The 2006 International Conference on MEMS, NANO and Smart Systems

Performance Enhancement of Gap Closing Electrostatic MEMSConverters

Mona S. Salem*, Marwa S. Salem*, A. A. Zekry*, H. F. Ragai**Ain Shams Univ., Fac. of Eng., ECE Dept

mona_marwa2002@yahoo.com

Abstract - This paper proposes new ideas to enhance theoutput power of the gap closing electrostatic MEMSconverters. This will be done by including the effect of theparallel capacitance of the converter in the output powerequation. In addition the output power of the converter willbe increased by increasing the converter thickness.

List of symbols

Symbol DefinitionE Output energy from the converter

Vmax Maximum allowable voltage for thesystem

Vmin Initial voltage on the converterC*max Total maximum capacitance of the

converterC*min Total minimum capacitance of the

converterCpar A constant capacitor, due to anchors,

added in parallel to the convertercapacitance

f Input vibration frequencyPout Output power of the converterWa Anchor widthLf Finger lengthWf Finger widtht Device wafer thicknessco Permittivity of air

dnominal Nominal distance between fingersNg Number of fixed or movable fingersLm Shuttle mass lengthLt Total length of the converterdmin Minimum dielectric gap distance

between fingersAanchor Anchor area

tox Oxide (SiO2) thicknessCOX Relative permittivity of SiO2m Mass of the movable partp Density of poly SiWm Shuttle mass widthk Spring constantE Modulus of elasticity for poly SiLb Spring shin lengthLa Spring thigh length

Wsp Spring beam width

I. INTRODUCTION

D uring the past several years, there has been an

increasing interest in the research community on smallwireless electronic devices. Wireless sensor networkshave many considerable applications in areas rangingfrom building monitoring and environment control tomilitary applications. Advances in low power VeryLarge Scale Integration (VLSI) design [1, 2] along withthe low duty cycles of wireless sensors have reducedpower requirements to the range of tens to hundreds ofmicrowatts. Such low power dissipation opens up thepossibility of powering the sensor nodes by scavengingambient energy from the environment, eliminating theneed for batteries and extending the lifetime indefinitely.

Energy scavenging system contains two main parts.The First part is an electrostatic MEMS converter, whichconverts the environmental vibration into electricity. Theother part is the controller circuits, which control theoperation of the electrostatic MEMS converter.

There are two well known topologies of electrostaticMEMS converters, gap closing and overlap. The gapclosing converter is better than the overlap converter. Itgives a higher capacitance range thus higher outputpower. Therefore, the gap closing converter is moresuitable for the energy scavenging applications [1].

This paper presents the output power equation of thegap closing converter. In addition it discusses thedifferent factors which lead to enhancement in theconverter output power. These factors include theparallel capacitance of the converter and the thickness ofthe moving plate.

II. THE OUTPUT POWER EQUATION OF GAPCLOSING CONVERTER

The output energy per cycle from the converter isgiven by

E = 1/2Vmax Vmin (C*max-C*min) (I)Vmax is one of the basic constraints for the system whichis set by some process and system requirement [3] to 8Vand C*max= (Cmax + Cpar), C mn= (Cmin + Cpar).

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The 2006 International Conference on MEMS, NANO and Smart Systems

On the other hand to satisfy the charge constrainedconversion [3] we have

Q = C*max v min = C *mln V max (2)The output power from the converter is expressed by

P = 2fE (3)f equals to 2.5 KHz in this case study. The factor of 2comes from the fact that the converter undergoes twocharging/discharging cycles for each mechanical cycle.The power depends on geometric design parameters,physical constraints, and the input voltage. Combiningequations (1), (2) and (3), one can derive the followinganalytical expression for the output power

Pout C*min V 2max( a)f (4)Where a - C mln /C *maxEquation (4) represents the output power from the gapclosing converter in terms of its capacitances.

Ill. EFFECT OF THE PARALLEL CAPACITANCE(Cpar) OF THE CONVERTER ON THE OUTPUT

POWER

Cpar is an important parameter which controls theoutput power of the converter, as it increases the outputenergy of the converter thus it increases its output power[3]. Figure 1 shows the MEMS converter cross-sectionalview representing Cpar. The parallel capacitance (Cpar) isincluded in the design essentially for free by exploitingthe parasitics that exist between the MEMS device andits substrate, and by tailoring the bonding oxidethickness between the two wafers making up the MEMSdevice.

Since Cpar acts as a parallel plate capacitor, one has toincrease W, in order to increase Cpar, thus increasing theoutput power.

CMEMSF7CParD)evice Wafeir

Ilandicl WVal.r

Silicon A\lIlllllull

Fig. 1: MEMS converter cross-sectional view representing Cpar

IV. GAP CLOSING CONVERTER DESIGN

In order to calculate the output power of theconverter, one has to design the converter dimensions.Figure 2 indicates the designed dimensions of the gapclosing converter. It shows that the converter is dividedinto two parts. The first part is the comb drive. The otherpart is the spring.

A. Comb Drive DesignThe overall chip area of the converter is taken to be

8mm X 8mm, in order to increase the output power ofthe converter. The effective electrical parameters in thepower equation, equation (eq. 4) , Cmax, Cm.n and Cparn arecalculated depending on the designed parameters of theconverter.

W,

WffLTl.

