mems comb drive actuator to vary tension and - imechanica

MEMS Fall 2005 Department of Mechanical Engineering Professor Wong Design Project Columbia University Submitted 12/12/2005

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MEMS Comb Drive Actuator to Vary Tension and Compression ofa Resonating Nano-Doubly Clamped Beam for High-Resolution

and High-Sensitivity Mass Detection

Adam Hurst1, Chou Ying-Chi1, John Regis1, Andrew Lie2, and Adrian Podpirka3

Department of Mechanical Engineering, Columbia University500 W. 120 Street, Room 220 Mudd, New York, NY 10027, USA

Abstract – Micro-electromechanical systems (MEMS) often provide cost effectivesolutions with rapid response times to many macroscopic engineering enigmas. WhileMEMS devices offer micro-scale actuation and sensing, nano-electromechanical systems(NEMS) give even greater sensitivity, faster response times, and a larger breadth ofapplications. Nano-sized resonating beams, specifically, provide promise in ultra-sensitive mass detection and substance sensing. Detection is achieved through thecoloration of resonant frequency shifts with the existence of specific environmentalconditions. In an effort to increase sensitivity, we have designed a micro-scale combdrive electrostatic actuator. Our MEMS device will have the versatility to load a 10 µmlong, 80 nm wide, and 100 nm thick gold/palladium beam with tensile and compressivestresses. The structure is made using a combination of electron beam evaporation of goldand palladium, Reactive Ion Etching (RIE), and 5:1 BHF etchant on a Si-SiO2-Si wafer.A voltage applied to the comb drive will change the compression and tension of thebeam. The beam will drive and the resonant frequency will be determined by amagnetomotive technique [13]. A DC voltage along with a sinusoidal current, which isout of phase with the resonating beam, will be applied to comb drive plates in order tokeep the structure stable and apply the desired tensile or compressive loading. The deviceis packaged using an innovative leadless contact approach, which increases stability overtime and environment. Potential applications include gas and homeland securitybioterrorism sensors.

Index Terms – Electrothermal tuning, thermal time constant, MEMS resonator, NEMSresonator, resonating beam sensor, leadless packaging.

1 Graduate Student in Mechanical Engineering, Columbia University2 Undergraduate Student in Mechanical Engineering, Columbia University3 Undergraduate Student in Material Science and Engineering, Columbia University

I. Introduction

M icro-electromechanical systems(MEMS) and nano-electromechanicalsystems (NEMS) have a wide range ofapplications from sensors that can detect

the finite amounts of organic compoundsor gases such as hydrogen. Delving intonano-structures has resulted in thediscovery of hypersensitive devices.Nanobeams, for example, experiencechanges in their lattice structure or massloading. As classical mechanics


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suggests, such changes in beamdimensions or loading causes a resonantfrequency shift. Frequency shifts of anano-scale beam are detected andcorrelated with the presence of aparticular substance. Due to theirminiscule size and intricate design,nano-electromechanical systemsroutinely reach high frequencies on theorder of GHz. The fabrication of aresonating beam leaves residual tensilestresses on the beam. It has beendiscovered that such resonating beamsare less sensitive under these tensileloads [13]. Therefore a motivation hasrisen to load the beam with tensile andcompressive stresses in order to furtherexamine beam sensitivity and resonance.The ideal beam loading device is aMEMS actuator.

In this paper we report anintricate design of a MEMS comb driveelectrostatic actuator tailored to applycompressive and tensile loads to thedoubly clamped NEMS resonating beamon the order of ≈ +/- 200 MPa. Thestructure will work on the application ofan electrostatic force from an appliedvoltage bias.

The research disclosed withinthis paper describes the properties of thenano-mechanical resonator, the thermaltime constant of such a resonator, thedesign, fabrication and packaging of thecomb drive electrostatic actuator tocreate an adjustable load on the NEMSresonating beam. An innovative leadlesspackaging system is also disclosed.Numerous applications exist for suchresonating beams. Some suchapplications include but are not limitedto bio-terrorism sensors for homelandsecurity issues or gas sensors.

