Piezoelectrics in Positioning - PZT & Piezo Actuators: Sub ...

Piezo • Nano • PositioningContentsPiezoelectrics in PositioningContents ............................................................2-172Features and Applications of Piezoelectric Positioning Systems ..............2-174Glossary ............................................................2-175Introduction .........................................................2-177Nanopositioning with Piezoelectric Technology ............................2-177Features of Piezoelectric Actuators ......................................2-177Quick Facts ..........................................................2-178ActuatorDesigns .....................................................2-178Operating Characteristics of Piezoelectric Actuators ........................2-179Fundamentals of Piezoelectricity ........................................2-181Material Properties ...................................................2-181PZT Ceramics Manufacturing Process ....................................2-182Definition of Piezoelectric Coefficients and Directions .......................2-182Resolution ...........................................................2-183Fundamentals of Piezomechanics .......................................2-184Displacement of Piezo Actuators (Stack & Contraction Type) .................2-184Hysteresis (Open-Loop Piezo Operation) ..................................2-185Creep / Drift (Open-Loop Piezo Operation) ................................2-186Aging...............................................................2-186© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.18Actuators and Sensors ................................................2-187Metrology for Nanopositioning Systems .................................2-187Indirect (Inferred) Metrology ............................................2-187Direct Metrology .....................................................2-187Parallel and Serial Metrology ...........................................2-187High-Resolution Sensors—Strain Gauge Sensors ..........................2-187Linear Variable Differential Transformers (LVDTs) ..........................2-188Capacitive Position Sensors ...........................................2-188Fundamentals of Piezoelectric Actuators .................................2-189Forces and Stiffness ..................................................2-189Maximum Applicable Forces (Compressive Load Limit, Tensile Load Limit) ....2-189Stiffness ............................................................2-189Force Generation .....................................................2-190Displacement and External Forces .......................................2-191Dynamic Operation Fundamentals ......................................2-192Dynamic Forces ......................................................2-192Resonant Frequency ..................................................2-193How Fast Can a Piezo Actuator Expand? ..................................2-1942-172

Piezo • Nano • PositioningPiezo Actuator Electrical Fundamentals ..................................2-195Electrical Requirements for Piezo Operation ...............................2-195Static Operation ......................................................2-195Dynamic Operation (Linear) ............................................2-196Dynamic Operating Current Coefficient (DOCC) ............................2-197Dynamic Operation (Switched) ..........................................2-197Heat Generation in a Piezo Actuator in Dynamic Operation ..................2-198Control of Piezo Actuators and Stages ...................................2-199Position Servo-Control ................................................2-199Open- and Closed-Loop Resolution ......................................2-200Piezo Metrology Protocol ..............................................2-200Methods to Improve Piezo Dynamics ....................................2-201InputShaping ® .......................................................2-201Signal Preshaping / Dynamic Digital Linearization (DDL) ....................2-202Dynamic Digital Linearization (DDL) .....................................2-203Environmental Conditions and Influences ................................2-204Temperature Effects ...................................................2-204Linear Thermal Expansion .............................................2-204Temperature Dependency of the Piezo Effect ..............................2-204Piezo Operation in High Humidity .......................................2-204Piezo Operation in Inert Gas Atmospheres ................................2-205Vacuum Operation of Piezo Actuators ....................................2-205LifetimeofPiezoActuators .............................................2-206Linear Actuators & MotorsNanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesPiezoelectrics in PositioningNanometrologyMicropositioningIndexBasic Designs of Piezoelectric Positioning Drives/Systems ..................2-207Stack Design (Translators) .............................................2-207Laminar Design (Contraction-Type Actuators) .............................2-207TubeDesign .........................................................2-208Bender Type Actuators (Bimorph and Multimorph Design) ..................2-209Shear Actuators ......................................................2-209Piezo Actuators with Integrated Lever Motion Amplifiers ....................2-210Piezo Flexure Nanopositioners ..........................................2-211Parallel and Serial Kinematics / Metrology ...............................2-212Direct and Indirect Metrology ..........................................2-212Parallel and Serial Kinematics ..........................................2-213PMN Compared to PZT ................................................2-214ElectrostrictiveActuators(PMN) ........................................2-214Summary ...........................................................2-215Mounting and Handling Guidelines for Piezo Translators ...................2-216SymbolsandUnits ...................................................2-2172-173

Piezo • Nano • PositioningProperties / ApplicationsFeatures of Piezoelectric Positioning SystemsUnlimited ResolutionPiezoelectric actuators convertelectrical energy directly to mechanicalenergy. They make motionin the sub-nanometer rangepossible. There are no movingparts in contact with each other tolimit resolution.Fast ExpansionPiezo actuators react in a matter ofmicroseconds. Acceleration ratesof more than 10,000 g can be obtained.High Force GenerationHigh-load piezo actuators capableof moving loads of several tons areavailable today. They can covertravel ranges of several 100 μmwith resolutions in the sub-nanometerrange (see examples likethe P-056, in the “Piezo Actuators& Components” section).No Magnetic FieldsThe piezoelectric effect is related toelectric fields. Piezo actuators donot produce magnetic fields norare they affected by them. Piezodevices are especially well suitedfor applications where magneticfields cannot be tolerated.Low Power ConsumptionStatic operation, even holdingheavy loads for long periods, consumesvirtually no power. A piezoactuator behaves very much like anelectrical capacitor. When at rest,no heat is generated.No Wear and TearA piezo actuator has no movingparts like gears or bearings. Its displacementis based on solid statedynamics and shows no wear andtear. PI has conducted endurancetests on piezo actuators in whichno measurable change in performancewas observed after severalbillion cycles.Vacuum and Clean RoomCompatiblePiezoelectric actuators neithercause wear nor require lubricants.The new PICMA ® actuators withceramic insulation have no polymercoating and are thus ideal forUHV (ultra-high vacuum) applications.Operation at CryogenicTemperaturesThe piezoelectric effect continuesto operate even at temperaturesclose to 0 kelvin. PI offers speciallyprepared actuators for use at cryogenictemperatures.Piezoelectric nanopositioning systems large(e.g. for precision machining), medium (e.g. forinterferometry), small (e.g. for data storagemedium testing)Applications for Piezo Positioning Technology© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.182-174Data Storage MR head testing Spin stands Disk testing Active vibration cancellation Pole-tip recession testSemiconductors, Microelectronics Nano & Microlithography Nanometrologie Wafer and mask positioning Critical-dimension-test Inspection systems Active vibration cancellationPrecision Mechanics Fast tool servos Non-circular grinding,drilling, turning Active vibration cancellation Structural deformation Tool adjustment Wear compensation Needle-valve actuation Micropumps Linear drives Knife edge control in extrusiontools Micro engraving systems Shock wave generationLife Science, Medical Technology Scanning microscopy Patch clamp Nanoliter pumps Gene manipulation Micromanipulation Cell penetration MicrodispensersOptics, Photonics,Nanometrologie Scanning mirrors Image stabilization,pixel multiplication Scanning microscopy Auto focus systems Interferometry Fiber optic alignment Fiber optics switching Adaptive and active optics Laser tuning Stimulation of vibrationsSelection of piezo nanopositioning stages

Piezo • Nano • PositioningGlossarySee also the MicropositioningFundamentals Glossary (p. 4-128).Actuator:A device that can produce force ormotion (displacement).Blocked Force:The maximum force an actuatorcan generate if blocked by an infinitelyrigid restraint.Ceramic:A polycrystalline, inorganic material.Closed-Loop Operation:The displacement of the actuatoris corrected by a servo-controllercompensating for nonlinearity,hysteresis and creep. See also“Open-Loop Operation“.Compliance:Displacement produced per unitforce. The reciprocal of stiffness.Creep:An unwanted change in the displacementover time.Curie Temperature:The temperature at which thecrystalline structure changes froma piezoelectric (non-symmetrical)to a non-piezoelectric (symmetrical)form. At this temperature PZTceramics looses the piezoelectricproperties.Drift:See “creep”Domain:A region of electric dipoles withsimilar orientation.HVPZT:Acronym for High-Voltage PZT(actuator).Piezoceramic layers in a “classical”stack actuator (HVPZT).Hysteresis:Hysteresis in piezo actuators isbased on crystalline polarizationand molecular effects and occurswhen reversing driving direction.Hysteresis is not to be confusedwith backlash.LVPZT:Acronym for low-voltage PZT(actuator).Piezoceramic layers in a monolithicactuator (LVPZT).Monolithic Multilayer Actuator:An actuator manufactured in afashion similar to multilayer ceramiccapacitors. Ceramic andelectrode material are cofired inone step. Layer thickness is typicallyon the order of 20 to 100 μm.Open-Loop Operation:The actuator is used without aposition sensor. Displacementroughly corresponds to the drivevoltage. Creep, nonlinearity andhysteresis remain uncompensated.Parallel Kinematics:Unlike in serial kinematics designs,all actuators act upon thesame moving platform. Advantages:Minimized inertia, nomoving cables, lower center ofLinear Actuators & MotorsNanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesPiezoelectrics in PositioningNanometrologyMicropositioningIndexNanopositioning system featuring parallelkinematics and parallel metrology.Equipment for fully automated screen printing of electrodes on piezoelectric and dielectric ceramics.gravity, no cumulative guidingerrors and more-compact construction.2-175

Piezo • Nano • PositioningGlossary (cont.)Parallel Metrology:Unlike in serial metrology designs,each sensor measures the positionof the same moving platform in therespective degree of freedom. Thiskeeps the off-axis runout of allactuators inside the servo-controlloop and allows it to be correctedautomatically (active guidance).Piezoelectric Materials:Materials that change their dimensionswhen a voltage is appliedand produce a charge when pressureis applied.Metrology” is not possible, cumulativeguiding errors, lower accuracy.Serial Metrology:One sensor is assigned to eachdegree of freedom to be servo-controlled.Undesired off-axis motion(guiding error) from other axes inthe direction of a given sensor, gounrecognized and uncorrected (seealso “Parallel Metrology”).Stiffness:Spring constant (for piezoelectricmaterials, not linear).Poling / Polarization:The procedure by which the bulkmaterial is made to take on piezoelectricproperties, i.e. the electricalalignment of the unit cells in a piezoelectricmaterial.PZT:Acronym for plumbum (lead) zirconatetitanate. Polycrystalline ceramicmaterial with piezoelectricproperties. Often also used to referto a piezo actuator or translator.© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.182-176Serial Kinematics:Unlike in parallel kinematics designs,each actuator acts upon aseparate platform of its own. Thereis a clear relationship betweenactuators and axes.Advantages: Simpler to assemble;simpler control algorithm.Disadvantages: Poorer dynamiccharacteristics, integrated “ParallelDesign principle of a stacked XY piezo stage(serial kinematics).Flatness of a nanopositioning stage with active trajectory control is better than1 nanometer over a 100 x 100 μm scanning range.Trajectory-Control:Provisions to prevent deviationfrom the specified trajectory. Canbe passive (e.g. flexure guidance)or active (e.g. using additional activeaxes).Translator:A linear actuator.

Piezo • Nano • PositioningIntroductionNanopositioning with Piezoelectric TechnologyBasicsThe piezoelectric effect is often encounteredin daily life, for examplein lighters, loudspeakers andbuzzers. In a gas lighter, pressureon a piezoceramic generates anelectric potential high enough tocreate a spark. Most electronicalarm clocks do not use electromagneticbuzzers anymore,because piezoelectric ceramicsare more compact and more efficient.In addition to such simpleapplications, piezo technology hasrecently established itself in theautomotive branch. Piezo-driveninjection valves in diesel enginesrequire much lower transitiontimes than conventional electromagneticvalves, providing quieteroperation and lower emissions.The term “piezo” is derived fromthe Greek word for pressure. In1880 Jacques and Pierre Curie discoveredthat an electric potentialcould be generated by applyingpressure to quarz crystals; theynamed this phenomenon the“piezo effect”. Later they ascertainedthat when exposed to anelectric potential, piezoelectricmaterials change shape. This theynamed the “inverse piezo effect”.The first commercial applicationsof the inverse piezo effect were forsonar systems that were used inWorld War I. A breakthrough wasmade in the 1940’s when scientistsdiscovered that barium titanatecould be bestowed with piezoelectricproperties by exposing it to anelectric field.Features of PiezoelectricActuators Piezo actuators can performsub-nanometer moves athigh frequencies becausethey derive their motionfrom solid-state crystalineeffects. They have no rotatingor sliding parts to causefriction Piezo actuators can movehigh loads, up to severaltons Piezo actuators presentcapacitive loads and dissipatevirtually no power instatic operation Piezo actuators require nomaintenance and are notsubject to wear because theyhave no moving parts in theclassical sense of the termPiezoelectric materials are used toconvert electrical energy to mechanicalenergy and vice-versa. Theprecise motion that results whenan electric potential is applied to apiezoelectric material is of primordialimportance for nanopositioning.Actuators using the piezoeffect have been commerciallyavailable for 35 years and in thattime have transformed the worldof precision positioning andmotion control.Linear Actuators & MotorsNanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesPiezoelectrics in PositioningNanometrologyMicropositioningIndex2-177

