Measurement techniques for piezoelectric nanogenerators

Cite this: DOI: 10.1039/c3ee41889h

Joe Briscoe,a Nimra Jalali,a Peter Woolliams,b Mark Stewart,b Paul M. Weaver,b Markys Cainb and Steve Dunn*a

Electromechanical energy harvesting converts mechanical energy from the environment, such as vibration or human activity, into electrical energy that can be used to power a low power electronic device. Nanostructured piezoelectric energy harvesting devices, often termed nanogenerators, have rapidly increased in measured output over recent years. With these improvements nanogenerators have the potential to compete with more traditional micro- or macroscopic energy harvesting devices based on piezoelectric ceramics such as lead zirconate titanate (PZT), polymers such as polyvinylidene fluoride (PVDF) or electrostatic, electret or electromagnetic kinetic energy harvesters. Power output from a nanogenerator is most commonly measured through open-circuit voltage and/or short-circuit current, where power may be estimated from the product of these values. Here we show that such measures do not provide a complete picture of the output of these devices, and can be misleading when attempting to compare alternative designs. In order to compare the power output from a nanogenerator, techniques must be improved in line with those used for more established technologies. We compare ZnO nanorod/poly(methyl methacrylate) (PMMA) and ZnO nanorod/poly(3,4-ethylenedioxythiophene) poly(styrenesulfonate) (PEDOT:PSS) devices, and show that despite an open-circuit voltage nearly three times lower the ZnO/PEDOT:PSS device generates 150 times more power on an optimum load. In addition, it is shown that the peak voltage and current output can be increased by straining the device more rapidly and therefore time-averaged power, or time-integrated measures of output such as total energy or total charge should be calculated. Finally, the internal impedance of the devices is characterised to develop an understanding of their behaviour and shows a much higher internal resistance but lower capacitive impedance for the ZnO/PMMA device. It is hoped that by following more rigorous testing procedures the performance of nanostructured piezoelectric devices can be compared more realistically to other energy harvesting technologies and improvements can be rapidly driven by a more complete understanding of their behaviour.

Received 3rd June 2013

Accepted 14th August 2013

DOI: 10.1039/c3ee41889h

www.rsc.org/ees

Broader context

Piezoelectric energy harvesting enables the conversion of movement and vibrations in the environment to electrical energy. Macro and micro scale devices based on ceramic piezoelectric materials have been demonstrated for some time and studied in detail. More recently devices using arrays of nanostructured piezoelectric crystals for the electromechanical harvesting of energy have been demonstrated. These can be deposited using low cost solution methods onto a wide range of substrates that include exible plastics. With the rapid increase in electrical output from such devices a number of potential applications seem achievable, such as on body charging of electronic equipment and utilisation of ambient vibrations from transport or industry. However, despite the increase in peak instantaneous voltage output, the characterisation of such nanostructured devices has not been performed in detail. In order to compare between the wide range of nanostructured device architectures, and between other energy harvesting technologies, we demonstrate a range of test methods that facilitate a more complete understanding of their output and behaviour than has been demonstrated previously.

1 Introduction

There is intense interest in the scavenging of energy from a variety of sources such as solar, wind and vibration or

a Centre for Materials Research, School of Engineering and Materials Science, Queen Mary University of London, E1 4NS, UK. E-mail: s.c.dunn@qmul.ac.uk

b National Physical Laboratory, Hampton Road, Teddington TW11 0LW, UK movement. These are seen as a vital technological development to increase energy security, reduce our reliance on fossil fuels, and potentially facilitate the development of autonomous selfpowered devices.1 The interest in vibrational energy harvesting, which has developed over the past 15 years,1–4 covers the full length scale of materials from large macro-sized devices to a plethora of micro- and increasingly nano-scaled systems. A variety of techniques have been used such as electromagnetic, electrostatic, electret designs and piezoelectric conversion to produce electrical work from mechanical energy for applications such as powering a sensor or charging a battery.1,2

To date the majority of piezoelectric energy harvesting devices have been based on ceramic piezoelectric materials, most commonly lead zirconate titanate (PZT).1,5,6 The most widely investigated device architecture is that of a resonant mass-spring system, typically a piezoelectric cantilever with a tip mass. These systems have been extensively studied with welldeveloped models for describing their performance in a variety of energy harvesting situations.7 A major limitation is that these devices are tuned to a specic frequency, and power output declines rapidly away from the resonant frequency. Increasingly, work is being performed to broaden this response,1,5,6 for example through the use of non-linear oscillators to power pacemakers,8 non-linear bistable laminates,9 tuneable resonators,10,11 or multi-frequency arrays.10 An aspect of increasing importance is the control of losses in energy harvesting systems, both internal to the device itself12 and in the transfer of energy from the harvesting transducer to the electronic load where electronic solutions using techniques such as synchronous switched harvesting13 and adaptive load matching14 can significantly enhance performance. Devices have also been designed with more novel structures to access a wider range of motion, for example in shoe-implant designs,15 ballistic energy converters,5 or other body motion harvesters.16 For such alternative designs where the piezoelectric element may have to bend or ex to harvest energy from motion, standard ceramic materials can quickly deteriorate in performance due to their brittle nature.5 An alternative to potentially overcome this problem is to use the piezoelectric polymer polyvinylidene uoride (PVDF),17 which can withstand large degrees of bending. This has been trialled in energy harvesting applications such as in backpack straps.18 However, it generally demonstrates lower output than ceramic-based piezoelectric materials, even when both are produced with similar morphologies.19 A good understanding of the range of possible designs and their outputs can be obtained from a number of reviews on the subject.1,2,5,6

