalized output power (power/frequency×acceleration) for AIN micro devices ranges between 2.034×10⁻⁵–757×10⁻⁵ µW/(Hz×m/s²). Ignoring the data from Stoppel et al., the spread is more reasonable 2.034×10⁻⁵–11×10⁻⁵ µW/(Hz×m/s²). These values are quite good and considering the compatibility of AlN with CMOS process and long history in optimizing the deposition process, we expect that this area will continue to grow.

3.4 Piezoelectric Thick Films by Powder/Granule Spray in Vacuum Process

The powder spray in vacuum process so called aerosol deposition (AD) is a unique ceramic film deposition technology that is able to fabricate highly dense thick films (submicron to several hundred μm) at room temperature. This process utilizes high kinetic energy of ejected aerosol consisting of a mixture of fine ceramic particles and carrier gas from a nozzle. The process was firstly introduced by Akedo and co-workers at AIST, Japan in late 1990s (Akedo and Lebedev 2000). The process has unique advantages compared to other thin/thick film deposition process such as high deposition rate (over several tens μm/min depending on the deposition area), low processing temperature, composition control, high adhesion strength between substrate and film as well as micro-patterning of ceramic thick films during deposition (Zhou et al. 2011). Due to its low temperature processing, low sinterability ceramic thick films such as KNN based lead-free piezoelectrics and PbTiO₃ ceramics with full density can be deposited on various types of substrates (Han et al. 2011b; Ryu et al. 2007, 2014; Wang et al. 2008). Figure 18 shows ferroelectric/piezoelectric property modulation of AD-PZT film according to the variation of residual stress level (Han et al. 2011a). By generating high compressive residual stress in the PZT thick films, the piezoelectric properties can be enhanced by ~2 ×. All these advantages are highly attractive for MEMS based piezoelectric device applications as mentioned in previous section.

Figure 18:

Conceptual diagram of high piezoelectric performance in PZT thick films grown on various substrates; the stresses were controlled by the thermal expansion mismatch between substrates and PZT films (Han et al. 2011a).

Lee and co-workers at National Taiwan University reported the MEMS devices based upon the AD process in 2008 (Lee et al. 2009; Wang et al. 2008). Figure 19 represents their device pictures. By using AD process, they succeeded to fabricate over 10 μm PZT thick film on the silicon wafer and realized MEMS energy harvesters and other piezoelectric devices. The output power from their MEMS energy harvester with AD PZT was in the vicinity of 2 μW at ~ 255 kHz under 2 g acceleration. This is reasonably good performance compared to the other MEMS based piezoelectric energy harvesters (Lee et al. 2009).

Figure 19:

Silicon based MEMS devices with AD-PZT by Lee et al. (a), (b) Suspended double-layer PZT structure released by XeF₂ dry etching (Wang et al. 2008), (c) piezoelectric MEMS energy harvester with AD-PZT thick film (Lee et al. 2009).

Park and co-workers at KIMS, Korea, have been conducting detailed study on optimization of deposition rate and uniformity in large area films by the granule spray in vacuum process. They have succeeded to overcome the limitation of AD by using intentionally granulated raw powder and feeding system, termed as ‘granule spray in vacuum process (GSV)’. Figure 20 shows the typical microstructure of patterned highly dense PZT thick films for MEMS ultrasonic transducers by GSV. The deposition rate of the PZT thick film by GSV was 1.4 μm/min in the area of 1440 cm³. That is over two orders of faster rate than that of the other thin film processes. The film was very uniform as shown in Figure 20(a). Directly patterned highly dense 11 μm thick PZT film was fabricated on 6 inch Si/SiO₂/Ti/Pt wafer by GSV, and the films were not damaged during post processes including back-DRIE process.

Figure 20:

(a) Large area PZT deposition by GSV process. (b) 6 inch Si/SiO₂/Ti/Pt wafer with directly patterned PZT thick film. (c) and (d) cross-sectional SEM micrographs of piezoelectric MEMS ultrasonic device by GSV.

