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Microsyst Technol
DOI 10.1007/s00542-015-2585-5
TECHNICAL PAPER
Design, optimization and simulation of a low‑voltage shunt
capacitive RF‑MEMS switch
Li‑Ya Ma1 · Anis Nurashikin Nordin2 · Norhayati Soin1
Received: 29 June 2014 / Accepted: 29 May 2015
© Springer-Verlag Berlin Heidelberg 2015
1 Introduction
Radio-frequency (RF) micro-electro-mechanical system
(MEMS) switches operating at RF to millimetre-wave fre-
quencies have many advantages over p-i-n diode or field-
effect transistor (FET) switches, such as low or near-zero
power consumption, high isolation, low insertion loss, and
high linearity (Lee et al. 2006). These RF-MEMS switches
use mechanical movements to short or open a transmission
line; and normally can be integrated with a planar or copla-
nar waveguide (CPW).
There are many varieties of RF-MEMS switches. The
switch can be in series or in shunt connected with the
signal path; coupling method can be either capacitive or
metal-to-metal (Chan et al. 2003); and actuation mecha-
nism can be electrostatic (Kim et al. 2010), electromagnetic
(Glickman et al. 2011), thermal (Daneshmand et al. 2009),
piezoelectric (Park et al. 2006) or combined actuations
(Cho and Yoon 2010). Electrostatic actuated RF-MEMS
switches are the most prevalent technique in use today; due
to their virtually zero power consumption, high switching
speed (Kim et al. 2010), small electrode size, thin layers
used, 50–200 µN of achievable contact forces, the possi-
bility of biasing the switch using high-resistance bias lines
(Rebeiz 2003), and the high compatibility with a standard
Integrated Circuitry (IC) process (Chu et al. 2007). How-
ever, the largest challenge for electrostatic switches is their
relative high actuation (or pull-in) voltage, which is around
20–80 V (Lee et al. 2006; Kim et al. 2010; Park et al. 2006;
Mafinejad et al. 2013).
