A Bulk Micro Machined Bistable Relay With u Shaped Thermal Actuators

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 14, NO. 5, OCTOBER 2005 1099

A Bulk-Micromachined Bistable RelayWith U-Shaped Thermal ActuatorsJin Qiu, Member, IEEE, Member, ASME, Jeffrey H. Lang, Fellow, IEEE,Alexander H. Slocum, Member, IEEE, Fellow, ASME, and Alexis C. Weber

Abstract—This paper reports a deep-reactive ion etching(DRIE)-through-etched laterally bistable MEMS relay for powerapplications, with a primary emphasis on the design and modelingof its U-shaped transient thermal actuators, and a secondaryemphasis on the design and fabrication of its contact element. Inthis relay, a contact crossbar is carried by a curved-beam bistablemechanism [1], which is toggled by transient U-shaped thermal ac-tuators with their hot beam adiabaticly heated by electrical pulses.Each U-shaped thermal actuator comprises uniform-thickness hotand cold beams with a gap between them so they bend differently.This paper develops both a basic model and a complete modelfor the actuator that are verified by Finite Element Analysis andserve as effective design tools. The DRIE process creates nonidealetched surfaces, which pose challenges for good relay contacts.Both contact design and process development are discussed to helpalleviate this problem. The fabricated relay exhibits a minimumtotal on-state resistance of 60 m, and a maximum currentcarrying capacity of 3 A. It switches with a 1 ms actuation pulse,and a maximum 5 Hz repetition rate. [1415]

Index Terms—Bistable relay, DRIE footing, microelectrome-chanical systems (MEMS) relay, nonlinear beam analysis, relaycontact, thermal actuator.

LIST OF SYMBOLS IN ACTUATOR MECHANICAL MODELING

The subscript and refer to parameters related to the hotbeam and the cold beam, respectively. Capital letters in paren-thesis in the following list refer to corresponding normalizedparameters.

Beam width (wafer thickness).Young’s modulus.Force, actuator force.Actuator blocked force.Beam moment of inertia.Beam initial length.Moment.Beam axial compression force.Beam thickness.Initial gap between hot and cold beam.Temperature rise in hot beam.Initial distance between hot and cold beam centerlines.

Manuscript received August 31, 2004; revised April 18, 2005. This work wasbased on the Ph.D. dissertation of J. Qiu [15]. This work was supported by ABBCorporate research, Baden-Dattwil, Switzerland. Fabrication was performed inthe Microsystems Technology Laboratories of MIT. Subject Editor C.-J. Kim.

J. Qiu is with WiSpry, Inc., Irvine, CA 92618 USA (e-mail: [email protected]).

J. H. Lang is with the Department of Electrical Engineering and ComputerScience, Massachusetts Institute of Technology, Cambridge, MA 02139 USA.

A. H. Slocum and A. C. Weber are with the Department of Mechanical Engi-neering, Massachusetts Institute of Technology, Cambridge, MA 02139 USA.

Digital Object Identifier 10.1109/JMEMS.2005.856676

Fig. 1. Basic fabrication method of the relay.

Lateral beam deflection.Beam coordinate.Thermal expansion coefficient.Beam tip lateral deflection.Actuator free displacement.Ratio of beam tip axial shortening, caused by beam lat-eral curving, to beam length.Beam tip rotation.

Note: In this paper, “axial” refers to the direction along theinitial beam length (the - direction), and “lateral” refers to thein-plane direction perpendicular to it. By such definition, bothdirections do not change with the bending of the beam. As canbe seen in Fig. 7(b), the direction of the axial force is alwayshorizontal, and the lateral forces and are always sideways.Both axial and lateral deflections of the beam are also definedin the above directions.

I. INTRODUCTION

THE development of MEMS relays has attracted consider-able attention in recent years. Relays have been fabricated

through surface [2], [4]–[6] and bulk [3], [7] micromachining,have employed electrical [3], [6], magnetic [4], [7] and thermal[2], [5] actuation, have employed monostable [2], [3], [5]–[7]and bistable [4] structures, and have employed lateral [2], [5]and vertical [3], [4], [6], [7] moving contacts. One relay hasemployed a liquid-metal movement [5]. The applications haveranged from signal [2], [4], [5] to power [3], [6], [7] switching.For power switching requirements, the lowest reported on-stateresistance is 14 [3] and the highest reported current-car-rying capacity is several Amperes [6]. None of these relays aredesigned to be mechanically bistable, which is a main feature ofthe relay developed by this paper. Some preliminary results ofthis paper are presented in [8].

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1100 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 14, NO. 5, OCTOBER 2005

Fig. 2. Relay plan view.

The relay reported here is a bulk micromachined thermallyactuated bistable lateral relay for power applications. The bulkmicromachined structure ensures good thermal conduction atthe relay contact, which together with a low contact resistance,contributes to a high current-carrying capacity. Compared withother actuators, the thermal actuator has a larger force andstroke, and requires a lower driving voltage. When coupledwith a bistable structure, the disadvantage of the high power re-quired for thermal actuation is minimized because only a smallamount of transient energy is needed to change the bistablestate. Contact resistance is a function of contact force amongother things. To have a low resistance, the desired force is set tobe more than 1 mN. In order to have a large stand-off voltagewhen the relay is in its off-state, a minimum gap between thecontacts is specified as 24 . One potential application ofthis relay is to disconnect ac loads at their zero current point.To achieve this, the switching time is required to be less than 4ms. Switching at the zero current point reduces the energy thatthe small MEMS contacts must absorb in the subsequent arc.Similarly, the relay must open quickly at its zero voltage pointto avoid an arc.

