Analytical Modeling and Simulation of MEMS Microstructure-Microcantilever Using FEM

8/11/2019 Analytical Modeling and Simulation of MEMS Microstructure-Microcantilever Using FEM

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International Journal of Exploring Emerging Trends in Engineering (IJEETE)

Vol. 01, Issue 01, Sept, 2014 WWW.IJEETE.COM

All Rights Reserved 2014 IJEETE Page 21

Analytical Modeling and Simulation of MEMS Microstructure-

Microcantilever Using FEM

1Anuj Kumar Goel,2Dr. H.P.Sinha,3Dr. Dushyant Gupta

1M.M.Engineering College,MMU , Mullana ,Haryana2M.M.Engineering College,MMU , Mullana ,Haryana3Guru Jambheshwar University, Hisar, Haryana

ABSTRACT-MEMS Devices ranges in size

from a few micrometers to millimeters. MEMS

provide very good scope for sensing physical,

chemical and biomedical parameters in an

efficient way which could be integrated with

VLSI chips. MEMS utilize the mechanical

properties of several elements such as

cantilever, beams, combdrive, membrane,

reservoirs and channels etc. In order to

optimally utilize the properties of these micro

mechanical elements, the mechanical behavior

of elements in presence of parameters has to be

study in detail. This paper presents the design

simulations of MEMS based micro-cantilever

made up of single crystal silicon using FEM

(COMSOL Multiphysics).The simulations

results into the stress and displacement

measurements of the cantilever.

Keywords MEMS, FEM, Microcantilevers.

I. INTRODUCTION

Now days, MEMS based Micro cantilevers has

been proven as an outstanding platform for

extremely sensitive chemical and biological

sensors [1]. In the past decade micro cantilevers

has become so popular due to its high sensitivityselectivity, ease of fabrication and flexibility of

on chip circuits. Also it has become interesting

due to convenience to calibrate, readily

deployable into integrated electromechanical

system and does not require external detection

devices [2-5]. Many previous researches

reported attempts made to improve the

cantilever sensitivity using piezoresistive

microcantilevers comprise of a polysilicon

piezoresistor integrated with silicon/ silicon-

nitride cantilever [6-7]. These researches

provided thorough understanding and strong

foundation on silicon- based microcantilevers.

This paper demonstrates the finite element

method to obtain the optimal performance of Sibased microcantilevers sensor by optimizing the

geometrical dimension of cantilever. COMSOL

Multiphysics, a commercial finite elementanalysis tool for MEMS was used to develop a

finite element model of the microcantilever.

II. DESIGN PARAMETERS

A cantilever is a beam anchored at only one

end. The beam carries the load to the support

where it is resisted by moment and stress. A

Cantilever structure consists of greater length as

compare to its width with optimal thickness.

Two equations are key to understand thebehavior of MEMS cantilevers. The first is

Stoney's formula, which relates cantilever end

deflection zto applied stress :

(1)

Where d and L are the cantilever beam

thickness and length, respectively; E and are

the elastic modulus and the Poisson ratio of the

cantilever material. Very sensitive optical and

capacitive methods have been developed to

measure changes in the static deflection of

cantilever beams. The second is the formula

relating the cantilever spring constant to

the cantilever dimensions and material

constants:


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(2)

where F is the point load applied at the end of

the cantilever, and z is the resulting end

deflection, E is the Youngs modulus of

elasticity for the cantilever material and w, d, L

are the width, thickness, and length of the

cantilever, respectively.

The movement of the cantilever is effected by

its length, width, thickness and various

properties of the material used to make the

structure. The geometric shape, as well as the

material used to build the cantilever

determines the cantilever's stiffness. The

analysis is done on the structure havingfollowing material properties which is shown

in table 1.

Table 1:Material properties of Silicon

S.No. Material Properties Values

1. Youngs Modulus 0.2GPa

2. Density 2330

3. Poissons ratio 0.33

The Micro cantilever designed using FEM(COMSOL Multiphysics) as shown in Fig. 1.

Figure 1:Microcantilever model in COMSOL

Also Silicon dioxide, Polysilicon and Silicon

nitride was used as Microcantilever materials

having properties and dimensions as given in

table 2:

Table 2:Material properties of different materials

S.

No.

Materia

l

Propert

ies

Dimen-

sions PolyS

i.

1.

Youngs

Modulus

Length

60E-6,Width10E-6,Thickne

ss 1.5E-6

160E9 250E9 70E9

2. Density 2320 3100 2200

3.Poissons ratio 0.22 0.23 0.17

III. SIMULATION RESULTS

The simulations of micro cantilevers with

varying the dimensions are performed.