Usage of standard complementary metal-oxide semi-
conductor (CMOS) technologies have always been of great
interest for the implementation of RF-MEMS devices due
to their mature fabrication process, higher levels of inte-
gration, and also lower manufacturing cost (Fouladi and
Abstract This paper presents the design, optimization
and simulation of a radio frequency (RF) micro-electro-
mechanical system (MEMS) switch. The capacitive RF-
MEMS switch is electrostatically actuated. The structure
contains a coplanar waveguide, a big suspended mem-
brane, four folded beams to support the membrane and four
straight beams to provide the bias voltage. The switch is
designed in standard 0.35 µm complementary metal oxide
semiconductor process and has a very low pull-in voltage
of 3.04 V. Taguchi method and weighted principal compo-
nent analysis is employed to optimize the geometric param-
eters of the beams, in order to obtain a low spring constant,
low pull-in voltage, and a robust design. The optimized
parameters were obtained as w = 2.5 µm, L1 = 30 µm,
L2 = 30 µm and L3 = 65 µm. The mechanical and elec-
trical behaviours of the RF-MEMS switch were simulated
by the finite element modeling in software of COMSOL
Multiphysics 4.3® and IntelliSuite v8.7®. RF performance
of the switch was obtained by simulation results, which are
insertion loss of −5.65 dB and isolation of −24.38 dB at
40 GHz.
* Li-Ya Ma
maliya8445@gmail.com
Anis Nurashikin Nordin
anisnn@iium.edu.my
Norhayati Soin
norhayatisoin@um.edu.my
1 Department of Electrical Engineering, University of Malaya,
50603 Kuala Lumpur, Malaysia
2 Department of Electrical and Computer Engineering,
International Islamic University Malaysia,
53100 Kuala Lumpur, Malaysia
Microsyst Technol
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Mansour 2010). Nevertheless, generally standard 0.35 µm
CMOS process fabricated devices require compatible oper-
ating voltage supply of 3.3 V or less than 3.3 V (Yusoff
et al. 2004; Wey et al. 2002), which is insufficient to actuate
the most developed electrostatically-actuated RF-MEMS
switches. In order to monolithically integrate these RF-
MEMS switches with active CMOS circuitry, an additional
voltage-upconverter or an external off-chip circuit is needed
Fig. 1 RF-MEMS switch design. a Overall view, b top view and c cross-section view (A–A′)
Table 1 Each layer thickness
Name Membrane (t) Dielectric layer
(td)
CPW lines Air gap (g)
Thickness 0.877 µm 0.1 µm 0.624 µm 1.397 µm
Fig. 2 Relationship of Vp and k
Table 2 Geometric parameters with their possible values
Factor Level 1 (µm) Level 2 (µm) Level 3 (µm)
Beam width (w)2 2.5 3
First length (L1) 20 25 30
Second length (L2)30 35 40
Third length (L3)60 65 70
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Fig. 3 Multi-response optimization methodology
Table 3 Simulated results
of spring constant (k)
and maximum von Mises
stress (σv(max)) with their
corresponding S/N
σv(max) is obtained with 1µN surface load
Simulation no. Parameter Simulation results Calculated S/N
w L1 L2 L3 k (N/m) σv(max) (MPa) k (dB) σv(max) (dB)
1 1 1 1 1 1.625 20.800 9.302 −26.361
2 1 2 2 2 1.182 21.987 19.939 −26.843
3 1 3 3 3 0.877 23.477 7.840 −27.413
4 2 1 2 3 1.446 18.306 15.740 −25.252
5 2 2 3 1 1.633 17.900 9.121 −25.057
6 2 3 1 2 1.300 18.496 35.494 −25.342
7 3 1 3 2 1.935 15.219 3.707 −23.648
8 3 2 1 3 1.528 16.081 12.220 −24.126
9 3 3 2 1 1.737 15.217 6.861 −23.647
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(Lee et al. 2006), which will make the whole chip larger,
more complex, and consume more power. Chan et al. and
Goldsmith et al. indicated that a high actuation voltage also
may lead to a shorter lifetime for capacitive RF-MEMS
switches which use dielectric layers for isolation (Shal-
aby et al. 2009). Diverse RF-MEMS switch designs have
been proposed by various researchers to reduce the actua-
tion voltages. A dedicated RF-MEMS switch fabricated
in 0.35 µm CMOS process has been reported to require a
pull-in voltage of 7 V (Dai and Chen 2006). A bi-stable
RF-MEMS switch was designed with a low actuation volt-
age of 5 V, but was not compatible with CMOS process
(Lakamraju and Phillips 2005). Afrang et al. (Afrang and
Abbaspour-Sani 2006) have introduced a CMOS fabricated
membrane-based switch with actuation voltage of 12.5 V.
Authors’ previous design on CMOS RF-MEMS switch
managed to achieve a low pull-in voltage of 3 V (Ya et al.
2013), however, the relatively wide beams cannot be eas-
ily released with membrane in one step; an additional mask
wet etch is needed. Moreover the long membrane design
is hard to keep it in-plane during fabrication and operation
which deteriorates a lot in its RF performance.
In this paper, an advanced low-voltage electrostatically-
actuated shunt capacitive RF-MEMS switch is proposed
by using MIMOS (Malaysia Institute of Microelectronic
Systems) standard 0.35 µm (double poly triple metal)
CMOS technology. The actuation voltage of 3.04 V was
achieved by reduction of the beams’ spring constant while
maintaining the structure’s robust using multi-response
optimization method, which comprises Taguchi method and
weighted principal component analysis (WPCA). The rest
of the paper is divided into the following sections: Sect. 2
presents the detail designs of RF-MEMS switch. Section 3
displays the beams’ geometric optimization by Taguchi
method and WPCA. Section 4 illustrates the simulation
results of applied voltage with the membrane displacement,
stress distributions, switching time, switch-on and switch-
off capacitances, insertion loss and isolation, as well as a
comparison of the designed switch with other related work.