The basic fabrication scheme is shown in Fig. 1. A silicon de-vice wafer is through-etched by DRIE and bonded to a handlewafer that has shallow etched pits, above which the device fea-tures can move. Fig. 2 shows the relay plan view, with shadedareas anchored to a handle wafer. As can be seen in Fig. 2, allrelay components move laterally in a direction parallel to thewafer plane, thus the relay contact happens through the side-walls of DRIE etched beams as they are pushed against eachother. The sidewalls are deep etched surfaces, which are not per-fectly planar. This poses challenges that are a main topic of thispaper.

At the center of the relay is a mechanically bistable precurveddouble beam [1] that moves laterally in the wafer plane. Acrossbar is attached to the double beam by a cantilever beam.When the double beam is in its as-etched position (solid lines inFig. 2) the two contacts below the crossbar are not connected,

Fig. 3. Contact geometry explored.

and the relay is open. When the double beam snaps toward itssecond stable position (dashed lines in Fig. 2), it pushes thecrossbar against the two contacts, and the relay is closed. Goodelectrical contact is ensured through metal deposited on theetched sidewalls; flat contacts have experimentally proven togive the best electrical contact. Thermal Actuator #1 in Fig. 2deflects downward to close the relay. Thermal Actuator #2deflects upward to open the relay.

II. RELAY CONTACT

The basic contact component employed in this relay com-prises a flat crossbar and two flat relay contacts. The crossbar,attached to the bistable double beam through a cantilever, is re-quired to provide balanced contact force on both contacts whenthe double beam’s deflection toward the second stable positionis blocked. The shape of the contact structure and the mechan-ical characteristics of the double beam can both vary with fab-rication errors. The flat-flat contact shapes and the compliantcantilever coupling are designed to lower the dependence of thetwo contact forces on fabrication variations.

Other crossbar and contact shapes have been fabricated andtested as shown in Fig. 3. In the figure, the upper element is thecrossbar, which can move laterally to close the two contacts atthe lower position. Even with the extra cantilever compliancediscussed later, all of these have worse contact resistance thanthe flat-flat contacts shown in Fig. 2. In most cases, the crossbarsshown in Fig. 3 make contact on only one of the two contacts;the other contact is not touched. Nonflat contact shapes havemore variation during the mask making and photolithographysteps, so the shape errors are larger than for flat ones. In addition,all of the nonflat shapes have a point contact in 2D, and so an


QIU et al.: BULK-MICROMACHINED BISTABLE RELAY WITH U-SHAPED THERMAL ACTUATORS 1101

Fig. 4. f-d characteristic of double beam and attached softspring-coupled crossbar. (a) f-d curve of double beam. (b) f-d curve of crossbar. The Bistable beam hasa thickness of 12 �m, an initial apex height of 72 �m, a length of 4 mm, a width (wafer thickness) of 0.3 mm, and a Yong’s modulus of 169 GPa; the cantileverbeam has a thickness of 12 �m, a length of 500 �m, a width (wafer thickness) of 0.3 mm; the crossbar has an initial distance to the contacts of 114 �m.

equal amount of shape variation is more significant for sharpcorners than for flat edges. Also, several configurations shownin Fig. 3 have their contact surfaces not perpendicular to thecrossbar motion. Friction can occur in these cases, which makesthe contact positions unpredictable.

Fig. 4(a) shows the force-displacement (f-d) relation of thebistable double beams with the design dimensions stated in thefigure description. These dimensions are chosen to meet therelay specification outlined in Section I. The relation has threeregions of different stiffness. They are two short regions of verylarge positive stiffness at the beginning and the end of the rela-tion, and a long region of low negative stiffness in between. [1]establishes that with , the f-d curve shown in Fig. 4(a)can be described with

(1)

(2)

where is the ratio of the double beam initial apex height tothe beam thickness , is the Young’s modulus, is the beammoment of inertia, and is the beam length. The center clampbetween the double beams is designed to constrain the twistingmode during beam deflection through the negative stiffness re-gion. Even though most of the twisting mode is constrained,some remains, which makes the orientation of beam center un-predictable. However, during the second positive stiffness re-gion, there is no twisting mode present so the beam center is per-fectly parallel to the contacts. Thus the second positive stiffnessregion is where the contact should be positioned. To have a totalcontact force of 4 mN, the contact point, as shown in Fig. 4(a),should be positioned at about 137 on the axis. However,two factors affect the relative position of the contact point onthe f-d curve. First, photolithography and DRIE through-etchingcan typically produce an etched feature width variation of about4 from the mask design. Second, the variation of doublebeam thickness can change the shape of the f-d curve. Both ef-fects can make the contact force unpredictable and may evenprevent contact.

