Sensors and Actuators A 148 (2008) 186–192

Contents lists available at ScienceDirect

Sensors and Actuators A: Physical

journa l homepage: www.e lsev ier .com/ locate /sna

Pre-shaped buckled-beam actuators: Theory and experiments

Seunghoon Park, Dooyoung Hah ∗

Department of Electrical and Computer Engineering, Louisiana State University, 102 S. Campus Dr., Baton Rouge, LA 70803, USA

a r t i c l e i n f o

Article history:Received 13 May 2008Received in revised form 15 July 2008Accepted 18 July 2008Available online 25 July 2008

Keywords:Bistable actuatorElectromagnetic actuator

a b s t r a c t

Bistability is one of the desirable features for a MEMS actuator to have in various applications such asmechanical memories, micro-relays, micro-valves, optical switches, digital micro-mirrors, etc. It allowswithdrawal of actuation force during idle periods without affecting an actuated state of a device, whichresults in minimal or even zero standing power consumption. One such actuator is a pre-shaped buckledbeam. In this paper, theoretical analysis reveals that existence of the second stable state in a buckled-beam actuator depends not only on a ratio of its initial rise to its thickness, but also on its residual stress.Buckled-beam actuators are pre-shaped by layout design, fabricated by SU-8 lithography and copperpulse electroplating, and actuated by Lorentz force using an external magnet and current flow through the

Pre-shaped buckled-beamMEMS actuator

beams. Forward and backward critical loads or switching currents of the actuators are measured for variousbeam dimensions, and compared to the theoretical values. Required switching currents and voltages arebetween 10 and 200 mA, and between 20 mV and 0.4 V, respectively, for 20–60 �m displacement. Effect

s to

1

sctbacpfepeldotuabcim

bcltncsdlbaaaaaswuT

0d

of electroplating condition

. Introduction

Actuators directly driven by electrical signals are attractive forystems that are built on, or controlled by electronics. In thatategory are electrostatic, electrothermal, piezoelectric, and elec-romagnetic actuators. Among them, electrostatic actuators haveeen most popular so far. However, they are generally operatedt high voltage, and as a result, often require voltage multiplierircuits. Electrothermal actuators exert high force with large dis-lacement, but ask for high power consumption, and also sufferrom low speed. Piezoelectric actuators can be operated at mod-rate voltage and negligible current level, but related material androcess technologies are yet far from maturity. In the meantime,lectromagnetic actuators have several attractive features, such asow operation voltage, high speed, high force exertion, and largeisplacement. Electromagnetic actuators, however, are not with-ut a drawback, i.e. high standing power consumption, usually inhe range of tens to hundreds of mW. This standing power, althoughsually inevitable to keep an actuator at an actuated state, can bevoided if the actuator has more than one stable position or can

e locked mechanically. However, mechanical locks usually requireomplicated structures as well as large extra areas [1,2]. Therefore,n many applications, actuators with multiple stable positions are

ore attractive.

∗ Corresponding author. Tel.: +1 225 578 5532.E-mail address: dyhah@lsu.edu (D. Hah).

pcacss

c

924-4247/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.sna.2008.07.009

bistability of actuators is studied as well.© 2008 Elsevier B.V. All rights reserved.

One of the well-known mechanical structures that have bista-ility is a beam or a membrane that is buckled. When alamped–clamped free standing structure is left with sufficientlyarge compressive stress, it buckles towards a direction parallel tohe smallest dimension [3]. Having smaller width than the thick-ess, it can be buckled laterally (or in-plane direction). However,reating buckled beams in this manner affects other free-standingtructures made out of the same layer as well, which should noteform. Still, there are other methods to make a beam have a buck-

ed shape without relying on compressive residual stress of theeam. One is to compress a beam from its ends using auxiliaryctuators until it buckles [4]. This method can precisely controldegree of buckling at any time. However, it requires not only

