Improving the Sensitivity and Bandwidth of In-Plane Capacitive Microaccelerometers Using Compliant Mechanical Amplifiers

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 23, NO. 4, AUGUST 2014 871

Improving the Sensitivity and Bandwidth ofIn-Plane Capacitive MicroaccelerometersUsing Compliant Mechanical Amplifiers

Sambuddha Khan, Student Member, IEEE, and G. K. Ananthasuresh

Abstract— This paper presents a method to enhance boththe sensitivity and bandwidth of in-plane capacitive microma-chined accelerometers by using compliant mechanical amplifiers,and thus obviating the compromise between the sensitivityand bandwidth. Here, we compare one of the most sensitivesingle-axis capacitive accelerometers and another with largeresonant frequency reported in the literature with the modifieddesigns that include displacement-amplifying compliant mecha-nisms (DaCMs) occupying the same footprint and under identicalconditions. We show that 62% improvement in sensitivity and34% improvement in bandwidth in the former, and 27% and25% in the latter can be achieved. Also presented here is a dual-axis accelerometer that uses a suspension that decouples andamplifies the displacements along the two in-plane orthogonalaxes. The new design was microfabricated, packaged, and tested.The device is 25-µm thick with the interfinger gap as large as4 µm. Despite the simplicity of the microfabrication process, themeasured axial sensitivity (static) of about 0.58 V/g for both theaxes was achieved with a cross-axis sensitivity of less than ±2%.The measured natural frequency along the two in-plane axes was920 Hz. Displacement amplification of 6.2 was obtained using theDaCMs in the dual-axis accelerometer. [2013-0083]

Index Terms— Compliant mechanism, displacement amplifica-tion, DaCM, dual-axis micromachined accelerometer, sensitivityenhancement.

I. INTRODUCTION

M ICROMACHINED accelerometers are increasinglyused in many applications because of their success-

ful miniaturization and cost-effective batch-fabrication. Someapplications such as inertial navigation, tilt-control in space-craft, surveillance, oil exploration, and earthquake detection,etc., require high sensitivity and low noise-floor. Some appli-cations also require large bandwidth, which requires high res-onance frequency and low damping. Simultaneously achievinghigh sensitivity and resonance frequency is difficult becausethere is inherent tradeoff between the two. Mechanical ampli-fication of the displacement helps to some extent in reducingthis compromise, as shown in this paper.

Manuscript received March 26, 2013; revised November 15, 2013; acceptedDecember 27, 2013. Date of publication February 7, 2014; date of currentversion July 29, 2014. This work was supported in part by the Indian SpaceResearch Organization, and in part by the Naval Physical and OceanographicLaboratory. Subject Editor A. M. Shkel.

The authors are with the Department of Mechanical Engineer-ing, Indian Institute of Science, Bangalore 560012, India (e-mail:[email protected]; [email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JMEMS.2014.2300231

Fig. 1. A Displacement-amplifying Compliant Mechanism (DaCM) inte-grated to the proof-mass of an accelerometer. A sense-comb is attached atthe output end of the DaCM whereas the input end, which hardly moves, isattached to the proof-mass.

Several techniques were developed in the last two decadesto address the need for high sensitivity. Some that use tun-neling current [1]–[7] or laser interferometry [8]–[10] are notsuitable for lightweight and portable applications. Among therelatively simple transduction principles, capacitive [11]–[19],piezoelectric [20], [21], piezoresistive [22]–[26], and reso-nant [27]–[30] techniques are dominant. The capacitive typeis reported in the literature with some of the most highlysensitive accelerometers [11]–[19]. They use either high-precision custom-made interface electronics (e.g., [19]) or verydemanding micromachining processes (e.g., [11]–[14], [17],and [18]). In this paper, we present a mechanical displacement-amplifying technique that can be used to improve the sensi-tivity further, by design.

A mechanical amplifier can be as simple as a lever [19],[29], [30] or as elaborate as a Displacement-amplifying Com-pliant Mechanism (DaCM) [31] shown in Fig. 1. The input ofthe DaCM is attached to the proof-mass. As can be seen inFig. 1, a sense-comb is attached at the output of the DaCMwhere the displacement is significantly more than that at theproof-mass. The ratio of the output and input displacementsof a DaCM is called its geometric advantage (GA). Since aDaCM is indeed a lever at the abstract level, their comparisonis pertinent.

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872 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 23, NO. 4, AUGUST 2014

Fig. 2. The lumped model of an accelerometer with a compliant lever thatuses a small-length flexural pivot reported in [19].

Shown in Fig. 2 is the main component of a compliant leverused in [19] for amplification of the displacement as well asto serve as the suspension for the proof-mass. It uses a small-length flexure pivot [32], which can be modeled as a hingedlever with a torsional spring of spring-constant κ in series witha linear spring with spring-constant ka . The deformation of thewide lever arm is neglected as it is shown in [19] to have littleinfluence. The two spring-constants are given by

ka = E A

L(1a)

κ = E I

L(1b)

where L is the length of the pivot, A = tw is the area ofcross-section of the pivot, and I = tw3/12 is the moment ofinertia with w denoting the in-plane width and t the thicknessof the beam; and E is the Young’s modulus. As per Fig. 2,the displacement uout of the sense-comb (denoted with alumped quantity msc) due to the inertial force experienced bythe proof-mass (denoted with m pm) and msc due to appliedacceleration a, can be computed as

uout =(m pm + msc

)a

ka+

li lo

(m pm + lo

limsc

)a

κ. (2)

It is clear from Eq. 1(a)–(b) that ka and κ are large when Lis small, as will be the case with small-length flexural pivots.Then, the absolute displacement of the sense-comb (i.e., uout)will be small. Additionally, as per the second term on the righthand side of Eq. 2, if the lever ratio (lo/ li in Fig. 2) is largerthan unity, uout will not be at its maximum; indeed, uout willbe the largest when li = lo. This means that the proof-massand the sense-comb should be combined and kept towards theother end of the lever, i.e., farthest from the flexural pivot, forgetting the largest value of uout . It must be noted that thisargument is valid under static conditions only; displacementunder dynamic conditions can be analyzed in a similar manner.

Further improvement in uout is possible if the lever arm ismade sufficiently narrow instead of using the flexural pivot,within the same footprint. Two possible drawbacks of this arethat the out-of-plane stiffness and the resonance frequencywill be reduced as compared to those with the lever based

on the flexural pivot. One way to alleviate this is to decreasethe size of the proof-mass. But reduced proof-mass decreasesthe inertial force and in turn decreases the displacementat the sense-comb, and hence the sensitivity too. Instead ofthis, the space relieved by decreasing the size of the proof-mass can be utilized to append a DaCM so that substantiallyamplified displacement at the sense-comb is obtained. Thedesign of the DaCM should be such that the out-of-plane stiff-ness and the resonance frequency are not hampered. DaCMsare also used in actuator applications for increasing the stroke[33], [34].

