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integrating them in devices permits the applications of devices without external power source or battery. Several examples of various materials and device confi gura-tions appear in the literature.

An example of piezoelectric materials that has been constantly studied is ZnO, mostly in nanowire (NW) form. [ 2–4 ] A nanogenerator (NG) based on ZnO NW was an application that utilizes the piezo-electric effect on NWs to harvest energy from the environment for electricity. [ 5 ] A high-level current of ≈500 nA and voltage of ≈10 mV were obtained. In order to solve the problems of the electrical output sta-bility and mechanical robustness in the previous design, Yang et al. [ 6 ] reported a fl exible power generator based on a piezoelectric fi ne wire that was fi rmly attached to the metal electrodes at both ends. Repeating stretching and releasing a single wire with a strain of 0.05–0.1% cre-ated an oscillating output voltage of up to ≈50 mV. Xu et al. [ 7 ] reported that a lateral integration of 700 rows of ZnO NWs pro-

vided promising capability to charge an AA battery as it yielded an output voltage of 1.26 V. ZnO NWs had also been used to develop a high-output nanogenerator (HONG) on plastic sub-strates that could generate power to light up a commercial light-emitting diode (LED). [ 8 ] Li et al. [ 9 ] showed the feasibility of harvesting energy from the pulmonary motions and heartbeat of animals.

PZT-based NGs have also been investigated as they can generate higher power outputs than other semiconductive

Measured Output Voltages of Piezoelectric Devices Depend on the Resistance of Voltmeter

Yewang Su , * Canan Dagdeviren , * and Rui Li

Piezoelectric mechanical energy harvester (MEH) has been developed as an important emerging variant of piezoelectric devices. Experiments in the literature show that the voltage–time curves of piezoelectric devices encom-pass both positive and negative characteristics even though the strain in the piezoelectric material is always positive during the applied cycling load. This does not agree with the results predicted by the piezoelectric theory of open circuit. Here, both the experiments and theory are performed to understand this important problem. A zirconate titanate (PZT) MEH is fabricated and the output voltages are recorded with three voltmeters. It is found that the measured voltages depend on the resistance of voltmeter. The peak value of voltage increases with the increase of the resistance of voltmeter, which is contrary to the established knowledge that the measurement results are independent of the instruments used. A theoretical model considering the voltmeter with fi nite resistance is established. The charge is allowed to go through the voltmeter and switch the directions during increasing and releasing of strain. The results by this model agree well with those from the experiments. The fi ndings suggest that the resistance of voltmeter should be reported for voltage measurement of the piezoelectric devices.

DOI: 10.1002/adfm.201502280

Prof. Y. Su State Key Laboratory of Nonlinear Mechanics Institute of Mechanics Chinese Academy of Sciences Beijing 100190 , China E-mail: yewangsu@imech.ac.cn Prof. Y. Su Department of Civil and Environmental Engineering Northwestern University Evanston , IL 60208 , USA Dr. C. Dagdeviren The David H. Koch Institute for Integrative Cancer Research Massachusetts Institute of Technology Cambridge , MA 02139 , USA E-mail: canand@mit.edu

Dr. C. Dagdeviren Department of Materials Science and Engineering Beckman Institute for Advanced Science and Technology Frederick Seitz Materials Research Laboratory University of Illinois at Urbana-Champaign Urbana , IL 61801 , USA Prof. R. Li State Key Laboratory of Structural Analysis for Industrial Equipment Department of Engineering Mechanics Dalian University of Technology Dalian 116024 , China

1. Introduction

As being power sources for wearable or implantable electronic devices, piezoelectric materials such as zinc oxide (ZnO), lead zirconate titanate (PZT), and polyvinylidene fl uoride (PVDF) offer potential for converting electrical power from mechanical motion associated with natural body processes (e.g., walking and breathing). [ 1 ] The prospective of utilizing piezoelectric materials to generate power from everyday activities and