dditional space but also standing power for the auxiliary actu-tors, which dilutes advantages of bistability. On the other hand,beam can be pre-shaped into a buckled fashion in a sinusoidal

hape that is defined at the layout stage [5–8]. Whether this beamill have bistability depends on its geometries as well as its resid-al stress, as will be described in the following section in detail.his method also can precisely control the level of buckling. Thesere-shaped buckled-beam actuators have been applied to opticalrossbar switches [6,7] and micro-relays [8], and yet have otherpplication areas as well, including mechanical memories, opti-

al shutters, digital micro-mirrors, and micro-valves. Other beamhapes that can offer similar bistability features include a chevronhape [9,10] and an H shape [11].

A buckled beam, either compressed or pre-shaped, reverses itsurvature when it is transversally loaded above some critical value.

Actua

Twtpsbtbct

2

prmtl

E

a

o

wmwHwteHb

e

wf

e

Ffl

s

ε

woa

U

wab

M

wU

U

N

W

U

S. Park, D. Hah / Sensors and

he analysis of this behavior, so-called snap-through buckling isell established [3,4,12–16]. However, literatures seldom present

he analysis of a pre-shaped buckled beam with residual stress. Thisaper models the pre-shaped buckled beam with non-zero residualtress. Even though there have been several publications regardinguckled-beam actuators in microscale, e.g. MEMS actuators, onehat reports experimental results of critical loads in relation to theeam dimensions is rare. This paper presents measured values ofritical loads for various beam dimensions, which are compared tohe theoretical ones as well.

. Theoretical analysis

Fig. 1 is a sketch of a pre-shaped buckled beam with designarameters indicated – width w, thickness t, length l, and initialise h. To analyze the deflection of the pre-shaped buckled beam, aode superposition method with the following eigenvalues nj and

he eigenmodes vj of a straight clamped–clamped beam under axiaload can be used as in [13–14,16].

ven modes : vj(x) = Cj

[1 − cos

(nj

x

l

)], nj = (j + 2)�,

j = 0, 2, 4, . . . (1)

nd

dd modes : vj(x) = Cj

[1 − cos

(nj

x

l

)− 2

x

l+ 2 sin(njx/l)

nj

],

nj = 2.86�, 4.92�, . . . j = 1, 3, 5, . . . (2)

here Cj are arbitrary coefficients. Using these buckling eigen-odes as an orthogonal set for the pre-shaped beam deflectionould best represent the nature of buckling features of the beam.owever, due to the nature of the load considered in the presentork, the odd modes of (2) will be constrained. It can be also proved

hat the coefficients of the odd modes become zero even when bothven and odd modes are considered in the following derivation.ence, using only the even modes, the shape of the beam e(x) cane expressed as

(x) =∞∑

n=1

an

(1 − cos

2n�x

l

), (3)

here an is an amplitude of the nth mode. The predetermined (as-

abricated) shape of the beam e0(x) is given as

0(x) = h sin2(

�x

l

)= h

2

(1 − cos

2�x

l

). (4)

ig. 1. A sketch of a pre-shaped buckled beam. e(x) represents distance of the beamrom the straight line between two fixed ends (or x-axis). q is uniformly distributedoad and B is applied magnetic flux.

s

(ata

d

bl

tors A 148 (2008) 186–192 187

When a transverse load q is applied to the pre-shaped beam,train ε and axial load P are generated;

(x) = P(x)EA

=

[√1 + (de/dx)2 −

√1 + (de0/dx)2

]√

1 + (de0/dx)2≈ 1

2

×[(

de

dx

)2

−(

de0

dx

)2]

≈ 12

[(∑∞

n=1

2n�

lan sin

2n�x

l

)2

−(

�h

l

)2

sin2 2�x

l

], (5)

here E and A are the Young’s modulus and the cross-sectional areaf the beam, respectively. Strain energy UP due to the axial load Pnd the residual stress of the beam �0 can be calculated as

