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TRANSACTIONS ON ELECTRICAL AND ELECTRONIC MATERIALS
Vol. 14, No. 5, pp. 225-230, October 25, 2013
pISSN: 1229-7607
Regular Paper
eISSN: 2092-7592
DOI: http://dx.doi.org/10.4313/TEEM.2013.14.5.225
Stress Analysis Using Finite Element Modeling of
a Novel RF Microelectromechanical System Shunt
Switch Designed on Quartz Substrate for Low-voltage
Applications
Tejinder Singh, Navjot K. Khaira, and Jitendra S. Sengar
Department of Electronics & Communication Engineering, Lovely Professional University, PB 144 402, India
Received June 24, 2013; Accepted June 30, 2013
This paper presents a novel shunt radio frequency microelectromechanical system switch on a quartz substrate with
stiff ribs around the membrane. The buckling effects in the switch membrane and stiction problem are the primary
concerns with RF MEMS switches. These effects can be reduced by the proposed design approach due to the stiffness
of the ribs around the membrane. A lower mass of the beam and a reduction in the squeeze film damping is achieved
due to the slots and holes in the membrane, which further aid in attaining high switching speeds. The proposed
switch is optimized to operate in the k-band, which results in a high isolation of -40 dB and low insertion loss of -0.047
dB at 21 GHz, with a low actuation voltage of only 14.6 V needed for the operation the switch. The membrane does not
bend with this membrane design approach. Finite element modeling is used to analyze the stress and pull-in voltage.
Keywords: RF MEMS, RF shunt switch, Capacitive MEMS, Low-voltage MEMS switch, Quartz substrate
1. INTRODUCTION
Microelectromechanical Systems (MEMS) switches [1] optimized to work at Radio Frequencies (RF) have been a primary
focus of intensive research over the past few years in both academia and industrial organizations. RF MEMS switches have
grown at very fast pace, and have entered into many applications
in wireless communication [2] and space systems. RF MEMS
switches have replaced the conventional GaAs FET and p-i-n
diode switches in RF and microwave systems, because of their
negligible power consumption of a few μ-watts, low insertion
loss, high isolation, much lower intermodulation distortion,
small footprints, low cost, and light weight [3]. Due to the enormous advantages of MEMS switches, these are widely used at RF
†
Author to whom all correspondence should be addressed:
E-mail: [email protected]
Copyright 2013 KIEEME. All rights reserved.
This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial
License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted noncommercial use,
distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright 2011 KIEEME. All rights reserved.
225
to millimeter-wave frequencies.
Typically MEMS switches are fabricated using surface micromachining processes, and have a suspended thin metal membrane called the “bridge,” which can be a fixed-fixed, cantilever,
or torsion beam). The bridge allows or blocks the electronic
transmission through mechanical movement of the membrane
above the electrode [3]. MEMS switches can be actuated by various methods, such as electrostatic [4-6], electromagnetic [7],
piezoelectric [8], and thermal [9] actuation. Due to the near-zero
power consumption and linearity, electrostatic actuation is most
widely used, in which electrostatic force is generated between a
fixed electrode and a movable membrane for switching operation. Several disadvantages include slow switching speeds, high
actuation voltage, and hot switching in high-power RF applications [10].
This paper presents a novel design for a RF MEMS capacitive
switch on quartz substrate, which results in excellent RF performance in the k-band with high isolation and low insertion loss.
With the inclusion of ribs around the membrane, the bucking
effect and stiction problem can be eliminated. The effect of this
http://www.transeem.org
226
Trans. Electr. Electron. Mater. 14(5) 225 (2013): T. Singh et al.
Ribs (around Membrane)
novel membrane design can be seen in stress analysis. The membrane can withstand several switching cycles. The spring constant, required voltage, and stress is analyzed using multiphysics
environment.
