A Survey on Piezoelectric Ceramics for Generator Applications

Thomas Rodigw and Andreas Schonecker

Fraunhofer IKTS, WinterbergstraXe 28, 01277 Dresden, Germany

Gerald Gerlach

TU Dresden, IFE, HelmholtzstraXe 18, Dresden, Germany

Piezoelectric generators enable maintenance-free power supplyfor integrated electronics in smart system applications. The ma-jority of publications consider the aspect of power transfer elec-tronics; however, the influence of the transducer materials wasrarely described. Recently, material characteristics received in-creased attention from the ceramics community. We set the fo-cus of the present paper to commercially available piezoelectricceramics. Different figures of merit are derived from systemanalysis using electromechanical modeling. They allow for thedescription of typical load scenarios and commercial piezoce-ramics. Derived rules are expected to be helpful for guiding ce-ramic engineers and system designers to succeed in improvedgenerator solutions.

I. Introduction

RECENT developments in sensing technology, electronics, andwireless communication together with the progress in the

harvest of electrical energy from sustainable sources, such assunlight, heat, and mechanical vibrations, enable a new gener-ation of smart structures and systems.1 Application scenariosinclude wireless, self-powered sensor nodes, which are capable ofreporting on operating conditions and monitoring ‘‘life experi-ence’’ to account for the current state of health. Growing mar-kets are seen in energy and environmental management,building management, process control, condition monitoring,logistics, and asset tracking.2

Wireless sensor networks require a flexible and maintenance-free power supply that works for decades. The use of solid-stategenerators has proved to be a competitive approach. In com-parison with other energy converters, the piezoelectric generatorfeatures a high-energy density at relatively low mechanicalstrain–stress levels.3 Furthermore, mechanical vibration energyis available at almost all locations allowing for the general im-plementation of piezoelectric power supply.

Historically, piezoelectric generators made of piezoceramichave existed since 19594 (Table I). An electric spark generatorfor the ignition of flammable or explosive gas mixtures5 was thefirst application, where a relatively long longitudinally poledpiezoceramic bar is mechanically stressed by a hammer stroke.6

Because of the piezoelectric effect, a high open-circuit voltage ofmore than 10 kV is generated.7 If this generated voltage exceedsthe breakdown voltage of the gas, an electric spark occursthereby igniting the gas (see Fig. 1).

In 1980, the application of a piezoelectric generator in com-bination with a low-power electronic was reported for thefirst time.8 A piezoelectric transducer is used to monitor thepressure level in tires of cars and trucks. While driving with lowpressure levels, the rubber of the tire and the piezoelectric trans-ducer are more prone to stress. The amount of energy convertedincreases and allows for sending a telegram to a receiver.

In 2003, Enocean GmbH began commercializing wirelesslight switches for building automation.9 The mechanical inputenergy is taken from the user while operating the light switch. Apiezoelectric bending transducer generates sufficient electricalenergy to send a message up to 300 m.9

We conclude that the performance of piezoelectric ceramicsallows for the implementation of wireless, self-powered sensornodes either as a part of smart structures and systems or as amore general maintenance-free, self-sufficient operation of low-power electronic through the complete life cycle.

Of course, product developments are based on the optimumselection and combinations of subassemblies. The main focus ofthe present paper is directed to the multifarious correlations be-tween the characteristic values of commercial piezoceramics andtheir effective implementation in generator architectures.

Section II reports on the individual modules of a piezoelectricgenerator, Section III illustrates the details of the piezoelectricenergy conversion, Section IV summarizes the commercial ma-terials basis, Section V considers the electronic, and Section VIends up with the conclusions.

II. Operating Principle of a Piezoelectric Generator System

A piezoelectric generator is divided in five major modules: me-chanical energy source, mechanical transformer, piezoelectrictransducer element, generator electronics as well as intelligent

Feature

J. Rodel—contributing editor

wAuthor to whom correspondence should be addressed. e-mail: thomas.roedig@ikts.fraunhofer.de

Manuscript No. 27155. Received February 8, 2010; approved February 9, 2010.

Journal

J. Am. Ceram. Soc., 93 [4] 901–912 (2010)

DOI: 10.1111/j.1551-2916.2010.03702.x

r 2010 The American Ceramic Society

energy and storage management (Fig. 2). These modules areconsidered in the following sections.

(1) Mechanical Energy SourcesA piezoelectric generator must be driven dynamically; hence, theachievable output power is proportional to the driving fre-quency. For understanding the influence of the material prop-erties, which is our motivation, it is more convenient to useenergy quantities instead of power.

We classify the mechanical energy sources in terms of energyforms and drive modes.

Three generalized mechanical energy forms are available:translational, rotational, and acoustic energy. In practice, pi-ezoelectric materials are usually driven under translationalloads. Alternatively, the shear case is also possible. Rotationalenergy is not directly usable.

Concerning mechanical drive modes, two principles are dis-tinguished:

1. Stress-driven mode: An applied mechanical stress leads toa specific strain value depending on the material’s Young’smodulus. Parallel loading paths to the piezoelectric materialmust be avoided. Otherwise, the stress energy is separated de-pending on the stiffness ratio and electrical boundary condition,see Section III. Stress-driven load cases can be resonant or non-resonant. The piezoelectric accelerometer sensor may serve as anexample.

2. Strain-driven mode: The generator is forced to follow anexternal strain, caused by an ‘‘infinite’’ stress. For example, con-sidering a large bridge with a small attached surface-mountedflat generator, like a Macro Fiber Composite (MFC),10 the gen-erator follows the deflection of the bridge, completely.

In both modes, the generator is assumed not to react on theexternal driver. Practical cases are sometimes more complex.This is especially true if the stiffness of the generator is influencedby the behavior of the piezoelectric material. In other words,

stiffness of the structure and stiffness of the piezoelectric materialare connected in parallel and establish a secondary load path.

Depending on electrical boundary conditions, the stiffnessand hence the mechanical energy in the piezoelectric materialsvary; see Section III(1). The effect can be monitored by reso-nant frequency shifts and damping effects,11 which are directlyrelated to change in stiffness and energy distribution. Change invibration amplitude can often be observed as is typical for res-onant generators.

