Micr o Actuator s
•Electrostatic actuator
- comb drive actuator
•Magnetic actuator
•Thermal actuator
•Piezoelectric actuator
•Shape memory alloy actuator
•Pneumatic actuator
Micr ovalve/pump
Electrostatic
Piezoelectric
Electromagnetic
Shape memory alloy
Thermal bimorph
Pneumatic
Fundamental of Electr ostatic For ce
(I) Energy in a battery-capacitance system:
(II) Capacitance of flat plate:
Constant Char ge Mode of Electr ostatic For ce
Switch is open
(i) Fixed gap Z=Z0, moving in x-direction
Fx =
(3)
Fx =
− ∂U c
1
Z
2
=
(
) q0
2
∂X
2kε 0 WX
1
Z
kε 0WX0V0 2 1
X0 2
1
2 W
(
)(
)
=
k
ε
V
(
)(
)
~
0 0
2kε 0 WX2
Z
2
Z X
X2
W ↑, Z ↓,
q0 = C0V0=εWX0V0/Z0
(ii) Fixed X=X0 position, moving in z-direction
Fz =
Fz =
X0
↑ ⇒ Fx ↑
X
− ∂U c
−1 1
2
=
(
) q0
∂Z
2kε 0 WX
− ∂U c
− 1 1 kε 0WXV0 2 1
1
2 WX
=
(
)(
) = kε 0V0 ( 2 ) = cons tan t ~ 2
∂Z
2kε 0 WX
Z0
2
Z0
Z0
Examples
Constant Voltage Mode of Electr ostatic For ce
Switch is closed
(i) Fixed gap z, moving in x-direction
(3)
(i) Fixed x position, moving in z-direction
Examples
X-dir ection motion of Comb Dr ive Device
Fr inged Field Cor r ection
A=Xt
Constant Voltage Mode
with fringed field correction
ε = kε 0
W=t
Z=d
For ce and Deflection (later al motion)
Electrostatic force:
2
2µm
100µm
V=15V, t=2µm, d=2µm, t/d =1, α(t/d)=2
8 combs
a
b
t 1
t
1
Fx = Nα ( ) εV 2 = 8 × 2 × × 8.854 ×10−12 ×152 ×1
d 2
d
2
Fx = 1.6 × 10 −8 N = 0.016 µN
Spring constant K(a,b,L):
Ea 3b 150 ×109 ( N / m2 )(2 ×10−6 m)3 (2 ×10 −6 m)
K (2,2,100) =
=
4 L3
4(100 ×10 −6 m) 3
N
K (2,2,100) = 0.6
m
Ver y small
F
−8
∆y = = 2.66 ×10 m = 0.027 µm
deflection!
K
How to get bigger for ce fr om combs ?
t 1
t
Fx = Nα ( ) εV 2
d 2
d
(1) Better lithography resolution
d↓, t/d↑, Fx ↑
(2) High aspect ratio structure (for example: LIGA)
t ↑, t/d↑, Fx ↑
(3) Submicron device:
(4) Leverage structure:
Z-dir ection motion of Comb Dr ive Device
Fr inged Field Cor r ection
t 1
Wt
t 1
t X
Fz ( d ) = − Nα ( ) kε 0V 2 ( 2 ) = − Nα ( ) εV 2 ( )( )
d 2
d
d 2
d d
d
x
Ex1: V=15V, t=2µm, d=2µm, t/d =1, α(t/d)=2, 8 combs
t 1
t X
1
Fz = − Nα ( ) εV 2 ( )( ) = −8 × 2 × × 8.854 ×10 −12 ×152 ×1× 5 = −1.6 ×10 −8 × 5 N = −0.08µN
d 2
d d
2
Ex2: X=10µm, K= 1 N/m, calculate voltage V for 1 µm deflection
Fz = − K • ∆z = −1µN
t 1
t X
1
Fz ( d ) = − Nα ( ) εV 2 ( )( ) = −8 × 2 × × 8.854 × 10 −12 × V 2 ×1× 5 = −1µN
d 2
d d
2
V = 53volt
y0
x
unstable
Spr ings for Folded Beams
2 2
µ
m
100µm
ab
Ea 3b
K0 (a , b, L) =
4 L3
K = 4 K0
Folded Beams
K = 8K0
Linear Resonator
m
Ea 3b
K = 4 K0 = 3 = 2.4 N / m
L
m = ρAt = ( 2.3 × 103 kg / m3 )(100 × 10 −6 m) 2 (2 × 10 −6 m) = 4.6 × 10 −11 kg
ω=
f=
K
2.4 N / m
=
= 228416
m
4.6 × 10 −11 kg
ω
= 36 KHz
2π
Metal
Poly0
Poly1
Homework #3
Magnetic For ce on a Cur r ent-car r ying Conductor
r
r r
F = IL × B
Magnetic Field of a Solenoid
For ce on a Cur r ent Loop in a unifor m magnetic Field
For ce on a Cur r ent Loop in a Solenoid
Magnetic Micr oflap
Poly1
Metal
coil