A new type of surface micromachined ratcheting actuation system has been developed at the Microelectronics Development Laboratory at Sandia National Laboratories. The actuator uses a torsional electrostatic comb drive that is coupled to an external ring gear through a ratcheting scheme. The actuator can be operated with a single square wave, has minimal rubbing surfaces, maximizes comb finger density, and can be used for open-loop position control. The prototypes function as intended with a minimum demonstrated operating voltage of 18V. The equations of motion are developed for the torsional electrostatic comb drive. The resonant frequency, voltage vs. displacement and force delivery characteristics are predicted and compared with the fabricated device's performance

BARNES,STEPHEN MATTHEW

BITSIE,FERNANDO

MILLER,SAMUEL L.

RODGERS,M. STEVEN

UNT Digital Library

5’%An72@Nz- c-Torsional Ratcheting Actuating SystemStephen M. Barnes, Samuel L. Miller, M. Steven Rodgers, Fernando Bitsie ~! ~~~~ ~~~Sandia National Laboratories JAN 3 t2NNIMS 1080, PO Box 5800, Albuquerque, NM, 87185smbarne@sandia.gov, (505)284-33 10, fax: (505)844-2991, http://mems.sandia.gov/ QsTj.1 ABSTRACTA new type of surface micromachined ratcheting actuationsystem has been developed at the MicroelectronicsDevelopment Laboratory at Sandia National Laboratories.The actuator uses a torsional electrostatic comb drive that iscoupled to an external ring gear through a ratcheting scheme.The actuator can be operated with a single square wave, hasminimal rubbing surfaces, maximizes comb finger density,and can be used for open-loop position control. Theprototypes fi,mction as intended with a minimumdemonstrated operating voltage of 18V. The equations ofmotion are developed for the torsional electrostatic combdrive. The resonant frequency, voltage vs. displacement andforce delivery characteristics are predicted and compared withthe fabricated device’s performance.Keywords: MEMS, Actuator, Electrostatic, Comb, Ratchet2 INTRODUCTIONThe development of actuation methods that meet thestringent requirements of MEMS applications has receivedlimited attention, and is a critical need. Numerous types ofMEMS actuators have been proposed based onelectromagnetic, piezoelectric, thermal, and electrostaticprinciples [1]. However, many of these actuators displaysmall displacement outputs, require complicated post-processing, are difficult to operate, and require large voltageinputs.The goal of this work is to develop and characterize areliable surface micromachined actuator that provides asignificant force and displacement output with precise openloop positioning using simple low voltage drive signals.Electrostatic actuation is readily implemented in surfacemicromachining and is well characterize~ so it was chosen toaddress this goal. The actuator presented herein is termed thetorsional ratcheting actuator or TRA.3 TORSIONAL RATCHETING ACTUATORThe TRA uses rotational comb drives for electrostaticoperation which are similar to previous gyro designs [2,3]. Alarge circular frame ties the movable banks of combstogether. See Figure 1 for a SEM of the fabricated device.Four cantilever beams support this frame in its center and actas the frame’s spring return. These four beams are resistantto any lateral motion of the fi-amebut allow it to rotate. Theframe is limited to 2.8° of rotation by stiff spring stops at itsoutside edge. To avoid stiction problems, the frame hasdimples fabricated in its bottom surface to ensure the frame isphysically separated from the underlying ground plane.The torsion frame is surrounded by a 375pm radius ringgear which has standard involute gear teeth on itscircumference that were designed to mesh with Sandia’sstandard MEMS components. Four overhanging clips hold itto the substrate and also constrain it to only rotationalmovement. The inside of the ring gear is lined with a rack ofratchet teeth that have a pitch of 13pm. Equally spacedaround the edge of the torsion frame are three ratchet pawlsthat engage with the ratchet teeth. To prevent any unwantedreverse motion of the gear, there are three anti-reversemechanisms that engage the ratchet teeth. The anti-reversemechanisms are anchored cantilever beams that engage withthe ratchet teeth.To prevent electrostatic attraction to the underlyingsubstrate, the frame is fabricated above a thin ground plane ofpolysilicon. The frame is connected to the ground plane atthe central torsion springs. The stationary sections of thecomb banks are connected using electrically isolated pieces ofthe ground plane. The interconnect to the stationary banks ofcombs is made using a signal line that passes above the gearand comects with one of the stationary comb banks.To actuate the TR& a periodic voltage signal is appliedthrough this interconnect to the stationary combs. As thesignal voltage increases, the torsion tie rotates counter-clockwise about its springs in response to the electrostaticattraction between the stationary and moving comb fingers.As the frame begins to rotate, the ratchet pawls engage thering gear and cause