A. How Effective Can a DaCM Be?

In order to substantiate the benefits of a DaCM, wefirst compare the results presented in this paper with otheraccelerometers that do not use DaCMs. Table I compares afew of the most sensitive in-plane capacitive accelerometersreported in the literature with the ones presented in thispaper. The accelerometers in Table I are arranged in the orderof increasing sensitivity (change in output voltage per unitapplied acceleration due to gravity, i.e., �V /g). Except the lasttwo rows (which show simulated results), all others contain themeasured sensitivities. It may be noted that sensitivity dependsnot only on the mechanical element but also on capacitivecomb design and electronic circuitry. Since the focus of thispaper is only mechanical design, we include a figure ofmerit (FoM) in Table I that combines static deflection of thesense-comb per unit g acceleration (u/g) and the resonancefrequency ( f in Hz and ω in rad/s).

FoM =(

u

g

)f 2 = 4π2

(u

g

)ω2. (3)

It is a non-dimensional number that is suitable for comparingsensors of different sizes.

Very small sense-gaps (1.3 μm and 1.2 μm) and thick(60 μm and 500 μm) proof-masses are used in [16] and[14] to achieve moderate sensitivity and resonant frequency.So, their FoM is low. By using a stiff suspension in a smallfootprint with a sense-gap of 2.3 μm, reference [15] reportedhigh resonance frequency (1.6 kHz) and good sensitivity. Buthigh stiffness leads to small deflection and hence, it has lowFoM. The high voltage sensitivity of [19] is mainly due to veryhigh circuit gain (22 V/pF) of the interface electronics eventhough its change in capacitance per unit applied gravitationacceleration (g = 9.81 m/s2) is comparatively low. Therefore,despite its high resonance frequency, it has low FoM. On theother hand, [18] has the highest sensitivity, which is due tothe thick structural layer of 100 μm and an additional largeproof-mass of 400 μm thick. But its resonance frequency islow. So, its FoM is not very high.

By juxtaposing the measured performance of the DaCM-aided dual-axis accelerometer presented in this paper withthe others in Table I, we note that the sizes, sensitivity, andresonance frequency compare well (0.58 V/g sensitivity and920 Hz resonant frequency). The remarkable improvement inFoM of the ones using DaCMs can be noticed in Table I.This is a direct consequence of overcoming the inherent

KHAN AND ANANTHASURESH: IMPROVING THE SENSITIVITY AND BANDWIDTH OF IN-PLANE CAPACITIVE MICROACCELEROMETERS 873

TABLE I

SENSITIVITY COMPARISON OF THE CAPACITIVE IN-PLANE ACCELEROMETERS FROM THE LITERATURE

tradeoff between mechanical sensitivity (i.e., sense-comb dis-placement) and the resonance frequency.

It should be noted that we used a comparatively less aggres-sive multi-user process (namely SOIMUMPs [35]) with a rel-atively large sense-gap of 4 μm and thickness of only 25 μm(the lowest among all); and interfaced with commerciallyavailable capacitance extraction chips (MS3110 from IrvineSensors Corp. [36]) of low circuit gain of 2 V/pF in compari-son to others. While the fabricated and packaged design withDaCMs (i.e., the third in Table I under experimental results)shows comparable performance due to the stated reasons of aless aggressive process, the simulated results of two designsshown in Table I show superior performance. The last but onerow in Table I shows that under identical conditions (includingthe footprint and circuit gain), the sensitivity of [18] canbe surpassed by using a DaCM. It may be noted that thesensitivity of [18] can be increased by 60% and resonancefrequency by 34%. Likewise, the accelerometer of [15] withthe largest resonance frequency can also be improved, againunder identical conditions with a DaCM, with 25% increasein resonance frequency and 27% in the sensitivity.

Based on the foregoing, we can conclude that by properdesign of DaCMs, the performance of an existing accelerom-eter can be improved in terms of sensitivity and reso-nance frequency (and hence the bandwidth). If either ofthese two performance characteristics is considered to bemore dominant than the other, one can expect to achieve

significant enhancement of one without overly compromisingon the other by using a DaCM as compared to without it. FoMin Eq. (17) helps in deciding this tradeoff.

B. Organization of the Paper

In Section II, we describe how a DaCM should be appendedto an accelerometer and then we present a lumped model ofthe DaCM that is used to design it as per the specificationsof the accelerometer. Two design case-studies pertaining tothe last two rows of Table I are presented in Section III.These two are single-axis accelerometers. Section IV containsthe details of the dual-axis accelerometer shown in the thirdrow of the experimental part of Table I. A distinguishingfeature of this is that it has a novel two-axis suspensionwhose axes are decoupled while combining two DaCMs fordisplacement-amplification. Its design, fabrication, die-levelcharacterization, packaging, testing, and calibration are pre-sented. Concluding remarks are in the last section.

II. DESIGN OF AN ACCELEROMETER WITH A DACM

The sensitivity of a capacitive accelerometer with differ-ential capacitor arrangement is linearly proportional to thedisplacement of the sense-comb, u:

�V

g= K

(�C

g

)= K

(2uCbase

gd0

)(4)


Fig. 3. Schematic of an accelerometer with a DaCM. The sense-comb areattached at the output side of the DaCM whereas the proof-mass is connectedat the input side of the DaCM.

where �V/g denotes the change in the output voltage per unitacceleration due to gravity g, K the gain of the electroniccircuit measured as V/pF, �C the change in capacitance,Cbase is the base capacitance, and d0 the gap betweenthe successive fingers of the sensing comb. Cbase and d0(i.e., how many fingers can be packed how narrowly intothe available space) are restricted by the capabilities of themicrofabrication process and the desired damping and indi-rectly by the natural frequency. The gain in the electronicinterface decides K . This leaves u for improving the sen-sitivity by suitably designing the mechanical sensing ele-ment of an accelerometer. DaCM helps increase the valueof u.

A. DaCM in an Accelerometer

The schematic of an in-plane capacitive accelerometer witha DaCM is shown in Fig. 3. It has a proof-mass along with itsmechanical suspension and electrostatic combs. The combsattached to the proof-mass are useful in testing the device atthe die-level through electrostatic actuation. They can also beused for feedback in closed-loop operation. Usually, the sense-comb is also appended to the proof-mass. However, here, asshown in Fig. 3, we use a DaCM that is attached to the proof-mass on one side and sensing-comb on the other side. Thepurpose of the DaCM is to amplify the displacement of theproof-mass (called the input side of the DaCM) and provideamplified displacement of the sensing comb (called the outputside of the DaCM). This amplification contributes to enhancedsensitivity. It may be noted that the sense-comb needs to havesufficient number of fingers in differential capacitive arrange-ment and hence has considerable mass. Therefore, it needs itsown suspension to prevent its swaying due to cross-axis accel-eration. This suspension, called the “external suspension”, isto be designed to have high cross-axis stiffness but very lowstiffness along the intended direction. The symbols indicatedin Fig. 3 refer to the lumped model of the device discussednext.

