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26-Nishida_MEMSacousticEnergy_JMicromech_2006

I NSTITUTE OF P HYSICS P UBLISHING J OURNAL OF M ICROMECHANICS AND M ICROENGINEERING J.Micromech.Microeng.16(2006)S174–S181doi:10.1088/0960-1317/16/9/S02

A MEMS acoustic energy harvester

S B Horowitz1,M Sheplak2,L N Cattafesta III2and T Nishida1

1Department of Electrical and Computer Engineering,Interdisciplinary Microsystems

Group,University of Florida,Gainesville,FL32611-6250,USA

2Department of Mechanical and Aerospace Engineering,Interdisciplinary Microsystems

Group,University of Florida,Gainesville,FL32611-6250,USA

E-mail:nishida@u?.edu

Received2February2006,in?nal form14June2006

Published9August2006

Online at https://www.sodocs.net/doc/4513877211.html,/JMM/16/S174

Abstract

This paper presents the development of a micromachined acoustic energy

harvester for aeroacoustic applications.The acoustic energy harvester

employs a silicon-micromachined circular,piezoelectric composite

diaphragm for electroacoustic transduction.Lumped element modeling,

design,fabrication and characterization of a micromachined acoustic energy

harvester prototype are presented.Experimental results indicate a maximum

output power density of0.34μW cm?2at149dB(ref.20μPa)and suggest

a potential output power density,for this design,of250μW cm?2with an

improved fabrication process.

Nomenclature

a radius of the Helmholtz resonator neck(m)

A eff effective area needed to maintain continuity of

volume velocity(m2)

C aC acoustic compliance of the resonator cavity

(m3Pa?1)

C a

D acoustic compliance of the diaphragm(m3Pa?1) C eb‘blocked’electrical capacitance of the piezoelectric

(F)

C ef‘free’electrical capacitance of a parallel plate

capacitor(F)

c o isentropic spee

d of sound(m s?1)

d31material dependent piezoelectric coef?cient

(C N?1or m V?1)

d A effectiv

e acoustic piezoelectric coef?cient

(m3V?1)

f d resonant frequency dominated by diaphragm(Hz) f HR resonant frequency dominated by Helmholtz

resonator(Hz)

k wavenumber,≡ω/c0(1/m)

k2c electroacoustic coupling factor(1)

L length of the Helmholtz resonator neck(m)

M aD acoustic mass of the diaphragm(kg m?4)

M aDrad acoustic radiation mass of the diaphragm(kg m?4) M aN acoustic mass of the resonator neck(kg m?4)

P acoustic pressure(Pa)

Q quality factor(l)

Q A volume velocity(m3s?1)

r radius of integration(m)r1inner radius of the piezoelectric ring(m)

r2outer radius of the piezoelectric ring(m)

R aDrad acoustic radiation resistance of the diaphragm (kg m?4s?1)

R load load resistance placed across the piezoelectric( ) R aN acoustic resistance of the resonator neck (kg m?4s?1)

R p dielectric loss resistance of the piezoelectric( ) t si thickness of the silicon diaphragm(m)

t p thickness of the piezoelectric ring(m)

V voltage across the piezoelectric ring(V)

V ol cav volume of the Helmholtz resonator cavity(m3)

Z in input impedance of the complete system( )

V ol volumetric displacement caused by de?ection of the diaphragm(m3)

ηoverall system ef?ciency(l)

φeffective acoustic piezoelectric transduction ratio (Pa V?1)

out output electrical power(W)

in input acoustical power(W)

ρmaterial density of each diaphragm layer(kg m?3)ρA areal density of the diaphragm(kg m?2)

ρo density of air(kg m?3)

σTiO

2

tensile stress in the TiO2(Pa)

ωangular frequency(rad s?1)

w(0)center de?ection of the diaphragm(m)

w(r)vertical de?ection as a function of the radius,r(m)

