RSM2011 Proc.

, 2011, Kota Kinabalu, Malaysia

Design, Modeling and Simulation of CMOS

MEMS Cantilever for Carbon Dioxide Gas
Sensing
1

Asif Mirza, Mohd Haris Md Khir, John Ojur Dennis a, Khalid Ashraf, Nor Hisham Hamid
Department of Electrical and Electronics Engineering,
a
Department of Fundamental and Applied Sciences,
Universiti Teknologi PETRONAS, Bander Seri Iskandar 31750, Perak, Malaysia.
1
asif_g01000@utp.edu.my

Abstract- Carbon dioxide sensors have potential applications in

medical diagnoses, health care, environmental monitoring, food
and medicine industry. In recent years, many novel biological,
physical and chemical sensors have employed microcantilevers
due to their simplicity, ease of fabrication and integration with
electronics. This paper presents design, modeling and simulation
of a microcantilever working in dynamic mode for CO2 gas
sensing with electromagnetic actuation and capacitive sensing
using comb fingers. The sensor is based upon 0.35 micron CMOS
technology. CoventorWare and MATLAB have been used as
simulation software. According to the developed model and
simulation results the resonator has a quality factor of 3333 in air
and mass sensitivity of 3.2 Hz/ng.
Key WordsCarbon dioxide, CMOS, Resonator, Sensor,
MEMS.

I. INTRODUCTION
The market potential for reliable and inexpensive CO 2
sensors is huge because of its wide range of field uses. Some
important areas of applications of CO2 sensors include
environmental monitoring to measure global warming and
indoor air quality, medical diagnostics, petroleum industry,
water treatment and the horticultural industry [1-2].The
simplest spectroscopic sensors are non-dispersive infrared
(NDIR) sensors used most commonly for CO2 detection.The
building blocks of NDIR sensors are an infrared source, an
infrared detector, a light tube, and an interference filter. The
major limitations of this technology are power consumption
and physical size. In recent years, microcantilevers have
attracted users due to their potential in the development of
many novel biological, chemical and physical sensors [3].
Microcantilever is very simple microelectromechanical
system (MEMS) whose micromachining and mass-production
is easy. It provides promising sensor solutions that are precise,
reliable, small, saleable, low power consuming and ultimately
portable. Monolithic fabrication of micromechanical
components with micro-electronics on a chip and fabrication
of multi element sensor arrays make these more advantageous
as compared to the conventional technologies. The mode of
cantilever operation can be referred to as either static or
dynamic depending upon the parameter measured. In the
This work was supported in part by UTP graduate assistantship scheme.

324

978-1-61284-846-4/11/$26.00 2011 IEEE

dynamic mode the cantilever is driven at resonance by an

excitation mechanism and change in resonance frequency due
to adsorption of gas by the functional layer deposited on the
surface of the cantilever is measured by a sensing mechanism,
while in static mode the deflection of cantilever on adsorption
of gas is monitored. The dynamic response of a cantilever
sensor depends on its quality factor which in turn depends
upon damping faced by it. A carefully designed cantilever, the
cost in the higher complexity of the dynamic mode in front of
the static mode is compensated with a much better sensitivity
of the sensor. In this paper design, analytical modeling and
simulation results of a dynamic mode cantilever are presented.
The methodology is discussed in Section-II, analytical model
is presented in Section-III, results and discussion is given in
Section-IV and Section-V concludes the paper.
II. METHODOLOGY
The microcantilever reported in this work has been designed
to be fabricated in 0.35 micron 2P3M (two poly-silicon and
three metal) CMOS technology in MIMOS foundry, Malaysia.
This technology allows two poly-silicon layers, three metal
layers, vias to connect the metal layers and dielectric layers for
insulation between metal layers. All metal layers are made of
aluminum, dielectric layers are made of silicon dioxide and the
contact/via holes are filled with tungsten plugs. Trenches can
be made on the top metal layers to isolate the conducting and
non conducting parts. The device has been designed and its
parameters are optimized using CoventorWare which provides
an integrated environment for the designing of MEMS devices.
Fig.1 shows a three dimensional picture of the designed
cantilever and its design parameters are given in Table I. A coil
of 36 turns is made in the metal-two layer to actuate the
cantilever electromagnetically by Lorentz force. Two sets of
capacitive comb fingers containing twenty fingers each has
been designed at the free end of the cantilever for capacitive
sensing.
The overlapping length and spacing between moveable and
fixed fingers are 90 m and 3 m respectively. Fingers of the
cantilever are composed of the three metal layers. In order to
increase the capacitance, all the three metal layers are joined
together in the sensing fingers through vias. As compared to
bottom sensing electrodes, the capacitive comb fingers not only
ease the fabrication process but also reduce air damping. To

