A viscoelastic-aware experimentally-derived model for analog RF MEMS varactors
ABSTRACT In this paper we present, for the first time, an experimentally-extracted model for the spring constant and tuning range of an analog RF-MEMS varactor that includes viscoelastic effects in RF-MEMS devices. By utilizing a bi-state bias condition with one state lasting 60 minutes and the other 1 minute, this model focuses on capturing the true electromechanical behavior of the varactor. An experimental setup with very high long-term accuracy is created to measure capacitance of the varactor up to 1,370 hours. The impact of these effects and the effectiveness of the model are demonstrated on a tunable-resonator loaded with RF-MEMS varactors.
Conference Proceeding: A Millimeter-wave Tunable Filter Using MEMS Varactors[show abstract] [hide abstract]
ABSTRACT: A mm-wave tunable 3-pole filter was developed using high-Q MEMS varactors on a quartz substrate using a coplanar-waveguide (CPW) implementation. The measured tuning range was 23.8 GHz (0 V) to 22.6 GHz (15 V) with an associated insertion loss of Â¿2.8 dB to Â¿3.8 dB, and a return loss better than Â¿12 dB over the entire tuning range. The measured 1-dB bandwidth was 8.4% at 23.8 GHz and 6.6% at 22.6 GHz. The extracted capacitance change in the analog MEMS varactors is 1.20. These numbers represent the best results achieved to-date for tunable filters. A larger tuning range can be obtained with the new of high-capacitance ratio varactors (2:1).Microwave Conference, 2002. 32nd European; 10/2002
Conference Proceeding: Evaluation of Creep in RF MEMS Devices[show abstract] [hide abstract]
ABSTRACT: RF MEMS are capacitive switches consisting of a suspended aluminum beam that can be pulled down by electrostatic force. At elevated temperatures and high mechanical stresses the aluminum beam can exhibit creep phenomena that result in shifting of device parameters as a function of time. Experimental and numerical methodologies are presented for measuring and predicting the effect of creep on the RF MEMS device performance. A constitutive creep model is implemented in a Finite Element code where the parameters of this constitutive model for creep in thin aluminum layers are determined by wafer curvature experiments. In order to distinguish creep effect from charging effects, special test structures are designed. Simulations on the test with different geometries indicate the effect of creep and can result in design rules for the RF MEMS switches. The numerical predictions and the measured degradation on the RF MEMS switches are compared and conclusions are drawn with respect to the methodology.Thermal, Mechanical and Multi-Physics Simulation Experiments in Microelectronics and Micro-Systems, 2007. EuroSime 2007. International Conference on; 05/2007
- [show abstract] [hide abstract]
ABSTRACT: The uniaxial tensile creep behavior of porosity-free nanocrystalline nickel with 30 nm grains produced by an electrodeposition processing has been investigated under constant and step-load conditions at room temperature and 373 K in a load range 500–1050 MPa. The experimental results showed that significant creep deformation occurred even at room temperature at an initial applied stress of 600 MPa or higher. The creep resistance was very sensitive to test temperature. The grain size and microstructure of the as received and post-creep specimens have been characterized by conventional TEM techniques. An attempt has been made to explain the deformation behavior and creep mechanisms based on current findings.Materials Science and Engineering: A. 01/2001; 301(1):18-22.
A VISCOELASTIC-AWARE EXPERIMENTALLY-DERIVED
MODEL FOR ANALOG RF MEMS VARACTORS
Hao-Han Hsu and Dimitrios Peroulis
Birck Nanotechnology Center, Purdue University, West Lafayette, IN 47907, USA
In this paper we present, for the first time, an
experimentally-extracted model for the spring con-
stant and tuning range of an analog RF-MEMS var-
actor that includes viscoelastic effects in RF-MEMS
devices. By utilizing a bi-state bias condition with
one state lasting 60 minutes and the other 1 minute,
this model focuses on capturing the true electrome-
chanical behavior of the varactor. An experimental
setup with very high long-term accuracy is created
to measure capacitance of the varactor up to 1,370
hours. The impact of these effects and the effective-
ness of the model are demonstrated on a tunable-
resonator loaded with RF-MEMS varactors.
