Effects of Structure Parameters and Stress for Capacitive SwitchesMEMS Bridge on Time ResponseXun-jun He" 2, Qun Wu*', Ming-xin Song9, Jing-hua Yin'

'School of Electronics and Information Technology, Harbin Institute of Technology, Harbin 150001, China2 School ofApplied Sciences, Harbin University of Science and Technology, Harbin 150080, China

*Email: qwughit.edu.cn

Abstract: In this paper, a novel method for analyzingthe switching time of the electrostatic driven RFMEMS capacitive switches is presented. The effects ofthe structure parameters which mainly include thewidth, length and thickness and stress for capacitiveswitches MEMS bridge on time response areinvestigated using the SYNPLE module ofIntelliSuiteTM tool. The result shows that the width ofMEMS bridge and the stress in bridge indistinctivelyaffect on time response, while the length andthickness of MEME bridge distinctively effect ontime response.

1. Introduction

The emergence and rapid development of radiofrequency microelectromechanical system (RF MEMS)have attracted much attention from around the world.The passive RF/microwave switches implemented withMEMS methods have been shown as a promising way todeveloping low-power, low-cost and miniaturized RFMEMS switches for high frequency applications, such asphase shifters for satellite-based radars, missile systems,long range radars, automotive radars, instrumentationsystems, satellite communication systems and wirelesscommunication systems 1-21 The advantages ofMEMS-based RF switches over FET or PIN diodes arenear-zero power consumption, high isolation, lowinsertion loss, low cost, light weight and IC processescompatibility, and so on. Currently the RF MEMScapacitive switches have been fabricated in both seriesand shunt configurations. In the shunt configurations, theRF MEMS capacitive switches are devices that usemechanical movement of MEMS components to achievea short circuit or an open circuit in the CPWtransmission line. However, the forces required for themechanical movement can be obtained usingelectrostatic, piezoelectric, or thermal designs. To date,only electrostatic-type switches have been demonstratedwith high reliability and wafer-scale manufacturingtechniques. It is for this reason that this paper willconcentrate on electrostatic driven RF MEMS capacitiveswitches. But they still have shortcomings, such ashigh-driven voltage and relatively low speedE3'.With the extensive applications of RF MEMS capacitive

switches, the sensitivity of RF MEMS capacitiveswitches which is the switching time is the vitalimportance for the distributed RF MEMS phase shiftersto precisely control phased-array antennas. It is thepurpose this paper to analyze effects of structureparameters and stress for the capacitive switches MEMSbridge on time response. We mainly focus on discussingthe effects of the width, length and thickness of thebridge and the stress in the MEMS bridge on theswitching time using the SYNPLE module ofIntelliSuiteTM that is an available CAD for MEMS tool.

2. Principle

2.1 Mechanical ModelIn order to present a systematic method of analyzingelectromechanical principles of electrostatic driven RFMEMS switches, the model problem of electrostaticswitches with simple geometry is first considered. Thesimplest model of electrostatic switches is thefixed-fixed MEMS metal bridge membrane witheffective spring constant k, which is constructed from atop electrode of width w and thickness to that issuspended above the signal line (bottom electrode) of thecoplanar waveguide (CPW) transmission line, thesimplified schematically representation of the MEMSswitch is shown in Figure 1. The bottom electrode iscoated with a dielectric layer of thickness do and

dielectric constant Er, and the initial height between thetop electrode and the dielectric is go. The top electrode iselectrically grounded and a voltage V may be applied tothe bottom electrode.

MEM bridge/ Diele ic layer

Figure 1 Simplified model of MEMS switch

2.2 Dynamic equationsBecause the RF MEMS capacitive switches are modeled

using a simple fixed-fixed MEMS bridge, the pull-downvoltage is derived from static calculation and given by:

8g3V = g (1)0

where w is the width of the MEMS metal bridgemembrane, W is the width of the signal line, and theeffective spring constant k depends on the geometricaldimensions of the MEMS metal bridge membrane andon the Young's modulus of the material used for afixed-fixed bridge design with a force distributed overthe center third of bridge length 41, k is given by:

32Et 3w 8((1 -v)tw (2)

where E is the Young's modulus, v is the Poisson's ratio,( is the residual stress in the fixed-fixed bridge, I and toare the length and thickness of the bridge, respectively.When a voltage V may be applied to the bottomelectrode, the top electrode will move to contact with thedielectric. The dynamic equation of capacitive switchesis derived using the Newtonian dynamic equation ofmotion and given by:

d2z dz 1 g0WWV2dt2 +bdt +kz 2 ( + do z)2Er

where m is the mass of the bridge, z is the displacementfrom the up-state position, and b is the dampingcoefficient and is dominated by the squeeze-filmdamping under the bridge. For two parallel plates, b isgiven byE5:

kW3b = Fpairl(-)c)ooQ go(4)

where ) 0 k- is the natural resonant frequency ofrm

the switch, Q is the quality factor of MEMS bridge,

andpj,Uis the viscosity ofair ( 1.8x1051kg/m3')3. Response time analysis and discussion

