A lateral-axis micromachined tuning fork gyroscope with torsional Z-sensing and electrostatic

force-balanced driving

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2010 J. Micromech. Microeng. 20 025007

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J. Micromech. Microeng. 20 (2010) 025007 (7pp) doi:10.1088/0960-1317/20/2/025007

A lateral-axis micromachined tuning forkgyroscope with torsional Z-sensing andelectrostatic force-balanced drivingZ Y Guo1,2, Z C Yang1, Q C Zhao1, L T Lin1, H T Ding1, X S Liu1, J Cui1,H Xie2 and G Z Yan1

1 National Key Laboratory of Science and Technology on Micro/Nano Fabrication, Institute ofMicroelectronics, Peking University, Beijing, 100871, People’s Republic of China2 Department of Electrical & Computer Engineering, University of Florida, Gainesville, FL 32611,USA

E-mail: gzyan@pku.edu.cn

Received 28 August 2009, in final form 27 October 2009Published 15 December 2009Online at stacks.iop.org/JMM/20/025007

AbstractA single-crystal silicon-based lateral-axis tuning-fork gyroscope (TFG) with electrostaticforce-balanced (EFB) driving and torsional z-sensing is presented. The EFB comb drive usedin this TFG can efficiently suppress the mechanical coupling in a simple manner. The TFGstructure is also optimized to further reduce the coupling. Moreover, the Coriolisacceleration-induced out-of-plane rotation of the sensing mode is detected by using bendingsprings and differential comb fingers. This z-sensing design has relatively high Q, so thisgyroscope can work at atmospheric pressure. This TFG design has been fabricated and tested.Measured in air, the device demonstrates a sensitivity of 2.9 mV/◦/s, a full range of 800◦ s−1

with a 0.9% nonlinearity and the noise floor of 0.035◦/s/Hz1/2. This TFG design also has verylow coupling, where the measured drive-to-sense coupling and sense-to-drive coupling are−45 dB and −51 dB, respectively.

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

1. Introduction

The demanding need for smaller and cheaper gyroscopeshas led to extensive research and development of MEMS-based vibratory gyroscopes in the past two decades. Themechanical resonator actuated by electrostatic interdigitatedcomb structures, or comb drives, proposed by Tang et al [1],has been widely used in MEMS gyroscopes [2, 3]. One of thefirst such MEMS tuning fork gyroscopes was demonstrated byCharles Draper Laboratory [2]. Thanks to the drive of variousmarkets and the creative efforts of many MEMS researchers,MEMS gyroscopes have been applied in consumer electronics,health care, space and defense [4].

In order to realize high-performance gyroscopes,researchers must face many challenges which may comefrom structural design, device fabrication, and interface andcontrol circuits design. For instance, the mechanical coupling

between the driving and sensing modes is one of the main errorsources, which not only deteriorates the bias stability but alsolimits the dynamic range of a MEMS gyroscope and causesother errors such as the quadrature error [5, 6]. Therefore,decoupling the mechanical crosstalk between the two workingmodes is crucial for improving the performance of a gyroscope[1–6]. Geiger et al [7–9] reported a mechanical decouplingmechanism using independent beams and/or a rigid frame toisolate the two modes mechanically. This method has beenadopted in a number of MEMS gyroscopes and can efficientlydecouple the mechanical coupling from the driving mode tothe sensing mode [5–10]. On the other hand, the mechanicalcoupling from the sensing mode to the driving mode alsoneeds to be suppressed [5, 9]. A doubly decoupled structureis commonly used to reduce the sense-to-drive coupling of z-axis gyroscopes, but it does not work well for lateral-axis TFGs

0960-1317/10/025007+07$30.00 1 © 2010 IOP Publishing Ltd Printed in the UK

J. Micromech. Microeng. 20 (2010) 025007 Z Y Guo et al

[2, 11]. Therefore, a method to minimize the sense-to-drivecoupling is needed for lateral-axis TFGs.