Piezo • Nano • PositioningQuick FactsActuator DesignsNoteThis section gives a brief summaryof the properties of piezoelectricdrives and their applications. Fordetailed information, see “Fundamentalsof Piezoelectricity” beginningon p. 2-181.Stack actuators are the most commonand can generate the highestforces. Units with travel ranges upto 500 μm are available. To protectthe piezoceramic against destructiveexternal conditions, they areoften provided with a metal casingand an integrated preload spring toabsorb tensile forces.times the displacement of the piezoelement, resulting in a travel rangeof several hundred μm.Piezomotors are used where evenlonger travel ranges are required.Piezomotors can be divided intotwo main categories: Ultrasonic Motors (Fig. 2a) Piezo-Walk ® Motors (Fig. 2b)The motion of ultrasonic piezomotorsis based on the frictionbetween parts oscillating withmicroscopic amplitudes. Linearultrasonic motors are very compactand can attain high speeds combinedwith resolutions of 0.1 μm orbetter. Rotary motors feature hightorques even at low rpm.Piezo-Walk ® linear drives (seep. 1-3 ff ) offer high positioning andholding forces (up to hundreds ofnewtons) with moderate speedsand resolutions in the subnanometerrange.All implementations are self-lockingwhen powered down.Piezo tube actuators exploit theradial contraction direction, andare often used in scanning microscopesand micropumps.Bender and bimorph actuatorsachieve travel ranges in the millimeterrange (despite their compactsize) but with relatively lowforce generation (a few newtons).Shear elements use the inversepiezo-effectshear component andachieve long travel and high force.© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.182-178For more information, see p.2-207 ff.Guided piezo actuators (1 to 6axes) are complex nanopositionerswith integrated piezo drives andsolid-state, friction-free linkages(flexures). They are used whenrequirements like the followingneed be met: Extremely straight and flatmotion, or multi-axis motionwith accuracy requirements inthe sub-nanometer or sub-microradianrange Isolation of the actuator fromexternal forces and torques, protectionfrom humidity and foreignparticlesSuch systems often also includelever amplification of up to 20Fig. 1a. Selection of classical piezo stack actuators, with adhesive used to join the layersFig. 1b. Selection of monolithic PICMA ® technology actuators

Piezo • Nano • PositioningOperating Characteristics of Piezoelectric ActuatorsOperating VoltageTwo types of piezo actuators havebecome established. Monolithicsintered,low-voltage actuators(LVPZT) operate with potential differencesup to about 100 V and aremade from ceramic layers from 20to 100 μm in thickness. Classicalhigh-voltage actuators (HVPZT),on the other hand, are made fromceramic layers of 0.5 to 1 mmthickness and operate with potentialdifferences of up to 1000 V.High-voltage actuators can bemade with larger cross-sections,making them suitable for largerloads than the more-compact,monolithic actuators.a casing with integrated preloador an external preload spring isrequired. Adequate measuresmust be taken to protect the piezoceramicfrom shear and bendingforces and from torque.Travel RangeTravel ranges of Piezo Actuatorsare typically between a few tensand a few hundreds of μm (linearactuators). Bender actuators andlever amplified systems canachieve a few mm. Ultrasonicpiezomotors and Piezo-Walk ®drives can be used for longer travelranges.concerning the sensor, actuatorand preload can induce micro-frictionwhich limits resolution andaccuracy.PI offers piezo actuators and positioningsystems that provide subnanometerresolution and stability.For more information, seep. 2-183 ff.Linear Actuators & MotorsNanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesStiffness, Load Capacity, ForceGenerationTo a first approximation, a piezoactuator is a spring-and-mass system.The stiffness of the actuatordepends on the Young’s modulusof the ceramic (approx. 25 % thatof steel), the cross-section andlength of the active material and anumber of other non-linearparameters (see p. 2-189). Typicalactuators have stiffnessesbetween 1 and 2,000 N/μm andcompressive limits between 10and 100,000 N. If the unit will beexposed to pulling (tensile) forces,ResolutionPiezoceramics are not subject tothe “stick slip” effect and thereforeoffer theoretically unlimitedresolution. In practice, the resolutionactually attainable is limitedby electronic and mechanical factors:a) Sensor and servo-control electronics(amplifier): amplifier noiseand sensitivity to electromagneticinterference (EMI) affect the positionstability.b) Mechanical parameters: designand mounting precision issuesFig. 2b. Custom linear drivewith integratedNEXLINE ® Piezo-Walk ® piezomotorPiezoelectrics in PositioningNanometrologyMicropositioningIndexFig. 2a. Ultrasonic piezo linear motorsFig. 3. Example of a compact piezonanopositioning and scanning systemwith integrated flexure guidance,sensor and motion amplifier2-179

Piezo • Nano • PositioningQuick Facts (cont.)© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.182-180Open- and Closed-Loop OperationIn contrast to many other types ofdrive systems, piezo actuators canbe operated without servo-control.The displacement is approximatelyequal to the drive voltage.Hysteresis, nonlinearity and creepeffects limit the absolute accuracy.For positioning tasks which requirehigh linearity, long-term stability,repeatability and absolute accuracy,closed-loop (servo-controlled) piezoactuators and systems areused (see p. 2-199). With suitablecontrollers, closed-loop operationenables reproducibilities in thesub-nanometer range.High-Resolution Sensors forClosed-Loop OperationLVDT (linear variable differentialtransformer), strain gauge andcapacitive sensors are the mostcommon sensor types used forclosed-loop operation. Capacitivesensors offer the greatest accuracy.For more information, see p. 2-187 ff.Dynamic BehaviorA piezo actuator can reach its nominaldisplacement in approximatelyone third of the period of its resonantfrequency. Rise times on theorder of microseconds and accelerationsof more than 10,000 g arepossible. This feature makes piezoactuators suitable for rapid switchingapplications such as controllinginjector nozzle valves, hydraulicvalves, electrical relays, opticalswitches and adaptive optics. Formore information, see p. 2-192 ff.Power RequirementsPiezo actuators behave as almostpure capacitive loads. Static operation,even holding heavy loads,consumes virtually no power. Indynamic applications the energyrequirement increases linearly withfrequency and actuator capacitance.At 1000 Hz with 10 μmamplitude, a compact piezo translatorwith a load capacity ofapprox. 100 N requires less than10 W, while a high-load actuator(> 10 kN capacity) would use severalhundred watts under the same conditions.For more information, seep. 2-195 ff.Protection from MechanicalDamagePZT ceramics are brittle and cannotwithstand high pulling or shearforces. The mechanical actuatordesign must thus isolate theseundesirable forces from the ceramic.This can be accomplished bymeasures such as spring preloads,use of ball tips, flexible couplings,etc. (for more mounting guidelines,see p. 2-216). In addition, theceramics must be protected frommoisture and the intrusion of foreignparticles. Close contactbetween the piezo mechanics manufacturerand the user facilitatesfinding an optimal match betweenthe piezo system and the applicationenvironment.Fig. 4. Piezo actuator with water-proof case and connection for flushing/cooling air

Piezo • Nano • PositioningFundamentals of PiezoelectricityMaterial PropertiesNotesThe following pages give adetailed look at piezo actuatortheory and their operation. Forbasic knowledge read “QuickFacts”, p. 2-178. For definitionof units, dimensions and terms,see “Symbols and Units”,p. 2-217 and “Glossary”, p.2-175.Since the piezo effect exhibitedby natural materials such asquartz, tourmaline, Rochellesalt, etc. is very small, polycrystallineferroelectric ceramicmaterials such as bariumtitanate and lead (plumbum)zirconate titanate (PZT) withimproved properties have beendeveloped.PZT ceramics (piezoceramics)are available in many variationsand are still the mostwidely used materials for actuatorapplications today.Before polarization, PZT crystalliteshave symmetric cubicunit cells. At temperaturesbelow the Curie temperature,the lattice structure becomesdeformed and asymmetric. Theunit cells exhibit spontaneouspolarization (see Fig. 5), i.e. theindividual PZT crystallites arepiezoelectric.thermal and electrical limits ofthe material). The ceramic nowexhibits piezoelectric propertiesand will change dimensionswhen an electric potentialis applied.Linear Actuators & MotorsNanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesPiezoelectrics in PositioningNanometrologyMicropositioningIndexGroups of unit cells with thesame orientation are calledWeiss domains. Because of therandom distribution of thedomain orientations in theceramic material no macroscopicpiezoelectric behavior isobservable. Due to the ferroelectricnature of the material,it is possible to force permanentalignment of the differentdomains using a strong electricfield. This process is called poling(see Fig. 6). Some PZTceramics must be poled at anelevated temperature. The materialnow has a remnant polarization(which can be degradedby exceeding the mechanical,Fig. 5. PZT unit cell:1) Perovskite-type lead zirconatetitanate (PZT) unit cell in the symmetriccubic state above the Curietemperature2) Tetragonally distorted unit cell belowthe Curie temperatureFig. 6. Electric dipoles in domains; (1) unpoled ferroelectricceramic, (2) during and (3) after poling (piezoelectric ceramic)2-181

Piezo • Nano • PositioningFundamentals of Piezoelectricity (cont.)PZT Ceramics Manufacturing ProcessPI develops and manufacturesits own piezo ceramic materialsat the PI Ceramic factory. Themanufacturing process forhigh-voltage piezoceramicstarts with mixing and ballmilling of the raw materials.Next, to accelerate reaction ofthe components, the mixture isheated to 75 % of the sinteringtemperature, and then milledagain. Granulation with thebinder is next, to improve processingproperties. After shapingand pressing, the greenceramic is heated to about750 °C to burn out the binder.The next phase is sintering, attemperatures between 1250 °Cand 1350 °C. Then the ceramicblock is cut, ground, polished,lapped, etc., to the desiredshape and tolerance. Electrodesare applied by sputteringor screen printing processes.The last step is the polingprocess which takes place in aheated oil bath at electricalfields up to several kV/mm.Only here does the ceramictake on macroscopic piezoelectricproperties.Multilayer piezo actuatorsrequire a different manufacturingprocess. After milling, aslurry is prepared for use in afoil casting process whichallows layer thickness down to20 μm. Next, electrodes arescreen printed and the sheetslaminated. A compactingprocess increases the densityof the green ceramics andremoves air trapped betweenthe layers. The final steps arethe binder burnout, sintering(co-firing) at temperaturesbelow 1100 °C , wire lead terminationand poling.All processes, especially theheating and sintering cycles,must be controlled to very tighttolerances. The smallest deviationwill affect the quality andproperties of the PZT material.One hundred percent final testingof the piezo material andcomponents at PI Ceramicguarantees the highest possibleproduct quality.Sputtering facility at PI CeramicDefinition of Piezoelectric Coefficients and Directions© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.18Because of the anisotropicnature of PZT ceramics, piezoelectriceffects are dependenton direction. To identify directions,the axes 1, 2, and 3 willbe introduced (correspondingto X, Y, Z of the classical righthandorthogonal axis set). Theaxes 4, 5 and 6 identify rotations(shear), X , Y , Z (alsoknown as U, V, W.)The direction of polarization(axis 3) is established duringthe poling process by a strongelectrical field applied betweentwo electrodes. For linear actuator(translator) applications,the piezo properties along thepoling axis are the most important(largest deflection).Piezoelectric materials arecharacterized by several coefficients.Examples are: d ij : Strain coefficients [m/V]or charge output coefficients[C/N]: Strain developed[m/m] per unit of electricfield strength applied [V/m]or (due to the sensor / actuatorproperties of PZT material)charge density developed[C/m 2 ] per given stress[N/m 2 ]. g ij : Voltage coefficients orfield output coefficients[Vm/N]: Open-circuit electricfield developed [V/m] perapplied mechanical stress[N/m 2 ] or (due to the sensor /actuator properties of PZTmaterial) strain developed[m/m] per applied chargedensity [C/m 2 ]. k ij : Coupling coefficients[dimensionless]. The coefficientsare energy ratiosdescribing the conversionfrom mechanical to electricalenergy or vice versa. k 2 is theratio of energy stored(mechanical or electrical) toenergy (mechanical or electrical)applied.Other important parametersare the Young’s modulus Y(describing the elastic propertiesof the material) and r therelative dielectric coefficients(permittivity).Double subscripts, as in d ij , areused to describe the relationshipsbetween mechanical andelectrical parameters. The firstindex indicates the direction ofthe stimulus, the second thedirection of the reaction of thesystem.Example: d 33 applies when theelectric field is along the polarizationaxis (direction 3) andthe strain (deflection) is alongthe same axis. d 31 appliesiftheelectric field is in the samedirection as before, but thedeflection of interest is thatalong axis 1 (orthogonal to thepolarization axis).In addition the superscripts S,T, E, D can be used to describean electrical or mechanicalboundary condition.Definition:S for strain = constant (mechanicallyclamped)T for stress = constant (notclamped)E for field = 0 (short circuit)D for charge displacement (current)= 0 (open circuit)The individual piezoelectriccoefficients are related to eachother by systems of equationsthat will not be explained here.2-182