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nanomaterials, and can offer high energy conversion effi ciency (≈80%). [ 10 ] Electrospinning process was performed to obtain PZT nanofi bers with extremely high piezoelectric voltage con-stant (g 33 , 0.079 Vm N −1 ). [ 11 ] Despite its excellent piezoelectric property, PZT has a disadvantage due to its brittleness and strain limitation (<1%). [ 12 ] To overcome this limitation, devices built with PZT, including other brittle piezoelectric materials, were typically integrated with stretchable substrates, as dem-onstrated by several research groups. [ 13–16 ] For instance, the integration of piezoelectric PZT ribbons onto fl exible rubber substrate (PDMS) offered an effi cient and fl exible energy con-version that opened a new opportunity for future energy har-vesting systems. [ 14,17 ] In recent years, many emerging piezoelec-tric devices have been presented with attractive performance. A co-integrated collection of such energy harvesting elements with rectifi ers and micro-batteries provided an entire fl exible system, being capable of viable integration with the beating heart via medical sutures and operation with a high peak voltage of 8.1 V and effi ciency of ≈2%. [ 16 ] Dagdeviren et al. [ 18 ] demonstrated composite structures of hard piezoelectric material, and stretch-able serpentine (spring-like) conducting metal traces with soft elastomer substrates forming an array of mechanical actuators and sensors. The array is softly and reversibly laminated on the surfaces of nearly any organ system of the human body, for rapid and precise measurement and spatial mapping of viscoe-lastic properties. Researchers also fabricated the directly written energy harvesters and sensors, which pave the way for a cost-effective, high-effi ciency manufacturing pathway in wearable, bio-integrated electronics with large deformability. [ 19,20 ]

The voltage output is an important parameter to determine the performance of piezoelectric devices. The literature shows that the voltage–time curves of piezoelectric devices are char-acterized by the positive and negative variations ( Figure 1 a), even though the strain or stress in the piezoelectric mate-rial is always positive during the cycling load. [ 6–9,21–25 ] The theory of open circuit is usually used to predict the peak of the voltage–time curve, [ 6–9,22–25 ] which will be shown and

described analytically in this study. Figure 1 c shows the sche-matic illustration of a piezoelectric ribbon with polarization direction along the thickness direction subject to stretching. By the theory of open circuit, the voltage is zero in the state without being stretched, reaches the maximum while the strain is maximum and restores to zero after being released. The output voltage is always positive during the stretch-release cycles (Figure 1 b). The voltage never goes to the range of nega-tive during the process, which confl icts with the experimental fi ndings (Figure 1 a). To address this important problem, we both investigated theory model and conducted experimental measurement.

2. Results

In order to study the measurement of output voltage, a PZT mechanical energy harvester (MEH) [ 16 ] that was fl ex-ible enough to wrap a glass tube was fabricated, as shown in Figure S1a (see Supporting Information for the fabrica-tion method details). The functional element of the MEH is a capacitor-type structure that consists of a layer of PZT (500 nm) between the bottom (Ti/Pt, 20 nm/300 nm) and top (Cr/Au, 10 nm/200 nm) electrodes (Figure S1b, Supporting Information). A MEH module consists of 12 groups of 10 capacitor structures that are electrically connected in parallel. Each of the twelve groups is connected in series to its neigh-boring group to increase the output voltage (Figure S1c, Sup-porting Information).

For the performance characterization of the MEH, a mechan-ical stage is used to cyclically compress the device from clamps at its ends, and allows doing measurements of output voltage during deformation, as shown in Figure 2 . The apparent length of the device is L = 2.5 cm, and the amplitude of the compres-sion LΔ between the two ends of the device is a periodic func-tion of time t . In the experiment, four groups of maximum value of the compression L 1.5, 3, 5, and 10 mmmaxΔ = are per-formed ( Figure 3 a), respectively. For each group of maximum compression, three voltmeters with different inner resistance

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b

c

0, 0VΔL 0, 0VΔL0, 0VΔL

Piezoelectric materials

without stretch stretch release

0time

V Piezoelectric theory a

0time

V Experiment results

Figure 1. Schematic illustrations of the curves of output voltage versus time from a) experiments and b) piezoelectric theory for open circuit. c) Schematic illustration of the voltage and charge distribution of piezoelec-tric materials subject to stretching.