Fig. 4. (a) Lumped Spring-Mass-Lever (SML) model of an accelerometerwith an inverting DaCM, (b) Lumped model of a conventional accelerometerwith proof-mass and suspension.

B. Lumped Model of an Accelerometer With a DaCM

A two degrees-of-freedom (dof) lumped spring-mass-lever(SML) [37] model of an accelerometer with a DaCM isshown in Fig. 4(a). The five lumped parameters pertainingto the DaCM, shown in the region enclosed with dashed redlines, capture its essential static and dynamic behavior. Theparameters kci and kco denote the stiffness of the DaCM onits input and output sides, respectively. Likewise, mci andmco denote the inertia felt on the input and output sides. Theinherent geometric advantage between the input and outputsides is denoted by n.

Also shown in Fig. 4(a) are the lumped parameters per-taining to the proof-mass (m pm) and its suspension (ks) aswell as the mass of the sense-comb (msc) and its suspension(kext). This should be contrasted with the lumped model of anaccelerometer without a DaCM, which is shown in Fig. 4(b).Here, k ′

s denotes the stiffness of the suspension and m′pm the

combined mass of the proof-mass and the sensing combs.Let us assume that the physical forms corresponding to

the two lumped models in Fig. 4(a) and (b) occupy thesame footprint on the chip and have the same minimumand maximum feature sizes of a microfabrication process.Fair comparison of the two is to be done by comparing thedisplacements of the sense-comb in the two cases and not justthe inherent amplification, n, which can be as large as 100 ormore. In the case of the one without a DaCM [Fig. 4(b)], thedisplacement of the sensing comb is the same as that of theproof-mass. Its steady-state value under applied accelerationa is given by

u′out = m′

pma/k ′s (5)

The case in Fig. 4(a) leads to the following expression for thesteady-state displacement of the sense-comb under the sameacceleration:

uout =(nkcom pm + msckci + mscks + n2msckco

)a

(kcokci + kcoks + kextkci + kext ks + n2kextkco

) (6)


The preceding equation is derived by writing the static equi-librium equations of the two-degree-of-freedom model inFig. 4(a) with Fin = m pm + mci a and Fout = mco + msca.Now, the net amplification (N A) between the two casesgiven by

N A = uout

u′out

=(nkcom pm + msckci + mscka + n2msckco

)k ′

s(kcokci +kcoks +kextkci +kextks +n2kextkco

)m′

pm(7)

is independent of the applied acceleration. It is this netamplification that should be made as large as possible to showthe effectiveness of a DaCM in increasing the sensitivity overthe case that does not use a DaCM. As can be seen in Eq. 5,it depends on all five lumped parameters of the DaCM as wellas those of the proof-mass, mass of the sense-comb, and theirsuspensions.

Another important consideration is the fundamental (i.e.,the lowest) resonant frequency of the model in Fig. 4(a). Bywriting the equation governing the free vibration of the lumpedsystem in Fig. 4(a), an analytical formula for the fundamentalresonance frequency can be obtained as [37]

f0 = 1

2√

2π

√

(α + β) −√(

(α − β)2 + γ)

(8)

where

α =(kci + ks + n2kco

)

(mci + m pm

)

β = (kco + kext )

(mco + msc)

γ = 4n2k2co(

mci + m pm)(mco + msc)

The frequency given by Eq. 8 using the lumped model isshown to be a good estimate of that of the complete modelcomputed using the modal analysis of the complete finiteelement model [37] of the system.

Before explaining how a DaCM is designed as per thespecifications on the sensitivity and resonance frequency, it ispertinent to explain how the lumped parameters are computedusing the complete model.

C. Computing the Lumped Parameters

In order to find the strain energy and the kinetic energyof the entire system, these lumped parameters are to beextracted properly. The four lumped parameters ka, ma, kext

and mext can easily be found using standard Finite Element(FE) analysis. The method to determine the other five lumpedparameters i.e. kci , kco, mci , mco, and n of a DaCM [37], [38],used in the accelerometer, is described next. Finding the valuesof these lumped parameters of a DaCM is neither a standaloneanalytical technique nor a complete FE analysis; it is a methodwhere both of them are utilized simultaneously.

Let the two-dof shown in the Fig. 2(a) are uin and uout ,which are the displacements corresponding to the forces Fin

and Fout acting at the input and output side of the DaCM.

The values of Kci and Kco can be found by applying staticequilibrium condition to this two-dof SML model using theequations

kci = Fin − ksuin − n (kextuout − Fout )

uin(9)

kco = (kext uout − Fout )

nuin − uout(10)

Equations (9) and (10) can be used to find the stiffnessparameters of the DaCM with the help of two simple FEanalysis runs of the meshed model of only the DaCM withtwo different load conditions. In the first load condition, uin

is found by applying a known value of Fin at the input side ofthe DaCM while keeping Fout = 0. Similarly, in the secondload condition, uout is found by applying a known value ofFout at the output side of the DaCM while keeping Fin = 0.The values of ks and Kest are zero in these two load conditionsas the analysis considers only the DaCM.

Extraction of mci and mco also requires the same two staticFE analysis with two different load conditions as used todetermine Kci and Kco. Here, we make use of all the dofsof the meshed FE model. The lumped masses of the DaCM,mci and mco, can be found by equating the kinetic energies ofthe SML model and those of the FE model under two differentload conditions.

1

2mci u

2in1 + 1

2mcou2

out1 = ρ

2

N∑

i=1

U21ivi (11)

1

2mci u

2in2 + 1

2mcou2

out2 = ρ

2

N∑

i=1

U22ivi (12)

where, U1 and U2 are the displacement vectors of all the dofsof the FE meshed model for two different load conditions, vi

is the volume of the i th finite element and ρ is the density ofthe material used for fabrication of the accelerometer with theDaCM. The quantities uin1 and uout1 are the input and outputside displacements of the DaCM in the first load conditionwhereas uin2 and uout2 are for the second load condition. Theparameters mci and mco can be found out by solving Eqs. (11)and (12). The value of n can be found by taking the ratio ofthe output side displacement to the input side displacement inthe first load condition, i.e., n = uout1/uin1.