Moreover, to further enhance the functionality, expand theapplicable range and explore the low-cost benefits, monolithicintegration of multi-axis inertial sensors including full 6-axisinertial measurement units (IMUs) is required, which needsnot only z-axis but also lateral-axis gyroscopes. Variable-gap capacitors are commonly used to sense the out-of-planemotion for a lateral-axis gyroscope, which requires high-costvacuum packaging to avoid air damping [2]. Vertical sensingcomb fingers help to lower the damping in air and severalvertical comb drives have been proposed to sense the out-of-plane motion [12–17]. Selvakumar et al used a conventionalcomb-finger design to sense the torsional motion of a z-axisaccelerometer [12], but such comb fingers cannot detect thedirection of the motion and cannot sense the rotational momentdifferentially. Tsuchiya et al and Yang et al proposed verticalcomb capacitors with one set of comb fingers thinner at theupper side [13] or the bottom side [14], respectively. This typeof combs can differentially sense vertical motion by properarrangements, but it has very small dynamic range [14]. Xieet al reported a vertical comb capacitor formed by multi-conductor thin-film stacks [15], but such vertical combs havesmall capacitance and large stress. Vertically offset combsproposed by Kim et al can also be used to sense the out-of-plane motion with large dynamic range [16]. Liu et al proposedan improved torsional comb capacitor which can differentiallysense rotation moments while avoiding the drawbacks of thepreviously proposed vertical sensing combs. However, thegyroscope is structurally asymmetrical, and hence is sensitiveto z-axis accelerations [17].

The gyroscope design presented in this paper addressesboth the sense-to-drive coupling and the vertical sensing combissues. In particular, an electrostatic force-balanced (EFB)comb drive design is proposed to suppress the sense-to-drivecoupling, and a torsional sensing comb based on single-crystalsilicon is used to pick up the out-of-plane motion. So theproposed TFG can not only work in the atmosphere butalso effectively suppress the drive-to-sense and sense-to-drivecouplings in a simple manner. Furthermore, the EFB combdrives are near the center while the proof-mass and sensingcapacitors are at the periphery, which helps to decrease thecoupling further.

In the proposed TFG, the mechanical decouplingmechanism is used to decouple the drive-to-sense couplingwhile the EFB lateral comb drive is adopted to decouple thesense-to-drive coupling. So the decoupling effectiveness ofthe EFB lateral comb drive can be demonstrated by comparingthe effectiveness of the two decoupling methods usedin the same TFG. The mechanical decoupling mechanism canefficiently decouple the mechanical coupling from the drivingmode to the sensing mode and has been widely used in manyMEMS gyroscopes [5, 10].

In this paper, the design of the device will be introduced insection 2, where the lateral EFB comb drive and the topologyof the TFG will be discussed in detail. In section 3, the mainsteps of the fabrication process will be given. Testing resultswill be presented in section 4 and discussions and conclusionswill be given in section 5.

Z X

Y

Comb drives Sensing combsAnchor

Sense beams Proof-massDrive beam2

Drive

beam1

Figure 1. Schematic diagram of the TFG.

2. Device design

2.1. Structure and working principle

The schematic of the proposed TFG is shown in figure 1. Theoverall structure is symmetric with respect to both x-and y-axes. The comb drives and spring beams for the driving modeare located in the middle, surrounded by the comb fingers andspring beams for the sensing mode. There are four foldedsensing beams which support the entire movable parts andfunction as a torsional spring for the out-of-plane rotationalmotion. The two proof masses of the TFG are electrostaticallyactuated to vibrate oppositely along the x-axis. When a y-axisangular rate is applied to the gyroscope, Coriolis accelerationwill be induced and the two proof masses will vibrate out ofphase along the z-axis, which in turn will cause an out-of-planerotational vibration of the moveable structure with respect tothe y-axis. This out-of-plane vibration will be differentiallypicked up by two sets of vertical comb fingers similar to theones reported in [17].

The decoupling method reported by Geiger et al [7–9] isemployed to minimize the coupling from the driving mode tothe sensing mode. The coupling from the sensing mode tothe driving mode is minimized by a novel comb drive designwhich is described in section 2.2.

In order to achieve high sensitivity when operating atatmospheric pressure, the working frequencies of the TFG areselected to be relatively low [18]. The driving and sensingmodes are simulated using ANSYSTM and are shown infigure 2. The resonant frequencies of the two modes are3.96 kHz and 4.38 kHz, respectively. The designed dimensionsand stiffness of the beams are given in table 1. Note that thesensing mode is slightly higher than the driving mode. Thisis to ensure that there is only a small and stable phase shiftbetween the sensing motion and driving motion.

