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Sensors and Actuators A 143 (2008) 352–359

Design, modeling and testing of a unidirectionalMEMS ring thermal actuator

Peng Yang a, Mathew Stevenson a, Yongjun Lai a,∗, Chris Mechefske a,Marek Kujath b, Ted Hubbard b

a Department of Mechanical and Materials Engineering, Queen’s University, Kingston, Ontario K7L 3N6, Canadab Department of Mechanical and Materials Engineering, Dalhousie University, Halifax, Nova Scotia, B3J 1Z1, Canada

Received 3 May 2007; received in revised form 19 October 2007; accepted 29 October 2007Available online 17 November 2007

bstract

This paper describes a novel design for polysilicon micro ring thermal actuators (RTA) fabricated using the multi-user-MEMS-process (MUMPs).RTA is comprised of a ring supported by 12 thin spokes. The spokes are 2 × 2 �m in cross section and 155 �m long. The inner diameter of the

ing is 390 �m, and its outer diameter is 440 �m. The spokes are placed almost radially with an offset distance r of 3 �m measured from the ring

enter to the spoke axes. The actuator design can generate linear motion of 6 �m measured at the end of a spoke. A theoretical model and a finitelement model have been developed in this paper. The actuator has been tested and these results agreed with the simulation results. In order totudy the behavior of the RTA at its natural resonant frequencies, modal analysis has also been conducted.

2007 Elsevier B.V. All rights reserved.

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eywords: MEMS; Micro thermal actuator; Unidirectional; Microsystems; Mo

. Introduction

In the past 20 years, a wide variety of micro-electro-echanical systems (MEMS) actuators, such as magnetic,

lectrostatic and electro-thermal actuators [1], have been investi-ated. Thermal actuators in particular have attracted a significantmount of research effort due to their compact geometry andapability to generate relatively large displacements perpendic-lar [1] or parallel [2] to the substrate. Applications of thermalctuators include driving optical/electrical switches and scan-ing mirror arrays [3]. Since Guckel [2] developed a nickelimorph thermal actuator, the design and modeling of ther-al actuators based on bimorph thermal actuating mechanisms

ave been well developed [4–7]. The principal of these ther-al actuators is to amplify the asymmetrical thermal expansion

f a microstructure with variable cross sections or different

aterials. The heating power comes from the ohmic heating

nder a driving current through the structure. A single polysil-con bimorph thermal actuator can only produce a small force,

∗ Corresponding author.E-mail address: lai@me.queensu.ca (Y. Lai).

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924-4247/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.sna.2007.10.085

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ypically <10 �N. Klaassen [8] and Williams [9] developedhevron actuators which could produce force up to several hun-red micro Newton with maximum 3 �m displacement [10].ater chevron actuators were developed with toggle ampli-ers which are able to provide moderate force and moderateisplacement [11]. A similar concept to bimorph thermal actu-tors has been used to develop out-of-plane thermal actuatorshich could provide a vertical actuating force [12,13]. The main

imitations of thermal actuators are high power consumptionnd low operating frequencies compared to electrostatic actua-ors. The operating frequency of thermal actuators is limited byeating and cooling times which depend on the actuator geom-try and the distance between the suspended device and theubstrate [14].

Most reported thermal actuators provide rectilinear motion.f rotational motion is required, it has usually been generated byicro-motors. Micro-motors consist of arrays of bent beam or

imorph actuators and a transmission mechanism that convertsectilinear motion into rotational motion [15]. The objective of

his work was to design an actuator that directly generated rota-ional motion. There are other examples of rotational thermalctuators that have two to four expansion arms attached to a cen-ral suspended platform and anchored at their outer ends [16].

Actuators A 143 (2008) 352–359 353

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P. Yang et al. / Sensors and

ur design is different because the expansion arms are anchoredt a central hub and an outer ring is rotated. This allows for manyxpansion arms to be used and the rotating body can be easilyttached to other devices. Applications for this rotational actua-or include scanning mirrors and optical switches [15] as well asunable capacitors [16] that operate by varying the overlappinglate area.

