Modeling of Metal-based Piezoelectric MEMS Energy Harvesters Yuichi Tsujiura, Eisaku Suwa, Fumiya Kurokawa, Hirotaka Hida, and Isaku Kanno

Department of Mechanical Engineering, Kobe University 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, JAPAN

Abstract: We fabricated a piezoelectric MEMS energy harvester (EH) of Pb(Zr,Ti)O3 (PZT) thin film on stainless steel cantilever. The use of metal substrates makes it possible to fabricate thin cantilevers owing to a large fracture toughness compared with Si substrates. The PZT thin film was directly deposited onto 50-μm-thick stainless steel substrate by rf-magnetron sputtering. By attaching a tip mass (weight: 480 mg) to the substrate, the resonant frequency of the cantilever (length: 10 mm, width: 10 mm) was dropped to about 75 Hz. From X-ray diffraction (XRD) measurement, we confirmed that the PZT thin film on Pt-coated stainless steel substrate had a perovskite structure with a random orientation. The relative dielectric constant εr and transverse piezoelectric coefficient e31,f were measured to be 650 and −1.7 C/m2, respectively. From the evaluation of the power generation performance of the PZT thin-film EH, we obtained a large average output power of 1.1 μW under vibration at a low frequency of 75 Hz (acceleration amplitude: 5 m/s2, load resistance: 20 kΩ). Moreover, the experimental output voltages with open circuit state were in good agreement with the theoretical values calculated using theoretical equation.

1. INTRODUCTION

In recent years, there have been a lot of studies on energy

harvesters (EHs) made of piezoelectric thin films functioning as power sources for small electronic devices such as autonomous wireless sensor nodes [1-3]. By using EHs instead of primary batteries, it is possible to produce long life and maintenance-free power sources. As vibrational energy widely exists in the environment, it is therefore particularly useful in areas where solar power cannot be used. Although the power consumed by small electronic devices has dropped to tens to hundreds of μW [4], the power generated by EHs is still insufficient and improvements in power generation efficiency are strongly demanded.

Vibration generators are broadly classified into three types: electromagnetic, electrostatic, and piezoelectric systems [4]. Among these types, piezoelectric ones have the simplest structure and the highest power density [5]. Furthermore, piezoelectric thin films are compatible with microelectromechanical systems (MEMS) process. Therefore, it is advantageous for piezoelectric EHs to be integrated into microdevices. Piezoelectric MEMS EHs usually have the structure of unimorph cantilevers of Pb(Zr,Ti)O3 (PZT) thin films on the Si substrates. However,

one of the problems is the fracture toughness of the cantilevers at a resonance because PZT/Si unimorph cantilevers are brittle materials. Furthermore, conventional MEMS EHs have a higher resonant frequency of more than 1 kHz because of the small size of the resonators, although the frequency of environmental vibrations is generally less than 200 Hz [4].

In this study, we fabricated the piezoelectric MEMS EH using a metal substrate to enhance fracture toughness. In addition, a low resonant frequency can be achieved by thin metal cantilever with large tip mass. We deposited the PZT thin film directly onto stainless steel substrate by rf-magnetron sputtering. Subsequently, we measured the frequency response, load resistance dependence, and acceleration dependence of the PZT thin-film EH to evaluate power generation performance.

2. DEVICE FABRICATION

We fabricated the piezoelectric MEMS EH of the PZT

thin film deposited on the ferritic stainless steel (SUS430) substrate using rf-magnetron sputtering. The coefficients of thermal expansion (CTE) of the PZT thin film and SUS430 are reported to be about 9.0 × 10−6 K−1 and 11.4 × 10−6 K−1, respectively [6,7]. Considering that the CTE of typical austenitic stainless steel (SUS304) is 18.4 × 10−6 K−1, the small difference in CTE between the PZT thin film and SUS430 can mitigate the initial bending of the unimorph cantilever.

Prior to PZT thin film deposition, Pt/Ti bottom electrodes and a (Pb,La)TiO3 (PLT) seed layer were deposited on the 50-μm-thick SUS430 substrate at the substrate temperature of 500 ~ 650°C by rf-magnetron sputtering. Then, the PZT thin film with a composition near the morphotropic phase boundary (MPB) of Zr/Ti = 53/47 was deposited on the substrate using an rf-magnetron sputtering. The sputtering conditions of the PZT thin film on PLT/Pt/Ti/SUS430 substrate are listed in Table 1.

Table 1: Sputtering conditions of the PZT thin film.

