INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF MICROMECHANICS AND MICROENGINEERING

J. Micromech. Microeng. 15 (2005) 1092–1101 doi:10.1088/0960-1317/15/5/028

Structurally decoupled micromachinedgyroscopes with post-release capacitanceenhancementCenk Acar and Andrei M Shkel

Department of Mechanical and Aerospace Engineering, Microsystems Laboratory,University of California at Irvine, Engineering Gateway 2110, Irvine, CA 92697, USA

E-mail: cacar@uci.edu and ashkel@uci.edu

Received 16 November 2004, in final form 25 February 2005Published 14 April 2005Online at stacks.iop.org/JMM/15/1092

AbstractThis paper reports a novel micromachined gyroscope design that providesenhanced decoupling of the drive and sense modes, and increased actuationand detection capacitances beyond the fabrication process limitations. Thedecoupling mechanism minimizes the effects of fabrication imperfectionsand the resulting anisoelasticities, by utilizing independent folded flexuresand constrained moving electrodes in the drive and sense modes. Thepost-release capacitance enhancement concept aims to increase the drive andsense capacitances beyond the minimum gap requirement of themicromachining process. The approach is based on designing the stationarycomponents of the electrodes attached to a moving stage that permanentlylocks into the desired position before the operation of the device, tominimize the electrode gap with a simple assembly step.Bulk-micromachined prototype gyroscopes have been fabricated, and theexperimental results have successfully demonstrated the feasibility of thedesign. It is experimentally shown that over an order of magnitude ofcapacitance, increase is achieved in the same foot print of the device,without additional fabrication steps. A noise floor of 0.25◦/s/

√Hz was

demonstrated at 50 Hz bandwidth in atmospheric pressure.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

Gyroscopes are among the most critical components affectingthe performance and cost of commercial and militarynavigation, guidance and vehicle control systems. Thecomplicated dynamics and extremely small detection signalshave made gyroscopes one of the most challenging devices tobe realized in micromachining, and only a few concepts havesucceeded in the market.

Even though an extensive variety of micromachinedgyroscope designs and operation principles exist, almostall of the reported micromachined gyroscopes use vibratingmechanical elements to sense angular rate. The concept ofutilizing vibrating elements to induce and detect Coriolis forceinvolves no rotating parts that require bearings, and has beenproven to be effectively implemented and batch fabricated indifferent micromachining processes.

The operation principle of the vast majority of all existingmicromachined vibratory gyroscopes relies on the generationof a sinusoidal Coriolis force due to the combination ofvibration of a proof-mass and an angular-rate input. Theproof mass is generally suspended above the substrate by asuspension system consisting of flexible beams. The overalldynamical system is typically a two degrees-of-freedom(2-DOF) mass–spring–damper system, where the rotation-induced Coriolis force causes energy transfer to the sensemode proportional to the angular rate input. In most ofthe reported micromachined vibratory rate gyroscopes, theproof mass is driven into resonance in the drive directionby an external sinusoidal force. When the gyroscope issubjected to an angular rotation, the sinusoidal Coriolisforce at the driving frequency is induced in the directionorthogonal to the drive-mode oscillation and the input angularrate.

0960-1317/05/051092+10$30.00 © 2005 IOP Publishing Ltd Printed in the UK 1092

Micromachined gyroscopes with capacitance enhancement

Figure 1. SEM image of the structurally decoupled micromachinedgyroscope with post-release capacitance enhancement.

Fabrication imperfections and residual stresses inMEMS gyroscopes generally introduce small imbalances andasymmetries in the gyroscope suspension structure. Dueto lack of perfect alignment of the intended and the actualprinciple axes of oscillation, anisoelasticity in the gyroscopestructure occurs, causing dynamic cross-coupling between thedrive and sense directions [16]. This results in mechanicalinterference between the modes, often much larger than theCoriolis motion. This undesired coupling, called quadratureerror, is in phase with the proof-mass displacement, and90◦ phase shifted from the Coriolis force proportional to theproof-mass velocity. Even though phase-sensitive detectiontechniques can partially discriminate the quadrature error,the device performance suffers. Various devices havebeen reported employing mode decoupling mechanisms andindependent suspension systems for the drive and sense modes[13, 17–19, 23] in order to suppress the resulting quadratureerror due to the coupled oscillation. The micromachinedgyroscope structure reported in this paper (figure 1) providesenhanced mechanical decoupling of the drive and sensevibration modes, and completely eliminates the undesiredsense-direction excitation force of the drive electrodes dueto fabrication imperfections of the actuator. Furthermore, apost-release assembly technique is implemented to enhancethe sensing and actuation capacitances beyond the fabricationprocess limitations.

