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Integrated Microelectromechanical GyroscopesHuikai Xie1 and Gary K. Fedder 2

Abstract: Microelectromechanical~MEMS! gyroscopes have wide-ranging applications including automotive and consumer electrmarkets. Among them, complementary metal-oxide semiconductor-compatible MEMS gyroscopes enable integration of signal coing circuitry, multiaxis integration, small size, and low cost. This paper reviews various designs and fabrication processes for intMEMS gyroscopes and compares their performance. Operational principles and design issues of MEMS vibratory gyroscopesaddressed.

DOI: 10.1061/~ASCE!0893-1321~2003!16:2~65!

CE Database subject headings: Sensors; Micromechanics; Design; Fabrication; Electronic equipment.

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IntroductionMicroelectromechanical system~MEMS! gyroscopes are widelybelieved to be a low-cost solution for medium-performancequirements. The automotive market is demanding low-cost gscopes for sensing yaw rate to compensate braking and susion systems for driving security and comfort. Consumelectronic markets desire handheld products with motion stabcontrol. Inspired by the successful commercialization of microcelerometers~Payne et al. 1995!, MEMS researchers in academand industry have studied gyroscopes extensively in the pasyears. In fact, Robert Bosch Corporation started to sell MEgyroscopes for dynamic control of automobiles a few years~Lutz et al. 1997!. Silicon Sensing Systems~SSS! is providingMEMS gyroscopes for Segway Human Transporters~Hombersley2002!. Analog Devices, Inc.~ADI ! just launched its first generation integrated MEMS gyroscope~Wisniowski 2002!. The ADIdevice is the first commercially available MEMS gyroscope tomonolithically integrated with circuits. In this paper, such monlithic integration is defined as an ‘‘integrated MEMS gyroscopOther MEMS gyroscopes are made in an assembled multisolution, with separate micromechanical and electronics chip

A brief outline of MEMS gyroscopes not integrated with eletronics indicates the breadth of operating principles and fabrtion processes that have been explored. Draper Lab, proposefirst silicon micromachined vibratory-rate gyroscope in 19~Greiff et al. 1991!. The mechanism was a suspended tuning-fstructure driven into resonance by electrostatic actuation. Athat, various mechanisms, such as vibrating beams or r~Maenaka et al. 1995; Putty and Najafi 1994!, tuning forks~Bern-stein et al. 1993!, spinning disks~Shearwood et al. 1995!, andsurface-acoustic waves~Kurosawa et al. 1998!, were investigated

1Assistant Professor, Dept. of Electrical and Computer EngineeUniv. of Florida, Gainesville, FL 32611. E-mail: [email protected]

2Professor, Dept. of Electrical and Computer Engineering, CarnMellon Univ., Pittsburgh, PA 15213-3890. E-mail: [email protected]

Note. Discussion open until September 1, 2003. Separate discusmust be submitted for individual papers. To extend the closing datone month, a written request must be filed with the ASCE ManagEditor. The manuscript for this paper was submitted for review andsible publication on November 27, 2002; approved on November2002. This paper is part of theJournal of Aerospace Engineering, Vol.16, No. 2, April 1, 2003. ©ASCE, ISSN 0893-1321/2003/65–75/$18.00.

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for use in gyroscopes. Spinning gyroscopes have contact bings, which pose a reliability problem. Surface-acoustic and fiboptic gyroscopes require substantial process and materials deopment and integration. Among the various kinds of mechanismthe suspended vibratory type, including tuning forks and vibratibeams or rings, is dominant because it is more suitable for bafabrication in current micromachining processes.

For example, Delphi used electroplated metal ring structu~Sparks et al. 1999!, University of Michigan explored both poly-silicon and single-crystal silicon ring structures~Ayazi and Najafi2001; He and Najafi 2002!, and SSS has a metal ring in theproduct~Hopkin 1994!. The majority of MEMS gyroscopes usevibrating beam structures, such as polysilicon structures by A~Geen et al. 2002!, Bosch ~Lutz et al. 1997; Funk et al. 1999!,Murata~Tanaka et al. 1995!, Samsung~Park et al. 1997! and UC-Berkeley ~Clark et al. 1996; Juneau et al. 1997!, single-crystalsilicon structures by Carnegie Mellon~Xie and Fedder 2002a!,JPL ~Tang et al. 1997!, Murata ~Mochida et al. 1999!, and Sam-sung ~Park et al. 1999!, and compound aluminum/silicon oxidestructures by Carnegie Mellon~Xie and Fedder 2001; Luo 2002!.

