Graphene/MoS2 based RF-NEMS Switches for Low
Actuation Voltage and Enhanced RF-Performance
Aakif Anjum, Mukesh Madhewar, Suhas S. Mohite
Vishram B. Sawant
Mechanical Engineering Department,
Government College of Engineering,
Vidyanagar, Karad, Maharashtra, India, 415124
anjumaakif@gmail.com
mmadhewar@gmail.com
Mechanical Engineering Department,
Rajiv Gandhi Institute of Technology,
Versova, Andheri (W), Mumbai, Maharashtra, India,
400097
sawantvb@gmail.com
Abstract—In this work, the modeling, simulation and
analysis of a contact type RF nano-electromechanical switches
(RF-NEMS) with very low actuation voltage and enhanced RFPerformance is presented. The switches are modeled using
previously known theory from literature and then optimized
geometrical dimensions for low actuation voltage, low insertion
loss and high isolation as objectives. The effects of the length,
width and thickness of Graphene/MoS2 beam on various
performance parameters are studied in details. Further, modal
analysis, force, capacitance, release time, actuation voltage and
S-parameters are computed using ANSYS and HFSS software’s.
The switch exhibits low actuation voltage <1V for different
thickness of Graphene/MoS2 as a beam material. The
mechanical resonant frequency and quality factor are 72.5 kHz,
28 kHz and around 2, respectively, with a simulated switching
time of 19 µs to 71 µs for optimum length of 10 µm are obtained
for all three layers with comparison of results. It is concluded
that low actuation voltage NEMS switches can be realised using
single/bilayer layer 2D material with enhanced RF performance.
Keywords—Graphene, MoS2, RF-NEMS, Actuation voltage,
Insertion loss, Isolation.
I.
INTRODUCTION
A Nano-electromechanical system (NEMS) is an emerging
field for future technology development. Radio frequency
based NEMS switches in future will be widely used over
MEMS switches to further reduce voltage, low power
consumption and to enhance RF performance [1]. The main
reason is that RF-NEMS switches have low resistive loss,
high isolation, low noise, low actuation voltage. RF-NEMS
switches work on a wide range of frequencies for various
applications such as wireless communications, satellite
system, cell phones, highly sensitive Sensors, military
applications, nano tweezers etc. [1-3].
There are various 2D materials which are used in
nanofabrication of devices to name a few are Graphene,
MoS2,
borophene,
germanene,
silicene,
stanene,
phosphorene[1-3].These materials can be used as a bridge
material in RF-NEMS switches by [3-5]. RF-NEMS switch
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with two layer of graphene as a bridge material is presented
by Milaninia et al. [3]. The dimensions used for beam is 20 ×
3 µm (L × w) and g = 500 nm. The pull in voltage is 4.5 V is
obtained. The drawback of this switch is the limitation of
contact resistance (200 kΩ). This is because of non-uniform
surface of graphene due to chemical vapour deposition
process. Fixed-fixed type RF-NEMS switch consisting of
graphene beam is modeled and simulated by Dragoman et al.
[4]. CPW transmission line is formed using 20 nm gold
which is patterned on silicon. The voltage obtained by this
switch is 2 V.Graphene based RF-NEMS switches are
modelled and analysed for fixed-fixed beam by Pankaj et. al.
in 2014 [5]. The main disadvantage of all above switches is
the actuation voltage’s are > 1V.Proper selection of 2D beam
material so as to give minimum voltage is still challenging
task and switch design has to be optimised at initial stage of
design before fabrication. Reliability issues and its effects are
not considered in this work. This motivates us to design RFNEMS Switch in order to get the minimum actuation voltage
with low insertion loss and high isolation at various operating
frequencies.
II.
SCHEMATIC
Figs. 1(a) and 1(b) represent the up and down state
position of graphene/MoS2 based cantilever type RF-NEMS
switch.