Although the design of the devices can vary widely, and as such the testing methods can also be fairly diverse, there are some general considerations for the characterisation of such devices that are well known. Energy harvesters present a source impedance to the load circuit, and power output is maximised when the load impedance is matched to the source impedance. Therefore it is common to vary the load impedance to nd the maximum power point.13,19,20 For harmonic excitation, the internal impedance and therefore the optimum matched load and power output are frequency-dependent. For non-sinusoidal excitation or response, the situation is more complex. The timeaveraged power delivered to the load is given generally by

$$P_{\mathrm{elec}}=\frac{1}{\tau }{\int }_0^{\tau }V\times I\mathrm{d}t,\text{\hspace{1em}(1)}$$

for a time period s. For a resistive load, the current (I) and voltage (V) are in phase, but most practical electrical loads are not resistors – they are generally much more complex comprising non-linear elements such as diodes, transistors, batteries as well as reactive components such as capacitors for energy storage, and inductors.

It is important to consider the implications of the time averaging in the measurement of power. A piezoelectric energy harvester produces a charge proportional to the stress or strain in the piezoelectric material following the piezoelectric relations:

$$D=dT+{\epsilon }^{T}E;\text{\hspace{1em}(2)}$$ $$D=eS+{\epsilon }^{S}E,\text{\hspace{1em}(3)}$$

where T is the stress, S is the strain, D is the electric displacement (charge per unit area), E is the electric eld, d and e are piezoelectric coefficients and 3 is the permittivity under conditions of constant stress or strain (superscripts T and S respectively). These elds and coefficients are in general expressed as vector and tensor quantities,21 but for ease of explanation, the tensor notation is omitted here. For a complex device such as a cantilever the stress and strain vary within the device, so the charge is integrated over the piezoelectric element.12 The current is the time derivative of the displacement eld. At constant electric eld, this is given by:

$$I=\frac{\mathrm{d}D}{\mathrm{d}t}=d\frac{\mathrm{d}T}{\mathrm{d}t};\text{\hspace{1em}(4)}$$ $$I=\frac{\mathrm{d}D}{\mathrm{d}t}=d\frac{\mathrm{d}S}{\mathrm{d}t}.\text{\hspace{1em}(5)}$$

This shows that the short circuit current (E 0) depends on the rate of strain of the piezoelectric element. A fast impulse excitation can therefore generate an arbitrarily large current (or voltage), and the instantaneous power generated can be quite high. For a high strain rate, the yield stress of the material will be reached in a short time, so achieving a high instantaneous power from an impulsive mechanical input does not imply that this power level can be sustained over a period of time.

A piezoelectric transducer converts mechanical to electrical energy in a proportion given by the electromechanical coupling coefficient, k:

$$k^2=\frac{\text{ mechanical energy converted to electrical energy }}{\text{ input mechanical energy }}.\text{\hspace{1em}(6)}$$

Again (subject to constraints such as yield and mechanical and electrical non-linearities), arbitrarily large electrical output could be achieved if the input power is unlimited. In practice, the power available from the mechanical source is nite, so in assessing the ability of an energy harvester to deliver useful energy to a device such as a wireless sensor it is necessary to take into account the ability of the mechanical system to deliver power into the transducer, and therefore the mechanical properties of the input used for testing should be measured and described.5,16,18,20

Many applications are not based on inertial coupling, e.g. power from human motion can employ direct (kinematic) strain coupling, but the same principles apply i.e. power density needs to be assessed in relation to the ability of the mechanical source to create strain in the piezoelectric material. For an impulsive type of excitation, a strain pulse induces a nite charge or energy per pulse. For an ideal piezoelectric element, the charge released for a given amount of strain does not depend on the rate. The energy per pulse can therefore be quantied, but average power delivery into the load depends on the pulse repetition rate. In some materials, charge transport processes or leakage currents can reduce the charge delivered to the load, in which case the measured energy per cycle will be rate-dependent.

Recently, alternative device designs to ceramic or polymer piezoelectrics have been demonstrated that use nano-to-microsized (normally single) crystals of piezoelectric materials deposited or grown across a substrate material.22–26 When deposited onto exible substrates these have the potential to access both the advantages of exible piezoelectrics such as PVDF or ceramicpolymer composites1 with the high coupling of single-crystal piezoelectrics. In most cases ZnO nanorods or nanowires are used as the nanostructured material, although $\mathbf{PZ}{\mathbf{T}}^{27}$ and ${\mathbf{BaTiO}}_3$ (ref. 28) nanostructures have also been used. By vibrating or compressing the structure in the case of rigid substrates, or bending when using exible substrates, the piezoelectric elements are strained and an external voltage is generated. In designs that use exible substrates the whole device can be bent to enable the harvesting of energy from a wide range of sources, including lowfrequency but high-displacement movements such as are found in everyday human motion.1,23

Such new device designs present a new range of challenges for testing and reporting of performance. Output from these devices has been reported in a variety of ways. Most commonly the open-circuit voltage $\left(V_{\mathrm{oc}}\right)$ and/or short-circuit current $\left(I_{\mathrm{sc}}\right)$ or current density $\left(J_{\mathrm{sc}}=I_{\mathrm{sc}}/\mathrm{area}\right)$ is reported versus time as an impulsive strain is induced in the device. Sometimes the peak values are used to calculate the peak power $(P_{\mathrm{peak}}=V_{\mathrm{oc}-\mathrm{peak}}\times$ $I_{\mathrm{sc}-\mathrm{peak}})$ or equivalent values per area or per volume. To date these have provided some useful means to compare the relative output of devices within this eld. However, in recent years the output of such devices has increased rapidly from the mV range to volts.25 This makes it increasingly necessary to be able to compare the performance of these devices with alternative energy harvester designs and to assess their suitability for integration into other electronic components such as batteries, capacitors and sensors.