(2) Mechanical TransformersMechanical transformers have two functions: the transfor-mation of nontranslational into translational energy and thematching of the mechanical impedance.

Typically, the mechanical sources produce only a limitedstress level and the piezoelectric materials are mostly stiff. Thisimplies the coupling of mechanical sources of high impedancewith piezoelectric materials of low mechanical impedance.Piezoelectric polymers represent an exception.

Mechanical transformers are known from actuator develop-ments, e.g. lever arms,12 bending structures,13 C-blocks,14 rain-bows,15 THUNDERS,16 recurves,17 telescope,18 moonie,19 andcymbal structures.20

Mechanical impedance matching enables an optimized energytransfer from the source to the transducer. This ensures a highermechanical, and hence a higher electrical converted energy. Itshould be noted that mechanical energy transformation and im-pedance matching are always accompanied with losses of trans-ferred energy. Typically, a certain amount of mechanical inputenergy is needed to deform the mechanical structure elastically.This energy is stored recoverably but is not used to stress thetransducer and to generate electrical energy. Additionally, reallosses like friction occur, but their contribution is comparablylow.

1

2

34

Fig. 1. A micro section of piezoelectric spark generator from a pocketlighter is shown. The acceleration (1) and retaining (2) spring is loadedby the human finger. Reaching a defined stress, a simple mechanic re-leases the energy stored in the acceleration spring and a hammer (3) hitsthe piezoceramics (4).

sources

mechanical impe-dance matching electrical impedance matching

mechanicaltransformer

piezoelectrictranducerelement

powertransfercircuit

intelligent energy andstorage management load

force

displacement

acceleration

pressure

massaPZT

F=m a

F Fin outoutin

lever

F l =F l

PZT

PZTF=A p

p p

membrane piston

FPZT

bending structures

plate

bulk

stack

multilayer

DC-DCconverter

rectifier

storage capacitor

management

pow

er d

ensi

ty

energy density

Li-ionNi-MH

Ni-CdDLC

electrolytic

ultra cap

µC

measure controlregulate

V

Fig. 2. Block diagram of a piezoelectric generator. Each column shows one of the five major modules with some typical examples.

Table I. Historical Review of Piezoelectric Generators

1880 Discovery of the piezoelectric effect28

1950 General use of piezoelectric generator claimed29

1959 Piezoelectric spark igniters claimed5

1972 U.S. patent6 about a gas ignition device as shown inFig. 1

1980 First possible application using piezoelectric generatorsin combination with low-power electronics28

2003 Enocean starts commercializing wireless light switches9

2009 Diversification of research objectives and markets1

902 Journal of the American Ceramic Society—Rodig et al. Vol. 93, No. 4

(3) Piezoelectric MaterialsThe three most common piezoelectric material groups are singlecrystals, ceramics, and polymers (Table II).

A deeper view into the crystal structure of single crystalsand ceramics proposes that 20 of the 32 crystallographicpoint groups are piezoelectric due to unsymmetrical lattice.21

Furthermore, 10 of them are polar and are called pyroelectric. Asubgroup has switchable polarization and is called ferroelectric.

The superposition of the piezoelectric and the ferroelectriceffects increases the electromechanical performance.21 Thisbehavior is well known from ferroelectric piezoelectrics with aperovskite structure such as lead–zirconate–titanate (PZT) andBaTiO3 but is also nonlinear. We always consider the linear ap-proximation in the present paper. For further interest in non-linear effects, Hall22 is recommended.

The tailoring of piezoelectric and ferroelectric material char-acteristics by compositional variations and the microstructure iswell known.23 In addition to being one of the best-known ce-ramics, PZT is also commercially available in large amounts andfor an affordable price.

Hard PZT ceramics are characterized by reduced hysteresis,low depolarization, and low losses, and therefore they are usedfor high-power ultrasound transducer and sensors with highertemperature stability. Soft PZT materials commonly exploit theferroelectric effect for high strain and high piezoelectric voltageconstant g. Typical application areas are low-frequency, high-strain actuators and sensors with high sensitivity.

Today, PZT materials for generator application, like gas ig-niters, play a secondary role in R&D activities. The materials areoptimized for high mechanical stress loads without depolariza-tion and high-voltage output (high g-constant), respectively.Two examples are the impact-type Sonox

s

P524 (see Fig. 1)and the squeeze-type Sonox

s

P41.24

Sometimes, piezoceramics for sensor applications are speci-fied as a possible candidate for generator applications. However,tailored ceramic materials for piezoelectric generators, especiallydesigned for the use with electronics, are not commercially avail-able. Therefore, the aim of this paper is to evaluate commercialhigh-performance piezoelectric ceramics for their possible use ingenerator applications.

(4) Power Transfer ElectronicsDynamically stimulated piezoelectric generators produce an al-ternating current (ac) output, which is not directly usable byelectronic loads. Usually, a direct current (dc) output is neededto power electronics. Rectification, filtering, and an optimumpower transfer are essential. Generally, power transfer circuitsfor piezoelectric generators are composed of up to four differentpower electronic components (Fig. 3).

Circuit design and layout, both depend on the topology used.Typical standard topologies are provided by the power elec-tronic literature.25

The power transfer electronic is aimed to match the electricalimpedances of the generator and the load. In order to improvethe amount of harvested energy, additional active electronicsmay be helpful. dc–dc converters, such as step-down and step-up

converters, inverter, and charge pumps, are used as standardcomponents in electronic design.25 The extremely low outputcurrent of the piezoelectric generators limits the design optionfor the dc–dc converters, which are normally used to transferhigher currents (10 mA–10 A). To handle the very low current ofa piezoelectric generator, the inductance or the switching fre-quency must be increased. Both approaches cause higher lossesresulting from the resistance of the inductor and the higheron-site power due to higher switching frequency of the transis-tor, respectively.