Figure 2. Photographs of a PZT MEH clamped on a bending stage in fl at (upper) and bent (lower) confi gurations.

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value R 34, 60, and 300 M= Ω were used to measure the voltage of the same MEH (see Supporting Information for details). The measured voltage values are different for the same compression LmaxΔ , as shown in Figure 3 b, d, f, and h, which is contrary to the established knowledge that the measured results should be independent of the instruments used. The peak value of the voltage output slightly increases with the resistance of the voltmeter ( Figure 4 ). The peak values of output voltage are 2.98, 3.61, and 3.85 V for the voltmeter with resistances R 34, 60, and 300 M= Ω, respectively, while 10maxLΔ = mm is the same for all cases. The measured results are dependent on not only the device itself, but also the instrument used.

Here, an analytic model coupling the piezoelectric behavior and the fi nite deformation of the device is developed, as shown

in Figure 5 a. When the length of the PZT ribbons is much smaller than that of the supporting substrate (polyimide, PI), the membrane strain in the PZT can be obtained as (see Sup-porting Information for details)

EI

EI

h

L

L

L4m

PI

compε π= Δ (1)

where EI comp and EIPI are the bending stiffness (per unit width) of the PI with and without the PZT devices, respectively; h is the distance from the center of the PZT layers to the neutral mechanical plane (Figure S1b, Supporting Information). The capacitor-type structure consists of layers in the following order {PI, PI, Ti, Pt, PZT, Cr, Au, PI}, as shown in Figure S1b (Sup-porting Information), where the corresponding moduli are {E1~8} = {2.83, 2.83, 129, 196, 69.2, 292, 96.7, 2.83} Gpa, and thicknesses { t 1~8 } = {75, 1.2, 0.02, 0.3, 0.5, 0.01, 0.2, 1.2} µm. These values yield EI EI/PI comp = 0.45, y neutral = 52.0 µm and h t t t t t y21 2 3 4 5 neutral( )= + + + + / − = 24.7 µm.

PZT in this system is transversely isotropic with a polariza-tion direction x 3 normal to the surface. Constitutive models give relations among the stress ijσ , strain ijε , electrical fi eld E i and electrical displacement D i as shown in Equations (S1) and (S2) (Supporting Information), where c ij , e ij , and k ij are the elastic, piezoelectric, and dielectric constants, respec-tively. For the plane-strain deformation ( 022ε = ) and traction free on the top surface of the structure ( 033σ = ), the strain

33ε and electrical fi eld E 3 along the polarization direction x 3 satisfy the constitutive relations c c e E0 11 11 13 33 31 3ε ε= + − and D e e k E3 31 11 33 33 33 3ε ε= + + , where the electrical displacement D 3 along the polarization direction is a constant to be deter-mined. The elimination of 33ε gives D e kE3 11 3ε= + , where

/31 13 33 33e e c c e( )= − and /33 332

33k k e c( )= + are the effective piezo-electric constants. The electrical displacement can be further obtained as

D ekV

Nt3 m

PZT

ε= + (2)

from the charge equation d /d 03 3D x = and the relation E x/3 3φ= − ∂ ∂ between the electrical fi eld and electrical poten-tial, together with the boundary condition that the voltage dif-ference between the bottom and top of PZT is V / N , where V is the total output voltage between the two ends of the N groups

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Figure 3. a) Displacement load and the comparison of voltage between b,d,f,h) experiments and c,e,g,i) theory as functions of time for resist-ance of 34, 60, and 300 MΩ and maximum displacement of 1.5, 3, 5, and 10 mm.

Figure 4. Comparison of the maximum output voltage between theory and experiments for the resistance of 34, 60, and 300 MΩ.

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of PZT ribbons in series, t PZT and mε are the thickness and membrane strain of PZT ribbons.