Silicon-based MEMS processes may be categorized into bmicromachining and surface micromachining. A large mass issired for a gyroscope because thermomechanical noise~Browniannoise! is inversely proportional to mass. Generally speakinbulk-micromachined gyroscopes have large mass and relativlarge readout capacitance or piezoresistive readout. Therefmost bulk-micromachined gyroscopes do not incorporate on-creadout electronics, but instead require wire bonding to sepaelectronic readout chips~a ‘‘two-chip’’ solution!. Two-chip gyro-scopes have a relatively large package size that restricts tapplications in consumer electronics regardless of price. In ctrast, surface-micromachining gyroscopes have small massrelatively small readout capacitance. However, the sensorsreadout electronics are usually integrated on a single chip, toduce parasitic capacitance. Some work has been conducteintroduce large mass into single-chip gyroscopes~Park et al.1999; Xie and Fedder 2002a!. The single-chip approach can significantly cut down both the price and package size of MEMgyroscopes, resulting in a much broader application range.

Complementary metal-oxide semiconductor~CMOS! process-ing has been the mainstream technology in the digital electronworld for about two decades. The enormous market volume

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Fig. 1. Two-dimensional conceptual model of vibrating gimbagyroscope
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in the y direction ~drive mode!. The structure is a two-fold, orthogonal spring-mass-damper system with stiffnessks and reso-nant frequencyv r ,s for the sense mode, and stiffnesskd and reso-nant frequencyv r ,d for the drive mode.

Suspended gyroscopes are usually underdamped, so theplacement amplitude,y, at the drive-mode resonance frequenv r ,d, is amplified.

y5Qd

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whereFdm5drive force amplitude; andQd5mechanical qualityfactor of the drive mode.

The vibrating drive motion in most micromachined gyroscopis driven at resonance to take advantage of this amplification.velocity ny at resonance is

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The second-order mechanical transfer function of the embedsense accelerometer changes the magnitude and phase of tsponse given in Eq.~3!, i.e., the displacement phasor is

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is the phase relative to the drive velocity andQs is the quality-factor of the sense mode. The drive frequency is chosen lessor equal to the accelerometer resonance, so the acceleromsignal is not attenuated. The two common design cases arKs

'1, ws'0° whenv r ,d!v r ,s , andKs5Qs , ws'90° whenv r ,d

5v r ,s .Assuming a sinusoidal rotation signalVz5Vzmcos(vVt) and

substituting Eq.~5! into Eq. ~6!

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where the magnitude termKs and phase termws are calculatedassumingvV is negligible compared tov r ,d .

Eq. ~9! shows that the mechanical sensitivity is determinedactuation amplitude, the drive and sense resonant frequenciesthe sense-mode quality factor~throughKs). Lowering the embed-ded accelerometer resonance frequency by increasing the pmass leads to high-gyroscope sensitivity. The drive amplituderesonance must be kept large for high sensitivity, so the dvoltage must be increased for larger proof mass. From Eq.~7!,sensitivity is maximized when the two modes are exacmatched, but the bandwidth in this case is inversely proportioto the Q factor. Vacuum packaging can be used to increase bofactors and thus the sensitivity. However, high-Q mechanstructures will ring with external disturbances, reducing theable bandwidth and increasing the settling time of the gyrosco

digital electronics has supported the growth of foundries thatcialize in CMOS processing and who continually improvetechnology. Design compatibility of gyroscopes with convetional CMOS processes provides potential low cost due tohigh availability and large market of CMOS.

This review focuses on vibratory-rate gyroscopes fabricatesingle-chip integrated micromachining processes. First, the optional principle and design issues are introduced. Next, varmicromachining processes are briefly described. Then, CMcompatible MEMS gyroscopes with different designs areviewed, followed by a discussion of future trends.

Theory

Sensitivity, resolution, and stability are the primary performameasures of gyroscopes@IEEE Std 528-1994#. An analysis ofthese metrics for vibrating gyroscopes begins with the Coriphenomena. When a particle or structure moves in a rotatingerence frame, this structure will experience a Coriolis force

FW c5maW c (1)

wherem5mass of the structure. The corresponding CorioliscelerationaW c is proportional to the velocitynW of the moving struc-ture and the rotation rateVW of the rotating reference frame.

aW c52nW 3VW (2)

If the structure is suspended by a spring with a stiffness ofk, thedisplacementxW due to the Coriolis force is expressed as

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wherev r5Ak/m5resonant frequency.Thus, from Eq.~3!, a vibratory gyroscope is indeed an acc

erometer. However, unlike accelerometers that detect translatmotion, the accelerometer in a gyroscope must vibrate andvibration velocityVW must be known and stable in order to derithe rotation rate according to Eq.~2!.