A step-down dc–dc converter working in a discontinuousconduction mode is proposed as the solution of choice.26 Ad-vantages arise from a smaller inductor and a comparably lowswitching frequency. However, the discontinuous mode is lessefficient.25 Alternatively, dc–dc converters with a relatively lowinductor and switching frequency working in a continuousconduction mode under intermittent duty cycle can also solveproblems.

A nonlinear technique called Synchronized Switch Harvest-ing on Inductor (SSHI) as an alternative power transfer elec-tronic is described in Guyomar.27 It can be understood as anenergy-level-triggered dc–dc converter in discontinuous conduc-tion mode. The idea behind SSHI is to work under open-circuitconditions until the maximum voltage is reached. Then, shortcircuiting is carried out by switching on an inductor, whichstarts the charge and power transfer. A practical self-poweredimplementation showing a high on-site power and low efficiencyis cited.27

Despite many activities in R&D, a few self-powered dc–dcconverters providing the lowest acceptable current in the 100 mArange are commercially available. One example, the LT1934 isused in the wireless light switch for building automation,9 show-ing an efficiency of approximately 50%–75% depending on theload current in the range of 100–1000 mA. This implies that thepiezoelectric generator must be roughly doubled in size to pro-vide the same amount of energy, but the output energy is welladjusted and regulated in the voltage level to the load.

Additional power transfer electronics consume a certainamount of energy, which has to be delivered by the generator.The efficiency of relatively small piezoelectric generators canhave an adverse balance due to the on-site power consumed bythe power transfer electronics, and therefore the output powercan be negative (see Fig. 4).

(5) Intelligent Energy and Storage ManagementAn intelligent energy management and storage technology isneeded to ensure reliable energy supply. This should be consid-ered as a part of the generator system in order to maximize theenergy output by switching the energy flow to empty storageunits. Furthermore, controlled and reliable wake-up and shut-down routines are required in accordance with the available en-ergy. This is necessary to increase the performance and ensurethe operation of the generator.

Table II. Piezoelectric Materials—Classification andExamples

Single crystal Quartz, tourmaline, lead magnesium niobate–lead titanate (PMN–PT)

CeramicsGeneral Zinc oxide, aluminum nitride, lead zirconium

titanate (PZT), sodium potassium niobate(KNN), barium titanate (BT)

Hard PZT4, PZT8Soft PZT5A, PZT5H

Polymers PVDF F

F

µCAC DC

piezoelectricgenerator

power transfer circuitgeneral topology load

Fig. 3. General topology of a power transfer circuit. An incoming al-ternating current (ac) is rectified by diodes and stored in capacitors.Switches and inductors are used for current regulation as well as currentlimiting and short-time energy storage, respectively. Sometimes, a mi-crocontroller (mC) for control purposes is used.

April 2010 Piezoelectric Ceramics for Generator Applications 903

A typical topology for a possible intelligent energy and stor-age management is shown in Fig. 5. The first energy path is usedto power up the microcontroller, which manages the energy.This path must be powered up first and put to sleep at last. Afterturning on the energy management microcontroller, the in-coming energy must be transferred to the load and to differentstorage elements, characterized by individual charge-up anddischarge times.

The reason for this is that the wake-up time should be as lowas possible. The charge time of a small capacitor storing enoughenergy for a few working cycles of the load needs less time than tocharge-up a super capacitor or a lithium ion secondary cell. Thehighest potential for reducing on-site power is the usage of low-power electronics and slim software code for the microcontroller.

Power transfer, intelligent energy/storage management areoften considered as one module. Here, in this paper, they arediscussed separately due to their different functionality and sys-tem relevance.

III. Piezoelectric Generator Effect

The direct piezoelectric effect used for piezoelectric generatorswas discovered by Jacques and Pierre Curie in 1880.28 By ap-plying a mechanical load to piezoelectric elements, the energy issplit into mechanical and electrical energy. We will consider theoperation conditions under which electrical work can be per-formed by a loaded piezoelectric generator. Let us start with thethree electrical loading conditions. They comprise:

1. Short-circuit conditions: A charge is generated propor-tional to the mechanical load. In turn, the strain is proportionalto the stress load although higher than in case 2. There is nocounter-acting electric field.

2. Open-circuit conditions: A voltage is generated propor-tional to the mechanical load. The strain is proportional to thestress load but lower than in case 1. The reason for this is thegeneration of an internal electric field acting in the opposite di-rection of the mechanical load and stiffens the generator.

3. Load circuit conditions, i.e. a voltage and charge per-forming an electric work are generated simultaneously. Thestrain is proportional to the stress; the strain level depends onthe voltage and charge output level, respectively, but lies be-tween short- and open-circuit conditions.

The first two cases are typically used in sensors, whereas thelatter case depicts the piezoelectric generator effect.

Considering piezoceramics like PZT and BaTiO3, the piezo-electric effect is superimposed by the nonlinear ferroelectriceffect. In this paper, the electromechanical behavior is assumedas linear when considering large signals.

(1) Energy DensityThe piezoelectric generator is stimulated by an external mechan-ical vibration. The total energy provided is split into mechanicaland electrical energy portions, i.e. the elastic deformation of asolid body and the free electric surface charge generating anelectric field. This electric field can drive the free electric surfacecharge as a current through a load to perform electric work.Simultaneously, the electric field decreases. For a continuouslyalternating stimulation, a permanent electric work is performed.

For a better understanding of the piezoelectric generatoreffect, we consider a theoretical working cycle as visualized inFig. 6. Starting at point 1 and applying a mechanical stress T2 toa piezoelectric material under open-circuit condition leads to astrain S2. The slope describes the compliance sD; see also the linefrom point 1 to point 2 in Fig. 6.

The superscript D denotes operation under a constant electricdisplacement field, e.g. open-circuit conditions. Vice versa, thesuperscript E indicates the regime with a constant electric field,e.g. short-circuit conditions. The projection of strain and stressinto quadrants II and IV describes the piezoelectric behavior.The external electric displacement field D2 remains zero but theelectric field strength E2 increases by d/(eTsD). The constants dand e are the piezoelectric charge constant and the permittivity,

F

µC

piezoelectricgenerator

power

power transfercircuit

intelligent energyand storage management

load

controlmonitor

Fig. 5. Typical topology for energy and storage management for pi-ezoelectric generators. The energy flow can be divided into three pathsself-supply, storage, and load supply.