In order to facilitate this comparison we present a wide range of methods to characterise and test the performance of nanostructured piezoelectric energy harvesting devices. The aim is to provide a thorough understanding of the output of the devices and to provide an improved test regime to enable comparison between devices of differing architectures, whether nanostructured or micro/macro-scale devices. Throughout the discussion this is related to the topics discussed above, such as measurement of power delivered to a range of loads, energy delivered per input pulse, and characterisation of the nature of the mechanical input. These aspects, as discussed, have been considered for some time in micro- and macro-scale energy harvesters, but have not routinely been included in the characterisation of nanoscale energy harvesting devices. We use the comparison between two common types of device to demonstrate that improved test regimes are required to properly assess energy harvesting performance.

In both types of device an array of ZnO nanorods are grown on a exible, conducting substrate using solution methods. All processing steps are at less than $100{}^{\circ }\mathbf{C},$ , making the process compatible with a wide range of polymer substrates. In the rst and most widely studied structure the nanorods are encapsulated in an insulator (typically PMMA) onto which a top electrode is deposited. These devices typically generate a large potential difference but have a relatively low current output due to the insulating layer.25,26 The second, and more recently reported, type of device uses a p–n junction between the asgrown n-type ZnO and a variety of p-type materials.22,29,30 These devices have tended to show lower voltages but higher current density than the ZnO-insulator structures. However, it should be noted that these structures are currently less well-studied than the insulator-type devices and so there is signicant room for improvement in the power output.

Benetting from intensive development, large improvements in the potential difference produced by the insulator-type devices have been recorded recently. These improvements are associated with reducing the carrier concentration in the ZnO either through ${\mathrm{doping}}^{31}$ or by surface passivation.25,32 The importance of reducing free-carrier concentration has been highlighted recently for p–n junction devices as relating to the screening effect, which is well-known for ferroelectric materials.22 This indicates that similar improvements can be made to both types of devices by understanding the fundamental principles that inuence the process of piezoelectric energy conversion. However, the impact of such modications on both device types has not been fully tested. Therefore, in order that the testing methods can be demonstrated and the two types of device can be compared, these processes are not used in this paper. The aim of this work is not to produce devices that out-compete others in the literature, but to demonstrate improved testing methods so that the output of a range of devices can be effectively compared. It is hoped that as a result of more complete reporting of device behaviour, improvements in performance can be more rapidly and effectively achieved in the future.

2 Experimental methods

ZnO nanorods were grown on 2 - 1 cm indium-tin oxide (ITO)- coated polyethylene terephthalate (PET) substrates (Aldrich) seeded with a sputtered ZnO lm (100 nm). Seeded substrates were suspended in solutions of 25 mM zinc nitrate and 25 mM hexamethylenetetramine and heated to 90 C for 2.5 hours. This process was repeated a total of 6 times in fresh solutions. ZnO nanorods were made into devices without further treatment by coating with either poly(methyl methacrylate) (PMMA) or poly(3,4- ethylenedioxythiophene) poly(styrenesulfonate) (PEDOT:PSS). Three layers of a 10 wt% solution of PMMA (Aldrich, $M_{\mathrm{w}}$ 120 000) in anisole (Sigma-Aldrich, 99%) were spin-coated onto the nanorods at 1000 rpm for 30 seconds, drying for 10 minutes at $100{}^{\circ }\mathrm{C}$ aer each layer. Two layers of as-received PEDOT:PSS (Aldrich, 1.3 wt% in water, conductive grade) were spin-coated onto the nanorods at 2000 rpm for 30 seconds, with ten minutes of drying at 100 C aer each layer. All devices were nished by evaporating gold contacts onto the top surface of the PMMA or PEDOT:PSS using thermal evaporation of 99.99+% gold wire (Goodfellows). Flat copper ribbons were bonded to both the ITO layer and gold contact using silver DAG followed by epoxy at one end of the device (as shown in Fig. 1e), which was clamped for testing. Scanning electron microscopy (SEM) micrographs of ZnO nanorods were recorded using an FEI Inspect-F SFEG SEM.

Kinetic energy harvesting performance was measured by mounting the devices on 0.5 mm thick, 6 2.5 cm PET substrates and bending using a cam attached to a motor rotating at 1–3 Hz so that the substrate tip opposite the contacts was bent by 10 mm and returned once per cycle. By using a cam it was possible to maintain a constant maximum displacement of the device while altering the strain frequency. Results presented are for strain rates of 1 Hz unless otherwise stated. The displacement prole of the motion was measured using a MEL M5 laser triangulation sensor. Velocity was calculated from time-dependent displacement measurements. Voltage generated by the devices was captured in open-circuit using a Tektronix TDS2012C oscilloscope in trigger mode and using a National Instruments NI PXIe-1062Q with NI DAQ support across a range of loads varied using a M-602 programmable resistance decade (MEATEST). Load resistance was corrected for the measurement input impedance of 1 MU.

DC current–voltage characteristics were measured using a Keithley 2400 SMU combined with NI Labview. The impedance of PMMA and PEDOT:PSS devices was measured using Agilent 4294A Impedance Analyser. The input frequency range was 40 Hz to 10 MHz.

3 Results and discussion

Characterisation of materials

To make reasonable comparison between the two types of nanostructured devices studied here it is rst necessary to characterise the structure of the materials in use (physical dimensions, morphology etc.). This enables the potential impact of nano- and micro-scale structural differences to be taken into account. In addition, full details of the methods used to fabricate the materials and devices are valuable, as these can give an indication of the expected material properties.