II. Theoretical Background & Design

H ypersensitivity may be achievedwhen a compressive force is applied tothe NEMS beam. In an effort tooptimize the sensitivity of NEMSresonating beams, our MEMSelectrostatic actuator has been designedto accurately place a compressive andtensile load on the beam. It has beenestimated that sensitivity optimizationwould occur within the load range of ≈+/- 200 MPa. The beam is assumed tobe constructed as a composite of goldand palladium. The effective Young’smodulus, SiPdeAuE &/ , and density,

SiPdeAu &/ρ , are given by

PdAu

PdPdAuAuPdeAu AA

AEAEE

+

+=/

Equation 1 [13]

PdAu

PdPdAuAuPdeAu AA

AA++

=ρρ

ρ /

Equation 2 [13]

where A is the area.

Similarly, the composite structure ofsilicon with evaporated gold andpalladium on its surface has an effectiveYoung’s modulus, Ee,Si,Au/Pd defined by

SiPdAu

SieSiPdAuPdeAuSiPdeAu AA

AEAEE

+

+=

/

//&/

Equation 3 [13]

SiPdAu

SieSiPdAuPdeAuSiPdeAu AA

AA

+

+=

/

//&/

ρρρ

Equation 4 [13]

Applying the classical pressureequation, displayed below, the required


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force on the beam is determined, with Prepresenting pressure, F as force, and Aequaling the cross sectional area of thebeam.

PdAuAF

P/

=

Equation 5 [15]

The beam axial deflection undersuch a load is calculated through theeffective young’s modulus and initialbeam length, L0. The axial deflection isgiven by

0/

LE

LPdAu

σ=Δ

Equation 6 [5]

These calculations indicate requiredforce and deflection that a MEMS devicemust create for effective testing. Whilemany appropriate MEMS actuators exist,we determined a comb drive to be thethe most effective based on a fabricationand performance analysis.

Our comb drive consists ofnumerous suspended finger structures.Comb drive electrostatic actuation offersa nearly linear resultant force due toinput voltage, which is desirable. OtherMEMS devices such as capacitiveelectrostatic or magneto motive actuatorspossess non-linear relationships betweenapplied bias and output force ordisplacement. While such force/voltagerelationships can be modeled, thevariability in fabrication is very likely toresult in inaccuracy betweentheoretically predicted and actualperformance. Such variability iseliminated with the use of a comb drive.

Comb drives actuate motion throughan applied voltage between two parallelplates. A lateral attractive force isgenerated when one grounded finger or

plate is surrounded by two additionalfingers or plates powered at a highvoltage. The electrical field generatedbetween these plates cause equal andopposite attractive forces that preventsnap down while generating a lateralforce. The energy in one of thesecharged parallel plate capacitors isdefined by

d

AVU r

20

21 εε

=

Equation 7

where U is the energy, ε0 is thepermittivity of free space, εr is therelative permittivity, A is area of the faceof the plate, V is the applied voltage, andd is the gap between the plates [7]. Thederivative of this energy equation withrespect to the lateral direction is thegenerated force in the horizontaldirection, which is displayed below.

d

wVF rx

20εε=

Equation 8

In this instance, w is the width of theparallel plates [7]. The equation aboveis valid only when the overlap distanceis assumed to be considerable incomparison to the other dimensions ofthe fingers. Figure 1 illustrates theeffective comb drive actuation.

Effective comb drive actuationFigure 1 [7]

Similar to capacitive plate snapdown, comb drives can experience side


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instability or snap down betweenadjacent plates. Side instability can existif the comb drive does not possessenough rigidity. Comb drives should bedimensioned such that the sideinstability voltage is significantly outsidethe operating range. The side instabilityvoltage is defined by

VSI = 2fo bnd2ky

2 ky

kx + d2

yo2

- dyo

d n

Equation 9

where d is the distance between combs,ky and kx is a comb drive finger springconstant along the vertical andhorizontal axis, respectively, b is thebase, n is the number of combs, d is thedistance between plates, and y0 is theinitial length of the finger [8].