2.2. Design of the lateral comb drive

For conventional lateral comb drives, when the movable combfingers have an offset or any asymmetry along the z-axis,an electrostatic force will be generated in the z-direction.Such out-of-plane electrostatic forces will produce errors tolateral TFGs with conventional lateral comb drives [2]. To

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J. Micromech. Microeng. 20 (2010) 025007 Z Y Guo et al

(a)

(b)

(b)

X-axis displacement Z-axis displacement

X

Y

Z XY

Z

Figure 2. The working modes of the TFG (simulated in ANSYSTM). (a) The driving mode, frequency = 3.96 kHz. (b) The sensing mode,frequency = 4.38 kHz.

Table 1. Dimensions and stiffnesses of the beams.

Width (μm) Length (μm) Thickness (μm) Stiffness Number Total stiffness

Drive beam 1 10.5 500 90 133.3 (N m−1) 4 533.2 (N m−1)Drive beam 2 10 500 90 126.9 (N m−1) 2 253.8 (N m−1)Sense beam 26 350 90 0.589 (Nm rad−1) 4 2.356 (Nm rad−1)

address this issue, the lateral comb drive used in this TFG iselectrostatic force balanced along the z-axis. The concept isillustrated in figure 3, where (a) and (b) are the perspectiveand cross-sectional view, respectively. All the fingers havethe same thickness, t, but different heights with a heightdifference of �h as shown in figure 3(b). In order to balancethe electrostatic force in the z-axis, the overall layout of allthe fingers is symmetric with respect to the y-axis as shownin figure 3(a). When a voltage is applied to the comb drive,electrostatic forces will be generated along the z-axis, i.e.Fz1 and Fz2 as shown in figure 3(b). These two forces willbe equal and counteracted. Thus, the net electrostatic force,Fz = Fz2 + Fz1, is zero. Consequently, the sense-to-drivecoupling can be greatly reduced in a simple manner.

The moments of the z-axis electrostatic forces, Fz, withrespect to the x-axis also need to be balanced as they mayexcite other undesired modes of the gyroscope. By properlyarranging the comb fingers of the lateral comb drive, zeromoments of the z-axis electrostatic forces can be realized. Todo this, the fingers are symmetrically distributed along all x-,y- and z-axes, as shown in figures 3(a) and (b) while figure 3(c)gives an example of other arrangement with non-zero z-axiselectrostatic forces moments.

To optimize the comb finger design, the electrostaticforces along the z-axis can be calculated using analyticalequations [19] or simulated using numerical tools such asANSYSTM. Based on the simulation, the parameters of thecomb fingers are chosen as follows: the thickness, t, andthe gap, g, are 80 μm and 4 μm, respectively and �h =10 μm. The electrostatic force of one pair of the combfingers versus the z-displacement dz is simulated and extractedby ANSYSTM, and the result is plotted in figure 4. Thenet z-axis electrostatic force Fz of the proposed comb driveis much smaller than the z-force Fz0 of a commonly usedequal-thickness, equal-height comb drive with the same finger

thickness and gap. As can be seen from figure 4, the net forceFz is nearly zero even when the vertical offset dz is as large ashalf of the finger gap g.

2.3. Topology of the TFG and the considerations

The lateral-axis comb drive design described above canbalance the z-axis electrostatic force. However, the net z-axis electrostatic force may not be zero in reality. This ismainly due to the fabrication imperfections, which can makethe structure of the fingers asymmetric with respect to the y-axis. In order to minimize the effect of the z-axis electrostaticforce on the TFG, the comb drives are placed near the rotationaxis of the sensing mode of the TFG while the proof massesare located at the two sides, as shown in figure 5. For such anarrangement, the moment of the z-axis electrostatic force canbe reduced and the coupling between the two working modescan be suppressed further.

As shown in figure 5, the moments induced by the Coriolisforce, Fc, and the residual electrostatic force, Fer, can bewritten as 2Fcrc and 2Ferrer respectively. So the momentratio

Mc/Mer = Fcrc/Ferrer. (1)

Many TFG designs have equal rc and rer. Therefore, forthe same Fc and Fe, the moment ratio for the proposed TFG isimproved by Rmr times, where

Rmr = rc/rer. (2)

For the proposed TFG, Rmr = 2.2, so the mechanical couplingbetween the two working modes of the TFG is furthersuppressed.