3.5 Nonlinear Resonance Based Energy Harvesting Structures

Most of the reported vibration energy harvesters use a linear cantilever resonator structure to amplify small ambient vibration. While such structures are easy to model, design and build, they typically have a narrow bandwidth. In contrast, nonlinear resonators have different dynamic response and greatly increase the bandwidth by hardening or softening the resonance characteristic of the beam structure. In addition, it has been found that non-linear resonating beams can extract more electrical energy than that of linear resonating beams (Hajati and Kim 2011; Marinkovic and Koser 2009) when external vibration source has variable frequency.

Nonlinearity may come from magnetic force or constrained mechanical structures. The magnetic forces between the magnets and the iron create a nonlinear spring, whose nonlinearity is determined by the strength of the magnets and the size of the air gap between the magnets and the iron stator. Due to the mutual attractions, the ferromagnetic beam has three equilibrium positions (statically bi-stable configuration), and the vibration mode has the form of the bi-stable Duffing resonance. Electromagnetic energy harvesters have been reported showing hardening or softening resonance characteristics (Ando et al. 2010; Barton, Burrow, and Clare 2010; Erturk and Inman 2011; Mann and Sims 2009). However, magnet-based beams require assembly of hard magnets, which is expected to be costly as the size of the device shrinks.

Nonlinear resonance could be better achieved by a monolithically fabricated MEMS structures. Efforts have been made to achieve wide bandwidth piezoelectric energy harvester by exerting an axial compression and forming a buckled configuration, to make a bi-stable oscillator (Cottone et al. 2012; Marinkovic and Koser 2009). Recently, Hajati et al. demonstrated a monolithic MEMS-based non-linear resonant piezoelectric micro energy harvester, which achieved an ultra-wide bandwidth of >>20 % of the center frequency and generated power more than 22 μW (see Figure 21) (Hajati and Kim 2011). More than one order of magnitude improvements were demonstrated in comparison to the devices previously reported in both the power bandwidth and the normalized power density (NPDV) (see Table 1). The basic design is based on a doubly clamped beam resonator with dimensions, 6 mm×6 mm×5.5 μm (L×W×H), PZT thickness 0.25 μm. Four of these resonators are arranged perpendicular to each other and form one energy harvester, which is about the size of a US quarter coin (Figure 21(a)). At large deflection (exceeding 2–3 times the thickness of the beam), a net stretching in addition to bending results, which changes the dynamic response to a non-linear one (Figure 21(b)).

Figure 21:

Non-linear beam MEMS energy harvester with ultra-wide bandwidth (a) Photo of fabricated device on a coin. (b) Simulated dynamic response of a nonlinear resonator. (c) Open circuit voltage versus frequency (note that nonlinear stretching happens twice in each excitation cycle). (d) Curve 1: estimated extractable power versus frequency, Curve 2: Generated power via the piezoelectrics (Hajati and Kim 2011).

Unlike a linear resonance system, where the electrical damping cannot exceed the mechanical damping (Dutoit, Wardle, and Kim 2005), it has been shown that electrical damping in a nonlinear resonance system could surpass the mechanical damping, extracting much higher output power than that of the linear systems. The nonlinear impedance serves as a negative feedback and stabilizes the deflection when the electrical damping changes (Hajati, Xu, and Kim 2011). This is why the power bandwidth of nonlinear systems can be much wider than that of linear systems at equivalent beam dimensions.

Bi-stable nonlinear resonant beams were recently developed not only to widen the power bandwidth but also to lower the working frequency range and input vibration amplitude of energy harvesters (Xu and Kim 2015). Electromechanical lumped model predicts both stiffening and softening frequency responses for the inter-well and intra-well oscillations of bi-stable systems. Preliminary meso-scale experiments match well with the dynamic simulation and show that the softening frequency response generates much higher power than mono-stable configuration at lower frequencies, providing opportunity for MEMS harvesters to be operated at low frequency and low g input vibrations. MEMS-scale multi-layer buckled plate test results show that at least 50 μW power could be generated below 100 Hz frequency and 0.2 g acceleration (Figure 22).

Figure 22:

Schematic view of a bi-stable beam energy harvester (Xu and Kim 2015).