0960-1317/06/090174+08$30.00?2006IOP Publishing Ltd Printed in the UK S174

A MEMS acoustic energy harvester

1.Introduction

We report progress toward a microelectromechanical systems (MEMS)acoustic energy harvester.To enable wireless sensor nodes that are not dependent on replaceable batteries,power needs to be collected locally from the environment.Most energy harvesting efforts have focused on vibrations [1],ambient light [2]and temperature gradients [3]as the environmental energy sources.Acoustic energy is another potential source in certain applications.Acoustic energy harvesting has been demonstrated recently using a mesoscale Helmholtz resonator machined in aluminum (dimensions on the order of 2cm),delivering 25mW to a resistive load at a sound pressure level (SPL)of 152dB (ref.20μPa)[4–6].This acoustic energy may be used to locally power a wireless active liner for suppression of engine noise in turbofan engine nacelles,where SPLs typically reach upwards of 150dB [5].The acoustic environment within an aircraft engine nacelle typically consists of broadband audio-range noise,permeated by large amplitude tones at the blade passage frequency and subsequent harmonics.The density and proximity of Helmholtz resonators within the active liner,however,may preclude the use of mesoscale fabrication approaches.

The goal of this work is the development of a silicon micromachined acoustic energy harvester (AEH),including lumped element modeling,scaling analysis,design,fabrication and characterization.Figure 1shows a schematic of the overall system,which is attached to a plane wave tube (PWT)for testing.Incident acoustic waves impinge on the AEH,shown in the dashed circle.A fraction of the incident acoustic energy is transferred to the harvester where it is converted into an ac voltage,recti?ed,and stored.In the current approach,the AEH utilizes a compliant piezoelectric backplate Helmholtz resonator (HR)to create a coupled resonant system.

This paper is organized as follows:section 2discusses the theoretical modeling of the AEH,including lumped element and ?nite element modeling.Section 3focuses on the fabrication and packaging of the energy harvesting device.The experimental setup for characterizing the energy harvester is presented in section 4.The results of these

experiments

Figure 1.Schematic of overall AEH.The overall AEH consists of a compliant piezoelectric backplate Helmholtz resonator for energy conversion,power electronics for recti?cation and regulation,and battery for energy storage.The AEH is attached to a PWT to provide a known acoustic input.

are discussed in section 5.Finally,concluding remarks are provided in section 6.

2.Theoretical background

Today’s designer of energy harvesting systems is faced with many choices and challenges.Most fundamental of these is the choice of energy domain from which to extract energy (e.g.,mechanical,acoustical,thermal,optical,etc)[1–6].In addition,the designer must choose to optimize the system for either broadband or resonant operation,or some combination of them.Often,however,these design decisions will be dictated by the application.Furthermore,an energy harvester can potentially be optimized for one of a number of output parameters (e.g.,maximum output power,ef?ciency,voltage,current,power density,etc),many of which limit optimization of the others.There are also many available modeling techniques,such as lumped element modeling (LEM),which offers physics-based insight into scaling behavior,and ?nite element modeling (FEM),which provides accurate numerical calculations of device behavior.The concept behind LEM is to reduce the complexity of an analytical or numerical expression by lumping a distributed system into discrete elements based on their interaction with energy [7].Whenever dealing with more than one lumped element,the concept of power ?ow between the elements must be considered.The net power ?ow is computed using conjugate power variables.In acoustic systems,the conjugate power variables are pressure,P ,and volume velocity,Q A .

For the work presented here,a combination of LEM and FEM was used to predict device behavior and facilitate the design,thereby incorporating advantages of both.First,the overall model of the system was developed using LEM and represented as an equivalent electrical circuit.FEM was used to verify lumped parameters generated via LEM.Once these values were found,the overall system performance was analyzed.