Viscoelasticity is one of the most important ar-
eas of concern in the long-term operation of MEMS
devices.It can be observed as the time depen-
dency of deflection, spring constant, elastic mod-
ulus, and yield strength, among others, in MEMS
devices [1,2]. Most thin-film metals that are widely
employed in metallic RF-MEMS devices, including
Au, Al, and Ni, exhibit viscoelastic behavior. This
behavior needs to be studied and modeled in or-
der to achieve the required reliability and long-term
Vicker-Kirby et al. reported anelastic phenomena
in MEMS cantilever accelerometers . Si, Ni, and
Au cantilevers were controlled electrostatically us-
ing a feedback circuit that sensed the tunneling cur-
rent at the cantilever tip and applied an appropriate
voltage to maintain a constant gap of 10˚ A. This
voltage decreased gradually within the measure-
ment duration of 30 hours. This experiment also
demonstrated that Au is most prone to creep among
the three materials. Gilz et al. performed an ex-
periment on an Al RF-MEMS switch . It was
pulled-in using electrostatic force and the deforma-
tion of the suspension beam was measured opti-
cally for 15 hours. A finite-element-analysis (FEA)
simulation was conducted based on a measured
macro-scale creep-response to verify the micro-scale
measurement. However, discrepancies were found
between the measurement and the FEA simulation.
Yan et al.performed a stress-relaxation test on
an Au thin-film using a bulge test technique .
The Au film was inflated pneumatically and the ca-
pacitance between the deformed Au-film and the
Figure 1. The confocal-microscopy image of the fab-
ricated analog RF-MEMS varactor. The gap be-
tween the Ni plate and Au electrodes is 3 µm. There
are no dielectric layers in this varactor.
electrode beneath was measured for 80 hours. A
cyclic-loading test was also carried out to demon-
strate the linearity of viscoelasticity in such film.
The decrease of restoring force in the RF-MEMS
switch was discussed based on the calculation and
measurement of the bulged Au-film. Chasiotis et al.
conducted an investigation into the strain-rate ef-
fects on the mechanical behvaior of nanocrystalline
Au films . Atomic force microscopy (AFM)
and digital image correlation (DIC) were utilized
in the tensile tests of dog-bone shaped specimens
at various strain-rates. The decrease of the maxi-
mum strength, effective Young’s modulus, and yield
strength in the Au thin-films at low strain-rates was
attributed to dislocation creep.
In this paper, we present an experimentally-
extracted model that can accurately describe spring
constant and tuning range of analog RF-MEMS
varactors, based on capacitance measurements up
to 1,370 hours. This measurement setup has been
carefully established to achieve high accuracy and
high long-term stability. A new parameter called
dynamic spring constant is proposed to reveal the
true electromechanical behavior of the analog RF-
MEMS varactor under the effect of viscoelastic-
ity. The impact of viscoelasticity is demonstrated
by applying the experimentally-extracted model to
a tunable-resonator loaded with RF-MEMS var-
actors. This model and dynamic spring constant
may improve the controllability of MEMS devices
in long-term operation and lead to more reliable
ANALOG RF-MEMS VARACTOR
The confocal microscopy image of the analog RF-
MEMS varactor is shown in Fig. 1. The moving
parts of the varactor consists of a 300-µm × 220-µm
Ni top-plate and 4 symmetric suspension-beams.
Three Au electrodes can be found underneath the
Ni plate. The bias voltage is applied to the two
electrodes at the side, and the capacitance is sensed
using the center electrode. The thickness and total
length of one suspension beam is about 3 µm and
200 µm respectively. The actuation voltage is about
50 V. Unlike switched RF-MEMS devices, there are
no dielectric layers in this design. This eliminates
the effect of dielectric charging and provides sub-
stantial insight into the viscoelastic behavior of ana-
log RF-MEMS devices.
The fabrication process of this Ni analog RF-
MEMS varactor is shown in Fig. 2.
tor is built on a p-type high-resistivity silicon sub-
strate with a 500-nm thick thermally-grown silicon-
dioxide film. An 1-µm thick Au-film is sputtered
and lifted-off to define the bottom electrodes and
electrical connections of the varactor in Fig. 2(a).