T

S

E

D

4

4

4

4

3

3

3

3

2

22

2

1

1

1

1

E4E2 E1

S4

S3

S1

S2

D1

D3

T2T1

WMechE

WmechD

WmechE − Wmech

D

Wel

IVIII

II I

εT εT

sEsD

− s )(sεd

DET

sεd

DT

d

Fig. 6. Energy density graph of a piezoelectric material. The diagram isnot to scale.

outp

ut p

ower

generator size

power transfer circuits

on-site power

topology 1without

topology 2

Fig. 4. General relationships between output power and generator sizedepending on the power transfer electronic used. Topology 1 is assumedas less complex than topology 2. A piezoelectric generator system withpower transfer circuit features a higher output power by better imped-ance matching but also suffers from higher power consumptions.

904 Journal of the American Ceramic Society—Rodig et al. Vol. 93, No. 4

respectively. Superscript T and S indicate constant stress orstrain field, respectively. This consideration is in accordancewith Eq. (A3) in Sidebar A.

Going now from point 2 to point 3, the electric boundarycondition are changed to short-circuit conditions. The stress levelremains constant whereas the strain increases to S3. This pointcan also be reached by applying the same stress level T2 startingfrom point 1 under a short-circuit condition with the slope sE.The electric field strength decreases to zero by a slope of!d/(eT(sE!sD)). The electric displacement field increases to D3.

Depending on the electrical boundary conditions, the strain–stress relation varies leading to two different constants for thecompliance, which are sE and sD.

The blue and green crosshatched triangles in quadrant I rep-resent the energy densities Wmech

D and WmechE for one half

cycle, respectively:

Wmech ¼ 12ST (1)

The difference between WmechD and Wmech

E is exactlythe electrical energy density Wel, shown as a red triangle inquadrant III. The electrical energy density Wel amounts to

Wel ¼ 12DE (2)

To finish the full working cycle, the stress T2 falls. Open-circuit conditions will be applied, eliminating the stress T2, point3 to point 4. A residual strain S4 remains. The electric fieldstrength falls below zero to E4 while the electric displacementfield remains on level D3. Short-circuiting the piezoelectric ele-ment again closes the working cycle, point 4 to point 1. Thelevels of stress T, strain S, electric field strength E, and electricdisplacement field D go finally to zero.

The working cycle is approximated by the SSHI technique.27

Generally, the efficiency can become complex if energy dissi-pation (real part) and storage (imaginary part) are consideredseparately. For piezoelectric materials, the storage is higher thanlosses. Therefore, the efficiency of the working cycle, shown inFig. 6, can be written as:

Z ¼ k2 ¼WE

mech !WDmech

WEmech

¼ Wel

WEmech

(3)

The definition of efficiency is the same as for the square of thecoupling coefficient.31

The ratio of mechanical and electrical energy k2 in Eq. (3)depicts a material constant. A high-efficient piezoelectric gener-ator material can be selected by a proper set of material con-stants defining a very high value of the coupling coefficient k; seethe known Eq. (4).30

k2 ¼ d2

eTsE(4)

For piezoelectric generators, it is more advantageous to pro-vide a maximum of electrical energy output by a given volumeindependent of the efficiency. For this case, another figure ofmerit applies.

It should be noted that piezoelectric generators are drivendynamically. The energy approach presented here does not in-clude the influence of the frequency. Considering the frequencybehavior, power density, which is defined as energy density cy-cles per time interval, must be used instead of energy density.

Sidebar A. Four-Terminal Network Theory Applied to the Constitutive Piezoelectric Equations

The constitutive piezoelectric equations30 can be written as hybrid fourterminal network equation (Eq. (A1)). The signs are defined by thedirection of the arrows in Fig. A1. The hybrid parameters are describedby the three fundamental material properties of the piezoelectricmaterial, sE, eT, and d. Therefore, the piezoelectric four terminal network can additionally be split to three sub-four-terminalnetworks representing the mechanical, piezoelectric, and electric behavior, respectively. Four-terminal network descriptions arethe admittance matrix Y (Eq. (A2)) and the inverse transmission matrix B (Eq. (A3)) used for electromechanical and analyticalmodeling, respectively. The electromechanical modeling allows the use of piezoelectric material properties including electricaland mechanical components and sources in circuit simulation tools, e.g. SPICE. The transformation among the differentmatrix equations does not provide additional information; however, it allows an easier approach to the requested information.For the inverse transmission matrix B, it should be noted that a stress or strain cannot be applied independently.

TD

! "¼ 1=sE d=sE

d=sE ! sE # eT ! d2# $

=sE

! "# S

E

! "¼ cE eE

eE !eS

! "# S

E

! "¼ Y½ % # S

E

! "ðA2Þ

ED

! "¼ !1=d sEd

eT=d ! sE # eT ! d2# $

=d

! "# S

T

! "¼ !1=d 1=eE

1=gT !eS=eE

! "# S

T

! "¼ B½ % # S

T

! "ðA3Þ

The transition from geometrically independent to geometrically dependent quantities, see Table A1, may apply.

T D

S E

mechanical electricalpiezoelectric

four terminal network

Fig A1. A four-terminal network representing a piezoelectric element.

Table A1. Correlation of Physical Variables

Geometrical independence Geometrical dependence

Strain S Displacement xVelocity v

Stress T Force FElectric displacementfield

D ’- Charge QCurrent I

Electric field strength E Voltage VEnergy density W Energy E

Power P

SD

! "¼ SE !d

d !eT

! "# T

E

! "¼ ½H% # T

E

! "ðA1Þ

April 2010 Piezoelectric Ceramics for Generator Applications 905

(2) Figures of MeritFor piezoelectric generators, the electrical energy output as wellas the electrical energy density of the considered material shouldbecome a maximum. The valid figures of merit depend on thestimulation mode of the piezoelectric generator and up ratedifferent material data. In Sidebar A, the constitutive piezoelec-tric equations are presented.