The output voltages measured with a conventional voltmeter are often recognized as the open-circuit voltage. In this case, the electric displacement D 3 is zero and the voltage is propor-tional to the membrane strain, according to Equation ( 2) ,

Ve Nt

km

PZT ε( )= − (3)

The results suggest that the sign of the voltage is always same as the membrane strain since e 0( )− > . Contrary to this, the reported measurements [ 6–9,22,23,25 ] and our experimental results (Figure 1 a and Figure 3 b,d,f,h) show alternating posi-tive and negative values, even for the tests in which the strains/stresses do not change in sign at any stage of the deformation.

This discrepancy arises from an assumption that the volt-meter has infi nite resistance, whereas its actual, fi nite resist-ance allows charge to pass, in a way that involves changes in direction as the strain increases and decreases, as shown in Figure 5 b. Here, the current I A D�PZT 3= − is related to the voltage V and resistance R of the voltmeter by I = V / R , where A m w l w lPZT PZT,1 PZT,1 PZT,2 PZT,2( )= + is the total area of PZT rib-bons in each group; m 10= is the number of PZT ribbons in each group; 100 mPZT,1w = μ , 140 mPZT,2w = μ , l 2.02 mmPZT,1 = and l 160 mPZT,2 μ= are the widths and lengths of the two rec-tangular parts of each PZT ribbon, respectively (Figure S1b, Supporting Information). The result is that / PZT 3V R A D= − � , i.e.,

V

t

Nt

A RkV

Net

k t

dd

dd

PZT

PZT

PZT mε+ = − (4)

Using the initial condition V t 0 0( )= = , the voltage is given by

d

ddPZT m

0

PZT

PZT

PZT

PZTVe Nt

ke

te t

Nt

A Rkt

Nt

A Rkt

t

∫ε( )=

− − (5)

Rewriting this equation with / PZTV kV e Nt[ ]( )= − as the dimensionless voltage yields

V et

e tt

R

t

R

t dd

dm

0∫

ε=−

(6)

where /t t T= and = [ ]/( )PZT PZTR A k Nt T R are the dimen-sionless time and resistance. For a representative strain

[1 cos(2 )]/2tmε π= − as a function of dimensionless time, the dimensionless voltage is

π

ππ π π

π=

+[ − ] +

+−

1 4sin 2 arctan(2 )

2

1 42 2

2 2

2 2/V

R

Rt R

R

Re t R (7)

where the fi rst term of the right side is a periodic function that switches between positive and negative; the second term repre-sents an exponential decay. For infi nite resistance, Equation ( 7) reduces to Equation ( 3) . Figure 6 shows the effect of dimen-sionless resistance on the dimensionless voltage. The second part of Equation ( 7) vanishes while R is small enough, and the voltage switches between the positive and negative as a periodic function and depends on the resistance. The dimensionless voltage moves to the range of the positive gradually with the increase of the dimensionless resistance. The dimensionless voltage becomes completely positive and is linearly proportional to the membrane strain when the dimensionless resistance is infi nitely large, i.e., the open circuit, which is exactly the case of Equation ( 3) . This phenomenon can be understood by the effect of the resistance of the voltmeter. With the increase of

c33

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PI PZT

2L

PIL - ΔL1x

2x

2x

1x

A2L

1w x

PIt

b

a

PZT PI

PZT PI

bending

release

V

V 0V

0V

Figure 5. Schematic illustrations of a) theoretical shape for buckling of a PZT MEH under compression and b) charge movement in the circuit during the cycling load.

543210-101-101-101-101-1010

1

t

0.01R

0.1R

1R

10R

100R

Figure 6. Effects of the dimensionless resistance on the dimensionless voltage.

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the resistance value, it becomes more diffi cult for the charge to go through the voltmeter, and the more stranded charge on electrodes yields higher voltage.