The anchors are then patterned through a 3-µm
thick photoresist sacrificial layer in Fig. 2(b). The
sacrificial layer is hard-baked at 190◦C for 5 min-
utes. A seed-layer of 50-nm sputtered Ti and 30-
nm evaporated Ni is deposited on the whole sam-
ple in Fig. 2(c). A 6-µm thick photoresist layer
is shaped to form the electroplating mold on the
seed layer. The Ni electroplating is carried out in
a nickel-sulfamate bath at a temperature of 50◦C
and a pH value of 4. The average grain-size is about
50 nm. A 3-µm thick Ni layer is electroplated on the
seed layer selectively based on the photoresist mold
as shown in Fig. 2(d). The Ni and Ti seed layers
are stripped with HCl : water = 1 : 1 and HF : wa-
ter = 1 : 20 at room temperature respectively af-
ter the removal of the photoresist mold. The pho-
toresist sacrificial layer is removed by immersion in
photoresist-stripper-2000 at 75◦C for 24 hours. Fi-
nally, the fabrication process is completed by drying
in a critical-point-dryer (CPD) in Fig. 2(e).
A commercial capacitance sensor, AD7746, from
Analog Devices, Inc., is employed to perform low-
noise, low-capacitance measurement on the ana-
log RF-MEMS varactors, which is wire-bonded
and mounted on an Au-electroplated pin-grid-array
(PGA) package. This AD7746 is a high-precision
capacitance-to-digital converter (CDC) consisting
of a 24-bit Σ-∆ modulator and a third-order dig-
ital filter. This circuit feeds a 32k-Hz square wave
to the capacitor-under-test and converts the charge
going through the capacitor to a binary code.
Two difficulties can be encountered during the
observation of viscoelastic behavior. First, sub-
Figure 2. Fabrication process of the Ni analog RF-
Figure 3. The experimental setup consists of opaque
shielding boxes, laptops equipped with AD7746, a
high-voltage power supply, and a multi-meter.
femto-farad accuracy is required.
measurement drifting needs to be minimized to re-
veal the true viscoelastic movement. The noise is
the limiting factor of the measurement uncertainty.
In this work, each data point is the average of
100 acquired-samples and the uncertainty of such a
point is defined as one standard-deviation of these
100 samples. The noise can be lowered by utilizing
an opaque electrically-grounded shielding box and
coaxial cables. The measurement uncertainty is less
than 200 aF in Fig. 4(a).
The long-term drift of the experimental setup
needs to be characterized to validate that the mea-
sured capacitance-change is due to the nature of
viscoelasticity and not the artificial drift of the ex-
perimental setup.A long-term drift test is car-
ried out by measuring the capacitance of the ana-
log RF-MEMS varactor without applying any bias
for 1,500 hours in Fig. 4(b). It’s confirmed that
the effect of the long-term drift can be neglected in
this work. The overall drift is less than 4 fF over
1,500 hours, which is about 1% of the varactor ca-
pacitance at 1,000 hour and beyond.
RESULTS AND DISCUSSION
The analog RF-MEMS varactors are measured
using a bi-state bias condition. In the first state
a constant bias-voltage Vbiasis applied to the var-
actor for 60 minutes. In the second state the bias
Figure 4. (a) The measurement uncertainty.
The measured long-term drift is less than 4 fF over
voltage is removed for 1 minute. In Fig. 5(a) the
biased curve represents the capacitance measured
in the first bias state when Vbiasis 40V. The capac-
itance measured in the second state when Vbias is
removed is shown in the unbiased curve. A 3-D elec-
trostatic model of the varactor that contains all the
electrodes, pads, and the substrate is established in
a FEA tool . The gap in Fig. 5(b) and the elec-
trostatic force (not shown) are extracted using this
model. The parasitics and the fringing field are in-
cluded in this FEA model, and thus a more accurate
extraction of the gap and electrostatic force than
the parallel-plate model is obtained. The measured
data and also the extracted data can be modeled us-
ing a series of decaying exponents by curve-fitting,
y(t) = Ao+
where Aiand τiare constant.
In contrast to the traditional point of view that
the capacitance of varactor returns to the initial ca-
pacitance Coafter the bias is removed, the capaci-
tance Cunbiasis determined by the loading history
and stays between Cbiasand Co. This phenomenon
is largely due to the viscoelasticity of the material
and not to dielectric charging because there are no
dielectric layers between the varactor.
Dynamic Spring Constant
The conventional spring constant in Fig. 6(a) is
where F(t) is the FEA-extracted force, gois the ini-
tal gap, and g(t) is the gap at time t. An assump-
Figure 5. The measured (black) and fitted (red) re-
sults of the analog RF-MEMS varactor. (a) The
measured capacitance. Cois the initial capacitance.
(b) The FEA-extracted gap. gorepresents the ini-
Figure 6. The measured (black) and fitted (red)
spring constant. (a) Conventional spring constant.