In order to achieve N A > 1 for a given values ofka, ma, m′

a, kext , and mext , a selection map-based method isused to design a stiffness-matched DaCM with optimal valuesof kci , kco and n.

D. Designing a Stiffness-Matched DaCM

Many working prototypes of DaCMs have been synthesizedand are reported in the literature [39]–[46]. A catalog has beencreated with quantitative details of these mechanisms. Most ofthem are designed using topology optimization [40], [43]–[46]as well as size and shape optimization [42] for piezoelectricand electrostatic actuation. In this paper, we do not design anew DaCM using an optimization method. Instead, we select aDaCM from the database and re-design it using interactive sizeand shape optimization for stiffness-matching. This method


uses a pragmatic design approach based on selection maps[37], [38]. An online version of this method is available athttp://www.mecheng.iisc.ernet.in~m2d2 CMdesign.

The selection map-based method allows the user to providethe user-specifications within bounds around their nominalvalues. This leads to a set of inequalities that bound the valuesfrom above and below:

FinL ≤ Fin ≤ FinH

uinL ≤ uin ≤ uinH

Fout L ≤ Fout ≤ Fout H

uout L ≤ uout ≤ uout H

ks L ≤ ks ≤ ks H

kext L ≤ kext ≤ kext H (13)

These inequalities are solved along with the equilibriumequations from SML model given in Eqs. (9) and (10) toget several continuous sets of the feasible values of kci , kco

and n. Using these values, the kco vs. kci map or the stiffnessmap is drawn. It should be noted that this map is a projectionof a feasible volume in the 3D space of kci -kco-n onto the2D space of kci − kco. Therefore, for every point inside thefeasible map there is a corresponding valid range for n. Onthe same map, the kci , kco, and n values of existing DaCMsare computed and plotted as individual points. If any point lieswithin the feasible map and the n value of the correspondingmechanism matches, then that particular DaCM satisfies theuser-specification. If any mechanism that does not lie insidethe feasible map, then that mechanism can be interactivelyoptimized and re-designed to bring that mechanism inside thefeasible map. To re-design the mechanism, the in-plane widthof the beams of the mechanism, the out-of-plane thicknessof the mechanism, the size of the mechanism along the twoin-plane directions can be varied. The procedure for solvingthe inequalities and equations is implemented in an interactiveprogram written in MATLAB. A complete example of re-designing a DaCM, using the selection map-based method isdiscussed in the next section.

III. CASE STUDIES

Development of high-sensitive and high-resolution capac-itive in-plane micromachined accelerometers with micro-fabrication constraints is the main challenge faced by theresearchers in this field. Development of highly-sensitive andhigh-resolution in-plane accelerometers requires high-aspect-ratio vertical electrodes with very small sense-gap as reportedin [13] and [18]. They both require sophisticated and henceexpensive microfabrication processes.

Here, two case studies were presented to show that improvedperformance can be achieved by incorporating DaCMs withexisting accelerometers. By performance, we mean the staticdisplacement sensitivity (i.e. the displacement of the sense-comb per unit applied acceleration due to gravity) and the reso-nance frequency of the device. Static displacement sensitivityis directly proportional to the static capacitance sensitivity,i.e., the change in capacitance per unit acceleration due to

Fig. 5. The solid models of an accelerometer with thick proof-mass developedby [18].

gravity. The two case studies were performed by two com-parisons that were made with the accelerometers reported in[18] and [15] with their modified versions containing smallerproof-masses and DaCMs. The incorporation of a DaCM doesnot require any extra microfabrication process step. It can befabricated along with the other parts of the accelerometer. But,it consumes extra space in the silicon wafer which is also anexpensive factor in microfabrication processes. Hence, to havefair case studies, the footprints of the modified designs werekept the same as that of the reported ones.

A. An In-Plane Capacitive Accelerometer byAbdolvand et al. 2007 [18]

In the reported design of the single-axis in-plane capacitiveaccelerometer in [18], the overall size of the accelerometer is7 mm × 7 mm with a top-side proof-mass as big as 5 mm ×7 mm shown in Fig. 5. The accelerometer was fabricated usinga silicon-on-insulator (SOI) wafer with 100 μm thick structuralsilicon layer. By backside Deep Reactive Ion Etching (DRIE)and Inductively Coupled Plasma (ICP) oxide etch; a part ofthe 400 μm thick substrate layer that is beneath the top-sideproof-mass was used as extra proof-mass. The size of thisadded proof-mass is 4.7 mm × 6.7 mm × 400 μm. A pitch of60 μm was used to accommodate 110 sense-comb on each sideof the accelerometer proof-mass. An initial sense-gap of 9 μm,between the dynamic comb and the static comb, was narroweddown to 4 - 5 μm by adding an extra process step of sidewalldeposition of polysilicon. The detailed design specification ofthe accelerometer is given in the second column of Table II.

The static FE analysis using COMSOL Multiphysics [47]shows that the static displacement sensitivity of the accelerom-eter is approximately 6.5 μm/g which corresponds to a staticcapacitance sensitivity of more than 30 pF/g. The effect ofgeometric nonlinearity was considered in all the FE simula-tions performed in this paper. The first mode of vibration wasfound to be an in-plane motion with a frequency of 195 Hzwhereas the second mode is an out-of-plane mode at 1900 Hz,which is much higher than the operational bandwidth of thedevice.

The effective in-plane stiffness (k ′s) of the accelerometer

is reported as approximately 58 N/m whereas the effectiveinertia (m′

s) of the accelerometer is given as approximately


TABLE II

COMPARISON BETWEEN THE EXISTING ACCELEROMETERS WITH THE MODIFIED DESIGNS USING DaCMS

Fig. 6. First two simulated modes of vibration of the accelerometer developedby Abdolvand et. al. 2007 [18].

38 × 10−6 kg. The simulated first two modes of vibration ofthe accelerometer are shown in Fig. 6.

B. Modified Design of [18] Using a DaCM

In comparison to the accelerometer reported in [18], wepropose a modified design of an accelerometer containing aDaCM and with an equal footprint area of 7 mm × 7 mm. Themodified design contains a smaller proof-mass of 3.9 mm ×5 mm, a properly selected and re-designed DaCM and a set ofcapacitive combs attached at the output port of the DaCM. Thethickness of the DaCM, combs and suspensions are consideredto be 100 μm as used in the design in [18]. The proof-mass inthe modified design is smaller but the thickness was consideredas 500 μm (i.e. 100 μm of structural layer + 400 μm thicksubstrate layer of the SOI wafer).

