NTHU ESS5850
F. G. Tseng
Micro System Design
Fall/2003, 8-2, p1
Lecture 8-2 Design Comb-drive Actuator through
Cronos/MUMPS Process: I
 Electrostatic actuator/sensor [1]
Actuator
z
Stator
y
W
z
x
x
1. Fundamental
a. Energy in a battery-capacitor system
U c1  VQ
U c1
+
V
U c 2  U c 2,b  U c 2,c
q
 V (Q  q )   Vdq
Q
-
V(Q  q)
C
1
 V (Q  CV )  CV 2
2
1
 VQ  CV 2
2
+
-
Energy stored in
capacitance
0
U c2
+
(8-1)
q
(q  CV )
(8  3)
System energy
reduced by
(8  2)
1
CV 2
2
NTHU ESS5850
F. G. Tseng
Micro System Design
Fall/2003, 8-2, p2
b. Capacitance of a flat plate
+
X
A=WX
W
z
W
q
Neglect end effect
Ck
0 A
z
k
 0WX
(8-4)
z
Here k: Dielectric constant, for vacuum: 1.0, air: 1.00059, Pyrex:
5.6, Teflon: 2.1, water 80.
0: Permittivity of free space: 8.85e-12 C2/Nm2
2. Constant Charge mode
U c2
+
V(Q  q)
C
U C ,Q
+
-
q
+
V
-
q
Energy stored:
q02
1
1
z
2
U c  CV0 

(
)q02
2
2C 2k 0 WX
(8-5)
NTHU ESS5850
F. G. Tseng
Micro System Design
Fall/2003, 8-2, p3
a. Fix gap z, move in X direction
Q Fx 
 U C
1
z
2

(
)
q
0
X
2k 0 WX 2
(8-6)
b. Fix X position, move in z direction
Q Fz 
 U C
1
1

(
)q02
z
2k 0 WX
(8-7)
Constant force!!
3. Constant Voltage mode
U C ,V
V
(Q  q)
+
C
-
+
q
-
Energy stored:
1
1 k WX 2
2
U c ,V  VQ0  CV0  VQ0  ( 0
)V0
2
2
z
(8-8)
a. Fix gap z, move in X direction
V
Fx 
 U C 1 k 0W 2
 (
)V0
X
2
z
Constant force!!
c. Fix X position, move in z direction
(8-9)
NTHU ESS5850
F. G. Tseng
Micro System Design
Fall/2003, 8-2, p4
V
Fz 
 U C  1 k 0WX 2

(
)V0
2
z
2
z
(8-10)
 Comb drive actuator (Tang et. Al., MEMS’89)[1]
Layout of a linear resonant plate with comb structures on both ends
and a 50 m long folded-beam on each side.
1. Driving force and displacement
a. Laterally driven
V
z
Fx,C
Kl
W
X
Kg
Ctotal  N 0
WX
z
Fx ,C 
(For W>>Z, N: # of gaps)
1
W
N 0V 2
2
z
(8-11)
(8-12)
NTHU ESS5850
F. G. Tseng
Micro System Design
Fall/2003, 8-2, p5
i. Large displacement
ii. Small force
iii. Constant force
b. Gap-closing driven
V
Fz+
z
Kl
W
X
Fz-
Ctotal, z  N z 0
Ctotal, y  N y 0
y
Kg
WX
z (For W>>z, Nz: # of closer gaps) (8-13)
WX
y (For W>>y, Ny: # of farer gaps)
(8-14)
k WX
k WX
1
1
N z ( 0 2 )V 2 
N y ( 0 2 )V 2
2
z
2
y
k WX
1

N z ( 0 2 )V 2
( for z  y )
2
z
Fz  Fz   Fz  
(8-15)
i. Nonlinear force
ii. Small displacement
NTHU ESS5850
F. G. Tseng
Micro System Design
Fall/2003, 8-2, p6
2. To get larger force
a. Gap closer-better lithography resolution
b. Higher aspect ratio- using LIGA, SCREAM,
Deep Silicon RIE, Thick PR...increase W
c. Special initial fixing technique [2]…decrease Z
d. Increase capacitive area: tooth like surface
e.
Increase capacitive area: Cylinder type surface
f.
Using buckling effect-scratch actuator
NTHU ESS5850
F. G. Tseng
Micro System Design
Fall/2003, 8-2, p7
3. To get larger Displacement
a. Laterally driven+gap closing [3]
Moving
b. Inch worm
c.
Transverse motion=> rotational motion (Sandia
national lab, comb drive-> gear set)
NTHU ESS5850
F. G. Tseng
Micro System Design
Fall/2003, 8-2, p8
 Spring System
Spring
Spring
1. Cantilever beam
b
a
L
F Ea3b
K (a, b, L) 

 K0
3
y 4 L
2. Two ends constrained beam:
y1
F
F y1
L
(8-16)
NTHU ESS5850
F. G. Tseng
Micro System Design
Fall/2003, 8-2, p9
k1 
F
1
L
 k (a, b, )  4 K 0
2y1 2
2
(8-17)
3. Crab lag
1
k2  K1  2 K 0
2
(8-18)
4. Folded beam
k fold  2 K 2  4 K 0
(8-19)
NTHU ESS5850
F. G. Tseng
Micro System Design
Fall/2003, 8-2, p10
 Viscous Damping [4]
Couette-type damper:
Qcd 
d
MK
A
(8-20)
Q: quality factor, Q=nM/b
Stokes-type damper:
1
1
1
1



Qs Qsd Qs Qsc
(8-21)
NTHU ESS5850
F. G. Tseng
Micro System Design
Fall/2003, 8-2, p11
total=(finger to ground) + (finger to ) + (finger to
finger)
(cosh 2 d  cos 2 d )
Q

Q
sd
cd
where
d (sinh 2 d  sin 2 d )
Qs  Qcd
1
d
(8-22)
(8-23)
Afinger (cosh 2z  cos 2z )
Qsc  Qcd
A d (sinh 2z  sin 2z )
(8-24)
where


,  : osillation frequency,  : dynamic viscousity,
2
M
z : finger gap, Q : quality factor 
b
 Dynamic Response
Laterally driven:
1
W
MX  bX  K ( X  X 0 )  Fx ,C  N 0V 2  cons tan t
2
z
NTHU ESS5850
F. G. Tseng
Micro System Design
Fall/2003, 8-2, p12
(8-25)
Gap closing:
Mz  bz  K ( z  z0 )  Fz ,C 
k WX
1
N z ( 0 2 )V 2
2
z
(8-26)
Frequency response

K
M
(8-27)
Reference
[1] William C. Tang, Tu-Cuong H. Nguyen, and Roger T. Howe, “Laterally Driven
Polysilicon Resonant Microstructres”, Proceedings of MEMS ’89, pp.187-193,
Feb., 1989.
[2] T. Hirano, T. Furuhata, K. J. Gabriel, and H. Fujita, “Operation of Sub-micron Gap
Electrostatic Comb-drive Actuators”, Proceedings of MEMS’91, pp. 873-876,
Feb. 1991.
[3] Reid A Brennen, Martin G. Lim, Albert P. Pisano, and Alan T. Chou, “Large
Displacement Linear Actuator”, Technical Digest IEEE Solid-State Sensors and
Actuators, pp. 135-139, June, 1990.
[4] Young-Ho Cho, Albert P. Pisano, and Roger T. Howe, “Viscous Damping Model
for Laterally Oscillation Microstructures”, Journal of MEMS, Vol. 3, No. 2, pp.
81-86, June, 1994.