ICSE2004 Proc. 2004, Kuala Lumpur, Malaysia

Mechanical Behaviour of a lOg MEMS Non-CrossingDifferential Capacitive Accelerometer

Azrif Manut, Badariah Bais, Member, IEEE and Burhanuddin Yeop Majlis, Senior Member, IEEEInstitute of Microengineering and Nanoelectronics (IMEN)

Universiti Kebangsaan Malaysia43600 Bangi, Selangor, MALAYSIA

Email: badariah(vlsi.eng.ukm.my, burhan(d&v1si.eng.ukm.my

Abstract A MEMS lateral capacitiveaccelerometer was designed and simulated. Theaccelerometer used in the study is based on gap-difference principle. It consists of 74 pairs offingers and the proofmass suspended by twostraight truss springs at both ends. Importantparameters such as displacement, differential IIcapacitance, harmonic response and sensitivity Lwere studied and results presented. The shockresistance was also simulated to ensure therobustness of the device against external shock.The accelerometer is 40,um thick and 0.6mm x0.7mm in size. It has a resonant frequency of (a)3.60 kHz at acceleration of lOg.

1. INTRODUCTION

MEMS accelerometers play an important role inthe field of sensors [1]. Markets for MEMSdevices has increased from a 2-5 billion dollarindustry in 2000 to 8-15 billion dollar industry in2004 [2]. There has been good progress in theresearch of accelerometers so far. Accelerometerscan be classified according to their form oftransduction mechanism: (a) capacitive, (b)piezoelectric, (c) piezoresistive, (d) thermal, (e)electron tunnelling and (f) Bragg grating.

The capacitive sensing scheme is one of themost widely used in MEMS-based accelerometers[3,4]. This is due to their high sensitivity, good dcresponse and noise performance, low drift, lowtemperature sensitivity, low power dissipation andsimple structure [5,6].

There are two types of differential capacitivesensing, crossing and non-crossing. Theadvantage of the non-crossing type compare to thecrossing type is that it can use a three-maskfabrication process [7]. But non-crossing types still

a 0lufl,i lulls|~~~~~I I-l

(b)

Fig. 1. (a) Non-crossing differentialaccelerometer (b) the top viewdifferential lateral accelerometer.

lateral capacitiveof non-crossing

have inherent non-linearity. In order to improvelinearity, the movement of the mass is limited to asmall range [I].

Good mechanical sensitivity is also animportant factor in the design of a capacitiveaccelerometer. The mechanical sensitivity of anaccelerometer can be defined as the change incapacitance with the change in acceleration [8].

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ICSE2004 Proc. 2004, Kuala Lumpur, Malaysia

II. WORKING PRINCIPLE

The accelerometer used in this study consists of 74pairs of fingers attached to the proofmass as shownin Fig. 1. The proofmass is suspended by twostraight truss springs on both sides. At the end ofthe proofmass, there are two small rectangularbeams acting as a limit stop. Movable combfingers are attached to the proofmass. They arecombined with fixed comb fingers to form thesensing units. Each of the fingers on the proofmassis I00l m long, 2pm wide and 40tm thick. Thecentre proofmass plate is 100gm wide and 568,mlong. The ratio of separation between the movablecomb fingers and fixed comb fingers, d1/d2 is 0.5.

C, (x)= NAf - + d2d, -Axc d2 + Ax

(2)

(3)C2 (X) =NAf4 I+ d IA

d, -Axc d2 + Ax

where the displacement of the mass, Ax can bederived as follows [6]:

pa3Ax pSaL

2 Ew a3(4)

where p is the density, E is the Young's modulus, Sis the surface area, a is the acceleration, La and wa,are the length and the width of the springrespectively.

The differential capacitance, AC can be writtenas follows [7]:

AC = CI(x) - C2(x)

(b) - 4(a)

Fig. 2. Top view of a finger in accelerometer (a) noacceleration (b) with acceleration.

