[email protected]

Novel Multilayer Electrostatic Solid-State Actuators with Elastic Dielectric

Helmut F. Schlaak, Markus Jungmann, Marc Matysek, Peter Lotz Institute for Electromechanical Design, Darmstadt University of Technology,

Merckstr. 25, D-64283 Darmstadt, Germany

ABSTRACT

Solid state actuators provide deformation and actuation forces mainly excited by electric fields. Piezoelectric actuators are well established providing high forces at low strain due to their material characteristic. Electrostatic solid-state actuators consist of elastic dielectric layers between compliant electrodes. Applying electric fields of up to 100 V/m at the electrodes the dielectric contracts due to electrostatic forces and expands in orthogonal direction. We use high elastic silicone elastomers with thin graphite powder electrodes. In order to increase the absolute strain values at limited voltage, we have developed a novel multilayer process technology to fabricate elastomer stack actuators with up to 100 layers. The electromechanical properties of the actuators have been evaluated theoretically and characterised experimentally. Maximum strain values up to 20 % for prestressed multilayer films have been achieved. The novel multilayer fabrication technology provides multilayer stack actuators with various electrode patterns like universal linear actuators or matrix arrays for a wide range of applications as tactile displays for telemanipulation or Braille displays.

The strain in vertical direction versus driving voltage shows a hysteresis due to viscous friction in the elastomer layers. These measurements correspond to a viscoelastic theoretical model. The mechanical stress versus strain characteristic shows a strong nonlinearity for strains > 30 %. The dynamic characteristic has been evaluated by measuring the mechanical impedance in the frequency range of 2 to 1000 Hz.

Keywords: electroactive polymer, multilayer, electrostatic actuator, dielectric elastomer, tactile display

1. INTRODUCTION

Almost all technical products contain actuators. The variety of actuators is increasing while their physical dimensions are shrinking. This fact enables totally new fields of applications. During the last years piezo-electric actuators captured more and more attention. Meanwhile they are very well analyzed concerning available materials, characterization and dimensioning. Even todays available piezo-electric ceramics (e.g. PZT) and polymers (e.g. PVDF) respectively achieve a maximum strain of about 0.2 % and 0.1 % respectively.1,2 However they provide high forces. To reduce the driving voltage multilayer cofired piezoelectric ceramic actuators with thin layers (down to 20 m thickness) have been developed.3 The transverse piezo-electric effect is used with multilayer bending beam actuators. Stack actuators are using the longitudinal piezo-electric effect in contrast.4 Often an additional mechanical transmission is required to achieve attended strain. One way to higher strain ratios is given by lower stiffness: the material can easily be distorted. Foams for example have a very low stiffness and therefore a high strain at low maximum forces. Predominantly they are used as sensors (e.g. in electret microphones) because their maximum load is quiet low.5 At this certain point the electrostatic solid-state actuators are concerned. They can be realised by an elastic dielectric layer between compliant electrodes. Applying a voltage at the electrodes the dielectric contracts due to electrostatic forces and expands in lateral direction (Fig. 1). Due to the large variety of materials that can be used as dielectric, restoring spring and as substrate carrying the electrodes at the same time the compromise between high pressure and high strain can easily be met. Another feature of these materials is their high structural flexibility and their low density. Using high elastic silicone elastomer with thin graphite powder electrodes a relative thickness strain up to 30 % can be achieved.6

Invited Paper

Smart Structures and Materials 2005: Electroactive Polymer Actuators and Devices (EAPAD), edited by Yoseph Bar-Cohen, Proceedings of SPIE Vol. 5759 (SPIE, Bellingham, WA, 2005) 0277-786X/05/$15 doi: 10.1117/12.604468

121

Downloaded From: http://proceedings.spiedigitallibrary.org/ on 05/19/2015 Terms of Use: http://spiedl.org/terms

