electrostatic zipping actuators and their application to...

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1

Electrostatic Zipping Actuators and Their Application to MEMS

Jian Li

B.S. Mechanical Engineering, Tsinghua University, 1997M.S. Mechanical Engineering, Tsinghua University, 2000

Ph.D CandidateDept. of Mechanical Engineering

Massachusetts Institute of Technology

01/15/2004

2

Introduction

ProblemNeed powerful electrostatic actuators for MEMS

power relay

Huge size using conventional designs

SolutionsZipping actuator with compliant

starting zone

Results

9 mm

~ 3 mm

2

3

Contributions

Design: Starting zone to reduce the pull-in voltageNumerical and analytical modeling: easy and accurateOptimization of the systemSpecified design for implementation in a relayFabrication and measurement of the actuator-relayWet-anisotropically-etched micro relay contact

4

Background: Electrostatic Actuators

Comb DriveForce independent

of stroke: large stroke

Very small force, large deflection

Parallel PlateConfliction

between stroke and force

“Zipper”Large force and

large deflection

High voltage for pull_in

3

5

F-D Curve of Three Electrostatic Actuators

Force-Displacement Character of the three actuatorsWith the same volume and same voltage, the “zipper” actuator achieves a

much larger force than comb drive an capacitor plate actuators

“Zipper” actuator is the only hope to secure milli Newtons of force with a reasonable volume

0

2

4

6

8

10

12

0 20 40 60 80

Displacement (µm)

Forc

e (m

N)

Parallel PlateComb DriveZipping Actutor

6

Zipping Actuators: A Survey

802 ~ 109 * 1RelayLateralThis thesis

100N/A(very small)1 * 0.2Fluid

controlLateralSherman

20N/A(very small)0.5 * 0.2Optical

shutterLateralPerregaux

300.020.8 * 0.5N/ALateralLegtenberg

60.10.8 * 0.8MirrorVerticalDivoux

220N/A (very small)5 * 5ValveVerticalShikida

Stroke (µm)

Force (mN)

Size(mm2)

Applica-tion

Actuation directionAuthor

4

7

Example Load: Double BeamA pre-curved bistable MEMS mechanismPromising as a micro relay structure

Simple structureNo residual stressHigh contact force: good for on-state performance

Need an electrostatic actuator to make the MEMS relay

F

Double beam Double beam working as a Relay

8

Why Is It Hard ? (1)

Stoke: >= 80 µmAsymmetric and high actuation/contact force: ~ 7 mN for the first 10 µm to get a 3mN of contact forceActuation voltage: < 200 V (as small as possible)Scale: 7 × 7 × 1 mm3

Fabrication: Deep Reactive Ion Etching

-4

-2

0

2

4

6

8

0 20 40 60 80 100 120Displacement δ (µm)

Act

uatio

n fo

rce

Fri

ght(

mN

)

~ 3 mN

~ 7.5 mN

5

9

Why Is It Hard ? (2)

Initial Design:DRIE etch throughAttach the cantilever

beam to the double beamApply voltage between

electrode and the cantilever beam.

Problem:Minimum gap due to

DRIE aspect ratio of ~5%Very High pull-in voltage

because of the gap, about 250 V for a 15 µm thick and 4.5 mm long zipping beam.

U

Minimum Gap

Cantilever Beam BeingElectrified

Cantilever Beam Electrode

Double Beam

Double beam actuated by "Zipper"

10

Contributions

Design: Starting zone to reduce the pull-in voltageNumerical and analytical modeling: easy and accurateOptimization of the systemSpecified design for implementation in a relayFabrication and measurement of the actuator-relayWet-anisotropically-etched micro relay contact

6

11

Design: Compliant Starting Zone

To reduce the pull-in voltage:

A compliant starting zoneReciprocity: remove

material not needed and not useful The starting zone

bends up when voltage is applied between electrode and the beamThe cantilever beam

pulls-in and keep zipping at low voltage

U

gmin

ActuatorCantilever Beam

Fixed electrode

Bistable RelayBeam

StartingCantilever a)

b)

12

Contributions

Design: Starting zone to reduce the pull-in voltage

Numerical and analytical modeling: easy and accurateOptimization of the systemSpecified design for implementation in a relayFabrication and measurement of the actuator-relayWet-anisotropically-etched micro relay contact

7

13

Modeling: Overview

( )2'''' 0

2

0

( ) ( )