Image of support beams and structureFigure 2

While effective comb driveelectrostatic actuation creates theappropriate forces, such structures mustbe released from the surface whileremaining attached to the wafer. Supportbeams successfully secure the resonatingnano-beam and released comb drivestructure to the wafer. These can beviewed in Figure 2 above. Such beamsact as springs, deflecting as a result ofthe force generated by the comb drives.They are assumed to act similar tocantilever beams. These beams can beviewed in the lower and upper sections

of Figure 3 as well. In this application,the effective spring constant, k , of acantilevered beam is dependent upon thecomposite Young’s modulus, Ee, thebase, b, height, h, and length, L of thebeam.

ky = 4L3

Eehb3

= L3

3Ee Iyy

Equation 10

kx = L3

3Ee Ixx = 4L3

Eebh3

Equation 11

Doubly Clamped NanobeamFigure 3

The effective spring constant ofseveral identical cantilever beams isdefined by

knkeff ⋅=Equation 12

where n is the number of identicalcantilever beams supporting the structureand k is the spring constant of one suchbeam.

The force related with bending sucha spring is defined by

xkF effx ⋅=Equation 13


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The vertical deflection of suchcantilevered beams used to suspend thecomb drive and resonating beam isdefined by

)3(6

)( 32

/

xLxIE

Fxv

PdeAu

−=

Equation 14 [5]

where v(x) is the vertical deflection, x isthe location on the beam of the force,and L, b, h represent the dimensions ofthe beam. Appropriate supportingbeams should deflect several orders ofmagnitudes less than the thickness of theNEMS resonating beam. Such minimaldeflection will eliminate the possibilityof gravitational forces loading the beam.

Adding support beams requires thecomb drive to create a greater amount offorce. Larger forces can be achieved byincreasing the number of fingers.

III. Thermal Time Constant

The resonating beam is heated using aDC voltage. Tuning provides controlover the resonant frequency of the beam.The speed at which the frequency of thebeam can be tuned is highly dependanton the thermal time constant. Thethermal time constant of an actuator isthe measure of time required for theactuator to cool down to ambienttemperature following actuation. It alsodetermines the maximum operatingfrequency, independent of the resonantfrequency.

Solving for the time constantrequires the setting of many equationsand conditions.

The one dimensional Heat FlowEquation states:

2t2u

- k dx2

22u= Cp

Q (x, t)

Equation 15 [5]

With the boundary conditions

B.C. (1):u (o, t) = Tw

B.C. (2):u (L, t) = Tw

I.C.: u (x,0) = f (x) = Tw

Equation 16 [1]

where Q(x,t) is the thermal energy perunit volume per unit time, k is thethermal conductivity, ω0 is the resonant

frequency and T = ~o

2r , and Cp is the

specific heat capacity. Applying a directcurrent gives

I = I0 tEquation 17

I2 = Io2 tEquation 18

Using this, as well as integrating the areaand thermal energy distribution;

QL = T1

A Q (x, t)^ h0

L

#0

T

# dxdt

Equation 19 [1]

gives the result of

QL = ~o

(I02) (R) (r)

Equation 20 [1]

Defining a new function allows for theboundary conditions to be equal to zero:

v(x, t) = u(x, t) - Tw

B.C. (1): v (0, t) = Tw - Tw = 0

B.C. (2):v (L, t) = Tw - Tw = 0

I.C.:v (x,0) = Tw - Tw = 0Equation 21 [1]


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∴

2t2v

- k dx2

22v= Q(x, t)

B.C. (1): v(0, t) = 0

B.C. (2):v(L, t) = 0

I.C.:v(x,0) = 0Equation 22 [1]

In order to match the boundaryconditions, there must be a combinationof plus and minus eigenfunctions, thusexpanding the eigenfunction equation:

v (x, t) = an(t)zn(x)n=1

3

/

where zn(x) = sin( Lnrx

)

Equation 23 [1]

This is a spatial sinusoid.