Fig. 1: Deformation of an elastic dielectric film under electrostatic pressure

The electrostatic pressure causing the deformation is

22

0 02r rVp T Ez

= = = (1)

where 0 is the relative permittivity in air, r the permittivity of the dielectric, z its thickness and V the applied voltage. Since polymers are nearly incompressible, the volume remains constant during deformation. By reducing the voltage the dielectric returns to its initial shape and can produce forces due to the stored elastic energy. To realise a sufficient strain with applicable voltages the thickness of the dielectric has to be in the range of a few microns, causing a further loss of absolute strain. The electrodes have to be very compliant not to constrain the deformation. Pelrine et al. have showed more than 30 % relative strain in thickness and electrostatic pressures of more than 1 MPa on prestrained silicone elastomer dielectric films between carbon electrodes.6 In order to increase the absolute strain values at limited voltages, certain arrangments are essential. Fig. 2 shows the three major assemblies.

Fig. 2: Configuration and function of electrostatic elastomer-actuators

A bending actuator (Fig. 2 a) consists of dielectric layers carrying electrodes on top of a passive layer. In operation the dielectrics elongation generates a tensile stress onto the passive layer causing the deflection. Hollow and solid cylinders (so called roll-actuators Fig. 2 b) are fabricated by a combination of only two dielectric layers and two electrodes convoluted as cylinder. The low number of layers reduces expenditure in manufacturing but a parallel fabrication of roll-actuators as an array is nearly impossible. As shown before stack actuators (Fig. 2 c) can be fabricated in different sizes and arrangements. Therefore the handling of a high number of thin dielectric and electrode layers is quiet challenging. We have developed a multilayer process technology to fabricate elastomer stack actuators with more than 100 layers. The according design of the electrodes allows even parallel fabrication of stack actuators in a matrix configuration.

2. TECHNOLOGY

2.1 Requirements There is a huge variety of parameters to be kept in mind while choosing the right elastomer for your special application with multilayer actuators. If you decide to use an elastomer with a high grade of hardness you can apply quiet large forces causing a low prestrain before electrostatic excitation. The remaining displacement is close to its idle-maximum. Therefore a high electrostatic pressure is required. The high electric field may lead to a breakdown. On the

122 Proc. of SPIE Vol. 5759


other hand you may choose a very soft elastomer. The required voltage for maximum displacement is relatively low but the prestrain causes high deformation and minimizes possible contraction.

Beside these considerations the elastomer material should have a low dynamic viscosity not to loose maximum displacement with increasing frequency. Furthermore the mechanical parameters of the dielectric should have a high disruptive strength and due to eq. (1) a high permittivity to maximize actuator performance. Technological demands are a low viscosity to realize thin dielectric films by spin coating and an addition curing silicone, not to get fission products. Dilution of the components is possible but requires a certain time to degasify, otherwise bubbles would be the consequence. A low pot life leads to an acceptable production time each dielectric layer has to cure before the electrode is put onto it. Often curing can be accelerated by thermal or optical radiation. Table 1 shows several silicones and their main parameters.

Table 1: Properties of applicable silicones

Manufacturer Name shore hardness viscosity, uncured [Pa s] permittivity

Bayer IS 5663/20 15 8,5 3 Dow Corning 96-082 31 1,1 3,14 Wacker Elastosil RT 607 55 10 3,7 Wacker Elastosil RT 675 80 35 6,1

The importance of the electrodes material is given by its conductivity. The electrical cut-off frequency is dominated by the (series-) resistance of the feed line. The sheet resistance of the feed line and the electrode has to stay low during planar expansion otherwise the time constant would change immensly and parts of the electrode may get lost due to interceptions. Furthermore the surface density of the electrode should stay high even under expansion to assure high effective electrostatic pressure. The mechanical requirements are influenced by the deformation of the electrode layer. The ideal electrode would have an infinite compliance, is thin compared to the dielectric layer and is patterned with high resolution.7 A good adhesion onto the dielectric layer is needed to prevent partial wash off effects reducing conductivity. The manufacturing process shouldnt be too complex, otherwise the time for fabrication of a stack would be too long.

2.2 Realisation We have developed an automatic fabrication process of multilayer actuators which is controlled by a computer. A special LABVIEW program is used to set the parameters and drive all the process sequences. Fig. 3 shows an overview of one cycle.