Prior studies have shown that the presence of nonlinearity based on magnetic interaction or buckled beams has a significant influence on the performance of energy harvesters. The bandwidth of nonlinear energy harvester was increased by bistable effect, however, it is obvious that the frequency response to input vibration was more complicated as compared to linear case. The instability of frequency response makes it difficult to precisely modulate the bandwidth and tune the resonance frequency of the energy harvester in realistic environment. We expect that nonlinearity can provide a solution for widening the bandwidth but it will require additional control features to exploit the enhancement in the output power.

3.6 Self-resonance Frequency Tuning Technique

To maximize output power, energy harvesters should be excited in resonance with external vibration sources. In the other words, the natural frequency of the energy harvester should be matched to those of external vibration sources. The typical linear energy harvester has only one dominant natural frequency which should be carefully selected in accordance with the external vibration frequency. However, when the excitation frequency is unknown or varies with time, the energy harvester with fixed natural frequency cannot achieve an optimal output power. Therefore, in practice, the resonance frequency tuning scheme is essential to increase its power output. Most reported frequency tuning mechanisms are passively adjusted or require additional energy in order to automatically tune the frequency. Hence, the self-frequency tuning mechanisms which do not require extra energy or very small amount energy for autonomous tuning are necessary.

Jo et al. presented the cantilever structure that can automatically switch its natural frequency and maintain its switched frequency without an additional energy consumption (Jo, Kim, and Kim 2011). The proposed harvester was composed of a cantilever couple with different lengths, similar to seesaw structure. The coupled cantilevers are able to move laterally and have two different optimal vibration phases at each resonance frequencies. As shown in Figure 23, the vibration phase of the coupled energy harvesters can shift to the other phase when the external frequency are closed to the resonance frequency of the other phase. The difference between the horizontal inertia forces by deflection difference of cantilevers is the key to switch the harvester between the two phases. This harvester is self-frequency tunable and no additional power is required for tuning. As shown in Figure 24, this harvester cannot cover whole frequency range but still is much more efficient than typical harvesters.

Figure 23:

Schematic view of resonance frequency switchable energy harvester (Jo, Kim, and Kim 2011).

Figure 24:

Output power of frequency switching scheme: (1) when the excited frequency increases from 10 Hz, the first output peak shows at 24 Hz and the second peak shows at 35 Hz, (2) when the excited frequency decreases from 40 Hz, the first output peak shows at 33 Hz and the second peak shows at 24 Hz (Jo, Kim, and Kim 2011).

The close loop active frequency tuning system have been proposed by Zhu et al. (2008). The schematic of tuning mechanism is described in Figure 25. The natural frequency of energy harvester can be adjusted by attraction force between two magnets. The magnetic force also can be controlled by changing distance of two magnets using the linear actuator. Thus, the axial load on the cantilever can be changed. Overall tuning process was controlled by a microcontroller which detects the output voltage of the generator periodically and gives an instruction to drive a linear actuator to adjust the distance between two magnets. When the output power reaches maximum, the system changes to sleep mode to save power. The microcontroller periodically wakes up to monitor the power output and execute natural frequency tuning process. They claimed that the microcontroller and linear actuator can be operated using only power generated from micro-generator itself. However, the power consumption for frequency tuning procedure was still very high on the order of 2.04 mJ/mm. If one can dramatically reduce the power consumption of the microcontroller and linear actuator, the closed loop frequency tuning system could be one of the promising candidate for self-resonance tuning technique except in continuously varied frequency or complex mode vibration environment.

Figure 25:

Schematic diagram of the closed loop tuning system (Zhu et al. 2008).

3.7 Low Frequency Energy Harvesting Structures

Micro scale low frequency energy harvester has been mainly dominated by inductive or electromagnetic devices. However, the miniaturization of such devices is limited by the size of the magnet used as the inertial mass and the size of the coil that can be fabricated on the MEMS scale. Consequently, for MEMS scale energy harvester, piezoelectricity is the transduction of choice and especially due to its compatibility with cleanroom based silicon micromachining techniques. Recent study by Mitcheson et al. (2007) has shown that at mm-scale, piezoelectric mechanism provides the best output power density at low frequencies as compared to other possible mechanisms for vibration EH. However, piezoelectric based energy harvester presents a fundamental challenge at the small dimensions since the resonance frequency of the structure increases (kHz range) as the dimension decreases. This challenge should be overcome in order to become compatible with the practical applications.