P =∫ l

0

[P(x) + �0A]2

2EAdx

= EA�4

8l3

[∑∞

n=16n4a4

n − 3h2a21 −

∑∞

n=22h2n2a2

n + 38

h4]

+�2A�0

4l

(∑∞

n=14n2a2

n − h2)

+ A�20 l

2E+ f (an), (6)

here f(an) represents cross-product terms such as a13a3, a1

2a22,

12a2a4, a1a2a3a4, a1a3, and so on. Next, bending moment M of the

eam generated can be derived to be

(x) = −EI

(d2e0

dx2− d2e

dx2

)

= EI�2

l2

[∑∞

n=14n2an cos

2n�x

l− 2h cos

2�x

l

], (7)

here I is the moment of inertia of the beam. Then, the strain energyM due to the bending moment can be found to be

M =∫ l

0

[M(x)]2

2EIdx = EI�4

l3

[∑∞

n=14n4a2

n − 4ha1 + h2]

. (8)

ext, the amount of work done W by the transverse load q is

=∫ l

0

q[e0(x) − e(x)]dx = ql(

h

2−

∑∞

n=1an

). (9)

Finally, the total energy Ut in the system is described as

t = UP + UM − W. (10)

Since the mode amplitude should minimize the total energy attatic equilibrium,

∂Ut

∂an= 0. (11)

11) can provide relationships between the load q and the modemplitudes an. Once the mode amplitudes are found in relation tohe load, deformation of the beam at the center (d) can be calculateds

= h − e(

l

2

)

= h −∑∞

an(1 − cos n�) = h −∑∞

2an. (12)

n=1 n=1,3,5,...

First, the higher modes (n > 1) will be ignored and zero stress wille assumed to gain some insight regarding the snap-through buck-

ing behavior. With only the first mode taken into consideration

1 Actuators A 148 (2008) 186–192

aa

q

sabHmdopdTscpbb

q

a

q

Ad

a

wt

d

Eps

Fbh

c

Ih

dmFtclretd

l

FDdtt

88 S. Park, D. Hah / Sensors and

nd zero stress, from (10) and through (11), the load q is obtaineds

= �4E

l4

[−3Aa3

1 +(

3Ah2

4− 8I

)a1 + 4Ih

]. (13)

Fig. 2 shows a conceptual plot of q versus a1 as well as deformedhape of the beam at some specific points on the graph. With O1s the initial stable position, when a small load is applied, theeam deformation increases monotonically as the load increases.owever, as the load increases further, it reaches a local maxi-um (point A). Beyond this critical deformation, the load starts to

ecrease as the deformation increases, which is unreal. Implicationf this is that when the beam passes the critical point, it snaps fromoint A to point B. When the load is withdrawn at point B, the beamoes not come back to O1 but rests at the second stable position (O2).o bring the beam back to O1, the load has to be applied in the oppo-ite direction (−y) and the beam has to be pulled beyond anotherritical deformation (point C). Then, the beam moves abruptly fromoint C to point D, and if the load is withdrawn at this point, theeam returns to O1. The critical loads (qcrf for forward and qcrb forackward) can be found at those local maximum and minimum as

crf = �4EI

l4

[9t2

(13

h2 − 827

t2)3/2

+ 4h

](14)

nd

crb = �4EI

l4

[− 9

t2

(13

h2 − 827

t2)3/2

+ 4h

]. (15)

mplitude of the first mode at the second stable position O2 can beerived by solving q = 0 from (13) and finding the lowest solution;

1 at O2 = − h

4−

√116

h2 − 29

t2, (16)

hich results in the distance between the two stable positions athe beam center (dstable; see Fig. 2) as

