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MEMS Actuation Basics: Electrostatic Actuation

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Two basic actuator types: Out of Plane(parallel plate) In Plane (lateral rezonator). N=15. V=0. k. z. V. F. V=0-150V. D gap =4 µm. MEMS Actuation Basics: Electrostatic Actuation. Out of plane actuator. MEMS Actuation Basics: Electrostatic Actuation. k. Zo-Z. V. Z. Zo. Unstable. - PowerPoint PPT Presentation
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E 5323 – Nonlinear Systems, Spring 2012 MEMS Actuation Basics: Electrostatic Actuation Two basic actuator types: Out of Plane(parallel plate) In Plane (lateral rezonator) V z k V=0-150V V=0 F N=15 Dgap=4µm
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Page 1: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

MEMS Actuation Basics: Electrostatic Actuation

Two basic actuator types: Out of Plane(parallel plate) In Plane (lateral

rezonator)

Vz

k

V=0-150V

V=0

F

N=15

Dgap=4µm

Page 2: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

MEMS Actuation Basics: Electrostatic Actuation

Out of plane actuator

VZo-Z

k

o

osnap

osnap

oo

o

o

kzV

zz

z

V

zzkz

V

kzzz

VF

27

8,

3,0

)(2

)(2

3

2

2

Z

V

Zo

0.33 Zo

Vsnap

Unstable

Stable

Hard StopsProblem: Snap-downoccurs in 2/3 of thetravel range.

Page 3: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

MEMS Actuation Basics: Electrostatic Actuation

Out of plane actuator

VZo-Z

k

zkAQ

kzA

QF

o

o

2

2

2

Solutions: Use hard stops:

reduced range of motion

Use charge control: requires on-chip circuitry

Stiffening mechanical spring: increases required voltage

Page 4: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

MEMS Actuation Basics: Electrostatic Actuation

Out of plane actuator

VZo-Z

k

zkAQ

kzA

QF

o

o

2

2

2

Solutions: Use hard stops:

reduced range of motion

Use charge control: requires on-chip circuitry

Stiffening mechanical spring: increases required voltage

Page 5: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

MEMS Actuation Basics: Electrostatic Actuation In plane MUMPS or DRIE comb drive

Linearized comb modelV=0

FKxdt

dxB

dt

xdM

QMB

L

WEhKV

d

hNF o

gapo

2

2

exp3

32 ,4,

V=0-150V

V=0

F

N=15

Dgap=4µm

Damping is given by a Couette flow Model.High K => High Q, high force.Low K => High displacement.

Page 6: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

MEMS Actuation Basics: Electrostatic Actuation General Formula T – actuator thickness

Xo – finger engagementL – finger lengthH(x)=g(x)-f(x+L-xo) – gap function

)(

)(2)(

)()(2)(

2

2

0

0

2

xh

TVF

xh

dxTxC

xLxfxg

dxTxC

x

CV

x

EF

ox

x

oo

x

ooo

oox

o

o

Only if the fingers are sufficiently Parallel to one another.

stationary

movable

xo

g(x)

f(x+L-xo)

L

x

)()( o

o

xLxfxg

TdxdC

Page 7: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

Page 8: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

Page 9: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

Page 10: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

Page 11: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

MEMS Actuation Basics: Electrostatic Actuation Example

Page 12: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

Page 13: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

Page 14: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

Page 15: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

Page 16: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

MEMS Actuation Basics: Electrothermal

Principle: Electrical current Joule Heating Thermal expansion Deflection and Force

Thermal governing equation: Fourier (Heat) Equation:

HWdt

dE

E - Thermal energy storedW - Power Generated by Joule HeatH - Heat Transferred to surroundings

radiationconductionconvection HHHHRIWcTE ,, 2

neglijibleTfH

TTKH

TH

radiation

airconvection

conduction

)(

),(

,

4

C- volumetric specific heat- thermal conductivityK – convection coefficient

Page 17: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

Electrothermal MEMS bimorph

If the driving input is voltage applied:

),()_),,((

)(),(),( 2

2

2

xtKT

xxtTR

tV

x

xtT

t

xtTc

“cold” arm“hot” arm

Elements n-1, n, n+1

FEA Approximation Model:

2

2

13121)(

)()()(

nn

nnnnnnnn

nn

R

tVTRTTT

dt

tdTc

In which Rn is the resistance of the n-th element which depends on temperature

+V-

Page 18: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

Thermal Bimorph: Electro-Thermal-Mechanical Model

The full linearized model is expressed by:

])[]([)(]][[][

]][[][]][[]][[

212

.

_

.

_

..

_

TRRtVTT

TNxKxBxM

In this equation and are vectors containing positions and temperature of the elements, while M, B, K, N, and are tri-diagonal matrices.

The governing equations are non-linear. An FEA package will simply integrate the equations using many elements to provide a solution.

][x ][

T

Page 19: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

Electrothermal MicroActuators

Rotary stage, tooth gap – 6 µm[Skidmore00]

Translation stage, scanning mirror 30 µm [Sin04]

Precision guided MEMS flexure stage And microgrippers using flexible hinges

Page 20: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

Silicon MEMS devices: Linear Stage

Electro-thermal actuation

Back-bent for power-off engagement

0.6mm / second operation speed

Page 21: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

Micro Optical Bench Assembly

--1212-- 7/31/20017/31/2001MOST Design TeamMOST Design Team

Prototype DesignPrototype Design

Wafer

Fiber

Fiber MountMolded Glass

Lens

Steering MirrorsMicrolens Aperture

TurningMirror

500 microns

200 microns

Page 22: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

Fiber Alignment – “Pigtailing”

1XN V-Groove array Pigtailing with Ferrules

Page 23: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

Nonlinearities during Fiber Alignment

Light transmission loss is parabolic with d and

2 2d tdB k d k

d

z

2

2 42 4

1 410log

1 5 4z

z z

k zdB

k z k z

-10-5

05

1015

-10

0

10

20-26

-24

-22

-20

-18

-16

x(um)y(um)

z(db

m)

Alignment Algorithms: Model Based Alignment Conical/circular scanning Gradient Based MethodsMBA decreased search time by a factor

of 10[Sin03]

2 2

1 22 2 2 2

1 1 2 2

1 1 2 2

1 1 2 2

1 1 2 2

1

1

1

,

x x

y z y z

x z x z

y z y z

dx y x y

x

y

z

r crr r c r r

r r cr r kr r cr r ckr r cr r

rrr

x

2 2 21 2 1 2 2 2 2 2 2 2z y y z z y z z y z yy z y z y A

y = Ax

Page 24: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

Fiber Alignment Algorithms

Model-based alignment method

2 2

1 22 2 2 2

1 1 2 2

1 1 2 2

1 1 2 2

1 1 2 2

1

1

1

,

x x

y z y z

x z x z

y z y z

dx y x y

x

y

z

r crr r c r r

r r cr r kr r cr r ckr r cr r

rrr

x

2 2 21 2 1 2 2 2 2 2 2 2z y y z z y z z y z yy z y z y Ay = Ax

X

Z

r1r3

r2

r4

actuated fiber (a) fixed fiber (b)

Gradient-based searchConical scanning search

a

r1r3

actuated fiber (a)

fixed fiber (b) Z

Y

scanning path

Page 25: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

Optical Fiber Insertion Into Ceramic Ferrule

Experimental setup

Connector hole with fiber

Page 26: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

Optical Fiber Insertion Into Ceramic Ferrule

MeasuredComputed

Laser intensity around the hole of connector

Laser intensity during insertion

Page 27: MEMS Actuation Basics: Electrostatic Actuation

EE 5323 – Nonlinear Systems, Spring 2012

Textbook Readings for Week 2

Chapter 2 from Slotine & Li text

Chapters 1,2 from F. Verlhurst

Chapters 1,2 from M. Vidyasagar


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