Simulations are also performed with use ofdifferent materials for micro cantilevers. The

simulated models of Micro cantilevers are

shown in fig. (2-5).

Figure 2:Simulated model of Microcantilever1



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The simulated results with varying dimensions

of microcantilevers are shown in table.

Table 3:Increase in resultant stress with increase in

length of Microcantilever

S.No. Dimensions Stress (Pa)

1. 1000*100 50.44

2. 800*100 44.703

3. 600*100 31.022

Figure 5:Simulated model of Micro cantilever 4

Micracantilevers are also designed with

different materials. The simulation results with

varying materials are shown in table

Table 4:Increase in resultant stress with material

S.No. Material Stress (Pa)

1. Polysilicon 34.29

2. SiliconNitride 34.117

3. Silicondioxide 34.727

IV. CONCLUSION

MEMS based Microcantilever has been

designed with varying dimensions and with

different materials.

With increase in length of beams the respective

displacement is increased. With asmaterial maximum displacement is achieved as

compare to Polysilicon and Siliconnitride.

V. REFERENCES

[1] Robert Littrell et.al. (2012) Modelling and

Characterization of cantilever based MEMS

piezoelectric sensors and actuators, Journal of

Microelectromechanical SystemsVol.21No.2pp.406-413.

[2] Antoine Ferreira et.al. (2011) A Survay of

Modeling and Control Techniques for Micro

and Nano Electromechanical Systems, IEEE

Transactions on Systems, man, and Cybernatics

Part C: Applications and Reviews Vol.41 No.3

pp.350-364.

[3] Zabilzham et.al. (2004) dynamic Simulation

of a resonant MEMS Magnetometer inSimulink, Sensors and Actuators A115 pp.392-

400.

[4] Ankit jain et.al. (2012) A Physics based

Predictive Modeling Framework for Dielectric

Charging and Creep in RF MEMS Capacitive

Switches and varactors, Journal of

Microelectromechanical Systems Vol.21 No.2

pp. 420-430.

[5] I.Gill et.al. (2011) Characterization andModeling of switchable stop-band filters based

on RF MEMS and complementary Splitring

resonators. Microelectronics Engineering 88

pp.1-5.

[6] Robert Littrell et.al. (2012) Modelling and

Characterization of cantilever based MEMS

piezoelectric sensors and actuators, Journal of

Microelectromechanical Systems Vol.21, No.2,

pp.406-413.


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[7] Antoine Ferreira et.al. (2011) A Survay of

Modeling and Control Techniques for Micro

and Nano Electromechanical Systems, IEEE

Transactions on Systems, man, and Cybernatics

Part C: Applications and Reviews Vol.41 No.3

pp.350-364.

[8] Zabilzham et.al. (2004) dynamic Simulation

of a resonant MEMS Magnetometer in

Simulink, Sensors and Actuators A115 pp.392-

400.

[9] Ankit jain et.al. (2012) A Physics based

Predictive Modeling Framework for Dielectric

Charging and Creep in RF MEMS Capacitive

Switches and varactors, Journal of

Microelectromechanical Systems Vol.21 No.2

pp. 420-430.

[10] I.Gill et.al. (2011) Characterization and

Modeling of switchable stop-band filters based

on RF MEMS and complementary Splitring

resonators. Microelectronics Engineering 88

pp.1-5.

[11] Francisc Attila Boloni et.al. (2011)

Stochastic Modeling of the pull-in voltage in a

MEMS beam structure. IEEE Transactions onMagnetics Vol.47 No.5 pp.974-977.

[12] Shivappa Goravar et.al. (2010)

Probabilistic Analysis of a comb drive actuator.

IEEE Sensors Journal Vol.10 No.4 pp.877-882.

[13] E. M. Abdel-Rahman et.al. (2002)

Characterization of the mechanical behavior of

an electrostatically actuated microbeam. Journal

of Micromechanics and Microengineering, 12

pp.759766.

[14] R. C. Ackerberg. (1969) On a nonlinear

differential equation of electrohydrodynamics.

Proc. Roy. Soc. A, 312 pp.129140.

[15] L. Azrar et.al. (2002) Nonlinear forced

vibrations of plates by an asymptotic numerical

method. Journal of Sound and Vibration,

252(4):657674.

AUTHORS BIBLOGRAPHY

Anuj Goel was born in

Haryana, India in 1983.He is

presently pursuing Ph.D. from

M.M. University,India and alsoworking as Assistant Professor

in ECE Department, MMEC,

M. M. University, Mullana, India. His research

interests include MEMS Modelling, VLSI

Design etc.

Analytical Modeling and Simulation of MEMS Microstructure-Microcantilever Using FEM

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