it to also rotate. As the gear is rotating,the anti-reverse mechanisms are forced out of theirengagement with the ratchet teeth an~ once the ring gear hasmoved sufficiently, they reengage the next tooth. When thevoltage is remove& the central torsion springs force the frameto return to its fabricated position. As the frame is returning,the ratchet pawls attempt to drag the ring gear in the reversedirection but the anti-reverse mechanisms have engaged andthe ratchet pawls are forced to skip over the tooth and finallyengage the next tooth. At this poin~ the frame has returned toits initial position, and the cycle can be repeated.This type of actuator has many inherent advantages. Oneimportant feature of the actuator is its high density ofelectrostatic force elements. This high density is the result ofa compact overall actuator layout. This density is importantfor applications because it minimizes the voltage required todrive a load while minimizing the area the actuator consumeson a die. Also, because the ring gear is only ratcheted in onedirection, the TRA requires only two electrical connections toDISCLAIMERThis report was prepared as an account of work sponsoredby an agency of the United States Government. Neither theUnited States Government nor any agency thereof, nor anyof their employees, make any warrantyt express or imPliedtor assumes any legal liability or responsibility for theaccuracy, completeness, or usefulness of any information,apparatus, product, or process disclosed, or represents thatits use would not infringe privately owned rights. Referenceherein to any specific commercial product, process, orservice by trade name, trademark, manufacturer, orotherwise does not necessarily constitute or imply itsendorsement, recommendation, or favoring by the UnitedStates Government or any agency thereof. The views andopinions of authors expressed herein do not necessarilystate or reflect those of the United States Government orany agency thereof.=., -T ,,,, ..>., ,, =..,,,, ,.. . n-, 7---? . . . . . ,>--=--’.. . ..> .: ,.msm.- -—.-—-——-- --- ---— - --DISCLAIMERPortions of this document may be illegiblein electronic image products. Images areproduced from the best available originaldocument.‘ )Figure 1. SEM of the fabricated torsional ratchetingactuator. a. shows an enlarged view of the central torsionsprings.run, and operates on extremely simple input signals. Finally,the use of a ratcheting system produces discrete displacementoutputs. This is highly relevant because the actuator can beused for open loop positioning of a load.4 THEORYModel-based design parameters that will result in lowvoltage operation require appropriate system models. Thetorsion frame is the focus of the modeling presented here.The ring gear is not included in the model due to stiction anddamping forces that are diftlcult to represent. The overallmodel for the torsion frame is obtained by summation ofmoments about its center torsion springs. This allows directextraction of torque-displacement voltage-displacemen~ andvoltage-force relationships. The model for the system isbased on:~c(v,e)+qc(v,e)-~(e) = I@# (1)where TiCis the torque produced by the inner banks of combfingers, Tm is the torque produced by the outer banks of combfingers, T, is the resisting torque of the center torsion springs,I is the moment of inertia of the torsion flame, 0 is theangular displacement of the torsion fmme, V is the appliedvoltage, and t is time.To model the torque output of the combs, linear combtheory was combined with parallel plate theory [4]. This wasdone to account for the linear clamping of the comb banksthat occurs at the end of each comb’s travel. Summing theindividual torque contributions of each comb finger yields:<C(V,8)= @-3c0mbS(2~f~,2+$)&v21 ,2,where n is the number of inner comb banks, A is the area ofthe tip of the comb, gt is the parallel plate gap between theend of a finger and the root of the opposing comb, h is thevertical thickness of the combs, g~is the gap between adjacentcomb fingers, &is the dielectric constant for air, and r is theradius of the individual comb finger. The ~ term in equation 2accounts for the decrease in the capacitance of theelectrostatic combs due to the underlying ground plane. Tang[5] shows this term can be approximately 0.7, whichrepresents a 30°/0reduction in the force output of the combs.All calculations in this analysis use 0.7 for ~. There is asimilar expression for TW.The torsion springs are not adequately described by linearbeam theory. The end of each beam that makes up the torsionsprings is forced to undergo an in-plane displacement alongwith an angular deflection. Also, while the torsion frame isrotating, the nearly clamped-clamped geometry of the torsionsprings requires the individual beams to be stretched duringthe displacement. In an attempt to alleviate this strain andgenerate linear spring behavior, relief springs were placed atthe root of each torsion beam.Due to the complicated spring displacement andgeometry, a three-dimensional non-linear finite elementanalysis (FEA) was performed to calculate their