One more issue that must be taken into consideration isthat it is necessary to eliminate the rotation movement of theproof mass on its own inertia axis, which means that for the

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J. Micromech. Microeng. 20 (2010) 025007 Z Y Guo et al

(c)

Y

ZFz

2

Fz2

Fz1 Fz1

MzxX

Y

Z Fz2Fz2

Fz1 Fz1 Vd

fixed

movable

Δh

Δhg

t

(b)

Z

X

Y

t

t

FixedMovable

Fixed

(a)

Figure 3. Schematic diagram one group (a), the sectional view(b) of the lateral comb drive and (c) an example of other comb drivelayout with non-zero moment with respect to x-axis.

-2 -1 0 1 2

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

Fz2

Fz0

Nor

mal

ized

forc

e F

/(0V

2 ) [

m-1]

Normalized displacement Dz/g

Fz1

Fz

Figure 4. Electrostatic force of one unit of the comb drive versusz-axis displacement simulated by ANSYSTM.

lateral TFG, there is no relative rotation between the proofmass and the support rigid frame. For most TFGs, two orfour uniform driving beams are arranged symmetrically withrespect to the principal inertia axis of the proof mass, so

Glass

Z

Fc

Fc

Fer Ferrer

rc

Sensing comb

Drivingcomb

Proof

Figure 5. Schematic diagram of cross-sectional view of the TFG.

Center of the TFG

Drive beam 1

Center of the total mass

Drive beam 2

l2l1Fa

kz1 kz2Center of the total mass

(a)

(b)

l2l1

Figure 6. (a) The proof mass and the drive spring beams of the leftpart of the TFG. (b) The schematic model for force analysis.

no moments arise under acceleration as acceleration-inducedforces pass through the inertia axis and will not cause anyrotation of the proof mass.

Note that with this new arrangement, the drive springbeams may not be symmetrically arranged with respect to thecenter of the proof mass. As shown in figure 6, in order toavoid the rotation, the two sets of drive spring beams musthave different z-stiffnesses since the displacements of the twosets of beams along the z-axis are the same under the inertiaforce, Fa . So, the z-stiffness ratio of the two beams is givenby

kz1/kz2 = l2/l1. (3)

For the proposed TFG here, the stiffness ratio is 2.10.

3. Device fabrication

The proposed TFG can be realized by a five-mask, silicon-on-glass (SOG) process using silicon/glass wafer bondingand DRIE, which is developed at Peking University [21].

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J. Micromech. Microeng. 20 (2010) 025007 Z Y Guo et al

(e)

Sense Drive Moveable Beam

( f )

SiO2PR Al

Au Si Glass

(a)

(b)

(c)

(d)

Figure 7. Main steps of the fabrication flow.

(a) (b)

(d )(c)

XZ

Y

Dr(+) Dr(-)

Ds(+)

Sen

Ds(-)

Dr(+)

Figure 8. Fabricated TFG. (a) Die photo. (b) SEM of the comb drive. (c) Close-up of the comb drive. (d) SEM of the torsional sensingcomb.

Figure 7 shows the main steps of the fabrication flow. Firstly,the bottom sides of the comb fingers are formed by DRIE (a).Then the space between the Pyrex7740 glass substrate and theproof masses is formed by the second DRIE (b). The electricalconnections are formed on the glass by Au lift-off (c). The Aulayer is about 200 nm thick. After anodic bonding and KOHthinning (d), the structure is pre-released by the third DRIE(e). Then the structure is released by the last DRIE and the topsides of the fingers are formed at the same time (f ).

Figure 8 shows the optical photo and scanning electronmicrographs (SEMs) of a fabricated gyroscope, where Dr,Ds and Sen denote drive electrodes, drive-sense electrodesand sense electrodes, respectively. Figure 8(a) is a die photowhere the die size is 3.5 × 6.5 mm2. Figures 8(b) and (c)show an SEM and a close-up view of the EFB lateral combdrive. The finger thickness is about 80 μm and the adjacentfingers have a height difference of about 10 μm. The fingergaps are 5 μm, which is 1 μm larger than the designed value

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J. Micromech. Microeng. 20 (2010) 025007 Z Y Guo et al

(a) (b)

Q = 7 Q = 270

Figure 9. Frequency response of driving mode (a) and sensing mode (b) of the TFG.

