MEMS VARIABLE CAPACITOR WITH SUPERIOR LINEARITY AND LARGE
TUNING RATIO BY MOVING THE PLATE TO THE INCREASING-GAP
DIRECTION
Chang-Hoon Han, Dong-Hoon Choi, Seon-Jin Choi and Jun-Bo Yoon
Department of Electrical Engineering, KAIST
373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Republic of Korea
response to the noise signal whose frequency exceeds the
mechanical resonant frequency of the moving actuator.
Thanks to the electrostatic actuation property, we do not need
to consider the forward biasing problem which is critical
supply voltage limit of p-n junction varactors [3].
However, common parallel-plate MEMS variable
capacitors show non-linear C-V response that most of the
capacitance change occurs near the highest control voltage
region because they increase the capacitance value by closing
the gap between two parallel plates.
This inherent
non-linearity is one of the main factors which result in
non-constant phase noise over the frequency tuning range in
VCOs [4] and loop bandwidth variation in LC-VCO based
PLL [5]. These properties make it difficult to set the voltage
for achieving a desired capacitance value.
Recently, a few MEMS variable capacitors showed high
linearity factor (98.5 ~ 99.6%) and larger capacitance tuning
ratio than the conventional parallel-plate type devices [6-7].
However, it was difficult to design capacitance value and
control voltage range since their main approach was
increasing the mechanical spring constant as the applied
voltage closes to the pull-in point. Therefore, they needed to
get through several trial and errors for optimization.
In this work, we paid our attention to the direction of the
moving plate. Opposing to the common closing-gap
direction, we found that by moving the plate simply to the
increasing-gap direction, we could achieve excellent C-V
linearity and large tuning ratio simultaneously.
ABSTRACT
This paper reports an innovative and simple method to
achieve highly linear capacitance vs. voltage response and
large tuning ratio in a parallel-plate MEMS variable
capacitor by moving the plate to the increasing-gap direction.
The proposed structure adopted a levering actuator to achieve
the opposite moving direction and large displacement of the
top plate. The proposed MEMS variable capacitor, which
was made by metal surface micromachining, showed
excellent linearity factor of 99.1% in C-V response and the
capacitance tuning ratio of 178% were achieved at 2GHz.
INTRODUCTION
Capacitance
Displacement
Capacitance
In RF applications, a parallel-plate MEMS variable
capacitor has been widely studied for its simple fabrication
and relatively high quality factor compared to other MEMS
variable capacitors and p-n junction varactors, which were
used in voltage-controlled oscillators (VCOs) and
phase-locked loop circuits (PLL) [1-2]. The parallel-plate
MEMS variable capacitor is generally made of metal
materials which have low electrical resistivity as a signal path
structure and air gap as an insulator, which leads to high
Q-factor. In hence, low loss and low phase noise of RF signal
are easily achievable. Additionally, since the MEMS
variable capacitors change its capacitance value by
mechanical movement, the moving parts does not sensitively
Voltage
Displacement
< Actuator >
< Capacitor >
Port 2
Voltage
Port 1
Capacitance
Displacement
Capacitance
(a)
Voltage
Displacement
< Actuator >
< Capacitor >
b
t
< C-V response>
L
Ground
Voltage
Bias Vctrl
< C-V response>
(a)
(b)
(b)
Figure 2: The proposed structure (a) Perspective view of
initial and pull-in state, (b) Magnified view of the actuator
part
Figure 1: Conceptual graphs of capacitance vs. voltage
response characteristics for (a) conventional MEMS
variable capacitor and (b) newly proposed device
978-1-4244-9633-4/11/$26.00 ©2011 IEEE
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772
MEMS 2011, Cancun, MEXICO, January 23-27, 2011
coefficient equation (inset of Figure 3) [8]. The LF value lets
us know how well the curve is close to the straight line.
When a curve is straight line, the LF value is 100%. The LF
value is independent from the number of samples. The beam
length ratio from the levering beam to each end of the
actuator beam was 7:1 (560μm: 80μm). The gap between
two parallel plates was initially 1.25μm and it was supposed
to be increased to 3.53μm when the applied voltage was 50V.
