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Sensors and Actuators A 172 (2011) 523– 532

Contents lists available at SciVerse ScienceDirect

Sensors and Actuators A: Physical

jo u rn al hom epage: www.elsev ier .com/ locate /sna

esign, damping estimation and experimental characterization of decoupled-DoF robust MEMS gyroscope

ashif Riaza,∗, Shafaat A. Bazazc, M. Mubasher Saleemb, Rana I. Shakoord

Faculty of Electronic Engineering, GIK Institute of Engineering Sciences and Technology, Topi, KhyberPakhtunkhaw, PakistanFaculty of Computer Science and Engineering, GIK Institute of Engineering Sciences and Technology, Topi, KhyberPakhtunkhaw, PakistanDepartment of Computer Science, Center for Advance Studies in Engineering (CASE), Islamabad, PakistanNano-Devices Group, National Institute of Lasers and Optronics (NILOP), Islamabad, Pakistan

r t i c l e i n f o

rticle history:eceived 6 April 2011eceived in revised form0 September 2011ccepted 25 September 2011vailable online 1 October 2011

eywords:icrogyroscopeynamic amplification

a b s t r a c t

This paper reports the design implementation of three degree-of-freedom (3-DoF) non-resonant MEMSgyroscope having 2-DoF drive-mode oscillator. The proposed architecture utilizes structurally decoupledactive-passive mass configuration to achieve dynamic amplification of oscillation in 2-DoF drive-mode.This results in higher sensitivity and eliminates the need of mode matching for resonance. A low coststandard Metal-Multi User MEMS Processes (MetalMUMPs) is used to fabricate 20 �m thick nickel basedgyroscope with an overall reduced size of 2.2 mm × 2.6 mm. The experimental characterization demon-strated that the frequency response of the 2-DoF drive-mode oscillator has two resonant peaks at 754 Hzand 2.170 kHz with a flat operational region of 1.4 kHz between the peaks. The sense-mode resonantfrequency lies at 1.868 kHz within this flat operational region where gain is less sensitive to structural

egree-of-freedom (DoF)ehavioral modelingamping modelsetalmumps

parameters and environmental variations. This results in improved robustness to fabrication imperfec-tions and environmental variations and long term stability without utilizing tuning and feedback control.Gyroscope dynamics and system level simulations using behavioral modeling are carried out to predictthe performance of the device. Experimental results show close agreement with the behavioral sim-ulation results due to incorporation of improved damping models in behavioral model developed inCoventorWare.

© 2011 Elsevier B.V. All rights reserved.

. Introduction

Conventional bulky gyroscopes have been replaced by micro-achined gyroscopes due to low cost, low power consumption

nd micro sizes. Advancements in micromachining technologyllow monolithic mechanical systems on a chip with their con-rol and sense electronics. Wider application spectrum has beenchieved from automotive navigation, guidance and safety systemso interactive consumer electronics by using precise and accuratengular rate microgyroscopes [1]. Micro-level adaptation inducesnwanted effects, so gyroscope needs improvement in gain, robust-ess and stability [2].

Conventional MEMS vibratory gyroscopes work on the Coriolisrinciple of vibratory proof mass suspended above the substrate bynchored flexures. This allows the mass to oscillate in two orthog-nal directions referred as drive and sense direction. The overallynamical system of gyroscope is a 2-DoF mass-spring-damper sys-em. Typically, the proof mass oscillates at resonance in the drive

∗ Corresponding author. Tel.: +92 3326486319.E-mail address: engrkashifrz@gmail.com (K. Riaz).

direction by electrostatic drive force. When an input angular rota-tion is applied to gyroscope, a Coriolis force proportional to theinput angular rate is induced. This force excites the proof mass inthe sense direction orthogonal to both drive force and the inputangular rate. Higher sensitivity is achieved by designing and tuningdrive and sense-mode resonant frequencies to match with reducedmechanical bandwidth [3].

Environmental variations and fabrication imperfections putan upper limit on fabrication of symmetric suspension andmode matched resonant systems. This lead to drastic variationsin the oscillatory system parameters limiting the resonant fre-quency matching which result in decreased sensitivity, robustness,stability and performance of MEMS gyroscopes. Thus, in reso-nant microgyroscopes, active tuning and feedback control systembecome inevitable to minimize the effects of these unavoid-able micro-fabrication flaws and environmental variations [2].The dynamical systems with slightly shifted sense-mode resonantfrequency from drive-mode have been designed with increasedbandwidth but at the expense of gain [4]. Recently, new designapproaches have been implemented either by utilizing multi-DoFin drive and sense-mode oscillatory system or by utilizing mul-tiple drive-mode oscillators with incrementally spaced resonant

