irut- Lebanon
Emails:
gke01@aub.edu.lb
&
mah29@aub.edu.lb



Abstract
This paper presents the design optimization and
fabrication of a low-voltage series radio frequency
(RF) Micro-electromechanical (MEMS) switch. The
simulation shows that the use of a pre-strained SMA
beam to actuate switching allows the excitation
voltage to be relatively much lower compared to
that needed for electrostatic actuation. The switch
structure has been optimized by the calculation of
the dependence of gap size on both the length and
the modulus of elasticity of cantilever beam. The
paper also describes two ways in which the
response of the SMA actuator is improved. To allow
rapid heating without over heating the beam a
temperature sensor along with a controller are
implemented in the design.

Keywords
RF Switch, MEMS, SMA, Nitinol

Nomenclature
e
temperatur
start
Martensitc
M
s
:

e
temperatur
finish
Martensitc
M
f
:

e
temperatur
start
Austenitic
A
s
:

e
temperatur
finish
Austnitic
A
f
:

e
temperatur
Operation
T
=

..)
,
(
,
:
As
Ms
e
temperatur
phase
any
be
could
T
where
Strain
T
e
temperatur
n
Transtitio
tr
=
t
coefficien
e
temperatur
to
Stress
C
=

strain
tion
Transforma
=
Stress
=
1. Introduction
The continuous advance in microelectro-mechanical
systems (MEMS) technology attracted researchers
towards the development of MEMS devices for
radio frequency (RF) applications. RF MEMS
devices have a broad range of potential applications
in wireless communication, navigation and sensor
systems. They could be used in switches, phase
shifters, signal routings, impedance matching
networks, exciters, transmitters, filters, and IF/RF
receivers [1]. Compared with the common electronic
solid state switches (FETs and PIN diodes), RF
MEMS based switches are characterized by very
low insertion loss, low power consumption, high
isolation (up to 100 GHz), low fabrication cost, and
very low intermodulation. The literature shows more
than 32 different types of RF MEMS with a variety
of
actuation
mechanisms
(electrostatic,
magnetostatic, piezoelectric or thermal), contact
modes (capacitive or metal-to-metal), and circuit
implementation (shunt or series) [2].
Electrostatic actuation is the most used
actuation scheme in RF MEMS. However, this type
of triggering requires a relatively high DC voltage
(up to 30 volts) and thus requires an additional
CMOS integrated up-converter to raise the usually
used 5 volts control voltage to the required level.
The current paper focuses on the design and
fabrication of RF MEMS switch using Shape
Memory Alloys (SMA) based actuator. Shape
memory alloys are thermally activated. At low
temperatures the crystalline structure of the alloy is
in the martensitic phase which provides flexibility
and allows relatively large deformations. When the
temperature is raised, transformation to austenitic
phase takes place and the material loses its
flexibility and thus the strain is recovered. Usually
heating of SMA actuators is based on joules
heating effect and the voltage needed could be
around 5 volts, which makes it superior to the
electrostatic actuator in that sense. In addition to the
low driving voltage, SMA actuators provide high
energy density and large forces. Unfortunately, the
drawback of SMA actuators is their relatively high
response time (~50 ms) compared to the
electrostatic actuators that have a response time on
the order of micro seconds. The paper provides a
scheme to improve the performance of SMA
actuation of the RF switch by allowing rapid heating and fast cooling of the SMA beam. Applying high
currnents results in rapid heating but requires
temperature monitoring in order to avoid
overheating of the SMA layer. A thermodiode
temperature sensor with a feedback control is used
to monitor the temperature of the SMA wire. As for
rapid cooling, different methods are available,
including water immersion, heat sinking and forced
air cooling. Heat sinking is herein used to improve
the cooling rate and thus provide faster switching
time.

2. Design and Fabrication of the RF Switch

2.1 Switch design

The model of the proposed SMA switch is shown in
figure 3. The switch is of series type which basically
consists of a free end cantilever Polyimide
1
beam.
We used Nitinol as the SMA material in our model
since it is the most used SMA material for actuation
purposes. Two Nitinol beams are attached to the
cantilever as shown in figure 1; one at the top and
the other at the bottom.


