mems transducers
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EEL5225: Principles of MEMS Transducers (Fall 2003)1
EEL5225: Principles of MEMS Transducers (Fall 2003)
Instructor: Dr. Hui-Kai Xie
Transducers
Today: Electrostatic
Capacitive
Reading: Senturia, Chapter 6, pp. 125-138
Last lecture
Piezoresistive
Pressure sensor
Lecture 22 by H.K. Xie 10/15/2003
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EEL5225: Principles of MEMS Transducers (Fall 2003)2
Capacitive Transducers
Electrostatic Transducer Sensor
Actuator
Advantages
Reciprocal
sensor and actuator in same device
Negligible temperature dependence
High accuracy
Challenges
Small signal magnitude
Effect of parasitic capacitance
Potential undesired electrostatic actuation
MEMS Applications
accelerometers
gyroscopes
actuators voltage controlled capacitance
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EEL5225: Principles of MEMS Transducers (Fall 2003)3
Capacitive Transducers
Geometrical configurations
Parallel plate
Vertical
Parallel
Interdigitated comb finger
Transverse comb Longitudinal comb
Vertical comb
Anchor
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4/21EEL5225: Principles of MEMS Transducers (Fall 2003)4
Parallel Plate
plates
of area
S
x
fixed
plates
x=0
x=x0
movable
plates
x0 x
1 1
0 0 0 0
0 0 0 0
0
0
0
The capacitance can be expressed as:
( ) ( )( ) 1 1 ,( )
where is the capacitance at rest,
: gap at rest, and x(t): gap change.
S S S x t x t C t Cx x x t x x x
SC
xx
= = = =
=
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Capacitive Transducers
0 0
The voltage, ( ), is related to the charge on the parallel
plate of the capacitor, ( ), through the capacitance, ( ).
( ) ( ) ( )( ) 1( )
( ) "behavior at rest" + "electromechanical
V t
Q t C t
Q t Q t x t V tC t C x
V t
= =
= coupling"
2* 2
0 0 0 0
By first principles, we find the electrostatic force from
potential energy stored in this capacitor:1
2 2
Q QV V
P P
Q QW QdV VCdV CV W VdQ dQ
C C= = = = = = =
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Parallel Plate
Charging Capacitor at Fixed GapQ2 2
0 02 2
Q Q
P
Q Q Q xW VdQ dQ
C C S= = = = CV
2 2 2*
2 2 2P
Q CV SV WC x
= = =
Lifting up one electrode at Fixed Charge
2
( , )2
PW QF x Qx S
= =0
( )x
PW F x dx=
Electrostatic force:
Note: Electrostatic force always tries to narrow the gap.
+QF(x)
x
-QFE(x)2
( , )2
PE
W QF F x Q
x S
= = =
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Parallel Plate
Lifting up one electrode at Fixed Voltage
* ( , ) ( , )W V x QV W Q x=
Electrostatic force:
Note: Electrostatic force always tries to narrow the gap.
+VF(x)
x
0* ( , ) ( , )where ( , )
dW V x QdV VdQ dW Q xdW Q x VdQ Fdx
= + = + FE(x)
*( , ) ( )dW V x QdV F x dx =
* ( , )( )
V
W V xF x
x
=
*21( , )
2
PE
W dCF F x V V
x dx
= = =
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Parallel Plate
x
fixedplate
x=0
x=x0
movable
plate
Cm =1/k
The sum of the mechical and electrical forces is
0EF F F= + =
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Electrostatic Spring Softening
2 22
22 2
0 020
0
The electrostatic force opposes motion in the x-direction as follows:
21
2 22 1
E
S SV SV xF V
x x xxxx
= = +
If x
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EEL5225: Principles of MEMS Transducers (Fall 2003)10
Pull-In
( )2
022net E m m
SVF F k x k x x
x
= + =
0 0Example: 1 , 1 ,
1 / , 0.54
E
PI
x um C pF
k N m V V
= =
= =
FM
FEFE,0
2
3
Consider the effect of a small perturbation in the gap
spacing, x+ x, on the net force, F:
ornetnet net mV
F SVF x F k x
x x
= =
x
net
2 2
,min3 3
F must oppose x to avoid collapse (pull-in),
which requires: orm mSV SV
k kx x
> =
( )
2
,min 0 min2
maxThus, 0 2
net m
SV
F k x xx
= =
min 0
30
0 PI
2Then we obtain =
3
82So, pull-in occurs at at which V
3 27PI
x x
kxx x
S
= =
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EEL5225: Principles of MEMS Transducers (Fall 2003)11