2.1.Lumped element modeling

The structure presented here consists of a cavity connected by a small opening or neck to the environment.Together,

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S B Horowitz et al

t diaphragm

Figure 2.The EMHR consists of a compliant

piezoelectric-composite diaphragm serving as a wall of a HR.The inner and outer radii of the piezoelectric ring are r 1and r 2,

respectively.The radius of the circular diaphragm is r 2,while t si and t p are the thicknesses of the silicon diaphragm and piezoelectric ring,respectively.The HR neck has a radius of a and a length of L .

these form a HR;however,we replace the back wall of the cavity with a compliant composite diaphragm possessing a piezoelectric annular ring to form an electromechanical HR (EMHR),as shown in ?gure 2.

An equivalent circuit [5]of the EMHR consists of the mass-spring-damper equivalent of the HR neck and cavity (M aN ,C aC ,R aN )augmented with the lumped diaphragm mass,M aD ,and compliance,C aD ,radiation resistance,R aDrad ,and mass,M aDrad ,as shown in ?gure 3.The electroacoustic transduction is represented by an ideal transformer representing the effective acoustic piezoelectric transduction ratio,φ,the blocked electrical capacitance,C eb ,dielectric loss resistance,R p ,and load resistance,R load .In the above notation,the ?rst subscript letter denotes the energy domain (e.g.,‘a’for acoustic and ‘e’for electric),while the remainder describes the functionality of the element (e.g.,‘D’for diaphragm,‘N’for neck,‘C’for cavity and ‘rad’for radiation).The load resistance,R load ,approximates the input impedance of the energy harvesting circuitry shown in ?gure 1.

The three components of the HR,M aN ,C aC and R aN ,are unchanged from those of a conventional HR [8].The additional components arise due to the presence of the composite piezoelectric diaphragm.The acoustical diaphragm compliance,C aD ,is found by placing a short circuit (V =0)across the piezoelectric and subsequently computing the potential energy stored in the diaphragm for an applied pressure,P ,and is thereby de?ned by [9]

C a

D = V ol P

V →0= r

20w(r)|V →02πr d r P ,(1)where V ol is the volumetric displacement and w(r)is the

de?ection as a function of the radius,r .The acoustic diaphragm mass,M aD ,is determined by equating the lumped

Figure https://www.sodocs.net/doc/4513877211.html,plete equivalent circuit for EMHR AEH.

kinetic energy of a point mass moving with the center velocity of the diaphragm to the total kinetic energy of the vibrating diaphragm and is therefore given by

M aD =2π r 2

0ρA w(r)|V =0 V |V =0 2

r d r,(2)

where ρA is the areal density of the composite plate de?ned

by integrating the density,ρ,through the thickness,

ρA = z 2

z 1

ρd z.(3)

An additional term of importance,the effective acoustic piezoelectric coef?cient,d A ,relates the free volumetric displacement to the applied voltage,when the differential pressure is zero,and is de?ned by

d A = V ol V

P →0= r 20w(r)P →02πr d r V .(4)Then,the electroacoustic transduction factor,φ,is

φ=?d A C aD

.(5)

Additionally,the radiation resistance can be found by approximating the de?ection of the diaphragm as a piston in an in?nite baf?e [9],for kr 2 1(where k =ω/c is the wavenumber and ωis the angular frequency)as

R aDrad ~=(kr 2)2ρo c o 2A eff

,(6)

while the radiation mass is approximated as

M aDrad ~=

8kr 2ρo c o

3πωA eff

,(7)where ρo and c o are the density and the isentropic speed of sound of air,respectively,and A eff is the effective area to maintain continuity of volume velocity de?ned by

A eff = r 2

w(r)2πr d r

w(0)

,(8)and w (0)is the center de?ection of the diaphragm.