The normalization factor isomitted because eigenfunctions ofdifferent n are always orthogonal. Thesolutions of the eigenfunction expansionformula gives a set of values known asSturm-Liouville Values. The SturmLiouville theory states that for a secondorder ordinary differential equation

dxd

p (x) dxdy

b l+ (m~(x) - q (x))y = 0

Equation 24 [2]

,where λ is a function and ω(x) is theweighting function. The solutions oflambda, with appropriate boundaryconditions, and the corresponding u(x)solutions are the eigenfunctions. Usingthe

Initial Condition: v (x,0) = 0

an(0)zn(x) = 0n=1

3

/

` an(0) = 0Equation 25 [10]

and the aforementioned heat flowequation provides the generalizedFourier series for Q(x,t):

Q (x, t) = ( dtdan

n=1

3

/ + mn kan(t))zn(x)

Equation 26

To solve for the Fourier coefficients,an, the equations of orthogonality can beused:

dtdan + mn kan =

Qn2(x)dx

0

L

#

Q (x, t)zn(x)dx0

L

#/ qn(t)

where Q (x, t) = qn(t)zn(x)n=1

3

/(weighting function= 1)

Equation 27 [1]

,where the numerator is

nPC1L (1 + (- 1) n+1)

Equation 28 [1]

and the denominator is simply L/2.Thus:

emn kt ( dtdan + mn kan) = qn(emn kt)

Equation 29 [2]

with emn kt being the integrating factor

thus making the function integratable.


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This results inan(t) = l (n)e-mn kt ((

mn2k2

emn kt

(mn kt- 1)) + (mn

2k2

1))

where l(n) =nPC12 (1 + (- 1) n+1)

Equation 30 [1]

The time associated with the longesttime to reach steady state corresponds tothe n=1 eigenmode. The term thatsupplies this is

e-mn kt

Equation 31 [2]

where

mn = ( Lnr

)2 = L2

n2r2

k = tCp

k0

Equation 32 a&b [13]

Thus,

x =mn k1

= ( L2

n2r2

) ( ko

tCp)

Equation 33 [5]

and the result is a thermal time constantequal to 1.69124 * 10-7s.

Important values for gold

Thermalconductivity Density

SpecificHeatCapacity Length

(W/(m*K)) (kg/m^3) (J/(kg*K)) (m)

148 19300 128 0.00001

We are assuming that most of thestructure will be gold and there will be aminimal effect from palladium.

IV. Design Results

The dimensions of the resonating beamand desired compressive and tensileloading are applied as the initial design

constraints. The initial dimensions ofthe beam are assumed to be ~10 µmlong, 80 nm wide, and 100 nm thick.Based on a beam loading of 200 MPa, adesired applied force of 1.6 µN can becalculated from equation 1. Theeffective Young’s modulus of acomposite gold/palladium beam is foundto be approximately 85 GPa. Thegold/palladium NEMS beam compressesunder such axial loading. As a result,the beam deflects axially by 25.6 nm,which is determined using equation 6.

Through these design requirementsof axial force generation and deflection,we have developed a comb drivesuspended in space by four supportbeams. Figure 4 illustrates an accuratelayout of the MEMS comb driveelectrostatic actuator.

Above view of the MEMS structureFigure 4

The four-support beams are 50 µmlong, 2 µm wide, and 5 µm thick. Theyare dimensioned to eliminate verticaldisplacement of the comb drive, beamsupport block, and the resonating beamitself. Vertical deflection of thecantilevered beams would result inundesirable loading of the resonatingbeam. Based upon the density of silicon,which is the comb drive and beamsupport block construction material, and


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the density of the gold/palladiumcomposite evaporated onto the silicon,we determined a combined mass of4*10-9 kg. Applying Newton’s secondlaw to determine a gravitational force,the cantilevered beam deflectionequation provides a vert icaldisplacement of 96.7 pm for the entirebeam support structure. This verticaldisplacement of the resonating beam isseveral orders of magnitude less than thethickness of the beam. Such minusculedeflection is acceptable.