(a)
(b)
Si/SiO2
Gold
Si3N4
Graphene/MoS2 Layer
Fig. 1. Graphene based RF-NEMS switch (a) Up state (b) Down
state
In schematic representation above three elements are
common in all radio frequency switches. One is transmission
line which transmits the radio frequency signals from one
port to another port that is from input to output port. The
second is substrate, beam which is moving element generally
cantilever or fixed-fixed beams are used for the actuation and
un-actuation of the switch. Due to supplied voltage the
electrostatic charges are developed which generates various
forces at nanoscale which causes the movement of beam. In
this study the thickness of beam is varied from 0.34 nm to
2nm while length and width is varied from 5 to 30 um to
achieve set objectives of design.
III.
(1)
Here EI represents effective bonding rigidity of the beam.
Deflection of beam is denoted by ω, x is the distance
measured from fixed end. Felec, Fc represents the electrostatic
and casimir force per unit length. While Fs represent elastic
force.
According to fringe field of first order, F elec per unit length of
cantilever beam is [6]
( )]
[
( )
]
(2)
Where b represents width of beam, g0 is the distance between
cantilever beam and central conductor ϵ0 is the permittivity of
vacuum and V is the applied voltage.
The force which is due to attraction between atoms is known
as casimir force. The casimir force per unit length of the
cantilever beam is [6]
(3)
*
(4)
This force may soften the cantilever type of switch. By
combining Equation 2,3,4 The governing equation will be
[6]
( )
( )
[
( )]
[
( )
( )]
( )+
Here c is the speed of light that is 2.998 × 108 m s−1, h is
planks constant/2 π. Material property does not affect the
casimir force.
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(5)
( )
[
]
(6)
,
( )
[
( )
MODELING
A. Mechanical Modeling
The mechanical modelling of RF-NEMS switch is involved
by the three types of forces. The electrostatic force which
acts due to the electrostatic charges induced between ground
conductor and graphene beam. The second is elastic force,
spring is modeled with the help of elastic force. This
electrostatic force depends on size, shape and material of
beam. The third is intermolecular forces. These forces
include van der waals and casimir forces. The consideration
of van der waals force is only when gap height g is less than
20nm. Practically fabrication of switch with gap height less
than 20nm faces difficulties. Packaging and population
becomes difficult to control. Due to this reason we have
considered the casimir force and designed the model with gap
height greater than 20nm. The consideration of casimir force
is only when gap height g is greater than 20nm [6]. The
governing equation of cantilever type switch is given as [6]
( )
Perpendicular load which acts due to small amount of
deformation in a beam is elastic or transverse force. This
Force is as [6]
Modeling of series type RF-NEMS switch can be done by
considering the capacitor which are parallel to each other.
The actuation voltage for cantilever type RF-NEMS switch is
as [7]
√
(
)
(7)
Where, gair=Air gap, εo=Permittivity of free space, w=
Cantilever width, W= Length of CPW, K= Stiffness of spring
The actuation voltage is dependent on stiffness and is given
( )
as [7]
(8)
Where
W, t, L is width, thickness and length of beam, E is Young’s
modulus of the beam.
Mechanical quality factor is amount of energy stored divided
by amount of energy released per cycle at the resonant
frequency. This mechanical quality factor is important
because higher the value of quality factor lower be amount of
energy loss. The frequency (f), quality factor (Q) and
dynamic viscosity (µ) are given as [8]
√
√
(
(9)
10)
)
√ (
)
(11)
The switching and release time also important parameters of
the RF-NEMS switch. The time taken by beam to come from
up state to down state position is known as switching time.
Switching time is as [5]
(12)
Vs=1.3* Vpull-in
(13)
Where,
is the angular frequency. Release time of switch
is given as [7]
(14)
Thus from above equation it is clear that release time is
inversely proportional to frequency.
Zs=Rs+jωL
(22)
(
(23)
and for
Zs=Rs, (ωL<<Rs)
)
B. Electrical Modeling
The series type RF-NEMS switch is modeled electrically.
This model depends on C, R and L. where C represents
capacitance. As there are two states up and down so there are
two values of capacitance. Capacitance in up state denoted by
Cu and the capacitance in down state is denoted by Cd. R and
L is the resistance and inductance respectively.
1) capacitance: The up state capacitance is combination
of parasitic capacitance denoted by Cp and series capacitance
denoted by Cs. Thus up state capacitance is given by [7]
Hence it is very simple to determine the series resistance with
the help of reflection coefficient.