Regarding the electrical elements,C eb ,the electrical capacitance when the diaphragm is blocked from moving,is given by

C eb =C ef 1?k 2

c ,(9)where C ef is the ‘free’electrical capacitance of a parallel plate capacitor,an

d k 2

c

is the electroacoustic coupling factor de?ned by

k 2c

=d 2A C ef C aD

.(10)

Physically,the coupling factor,k 2

c ,represents the fraction of energy that is ideally couple

d between th

e acoustical and electrical energy domains.It does not account for losses in

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A MEMS acoustic energy harvester

the system that are unrelated to the actual coupling.It is a function of the effective acoustic piezoelectric coef?cient,d A ,which represents coupled energy,and the two elements which store potential energy associated with the transduction,C ef and C aD .The coupling factor is therefore related to the ideal ratio of the coupled energy to the stored energy,but does not account for losses [7]https://www.sodocs.net/doc/4513877211.html,posite plate modeling

In order to obtain the equivalent circuit parameters related to the diaphragm mechanics,an analytical model was employed for a piezoelectric composite circular plate [9,10].Using this approach,analytical modeling was accomplished by dividing the structure into two portions:an inner circular plate surrounded by a clamped annular composite ring with matching boundary conditions at the interface.The matching conditions consist of equal moments and forces at the interface as well as equal slope and transverse displacement,resulting in a piecewise de?ection equation for each region.Next,the lumped element values are found using the computed de?ection.Shown in ?gure 4are the effective acoustic short-circuit compliance (a )and mass (b )as a function of the radius ratio,r 1/r 2,and the thickness,t p .The thickness range,as shown,was constrained by physically realizable values for the chosen piezoelectric material and deposition method.

2.3.System analysis

Once all the lumped element values are known,the overall system behavior can be analyzed.One important ?gure of merit for an energy harvester is the overall system ef?ciency,η,de?ned as the ratio of output electrical power, out ,to input acoustical power, in ,given by

Re {η}=Re { out }

Re { in .(11)

The theoretical ef?ciency was calculated for an illustrative set of dimensions and is plotted in ?gure 5for an assumed incident pressure of 1Pa (94dB).The ef?ciency of the

-12

r 1/r 2

C a

D [m 5/N ]

500

10001500200025003000

3500r 1/r 2

M a D [k g /m 4]

(a )

(b )

Figure 4.Effective acoustic short-circuit compliance (a )and mass (b )as a function of r 1/r 2and t p .For illustrative purposes,in these calculations,t s =3μm,r 2=2mm,and t p =0.6,1.2,1.8,2.4,3.0(μm ).

Figure 5.Simulated magnitude of the acoustic energy harvester ef?ciency.(L =3.18mm,a =2.36mm,V ol cav =1950mm 3,t s =3μm,t p =0.266μm,r 2=1.95mm,r 1=1.85mm.)

composite plate alone (without HR)exhibits a single peak at the diaphragm resonance (3.7kHz),while the ef?ciency of the coupled EMHR has two peaks [11],one,at 1.8kHz,due primarily to the HR and the other,at 3.9kHz ,due primarily to the diaphragm.By designing these peaks to occur at one of the blade passage frequencies,where acoustic energy is most available,the amount of harvested energy can be increased.

Under the constraint of a purely resistive load presented by the energy harvesting circuitry,the output power,

out =V 2/R load ,

(12)

is maximized when the load resistance is equal to the magnitude of the output impedance [4,5].Theoretical values for the output power were then computed as a function of load resistance when the composite plate alone (diaphragm)and the EMHR (diaphragm /HR)are excited at their respective resonant frequencies,3.7kHz and 3.9kHz.The output power exhibits a peak,as expected,for load resistances equal to the magnitude of the Th′e venin impedances (1.03k and 1.09k )as shown in ?gure 6.Additionally,the acoustical input power, in ,included on this graph for reference,can be obtained from the input acoustic pressure,P ,and the input impedance,Z in [12],and is given by

Re { in }=P 2

Re {Z in }

.

(13)

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S B Horowitz et al

10

2

10

3

10

4

10

-8

10

-7

10

-6

10

-5

10

-4

Load Resistance [?]

P o w e r D e l i v e r e d t o L o a d [W ]

Πin

- Diaphragm Πin

-Diaphragm/HR Πout

- Diaphragm Πout

- Diaphragm/HR Figure 6.Simulated output power versus load resistance.(f HR =3.9kHz,f d =3.7kHz,P =1Pa or 94dB re 20μPa.)