2 ( ) ( )r

U bE I x y xhy x c x

ε

ε

−=

⎡ ⎤− +⎢ ⎥

⎣ ⎦

Beam bending equation in electric field

Electrode Insulator

h0

h

U

x

y

z

Actuator Cantilever

Starting Cantilever(Component III)

b

L1 L2

L

Component I Component II

WaferNormal

c(x)

14

Numerical Modeling: Before “Pull-in”

Deflection profiles of the cantilever beam and the starting beam at different voltages when the tip is constrained at zero displacement

Numerical MethodModeled as a device

with Multiple-beams.Each beam is bent by

the electrostatic force.The ODEs are solved

simultaneously for each beamDeflection profiles for

each beam are given out at different voltages.Actuation force can be

calculated.Pull-in voltage can be

found

8

15

Numerical Modeling: After “Pull-in”

sL

δ

c(x)

p(x)

Fright

Fleft

sL

δ

x

y

δmax

d

h0

Numerical solutionsEliminate varying B.C by adding parameter

Cantilever Beam Deflection profiles when the tip is constrained at zero displacement(different voltages)

Ls /1−=λ

Model after pull-in

[ ]2

02

0

''''( ) ( )2 ( ) ( ) / r

bUEIy x p xy x c x h

εε

= = −− +

Beam equation: s x L≤ ≤

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Analytical Modeling: After Pull-in3/ 421/ 4

0

0

~ rright

U hE bFhd

ε ε⎛ ⎞⎜ ⎟⎝ ⎠

0

1

2

3

4

5

6

7

100 120 140 160 180 200 220 240 260

Voltage (V)

Forc

e (m

N)

Device I, Numerical results

Device I, Analytical Results

Device II, Numerical Results

Device II, Analytical results

Approximation equation:

Comparisons between analytical approximations and numerical results:

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Forces: Actuator vs. Switch Beam

Force-Displacement curves of the actuator and the double beam

> 160V is needed to actuate the double beam with ~ 3 mN of contact forceCan we change the

force-displacement curve of the double beam without reducing the contact force?


-5

0

5

10

15

20

0 20 40 60 80 100 120

Displacement δ (µm)

Act

uatio

n fo

rce

Fri

ght(

mN

)

Relay with Uniform Thickness, FEA Actuator, U = 100 V

Actuator, U = 120 V Actuator, U = 140 V

Actuator, U = 160 V

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Contributions

Design: Starting zone to reduce the pull-in voltageNumerical modeling: easier and more accurate

Optimization of the systemSpecified design for implementation in a relayFabrication and measurement of the actuator-relayWet-anisotropically-etched micro relay contact

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Force ratio R = C(τ0,τ2)1

Optimization of The Double Beam

0 2 0 2 0 2( , ) ( ) ( , , , )C I w wδ τ τ δ τ τ= Λ∫Start with constant I(x)

Numerically calculate eigen-functions and eigenvalues [wi , τi]

choose δI = εΛ(τ0, τ2, w0, w2),satisfying thickness constraints.

Small enough R?No

YesEnd

I(x) = I(x) +δI

20

Optimization of The Double Beam (II)


-5

0

5

10

15

20


Act

uatio

n fo

rce

Fri

ght(

mN

)

Relay with Uniform Thickness, FEA Optimized Relay, FEAActuator, U = 100 V Actuator, U = 120 VActuator, U = 140 V Actuator, U = 160 V

7.5 mN4.5 mN

Actuation force/Contact force ratio starts from~ 2.5:1.Beam was modulated, force ratio was optimized to ~1.5 :1.~ 120 V is needed to actuate the relay.

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Contributions

Design: Starting zone to reduce the pull-in voltageNumerical modeling: easier and more accurateOptimization of the system

Specified design for implementation in a relayFabrication and measurement of the actuator-relayWet-anisotropically-etched micro relay contact

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The Relay

UU

UU

U

a)

b)

c)

d)9 mm

~1.5 mm

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Contributions

Design: Starting zone to reduce the pull-in voltageNumerical modeling: easier and more accurateOptimization of the systemSpecified design for implementation in a relay

Fabrication and measurement of the actuator-relayWet-anisotropically-etched micro relay contact

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Fabrication: Process Flow (1)

Starting substrate: 4''DSP <100> Si Wafer

Spin and pattern 10 µmof photoresist

DRIE etch through

Grow 0.2 µm ofthermal oxide

Strip photoresist inPiranha, RCA clean

v

Silicon Silicon Oxide Photoresist

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Bond shadow waferand device wafer, etchoxide selectively