Inclusion of a cantilever beam having dimensions describedin the caption of Fig. 4 solves this problem. Fig. 4(b) also showsthe f-d curve of the crossbar attached to the cantilever. With theextra compliance of the cantilever, both the positive stiffness re-gions of the double beam become much more compliant, whilethe negative stiffness region becomes stiffer. Now the contactsshould be designed to be 114 away from the etched posi-

Fig. 5. Microscope picture of the cantilever and the closed contacts.

Fig. 6. Schematic of the electrothermal actuator.

tion of the crossbar, closer than without the extra compliance, tohave the desired contact force of 4 mN. The contact force vari-ance resulted from an etched gap variance of 4 is reducedto 0.6 mN with the modified f-d curve. The center of the twocontacts, the crossbar, and the double beam are aligned in themoving direction of the double beam. In this way the crossbarremains parallel to the contacts when pushed against the twocontacts and the force on the two contacts are equal. The can-tilever beam can also mechanically self-adjust to balance theforce on each contact, as well as to conform the crossbar to thecontacts when opposite contact sidewalls are slightly verticallyunparallel. Fig. 5 shows a closed crossbar with contacts.

DRIE through-etch creates deep nonideal etched sidewalls,which pose challenges to good relay contact and metallization.The fabrication steps for creating better etched sidewalls andachieving better sidewall metallization are described later inSection IV of this paper.

III. ELECTROTHERMAL ACTUATION OF

THE BISTABLE MECHANISM

A. Design and Modeling Overview

Electrothermal actuators are commonly used in MEMS[9]–[12]. Fig. 6 shows the schematic of the U-shaped thermal



Fig. 7. Thermal actuator mechanical model. (a) Deflection of thermal actuator. (b) Free body diagram of the three segments. Note: The axial direction is horizontaland the lateral direction is vertical, they do not change with the beam bending.

Fig. 8. Treatment of beam segments in the mechanical modeling of thermalactuator. (a) Basic model. (b) Complete model.

actuator developed in this paper. Two beams are mechanicallyanchored at one end, and joined together at the other end. Onebeam is coated with metal while the other is not, so a currentgoing around the beams generates heat in the bare silicon beamwhile the coated beam remains cold due to the high metal elec-trical conductance. The hot beam expands thermally, but dueto the constraint of the cold beam, both deflect laterally at thejoint tip. This tip motion is used as the actuation. The heatingof the hot beam is controlled to be very short, so the actuatoris in a thermal transient during the actuation. During actuation,the gap between the two beams varies in time along the beams.This is different from a bimorph type thermal actuator where nogap exists thus all layers of the bending structure would deflectin the same shape. While the treatment of the bimorph thermalactuator can be found in literature such as in [9], no analyticmodeling of the U-shaped thermal actuator in the literature hasbeen found. The detailed mechanical modeling of the actuatoris therefore developed and presented here.

Two important characteristics of the actuator are 1) itsblocked force at the tip when the tip displacement isblocked and 2) its free displacement at the tip when no tipforce is applied. These characteristics will be set by the needsof the relay. In the modeling, the temperature rise of the hotbeam is assumed to be uniform, and the temperature rise of thecold beam is assumed to be zero. The modeling approach is1) separate the actuator, as shown in Fig. 7(a), into three freebodies as shown in Fig. 7(b): the hot beam, the cold beam andthe connector beam; 2) write the relations of force/momentand displacement/rotation for each of these three memberstogether with the coupling boundary conditions; and (3) solvethe equation array.

As shown in Fig. 8(a), the basic model assumes that the lateralbeam deflection is only affected by moment and lateral force,and the axial beam deflection is only affected by axial force. Thebasic model neglects two higher-order effects, which are takeninto account in the complete model as shown by the two extra

arrows in Fig. 8(b). First, when the beam tip lateral deflection isnonzero, the axial force contributes a moment on the beam soit affects its lateral deflection. Second, the lateral curving of thebeam causes its tip to shrink back axially. The basic model givesa closed form solution and design, which can be verified andrefined by the complete model. Fig. 7(a) shows that the hot beam“buckles” in the center during the beam deflection, it should benoted that this is not mainly caused by axial force such as ina clamped-clamped beam case. The “buckling” exists in bothbasic and complete models, though axial force does amplify thebuckling in the complete model.

In both the basic and complete models for the thermal actu-ator shown in Fig. 7, assume a top hot beam length of , thick-ness of and moment of inertial of , a bottom cold beamlength of , thickness of and moment of inertial of , aninitial gap between the two beams of , a beam width (waferthickness) into the paper of , a uniform temperature rise in thehot beam of and in the cold beam of zero, a thermal expan-sion coefficient of , a compression force inside the hot beamat the top (which means a tension force inside the cold beam),upward forces and on the hot and cold beam tips and anupward net force on actuator tip of , a clockwise moment onthe hot beam tip of , a clockwise moment on the cold beamtip of , a downward tip lateral displacement , and a clock-wise tip rotation .