In the experiments, the compression LΔ between the two ends of the device is a periodic function of time t , given by

L

L t

Tt T

L T t T T

L t T T

TT T t T T

T T t T T

41 cos , 0

,

41 cos

2, 2

0, 2 2

max

1

2

1

max 1 1 2

max 1 2

1

2

1 2 1 2

1 2 1 2

π

π ( )

( )

Δ =

Δ − ⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥ ≤ <

Δ ≤ < +

Δ − − −⎡⎣⎢

⎤⎦⎥

⎧⎨⎩

⎫⎬⎭

+ ≤ < +

+ ≤ << +

⎧

⎨

⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

(8)

in the fi rst period, where LmaxΔ is the maximum compres-sion, and T T T2 1 2( )= + is the period. For T 0.81 = s, T 1.22 = s, and A PZT = 2.24 mm 2 in the experiment, 6.2 Cm 2e = − − and

2 10 C(Vm)8 1k = × − − , consistent with values in the literature, [ 26 ] Figure 3 c,e,g,i show the voltage V versus time t obtained from Equation ( 6) , and the peaks are plotted in Figure 6 . The theoret-ical results agree well with the experimental fi ndings, including both peaks and shapes of the voltage–time curves. The peak value of the voltage increases with the resistance of the volt-meter. It confi rms that, for piezoelectric devices, the measured output voltages indeed depend on the resistance of the volt-meter. To evaluate the performance of the piezoelectric devices reasonably, the resistance of the voltmeter should be reported in the measurement.

3. Conclusions

In summary, output voltage measurement represents a fun-damental importance in the performance characterization of emerging classes of fl exible and stretchable piezoelectric devices. The literature shows that most of voltage–time curves of piezoelectric devices are characterized by the alternatively positive and negative variations, even though the strain in the piezoelectric material is always positive during the applied cycling load. This phenomenon does not obey the piezoelectric theory for open circuit, which is usually adopted for the quan-titative calculation of peak voltages in the literature. Here, we studied this important problem experimentally and theoreti-cally. Collective results show that the measured output voltage depends on the resistance of the voltmeter. The peak of voltage increases with the increase of the resistance of voltmeter. As a signifi cant conclusion, the resistance value of the measure-ment systems, i.e., voltmeters should be reported in the voltage measurement studies of piezoelectric devices. This conclusion is applicable not only to PZT energy harvester consisting of PZT ribbons, but also to other piezoelectric devices with dif-ferent confi gurations, such as sensors and piezoelectric poly-mers in the form of wire/fi bers. [ 27,28 ] The established model can be also extended to those piezoelectric devices by reana-lyzing the mechanical deformation and piezoelectric behavior. It should be pointed out that the effect described here does not

exist for current measurement because the inner resistance of the ampere meter is usually very small or even zero. Our ongoing work based on the fi ndings here is to develop a new voltmeter with infi nite or approximately infi nite inner resist-ance for precise characterization of the properties of piezoelec-tric devices.

Supporting Information Supporting Information is available from the Wiley Online Library or from the author.

Acknowledgements The authors thank Prof. John A. Rogers of the University of Illinois for his helpful discussions and continued support. C.D. thanks P. Joe for her assistance on experimental part. This work was supported by the National Natural Science Foundation of China (grant 11302038) and Fundamental Research Funds for the Central Universities of China (grant DUT15LK14).

Received: June 4, 2015 Revised: June 25, 2015

Published online:

[1] T. Starner , IBM Syst. J. 1996 , 35 , 618 . [2] C. Dagdeviren , S.-W. Hwang , Y. Su , S. Kim , H. Cheng , O. Gur ,

R. Haney , F. G. Omenetto , Y. Huang , J. A. Rogers , Small 2013 , 9 , 3398 .

[3] C. Dagdeviren , M. Papila , Polym. Compos. 2010 , 31 , 1003 . [4] S. Xu , Y. Wei , J. Liu , R. Yang , Z. L. Wang , Nano Lett. 2008 , 8 , 4027 . [5] J. Liu , P. Fei , J. Zhou , R. Tummala , Z. L. Wang , Appl. Phys. Lett.