3250 3750 4200

-75

-65

-55

-45

Freq (Hz)

Mag

(dB

)

drive-to-sensesense-to-drive

Figure 10. Coupling test of the TFG.

-400 -200 0 200 400

-1

-0.5

0

0.5

1

Angular rate ( o/s )

TF

G O

utpu

t (V

)

y=0.0029x-0.304R2=0.9998

Figure 11. Output of the TFG versus angular rate input.

because of the CD loss. In figure 8(b), residues can be found atthe edges of the thinned part of the combs. The residues maycome from the passivation or sidewall deposition during DRIEand can be reduced by optimizing the fabrication process orthrough wet etching [20]. Figure 8(d) shows an SEM of thevertical sensing comb. The sensing fingers have a length of450 μm and a width of 12 μm while the step and gap ofneighboring fingers are about the same with those of the lateralcomb drive.

X:4.25 Hz Y:102.2083 uV/rtHz

10V/rtHz

rms

1E-05

Mag (Log)

Hz100 0 Hz

Figure 12. Noise spectrum analysis of the TFG.

4. Testing

The TFG was tested in the atmosphere. The interfaceelectronic circuitry is the same as the one reported in [22].The dc bias and the amplitude of the ac signal applied on thedriving electrodes were 10 V dc and 3.5 V ac, respectively.An HP35670 spectrum analyzer was used to measure thefrequency responses of the driving and sensing modes.Figure 9 shows the measured resonant frequencies of thesensing and driving modes. Their resonant frequencies are3.75 kHz and 4.34 kHz, respectively. The measured drivingmode frequency has a larger difference from the simulatedresult than that of the sensing mode. This is because thestiffness of the driving (in-plane bending) beams is moresensitive to the CD loss than that of the sensing (out-of-plane bending) beams. When the CD loss, which is about0.5 μm, is taken into consideration, the simulated drivingresonant frequency is 3.74 kHz. The quality factor of thedriving mode is 270 while the quality factor of the sensingmode is only 7 because of the squeeze-film damping betweenthe proof mass and the glass substrate. The gap betweenthe proof mass and the glass substrate is about 30 μm. TheHP35670 spectrum analyzer was also used to measure thecouplings between the two working modes. Figure 10 showsthe measured results of the couplings between the two modes.The drive-to-sense coupling is −45 dB while the sense-to-drive

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coupling is −51 dB, which demonstrates that the electrostaticbalanced comb drive can efficiently suppress the sense-to-drivecoupling. The outputs of the TFG under different constantinput angular rates were tested on a TVP1 turntable, a productof the Changcheng Institute of Metrology & Measurement.Figure 11 shows the outputs with a full range of 800◦ s−1.The measured sensitivity is 2.9 mV/◦/s and the nonlinearityis 0.9% in the full range. The zero input offset mainly comesfrom the quadrature error though decoupling mechanismsare employed [5, 23]. Figure 12 shows the noise spectrumanalysis. The noise floor is about 0.035◦/s/Hz1/2.

5. Conclusion

A lateral-axis tuning-fork gyroscope (TFG) with anelectrostatic force-balanced (EFB) comb drive and a torsionalvertical sensing comb capacitor is designed and demonstrated.The proposed EFB comb drive can efficiently suppress thecoupling from the sensing mode to the driving mode. Thetopology of the TFG also helps to lower the sense-to-drivecoupling further. The TFG can work at atmospheric pressurewith a sensitivity of 2.9 mV/◦/s and a nonlinearity of 0.9%for the full scale of 800◦s−1. The noise floor is about0.035◦/s/Hz1/2. Though vertical comb sensing capacitorsare used to pick up the out-of-plane displacements, the qualityfactor of the sensing mode is still only about 7 because ofthe squeeze-film air damping between the proof mass andthe substrate. Better performance can be anticipated whenoperating in vacuum and mode matching mechanisms adopted.

Acknowledgments

The authors would like to thank the technical staff ofthe National Key Laboratory of Micro/Nano FabricationTechnology for their support on device fabrication. Thework was partially supported by NSFC (grant no 50575001),National High Technology Research and DevelopmentProgram of China (grant no 2006AA04Z371) and the ChineseGovernment Scholarships for Postgraduates.

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