A simplified two-dimensional model of a vibrating gimbalegyroscope is shown in Fig. 1. The suspensions provide apprate elastic stiffness and constraints such that the central pmass relative to the frame may only move in thex direction~sense mode! while the frame relative to the chip may only mov

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Eq. ~9! also shows that the output is a modulated signal.electronic demodulator is needed to recover the rotation sigThe modulation shifts the rotation signal from low frequency~0–300 Hz! to a much higher-frequency band, typically aroundkHz, for accelerometer displacement. Therefore, translationaceleration with a frequency lower than the drive frequency canrejected through filtering if the accelerometer has a linearsponse. If the accelerometer has a certain nonlinearity or limlinear range, external vibration noise will be mixed with the Criolis signal~Xie 2002!. In that case, differencing the signals frotwo matched antiphase gyroscopes, or from one gyroscopetwo matched antiphase oscillating proof masses, will reject exnal translational acceleration.

Another important specification for a gyroscope is resolutor noise floor. The input-referred thermomechanical noiseBrownian noise, of a gyroscope is given by

Vzm

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where ms5accelerometer proof mass;BW5gyroscope bandwidth; and ydm5QdFdm /kd5vibration amplitude of the drivemode. A typical surface micromachined gyroscope has paramms510mg, Qs5100, v r ,s5v r ,d510 kHz, and ydm55 mm,leading to a Brownian noise of 0.03°/s/AHz. The thermome-chanical noise spectral density, which is white, is integrated othe desired gyroscope bandwidth of around 300 Hz. As withsensitivity, noise performance is improved by increasing the damplitude, drive resonance, and both Q factors, while decreathe accelerometer resonant frequency.

The displacement due to Coriolis force is very small. The aplitude ratio of the sense motion and drive motion is obtainfrom Eq. ~7!, i.e.

xsm

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v r ,d

v r ,s2 @°/s#21 (11)

For Ks510, andv r ,s5v r ,d510 kHz, this ratio is 6 ppm/°/sTherefore, even a very small motion coupled from the drive mwill overwhelm the rotation signal. So, highly symmetric desiand careful process tuning are required to minimize the coupThere are two types of motion coupling:~1! quadrature and~2!direct motion coupling. Quadrature refers to the motion coupthat arises from anisoelasticity and other asymmetry. Forample, suppose the gyroscope has driven motion in they directionas assumed in the prior analysis. Due to the imperfections instructure, small motions are coupled into thex and z directionstoo. The coupledx-axis motion is detected by the acceleromeand added to the Coriolis signal. The coupled motion is in phwith the primary drive motion. Therefore, since it is shiftedphase by 90° with respect to the Coriolis acceleration, the coumotion is called quadrature or quadrature error@Clark et al.1996#. This implies that the quadrature can be canceled ouproperly tuning the phase of the carrier signal of the demodula

The second kind of coupling originates from the imperfectioof the actuator. For example, interdigitated-finger ‘‘comb’’ drivare often used as electrostatic actuators. Due to process variathere may be small geometric mismatches of a comb drivecreate additional electrostatic forces in the cross-axis~x,z! direc-tions. Typically, the structure is much stiffer in the two cross axand thus these direct motions are shifted in phase by690° withrespect to they-axis resonant motion. Since there is anotherphase shift between they-axis oscillation and the Coriolis acceeration@see Eq.~1!#, the direct motion coupling has a 0° or 18

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phase shift from the Coriolis signal, implying that this direct mtion coupling cannot be rejected by simply controlling the phaof the carrier of the demodulator~Xie et al. 2002b!.

From Eq.~9!, the output signal of the gyroscope is dependon the drive amplitude and phase, the drive and sense resonfrequencies, and the accelerometer damping. All of these facmust be held constant, or the output will drift over time. In paticular, the phase relationship at frequencies near resonanvery sensitive to small changes in these factors. For exampackaging stress can induce changes in spring constants, leto changes in resonance frequency. All high-performance migyroscopes require attention to packaging and closed-loop sof amplitude and phase to null variations of this kind.

Integrated Micromechanical System Processes

Large sensitivity, low noise, selective mode matching and seption, undesired vibration coupling, and external translationalceleration rejection must be carefully considered during gyscope design. Of prime importance is that the gyroscope desimust consider the structural imperfections due to material behior and process variations, which affect these performance mrics.