2 RF‑MEMS switch design
The structure of the RF-MEMS switch is illustrated in
Fig. 1a. The RF-MEMS switch consists of a membrane,
four folded beams, four straight beams, anchors and copla-
nar waveguide (CPW) lines. The four folded beams mainly
provide support to the large membrane and the four straight
beams are used to supply the DC bias. Figure 1b displays
the geometric parameters of the membrane and beams,
Table 4 Average values of S/N
ratio for each response
For each parameter, the bold values are the largest mean S/N ratio among three levels, as highlightedcor-
responding point in Figs. 4 and 6
Parameter Mean S/N ratio for k (dB) Parameter Mean S/N ratio for σv(max) (dB)
Level 1 Level 2 Level 3 Max-Min Level 1 Level 2 Level 3 Max-Min
w 12.360 20.118 7.596 12.522 w -26.873 -25.217 ‑23.807 3.066
L1 9.583 13.760 16.732 7.149 L1 ‑25.087 -25.342 -25.467 0.380
L2 19.005 14.180 6.890 12.116 L2 -25.276 ‑25.247 -25.373 0.125
L3 8.428 19.713 11.934 11.286 L3 ‑25.022 -25.278 -25.597 0.575
Fig. 4 Mean S/N plots. a Mean S/N of spring constant and b Mean S/N of maximum von Mises stress
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where the holes are used to release the membrane during
the post-CMOS process. And Fig. 1c shows the cross-sec-
tion view of the switch, where the four folded beams are
connected to the ground lines of the CPW by via; and a
very thin dielectric layer covers the CPW lines to consist
the coupling capacitor during actuated state.
When a DC bias voltage is applied between the mem-
brane and signal line, there is a positive feedback between
the electrostatic forces and the deformation of the mem-
brane. The applied voltage creates electrostatic forces that
bend down the beam and thereby reducing the gap to the
ground substrate. The reduced gap between the membrane
and signal line, in turn, increases the electrostatic forces.
At a certain voltage, the electrostatic force overcomes the
mechanical stress limit of the beam causing the system to
be unstable, and the gap collapses. This critical voltage
is called pull-in voltage or actuation voltage (Vp) and can
be described as shown in (1) (Rebeiz 2003; Gupta 1997).
Once the switch is actuated, a coupling capacitor induced
between the membrane and signal line prevents the signal
to be passed the signal line.
where, k is the spring constant of the membrane and beams;
g0 is the initial gap between the membrane and the signal
line; ε0 is the permittivity of air, 8.854 × 10−12 F/m; and
A is the area of the membrane, namely the product of the
membrane’s width and length (Wm × Lm).
(1)
V
p=
8kg3
0
27ε
0
A
Fig. 5 Percentage contribu-
tion of each factor to the both
responses. a Spring constant,
and b Maximum von Mises
stress
Table 5 Normalized S/N
values and computed MPI Simulation No Parameter Normalized S/N MPI
w L1 L2 L3 k (xi
*(1)) σv(max) (xi
*(2))
1 1 1 1 1 0.1760 0.2792 0.0774
2 1 2 2 2 0.5107 0.1512 0.3356
3 1 3 3 3 0.1300 0.0000 0.0919
4 2 1 2 3 0.3786 0.5738 0.1710
5 2 2 3 1 0.1703 0.6255 0.0151
6 2 3 1 2 1.0000 0.5500 0.6145
7 3 1 3 2 0.0000 0.9997 -0.1684
8 3 2 1 3 0.2678 0.8726 0.0424
9 3 3 2 1 0.0992 1.0000 -0.0983
Table 6 Explained variation and eigenvector
Principal component Eigen value Explained variation (%) Cumulative variation (%) Eigenvector [k, σv(max)]
Z1 1.238 61.913 61.913 [0.707, −0.707]
Z2 0.762 38.087 100.000 [0.707, 0.707]
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The materials and thickness of each layer are determined
by the CMOS fabrication process and is listed in Table 1.
The membrane and CPW lines are made from aluminum
(Al) and built by Metal3 and Metal1 layers of the standard
process. The permittivity of the dielectric material between
two metal layers is 4.99.
From (1) it can be seen that to achieve a low Vp, the
capacitive switch should have a small spring constant (k),
large membrane area (A) and big initial gap (g0). In this
design, the initial gap is determined by the CMOS process
(g0 = gair + td); the membrane area is generally decided
by the coupling capacitance which is in pF range and does
not have much space and flexibility to be modified here.
Therefore, the main parameter that can be designed and
controlled by the researchers is the spring constant (Dai
and Chen 2006; Peroulis et al. 2003; Balaraman et al. 2002;
Kuwabara et al. 2006; Jaafar et al. 2009). The relationship
of Vp and k can be observed in Fig. 2. Basically, in order to
own a lower spring constant, the beam should have a less
beam width or thinner beam thickness; but this will make
the structure to become fragile and short-lived (Bao 2000).