2. The mode-decoupling structure

The novel decoupling mechanism is based on providing 2-DOFoscillation capability to the gyroscope proof mass, while thedegree of freedom of the actuation and detection electrodesare restricted to 1-DOF. This is achieved by structurallydecoupling the rotors of the drive and sense electrodes fromthe proof mass (figures 2 and 3).

In the proposed approach, the moving electrode (rotor)of the drive-mode actuator is directly connected to an anchorpoint through a folded suspension beam (figure 2). The foldedsuspension completely restricts the sense-direction motion,and forces the drive-mode electrode rotor to oscillate purelyin the drive direction. Thus, the undesired electrostatic force

Figure 2. Conceptual schematic of the structurally decoupledmicromachined gyroscope.

generated in the sense direction by the drive electrodes dueto fabrication imperfections is drastically suppressed. Also,the lateral stability of the actuation electrodes is significantlyenhanced.

The drive-mode excitation force is applied to thegyroscope proof mass through a folded suspension, whichdirectly transfers the drive-mode oscillation of the driveelectrode rotor, while allowing the proof mass to oscillateindependently in the sense direction.

Similarly, the moving electrode of the sense capacitorsis directly connected to an anchor point through a foldedsuspension beam (figure 2). Thus, transfer of the drive-modeoscillations of the gyroscope proof mass to the sense electrodesis completely eliminated. The sense-mode oscillations ofthe proof mass due to the rotation-induced Coriolis forceare directly transferred to the sense-electrode rotor throughanother folded beam, which also allows relative drive-modeoscillations.

Thus, the benefits of the structural decoupling mechanismcan be summarized as follows:

• The mechanical coupling between the drive and sensemodes is minimized. Thus, zero-rate-output andquadrature error are significantly reduced in the presenceof structural imperfections.

• Due to fabrication imperfections and asymmetries, driveelectrodes generally generate undesired electrostaticforces in the sense direction that excite the sense mode.The structure drastically suppresses the effect of thisparasitic force.

• The sensing electrodes do not respond to the drive-mode vibrations owing to the structural decoupling. Thespurious capacitance changes in the sense electrodesdue to the drive mode oscillations, and the resultingerror signal 90◦ phase shifted from the Coriolis signalis minimized.

1093

C Acar and A M Shkel

(a)

(b)

(c)

Figure 3. (a) Microscope photograph of the mode-decouplingstructure. (b) The drive-mode oscillations (blurred), where only thedrive-electrode rotor deflects. (c) The sense-mode oscillations(blurred), where only the sense-electrode rotor deflects.

3. Post-release capacitance enhancement

In micromachined inertial sensors, capacitive sensing andactuation offer several benefits when compared to othersensing and actuation means (piezoresistive, piezoelectric,optical, magnetic, etc) with their ease of fabrication andintegration, good dc response and noise performance, highsensitivity, low drift and low temperature sensitivity.

The performance of micromachined sensors employingcapacitive detection is generally determined by the nominalcapacitance of the sensing electrodes. Even thoughincreasing the overall sensing area provides improved sensing

Figure 4. SEM images of post-release positioned comb drivesintegrated in a micromachined gyroscope. The resulting finger gapafter the assembly is 1 µm, while the process minimum-gaprequirement is 10 µm.

capacitance, the sensing electrode gap is the foremost factorthat defines the upper bound. Similarly, the force generatedby the electrostatic actuation electrodes (comb drives orparallel plates) is limited by the minimum gap attainable inthe fabrication process. In electrostatically actuated devicessuch as micromachined gyroscopes, the nominal actuationcapacitance determines the required drive voltages. For a smallactuation capacitance, large voltages are needed to achievesufficient forces, which in turn results in a large drive signalfeed-through.

