mems transducers

7/25/2019 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


2/21


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


3/21



Geometrical configurations

Parallel plate

Vertical

Parallel

Interdigitated comb finger

Transverse comb Longitudinal comb

Vertical comb

Anchor


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

= = = =

=




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= = = = = = =



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

= = =



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

= = =



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= + =



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


10/21


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

= =


11/21



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

= + =

+ +


12/21


Capacitive Sensor

Transverse comb Flexture

Anchor

Fixed Plates

Ref. Analog Devices ADXL-50


13/21


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


14/21


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


15/21


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


16/21


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


17/21



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


18/21


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)


19/21


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


20/21


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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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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