Dielectric
Air-Gap
Up-State Position of Switch
CPW
Meanders
Membrane
Anchors
2. EXPERIMENTS
2.1 Structure and principle of operation
The proposed RF MEMS switch has a coplanar waveguide
(CPW) line for RF signal transmission on a 100-μm-thick quartz
substrate. A dielectric layer of hafnium dioxide (HfO2) is used
due to its very high dielectric constant over the substrate. The
working principle of the switch is shown in Fig. 1. The CPW consists of a 70-μm-wide signal line with a gap of 90 μm. The same
dielectric material is used on top of the signal line. The characteristics of the switch are mainly governed by the design of the
membrane.
To lower the pull-down voltage, meanders are included on
the sides of the membrane, which helps to lower the spring
constant of the membrane. The membrane is thin on the inside and thick at its boundary. Four anchors 4-μm thick are
attached to the ground plane, and meanders are present on the
top end to give the membrane a proper space for movement
above the RF line. A gap height g0 of 3 μm is maintained between the membrane and pull-down electrode, as it is needed
to optimize the pull-down voltage and gap. Otherwise, the
membrane may become prone to self-biasing and external
vibrations, and then it would not be possible to recover the
membrane’s position due to elastic recovery forces. A 3D view
of the proposed switch is shown in Fig. 2, and a tilted view of
the switch membrane is shown in Fig. 3, showing the varying
height of membrane.
The proposed switch is actuated by electrostatic force. When
a voltage is applied to the pull-down electrode, the membrane
connected to the grounds of the CPW line snaps down onto the
signal line. As the dielectric layer is applied to the signal line, it
reduces the gap g0, and the down-state capacitance value is increased. When the membrane is in the up-state, the capacitance
value becomes low, thus giving a good capacitance ratio. The
design is optimized after the analysis of the von Mises stress and
spring constant constraints.
Down-State Position of Switch
Fig. 1. Operation principle of proposed switch in up and down states.
Hafnium Dioxide (Dielectric) Meanders
CPW
Quartz (Substrate)
Membrane
Transmission Line
Fig. 2. 3D view of designed switch.
Fig. 3. Tilted view of membrane on co-planar waveguides.
70 μm
15 μm
Slots
5 μm
2.2 Design of membrane
The inclusion of holes of 5-μm diameter and slots in the
membrane help to reduce the biaxial residual stress, and thus
reduce the buckling effect of the membrane after the removal
of the sacrificial layer during fabrication. The membrane is
reliable in terms of switching life due to the flatbed internal
structure. Hence, the membrane does not bend when pulled
in towards the signal line. The bending only occurs at the meanders. The holes also help in reducing the principle strain on
the membrane at the pull down electrode area. The diameter
of the holes in the membrane should be less than 2g0, so as
not to affect the capacitance value. In MEMS switches, if the
spring constant k is very low and the membrane gap is less
than 3 μm, then during switching, the membrane sometimes
is not restored to its original rest position due to stiction at the
electrode. The top view of the membrane is shown in Fig. 4. The
thin internal membrane helps in reducing the overall mass and
squeeze-film damping of the membrane. The meanders help to
restore the membrane. Overall, the switching speed is increased
due to the holes and slots. The dimensions of the meanders are
shown in Fig. 4.
Ribs
Anchors
Holes
Meanders
Fig. 4. Top view of membrane and dimensions of meanders.
2.3 Switch specifications
The proposed shunt switch is designed in Ansoft HFSS v13,
which was also used to measure the RF performance. A combined multiphysics environment, COMSOL Multiphysics 4.3b, is
used to compute stress, the required actuation voltage, and the
spring constant. The specifications, dimensions, and materials
used to design the switch are presented in Table 1.
2.4 Selection of materials
A flat and smooth substrate surface is preferred to fabricate
the switch, as the substrate is the base over which the switch
operates. It should have uniform electrical properties and
Trans. Electr. Electron. Mater. 14(5) 225 (2013): T. Singh et al.
2.6 Electromagnetic circuit modeling
Table 1. Switch specifications.