Figure 3: Process steps of one cycle of the automated fabrication for elastomeric actuators

Proc. of SPIE Vol. 5759 123


By spinning on silicone elastomeric dielectric films are realized. Spin coating is used to achieve homogeneous coating thickness of only a view microns. As mentioned in subsection 2.1 an addition curing silicone consisting of two components is used to avoid decomposition products on the surface while curing. The two components are stored in cartridges and are squeezed out by stepping motors. Flexible tubes head the components into a static mixer where they get mixed consistently without embedding any bubbles. The use of materials without any catalytic poison (e.g. plasticizer) is very important, otherwise curing may be disturbed or prevented. The volume of the mixer and the pot life have to be coordinated that way, that already mixed elastomer within the mixer will not be cured until its displacement after the further process cycles. The spun on silicones curing is accelerated by thermal radiation. Finally cooling down the elastomer and the spincoater prevents the new silicone layer from curing before the end of the spin coating process. The electrodes are deposited onto the elastomeric film. To contact the actuator to its supply voltage easily it is necessary to turn the leads of every second electrode. Fig. 4 shows the schematic cross section of an actuator stack with a parallel interconnection. The fabrication device for a structured spray-coating of conductive powder on elastomeric layers has to realize three major cycles:

masking the dielectric layer dosing the graphite powder spraying on the pressurized air-graphite powder mixture

Masking is realised by a spray head carrying a shadow mask patterned by photolithography. The graphite powder is stored in a pressure vessel. By whirling up the particles the mixture is generated in the upper parts of the vessel. Out of a nozzle the air-graphite powder mixture is sprayed onto the mask.

2.3 Results Prototypes with up to 200 dielectric layers have been fabricated with silicone elastomer Wacker Elastosil P7670. Various electrode patterns, e.g. single electrodes as well as electrode matrix arrays have been realised. The minimum thickness of dielectric layers has been limited to approximately 25 m due to the decreasing yield for thicknesses below 20 m. The particle-electrode thickness is about 5 m while the primary particle size of the graphite powder is 2 m. Fig. 5 shows a micrograph of a 100-layer actuator stack. If you compare the realised actuator stack to the schematic assembly (Fig. 4) you can see, that the electrodes or graphite particles do not immerse into the silicone layer nor a wash-off effect of the particles occurs. The reproducibility of the electrodes edge is within a few microns as the graphite stands out against the clear silicone layers (Fig. 5 a).

Figure 5: Micrograph: a) boundary between supply region and active region (scaling bar: 50m); b) active region (scaling bar: 20m)

a) b)

Figure 4: schematic cross section of an actuator stack



In addition we investigated the reproducibility of the thickness of the spun on silicone layers. With a line width measuring system the thickness of each dielectric layer of a 50 layer stack has been determined (Fig. 6 a). It can be seen that the first spun on layers are thinner than the last ones: the mean value is slightly rising by the number of layers.

10

15

20

25

30

35

1 6 11 16 21 26 31 36 41 46film n

film

th

ickn

ess

[m

]

measured valueslinear fit

-40%-30%-20%-10%

0%10%20%30%40%

1 6 11 16 21 26 31 36 41 46film n

rela

tive

de

via

tion

Actuator 1Actuator 2Actuator 3

a) b) Figure 6: a) Measured absolute film thickness. b) Deviation of film thickness from mean thickness for three different actuators

To verify this effect another three actuators have been measured (Fig. 6 b). The effect of a growing film thickness has been proven. As mentioned before the electrode and its conductivity are of high importance. Not only the material but also the way of deposition affects its quality. Since two methods are applicable spraying and brushing both results have been analysed in Fig. 7. Even if both both types have low starting sheet resistance (< 10 k/cm), the sprayed electrode has more than two times greater resistance. This difference is rising with transverse strain that is applied manually by a mechanical device. Actuators with a high strain should carry brushed electrodes even if there are still difficulties by brushing graphite powder onto a micro patterned shadow mask (and not under it).