Scanning-electron microscope (SEM) images give a good impression of the size and morphology of the nanostructures used and are shown for the ZnO nanorods used in the energy harvesting devices in Fig. 1. Here, the nanorods are 1–1.5 mm long (average 1.2 mm) and 30–80 nm wide (average 64 nm), giving an aspect ratio of nearly 20 : 1. Aspect ratio of the nanorods has previously been shown to affect the device output.22,33 Clear spaces can be seen between the rods in the tilted view (Fig. 1a), which allows penetration of the coating layer. Characterisation of the coating material structure is important as it is expected to impact the device performance through mechanical and electrical changes, though a systematic study of the effect of factors such as PMMA thickness has not been published previously. Here the PMMA penetrates completely between the rods, as shown in Fig. 1c. The PMMA also covers the top of the rods with a uniform layer that continues 3.5 mm above the top of the rods. Unlike PMMA, PEDOT:PSS does not penetrate completely between the rods (Fig. 4d) as seen in previous studies.22,34 There is a continuous layer of PEDOT:PSS above the rods that is 1 mm thick. The layers used in the devices are shown in the schematic in Fig. 1e, which represents the different lling of the two materials as well as the overall layout of the devices as described in Section 2. It is possible that the difference in lling between the PEDOT:PSS and PMMA may lead to different mechanical behaviour when the device is bent. However, further study is required to establish the effect of the interface morphology, possibly through modelling. The PMMA layer in our devices is slightly thicker than reported for the majority of devices in the literature where thicknesses of 1–2 mm are common,35,36 although layers up to 3 mm have been used previously.37

natural_image

Microscopic view of nanoscale fibrous structures with 1 μm scale bar (no text or symbols beyond label)

natural_image

Microscopic view of nanofiber structures with 500 nm scale bar (no text or symbols on fibers)

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Microscopic view of a textured surface with labeled PMMA and 1 μm scale bar (no other text or symbols)

text_image

(d) PEDOT:PSS 1 µm

text_image

(e) Au ITO PEDOT:PSS Au PET PMMA Au PET ZnO

SEM micrographs and schematics of uncoated and polymer-coated ZnO Fig. 1nanorods used in the study. (a) 30 tilt of the uncoated ZnO nanorods. (b) Crosssection of ZnO nanorods. (c) Cross-section of PMMA-coated ZnO nanorods. The PMMA fills between the nanorods to the base, and covers them by 3.5 mm. The top of the PMMA layer is truncated in the image to show detail of filling. (d) Cross-section of PEDOT:PSS-coated ZnO nanorods. The PEDOT:PSS only coats the tips, and covers the nanorods by 1 mm. (e) Schematic of device construction with cross-sections of PMMA and PEDOT:PSS devices showing the different filling as seen in (c) and (d).

Characterisation of input

There are a wide variety of methods to strain energy harvesting devices. These can have an impact on the output such as through rate-dependent variations in peak voltage discussed in

line chart

Time (s)	Displacement (mm)
0.00	0.0
0.05	4.0
0.10	6.0
0.15	6.0
0.20	1.0
0.25	0.5
0.30	0.0

Measured displacement of the tip of the active area of the device during Fig. 2bending with the cam. Maximum displacement was calculated from the average of 10 measurements. The stiffness of the substrate means that it does not follow the shape of the cam exactly, but instead drops from the maximum displacement point after it has been released by the cam, as indicated.

Section 1 (see below). As such it is useful to characterise as fully as possible the method of straining the device. Nanostructured energy harvesting devices are most commonly strained with impulse-type excitations. Where, as in this paper, the device is produced on a exible substrate and bent the extent and rate of bending should be characterised through the maximum displacement or radius of curvature and the acceleration or velocity. In some cases, when programmable actuators are used to bend the devices27 this can be ascertained from the pre-programmed bending prole. However, for the devices discussed herein a cam is used to bend the device. Therefore the displacement and motion was measured using a simple laser triangulation sensor (see Section 2 and Fig. 2). From this the maximum displacement of the tip of the active area was measured as 6.02 mm, and the maximum velocity measured from a number of bending proles was 0.8–0.9 ms1 . As the device dropped from the maximum displacement point it was found to undergo acceleration that peaked at around 50 g (480 ms2 ) for a very short time (<3 ms).

For many applications, the nanogenerator will not present a signicant mechanical load to the source of the motion being harvested. In such a case the main consideration is to evaluate generated power under well-dened test conditions as discussed below. However, there are situations where the loading of the energy source needs to be known in which case a measure of the power out relative to the power in, i.e. efficiency, would be required. Measurements of efficiency in nanogenerator devices using measurement of the input force have been previously reported.29

Measurement of output

The most common method to represent output in such energy harvesting devices is to show $V_{\mathrm{oc}}$ and/or $J_{\mathrm{sc}}$ output versus time over a number of bending cycles. Example $V_{\mathrm{oc}}$ outputs are shown in Fig. 3 for both PMMA and PEDOT:PSS devices. This provides a useful visual representation of the output of the device. From such plots the peak voltage is generally obtained, here 252 mV for PMMA and 90 mV for PEDOT:PSS. As discussed, recent optimisation treatments such as annealing, compensation doping and surface functionalisation have not been used in this study, hence the peak $V_{\mathrm{oc}}$ of the PMMA device is not as high as values such as 20 V recently demonstrated in the literature.25 In this study, by using nanorods produced and tested with the same methods the two architectures can be compared, which shows the PMMA device has around three times higher peak $V_{\mathrm{oc}}$ than the PEDOT:PSS device.