Various advanced fabrication technologies have beenreported to minimize electrode gap, based on deposition ofthin layers on electrode sidewalls [1, 2, 5]. For example, in onereported approach, high aspect-ratio polysilicon structures arecreated by refilling deep trenches with polysilicon depositedover a sacrificial oxide layer. Thick single-crystal siliconstructures are released from the substrate through the frontside of the wafer by means of a combined directional andisotropic silicon dry etch and are protected on the sides byrefilled trenches. This process involves one layer of low-pressure chemical vapor deposited (LPCVD) silicon nitride,one layer of LPCVD silicon dioxide and one layer of LPCVDpolysilicon [2]. This process and similar approaches requireadditional fabrication steps.

The post-release assembly technique presented in thispaper aims to increase the sensing and actuation capacitances

1094

Micromachined gyroscopes with capacitance enhancement

Figure 5. Comparison of a conventional comb-drive structure, and the post-release positioning approach designed for the same fabricationprocess. Note the difference in the resulting gap, and the number of fingers per unit area.

in micromachined devices, without any modification of thefabrication process. With a simple additional assembly step,the performance and noise characteristics are enhanced beyondthe fabrication process limitations.

3.1. Enhancement of comb-drive capacitance

Interdigitated comb drives are one of the most commonactuation structures used in MEMS devices, and are utilizedfor actuation in the proposed device. The primary advantagesof comb drives are long-stroke actuation capability, thelinearity of the generated forces and the ability of applyingdisplacement-independent forces for high-stability actuators.With a balanced interdigitated comb-drive scheme imposedby applying V1 = Vdc + νac to one set of comb drives andV2 = Vdc − νac to the other set, the net electrostatic forcereduces to [11]

Fcomb = 4ε0z0N

y0Vdcνac, (1)

where Vdc is the dc bias voltage, νac is the sinusoidal ac voltage,z0 is the finger thickness and y0 is the finger separation. Inconventional interdigitated comb drives, the gap between eachstationary and moving finger is determined by the minimum-gap requirement of the fabrication process (figure 5). Forexample, if the minimum gap is 10 µm, the gap between theconventional comb-drive fingers is 10 µm.

In the presented post-release positioning approach, thefingers attached to opposing electrodes are designed initiallyapart, and interdigitated after the release. Thus, the gapbetween the fingers after interdigitating can be much smallerthan the minimum-gap requirement (figure 5). For the sameexample, if the width of one finger is 8 µm and the minimumgap is 10 µm, the resulting gap between the stationary andmoving fingers after the assembly is 1 µm. This results ina ten times increase in the force per finger. Furthermore,the number of fingers per unit area is increased by allowingsmaller gaps. In this example, exactly two times as manyfingers can be used in the same area, resulting in a total of 20times increase in the drive force.

Figures 4 and 6 present microscope photographs of theassembled post-release positioning comb drives integratedin the decoupled micromachined gyroscope. It is observedthat excellent positioning is achieved, providing uniform gapsacross the comb-drive structure. The gyroscope proof mass issuccessfully driven into resonance in the drive mode with theassembled comb fingers (figure 7). In the presented device,thermal actuators have been used (figure 9) for displacing and

(a)

(b)

Figure 6. SEM images of post-release positioning comb drivesintegrated in a micromachined gyroscope, (a) before and (b) afterassembly.

Figure 7. Microscope photographs of the assembled post-releasepositioning comb drives integrated in a micromachined gyroscope.The gyroscope is successfully driven into resonance in the drivemode with the assembled comb fingers.

assembling the moving stages. Bistable locking mechanismsand self-assembly approaches have also been explored(figure 8) [3].

1095

C Acar and A M Shkel

Figure 8. Microscope photographs of the ratchet structure utilizedas the locking mechanism for post-release positioning.

Before Assembly

During Assembly

After Assembly

Figure 9. The assembly sequence of the post-release positioningcomb drives using thermal actuators.