924-4247/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.sna.2011.09.032

524 K. Riaz et al. / Sensors and Actuators A 172 (2011) 523– 532

Nomenclature

m1 active massm2 + mf passive mass

angular velocityk1x drive direction spring constant for mass m1k2x drive direction spring constant for mass m2k2y sense direction spring constant for mass m2c1x drive direction damping coefficient for mass m1c2x drive direction damping coefficient for mass m2c2y sense direction damping coefficient for mass m2w flexure beam widtht flexure beam thickness˝1x, ˝2x resonant frequencies of active and passive mass-

spring system�x frequency ratio�x mass ratiofx−n1, fx−n2 expected resonance peaks in drive-modeX1, X2 steady state response of 2-DoF drive-mode oscilla-

tor system� effective coefficient of viscosity

fr

mot2nadioivfoMmtf

feTM[awmftebaCd

bdae

CoventorWare are discussed in Section 4. Section 5 presents exper-imental characterization of the fabricated prototype.

2. Microgyroscope design concept and dynamics

2.1. 3-DoF design concept with 2-DoF drive-mode oscillator

In this paper, we propose a 3-DoF MEMS gyroscope consistingof two interconnected masses m1 and m2. The scanning electronmicroscope (SEM) image of the proposed microgyroscope is shownin Fig. 1. The mass m1 is electrostatically actuated using comb drives[11] and oscillates in the drive direction (x-axis) only whereas itsmotion is constrained in the sense direction (y-axis). The mass m2can oscillate in both drive and sense direction. The combination ofthe masses m1 and m2 form the 2-DoF drive-mode oscillator. Themass m2 forms the 1-DoF sense-mode oscillator. The mass m1 formsthe active mass and the mass m2 + mf forms the passive mass of 2-DoF drive-mode oscillator. The passive mass acts as the vibrationabsorber of the active mass. This active-passive mass configurationis designed to achieve dynamic amplification in the drive-mode foramplified response amplitude of the sense mass m2.

Small imbalance in the suspension system of gyroscope dueto unavoidable fabrication imperfections results in dynamic modecoupling between drive and sense modes. To minimize theseeffects, decoupled drive and sense modes or independent sus-pension systems have been utilized [12,13]. In our design, thedrive and sense-mode oscillators are mechanically decoupled byusing unidirectional decoupling frame of mass mf and indepen-dent suspension system. This configuration suppresses dynamicmode coupling between the drive and sense modes. Effects of smallimbalance in the drive-mode suspension system are suppressed byindependent constrained suspension system in the sense directionand vice versa.

The proposed 3-DoF design concept utilizes resonance in thesense-mode, but not in the drive-mode to improve the sensitivitywhile maintaining the robust operational characteristics. The 2-DoFdrive-mode oscillator has two resonant peaks with a flat opera-tional region between them. This region defines the operationalfrequency region of the microgyroscope where response amplitudeis less sensitive to parameter variations. The 1-DoF sense-modeoscillator is designed so that its resonant peak overlap the flat oper-ational region of the 2-DoF drive-mode oscillator, which results inhigh robustness and stability. By utilizing the dynamic amplifica-tion, large oscillation amplitude of the sense mass is achieved inthe drive-mode with the small actuation amplitudes, generated bythe comb drive based electrostatic actuation.

2.2. Proposed microgyroscope dynamics

Fig. 2 shows the lumped mass-spring-damper model of theproposed microgyroscope design. The 3-DoF gyroscope dynamicsystem is analyzed in the non-inertial frame of reference associatedwith the microgyroscope. Each of the interconnected proof massesis assumed to be a rigid body with a position vector �r attached to arotating microgyroscope reference frame with an angular velocityof �� resulting in an absolute acceleration in the inertial frame givenas

�arot = �ain − �� × �r − 2 �� × �vrot − �� × ( �� × �r). (1)

Thus the equation of motion of m1 and m2 can be expressed ininertial frame as

effKn knudsen number

requencies resulting in increased stability and robustness to fab-ication imperfections and environmental variations [5,6].

In this paper, an electrostatically actuated 3-DoF non-resonanticrogyroscope, having 2-DoF drive-mode and 1-DoF sense-mode

scillator, with wider bandwidth is proposed. Dynamic amplifica-ion is achieved by using active-passive mass configuration in the-DoF drive-mode which results in higher sensitivity and elimi-ates the need of resonance. The drive and sense-mode oscillatorsre structurally decoupled. This lowers mode coupling between therive and sense modes which results in less instability. The device

s operated in flat operational region between two drive-mode res-nant peaks where gain is less sensitive to parameter variations,

.e. structural and environmental parameter variations. This pro-ides high robustness and stability, thus eliminates the need ofeedback control circuitry. Furthermore, the fabrication of micr-gyroscope has been tuned for MetalMUMPs [16] for the first time.etalMUMPs is a low cost commercially available surface micro-achining process which facilitates the researchers to fabricate

heir MEMS based devices who do not have in-house fabricationacility.