The spring constant of the fouridentical support beams is determinedusing equation 10 &11. We determinedthis spring constant of one individualbeam to be 100.8 N/m. Multiplying thisvalue by four for each support beam, acomplete spring constant is determined.This combined spring constant alongwith the known axial deflection of theresonating beam are multiplied, asequations 13 indicates. The result of10.5 µN is the force necessary to movethe entire beam support structure alateral distance of 25.6 nm. From thesecalculations, we found the total combdrive force required to be 12.1 µN. Sucha force will result in a support blockdisplacement and beam axial deflectionof 25.6 nm. In addition, the beam willexperience 200 MPa of loading with acomb drive generating 12.1 µN.

The comb drive designed to generate12.1 µN of lateral force has 50 fingersthat are each 8 µm long, 2 µm wide, and5 µm thick. The overlap betweeninterlocked fingers is 6 µm. Figure 4also shows a dimensioned view ofseveral fingers of the comb drive system.

Applying the comb drive lateralforce generation equation yields thedesired force output at an input voltageof 127.99 V. If during experimentationgreater or smaller loading is required, a

nearly linear relationship exists betweenforce and input voltage, which is asignificant advantage to comb driveelectrostatic actuation. This relationshipbetween force and applied voltage isillustrated in figure 5.

Voltage Input vs. Comb Drive Lateral Force

0.00E+00

2.00E-06

4.00E-06

6.00E-06

8.00E-06

1.00E-05

1.20E-05

1.40E-05

1.60E-05

0 20 40 60 80 100 120 140 160

Voltage (V)

Co

mb

Dri

ve L

ater

al F

orc

e (N

)

Force Dependence on Voltage 200MPa on Beam

Voltage Input vs. Comb Drive LateralForce

Figure 5

Similar to force, lateral displacementalso maintains almost a linearrelationship with input voltage, which isshown in figure 6.

Voltage vs. Lateral Displacement

0

5

10

15

20

25

30

35

40

0 20 40 60 80 100 120 140 160

Voltage (V)

Lat

eral

Dis

pla

cem

ent

(nm

)

Lateral Displacement Dependence on Voltage Lateral Displacement at 200MPa

Voltage vs. Lateral DisplacementFigure 6

While designing a comb drivesystem, we also took into account sideinstability. To ensure that the combdrive network would not experiencesnap down, the comb drive fingerdimensions are such that side instabilityvoltage is 1320 V, which is two orders


9

of magnitude larger than the workingrange.

IV. Fabrication

T he fabrication starts with a SOI(Silicon on Insulator) wafer. A SOI chipworks by placing a thin, insulating layer,such as silicon oxide below the thinsilicon wafer. For the purpose of ourexperiment we will be using a Si-SiO2-Siwafer. This is illustrated in figure 7. Thedepth of this wafer will 5 µm-1 µm-125µm, respectively. The processing stepsbegin with a SIO p-type doped wafer.We use the RCA clean to prepare thewafer and then spin on positivephotoresist.

Silicon/Silicon Dioxide/Silicon WaferFigure 7

The wafer is then expose usingthe Mask #1, which is shown in Figure8. After baking the photoresist andremoving the unexposed area, E-beamlithography is used to evaporate thegold/palladium substance. Thegold /pa l lad ium, due to i t sinsusceptibility to 5:1 BHF etching andhigh conductivity, is used as theresonating beam and contacts [12]. Thephotoresist is now lifted leaving only thebeam and contact pattern on the surfaceof the silicon, as can be seen in Figure 8.The wafer is now cleaned for preparationfor Reactive Ion Etching.

Mask #1: Contact PlacementFigure 8

A positive photoresist is againspun on and developed using Mask #2.Reactive Ion Etching (RIE) is used tovertically etch to the silicon dioxidelayer 5 µm below. The RIE process useslow-density diode plasma. This processtypically uses a chloride or Brominebased corrosive chemistry with orwithout fluorine based pre-cursors. Thistypically leads to lower silicon etch ratesof < 1µm/min giving lower systemoutput. Mask selectivity requires either ahard oxide mask or a thick photoresist.Since it is hard to control beyond 10µm,the structure we etch into is 5µm thick.At a rate of about 1µm/minute, it willtake roughly 5 minutes to complete butthis variable might change from machineto machine.