Optimization of beam lengths L1, L2 and L3, as well as
beam width w to obtain a low spring constant while main-
tain a robust structure becomes an important problem for
this low Vp RF-MEMS switch design.
3 Multi‑response optimization method
There are four geometric parameters in the RF-MEMS
switch as shown in Fig. 1b and the possible dimensions
are listed in Table 2. These parameters need to be modi-
fied to obtain a low k and small maximum von Mises stress
(σv(max)) simultaneously, where the low k can led to a low
Vp as shown in Fig. 2 and the small σv(max) can guarantee
a robust structure (Chen and Harichandran 1998). Since
every geometric parameter could be set with three differ-
ent values, it will be tedious to simulate all their possible
combinations (34 = 91 times). Therefore, a proper optimi-
zation technique is necessary here; it is also a general prob-
lem to be encountered by most RF-MEMS switches’ design
(Shalaby et al. 2009; Philippine et al. 2013). The only dif-
ference from each work could be the optimized responses
(such as switching speed, power handling capability or
RF performance) (Shalaby et al. 2009; Badia et al. 2012)
or geometric design (shapes or dimensions) (Peroulis et al.
2003; Gong et al. 2009).
In this work, a multi-response optimization method
which comprises Taguchi method and WPCA was
employed to optimize the responses of the spring constant
and maximum von Mises stress. This method could be sim-
ply implemented into other optimization problems which
have single or multiple responses with diverse parameters.
Figure 3 shows the multi-response optimization methodol-
ogy. The optimized values are based on a 3-D structural-
Electro-mechanics Finite Element Modeling (FEM) simu-
lation results.
3.1 Taguchi method
Taguchi’s parameter optimization is an important
method for robust design. Taguchi defines robustness as
the “insensitivity of the system performance to param-
eters that are uncontrollable by the designer” (Taguchi
et al. 1987). A robust design incorporates this concept of
robustness into design optimization and aims at achiev-
ing designs that optimize given performance measures
while minimizing sensitivities against uncontrollable
parameters using different approaches, such as signal to
noise ratio (Shalaby et al. 2009). The Taguchi approach
itself can be utilized to determine the best parameters for
the optimum design configuration with the least number
of analytical investigations. Comparing with other opti-
mization methods, such as Genetic Algorithm (GA) (Li
et al. 2003) or Neural Network (Meng and Butler 1997),
the proposed multi-response optimization does not need
much statistical or technical background in that specific
Table 7 Average MPI for each factor at each level
For each parameter, the bold values are the largest mean S/N ratio
among three levels, as highlightedcorresponding point in Figs. 4 and 6
Factor MPI Max-Min
Level 1 Level 2 Level 3
w 0.168 0.267 -0.075 0.342
L1 0.027 0.131 0.203 0.176
L2 0.245 0.136 -0.020 0.265
L3 -0.002 0.261 0.102 0.262
Fig. 6 Mean value of MPI
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field, which can be easily implemented by engineering
researchers (Roy 2010; Liao 2006). This method has not
been widely employed for the optimization of RF-MEMS
switch geometry but is more commonly used for process
or product optimization. There are two major tools to be
used in this method, which are orthogonal array (OA) and
signal-to-noise ratio (S/N).
The folded and straight beams of the RF-MEMS switch
will be analysed in terms of whole system’s k and σv(max).
In order to develop a RF-MEMS switch which could be
implemented together with normal active CMOS circuitry
as mentioned in part 1, a Vp of 3 V is proposed. From
Fig. 2, it can be seen that for our model, a Vp = 3 V RF-
MEMS switch should have a k of 1.2827 N/m. Therefore,
in Taguchi method, the S/N of k is calculated according to
the characteristics of the nominal the best; such a ratio is
selected when a specific target value is desired. The opti-
mum of σv(max) on the other hand employed the smaller the
better characteristic. This is because in order to avoid the
structure failure, with the applied voltage load, the beams
and membrane’s total σv(max) should be less than their mate-
rial’s yield strength (Chen and Harichandran 1998). With
smaller σv(max), the structure experiences less stretch. The
equations of both characteristics are shown in (2) and (3),
respectively (Roy 2010).
Nominal the best:
Smaller the better:
where y1, y2, etc., are the simulation results,
y0 = 1.2827 N/m is the target value of results; and n is the
number of observations with the same values of factors
(here n = 1).