RSM2011 Proc., 2011, Kota Kinabalu, Malaysia

Fig. 2. Lumped parameter equivalent model of the cantilever.

(3)
() =   ( ) +  ( )
where c1 and c2 are arbitrary constants. By using (3) in (2) we
get
(( ) + )(  ( ) +  ( )) = 0.
(4)
The non-trivial solution of (4) can be rearranged to give

Fig.1. Cantilever with capacitive sensing and electromagnetic

actuation.

 = 


TABLE 1
DEVICE DESIGHN PARAMETERS
Parameter
Length of cantilever
Width of cantilever
Thickness of cantilever
Length of comb finger
Width of comb finger
Overlapping area of fingers
Spacing between fingers
No of comb finger pairs
Width of coil
Length of coil
Spacing between consecutive turns
Width of coil wire
Thickness of coil wire
Conducting layers thickness

 =

=

+




+   =

(1)

A. Natural Frequency
The natural frequency of an oscillator is the frequency with
which it vibrates freely in the absence of damping, so assuming
damping and driving force zero. Equation (1) can be written as



+  = 0

(6)





(2)

which is a simple homogeneous equation. The general solution

of (2) can be written as

(7)

!"

#$$ =

where m, c, k, F and x are effective mass of cantilever, damping

constant, spring constant, external force and instantaneous
displacement respectively.



and

The cantilever sensor driven by an external force in the first

mode of vibration can be modeled as a mass-spring-damper
equivalent as shown in Fig. 2.
The governing equation for the motion of such a driven
damped oscillator with single degree of freedom can be written
as





where meff and k are the effective mass and stiffness coefficient
of the resonator respectively given in [4] as

III. ANALYTICAL MODELING



(5)

which can be simplified into the following form

Value(m)
1000
300
45
100
6
90
3
76
250
900
0.12
0.8
0.612
2.113

avoid buckling of the structure due to residual stress, a silicon

substrate of thickness 40 m is added with the thin film.



%
&*
'

(8)

E, b, h, L, m are the Youngs modulus, width, thickness, length

and mass of cantilever respectively and , is a constant whose
value depends upon the mode of vibration. For the first mode
its value is 1.88.
Equation (6) can be rearranged using (7) and (8) to give
 =

&
'

 "

/ .

(9)

The comb fingers created at the free end of the cantilever act
as loaded mass and cause the resonance frequency to reduce.
The effective [5] mass of each finger can be determined as
%4

 5

(10)
2 = 2 (1 +  )
"
"
where 2 , a and L are mass of individual finger, distance of
finger from free end and length of cantilever respectively.
Finally total effective mass meff of the cantilever can be
determined by adding effective masses of all the fingers $#$$
and effective mass of the beam mbeff. The resonance frequency,
then, can be calculated using
=






 6#$$

(11)

B. Resonant Response
The steady state solution of (1) is given as
7/
sin 
=
:
:

(12)

(9(: ) ) 6(;: )
'

'

where ,  and are frequency of driving force, natural

frequency of the oscillator and dimensionless damping ratio
respectively.