3√

1 8

stable =

2h +

4h2 −

9t2. (17)

q. (16) contains an important fact about bistability. In order for are-shaped buckled beam to have bistability, the term inside thequare-root must be a positive value, which gives the following

riaii

ig. 2. (Left) Applied load (q) versus amplitude of the first mode (a1) of a buckled beameformed shape of the beam at some specific points. The beam deformation at the centereforming downward, as the beam reaches the position A at critical load qcrf, it snaps to the second stable position. When deforming upward, as the beam reaches the position C ahe beam returns to the position O1. dstable is the distance between the two stable position

ig. 3. Applied load (q) versus beam deformation at the center (d) of the pre-shapeduckled beam calculated with (solid line) and without (dashed line) consideringigher modes. Beam dimensions: l = 3000 �m, w = 10 �m, t = 5 �m, and h = 10 �m.

ondition to the beam geometries.

h

t>

4√

23

= 1.886 (18)

t should be noted that this criterion needs to be changed whenigher modes and non-zero residual stress are taken into account.

Next, higher modes will be included in the analysis. This can beone in the same manner except that it needs aid from a mathe-atical software such as MATLAB® due to complexity in calculation.

ig. 3 compares calculated results of the load versus beam deforma-ion at the center of the beam between one with and one withoutonsidering higher modes. It shows that for such a long beam withow initial rise, the result from the first order approximation iseasonably close to that from the more rigorous calculation. How-ver, as can be seen later from Fig. 9, the shorter the beam is andhe higher the initial rise is, the bigger becomes the calculationiscrepancy between them.

Finally, Fig. 4 shows an effect of residual stress on the criticaloads of the buckled beams. It was found that tensile residual stress

educes the initial rise and hence the magnitudes of critical loadsn both forward and backward directions. It also shows that whenbeam has tensile stress higher than a certain value (e.g. 100 MPa

n the figure), it has no backward critical load, which implies thatt is devoid of bistability. On the other hand, compressive residual

when the higher modes are ignored and the beam has no residual stress. (Right)can be calculated as h − 2a1. O1 is the initial (as-fabricated) stable position. While

he position B. If the load is withdrawn after this, the beam rests at the position O2,t the critical load qcrb, it snaps to the position D. If the load is withdrawn after this,s at the beam center.

S. Park, D. Hah / Sensors and Actuators A 148 (2008) 186–192 189

Fig. 4. Calculated critical load (qcr) versus tensile residual stress (�0) of the pre-shaped buckled beam. Beam dimensions: l = 2000 �m, w = 10 �m, t = 5 �m, andh = 30 �m. The beam loses the bistability when its tensile stress is greater than100 MPa although it shows there still will be forward snap – in this situation, evenad

sl

lndFrdbbdo

Table 1Composition of copper acid electrolyte solution used in the electroplating

Chemicals Amount/liter Remarks

Copper sulfate 150 gSulfuric acid 50 mlCopper chloride 120 mgMPJ

3

sdir(ftpT(pwcW3iTlstlbeneficial to reduce operation voltage. Composition of the copperacid electrolyte solution used in the electroplating is summarized in

Fr

fter snapping, the beam returns to its original position (O1) when the load is with-rawn.

tress increases the initial rise and hence the magnitudes of criticaloads.

In this work, for buckled-beam actuation, Lorentz force was uti-ized, which requires a small footprint, low actuation voltage, ando other structures than a beam itself. If current (I) is applied in xirection in the presence of magnetic flux (B) in −z direction (seeig. 1), uniform load (q = BI) is generated in y direction. If the cur-ent is applied in −x direction, q is generated in −y direction. Exactirection of q varies over the beam length because direction of theeam cross-section varies by both position on and deflection of the

eam. However, for a buckled-beam actuator whose initial rise andeflection are much smaller compared to its length, the directionf q can be assumed invariant in the analysis.

T(i

ig. 5. Fabrication process flow of the buckled-beam actuators. (a) Seed metal (titanium/emoval, (e) seed metal removal, and (f) release of actuators by glass substrate etching.