The most commonly used approach for reducing the natural frequency involves the addition of a large inertial tip mass to the free end of a simple single cantilever beam structures (Choi et al. 2006; Liu et al. 2012; Tsujiura et al. 2013; Xu et al. 2012a). Other methods involve the use of increased effective surface area cantilevers such as spirals (Deterre et al. 2013). Recently, Song et al. demonstrated the spiral MEMS energy harvesters using typical silicon MEMS process as shown in Figure 26. In order to understand the natural frequency characteristics of the spiral cantilever structure, different turns of spiral MEMS harvesters were fabricated as illustrated in Figure 26(b). The natural frequency of the spiral MEMS harvester was inversely proportional to number of turns and can be reduced to less than 50 Hz within 1.85 mm diameter circle active dimension. The generated output voltage was gradually increased until 5 turns and then started to slightly decrease with increasing number of turns. This might be because the active dimension of spiral region was gradually increased and thus voltage cancelation mode due to torsion are more likely to dominate with higher number of turns. Five turn spiral energy harvester showed the maximum generated voltage. More precise MEMS fabrication process and structural modification to reduce the complex vibration modes are required in producing higher turn spiral energy harvesters.

Figure 26:

(a) Spiral MEMS energy harvester with low natural frequency (a) photo of fabricated device on a coin, (b) spiral MEMS energy harvesters with variation of number of turns, (c) open circuit output voltage versus frequency with number of turns of spiral MEMS energy harvesters, and (d) natural frequency variation with number of turns.

The use of tip masses severely affects the structural integrity and durability of the harvesters while the increased effective surface area designs exhibit torsion (causing voltage cancellation effect) in the very important first vibration mode. Therefore, it is of great importance to create a more effective method by developing uniquely shaped cantilevers, such as arc-based cantilevers, which exhibit low natural frequencies. To harvest energy at the low frequency of ambient vibrations, extensive research has led us to the development of circular Zigzag structure that permits inertial mass free attainment of such low frequencies. Recently, Varghese et al. reported a set of new tip mass free vibration energy structures that are capable of attaining resonant frequency of less than 100 Hz with less torsion than spiral designs and with a smaller foot print than zigzag or meandering structures, as shown in Figure 27 (Apo 2014; Varghese 2013). This design, termed as arc-based cantilever (ABC), has achieved <100 Hz resonant operation both on the Si MEMS platform and with bulk piezo material as compared to traditional cantilevers. The arc-based cantilever is a continuous cantilever that can be divided into purely circular arc segments, thereby making it a low frequency structure with dominant bending characteristic in the first (or fundamental) frequency mode (Apo, Sanghadasa, and Priya 2013). Different configurations of micro ABCs were investigated through analytical modeling and validation experiments. As shown in Figure 27(a), two arc-based micro-cantilevers (S-shaped, C-shaped) were designed based on the well-known linear configurations (simple and zigzag.) In addition to the metal micro-milling, [Figure 27(b)] such structures were also fabricated and demonstrated using a silicon micromachining process [Figure 27(c)]. All the arc-based cantilevers were shown to resonate below 100 Hz and they exhibited dominant bending behavior in the fundamental mode (Apo, Sanghadasa, and Priya 2013, 2014). These designs therefore provide a foundation for the development of standalone arc-based micro-cantilevers which can be used for energy harvesting, actuation and sensing applications. The model for ABC structures is based on the classical Timoshenko beam theory and includes the effects of bending, torsion, transverse shear deformation and rotary inertia. It was developed with a provision for multilayered beam modeling (Apo 2014). The micro-cantilever can be modified and optimized to fit desired configurations based on the numbers of arcs, longest side length, spacing and width.

Figure 27:

Arc-based microcantilvers: (a) Design development of the cantilevers, (b) Micromilled S-shaped cantilevers (Apo 2014), (c) As fabricated silicon MEMS cantilever structures (Varghese 2013).