Two views of our Mask areshown. Figure 8 shows the far out viewof Mask #2, which illustrates whereetching exists to form electricallyisolated regions. Figure 9 shows theclose up view of the mask where thestructure will be cut.

Due to the ratio of roughly 100:1between the depth and resonating beamwidth, the RIE will remove the siliconunder the gold beam. If SEM imagineindicates that the resonating beam wasnot fully released from its siliconsubstrate, we will purge the structurewith XeF2 gas to etch the thin layer ofsilicon. Due to the highly reactivenature of the XeF2 etch with silicon, thisstep would take roughly 5-10 seconds


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and must be immediately purged with aninert gas. The beam is now fullyreleased.

Mask #2: Far Out ViewFigure 9

Mask #2: Close Up ViewFigure 10

The reason electrical isolation ofregions within our design is to enableseparate voltage bias to be applied to thecomb drive and resonating beam.

In order to release the structurefrom the wafer, the silicon oxide must becut. Due to the sensitive nature of siliconand gold, a 5:1 BHF etch is used [12].This etch will take approximately 30minutes in order to guarantee thestructure being released. Due to the“wet” nature of the etch and the smallarea between the silicon substrates,supercritical drying must be used toprevent the appearance of water oretchant which could lead to stiction anddestroy the structure. Supercriticaldrying is a process to remove liquid in aprecisely controlled way, similar tofreeze-drying.

As a substance crosses fromliquid to gas, the size of the liquiddecreases. As this happens, surfacetension at the solid-liquid interface pullsagainst any structures that the liquid isattached to. Delicate structures such as aMEMS device, tend to break due tosurface tension.

In supercritical drying, the routefrom liquid to gas does not cross anyphase boundary, instead passing troughthe supercritical region, where thedistinction between gas and liquid doesnot apply.

For the purpose of this step, CO2will be used since it is readily availableand has a critical point at 31.1˚C at 1072psi.

Complete structureFigure 11

The device is now tested andprepared for mounting and packaging asfigure 11 above illustrates.

V. Packaging

I n the NEMS and MEMS fields,packaging is often one of the morechallenging and limiting componentsdue to size constraints. The integratedNEMS/MEMS sensor expounded upon


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requires a complex packaging methodthat enables complete conductancebetween the micro-machined device andinput/output wires, while alsomaintaining stability over time andenvironmental. Moreover, suchresonators must be exposed to themediums under examination in order todetect mass or compute quantummeasurements.

Whi le current researche x p e r i m e n t a t i o n r e q u i r e s asuperconducting magnet in a cryostat,successful implementation will involve asmaller, portable magnet and properfunctioning under ambient pressure andtemperature. With parametricamplification, detection of mass orspecific organic compounds is morelikely possible. The ideal packagingschematic involves the micro-machinedNEMS resonator and MEMS actuatormounted in a leadless configuration ontoPyrex with a protective steel casing, asillustrated in figures 12 [6]. Since all ofthe applications for such a device havenot fully been explored, the packagingwill be uniquely tailored for eachapplication. The packaging schematicdiscussed and illustrated here assumesimplementation as a mass detection ororganic sensing device.

Device packagingFigure 12

The holes within the steelencasement will allow a flow of thesubstance under inspection to the sensor.For example, a gas can flow into thesteel chamber through these holes andthe NEMS/MEMS device coulddetermine if hydrogen is present. Thepresence of hydrogen would combinewith the palladium in the compositegold/palladium beam. Consequently, thelattice structure of the beam wouldchange which would result in a resonantfrequency shift. The frequency shiftwould be detected through the contactpins, and the presence of hydrogenwould be known.

The superconducting magnet,which is necessary for the detection ofsuch frequency shifts, will be mountedwith epoxy into the steel cover. Thesteel cover will serve as a protectiveencasing and a support for the magnet.