PS 10 mg BrightenerEG 100 mg SuppressorGB 1 mg Leveler

. Fabrication

Based on the theoretical analysis described in the previousection, buckled-beam actuators with various dimensions wereesigned and fabricated by using an SU-8 LIGA-like process. Fig. 5

llustrates the process flow of the buckled-beam actuator fab-ication. Devices were fabricated on a 4′′ Borofloat glass waferthickness: 700 �m). The Borofloat glass wafer was selected for itsast etch rate (∼7 �m/min) in 49% hydrofluoric acid, which helpso reduce etching damage to main copper structures. First, as areparation step for the electroplating process, a seed metal layer,i (20 nm)/Cu (30 nm) was deposited using a thermal evaporatorFig. 5a). Next, to create electroplating molds, SU-8 lithography waserformed using a Quintel Q-4000 aligner (Fig. 5b). UV exposureas carried out through a cut-off filter (PL-360-LP, Omega Opti-

al, cut-off at 360 nm) to prevent a so-called T-topping problem.ithout the filter, most of light whose wavelength is shorter than

60 nm is absorbed near the surface of a SU-8 layer, which resultsn a T-shape cross-section: a broader top and a narrower base.ransmission through the filter at 365, 405, and 436 nm mercuryines is better than 90% [17]. Next, copper was electroplated as atructural layer (Fig. 5c). Copper was selected for its high conduc-ivity (5.96 × 107 S/m), moderate Young’s modulus (128 GPa) [18],ow residual stress, and good resistance to HF. High conductivity is

able 1. Mercaptopropane sulfonic acid (MPS), polyethylene glycolPEG), and Janus green B (JGB) are additives for better film qual-ty, e.g. reduced residual stress and improved film density. Both

copper) deposition, (b) SU-8 lithography, (c) copper pulse electroplating, (d) SU-8

190 S. Park, D. Hah / Sensors and Actuators A 148 (2008) 186–192

Table 2Conditions of the copper pulse electroplating

Parameters Descriptions

Anode 99.9% copperTemperature Room temperatureCurrent density 6.6 mA/cm2

Pulse duty ratio 50%Frequency 100 Hz

piairprThrHa47lrdfbb

3

eisaem

TC

S

ABC

Fig. 7. Microimages showing parts of fabricated buckled beams. (a)–(c) Copperwhose electroplating conditions are (a) without brightener at 6.6 mA/cm2 (sam-p1tt

teawere tested. First, effects of brightener and current density on theresidual stress were investigated by observing released buckledbeams. As can be seen from Fig. 7a and c, traces of buckled beamsthat are left on a glass wafer during the release step can be clearlydistinguished from the released buckled beams – in those cases,

Fig. 6. An SEM image of the fabricated pre-shaped buckled beams.

ulse and DC electroplating were attempted with different resultsn film quality. The former provided significantly better topologynd uniformity than the latter. Conditions for the pulse electroplat-ng are presented in Table 2. Effect of electroplating conditions onesidual stress of the film will be discussed later. After the electro-lating process, SU-8 molds were removed (Fig. 5d) by the Nano PGemover (MicrochemTM). Then, the seed layer was stripped (Fig. 5e).he copper seed layer was etched by a mixture of sulfuric acid,ydrogen peroxide, and deionized water in 1:1:30 ratios. The etchate was 2.7 nm/s. The titanium adhesion layer was removed byF in the subsequent substrate etch process. The buckled-beamctuators were released by underetching the glass substrate in9% concentrated HF (Fig. 5f). The etch rate was approximately�m/min. The actuators are anchored to the glass substrate via

arge probing pads which are not completely underetched in theelease step. Finally, samples were dehydrated with a critical pointryer (CPD, Autosamdri®-815B, Tousimis). An SEM image of the

abricated buckled beams is presented in Fig. 6. Square patternsetween the buckled beams were inserted as crude references ofeam positions during actuation.