Parameter Conditions Substrate PLT/Pt/Ti/SUS430 Target [Pb(Zr0.53,Ti0.47)O3]0.8 + [PbO]0.2

Growth temperature [°C] 600 Gas composition Ar(9.0 sccm) + O2(1.0 sccm) Gas pressure [Pa] 0.4 RF power [W] 160 Sputtering time [min] 180

The substrate was heated to around 600°C, and deposition was performed under a mixed gas atmosphere of Ar/O2 with a flow of 9.0/1.0 sccm. The thickness of the PZT thin film was 3.55 μm. The Pt top electrode was prepared through a shadow mask. Annealing treatment was performed at the temperature of 650°C. After that, a metal tip mass (weight: 480 mg) was attached to the back-side of the unimorph cantilever.

Figure 1 shows a photograph of the PZT thin-film EH (length: 10 mm, width: 10 mm) based on SUS430 substrate with a tip mass (weight: 480 mg) and cross-sectional image of the PZT thin-film EH. We can confirm the unimorph cantilever are straight with little initial bending.

3. CHARACTERISTICS OF PZT THIN FILM

We evaluated the crystal structure of the PZT thin film

using X-ray diffraction (XRD) measurement. Figure 2 shows XRD patterns of the PZT thin film on the SUS430 substrate. The diffractions of the perovskite PZT with a random orientation were clearly observed.

We then measured the dielectric properties of PZT thin film using an LCR meter. The relative dielectric constant εr was as low as 650, which is lower than that of the PZT thin film on Si substrate (εr ~ 1000). The low relative dielectric

constant of the PZT thin film is attributed to the in-plane

compressive stress produced by the difference in CTE between the PZT thin film and the SUS430 substrate [8]. The dielectric loss tan δ was 0.059.

The transverse piezoelectric properties of the PZT thin film were assessed by considering the inverse piezoelectric effect for the unimorph cantilevers [9]. We applied a unipolar sinusoidal electric voltage across the top and bottom electrodes at a frequency sufficiently lower than the resonant frequency of the cantilever, and measured cantilever displacements using a laser Doppler vibrometer. Figure 3 shows the cantilever displacements and the transverse piezoelectric coefficient e31,f as functions of applied voltage from 1 to 10 Vp-p. The laser beam was focused at 9.0 mm from the fixed end of the cantilever. From the relationship between the measured cantilever displacement and the applied voltage, the e31,f was calculated using [9]

VLEh

es

ss

2

2

f,31 13 (1)

where hs, Es, νs are the thickness, Young’s modulus, and Poisson’s ratio of SUS430; L, V, and δ are the distance from the fixed end of the cantilever, applied voltage, and cantilever displacement, respectively. Young’s modulus and Poisson’s ratio of SUS430 are 200 MPa and 0.27, respectively. From Eq. (1), the e31,f was calculated to be about −1.7 C/m2 (see Fig. 3).

The figure of merit (FOM) for the power generation of the PZT thin-film EH was determined using [10]

r

2f31,e

FOM (2)

For PZT thin films on SUS430 substrate, FOM was calculated to be about 4.45 × 10−3, which was quite lower than that of the PZT thin film on Si substrate (FOM: 2.98 × 10−2, e31,f: -5.18 C/m2, εr: 900) [11].

Figure 2: XRD patterns of the PZT thin film deposited on PLT/Pt/Ti/SUS430 substrate.

20 30 40 50101

102

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2 [deg]

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nsity

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S]

(001

)PZT (1

01)P

ZT

(111

)PZT

(111

)Pt

(002

)PZT

(102

)PZT

Figure 1: (a) A photograph of the PZT thin-film EH based on SUS430 substrate with a tip mass. (b) Cross-sectional image of the PZT thin-film EH.

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]

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/m2]

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Figure 3: Cantilever displacements and transverse piezoelectric coefficient e31,f as functions of applied voltage for PZT/SUS430 unimorph cantilever.

4. POWER GENERATION PERFORMANCE

Figure 4 shows a schematic diagram of the measurement

setup for a vibration EH. The EH was mounted on the vibration exciter and the acceleration pickup was attached to the base of the cantilever for monitoring the acceleration amplitude. The top and bottom electrodes of the PZT thin film were connected to a load resistance and the generated voltage was measured using a frequency response analyzer (FRA). We evaluated the power generation performance (frequency response, load resistance dependence, and

acceleration dependence) of the PZT thin-film EH based on SUS430 substrate.