B. Basic Mechanical Model of Actuator

In the basic model, the beam bending equation is

(3)

where is the Young’s modulus, is the beam momentof inertia, and is the beam lateral displacement.Equation (3) together with clamped boundary conditions andsmall approximation, yields the deflections of the hot andcold beam tips as

(4)

(5)

(6)

(7)



With a small approximation, the moment balance of the con-nector beam gives

(8)

A force balance of the connector beam between the hot and coldbeams gives the actuator force as a sum of both hot and coldbeams tip forces,

(9)

The short connector beam is assumed to be a rigid body duringthe actuation, so the axial deflection geometric compatibility ofthe hot and cold beams gives

(10)

Equations (8)–(10) are linear equations, so the tip displacementis a linear function of tip force. The blocked force and free dis-placement can be obtained as follows. For simplicity, assumeboth initial lengths are equal, and define .Then

(11)

(12)

(13)

This completes the simple model, with (11)–(13) summarizingthe behavior of the linear f-d relation.

C. Complete Mechanical Model of Actuator

In the complete model, the lateral deflection is caused by thelateral force and moment, and also amplified by axial compres-sion, or deamplified by axial tension. The self-enhancing ampli-fication effect of axial compression is usually more significantthan the self-limiting deamplification effect of axial tension. Onthe other hand, besides thermal strain and Hooke’s law, the axialdeformation is also determined by the curving of the beam. Thetwo effects shown in Fig. 8(b) are both very nonlinear, whichmakes the complete model algebraically complex.

To start the complete model, first consider a beam with sim-ilar conditions as the hot beam shown in Fig. 7(b). The beambending equation used is

(14)

which has the moment contribution of the axial force , ex-pressed by the first term on the right hand side, as an extra mo-ment contribution than what is shown in (3). Note that , thebeam tip deflection, is an unknown constant that must be deter-mined. The beam tip rotation is

(15)

To clarify the analysis, define the normalized variables

(16)

With these normalizations, (14) takes the form

(17)

The solution of (17) is

(18)

Note that the unknown constant does not appear in this so-lution. Although (18) is highly nonlinear in , it is linear for agiven . As can be seen in the development below, all equationsare linear for a given . This ensures a linear numerical solu-tion of the actuator behavior with the normalized compressionforce acting as a free varying parameter. Equation (18) givesa constitutive relation at the beam tip of

(19)

and

(20)

The axial deflection of the beam tip is caused by three factors:the thermal expansion, the axial compression, and the beamshortening caused by the lateral curving of the beam. With asmall deflection assumption, the ratio of the beam shorteningby lateral curving to the beam length can be calculated as

(21)

We can now consider the thermal actuator, shown in Fig. 7(a),using analytic notation defined in (16)–(21) with the subscripts



and denoting the hot beam and cold beam as shown inFig. 7(b). To continue the analysis, define

(22)

Next, the two axial forces must have equal value but oppositesign so that

(23)

Equation (23) yields an imaginary for the cold beam, whichmeans that its force is in tension instead of compression. Notethat (18)–(21) hold for an imaginary too, with all terms inthe equations still reducing to real numbers. Similar to (8), themoment balance of the connector beam is

(24)

According to and (19) and (20), the constitutive behavior ofboth beam tips is described by

(25)

(26)

(27)

(28)

The geometric constraints of the rigid connector beam are

(29)

(30)

(31)

In the left hand side of (31), the first term is the thermal strain(heat expansion) of the hot beam; the terms in the second paren-thesis are the axial strain for both beams; the terms in the secondparenthesis are the beam shortening effect for both beams; andthe last term is the deflection difference of the two beam tipscaused by the rotation of the connector beam. Note that ex-cept for the extra terms in the second parenthesis of (31), it isthe same equation as (10). Combining (21) and (31) gives (32)shown at the bottom of the page. Assuming a given , (23)gives , and then (24)–(30) are linear equations which can besummarized by

(33)

where and are both seven-element vector functions of. Substitution of (33) into (32) gives a quadratic equation

(34)

that can be solved for . Given , (33) then gives solutionsfor all other variables.

Returning to dimensional form, (16) gives

(35)

From a force balance and (16)

(36)

Note that (35) and (36) together give the force-displacementcharacteristic of the thermal actuator, parametrically over .Therefore, varying over a reasonable range sweeps the tra-jectory of the actuator force-displacement characteristic. Thecomplete model is implemented in Matlab code. (Readers canemail the first author for the code).

Both basic and complete models can be compared with non-linear FEA to show their effectiveness. A MatLab implementa-tion of both models gives a result in less than 1 second, whileconstruction and running of an FEA model usually takes morethan 10 minutes for a specific design. Fig. 9 shows the modelcomparison for a thermal actuator having dimensions describedin the figure caption. (Young’s modulus of Si at 220 is veryclose to its room temperature value according to [13], [14].) Thecomplete model agrees very well with the FEA, while the basicmodel is only effective over low temperature rise.