Generally, the design and analysis of MEMS devices are per-ormed without considering fabrication process, using the finitelement method (FEM) and boundary element method (BEM).hese methods require high computational time and memory.oreover, optimization analysis may vary from days to weeks

7,8]. In this paper, we present behavioral modeling and simulationpproach using CoventorWare which provides fast computationith less memory requirement [9]. CoventorWare ARCHITECTodule has been utilized as behavioral simulation tool, which per-

orms simulations based on the behavior of device as expressed byhe reduced order models. Complete fabrication process is mod-led using different fabrication steps such as deposition and etchingefore simulation and analysis [10]. Improved reduced order slidend squeeze film flow damping macro-models are extracted usingoventorWare DampingMM solvers to incorporate the effect of theamping in the developed behavioral model in CoventorWare.

The rest of the paper is organized as follows, Section 2 describes

riefly the concept of 3-DoF non-resonant microgyroscope and itsynamics. In Section 3, mechanical design of device is presentedlong with prototype modeling and fabrication. Damping modelxtraction and simulation results through behavioral modeling in

m1 �a1= �F1+ �Fd+ �Fr − 2m1�� × �v1 − m1

�� × ( �ω × r1) − m1�� × �r1 (2)

m2 �a2 = �F2 + �Fr − 2m2�� × �v2 − m2

�� × ( �ω × r2) − m2�� × �r2 (3)

K. Riaz et al. / Sensors and Actuators A 172 (2011) 523– 532 525

Fig. 1. SEM image of proposed gyroscope model with 2-DoF drive-mode and 1-DoF sense-mode oscillator.

where �Fd is the driving force applied to mass m1, �F1 is the net exter-nal force applied to mass m1 including the elastic and dampingforces from the substrate, �F2 is the net external force applied tothe mass m2 including the damping force from the substrate and�Fr is the elastic reaction force between m1 and m2. Following con-straints are applied on the dynamical system so that the equationof motion of m1 and m2 can be further simplified and decomposedinto the drive and sense directions: (a) the structure is stiff in out-of-plane direction, (b) the position vector of m1 and the decouplingframe are forced to lie along the drive direction, i.e. y1(t) = 0, (c) thedecoupling frame and the sense mass m2 move together in the drivedirection, (d) the mass m2 oscillates purely in the sense directionrelative to the decoupling frame, and (e) the rotation of the driveand sense masses about the z-axis in the absence of external rota-tion has been neglected which is still possible due to the presenceof the comb drive structures.

The equations of motion for the active mass (m1), the passivemass (m2 + mf) and the sense mass (m2) when subjected to angularvelocity, �z about the z-axis become

m1x1 + c1xx1 + k1xx1 = k2x(x2 − x1) + m1�2z x1 + Fd(t) (4)

(m2 + mf )x2 + c2xx2 + k2x(x2 − x1) = (m2 + mf )�2z x2 (5)

m2y2 + c2yy2 + k2yy2 = m2�2z y2 − 2m2�zx2 − m2�zx2 (6)

where mf is the mass of the decoupling frame, Fd(t) is the driv-ing electrostatic force applied to the active mass through thecomb drive based electrostatic actuation mechanism at the driv-ing frequency ωd and �z is the angular velocity applied to the

microgyroscope about the z-axis. It is assumed that there is noanisoelasticity or anisodamping in the system. The Coriolis force�Fc that excites the mass m2 in the sense direction is 2m2�zx2 andthis Coriolis response of the mass m2 in the sense direction (y2) isdetected for the angular rate measurement.

3. Mechanical design

This section describes the mechanical design implementationof the proposed design discussed in the Section 2. The suspen-sion system design for the 3-DoF microgyroscope is described first,followed by the prototype design and fabrication discussion.

Fig. 3 shows the complete suspension system of the proposeddevice which is designed so that the first mass m1 with 1-DoF isfixed in the sense direction and free to oscillate in the drive directiononly. The second mass m2 has 2-DoF, free to oscillate in both driveand sense direction.