Piezo • Nano • PositioningNotesThe piezoelectric coefficientsdescribed here are often presentedas constants. It shouldbe clearly understood that theirvalues are not invariable. Thecoefficients describe materialproperties under small-signalconditions only. They vary withtemperature, pressure, electricfield, form factor, mechanicaland electrical boundary conditions,etc. Compound components,such as piezo stack actuators,let alone preloaded actuatorsor lever-amplified systems,cannot be described sufficientlyby these materialparameters alone. This is whyeach component or systemmanufactured by PI is accompaniedby specific data such asstiffness, load capacity, displacement,resonant frequency,etc., determined by individualmeasurements. The parametersdescribing these systemsare to be found in the technicaldata table for the product.Important: There are no internationalstandards for definingthese specifications. Thismeans that claims of differentmanufacturers can not necessarilybe compared directlywith one another.PolarisationFig. 7. Orthogonal system describing theproperties of a poled piezoelectric ceramic.Axis 3 is the poling direction.Linear Actuators & MotorsNanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesPiezoelectrics in PositioningResolutionNanometrologySince the displacement of apiezo actuator is based on ionicshift and orientation of the PZTunit cells, the resolutiondepends on the electrical fieldapplied. Resolution is theoreticallyunlimited. Because thereare no threshold voltages, thestability of the voltage source iscritical; noise even in the μVrange causes position changes.When driven with a low-noiseamplifier, piezo actuators canbe used in tunneling and atomicforce microscopes providingsmooth, continuous motionwith sub-atomic resolution (seeFig. 8).Amplifier NoiseOne factor determining theposition stability (resolution) ofa piezo actuator is noise in thedrive voltage. Specifying thenoise value of the piezo driverelectronics in millivolts, however,is of little practical usewithout spectral information. Ifthe noise occurs in a frequencyband far beyond the resonantfrequency of the mechanicalsystem, its influence onmechanical resolution and stabilitycan be neglected. If itcoincides with the resonant frequency,it will have a far moresignificant influence on the systemstability.Therefore, meaningful informationabout the stability andresolution of a piezo positioningsystem can only beacquired if the resolution of thecomplete system—piezo actuatorand drive electronics—ismeasured in terms of nanometersrather than millivolts. Forfurther information see p. 2-10and p. 2-199 ff.NotesThe smooth motion in the subnanometerrange shown inFig. 8 can only be attained byfrictionless and stictionlesssolid state actuators and guidancesuch as piezo actuatorsand flexures. “Traditional”technologies used in motionpositioners (stepper or DCservo-motor drives in combinationwith dovetail slides, ballbearings, and roller bearings)all have excessive amounts offriction and stiction. This fundamentalproperty limits resolution,causes wobble, hysteresis,backlash, and an uncertaintyin position repeatability.Their practical usefulness isthus limited to a precision ofseveral orders of magnitudebelow that obtainable with PIpiezo nanopositioners.MicropositioningIndexFig. 8. Smooth response of a P-170 HVPZT translator to a1V,200Hztriangulardrive signal. Note that one division is only 2 nanometers2-183

Piezo • Nano • PositioningFundamentals of PiezomechanicsDisplacement of Piezo Actuators (Stack & Contraction Type)© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.18Commonly used stack actuatorsachieve a relative displacementof up to 0.2 %.Displacement of piezoceramicactuators is primarily a functionof the applied electric fieldstrength E, the length L of theactuator, the forces applied to itand the properties of the piezoelectricmaterial used. Thematerial properties can bedescribed by the piezoelectricstrain coefficients d ij . Thesecoefficients describe the relationshipbetween the appliedelectric field and the mechanicalstrain produced.The change in length, L, of anunloaded single-layer piezoactuator can be estimated bythe following equation:(Equation 1)Where:S = strain (relative lengthchange L/L, dimensionless)L 0 = ceramic length [m]E = electric field strength[V/m]d ij = piezoelectric coefficientof the material[m/V]d 33 describes the strain parallelto the polarization vector of theceramics (thickness) and isused when calculating the displacementof stack actuators;d 31 is the strain orthogonal tothe polarization vector (width)and is used for calculating tubeand strip actuators (see Fig. 9).d 33 and d 31 are sometimesreferred to as “piezo gain”.NotesFor the materials used in standardPI piezo actuators, d 33is on the order of 250 to550 pm/V, d 31 is on the order of2-184-180 to -210 pm/V. The highestvalues are attainable withshear actuators in d 15 mode.These figures only apply to theraw material at room temperatureunder small-signal conditions.The maximum allowable fieldstrength in piezo actuators isbetween 1 and 2 kV/mm in thepolarization direction. In thereverse direction (semi-bipolaroperation), at most 300 V/mmis allowable (see Fig. 10). Themaximum voltage depends onthe ceramic and insulationmaterials.Exceeding the maximum voltagemay cause dielectric breakdownand irreversible damageto the piezo actuator.With the reverse field, negativeexpansion (contraction) occurs,giving an additional 20 % of thenominal displacement. If boththe regular and reverse fieldsare used, a relative expansion(strain) up to 0.2 % is achievablewith piezo stack actuators.This technique can reduce theaverage applied voltage withoutloss of displacement andthereby increase piezo lifetime.Stacks can be built with aspectratios up to 12:1(length:diameter). This meansthat the maximum travel rangeof an actuator with 15 mmpiezo diameter is limited toabout 200 μm. Longer travelranges can be achieved bymechanical amplification techniques(see “Lever MotionAmplifiers” p. 2-210).Fig. 9. Expansion and contraction of a piezoelectric disk in response to an appliedvoltage. Note that d 31 , which describes the lateral motion, D, is negativeFig. 10. Typical response of a “soft PZT” actuator to a bipolar drivevoltage. When a certain threshold voltage negative to the polarizationdirection is exceeded, reversal of polarization can occurPolarisationV

Piezo • Nano • PositioningNote:PI piezo actuators and stagesare designed for high reliabilityin industrial applications. Thetravel, voltage and load rangesin the technical data tables canactually be used in practice.They have been collected overmany years of experience inpiezo actuator production andin numerous industrial applications.In contrast to many other piezosuppliers, PI has its own piezoceramic development and productionfacilities together withthe necessary equipment andknowhow. The goal is alwaysreliability and practical usefulness.Maximizing isolatedparameters, such as expansionor stiffness, at the cost of piezolifetime might be interesting toan experimenter, but has noplace in practical application.When selecting a suitablepiezo actuator or stage, considercarefully the fact that “maximumtravel” may not be theonly critical design parameter.Hysteresis(Open-Loop Piezo Operation)Hysteresis is observable inopen-loop operation; it can bereduced by charge control andvirtually eliminated by closedloopoperation (see p. 2-199 ff ).widenstoamaximumof10%to 15 % under large-signal conditions.The highest values areattainable with shear actuatorsin d 15 mode.For example, if the drive voltageof a 50 μm piezo actuatoris changed by 10 %, (equivalentto about 5 μm displacement)the position repeatabilityis still on the order of 1%offull travel or better than 1 μm.The smaller the move, thesmaller the uncertainty.Hysteresis must not be confusedwith the backlash of conventionalmechanics. Backlashis virtually independent of travel,so its relative importanceincreases for smaller moves.For tasks where it is not theabsolute position that counts,hysteresis is of secondaryimportance and open-loopactuators can be used, even ifhigh resolution is required.LIn closed-loop piezo actuatorsystems hysteresis is fullycompensated. PI offers thesesystems for applications requiringabsolute position information,as well as motion withhigh linearity, repeatability andaccuracy in the nanometer andsub-nanometer range (see p.2-199 ff ).Example: Piezoelectrically drivenfiber aligners and trackingsystems derive the control signalfrom an optical powermeter in the system. There, thegoal is to maximize the opticalsignal level as quickly as possible,not to attain a predeterminedposition value. An openlooppiezo system is sufficientfor such applications. Advantageslike unlimited resolution,fast response, zero backlashand zero stick/slip effectare most welcome, even withoutposition control.Linear Actuators & MotorsNanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesPiezoelectrics in PositioningNanometrologyMicropositioningIndexOpen-loop piezo actuatorsexhibit hysteresis in theirdielectric and electromagneticlarge-signal behavior. Hysteresisis based on crystallinepolarization effects and moleculareffects within the piezoelectricmaterial.The amount of hysteresisincreases with increasing voltage(field strength) applied tothe actuator. The “gap” in thevoltage/displacement curve(see Fig. 11) typically beginsaround 2%(small-signal) andFig. 11. Hysteresis curves of an open-loop piezo actuator for variouspeak voltages. The hysteresis is related to the distance moved, notto the nominal travel rangeV2-185

Piezo • Nano • PositioningFundamentals of Piezomechanics (cont.)Creep / Drift (Open-Loop PiezoOperation)The same material propertiesresponsible for hysteresis alsocause creep or drift. Creep is achange in displacement withtime without any accompanyingchange in the control voltage.If the operating voltage ofa piezo actuator is changed,the remnant polarization (piezogain) continues to change,manifesting itself in a slowchange of position. The rate ofcreep decreases logarithmicallywith time (see Fig. 12). Thefollowing equation describesthis effect:piezo effect). With actuatorapplications it is negligible,because repoling occurs everytime a higher electric field isapplied to the actuator materialin the poling direction.NoteFor periodic motion, creep andhysteresis have only a minimaleffect on repeatability.(Equation 2)Creep of PZT motion as a functionof time.© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.182-186Where:t = time [s]L(t) = change in positionasafunctionoftimeL t= 0.1 = displacement 0.1seconds after thevoltage change iscomplete [m]. = creep factor,which is dependenton the propertiesof the actuator(on the orderof 0.01 to 0.02,whichis1%to2%pertime decade).In practice, maximum creep(after a few hours) can add upto a few percent of the commandedmotion.AgingAging refers to reduction inremnant polarization; it can bean issue for sensor or chargegenerationapplications (directFig. 12. Creep of open-loop PZT motion after a 60 μm change in length as a functionof time. Creep is on the order of 1%ofthelast commanded motion per time decade

Piezo • Nano • PositioningActuators and SensorsMetrology for Nanopositioning SystemsThere are two basic techniquesfor determining the position ofpiezoelectric motion systems:Direct metrology and indirectmetrology.Indirect (Inferred) MetrologyIndirect metrology involvesinferring the position of theplatform by measuring positionor deformation at the actuatoror other component in thedrive train. Motion inaccuracieswhich arise between the driveand the platform can not beaccounted for.Direct MetrologyWith direct metrology, however,motion is measured at thepoint of interest; this can bedone, for example, with aninterferometer or capacitivesensor.Direct metrology is more accurateand thus better suited toapplications which needabsolute position measurements.Direct metrology alsoeliminates phase shiftsbetween the measuring pointand the point of interest. Thisdifference is apparent in higher-load,multi-axis dynamicapplications.Parallel and Serial MetrologyIn multi-axis positioning systemsparallel and serial metrologymust also be distinguished.With parallel metrology, allsensors measure the positionof the same moving platformagainst the same stationary reference.This means that allmotion is inside the servo-loop,no matter which actuatorcaused it (see Active TrajectoryControl). Parallel metrologyand parallel kinematics can beeasily integrated.With serial metrology the referenceplane of one or more sensorsis moved by one or moreactuators. Because the off-axismotion of any moving referenceplane is never measured,it can not be compensated.Seealsop.2-8ff.Linear Actuators & MotorsNanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesPiezoelectrics in PositioningNanometrologyHigh-Resolution SensorsMicropositioningStrain Gauge SensorsSGS sensors are an implementationof inferred metrologyand are typically chosen forcost-sensitive applications. AnSGS sensor consists of a resistivefilm bonded to the piezostack or a guidance element;the film resistance changeswhen strain occurs. Up to fourstrain gauges (the actual configurationvaries with the actuatorconstruction) form aWheatstone bridge driven by aDC voltage (5 to 10 V). Whenthe bridge resistance changes,the sensor electronics convertsthe resulting voltage changeinto a signal proportional to thedisplacement.Bandwidth: to5kHzIndexAdvantages High Bandwidth Vacuum Compatible Highly CompactOther characteristics: Low heat generation (0.01 to0.05 W sensor excitationpower) Long-term position stabilitydepends on adhesive quality Indirect metrologyExamplesMost PI LVPZT and HVPZT actuatorsare available with straingauge sensors for closed-loopcontrol (see the “Piezo Actuators& Components” section p. 1-61 ff).Fig. 13. Strain gauge sensors.Paper clip for size comparisonA special type of SGS is knownas a piezoresistive sensor. Ithas good sensitivity, butmediocre linearity and temperaturestability. See also p. 2-8 ff.Resolution: better than 1 nm(for short travel ranges, up toabout 15 μm)NoteThe sensor bandwidth for thesensors described here shouldnot be confused with the bandwidthof the piezo mechanicsservo-control loop, which isfurther limited by the electronicand mechanical properties ofthe system.2-187