y = 7,21x + 10

y = 3,28x + 7

020406080

100120140160

0 5 10 15 20 25transverse strain Sx,y [%]

she

et r

es

ista

nc

e [k

/cm

]

graphite, sprayedgraphite, brushed

Figure 7: Sheet resistance of graphite electrodes

The two micrographs in Fig. 8 show the surface of a brushed (Fig. 8 a) and a sprayed (Fig. 8 b) electrode. The sprayed electrode shows an inhomogenous surface that influences the conductivity obviously. The homogeneous layer of the brushed graphite may be the reason for a better conductivity for prestrained electrodes.



a) b) Figure 8: SEM Micrographs of a) brushed and b) sprayed graphite electrode

3. MODELLING

Due to high strain of the dielectric films of an actuator stack there is a nonlinearity of the stress-strain-characteristic. Furthermore viscoelastic behavior is typical to elastomeric materials, hysteresis and damping effects are the consequence. In this section a model is derivated, characterizing the actuators behavior under the mentioned restrictions.

3.1 Geometrical Nonlinearities Geometrical nonlinearities are typical characteristics of elastomers, caused by a very low compressibility. Therefore the volume V of a deformed elastomer stays nearly constant8. If we assume a constant volume, vertical strain of an elastomer probe caused by the force F deforms the probe (Fig. 9). The relation between vertical strain dz and area strain dAz is given by 0 0 0 0 0 0 0( ) ( )Z Z ZV const x y z A z A dA z dz= = = = + (2)

Figure 9: Geometrical proportions of a probe deformed by force F

The transverse strain Sx and the area strain SA of an uniaxial compressed elastomer volume are given by

0

1 11X Z

dxSx S

= =

; 0 1Z Z

AZ Z

dA SSA S

= =

(3)

Fig. 10 shows the transverse and area strain as a function of the vertical compression. Exceeding 61.9 % compression strain the transverse strain is larger than the compression strain.

At quasi-static deformation the stored mechanical energy W caused by the Force F complies with the sum of the three expansion energies in each dimension:

z y xdW F dz F dz F dy F dx= = + + (4) Here Fi = Ti Ai corresponds to the force acting onto the boundary face.



00,5

11,5

22,5

33,5

4

0 0,2 0,4 0,6 0,8 compression strain Sz

s

tra

in S x

, S A

transverse strainarea strainSx=Sz

Fig. 10: Transverse and area strain depending on the compression strain

Converting eq. (2) and (4) leads to Z Y XT T T T= (5) TY and TX are negative because they are tensile stress assuming TZ as compression. If we assume isotropic material properties and a constant, isotropic Youngs modulus Y = Ti/Si we get the externally affecting stress T (using Sn from eq. (3)) causing the compression SZ :

1( 2 ) 2 11Z X Z nZ

T Y S S Y S Y SS

= + = + =

(6)

3.2 Viscoelastic Performance The viscoelastic performance is another important characteristic of elastomers. Abrupt distention of these materials leads to an excursive increasing of the mechanical stress followed by asymptotic decreasing to the minimum. This effect is called relaxation. If there is a jump of stress, strain increases gradually asymptotic to its maximum. This effect is called creeping. Viscoelastic behaviour is represented by the Thompson model (Fig. 11), consisting of stiffnesses c1,2 and the viscous friction d2. The model is upgraded by another damper d1 and a mass element m.

Figure 11: Modified Thompson model

The mechanical impedance of this equivalent network is given by the following complex equation 1

1

2 2

11mech

cFZ d j mjv jc d

= = + + ++

(7)

Including accounted corpus geometry (face A0, height z0), concentrated parameters (d1,2, c1,2, m) can be converted into material specific terms (Youngs modulus Y1,2, viscosity-modulus 1,2 and inertia-modulus M): 0

1 10

2 2

1 11 1mech Z

z TZ Y j MA jS j

Y

= = + + ++&

(8)

Multiplying eq. (8) by j the stress-strain-transfer function G can be calculated (for small S):



21 1

2 2

11 1

T TG j j Y MS S j

Y

= = = + +

&

(9)

Assuming isotropic material parameters and keeping geometrical nonlinearities in mind (equation (5) and (6)) we get the complex stress-strain-characteristic:

nT G S= (10)

3.3 Electrical model The equivalent electrical circuit of an electrostatic multilayer actuator is shown in fig. 12. RS represents the resistance of the feed line of each electrode, RP the resistance of the dielectric layer (leakage current) and C the strain dependant capacity (C(SZ)).