Spin and pattern 10 µmof photoresist

Starting substrate: 4''DSP <100> Si Wafer

DRIE etch through

Strip photoresist inPiranha

Separate wafers, cleandevice wafer in Piranha

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Starting substrate: 4''Pyrex 7740 wafer, 500mm thick

Deposite 0.005 mm Ti,0.03 mm Cr

Pattern Cr in CR-7

Etch Pyrex 50 mm in49% HF

Bond device wafer toPyrex wafer at 800 Vand 350 degree C

Titanium Chromium

Sputter Au on relaycontacts

Gold

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Fabrication: Transparency Mask

Device made using Transparency Mask

Device made using transparency mask and 10:1 Stepper

Transparency mask for device wafer:

Much faster and much cheaperLow resolution: 3-4 µm

Electrostatic force is very sensitive to the recess at electrode

Print the mask 10 times larger and use 10:1 stepper to shrink it down

Electrode

Cantilever Beam

Cantilever Beam

Electrode

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Fabrication Results: Overview

13 7

2 1 11 6

54

12

500 µm

8

10

3 12

9

15

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Measurement: Pull_in of the Starting Zone

The starting beam bends up and closes the gap between zipper beam and fixed electrode

Pull-in at 75V

140 V. Zipper beam collapse to the fixed electrode, relay is closed

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Force Measurement

-4

-2

0

2

4

6

8

10

12


Forc

e (m

N)

Relay FEA Relay ExperimentalActuator Numerical Simulation at 140V Actuator Experimental at 140VRelay FEA (Adjusted model)

Flextester

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A Bipolar Drive to Avoid Stiction

74LS74

D

C

Q

Q

74LS74

D

C

Q

Q

+5V

+15V

+15V

+100V

+100V+15V

+100V TopElectrode

BottomElectrode

MiddleElectrode

InputSignal

1k

5k

5k

1k

4k

5k

5k

5k

5k1k

STP6NB50

STP6NB50

STP6NB50

2N3904

2N3904

2N3904

2N3904

InputSignal

TopElectrode

BottomElectrode

MiddleElectrode

t

t

t

t

Change polarity every two actuation cycles

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Relay Actuated by Zipping Actuator

> 40 millions of life cycles were achieved

Maximum toggling speed: 160 Hz

Shortest excitation pulse: 400 µs

Click for a movie

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33

Switching Time

Contact bounce time ~ 0.5 ms

Switching time ~ 3ms

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Contributions

Design: Starting zone to reduce the pull-in voltageNumerical modeling: easier and more accurateOptimization of the systemSpecified design for implementation in a relayFabrication and measurement of the actuator-relay

Wet-anisotropically-etched micro relay contact

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DRIE-etched Relay Contacts

Relay contactsVertical sidewallsSputter Au: low efficiency.Sidewall/surface thickness ratio = 1/9Contact resistance:~1 Ω

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KOH-etched Relay Contacts: Design

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KOH-etched Relay Contacts: Experiments

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KOH-etched Relay Contacts: Tests

Sputter Au: high efficiency.Sidewall/surface thickness = 1/1.4 Very low contact resistance: ~ 50 mΩ

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39

Proposed Full Relay Process Flow

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Conclusions and Future Work

Conclusions:Design, modeling, optimization, fabrication and measurement of an actuator-relay systemDevelop wet-anisotropically-etched relay contacts

Future work:Combine the actuator and the KOH-etched contactsVertically moving zipping actuators

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Acknowledgements

Advisors: Prof. Alexander Slocum, Prof. Jeffrey Lang, Prof. Michael Brenner (Harvard University)Discussion (PERG): Dr. Jin Qiu, Dr. Joachim SihlerFabrication (at MTL): Kurt Broderick, Dennis Ward, Paul Tierney, Linvhu Hol, Dr. Hongwei Sun …Testing (at ABB Research): Dr. Ralf Struempler, Dr. SamiKotilainen, Dr. Jan-henning Fabian, Eric Wapelhorst, Jeff Renaud

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22

43

44

Actuator Beam Profile

DRIE Etchdirection

15.24 µm

13.00 µm

15.78 µm

285.8 µm

12.78 µm

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45

Optimization: Algorithm (1)