Piezo • Nano • PositioningActuators and Sensors (cont.)Fig. 14. LVDT sensor, coil and core. Paperclip for size comparisonFig. 16. Capacitive sensors canattain resolution 10,000 timesbetter than calipers© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.18Linear Variable DifferentialTransformers (LVDTs)LVDTs are well suited for directmetrology. A magnetic core,attached to the moving part,determines the amount ofmagnetic energy induced fromthe primary windings into thetwo differential secondarywindings (Fig. 15). The carrierfrequency is typically 10 kHz.Resolution: to5nmBandwidth: to1kHzRepeatability: to5nmAdvantages: Good temperature stability Very good long-termstability Non-contactingFig. 15. Working principle of an LVDT sensor Controls the position of themoving part rather than theposition of the piezo stack Cost-effectiveOther characteristics: Outgassing of insulationmaterials may limit applicationsin very high vacuum Generates magnetic fieldCapacitive Position SensorsCapacitive sensors are themetrology system of choice forthe most demanding applications.Two-plate capacitive sensorsconsist of two RF-excitedplates that are part of a capacitivebridge (Fig. 17). One plateis fixed, the other plate is connectedto the object to be positioned(e.g. the platform of astage). The distance betweenthe plates is inversely proportionalto the capacitance, fromwhich the displacement is calculated.Short-range, two-platesensors can achieve resolutionon the order of picometers.See the “Nanometrology”section (p. 3-1 ff ). for details.Resolution: Better than 0.1 nmpossibleFig. 17. Working principle of two-plate capacitive position sensorsRepeatability: Better than0.1 nm possibleBandwidth: Up to 10 kHzAdvantages: Highest resolution of allcommercially available sensors Ideally suited for parallelmetrology Non-contacting Excellent long-term stability Excellent frequency response No magnetic field Excellent linearityOther characteristics: Ideally suited for integrationin flexure guidance systems,which maintain the necessaryparallelism of the plates.Residual tip/tilt errorsare greatly reduced by theILS linearization system (seep. 3-18) developed by PI.ExamplesP-733 parallel kinematic nanopositioningsystem with parallelmetrology (see p. 2-62).P-753 LISA NanoAutomation ®actuators (see p. 2-16); additionalexamples in the “PiezoFlexure Stages / High-SpeedScanning Systems” section.2-188

Piezo • Nano • PositioningFundamentals of Piezoelectric ActuatorsForces and StiffnessMaximum Applicable Forces(Compressive Load Limit,Tensile Load Limit)The mechanical strength valuesof PZT ceramic material(given in the literature) areoften confused with the practicallong-term load capacity of apiezo actuator. PZT ceramicmaterial can withstand pressuresup to 250 MPa (250 x 10 6N/m 2 ) without breaking. Thisvalue must never beapproached in practical applications,however, becausedepolarization occurs at pressureson the order of 20 % to30 % of the mechanical limit.For stacked actuators andstages (which are a combinationof several materials) additionallimitations apply. Parameterssuch aspect ratio, buckling,interaction at the interfaces,etc. must be considered.ness is normally expressed interms of the spring constant k T ,which describes the deformationof the body in response toan external force.This narrow definition is of limitedapplication for piezoceramicsbecause the cases ofstatic, dynamic, large-signaland small-signal operationwith open and shorted electrodesmust all be distinguished.The poling process ofpiezoceramics leaves a remnantstrain in the materialwhich depends on the magnitudeof polarization. The pola-imposed on the stiffness (k T ).Since piezo ceramics are activematerials, they produce anelectrical response (charge)when mechanically stressed(e.g. in dynamic operation). Ifthe electric charge cannot bedrained from the PZT ceramics,it generates a counterforceopposing the mechanicalstress. This is why a piezo elementwith open electrodesappears stiffer than one withshorted electrodes. Commonvoltage amplifiers with theirlow output impedances looklike a short circuit to a piezoactuator.Linear Actuators & MotorsNanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesPiezoelectrics in PositioningNanometrologyMicropositioningThe load capacity data listedfor PI actuators are conservativevalues which allow longlifetime.IndexTensile loads of non-preloadedpiezo actuators are limited to5% to 10% of the compressiveload limit. PI offers a variety ofpiezo actuators with internalspring preload for increasedtensile load capacity. Preloadedelements are highly recommendedfor dynamic applications.The PZT ceramic is especiallysensitive to shear forces; theymust be intercepted by externalmeasures (flexure guides,etc.).StiffnessActuator stiffness is an importantparameter for calculatingforce generation, resonant frequency,full-system behavior,etc. The stiffness of a solidbody depends on Young’smodulus of the material. Stiff-Fig. 18. Quasi-static characteristic mechanical stress/strain curves for piezo ceramic actuatorsand the derived stiffness values. Curve 1 is with the nominal operating voltage on theelectrodes, Curve 2 is with the electrodes shorted (showing ceramics after depolarization)rization is affected by both theapplied voltage and externalforces. When an external forceis applied to poled piezoceramics,the dimensional changedepends on the stiffness of theceramic material and thechange of the remnant strain(caused by the polarizationchange). The equation L N =F/k T is only valid for smallforces and small-signal conditions.For larger forces, anadditional term, describing theinfluence of the polarizationchanges, must be super-Mechanical stressing of piezoactuators with open electrodes,e.g. open wire leads, should beavoided, because the resultinginduced voltage might damagethe stack electrically.NoteThere is no international standardfor measuring piezo actuatorstiffness. Therefore stiffnessdata from different manufacturerscannot be comparedwithout additional information.2-189

Piezo • Nano • PositioningFundamentals of Piezoelectric Actuators (cont.)Force GenerationIn most applications, piezoactuators are used to producedisplacement. If used in arestraint, they can be used togenerate forces, e.g. for stamping.Force generation is alwayscoupled with a reduction in displacement.The maximumforce (blocked force) a piezoactuator can generate dependson its stiffness and maximumdisplacement (see also p. 2-191).At maximum force generation,displacement drops to zero.(Equation 3)Maximum force that can begenerated in an infinitely rigidrestraint (infinite spring constant).Where:L 0k T= max. nominal displacementwithout externalforce or restraint [m]= piezo actuator stiffness[N/m]ExampleWhat is the force generation ofa piezo actuator with nominaldisplacement of 30 μm andstiffness of 200 N/μm? Thepiezo actuator can produce amaximum force of 30 μm x 200N/μm = 6000 N When forcegeneration is maximum, displacementis zero and viceversa (see Fig. 19 for details).ExampleA piezo actuator is to be usedin a nano imprint application.At rest (zero position) the distancebetween the piezo actuatortip and the material is 30microns (given by mechanicalsystem tolerances). A force of500 N is required to embossthe material.Q: Can a 60 μm actuator with astiffness of 100 N/μm be used?A: Under ideal conditionsthis actuator can generate aforce of 30 x 100 N = 3000 N(30 microns are lost motiondue to the distance betweenthe sheet and the piezo actuatortip). In practice the forcegeneration depends on thestiffness of the metal and thesupport. If the support were asoft material, with a stiffness of10 N/μm, the piezo actuatorcould only generate a force of300 N onto the metal whenoperated at maximum drivevoltage. If the support werestiff but the material to beembossed itself were very softit would yield and the piezoactuator still could not generatethe required force. If boththe support and the metal werestiff enough, but the piezo actuatormount was too soft, theforce generated by the piezowould push the actuator awayfrom the material to beembossed.The situation is similar to liftinga car with a jack. If the ground(or the car’s body) is too soft,the jack will run out of travelbefore it generates enoughforce to lift the wheels off theground.© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.18In actual applications thespring constant of the load canbe larger or smaller than thepiezo spring constant. Theforce generated by the piezoactuator is:(Equation 4)Effective force a piezo actuatorcan generate in a yieldingrestraintWhere:L 0k Tk S= max. nominal displacementwithout externalforce or restraint [m]= piezo actuator stiffness[N/m]= stiffness of externalspring [N/m]Fig. 19. Force generation vs. displacementof a piezo actuator (displacement30 μm, stiffness 200N/μm). Stiffness at various operatingvoltages. The points where thedashed lines (external springcurves) intersect the piezo actuatorforce/displacement curvesdetermine the force and displacementfor a given setup with anexternal spring. The stiffer theexternal spring (flatter dashedline), the less the displacementand the greater the force generatedby the actuator. Maximumwork can be done when the stiffnessof the piezo actuator andexternal spring are identical2-190

Piezo • Nano • PositioningDisplacement andExternal ForcesaConstant ForcebChanging ForceLike any other actuator, a piezoactuator is compressed when aforce is applied. Two casesmust be considered when operatinga piezo actuator with aload:a) The load remains constantduring the motion process.b) The load changes during themotion process.NoteTo keep down the loss of travel,the stiffness of the preloadspring should be under 1/10that of the piezo actuator stiffness.If the preload stiffnesswere equal to the piezo actuatorstiffness, the travel wouldbe reduced by 50 %. For primarilydynamic applications, theresonant frequency of the preloadmust be above that of thepiezo actuator.Zero-point is offsetA mass is installed on thepiezo actuator which appliesa force F = M · g (M is themass, g the acceleration dueto gravity).The zero-point will be shiftedby L N ≈ F/k T , where k T is thestiffness of the actuator.If this force is below the specifiedload limit (see producttechnical data), full displacementcan be obtained at fulloperating voltage (see Fig. 20).(Equation 5)Zero-point offset with constantforceWhere:L NFk T= zero-point offset [m]= force (mass x accelerationdue to gravity)[N]= piezo actuator stiffness[N/m]Displacement is reducedFor piezo actuator operationagainst an elastic load differentrules apply. Part of thedisplacementgeneratedby thepiezo effectis lost dueto the elasticityof thepiezo element(Fig.21). The totalavailabledisplacementcanbe related to the spring stiffnessby the following equations:(Equation 6)Maximum displacement of apiezo actuator acting againsta spring load.(Equation 7)Fig. 21. Case b: Effectivedisplacement of a piezo actuatoracting against a spring loadExampleMFig. 20. Case a: Zero-point offsetwith constant forceHow large is the zero-pointoffset of a 30 μm piezo actuatorwith a stiffness of 100N/μm if a load of 20 kg isapplied, andwhat is themaximum displacementwiththis load?The load of20 kg generatesa force of 20 kgx 9.81 m/s 2 =196 N. Witha stiffness of100 N/μm, the piezo actuatoris compressed slightly lessthan 2 μm. The maximumdisplacement of 30 μm is notreduced by this constantforce.Maximum loss of displacementdue to external springforce. In the case where therestraint is infinitely rigid (k s= ∞), the piezo actuator canproduce no displacement butacts only as a force generator.Where:LL 0L Rk sk T= displacement with externalspring load [m]= nominal displacementwithout external forceor restraint [m]= lost displacementcaused by the externalspring [m]= spring stiffness [N/m]= piezo actuator stiffness[N/m]ExampleQ: What is the maximum displacementof a 15 μm piezotranslator with a stiffness of50 N/μm, mounted in an elasticrestraint with a springconstant k S (stiffness) of100 N/μm?A: Equation 6 shows that thedisplacement is reduced in anelastic restraint. The springconstant of the externalrestraint is twice the value ofthe piezo translator. Theachievable displacement istherefore limited to 5 μm(1/3 of the nominal travel).2-191

Piezo • Nano • PositioningDynamic Operation FundamentalsDynamic ForcesEvery time the piezo drive voltagechanges, the piezo elementchanges its dimensions. Due tothe inertia of the piezo actuatormass (plus any additionalload), a rapid move will generatea force acting on (pushingor pulling) the piezo. The maximumforce that can be generatedis equal to the blocked force,described by:(Equation 8)Maximum force available toaccelerate the piezo mass plusany additional load. Tensileforces must be compensated,for example, by a spring preload.Where:F max = max. force [N]The preload force should bearound 20% of the compressiveload limit. The preload shouldbe soft compared to the piezoactuator, at most 10% the actuatorstiffness.In sinusoidal operation peakforces can be expressed as:(Equation 9)Dynamic forces on a piezoactuator in sinusoidal operationat frequency f.Where:F dyn = dynamic force [N]m eff = effective mass [kg],see p. 4-25L = peak-to-peak displacement[m]f = frequency [Hz]The maximum permissibleforces must be consideredwhen choosing an operatingfrequency.Example:Dynamic forces at 1000 Hz, 2 mpeak-to-peak and 1 kg loadreach approximately ±40 N.NoteA guiding system (e.g.diaphragm type) is essentialwhen loads which are heavy orlarge (relative to the piezo actuatordiameter) are moveddynamically. Without a guidingsystem, there is a potential fortilt oscillations that may damagethe piezoceramics.L 0k T= max. nominal displacementwithout externalforce or restraint [m]= piezo actuator stiffness[N/m]© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.18Fig. 22. Recommended guiding for large masses2-192