Considering a piezoelectric generator driven under a stressload, the appropriate figure of merit can be derived fromEq. (A3) in Sidebar A.

WTel ¼

1

wTel

T2 ¼ d2

eTT2 (5)

For both exceptional electrical loading cases, short circuit,i.e. E5 0, and open circuit, i.e. D5 0, the Eqs. (9) and (10)shown in Table III, can be derived. The strain S in the stress–load condition is set equal in the Eq. (A3). Equation (5) canbe obtained by replacing D and E in Eq. (2) using the Eqs. (9)and (10).

WelT and wel

T are the electrical energy density and the piezo-electric energy density constant under stress load, respectively.This figure of merit was also found by Priya.32 Further relevantdependencies on the up-rated materials data are summarized inTable III.

It should be noted that the stiffness of the piezoelectric gen-erator material has no influence on both the energy density andthe energy output, respectively. The material selection should beperformed based on the energy output.

Considering a piezoelectric generator driven under a strainload, another figure of merit applies:

WSel ¼ wS

elS2 ¼ d2

eTsEsDS2 (6)

The derivation of Eq. (6) follows similarly to Eq. (5), butunder strain-drive conditions. Wel

S and welS are the electrical en-

ergy density and the piezoelectric energy density constant understrain load, respectively. Table IV summarizes the relations forthis load case.

In the case of strain-driven mechanical energy sources, com-pliance becomes important. A stiffer, i.e. less compliant piezo-electric material leads to a higher energy output. The reason forthis is the high mechanical stress forced by the strain energysource. Therefore, the mechanical energy applied to the gener-ator is comparatively high. This leads to a higher amount ofenergy converted even if the material efficiency is low.

It is essential to keep in mind that the highest efficiency doesnot necessarily mean the highest energy output. This can be seenby the different values for energy density constants wel

T or welS and

coupling coefficient k. See also Fig. 13 in Section V.In discussing energy transfer and efficiency, three issues must

be taken into considerations.1. The piezoelectric generator material should be able to

absorb huge amounts of mechanical energy. Therefore, the com-pliance smust be adapted to the mechanical source. Considering

stress- or strain-driven sources, a high or low compliance is es-sential, respectively (see Tables III and IV).

2. The piezoelectric charge constant d represents the cou-pling between mechanical input and electrical output. A highvalue for piezoelectric coupling is essential in order to obtainlarge energy transfer as well as high efficiency.

3. The piezoelectric generator material should be character-ized by a low ability to transmit electric fields. This means a lowpolarization under electric field load, represented by a low per-mittivity.

All these requirements are expressed in the well-knownEq. (4) for the coupling coefficient. In this equation, the squareof the piezoelectric charge constant d plays the key role, butthe compliance s and the permittivity e should also be takeninto account.

IV. Material Survey

Currently, more than 200 different piezoelectric ceramics frommore than 14 suppliers are commercially available. Most ofthese materials are based on PZT solid solutions.

Furthermore, there are ongoing research activities in theoptimization of PZT materials,33 development of lead-freepiezoelectric ceramics,34 and the special structural design of pi-ezoelectric materials such as ZnO nanowires.35 All these newdevelopments are not considered here. We focus on commercialpiezoceramics with fully documented values.

The properties of a piezoelectric material are defined by theelastic, dielectric, and piezoelectric tensor components. They arerepresented by the compliance sE, the permittivity eT, and thepiezoelectric charge constant d, respectively. The materials dataused in following sections are taken from the datasheets pro-vided by different vendors.36–49 In this analysis, we consider onlymaterial properties at room temperature assuming that they areconstant under the generator load conditions, e.g. temperatureprofiles and depolarization effects will not be considered here.

One result is that the investigated materials data in the dia-gram (Fig. 7) are correlated to each other linearly and are lo-cated along certain lines. These lines are labeled as the ‘‘PZTlines.’’ Understanding this correlation between permittivity, eT,and piezoelectric charge constant, d, requires a deeper view intothe structural properties of the lattice.21,30 Both materials datadepend on the mobility of the ions in the lattice and are thereforelinearly related to each other.

The statistical analysis of the material data encompassingmore than 200 different piezoelectric materials shown in Fig. 7,is presented in Table V. The compliance range is comparativelylow, whereas the permittivity and piezoelectric charge constantvary by one order of magnitude.

More specifically, six commonly used standard materials areassessed in the following sections. These ceramics correspond toPZT 4, 5A, 5H, 8, BaTiO3, and KNN. They are labeled in thederived diagrams and are listed in Table VI. All other materialsare marked by a data point. The selected materials cover thewhole interesting variation range of piezoelectric materials data.Because of limited availability, noncommercial ceramics have

Table III. Equations for Stress-Driven PiezoelectricGenerators

Property Material constant Equation

Strain Elastic SD ¼ sDT ð7Þcompliance SE ¼ sET ð8Þ

Electricdisplacementfield

Piezoelectriccharge constant

D ¼ dT ð9Þ

Electric fieldstrength

Piezoelectricvoltage constant

E ¼ gTT ¼ d=eTT ð10Þ

Table IV. Equations for Strain-Driven PiezoelectricGenerators

Property Material constant Equation

Stress Elastic stiffness TD ¼ cDS ð11ÞTE ¼ cES ð12Þ

Electricdisplacementfield

Piezoelectric chargedensity constant

D ¼ eES ¼ d=sES ð13Þ

Electric fieldstrength

Piezoelectric electricfield constant

E ¼ hS ¼ d=ðeTsDÞS ð14Þ

906 Journal of the American Ceramic Society—Rodig et al. Vol. 93, No. 4

been excluded in this study. The next two sections present moredetailed material analyses, where we differentiate between stress-and strain-driven modes and the directions of the acting me-chanical and electric fields (d33, d31, d15).