Figure 5 and 6 show the frequency response of output voltage with open circuit state (R = 1 MΩ) and vibration amplitude of the PZT thin-film EH, respectively. We swept up the excitation frequency, and the output voltage and vibration amplitude were respectively measured using a FRA and a laser Doppler vibrometer at each vibration acceleration. The vibration amplitude was measured at the center of gravity of the tip mass (8.5 mm from the fixed end of the cantilever). From Fig. 5 and 6, the nonlinear resonance behavior due to the softening spring effects was gradually appeared with increasing the vibration acceleration. Resonance curves of the output voltage and the vibration amplitude were in good agreement. Under vibration of 75 Hz and 5 m/s2, the output voltage and the vibration amplitude reached 326 mV and 435 μm, respectively.

Figure 7 shows the output power and the output voltage as functions of load resistance at the resonant frequency under the acceleration of 5 m/s2. The averaged output power (P = V2/2R) reached 1.1 μW at the optimum load resistance of 20 kΩ. We define the power density as the maximum output power divided by the active area of the cantilever, and the power density was calculated to be 1.1 μW/cm2.

Figure 8 shows the resonant frequency and the Q factor as functions of vibration acceleration. Both the resonant frequency and the Q factor decreased with increasing the vibration acceleration. The Q factor was evaluated as vibration magnification at resonance. Figure 9 shows the cantilever displacements at each position from the fixed end of the cantilever. Cantilever displacements linearly increased with increasing the vibration acceleration.

Theoretical values of the output voltage with open circuit state of unimorph cantilever were calculated using [12]

smss

mspss

lllllthe

V34

31 2

2

r0

f,31 (3)

222r

0

36434

2 mmss

msss

lllllll

fQa

(4)

Figure 4: Experimental setup for measuring power generation performance of a vibration EH.

60 65 70 75 80 85 900

100

200

300

400

Frequency [Hz]

Out

put v

olta

ge (o

pen)

[mV] 0.5 [m/s2]

1 [m/s2] 2 [m/s2] 3 [m/s2] 5 [m/s2]

Figure 5: Output voltage with open circuit state of the PZT thin-film EH as a function of frequency at each vibration acceleration.

60 65 70 75 80 85 900

100

200

300

400

500

Frequency [Hz]

Vibr

atio

n am

plitu

de [

m] 0.5 [m/s2]

1 [m/s2] 2 [m/s2] 3 [m/s2] 5 [m/s2]

Figure 6: Vibration amplitude at 8.5 mm from the fixed end of the cantilever as a function of frequency at each vibration acceleration.

1 10 1000

0.4

0.8

1.2

0

100

200

300

Load resistance [k ]

Output voltage [m

V]O

utpu

t pow

er [

W]

Output power Output voltage

Figure 7: Output power and output voltage of the PZT thin-film EH as functions of load resistance at 75 Hz and 5 m/s2.

where tp, ls, lm, and δs are the thickness of the PZT thin film, the length of the beam and tip mass, and the cantilever displacement at the boundary between the beam and tip mass, respectively; Q, a0, and fr are the Q factor, vibration acceleration, and resonant frequency, respectively.

Figure 10 shows the output power and the output voltage with open circuit state at resonant frequency and optimum load resistance as functions of vibration acceleration. Experimental output voltages were in good agreement with

theoretical values calculated using Eq. (3). The output power was quadratically increased with increasing the vibration acceleration. From these results, output voltage can be expected from the dielectric and piezoelectric properties of the PZT thin film and the vibrational characteristics of the cantilever.

5. CONCLUSIONS

In this study, we presented the fabrication and the

evaluation of piezoelectric MEMS EHs of the PZT thin film based on SUS430 cantilever. The PZT thin film was directly deposited on Pt-coated 50-μm-thick SUS430 substrate by rf-magnetron sputtering. The PZT thin film has a perovskite structure with a random orientation. The relative dielectric constant εr and the transverse piezoelectric coefficient e31,f were 650 and −1.7 C/m2, respectively. From the evaluation of the power generation performance of the PZT thin-film EH (length: 10 mm, width: 10 mm, weight of tip mass: 480 mg), the nonlinear resonance behavior due to the softening spring effects was observed around the resonant frequency of the cantilever. The maximum output power was 1.1 μW under the vibration of 75 Hz, 20 kΩ, and 5 m/s2.

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onan

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Figure 8: Resonant frequency and Q factor of the PZT thin-film EH as functions of vibration acceleration.

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Figure 9: Cantilever displacements at each position from fixed end of the cantilever.

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Figure 10: Output power and output voltage with open circuit state of the PZT thin-film EH at resonant frequency and optimum load resistance as functions of vibration acceleration.