D. Electrothermal Model of the Actuator

The basic actuator design covers the cold beam with metalto make it more electrically conductive than the hot beam. Thispermits differential heating and expansion of the beams as anelectrical current is passed around them to produce the desireddeflection. Heat transfer has three mechanisms: conduction,convection and radiation. Over the MEMS scale, conduction isthe dominant mechanism. To verify this, the heat transport ofthe other two mechanisms can be estimated. Assuming a forcedair convection constant of 100 - , a Stefan-Boltzmannradiation constant of 5.67e-8 - , a room temperatureof 25 , a hot beam temperature of 220 higher than roomtemperature, and a total surface area of the hot beam of 4.6e-6

, the convective power lost is 0.1 W and the radiation powerlost is 0.019 W, both negligible compared to the 50 W dissipa-tion of electrothermal power generated in the thermal actuatordesign described in Fig. 9. To model the thermal operation ofthe thermal actuator, it is first important to know how fast the

(32)



Fig. 9. Comparison of thermal actuator model results. (a) Blocked force versustemperature. (b) Free displacement versus temperature. The U-shaped thermalactuator has a 6 mm length, an 80 �m hot beam thickness, a 60 �m cold beamthickness, a 20 �m gap, a 300 �m width (wafer thickness), and a 169 GPaYoung’s modulus.

heat diffuses by conduction in the silicon structure. A simpleestimate is

(37)

where is the thermal diffusion time, is the thermaldiffusion length, and thermal capacity (or volumetric heat ca-pacity) and thermal conductivity refer to the values of silicon.Equation (37) can also be written as

(38)

The electrical pulse used to heat the thermal actuator ischosen to be 1 ms. Equation (38) states that the thermal diffu-sion length over 1 ms is 315 , which is much less than 6mm, the actuator length in the final design. Therefore thermaldiffusion along the beam length is to first order negligible.Unlike many other thermal actuators, the actuator describedhere is a transient one. In this way, uniform temperature ismaintained inside the hot beam and little heat flows into thecold beam, so the maximum expansion difference between thebeams is obtained. If left excited for more than several ms, thetemperatures of the two beams partially equilibrate and theactuator retracts. To thermally diffuse through the whole 6 mm

length of the actuator, (37) states that the required diffusiontime is 0.37 s, which is an estimate of how fast the thermalactuator can cool down. This is reasonably consistent with theexperimentally measured maximum repetition rate of 5 Hz.

The electrical energy required for actuation is equal to theheat energy stored inside the hot beam. For the thermal actu-ator shown in Fig. 9, a heat capacitance calculation estimatesthat 50 mJ of electrical energy is needed to heat the hot beamup by 220 . (The temperature of 220 is chosen based onthe complete model and/or FEA for the desired blocked forceof 13 mN and free deflection of 120 .) The silicon resis-tivity determines the required excitation voltage and current. Ifan actuation voltage of 50 V and pulse width of 1 ms is desired,the resistivity of the wafer should be chosen as 0.02 ohm-cm.The corresponding current at actuation is . The metal layershould provide a much lower electrical resistance than the sil-icon it covers. Assuming only the top surface is covered by gold,to have one tenth resistance of the silicon, its thickness is cal-culated to be 0.35 . This means a 0.35 gold layer shouldbe enough to provide the high conductance. With this thickness,approximately equal to one tenth of the heat generated in the hotbeam would be generated in the gold layer. Heat diffusion es-timation shows that this heat would diffuse across the 300silicon depth, so the temperature rise in the gold layer would beone order of magnitude lower than in the hot beam. However,even with this transient actuator, the heat will still flow from thehot beam to the cold beam through their connection after theelectrical pulse. So the gold layer near the junction point willexperience a temperature close to that of the hot beam temper-ature. Failure of the gold layer at the junction was indeed ob-served during the operation of some of the devices.

A thermal FEA study of the transient conduction in thethermal actuator described in Fig. 9 was carried out. Boththe hot beam and cold beam have zero temperature boundarycondition at their clamping bases. The connection beam is setto be 50 wide. 50 W is applied to the whole body of the hotbeam to simulate the ohmic heating, and 1 W is applied to thetop surface (wafer top) of the cold beam to simulate heat sourcewithin its metal coating. The resulting temperature rise profileat the end of a 1 ms heating pulse is shown in Fig. 10. It can beseen that the hot beam rises for about 220 degree C and the coldbeam rises for less than 10 degree C. The transition temperatureregion at bases and connection ends are much shorter than thetotal beam length, which verifies the diffusion estimation by(38).

E. Dynamics of the Actuation

The mechanical models presented in Sections III-B and C arestatic. The thermal actuator is designed to operate in transientfashion; dynamics exists for the coupled actuator-double beamsystem. Due to the component’s high nonlinearity, even the tran-sient FEA for the double beam alone has convergence problems.On the other hand, due to the small size of MEMS elements, in-ertial effects are usually small thus the mechanical system couldbe considered quasistatic. To evaluate this, a first order estima-tion is presented here.

With reference to Fig. 9, the system has a total mass of 6e-7kg, a block force of 13 mN and a free displacement of 120 .



Fig. 10. FEA modeling of the transient heating in thermal actuator.

Fig. 11. The actuation pulse (top curve) and resulting contact closure (bottom curve).

To estimate how fast the actuator will bend, we treat it as a singledegree of freedom mass-spring system, with the effective massto be its total mass, and the effective spring constant to be itsblocked force divided by its free displacement. The total timefor it to reach fully bent shape, as estimated to be one fourth ofits vibration period, is about 0.12 ms, almost 10 times smallerthan the heating time of 1 ms. The double beam is even fasterconsidering its mass of more than 10 times smaller than the ac-tuator. This indicates that the mechanical response of the actu-ator is much faster than its thermal response, so we can treat theactuation as a quasistatic mechanical event with the speed dom-inated by the heating.