Piezo • Nano • PositioningResonant FrequencyIn general, the resonant frequencyof any spring/mass systemis a function of its stiffnessand effective mass (see Fig.23). Unless otherwise stated,the resonant frequency givenin the technical data tables foractuators always refer to theunloaded actuator with oneend rigidly attached. For piezopositioning systems, the datarefers to the unloaded systemfirmly attached to a significantlylarger mass.(Equation 10)Note:In positioning applications,piezo actuators are operatedwell below their resonant frequencies.Due to the non-idealspring behavior of piezoceramics,the theoretical result fromthe above equation does notnecessarily match the realworldbehavior of the piezoactuator system under largesignal conditions. Whenadding a mass M to the actuator,the resonant frequencydrops according to the followingequation:(Equation 11)is well above that of the actuator,forces it introduces do notsignificantly affect the actuator’sresonant frequency.The phase response of a piezoactuator system can be approximatedby a second order systemand is described by the followingequation:(Equation 12)Where:= phase angle [deg]Linear Actuators & MotorsNanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesF max = resonant frequency [Hz]Piezoelectrics in PositioningResonant frequency of an idealspring/mass system.Where:f Ok T= resonant frequency ofunloaded actuator [Hz]= piezo actuator stiffness[N/m]m eff = effective mass (about1/3 of the mass of theceramic stack plus anyinstalled end pieces)[kg]Resonant frequency withadded mass.m´eff = additional massM+m eff .The above equations show thatto double the resonant frequencyof a spring-mass system,it is necessary to eitherincrease the stiffness by a factorof 4 or decrease the effectivemass to 25 % of its originalvalue. As long as the resonantfrequency of a preload springf= operating frequency[Hz]NanometrologyMicropositioningIndexFig. 23. Effective mass of an actuator fixed at one end2-193

Piezo • Nano • PositioningDynamic Operation Fundamentals (cont.)How Fast Can a PiezoActuator Expand?Fast response is one of thecharacteristic features of piezoactuators. A rapid drive voltagechange results in a rapid positionchange. This property isespecially welcome in dynamicapplications such as scanningmicroscopy, image stabilization,switching ofvalves/shutters, shock-wavegeneration, vibration cancellationsystems, etc.A piezo actuator can reach itsnominal displacement inapproximately 1/3 of the periodof the resonant frequency, providedthe controller can deliverthe necessary current. If notcompensated by appropriatemeasures (e.g. notch filter,InputShaping ® , see p. 2-201) inthe servo-loop, such rapidexpansion will be accompaniedby significant overshoot.(Equation 13)Minimumrisetimeofapiezoactuator (requires an amplifierwith sufficient output currentand slew rate).Where:T min = time [s]f 0= resonant frequency[Hz]]Example: A piezo translatorwith a 10 kHz resonant frequencycan reach its nominal displacementwithin 30 μs.© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.18Fig. 24. Response of an undamped, lever-amplified piezo actuator (low resonant frequency) to a rapid drive-voltage change. Thisbehavior can be prevented by intelligent control techniques or position servo-control2-194

Piezo • Nano • PositioningPiezo Actuator Electrical FundamentalsElectrical Requirements for Piezo OperationGeneralWhen operated well below theresonant frequency, a piezoactuator behaves as a capacitor:The actuator displacementis proportional to stored charge(first order estimate). Thecapacitance of the actuatordepends on the area and thicknessof the ceramic, as well ason its material properties. Forpiezo stack actuators, whichare assembled with thin, laminarwafers of electroactiveceramic material electricallyconnected in parallel, thecapacitance also depends onthe number of layers.The small-signal capacitance ofa stack actuator can be estimatedby:100 times as much current, thepower requirements of the twoactuators in this example areabout the same. The PI highvoltageand low-voltage amplifiersin this catalog are designedto meet the requirementsof the respective actuatortypes.Static OperationWhen electrically charged, theamount of energy stored in thepiezo actuator is E = (1/2) CU 2Every change in the charge(and therefore in displacement)of the PZT ceramics requires acurrent i:(Equation 15)one second. Suitable amplifierscan be found using the “PiezoDrivers / Servo Controllers”Selection Guide on p. 2-100 ff.NoteThe actuator capacitance valuesindicated in the technicaldata tables are small-signal values(measured at 1 V, 1000 Hz,20 °C, unloaded) The capacitanceof piezoceramics changeswith amplitude, temperature,and load, to up to 200 % ofthe unloaded, small-signal,room-temperature value. Fordetailed information on powerrequirements, refer to theamplifier frequency responsecurves in the “Piezo Drivers /Servo Controllers” (see p.2-99 ff ) section.Linear Actuators & MotorsNanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesPiezoelectrics in PositioningNanometrology(Equation 14)Relationship of current andvoltage for the piezo actuatorMicropositioningWhere:IndexWhere:i= current [A]C= capacitance [F (As/V)]Q = charge [coulomb (As)]n = number of layers =C = capacitance [F] 33 T= dielectric constant[As/Vm]U = voltage [V]Ad SI 0= electrode surface areaof a single layer [m 2 ]= distance between theindividual electrodes(layer-thickness) [m]= actuator lengthThe equation shows that for agiven actuator length, thecapacitance increases with thesquare of the number of layers.Therefore, the capacitance of apiezo actuator constructed of100 μm thick layers is 100 timesthe capacitance of an actuatorwith 1 mm layers, if the twoactuators have the samedimensions. Although the actuatorwith thinner layers drawst= time [s]For static operation, only theleakage current need be supplied.The high internal resistancereduces leakage currentsto the micro-amp range or less.Even when suddenly disconnectedfrom the electricalsource, the charged actuatorwill not make a sudden move,but return to its unchargeddimensions very slowly.For slow position changes,only very low current isrequired.Example: An amplifier with anoutput current of 20 μA canfully expand a 20 nF actuator inFig. 25. Design of a piezo stack actuator2-195

Piezo • Nano • PositioningPiezo Actuator Electrical Fundamentals (cont.)Dynamic Operation (Linear)Piezo actuators can provideaccelerations of thousands ofg’s and are ideally suited fordynamic applications.Several parameters influencethe dynamics of a piezo positioningsystem: The slew rate [V/s] and themaximum current capacityof the amplifier limit theoperating frequency of thepiezo system. If sufficient electrical poweris available from the amplifier,the maximum drive frequencymay be limited bydynamic forces (see “DynamicOperation”, p. 2-192).(Equation 16)Long-term average currentrequired for sinusoidal operation(Equation 17)Peak current required for sinusoidaloperation(Equation 18)Maximum operating frequencywith triangular waveform, as afunction of the amplifier outputcurrent limitA: The 20 μm displacementrequires a drive voltage ofabout 500 V peak-to-peak. WithEquation 17 the required peakcurrent is calculated at ≈ 63 mA.For appropriate amplifiers, seethe “Piezo Drivers / ServoControllers” section (p. 2-99 ff ).The following equationsdescribe the relationship between(reactive) drive power,actuator capacitance, operatingfrequency and drive voltage.The average power a piezodriver has to be able to providefor sinusoidal operation isgiven by:(Equation 19)© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.18 In closed-loop operation, themaximum operating frequencyis also limited by thephase and amplituderesponse of the system. Ruleof thumb: The higher thesystem resonant frequency,the better the phase andamplitude response, and thehigher the maximum usablefrequency. The sensor bandwidthand performance ofthe servo-controller (digitaland analog filters, controlalgorithm, servo-bandwidth)determine the maximumoperating frequency of apiezoelectric system. In continuous operation,heat generation can alsolimit the operating frequency.The following equationsdescribe the relationshipbetween amplifier output current,voltage and operating frequency.They help determinethe minimum specifications ofa piezo amplifier for dynamicoperation.Where:i a *= average amplifiersource/sink current [A]i max * = peak amplifiersource/sink current [A]f maxC**U p-pf= maximum operatingfrequency [Hz]= piezo actuator capacitance[Farad (As/V)]= peak-to-peak drivevoltage [V]= operating frequency[Hz]The average and maximumcurrent capacity for each PIpiezo amplifier can be found inthe product technical datatables.ExampleQ: What peak current isrequired to obtain a sinewavedisplacement of 20 μm at 1000Hz from a 40 nF HVPZT actuatorwith a nominal displacementof 40 μm at 1000 V?Peak power for sinusoidaloperation is:(Equation 20)Where:P aP maxC**fU p-pU max= average power [W]= peak power [W]= piezo actuator capacitance[F]= operating frequency[Hz]= peak-to-peak drivevoltage [V]= nominal voltage ofthe amplifier [V]It is also essential that thepower supply be able to supplysufficient current.* The power supply must be able to provideenough current.** For large-signal conditions a margin of70% of the small-signal value should beadded.2-196

Piezo • Nano • PositioningDynamic Operating CurrentCoefficient (DOCC)Instead of calculating therequired drive power for agiven application, it is easier tocalculate the drive current,because it increases linearlywith both frequency and voltage(displacement). For thispurpose, the DynamicOperating Current Coefficient(DOCC) has been introduced.The DOCC is the current thatmust be supplied by the amplifierto drive the piezo actuatorper unit frequency (Hz) andunit displacement. DOCC valuesare valid for sinewaveoperation in open-loop mode.In closed-loop operation thecurrent requirement can be upto 50% higher.The peak and long-term averagecurrent capacities of thedifferent piezo amplifiers canbe found in the technical datatables for the electronics, theDOCC values in the tables forthe piezo actuators.Example: To determinewhether a selected amplifiercan drive a given piezo actuatorat 50 Hz with 30 μm peakto-peakdisplacement, multiplythe actuator’s DOCC by 50 x 30and compare the result withthe average output current ofthe selected amplifier. If thecurrent required is less than orequal to the amplifier output,then the amplifier has sufficientcapacity for the application.Dynamic Operation(Switched)For applications such as shockwave generation or valve control,switched operation (on/off) may be sufficient. Piezoactuators can provide motionwith rapid rise and fall timeswith accelerations in the thousandsof g’s. For informationon estimating the forcesinvolved, see “DynamicForces,” p. 2-192).The simplest form of binarydrive electronics for piezoapplications would consist of alarge capacitor that is slowlycharged and rapidly dischargedacross the PZT ceramics.The following equation relatesapplied voltage (which correspondsto displacement) totime.(Equation 21)Voltage on the piezo afterswitching event.Where:U 0U p-pRCt= start voltage [V]= source output voltage(peak-to-peak) [V]= source output resistance[ohm]= piezo actuator capacitance[F]= time [s]The voltage rises or falls exponentiallywith the RC time constant.Under quasi-static conditions,the expansion of the PZTceramics is proportional to thevoltage. In reality, dynamicpiezo processes cannot bedescribed by a simple equation.If the drive voltage risestoo quickly, resonance occurs,causing ringing and overshoot.Furthermore, whenever thepiezo actuator expands or contracts,dynamic forces act onthe ceramic material. Theseforces generate a (positive ornegative) voltage in the piezoelement which is superimposedon the drive voltage. Apiezo actuator can reach itsnominal displacement inapproximately 30 % of the periodof the resonant frequency,provided the controller candeliver the necessary current.(see p. 2-194).The following equation appliesfor constant-current charging(as with a linear amplifier):(Equation 22)Time to charge a piezoceramicwith constant current. Withlower-capacity electronics,amplifier slew rate can be alimiting factor.Where:tCU p-pi max= time to charge piezoto U p-p [s]= piezo actuator capacitance[F]= voltage change(peak-to-peak) [V]= peak amplifiersource/sink current [A]For fastest settling, switchedoperation is not the best solutionbecause of the resultingovershoot. Modern techniqueslike InputShaping ® (see p. 2-201)solve the problem of resonancesin and around the actuatorwith complex signal processingalgorithms.NotePiezo drives are becomingmore and more popularbecause they can deliverextremely high accelerations.This property is very importantin applications such as beamsteering and optics stabilization.Often, however, the actuatorscan accelerate faster thanthe mechanics they drive canLinear Actuators & MotorsNanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesPiezoelectrics in PositioningNanometrologyMicropositioningIndex2-197

Piezo • Nano • PositioningPiezo Actuator Electrical Fundamentals (cont.)© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.18follow. Rapid actuation ofnanomechanisms can causerecoil-generated ringing of theactuator and any adjacent components.The time required forthis ringing to damp out can bemany times longer than themove itself. In time-criticalindustrial nanopositioningapplications, this problemobviously grows more seriousas motion throughputsincrease and resolutionrequirements tighten.Classical servo-control techniquescannot solve this problem,especially when resonancesoccur outside theservo-loop such as when ringingis excited in a sample on afast piezo scanning stage as itreverses direction. A solution isoften sought in reducing thescanning rate, thereby sacrificingpart of the advantage of apiezo drive.A patented real-time feedforwardtechnology calledInputShaping ® nullifies resonancesboth inside and outsidethe servo-loop and thus eliminatesthe settling phase. Formore information see p. 2-201or visit www.Convolve.com.2-198Heat Generation in a PiezoActuator in DynamicOperationPZT ceramics are (reactive)capacitive loads and thereforerequire charge and dischargecurrents that increase withoperating frequency. The thermalactive power, P (apparentpower x power factor, cos ),generated in the actuator duringharmonic excitation can beestimated with the followingequation:(Equation 23)Heat generation in a piezo actuator.Where:P= power converted toheat [W]tan = dielectric factor (≈ powerfactor, cos , for smallangles and )fC= operating frequency[Hz]= actuator capacitance[F]U p-p = voltage (peak-to-peak)For the description of the losspower, we use the loss factortan instead of the power factorcos , because it is themore common parameter forcharacterizing dielectric materials.For standard actuatorpiezoceramics under small-signalconditions the loss factor ison the order of 0.01 to 0.02.Thismeansthatupto2%ofthe electrical “power” flowingthrough the actuator is convertedinto heat. In large-signalconditions however, 8 to 12 %of the electrical power pumpedinto the actuator is convertedto heat (varies with frequency,temperature, amplitude etc.).Therefore, maximum operatingtemperature can limit the piezoactuator dynamics. For largeamplitudes and high frequencies,cooling measures may benecessary. A temperature sensormounted on the ceramics issuggested for monitoring purposes.For higher frequency operationof high-load actuators withhigh capacitance (such asPICA-Power actuators, see p.1-88), a special amplifiersemploying energy recoverytechnology has been developed.Instead of dissipating thereactive power at the heatsinks, only the active powerused by the piezo actuator hasto be delivered.The energy not used in theactuator is returned to theamplifier and reused, as shownin the block diagram in Fig. 26.The combination of low-loss,high-energy piezoceramics andamplifiers with energy recoveryare the key to new highleveldynamic piezo actuatorapplications.Fig. 26. Block diagram of an amplifier with energy recovery forhigher frequency applicationsFor dynamic applications withlow to medium loads, thenewly developed PICMA ® actuatorsare also quite well suited.With their high Curie temperatureof 320 °C, they can beoperated with internal temperaturesof up to 150 °C.