Many nanostructured piezoelectric energy harvesting devices have been judged solely on equivalent peak open-circuit voltage values.25,35 By this measure the PMMA-based device is superior to the PEDOT:PSS device. However, as discussed above, for useful implementation of the harvested energy the device cannot operate in open circuit, but instead must be connected to a load. Although there are a number of complex circuits that have been developed for optimum transfer of power,13 the most basic test that is common for other energy harvesting technologies is to measure the voltage generated when the harvester is connected directly to a range of resistive loads.19,20 This was performed for the ZnO/PMMA and ZnO/PEDOT:PSS devices by bending them using a cam and recording the peak voltage across a load resistance that was varied between 100 U and 10 MU (Section 2). In this case this was performed automatically using a programmable variable resistor (Section 2). The instantaneous power generated by the device can be calculated approximately using the equation,

(a)

line chart

Time (s)	Open-circuit voltage (mV)
0.5	-40
1.5	240
2.5	-40
3.5	240

line chart

Time (s)	Open-circuit voltage (mV)
0.0	0
0.5	90
1.0	0
1.5	85
2.0	0
2.5	90
3.0	0
3.5	75
4.0	0

Open-circuit voltage output of ZnO/PMMA (a) and ZnO/PEDOT:PSS (b) piezoelectric energy harvesting devices. Devices were bent once per second using a rotating cam.

$$P=\frac{V^2}{R},\text{\hspace{1em}(7)}$$

where P is the power and V the peak voltage measured across the load R. It should be noted that this expression is only approximate due to the effects of stray reactance in the load and measuring circuits. Whilst this is not expected to have a major effect on results presented here, accuracy could be improved by minimising these effects and compensating for them. This is beyond the scope of the current paper, but care would be needed for small samples with high source impedance which could be signicantly affected by stray reactance.

In general, nanostructured piezoelectric energy harvesting devices are deposited on a planar substrate. Therefore the power scales with the active area (A) of the device. Hence, it is useful to calculate the area power density, $P_{\mathrm{A}}=P/A$ . In addition, for many piezoelectric energy harvesting devices based on ceramic piezoelectric materials the volume power density $\left(P_{\mathrm{V}}\right)$ is oen quoted. This is obtained by dividing the power by the volume of the device,1,2,6 although different ways of calculating the volume (volume of active material or working volume required to accommodate the mechanical displacement) can lead to large discrepancies in reported power densities. In this paper, to aid comparison between nanostructured devices, the thickness of the device was taken as that of the active portion of the device, i.e. the piezoelectric plus any encapsulating material (here PMMA or PEDOT:PSS) and electrodes, but not the supporting substrate. This is because the active layers could in principle be added to an existing surface, such as the casing of machinery, or onto fabric for clothing.38 Here the ZnO/PMMA structure is 5.5 mm thick, and the ZnO/PEDOT:PSS is 2.5 mm.

The volume power density can be used to compare to other technologies, but in general the area power density may be more useful as a working gure when comparing the output of nanostructured devices.

The value of $P_{\mathbf{A}}\cdot$ -versus-resistance for the PMMA and PEDOT:PSS devices are shown in Fig. 4. From these plots the peak area (volume) power densities for PMMA and PEDOT:PSS devices are found to be $0.243\mu \mathrm{W}{\mathrm{cm}}^{-2}\left(0.44\mathrm{mW}{\mathrm{cm}}^{-3}\right)$ and 36 $\mu \mathrm{W}{\mathrm{cm}}^{-2}\left(144\mathrm{mW}{\mathrm{cm}}^{-3}\right)$ respectively. Therefore the PEDOT:PSS devices generates a maximum area power density over 150 times greater than the PMMA device on an optimum load. In addition, it compares well with other piezoelectric energy harvestors, which generally have power outputs in the $\mu \mathrm{W}\cdot \mathrm{mW}{\mathrm{cm}}^{-3}$ range.2,6 However, in some cases these are average rather than peak power densities, which is discussed below.

For comparison the $V_{\mathrm{oc}}$ and $J_{\mathrm{sc}}$ of the devices can be estimated from the voltage measured across a high resistance, and current across a low resistance respectively. These give $V_{\mathrm{oc}}$ and $J_{\mathrm{sc}}$ of 200 mV and $3.6\mu {\mathrm{Acm}}^{-2}$ for the PMMA device, and 154 mV and $867\mu {\mathrm{Acm}}^{-2}$ for the PEDOT:PSS device. It should be noted that these are only estimates: the $V_{\mathrm{oc}}$ values differ slightly from the peak values taken from Fig. 3. Previously output power has been calculated by taking the product of $V_{\mathrm{oc}}$ and $J_{\mathrm{sc}},$ which gives $P_{\mathbf{A}}$ values of $0.71\mu \mathrm{W}{\mathrm{cm}}^{-2}$ and 134 mW cm2 for PMMA and PEDOT:PSS devices respectively. These overestimate the peak power value measured on the load by a factor of 2.9 and 3.7. This demonstrates the importance of measuring the power generated across a load rather than using $V_{\mathrm{oc}}\times J_{\mathrm{sc}},$ as the latter can lead to large overestimations of the generated power. In addition, when established for a particular device architecture, this overestimation factor can be used to scale previous power values calculated using only $V_{\mathrm{oc}}$ and $J_{\mathrm{sc}}$ to the actual maximum power generated on a load. This will vary depending on the exact device due to differences in the electrical properties of the device (see below), therefore in future work P should always be measured across a load to calculate at least $P_{\mathbf{A}},$ and ideally also $P_{\mathbf{V}}$ (if the thickness is known). Comparison of the two ZnO nanorod-based device structures herein using both $V_{\mathrm{oc}}$ and peak power on a load thus demonstrates the importance of generating such load curves for energy harvesting devices.