2008 , 92 , 173105 . [6] R. Yang , Y. Qin , L. Dai , Z. L. Wang , Nat. Nanotechnol. 2009 , 4 , 34 . [7] S. Xu , Y. Qin , C. Xu , Y. Wei , R. Yang , Z. L. Wang , Nat. Nanotechnol.

2010 , 5 , 366 . [8] G. Zhu , R. Yang , S. Wang , Z. L. Wang , Nano Lett. 2010 , 10 , 3151 . [9] Z. Li , G. Zhu , R. Yang , A. C. Wang , Z. L. Wang , Adv. Mater. 2010 , 22 ,

2534 . [10] A. M. Flynn , S. R. Sanders , IEEE Trans. Power Electron. 2002 , 17 , 8 . [11] X. Chen , S. Xu , N. Yao , Y. Shi , Nano Lett. 2010 , 10 , 2133 . [12] T. Tanimoto , K. Okazaki , K. Yamamoto , Jpn. J. Appl. Phys., Part 1

1993 , 32 , 4233 . [13] E. M. Alkoy , C. Dagdeviren , M. Papila , J. Am. Ceram. Soc. 2009 , 92 ,

2566 . [14] X. Feng , B. D. Yang , Y. Liu , Y. Wang , C. Dagdeviren , Z. Liu ,

A. Carlson , J. Li , Y. Huang , J. A. Rogers , ACS Nano 2011 , 5 , 3326 . [15] Y. Qi , J. Kim , T. D. Nguyen , B. Lisko , P. K. Purohit , M. C. McAlpine ,

Nano Lett. 2011 , 11 , 1331 . [16] C. Dagdeviren , B. D. Yang , Y. Su , P. l. Tran , P. Joe , E. Anderson ,

J. Xia , V. Doraiswamy , B. Dehdashti , X. Feng , B. Lu , R. Poston , Z. Khapley , R. Ghaffari , Y. Huang , M. J. Slepian , J. A. Rogers , Proc. Natl. Acad. Sci. U.S.A. 2014 , 111 , 1927 .

[17] Y. Qi , N. T. Jafferis , K. Lyons Jr. , C. M. Lee , H. Ahmad , M. C. McAlpine , Nano Lett. 2010 , 10 , 524 .

[18] C. Dagdeviren , Y. Shi , P. Joe , R. Ghaffari , G. Balooch , K. Usgaonkar , O. Gur , P. L. Tran , J. R. Cosby , M. Meyer , Y. Su , R. C. Webb , A. S. Tedesco , M. J. Slepian , Y. Huang , J. A. Rogers , Nat. Mater. 2015 , 14728 .

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[19] Y. Duan , Y. Huang , Z. Yin , N. Bu , W. Dong , Nanoscale 2014 , 6 , 3289 . [20] Y. Ding , Y. Duan , Y. Huang , Energy Technol. 2015 , 3 , 351 . [21] L. Persano , C. Dagdeviren , Y. W. Su , Y. H. Zhang , S. Girardo ,

D. Pisignano , Y. Huang , J. A. Rogers , Nat. Commun. 2013 , 4 , 1633 . [22] Y. Qi , M. C. McAlpine , Energy Environ. Sci. 2010 , 3 , 1275 . [23] K.-I. Park , S. Xu , Y. Liu , G.-T. Hwang , S.-J. L. Kang , Z. L. Wang ,

K. J. Lee , Nano Lett. 2010 , 10 , 4939 .

[24] Y. Yang , Y. Zhou , J. M. Wu , Z. L. Wang , ACS Nano 2012 , 6 , 8456 . [25] S. Xu , B. J. Hansen , Z. L. Wang , Nat. Commun. 2010 , 1 , 93 . [26] S. B. Park , C. T. Sun , Int. J. Fracture 1995 , 70 , 203 . [27] J. Fang , H. Niu , H. Wang , X. Wang , T. Lin , Energy Environ. Sci. 2013 ,

6 , 2196 . [28] L. Persano , C. Dagdeviren , C. Maruccio , L. De Lorenzis ,

D. Pisignano , Adv. Mater. 2014 , 26 , 7574 .

Copyright WILEY-VCH Verlag GmbH & Co. KGaA, 69469 Weinheim, Germany, 2015.