(1) Stress-Driven ScenarioRegarding the piezoelectric stress energy density constant wel

T,most of the materials data are located close together forming apiled cloud (Fig. 8). There are only a few data points, which areseparated in both directions, to lower or to higher wel

T. Points inFig. 8, which are located closer to the origin of the diagram—among them BaTiO3 and KNN—are of minor interest, becausethe energy density is low. Present lead-free materials are char-acterized by lower energy density Wel

T.34 It should be noted thatthe correlation between the piezoelectric stress energy densityconstant wel

T and energy density WelT is inverse (Eq. (5)).

Few data points were found to be located distant from theorigin. One example is a single crystal based on PMN–PT,having w33el

T 5 1.4( 1010 J/m3 in Fig. 8. In addition, there are a

Table V. Statistical Evaluation of the Material Properties

Property Symbol Unit Minimum 90% range Maximum

Permittivity e11T /e0 — 127 500–5000 6500

e33T /e0 4.86 200–5000 8000

Compliance s11E 10!12 m2/N 7.19 8–20 59.7

s33E 6.94 8–25 86.5

s55E 11.5 25–55 57.8

Piezoelectriccharge constant

d31 10!12 C/N !1050!300 to !30 2.26

d33 2.3 100–1000 2250

d15 7.79 160–1000 1160

Piezoelectricenergy densityconstant

w31T 1010 J/m3 6.42 40–400 21600

w33T 1.4 6.5–50 1430

w55T 3.16 4–30 1860

w31S 0.00412 0.21–2.1 1.74

w33S 0.0171 1–30 58.5

w55S 0.00809 0.5–4 4.17

Fig. 7. Materials data of more than 200 different commercially avail-able piezoelectric materials. Each single point represents a material de-scribed by its three characteristic values (compliance sE, permittivity eT,and piezoelectric charge constant d). The best-fit lines are shown. Thegray net surface depicts the theoretical limit (k51).

Table

VI.

StandardPiezoelectricMaterialin

Com

parison

Property

material

Permittivity

Complia

nce

atconstan

telectric

fieldstrength

Piezoelectric

charge

constan

tCouplin

gcoefficient

Piezoelectric

energy

constan

t

Stressdriven

Straindriven

Unit

—10

!12m

2/N

10!12C/N

—10

10J/m

310

10J/m

3

Sym

bol

e 11T/e

0e 3

3T/e

0s 11E

s 33E

s 55E

d 31

d 33

d 15

k31

k 33

k 15

w31T

w33T

w15T

w31S

w33S

w15S

BaT

iO350

1620

1900

8.55

8.93

22.3

!79

191

270

0.21

0.49

0.48

269

46.1

19.7

0.53

3.59

1.32

KNN

31

938

496

8.2

10.1

27.1

!51

127

306

0.27

0.61

0.64

168

27.2

8.87

0.95

5.66

2.63

PZT45

11475

1300

12.3

15.5

32.7

!123

289

496

0.33

0.70

0.71

76.1

13.8

5.31

0.97

5.79

4.16

PZT5A

51

1730

1700

16.4

18.8

44.3

!171

374

584

0.34

0.71

0.69

51.5

10.8

4.49

0.82

5.20

2.28

PZT5H

51

3130

3400

16.5

20.7

42.6

!274

593

741

0.39

0.75

0.68

40.1

8.6

5.05

1.08

6.26

2.04

PZT85

11500

1200

11.8

14.2

30.4

!120

265

306

0.30

0.64

0.55

73.8

15.1

5.89

1.10

6.13

4.17

April 2010 Piezoelectric Ceramics for Generator Applications 907

number of ceramic materials showing an interesting materialproperty combination. It should be considered worth investi-gating these combinations before starting a complete new ma-terial development.

The location of the data points in Fig. 8 depends on the rel-ative directions of polarization, and the mechanical and electricfields, which is represented by the characteristic tensor compo-nents d33, d31, and d15. In comparison, a d31-mode-driven piezo-electric transducer has the lowest energy density and is,therefore, less efficient. An interesting fact is that shear mode(d15) enables a higher energy density than the d33-mode. Thereason is the typically higher piezoelectric charge constant d15compared with d33 used quadratic in Eq. (5). The typically higherrelative permittivity e11 compared with e33 is of minor effect.

Despite the wide range of variation of the piezoelectric chargeconstant d and the piezoelectric voltage constant g, the variationrange of the resulting product, the piezoelectric stress energydensity constant wel

T, is relatively low. We find the energydensity values of commercial PZT-based piezoelectric materialsin the same range. Both properties, d and g constant, can betailored, but not independently.

It is clearly demonstrated that different piezoelectric materialshave similar energy densities, but they differ with respect tothe piezoelectric voltage constant g and piezoelectric chargeconstant d enabling a high open-circuit voltage or high short-circuit charge output, respectively.

Proper material selection enables a better electrical imped-ance matching to the load. This can be a substantial advantage,compared with the additional use of complex power transfercircuits. Moreover, this can be of great importance when con-sidering technologies where the thickness of the piezoelectriclayer mainly influences the value of the output voltage. This isdiscussed more detailed in the Section III.

(2) Strain Driven ScenarioWhen comparing stress-driven piezoelectric generators, thestudy considered more than 200 commercial materials locatedas a band in the diagram of Fig. 9. For the majority of the ma-terials under consideration, the variation of energy density andthe variation of piezoelectric strain energy density constant wel

S,were found to be low.

1 10 100 1000

10

20

30

40

50

60

piezoelectric stress energy density constant w [10 J/m ]

piez

oele

ctric

vol

tage

con

stan

tg[

10−3

Vm

/N]

piezoelectric charge constant d [10−12 C/N]

13.161031.6100316

3160

1000

Fig. 8. Piezoelectric charge constant d vs. piezoelectric voltage constant g for more than 200 different materials, each represented by a point, is shown.Additionally, the piezoelectric stress energy density constant wT is visualized as contour lines.

0.010 10 20 30 40 50

0.1

1

10

100 piezoelectric strain energydensity constant w [10 J/m ]

piez

oele

ctric

elec

tric

field

cons

tant

h[1

0V

/m]

piezoelectric charge density constant e [C/m ]

0.1 0.3161

3.1610

31.6

100

316

Fig. 9. Piezoelectric charge density constant eE vs. piezoelectric electric field constant hD for more than 200 different materials is shown. Additionally,the piezoelectric stress energy density constant wS is visualized as contour lines.