The insulating Pyrex structuresupports the contact pins onto which the


12

NEMS/MEMS device will be mounted.This Pyrex piece will be manufacturedby powder injection molding. A Pyrexpowder will be compressed in a diecavity that possesses the desired shape ofthe final structure. The piece is thenfired into solid Pyrex, and the brasscontact pins are sealed into the structure.

The leadless Pyrex contactstructure manufactured from a 381 µmPyrex wafer. This Pyrex piece is astructural support for the NEMS/MEMSdevice. Holes for the brass pins and alarge volume cavity for beam exposureare then drilled with a cavitron into it.Next, the holes of the Pyrex contactstructure are aligned with the goldcontacts on the micro-machined NEMSresonator wafer. The silicon wafercontaining the device is then anodicallybonded to the drilled, leadless Pyrexcontact structure. The device mountedto the leadless Pyrex structure isillustrated below in figure 13.

Resonator and actuator mounted on aninsulating leadless support.

Figure 13

The pin holes in the Pyrex arethen filled with a conductive paste, andthe entire leadless setup is mounted ontothe brass contact pins protruding throughthe insulating Pyrex support. Theassembly is then heated to harden thepaste, which ensures structural stabilityof the device and excellent conductivitybetween the brass pins and the

NEMS/MEMS device. A preassembledview is shown in figure 14.

Leadless contact approachFigure 14

The traditional packagingmethod would involve ball bonding thecontacts in order to create electricalcontact between the brass pins and theNEMS/MEMS device. While thismethod is a well developed industrystandard, it has several disadvantagesthat do not exist within this leadlessdesign. The ball bonding techniqueentails soldering tiny wires between thegold contacts on the NEMS/MEMSdevice and the brass pins. These wiresare approximately the size of a humanhair and easily break under significantvibration. Moreover, ball bondingbecomes less reliable at highertemperatures. The leadless designpresented forms excellent electricalcontact between the NEMS/MEMSdevice and the brass pins. In addition,its robust contacts eliminate thepossibility of losing conductivity inextreme environments, where significantvibration is present.

Many of the applications of thisdevice are related to antiterrorism. Sucha device along with this packaging


13

schematic would be suitable fordetecting finite amounts of organiccompounds that would naturally bepresent in explosives. This is a short listof the numerous applications for such adevice.

VI. Device Operation

The device works through the use of theLabView program software, which isattached to the contacts. As one mightnotice from the drawings, there are morecontacts then necessary to use thestructure in its simplest form. Thisallows the user to change parameters anddifferent biases to push the designslimits. Also, it allows the user to havegrounds and to be able to measure thevoltage at the silicon level for activefeedback.

The operation of the comb drivestructure can be seen in figure 3. Avoltage bias is applied to contactsleading to each side of the comb drive.This difference in voltage between theleft and right side of the structuresactuates the comb. The difference formaximum output has to be a differenceof 127.99V.

Due to the fact that beam will beresonating, an AC current must beapplied on top of the DC current thatplaces the bias on the comb drive. Thisis done 180˚ out of phase from thecurrent applied to the resonating beam.This will be applied through one of theleft hand side contacts, using figure 13as a reference.

The nano resonating beam willbe driven magnetomotively by a Lorentzforce. The beam’s frequency will betuned by applying a DC bias to the goldcontacts attached to the beam. Thedirect current heats the beam whichshifts its resonant frequency downward.

The tuning DC bias can be placed usingthe upper right two contacts attached tothe beam. The middle contacts, whichconnect to one side of the beam and oneside of the comb drive, will both beconnected to ground or a referencevoltage. The resonant frequency shiftscan be measured using a magnetomotivetechnique [13].

VII. Conclusion

A relationship characterizing theelectromechanical behavior of the combdriven structure on the doubly clampedresonating beam has been formed. Themodel, masks, fabrication steps andcalculations have all been derived forease in manufacturing and packaging. Asuggestion for further research would bea feed back loop in order to determinethe distance traveled by the blockstructure. This would most likely be asmall electrostatic capacitive parallelplate sensor on the edge of the combdrive. We are currently evaluatingalternative approaches to excitation andcapacitive detection in order to expandthe applicability of the device.