Capacitive Transducers
Position Sensing ac input voltage
parasitic electrostatic force
capacitive divider
need to match Cr to C0 to minimize offset
output proportional to x
00 0
0 0 0
0
0 0 0
out 00 0 0 0 0
Ssense capacitor= 1x
If , then we have
V if 1.2 2 2
S
ref
i
i i
CxC C C xx x x
C C
C x x x x V x
V V x xC C x x x x x
= + = +
=
= + +
Vi
CS Vout
CrBuffer
-Vi
( )out
The output of the capacitor divider is:
V 2s r si i is r s r
C C CV V V
C C C C
= + =
+ +
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EEL5225: Principles of MEMS Transducers (Fall 2003)12
Capacitive Sensor
Transverse comb Flexture
Anchor
Fixed Plates
Ref. Analog Devices ADXL-50
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EEL5225: Principles of MEMS Transducers (Fall 2003)13
Capacitive Sensor
Transverse comb
Thickness=t
LCs1 Cs2
S1 S2
1
0
2
0
where C and C are given by:
S fringe
S fringe
LtC N C
x x
LtC N C
x x
= + +
= +
x0+x
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EEL5225: Principles of MEMS Transducers (Fall 2003)14
Capacitive Sensor
Transverse comb for senseVout
Vi -Vi
Cs1
1 0
2 0
x=0 0
0
0
0
0
For small displacements,
|
|
where C|
S x
S x
ringe
out i
CC C xx
CC C x
xNLt
C Cx
CC sensitivityx x
xV V
x
=
=
+
= = +
=
Cs2
Differential Capacitive Bridge
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EEL5225: Principles of MEMS Transducers (Fall 2003)15
Electrostatic Actuator
Transverse comb for actuation
Differential force (x=0)
( ) ( )
( ) ( )
1 2
2 2
0 0
2 200 0
0
0 0
0
1
2
1
2
2
Differential force is proportional to voltage, .
x x
x x
x
x
F F F
dCV V V V
dx
C V V V V x
C V
Vx
V
=
=
=
x
+V0 -V0+Vx
F1 F2
F
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EEL5225: Principles of MEMS Transducers (Fall 2003)16
Electrostatic Actuator
Electrostatic spring (Vx=0)
1 2
2 22
0
0 0
2
0 0
20
( )
1 12
2
el
dk F F
dx
SVddx x x x x
C V
x
=
= +
x
+V0 -V0Vx=0
F1 F2
Electrostatic Softening Effect
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EEL5225: Principles of MEMS Transducers (Fall 2003)17
Capacitive Transducers
Lateral comb
x00
2 20
2
( )
( )12 2
N ote: non -linear w ith V .2
N ote that the spring constant, 0 !
p
p
E
Ee
t x xC
d
t x xW C V V d
W tF V
x d
Fkx
+=
+= =
= =
= =
d
No electrostaticsoftening effect for
longitudinal actuation!
( )22 2
2 2 2
If sin
( sin ) ( 2 sin sin )2 2
( 0.5 2 sin 0.5 cos 2 )
2
dc ac
dc ac dc dc ac ac
dc ac dc ac ac
V V V t
t tF V V t V V V t V td d
tV V V V t V t
d
= +
= + = + +
= + +
Second harmonic
x
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EEL5225: Principles of MEMS Transducers (Fall 2003)18
Vertical Comb
Z-axis sensing X-axis sensing
stator statorrotor
z
xy
C1 C2
Vm+ Vm-
Vs
C2
C1 Vm+
Vm-
C1 C2 (at zero displacement)C1 = C2 (at zero displacement)
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EEL5225: Principles of MEMS Transducers (Fall 2003)19
Vertical Comb
Maxwell 2D Field Simulation
C1
C2
C2-C1
C2+C1
Z (m) Z (m)
Capacitance(aF/finger
/mm)
Normalized
diff.capacitance
C1 and C2 have high nonlinearity However, their normalized difference has wide linear range
A large offset exists
C
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EEL5225: Principles of MEMS Transducers (Fall 2003)20
Vertical Comb
Wiring for x-axis actuation But we can make wiring like this
Fz
Fz
V
z
x
yFxFx
V
2
2
1V
dx
dCFx=
Total of 25 different combinations
2
2
1V
dz
dCFz=
V ti l C b
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EEL5225: Principles of MEMS Transducers (Fall 2003)21
Vertical Comb
x
z
C2
C1
V2
V1
Z-axis
spring
Z-axiscomb
C1
C2
dz
dC1
dz
dC2
Capacitanc
e(aF/m)
Z-axis displacement (m)-4 -2 0 2-3 -1 1 3 40
5
10
15
20
-5
-2.5
0
2.5
5
C
apacitancegradient(aF/m2
)
H. Xie, et al, MSM 2000, San Diego
Z-axisdispla
cement(m)
Applied voltage, V1 (V)
0
100
200
300
400
0 4 8 12
Experimental data
Simulation
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