The dynamic coupling is unavoidable in multi-DoF systems evenin the perfectly fabricated micro-devices due to structural non-linearities. However, in order to minimize the dynamic couplingbetween the drive and sense modes, the drive and sense-modeoscillators have been decoupled mechanically with a frame struc-ture. The drive mass m1 oscillates only in the drive direction dueto suspension fixed in the sense direction. When the mass m2 isnested inside the drive-mode frame, the sense-mode oscillationsof the frame are constrained, and the drive-mode oscillations areautomatically forced to be in the designed drive direction. Then,m2 is free to oscillate only in the sense direction with respect to the

m1m2+m f

k1x

c1x

k2x

c2x

Fd

x1

x2

m2

c2y

k2y

y2

Fc

(a) (b)

Fig. 2. (a) Lumped mass-spring-damper model for the 2-DoF drive-mode oscillator. (b) Lumped mass-spring-damper model for the 1-DoF sense-mode oscillator of 3-DoFmicrogyroscope.

526 K. Riaz et al. / Sensors and Actuators A 172 (2011) 523– 532

ftb

3

vlbl

k

wibacdfbs

k

fttarf

k

3.2. Prototype design and fabrication

Various gyroscope based on the multi-DoF design concept havebeen prototyped using customized silicon-on-insulator (SOI) andsilicon-on-glass (SiOG) based bulk micromachining process withhigher structural layer thickness, less operational bandwidth andincreased device size [5,14,15]. we have prototyped our micro-gyroscope designs with reduced device size of 2.2 mm × 2.6 mmusing standard surface micromachining MetalMUMPs process [16].This process provides structural layer (Nickel) thickness of 20 �mas compared to other available MUMPs processes. MEMSPro hasbeen used for the designing of mask layouts, design rule checksand process simulations for MetalMUMPs.

The proof mass values for prototype design arem1 = 3.86 × 10−7 kg, m2 = 1.346 × 10−7 kg and the decouplingframe mass is mf = 4.8 × 10−8 kg. The spring constants are k1x= 63.59 N/m, k2x = 15.96 N/m, k2y = 13.8 N/m with beam lengthsL1x = 410 �m, L2x = 650 �m, L2y = 502 �m, t = 20 �m is beamthickness and w = 8 �m is the beam width. The Young’s Mod-ulus for structural layer Ni was assumed to be E = 214 GPa. Thesense-mode resonant frequency is designed to be 1.649 kHz. Inthe drive-mode, resonant frequencies of the isolated active andpassive mass-spring system are ω1x =

√k1x/m1 = 2.043 kHz

and ω2x =√

k2x/(m2 + mf ) = 1.490 kHz, respectively. Thefrequency ratio is �x = ω2x/ω1x = 0.7296 and mass ratio is�x = (m2 + mf)/m1 = 0.47. The location of the two expectedresonance peaks in the drive-mode frequency responsefx−n1 = 1.25 kHz and fx−n2 = 2.42 kHz are calculated by usingthe relations [5]:

fx−n1=

√√√√√12

⎛⎝1 + �x + 1

�2x

−

√(1 + �x + 1

�2x

)2

− 4

�2x

⎞⎠ω2x (10)

fx−n2=

√√√√√12

⎛⎝1 + �x + 1

�2x

+

√(1 + �x + 1

�2x

)2

− 4

�2x

⎞⎠ω2x. (11)

4. Behavioral model development and simulation results

A behavioral modeling and simulation tool at system level per-forms simulation based on the behavior of device as expressedby reduced order equations. The designed microgyroscope per-formance is verified by modeling complete fabrication processMetalMUMPS and through behavioral modeling using Coventor-Ware ARCHITECT module [10]. The main components used forthe behavioral modeling of design in CoventorWare are beam,comb drive, rigid plate and extracted slide and squeeze film damp-ing macro-models. Fig. 4 shows the complete schematic of theMEMS gyroscope behavioral model developed using CoventorWarewith the illustration of the physical geometry represented by theschematic components. The wires linking electrical symbols in anelectrical schematic have a direct analogy in the physical world:they represent a physical wire that keeps its two ends constrainedto the same voltage [10]. In schematic, mechanical wires are a bun-dle of 6 individual wires containing three translational and threerotational wires. These wires define the motion and rotation of a

Fig. 3. 3-DoF non-resonant microgyroscope suspension system layout.

rame, and the sense-mode response of m2 will be orthogonal tohe drive direction significantly minimizing the dynamic couplingetween the drive and sense-mode.