Large proof mass, desirable for high sensitivity, is hardrealize in surface micromachining processes. Structural thickis limited to around 10mm for uniform thin-film deposition andstructural area is limited to around 1 mm on a side to avproblems with out-of-plane structural curling and with stickingthe substrate. However, wet etched bulk silicon gyroscopes hrelatively large problems with spring and mass geometry conMuch better control of geometry is enabled with the adventdeep reactive-ion etching~DRIE! of silicon.

The capacitive sense interface circuit design is also a vchallenging problem for both surface- and bulk-micromachingyroscopes. Surface-micromachined gyroscopes have a tysense capacitance of 0.1 pF. Bulk-micromachined gyrosconormally have a relatively larger sense capacitance of 1 pFgreater, but most bulk silicon gyroscopes have not been integrwith electronics. The parasitic capacitance introduced by the wbonding to electronic chips can greatly attenuate the signal.dearth of integrated bulk silicon gyroscopes is partly due toincompatibility of wet silicon through-wafer etching and wafbonding with foundry electronics processes. The Si DRIE tenology is still relatively new, and is expected to enable futugenerations of high-performance integrated microgyroscopescause of the ability to create precision bulk silicon structuresrectly in electronics processes.

For CMOS-compatible MEMS technology, micromachininsteps can be performed before, after, or mixed with CMOS stnamely, pre-CMOS, post-CMOS, and intra-CMOS micromaching, respectively~Baltes et al. 2002!. Table 1 lists the comparisonof these three types of process approaches. A CMOS-MEMScess may involve combinations of surface- and bumicromachining steps.

Pre-CMOS Micromachining

Pre-CMOS micromachining processes start with building MEMstructures on bare silicon wafers. Therefore, processing tempture can be high~.800°C!, and thus the structures can be opmized to achieve excellent planarity. However, CMOS foundr


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Table 1. Comparison of Complementary Metal-Oxide Semiconductor-Micromechanical System Processes

Micromechanical system planarityTemperature constraint formicromechanical system Contamination constraint Vendor accessib

Pre-CMOS Best None Yes LimitedIntra-CMOS Good Yes Yes Very limitedPost-CMOS Varies yes No Good

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One example of pre-CMOS micromachining processes isSandia National Laboratories~SNL! IMEMS technology~Smithet al. 1995!. The cross-sectional view of the process is shownFig. 2. Micromechanical devices are created within a shaltrench in the Si substrate, which is formed using an anisotroetchant. Multiple layers of polysilicon and sacrificial silicon oxidare then deposited and patterned. Electrical contact betweemicrostructures and the CMOS electronics is made via polycon studs. Next, the shallow trenches are filled with silicon oxiplanarized with chemical-mechanical polishing~CMP! and an-nealed at high temperature to relieve stress in the structural psilicon. At this point, the wafer is ready for conventional CMOprocessing. After the CMOS processing is completed, a silinitride layer is deposited for the protection of the CMOS frowet HF of the final release step.

Intra-CMOS Micromachining

High-temperature annealing of certain microstructural materisuch as polysilicon, must be completed before the CMOS inconnect processing to avoid the melting temperature of the inconnect metals. The insertion of MEMS steps into the CMprocess steps posts potential compatibility problems with etronic doping that must be solved. This fully customized proceing requires a dedicated production line.

A well-known example is Analog Devices, Inc.’s iMEMStechnology~Core et al. 1993!. The fabrication is based on a stadard 24V 3mm BiCMOS process with trimable thin-film resistorIn this process, the deposition and annealing of structural maals is inserted prior to metallization. Si3N4 is used to protect theCMOS/BiCMOS area during the final wet etch release step. Fishows the cross-sectional view. Compared to the pre-CMOScromachining process shown in Fig. 2, no trench etch and Care needed in this process. However, after the structural lay

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ig. 3. Cross-section view of Analog Devices, Inc.’s iMEMS tech-ology @Core et al. 1993#. Courtesy of John Geen.

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patterned, the wafer is not planar any more because the structlayer is typically a few microns above the rest of the wafer.

Consequently, only one interconnect layer may be feasiband the electrical connection of the structural layer has to bediffusion layer. Moreover, the influence of the high-temperatuannealing to the performance of transistors must be considewhen designing on-chip circuits.

Post-CMOS Micromachining

Post-CMOS micromachining processes build structures afcompletion of all conventional CMOS steps, enabling foundproduction of the CMOS. Highly planar structures are more dficult to make, because processing temperatures must be uaround 400°C so that the CMOS metallization does not meContamination of the CMOS transistors from diffusion of MEMSmaterials is not an issue at such low temperatures.