The selection and re-design of the DaCM used for thismodified model is performed using the stiffness map- basedmethod discussed in Section II.D. For this, the lumped mass(ms) and stiffness (ks) values of the input side of the

modified accelerometer model are simulated using FE analysisas 20.8 × 10−6 kg and 58 N/m respectively. The lumpedmass (mext ) and stiffness (kext) values of the output side ofthe same model are also simulated as 0.4 × 10−6 kg and0.3261 N/m respectively. We used these values as the inputuser-specifications to the method to arrive at the inequalities:

190 μN ≤ Fin ≤ 210 μN

2 μm ≤ uin ≤ 3 μm

3μN ≤ Fout ≤ 4 μN

7 μm ≤ uout ≤ 11 μm

50 N/m ≤ ks ≤ 70 N/m

0.3 N/m ≤ kext ≤ 0.4 N/m (14)

These values are used to draw the feasible kco vs. kci

map shown in Fig. 7. It can be observed that none of themechanisms from the literature lie inside this feasible map.Therefore, the first closest mechanism taken from [34] ischosen for re-designing. The initial position of the DaCM withits current feature size is shown as a point on the graph. Byvarying the dimensional parameters, such as in-plane beamwidth, thickness, size of the mechanism along X and Y axes,a few parameter curves are drawn. It is observed that a feasibledesign of the mechanism is possible by moving along theparameter curves. The optimal design of the DaCM is attainedas shown in Fig. 8 with in-plane beam width of 6.5 μm,thickness 100 μm and size of the DaCM along X and Yas 6.9 mm and 0.758 mm respectively. It can also be notedthat the value of n of the modified mechanism lies withinits maximum and minimum value as shown in Fig. 8. Theoptimal design of the DaCM has the values of kci and kco

as 31.06 N/m and 18.23 N/m respectively. The values of mci

and mco for the mechanism are found to be 0.124 × 10−6 Kgand 0.1 × 10−8 kg respectively using Eqs. (10) and (11)respectively.

The isometric view of the modified accelerometer alongwith the re-designed DaCM are shown in Fig. 9(a) and (b).The first in-plane modal frequency of the modified design canbe analytically estimated using Eq. 7 as 265 Hz whereas thestatic displacement sensitivity of the model is calculated as10.39 μm/g using the Eq. 5. By using Eq. 6, the value of NAis found to be 1.62 approximately.

The static FE analysis is also performed on the solid 3Dmodel of the modified design of the accelerometer. It shows


Fig. 7. The graphical user interface (GUI) for the selection map based method describing the re-design of an existing DaCM from [34] using parametercurves. The initial position of the DaCM to be used with the current feature size is shown as a point on the graph. The area enclosed by a green curve showsthe feasible stiffness map for the given specification. The parameter curves are drawn from the initial position of the mechanism shows that the selectedmechanism can be brought inside the feasible stiffness map by varying the parameters e.g. in-plane beam width, thickness, size of the mechanism along Xand Y of the mechanism.

Fig. 8. Re-design of the DaCM by varying the parameters along the parametercurves to achieve feasible kci , kco, and n values for the mechanism.

that the static displacement sensitivity of the sense-combof the accelerometer is 10.51 μm/g with the first in-planenatural frequency at 267 Hz. The simulated value of NAis found to be 1.6. This validates the effectiveness of thelumped SML model. The modal responses of the modifieddesign are shown in Fig. 10.

The static FE analysis is also performed on the solid 3Dmodel of the modified design of the accelerometer. It showsthat the static displacement sensitivity of the sense-comb ofthe accelerometer is 10.51 μm/g with the first in-plane modalfrequency at 267 Hz. The simulated value of NA is foundto be 1.6. This validates the effectiveness of the lumped SMLmodel. The modal responses of the modified design are shownin Fig. 10.

Fig. 9. (a) The design of the DaCM used in the modified design of [18], and(b) Solid model of the modified design of [18] with a smaller proof-mass, astiffness matched DaCM occupying an area of 7 mm × 7 mm.

The analysis confirms that, by design, we have achieved asensitivity enhancement of 60% as compared to the reporteddesign in [18]. By design, an improvement of the resonanceby approximately 34% is also achieved. The detailed simu-lated performance specifications for the modified single-axisaccelerometer with a DaCM are given in the third column ofTable II.


Fig. 10. First five modes of vibration of the modified version of a similaraccelerometer with a DaCM and with equal footprint.

Fig. 11. (a) The design of the SOI accelerometer reported in [15], (b) Thefirst two modes of the accelerometer reported in [15].

C. In-Plane SOI Accelerometer by Amini 2006 [15]

The accelerometer reported by Amini [15] is a micro-gravitysingle-axis capacitive accelerometer with overall device size of5 mm × 6 mm. The device contains a proof-mass as big as2 mm × 6 mm with 90 sensing electrodes along each

Fig. 12. (a) The modified design of [15] using a DaCM, and (b) The designof the DaCM used in modified design of [15].

side of the accelerometer. The weight of the proof-masswas 1.6 mg as the device was fabricated using SOI waferswith structural layer thickness of 50 μm. The pitch betweentwo sense-comb was kept as 60 μm with a sense-gapof 2.3 μm. The base capacitance of the sense-comb was7.5 pF with a static capacitance sensitivity of 0.8 pF/g anda voltage sensitivity of 0.8 V/g. The corresponding staticdisplacement sensitivity was simulated to be 0.102 μm/g.The first natural frequency of the device was found to bearound 1.6 kHz. Fig. 11(a) shows the detailed dimensionsof the device. The first two modal frequencies are shownin Fig. 11(b).

D. Modified Accelerometer by [15] Using a DaCM

The same stiffness map-based method that is used to designthe DaCM for the improved version of [15] is used herealso. The specifications for the selection-based method are asfollows:

8 μN ≤ Fin ≤ 12 μN

40 nm ≤ uin ≤ 3 μm

0.1 μN ≤ Fout ≤ 0.2 μN

0.125 μm ≤ uout ≤ 0.225 μm

240 N/m ≤ ks ≤ 260 N/m

0.1 N/m ≤ kext ≤ 0.2 N/m (15)

The bounds were chosen as per the design of [15]and the anticipated enhancement in the modified design.The feasible stiffness map was drawn and a suitable


Fig. 13. The first five modes of vibration of the modified design of [15]using a stiffness matched DaCM.

mechanism was selected and interactively designed. Thedetails are not presented for the sake of brevity.

The values of the re-designed DaCM are: kci = 151.8 N/m,kco = 106.5 N/m, n = −6.08, mci = 1.88311 × 10−8 kg,and mco = 1.61055 × 10−9 kg. It has static displacementsensitivity of 0.127 μm/g, NA = 1.27, effective in-planestiffness = 320.6 N/m and effective mass = 1.07 mg, andresonance frequency of 1947 Hz. The detailed design of themodified accelerometer and the re-designed DaCM are shownin Fig. 12(a) and (b). The first five simulated modes of themodified design are shown in Fig. 13.