An analytical model combining electro-thermal and thermal–echanical analysis of the actuator was developed for the

alidation and optimization of the design. The finite ele-ent analysis was performed to evaluate the performance of

he design. It should be noted that a full analysis (model-

ng and testing) of the force characteristics of this designre not included here, but will be reported in a futureaper.

ig. 1. Unidirectional ring thermal actuator: (a) SEM image and (b) simplifiedinematics model with four spokes only.

earwTkisj(ePhclsc

ctTaprrarcrttrc

3

3

stmc

Fig. 2. The cross sectional view of RTA for thermal analysis.

. Mechanical design of the unidirectional ring actuator

The RTA consists of 12 identical spokes which are distributedvenly along the rigid ring as shown in Fig. 1a. Each spoke hasn offset distance of r = 3 �m measured from the center of theing to the axis of the spoke. The spokes are attached to a ringith an inner diameter of 390 �m and outer diameter of 440 �m.he spokes are 155 �m long with 2 × 2 �m in cross section. Ainematic model of the RTA has been developed and is illustratedn Fig. 1b. The ring is modeled as a rigid body. Each flexiblepoke is modeled as two rigid links connected by a prismaticoint. The rigid links are connected to the ring and an anchoror frame) via rotary joints. The prismatic joint mimics thermalxpansion of the spoke. Due to the minimum spacing rule of theolyMUMPs process [18], it is not possible to connect all theot spokes to their anchors at the tangential point on the offsetircle (see Fig. 1b). Instead, the spokes are anchored on a dashedine circle with a diameter of 80 �m, called the base circle ashown in Fig. 1b. The base circle is concentric with the offsetircle and the ring.

The spokes are divided into two groups by the horizontalenter line of the ring. The two groups of spokes are anchoredo the poly0 layer (see Fig. 2) on the base circle (see Fig. 1a).he anchors of the two spoke groups are separated by a gapnd each of the anchors is connected to a probe pad through theoly0 layer. Through the probe pads, the applied electrical cur-ent flows from one anchor to the connected spokes, then to theing, and flows back through the other group of spokes to theirnchor. The ring is more than 12 times wider than the spokesesulting in the heat generated in the ring being insignificantompared to the heat generated in the spokes. Therefore, theesulting thermal expansion of the ring in both the circumferen-ial and radial directions is negligible. The thermal expansion ofhe spokes causes compressive forces due to the constraint of theing. The compressive forces combined with the spoke offsetsause the ring’s rotation.

. Analytical model

.1. Electrothermal analysis

Since the length of each spoke is much larger than its cross-

ection size, the electrothermal analysis of the RTA is simplifiedo a one-dimensional heat transfer problem similar to other ther-

al actuators [6,12]. The resistance of the ring is relatively smallompared to that of the spokes and consequently it is ignored.

3 Actuators A 143 (2008) 352–359

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ρ

R

waci

S

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pθ

t

F

t

T

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T

r

T

pd

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q

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T

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54 P. Yang et al. / Sensors and

ue to the characteristics of symmetry, the ring thermal actuatoran be divided into 12 identical sections. Each section consistsf one spoke and one portion of the ring between the spoke beingodeled and the next one in a clockwise direction.When the actuator is heated up by ohmic heating, the actuator

ill transfer heat to the ambient air and substrate by conduc-ion, convection and radiation. It has been observed that theonduction mode dominates the heat transfer when the devicesre scaled down to the micron level [14]. In the MUMPs process,here the devices are released above the substrate with a 2 �m

ir gap, it has been proved that the major mode of heat transferhrough the air is conduction [7,19]. Therefore, only conductionill be considered in the analysis of the RTA. Fig. 2 illustratesgeneral cross sectional view of the layers involved in the RTA

hermal analysis.Under steady-state conditions, the second order differential

quation describing the temperature distribution is

pd2T

dx2 + J2ρ = S

t

(T − TS)