The down state inductance can also be calculated. In this case
reflection coefficient is fixed with RL model impedance is
given as [7]
And for Zs=jωL, (ωL>>Rs)
(15)
The series capacitance is the sum of parallel plate capacitance
(Cpp) and fringing component Cf which is 0.3-0.6 of Cpp. Cp
can be calculated using simulation software such as Sonnet,
IE3D and HFSS.
The parallel plate capacitance is given by [7]
C. Material Properties of Graphene and MoS2
Graphene, which is a typical flat monolayer of carbon atoms
arranged in a honeycomb lattice and has great interest in
electronic devices [1]. It was first mechanically exfoliated
from graphite in 2004 [1].
Molybdenum disulphide is silvery black two
dimensional material can also be used for switching of RFNEMS switches. MoS2 is an inorganic and comes in a class
of transition metal. It looks like graphite but same plane is
not shared by MoS2 as graphene shares the same plane. This
is because the graphene’s orbital are planer. Monolayer
MoS2 is a semiconductor with a direct bandgap of 1.8 eV.
This property of MoS2 will largely compensate the weakness
of gapless graphene, thus next generation switching devices
can be fabricated from them.
(16)
In above equation td/εr is because of dielectric thickness. For
Si3N4 the relative dielectric constant is 7.6.
The down state capacitance is given as [7]
(17)
The capacitance ratio is nothing but ratio of down state
capacitance to the up state capacitance. [7]
Cr=Cd/Cu
(18)
In order to get lower insertion loss and higher isolation
capacitance ratio should be high. Capacitance ratio is high
only when capacitance in down state is high and capacitance
in up state is low.
2) Scattering parameters:The scattering parameters can
be calculated with the help of up state and down state
capacitance in off and on states. These scattering parameters
will help in extracting the CLR values.
In up state position, insertion loss and isolation can be
calculate as [7]
(19)
(20)
For extracting CLR value the effect of inductance and
capacitance is not considered, as in case of up state effect of
L and R is negligible.
Loss of cantilever NEMS switch can be calculated with the
help of extracted values of S11 and S12 [7]. Thus
Loss= 1-|S11|2-|S12|2
(21)
In case of down state resistance and inductance can be
calculated with the help of reflection coefficient.
The equivalent series impedance for down state position is as
[7]
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(
)
(24)
Thus from above we can measure inductance in down state.
TABLE I
Material properties of Graphene and MoS2
Reference
Graphene
MoS2
p-doped
p-doped
[5]
Doping
Single layer
thickness (SL)
Bilayer
thickness (BL)
Multilayer
thickness (ML)
Young’s
modulus
Density
Poisson’s ratio
IV.
0.34 nm
0.3 nm
[5], [11],[13]
0.64 nm
0.6 nm
[5], [11],[13]
2 nm
1.7 to 1.8 nm
[5]
0.3 Tpa
[5],[10]
0.8 to 1 Tpa
3
2200 k.g/m
0.4
3
5060 k.g/m
0.125
[5],[10]
[5],[10]
RESULTS AND DISCUSSIONS
A. Modal Analysis
In an attempt to study the effect of the cantilever beam
length, width, and thickness variations, the simulations of
resonant frequency and deflection of cantilever beam were
carried out. Each geometrical parameter of the micro
structure is varied one at a time in order to interpret its effect
on the frequency and deflection of cantilever beam.
The Fig. 2 shows the cantilever type of
graphene/MoS2 based RF-NEMS switch. Resonant frequency
of the switch is obtained with the help of modal analysis.
Resonant frequency of Graphene based beam for first, second
and third mode are 72.5 KHz, 299 KHz and 582 KHz
respectively while for MoS2 based beam 28, 131 and 227
KHz respectively.
switches is studied. Both casimir and electrostatic force
increases nonlinear with respect to deflection. Fig. 3 and 4
shows the nonlinear effect of casimir as well as electrostatic
force. The length at which cantilever beam will not adhere to
the surface due to casimir force is known as detachment
length. Detachment length of 1.5 um is noted. All RF-NEMS
switches require large down to up capacitance ratio of the
State's ability to maintain high isolation and low insertion
loss. Capacitance ratio of 1.59e-9 F is noted.