CONCEPT AND SIMULATION
Concept
As depicted in Figure 1 (a), a conventional closing-gap
parallel-plate MEMS variable capacitor shows non-linear
C-V response because as the voltage increases, gap decreases
fast, and as the gap decreases, capacitance increases faster.
On the other hand, if the gap increases fast as the voltage
increases, capacitance decreases linearly to the voltage since
capacitance decreases slow as the gap increases, as shown in
Figure 1 (b). This concept is presented for the first time to
our knowledge. To realize this concept, we need an actuator
that can increase the gap between two parallel plates as the
actuation voltage increases. Figure 2 shows a schematic
view of the proposed structure which transforms the common
closing-gap electrostatic actuation in the actuator part into
the increasing-gap actuation in the central parallel plates by
means of the levering beam. When the voltage is applied
between the actuator plate and the bottom DC pad which is
located underneath the actuator plate, the actuator plate
moves down but the opposite side of the actuator beam is
lifted up due to the torsion of levering beam. As a result, we
can achieve increasing-gap actuation of the parallel plates as
the applied voltage increases. Additionally, this structure
makes it possible to separately design the capacitance value,
actuation voltage range and the linearity in C-V response.
The capacitor plate’s size and the length of ‘b’ in actuator
part determine the capacitance value and actuation voltage
range respectively. The beam length ratio from the levering
beam position to the capacitor plate connector and to the end
of actuator plate is supposed to determine the linearity solely.
FABRICATION
Figure 4 represents the fabrication process of the
actuator part of the proposed MEMS variable capacitor. The
process started with a glass substrate for low substrate loss of
RF signal. Thermal evaporated Au (1000Ǻ) made the bottom
capacitor plate and bias pad pattern. To prevent DC electrical
short, silicon nitride was deposited on the bottom layer using
PECVD and patterned by plasma etcher. The sacrificial layer
was then formed using sputtered Cr (1500Ǻ), Al (4000Ǻ) and
Cr (6500 Ǻ) in order (step A). Thick photoresist was
spin-coated and patterned to form the 1st mold. 6μm thick Cu
was electroplated to form the levering beam and the
connector for the capacitor plate (step B). The photoresist
used in step B was totally removed and thicker 2nd photoresist
was patterned for 25μm thick electroplated Cu (step C). In
the last step, the 2nd photoresist was removed and the
sacrificial layer was wet-etched. Finally, the structure was
A
Simulation
The proposed concept was verified using
CoventorWareTM and HFSSTM, and the result was shown in
Figure 3. An excellent linearity factor of 99.9% was
anticipated in the voltage range of 10 ~ 50V.
The linearity factor (LF) was defined by the correlation
Capacitance (pF)
2.0
1.6
B
Cu 6μm
Si3N4 4000Ǻ
Cu 25μm
LF = 0.992 (total)
0.999 (10~50V)
1.4
Au 1000Ǻ
PR mold
1GHz
2
400x400μm , b=300μm
W=10μm, L=20μm, t=6μm
1.8
Cr 1500Ǻ / Al 4000Ǻ / Cr 6500Ǻ
C
1.2
1.0
0.8
0.6
0
LF =
n∑ CiVi − ∑ Ci ∑ Vi
[n∑ C − (∑ Ci ) 2 ][n∑ Vi 2 − (∑ Vi ) 2 ]
2
i
10
20
30
Voltage (V)
40
D
50
Figure 3: Simulated capacitance vs. voltage response using
CoventorWareTM and HFSSTM
Glass substrate
Au
Cu
Cr / Al / Cr layer
Actuator part
Si3N4
PR
Figure 4: Simplified fabrication process of the proposed
structure
773
at 0V. This is relatively low compared to the conventional
parallel-plate MEMS variable capacitors. Because the RF
signal should pass through the long actuator beam which acts
as an inductive component in the device.