3.Fabrication and packaging

The fabrication process ?ow (?gure 7)utilizes the epitaxial silicon layer of a silicon-on-insulator (SOI)wafer as the primary mechanical material of the diaphragm and a ring-shaped layer of lead zirconate titanate (PZT)as the piezoelectric material [12].The energy harvester consists of a 3μm thick,silicon diaphragm with a thin ring of PZT placed near the clamped boundary of the diaphragm as shown in ?gure 2.The 270nm thick PZT was sol–gel deposited above a patterned 220nm Ti /Pt layer,serving as a bottom electrode,and wet etched using a patterned 180nm Pt layer that also serves as the top electrode.The entire ring structure is separated from the silicon diaphragm by a 100nm thick TiO 2layer that serves as a diffusion barrier for the PZT during processing.The TiO 2layer was created by evaporating a titanium layer and oxidizing at 650?C.An unfortunate result of this particular step was the generation of a large in-plane tensile stress which degraded the device performance.The piezoelectric ring was placed near the clamped boundary since the largest stress concentrations occur in this region during

(a )(b )(c )(d )(e )

(f )

(g )

(h )

Figure 7.Concise process ?ow for the MEMS acoustic energy harvester.(a )Deposit 100nm of Ti and oxidize to TiO 2.(b )Deposit and liftoff Ti /Pt (40/180nm).(c )Spin PZT 52/48solution and pyrolize (four layers for 267nm total).(d )Deposit and liftoff Pt (180nm).(e )Wet etch PZT in 3:1:1of (NH 4)HF 2/HCl /DI water.(f )Spin and pattern thick photoresist on back.(g )Deep reactive ion etch to buried oxide (BOX)layer.(h )Ash resist and wet etch BOX.

Figure 8.Lucite package with leads and ?ush mounted chip.All dimensions in mm unless otherwise marked.

5.25 mm

(a )

38 mm

(b )

Figure 9.(a )Fabricated MEMS AEH chip.(b )Packaged device.

de?ection,leading to a higher transduction capability and a correspondingly higher sensitivity.Furthermore,the ring shaped piezoelectric facilitates the connection of electrical lines to and from the bond pads without having to traverse across the diaphragm.

The chip was ?ush mounted in a Lucite package shown in ?gure 8and bonded with epoxy.The electrical connections to the package leads were accomplished via short lengths of wire that were bonded using silver epoxy (Epotek H20E)on the chip bond pads as well as to the copper pads on the package.A fabricated AEH chip,shown in ?gure 9(a ),was packaged

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A MEMS acoustic energy harvester

2.54 cm

BMS

Figure10.Experimental setup for energy harvesting measurements.

Table1.Geometric properties of tested devices.

Device r1(mm)r2(mm)t p(μm)t si(μm)

1 1.115 1.2000.2673

2 1.685 1.8000.2673

as shown in?gure9(b).As such,the fabricated chip was used without the Helmholtz resonator.After packaging,the chip was poled at5.33V(20Vμm?1)for30min.

4.Experimental setup

The packaged device was mounted in a2.54cm×2.54cm acoustic PWT that was acoustically driven by a BMS4590P coaxial compression driver,as shown in?gure10[12]. Using a Stanford Research Systems SRS785Dynamic Signal Analyzer,the AEH resonant frequency values were obtained ?rst.The SRS785recorded500averages of800frequency bins over a frequency span from dc to25.6kHz.The measured resonant frequencies are13.6kHz and5.2kHz for two MEMS AEH designs,device1and device2,with geometries as de?ned in table1.The choice in these designs was governed by the desire to achieve a resonant frequency within a measurable range,while maintaining a manufacturable geometry.

Once the resonant frequencies were found,the optimal resistance for maximum power transfer at resonance was determined.The source was changed to a sinusoidal signal at the resonant frequencies for the respective devices.The output voltage was then measured while the load resistance was varied from46.4 to1.0M .From the measured output voltage,the output power was then calculated via equation(12).