stiffhess.The finite element model used was of a single cantilever andits strain relief structures. The boundary conditions usedwere deflection and angle specifications at the free end of thespring and fixed conditions at the base of the spring. I-DEASwas used to mesh the spring and Abacus was used to do thenon-linear calculations. The total end moment required todeflect the beam to the end conditions was calculated at onedegree displacements. A polynomial fit was then used to findthe torque-deflection relationship:z =149e+l1.802–1.65e3 (3)5 EXPERIMENTAL RESULTSThe TIM was fabricated in SUMMiT at theMicroelectronics Development Laboratory at Sandia NationalLaboratories (see Figure 1). To conserve space, thefabrication details are omitted from this article and can befound in [6].The fabricated devices demonstrated behavior aspredicted from the models. Design variations producedminimum actuation voltages between 18V and 35V. TheTRA has also shown to be very robust to larger voltageinputs. Up to 150V has been applied with no observeddetrimental effects.Initial lifetime tests have demonstrated up to 108cycles tofailure. This is equivalent to 600,000 gear revolutions. Thisnumber of actuation cycles drives the ring gear a lineardistance of nearly 1.5 km. Also, initial testing has shown a2000 I I I I 1 I I.. ......... ......... ............ .......................... .IOv I I I I IoA!$tar Displacement o;fe Toraion%rame (d$gf3Figure 2, Resisting spring torque as a fimctionof the angulardisplacement of the torsion flame. The FEA calculations arecompared with the experimentallyderived spring stiflhess. The‘Experiment’ curve was obtained by measuring the naturalfrequencyof the torsion tlame at one displacementand determiningan “effective”stiffhess.greater than 90’% yield of the unpackaged devices with noprior manipulation required.In previous comb driven actuator designs [7], lateralclamping of the comb fingers was a serious issue. Lateralclamping is directly related to the lateral stiffness of thesupport springs and this spring design was chosen due to itsinherent stiffness. Spiral springs were initially consideredbecause simple models exis~ but they were rejected due totheir inherent vertical and lateral compliance. The stiffness ofthe torsion springs has contributed strongly to the TRA’srobustness to release and over-voltage.The type of signal that is used to drive the TR4 affects theratcheting performance of the device. This is due to therelatively large inertia of the ring gear. If a pure square waveis applied to the combs, the strong impulse that is given to thering gear can impart enough momentum to cause the gear tomove past multiple ratchet steps. If a signal with a slowerinitial rise time is use~ the gear is only moved one step. Atriangle wave has shown to work well for driving the TRA.Because the torsion springs are an important parameter inthe models, their widths were measured using SEM. Thesprings showed clean definition and were approximately80nm thinner than defined. This type of close match isrequired for the FEA analysis to be accurate because thestiffness of cantilever beams is typically related to the widthof the springs cubed [8].The natural frequency of the device at atmosphericpressure and temperature was measured by applying a lowfrequency square wave signal and observing its dynamicbehavior using stroboscopic illumination. This allowedrecording the torsion frame’s free oscillations in a knowntime. This was performed on TRAs that did not have ratchetpawls so that the torsion frame was not making contact withthe ring gear. The measured natural frequency of the torsionframe was 3800Hz. The FEA predicts a slightly fasterresponse of approximately 3900 Hz. Using the measured3 I I I 1 I I Ig:2.5 -----gk52 . . ........ ........... .... ...... ....... ..... ..... ... ... ........ ... .. .. . .. ..f!?E~ 1.5zE;gl~.%n& 0.5x0) qOazo0 100 200 300 400 500 600 700 800Input Voltage Squared (V 2,Figure 3. Comparison between the experimental and theoreticalangular displacement of the torsion frame due to appliedvoltage.natural frequency, a linear torsional spring constant wascalculated for the device. This was done using a calculatedmoment of inertia of the torsion flame and assuming a linearspring response. Figure 2 shows the force-displacementresponse of the torsion springs as calculated by FEA andexperiment. The FEA results match with the experimentalmeasurement quite well and show a slight spring stiffening asthe frame is displaced.The fi-ame’sangular displacement response to voltage wasalso measured. DC signals from OV to 30V were applied andthe steady state angular displacement of the fi-ame wasrecorded for each. The fizune’s displacement was measuredusing a pointer fabricated on the outside edge of the framethat indicates the frame’s angular displacement in degrees.This pointer gives a 0.25° resolution because of the largeoutside radius of the TRA. These data are plotted against thetheoretical response in Figure 3. As the figure shows, thetheory predicts the electrostatic pull-in of the torsion time towithin