Switching and Release Dynamics of an Electrostatically Actuated MEMS Switch
under the influence of Squeeze-film Damping
S. Shekhar*, K. J. Vinoy* and G. K. Ananthasuresh**
*
Department of ECE, Indian Institute of Science, Bangalore, INDIA,
{sshekhar, kjvinoy}@ece.iisc.ernet.in
**
Department of Mechanical Engineering, Indian Institute of Science, Bangalore, INDIA,
suresh@mecheng.iisc.ernet.in
ABSTRACT
This paper reports experimental validation for switching
and release times of an electrostatically actuated
micromachined switch. Switching dynamics is investigated
under the influence of squeeze-film damping and tests were
performed on SOI (silicon-on-insulator) based parallel
beams of varied dimensions. Measurement results also
show the oscillation during the release and confirm that the
quality factor Q has appreciable effect on the release time
compared to the switching time. The quality factor Q is
extracted from the response measurement and compared
with the simulation result. Switching time is of the order of
few µs (5-18 µs) whereas release time less than 8 µs. . In
addition, the dynamic pull-in and frequency pull-in effects
have also been studied and reported in this paper. For a
parallel-plate actuator pull-in can be achieved with only
91.9 % of the predicted pull-in voltage and is been vrified
experimentally.
Keywords: RF MEMS switch, switching speed, squeezefilm damping, dynamic pull-in, SOI MUMPs
1
INTRODUCTION
Microelectromechanical systems (MEMS) switches
have always been the most favored area of research after
the successful developement of MEMS technology. Among
various applications RF (radio frequency) MEMS switch is
one of the potential application and the reason behind the
popularity are low insertion loss, high isolation, low power
consumption, and high linearity as compared to
semiconductor switches (e.g., p-i-n diodes, field effect
transistors (FETs), etc.) even at very high frequencies [1-2].
However, switching time is of the major concerns of
MEMS switches. In recent years many MEMS switches
have been fabricated and reported but the effect of various
phenomena such as squeeze-film damping, frequency pullin effect, dynamics pull-in etc. on the switching and release
times have not been explored substantially. Low actuation
voltage and fast switching speed are key parameters. Low
actuation voltage can be achieved by making the switch
geometry more flexible but penalty is paid in the form of
low switching speed. Swithcing speed depends not only on
the actuation voltage but on other factors too and damping
is one of the critical parameter. Squeeze-film damping has a
very strong influnce on the dymanics of MEMS structures
and have been studied extensively in the past [3-5].
Damping not only affects the quality factor of the switch
but also the switching speed. Therefore, to design and
develope a high speed MEMS switch it is desirable to have
a better unserstading of damping and its effects on the
switching and release times.
In our previous work [6], we presented expalnations for
pull-in (switching) time being more than the pull-up
(release) time of an RF MEMS switch at voltage
comparable to the pull-in voltage. However, our analysis
did not consider damping. In section 2 of the present paper,
effects of squeeze-film daming on the switching and release
times are studied and demontrated experimentally.
For switching mechanism in MEMS switches pull-in
phenomenon is extensively used. In elctrostaticlly actuated
MEMS switches, when the applied voltage reaches a
particular value termed as Pull-in volatge, the switch snaps
down to the bottom electrode and makes or breaks the
signal. It has been observed that pull-in happens before the
actual pull-in volatge. Section 3 of this paper deals with the
dynamic pull-in phenomenon. Simulation as well as
measurement results are presented.
2
2.1
SQUEEZE-FILM DAMPING
Theory
A gas (air) fills the space between the two plates and
when the plate moves downwards because of the force
applied on the plate, the pressure inside the gas increases as
a result the gas is squeezed out from the edges of the plate.
The viscous drag of the air creates a dissipative mechanical
force which opposes the motion. This dissipative force is
called squeeze-film damping. A simple squeeze-film
damping configuration is illustrated in figure 1. Most
oftenly in MEMS devices geometries used are of very small
feature size therefore the squeeze-film daming is dominated
by viscosity of the fluid and inertial damping is neglected.
The behavior of the fluid is governed by Reynold’s
equation which is a function of density and the temperature.
Assumptions made to derive the Reynold’s equation are [7]:
•
Fluid obeys ideal gal law
•
•
•
The width of gas trapped between the two
plates is very samll compared to the lateral
dimension of the plate (g << L,W)
The variation of the pressure across the fluid
folw is negligibly small
The system is isothermal
Based on the above assumptions the Reynold’s equation
is simplified as:
12η
∂ ( Pg )
= ∇ ⋅ (1 + 6 K n ) g 3 P∇P 


∂t
ω0 = k m
is the
resonant
(5)
frequency and
Q = k ω0 b is the quality factor of the beam.
k
b
Fs
+
∂ ( Pg ) g 3  1 2 2 
=
∇ P 
∂t
12η  2

(2)
and the damping constant is given by:
96η LW 3
(3)
π 4 g03
form the above equation it clear that damping has strong
dependence on the gap height, g0 .
F
g (t)
Figure 1. Squeeze-film damping between two plates.
2.2
where
(1)
where η is the viscosity and K n is the Knudsen number,
which is the ratio of mean free path of the gas molecule to
the gap. In case of MEMS structure when the gap is very
small and for small amplitude motion the Knudsen number
is negligibly small. Under these assumptions, the Reynold’s
equation becomes:
b=