As can be seen in the fourth and fifth columns of Table II,the sensitivity of [15] is enhanced from 0.102 μm/g to0.127 μm/g, by 25%. At the same time, the first resonancefrequency too went up from 1556 Hz to 1947 Hz, by 25%.

Based on the two case-studies and our general under-standing of DaCMs, we claim that the sensitivity of anydisplacement-based conventional accelerometers with a proof-mass and sensing mechanism could be improved by designingand incorporating a properly designed DaCM within the samefootprint area and without compromising the bandwidth of thedevice. This also indicates that, for a given microfabricationprocess, the sensitivity of any capacitive accelerometers canbe enhanced by using a DaCM instead of increasing the sizeof the proof-mass. If the natural frequency were not consid-ered as a design constraint or if the natural frequency werekept the same, further improvement in sensitivity is possible.In addition to these two case studies that show the advantageof using a DaCM in a single-axis in-plane accelerometer, wealso present a dual-axis in-plane capacitive accelerometer with

Fig. 14. (a) A schematic showing two independent actuations of the Proof-mass using the XY flexure mechanism, (b) A parallel arrangement of an XYStage.

two DaCMs. This was fabricated, characterized, packaged andtested to prove the functionality of DaCMs in a micromachinedaccelerometer.

IV. A DUAL-AXIS ACCELEROMETER WITH TWO DaCMS

A dual-axis accelerometer is designed to sense both theorthogonal components of acceleration along any arbitrarydirection in a plane. It requires two independent motions ofthe proof-mass. This can be achieved by designing a suitablemechanism that is capable of de-coupling one axis from theother.

A. Mechanical Design of the Accelerometer

De-coupling can be obtained by arranging four sliding jointsas shown in Fig. 14(a). The arrangement works perfectly ifthe design of the sliding joints offers zero axial stiffness andinfinite cross-axial stiffness but this is not so in practice. Thedesign shown in Fig. 14(b) uses the compliant equivalentsof sliding joints to obtain de-coupling among the axes [48].The design has symmetry with eight folded-beam suspensionsreplacing the sliding joints in a monolithic compliant design.This arrangement is used for creating a compliant XY stage.The arrangement provides good isolation of the stage (i.e., thestage would move along only one direction when it is actuated)and isolation of the actuator (i.e., when the stage is actuatedin one direction, the location of the other actuator remainsunaffected).

Here, we use the de-coupling mechanism for the purposeof sensing. That is, the stage is used as the proof-masswhose motion is sensed. The folded beam suspensions allowthe proof-mass to move along the direction of the appliedacceleration in the plane of actuation whereas the ports Xand Y move by the respective X and Y components of thedisplacement of the proof-mass in that plane. The actuation ofthe Ports X and X do not undergo any disturbance when thedevice is actuated along the Y direction and vice versa.

For capacitive sensing, we add sense-comb with consider-able mass, which disturbs the perfect de-coupling arrangementof Fig. 14(b) under body-force of acceleration. In particular,sense-comb tends to rotate about the out-of-plane axis war-ranting an additional suspension that limits this rotation. But


Fig. 15. (a) The schematic and (b) the layout of a dual-axis capacitive lateralaccelerometer with a decoupling mechanism and two inverting DaCMs.

the use of this additional folded beam suspension increasesthe in-plane stiffness and thus reduces the in-plane sensitivity.Fig. 15(a) shows the schematic of the sensing element with12 folded-beam suspensions [49] and two inverting DaCMs.This special configuration retains decoupling of the two axeseven after appending the inverting DaCMs, the sense-comb,and the external suspensions at the sensing ports of both axesas opposed to de-coupling layout of the XY stage shown inFig. 14(b). It may be noted that there is a direct correspondencebetween the configuration of the schematic in Fig. 15(a) andthat of the designed device layout in Fig. 15(b). De-couplingensures low cross-axis sensitivity as input in one direction doesnot affect the other.

In addition to achieving de-coupling of the two axes withthe special configuration of Fig. 15(a) and displacementamplification, the inverting DaCM was designed to have lowstiffness along the intended axis and high stiffness along thecross axes. The stiffness-matched inverting DaCM was againobtained using the selection map-based method described inthe Section II.D.

TABLE III

LUMPED PARAMETERS OF THE ACCELEROMETER

TABLE IV

PERFORMANCE SPECIFICATIONS OF THE ACCELEROMETER

The design is symmetric about the X and Y axes. Thethickness of the device of the entire device was kept as 25μm.The minimum feature size is kept as 6 μm and the sense-gapis kept as 4 μm. The total size of the designed accelerometeris 8.5 mm × 8.5 mm along with a proof-mass that is as big as3mm × 3 mm. The design is deliberately conservative becausewe used a multi-user fabrication process.

B. Modeling

The design of the dual-axis accelerometer with two DaCMsin two orthogonal directions can be represented as two identi-cal single-axis accelerometers with DaCM mounted orthogo-nally to each other. Thus, the lumped mass and stiffness valuesof the dual-axis accelerometer will be same along both theaxes. Therefore, the analytical modeling and the FE analysisof the accelerometer along one axis can be used to predict theresponse of the accelerometer in the other axis.

All the lumped parameters of the accelerometer with theDaCMs are found using the selection map-based method asdiscussed in previous sections II.D and III.B. The optimizeddesign of the DaCM used in the accelerometer was foundusing the method. The lumped stiffness and mass values of theaccelerometer including the DaCMs are given in Table III. Theperformance specifications (e.g., static displacement sensitivityand the first in-plane natural frequency) found using analyticalexpressions in Eqs. (5) and (7) and 3D FE analysis usingCOMSOL multiphysics are given in Table IV.

Fig. 16 shows a simulated image where static 1g acceler-ation in the form of a body force is applied along both theX and Y axes. It is worth noticing that the proof-mass movesalong the resultant direction of the applied acceleration butthe outputs of the DaCMs move only along the intended axes.It can also be seen that the DaCMs amplify the displacement


Fig. 16. Simulated image of the device under 1 g body-load along both theaxes. The decoupling mechanism decouples the applied acceleration into itscorresponding axial components and the two DaCMs amplify the displacementof the proof-mass along both the axes.

from their inputs to their outputs by a certain factor but thedirection of the displacement reverses. The first three modes ofvibration of the dual-axis in-plane accelerometer with DaCMssimulated using COMSOL Multiphysics are shown in Fig. 17.The identical values of the first two modal frequencies ensurestructural symmetric along both the axes.

