Multiple Mode Resonator

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    MULTIPLE ODEMICROMECHANICALESONATORSReid A. Brennen, Albert P. Pismo, and William C. Tang

    Berkeley Sensor 6 Actuator CenterElectronics Research LaboratoryDepartment of Electrical Engineering and Computer ScienceUniversity of California Berkeley CA 94720

    ABSTRACTIn this paper are described two resonant micromechanicalstructures that have been designed, fabricated, and tested and whichexhibited multiple modes of v ibration. The first had a cantileveredinertial mass that was actuated by a curved-comb electrostatic-driveattached near the root of the cantilever. The second structure had astraightamb electrostatic-drive with a folded flexure suspension thatwas used to actuate the cantilevered inertial mass. The first structureexhibited 2 distinct vibration modes, and the second structure actuallyexhibited 3 distinct vibration modes. An analytic dynamic model hasbeen developed and it predicted the vibrational mode shapes of thestructures. Tests of the fabricated structures have demonstrated thatpeak-to-peak lateral displacements greater than 10 microns werefeasible. Further, peak-to-peak angular displacements greater than100 have been measured dur ing second mode vibration. The resonantfrequencies of the structures varied from 1.7 to 33 kHz depending onstructure geometry. Cantilever structures with overhang lengths asgreat as 864 microns have been fabricated and operated with noperceptible contact between the inertial mass and the substrate.INTRODUCTIONMicro electromechanical resonant systems hold out the promiseof providing extremely fine position control at very high mechanicalfrequencies with extremely low power input. Some microresonatorshave been shown capable of achieving high frequency resonance (750kHz) at high Q (above 35,000), when fabricated of polycrystallinesilicon and operated in a vacuum [l]. Other microresonators have beendesigned for relatively large linear motion of a rigid body vibrationmode asopposed to a continuum vibration mode) and these, too, havebeen shown to achieve significant values of Q 49,000) for largeamplitude motion 20 micrometers) at 31 kHz as reported by [21, I31 as

    well asby [41.The common feature of all these microresonators is that theirvibration mode is purely linear. This is an artifact of the mechanicaldesign featuresof the flexural suspension systems and the mechanics ofthe boundary conditions where the flexures are anchored to thesubstrate. Clearly the designers have explicitly chosen mechanicaldesigns that deliberately preclude rotational motion. Other designshave been tailored to flexural suspensions suitable for purely angularresonance,and such a device is described in [21.In this esearch effort,a microresonator has been designed witha flexural suspension that admits resonances in all of translational,rotational, and coupled translational/rotationalmodes of vibration.These modes are not only well-separated in frequency, but can beselectively excited and analytically predicted. This makes it possibleto design a new class of resonant structure micromotors with selectablemodes of operation.Micromotors that attempt to achieve rotational motionwithout the use of flexures must implement some sort of mechanicalbearing in which surface-to-surface contact friction is inevitable [5], [61.Such micxomotors have the advantage of limitless rotation, but this isobtained at the cost of friction and wear. Rotational resonant-structuremicromotors may not provide full rotation motion, but operate at highfrequency with substantial Q in the complete absence of mechanicalfriction and wear. Until research in the complete and controlledlevitation of armatures in micromechanical rotation motors provides aworkable engineering design [71, rotational resonant-structuremicromotors s e m o offer the only solution to high-frequency, zero wearrotational motion.CH2832-4/90/0000-0009 01.0001990 IEEE 9

    In this research, two mechanical designs for multiplemode,micromechanical resonators have been developed, fabricated,operated, and quantified experimentally. Analytic, dynamic modeshave been developed for each, and it is Seen that these models predictvibration mode shapes and vibration frequencies.

    DESIGNThe two basic designs of the multiple mode resonating structuresare shown inFigs.1and 2. Both designs are modular two componentsystems that consist of a semaphore and a driving base . Thesemaphore section in both designs is the resonator proper, and is madeu p of a single cantilever beam with an end mass. The beam can beattached at one edge of the plate mass, or, as shown inFigs.1and 2, thebeam can be attached at the gravity center of the mass. The other endof the semaphore beam is attached to the drive-base, of which twodistinct designs are presented below. The drive-base in each caseconsists of an electrostatic comb drive [31 which is supported by afl ex w suspension. The electrostatic driveused two comb elements, onewhich was used for driving the structure and one which was used to

    A canhkver design, as opposed to some variation of a resonantbridge form [3], was used for the semaphore for several reasons. Acantilever be mhas 64 imes the compliance of a n equal length beamthat is fixed at the ends, and thus, he cantilever design affords greatercompliance in a shor ter distance. Further, the canti lever design is acompletely released structure that does not retain any residual stressesinduced by the fabrication process. Lastly, this design allows anadditional degree of freedom in the semaphore mass, a rotationalvibration, which can be exploited.