According to OA selector (Fraley et al. 2006), with
four parameters and three levels of each parameter, OA of
L9 is selected as shown in Table 3, where the level of “1”,
“2” and “3” under parameter columns represent the corre-
sponding parameter’s least, middle and largest values. The
OA of Taguchi method has the capability to reduce the full
factorial designs into highly fractionated factorial designs
and to make the design of experiments very easy and con-
sistent. In Table 3, each row signifies random single simu-
lation run that has been carried out. The simulation results
for both responses of spring constant and maximum von
Mises stress were obtained by FEM simulations using soft-
ware of Comsol Multiphysics 4.3®, where Electro-mechan-
ics model was employed with the boundary condition of
eight beams’ end fixed. By applying (2) and (3) for simu-
lated k and σv(max), the S/N for each simulation run can be
calculated as listed in Calculated S/N columns. In order to
get the parameters’ optimum condition for each response,
the average S/N at each level for k and σv(max) are calcu-
lated separately in Table 4 and plotted in Fig. 4. For all of
these characteristics, the largest value of S/N represents a
more desirable condition (Roy 2010); and the bigger Max–
Min value means that corresponding parameter has more
effect on the response, vice versa.
Figure 4a suggests that in order to obtain the desired
spring constant of 1.2827 N/m, the four parameters
should be set as: w = w2 = 2.5 µm, L1 = (L1)3 = 30 µm,
L2 = (L2)1 = 30 µm and L3 = (L3)2 = 65 µm. Fig-
ure 4b illustrates that to obtain a structure with small-
est von Mises stress and longer lifetime, the parameters
should be set as: w = w3 = 3 µm, L1 = (L1)1 = 20 µm,
L2 = (L2)2 = 35 µm and L3 = (L3)1 = 60 µm. The con-
tribution of each parameter to the spring constant and
von Mises stress was calculated using Pareto analy-
sis of variance (ANOVA) technique (Park and Antony
2008) and is shown in Fig. 5. These optimization results
(2)
S
/N=−10 log10
(y1−y0)2+(y2−y0)2+··· +(yn−y0)2
n
(3)
S
/N=−10 log10
y2
1+y2
2+··· +y2
n
n
Table 8 Geometric parameters’ setting with different motivated opti-
mization
Factor The lowest spring
constant design
(model a) (µm)
The smallest von
Mises stress design
(model b) (µm)
The multi-response
optimization design
by WPCA
(model c) (µm)
w 2.5 3 2.5
L1 30 20 30
L2 30 35 30
L3 65 60 65
Fig. 7 Spring constant simulations for the optimized models
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illustrate that the geometric parameters’ settings for
achieving both low spring constant and small von Mises
stress simultaneously do not coincide. Generally, Tagu-
chi method is better to be used for optimizing a single
response or one design objective with many controlla-
ble parameters or factors, as in (Fahsyar and Soin 2012;
Su and Yeh 2011). For this multi-response optimiza-
tion, if all the responses have same parameters’ setting,
then the optimized result is obtained; if the responses
have conflict parameters’ setting, then a trade-off tech-
nique among them is needed. Here, in order to obtain the
trade-off parameters for low spring constant and small
von Mises stress designs, a further calculation of multi-
response optimization, namely WPCA was conducted, as
mentioned in Fig. 3.
3.2 Weighted principal component analysis
Principal component analysis (PCA) is a multivariate
statistical method used for data reduction purpose. The
basic idea is to represent a set of variables by a smaller
number of variables known as principal components.
It involves a mathematical procedure that reduces the
dimensions of a set of variables by reconstructing them
into uncorrelated combinations (Wu and Chyu 2004).
However, there are still some obvious shortcomings in
the PCA method. First, only the principal components
with eigenvalues ≥1 are chosen to be analysed in PCA.
Second, when more than one principal component (eigen-
value ≥1) is selected, the required trade-off for a feasible
solution is unknown; and third, the multi-response per-
formance index cannot replace the multi-response solu-
tion when the chosen principal component can only be
explained by total variation (Liao 2006). WPCA is a
method bases on PCA while all principal components
and their weights are taken into consideration. In order
to completely explain variation for all responses, WPCA
uses the explained variation as the weight to combine
all principal components into a multi-response perfor-
mance index (MPI) for the further optimization results
produced (Liao 2006). Experimental results using WPCA
have been reported by some researchers to provide higher
accuracy than the conventional PCA (Fan et al. 2011;
Pinto da Costa et al. 2011).