Component
Substrate
Dimensions (μm)
Length
Width
Depth
810
350
100
Material
Quartz
Hafnium
Dioxide
Substrate Dielectric
810
350
0.5
CPW Lines
90 (G)
70 (G)
90 (G)
Gold
Signal Line Dielectric
80
70
0.5
Hafnium
Dioxide
Membrane with Meanders
310
110
1
Gold
Membrane Ribs
250
10
2
Gold
Membrane without
Meanders
250
80
1
Gold
2.5 Switch characteristics
A lumped CLR model [13,14] of the membrane and two sections of the transmission line are used to model the capacitive
switch with a capacitance having the down-state/up-state values. Figure 5 shows the equivalent circuit model of the switch.
The sections of the transmission line are of length l+(w/2), where
l = 15 μm is the distance from the reference plane to the edge of
the membrane. For the k-band switch, the calculated value of the
capacitance is 2.47 pF / 16.41 fF with an inductance of 5-6 pH
and series resistance of 0.15 Ω.
The shunt impedance of the switch is given by:
Z s =Rs + jω L +
chemical resistance (as required during fabrication) [11,16].
These requirements make quartz a good candidate, as it fulfills
all these requirements. Quartz has a high melting point compared to silicon, so a switch designed with a quartz substrate
can withstand higher temperatures than one made with a silicon substrate [3].
Hafnium dioxide (HfO2) of 0.5-μm thickness is used over the
substrate beneath a CPW line made of Gold (Au). HfO2 has a
dielectric constant of k~25. It is always preferable to use materials that have high k [12]. Most of the conventionally designed
MEMS switches have used silicon dioxide (SiO 2) or silicon
nitride (Si3N4) as dielectric materials, with k~3.9 and k~7.5, respectively. As the research evolved, more advanced materials
came into existence. We compared these materials with the one
actually used in the switch, and the results indicate that HfO2
provides higher isolation compared to other dielectric materials.
1
jωC
Due to the approach used to design the membrane, the load
on the membrane is shifted toward the ends, and it has meanders to lower the overall spring constant k. The load is distributed because of the ribs around the edges of the membrane. The
residual stress component can be neglected during calculation
due to the stiffness of the membrane.
The actuation voltage Vp of a MEMS switch with a spring constant k is given by:
(1)
where ε0 is the permittivity of free space, g0 is the gap between
the membrane and the electrode, and A is the area of the membrane actually covering the dielectric on the signal line.
The analytical value of the actuation voltage is 14.6 V for the
dimensions of the switch given in Table 1. The permittivity ε0 and
spring constant k are fixed, so the value of the actuation voltage
completely depends upon the gap height between the membrane and the signal line [15].
The power handling capability is augmented in comparison to
various designs due to the use of a single electrode. The switch
relies on the elastic recovery force of the meanders instead of
the force of the membrane to pull it upwards, because the membrane is stiff around edges.
(2)
with C=Cup or Cdown depending on the position of the switch. The
LC resonant frequency of the switch is given by:
1
f0 =
2π LC
(3)
The CLR model behaves purely as a capacitor for frequencies
below the LC series resonant frequency, and as an inductor at
higher frequency. At resonance, the CLR model behaves as series resistance of the membrane. For Cdown / Cup = 2.47 pF / 16.41
fF and L = 5 pH, the resonance occurs at f0 = 45.28 GHz at the
down-state position, and 555 GHz at the up-state position of the
switch. The impedance is approximated by:
for f ≪
� f0 ;
1/ jωC ,

Z s =
Rs ,
for f
f0 ;
=
 jω L,
for
f
f
�
≪ 0;

2.5.1 Actuation mechanics and power handling
capabilities
8k
3
Vp =
g0
27ε 0 A
227
(4)
When the resonant frequency is 555 GHz, the inductance of
the membrane plays absolutely no role in the up-state for f < 100
GHz, but plays a significant role in the down-state position of
the switch. The cut-off frequency of the switch is stated as fc =
1/2πCupRs and fc = 64.65 THz for Cup = 16.41 fF and Rs = 0.15 Ω.