X ( jω ) 1 
1

=
F ( jω ) k  1 − (ω / ω )2 + jω /(Qω ) 
0
0 

Lumped parameter model
V
-
g0
x
Fe
Figure 2. Lumped model of a parallel-plate actuator.
A high quality factor Q structure does not effect
switching time but has a large effect on the the setteling
time of the switch. Figure 3 shows the typical frequency
response of equation 5 for different values of Q (0.1, 0.5, 1,
2 and 5). Simulation results show that Q ≤ 0.5 results in
slow switching time while Q ≥ 1 results in long setteling
and hence the release time.
2.3
Experimental results
For dynamic characterization PolyTech MSA-500 laser
vibrometer [8] has been used. A laser vibrometer uses
Doppler’s shift effect to measure the displacement as well
as velocity of the beam. Test structures investigated for the
study are fabricated using SOI MUMPs (Silicon-oninsulator Muli-user MEMS Precesses) in MEMSCAP,
USA. Length of parallel-beams are 450 µ m to 550 µ m ,
thickness 2 µ m to 4 µ m , width 25 µ m and the gap is
2 µ m . These parallel-beam test structures are shown in
figure 3 and 4.
One dimensional model (1D) treats a switch as a
lumped mass and spring model. Figure 2 shows the lumped
model of a MEMS switch and the governing dynamic
equation of motion is given by:
mxɺɺ + bxɺ + kx = f ext
(4)
where x is the displacement, m is the mass, b is the
damping co-efficient, k is the stiffness and f ext is an
external force. Frequency response of the system can be
found by taling the Laplace transforms of equation 4 and
given by:
Figure 2. SEM image of parallel-beam test structures.
L = 550um t = 3um
w = 25um g = 2um
Displacement [um]
1
V=
V=
V=
V=
V=
V=
0.8
0.6
25V
26V
27V
27.5V
28V
29V
0.4
0.2
0
All the experiments are performed at normal
atmospheric pressure. Measurement setup can be seen in
figure 5. Switching characteristics of the switch for various
actuation volatges are studied. Measurement results of
switching and release times can be seen in figures 6 and 7.
Switching time decreases with increase in actuation
voltage. It is found that switch closing time is of the order
of 5-18 µ sec while the opening time is less than 8 µ sec .
Measurement results also show the oscillation during the
release and confirm that the quality factor Q has
appreciable effect on the release time compared to the
switching time.
10
15
20
Time [us]
Figure 6. Measurement results of switching response for
various applied voltages Vs.
0
5
0.2
Displacement [um]
Figure 4. SEM image of parallel-beam test structure.
0
-0.2
-0.4
-0.6
-0.8
-1
0
10
20
30
Time [us]
40
50
Figure 7. Release time response of the switch .
3
DYNAMIC PULL-IN
It has been observed that pull-in voltage is influenced by
the inertia of the beam [9]. To study this effect a ramp DC
voltage is applied instead of step input voltage and it has
been found that pull-in occurs before the quasi-static pull-in
voltage. The simulation results for 1D model without
damping is shwon in figure where wich shows that actual
pull-in happens when the applied voltage is 91.9% of the
actual pull-in voltage and this voltage is termed as dynamic
pull-in voltage. Pull-in voltage for a 1D model lumped
system is given by:
VPI =
Figure 5. Laser Doppler Vibrometer measurement setup.
8kg03
27ε 0 A
(5)
It has also been oberved that dynamic pull-in volage is
influenced by damping. Figure 9 shows effect of damping
on dynamic pull-in voltage and as damping increases
1
Vs = Vpi
Vs = 0.919Vpi
Vs = 0.91Vpi
0.8
0.6
-0.4
-0.6
-1
0.2
2
4
6
8
10
Normalized Time [time*freq]
Figure 8. Dynamic pull-in phenomenon without damping.
Normalized Displacement [x/g0]
-0.2
-0.8
0.4
0
0
Displacement[ um ]
Normalized Displacement [x/g0]
dynamic pull-in voltage approaches to the actual pull-in
voltage.
0
1
Vs = 0.919*Vpi
Vs = 0.954*Vpi
0.8
5
10
15
Time [ usec ]
20
25
Figure 10. Mesurement results of the shift in dynamic pullin with damping.
5
ACKNOWLEDGEMENT
The author wolud like to thank Micro and Nano
Characterization facility (MNCF), Centre for Nano Science
and Engineering (CeNSE), IISc, Bangalore for the facilities
used for device characterizaion.
REFERENCES
0.6
0.4
0.2
0
0
0
2
4
6
8
10
Normalized Time [time*freq]
Figure 9. Shift in dynamic pull-in volatge with damping.
In order to support the effect of squeeze-film damping
on the shift of dynamic pull-in voltage, LDV measurement
was done. Measurement results can be seen figure 10.
4
CONCLUSIONS
In this paper, we have presented the effcet of squeezefilm damping on the switching and release times. A
lumped parameter squeeze film model has been discussed.
Experimental results presented are in close agreement with
analytical and simulation results presented in previous
work.
In addition, we also have discussed dynamic pull-in
effect which shows that pull-in can be achieved with only
91.9% of the predicted pull-in voltage. This dynamic pullin technique can be used in developing low actuation
voltage MEMS switches (RF, Optical etc.) without
sacrificing mechnaical stiffness.
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