Fig. 8 Von Mises stress simulations for the optimized models. a Model a and Model c and b Model b
Table 9 Materials’ properties
Material Density
(g/cm3)
Young’s
modulus (GPa)
Poisson
ratio
Dielectric
constant
Si 2.3 170 0.26 –
SiOx2.2 73 0.17 4.99
Al 2.7 70 0.36 –
Fig. 9 Applied voltages vs. membrane’s vertical displacement
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3.2.1 WPCA procedure
In order to compute WPCA and obtain the MPI, a simple
procedure needs to be carried out as follows. First, using
(4) (Jaafar et al. 2009) normalizes the S/N values for all the
responses. The normalized value can get rid of the differ-
ence between different units and it should be located in the
range of 0 to 1. Second, PCA is performed by using the
normalized S/N values to obtain the values of explained
variation of all the responses, the eigenvalues and eigenvec-
tors of each principal component. Last step is to calculate
MPI by (5), where all the principal components and their
explained variations or weights are considered (Liao 2006).
where, xi(j) means the S/N value of jth response at ith
experiment number, xi
*(j) is the normalized response, xi(j)+
(4)
x
∗
i(j)=
x
i
(j)
−
x
i
(j)−
xi(j)
+−
xi(j)
−
is the maximum value of xi(j) at jth response, and xi(j)− is
the minimum value of xi(j) at jth response.
where, Zj is the jth principal component which can be
obtained by (6); Wj is the weight (or explained variation)
of jth principal component; and r refers to the total of
response number.
where, aji is the eigenvector which satisfies the relation of
∑ p
i=1aji
2 = 1.
3.2.2 Multi‑response optimization by WPCA
Following the WPCA procedures introduced in last part,
the S/N normalized values for both spring constant and
maximum von Mises stress were calculated by (4), as
shown in Table 5. Add-Ins tool of XLSTAT in Microsoft
Excel® has been used to compute PCA, where the normal-
ized S/N values of k and σv(max) were set as the Observa-
tions or variables; and the simulation run numbers were set
as the Observation labels. After the calculation, a complete
PCA datasheet was displayed in Microsoft Excel®. Table 6
summarized some important PCA data.
By using (5), MPI can be calculated as below (7) and
the values were displayed in the form of the standard OA
of L9, as shown in Table 5. Calculation of the mean values
(5)
MPI
=
r
j
=
1
WjZ
j
(6)
Z
j=
p
i=1
ajix∗
i(j
)
Fig. 10 3D view of the optimized RF-MEMS switch’s simulations with Vp = 3.04 V. a Z-displacement distribution and b Von Mises stress dis-
tribution
Fig. 11 Voltage load in time domain
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of MPI at each level for each factor allows us to obtain the
final optimized combinations for the multiple responses.
Specific to this case, the values are w2(L1)3(L2)1(L3)2, as
displayed in Table 7 and Fig. 6, where w = w2 = 2.5 μm,
L1 = (L1)3 = 30 µm, L2 = (L2)1 = 30 µm, and
L3 = (L3)2 = 65 μm.
3.3 Summary of the optimized results
The RF-MEMS switch’s beams geometric optimization
with the objectives of (1) low spring constant, (2) small
maximum von Mises stress, (3) multiple responses has
been done separately in the aforementioned sections.