VIII. Acknowledgements

This paper was supported by ProfessorChee Wei Wong and Professor JamesHone of the Department of MechanicalEngineering at the Fu School ofEngineering and Applied Sciences ofColumbia University in the City of NewYork.


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IX. References

[1]Haberman, Richard. Applied PartialDifferential Equations. Prentice Hall.2004.

[2] MathWorld. Stephen Wolfram.March 10, 2005. Wolfram Research, Inc.December 10, 20005.<http://mathworld.wolfram.com/>.

[3] G. Abadal. “Electromechanicalmodel of a resonating nano-cantilever-based sensor for high resolution andhigh-sensitivity mass detection”,Nanotechnology 12 (2001) 100-104.

[4] Z.J. Davis. “High mass and spatialresolution mass sensor based on Nano-cantilever Integrated with CMOS”,Transducers’01 Conference TechnicalDigest, pp72-75 (2001).

[5] Senturia, Stephen D. MicrosystemDesign. Springer. 2001.

[6] Kulite Semiconductor Products Inc.(2005) Apparatus And Method ForInterconnecting Leads In A HighTemperature Pressure Transducer. USpatent number 6,895,822 B2. May 24,2005.

[7] MEMS class. Fall 2005. Prof. CheeWei Wong. Columbia University.Lecture 7.

[8] Rob Legtenber, A W Groeneveld andM Elwenspoek. “Comb-drive actuatorsfor large displacement.” J. Micromech.Microeng. 6 (1996) 320-329.

[9] Ki Bang Lee, Liwei Lin. “Verticallysupported two-directional comb drive.”J. Micromech. Microeng. 15 (2005)1439-1445.

[10] Michael Mendalaous, GraduateStudent, Mechanical Engineering.Columbia University.

[11] Tam Pandhumsopron. “High etchrate, deep anisotropic plasma etching ofsilicon for MEMS fabrication” AlcatelVacuum Technology.

[12] Kirt R. William. “Etch rates formicromachining processing – Part II.”Journal of Microelectromechanicalsystems, Vol. 12, No.6, December 2003.

[13] James Hone. “Electrothermal tuningof composite Al-SiC nanomechanicalresonators.”

X. Biography

Adam Hurst recently received hisBachelors of Science in MechanicalEngineering from Columbia University.He is currently working at Kulite®Semiconductor Products as a design anddevelopment engineer. In addition, he isworking on his Master of Science degreeat Columbia University. He also likes torun and climb walls with Prof. Hone.

Chou Ying-Chi is currently a graduatestudent in department of MechanicalEngineering at Columbia University. Hereceived his Bachelors of Science fromTamkang University where he studiedMechanical Engineering.

John Regis has received his Bachelor ofScience degree in Physics from AdelphiUniversity, as well as his Bachelor ofScience degree in MechanicalEngineering from Columbia Universityin 2003 and 2005, respectively. He iscurrently a 1st year graduate student inthe department of Mechanical


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Engineering at Columbia University.Some of his research interests include:Controls, Manufacturing, and ProductDesign/Analysis. After getting hisMaster’s degree, he will seekemployment at an engineering companywhere he can work exclusively onmanufacturing and product design.

Andrew Lie is currently a seniorundergraduate student in the Departmentof Mechanical Engineering at ColumbiaUniversity. Upon graduating, he will beworking as a strategy consultant forAccenture in California while pursuinghis Silicon Valley start-up company.

Adrian Podpirka is currently a seniorundergraduate engineering student in theDepartment of Material Science atColumbia University pursuing aBachelors of Science. At the moment,he is applying to graduate school wherehe hopes to continue his studies andwork towards a doctorate degree inMaterial Science. His research interestsinclude fuel cell membranes andsemiconducting materials. He is also afour-year member of the varsitylightweight crew team.

mems comb drive actuator to vary tension and - imechanica

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