Figure 12: Equivalent circuit of an electrostatic multilayer actuator

The effective voltage drop across the dielectric layer is given by

01

11 2 ( )C

S ZP

V VR j C S

R

=

+ +

(11)

and the strain dependant capacity C(SZ) is given by

0 00 0 0

0 0

(1 )( ) (1 )A

Z r r rZ

A dA A SAC Sz z dz z S

+ +

= = =

. (12)

With eq. (3) we can simplify the term, yielding

00 2

0

1( ) (1 )Z r ZAC Sz S

=

. (13)

Combining eq. (11) and (13) we get:

00

0 20

11 11 2 (1 )

C

S rZ P

V VAR jz S R

=

+ +

(14)

By equating relation (1) for the electrostatic pressure and relation (10) for the mechanical stress we get the voltage VC, needed to achieve the strain SZ:

00 0

1(1 )C z nr r

TV z z S G S

= = (15)

The coupling of mechanical and electrical model is given by eq. (14) and eq. (15). With known model-parameters quasi-static and dynamic performance can be developed. During deformation of an active stack the dielectric layer is getting thinner. This causes a faster increase of the electrostatic pressure (by the electric field) than of the mechanical stress. At strain of SZ = 38.8 % electrostatic pressure becomes larger than the mechanical stress. This causes a pull-in effect until the destruction of the actuator due to dielectrical breakdown.



4. CHARACTERISATION

To characterise the dynamic behaviour of stack actuators special prototypes have been realised. Fig. 13 shows the prototype design and its dimensions. The thickness of the dielectric layer (silicone: Wacker Elastosil P 7670) is 25 m, electrodes are 5 m high. The permittivity of the elastomer is r = 3. Stacks with 22 and 52 layers have been investigated the two layers on the surfaces of the stack are to protect the electrodes. Material parameters are ascertained by cast cylindrical probes.

Figure 13: Actuator design

4.1 Quasi-static behaviour The stress-strain characteristics is used to determine the quasi-static material parameters. Therefore a silicone probe ( 10 mm; height 10 mm) has been compressed unaxially and the force-deflection characteristic has been determined. The proceeding velocity is 10 m/s. Fig. 14 shows the stress-strain-characteristic compared to the theoretical model (eq. (6)). Stress values concern the face of the uncompressed probe (A0) the systematic error for small deflection is quiet low.

0

0,1

0,2

0,3

0,4

0,5

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7strain Sz

str

es

s T

m [M

Pa]

modelmeasurement

Figure 14: Stress-strain characteristic

We can see the hysteresis in the measurement, due to viscosity-modulus (1,2) and the friction on the contact surface. This friction is minimized by using vaselin. To eliminate the hysteresis for calculation, the model has been approximated to a minimum mean error of 7.8 %. The determined Youngs modulus is Y1= 123.717 kPa. This Youngs modulus can be used to calculate (eq. (15)) the strain of an actuator for an applied voltage. The real strain as function of the supplied voltage is determined with a 20 layer actuator. To measure the deflection the actuator is put into a mechanical frame to prevent several sources of error (e.g. cambers). The deflection is measured by an optical surface-profilometer. This characteristic is shown in Fig. 15.



00,05

0,1

0,15

0,2

0 500 1000 1500 2000voltage [V]

str

ain

S z

measuredmodelcorr. Modell

Figure 15: strain-voltage-characteristic

We obtain a similar characteristic between model and measurement, the latter shows a gradient. For this purpose we assume the following reasons:

the outer silicone layers are not under electrostatic pressure: they impede transverse strain reducing the linear compression

the passive elastomer surrounding the electrodes constricts plane expansion and impedes linear compression, too

the graphite-powder layers are non-ideal electrodes : incomplete coverage and contact resistances between particles may cause field-free areas ending up in a lower effective electrostatic pressure

the Youngs modulus is determined with a larger probe: the stiffness of a thin actuator slice is clearly higher

By establishing a constant correction factor (kf = 0.14) the model characteristics can be fitted to the measurement. This leads to a mean error of only 2.9 %. At high strain (SZ > 12 %) there is an increasing deviation, probably caused by the decreasing charge density with rising strain. The corrected model is based on a (mathematically determined) electrostatic pressure of only 14 %. This corresponds to a reduced effective field strength of 37.4 %.