.1. Effect of residual stress

Residual stress of a buckled-beam actuator has a significantffect to its operation characteristics. High compressive stressncreases the initial rise demanding high actuation force. High ten-

ile stress has even more drastic effect; it deprives a buckled-beamctuator of bistability, which was proven both theoretically andxperimentally. Therefore, it is important for the actuator to haveild residual stress.

able 3onditions of copper electroplating to examine effects on residual stress

ample Current density Brightener

6.6 mA/cm2 No6.6 mA/cm2 Yes10.0 mA/cm2 Yes

Ftah

le A), (b) with brightener at 6.6 mA/cm2 (sample B), and (c) with brightener at0 mA/cm2 (sample C). (d) Nickel electroplated at 6.6 mA/cm2. Distance between arace of a buckled beam and the beam itself indicates amount of residual stress inhe structure.

It was reported that adding brightener to electroplating solu-ion or using low current density can reduce tensile stress in copperlectroplating [19,20]. This trend was verified in the present works well. Three different conditions of copper electroplating (Table 3)

ig. 8. Images of a buckled beam at (a) the original, and (b) the second stable posi-ions. A trace of the buckled beam can be also seen in (b), which is produced duringrelease step (Fig. 5f). Beam dimensions: l = 3000 �m, w = 10 �m, t = 5 �m, and= 25 �m.

Actua

iblsfAetsbfi

Fcaa

t[

wfeT

S. Park, D. Hah / Sensors and

nitial rises of the beams were reduced, which implies that thoseeams have significant tensile stress. Distance of a released buck-

ed beam from its original location indicates strength of the tensiletress in the beam. In the case of Fig. 7b, the trace is not discerniblerom the beam, i.e. it has negligible stress. Comparing the samples

and B, it is plain that adding brightener has an effect of less-ning tensile stress. It is also evident from the samples B and C

hat using low current density in electroplating diminishes tensiletress. However, the current density could not be lowered furtherelow 6.6 mA/cm2 because that caused detrimental effect to thelm quality. Then, approximate value of residual stress of copper in

ig. 9. Measured (circles) and calculated (lines), forward and backward switchingurrents of buckled-beam actuators whose lengths (l) are (a) 2000 �m, (b) 2500 �m,nd (c) 3000 �m. For all devices, thickness (t) and width of the beam (w) are 5 �mnd 10 �m, respectively. Magnetic flux density (B) applied is 0.7 T.

T

4

TfladtbtoatcftmctwsbFtcbomwnwmwnl

5

s1af6estfc

A

ST

tors A 148 (2008) 186–192 191

he case of sample B was measured from stress indicator patterns21]. The measured value was less than 10 MPa (tensile).

In addition to copper, nickel electroplating was attempted asell to examine an effect of electroplating material. As can be seen

rom Fig. 7d, electroplated nickel showed very high tensile stressven though it was plated at low current density, i.e. 6.6 mA/cm2.his observation agrees with a previous report by Larsen, et al. [22].heir electroplated nickel had tensile stress of 700 MPa.

. Results

Fabricated buckled beams were electromagnetically actuated.he wafer was placed on a permanent magnet that exerts magneticux density of 0.7 T, and dc current was applied through the actu-tors. It was experimentally confirmed that a buckled beam withimensions satisfying the criterion (18) can be switched betweenwo stable positions. Fig. 8 shows bistable actuation of a buckled-eam actuator. When the applied current was in an amount enougho create the forward critical load, the beam was snapped to thepposite side, and as the current was withdrawn, it moved to restt the second stable state (Fig. 8b). When current was applied inhe opposite direction in an amount to generate the backwardritical load, and then withdrawn, it moved back to the original (as-abricated) stable state (Fig. 8a). Two square patterns by the side ofhe beam and the trace of the beam make this bistable actuation

ore notable. As was expected from the theoretical analysis, theseritical currents or switching currents of a buckled-beam actua-or were dependent on its dimensions (Fig. 9). Switching currentsere recorded for both forward and backward transitions when

nap was observed. For comparison, calculated switching currentsoth with and without considering higher modes are also plotted inig. 9. The measured switching currents reasonably well agree withhe calculated ones. Discrepancy of the measured results from thealculated ones is thought to be caused by changes in fabricatedeam dimensions from designed values. In addition, possible sec-ndary effects including an electrothermal (Joule heating) effectight have played a role. The actuators made by electroplatingith conditions A and C of Table 3, and those made of electroplatedickel, having large tensile stress, did not show bistability, whichas expected from the theory. In addition to the static measure-ent, dynamic actuation behaviors of the buckled-beam actuatorsere investigated by applying a bipolar square-wave current sig-al to the actuators. Actuators showed bistability characteristics at

east up to 10 kHz.