Figure 1: RF switch model

At the equilibrium position, the lower nitinol
actuator is initially deformed in the longitudinal
direction. When a voltage applied to the lower
actuator, current will pass through the actuator
causing it to heat up by joule heating and thus
retain its initial deformation and contracts. The
contraction of the beam causes the cantilever to
bend down wards and metal-to-metal contact
will occur. To enhance switching time, the
upper nitinol actuator is heated up and the strain
induced in the pull down phase will be retained
and will aid the cantilever to go back to its
equilibrium position in smaller time.


1

The choice of Polyimide is based on the optimization that will
be illustrated later

2.2 Constitutive relations of SMA

Many constitutive models have been proposed for
the stress-train relations as a function of
temperature. In this study, a simplified model is
used for simulation purposes and that approximates
the stress-strain curve as multi-linear segments with
variable modulus of elasticity that is dependant on
the operating temperature. The stress-strain curve
for a given temperature is as shown in figure 2. The
model is determined by the following parameters [3,
4, 5, 6].


Figure 2: Stress Strain curve at a given temperature

a) Transition Stresses:
(
)
s
Ms
M
T
C =


(1)
(
)
f
Mf
M
T
C =


(2)
(
)
s
As
A
T
C =


(3)
(
)
f
Af
A
T
C =


(4)


b)
Transitions Strains
(
)
A
s
Ms
E
M
T
C =


(5)
(
)
M
f
Mf
E
M
T
C + =

(6)
(
)
M
s
As
E
A
T
C + =

(7)
(
)
A
f
Af
E
A
T
C =


(8)

The constitutive relations for the five regions
depicted figure 2:


Cantilever
Nitinol Actuator

1) Region I

(0<
I <
Ms )



I
A
I
E =




(9)


2) Region II

(
Ms <
II <
Mf ) =
Ms
Mf
Ms
II
II
tr ,

(10)
(
)
Ms
Mf
II
tr
Ms
II +
=
,
(11)

3) Region III

Mf <
III <
max ) =
III
tr
,


(12)
(
)
Mf
III
M
Mf
III
E +
=

(13)


4) Region IV

(
As <
IV <
Mf )
=
IV
tr
,


(14)
(
)
Mf
IV
M
Mf
IV
E +
=
(15)


5) Region V

(
Af <
V <
As ) =
Af
As
V
tr
As
V
tr ,
,
(16)
(
)
+
=
Af
As
V
tr
Af
V ,
(17)



Figure 2 shows the stress strain curve for different
temperatures. It should be noted that increasing the
temperature is equivalent to reducing the applied
stress.


Figure 3: Stress Strain curve of Nitinol for different T

2.3 Temperature Control

Large currents heat SMA layer quickly and reduce
contraction time. However, applying large currents
for too long leads to overheating which can destroy
the shape memory effect and in extreme cases lead
to break of the SMA layer. In order to prevent such
damage a thermodiode is used to sense the
temperature. When the temperature of the SMA
reaches a certain value the controller automatically
cuts-off the current to the SMA element.

Thermo-diode Sensor

If a voltage source is connected to a p-n junction
diode, current will flow continuously and the
junction is sid to be forward-biased, provided that
the applied voltage V is greater than the forward bias
voltage V
s

of the diode. The voltage dependence on
temperature of the diode is given by:

ln
1
s
KT
I
V
e
I =
+


(18)
where : Non ideality multiplicative factor
e: Electron charge (C)
K: Boltzmans constant (J/K)
T: Absolute temperature

Equation (18) indicates that the voltage is directly
proportional to absolute temperature. Because diode
voltage V is a function of current, a stable constant
current source is essential.
In the current application the pn-junction will be
placed in contact with the shape memory alloy and
an amplifier circuit is used to measure the forward
bias voltage across a thermodiode. Figure 4 shows the basic circuit for the thermodiode; resistors R
1

and R
2

limit the current I which flows through the
junction. The output from the differential opamp is
linearly related to temperature and is converted into
a digital value by analog to digital conversion (data
acquisition card).


Figure 4: Controller flow chart


The value of the voltage is monitored and when the
voltage value exceeds Vref, the voltage
corresponding to the rating temperature, the voltage
input to the SMA layer drops to zero to cut-off the
current.

2.4 Switch Dynamic model

A simplified dynamic model for the switch is given
by [2]. The motions equation:

Fc
X
K
X
B
X
M
=
+
+
.
..


(19)




where
..
X
,
.
X
, and
X
ar