.1. Suspension system

The suspension that connects the mass m1 with the substrateia anchors comprises four double-folded flexures. Each beam ofength L1x in the folded flexure can be modeled as a fixed-guidedeam deforming in the orthogonal direction to the axis of the beam,

eading to an overall stiffness of [11]:

1x = 42

(12

3EI

(L1x/2)3

)= 2Etw3

L31x

(7)

here E is the Young’s Modulus, I = tw3/12 is the second moment ofnertia of the beam cross section, t is the beam thickness and w is theeam width. Possible anisoelasticities due to manufacturing flawsre suppressed by driving the mass m1 purely along the geometri-al drive axis by this suspension and constraining m1 in the senseirection. Decoupling frame having mass mf is connected to m1 viaour double-folded flexure with a beam length of L2x which cane deformed in the drive direction resulting in the drive directiontiffness value of [11]:

2x = 42

(12

3EI

(L2x/2)3

)= 2Etw3

L32x

. (8)

The sensing mass m2 is connected to the decoupling frame withour five-folded flexures, each having beam length of L2y. Sincehese flexures are stiff in the drive direction and deform only inhe sense direction, dynamic coupling instability between the drivend sense modes is reduced and the zero rate drift of the microgy-oscope is also minimized. The overall stiffness with a length of L2yor each beam is [11]:

2y = 45

(12

3EI

(L2y/2)3

)= 4Etw3

5L32y

. (9)mechanical point in space. This point referred as knot and it canbe seen as the physical connection point between two or moremechanical elements [17].

K. Riaz et al. / Sensors and Actuators A 172 (2011) 523– 532 527

Fig. 4. Behavioral model schematic of the proposed microgyroscope design developed using CoventorWare.

4.1. Damping model extraction

In our design, for the mass m1 in the drive-mode, total dampingcan be estimated as combination of slide film damping between themass and the substrate and between comb drive fingers. This damp-ing is represented by damping coefficient c1x. For the mass m2 in thedrive-mode, total damping can be approximated due to slide filmdamping between mass and substrate and between sense capacitorelectrodes. This damping is represented by damping coefficient c2x.In the sense-mode, the total damping due to the mass m2 resultsfrom slide film damping between mass and substrate and squeezefilm damping between sense capacitor electrodes. This damping isrepresented by damping coefficient c2y.

To incorporate damping effects in behavioral modeling, reducedorder slide film and squeeze film damping models are extractedusing DampingMM solver in CoventorWare [10]. By consideringgas rarefaction effects, narrow gaps and kinetic gas models [18],more accurate slide film models have been extracted. Squeeze filmmodels are improved by incorporating non-linear effects [19].

The squeezed film solver in CoventorWare uses flow resistancemodels to set up a finite element representation of the linearizedReynolds equation [19] for a given input geometry. The solver notonly solves for damping due to viscous effects, but also for springeffects due to the compressibility of a fluid. DampingMM solverthen applies the Arnoldi algorithm [18] to reduce the order of thesystem matrix required to adequately model the squeezed film flowwhile preserving its frequency dependent properties [20].

The Reynolds equation is used to represent the gas pressuredistribution in the gap between sense capacitor electrodes for acompressible gas film which is air. The linearized Reynolds equa-tion is given as [19]:

Poh2o

12�eff�2

(�P

Po

)− ∂

∂t

(�P

Po

)= ∂

∂t

(h

ho

)(12)

where Po is the undisturbed pressure, �P is the small variation inpressure, (h/ho) is the normalized gap dimension, ho is the width ofthe gap, and �eff is the effective viscosity.

The molecular mean free path � is not negligible at low pressuresas compare to gap widths. The gas flow in this case can be modeledby modified Reynolds equation [19]. This modification can be rep-resented by using the effective coefficient of viscosity, �eff. A simpleempirical approximation for the effective coefficient of viscosity isgiven as [19]:

�eff = �

1 + 9.368k1.159n

. (13)

where Kn = �/d is Knudsen number, � is the mean free path ofmolecules, d is the gap distance between the mass and the sub-strate and � is the viscosity coefficient. The effective coefficientof viscosity �eff depends on pressure as the mean free path � isinversely proportional to pressure [19].

The Squeezed film solver in CoventorWare uses a hybridNavier–Stokes/Reynolds (NSR) approach in the compressed gasfilm. Navier–Stokes equations are used to model non-linear effectsand additional flow resistance from the fluid turning across thecorner to flow out of an edge or hole [21] for increased accuracy.

The slide film damping model is a closed form expressionderived from the one-dimensional diffusion equation as [18]:

∂v(z)∂t

= v∂2v(z)

∂2z

(14)

where v is the kinematic viscosity, v = �/ and is the density ofgas. The damping coefficient is obtained by simplifying closed formexpression as

= �effA

h(15)

528 K. Riaz et al. / Sensors and Actuators A 172 (2011) 523– 532

Table 1Data related to damping such as layer properties, operating conditions and dampingcoefficient imported with damping models to CoventorWare behavioral model.