Wm

WsI'y1 -FLb

Fig.2: Designed dimensions of gap closing converter

The main objective of the design is to increase theoutput power of the converter (Pout). The convertercapacitances are given by the following equations

C max = (2NgCoLft) /dmin (5)C mn = (2NgcOLf t) / dnominal (6)Cpar= (cocoxAanchorVtox (7)

The designed dimensions of the converter areconstrained by the SOIMUMPs technology file [4],which is the chosen technology for implementing theconverter.

Lf must be maximized in order to increase theconverter capacitance. The maximum value for Lf islimited to 10Om as the converter is anchored at one endonly. In addition Wf will be 6Rm. t equals to 25iim forSOI technology. C0 is 8.85 x10-'2 F/m. It is better todecrease dnominal. Therefore Ng is increased, thusincreasing the capacitances. So dnominal is set to be 6Rm.Ng given by the following equation

Ng Lm / (Wf + 2 dnominal) (8)Lm is taken to be 7.5mm. The rest of L, is left for thespring design. Thus Ng is 417 fingers. For dmn,, it isbetter to decrease it as much as possible in order toincrease Cmax. Thus dmn, is taken to be 0.25pm.Substituting in equations (5) and (6), one gets C maxequals to 74pF and C min equals to 3pF. Recallingequation (7) to calculate Cpar,Aanchor equals to WaLm. In addition t0,, equals to 1.mfrom the SOIMUMPs technology file. co,, is 4. AssumingWa, to be 1.5mm in order to increase Cpar. Cpar total forthe converter found to be 796.5pF.

Neglecting Cm,n with respect to Cpar, the powerequation (4) becomes

Pout= Cpar V 2max ( - a) f (9)

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The 2006 International Conference on MEMS, NANO and Smart Systems

Since a is given by Cpar/ (Cmax + Cpar), thensubstituting by Cma, Cmin and Cpar in equation (9), Pout isfound to be 12.711W.

be 148OpF. Thus P0,,o will be 82.8iW. It is obvious that,by increasing the converter thickness, the output powerof the converter can be enhanced.

B. Spring DesignThere are many types of springs. The most suitable

one for the gap closing converter design is the crab - legspring [5]. Figure 3 shows the crab - leg spring with itsdimensions.

hinThigh

/

Lb

Wb

N N

Fig.3: Crab - leg spring

As for the design of the spring, the spring constantmust be determined from the following equation

f = I/2i 1 (k/m) (10)m is given by

m = p t Wm Lm (1 1)

p equals to 2.33g/cm3 [6]. Wm is taken to be 4.78mm.Combining equations (10) and (11), k is 515.19N/m.Recalling the crab - leg spring equations [5], the springconstant in X - direction is given by

kx = (EtW3 b (4Lb + C La))/ L3b(Lb + C La) (12)E is 15OGpa [6]. C is defined as (Wb / Wa)3.

Assuming that Wa = Wb = Wsp, C equals to 1. Thespring constant in Y - direction is given by

ky=(EtW3a (Lb + 4C La))/ L a(Lb + C La) (13)From equations (12) and (13), there are three unknownswhich are Lb, La and Wap thus one must make someassumptions. Lb is assumed to be 1.66mm to bephysically feasible. ky must be larger than k, to preventthe motion of the converter in the Y - direction. Thus ky/k, is taken to be 500. So La found to be 131.75jtm andW,p equals to 53.95,um. The output power of theconverter is small (12.7ptW).

VI. CONCLUSION

The equation of the output power from the converterincluding the effect of Cpar is presented. The outputpower of the converter is 12.71tW if the converterthickness is 251tm. By increasing the converter thicknessto 500pim the output power becomes 82.8VW.

REFERENCES

[1] S. Roundy, P. K. Wright and K. S. J. Pister, David A.Domfeld "Energy Scavenging for Wireless Sensor Nodes witha Focus on Vibration to Electricity Conversion", A dissertationof Philosophy in Engineering-Mechanical Engineering in theUNIVERSITY OF CALIFORNIA, BERKELEY, Spring 2003.[2] S. Meninger, "A Low Power Controller for a MEMS BasedEnergy Converter", Master of Science at the MassachusettsInstitute of Technology, 1999.[3] Scott Meninger, Jose Oscar Mur-Miranda, RajeevanAmirtharajah, Anantha P. Chandrakasan, and Jeffrey H. Lang,,"Vibration-to-Electric Energy Conversion", IEEETRANSACTIONS ON VERY LARGE SCALEINTEGRATION (VLSI) SYSTEMS, VOL. 9, NO. 1,FEBRUARY 2001[4] http://www.memscap.com/memsrus/crmumps.html[5] Gary Keith Fedder, "Simulation of Micro-electromechanical Systems", a dissertation of Philosophy inEngineering-Mechanical Engineering in the UNIVERSITY OFCALIFORNIA, BERKELEY, 1994.[6] http:H/www.Silicon Properties.html.

V. INCREASING THE OUTPUT POWER BYINCREASING THE CONVERTER THICKNESS

From equation (9), to increase Pout one has todecrease the factor a. This can be achieved by increasingCmax for a certain value of Cpar By increasing the devicethickness (t), Cmax increases. As a case study, let thedevice thickness (t) be 5OOjm [3]. Therefore Cmax will

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