Fig. 1(a) shows the non-crossing capacitivefingers that were used in this design. CapacitanceC, and C2 consists of movable and fixed fingers. Ifthere is no acceleration, then the capacitance of C,and C2 is the same (see Fig. 2(a)). Se1 staticcapacitance, C. can be written as follows.

C1 =C2 s d d (1)

where N is the number of the fingers, c is qUpermittivity, A is the area of sensing fingers and d;and d2 are the small gap and big gap between theelectrodes respectivelyd2

However, when there is acceleration along thex-direction (see Fig. 2(b)), the capacitance Cl andC2 will change. This is shown as:

(5)

and the total capacitance, EC is represented asfollows:

IC= Cl(x) + C2(x) (6)The sensitivity, AC/EC can be given in terms

of displacement as the following equation:

AC 2 d2-_ d2AY2C d2 -AX2 + d2 _AX2 AX (7)

In this design, we used folded straight trussspring with a spring constant of 6.86J N/M2 andweight of the proofmass is 13.5tg.

III. SIMULATION RESULTS AND DISCUSSION

Simulation was done using Coventorware 2001.3software. Fig. 3 shows the analytical andsimulation results of the displacement di toacceleration. The calculated deviation o f theanalytic expression in Eq. (4) and the simulationresults is less 4i?n'90.

The calculated static capacitance for theaccelerometer is 2279 fF while the simulatedvalue is 2566 fW. From Fig. 4, it is seen thesimulation results deviate from the theoretical

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ICSE2004 Proc. 2004, Kuala Lumpur, Malaysia

(a)

2 4 6Acceleration (g)

(b)IAnalytical

Simulation -

8 101

(c) (d)Fig. 3. Comparison of analytical and simulateddisplacement as a function of acceleration.

r-

53800 X

Xi

4800

2800100

0 0.5 1 1.5Displacement (umr)

Fig. 4. Variation of differentialfunction of lateral displacement.

capacitance as a

Fig. 5. Linearity of capacitance due to smalldisplacemenet.

(e) (f)

Fig. 6. Mode shapes of the device (a) first mode, (b)second mode, (c) third mode, (d) fourth mode, (e)fifth mode and (f) sixth mode.

results by 13% to 7% as the displacementincreases. The difference between the theoreticaland the simulation results is caused by parasiticand fringe capacitances. The simulation andtheoretical results show that the non-linearity ofthe capacitance increases as the displacementincreases. To get a linear response, thedisplacement is limited to 10% of the small gap,dl. Fig. 5 depicts the linearity of capacitance C1and C2 due to small displacement.

Finite-element analysis of the harmonic modeswas also performed. The mode shapes, amplitudeof displacement and the resonant frequency wereobserved to ensure the stability and the linearity ofthe dominant mode. The first six modes of theharmonic behaviour from the simulation are shownin Fig. 6.

The analysis shows that the first mode occursat a frequency of 3.60 kHz. At this mode, thesensor moves backward and forward in the lateralx-direction. This is the normal mode of operation.The second mode which occurs at the frequency of16.88 kHz describes the tilting of the proofmass.The third mode occurs at a frequency of 34.68 kHzwhile the fourth, fifth and sixth modes occur at thefrequencies of 39.50 kHz, 54.40 kHz and 59.50kHz respectively.

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0.25

0.20

0.15

0.10

0.05

0.00

i2

I1;

2750

2700 _

- 2650

o 2600 C1° C2Cu

° 2500

2450

24000 0.05 0.1 0.15 0.2

Displacement (um)

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ICSE2004 Proc. 2004, Kuala Lumpur, Malaysia

0 1001 10Frequency (kHz)

Fig 7. Frequency response of the accelerometer atacceleration of lOg.

(b)

Fig 8. Stress distributions(a) y-axis, (b) z-axis

from an external shock

Fig 7 shows the plot of the harmonic amplituderesponse with frequency from 0 to 100 kHz. It isseen that the resonant frequency peaks at 3.60 kHz.This agrees with the prior modal analysis. Theamplitude response has a fair linearity below the

frequency of 200 Hz. The result also shows that thefirst mode is the desired dominant mode.