908 Journal of the American Ceramic Society—Rodig et al. Vol. 93, No. 4

The quadratic influence of the piezoelectric charge constant inEq. (6) is nearly completely compensated by compliance in com-bination with its permittivity. The values for wel

S for five of thesix materials considered vary minimally (Table VI). For BaTiO3,the values for wel

S are deviated from the other figures. It is quiteinteresting to see the ferroelectric soft material PZT 5H and theferroelectric hard material PZT 8 bearing nearly the same valuefor wel

S, i.e. w31elS )1.1( 1010 J/m3 or w33

S )6.2( 1010 J/m3. Tak-ing into consideration only the piezoelectric charge constant d,one would expect that the energy densities of the two materialsare quite different with PZT 5H showing the higher value.

In strain-driven generators, compliance plays a key role forenergy density considerations. As an example, the comparablystiff lead-free material KNN, characterized by a low piezoelec-tric coupling, shows a high piezoelectric strain energy densityconstant wel

S due to its ability to absorb a high amount ofmechanical energy.

Materials with a comparable low stiffness, e.g. single crystalsbased on PMN–PT, suffer from low mechanical input energy,even when they are more efficient in energy transforming.

Considering the relative directions of polarization, and themechanical and electric fields (d33, d31, and d15) the d33-mode isthe most energized. In comparison with the stress-driven sce-narios, the d15-mode has a lower energy density, due to highercompliance. The d31-mode again shows the lowest values forpiezoelectric strain energy density constant wel

S.From the present investigation comprising commercial PZT

ceramics, the highest value ofwelS530.5( 1010 J/m3 was identified.

(3) Technological AspectsThe piezoelectric layer’s thickness plays a key role in the designof the generator. It defines the open-circuit voltage, which isproportional to the layer thickness. Given the device volume andthe layer thickness, the charge output can be derived. This out-put, in turn, is proportional to the electrical active cross section.

There are several manufacturing technologies for piezoce-ramics ready to be used33 (Fig. 10).

By varying the layer thickness and the cross section, a piezo-electric generator can be specifically designed for high-voltageor high-current applications carrying the same volume. Thus,the corresponding electrical output impedance can be matchedto the electrical load impedance by device design avoiding com-plex power transfer circuits. The maximum achievable electricaloutput power, defined by the material properties, will not beinfluenced.

Optima can be found for specific mechanical load values andoutput requirements. For applications requiring a load voltage,for example, of 3.3 V, several technologies including sputtering,sol–gel, thick film, well known for its relative thin piezoelectriclayers, cannot be used directly. The reason is that an open-cir-cuit output voltage larger than 3.3 V cannot be reached. Other

technologies, e.g. solid fabrication, well known for its relativethick piezoelectric layers, are usable but less powerful (Fig. 11).

For layers that are either too thin or too thick, additionalactive power transfer circuits may increase the output power.However, power transfer circuits suffer from on-site power. Thisposes the issue of whether the generator system can be moreefficient with or without power transfer electronic.

It should be noted that a limited number of piezoceramicmaterials are compatible with a specific technology. Further-more, processing may influence the material properties and theymay differ from the properties of bulk ceramics given in thedatasheets.

At times, there are technological limits in the reduction orincrease of layer thicknesses. Two examples are tape casting incombination with the co-firing of stack transducer and sputter-ing, respectively. In both of these cases, optimal electrical im-pedance to the load cannot be obtained. By choosing a differentmaterial characterized by a high charge output or a high open-circuit voltage, the technological limit can be extended to ensureoptimal electrical impedance matching.

V. Piezoelectric Generator and Electronics

In this section, the aspects of electronics are considered. For thispurpose, a complete transition from geometrically independentto geometrically dependent physical values is more practical. Tooperate with time-independent quantities, it is more convenientto use velocity, current, and power rather than displacement,charge, and energy (Table A1).

Figure 12 shows a block diagram of a simple piezoelectricgenerator. Assuming that the diodes and capacitors are ideal, i.e.the forward voltage, backward current, and equivalent seriesresistance (ESR) are zero and the leakage resistance (Rleak) isinfinite.

(1) Resistive LoadConsidering only a variable resistive load without the blocks 1and 2 (in Fig. 12), the electrical condition of the piezoelectricgenerator varies from short circuit (low resistance) to open cir-cuit (high resistance). A small window exists in between thesetwo states where electrical work can be performed. For lowresistor values, the mechanical input power is high, while theoutput power and the efficiency are low. Under a high resistiveload, the output power and the efficiency are low.

Figure 13 illustrates that the resistor value for maximum out-put power is not the same for maximum efficiency. It should also

tech

nolo

gies

com

mer

cial

prod

ucts

1nm 1µm 1mm

sputtering

sol-gel

thick film stacks

tape casting

dicing

solids

layer

thickness

MFC gasigniterstack transducer

cofired stacktransducer

ferroelectricmemory

Fig. 10. Different technologies for processing piezoceramics are classi-fied by layer thickness. Commercial products placed by its characteristiclayer thickness.

0.0

0.2

0.4

0.6

0.8

1.0

norm

alis

ed o

utpu

t pow

er

normalised layer thickness

1 10

increasingoutput voltage

increasinginputpower

Fig. 11. The dependency of layer thickness and output power under thegiven mechanical load and required output voltage level is shown. Forhigher output voltage requirements or higher input power levels, thelayer thickness has to be increased or decreased, respectively. The nor-malizations are with respect to optimal layer thickness and maximumoutput.

April 2010 Piezoelectric Ceramics for Generator Applications 909

be noticed that the stiffness, and hence mechanical input powervariation depend on the electrical conditions, represented by thecompliance sE and sD, respectively.

Figure 14 portrays strain-driven piezoelectric generatorsunder variable load resistor electrical conditions where thebehavior is different. The mechanical input power changes inthe opposite direction, as more force and hence more energyis needed to induce a stiffer material to the same deflectionpoint. An interesting result occurs when a stiff but less-efficient piezoelectric material like KNN can produce a rela-tively high electrical output power compared with the othermaterials.