. Conclusion

Pre-shaped buckled beams with various dimensions wereuccessfully fabricated and actuated by current in a range of0–200 mA which corresponds to a voltage range of 20–400 mVnd to a switching power range of 0.2–80 mW. Driving force rangedrom 10 to 200 �N and the beam displacement was from 20 to0 �m. The measured results agree well with the theory. Effects oflectroplating parameters on residual stress, and in turn, of residualtress on bistability were studied. Since a buckled-beam actua-or consumes no power at each of the stable states, it is usefulor various applications, especially those which have tight poweronsumption constraints, such as RF MEMS switches.

cknowledgements

The authors would like to thank Mr. Golden Hwaung at Louisianatate University (LSU) and Dr. Myung Lae Lee at Electronics andelecommunications Research Institute (ETRI), Korea for their tech-

1 Actua

nR

R

[

[

[

[

[

[

[

[[

[

[

[

[

B

SUEDaA

Dt1Bt2Ka

92 S. Park, D. Hah / Sensors and

ical assistances. This work is partially supported by Council onesearch, LSU through the Faculty Research Grant Program.

eferences

[1] M. Hoffmann, P. Kopka, E. Voges, All-silicon bistable micromechanical fiberswitch based on advanced bulk micromachining, IEEE J. Select. Top QuantumElectron 5 (1999) 46–51.

[2] X. Liu, et al., Optical add and drop multiplexer using on-chip integration ofplanar light circuits and optical microelectromechanical system switching, J.Vac. Sci. Technol. A 22 (2004) 826–830.

[3] W. Fang, J.A. Wickert, Post buckling of micromachined beams, J. Micromech.Microeng. 4 (1994) 116–122.

[4] M.T.A. Saif, On a tunable bistable MEMS-theory and experiment, IEEE J. Micro-electromech. Syst. 9 (2000) 157–170.

[5] J. Lee, M. Lee, W. Jang, C. Choi, J. Joo, Bi-stable planar polysilicon microac-tuators with shallow arch-shaped leaf springs, in: Proceedings of SPIEConference on Micromachined Devices and Components V, 1999, pp.274–279.

[6] L. Dellmann, W. Noell, C. Marxer, K. Weible, M. Hoffmann, N.F. de Rooij,4 × 4 matrix switch based on MEMS switches and integrated waveguides,Proc. Transducers’ 01 Eurosensors XV Int. Conf. Solid-State Sensors Actuators,Munich, Germany, Jun. 10–14, 2001, pp 1332–1335.

[7] J.S. Ko, M.L. Lee, D.S. Lee, C.A. Choi, Y.T. Kim, Development and application ofa laterally driven electromagnetic microactuator, Appl. Phys. Lett. 81 (2002)547–549.

[8] J.S. Ko, M.G. Lee, J.S. Han, J.S. Go, B. Shin, D.S. Lee, A laterally-driven bistableelectromagnetic microrelay, ETRI J. 28 (2006) 389–392.

[9] I.H. Hwang, Y.S. Shim, H.N. Kwon, J.H. Lee, Design and experimental character-ization of the chevron-type bi-stable actuator for optical switch applications,Proc. IEEE/LEOS Int. Conf. Optical MEMS, Waikoloa, HI, USA, Aug. 18–21, 2003,pp. 135–136.

10] C. Lee, C.Y. Wu, Study of electrothermal V-beam actuators and latched mecha-nism for optical switch, J. Micromech. Microeng. 15 (2005) 11–19.