RT(1)

here kp represents the thermal conductivity of polysilicon, Jenotes the current density, t is the thickness of the actuator, Ss a shape factor accounting for heat flux out of the top and sideurfaces, RT is the thermal resistance between the suspendedicrostructure and the substrate, T is the temperature of theTA at position x, and TS the substrate temperature, is assumed

o be 300 K. The symbol ρ denotes the resistivity of polysili-on, a temperature dependent parameter, and ρ0 is the resistivityf polysilicon at 300 K. A linear temperature coefficient, ξ, isntroduced to calculate the resistivity [6] as follows.

(T ) = ρ0[1 + ξ(T − TS)] (2)

The thermal resistance RT is given by [6]

T = ta

kv+ tp

kp+ tn

kn(3)

here ta, tp and tn are the thicknesses of the air gap, poly0nd nitride layer, respectively, and kv and kn are the thermalonductivities of air and nitride, respectively. The shape factors given by [19]

= t

w

(2ta

t+ 1

)+ 1 (4)

here w and t are the width and thickness of the spoke, respec-ively.

The physical meaning of the first term on the left side of Eq.1) is the net rate of heat conduction into the element per unitolume. The second term is the rate of heat energy generationnside the element per unit volume. The right hand side of thequation represents the heat loss in the element per unit volume.or simplicity, only one of the 12 identical parts will be used in

he analysis. The boundary conditions are illustrated in Fig. 3.

The symbols Tr(θ), Ta(x) and TS in Fig. 3 represent the tem-

eratures on the ring, spoke and substrate, respectively, whereranges from 0 to β and x varies from 0 to l. The anchor of

he spoke is connected to the substrate. It is assumed to have a

m

ct

ig. 3. The boundary conditions of the electrothermal model of the actuator.

emperature equal to the temperature of the substrate.

a(0) = TS (5)

rom the continuity requirement, the temperature of the spokend the ring at the joint point should be equal.

a(l) = Tr(0) (6)

Considering the symmetric condition, the two ends of theing segment should have the same temperature.

r(β) = Tr(0) (7)

Furthermore, the rate of heat conduction across the joiningoint of the spoke and the ring must be balanced. For one-imensional analysis, the rate is given by:

(x) = kpAdT (x)

dx(8)

here A is the cross section area that the heat flux enters oreaves. According to the symmetric condition, the balanced ratef heat conduction at the joining point is given by

a(l) = qr(0) + qr(β) (9)

After solving Eq. (1) under the conditions of the spoke anding separately, the temperature distributions of the spoke andhe ring segments are shown as follows.

a(x) = TS + J2a ρ0

kpm2a

+ c1emax + c2e−max (10)

r(θ) = TS + c3emrθ + c4e−mrθ (11)

here

2 = Sa

kptRT− J2

a ρ0ξ

kp(12)

2

2 = Sr

kptRT− Jr ρ0ξ

kp(13)

i(i = 1–4) are constants to be solved by the boundary condi-ions, Ja and Jr are current densities of the spoke and the ring,

P. Yang et al. / Sensors and Actuators A 143 (2008) 352–359 355

Table 1Material properties and geometry dimension

Parameter Value Unit

Spoke length, l 155 �mActuator thickness, t 2 �mSpoke width, wa 2 �mRing width, wr 25 �mAir gap, ta 2 �mNitride thickness, tn 0.6 �mYoung’s modulus, E 169 × 103 MPaCoefficeint of thermal expansion, α 3.5 × 10−6 K−1

Thermal conductivity of polysilicon, kp 41 pW m−1 K−1

Thermal conductivity of air, kv 0.026 pW m−1 K−1

Thermal conductivity of nitride, kn 2.25 pW m−1 K−1

Resistivity of polysilicon, ρ0 2 × 10−5 T � mT

rt

t

T

T

�

wti

3

maad

saftr

r

Wftll

Fig. 4. Geometric relations (not to scale).