3.2. Enhancement of parallel-plate capacitance

Parallel-plate actuation provides much larger forces per unitarea compared to comb drives, with the expense of limitedstable actuation range, and nonlinear actuation forces. The netforce generated by a parallel-plate actuator is

�F pp = − ε0V2

dcz0x0

2(d0 − x)2ey, (2)

where ε0 = 8.854 × 10−12 F m−1 is the dielectric constant, A

is the total actuation area, d0 is the electrode gap and Vdc isthe dc bias voltage. The nonlinear electrostatic force profilein parallel-plate actuation electrodes is usually exploited forresonance frequency tuning. The negative electrostatic springconstant that reduces the resonant frequency with increasingdc bias can be found by taking the derivative of the electrostaticforce Fpp with respect to displacement

kel = ∂Fpp

∂x= −ε0A

d30

Vdc2. (3)

Thus, the shrinking of the electrode gap enhances both theactuation force and the electrostatic frequency tuning range.

3.2.1. Capacitive detection. In micromachined inertialsensors, differential capacitance sensing is generally employedto enhance and linearize the capacitance change with

Figure 10. SEM images of post-release positioning sensingelectrodes integrated in a micromachined gyroscope, before andafter assembly.

deflection. Defining y0 as the finger separation, l as thelength of the fingers and t as the thickness of the fingers,the differential capacitance values become

Cs± = Nε0t l

y0 ∓ y, �C = Cs+ − Cs− = 2N

ε0t l

y20

y. (4)

It is observed that the capacitance change is inverselyproportional to the square of the initial gap. Thus, theperformance of the sensor (i.e. sensitivity, resolution andsignal-to-noise ratio) is improved quadratically by decreasingthe initial gap of the sensing electrodes.

Similarly, the post-release positioning concept isimplemented in parallel-plate detection electrodes by attachingthe stationary fingers of the sensing electrodes to a movingstage that locks into the desired position before operation.Figure 10 presents scanning-electron-microscope images ofthe post-release positioning sensing electrodes integrated ina micromachined gyroscope, before and after assembly. Itis observed that excellent positioning is achieved, providinguniform gaps across the sensing electrode structure. Electrodegaps in the order of 1–2 µm have been achieved with100 µm thick structures (figure 11), while the minimum-gaprequirement of the fabrication process is 10 µm.

4. Experimental results

4.1. Fabrication of prototypes

The structurally decoupled micromachined gyroscopedesign concept with post-release capacitance enhancementwas analyzed experimentally on the bulk-micromachinedprototype structures, fabricated in the UCI Integrated Nano-Systems Research Facility. For the fabrication of prototypes,

1096

Micromachined gyroscopes with capacitance enhancement

Figure 11. Electrode gaps in the order of 1–2 µm have beenachieved with 100 µm thick structures, while the minimum-gaprequirement of the fabrication process is 10 µm.

a one-mask process was developed, based on deep-reactiveion etching (DRIE) through the 100 µm device layer of SOI(silicon-on-insulator) wafers, and front-side release of thestructures by etching the oxide layer in HF solution. TheDRIE process was performed in an STS ICP, using an 8 setch step cycle with 130 sccm SF6 and 13 sccm O2, 600 Wcoil power and 15 W platen power; and 5 s passivation stepcycle time with 85 sccm C4F6, 600 W coil power and 0 Wplaten power. In the device, 15 µm × 15 µm holes wereused to perforate the suspended structures, and 10 µm gapswere used in the sensing and actuation electrodes. The lowestetch rates were observed for the 15 µm × 15 µm holes,at approximately 1.25 µm min−1, and 85 min DRIE timewas used to assure complete through-etch while minimizingexcessive undercutting in larger areas. The anchors weredesigned as unperforated areas larger than 40 µm × 40 µmfor 25 min release in 49% HF solution.

4.2. System identification

The fabricated prototype devices were characterized in theUCI MicroSystems laboratory. The drive- and sense-mode frequency responses were experimentally acquired byelectrostatic excitation with a sinusoidal signal in frequencysweep mode and simultaneous capacitive detection. Inpractice, the acquired frequency response signal is generallycorrupted (figure 12) by the feed-through of the excitation

signal to the output signal over a lumped parasitic capacitanceCp between the bonding pads and the substrate, and a finitesubstrate resistance Rp in parallel to the ideal system dynamics(figure 13).