4.2 Dynamic behaviour Dynamic material parameters have been determined by measuring the mechanical impedance. The impedance measurement head consists of an electrodynamic oscillator, a force sensor and an acceleration sensor. This head is pressed onto the silicone probe with a force F0 = 0.5 N. The oscillation of the head causes the measured acceleration, integrated to its corresponding velocity. The resulting velocity-force-ratio delivers the mechanical impedance. Fig. 16 shows the absolute value of the measurement at frequencies of 10 Hz to 1000 Hz

0,1

1

10

100

10 100 1000frequency [Hz]

lZ

me

chl [N

s/m

]

measurementmodelcorr. model

Figure 16: Mechanical impedance compared to calculated model



The model parameters (eq. (8)) were determined by a curve-fitting using MATHEMATICA. The static parameter Y1 is already known. It has to be mentioned, that the resulting mass of the calculation includes the mass of parts of the measuring equipment. This mass can be determined by an idle-measurement and is substracted from the calculated mass (corr. model in Fig. 16). Table 2 shows the resulting specific material parameters.

Table 2: determined specific material parameters (Elastosil P7670) Y1 Y2 1 2 M

138948 Pa 676204 Pa 198 Pa s 13487 Pa s 0,1 Pa s2

These parameters are used in eq. (9) to determine the transfer function of strain S and mechanical stress T. To get the frequency response of a 50-layer actuator stack it has been supplied with a sinusoidal AC voltage superposed with a DC voltage at frequencies from 10 Hz upto 1000 Hz. Fig. 17 shows the measured frequency response and the qulitative comparison of the force-deflection-frequency resonse.

1E-5

1E-4

1E-3

1E-2

1E-1

1E+0

1E+1

10 100 1000frequency [Hz]

z/F

z/

U

model z/Fmeasurement z/U

Figure 17: Frequency response of an actuator and force-strain-ratio frequency response of the dielectric.

Both curves show a slight decay for low frequencies. The actuators lower resonant frequency (compared with the model) with a higher resonance magnification is obviously a result of the higher mass that results from the passive silicone surrounding the electrodes. Assuming an actuator without silicone surrounding silicone ring the frequency response will be close to the models course.

5. APPLICATIONS

As mentioned in section 1 electrostatic solid-state actuators fabricated as multilayer-stacks are primarily used for linear motion. They provide low forces at high deflection. This combination establishes new applications particularly in microelectromechanical systems (MEMS). As a result of the perpendicular effective motion direction actuators can easily be grouped close to each other. Multilayer elastomer stack actuators can meet a variety of applications in optics (micromirros), switches, acoustics (micro loudspeakers) and microfluidics (valves, pumps).9 A further field of application is the human tactile sense. The actuators performance is ideal to adapt actuators onto human skin, even if the actual needed supply voltage is very high. As an actuator for a braille-display (Fig. 18) there is only a 4x2 actuator matrix needed. 10



Figure 18: Braille display as a possible application of mulilayer actuators

But this is quite far away from the achievable potential of elastomer stack actuators. If we think of a tactile display integrated into a data-glove we have to meet enormous requirements. For stimulating the whole human hand there are some hundred actuators needed due to the high selectivity and spatial resolution of the human sense. These actuators have to be integrated into a compliant body enclosing human hand a complex structure. As we see, the possibility to fabricate (stack-) actuators simultaneously in arrays is predicted for these applications. Fig. 19 a shows a design concept for a tactile display. The planar arrangement of the actuators into a hexagonal shape assures equivalent distances between all adjacent actuators. Embedded bumps between actuator and skin realise the force transmission: passive (non excited) actuators are displacing the skin (fig. 19 b).