Figure 7 shows measured Q-factor with respect to the
frequency sweep. The values were between 7.3 and 13.5 at
1GHz. These values are very low at this moment because the
RF signal should pass through the narrow torsional spring
structures (connector between capacitor plate and actuator
beam, levering beam). However, these problems as well as
the low SRF can be solved by adopting the split bottom plate
structure developed in our group previously [10].
400x400μm2
Capacitor Plate
20 μm
Actuator
Beam
Levering
Beam
Actuator Plate
CONCLUSION
50 μm
A new MEMS variable capacitor with highly linear C-V
response and large tuning ratio by only changing the
Figure 5: SEM photographs of the fabricated MEMS
variable capacitor. Over-view (large), magnified view
(small)
released using critical point dryer (CPD) to prevent stiction
between parallel capacitor plates.
Figure 5 shows the scanning electron microscope (SEM)
photographs of the fabricated MEMS variable capacitor. All
four levering actuators were successfully fabricated without
any bending which can critically affect the C-V response
characteristic.
MEASUREMENT
Capacitance (pF)
200 μm
0V
5V
10V
15V
20V
25V
30V
35V
40V
45V
1.4
1.2
1.0
0.8
0.6
0.4
0.5
Figure 6 shows the measured frequency characteristics
of the capacitance (a) and C-V response extracted at specific
frequencies (b). The linearity factor was 98.4% at 1GHz and
99.1% at 2GHz in the total range without any abrupt changes.
Capacitance tuning ratio was 134% at 1GHz and 178% at
2GHz. Since there is little capacitance change in the first few
voltages (0 ~ 10V), the device is expected to be used in the
region from 10V to 45V. In this actual usage region, the
linearity was 99.5% at 1GHz and 99.9% at 2GHz. These are
extremely improved values compared to the conventional
closing-gap MEMS variable capacitor whose linearity factor
is typically about 85%. The capacitance tuning ratio of the
highly linear region was 125% at 1GHz and 164% at 2GHz
(10 ~ 45V), respectively, and these values are remarkably
higher than 50% which is the highest value that can be
achievable from the conventional closing-gap parallel-plate
MEMS variable capacitors.
Suppose that the conventional parallel-plate MEMS
variable capacitor with separate actuator is used to achieve
the same amount of the capacitance tuning ratio as in the
proposed device, the linearity factor becomes lower than the
conventional 85% since, in order to increase the capacitance
tuning ratio, the top plate moves down lower than two thirds
of the initial gap deteriorating linearity in C-V response
severely as shown in [9].
Self-resonant frequency (SRF) was measured to 3.5GHz
1.0
1.5
2.0
Frequency (GHz)
2.5
Capacitance (pF)
(a)
1.4
1GHz
2GHz
2
400x400μm , b=300μm
W=10μm, L=20μm, t=6μm
1.2
LF = 0.991 (total)
0.999 (10~45V)
1.0
0.8
LF = 0.984 (total)
0.995 (10~45V)
0.6
0.4
0
5
10 15 20 25 30 35 40 45
Voltage (V)
(b)
Figure 6: Measured results (a) Capacitance vs. frequency
sweep, SRF is 3.5GHz at 0V (b) Capacitance vs. voltage
response at 1GHz and 2GHz
774
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0V
45V
15
10
5
0
-5
1
2
3
4
Frequency (GHz)
5
Figure 7: Q-factor vs. frequency sweep, Q-factor is 7.3 (0V)
and 13.5 (45V) at 1GHz
direction of the moving plate is proposed and developed
successfully to demonstrate its performance with the
experimental results. The fabricated device showed over
99% linearity factor in C-V response and over 100%
capacitance tuning ratio without any abrupt capacitance
change region. The device is expected to be favorably used
in MEMS VCOs and various electrical circuits with its
remarkably high linearity and large tuning ratio.
ACKNOWLEDGEMENT
The authors would like to thank to the graduate students
of 3D Micro-Nano Structures laboratory in KAIST. This
work was partially supported by the Korea Science and
Engineering Foundation (KOSEF) grant funded by the Korea
government (MEST) (No.R11-2007-045-03003-0).
REFERENCES
[1] A. Dec, K. Suyama, “Microwave MEMS-Based
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