Recently, Sharpes et al. also demonstrated a strategy of using highly compliant two-dimensional beam shapes to harvest energy from low frequency excitations (Sharpes, Abdelkefi, and Priya 2015). They fabricated 3 different 2D shapes of Zigzag, Flex and Elephant configurations as shown in insets of Figure 28(a), (b) and (c). All of samples occupy a 25.4×25.4 mm² (1 inch²) area and fabricated using mild steel and APC850 piezoelectric ceramics. In order to maintain the low natural frequency, the piezoelectric layers were placed at the most stress concentrated single area of each shapes rather than whole area through a finite element simulation. Neodymium magnet tip masses of 1.88 g weight were attached to the end of each beams to decrease resonance frequency and increase out power. As shown in Figure 28(a), the Zigzag harvester is capable of producing 2.93 μW across 0.75 MΩ at 65.6 Hz. The Flex harvester produced 32.2 μW across 1 MΩ at 62.0 Hz base excitation frequency in Figure 28(b). In both designs, the electromechanical coupling is quite small, as no frequency shift was observable between the short-circuit (R_L=10³ Ω) and open-circuit (R_L=10⁷ Ω) frequencies. However, for the Elephant harvester, we note a substantial shift between short-circuit and open-circuit frequencies, as well as, a large power output of 81.3 μW across 1 M Ω at 68.125 Hz, as shown in Figure 28(c). From these findings, we can conclude the merits of Elephant design, and how it is beneficial towards efficient low-frequency piezoelectric energy harvesting compared to the other shapes.

Figure 28:

Experimental results for average power production as a function of frequency and electrical load resistance for (a) Zigzag, (b) Flex, and (c) Elephant configurations, with (d) Average power as a function of electrical load resistance at each harvester’s respective resonance frequency. All input vibrations were at 0.1 g base acceleration (Sharpes, Abdelkefi, and Priya 2015).

Two main issues in realizing MEMS energy harvesters are the broadband and low operational resonance frequency. Previously discussed low resonance frequency structures with nonlinear behavior excited through the magnetic coupling or the buckled structure could provide breakthrough. In addition to design of nonlinear broadband vibration structure for low resonance frequency, the MEMS fabrication process for incorporating complex structures should be developed.

3.8 Development of New Fabrication and Characterization Methodologies

Unlike inductive harvesting, piezoelectric and magneto-electric devices lend easily to MEMS scaling. The processing of such Piezo-MEMS devices often requires special fabrication, characterization and testing techniques. Generally, MEMS devices are fabricated on silicon wafer starting with growth of high quality piezoelectric films. Ron et al. developed a novel fabrication methodology to realize these structures with reduced number of processing steps (Varghese 2013). They also described the extensive work on MEMS wafer test bench setup.

The MEMS fabrication process flow consisted of two modules as shown in Figure 29: (a) the electrical module for PZT capacitor formation and (b) the mechanical module wherein the Si based micro-cantilever structures were created (Varghese 2013). When the modules are combined, this simplified process flow reduces the number of fabrication steps by ~40 %. Using this modular approach, a self-aligned and self-isolated MEMS fabrication process with only two photolithography steps was demonstrated, as shown in Figure 29(c). The key feature of this process is the use of a patterned SiO₂ hard mask to define the beam thickness in the DRIE and then after removal of that SiO₂ hard mask, using a 2^nd patterned photoresist mask to proceed with a 2^nd DRIE to release the cantilever. Unlike the process used for the unreleased MEMS structure of a Piezo accelerometer (Durou et al. 2010), this process is developed to a) in-situ remove the SiO₂ hard mask before the 2^nd DRIE and b) then conduct the 2^nd DRIE on the front side for release. The removal of the SiO₂ hard mask after the 1^st DRIE can be skipped in some cases and the DRIE SiO₂:Si etch rate selectivity can be utilized to define the cantilever beam thickness. That is, after SiO₂ hard mask definition, 1^st DRIE and 2^nd DRIE mask pattern is applied, but SiO₂ need not be removed. This inorganic hard mask will etch slower than Si and thus when the Si DRIE reaches the front of the wafer, the sections that were covered by SiO₂ would have lagged behind during etch and would be thicker. Using this modular approach, different cantilever structural designs were investigated and based on this learning, a low frequency structure that resembles an arc-based cantilever was developed [Figure 29(c)].

Figure 29:

Fabrication process details of the modules in a Piezo-MEMS process flow (a) Electrical module, (b) Mechanical module, and (c) Schematic of the MEMS fabrication process with two lithography steps (Varghese 2013).