Property Value

Structural layer NickelGas AirAmbient viscosity (MPa-s) 1.86e−11

Ambient density (kg/�m3) 1.16e−18

Ambient mean free path (�m) 6.7e−2

Input temperature (K) 300Input pressure (MPa) 1.01325e−1

Damping coefficient of mass m1 in drive-mode, c1x 1.33e−5

wao

�

tumddtf

cidfisttsqdc

4

ce

m

(

m

m

qs

X

[

X2 = Fo

k1x

[{1 + k2x

k1x−(

ω

ω1x

)2

+ jωc1x

k1x

}{1 −

(ω

ω2x

)2

+ jωc2x

k2x

}− k2x

k1x

]−1

(21)

where ω1x =√

k1x/m1 and ω2x =√

k2x/(mf + m2) are the reso-nant frequencies of the isolated active and passive mass-springsystem, respectively. When the driving frequency, ωd = ω2x, thepassive mass moves to exactly cancel out the applied input forceFd on the active mass, and maximum dynamic amplification isachieved. Since Coriolis force Fc = 2m�z ˙x2 is directly proportionalto the oscillations of the passive mass in the drive direction, largeoscillation amplitude of the passive mass results in increased sen-sitivity of the device in the sense direction.

To understand and verify the device frequency characteristicsand dynamic amplification concept, small signal AC analysis isconducted at Vac = 60 V and Vdc = 100 V through developed Coven-torWare behavioral model by varying the frequency from 1 Hzto 5 kHz at atmospheric pressure. Fig. 6(a) shows that two reso-nance frequencies for the 2-DoF drive-mode oscillator are locatedat 1.046 kHz and 2.042 kHz, which compares well to the analyti-cally calculated values of 1.25 kHz and 2.42 kHz. The sense-moderesonance frequency is located at 1.407 kHz and lies within thedrive-mode flat operational region of ∼1 kHz as shown in Fig. 6(b).Therefore, microgyroscope is operated in the flat operational regionof the drive-mode for high robustness, sensitivity and stability.

In case of dual mass oscillators as in our design, it is observedthat at first resonant frequency, active and passive masses are inphase and maximum dynamic amplification is achieved. At the sec-ond resonant frequency, the active and passive masses are out ofphase and the dynamic amplification is negligible [6]. Simulationresults show that in the drive-mode, at first resonant frequency(1.046 kHz), the active and passive masses with response ampli-tudes of 939.25 nm and 247.12 nm, respectively, are in phase anddynamic amplification of 3.8 times is achieved as shown in Fig. 7.At second resonant frequency (2.042 kHz), both the masses are178.5◦ out of phase and dynamic amplification is negligible. Thus,large oscillations amplitude of the passive mass results in increasedsensitivity of the device in the sense direction. The frequency anal-ysis verifies the working of the proposed design as dual massoscillator and thus achieving dynamic amplification for increasedsensitivity.

4.3. Robustness analysis

Maximum robustness to system parameter variations isachieved by designing the sense-mode oscillator to operate inthe flat operational region between the two resonant peaks ofthe 2-DoF drive-mode oscillator. In this region, gain is less sen-sitive to system parameter variations. The wide operational regionbetween the two resonant peaks avoids the need of active tuningand feedback control in the presence of unavoidable fabricationimperfections. These imperfections cause asymmetries in suspen-sion system and shift in resonance frequencies. Absolute tolerancesfor both the lengths and widths of flexures used in our proposedsuspension system design in the MetalMUMPs process in worstcase are ±0.5 �m [16]. The performance of the design is ana-lyzed with these absolute tolerances. In 2-DoF drive-mode, the

Damping coefficient of mass m2 in drive-mode, c2x 4.62e−6

Damping coefficient of mass m2 in sense-mode, c2y 8.54e−5

here A is the area, h is the gap and �eff is the effective viscosity ofir. The effective coefficient of viscosity is used instead of coefficientf viscosity to include the gas rarefaction effects and given as [18]:

eff = �

1 + 2kn + 0.2k0.788e−kn/10n

. (16)

Solid meshed models of the masses m1 and m2 with Manhattanype elements are developed using CoventorWare DESIGNER mod-le. All the necessary boundary conditions are applied and dampingodels are extracted using above developed expressions through

amping solvers using CoventorWare ANALYZER module. Theseamping models are symbols carrying data such as layer proper-ies, operating conditions, damping coefficient, damping and springorces over a predefined frequency range.