Experiments were done to observe the closing speed of therelay. One relay contact was connected to ground through a re-sistor, and the other contact was connected to a voltage source.The potential of the first contact was monitored by a voltmeter,so that a zero potential indicated an open relay and a highpotential indicated a closed relay. Actuation power of the 1 mspulse was ramped up until the relay can be just switched. Fig. 11shows a typical timing of the actuation and relay closure. Asthe figure shows, the first contact occurs less than 0.1 ms after

the down ramp of the actuation pulse, which agrees well withthe dynamic approximation given above (heating dominatesswitching speed). Five relays were tested from one fabricatedlot and similar closing phenomena were observed. Among therelay tested, the first closing occurred 65–75 after the downramp of the actuation pulse; the contact lasted for 80–90before the crossbar bounced back for 400–440 and returnedto close the relay again. Though the timing of the first contactand bounce were quite consistent, some devices settled to fullcontact after the first bounce, while others bounced for 1–4more times such as shown in Fig. 11. The full bouncing tookbetween 0.5 to 1.5 ms depending on number of bounces. Withthe 1 ms actuation time, the total relay closing time is less than2.5 ms. Due to the asymmetry of the double beam f-d curveas shown in Fig. 4, the opening of the relay is faster than itsclosing. So the total switching time of the relay is within thedesign requirement of 4 ms.

F. Design Procedure of the Actuator-Double Beam System

The actuator must have both enough force and enough dis-placement to toggle the double beam. To be effective, the ratio



of its blocked force over free displacement should be equal tothe negative slope of the double beam f-d curve as shown inFig. 4(a). In designing a thermal actuator, (13) can be used firstto quickly identify the ratio of thickness over length, and thenthe simple form of (11) assuming equal thicknesses can be usedto determine the length of the thermal actuator. Then, the relativeratio of thicknesses could be fine tuned with the exact formulain (11) and (12), or they can be substituted into the completemodel to verify the results.

For practical purposes, the temperature rise in the hot beamshould be kept below 300 degree C. For this temperature rangeFig. 9 shows that the basic model is good enough for predictingthe thermal actuator behavior. However, it must be emphasizedthat if the basic model is used without confirmation from thecomplete model, a thin-hot-beam (compared to the cold beam)design could easily become the “optimized” result. Such a de-sign does not give the desired result even at low temperature,because the thinner the hot beam compared to the cold beam,the lower is the temperature range over which the basic modelis effective. It is found that to have an effective transformationof axial expansion to lateral motion, a hot beam thickness ap-proximately equal to the cold beam thickness is preferred.

The U-shaped thermal actuator with the dimensions shown inFig. 9 is designed to have 13 mN of blocked force and 120of free deflection at a temperature difference of 220 . Thisactuator can actuate the bistable double beam whose f-d curveis shown in Fig. 4(a). The slightly larger force and displacementrequired of the thermal actuator over those of the double beamare the results of the 20- -etch gap between the actuator anddouble beam.

The temperature profile of the thermal actuator, and itsblocked force and free displacement capability during actuationare difficult to measure experimentally due to the small devicedimensions and the transient nature of the actuation. However,by ramping the actuation current pulse, it is easy to establish theminimum energy that causes the actuator to toggle the bistablestructure. The actuation energy determines the temperature riseof the hot beam in the electrothermal model, and the f-d relationof the bistable structure determines the blocked force and freedisplacement of the actuator. The experimentally measuredminimum energy pulse to toggle the bistable structure is typi-cally within 20% of the value estimated by the actuator models.

IV. FABRICATION AND TESTING

The MEMS relay shown in Figs. 2 and 5 has been fabri-cated and successfully tested. The N-type 4-inch silicon waferused for fabrication has a typical 0.02 - resistivity, and a315- thickness. The 4-inch Pyrex handle wafer has a 500-thickness. In the etch masks for the silicon through etch, filletsare added at the sharp corners to lower any stress concentra-tion. Further, a halo is included in the mask, so that the etchspace has the same width throughout the mask. This arrange-ment ensures that etching occurs at the same rate across all de-vices. Fast-turnaround and economic mask printing is adoptedfor fabrication. The mask pattern is first printed on a trans-parency by a commercial service with a feature resolution ofabout 5 . Then the transparency pattern is transferred to a re-sist-covered chrome glass plate by photolithography. Finally the

Fig. 12. Fabrication process flow.

chrome plate is etched and cleaned, ready to be used as a mask.The time required to turn a mask drawing into a real mask istwo days. For better resolution than 5 , a stepper exposureprocess can be used, which has a 10:1 feature reduction capa-bility from the mask onto the wafer. This improves the resolu-tion by a factor of ten.