325

RSM2011 Proc., 2011, Kota Kinabalu, Malaysia

The frequency of the driving Lorentz force can be adjusted
to match the resonance frequency of the oscillator so that form
(12) amplitude in dynamic mode at resonance can be written as
7/
.
(13)
? =
;

As quality factor of a resonator is given as


@=

(14)

;

and by Hooks law static deflecting under a force F is given as

AB =

So (13) can be rearranged to give
(15)
? = @AB.
Equation (15) shows that, for a carefully designed resonator
with large quality factor, the dynamic response is much higher
than that of static response and hence a resonant sensor can
exhibit high sensitivity as compared to the static one. The
mentioned equation also highlights the important role of
quality factor in dynamic response of the resonator. As can be
seen from (14) quality factor of a resonator depends on
damping experienced by it which must be minimized to obtain
a high quality factor.
C. Damping Estimation
Damping in a resonant cantilever sensor comes from many
parasitic complex sources and is the resultant of air flow
damping, squeeze film damping, acoustic damping, structural
damping and damping due to anchor losses. For a cantilever
based resonator the damping ratio [6] is given as


C=

D%E6D*F  G/H IJ' F

O?.% P

/K   J'

I  

/K LM

N
J'

actuation. Fig.3 shows schematically the electromagnetic

actuation mechanism. When an AC current is passed through
the coil, an out of plane force acts on the wire segments held
parallel to the free end of the cantilever.
So that the effective length of the coil for Lorentz force can be
determined as
Y 6Y
(18)
X#$$ =  M Z

where n, wo and wi are number of turns, outer width and inner
width of the coil respectively.
For small amplitude of vibration, the magnetic field remains
perpendicular to the effective segments of current carrying
conductor so that when a sinusoidal alternating current of peak
value i0 is passed, the Lorentz force acting is given as

= ? X#$$ [\()

where  is angular frequency of current and B is magnetic

field induction. Using ohms law force can be determined as a
function of applied voltage as

]M ^ _

. 2#$$ 
(16)
Where R is the viscosity of air (1.8x 10-5 Pas), S4 is the density
of air (1.3 kg/m3), S is the density of the cantilever T is the
width of the cantilever, is the thickness of the cantilever, Vo
is the distance between the cantilever and the nearby rigid
wall, W is the structural damping coefficient which is 5x10-6 for
silicon and  is the natural frequency of the cantilever.
Equation (16) above , shows nonlinear dependence of
damping factor on cantilever dimensions which has been
studied [7] in detail by showing that high quality factor can be
achieved in air at a thickness to length ratio of 1:20 and
thickness to width ratio of 1:3.
The electrical sensing mechanism also draws energy from the
resonator and hence damps the motion of the resonator;
however the amount of damping is negligible in comparison
with mechanical damping.

\()

(20)

where z is impedance of the coil. As the inductive reactance of

the coil is much smaller than its resistance so it can be
neglected and the impedance can be written as
a=b=

/^

(21)

where S is resistivity of material of coil, l total length of coil

and A is cross-sectional area of coil. Using aforementioned
value of z, (20) can be rearranged as

+

"

(19)

c]M ^ _
/^

\() .

(22)

Using this value of force in (11) the displacement can be

written as
=

c]M ^ _
:  
:
) ) 6(d )
:M
:M

/^ (9(

 .

(23)

F. Electrostatic Sensing
The fixed and free comb fingers are arranged in such a way
that they behave as parallel plate capacitors connected in series
so that their equivalent capacitance can be written as
f ^ 
(24)
e? = g g g

where , h?, X? , ? and l are number of capacitive pairs,
permittivity of free space, length of overlapping area of
capacitive fingers, thickness of conducting layer in fingers and
separation between opposing fingers respectively. A

D. Mass Sensitivity
With a small mass m loaded on the tip of the cantilever, the
shift in frequency of the cantilever is
$
 $M
=
.
(17)


 

E.

Electromagnetic Actuation
Electromagnetic actuation has the advantage of producing
large force and is the most suitable mechanism for out of plane
Fig.3. Schematic diagram of electromagnetic actuation mechanism

326

RSM2011 Proc., 2011, Kota Kinabalu, Malaysia

displacement x of the free end of the cantilever causes the
overlapping thickness (t0) to change to (? ) so that the
capacitance becomes
e=

fg ^g (g 9 )


(25)
IV. RESULT AND DISCUSSION

Using (24), above (25) can be rearranged as



e = e? D1

g

F.

(26)

As in dynamic mode displacement x is a periodic function of

time therefore above equation can be rearranged to give
e = e? D1

g o2 (J)
g

F.