F

m

(

l

d

Bpok5dpw

4

emperature coefficient of resistivity ofpolysilicon, ξ

1.25 × 10−3 K−1

espectively, Sa and Sr are the shape factors for the spoke andhe ring, respectively.

Once ci (i = 1–4) are obtained by Eqs. (5)–(13), the averageemperature can be obtained by

¯a = 1

l

∫ l

0Ta(x)dx (14)

¯r = 1

β

∫ β

0Tr(θ)dθ (15)

The thermal expansion of the spoke can be calculated by

L = α

∫ l

0(Ta(x) − TS)dx = α(T̄a − TS)l (16)

here α is the thermal expansion coefficient of polysilicon. Allhe material properties and geometry dimensions that were usedn the electrothermal analysis are listed in Table 1 [13,20].

.2. Deflection analysis

Instead of using a common solid mechanics model, a kine-atics model has been developed to predict the behavior of the

ctuator designed. Combined with the electrothermal model, thenalysis will provide a fast guide to justify and optimize theesign.

The geometric relation of the RTA is shown in Fig. 4. Theymbols R, r and e represent the radii of the inner ring, base circlend the offset circle, respectively. The symbol b is the distancerom the anchor to the ring center and γ is the angle between theoggle alignment and the virtual linkage. The relation between, e and b can be found as

2 = e2 + b2 (17)

hen the spoke is heated up, the length of the spoke increases

rom l to l + dl. The expansion dl will force the tip of the spokeo move from A to A′. The horizontal displacement at the tip isabeled as dx. The corresponding rotation angle of the virtualinkage is marked as dγ . For a rotation angle dγ , the trigono-

bMt

ig. 5. The displacement vs. the spoke expansion in the analytical model.

etric relation gives

l + dl)2 = R2 + r2 − 2R × r × cos(γ + dγ) (18)

2 = R2 + r2 − 2R × r × cos γ (19)

x = R × dγ (20)

y solving Eqs. (17)–(20), the relationship between dx (out-ut displacement) and dl (thermal expansion of spokes) can bebtained. Fig. 5 illustrates the dx vs. dl of the RTAs using theinematic model. Three different offset circle radii of e = 3 �m,�m, and 7 �m are simulated. In Fig. 5, it is observed that theesign with the smaller offset circle generates larger output dis-lacements. Therefore, in this paper, only the RTA with e = 3 �mill be examined.

. Finite element analysis

The finite element analysis (FEA) of the RTA haseen conducted using the commercial software COMSOLultiPhysicsTM. Similar to the former analytical model,

he analysis is divided into two parts. First, the electro-

3 Actuators A 143 (2008) 352–359

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swlst

56 P. Yang et al. / Sensors and

hermal analysis was conducted. In this step, the temperatureistribution was obtained using a non-linear solver of COM-OL MultiPhysicsTM. Then the temperature distribution was

mported as the initial condition to calculate the thermal expan-ion and displacement in thermal–mechanical analysis.

The finite element model of the RTA consists of the structureayer of the actuator, a 2 �m thick air gap between the structurend the substrate and an 800 × 800 × 100 �m air block on the topf the substrate. It has been found that increasing the boundaryize above 100 �m had no effect on the final solution [21]. Theottom of the air gap contacts the substrate directly. The siliconubstrate was considered as a large heat sink at room tempera-ure. Therefore, a constant temperature of 300 K is applied as theottom boundary condition of the air block. The inner ends ofhe spokes are also considered to be at a constant temperature of00 K. The top and side walls of the air block were consideredo be at room temperature 300 K. In the FEA the coefficient ofhermal expansion and thermal conductivity of polysilicon areemperature dependent [13]:

(T ) = (3.725 × (1 − e−5.88×10−3×(T−125)) + 5.548 × 10−4T )

