Transcript Class 8
MEMS
Class 6
Modeling of MEMS Devices
Mohammad Kilani
The Scaling of MEMS Devices
20 mm
2 mm
1 mm
Isometric Scaling
10 mm
How does electrostatic force change?
How does electrostatic force change relative to other forces?
How does response time change?
The Scaling of MEMS Devices
20 mm
2 mm
1 mm
Isometric Scaling
10 mm
L S, W S, H S
A L W S S S 2
V L W H S S S S 3
Water Bug
Weight = V S3
Surface Tension = kA S2
Man : 2m
Bug: 2 mm
Water bug uses surface
tension to walk on water
S = 1/1000
Surface Tension / Weight S2/S3 = S-1 = 1000
The Scaling of Forces
20 µm
2000 µm
10 μm
Isometric Scaling
1000 μm
S = 1/100
Weight = gm = gV S3
Electrostatic Force = kA S2
Electrostatic Force / Weight S2/ S3 = S-1 = 100
1
F1 S
F 2
2 S
F3 S 3
4
F4 S
The Scaling of Work or Mechanical Energy
1
F1 S
F 2
2 S
F3 S 3
4
F4 S
W F D
1
1
2
W 1 S S S
W 2 1 3
2 S S S
W 3 S 3 S 1 S 4
4 1 5
W 4 S S S
Gravitational force S3
Wok of gravity S4
If S = 1/100 the gravitational energy required to move an object
from the bottom to the top of the machine under consideration
decreases by (1/100)4 1/100,000,000.
Drop an ant from ten times his height, and he walks away.
Please do not try this with a horse!
The Scaling of Acceleration
1
F1 S
F 2
2 S
F3 S 3
4
F4 S
aF m
1
3
2
a1 S S S
a 2 3 1
2 S / S S
a3 S 3 S 3 S 0
4 3 1
a4 S S S
A predominance of the forces we use in the microdomain scale as S2.
For these forces, the acceleration scales as S 1. If S = 1/100, a
increases by a factor of 100.
Small systems tend to accelerate very rapidly.
The Scaling of Velocity
adx vdv , v 2 ax
1
F1 S
F 2
2 S
F3 S 3
4
F4 S
v 2xa x 0.5a 0.5
0.5
1
0.5
v 1 S S S
v 0.5 0.5 0
2 S S S
v 3 S 0.5 S 0 S 0.5
0.5 0.5 1
v 4 S S S
For the case where the force scales as S2, velocity scales as S-0.5.
If S = 1/100, the velocity increases by a factor of 10.
Small things tend to be fast.
The Scaling of Response Time
The time needed to travel a certain distance, x is given from the
relation
t
t t
x vd ad d
0
1
F1 S
F 2
2 S
F3 S 3
4
F4 S
0 0
Assume
constant a
2x
t
x 0.5a 0.5
a
1 2
x at
2
0.5
1
1.5
t 1 S S S
t 0.5 0.5 1
2 S S S
t 3 S 0.5 S 0 S 0.5
0.5 0.5 0
t 4 S S S
For the case where the force scales as S2, transit time t scales
as S1. If S = 1/100, the transit time decreases by a factor of 100.
Small things tend to be fast.
The Scaling of Mechanical Power
The time needed to travel a certain distance, x is given from the
relation
P F v
1
0.5
0.5
P1 S S S
P 2 0 2
2 S S S
P3 S 3 S 0.5 S 3.5
4 1 5
P4 S S S
For the case where the force scales as S2, power scales as S2.
If S = 1/100, the power decreases by a factor of 10000.
Small things have very small mechanical power.
The Scaling of Magnetic Forces
1. Constant current density
o
L
F
I aIb
2
d
Ib
Ia
L
I J .dA JA
Ia S 2, Ib S 2,
F S
4
The Scaling of Magnetic Forces
2. Constant heat flow through the surface of the wire
Q
S 0
As
Ib
L
Q P I R I
A
e
2
Q
I
L
0
[S ]
I 2 [S 3 ]
As
A s Ae
2
Ia
L
I S 1.5
F S 3
2
The Scaling of Magnetic Forces
3. Constant temperature rise of the wire
Ib
Ia
L
F S
2
The Scaling of Magnetic Forces
4. Wire and permanent magnet
Ia
L
1. Constant current density: F S3
2. Constant heat flow: F S2.5
3. Constant temperature rise: F S2
The Scaling of Different Forces