11] W.C. Chen, C. Lee, C.Y. Wu, W. Fang, A new latched 2 × 2 optical switch usingbi-directional movable electrothermal H-beam actuators, Sens. Actuators A(Physical) 123–124 (2005) 563–569.

12] A. Michael, C.Y. Kwok, Thermo-mechanical behavior of buckled multi-layered

micro-bridges, Sens. Actuators A (Physical) 137 (2007) 157–168.

13] J. Qiu, J.H. Lang, A.H. Slocum, A curved-beam bistable mechanism, IEEE J. Micro-electromech. Syst. 13 (2004) 137–146.

14] J. Qiu, A thermally-actuated bistable MEMS relay for power applications, Ph.D.dissertation, Dept. Mechanical Eng., Massachusetts Inst. Technol., Cambridge,June 2003.

ansboa

tors A 148 (2008) 186–192

15] S. Krylov, B.R. Ilic, D. Schreiber, S. Seretensky, H. Craighead, The pull-in behaviorof electrostatically actuated bistable microstructures, J. Micromech. Microeng.18 (2008) 055026.

16] M. Vangbo, An analytical analysis of a compressed bistable buckled beam, Sens.Actuators A (Physical) 69 (1998) 212–216.

17] Omega Optical Inc., https://www.omegafilters.com/.18] Z. Dolbow, M. Gosz, Effect of out-of-plane properties of a polyimide film on the

stress fields in microelectronic structures, Mech. Mater. 23 (1996) 311–321.19] V.A. Vas’ko, I. Tabakovic, S.C. Riemer, M.T. Kief, Effect of organic additives

on structure, resistivity, and room-temperature recrystallization of electrode-posited copper, Microelectron. Eng. 75 (2004) 71–77.

20] S.H. Brongersma, E. Kerr, I. Vervoort, A. Saerens, K. Maex, Grain growth, stress,and impurities in electroplated copper, J. Mater. Res. 17 (2002) 582–589.

21] F. Ericson, S. Greek, J. Soderkvist, J. Schweitz, High sensitivity surface micro-machined structures for internal stress and stress gradient evaluation, J.Micromech. Microeng. 7 (1997) 30–36.

22] K.P. Larsen, J.T. Ravnkilde, M. Ginnerup, O. Hansen, Devices for fatigue testingof electroplated nickel (MEMS), Proc. IEEE Int. Conf. Micro Electro MechanicalSystem, Las Vegas, NV, USA, Jan. 20–24, 2002, pp. 443–446.

iographies

eunghoon Park obtained his B.S. degree in Electronics Engineering from Dong-Aniversity, Busan, South Korea in February 2005. He received the M.S. degree inlectrical & Computer Engineering from Louisiana State University, Baton Rouge inecember 2007. His master thesis topic was in the area of RF MEMS and microctuators. Since July 2008, he has been working as a field application engineer atSML Korea, Ltd.

ooyoung Hah received the M.S. and Ph.D. degrees in electrical engineering fromhe Korea Advanced Institute of Science and Technology (KAIST), Daejon, Korea, in996 and 2000, respectively. Before joining the Louisiana State University (LSU),aton Rouge, he was with the University of California, Los Angeles, as a Postdoc-oral Researcher from 2000 to 2001 and as a Staff Research Associate from 2004 to005, and with the Electronics and Telecommunications Research Institute (ETRI),orea, as a Senior Member of the Research Staff from 2002 to 2004. He is currentlyn Assistant Professor of Electrical and Computer Engineering at the LSU. He has

uthored and coauthored over 50 publications including journal papers and inter-ational conference proceedings in the field of MEMS. He also holds six U.S. andix Korean patents. His research interests include MOEMS, RF MEMS, MEMS foriomedical applications, microactuators, sensors, microdischarge devices, and nan-technology. Dr. Hah was the third place winner at the student paper competitiont the 2000 IEEE MTT-s.