Fig. 12 shows the main fabrication process steps for the relay.First, a backside shallow pit of about 20 is etched by DRIEon the device wafer. This backside shallow etch step is designedto alleviate the bottom etching problem of a DRIE through etch.Typical DRIE through etching does not yield an ideal etch at thebottom of the wafer due to footing erosion and footing radius.The footing erosion refers to the eroded silicon structure at thebottom by reflected plasma attack on the unprotected silicon;this reflected plasma is from the adhesion photoresist on thehandle wafer carrying the device wafer being etched through.The footing radius refers to the thicker feature size at the bottomdue to weakened plasma etching from above. The shallow back-side etch lifts the bottom of the etch surface, thus effectivelyalleviating both problems. It prevents the relay contacts frommaking only point contact along their bottom edge. It also helpsincrease the fracture strength of the structure by avoiding ero-sion. Fig. 13 shows SEM pictures of the bottom part of threepieces of silicon. Without the backside etch, (a) has an erodedbottom, and (b) has a widened bottom, while with the techniqueof backside etching, (c) has a smooth and straight bottom.

Second, the device feature is through-etched by DRIE fromthe front side. All isolated parts etched in this step remainattached to the wafer by break-off tabs so that they do not falloff. The DRIE etch recipe “MIT69A” was used as developed inthe Microsystems Technology Laboratories (MTL) of MIT. Thetotal time taken to etch through the wafer thickness of 300was about three hours with a 20 halo. After the DRIEthrough etch, it is necessary to remove the Teflon residue fromthe DRIE process, and also to smooth the sidewalls for bettermetallization results. To do so, a DRIE isotropic etch usingfor 20 seconds follows the through etch. A half-hour O plasmaashing, a 0.5 thermal oxide growth at the temperature of1100 C, and a BOE (Buffered Oxide Etching) striping of oxidefollows. Experiments with these process steps prove they arehelpful for better metallization adhesion and contact resistance.



Fig. 13. SEM pictures of DRIE structures at the wafer bottom. (a) Typical footing erosion. (b) Typical footing radius. (c) Smooth bottom fabricated with thebackside shallow etch method.

In the third step, a Pyrex handle wafer receives an optionalshallow etch of 50 to define pits below the device-wafercomponents that will move. Fourth, the device wafer is anodi-cally bonded to the handle wafer. Fifth, a shadow wafer is etchedby DRIE and is placed on top of the device wafer. The devicewafer is sputtered with 100 A of Ti and 1 of Au with theshadow wafer acting as a mechanical mask. The shadow waferis designed so that all sputtered metal on the relay contactsare wired together. This provides a current path for subsequentelectroplating. The sputtering machine locates the metal sourceabove the wafer. It does not give metal coverage sufficient forsidewall contacts; our estimation of the average gold thicknesson the sidewalls is only 10% of that on the top wafer surface.

In the sixth step, about 2 of copper or gold are electro-plated on the device wafer. The copper plating for example isfrom a commercial acid sulfate solution. Periodic pulse platingwith a 5-ms on time and a 1-ms off time is used to improvethe uniformity of the film thickness and sidewall coverage.The plating was done under constant temperature of 18 C withmild agitation of the plating solution. The current amplitudeand plating time is determined by the desired plating thicknessand area. In a typical setting, 0.1 A of current lasting for 9 minplates 2 of Cu on a 10 area. After electroplating,thorough rinsing and drying is performed to remove any sulfatefrom the device to avoid fast oxidation.

After fabrication, the break-off tabs in the device wafer aremanually broken to achieve electrical isolation between devicefeatures, and the relay is ready for testing. Probes electricallyconnect the relay. An external source provides pulses for thethermal actuators. Typically, 1-ms pulses with between 50 and60 Volt amplitudes are required to actuate the relay, whichagrees well with our thermal actuator model. Thermal relax-ation limits repeated actuation to approximately 5 Hz. Cycletests with 1 Hz actuation have switched the relay 100 000 times,before the metal on the thermal actuator fails. A four-pointtest is performed to measure the total contact resistance; thebest result measured is 60 with a plated Cu thickness ofabout 2.5 . The same contact carried 3 A of current withoutcontact metal failure. The testing of relay switching dynamicsis described in Section III-E and Fig. 11.

V. SUMMARY AND CONCLUSION

This paper proposed, modeled, designed and fabricated anelectrothermally-actuated bistable MEMS relay for power ap-

plications. This paper selected a straightforward deep etch andbonding fabrication sequence that facilitates the flexure designof relay components to meet the functional requirements. Onekey requirement for this relay is its mechanical bistability, whichwas realized with double-curved beam discussed in detail in [1].To actuate the bistable component, a U-shaped thermal actuatorwas selected for its good actuation capability and simple fabrica-tion. Detailed modeling and design were developed and verifiedwith FEA. Two mechanical models were created, with the basicmodel giving closed-form solutions as shown by (11) and (12),and the complete model accurately capturing the cross couplingrelation of the beam force and deflection between lateral andaxial directions as shown by (18) and (21). Differential heatingwas achieved by coating the cold beam with highly conductivemetal. Electrothermal modeling showed the transient nature ofthe electrothermal actuator, which could be actuated by an elec-trical pulse generated by a specialized external circuit.

For the relay contact, this paper used a crossbar-contactstructure. Different shapes of the contact structure were fabri-cated and tested, and the flat-flat structure was selected as best.Crossbar compliance was designed so the crossbar can contactthe two contacts reliably by using a spring action to equalizeboth contact forces. To achieve good metallization and contactthrough the DRIE sidewalls, a backside shallow etch was usedto alleviate problems at the wafer bottom (footing erosion,footing radius) that tend to cause undesired point contact be-tween the crossbar and relay contacts. Several processes wereused to clean the Teflon residue from the DRIE process, whichcaused metal adhesion problems. A three-step metallizationprocess including cleaning, seed metal deposition by sputtering,and more metal deposition by electroplating was developed.The current carrying capacity with the electroplated contactswas about 2–3 A, and the on-state resistance was on the orderof 60 mohm, which are comparable to the best MEMS relaysfound in the literature.