Although the corrupted frequency response could be usedto obtain a rough approximation of the system parameters,close estimation of parameters, even the resonance frequency,is not possible. Fortunately, the ideal system response can beextracted from the corrupted response based on the analysisof the real and imaginary components of the response. Thetransfer function of the overall system, and the real andimaginary parts of the frequency response are

Vo

Vin= K

αs

ms2 + cs + k+ K

Cps

RpCps + 1,

Re

(Vo

Vin

)= Kαcω2

(k − mω2)2 + c2ω2+

KRpC2pω

2

(RpCpω)2 + 1,

Im

(Vo

Vin

)= Kα(k − mω2)ω

(k − mω2)2 + c2ω2+

KCpω

(RpCpω)2 + 1,

where K is the transimpedance amplifier gain, and α =12

∂Cdrive∂x

Vdc × ∂Csense∂x

Vdc contains the coefficients for conversionof the input sine wave to the mechanical force, and themechanical displacement to the motion induced current. Theexact mechanical resonance point is very easily identifiedfrom real part of the response, since the real part reachesits maximum at the resonant frequency ωn =

√km

regardlessof the parasitics.

The real part of the response includes only the parasiticeffects at frequencies away from the resonance point, and theimaginary part of an ideal system’s response is zero at theresonance point. Evaluating the real part at one frequencyωl away from ωn, and the imaginary part at ωn yields twononlinear equations with two unknowns Rp and Cp,

Re

[Vo

Vin(ωl)

]= RpC

2pω

2l

(RpCpωl)2 + 1,

Im

[Vo

Vin(ωn)

]= Cpωn

(RpCpωn)2 + 1.

These two equations are solved simultaneously to identifythe values of Rp and Cp. Evaluating the real part at theresonance point, and the imaginary part of the response slightlyaway from resonance (ωm) yields two equations for the twounknowns α and c,

Re

[Vo

Vin(ωn)

]= α

c+

RpC2pω

2n

(RpCpωn)2 + 1,

Im

[Vo

Vin(ωm)

]= α

(k − mω2

m

)ω(

k − mω2m

)2+ c2ω2

m

+Cpωm

(RpCpωm)2 + 1.

Solving these two equations simultaneously, the values of theelectrical gain α and the damping coefficient c are identified,yielding an accurate estimation of the Q factor and thebandwidth. Figure 12 shows the experimentally acquiredresponse with the parasitics, and the simulated response ofthe identified model. It is observed that the system parametersand the parasitics are effectively identified with the presented

1097

C Acar and A M Shkel

Figure 12. The measured drive-mode frequency response, corrupted by the drive feed-through signal. The system parameters and theparasitics are effectively identified with the presented algorithm, and the simulated response of the identified system closely matches theexperimental data.

(a)

(b)

Parasitic Signal

ElectrostaticActuator

MechanicalResonator

DetectionCapacitor

TransimpedanceAmplifier

Figure 13. (a) The parasitic signal runs over the parasitic capacitances through the substrate. (b) The transfer function model of the overallsystem, including the lumped parasitic capacitance, and the substrate resistance.

algorithm, and the simulated response of the identified systemclosely matches the experimental data. For the oscillator massof 2.31×10−6 kg, the identified parameters are Cp = 7.62 pF,Rp = 2.449 M�, and α = 2.226 × 10−13 (V F m−1)2 with6 V dc voltage. This yields ∂Cd

∂x= 1.112 × 10−7 F m−1.

When an identical gyroscope structure employingconventional comb drives with 10 µm gaps was characterizedwith the same technique, the system identification algorithmyielded ∂Cd

∂x= 1.54 × 10−8 F m−1. This experimentally

demonstrates that 7.22 times larger actuation force is

achieved with the post-release capacitance enhancementmethod compared to conventional comb drives.

Having identified the parasitic terms in the real andimaginary parts of the response, these terms can be numericallyfiltered from the measured signal to reflect the actualmechanical dynamics, by subtracting the evaluated parasiticterm at each frequency from the acquired trace. Figure 14presents the amplitude and phase of the experimentallyacquired frequency response at 250 mTorr pressure withnumerical filtering of parasitics.

1098

Micromachined gyroscopes with capacitance enhancement

(a)

(b)

Figure 14. Experimental measurements of the drive-modefrequency response, with numerical filtering of the parasitics.

4.3. Rate-table characterization

The synchronous demodulation technique was used to detectthe Coriolis response of the gyroscope proof mass in thesense mode. A high-frequency carrier signal was imposedon the structure, which is the common mode of the differentialcapacitive bridge in the sense mode. The current outputfrom each sensing capacitor due to the carrier signal wasconverted into a voltage signal and amplified. The differenceof the outputs was amplitude demodulated at the carrier signalfrequency, yielding the Coriolis response signal at the drivingfrequency (figure 15).