Piezo • Nano • PositioningControl of Piezo Actuators and StagesPosition Servo-ControlPosition servo-control eliminatesnonlinear behavior ofpiezoceramics such as hysteresisand creep and is the key tohighly repeatable nanometricmotion.PI offers the largest selection ofclosed-loop piezo mechanismsand control electronics worldwide.The advantages of positionservo-control are:Fig. 27. Variety of digital piezo controllers High linearity, stability,repeatability and accuracy Automatic compensation forvarying loads or forces Virtually infinite stiffness(within load limits) Elimination of hysteresisand creep effectsPI closed-loop piezo actuatorsand systems are equipped withposition measuring systemsproviding sub-nanometer resolution,linearity to 0.01 %, andbandwidths up to 10 kHz. Aservo-controller (digital or analog)determines the outputvoltage to the PZT ceramics bycomparing a reference signal(commanded position) to theactual sensor position signal(see Fig. 28).For maximum accuracy, it isbest if the sensor measures themotion of the part whose positionis of interest (direct metrology).PI offers a large variety ofpiezo actuators with integrateddirect-metrology sensors.Capacitive sensors provide thebest accuracy (see “Nanometrology”p. 3-1 ff ). Simpler,less accurate systems measurethings like strain in drive elements.Linear Actuators & MotorsNanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesPiezoelectrics in PositioningNanometrologyMicropositioningIndexFig. 28. Block diagram of a typical PI closed-loop piezo positioning systemFig. 29. Closed-loop position servo-control. For optimum performance, the sensoris mounted directly on the object to be positioned (direct metrology)2-199

Piezo • Nano • PositioningControl of Piezo Actuators and Stages (cont.)Open- and Closed-LoopResolutionPosition servo-controlled piezodrives offer linearity and repeatabilitymany times betterthan that of open-loop systems.The resolution (minimum incrementalmotion) of piezoactuators is actually better foropen-loop than for closed-loopsystems. This is because piezoresolution is not limited by frictionbut rather by electronicnoise. In open-loop, there is nosensor or servo-electronics toput additional noise on the controlsignal. In a servo-controlledpiezo system, the sensor andcontrol electronics are thus ofconsiderable importance. Withappropriate, high-quality systems,subnanometer resolutionis also possible in closed-loopmode, as can be seen in Fig. 30and 31. Capacitive sensorsattain the highest resolution,linearity and stability.Fig. 30. Response of a closed-loop PI piezo actuator (P-841.10, 15 μm, strain gaugesensor) to a3nmpeak-to-peak square-wave control input signal, measured withservo-control bandwidth set to 240 Hz and 2 msec settling time. Note the crisp,backlash-free behavior in the nanometer range© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.18Piezo Metrology ProtocolEach PI piezo position servocontrolleris matched to thespecific closed-loop piezo positioningsystem to achieve optimumdisplacement range, frequencyresponse and settlingtime. The adjustment is performedat the factory and a reportwith plotted and tabulated positioningaccuracy data is suppliedwith the system (seep. 2-87). To optimize the settings,information about thespecific application is needed.For details see p. 2-11.Digital controllers can automaticallyread important devicespecific values from an ID-chipintegrated in the piezo mechanics.This feature facilitatesusing a controller with variousstages/actuators and viceversa.Fig. 31. PI piezo actuators with capacitive position sensors can achieve extremelyhigh resolutions, as seen in the above result of a 250 picometerstep by a S-303 phase corrector (Controller: E-509.C1A servo-controller andE-503 amplifier). The measurements were made with an ultra-sensitivecapacitive sensor having a resolution of ±0.02 nmFig. 32. Open-loop vs. closed-loop performance graph of a typical PI piezo actuator2-200

Piezo • Nano • PositioningMethods to Improve Piezo DynamicsThe dynamic behavior of apiezo positioning systemdepends on factors includingthe system’s resonant frequency,the position sensor and thecontroller used. Simple controllerdesigns limit the usableclosed-loop tracking bandwidthof a piezoelectric systemto 1/10 of the system’s resonantfrequency. PI offers controllersthat significantly increasepiezo actuator systemdynamics (see table). Two ofthe methods are describedbelow; additional informationis available on request.InputShaping ® StopsStructural Ringing Caused byHigh-Throughput MotionA patented, real-time, feedforwardtechnology calledInputShaping ® nullifies resonancesboth inside and outsidethe servo-loop and virtuallyeliminates the settling phase.The procedure requires determinationof all critical resonantfrequencies in the system. Anon-contact instrument like aPolytec Laser Doppler Vibrometeris especially well-suitedfor such measurements. Thevalues, most importantly theresonant frequency of the sampleon the platform, are thenfed into the InputShaping ®Signal processor. There thesophisticated signal processingalgorithms assure thatnone of the undesired resonancesin the system or its auxillarycomponents is excited.Because the processor is outsidethe servo-loop, it works inopen-loop operation as well.The result: the fastest possiblemotion, with settling within atime equal one period of thelowest resonant frequency.InputShaping ® was developedbased on research at theMassachusetts Institute ofTechnology and commercializedby Convolve, Inc.(www.convolve.com). It is anoption in several PI digitalpiezo controllers.Linear Actuators & MotorsNanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesPiezoelectrics in PositioningNanometrologyMicropositioningIndexFig. 33. InputShaping ® eliminates therecoil-driven resonant reaction of loadsand neighboring components due torapid nanopositioner actuation.Top: Polytec Laser Vibrometer revealsthe resonant behavior of an undampedfixture when the nanomechanism isstepped.Bottom: Same setup, same step, butwith InputShaping ® . Structural ringingis eliminated. With no excitation ofvibration in the moved components,the target position is attained in a timesmaller than one period of the resonantfrequencyVarious Methods to Improve Piezo DynamicsMethodFeedforwardSignal preshaping (software)Adaptive preshaping (hardware)Linearization (digital, in DSP)InputShaping ®Dynamic Digital Linearization (DDL)GoalsReduce phase difference between output and input (tracking error)Increase operating frequency of the system, correct amplitude and phaseresponse. Two learning phases required; only for periodic signals.Increase operating frequency of the system, correct amplitude and phaseresponse. No learning phase, but settling phase required;only for periodic signals.Compensate for piezo hysteresis and creep effectsCancel recoil-generated ringing, whether inside or outside theservo-loop. Reduce the settling time. Closed- and open-loop.Increase operating frequency of the system, correct amplitudeand phase response. Integrated in digital controller.No external metrology necessary, for periodic signals only.2-201

Piezo • Nano • PositioningMethods to Improve Piezo Dynamics (cont.)Fig. 34 a. Signal preshaping, phase 1Signal Preshaping / DynamicDigital Linearization (DDL)Signal Preshaping, a patentedtechnique, can reduce rolloff,phase error and hysteresis inapplications with repetitive(periodic) inputs. The result isto improve the effective bandwidth,especially for trackingapplications such as out-ofroundturning of precisionmechanical or optical parts.Signal Preshaping is implementedin object code, basedon an analytical approach inwhich the complex transferfunction of the system is calculated,then mathematicallytransformed and applied in afeedforward manner to reducethe tracking error.For example, it is possible toincrease the command ratefrom 20 Hz to 200 Hz for a piezosystem with a resonant frequencyof 400 Hz without compromisingstability. At the sametime, the tracking error isreduced by a factor of about 50.Signal Preshaping is moreeffective than simple phaseshiftingapproaches and canimprove the effective bandwidthby a factor of 10 and inmulti-frequency applications.© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.18Fig. 34 b. Signal preshaping, phase 2Fig. 35. No preshapingA: Control input signal (expected motion)B: Actual motion of systemC: Tracking errorFrequency response and harmonics(caused by nonlinearityof the piezo-effect) are determinedin two steps using FastFourier Transformation (FFT),and the results are used to calculatethe new control profilefor the trajectory. The new controlsignal compensates for thesystem non-linearities.Fig. 36. Signal after preshaping phase 2A: Expected Motion (old control signal)B: Actual motion of systemC: New control input (producted by preshaping)D: Tracking error2-202

Piezo • Nano • PositioningDynamic Digital Linearization(DDL)DDL is similar in performanceto Input Preshaping, but is simplerto use. In addition, it canoptimize multi-axis motionsuch as a raster scan or tracingan ellipse. This methodrequires no external metrologyor signal processing (see p.2-108). DDL uses the positioninformation from capacitivesensors integrated in the piezomechanics (requires directmetrology) to calculate theoptimum control signal. Aswith preshaping, the result isan improvement in linearityand tracking accuracy of up to 3orders of magnitude.Fig. 37 a. Elliptical scan in a laser micro-drilling application with XYpiezo scanning stage, conventional PID controller. The outer ellipsedescribes the target position, the inner ellipse shows the actualmotion at the stageLinear Actuators & MotorsNanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesPiezoelectrics in PositioningNanometrologyMicropositioningIndexFig. 37 b. Same scan as before, with a DDL controller. Targetand actual data can hardly be discerned. The tracking error hasbeen reduced to a few nanometers2-203

Piezo • Nano • PositioningEnvironmental Conditions and InfluencesTemperature EffectsTwo effectsmust be considered: Linear Thermal Expansion Temperature Dependency ofthe Piezo EffectLinear Thermal ExpansionThermal stability of piezoceramicsis better than that ofmost other materials. Fig. 38ashows the behavior of severaltypes of piezoceramics used byPI. The curves only describethe behavior of the piezoceramics.Actuators and positioningsystems consist of a combinationof piezoceramics andother materials and their overallbehavior differs accordingly.NoteClosed-loop piezo positioningsystems are less sensitive totemperature changes thanopen-loop systems. Optimumaccuracy is achieved if theoperating temperature is identicalto the calibration temperature.If not otherwise specified,PI piezomechanics are calibratedat 22 °C.Piezo Operationin High HumidityThe polymer insulation materialsused in piezoceramic actuatorsare sensitive to humidity.Water molecules diffusethrough the polymer layer andcan cause short circuiting ofthe piezoelectric layers. Theinsulation materials used inpiezo actuators are sensitive tohumidity. For higher humidityenvironments, PI offers specialsystems with waterproofedenclosed stacks, or integrateddry-air flushing mechanisms.A better solution are PICMA ®actuators (see Fig. 39a), whichhave ceramic-only insulationwithout any polymer coveringand are thus less sensitive towater diffusion (see Fig. 39c).Temperature Dependency ofthe Piezo EffectPiezo translators work in awide temperature range. Thepiezo effect in PZT ceramics isknown to function down toalmost zero kelvin, but themagnitude of the piezo coefficientsis temperature dependent.© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.18At liquid helium temperaturepiezo gain drops to approximately10–20 % of its roomtemperaturevalue.Piezoceramics must be poledto exhibit the piezo effect. Apoled PZT ceramic may depolewhen heated above the maximumallowable operating temperature.The “rate” of depolingis related to the Curie temperatureof the material. PIHVPZT actuators have a Curietemperature of 350 °C and canbe operated at up to 150 °C.LVPZT actuators have a Curietemperature of 150 °C and canbe operated at up to 80 °C. Thenew monolithic PICMA ® ceramicswith their high Curie temperatureof 320 °C allow operatingat temperatures of up to150 °C.2-204Fig. 38 a. Linear thermal expansion of different PZT ceramicsFig. 38 b. The expansion of PICMA ® piezoceramics is only slightly temperaturedependent. This, and their low heat generation, makes themideal for dynamic applications