Post-CMOS micromachining processes can be divided intwo categories depending on how structural materials are maOne category is post-CMOS deposition, in which structural mterials are deposited after standard CMOS processing. Anotcategory is post-CMOS etching, in which microstructures aformed directly from the substrate and CMOS thin-film materiaby etching.

Post-Complementary Metal-Oxide Semiconductor DepositionProcess temperatures for thin-film deposition and annealing mbe lower than the melting point of the CMOS interconnect metTherefore, either high-temperature refractory metals are usedstructural materials with low-deposition temperature and lostress must be found.

Researchers at University of California at Berkeley developa Modular Integration of CMOS microStructures process usitungsten as the interconnect, TiSi2 as the contact barrier, andSi3Ni4 for wet etch or vapor etch protection~Yun et al. 1992!.However, high-temperature refractory metals have poor manufturability and are not used as an interconnect in commercCMOS processes. Recently, the same group proposed thin-polycrystalline SiGe microstructures with low-deposition temperature to avoid the use of refractory interconnect metal~Franke1999; Franke 2000!. High-temperature annealing is not require

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Fig. 4. Cross-sectional views of Carnegie Mellon CMOS-MEMprocesses.~a! Thin-film process@Fedder et al. 1996#. ~b! Backsideetch process@Xie et al. 2002#.

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The main difference between the thin-film and DRIE CMOMEMS processes is that the latter incorporates single-crystalcon ~SCS! into mechanical structures by introducing a backsisilicon etch into the process sequence. The SCS layer is typicabout 60mm thick. The cavity formed by the backside etch allowthe completed die to be bonded directly to a package withinterference from the released microstructures. As a final stepoptional timed isotropic Si etch may be performed. This step pvides a specific undercut of bulk Si to create compliant structuor achieve electrical isolation of single-crystal silicon.

Integrated Micromechanical System Gyroscopes

Choice of topology is a critical step in gyroscope design. Vibring gyroscopes may be categorized into single or dual sprmass or gimbaled mass, as summarized in Fig. 5. A single mspring system shares the same flexure for both the drive and smodes, and thus suppressing mode coupling is a design isDual mass structures can be arranged to form tuning fork resotors to reject transnational vibration. Single-gimbaled structuhave an advantage of decoupling the drive and sense modesmay have poor linear acceleration rejection and temperatureformance. The dual-gimbaled structure in Fig. 5~e! is employed toimprove the linear acceleration rejection and stability at the prof increased structural complexity.

Translational Vibration

Most vibrating microgyroscopes use translational actuation.polysilicon processes, the movable part can be used as onlyelectrode, so both the drive comb and sense comb must haveelectrode anchored on the substrate. MEMS processes that

Fig. 5. Vibrating gyroscope topologies. Subscriptd is drive mode,and subscripts is sense mode.~a! Single spring mass with translational drive. ~b! Dual mass spring~tuning fork! with translationaldrive. ~c! Single gimbaled mass with translational drive.~d! Singlegimbaled mass with torsional drive.~e! Dual gimbaled mass withtranslational drive.

since the poly-SiGe structural layer has lower strain and stgradient than poly-Si. In the process, poly-Ge, instead of oxideused as the sacrificial layer.

Delphi has developed electroplated metal structures on toCMOS chips~Sparks et al. 1999!. In the process, photoresistused to form the mold and then a metal structure is electroplat low temperature.

Post-Complementary Metal-Oxide Semiconductor EtchingIn post-CMOS etching processes, microstructures are formedrectly from the silicon substrate as well as the dielectric and mlayers normally used for interconnect. Baltes’ group at ETH Zrich first used this approach to make CMOS sensors~Baltes et al.1998!. Wet silicon etching was employed to release microstrtures.

Carnegie Mellon used a similar approach and developedversions of CMOS-MEMS processes: thin-film and DRCMOS-MEMS processes@Fedder et al. 1996; Xie et al. 2002a#.Both post-CMOS processes involve only dry etch steps andinterconnect metal layers as etch masks. The process crosstions are shown in Fig. 4. When the chips come back fromCMOS vendor, the CMOS circuits are covered by the top meand oxide, and the microstructures are predesigned by usinginterconnect metal layers. The anisotropic dielectric etch is pformed in a RIE etcher with a CHF3 /O2 plasma. The deep siliconetch is performed by using the Bosch Advanced Silicon Eprocess@Laermer and Schlip, U.S. Patent No. 5,501,893~1996!#in a Surface Technology Systems system. The dry etch for releliminates any sticking problems. Three-dimensional capacimotion sensing and electrostatic actuation has been realizeboth processes@Xie and Fedder 2002b; Xie et al. 2002a#.