Additionally,a Br¨u el and Kj?r Pulse Multi-Analyzer System recorded acoustic signals from two Br¨u el and Kj?r type4138microphones.The microphone positions were then switched and the measurements averaged to remove any differences due to the individual microphone calibrations.This averaged frequency response was then used with the standard two-microphone method(TMM)to determine the acoustic impedance[13].Once the acoustic impedance was known, equation(13)was then used to calculate the input power. 5.Results and discussion

The experiments were performed on the two devices listed in table1and packaged without a HR as shown in?gure9.

10

1010101010 10

10

10

10

10

10

10

Load Resistance [?]

P

o

w

e

r

D

e

l

i

v

e

r

e

d

t

o

L

o

a

d

[

W

]

Figure11.Measured power delivered to the load versus load resistance,compared to theory.Note that device1and device2data were taken with0.804Pa and2.28Pa input signals,respectively. For comparison to device1,the device2data and corresponding theory were adjusted down to an equivalent power based on a

0.804Pa rms input.

The output power delivered to the load was calculated and plotted versus the value of the load resistance,as shown in ?gure11.The?gure is overlaid with the theoretical values for comparison.The theoretical values were computed using a d A that was determined from an experimentally measured mode shape that differed from the predicted mode shape due to large residual stress effects[12].The experimentally determined resistance for maximum power for both of these devices was found to be980 .

Note that the position of the peak in the measured power curves,which occurs when the load resistance is nearly equal to the magnitude of the output impedance,was fairly well predicted by theory,whereas the magnitude of the measured peak was not well predicted.This suggests that the power conversion ef?ciency,which strongly affects the output power, was not as well predicted as the output impedance.Most likely, this arises from uncertainties in d A due to uncertainties in the PZT material quality,the poling capability and the residual stress,which affect the conversion ef?ciency,whereas the output impedance is dominated by the electrical capacitance of the piezoelectric and is a fairly well controlled quantity. It is also useful to note that the smaller of the two devices yields the larger output power.This results from the larger value of kr2arising from the higher resonant frequency.The larger value of kr2leads to a higher radiation resistance and correspondingly better coupling to the PWT.The transmission of acoustic energy from the PWT to the AEH is maximized when the acoustic input impedance of the AEH is equal to the acoustic impedance of the PWT.Under this condition,acoustic re?ections are eliminated at the interface.At resonance,the input impedance of the AEH is governed solely by the resistive elements.Due to the geometries of both the PWT and AEH, the impedance of the PWT is an order of magnitude larger than the AEH.Thus,an increase in the radiation resistance improves the impedance matching and so will reduce the amount of re?ected acoustic energy,thereby increasing the energy available for harvesting.

Next,using the resonant frequency and optimal load resistance measured previously,the input signal was steadily

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S B Horowitz et al

10

10

10

10

-8

10-6

Acoustic Input Pressure [dB]

P o w e r D e l i v e r e d t o L o a d [m W ]

10

10

10

10

-8

10

-6

10

-4

Acoustic Input Pressure [dB]

P o w e r D e n s i t y [W /c m 2]

(a )

(b )

Figure 12.Measured power (a )and power density (b )delivered to load versus acoustic pressure,compared to theory.

increased in amplitude while the output voltage was measured.The output voltage was found to be linear up to 125dB for device 1and up to 133dB for device 2and was seen to range between 22μV and 4.6mV .The power delivered to the load was then found (?gure 12(a ))based on the voltage and resistance measurements.For the theoretical overlays in these ?gures,a linear model was employed and was therefore not expected to accurately model the devices at suf?ciently high SPLs.