Piezo • Nano • PositioningPiezo Operation in Inert GasAtmospheresCeramic-insulated PICMA ®actuators are also recommendedfor use in inert gases, suchas helium. To reduce the dangerof flashover with high-voltagepiezos, the maximum operatingvoltage must be reduced.Semi-bipolar operation is recommended,because the averageoperating voltage can bekept very low.Vacuum Operationof Piezo ActuatorsAll PI piezo actuators can beoperated at pressures below100 Pa (~1 torr). When piezoactuators are used in a vacuum,two factors must be considered:I. Dielectric stabilityII. OutgassingI. The dielectric breakdown voltageof a sample in a specificgas is a function of the pressurep times the electrode distances. Air displays a highinsulation capacity at atmosphericpressure and at very lowpressures. The minimumbreakdown voltage of ~300 Vcan be found at a ps-product of1000 mm Pa (~10 mm torr).That is why PICMA ® actuatorswith a maximum operatingvoltage of 120 V can be used inany vacuum condition. However,the operation of HVPZTactuators with dielectric layerthicknesses of 0.2 – 1.0 mm andnominal voltages to 1000 V isnot recommended in the pressurerange of 100 – 50000 Pa(~1 – 500 torr).II. Outgassing behavior variesfrom model to model dependingon design. Ultra-high-vacuumoptions for minimum outgassingare available for manystandard low-voltage and highvoltagepiezo actuators. Bestsuited are PICMA ® ceramics(see Fig. 39a), because theyhave no polymers and canwithstand bakeout to 150 °C(see also “Options” in the“Piezo Actuators & Components”sections, p. 2-104 ff ).All materials used in UHV-compatiblepiezo nanopositioners,including cables and connectors,are optimized for minimaloutgassing rates (see Fig. 39b).Materials lists are available onrequest.Linear Actuators & MotorsNanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesPiezoelectrics in PositioningNanometrologyMicropositioningIndexFig. 39 a. PICMA ® actuators are made with ceramic-only insulation and candispense with any polymer coating. Result No measurable outgasing, insensitiveto atmospheric humidity and a wider operating temperature rangeFig. 39 b. P-733.UUD UHV-compatible XY stage for scanning microscopyapplications. PICMA ® ceramics are used here too. All materials used areoptimized for minimal outgassing. Materials lists are available on request2-205

Piezo • Nano • PositioningEnvironmental Conditions and Influences (cont.)Lifetime of Piezo Actuators© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.18The lifetime of a piezo actuatoris not limited by wear and tear.Tests have shown that PI piezoactuators can perform billions(10 9 ) of cycles without anymeasurable wear.As with capacitors, however,the field strength does have aninfluence on lifetime. The averagevoltage should be kept aslow as possible. Most PI piezoactuators and electronics aredesigned for semi-bipolaroperation.There is no generic formula todetermine the lifetime of apiezo actuator because of themany parameters, such as temperature,humidity, voltage,acceleration, load, preload,operating frequency, insulationmaterials, etc., which have(nonlinear) influences. PI piezoactuators are not only optimizedfor maximum travel, butalso designed for maximumlifetime under actual operatingconditions.The operating voltage rangevalues in the technical datatables are based on decades ofexperience with nanomechanismsand piezo applicationsin industry. Longer travel canonly be obtained with highervoltages at the cost of reducedreliability.Example:An P-842.60 LVPZT actuator(see p. 1-76 in the “PiezoActuators & Components” section)is to operate a switch witha stroke of 100 μm. Of its operatingtime, it is to be open for70 % and closed for 30 %.Optimum solution: The actuatorshould be linked to theswitch in such a way that theopen position is achieved withthe lowest possible operatingvoltage. To reach a displacementof 100 μm, a voltage2-206amplitude of approximately110 volts is required (nominaldisplacement at 100 V is only90 μm).Since the P-842.60 can be operateddown to -20 volts, theclosed position should beachieved with 90 V, and theopen position with -20 volts.When the switch is not in use atall, the voltage on the piezoactuator should be 0 volts.Statistics show that most failureswith piezo actuators occurbecause of excessive mechanicalstress. Particularly destructiveare tensile and shearforces, torque and mechanicalshock. To protect the ceramicfrom such forces PI offers avariety of actuators with preloads,ball tips, flexible tips aswell as custom designs.Failures can also occur whenhumidity or conductive materialssuch as metal dust degradethe PZT ceramic insulation,leading to irreparable dielectricbreakdown. In environmentspresenting these hazards,PICMA ® actuators with theirceramic-only insulation arestrongly recommended. PI alsooffers hermetically sealed actuatorsand stages.Fig. 39 c. PICMA ® piezo actuators (lower curve) compared with conventional multilayerpiezo actuators with polymer insulation. PICMA ® actuators are insensitve tohigh humidity in this test. In conventional actuators, the leakage current beginsto rise after only a few hours—an indication of degradation of the insulation andreduced lifetime.Test conditions: U = 100 VDC, T = 25 °C, RH = 70%Fig. 39 d. P-885.50 PICMA ® actuators with 15 MPa preload in dynamic motion test at116 Hz. No observable wear after 1.2 billion (10 9 ) cycles

Piezo • Nano • PositioningBasic Designs of Piezoelectric Positioning Drives/SystemsStack Design (Translators)The active part of the positioningelement consists of a stackof ceramic disks separated bythin metallic electrodes. Themaximum operating voltage isproportional to the thickness ofthe disks. Most high-voltageactuators consist of ceramiclayers measuring 0.4 to 1 mmin thickness. In low-voltagestack actuators, the layers arefrom 25 to 100 μm in thicknessand are cofired with the electrodesto form a monolithicunit.Stack elements can withstandhigh pressures and exhibit thehighest stiffness of all piezoactuator designs. Standarddesigns which can withstandpressures of up to 100 kN areavailable, and preloaded actuatorscan also be operated inpush-pull mode. For furtherinformation see “MaximumApplicable Forces”, p. 2-189.Laminar Design(Contraction-Type Actuators)The active material in the laminaractuators consists of thin,laminated ceramic strips. Thedisplacement exploited inthese devices is that perpendicularto the direction of polarizationand electric field application.When the voltage isincreased, the strip contracts.The piezo strain coefficient d 31(negative!) describes the relativechange in length. Itsabsolute value is on the orderof 50 % of d 33 .The maximum travel is a functionof the length of the strips,while the number of stripsarranged in parallel determinesthe stiffness and force generationof the element.Displacement of a piezo contractionactuator can be estimatedby the following equation:Fig. 40. Electrical design of a stack translatorLinear Actuators & MotorsNanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesPiezoelectrics in PositioningNanometrologyMicropositioningIndexDisplacement of a piezo stackactuator can be estimated bythe following equation:(Equation 25)(Equation 24)where:L = displacement [m]where:L = displacement [m]d 33 = strain coefficient (fieldand displacement inpolarization direction)[m/V]d 31 = strain coefficient(displacement normalto polarization direction)[m/V]L= length of the piezoceramicsin the electricfield direction [m]Fig. 41. Mechanical design of a stack translatorn= number of ceramic layersU= operating voltage [V]U= operating voltage [V]d= thickness of one ceramiclayer [m]Example:P-845, p. 1-76, etc. (see the“Piezo Actuators & Components”section)Fig. 42. Laminar actuator design2-207

Piezo • Nano • PositioningBasic Designs of Piezoelectric Positioning Drives/Systems (cont.)Tube DesignMonolithic ceramic tubes areyet another form of piezo actuator.Tubes are silvered insideand out and operate on thetransversal piezo effect. Whenan electric voltage is appliedbetween the outer and innerdiameter of a thin-walled tube,the tube contracts axially andradially. Axial contraction canbe estimated by the followingequation:(Equation 26 a)When the outside electrode ofa tube is separated into four90° segments, placing differentialdrive voltages ±U onopposing electrodes will leadto bending of one end. Suchscanner tubes that flex in X andY are widely used in scanningprobemicroscopes, such asscanning tunneling microscopes.The scanning range can beestimated as follows:(Equation 27)© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.18where:d 31 = strain coefficient (displacementnormal topolarization direction)[m/V]LUd= length of the piezoceramic tube [m]= operating voltage [V]= wall thickness [m]The radial displacement is theresult of the superposition ofincrease in wall thickness(Equation 26 b) and the tangentialcontraction:(Equation 26 b)r = tube radius(Equation 26 c)where:d = change in wall thickness[m]d 33 = strain coefficient (fieldand displacement inpolarization direction)[m/V]U = operating voltage [V]where:x = scan range in X and Y(for symmetrical electrodes)[m]d 31 = strain coefficient (displacementnormal topolarization direction)[m/V]ULIDd= differential operatingvoltage [V]= length [m]= inside diameter [m]= wall thickness [m]Tube actuators cannot generateor withstand large forces.Application examples: Microdosing,nanoliter pumping,scanning microscopy, ink jetprinters.Examples:PT120, PT130, PT140 (p. 1-100).Fig. 43. Tube actuator designFig. 44. Piezo scanner tube working principle2-208

Piezo • Nano • PositioningBender Type Actuators(Bimorph and MultimorphDesign)A simple bender actuator(bimorph design) consists of apassive metal substrate gluedto a piezoceramic strip (seeFig. 45a). A piezo bimorphreacts to voltage changes theway the bimetallic strip in athermostat reacts to temperaturechanges. When the ceramicis energized it contracts orexpands proportional to theapplied voltage. Since themetal substrate does notchange its length, a deflectionproportional to the appliedvoltage occurs. The bimorphdesign amplifies the dimensionchange of the piezo, providingmotion up to severalmillimeters in an extremelysmall package. In addition tothe classical strip form,bimorph disk actuators wherethe center arches when a voltageis applied, are also available.PZT/PZT combinations, whereindividual PZT layers are operatedin opposite modes (contraction/expansion),are alsoavailable.Two basic versions exist: thetwo-electrode bimorph (serialbimorph) and the three-electrodebimorph (parallelbimorph), as shown in Fig. 45b.In the serial type, one of thetwo ceramic plates is alwaysoperated opposite to the directionof polarization. To avoiddepolarization, the maximumelectric field is limited to a fewhundred volts per millimeter.Serial bimorph benders arewidely used as force and accelerationsensors.operating voltage (60 to 100 V).Bender type actuators providelarge motion in a small packageat the cost of low stiffness,force and resonant frequency.Examples:PL122 multilayer bender actuators(p. 1-94).Shear ActuatorsShear actuators can generatehigh forces and large displacements.A further advantage istheir suitability for bipolaroperation, whereby the midpositioncorresponds to a drivevoltage of 0 V. In shear mode,unlike in the other modes, theelectric field is applied perpendicularto the polarizationdirection. (see Fig. 46). The correspondingstrain coefficient,d 15 , has large-signal values ashigh as 1100 pm/V, providingdouble the displacement of linearactuators of comparablesize based on d 33 .Shear actuators are suitable forapplications like piezo linearmotors, and are available asboth single-axis and two-axispositioning elements.Examples:P-363 (p. 2-66),N-214 NEXLINE ® Piezo-Walk ®motor (p. 1-10).Fig. 45a. Bimorph design (strip and disk translator).Fig. 45b. Bender Actuators: Serial and parallel bimorphsmetalLinear Actuators & MotorsNanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesPiezoelectrics in PositioningNanometrologyMicropositioningIndexIn addition to the two-layerbenders, monolithic multilayerpiezo benders are also available.As with multilayer stackactuators, they run on a lowerFig. 46. Material deformation in a shear actuator2-209

Piezo • Nano • PositioningBasic Designs of Piezoelectric Positioning Drives/Systems (cont.)© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.18Piezo Actuators withIntegrated Lever MotionAmplifiersPiezo actuators or positioningstages can be designed in sucha way that a lever motionamplifier is integrated into thesystem. To maintain subnanometerresolution with theincreased travel range, thelever system must be extremelystiff, backlash- and frictionfree,which means ball or rollerbearings cannot be used.Flexures are ideally suited aslinkage elements. Using flexures,it is also possibleto design multi-axis positioningsystems with excellentguidance characteristics (seep. 2-211).PI employs finite elementanalysis (FEA) computer simulationto optimize flexurenanopositioners for the bestpossible straightness and flatness(see Fig. 49 and Fig. 51).Piezo positioners with integratedmotion amplifiers have bothadvantages and disadvantagescompared to standard piezoactuators:Advantages: Longer travel Compact size compared tostack actuators with equaldisplacement Reduced capacitance(= reduced drive current)Disadvantages: Reduced stiffness Lower resonant frequencyThe following relations applyto (ideal) levers used to amplifymotion of any primary drivesystem:where:r = lever transmissionratioL 0 = travel of the primarydrive [m]L Sys = travel of the leveramplifiedsystem [m]k sys = stiffness of the leveramplifiedsystem[N/m]k 0= stiffness of the primarydrive system(piezo stack andjoints) [N/m]f res-sys = resonant frequency ofthe amplified system[Hz]f res-0= resonant frequency ofthe primary drive system(piezo stack andjoints) [Hz]Fig. 47. Simple lever motion amplifierNote:The above equations are basedon an ideal lever design withinfinite stiffness and zero mass.They also imply that no stiffnessis lost at the couplinginterface between the piezostack and the lever. In realapplications, the design of agood lever requires long experiencein micromechanics andnanomechanisms. A balancebetween mass, stiffness andcost must be found, whilemaintaining zero-friction andzero-backlash conditions.Coupling the piezo stack to thelever system is crucial. Thecoupling must be very stiff inthe pushing direction butshould be soft in all otherdegrees of freedom to avoiddamage to the ceramics. Evenif the stiffness of each of thetwo interfaces is as high as thatof the piezo stack alone, a 67 %loss of overall stiffness stillresults. In many piezo-drivensystems, the piezo stiffness isthus not the limiting factor indetermining the stiffness of themechanism as a whole.PI piezomechanics are optimizedin this regard as a resultof more than 30 years experiencewith micromechanics,nanopositioning and flexures.2-210