Slide film damping model attached with mass m1 gives dampingoefficient c1x in drive-mode as shown in Fig. 4. Slide film damp-ng model attached with mass m2 gives damping coefficient c2x inrive-mode as shown in Fig. 4. The combination of slide and squeezelm models attached with mass m2 gives damping coefficient c2y inense-mode as shown in Fig. 4. These damping models are importedo CoventorWare behavioral model as shown in Fig. 4 to includehe effect of damping in behavioral simulations. The damping andpring forces for extracted damping models over a predefined fre-uency range are shown in Fig. 5. Table 1 shows data related toamping such layer properties, operating conditions and dampingoefficients.

.2. Frequency and dynamic amplification analysis

The sinusoidal force is applied to the drive mass m1 by theomb drives. The equation of motion in the drive direction can bexpressed as

1x1 + c1x ˙x1 + k1xx1 = k2x(x2 − x1) + Fd(t) (17)

m2 + mf )x2 + c2x ˙x2 + k2x(x2 − x1) = 0. (18)

The equation of motion of the lumped mass-spring-damperodel of the 1-DoF sense-mode as shown in Fig. 2(b) becomes

2y2 + c2yy2 + k2yy2 = 2m2�z ˙x2. (19)

When a constant amplitude sinusoidal force with driving fre-uency ω, Fd = Fo sin (ωt) is applied on the active mass m1, the steadytate response of the 2-DoF drive-mode oscillator system is [6]:

1 = Fo

k1x

(1 −

(ω

ω2x

)2

+ jωc2x

k2x

){

1 + k2x

k1x−(

ω

ω1x

)2

+ jωc1x

k1x

}{1 −

(ω

ω2x

)2

+ jωc2x

k2x

}− k2x

k1x

]−1

(20)

results depicted 4.62% and 5.87% deviation from the nominal valueat first and second resonance frequency, respectively. In 1-DoFsense-mode, 2.13% deviation is observed from nominal value atsense-mode resonance frequency as shown in Fig. 8. It can beobserved that the proposed design is robust to structural parame-ter variations within the fabrication process tolerances. Moreover,there is a minimal change in gain in the flat operational region

K. Riaz et al. / Sensors and Actuators A 172 (2011) 523– 532 529

Fig. 5. Frequency dependent damping and spring forces for slide and squeeze film damping models.

and the flat operational region is still overlapped by sense-moderesponse.

Simulations of 2-DoF drive-mode oscillator frequencyresponse shows that gain in the flat operational region

between two resonance frequencies remain insensitive toenvironmental parameter variations such as the pressurevariations and thus to damping variations as shown inFig. 9.

Fig. 6. Frequency response. (a) 2-DoF drive-mode oscillator. (b) 1-DoF sense-mode oscillator.

530 K. Riaz et al. / Sensors and Actuators A 172 (2011) 523– 532

Fig. 7. Active and passive mass drive-mode magnitude and phase response.

Fig. 8. Frequency response by varying suspension system width ±0.5 �m with nominal value of 8 �m. (a) Passive mass drive-mode response and (b) passive mass sense-moderesponse.

Fig. 9. Passive mass drive-mode response by varying pressure from 100–101,325 MPa.

K. Riaz et al. / Sensors and Actuators A 172 (2011) 523– 532 531

Fig. 10. (a) 3-DoF microgyroscope drive-mode response (first resonant frequency). (b) 3-DoF microgyroscope drive-mode response (second resonant frequency). (c) 3-DoFmicrogyroscope sense-mode response.

5. Experimental characterization

The frequency response of 2-DoF drive-mode oscillator and1-DoF sense-mode oscillator of the prototype 3-DoF microma-chined vibratory gyroscope was characterized at Nanoscale SystemIntegration Group at Southampton University, UK, using PolytecMicrosystem analyzer, MSA-400. All measurements were taken atatmospheric pressure.

A peak-to-peak voltage signal was generated by an onboard sig-nal generator from the MSA-400, which was then fed to the ACpower amplifier for signal amplification. This amplified signal wasapplied to the electrostatic actuator. Finally, using the PMA-400in-plane frequency response was extracted. For drive-mode char-acterization, two probes were used to apply ±DC bias voltage, Vdcon the fixed comb drives on either sides of the microgyroscopewhereas one probe was used to apply AC signal, Vac to the proofmass through the anchor. Fig. 10(a) and (b) presents the frequencyresponses of the active mass, m1 and passive mass, m2 + mf. The firstresonant frequency was observed at 754 Hz where the passive masswas observed to reach a displacement of 658 nm at Vdc = 100 V andVac = 60 V, achieving a 3 times dynamic amplification of the activemass.

