ee 5323 – nonlinear systems, spring 2012 mems actuation basics: electrostatic actuation two basic...
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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
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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.
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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
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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
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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.
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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
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EE 5323 – Nonlinear Systems, Spring 2012
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EE 5323 – Nonlinear Systems, Spring 2012
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EE 5323 – Nonlinear Systems, Spring 2012
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EE 5323 – Nonlinear Systems, Spring 2012
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EE 5323 – Nonlinear Systems, Spring 2012
MEMS Actuation Basics: Electrostatic Actuation Example
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EE 5323 – Nonlinear Systems, Spring 2012
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EE 5323 – Nonlinear Systems, Spring 2012
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EE 5323 – Nonlinear Systems, Spring 2012
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EE 5323 – Nonlinear Systems, Spring 2012
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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
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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-
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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
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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
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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
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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
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EE 5323 – Nonlinear Systems, Spring 2012
Fiber Alignment – “Pigtailing”
1XN V-Groove array Pigtailing with Ferrules
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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
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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
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EE 5323 – Nonlinear Systems, Spring 2012
Optical Fiber Insertion Into Ceramic Ferrule
Experimental setup
Connector hole with fiber
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EE 5323 – Nonlinear Systems, Spring 2012
Optical Fiber Insertion Into Ceramic Ferrule
MeasuredComputed
Laser intensity around the hole of connector
Laser intensity during insertion
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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