Piezo • Nano • PositioningPiezo Flexure NanopositionersFor applications whereextremely straight motion inone or more axes is neededand only nanometer or microraddeviation from the idealtrajectory can be tolerated,flexures provide an excellentsolution.A flexure is a frictionless, stictionlessdevice based on theelastic deformation (flexing) ofa solid material (e.g. steel).Sliding and rolling are entirelyeliminated. In addition, flexuredevices can be designed withhigh stiffness, high load capacityand do not wear. They arealso less sensitive to shock andvibration than other guidingsystems. They are also maintenance-free,can be fabricatedfrom non-magnetic materials,require no lubricants or consumablesand hence, unlike aircushion bearings, are suitablefor vacuum operation.Parallelogram flexures exhibitexcellent guidance characteristics.Depending on complexityand tolerances, they havestraightness/flatness values inthe nanometer range or better.Basic parallelogram flexurescause arcuate motion (travel inan arc) which introduces anout-of-plane error of about0.1% of the travel range (seeFig. 48). The error can be estimatedby the following equation:(Equation 28)Fig. 48. Basic parallelogram flexure guiding system with motion amplification.The amplification r (transmission ratio) is given by (a+b)/aFig. 49. Zero-arcuate-error multi-flexure guiding systemFor applications where thiserror is intolerable, PI hasdesigned a zero-arcuate-errormulti-flexure guiding system.This special design, employedin most PI flexure stages,makes possible straightness/flatness in the nanometeror microradian range (seeFig. 49).Note:Flexure positioners are farsuperior to traditional positioners(ball bearings, crossedroller bearings, etc.) in terms ofresolution, straightness andflatness. Inherent friction andstiction in these traditionaldesigns limit applications tothose with repeatability requirementson the order of 0.5to 0.1 μm. Piezo flexurenanopositioning systems haveresolutions and repeatabilitieswhich are superior by severalorders of magnitude.Linear Actuators & MotorsNanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesPiezoelectrics in PositioningNanometrologyMicropositioningIndexwhere:H = out-of-plane error [m]L = distance traveled [m]H= length of flexures [m]2-211

Piezo • Nano • PositioningParallel and Serial Kinematics / MetrologyDirect and Indirect MetrologyNon-contact sensors are usedto obtain the most accurateposition values possible forposition servo-control systems.Two-plate capacitive sensorsinstalled directly on the movingplatform and measuring on theaxis of motion offer the bestperformance. Resolution andrepeatability can attain 0.1nanometer in such systems.Indirect metrology—measuringstrain at some point in the drivetrain—cannot be used in systemswith the highest accuracyrequirements.Fig. 50 a. Working principle of a stacked XY piezo stage (serial kinematics).Advantages: Modular, simple design. Disadvantages compared with parallelkinematics: More inertia, higher center of gravity, moving cables (can causefriction and hysteresis). Integrated parallel metrology and active trajectorycontrol (automatic off-axis error correction) are not possible© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.18Fig. 50 b. Working principle of a nested XY piezo stage (serial kinematics).Lower center of gravity and somewhat better dynamics compared withstacked system, but retains all the other disadvantages of a stacked system,including asymmetric dynamic behavior of X and Y axesFig. 50 c. Working principle of a monolithic XY Z parallel kinematics piezo stage. Allactuators act directly on the central platform. Integrated parallel metrology keeps allmotion in all controlled degrees of freedom inside the servo-loop. The position of thecentral, moving platform is measured directly with capacitive sensors, permitting alldeviations from the prescribed trajectory to be corrected in real-time. This feature,called active trajectory control, is not possible with serial metrology2-212

Piezo • Nano • PositioningParallel andSerial KinematicsThere are two basic ways todesign multi-axis positioningsystems: Serial kinematics andparallel kinematics. Serial kinematicsare easier to design andbuild and can be operated withsimpler controllers. They do,however, have a number of disadvantagescompared to higher-performanceand more elegantparallel kinematics systems.In a multi-axis serial kinematicssystem, each actuator isassigned to exactly one degreeof freedom. If there are integratedposition sensors, theyare also each assigned to onedrive and measure only themotion caused by that driveand in its direction of motion.All undesired motion (guidingerror) in the other five degreesof freedom are not seen andhence cannot be corrected inthe servo-loop, which leads tocumulative error.In a parallel kinematics multiaxissystem, all actuators actdirectly on the same movingplatform.Only in this way can the sameresonant frequency anddynamic behavior be obtainedfor the X and Y axes. It is alsoeasy to implement parallelmetrology in parallel kinematicssystems. A parallel metrologysensor sees all motion in itsmeasurement direction, notjust that of one actuator, sorunout from all actuators canbe compensated in real-time(active trajectory control). Theresults are significantly lessdeviation from the ideal trajectory,better repeatability andflatness, as shown in Fig. 51.Examples:P-734, P-561 (p. 2-64, p. 2-72) .in the “Piezo Flexure Stages /High-Speed Scanning Systems”section.Linear Actuators & MotorsNanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesPiezoelectrics in PositioningNanometrologyMicropositioningIndexFig. 51. Flatness (Z-axis) of a 6-axis nanopositioning system with active trajectorycontrol over a 100 x 100 μm scanning range. The moving portion of this parallelmetrology positioner is equipped with ultra-precise parallel metrology capacitivesensors in all six degrees of freedom. The sensors are continually measuring theactual position against the stationary external reference.A digital controller compares the six coordinates of the actual position with therespective target positions. In addition to controlling the scanning motion in theX and Y directions, the controller also ensures that any deviations that occur inthe other four degrees of freedom are corrected in real-time2-213

Piezo • Nano • PositioningPMN Compared to PZTElectrostrictive Actuators(PMN)Electrostrictive actuators operateon a principle similar to thatof PZT actuators. The electrostrictiveeffect can beobserved in all dielectric materials,even in liquids.is greatest hysteresis increases(see Fig. 53 b). PMN actuatorsare thus best for applicationswith little or no temperaturevariations of the ceramic, bethey caused by dynamic operationor by environmental factors.PMNLElectrostrictive actuators aremade of an unpolarized leadmagnesium niobate (PMN)ceramic material. PMN is aceramic exhibiting displacementproportional to thesquare of the applied voltageunder small-signal conditions.Under these conditions PMNunit cells are centro-symmetricat zero volts. An electrical fieldseparates the positively andnegatively charged ions,changing the dimensions of thecell and resulting in an expansion.Electrostrictive actuatorsmust be operated above theCurie temperature, which istypically very low when comparedto PZT materials.PZTFig. 52. Comparison of PMN and PZT material: displacementas a function of field strength (generalized)L16PMNV© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.18The quadratic relationshipbetween drive voltage and displacementmeans that PMNactuator are intrinsically nonlinear,in contrast to PZT actuators.PMN actuators have anelectrical capacitance severaltimes as high as piezo actuatorsand hence require higherdrive currents for dynamicapplications. However, in a limitedtemperature range, electrostrictiveactuators exhibitless hysteresis (on the order of3 %) than piezo actuators. Anadditional advantage is theirgreater ability to withstandpulling forces.PZT materials have greatertemperature stability than electrostrictivematerials, especiallywith temperature variationsof over 10 °C.As temperature increases,available travel is reduced; atlow temperatures where travel2-214Fig. 53 a. Comparison of PMN and PZT material: displacementas a function of temperaturePMNFig. 53 b. Comparison of PMN and PZT material: hysteresis as afunction of temperature

Piezo • Nano • PositioningSummaryPiezoelectric actuators offer asolution to many positioningtasks that depend on highestaccuracy, speed and resolution.Examples given in this tutorialindicate a selection of themany applications commontoday. The relentless push formore accuracy and speed—whether in the further miniaturizationof microelectronics,production of optics and higher-performancedata storagedevices, precise positioning ofoptical fiber components fortelecommunications, or in thefabrication of micromechanisms—drivesboth the applicationand the further developmentof piezo technology.To use the advantages of piezopositioners to their full extent,it is important to carefully analyzethe system in which apiezo actuator is used as awhole. Close contact betweenuser and manufacturer is thebest recipe for success.Piezoelectric actuators will inthe future partially replace, partiallycomplement, conventionaldrive technologies. They willwiden the realm of the possible,and will usher in developmentsin areas like nanotechnologywhich would beunthinkable with conventionaldrive technologies.Linear Actuators & MotorsNanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesPiezoelectrics in PositioningNanometrologyMicropositioningIndex2-215

Piezo • Nano • PositioningMounting and Handling Guidelines© Physik Instrumente (PI) GmbH & Co. KG 2008. Subject to change without notice.Cat120E Inspirations2009 08/10.18Adherence to the followingguidelines will help you obtainmaximum performance andlifetime from your piezo actuators:Do not use metal toolsfor actuator handling. Do notscratch the coating on the sidesurfaces. The following precautionsare recommended duringhandling of piezoelectric actuators:I. Piezoelectric stack actuatorswithout axial preload aresensitive to pulling forces. Apreload of up to 50% of theblocking force is generallyrecommended.II. Piezoelectric stack actuatorsmay be stressed in the axialdirection only. The appliedforce must be centered verywell. Tilting and shearingforces, which can also be inducedby parallelism errorsof the endplates, have to beavoided because they willdamage the actuator. Thiscan be ensured by the useof ball tips, flexible tips,adequate guiding mechanismsetc. An exception tothis requirement is made forthe PICAShear actuators,because they operate in theshear direction.III. Piezoelectric stack actuatorscan be mounted by gluingthem between even metalor ceramic surfaces by acold or hot curing epoxy,respectively. Ground surfacesare preferred. Please,do not exceed the specifiedworking temperature rangeof the actuator during curing.IV. The environment of all actuatorsshould be as dry aspossible. PICMA ® actuatorsare guarded against humidityby their ceramic coating.Other actuators must be protectedby other measures(hermetic sealing, dry airflow, etc).2-216The combination of longtermhigh electric DC fieldsand high relative humidityvalues should be avoidedwith all piezoelectric actuators.V. It is important to shortcircuitthe piezoelectric stackactuators during any handlingoperation. Temperaturechanges and load changeswill induce charges on thestack electrodes whichmight result in high electricfields if the leads are notshorted: Should the stackbecome charged, rapid discharging—especiallywithouta preload—might damagethe stack. Use a resistorfor discharging.VI. Prevent any contaminationof the piezo ceramic surfaceswith conductive orcorrosive substances. Isopropanolis recommendedfor cleaning. Avoid acetoneand excessive ultrasoniccleaning at higher temperatures.No pulling force without preloadNo lateral force or torqueBall tips or flexures to decouple lateral forces orbending forcesBall tips or flexures to decouple bending forcesBolting between plates is not recommended

Piezo • Nano • PositioningSymbols and UnitsA Surface area [m 2 ](meter 2 )Linear Actuators & MotorsCd ijd sEfFf 0Coefficient of Thermal Expansion (CTE) [K -1 ] (1 / kelvin)Capacitance (F) [As/V]Piezo modulus (tensor components) [m/V] (meter/volt)Distance, thickness [m] (meter)Dielectric constant [As/Vm](ampere · second / volt · meter)Electric field strength [V/m] (volt/meter)Operating frequency [Hz] (hertz = 1/second)Force [N] (newton)Unloaded resonant frequency [Hz] (hertz = 1/second)Nanopositioning / PiezoelectricsPiezo Flexure Stages /High-Speed Scanning SystemsLinearVertical & Tip/Tilt2- and 3-Axis6-AxisFast Steering Mirrors /Active OpticsPiezo Drivers /Servo ControllersSingle-ChannelMulti-ChannelModularAccessoriesPiezoelectrics in Positioningg Acceleration due to gravity: 9.81 m/s 2 (meter/second 2 )Nanometrologyik Sk TCurrent [A] (ampere)Stiffness of restraint (load) [N/m] (newton/meter)Stiffness of piezo actuators [N/m] (newton/meter)MicropositioningIndexL 0Length of non-energized actuator [m] (meter)LL 0Change in length (displacement) [m] (meter)Nominal displacement with zero applied force, [m] (meter)L t=0.1Displacement at time t = 0.1 sec after voltage change, [m] (meter)mPQStMass [kg] (kilogram)Power [W] (watt)Charge [C] (coulomb = ampere x second)Strain [L/L] (dimensionless)Time [s] (second)T C Curie temperature [° C]UVoltage [V] (volt)U p-pPeak-to-peak voltage [V] (volt)2-217