ACKNOWLEDGMENT

The authors would like to thank Prof M. Schmidt, J. Li,J. Sihler, K. Broderick, V. Diadiuk, and R. Krishnan of MITfor helpful discussions and fabrication/testing assistance.They thank O. Yaglioglu of MIT for reading this paper andgiving helpful comments. They also thank R. Struempler,S. Kotilainen, and J. Henning of ABB for helpful discussionsand testing assistance.



REFERENCES

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[7] W. Taylor, O. Brand, and M. Allen, “Fully integrated magnetically ac-tuated micromachined relays,” J. Microelectromech. Syst., vol. 7, pp.181–191, 1998.

[8] J. Qiu, J. Lang, A. Slocum, and R. Struempler, “A high-current elec-trothermal bistable MEMS relay,” in Proc. MEMS ’03, pp. 64–67.

[9] W. Chu, M. Mehregany, and R. Mullen, “Analysis of tip deflection andforce of a bimetallic cantilever microactuator,” J. Micromech. Microeng.,no. 3, pp. 4–7, 1993.

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[14] K.-S. Chen, “Materials Characterization and Structural Design of Ce-ramic Micro Turbomachinery,” Ph.D. dissertation, Department of Me-chanical Engineering, Massachusetts Institute of Technology, 1998.

[15] J. Qiu, “An Electrothermally-Actuated Bistable MEMS Relay forPower Applications,” Ph.D. dissertation, Department of MechanicalEngineering, Massachusetts Institute of Technology, 2003.

Jin Qiu (M’04) received the Ph.D. degree in me-chanical engineering from Massachusetts Instituteof Technology (MIT), Cambridge, in 2003, with aminor in business. His doctoral project was ranked asthe top one among 20 others by its industry sponsor.He also received the B.S. degree in electrical en-gineering from Nanjing University in 1997 and theM.S. degree in mechanical engineering from MIT in1999.

He is with WiSpry, Inc., Irvine, CA, working on RFMEMS. Previously, he was with Tyco Electronics.

He has one issued patent and several others pending. His interests focus on thedevelopment of MEMS, semiconductor devices, and instruments.

Dr. Qiu is a Member of the American Society of Mechanical Engineers(ASME).

Jeffrey H. Lang (S’78–M’79–SM’95–F’98) re-ceived the S.B., S.M., and Ph.D. degrees in electricalengineering from the Massachusetts Institute ofTechnology (MIT), Cambridge, in 1975, 1977, and1980, respectively.

Currently, he is a Professor of Electrical Engi-neering at MIT. He has been an MIT faculty membersince receiving his Ph.D. degree and his researchand teaching interests focus on the analysis, design,and control of electromechanical systems withan emphasis on rotating machinery, microsensors

and actuators, and flexible structures. He has written over 160 papers andholds 10 patents in the areas of electromechanics, power electronics, andapplied control.

Dr. Lang and has been awarded four Best Paper prizes from various IEEEsocieties. He is a former Hertz Foundation Fellow and a former Associate Editorof Sensors and Actuators.

Alexander H. Slocum (M’03) received the Ph.D.degree from the Massachusetts Institute of Tech-nology (MIT), Cambridge, while simultaneouslyworking from 1983 to 1985 at the National Bureau ofStandards, where he also earned 12 superior serviceawards and a Department of Commerce Medal.

He is currently a Professor of Mechanical En-gineering at MIT and a MacVicar Faculty Fellow.He has about 60 patents issued/pending and hedesigns manufacturing equipment for the automo-tive, aerospace, semiconductor, and entertainment

industries. He has been involved in several manufacturing equipment companystart-ups, and he has helped many different companies bring many differentmachines to the marketplace. In addition, he has also been involved with nineproducts that have been awarded R&D 100 awards, each for annually being oneof one hundred most technologically significant new products. His researchhas involved three dozens Ph.D. students. His current interests focus on thedevelopment of instruments, MEMS, and nanotechnology.

Dr. Slocum is the recipient of the Society of Manufacturing Engineer’s Fred-erick W. Taylor Research Medal and is a Fellow of the American Society ofMechanical Engineers (ASME).

Alexis C. Weber received the B.S. degree in me-chanical and electrical engineering from InstitutoTecnologico y de Estudios Superiores de Monterrey(ITESM-CEM), Mexico, and the M.S. degree inmechanical engineering from the MassachusettsInstitute of Technology (MIT), Cambridge, in2002. He is currently pursuing the Ph.D. degree inmechanical engineering at MIT.

From 1999 to 2003, he was employed by DelphiCorporation, where he designed electromagnetic ac-tuators for automotive applications. His research in-

terests include design, modeling and fabrication of microelectromechancial sys-tems (MEMS), as well as macroscale precision machine design.

Mr. Weber is a Member of Sigma Xi.


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