It is preferred to use the down-state resonant frequency (f0
or 2f0), because the switch results in isolation up to twice the
resonant frequency f0 in the down-state position [5]. The switch
inductance limits the down-state performance at a much lower
frequency than cut-off frequency fc.
Silicon is used for the membrane, as it is robust and has a
low initial stress for bending compared to Au or Al membranes.
Hence, it has no residual stress component, which results in locally different bending of the membrane, and a constant gap is
maintained between the membrane and transmission line. The
various parameters of the silicon material used in the membrane
design are given in Table 2.
2.6.1 Up-state capacitance
The parallel plate capacitance of a shunt switch is given calculated as:
ε0 A
Cup =
g 0 + ( td / ε r )
(5)
The dielectric constant k of HfO2 is 25, and a dielectric layer of
Trans. Electr. Electron. Mater. 14(5) 225 (2013): T. Singh et al.
228
α=
Rs1 / l
2Z0
(8)
To model the inductance in the down-state position of the
switch, it is assumed that the capacitance is large enough for it to
act as a short circuit. The short circuit model can be analyzed numerically or by using an electromagnetic tool like Ansoft HFSS.
The inductance in the down-state is given as:
Fig. 5. Magnified top view of stiff membrane with meanders and
holes.
0.5-μm thickness is used with a gap height g0 of 3 μm. The fringing field capacitance of switch Cf is a substantial portion of the
total switch capacitance. The calculation is done by solving the
total capacitance using a 3D electrostatic simulation tool called
Maxwell 3D by Ansoft, and then subtracting the analytically derived capacitance. As the diameter of holes in the membrane is 5
μm, the fringing field does not affect the capacitance.
2.6.2 Down-state capacitance
The down-state capacitance of the switch is calculated for
when the membrane is in the down position. The calculated value of the down-state capacitance is 2.47 pF. In the down position,
the thickness of the dielectric layer is so small that the fringing
capacitance can be neglected. The down-state capacitance can
be calculated by:
ε 0ε r A
Cdown =
(6)
td
2.6.3 Capacitance ratio
The preferred value of the capacitance ratio should be greater
than 100:1 [3]. In the calculation of the capacitance ratio, the
result is 150:1 with an up-state capacitance of Cup = 16.41 fF and
down-state capacitance of Cdown = 2.47 pF. The down-state and
up-state capacitance ratio is given by:
Cdown
Cup
td
ε0 A


 g + (t / ε )  + C f
 0
d
r 
(9)
3. RESULTS AND DISCUSSION
3.1 RF performance analysis
The isolation loss, return loss, and insertion loss of the proposed switch are measured using Ansoft HFSS v13. The RF
performance of the switch is observed between frequencies of 1
GHz and 40 GHz. From Fig. 6, it is clear that the switch gives an
excellent isolation S12 of -40 dB at 21 GHz in the down-state.
Table 2 manifests the switch performance for the k-band.For
the up-state position, the insertion loss S12 is analyzed, and the
results in Fig. 7 show a low insertion loss of -0.047 dB in the upstate. The return loss S11 is calculated, and Fig. 8 presents a plot
of the return loss. The results show that the switch has excellent
performance in the k-band.
3.2 Stress analysis
The von Mises Stress is analyzed to check the deflection of the
membrane due to stress for the desired height. The membrane
is made of gold, which has a maximum stress of 25 MPa. This
value is good enough to handle higher switching under the given
maximum stress. Figure 9 shows the deflection of the membrane
under stress.
3.3 Spring constant
The spring constant k is given as the deflection of the membrane per unit meter under applied force. The plot is obtained by
setting a parametric sweep of the force applied. Figure 10 shows
the spring constant plot. The plotted value, 1.32 (N/m), is quite
close to the analytical calculations.
ε 0ε r A
=
Z s = jω L; ω L≫
�R
(7)
By varying the thickness of the dielectric layer to improve
the capacitance ratio, the optimized thickness of the dielectric
is used, as we cannot go beyond one particular value. The RF
MEMS switch needs an actuation voltage, and if the dielectric
layer is very thin, it can cause dielectric breakdown.