C. Pull in voltage, quality factor, switching time:
Analytical and simulation results are performed to study the
mechanical and electrical parameters.
B. Force and capacitance
13
40
tr for 0.34nm
35
tr for 0.64nm
30
tr for 2nm
7
20
5
15
3
0
-1
6
8
10
12
Length (um)
Fig. 5. Release time and stiffness as a function of length for
different values of beam thickness
0
2
4
From the graph it is clear that release time is inversely
proportional to voltage. And it is observed that the release
response time for 0.34 nm is 27% more than that of 0.64 nm.
20
100
200
300
tr for 0.34nm
tr for 0.64nm
tr for 2nm
18
Deflection (nm)
Release time (us)
16
Fig. 3.Casimir force as a function of deflection
20000
18000
16000
14000
12000
10000
8000
6000
4000
2000
0
100
90
80
14
70
12
60
10
50
8
40
6
30
4
20
2
10
Pull-in voltage(mv)
Casimir force (µN)
1
5
0
Electrostatic force (µN)
9
25
10
50
45
40
35
30
25
20
15
10
5
0
11
Stiffness (uN/m)
Fig.2. Modal patterns of the beam structure for Graphene/MoS2
Release time (us)
45
0
0
5
7
9
11
Width (um)
Fig. 6. Release time and voltage as a function of width for different
values of beam thickness
1
0
100
200
300
Deflection (nm)
Fig. 4.Electrostatic force as a function of deflection
Casimir effect as well as electrostatic effect on the critical
pull-in gap and actuation voltage of nanoelectromechanical
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3
Fig.6 shows the variation of release time and voltage with
width variation the optimum width (3um) and the thickness
t=0.34 nm, 0.64 nm and 2nm respectively. The dynamic
response shows that the fast switching that is less than 10 us
for NEMS Switch with width 3 um shows actuation voltage
of (<2mv).
35
10
11
9
30
25
7
20
5
15
3
10
6
4
2
1
5
0
-1
5
7
9
11
Length (um)
Fig. 7. Release time and voltage as a function of length for different
values of beam thickness
0
Fig.7 shows the variation of release time and voltage with
length variation the optimum length (10um) and the thickness
t=0.34 nm, 0.64 nm and 2 nm respectively. The dynamic
response shows that the fast switching that is less than 20 us
for NEMS Switch with length 10 um shows actuation voltage
of (<2mv).
160
3
Switching time (us)
13
ts for 0.34nm
70
ts for 0.64nm
60
ts for 2nm
11
9
50
7
40
5
30
3
20
1
10
0
-1
1
3
5
7
9
11
Length (um)
Fig. 8. Switching time and voltage as a function of length for
different values of beam thickness
From the graph it is clear that switching time is inversely
proportional to voltage. And it is observed that the switching
response time for 0.34 nm is 28% more than that of 0.64 nm.
As the quality factor of the NEMS switch depends
upon the cantilever length, width, in Fig. 9, the effect of
geometric dimensions on quality factor of the RF-NEMS
switch is plotted with the cantilever length, width as the
variables for thickness of 0.34, 0.64 and 2 nm. The results
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0
10
20
30
40
Length (um)
(a)
140
Quality factor
80
Pull-in voltage(mv)
1
Q for 0.34nm
Q for 0.64nm
Q for 2nm
8
Quality factor
40
Release time (us)
13
tr for 0.34nm
tr for 0.64nm
tr for 2nm
Pull-in voltage(mv)
45
show that the quality factor decreases for a given cantilever
length and width.
Q for 0.34nm
120
Q for 0.64nm
100
Q for 2nm
80
60
40
20
0
0
10
20
30
40
Length (um)
(b)
Fig. 9. Quality factor of beam as a function of (a) length (b) width
Fig. 9(a) shows the decline of quality factor with increase in
length. For thickness of 0.34 nm at optimum length of 10 um
the quality factor is 0.4. While for 0.64 nm thickness it is 1.6.