IV.Finally, a measurement of the device’s force outputagainst voltage was done. To accomplish this, some of thedevices were fabricated with folded springs attached asshown in Figure 4. The folded springs are attached to a lineargear rack that connects to the TRA’s ring gear. A smallperiodic voltage was applied and the displacement amplitudeof the folded springs was observed using a gauge fabricatedon the springs. The displacement of the springs was recordedat each amplitude of the input signal. Using linear beamtheory, the spring constant of the test structure was calculated.Using the displacement data and spring constant calculation,the force output was experimentally determined. The resultsof the experiment are shown in Figure 5.In equation 2, it can be seen that the torque output of thecomb banks depends on the voltage applied but also on thedisplacement of the fi-ame. This is due to the parallel plateattraction of the ends of the comb fingers as they furtherengage with the opposing combs. Because of this. . .. -5Figure 4. SEM of the force test structure after the experimentwas performed. Note that the beams are held in the deflectedposition due to the action of the anti-reverse mechanisms. Thebeams have a stiffness of approximately lpN/pm.dependence, there is a range of possible force outputs for eachapplied voltage. The minimum and maximum force outputsfor the voltage range were calculated from equation 1 and areplotted in Figure 5. The predictions bound the experimentalresults well.6 CONCLUSIONSWe have designed and fabricated a new type ofelectrostatic actuator based upon ratcheting small angulardisplacements to allow significant force output with a discretedisplacement output. The TRA has demonstrated reliableactuation and usable force at small voltages using very simpleinput signals. A dynamic model of the TR4 has beendeveloped and shown to accurately match the measuredbehavior of the fabricated devices. The model predicts thevoltage requirements for actuation of the TRA to within lVand accurately bounds the force output of the device.One objective of the TRA design is low voltage operation.The system model was developed to address this objective bypredicting the voltage response of the fabricated devices. Asthe model has been demonstrated to be accurate, improveddesigns can now be confidently developed. In order toachieve a higher force to voltage ratio, the fimdamentalactuation method of the TRA may be changed. This is thereason a full dynamic model was generated. Other actuationmethods that are based on the dynamic behavior of the TRAcould be used to dramatically reduce the voltagerequirements. New designs are being considered which useresonant mode actuation and reverse mode actuation. Inreverse mode actuation, the comb banks are used to initiallydisplace the center torsion springs. This stored energy is thenreleased to ratchet the ring gear and load. Additionally, theinertia of the torsion flame can be exploited in this mode toachieve larger initial frame/spring displacements than thesteady state voltage would allow. To confidently design boththe resonant mode and reverse mode actuators, this fulldynamic model is required.The torsional ratcheting actuator has demonstrated manydesirable features as a MEMS actuator. Its size, simplicity ofn. . . . ..“ o “’”20 40 100 120 140Ap$?ed Voit~~e (V)Figure 5. Comparison between the measured force output ofthe TRA with the maximum and minimum calculations. Theparticular TRAs used in this test had springs twice as stiff as theTMs tested in Figure 3.operatio~ and use in open loop control applications couldmake it a commonplace actuator design in MEMS.Sandia is a multiprogram laboratory operated by SandiaCorporation, a Lockheed Martin Company, for the UnitedStates Department of Energy under Contract DE-AC04-94AL85000.7 REFERENCES[1] H. Fuji@ H Toshiyoshi, “Micro actuators and theirapplications”, Microelectronics Journal 29, 1998, pp. 637-640[2] W. Geiger, B. Fokrner, U. Sobe, H. Sandmaier, W. Lang, “Newdesigns of micromachined vibrating rate gyroscopes withdecoupled oscillation modes”, Sensors and Actmators A 66,1998, pp. 118-124[3] S. An, Y.S. Oh, K. Y. Park, S. S. Lee, C. M. Song, “Dual-axismicrogyroscope with closed-loop detection”, Sensors andActuators 73,1999, pp. 1-6[4] J. J. Sniegowsld, E. J. Garci~ “Microfabncated Actuatom andTheir Application to Optics”, Proc. SPIE Miniaturized Systemswith Micro-Optics and Micromechanics, 2383, 1995, pp. 46-64.[5] W. Tang, “Electrostatic Comb Drive for Resonant Sensor andActuator Applications”, University of California at Berkeley,1990, pp. 15[6] J. J. Sniegowski, M. S. Rodgers, “Multi-layer enhancement topolysilicon stiace micromachining technology”, IEDM Tech.Digest pp. 903-906,1997[q E. J. Garci~ J. J. Sniegowski, “Stiace MicromachinedMicroengine”, Sensors and Actuatom A 48,1995, pp. 203-214.[8] W. C. Young, Roark’s Formulas for Stress& Strain, 61hEd.,Chap. 7, McGraw-Hill, Inc., New York, 1989, pp. 100.—- ~—.. — -7c-—.— — ----- - T - I

Torsional Ratcheting Actuating System

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