(27)

Fig. 4 shows an equivalent circuit for the capacitive sensing

mechanism. When the capacitance of variable capacitor
changes in response to vibration of the cantilever, the charge
stored also changes which causes an alternating current in the
circuit given as
=

p


= q_

r


(28)

Using (27), (28) can be simplified to give

=

]t M JrM
g

 ( + u)

(29)

where  is the amplitude of vibration. The voltage drop across

the capacitor, with the flow of above mentioned alternating
current during periodic motion [8], which lags current by v/2
can be written as
w4x =

]t M
g

\( + u).

(30)

As in the absence of periodic motion the capacitor acts as

open circuit for the DC bias so the voltage drop across it is
equal to that of biasing voltage q_ . Therefore the resultant
voltage at the point-A during continuous motion can be written
as
q_y = w4x + q_ = q_ (1 +

M
g

by mass loading the frequency of oscillation changes which

cause that of w4x to change. The shift in frequency of signal
can be digitally processed to determine the amount of loaded
mass.

\( + u)).

The parameters of the device for electromagnetic actuation

mechanism are calculated by the analytical model described in
above section are given in Table II. Fig. 5 shows the amplitude
of oscillation for different values of applied voltage and
magnetic field. It can be seen that with an applied voltage of
peak value 5 V and a magnetic field of 0.1 T amplitude of 2.8
m is produced. Fig. 6 shows frequency response of the device
obtained by finite element analysis and theoretical model and
Fig. 7 shows model shape and amplitude of vibration obtained
by FEM. It can be seen that both resonance frequency and
amplitude of vibration under similar forcing conditions are
closely agreeing, which authenticate the validity of the
developed model. From the frequency response curve the
quality factor of the device has been determined to be 3331 by
FEM and 3333 by analytical model which are again in close
agreement. Fig. 8 shows variation of resonance frequency with
loaded mass, the solid line is obtained by analytical model and
the square boxes represent the result by finite element analysis.
Again the two are in close agreement.
The capacitance of the comb fingers is calculated to be 0.043
pF. The initial overlapping thickness of the comb capacitors is
equal to the combined thickness of the three metallic layers i.e.
2.11 m in the technology we are using. As discussed above it
is possible to achieve a displacement equal to this initial
overlapping thickness so that the capacitance will drop to zero
TABLE II
ELECTRICMAGNETIC ACTUATION
MECHANSIM
Parameter
Value
Total length of wire in coil
62200 m
Effective length of coil
6200 m
Resistance of coil
3.3 K
PARAMETERS

FOR

(31)

The voltage w4x can be converted to a low impedance signal

using a follower and then amplified. As can be seen from (17)

Fig.4. DC bias capacitive sensing scheme.

Fig.5.Variation of dynamic amplitude with excitation voltage, at different

values of magnetic field.

327

RSM2011 Proc., 2011, Kota Kinabalu, Malaysia

TABLE III
COMPARISION OF FEM RESULTS
Parameter
Analytical
Resonance frequency
57393 Hz
Mass sensitivity
3.2 Hz/ng
Quality factor
3331
Amplitude under 1N force
2.8 m

FEM
57405 Hz
3 Hz/ng
3333
2.7 m

V. CONCLUSION AND FUTURE WORK

Fig.6. Frequency response of the device obtained by analytical model

and FEM.

A high quality factor cantilever resonator has been designed

and optimized for CO2 sensing. Analytical model for the device
has been presented and compared with FEM simulation results
using CoventorWare software. The close agreement of the
results as shown in Table III validates the authentication of the
model. The device works in dynamic mode using
electromagnetic actuation and capacitive sensing mechanisms
and has a quality factor of 3333, mass sensitivity of 3.23
Hz/ng. It consumes 7.5 mW power for actuation mechanism.
The wide surface area of the cantilever makes it suitable for
chemical sensing applications.
The device is currently under post processing phase of
fabrication. In future the fabricated device will be coated with a
suitable functional layer for CO2 detection by adsorption.
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Fig. 7. Model shape in first mode showing resonance frequency and

amplitude.

[2]

[3]

at maximum amplitude and from (30) the peak value of the

AC voltage in output signal will be almost equal to the applied
DC biasing voltage. A comparison of FEM and analytical
results is given in Table III.

[4]
[5]
[6]

[7]

[8]

Fig.8. Shift in resonance frequency with loaded mass. The solid line is
obtained by analytical model while square boxes show FEM result .

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