For electrical testing, MEMS harvesters are generally tested individually after the wafer has been singulated by dicing. This requires that the MEMS device be packaged or temporarily glued to a special carrier wafer without damage. Prior to packaging and simulation, Ron et al. introduced a novel concept of wafer level testing (Varghese 2013). As shown in Figure 30(a), wafer probe card is fabricated from a custom printed circuit board (PCB) with gold plated pogo pin probes, where all the pogo pin locations and wiring were designed according to the MEMS device layout on the wafer. All wiring is thus confined to the outside of the test setup and does not interfere with the laser vibrometry measurement [Figure 30(b)]. For mechanical testing of MEMS wafers, a Polytec MSA 500 was used with a special clamp that holds the wafer along its edges, as shown in Figure 30(c). As the shaker is moving, the whole wafer and all its MEMS devices move simultaneously, thus, one can scan each cantilever from tip to base and take the transfer function between the tip and base to compute the resonance frequency. Typical 3D animation plot of the actual vibration characteristics is illustrated in Figure 30(d). This approach is especially useful if one has numerous devices on a wafer.

Figure 30:

(a) As manufactured PCB board with pogo pins soldered on and (b) Clamped over a device wafer, (c) Vibration measurement setup with 3D laser vibrometer, (d) Animation plots of the velocity FRF at fundamental resonance of a arc-based micro cantilever (Varghese. 2013).

4.1 Maximum Power Point Tracking for PZT Resistive Matching

The source impedance of a transducer such as piezoelectric generator and photovoltaic cell changes as the operating condition changes, which requires MPPT. Deployment of an MPPT scheme is advantageous only when the additional power harvested owing to the MPPT is greater than the power dissipated by the MPPT circuit itself. As the additional power, which can be harvested through the MPPT, is limited by the transducer and its operating condition, there exists a breakeven point for adoption of an MPPT scheme. Another design issue with MPPT is accuracy and speed of the tracking, which are often traded. Also, a more accurate and hence more sophisticated MPPT scheme dissipates more power for the MPPT circuit. So adoption of an accurate scheme does not necessarily increase the net energy harvested.

Two commonly adopted MPPT algorithms for energy harvesting are hill climbing and fractional open circuit voltage (FOCV). The hill climbing algorithm, also called “perturb and observe”, for the dynamic resistive matching is illustrated in Figure 32. It increments the load resistance by a predetermined step and then measures the power, often the average current, delivered to the load. If the power increases, the search direction is correct, and it increments the resistance again in the next cycle. If the power decreases, it reverses the direction. The algorithm guarantees convergence to the optimal point if there is no local maxima, and it is the case for piezoelectric generators. The hill climbing algorithm can be implemented with a microcontroller unit (MCU) or a mixed-signal circuit (Kong, Deyerle, Ha, 2011; Sankman and Ma 2014). Considering the voltage of a storage device roughly remains the same for each cycle, the power can be measured through measurement of the average current into the storage device. The FOCV algorithm relies on the fact that the voltage across the load is one half of the open circuit voltage of the source (Lu, Tsui, and Ki 2011, Shim et al. 2015). The FOCV algorithm is simpler to implement compared with the hill climbing algorithm. However, the FOCV algorithm necessitates the load be open once in a while to measure the open circuit voltage, and the energy harvesting is interrupted during the time.

Figure 32:

Schematic description of the Hill climbing algorithm.

As noted earlier, the optimal load resistance for a resistive matching for a piezoelectric generator is RL=Rs2+Xs2 The load resistance seen by the piezoelectric generator is the input resistance of the converter connected to the generator. The effective input resistance of a buck-boost converter in the discontinuous conduction mode (DCM) is obtained as Rin=2LD2Ts, where L is the inductance, D is the duty cycle, and T_S is the switching period. So the duty cycle D can be controlled to change the effective input resistance of the converter. It should be noted that the duty cycle D is changed to control the input resistance, and the output voltage of the converter is also changed accordingly. To regulate the output voltage, it needs another converter stage or some other means such as use of a Zener diode.

Once MPPT achieves the optimal or near optimal resistor value, the MPPT operation can be halted to save power until the operation condition changes. A design issue is to set the optimal wake up and sleep periods or duty cycle, which depends on several factors such as the speed and amount of the operating condition change and the speed of MPPT.