Supporting Information

for Adv. Funct. Mater., DOI: 10.1002/adfm.201502280

Measured Output Voltages of Piezoelectric Devices Dependon the Resistance of Voltmeter

Yewang Su,* Canan Dagdeviren,* and Rui Li

1  

Supplemental Material

Measured output voltages of piezoelectric devices depend on the resistance of

voltmeter

Yewang Su, a,b,* Canan Dagdeviren, c,d,* Rui Lie  

a State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences,

Beijing 100190, China

b Department of Civil and Environmental Engineering, Northwestern University, Evanston, IL 60208,

USA

c Department of Materials Science and Engineering, Beckman Institute for Advanced Science and

Technology, and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-

Champaign, Urbana, IL 61801, USA

d The David H. Koch Institute for Integrative Cancer Research, Massachusetts Institute of Technology,

Cambridge, MA 02139, USA

eState Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering

Mechanics, Dalian University of Technology, Dalian 116024, China

* To whom all correspondence should be addressed:

yewangsu@imech.ac.cn (YS); canand@mit.edu (CD)

2  

1. Strain of the PZT ribbon

Figure. 2 and Fig. 5a show the compression of a device with length L that leads to buckling with an

out-of-plane displacement 11 cos 2 2w A x L , where the origin of the coordinate system is at

the center of the device. The bending energy in PI for plane-strain analysis ( 22 0 ) is related to the

curvature w by 22 dPIEI w s , where the integration is over the PI length; 3 12PI PI PIEI E t , PIE

and PIt are the plane-strain bending stiffness, plane-strain modulus, and thickness of PI, respectively.

Following the same approach as in Song et al.[1], minimization of the total energy (sum of bending and

membrane energies) gives the amplitude as 2A L L . The bending moment M in PI is related

to the curvature w by PIM EI w . For the part of PI covered by the PZT ribbons (Fig. S1b), the

local curvature is reduced to compM EI due to the additional bending stiffness of PZT ribbons, where

2

1 1 1

3n i i

comp i i i j neutral j neutral ii j j

EI E t t t y t y t

is the effective bending stiffness of multi-layer

structure (Fig. S1b) with PI as the 1st layer (i=1) and the summation over all n layers, iE and ti are the

plane-strain modulus and thickness of the ith layer, respectively, and

1 1 1

2 2n i n

neutral i i j i i ii j i

y E t t t E t

is the distance from the neutral mechanical plane to the

bottom of 1st (PI) layer. The membrane strain in PZT is the axial strain at the center of PZT ribbons,

and is given by PI compm EI EI w h , where h is the distance from the center of each PZT ribbon to

the neutral mechanical plane of the cross section, as shown in Fig. S1b. For the length of PZT ribbons

much smaller than that of the PI, w is evaluated at the center x1=0 of PZT ribbons as

4w L L L , which gives the membrane strain given in Eq. (1) in the main text.

3  

2. Constitutive relations for PZT

PZT in this system is transversely isotropic with a polarization direction x3 normal to the surface.

Constitutive models give relations among the stress ij , strain

ij , electrical field Ei and electrical

displacement Di as

11 12 1311 11 31

12 11 1322 22 31

13 13 3333 33 33

4423 23 15

4431 31 15

11 1212 12

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0

0 0 0 0 0 2 0 0

0 0 0 0 0 2 0 0

0 0 0 0 0 2 2 0 0 0

c c c e

c c c e

c c c e

c e

c e

c c

1

2

3

E

E

E

, (S1)

11

221 15 11 1

332 15 22 2

233 31 31 33 33 3

31

12

0 0 0 0 0 0 0

0 0 0 0 0 0 02

0 0 0 0 02

2

D e k E

D e k E

D e e e k E

. (S2)

where cij, eij, and kij are the elastic, piezoelectric, and dielectric constants, respectively.

