Berkeley ELENG C245 - Lecture Notes - D2143367

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Berkeley ELENG C245 - Lecture Notes

School name University of California, Berkeley

Course Eleng C245- Introduction to MEMS Design

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OverviewLimits to electrostaticsForce/AreaEnergy-Area RatioInchworm Motor DesignMUMPs Inchworm MotorsSilicon Inchworm MotorsPower Dissipation of the ActuatorSpringsSlide 10Spring constant worksheetDampingDynamic forces, fixed amplitude xoSlide 14Slide 15Dynamic forces, fixed amplitude qoMechanical Digital to Analog ConverterBasic Lever Arm Design6-bit DAC ImplementationOutput of a 6-bit DACksjp, 7/01MEMS Design & FabOverview•Integrating multiple steps of a single actuator•Simple beam theory•Mechanical Digital to Analog Converterksjp, 7/01MEMS Design & FabLimits to electrostatics•Residual stress (limits size)•Pull-in•Gap-closing•Comb drive•Tooth (for comb and gap-closing)•Thermal noiseksjp, 7/01MEMS Design & FabForce/Area nLW2max/4.030VV m,50 tm,3 If7.1ax when mmmNAFnMksjp, 7/01MEMS Design & FabEnergy-Area RationLW222/4.930VV m,50 tm,3 If2121mmnJAUVWtVWLCAUksjp, 7/01MEMS Design & FabInchworm Motor DesignFFshoeFFshoeshuttleVs1Va2Vs2Va1shoeshuttleFFshoeAdd ShoeActuatorsksjp, 7/01MEMS Design & FabguidesMUMPs Inchworm MotorsGap StopShoe ActuatorsShuttleLarge ForceLarge StructuresResidual StressStictionshoesksjp, 7/01MEMS Design & FabSilicon Inchworm Motors1mmksjp, 7/01MEMS Design & FabPower Dissipation of the ActuatorWPKhzfVVfCVPpFCmNFVFCVCFpFCmmmAmmAggeparasit icpathspad s6.271,30For 7.61For 22124102.71035412108.41004122222532522ksjp, 7/01MEMS Design & FabSprings•Linear beam theory leads to•Ka = Ea3b / (4L3)•Kb = Eab3 / (4L3)LbaFaFbksjp, 7/01MEMS Design & FabSprings•Linear beam theory leads to•Ka = Ea3b / (12L)•Kz = Ea3b / (3(1+2) L)•Note that Tz results in pure torsion, whereas Ta results in bending as well.TaTzksjp, 7/01MEMS Design & FabSpring constant worksheet•Assume that you have a silicon beam that is 100 microns long, and 2um wide by 20um tall. Calculate the various spring constants. •Esi ~ 150 GPa; Gsi = Esi / (1+ 2) = 80 GPaa3b=Ka=Kb=Ka =Kz =ksjp, 7/01MEMS Design & FabDamping•Two kinds of viscous (fluid) damping•Couette: b =  A/g ;  = 1.8x10-5 Ns/m2 •Squeeze-film: b ~  W3L/g3 •  proportional to pressure•Dynamics:•m a + b v +k x = Fext •If x(t) = xo sin(t) then•v(t) =  xo cos(t)•a(t) = - 2xo sin(t)•-m2xosin(t) + bxocos(t) +kxosin(t) = Fextksjp, 7/01MEMS Design & FabDynamic forces, fixed amplitude xo•-m2xosin(t) + bxocos(t) +kxosin(t) = FextfrequencyForcenLow dampingQ~10High damping~10ksjp, 7/01MEMS Design & FabDynamic forces, fixed amplitude xo•-m2xosin(t) + bxocos(t) +kxosin(t) = FextfrequencyForcenincrease kIncreasing k raises n but at costof more force or less deflectionn’ksjp, 7/01MEMS Design & FabDynamic forces, fixed amplitude xo•-m2xosin(t) + bxocos(t) +kxosin(t) = FextfrequencyForcenn’Decreasing m raises n atno cost in force or deflectiondecrease mksjp, 7/01MEMS Design & FabDynamic forces, fixed amplitude o•-J2osin(t) + bocos(t) +kosin(t) = FextfrequencyTorquenn’Identical result for angular systems withJ (angular momentum) instead of mdecrease mksjp, 7/01MEMS Design & FabMechanical Digital to Analog Converterksjp, 7/01MEMS Design & FabBasic Lever Arm DesignStops6m6mFolded spring supportInput Beam (digital)Input Beam (analog)Output Beam (analog)ksjp, 7/01MEMS Design & Fab6-bit DAC Implementation(Courtesy of Matthew Last)ksjp, 7/01MEMS Design & FabOutput of a 6-bit DAC0 10 20 30 40 50 6000.20.40.60.81DNL = 1.4 LSBINL = 6.3 LSBDigital inputNormalized beam position19

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