The quality factor for 2 nm thickness is 15 for 10 um length
and 1.7 for 30 um length. In Fig. 9(b) at optimum length,
quality factor of 1 and 3 for thickness of 0.34 nm and 0.64
nm respectively noted. The results show that the variation in
the micro beam width has comparatively greater effect on the
quality factor of the switch than the beam length.
For better performance of cantilever switch, actuation
voltage should be low and quality factor should be high. By
comparing calculated performance parameter values of
actuation voltage of graphene is low and quality factor is
greater than others. If actuation voltage is high, then a chance
of switch failure increases.
D. Insertion loss, Isolation of RF-NEMS Switches:
The S-parameters in the down state position is shown in
Figs.10 and 11. The isolation and insertion loss values are
obtained by simulations using ANSYS HFSS (High
Frequency Structural Simulator) for cantilever type RFNEMS switches. The isolation and insertion loss values
obtained are in the range of 62-69 dB and 0.0342-0.0379 for
graphene and MoS2 switches.
The isolation 69 dB for bilayer graphene and 63 dB
for bilayer MoS2 are obtained. The bilayer of graphene and
MoS2 switch offers a superior isolation as compared to the
monolayer and multilayer because of the lower surface
resistance.
TABLE II
Comparisons of Graphene and MoS2 based RF-NEMS Switch
Ref.
Milaninia
et al. 2009
[3]
Dragoman
et al.
2009[4]
Material
Pull-in
voltage,
Vpi(V)
Graphene
4.5 V
Graphene
2V
SLG
0.3 V
MLG
1.4 V
SLG
1.38 mV
BLG
3.56 mV
MLG
19.71 mV
SLG
0.543 mV
BLG
1.4 mV
MLG
7.75 mV
Isolation
-30dB at
60GHz
Pankaj et al
in 2014 [5]
Fig. 10. S11 and S12vs frequency in down state position of the NEMS
switches for graphene
Proposed
MoS2
VI.
Fig. 11. S11 and S12vs frequency in down state position of the NEMS
switches for MoS2
V.
COMPARISION
We have further studied the MoS2 based RF-NEMS switch
and compared with the graphene based RF-NEMS switch.
These Graphene/MoS2 based switches are compared with the
work done by various researchers previously. From TABLE
II, it is noted that Graphene/MoS2 based switches show low
actuation voltage, low insertion loss and high isolation than
that of work done by other researchers. The cantilever type
RF-NEMS switches show good performance in terms of
electrical and RF characteristics.
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----------
-40dB at
60GHz
>10db @
Proposed
Graphene
Insertion
Loss
----------
1-60 GHz
0.01–0.3
dB
>20db @
0.01–0.2
1-60 GHz
dB
-65.3441
-0.0352 at
at 9GHz
10GHz
-69.2384
-0.0344 at
at 7GHz
9GHz
-62.674at
7GHz
-62.38 at
11 GHz
-63.43 at
17 GHz
-62.9968
at 7GHz
-0.0379 at
14 GHz
-0.0342 at
9 GHz
-0.0374 at
GHz
-0.0379 at
14 GHz
CONCLUSIONS
The performance of cantilever type RF-NEMS switch
based on 2D material is calculated and by comparing the
performance parameters viz., actuation voltage and quality
factor, insertion loss and isolation are computed using
simulation. The switch exhibits low actuation voltage <1V
for different thickness of Graphene/ MoS2 as a beam
material. The mechanical resonant frequency and quality
factor are 72.5 kHz, 28 kHz and around 2, respectively, with
a simulated switching time of 19 µs to 71 µs for optimum
length of 10 µm are obtained for all three layers with
comparison of results. It is concluded that low actuation
voltage NEMS switches can be realised using single layer 2D
material with low insertion loss.
ACKNOWLEDGMENTS
The support and financial assistance received through TEQIP
program at CIM Laboratory of Mechanical Engineering
Department, Government College of Engineering Karad.
Thanks to Senior Facility Technologist at CeNSE, Indian
Institute of Science, Bangalore, for interaction related to
design and fabrication issues with 2D materials.
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