0''')'''( =+ wTwIE

( '') '' '' '' ( '') ''i i i i i iE I w T w T w E I wδ δ δ δ+ = − −

( )'' ( '') '' 0i i i iT w E I w w dxδ δ+ =∫

Beam equation:

Fredholm alternative:

( '') ''

''i i

ii i

w E I w dxT

w w dx

δδ = − ∫

∫Cost function variation:

( )( )

2

2

''

'i

ii

I w dxT E

w dx

δδ = ∫

∫

( )( )

2

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''( ) ( , )

'i

i i ii i i

wdCC T I I T wdT w

δ δ δ∞

=

⎡ ⎤⎢ ⎥= = Λ⎢ ⎥⎣ ⎦∑∫ ∫∫

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Optimization: Algorithm (2)Beam equation:

Transition state

( )( )

2

2

''

'i

ii

I w dxT E

w dx

δδ = ∫

∫0 0.5 1 1.5 2

-400

-200

0

200

400

600

800

force

displacement

20( ( ) '') '' '' ( / 2)E I w w w f x Lτ δ− + = −

0 ( )t nw w x A w= Γ +

120 ))/(1( −−=Γ ττ

( )*

*

12 2 (1 )

R− Γ∆

= =− ∆ − − Γ

* 1∆ = − Γ

*∆

22 0

22 0

( )2 ( )

τ ττ τ

=−

24

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Analytical Analysis (1)Beam equation:

[ ]2''''( ) ( )( )

EIy x p xy x β

Γ= = −

+

[ ]1 ( ) ( )

1 ( ) ( )

L

left s

L

right s

F p x L s x dxL s

F p x x s dxL s

⎧ = ⋅ − ⋅ − −⎪⎪ −⇒ ⎨⎪ = ⋅ ⋅ −⎪ −⎩

∫

∫

4 32( ) ( ) ( )

24y x x s A x s

EIβΓ

= − − + −

Near x = s

'''( ) 6leftF EIy s EIA= =

⇒

⇒

sL

δ

c(x)

p(x)

Fright

Fleft

sL

δ

x

y

δmax

d

h0

48

Analytical Analysis (2)

* * 3 * 42( ) ( ) ( )

246left

y x A x s x sEI

F EIA

ββ

Γ ⎫= = ⋅ − − − ⎪⎬⎪= ⎭

[ ]* *

2 2

* 2*

2

1 ( )~ ( ) ~

1 ( )~ ( ) ( )

x

left s

x

right s

x sF L s x dxL s

x sF p x x s dxL s L s

β β

β

⎧ Γ Γ −⋅ ⋅ − −⎪ −⎪

⎨Γ −⎪ ⋅ ⋅ − =⎪ − −⎩

∫

∫

* 3 * 42

*

2

~ ( ) ( )6 24

( )~

left

left

Fx s x s

EI EIx sF

ββ

β

⎫Γ⋅ − − − ⎪

⎪⎬

Γ − ⎪⎪⎭

Assume most of the force comes from s<x<x*

⇒

⇒1~right

EIFL s β

Γ−

3* 1/ 4

* 2

2

( ) ~ ( )

( )~right

EIx s

x sFL s

β

β

⎫− ⎪Γ ⎪

⎬Γ − ⎪

⎪− ⎭

⇒

⇒

25

49

1/ 4

~

1~right

EIL s d

EIFL s

β

β

⎫⎛ ⎞− ⎪⎜ ⎟Γ⎝ ⎠ ⎪⎬

Γ ⎪⎪− ⎭

3/ 41/ 41~ ( )rightF EI

d β⎛ ⎞Γ⎜ ⎟⎝ ⎠

3/ 421/ 40

0

~ rright

U hE bFhd

ε ε⎛ ⎞⎜ ⎟⎝ ⎠

2( ) ( )y x B x s= − ( )2*2

3* 1/ 4

~2

( ) ~ ( )

B x sEI

EIx s

ββ

Γ ⎫− ⎪⎪⎬⎪− ⎪Γ ⎭

Far from x = s

⇒

⇒⇒ ⇒


⇒

2

~

( )

BEI

d B L s

β⎫Γ⎪⎬⎪= − ⎭

⇒

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0

1

2

3

4

5

6

7

100 120 140 160 180 200 220 240 260

Voltage (V)

Forc

e (m

N)

Device I, Numerical results

Device I, Analytical Results

Device II, Numerical Results

Device II, Analytical results

electrostatic zipping actuators and their application to...

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