3. Fabrication and voltage measurement of the PZT mechanical energy harvester

The PZT MEH consists of an array of capacitors that are formed from PZT strips with top and

bottom electrodes which are fabricated using the following process. The base material is a multistack

layer of Pb(Zr0.52Ti0.48)O3/Pt/Ti/SiO2 (500 nm/300 nm/20 nm/600 nm) on Si from INOSTEK. A layer of

Au/Cr (200 nm/10 nm), which would become the top electrode, was deposited using e-beam

evaporation. The wafer was then coated in PR (AZ5214E) and photolithographically patterned to

define the top electrodes (50 μm x 2 mm) of each PZT strip. The Au and Cr layers were etched using

Gold etch-type TFA (Transene Company Inc., USA) and CR-7 chrome mask etchant (OM Group,

USA) respectively. The PZT strips with thickness of 500 nm were formed with dimensions of 100 μm

4  

by 2.02 mm by wet etching with a solution of nitric acid (HNO3), buffered hydrogen fluoride (BHF)

and DI water (H2O) with a ratio of 4.51:4.55:90.95 respectively (see Fig. S1A). The PR mask was

hard-baked with a controlled temperature treatment of 80 °C for 5 min, 110 °C for 30 min, and 80 °C

for 5 min. The bottom Pt/Ti electrodes, with final area of 140 μm by 2.02 mm, was patterned by wet

etching with a solution of HCl (hydrochloric acid), HNO3, and DI water with ratio 3:1:4 at 95 °C. A

photolithographically patterned mask was then spun onto the sample to protect the PZT layers while

the SiO2 sacrificial layer was partially removed with diluted HF (hydrofluoric acid) (DI water: 49%

HF = 1:3). The PR mask was removed in hot acetone bath for 3 hours. The PDMS (Sylgard 184, Dow

Corning) stamp was fabricated from a 10:1 ratio mixture of prepolmer and curing agent, and was cured

at room temperature for 24 hours. The stamp was then placed in conformal contact with the strips and

then lifted to remove the device from the Si wafer. A piece of Kapton (75μm, DuPont, USA) was spin-

coated with a layer of PI (poly(pyromellitic dianhydride-co-4,4’-oxydianiline)) amic acid solution

which would serve as an adhesion layer. The device was then transfer-printed onto the Kapton from

the PDMS stamp, followed by coating the sample with another layer of PI to encapsulation the device,

which was cured in a vacuum oven at 250 °C.  A layer of PR (AZ 4620) was spun onto the

Kapton/device and photolithographically patterned to open contact holes for the top and bottom

electrodes, and then developed with diluted AZ 400K developer (AZ Electronic Materials, USA) (DI

water : 400 K developer = 1:2). The contact holes were opened by etching the PI in a March RIE. A

layer of Au/Cr (200 nm/10 nm) was deposited with e-beam evaporation to form the interconnect lines,

followed by encapsulating the entire device with a final layer of PI which was hard-baked at 250 °C in

the vacuum oven. 

The PZT thin film was polled for two hours with a 100kV/cm electric field at 150 °C. The

mechanical stage was constructed with a high-precision linear stage (ATS100-150; Aerotech, Inc;

USA), equipped with a precision ground ball screw, noncontact rotary encoder with 1000 line/rev, and

5  

brushless servomotor to achieve a motion with an accuracy within 0.5μm and a bidirectional

repeatability of ±0.3μm over 150 mm stage motion range. To perform the test cycle, a LabVIEW

(National Instruments Corporation; USA) based program was aimed to maneuver the stage.

Piezoelectric device voltage output was measured by three different multimeters that have different

inner resistance value as following: a 6½ digit USB Multimeter (Signametrics, SMU2055): 34 M , a

semiconductor parameter analyzer (HP 4155C, Agilent): 60 M , and a Personal Daq/3000 Series 16-

bit/1-MHz: 300 M .

References

[1]  J. Song, Y. Huang, J. Xiao, S. Wang, K. C. Hwang, H. C. Ko, D. H. Kim, M. P. Stoykovich, and J. A. Rogers, Journal of Applied Physics 105, 123516 (2009).