4.2 Synchronized Switch Harvesting on Inductor (SSHI) and Synchronous Electric Charge Extraction (SECE)

Synchronized Switch Harvesting on Inductor (SSHI) aims to eliminate the effect of the capacitive term of piezoelectric generators (Guyomar et al. 2005; Ramadass and Chandrakasan 2010, Wu et al. to appear). Figure 33 shows an SSHI circuit composed of an inductor L and a switch S. Note that the PZT model in the figure is a simplified Norton equivalent circuit. The PZT capacitor C_p is negatively charged at the crossing point of the PZT current I_p from negative to positive. The SSHI scheme minimizes the wasted energy to charge the capacitor positively using an LC resonant circuit. The switch SW is closed momentarily right after the zero crossing of the PZT current i_p. The capacitor C_p and the inductor L form a resonant circuit with a resonant frequency much higher than the PZT vibration frequency. The capacitor voltage V_P rises quickly due to the oscillation of the resonant circuit, and then the switch is opened at the opposite peak value of V_P, reducing dispense of the PZT energy to discharge the capacitor. When PZT current I_p changes from positive to negative, the same operation is performed to save the energy for charging the capacitor negatively. An SSHI circuit increases the energy harvested when compared with a rectifier only circuit at the cost of higher circuit complexity.

Figure 33:

Synchronized Switch Harvesting on Inductor (SSHI).

The SSHI scheme requires impedance matching for maximum power transfer. Synchronous Electric Charge Extraction (SECE), which is an extension of the SSHI method, eliminates such a need. The SECE scheme uses an LC resonant circuit to transfer the energy stored in the PZT capacitor to the inductor first and then the inductor energy is transferred to the load through a DC-DC converter (Lefeuvre et al. 2005, Gasnier et al. 2014, and Dini et al. 2016). The extracted power of the SECE method does not depend on the load, and so the load can vary without affecting the efficiency.

4.3 Rectifiers and Voltage Doublers

Piezoelectric generators require rectification in order to convert output AC voltage in to DC. A full bride rectifier with passive diodes can be easily incorporated but the forward diode voltage drop can cause substantial power loss. Active or synchronous rectifiers reduce losses associated with passive diodes. An active rectifier turns on or off a MOSFET in appropriate time periods to effectively rectify the voltage (Hashemi, Sawan, and Savaria 2012; Lam, Ki, and Tsui 2006; Le et al. 2006). Figure 34 shows a comparator based active rectification, which senses the polarity of the input voltage to turn on or off the MOSFET. If the current through the MOSFET is small, e. g. near crossing zero points, the difference in the drain and source voltage is small to cause an operation error. Various circuit configurations for rectifications have been suggested (Rincón-Mora and Yang, 2016; Hwang et al. 2015), and a major design issue is to lower power dissipation of the gate control circuit, such as the comparator shown in Figure 34. Another issue with piezoelectric generator is that the rectified voltage is very small, which leads to low efficiency of the boost converter. A voltage doubler can be used to mitigate this issue (Tabesh and Fréchette 2010). A voltage doubler increases the output voltage by 2X while rectification. It is possible to combine the voltage doubling technique and active diodes.

Figure 34:

Circuit diagram for active rectification.

Recently, reconfigurable power management circuit using a 0.25 μm complementary metal-oxide semiconductor (CMOS) process has been developed by KAIST and SNU team (Hwang et al. 2015) as shown in Figure 35. The multiple storage capacitors of the reconfigurable charger array can adjust the magnitude of capacitance by controlling serial and parallel alignments of capacitors. At the charging stage, impedance is matched between the reconfigurable capacitor array and the energy harvester to extract maximum energy while minimizing energy loss, whereas at the discharging stage, the capacitors are rearranged to supply the demanded constant low-voltage into the external load. The reconfigurable rectifying circuit can transfer four times higher electric energy to the load resistor compared to the traditional rectifying circuit.

Figure 35:

(a) A top-view optical microscopy image and (b) schematic circuit diagram of the reconfigurable rectifying circuit system integrated with energy harvester, bridge rectifier, reconfigurable capacitor charger array, and external load. (Hwang et al., 2015)