The geometric parameters were set differently accord-
ing to the different objectives, as shown the summary in
Table 8. The same optimized result for multi-response
design (Model c) and low spring constant design
(Model a) is mainly due to the selection of the param-
eters’ value range (in Table 2). This reasonable values
range was estimated and selected by the limitations of
whole chip design dimension, fabrication, as well as
the design specifications. A trade-off Model c is sup-
posed to be different from both Model a and Model b;
Model b stands for the optimum condition for small von
Mises stress (σv(max)) design. But after the calculation,
Model c is more inclined to Model a, this is because:
(1) the beam lengths of L1, L2 and L3 have much less
effect on the σv(max) (Fig. 5b, totally around 5 %) com-
paring k (Fig. 5a, totally around 68 %); (2) the opti-
mized beam width for both σv(max) (w = 3 µm) and k
(w = 2.5 µm) are very close. Moreover, both Model a
and Model b’s contribution has been considered and
calculated by (7). After validation, Model c has spring
constant of Vp = 3.04 V and maximum von Mises stress
of σv(max) = 20.255 MPa, as shown in Figs. 7 and 8,
which meets with our design objective, further different
(7)
MPI
=
W
1
Z
1+
W
2
Z
2
=0.61913 ×Z1(k)×x∗
i(1)+Z1(σv(max))×x∗
i(2)
+0.38087 ×
Z2(k)×x∗
i(1)+Z2(σv(max))×x∗
i(2)
Fig. 12 Simulation of the optimized RF-MEMS switch in time domain. a Membrane’s movement, and b capacitances of switch-on and switch-
off
Fig. 13 S-parameters of switch-on state
Fig. 14 S-parameters of switch-off state
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parameters’ value range has not been tried (as shown
the work flow in Fig. 3). However, WPCA is a neces-
sary step when there is different optimized parameters’
setting for different responses.
4 Simulations of the optimized RF‑MEMS switch
The optimized geometric dimensions have been obtained
by Taguchi method and WPCA. In this part, its static prop-
erty, dynamic property, and RF performance is investigated
by FEM simulations.
4.1 Electro‑mechanical analysis
The simulation model is established in accordance with the
dimensions in Table 1 and the multi-response optimized
values in part 3. The materials’ properties of each layer can
be found in Table 9, which directly follows the setting from
the IntelliSuite v8.7® software’s material library, except the
thin silicon dioxide layer’s dielectric constant of 4.99. The
boundary conditions are set as: (1) the bottom plate of sili-
con (Si) substrate is fixed; (2) all the beams’ ends are set as
fixed face; and (3) potential of the signal line is set to zero
to simplify the simulation; and the membrane is assigned
with varying voltage load, in order to find Vp. The model is
then meshed using rectangular elements of less than 10 µm.
The simulation result of membrane’s vertical displace-
ment with the varying applied voltage is displayed in
Fig. 9. It can be seen that the membrane totally collapses
on the bottom plate at the voltage of 3.04 V which is the
optimized switch’s Vp. Figure 10 shows 3D results of the
membrane’s vertical displacement and stress distribution
during actuated state, respectively, where the obtained
σv(max) of 20.255 MPa is much less than the yield strength
of Al, 90 MPa (Dai et al. 2005).
4.2 Actuation time and capacitance
The RF-MEMS switch’s actuation time is limited by the
mechanical structure and basically is inversely proportional
to the membrane and beam’s total resonant frequency
(Mafinejad et al. 2013). A time dependent simulation by
Comsol Multiphysics 4.3® has been conducted to estimate
this optimized RF-MEMS switch’s actuation time. The
boundary conditions are set similar as the previous simula-
tion, except a step-up voltage load is applied on the mem-
brane, as shown in Fig. 11. The high level voltage of the
step function of 3.5 V is a bit higher than the Vp; and its ris-
ing time is adjusted within 1 µs. Then the simulated results
of membrane’s movement and switch’s capacitances are
presented in Fig. 12. Figure 12a shows that, when applied
voltage at low stage (near to 0 V), the membrane almost
Table 10 Comparison of developed capacitive RF-MEMS switches
Electrostatic capacitive
RF-MEMS Switch
Dai et al. (2006) Fouladi et al. (2010) Badia et al. (2012) Persano et al. (2012) Ya et al. (2013) This work
Structure
Actuation Voltage 7 V 82 V 23.6 V 25 V 3 V 3.04 V
Spring Constant 0.27 N/m – 1.43 N/m – 0.65 N/m 1.3 N/m
Air Gap 3.5 µm – 3 µm 3 µm 2.2 µm 1.397 µm
Dielectric 1.1 µm SiO2 εr = 3.9 0.73 µm SiO2 εr = 3.9 300 nm AIN εr = 9.8 300 nm Si3N4 εr = 6~7 0.1 µm SiO2 εr = 4.99 0.1 µm SiO2 εr = 4.99
Insertion Loss −3.1 dB @40 GHz −0.98 dB @20 GHz −0.68 dB @40 GHz <0.8 dB @ K-band – −5.65 dB @40 GHz
Isolation −15 dB @40 GHz −17.9 dB @20 GHz −35.75 dB @40 GHz >30 dB @ K-band – −24.38 dB @40 GHz
Capacitance Ratio Cr
(= Cd/Cu)
– 91 (2.1pF/23fF) 9.87 (1.266pF/128.32fF) 16.3 (2.2pF/0.135pF) 100 (10.36pF/0.1pF) 52 (7.31pF/0.14pF)
Actuation Time 8.2 µs 49 µs – – – 13.5 µs
Fabrication Process TSMC0.35 µm CMOS
+ post-process
TSMC0.35 µm CMOS
+ post-process
Seven-mask process
(not CMOS)
Eight-mask process
(not CMOS)
MIMOS0.35 µm CMOS
+ post-process (one
mask)
MIMOS0.35 µm CMOS
+ post-process
(maskless)
Microsyst Technol
1 3
keeps at its original position (z-displacement = 0 µm).