Figure 19: Matrix design for tactile displays

The excitation of a single actuator inside an actuator array is a challenge. If the actuators are arranged as a passive matrix every single line and column can be selected and the actuator gets charged or discharged. Fig. 20 shows the principle with periodically switched column and row lines. Due to the slow discharging (through the non-ideal isolator between the electrodes) the display needs to be refreshed at certain clearances. Such a passive matrix shows the principle disadvantage of crosstalk. If this crosstalk leads to noticeable displacements of the surrounding actuators an active-matrix-arrangement has to be used (e.g. known from TFT-displays).

Figure 20: Passive-matrix-arrangement with periodic refreshment

It is obvious to use such a matrix as sensor, too. The changing of the capacity due to external displacement can be measured. Current investigations are about an actuator-sensor-system by the use of elastomeric stack-actuators with embedded sensor-capacities.

V



6. CONCLUSIONS

An automatic fabrication technology has been developed to provide electrostatic multilayer stack actuators with elastic dielectric. Its function has been determined by several prototypes with different electrode-designs and different numbers of layers. Further developments have to investigate the material of the electrodes and their fabrication. There are already some known materials having better properties (eg. low contamination of the dielectric layer, higher area coverage, lower sheet resistance) but to determine their exact characteristics as electrode they have to be implemented into the existing process. Otherwise reproducibility will be very hard to achieve. To obtain a fabrication technology suited to different applications elastomers with different mechanical properties e.g. compliance have to be qualified. The developed dynamic, nonlinear model has been verified for a wide frequency range. So the model can be used to design electrostatic polymer actuators with elastic dielectric. Theoretical examinations of the actuator with load can be done easily by using the determined impedance. Further investigations are necessary to understand the deviations between model and real actuator: the description of an effective field strength is probably the best way to identify imperfections of the real actuator. The electrical interconnects of the multilayer electrodes have to be improved in order to assure the function of each layer. Three-dimensional analysis of integrated actuator arrays have to be performed (e.g. FEM-analysis) to describe the displacement and dynamic behaviour using integrated field simulation as well.

7. REFERENCES

1. Heartling, G. H.: Ferroelectric Ceramics History and Technology, J. Am. Ceramic Soc., 82, 4, pp. 77-818, 1999. 2. Tiersten, H. F.: Linear Piezoelectric Plate Vibrations Element of the Linear Theory of Piezoelectricity and the

Vibrations of Piezoelectric Plates, Plenum Press, New York, 1969. 3. Yao, K. et al.: Design and Fabrication of a High Performance Multilayer Piezoelectric Actuator with Bending

Deformation, IEEE Trans. Ultrasonics, Vol. 46, No. 4, 1999. 4. Rogacheva, N.: The Theory of Piezoelectric Shells and Plates, CRC Press, 1994. 5. Bauer, S.; Gerhard-Multhaupt, R.; Sessler, G.: Ferroelectrets: Soft Electroactive Foams for Transducers, Physics

Today, 37-43, Feb. 2004. 6. Pelrine, R.; Kornbluh, R.; Joseph, J.; Heydt, R.; Pei, Q.; Chiba, S.:High-field deformation of elastomeric dielectrics

for actuators, Materials Science and Engineering, C11, Elsevier Science, pp. 89-100, 2000. 7. Pelrine, R.; Kornbluh, R.; Joseph, J.; Chiba, S.: Electrostriction of Polymer Films for Microactuators, IEEE

Proceedings of the 10th Annual International Workshop on Micro Electro Mechanical Systems, MEMS 97, Nagoya, Japan, pp. 238-243, 1997.

8. Carpi, F.; Chiarelli, P.; Mazzoldi, A.; De Rossi, D.: Electromechanical characterisation of dielectric elastomer planar actuators: comparative evaluation of different electrode materials and different counterloads, Sensors and Actuators, A107, Elsevier Science, pp. 85-95, 2003.

9. Kornbluh, R. et. al.: Electroactive polymers: An emerging technology for MEMS. SPIE Vol. 5344, 2004. 10. Heydt, R.; Chhokar, S.: Refreshable Braille Display Based on Electroactive Polymers. Int. Display Res. Conf.

IDRC 03, SID Soc. Information Display, 2003, P7.5.



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