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Fig. 6. A z-axis gyroscope fabricated using Analog Devices, InciMEMS technology@Clark et al. 1996#.

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of commonly used longitudinal actuation, of comb drives wused for electrostatic actuation in this gyroscope design.parallel-plate actuation provides larger electrostatic force fogiven voltage at the expense of a limiting vibrational stroke. Tdrive comb fingers in the center are oriented 90° to the secomb fingers on the two sides. Vibration amplitude of 1mm wasachieved with a 3 V drive voltage. The compliant suspensiosimilar to that of Clark’s design shown in Fig. 6, but the whostructure is more compact and has higher area efficiency. A cscheme was developed that decouples the drive and sensetronics. Offset, switch charge injection and other sampling errincluding kT/C noise were canceled using correlated double spling in the switched-capacitor sense interface circuit. A nofloor of 3°/s/AHz was measured at atmospheric pressure.

The two designs described above use capacitive bridgemeasure the displacement induced by Coriolis force. Seshia@Seshia et al. 2002# reported an integrated MEMS gyroscobased on resonant sensing. The schematic and SEM of thisscope design is shown in Fig. 8. The device was fabricated uthe SNL IMEMS technology. The polysilicon sensor is aboutmm by 1.2 mm in size and 2.25mm thick. When there is anexternal rotation along thez axis, a Coriolis force induced by thvibration of the center proof mass acts on one end of a lemechanism. The force is amplified by the lever and transmittea double-ended tuning fork~DETF! along the axial direction othe DETF. The resonant frequency of the DETF is sensitiveaxial stress. Therefore, the DETF self-oscillation frequencymeasure of the external rotation rate.

There is one DETF on either side of the structure to formdifferential output. The output of the gyroscope is a frequenmodulated signal that can be easily converted to a digital sigNote that it is the proof mass, not the outer frame, that was drto oscillation in thex direction during the operation of this devicThe measured noise floor is 0.3°/s/AHz, limited by electronicnoise of the oscillator circuit.

The single-resonator gyroscope designs discussed abovprone to environmental vibrations. Geen et al.@Geen et al. 2002#reported a dual-resonatorz-axis gyroscope fabricated using ADIiMEMS technology with 4mm-thick structural polysilicon. Asshown in Fig. 9, the sensor consists of two identical resonadriven with equal amplitude in opposite directions. The differtial output of the two Coriolis signals effectively rejects externlinear acceleration. On-chip electronics include circuits for soscillation, phase control, demodulation, and temperature cpensation. A unique controlled-impedance field-effect transistoused to bias the input~the capacitive sense node! of the transre-sistance pre-amplifier. The bias transistor provides an equivaresistance of 2.5 GV. The resonance frequency of the drive mo

Fig. 8. Schematic and SEM of the mechanical structure of the renant output gyroscope@Seshia et al. 2002#.

vide multiple conducting layers have much higher-design flexiity, but the multiple layers of interconnect usually increases stgradients in the structures.

Polysilicon StructuresClark et al. demonstrated az-axis gyroscope using ADI’s iMEMStechnology~Fig. 3! in 1996 ~Clark et al. 1996!. A scanning elec-tron micrograph~SEM! of the device is shown in Fig. 6, wherthe sensor area is about 1 mm by 1 mm. The fixed-fixed flexrestricts motion to thex axis for the drive mode and to they axisfor the sense mode. The drive combs are located in the middthe device, and the sense combs are on both sides to fodifferential capacitance divider. Ideally, this capacitance pcompensates the capacitance changes in the drive direction aonly sensitive to the Coriolis motion in the orthogonal directioOn-chip circuits include a transresistance amplifier to detectmotional current from the capacitor divider and an integrator.resonant frequency of the drive mode is about 12 kHz. Elecstatic frequency tuning of the sense mode was used to enhsensitivity by matching drive and sense resonant frequenQuadrature error due to asymmetries in the vibrating strucwas minimized electrostatically by controlling the voltages onsense comb fingers. The measured noise floor was1°/s/AHz.

Jiang et al. took further the advantage of the CMOS comibility of the SNL IMEMS technology@Jiang et al. 2000#. Asigma-delta digital force-feedback circuit was integrated withsensor. A SEM of the sensor structure is shown in Fig. 7.sensor area is about 0.7 mm30.8 mm, and the thickness of thmechanical structure is 2.25mm. Parallel-plate actuation, instea

Fig. 7. SEM of a z-axis vibratory gyroscope with digital outpu@Jiang et al. 2000#. Courtesy of X. Jiang.