× 10−6 K−1 (21)

p(T ) = [(−2.2 × 10−11)T 3 + (9.0 × 10−8)T 2

+ (−1.0 × 10−5)T + 0.014]−1

pW m−1 K−1 (22)

. Results and discussion

Due to the structure of the RTA and the resistance of the ring,he electrical current going through each spoke will be differ-nt. Consequently, some spokes will be heated more than others.

ig. 6 demonstrates the steady-state temperature profiles of theTA driven by a total electrical current of 31.2 mA. The aver-ge current passing through each spoke is 2.6 mA. The spokesith the highest and lowest temperatures are compared with the

ig. 6. The temperature distribution in the spoke of the lumped model and FEAodel.

tfHtiotofspemsmw

fwamt

Fig. 7. Simulation and experimental results of displacement vs. current.

nalytical model. In FEA, the difference between the maximumemperatures of the two spokes is 81 K. The temperature pro-le of the analytical model is located between the spokes with

he highest and the lowest temperatures, therefore, the analyti-al model for electrothermal analysis is reasonable. The spokesill experience different amounts of thermal stress which will

ntroduce internal forces and reduce the output force and dis-lacement generated by the RTA. To solve this problem, a highlyonductive metal layer in the PolyMUMPs process should beeposited on the ring. The deposited metal (gold and nickel) canignificantly reduce the resistance of the ring and minimize theifference between the currents in the spokes.

The experimental setup included a dc power supply, probetation and microscopes. Digital images of the displaced actuatorere captured at various applied currents. The images were ana-

yzed using National Instruments machine vision software withub-pixel accuracy giving displacement measurements accurateo within 0.15 �m. Fig. 7 shows test and simulation results ofhe average spoke current vs. displacement. The predicted trendrom the analytical model agrees with the experimental trend.owever, the analytical results have relatively large overestima-

ions. In the thermal–mechanical analysis, the kinematic models used. The bending of a flexible spoke is modeled as a rotationf the links. However, the strain energy stored in the spoke is notaken into account in the kinematic model, which introduces theverestimation of the output displacement. Secondly, the simpli-ying assumption that all the arms experience the same thermaltress contributes to the overestimation. From a modeling view-oint, the overestimation could be reduced by introducing anlastic coil spring to the rotating links in the thermal–mechanicalodel. The developed analytical model is relatively simple and

traightforward. Though it overestimates the output displace-ent of the RTA, it predicts the trend of the output displacementell and it is valuable for proving the design concept.Thermal actuators have been successfully operated at high

requencies [22–24]. A popular application is scanning mirrors

ith low voltage requirements. These systems usually operate

t mechanical resonant frequencies which are well above theaximum thermal operational frequencies [22]. The response

o a high frequency ac signal is a static offset displacement

P. Yang et al. / Sensors and Actuators A 143 (2008) 352–359 357

(a) M

dtdwnda2wti3ti

avt

n3fnpredicted frequency of 28.6 kHz. All measured frequencies arelower than predicted ones. One major reason is because in FEAthe stiffness of the RTA anchors is assumed to be infinitely large,but in reality, it is a finite value.

Table 2Comparison of predicted and measured resonant frequencies

Mode Natural resonant frequencies (kHz)

Fig. 8. The simulated mode shapes of the RTA:

ue to RMS heating as well as a superimposed vibration. Sincehe RTA was designed with optical applications in mind, theynamic behavior of the device was studied. A modal analysisas conducted and the first four modes and their correspondingatural frequencies were found. The shapes of the modes areemonstrated in Fig. 8. Modes 1, 2 and 3 are out-of-plane modesnd mode-4 is an in-plane mode at frequencies of 22.1 kHz,2.1 kHz, 28.6 kHz, and 43.8 kHz respectively. Modes 1 and 2,obble out-of-plane around the centerline of the ring and have

he same resonant frequency with identical mode shapes, whichs common to structures with symmetric geometry [25]. In mode, all spokes bend vertically together. Mode 4 is an in-plane rota-ional mode where all the spokes bend in-plane homogeneouslyn one direction.