Power and efficiency are both influenced by the electricalload. Electrical output power and efficiency can be increased byoptimized impedance matching.

(2) Charging a CapacitorCharging a capacitor is an important issue for a piezoelectricgenerator system, due to the task of separating, filtering, andstoring the energy (see Fig. 12 without the block 3).

In Fig. 15, a generalized charge-up cycle is illustrated. At low-voltage levels, the piezoelectric generator acts under a short-cir-cuit condition, e.g. high currents. The input power is relativelylarge due to the larger compliance sE. The electrical outputpower and efficiency are low.

When the storage capacitor reaches the open-circuit voltageof the piezoelectric generator, the output power and efficiencyreturns to a low level. The mechanical input power is low due tothe smaller compliance sD.

Between the electrical short-circuit (t5 0) and open-circuitcondition (t5 1), there is a range with high-power transfer andhigh efficiency. The optimum point of power transfer and effi-ciency occurs when the voltage of the storage capacitor reachesapproximately 50% of the open-circuit voltage of the generator.The power flow from the generator through a bridge rectifierand a filtering/storage capacitor to the load can be optimized byshifting the working point.52

To compare different materials, a diagram is proposed graph-ing the time with charge up the capacitor to the open-circuitvoltage of the generator (see Fig. 16).

The maximum reachable voltages are the same for PZT 4,PZT 5A, and PZT 8, but the charge-up time is different, e.g. thesame energy level is reached at different power levels.

The analysis of charge time plays a key role in the intelligentenergy and storage management and allows for a generatorcomparison of various designs.

VI. Conclusions

Market analysis shows a broad offer of commercial piezoce-ramics usable in generator applications. Material selection fora generator depends on the type of mechanical energy source,the mechanical transformer, the electrical load, and the usablefabrication technology. Ceramic performance data must beevaluated in the context of the considered system. Dependingon the mechanical load conditions, different figures of merit arevalid.

Fig. 15. A typical capacitor charge-up cycle performed by a piezoelec-tric generator is shown. Highest electrical output power and efficiencyoccur only in a short first-time range. The average power over a definedperiod, e.g. full cycle of the stimulation frequency, is displayed. The timeand values are normalized to the charge-up end-time and to the max-imum achieved values, respectively.

Fig. 13. Normalized power and efficiency of different piezoelectric gen-erator materials under a stress-driven condition. The resistance is nor-malized to optimal resistor where the highest output power can beachieved. The normalization to power and efficiency is with respect tomaximum values.

Fig. 14. Normalized power and efficiency of different piezoelectric gen-erator materials under a strain-driven condition. The normalization iscomparable with Fig. 13.

F

F

piezoelectricgenerator

bridgerectifier

storagecapacitor

loadresistor

block 1 block 2 block 3

Fig. 12. Simple piezoelectric generator system, containing a dynami-cally stress-driven piezoelectric transducer element, a bridge rectifier,a storage capacitor, and a load resistor.

910 Journal of the American Ceramic Society—Rodig et al. Vol. 93, No. 4

We state, that the distribution of mechanical and electricalenergy in a stressed piezoelectric generator is defined by theproperties of the piezoelectric material used. The relation cannotbe changed by system design. It is the demanding task of thesystem designer to adjust the mechanical source and electricalload of the generator by a process of impedance matching toachieve the lowest loss of harvested electrical energy.

As a general consideration, the overall system efficiency of apiezoelectric generator is estimated to be 25%. This estimationassumes the efficiency of the piezoceramic of approximately50% (coupling coefficient k5 70%) and a 50% electrical energytransfer rate from the generator to the system. While this soundsless, the efficiency of other solid-state generators is lower (com-mercial solar cell o20%, thermal electric generator o10%),which opens up a secure perspective for the piezoelectric gener-ator principal.

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BaTiO3KNN

PZT 5HPZT 5APZT 4

PZT 8

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0ch

arge

tim

e [n

orm

alis

ed]

maximum voltage [normalised]

Fig. 16. The capacity of capacitor to be charged is adjusted with regardto always reaching the same energy level. The normalization to maxi-mum achieved values is used.

April 2010 Piezoelectric Ceramics for Generator Applications 911

Thomas Rodig received M.Sc. de-gree in electrical engineering fromthe Technische Universitat Dres-den in 2003. After graduation hejoined the Smart Materials andSystems Department at Fraun-hofer IKTS working as researchassociate. The main focus ofhis work is set to the developmentof piezoelectric actuators, sensors,ultrasound transducers and gen-erators and their integration into

systems. Since 2010 Mr. Rodig is the head of the group‘‘Actuators, Sensors and Intelligent Systems’’ at FraunhoferIKTS.

Andreas Schonecker studied Phy-sics at the Technical University ofDresden, Germany, and receivedhis Ph.D. in Solid State Physicsfrom here in 1976. In 1975 hejoined the Institute of Solid StatePhysics and Materials ScienceDresden, working as senior re-searcher in electronic materialsand ceramics. With FraunhoferIKTS since its inspection (1990),Dr. Schonecker heads the devel-

opment of smart materials and systems for the client compa-nies that contract the Organization’s service. He strives tocreate new, original materials that are beneficial to and arecompatible with existing materials already used. Working witha team of scientists, he is also involved in administrativeduties, marketing, business development and strategic plan-ning.

Gerald Gerlach received M.Sc.and Ph.D. degrees in electricalengineering from the TechnischeUniversitat Dresden in 1983 and1987, respectively. He worked inresearch and development in thefield of measuring devices andsensors at several companies. In1993 he became a professor at theDepartment of Electrical Engi-neering at TU Dresden. Since1996 Professor Gerlach has been

there the head of the Solid-State Electronics Laboratory. Hisresearch is focused on sensor and semiconductor technology,microsystem technology and simulation and modelling ofMEMS devices.

912 Journal of the American Ceramic Society—Rodig et al. Vol. 93, No. 4