Once the applied voltage is increased to 3.5 V at t = 20 µs;
the beams start to bend down until the membrane reaches
the maximum displacement at t = 33.5 µs. Therefore, the
actuation time of the optimized switch is 13.5 µs. Fig-
ure 12b illustrates the switch-on and switch-off capaci-
tances are 0.14 and 7.31 pF, respectively. The capacitance
ratio of the optimized switch is around 52.
4.3 RF performance
Electromagnetic (EM) simulator of AWR Design Envi-
ronment 10® has been used to compute the RF responses
(S-parameters) of the RF-MEMS switch. When the switch
state is ON, no actuation occurs and the RF signal passes
underneath the membrane with relatively little attenuation.
Its return loss (S11) and insertion loss (S21) is presented in
Fig. 13, where return loss is −1.51 dB and insertion loss is
−5.65 dB at 42 GHz. This relatively high insertion loss is
mainly due to the small fixed gap (g0) between two meal
layers and low-resistivity silicon substrate which is lim-
ited by the CMOS fabrication process. When the switch
is actuated, the metal-dielectric-metal sandwich produces
a low impedance path to the surrounding CPW grounds
(Yao et al. 1999); this prevents the RF signal from travers-
ing beyond the switch, and the switch state is OFF. During
this state, the return loss (S11) of −0.60 dB and isolation
(S21) of −24.38 dB at the frequency of 40 GHz is shown
in Fig. 14.
Table 10 presents the comparison of our work with some
typical developed capacitive RF-MEMS switches. It shows
our proposed switch’s Vp is low enough to be integrated
with most CMOS circuitry while other properties are kept
in a reasonable range.
5 Conclusion
A novel shunt capacitive RF-MEMS switch using standard
0.35 µm CMOS process has been designed, optimized and
simulated. The RF-MEMS switch employs four supporting
folded beams and four straight beams as DC voltage sup-
ply paths. Both Taguchi method and WPCA have been used
to optimize the switch’s geometric parameters. A com-
plete optimization methodology for multiple responses has
been developed in this work. By employing a L9 orthogo-
nal array and calculation of the S/N from each simulation
results, the best combination of the four parameters for the
nominated spring constant design is w2(L1)3(L2)1(L3)2;
and the best combination for smallest von Mises stress
design is w3(L1)1(L2)2(L3)1. By using WPCA and cal-
culating the MPI as well as their mean values at each
level for each parameter, the multi-response optimized
design is w2(L1)3(L2)1(L3)2, where, w = w2 = 2.5 µm,
L1 = (L1)3 = 30 µm, L2 = (L2)1 = 30 µm and
L3 = (L3)2 = 65 µm.
For the multi-response optimized RF-MEMS switch,
a very low pull-in voltage of 3.04 V can be achieved and
compatible with the most CMOS power supply require-
ments. The simulated actuation time of the optimized
switch is 13.5 µs and the capacitance ratio is 52. The inser-
tion loss and isolation is −5.65 dB and −24.38 dB at the
frequency of 40 GHz, respectively. The whole optimiza-
tion methodology not only can be applied for RF-MEMS
switch’s geometric parameters’ optimization, but also can
be used for other RF-MEMS devices’ optimization process,
especially with multiple responses or objectives.
Acknowledgments The research is collaborative effort between
University of Malaya and International Islamic University Malaysia.
All authors would like to thank the financial support by the RACE
fund (RACE 12-006-0006), UM CR 004-2013, and University
Malaya High Impact Research Grant (UM.C/HIR/MOHE/ENG/19).
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