Fig. 9. Micrograph of ADI dual-resonator gyroscope@Geen et al.2002#. Courtesy of John Geen.

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is 15 kHz with a mechanical Q of about 45, leading to a 10mmpeak-peak drive displacement generated with 12 Vac. The msured noise floor of the device is 0.05°/s/AHz.

Multilayer Thin-Film StructuresThe CMOS-MEMS process shown in Fig. 4~a! provides struc-tures with multiple conducting layers isolated by dielectriceliminating the electrical isolation constraint existing in moother MEMS processes. Thus, elastically gimbaled structuresdecoupled sense and drive modes can be realized. Both lataxis andz-axis gyroscopes have been demonstrated@Xie and Fed-der 2001; Luo et al. 2002#.

The gimbaled lateral-axis gyroscope shown in Fig. 10 wfabricated by a thin-film CMOS micromachining, starting wiAgilent 0.5 mm three-metal CMOS~Xie and Fedder 2001!. Themicrostructure is 5mm thick and 0.8 mm by 0.6 mm in size. Thcentral y-axis accelerometer is anchored on a rigid frame. Trigid frame is connected to the substrate via a flexure thacompliant in thez direction. Az-axis comb drive is employed, sthat the embedded accelerometer is driven in vertical oscillatandx-axis rotation is then detected.

The out-of-plane curling of the drive spring beams is duethe residual stress and thermal expansion coefficient differencthe materials in the beams. An on-chip buffer circuit detectsmotional capacitance of the accelerometer. The on-chip bufferlow-parasitic capacitance, so input attenuation of the motiosignal is minimal. The resonant frequency of the drive mode

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kHz, and matching to the sense-mode resonance was achusing thermomechanical tuning of the springs. The noise floothe sensor at atmospheric pressure is 0.5°/s/AHz, limited by elec-tronics noise.

Luo et al. demonstrated az-axis integrated gyroscope bCMOS micromachining, starting with UMC 0.18mm six-copperlayer CMOS~Luo 2002!. Fig. 11 shows a SEM of the mechanicstructure of a fabricated device. The thickness of the structuabout 8mm with a sensor area of 410mm3330mm. Though itstopology is similar to the one shown in Fig. 10, thisz-axis gyro-scope employs in-plane comb drives for both excitation andriolis acceleration sensing. The resonant frequency of the dmode is 8.8 kHz. The device operates at the atmospheric preand a noise floor of 0.5°/s/AHz was achieved.

Combining the above two types of gyroscopes can direresult in single-chip integrated three-axis gyroscopes. The missues of this type of thin-film CMOS-MEMS gyroscopes inclusize limitation due to curling, and strong temperature dependof multilayer structures.

Combined Single-Crystal Silicon and Thin-Film StructuresMEMS processes with the ability to create both SCS and thin-microstructures provide flatness and large mass as well as taxis compliance and three-axis actuation.

The writers fabricated a bulk silicon vibratory gyroscope@Xieand Fedder 2002a# using a DRIE CMOS-MEMS process that usAustria Microsystems three-metal 0.6mm CMOS. Fig. 12 is aSEM of a released device, which is a lateral-axis angularsensor with in-plane vibration and out-of-plane Coriolis acceletion sensing. The sensor plus on-chip CMOS circuitry is 1 mm1 mm in size. It incorporates both 1.8mm-thick thin-film struc-tures for spring beams with out-of-plane compliance and 60mm-thick bulk Si structures for spring beams with in-plane compance. The microstructure is flat because of the underlying tsilicon layer and thereby avoids potential curling problems, whexist in some thin-film CMOS-MEMS gyroscopes. A unique scon electrical isolation technique is used to obtain individuacontrollable comb fingers@Xie et al. 2002a#. The noise floor of

Fig. 10. SEM of integratedx-axis gyroscope fabricated by a thinfilm CMOS-MEMS process@Xie and Fedder 2001#


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iMEMS technology@Juneau et al. 1997#. As shown in Fig. 13~a!,the inertial rotor is suspended by four beams, which are anchoto the substrate and provide torsional compliance about all thaxes. The rotor has a diameter of 300mm and is made of 2-mm-thick polysilicon with a 1.6mm gap to the substrate. The rotor issurrounded by radial electrostatic comb drives, which generthe torsional oscillation along thez axis. When an external rota-tion exists around thex or y axis, the rotor will tilt along they orx axis, respectively, according to Eq.~1!. Two pairs of parallel-plate capacitance electrodes are placed underneath the roton1 diffusion in the substrate, with the rotor used as a commoutput electrode. Thus, two sets of differential capacitive bridgare formed. One set measures thex axis tilt and the other setmeasures they axis tilt. Since the rotor is a single electrode, thsignals for both axes share the same signal node. In ordedistinguish the two axis signals, two different modulation frequencies are applied, as shown in Fig. 13~b!.