A laser Doppler vibrometer (Polytec MSA-400) was used tonalyze the dynamic behavior of the fabricated actuator. Theibrometer system measures out-of-plane vibrations by sensinghe frequency shift of laser light reflected by a moving surface.

134

ode 1, (b) Mode 2, (c) Mode 3, and (d) Mode 4.

When the actuator was excited with a wide band-width white-oise signal, there were clear resonant responses at 21.6 kHz and7.1 kHz. Table 2 compares the predicted resonant frequenciesrom FEA simulations with the experimentally identified reso-ant frequencies. There was not a measurable response near the

Predicted Measured

and 2 22.1 21.628.6 –43.8 37.1

358 P. Yang et al. / Sensors and Actua

Fig. 9. Out-of-plane vibration frequency response of an RTA.

eotcsaibs

Fa

lMptdmoqis

iara

rtSwatsWvut

6

pMehb

Fig. 10. Out-of-plane displacement-shape visualization.

Fig. 9 shows the frequency response to a 2 V white-noisexcitation signal. To better understand the out-of-plane motionf the actuator, measurements were taken at multiple points onhe ring. Fig. 10 shows the ring’s upper surface displaced verti-ally above the substrate. This is a still frame of an animationequence (from experimental results) of the actuator’s response

t 37.1 kHz. The maximum vertical displacement is 150 pm. Its thought that since the beams have equal bending stiffness inoth in-plane and out-of-plane direction, the ring is being liftedlightly as it rotates.

ig. 11. In-plane vibration frequency response of an RTA with a resonant peakt 37.1 kHz.

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n

R

tors A 143 (2008) 352–359

To further the modal analysis, in-plane motion was ana-yzed with a stroboscopic video microscopy system (Polytec

SA-400). For this testing the actuator was excited with 2 Veak-to-peak sinusoidal signals at several high frequencies upo 100 kHz. The frequency response in Fig. 11 shows an in-planeisplacement peak at 37.1 kHz. At this frequency, the in-planeotion (∼1000 nm) is over six thousand times larger than the

ut-of-plane motion (150pm). It confirms the mode at this fre-uency is an in-plane mode. The measured resonant frequencys in good agreement with the frequency predicted by the FEAimulations.

The maximum measured rotation of the RTA was 1.9◦ with annput power of 119 mW. In comparison, the actuator in [17,26],lso fabricated with PolyMUMPs could rotate 1.7◦ and 1.9◦,espectively. The AlSi alloy actuator in [16] could rotate 7◦ withn input power of 300 mW.

One disadvantage of the proposed actuator is its size. Theequired area can be efficiently used by adding more arms insidehe ring. The output force increases with the number of arms.ince all of the arms are heated and do work, there is no energyasted deforming cold arms like those found in bimorph type

ctuators. A design flaw was discovered during the vibrationesting. The arms have square cross sections with equal bendingtiffness in the planes parallel and perpendicular to the substrate.

hen the arms expand there is rotation combined with undesiredertical lifting of the ring. This could be easily remedied bysing a different fabrication process with a thicker device layero prevent out of plane bending.

. Conclusions

A novel design of a micro electrothermal actuator has beenresented in this paper. The actuator has been fabricated usingUMPs process and tested. Analytical and finite element mod-

ls of the actuator have been developed. The simulated resultsave been compared with tested results, and agreements haveeen observed. The advantages and disadvantages of the simpli-ed analytical model have been discussed. Finite element modalnalysis has been conducted as well. The finite element analysisnd testing of the resonance frequency and mode shape are alsoresented. Good agreement has been achieved.

cknowledgements

This work was supported by the Natural Sciences and Engi-eering Research Council of Canada.

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