line chart

Resistance (Ω)	Power Density (μW/cm²)
100	0.005
200	0.004
500	0.003
1000	0.002
2000	0.008
5000	0.02
10000	0.06
20000	0.1
50000	0.18
100000	0.22
200000	0.24
500000	0.23
1M	0.21

line chart

Resistance (Ω)	Power Density (μW/cm²)
100	7
200	10
300	14
400	18
500	22
600	26
700	30
800	34
900	36
1000	35
2000	32
3000	28
4000	24
5000	20
6000	16
7000	12
8000	8
9000	4
10000	2
20000	1
30000	0.5
40000	0.3
50000	0.2
60000	0.1
70000	0.1
80000	0.1
90000	0.1
1M	0.1

Area power density output of ZnO/PMMA (a) and ZnO/PEDOT:PSS (b) devices measured across a range of load resistances. PMMA device peaks at 0.243 $\mu \mathsf{W}$ ${\mathsf{cm}}^{-2}\mathsf{at}488$ kU and PEDOT:PSS 36 $\mu \mathsf{W}{\mathsf{cm}}^{-2}\mathsf{at}1.67$ kU. Resistance is corrected for a 1 MU input impedance.

Time-dependent open-circuit voltage output of a ZnO/PEDOT:PSS piezoelectric energy harvesting device. Measurements (a)–(c) were obtained when the cam was set to rotate at 1, 2 and 3 Hz. With the increase in bending rate the peak voltage increases from around 80–100 mV. This demonstrates that the voltage generated by a device can be increased by increasing the strain rate. Hence time-integrated measurements such as total energy and charge are useful for comparison (see main text).

line chart

Time (s)	Voltage (mV)
0.00	0
0.005	105
0.01	-15
0.015	25
0.02	-20
0.025	15
0.03	0
0.035	0
0.04	-5

line chart

Time (s)	Voltage (mV)
0.00	0
0.01	80
0.02	-30
0.03	0
0.04	0

Time-dependent voltage output of ZnO/PMMA (a) and ZnO/PEDOT:PSS (b) devices measured across the optimum load for each device, as indicated.

Using power values measured across a load allows signi- cantly more realistic comparison to be made both between different nanostructured energy harvesting devices and between them and other energy harvesting devices. However, this peak output power is still based on the maximum voltage generated in a cycle. It does not reect the duration or shape of the cycle. It is therefore possible to increase this peak value merely by increasing the rate of strain of the device, as discussed above (see also Fig. 5). A better performance measure for device application is the average power delivered to the load over a period of time, or the energy per cycle for intermittent duty. This requires time-resolved measurement of voltage output using an instrument such as an oscilloscope. Such measurements for the PMMA and PEDOT:PSS devices are shown in Fig. 6. This voltage was measured across the optimum load for each device, as established from Fig. 4. From these data a wide range of metrics can be calculated. By integrating the power generated from the start (t ) to end (t ) of a cycle the total electrical energy delivered to the load can be calculated:

$$E={\int }_{t_1}^{t_2}\frac{V(t{)}^2}{R}\mathrm{d}t.\text{\hspace{1em}(8)}$$

For the PMMA and PEDOT:PSS devices the energy generated was calculated to be 0.22 nJ ${\mathrm{cm}}^{-2}$ and 38.6 nJ ${\mathrm{cm}}^{-2}$ respectively. Here, the PEDOT:PSS device transfers around 170 times more energy, consistent with the increased peak power level. As with power, this value is scaled per area to enable comparison between devices of different sizes. In principle, this output energy can be compared to the input energy to establish a mechanical-to-electrical conversion efficiency, as demonstrated previously.29 However, care must be taken to accurately dene the input energy to ensure accurate values are obtained. It is also possible to divide the energy by the duration of the cycle to calculate the average power (eqn (1)). This is most useful where the mechanical source consists of continuous vibrations or oscillations and therefore the output does not contain large gaps. In this case average power can give an indication of the level of demand that can be directly served by the energy harvester without the need for storage. When stress is applied infrequently as in the tests discussed herein the average power

over a long period will be very low due to the large periods of inactivity between impulses. Therefore in this case values totalled over a single cycle, such as energy, are more useful. However, it is possible to estimate the average power in a single cycle by dividing the total energy by the duration of the pulse. Although the value is somewhat arbitrary depending on the choice of pulse duration, here is was calculated for each device using the total energy over a duration of approximately 10 ms, which covered the single impulse output without additional minor oscillations $\left(\mathrm{Fig}.6\right)$ . To deliver this average power over an extended period the impulse would have to be repeated every 10 ms (100 Hz) without the device failing. This gives average area power densities of $0.020\mu \mathrm{W}{\mathrm{cm}}^{-2}$ and $5.2\mu \mathrm{W}{\mathrm{cm}}^{-2}$ for the PMMA and PEDOT:PSS devices respectively. This demonstrates that the average power – even over the duration of only one impulse – is many orders of magnitude lower than the peak power. This value also assists comparison as it is oen calculated for other energy harvesting devices that are tested under continuous vibrations or oscillations. In this study the maximum strain frequency tested was 3 Hz, and no deterioration of output was observed while sustaining this strain rate. However, to ascertain experimentally whether the calculated average power output would be sustainable without rapid device fatigue a system that could strain the device at high displacement at such high strain rates (100 Hz) would have to be used.

If the current can be measured or calculated across the load, another useful quantity to calculate is the total charge, Q, transferred from the device:

$$Q={\int }_{t_1}^{t_2}I(t)\mathrm{d}t.\text{\hspace{1em}(9)}$$

This is useful when the device is being used to charge a capacitor or battery for later use, as it indicates the total charge transferred to the storage medium.