    The first of the two designs for the drive-base (Fig. 1 is alinear drive design that uses a folded beam suspension [3] support.

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    Fig. 1. Photograph of the h e a r drive multimode resonator structure.Note Gshaped breakaway upport attached to the mas8 to the right.

    Fig. 2. Photograph of the angulardrive multimode resonator structure.

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    Fig. 3. The center of curvature of the curved comb teeth is set at U3 thedistancefrom thebeam root to the comb mass. Fig. 4. SEM micrographof the electrostatic comb drive portion of thelinea drive structure.

    This design forces the drivebase to undergo translational motion only,and the semaphore is therefore driven at its beam root only by atranslational motion. In contrast, the design shown in Fig. 2is anangular drive design that employs a drive-base with coupledtranslational and rotational motion. One way of regarding this seconddesign is to consider it a staged pair of cantilever beams, one each forthe drive-base and the semaphore. The complexity of the motion ofthe drive-base forces the use of curved comb teeth with varying radiusof curvature, since displacements are large enough that kinematicnonlinearities must be accounted for. Empirical calculations were usedto determine that to provide the maximum clearance between thedrive-base comb teeth and the fixed teeth as the drive moves, thecenter of curvature of the comb eeth must be set to 2/3 thedistance fromthe beam/comb-structure unction to the supportingbeam root, as shownin Fig. 3. Attaching the comb teeth directly to the beam, without localstiffening of the beam at the root of the comb would allow a largerdeflection but the resulting design would not allow the use of theempirical tooth curvature result stated above at high resonantfrequencies. This design would be undesirable since there would becontactbetween the fixed- and moving-comb teeth, effectively shortingout the electrostatic comb drive.The two component system allows a mechanical impedancematchmg in that the high-amplitude semaphore motion can be driveneither by large or small base motions. By tuning the physicaldimensions and masses of the device components and selecting whichresonant mode to excite, the maximum response of the semaphore canbeachieved with either large or small base amplitude motion. Since thesemaphore cantilever beam is attached to the gravity center, theangular motion of the mass has been decoupled from the translationalmotion of the beam, and likewise, the translational motion of the massfrom the angular motion of the beam. This decoupling makes itpossible to selectively excite either translational or angular vibrationmodesof themass.In all structures fabricated, the beam widths as well as thebeam thicknesses were nominally 2p. he semaphore mass was 116by 196p.m. Each tooth of the electrostatic comb drive was 2 by 2 pm incross section and was separated laterally from the fixedcomb teeth by2 pm, as shown inFigs.4and 5.Due to the arge sizeof some of the resonant structures, the totalspan of the cantilevered section reaches as much as 864 pm and atemporary restraint was necessary to prevent structure deflection anddamage during the fabrication process. All structures are suspendedabove the substrate at a 2 pm height. Temporary breakaway supports,which c n be seen inFigures1and 2, were attached to the outside of themass of the semaphore. These breakaway supports were used toprovide strength to the structure during fabrication so that the longstructures were not destroyed during wet etching and rinsing. Afterfabrication, the breakaway support was mechanically removed byphysically rupturing it with two probes.

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    Fig. 5. SEM miaogmph of the electrostatic comb drive portion of theangulardrive structurr .

    DYNAMIC MODELLINGTwo separate dynamic models were developed to simulate thebehavior of the two types of resonant, multimode structures, since eachof the drive-bases were fundamentally different for the two designs.The linear-motion drive-base structure with the folded flexuresuspension (Fig. 6) had 4 degrees of freedom 3 translational and 1rotational. The base drive of thisdesign had 2 degreesof freedom,onebeing the comb structure mass, the other being the fo ld piece in thefolded flexure. As no

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