This scheme can be modeled as a sinusoidal carriersignal Vc imposed over the variable sensing capacitor Cs, andthe sense current is amplitude modulated by the change incapacitance. The carrier signal and the sensing capacitancewill then be of the form

Vc = υc sin ωct (5)

Cs = Csn + Cso sin ωdt, (6)

Figure 15. The circuit-level model of the synchronousdemodulation technique, including the trimming capacitors forcapacitance matching.

where Csn is the nominal sensing capacitance, Cso is theamplitude of capacitance change due to the Coriolis response,ωd is the driving frequency (and thus, the sense-modeoscillation frequency) and ωc is the carrier signal frequency.Thus, the sense current becomes

is = d

dt[Vc(t)Cs(t)]

= d

dt[Csnυc sin ωct + Csoυc sin ωct sin ωdt]. (7)

The sense current is amplified by the trans-impedanceamplifier with a gain of K, and converted into a voltage signalVs,

Vs = KωcCsnυc cos ωct +KCsoυc

2[(ωc + ωd) sin(ωc + ωd)t

− (ωc − ωd) sin(ωc − ωd)t].

Vs is then amplitude demodulated at the carrier frequency ωc.By multiplying the sense signal Vs with a sinusoidal signal atωc, the amplitude demodulated signal Vsd is obtained as

Vsd = KωcCsnυc cos ωct sin ωct

+ 12KCsoυc[(ωc + ωd) sin(ωc + ωd)t sin ωct

− (ωc − ωd) sin(ωc − ωd)t sin ωct]

and after regrouping the corresponding terms,

Vsd = 12KωcCsnυc sin 2ωct

+ 14KCsoυc(ωc + ωd)[cos ωdt − cos(2ωc + ωd)t]

− 14KCsoυc(ωc − ωd)[cos ωdt − cos(2ωc − ωd)t].

When the amplitude demodulated signal Vsd is band-passfiltered at the drive frequency ωd, the high-frequency signalsat 2ωc, (2ωc + ωd) and (2ωc − ωd) are attenuated, leaving

Vsd = 12KωdCsoυc cos ωdt. (8)

When the signal Vsd is further amplitude demodulated atthe driving frequency using the drive signal as the referencesignal, the output voltage proportional to the angular rate inputis obtained as

Vo = 12KωdCsoυc. (9)

In the practical implementation of the synchronousdemodulation technique, the imbalance in the parasitic

1099

C Acar and A M Shkel

Figure 16. The experimental setup utilized for rate-tablecharacterization of prototype gyroscopes.

Figure 17. The angular-rate input versus voltage output plotobtained from the structurally decoupled gyroscopes with thepost-release assembled comb drives and sensing electrodes.

capacitances of the sense-mode differential capacitive bridgeresults in a large dc offset, corrupting the Coriolis signal.Utilizing trimming capacitors in parallel to the capacitorsin the differential capacitive bridge, capacitance matching isachieved, and the dc offset is nulled.

During the rate-table characterization, a 2 Vrms carriersignal at 20 kHz was imposed on the gyroscope structurewith 10 V dc bias. The current output from each sensingcapacitor due to the carrier signal was converted into a voltagesignal and amplified using two transimpedance amplifiers with1 M� feedback resistors. A lock-in amplifier was utilizedto provide the 1 V ac drive signal, and to synchronouslydemodulate the difference of the transimpedance amplifieroutputs at the drive frequency in the internal reference mode.The drive-mode amplitude was measured optically as 12 µmin atmospheric pressure (figure 16).

Using the synchronous demodulation technique, asensitivity of 0.921 mV s/◦ (figure 17) and a noise floor of0.231 mV/

√Hz at 50 Hz bandwidth was measured. This

yields a measured resolution of 0.25◦/s/√

Hz at 50 Hzbandwidth, with the post-release assembled comb drives andsensing electrodes.