These metrics therefore provide a more complete picture of the time-dependent output of the devices, removing some of the inherent variability that exists due to the widely varying straining methods used. This could also be useful to establish whether the total energy or charge generated is independent of strain rate, or whether it differs due to the different loss mechanisms discussed above such as leakage or screening22 within the devices.

line chart

Voltage (V)	Current Density (mAcm⁻²)
-2.0	-1.8
-1.5	-0.5
-1.0	0.0
-0.5	0.0
0.0	0.0
0.5	0.0
1.0	0.0
1.5	1.0
2.0	4.5

line chart

Voltage (V)	Current Density (mAcm⁻²)
-2	-18
-1	-5
0	0
1	15
2	80

Current density–voltage characteristics of ZnO/PMMA (a) and ZnO/PEDOT:PSS (b) devices.

line chart

Z_Re (kΩ)	Z_Im (kΩ)
0	0
100	-100
200	-200
300	-200
400	-100
500	0

line chart

Z_Re (kΩ)	Z_Im (kΩ)
0.0	0.0
0.2	-0.1
0.4	-0.2
0.6	-0.3
0.8	-0.2
1.0	-0.1

Nyquist plots for ZnO/PMMA (a) and ZnO/PEDOT:PSS (b) devices showing real and imaginary components of impedance ( ) measured between 40 Hz and Fig. 8 Z10 MHz. Arrows denote direction of increasing frequency. Approximate internal resistance and capacitance values obtained from analysis of the plots assuming a simple RC circuit are given in Table 1.

Key parameters for the two device types measured in this work

Electrical characterisation of devices

Measurement of the electrical properties such as current– voltage (I–V), capacitance–voltage (C–V) and impedance spectroscopy can provide valuable insight into the device performance and its relation to the structure and mechanism of energy conversion. Such measurements give useful information about the internal resistance, capacitance and rectication behaviour of the devices.

The direct current-density–voltage behaviour (J–V) of the ZnO/PMMA and ZnO/PEDOT:PSS devices is shown in Fig. 7. The ZnO/PMMA structure (Fig. 7a) shows non-linear behaviour with high resistance of 1.48 MU at low voltage, and breakdown to much lower resistance of around 530 U above 1–2 V. The ZnO/ PEDOT:PSS behaves like a non-ideal p–n junction, which is expected since as-grown ZnO is n-type,39 and PEDOT:PSS is ptype.22 As discussed previously, the diode structure helps to slow the screening of the polarisation aer strain allowing a voltage to develop,22 which in the case of ZnO/PMMA may also be served by the insulating nature of the PMMA and the capacitance of the junction. For ZnO/PEDOT:PSS using the non-ideal diode equation,40 with a resistance in series and parallel (shunt) to the diode, the series $\left(R_s\right)$ and shunt $\left(R_{\mathrm{sh}}\right)$ resistance can be estimated from the current–voltage behaviour at high forward voltage and at reverse saturation respectively. This gives $R_{\mathrm{s}}=$ 165 U and $R_{\mathrm{sh}}=1.55$ kU for the ZnO/PEDOT:PSS diode.

Nyquist plots showing the frequency-dependent reactive impedance $\left(Z_{\mathrm{Im}}\right)$ and frequency-independent resistive impedance $\left(Z_{\mathrm{Re}}\right)$ for the ZnO/PMMA and ZnO/PEDOT:PSS devices are shown in Fig. 8 with arrows denoting increasing frequency of measurement from 40 Hz to 10 MHz. The purely negative imaginary impedance indicates the reactive component is capacitive. Therefore, to provide an approximation of the resistive and capacitive properties of the devices, analysis was performed assuming a simple RC circuit.41 In this case, the internal resistance can be approximated from the diameter of the curve along the axis denoting the real component of the impedance $\left(Z_{\mathrm{Re}}\right)$ , as at low frequency the RC impedance is purely resistive.41 This gives internal resistance $\left(R_{\mathrm{int}}\right)$ values of approximately 475 kU for the PMMA device, and 1 kU for the PEDOT:PSS device. This is consistent with the higher resistance values derived from the current–voltage relationship for the PMMA device. In addition, the internal resistance for both devices are very close to the values of the optimum load resistances (Table 1), which is expected since the internal resistance determines the optimum load resistance (see Section 1).

For an RC circuit $Z_{\mathrm{Im}}$ is at a maximum at the cut-off or critical frequency, $f_{\mathrm{c}}{,}^{41}$ which is 980 Hz for PMMA and 6.7 kHz for PEDOT:PSS. At this frequency:

$$RC=\frac{1}{2\pi f_c}.\text{\hspace{1em}(10)}$$

From this it is possible to calculate the internal capacitance, $C_{\mathrm{int}},$ which is 0.32 nF for the PMMA device and 24 nF for PEDOT:PSS. This approximation is likely to be more accurate for the PMMA device as it follows RC behaviour more closely where the capacitive reactance $X_{\mathrm{c}}=R_{\mathrm{int}}/2$ at $f_{\mathrm{c}},$ whereas for PEDOT:PSS $X_{\mathrm{c}}$ is closer to $R_{\mathrm{int}}/4$ at $f_{\mathrm{c}}.$ . Although these are only approximate values, the lower capacitance for the PMMA device would deliver less power to a reactive load, as this is proportional to capacitance.41 These impedance plots can provide much more important information on some of the complexities of the electrical performance of these devices through a more in-depth analysis and tting of more complex model circuits. This is on-going, and aims to provide a thorough understanding of the devices’ operating principles.