The base capacitance (Cbase) of the sense comb is analyt-ically estimated to be 0.977 pF. Assuming the circuit gain Kas 2 V/pF, the design values of the axial voltage sensitivityof the accelerometer can be found by using the Eq. 3 to be0.572 V/g.

In order to find the NA value, a similar type of a dual-axis accelerometer is designed without any DaCM but theproof-mass size is increased to make the footprint of theaccelerometer the same as the dual-axis accelerometer withDaCMs. The effective in-plane stiffness (k ′

s) and the effectivemass (m′

pm) of this accelerometer design are simulated as23.14 N/m and 0.896 × 10−6 kg respectively. The staticdisplacement sensitivity of the accelerometer without a DaCMis found to be 0.382 μm/g and the first two modal frequenciesare also simulated to be at 808.85 Hz and 808.93 Hz. Theanalytically estimated and FE simulated values of NA arefound to be 1.56 and 1.53 respectively. Thus, the improvementof sensitivity by the use of mechanical amplifiers (DaCMs) canbe estimated as more than 50% along with an enhancementof operational bandwidth by about 25%.

C. Fabrication

The dual-axis accelerometer was fabricated using theSilicon-on-insulator Multi-user MEMS Process (SOIMUMPs)[35]. This process uses Silicon-on-Insulator (SOI) wafer with25 μm thick structural layer, 2 μm buried oxide layer and400 μm substrate layer as shown in Fig. 18. A few opticaland SEM micrographs of the fabricated device are shown inthe Fig. 19(a)–(e).

Fig. 17. First three modes of vibration of the dual-axis accelerometer withDaCMs.

Fig. 18. Cross-section of a typical device fabricated using SOIMUMPs [48]process. The top layer is the 25 μm thick structural silicon layer which isused to pattern the designed devices.

V. DYNAMIC CHARACTERIZATION OF THE DUAL-AXIS

ACCELEROMETER WITH DaCMS

The die-level dynamic measurements were performed onthe fabricated dual-axis accelerometer die using the PMAmodule of POLYTEC MSA 500 Micro System Analyzer. ThePMA module uses stroboscopic video microscopy for in-planemeasurements [50]. The PMA module in the equipment usesLight-emitting Diodes (LED) for imaging and measurementof the lateral displacement. The time response, frequencyresponse, the step response, and the coefficient of dampingof the device were captured optically using the equipmentand analyzed to study the dynamic behavior of the device.It may be noted that applying equivalent electrostatic forceis not exactly the same as what happens when in-planeacceleration is applied on the sensor but this is easy to do in anexperimental setup to capture time and frequency responses.


Fig. 19. (a)–(c) Optical micrographs (top view) of the fabricated dual-axisaccelerometer die, (d)–(e) Tilted SEM images of the device showing parts ofthe DaCM and the sense-comb present in the accelerometer.

A. Time Response

The fabricated device was actuated by applying an alternat-ing voltage (Vac) of 5 V over a DC bias (Vdc) of 5 V on theactuating combs along both the axes separately. The actuationfrequency was set to 100 Hz. The magnitude of displacementsat both the proof-mass and the sense-comb along both theaxes were measured and plotted in Fig. 20. The geometricamplification (n), which is the ratio of the displacement atthe sense-comb attached to the output end of the DaCM tothe displacement at the proof-mass attached at the input endof the DaCM, is measured as −6.24 approximately. A phasedifference of 180° between the proof-mass and sense-combdisplacements confirms that the DaCM is of an inverting typethat reverses the direction of displacement from its output portto input port.

B. In-Plane Frequency Response

The device was actuated electrostatically once again alongboth the axes using an alternating voltage of 3 V over a DC

Fig. 20. Time vs. Displacement plot, captured by Laser Doppler Vibrometer,of the input and output ports of the DaCMs present in the dual-axisaccelerometer along both the axes. The displacement amplification by theDaCMs can be measured by taking ratios of the displacement amplitudes atany time at the output to the input ports of the DaCMs.

bias of 5 V with frequency varying from 10 Hz to 1500 Hz.The amplitudes of the displacement of the sense-comb alongboth X and Y axes at each frequency step were recordedand plotted using a software called Planar Motion Analyzer(PMA) version 2.6. The in-plane frequency responses alongboth the axes of the device is shown in the Fig. 21. Thefrequency response of the input side, i.e., the actuation sidecan also be observed in the figure. Experimentally obtainedin-plane modal frequencies were found to be 920 Hz forthe X-axis and 918Hz for the Y-axis. An average valueof the absolute geometric amplification (|n|) of 6.2 wasextracted from the Bode plot. The phase response in alsogiven in Fig. 21(b). The 3dB bandwidth of the accelerometerwas measured to be approximately 505 Hz for both theaxes.

C. Step Response

Step-response of the fabricated accelerometer was obtainedby actuating the device using a DC voltage of 10 V inthe form of a square pulse along both the axes at thesame time.

As the device is actuated, both the displacement of theproof-mass at the actuation side and the sense-comb at theoutput of the DaCMs along both the axes were capturedoptically and then plotted with respect to time to achieve thestep response of the device shown in Fig. 22.

2πξ√

1 − ξ2= ln

x1

x2(16)

Q = 1/

2ξ (17)

The dynamic behavior of the device was extracted from thestep response of the device by finding the damping ratio ξ ofthe response using Eq. 15 [51]. Where x1 and x2 are the two


Fig. 21. Experimentally obtained Bode plot (Displacement amplitude in (a)and Phase in (b)) of the accelerometer showing the frequency response of thedevice at both the input and output of the DaCMs.

consecutive peaks of the damped oscillation of the sensingside. The measure value of ξ is 0.2118. The measured valueof the time constant of the damped oscillation τd was 1.087ms. The Quality factor Q was also found using Eq. 17 as 2.36.It may also be noted that the damping can be easily measuredfrom the response of the sensing side rather than that of theactuation side as the sensing side moves more than the latterbecause of the presence of the DaCMs.

VI. PACKAGING AND TESTING

A. Packaging

The fabricated accelerometer was packaged along with com-mercially available universal capacitance readout ASIC dieMS3110D [51]. A hybrid die-to-die System-in-Package (SiP)technique was adopted to package the device inside a hybridceramic package. A custom designed Low Temperature Co-fired Ceramic (LTCC) substrate was used as the base for both

Fig. 22. Experimentally obtained step response of the accelerometer capturedusing Laser Doppler Vibrometer to study the dynamic behaviour of the devicealong both the axes.