5. Conclusion

The post-release capacitance enhancement technique hasbeen successfully implemented in the comb drives andthe sensing electrodes of bulk-micromachined prototypestructurally decoupled gyroscopes. System identificationalgorithms applied to the electrostatically acquired drive-mode frequency responses of the gyroscope revealed that7.22 times larger actuation force is achieved compared toconventional comb drives implemented in the exact samegyroscope structure. With the assembled comb drives, 12 µmdrive amplitude was achieved with 10 V dc and 1 V ac actuationvoltages in air. The gyroscope with assembled comb drivesand detection electrodes exhibited a sensitivity of 0.91 mV s/◦,excellent linearity, and a noise floor of 0.25◦/ s/

√Hz at 50 Hz

bandwidth in atmospheric pressure.

References

[1] Hirano T, Furuhata T, Gabriel K J and Fujita H 1992 Design,fabrication and operation of submicron gap comb-drivemicroactuators J. Microelectromech. Syst. 1 52–9

[2] Ayazi F and Najafi K 2000 High aspect-ratio combined polyand single-crystal silicon (HARPSS) MEMS technologyJ. Microelectromech. Syst. 9 288–94

[3] Acar C and Shkel A 2004 Post-release capacitanceenhancement in micromachined devices IEEE SensorsConf. (Vienna, Austria, October 2004)

[4] Acar C 2004 Robust micromachined vibratory gyroscopesPhD Thesis University of California Irvine

[5] Pourkamali S and Ayazi F 2003 SOI-based HF and VHFsingle-crystal silicon resonators with sub-100 nanometervertical capacitive gaps Proc. Solid-State Sensor andActuator Workshop

[6] Clark W A, Howe R T and Horowitz R 1994 Surfacemicromachined Z-axis vibratory rate gyroscope Solid-StateSensor and Actuator Workshop

[7] Barbour N and Schmidt G 2001 Inertial sensor technologytrends IEEE Sensors J. 1 332–9

[8] Yazdi N, Ayazi F and Najafi K 1998 Micromachined inertialsensors Proc. IEEE 86 1640–58

[9] http://www.analogdevices.com[10] Alper S E and Akin T 2000 A planar gyroscope using standard

surface micromachining process Conf. Solid-StateTransducers (Copenhagen, Denmark) pp 387–90

[11] Clark W A, Howe R T and Horowitz R 1994 Surfacemicromachined Z-axis vibratory rate gyroscope Proc.Solid-State Sensor and Actuator Workshop (June 1994)pp 199–202

[12] Hong Y S, Lee J H and Kim S H 2000 A laterally drivensymmetric micro-resonator for gyroscopic applicationsJ. Micromech. Microeng. 10 452–8

[13] Alper S E and Akin T 2002 A symmetric surfacemicromachined gyroscope with decoupled oscillationmodes Sensors Actuators A 97 347–58

[14] Park S and Horowitz R 2001 Adaptive control for Z-axisMEMS gyroscopes American Control Conf. (Arlington, VA,June 2001)

[15] Shkel A, Horowitz R, Seshia A, Park S and Howe R T 1999Dynamics and control of micromachined gyroscopesAmerican Control Conf. (CA) pp 2119–24

[16] Shkel A, Howe R T and Horowitz R 1999 Modeling andsimulation of micromachined gyroscopes in the presence ofimperfections Int. Conf. on Modeling and Simulation ofMicrosystems (Puerto Rico) pp 605–8

[17] Geen J A 1998 A path to low cost gyroscopy Solid-StateSensor and Actuator Workshop (Hilton Head, SJ) pp 51–4

1100

Micromachined gyroscopes with capacitance enhancement

[18] Geiger W et al 2001 Decoupled microgyros and the designprinciple DAVED IEEE Sensors J. 170–3

[19] Mochida Y et al 2000 A micromachined vibratingrate gyroscope with independent beams for driveand detection modes Sensors Actuators A 80170–8

[20] Geen J A and Carow D W 2000 Micromachined gyrosUS Patent 6,122,961

[21] Hsu Y W 1999 Multi-element microd gyro US Patent6,089,089

[22] Boser B E 1997 Electronics for micromachined inertialsensors Proc. Transducers

[23] Niu M, Xue W, Wang X, Xie J, Yang G and Wang W 1997Design and characteristics of two-gimbals micro-gyroscopes fabricated with quasi-LIGA process Int. Conf.on Solid-State Sensor and Actuators pp 891–4

1101