In drive-mode frequency response, a flat operational regionof 1.4 kHz was experimentally demonstrated. The two resonancepeaks in the drive-mode frequency response were observedas f(x−n1) = 754 Hz and f(x−n2) = 2.170 kHz instead of designedf(x−n1) = 1.160 kHz and f(x−n2) = 2.340 kHz. At the second resonantfrequency of 2.170 kHz, the passive mass was observed to reach adisplacement of 460 nm at Vdc = 100 V and Vac = 60 V, achieving a 9

times dynamic amplification of the active mass having a displace-ment of 55 nm.

Similar testing methodology was adopted to characterize sense-mode characterization. Two probes were used to apply ±Vdc = 60 Vbias voltage on the fixed sides of the sensing parallel plate elec-trodes. One other probe was used to apply sinusoidal Vac = 45 Von the proof mass through the anchor. Fig. 10(c) shows thefrequency response of the 1-DoF sense-mode oscillator. The loca-tion of the peak was observed at 1.868 kHz instead of designedvalue 1.639 kHz. When the drive and sense-mode frequencyresponses of the 3-DoF microgyroscope prototype were investi-gated together, a flat operational region of 1.4 kHz was overlappedby the sense-mode resonant frequency, defining the operationalfrequency region of the proposed device. These results experimen-tally demonstrate and verify the feasibility of the design concept.Table 2 summarizes the comparison of the simulation and testresults.

The experimental verification of drive as well as sense-modefrequency responses demonstrated a difference, although not verylarge, between the simulated and tested resonant frequencies.The probable cause of these differences in tested and simu-lated results could be due to the fabrication imperfections. Indesign, analysis and optimization of MEMS devices, mechani-cal properties, i.e. young’s modulus of thin film structural layerare important and exact values of these properties should beknown for high performance design, analysis and optimiza-tion. Diversified values of thin film properties are availablewhich may or may not match with fabricated material val-ues.

Table 2Comparison of the simulated and test results for resonant frequencies of drive and sense-modes.

Parameter Simulated frequencies Simulated amplitudes Tested frequencies Tested amplitudes

Drive-mode first resonant frequency 1.046 kHz 866.46 nm 754 Hz 658 nmDrive-mode second resonant frequency 2.042 kHz 465.32 nm 2.710 kHz 460 nmSense-mode resonant frequency 1.407 kHz 4.586 �m 1.868 kHz 4 �m

532 K. Riaz et al. / Sensors and Actuators A 172 (2011) 523– 532

Moreover, the experimentally achieved drive and sense modefrequency responses clearly show a rapid rise in the ampli-tude at resonant frequencies. This nonlinear behavior at resonantpoint strongly suggests spring softening type nonlinearity mainlyinduced by the large electrostatic force generated due to applied dcbias voltage.

Fabrication imperfections also affect the geometry of MEMSdevices. In surface micromachined gyroscopes, thin film depositionprocess determines the thickness of the structural layer includ-ing its suspension elements, whereas etching process affects itswidth. Lateral over-etching often causes variation in the width andcross section of the suspension beams in micromachined devices.Residual stress with small magnitudes can cause undesirable defor-mation of suspended micromachined structures. These parametricvariations affect the dynamic response of micromachined gyro-scopes causing differences in the simulated and tested results.

6. Conclusion

A 3-DoF non-resonant microgyroscope design concept withstructurally decoupled 2-DoF drive-mode and 1-DoF sense-modeoscillator was presented. The prototype of the proposed designwas fabricated using a low cost standard fabrication process Metal-MUMPs to obtain large actuation force along with reduced devicesize to 2.2 mm × 2.6 mm. In drive-mode frequency response, a widebandwidth of 1.4 kHz is experimentally demonstrated having tworesonant peaks at 754 Hz and 2.170 kHz. The passive mass achieveda dynamic amplification of 3 times at first resonant frequency and 9times at second resonant frequency in comparison with the activemass. The resonant frequency of the 1-DoF sense-mode oscillatorwas experimentally observed at 1.868 kHz and found overlappingthe flat region of 1.4 kHz without any feedback control allowingthe robust, more stable and wide bandwidth operational device.Improved damping models extraction using behavioral modeling inCoventorWare is also presented which show excellent estimationof amplitude response which is very close to experimental values.

Acknowledgements

This research work was supported by Higher EducationCommission (HEC) of Pakistan and National ICT Fund, Min-istry of Information Technology of Pakistan through grant No.ICTRDF/TRED/2008/02. The authors would like to thank Prof.Michael Kraft at Southampton University, UK for his help duringdevice characterization using MSA-400 in his lab and Canon Foun-dation for Scientific Research (CFSR), UK for their financial supportthe visit of Dr. Rana I. Shakoor to Southampton University, UK fordevice characterization.

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