Fig. 23. (a) LTCC substrate developed for packaging the dual-axis accelerom-eter with DaCMs, (b) Hybrid die-to-die packaging of a dual-axis accelerometerdie along with two MS3110 dies inside a ceramic flat pin package.

the micromachined device and the interface electronic ASICdies shown in Fig. 23(a). Electrical connections are routed byscreen printing of silver paste on LTCC substrate. Conductive


Fig. 24. (a) Experimental setup for static calibration of the packaged dual-axis accelerometer using a turn table. The MS3110 evaluation board wasrequired only at the beginning of the test to program the MS3110 ASICdies. Once programmed, the evaluation board was disconnected while testing.(b) Both the static and dynamic calibration curve for the dual-axis accelerom-eter along the X and Y axes where the sensitivities of the packaged dual-axisaccelerometer can be found from the slope of the calibration curves, and(c) the off-axis sensitivity curve which is obtained by rotating the devicewhile keeping the sensitive axis horizontal.

silver epoxy was used to perform die-to-substrate attachmentsand non-conductive epoxy was used to attach the ceramicsubstrate to the package. All the electrical connections between

the accelerometer die to the capacitance extraction ASIC diesand between the ASIC dies to the contact pads on the LTCCsubstrate were established by performing thermosonic ball-to-wedge gold wire bonding. Fig. 23(b) shows an optical imageof the accelerometer wire-bonded to the capacitance extractionASIC dies. An evaluation board was designed and fabricatedfor testing the packaged accelerometer.

B. Testing and Calibration

Both static and dynamic calibration were performed onthe packaged dual-axis accelerometer. The static calibrationwas performed by mounting the packaged accelerometer ona vertical turn-table while the dynamic calibration was per-formed by mounting the device on vibration shaker. Theexperimental setup showing the packaged device on the turn-table is shown in Fig. 24(a). During the static calibration, theturn-table was rotated precisely to vary the applied accelerationon the device where as the platform of the shaker table wasexcited at 20 Hz for different values of g. Both the open-loop static and dynamic response of the packaged device areshown in Fig. 24(b). The static sensitivity was measured as580 mV/g and 589 mV/g while the dynamic sensitivity wasfound to be 762 mV/g and 778 mV/g for X and Y axesrespectively. The difference between the static and dynamicsensitivities could be because of the presence of the over-shoot in the dynamic response of the accelerometer. It canbe noted that the measured static axial voltage sensitivityclosely matches to the design value of the axial voltagesensitivity (static) which is 572 mV/g for both the axes. Themeasured static and dynamic linearity was found to be wellwithin 2% of the full-scale output (FSO) along both the axes.The cross-axis sensitivity of the packaged accelerometer wasalso measured by mounting the packaged accelerometer suchthat the acceleration due to gravity acts perpendicularly tothe measuring axis. The cross-axis sensitivity of the pack-aged dual-axis accelerometer was measured to be less than±2% of the axial sensitivity for both the axes as shownin Fig. 24(c).

VII. CONCLUSION

Large proof-mass, low stiffness of the suspension, smallinter-finger-gap in capacitive combs, high circuit gain of theinterface electronics, and low damping help enhance the sensi-tivity and resolution of micromachined capacitive accelerom-eters. But large proof-mass and low stiffness decrease theresonance frequency and hence the bandwidth. In this paper,it is shown that mechanical amplification using Displacement-amplifying compliant mechanisms (DaCMs) help increaseboth the sensitivity and resonance frequency. An importantpoint to note is that a DaCM occupies the space relieved bythe reduced proof-mass. Consequently, the overall footprintremains the same as that of the devices without the DaCMs.The fabrication process is also simple.

Two of the best single-axis accelerometers from the lit-erature are used to show that the design method presentedhere enhances their sensitivity and resonance frequency. Themethod uses a selection-based interactive design that begins


with user-specifications and accounts for practical considera-tions such as maximum stress and minimum feature sizes.

A new dual-axis accelerometer that includes two DaCMsis designed, fabricated, integrated with electronics, packagedand tested successfully.

The main conclusions from the work are:(1) An existing capacitive accelerometer can be modified

using DaCM to increase sensitivity and bandwidth withoutincreasing the footprint or changing the process.

(2) A monolithic dual-axis in-plane capacitive accelerom-eter that has good sensitivity and bandwidth is feasible, aspractically demonstrated here.

(3) A systematic and pragmatic selection-based designmethod can be used to design DaCMs. The details beyondwhat are presented here are in [37] and [38].

The future work will focus on the role of damping and noisewhen DaCMs are appended to accelerometers.

ACKNOWLEDGMENT

We are thankful to Centre for materials for electronicstechnology (CMET), Pune for their help in fabricating theLTCC substrates. We are also thankful to Si2 Microsystem,Bangalore for their generous help in packaging and wire-bonding the accelerometers.

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Sambuddha Khan received the B. Tech. degree ininstrumentation engineering from the Haldia Insti-tute of Technology, West Bengal, India, in 2003,and the M.E. degree in biomedical engineering fromJadavpur University, Kolkata, India, in 2005.

He is currently a doctoral student in the IntegratedNanoengineering Ph.D. programme at the IndianInstitute of Science (IISc), Bangalore, India. Hetaught at the Haldia Institute of Technology as aLecturer from 2005 to 2006 and then joined IISc.His research interests include micromachined inertial

sensors, microfabrication and packaging of microsystems, biosensors, andbiomedical instrumentation.

G. K. Ananthasuresh received the B. Tech. degreefrom IIT, Madras, India, in 1989; the M.S. degreefrom the University of Toledo, Toledo, OH, USA, in1991; and the Ph.D. degree from the University ofMichigan, Ann Arbor, MI, USA, in 1994.

He is Professor of Mechanical Engineering atthe Indian Institute of Science, Bangalore, India.His previous positions include Post-Doctoral Asso-ciate at the Massachusetts Institute of Technology,Cambridge, MA, USA; Associate Professor at theUniversity of Pennsylvania, Philadelphia, PA, USA;

and Visiting Professorships at the University of Cambridge, Cambridge, UK,and Katholike Univesiteit, Leuven, Belgium. His current research interestsinclude compliant mechanisms, kinematics, multi-disciplinary design opti-mization, microsystems technology, micro and meso-scale manufacturing,protein design, micromanipulation, and bio-design. He served on the editorialboards of eight journals and is a co-author of 200 papers in journals andconferences, as well as two edited books, one textbook, and 12 book-chapters.He has seven patents; three granted and four pending.

Dr. Ananthasuresh is a recipient of the NSF Career Award and SAE RalphO. Teeter Educational Award in the USA, and the Swarnajayanthi Fellowshipand Shanti Swarup Bhatnagar Prize in India, as well as seven Best Paperawards in international and national conferences.

Documents

Improving the Sensitivity and Bandwidth of In-Plane Capacitive Microaccelerometers Using Compliant Mechanical Amplifiers