A SEM of a fabricated device is shown Fig. 13~c!. The sus-pension beams were designed to match the resonant frequenc28 kHz in all three axes. Additional electrostatic tuning was alused to obtain better mode matching. The device achiev0.3°/s/AHz noise floor with cross sensitivity as much as 16%under open-loop conditions. A close-loop force balancing contscheme was proposed to reduce cross sensitivity and caquadrature error.

Bosch also reported a thick-polysilicon lateral-axis gyroscowith torsional actuation@Funk et al. 1999#. However, the fabrica-tion process is not compatible with CMOS processing.

Fig. 13. Dual-axis integrated gyroscope@Juneau et al. 1997#. ~a! Schematic;~b! modulation signals; and~c! micrograph of a fabricated device.

the gyroscope is 0.02°/s/AHz at 5 Hz. The resolution of thisDRIE gyroscope is one order of magnitude higher than thatthin-film counterparts.

Rotational Vibration

Rotational vibration around thez-axis makes it possible to deteclateral-axis angular rate with out-of-plane Coriolis acceleratisensing. Juneau et al. reported a dual axis gyroscope with a qsymmetry of a circular oscillating rotor design in the SN

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Summary and Future Trends

There are various structural topologies for vibrating gyroscopDual-resonator and ring structures have good vibration rejecand temperature performance. Translationally vibrating structcan be designed to sense both lateral-axis and vertical-axistion. Torsionally vibrating structures provide lateral-axis angurate detection. The choice of a topology for a gyroscope strondepends on the capability of the available fabrication process

Pre-CMOS, intra-CMOS, and post-CMOS micromachiniprocesses have their advantages and disadvantages. Pre-Cand inter-CMOS processes require a dedicated productionand thus require a large engineering investment. Post-CMOScromachining processes provide high accessibility and mlower cost. The key for post-CMOS micromachining processehow to form and process the structural materials. Polysiliconthe most popular and most explored material for pre- and inCMOS micromachining processes. However, it cannot be adointo post-CMOS micromachining processes because of theperature constraint. Alternative materials such as low-depostemperature SiGe or electroplating metals have been studiedhave very high potential for future gyroscopes.

The post-CMOS etching of MEMS approach is a relativesimple process and thus can produce inexpensive integrMEMS devices by using the materials directly from CMOS prcessing. The temperature performance is a major concern forcrostructures made of only metal and dielectric materials. Hever, microstructures with combined single-crystal silicon ametal/dielectric layers are flat and have electrical isolationgood temperature stability, allowing their potential applicationfuture gyroscopes.

Analog Devices just launched the first commercially availaintegrated MEMS gyroscope in October 2002. Though timeneeded to see how markets evolve, the small size, ease of userelatively low cost of the integrated gyroscope is expected to onew application areas. Nevertheless, technology developmestill needed to improve the CMOS compatibility to further reduthe price. Microgyroscope resolution and stability needs toimproved to broaden the range of applications. In particular,bias stability of current micromachined gyroscopes is not ablemeet navigation-grade specifications.

Multiple-axis integration is important to reduce the overpackage size and cost. The integration of electronics is not limto interface, signal conditioning, and analog-to-digital circuitThe CMOS compatibility assures the possibility of addingmuch circuits as needed. Self-powered, single-chip gyroscoplus accelerometers with wireless communications are ultimapossible. The applications then will not just be in automobilcomputer games or space navigation systems, but widespreconsumer electronics and appliances.

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In a vibrating ring gyroscope@Putty and Najafi 1994; Sparks et a1999#, the ring structure is driven into resonance in the planethe chip. The vibration of the ring forms an elliptically shappattern. In the absence of an external rotation, the four npoints at1/2 45° from the drive axis on the ring remain statioary, as shown in Fig. 14. An external rotation about thez axisgenerates a Coriolis force that excites the resonant mode athe 45° axes. The resulting displacement is sensed capacitivea series of electrodes around the ring. The symmetry of the sture provides identical drive and sense resonance if manufaing is perfect.

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