It is obviously that equation (3) is a non-linear,complicated differential equation. For years, it has beeninvestigated by many researchers using the methods ofnumerical analysis, and several perfect approximationsare adopted to computer the switching time 6-81. However,the effects of the width, length and thickness of thebridge and the stress in the bridge on the switching timeare not accurately given in their discussions. Therefore,this paper mainly analyzes the effects of the width,length and thickness of MEMS bridge and the stress in

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MEMS bridge on the switching time by the SYNPLEmodule of IntelliSuite'TM software, the switching time ofthe electrostatic driven RF MEMS capacitive switcheswill be computed for the following input data: go =2.5

um, W=100 um, do=0.3 um and cr =7.6. The results areshown in Figure.2 - Figure 5 for the different structureparameters and stress.The Figure 2 shows the relations between the length ofthe MEMS bridge and the time response of thecapacitive switches, it is observed that the switchingtime decreases as the length increases from Figure 2.When the length is 150um the response time is about23us. However, the response time is about 3us andalmost no change when the length increases to 200um,250um, 300um and 400um respectively. Thisdemonstrates that the effects of the length on timeresponse nearly was neglected when the length increaseto a certainty extent. Therefore, for the high sensitivecapacitive switches, the length of MEMS bridge can notbe extremely length.

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Figure 2 Time response of the different length

0 2 4 6 8 10 12time/us

Figure 3 Time response of the different thickness

The Figure 3 shows the time response of the capacitiveswitches for different thickness, it illustrates that theswitching time increases as the thickness of bridgeincreases. For instance, the thickness will be increasedby 3 times, yet the switching time will be increased by5.5 times. Therefore, the lower thickness of bridge canreduce the switching time and the driven voltage of

capacitive switches, but the thickness of the MEMSbridge can not be especially low to avoid the stictionfailure of capacitive switches. Consequently, theoptimization of the thickness may be importance toreduce the switching time and the driven voltage.The Figure 4 shows the time response of the capacitiveswitches for different width at the different appliedvoltages, it is observed that the switching time isunvarying as the width of MEMS bridge increases atsame applied voltage from Figure 4. This demonstratesno effects of the width on time response. But, for thecapacitive switches, we must select proper the width sothat the driven voltage can be decreased according toequation (1) and the proper capacitive ratio between theup-state and the down-state can be obtained, which willclearly improve capacitive performance.

3.E

(,, 3.2*,E

2.4-

2.0 l10 60 80 100 12

MEMS bridge width/um

Figure 4 Time response of the different width

The Figure 5 shows time response for different stress inthe MEMS bridge, it illustrates that the switching timeincreases as the stress in the MEMS bridge increases.The stress in the MEMS bridge mainly come fromfabrication processes. While, the stress are increased by50 times, the switching time will be increased by about 5times. This demonstrates that the stress indistinctivelyaffect on the time response. But, the stress can notextremely high to void the ruptured failure of the MEMSbridge. Currently, the capacitive switches are fabricatedcommonly using the low stress processes, the stress isapproximate 2OMPa.

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4. Summary

The influences of the width, length, thickness and stresson time response have been analyzed using the SYNPLEmodule of IntelliSuite'TM tool. The results show that theswitching time increase as the thickness and stressincrease respectively, the switching time decreases as thelength increases, while the switching time almost isunvarying as the width increases at same applied voltage.Moreover, the width and the stress indistinctively affecton time response, and the length and thickness ofdistinctively effect on time response. These results fitvery well with the experiment and theory. Therefore, thestructure parameters of MEMS bridge must properly beoptimized to enhance the response insensitivity andelectromechanical performance of RF MEMS capacitiveswitches.

Acknowledgments

The project was supported by the MultidisciplineScientific Research Foundation of Harbin Institute ofTechnology (HIT MD. 2003.07).

References

[1] Goldsmith C, Lin T H Powers B, IEEE MTT-S nt.Microwave Symp. Dig., p.91 (1995).

[2] Scott Barker N and Rebeiz G M, IEEE Trans.Microwave Theory Tech., 46, p.1881 (1998).

[3] Rebeiz G M, Muldavin J B., IEEE MicrowaveMagazine, 45, p.59(2001).

[4] Roark R J, Young W C., 6th ed. New York:McGraw-Hill, p.169(1989).

[5] Howe R T and Muller R S, IEEE Trans. on

Electron Devices, 33, p.499(1998)..

[6] Chan E K, Kan E C, Dutton R W., IEEE MTT-SInt. Microwave Symp. Dig.,p. 1511(1997).

[7] Shi F., J. Numer. Methods Eng.,39, p.4119(1996).

[8] Elata D and Leus V. ICMENS, p.1189(2005).

Time/usFigure5 Time response of the different stress

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