Shock resistance is also simulated to evaluatethe device robustness against external unexpectedshocks [9]. In this simulation, we observed theMises stress of the device. Mises stress is used as acriterion in determining the onset of failure inductile materials. The failure criterion states thatMises stress should be less than the yield stress ofthe material [7]. In this design, we use silicon asthe material and yield stress of silicon is 2.8GPa-6.8GPa.

Since the movement of the proof mass isconstrained in the sensing axis (in this design is x-axis), the limit stop will protect the device from anexternal shock. For the y and z axes (see Fig. 8), a1OOOg external shock is applied at the side and thetop of the device. Maximum Mises stress of1 1.1 MPa occurs at the edge of truss suspension forthe y-axis and 77.7MPa for the z-axis. These stressvalues are lower than the yield stress of silicon.Therefore, the sensor should be able to surviveunder a I OOOg shock.

W

e)

0.90.8

0.70.60.5

0.40.3

0.20.1^ f%.

*--Theoretical!:-*--Simulation

u.u

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8Displacement (um)

Fig 9. Sensitivity of the accelerometer as afunction of displacement.

Fig. 9 shows the plot of sensitivity of theaccelerometer as a function of displacement. It isseen that the sensitivity increases as thedisplacement increases and for the displacementranging from 0-0.2pim, the results are linear. Thesimulated result deviates from the calculatedvalues by 2%.

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ICSE2004 Proc. 2004, Kuala Lumpur, Malaysia

IV. CONCLUSION

We have presented theoretical and simulationresults on the mechanical behaviour of a MEMSnon-crossing dlfferential capacitive accelerometer.Displacement, modal and harmonic analysis, shockresistance and sensitivity results were compared.Although the sensitivity increased withdisplacement, the displacement was limited to asmall range in order to avoid non-linearity of thecapacitance value of C, and C2.

[81 S. Mutlu, "Surface MicromachinedCapacitive Accelerometer with Closed-Loop Feedback", Electrical Eng. AndComp. Sci. Dept., Univ. of Michigan.

[9] J. Chae, H. Kulah and K. Najafi, "A HighSensitivity Silicon-On-Glass Lateral pgMicroacceleromater", The Proceedings ofthe 3rd International Conference onIntegrated Nano/Microtechnology forSpace Applications (Nanospace 2000),Houston, TX, January 2000

V. ACKNOWLEDGEMENT

This work has been supported by the MalaysianMinistry of Science, Technology and Environmentunder the project title "Development of MEMSTechnology for Automotive Application".

REFERENCES

[l] B. Bais and B.Y. Majlis, "MechanicalSensitivity Enhancement of an Area-changed Capacitive Accelerometer byOptimization of the Device Geometry",Proceedings of DTIP of MOEMS &MEMS, Switzerland, 2004.

[2] MEMS Industry Group, "ExecutiveSummary", Industry Report, 2003.

[3] S.D. Senturia, "Microsystem Design",Kluwer Academic Publisher, 2001.

[4] N. Yazdi, A. Salian and K. Najafi, "AHigh Sensitivity CapacitiveMicroaccelerometer with a Folded-Electrode Structure", Tech. Dig. IEEEMicro Electro Mechanical SystemsWorkshop (MEMS'99), 1999.

[5] L.K. Baxter, "Capacitive Sensors", IEEEPress, Piscataway, N.J, 1997.

[6] B. Bais and B.Y. Majlis, "Analysis of theMechanical Behaviour of a MEMS Area-changed Lateral CapacitiveAccelerometer", Proc. of NationalSymposium on Microelectronics, Malaysia,2003.

[7] A.S. Tamsir, F. Saharil and B.Y, Majlis,"Spring Constant and von-Misses Stress ofa Non-Crossing Differential CapacitiveAccelerometer", Proc. of NationalSymposium on Microelectronics, Malaysia,2003.

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