3.4 Pull-In voltage vs. gap
The pull-in voltage or the electrostatic actuation voltage required to pull the membrane down to change the state of the
switch can be calculated by eq. (1). The pull-in voltage is plotted
vs. the gap in between the membrane and the signal line in Fig.
11. The graph is plotted for the spring constants k = 1, 2, and 1.32
(N/m). It is clear from the plot that as the gap and spring constant increase, higher pull-in voltages are required for switching
actions. Hence, the design is optimized to work at 14.6 V for a
3-μm gap height with low k.
2.6.4 Series resistance and inductance
The main factors for the calculation of series resistance are
Rsl and Rs, which are due to the transmission line loss and to the
membrane of the switch, respectively. The series resistance is
given by:
4. CONCLUSIONS
The proposed design utilizes a novel approach of membrane
design, as the membrane is a hybrid in terms of thickness, and it
Trans. Electr. Electron. Mater. 14(5) 225 (2013): T. Singh et al.
229
Isolation
0.00
-7.00
Isolation (S12) dB
-14.00
-21.00
-28.00
Curve Info
-35.00
-42.00
dB(S(1,2))
Setup1 : Sweep
0.00
5.00
10.00
15.00
20.00
25.00
Frequency (GHz)
30.00
35.00
40.00
Fig. 6. Isolation performance S12 for frequency range 1 - 40 GHz.
Spring Constant, k (N/m)
Insertion Loss
0.000
Fig. 9. von Mises stress showing deflection of 3 μm for applied force.
Curve Info
dB(S(1,2))
Setup1 : Sweep
Insertion Loss (S12) dB
-0.015
-0.030
-0.045
-0.060
-0.075
-0.090
0.00
5.00
10.00
15.00
20.00
25.00
Frequency (GHz)
30.00
35.00
40.00
Fig. 7. Insertion loss S12 for frequency range 1 - 40 GHz.
Fig. 10. Spring constant k calculations for different membrane
heights.
Return Loss
0.00
Pull-in Voltage (V) Vs Gap, g 0 (um)
Return Loss (S11) dB
-0.62
-1.25
-1.87
-2.50
Curve Info
-3.12
-3.75
dB(S(1,1))
Setup1 : Sweep
0.00
5.00
10.00
15.00
20.00
25.00
Frequency (GHz)
30.00
35.00
40.00
Fig. 8. Return loss S11 for frequency range 1 - 40 GHz.
Fig. 11. Pull-in voltage vs. gap g0 for different spring constant k.
is designed to reduce the buckling effect and to reduce the overall spring constant. From the numerical calculations and simulations, it is clear that the switch shows excellent isolation and
insertion loss in the k-band. The meanders and ribs are designed
so that the stiction problem in the switch can be reduced, and
holes and slots in the membrane reduce the fringing fields and
air resistance under the membrane, allowing the switching speed
to be increased. The reliability of the switch can be approximated
by the von Mises stress analysis.
The switch operates at lower actuation voltage than other capacitive switches. This results in excellent RF response, which allows the switch to be used in applications where low power and
low loss are a primary concerns, such as in wireless communication and space systems.
Trans. Electr. Electron. Mater. 14(5) 225 (2013): T. Singh et al.
230
Table 2. Performance analysis.
Parameter
Switch Membrane
Membrane Material
Air Gap, g0
Spring Constant, k
Up-State Capacitance, Cup
Down-State Capacitance, Cdown
Insertion Loss
Isolation
Capacitance Ratio, Cr
Actuation Voltage, Vp
von Mises Stress
Stress per unit meter
Value
1 μm (incl. meanders),
2 μm (ribs)
Gold with E = 79 GPa
3 μm
1.32 N/m
16.41 fF
2.47 pF
0.047 dB
40 dB
150:1
14.6 V
25 MPa (max) at the
edges of meanders
3.4 MPa
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