The power density was then calculated based on a square unit cell with lateral dimensions equal to the diameter of the diaphragm.The resulting values are shown in ?gure 12(b )and are again overlaid with theoretical values.Note from the graph that the maximum power density measured was around 0.34μW cm ?2for 149dB,which is considerably lower than the available acoustic power density,80mW cm ?2over the 6.45cm 2cross-sectional area of the PWT at the acoustic pressure of 149dB.This available power density was calculated from the acoustic input pressure and the cross sectional area of the PWT.The output power density was also lower than was measured for a similar mesoscale device,capable of producing 1.15mW cm ?2for an acoustic input pressure of 157dB [4].Finally,the ef?ciency,η= out / in ,was calculated for each of the devices.The ef?ciency was found to be fairly constant near 0.012%for device 1and 4×10?4%for device 2in the linear regime as a function of pressure.For comparison,the mesoscale devices demonstrated an overall ef?ciency of 0.24%.

A question then arises regarding the origin of the low ef?ciency and whether improvements in either the manufacturing or design of the devices could improve the ef?ciency,and thereby the output power.Several issues were faced during the fabrication process that limited the ef?ciency of the devices.First,the materials and processes led to a large residual stress in several layers of the device,most notably the titanium dioxide,as discussed above.The effect of this large tensile stress,σTiO 2,is threefold:(1)an alteration of the de?ection mode shape of the devices leading to a stiffening effect and a resulting decrease in C aD and d A ,(2)a large,nonlinear,initial de?ection of the diaphragm,and (3)a

decrease in the remanent polarization and a resulting decrease in the piezoelectric coef?cient.The power density is then reduced by a factor of 4.3from the zero-stress case.10

101010

-8

10-6

10

-4

10-2

Acoustic Input Pressure [dB]

P o w e r D e n s i t y [W /c m 2]

Figure 13.Currently and potentially achievable power density for device 2under improved fabrication conditions.

A second issue arising from the fabrication was overhanging metal on the electrodes that created short circuits under high electric ?elds.This ?eld limitation imposed a maximum poling voltage of 5.34V ,or 20V μm ?1and limited the resulting remanent polarization to roughly 6.26μC cm ?2.The poling limitation reduced the power density by a factor of 24.6versus a typically poled device.The ?nal fabrication issue concerns the piezoelectric material and the process by which it is deposited on the wafer.The piezoelectric coef?cient,d 31,relates electrical displacement to applied mechanical stress in a structure undergoing bending [14].The particular sol–gel technique that was employed produces a typical d 31of ?50pC N ?1,whereas other variations of the sol–gel process can produce a ?lm with a d 31of ?110pC N ?1[15].The output power density was reduced by a factor of 2.8as a result of the lower value of d 31as compared to other reported PZT thin ?lms.Finally,if the quality factor,Q ,were increased from a measured value of 10for device 2to a realistically achievable value [16]of 25,then the output power density would increase by a factor of 2.5.

Provided that these sources of inef?ciency are addressed,including the PZT material quality,the poling capability and the residual stress,the overall power density would increase by an estimated factor of 740.The resulting power density curve is shown in ?gure 13overlaid with the currently achievable results.With these improvements,at 149dB,the estimated

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A MEMS acoustic energy harvester

output power density would be on the order of250μW cm?2 and the overall ef?ciency would be8.8%for device1and 0.29%for device2,compared to the mesoscale value of0.24%.

6.Conclusions

The development of an AEH for aeroacoustic applications that employs a micromachined piezoelectric diaphragm was presented.Theoretical aspects of the design were addressed, along with a brief overview of the fabrication process and packaging scheme.Preliminary energy harvesting experiments indicate a power density of0.34μW cm?2for an acoustic input of149dB.Furthermore,calculations indicate a potentially achievable power density of250μW cm?2at 149dB using the same design but with improved fabrication. While the results show no scaling advantage to miniaturization, the smaller form factor makes this energy harvester an enabling technology for space-constrained applications such as the wireless active liner for aircraft engine nacelles. Acknowledgments

Financial and fabrication support for this research was provided by Sandia National Labs and monitored by Kent Pfeifer.The authors are also grateful for signi?cant fabrication assistance provided by Stephanie Jones of Sandia National Labs.Finally,the authors are grateful for clean-room access provided by the Army Research Lab.

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