This analysis demonstrates that an understanding of the load-dependent output can be gained by comparison with the electrical properties of the devices themselves. It demonstrates that the high internal resistive impedance of the PMMA device leads to it matching a high load resistance as expected, and therefore giving a low output power compared to the PEDOT:PSS device despite slightly higher open-circuit voltage. The different capacitance of the two devices also indicates that a comparison of the device outputs across a range of capacitive loads would add to the understanding gained from resistive load matching and allow a more complete understanding of their behaviour when used in energy harvesting applications. Although the lower internal capacitance of the PMMA device may lead to less energy being transferred if a reactive load were used, as mentioned above, such a comparison is complex as it would require the use non-linear elements such as a rectier or d.c. to d.c. converter and would depend on factors such as the duty cycle of the application $e.g.$ sensor/transmittor. Therefore, performance under real load conditions is likely to be complicated and highly application dependent, but is essential to evaluate performance in an application, and is therefore an important topic of further research. In addition, the varying frequency-dependent behaviour indicates analysis of frequencydependent output would further contribute to complete device characterisation. Finally, with understanding of the operating principles of these devices gained through equivalent circuit modelling, guidance for design of such devices can be directed for optimum performance.

4 Conclusions

Novel designs and materials for piezoelectric energy harvesting devices offer many potential benets, but also challenges for testing and characterisation. Devices using piezoelectric ceramics have been developed for over 15 years, and as such a wide range of in-depth testing procedures have been established. There is therefore a great potential benet for nanostructured piezoelectric energy harvesting (nanogenerators) to draw on these testing techniques. To date, nanogenerators have almost exclusively only been characterised through open-circuit voltage $\left(V_{\mathrm{oc}}\right)$ or short-circuit current $\left(I_{\mathrm{sc}}\right)$ measurements. By comparing two ZnO/polymer devices we have shown that such measures, and especially power values calculated from the product of their amplitudes, are an insufficient metric for the comparison of different device architectures. It has been shown that the power output measured across a range of resistive loads is needed to establish the peak power output. It is useful also to divide this by device area or volume to calculate a power density. Thus, despite having a higher $V_{\mathrm{oc}}$ of 252 mV, a ZnO/PMMA device has a maximum instantaneous power density of only 0.243 mW cm2 compared to $V_{\mathrm{oc}}$ of 90 mV, and power density of $36\mu \mathrm{W}{\mathrm{cm}}^{-2}$ for a ZnO/PEDOT:PSS device. Such load-dependent output is therefore essential in future reports of device behaviour.

The power output from the product of voltage and current is critically dependent on the rate of application of the mechanical strain, even for an ideal piezoelectric, so it is important to measure the ability of the device to deliver energy over a period of time. In this paper we report measurement of the energy per cycle, which was calculated by integrating the power transferred to a load across the duration of a cycle. This was calculated as 0.22 nJ cm2 and 38.6 nJ cm2 for the ZnO/PMMA and ZnO/ PEDOT:PSS devices respectively. In addition, the current transferred to a load or capacitor can be integrated over time to calculate the total charge generated by the device. Alternatively, for continuous cycle measurements calculation of average power can be useful to ascertain the potential for continuous power output. This is also calculated here, but depends greatly on the chosen duration over which to average for impulse-type tests. It is therefore useful wherever possible to measure some form of time-integrated or averaged output, and provide characteristics of the input such as maximum displacement, velocity, acceleration or frequency. Such measurements allow differences in peak output due to varying strain rates to be taken into consideration.

As well as measuring the output of the devices across a load, it has been shown that electrical characterisation of the devices themselves allows an understanding to be gained of their relative behaviour. Hence, current–voltage measurements and impedance spectra have been performed to ascertain the internal impedance of the devices. Using a simple RC circuit model to t the data approximate internal resistance values for the PMMA and PEDOT:PSS devices of 475 kU and 1 kU were calculated, which are very close to the optimum load resistances of each device. The internal capacitance was estimated to be 0.32 nF and 24 nF for PMMA and PEDOT:PSS devices respectively.

With this level of characterisation of the devices, it should be possible not only to compare them with other energy harvesting designs, but also to further develop our understanding of their behaviour leading to improved design at both the macro and nano-scale. For example, long-term stability and fatigue testing could be studied to determine how the output of the devices may change over time and with usage. In addition, further characterisation of their internal properties could allow accurate equivalent circuit models to be developed, which would facilitate their integration into optimised energy harvesting circuits. Although we have stressed the importance of output measurements across resistive loads, it would also be benecial in future to characterise the output across capacitive loads and potentially more complex harvesting circuits, as this will also depend strongly on the electrical characteristics of the devices.

With the two devices tested here based on the same substrate dimensions, material and structure, and using the same strain rate and amplitude, the measurements presented allow direct comparison of performance and properties. It should be considered, however, that structural variations in devices such as substrate thickness, the position of the neutral axis with respect to the active layer and the length and aspect ratio of the cantilever is likely to vary considerably for devices produced in other laboratories. This, as well as different straining methods is likely to impact upon the measured output. However, the testing methods demonstrated here provide an improved ability to compare the output of devices produced and tested with different techniques compared to those used previously. It is hoped that with these more rigorous testing techniques, and with further standardisation of testing, the performance of nanostructured piezoelectric energy harvesters can be compared effectively with other energy harvesting technologies in order to understand their potential for implementation in real-world applications. Furthermore, the understanding gained by thorough characterisation should enable more focussed improvements of their output, accelerating their development into a competitive technology.

Acknowledgements

The authors would like to acknowledge nancial support from the European Metrology Research Programme (EMRP) Project ENG02 “Metrology for Energy Harvesting”, the UK National Measurement System, and the EPSRC. The EMRP is jointly funded by the EMRP participating countries within EURAMET and the European Union.

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