(b) Dynamic spring constant.
tion is made that the varactor reverts to the initial
gap gowhen the bias voltage is removed. This as-
sumption is not true according to the extracted gap
in Fig. 5(b). The conventional spring constant is
not sufficient to describe the viscoelastic behavior of
the analog RF-MEMS varactor. Nevertheless, the
extracted conventional spring constant decays over
time and is consistent with the measurement results
of relaxation modulus in other literature [1,6].
In order to correctly capture the actual behavior
of the analog RF-MEMS varactor, a new parameter
called dynamic spring constant is defined,
(gunbias(t) − g(t))
where F(t) is the force, g(t) is the gap at time t, and
gunbias(t) is the gap at time t if the bias voltage is
removed. The force required for the desired deflec-
tion in the varactor can be correctly derived using
this spring constant since the viscoelastic behavior
that the varactor doesn’t revert to the initial gap
go is considered. This spring constant along with
the function gunbias(t) provides the ability to accu-
rately control the gap of the varactor in the long-
term operation. The measurement shows that the
dynamic spring constant may rise by as much as 8
times after the operation of 1,370 hours. The cause
of the increase in this spring constant is related to
The impact of viscoelastic behavior on tuning
range can be demonstrated using a tunable RF-
MEMS resonator. The tunable resonator consists of
an open-ended λ/2 transmission-line resonator sym-
metrically loaded with two analog RF-MEMS var-
actors as shown in Fig. 7. The resonant frequency
of this resonator is given by 
Bp− cotθ2+ tanθ1= 0(4)
where θ1and θ2are the equivalent electrical length
of l1and l2, and Bpis the normalized total shunt
susceptance, which is mainly contributed by the
varactors. An assumption that the tuning ratio re-
mains 1.5 is made in the calculation of tuning range.
A 906-µm long coplanar-waveguide (CPW) of 50-
Ω is loaded with two analog RF-MEMS varactor at
l1=100 µm. The model extracted from the previous
measurements is applied to this resonator. In Fig. 8,
region I shows the actual tuning range, while region
II is based on the concept of the conventional spring
constant. Because the varactor can not revert to the
initial position, the actual tuning range is reduced
by 60% compared to the conventional tuning range
at the 1,370 hour.
An experiementally-extracted model for vis-
coelastic behavior in analog RF-MEMS devices is
presented based on high-accuracy, high long-term
stability measurement up to 1,370 hours. A new
parameter named dynamic spring constant that can
reveal the true electromechanical behavior of analog
RF-MEMS devices is proposed. The impact of this
behavior is demonstrated using a simulation of a
tunable RF-MEMS resonator. This model and dy-
namic spring constant may improve the controlla-
bility of MEMS devices in long-term operation and
lead to more reliable designs.
Figure 7. Schematic of the tunable resonator loaded
with two RF-MEMS varactors.
Figure 8. The simulated tuning range of the tunable
RF-MEMS resonator. (I) The actual tuning range.
(II) Based on conventional spring constant.
This material is based upon work supported by
NNSA Center of Prediction of Reliability, Integrity,
and Survivability of Microsystems, and Depart-
ment of Energy under Award Number DE-FC52-
 X. Yan et al., “Anelastic stress relaxation in
gold films and its impact on restoring forces
in mems devices,” J. Microelectromech. Syst.,
vol. 18, no. 3, pp. 570–576, Jun. 2009.
 I. Chasiotis et al., “Strain rate effects on the me-
chanical behavior of nanocrystalline au films,”
Thin Solid Films, vol. 515, no. 6, pp. 3183–3189,
 D. J. Vickers-Kirby et al., “Anelastic creep phe-
nomena in thin metal plated cantilevers for
mems,” in Mat. Res. Soc. Symp., vol. 657, 2001,
 M. van Gils et al., “Evaluation of creep in rf
mems devices,” in EuroSime, Apr. 2007, pp. 1–
 Ansoft maxwell 3d. Ansoft LCC. Version 12,
2008. [Online]. Available: http://www.ansoft.
 W. Yin et al., “Creep behavior of nanocrys-
talline nickel at 290 and 373 k,” Mat. Sci. Eng.,
vol. 301, pp. 18–22, 2001.
 A. Abbaspour-Tamijani et al., “A millimeter-
wave tunable filter using mems varactor,” in
IEEE MTT-S Int. Micro. Symp. Dig., Jun.
2003, pp. 1785–1788.