Design and simulation of Bulk acoustic wave MEMS resonator

International Journal of Exploring Emerging Trends in Engineering (IJEETE)
Vol. 01, Issue 01, Sept, 2014 WWW.IJEETE.COM
Design and simulation of Bulk acoustic wave MEMS resonator
1
Wahengbam Kanan Kumar , 2Anuj Goel
1
M.Tech. (VLSI Design) , ECE Deptt., MMEC ,Mullana ,Haryana
2
Assistant Professor , ECE Deptt., MMEC ,Mullana ,Haryana
Abstract:- A brief review on the use of acoustic
waves in designing MEMS based resonator is
described in this paper. Acoustic devices can be
further classified into two basic types – Surface
acoustic wave (SAW) and Bulk acoustic wave
(BAW) devices. A BAW resonator is modeled
and simulated using COMSOL Multiphysics 4.3.
In this model variation in thickness and
piezoelectric material is the prime focus for
studying the basic variation in series resonance
and surface deformation of the device.
Keywords: Acoustic wave resonator, SAW,
BAW, Comsol Multiphysics 4.3, Piezoelectric
material.
I. INTRODUCTION
Acoustics is the study of time-varying
deformations or vibrations within a given
material medium. In case of solid, it is the result
of deformation of the material. Deformation
occurs when atoms within the material move
from their equilibrium position which results in
internal restoring forces that return the material
back to equilibrium. Figure 1 depicts the
equilibrium and deformed states of particles in
an arbitrary solid body- the equilibrium state is
shown by solid dots and the deformed state is
shown by circles [16].
Plane wave is the most general type of acoustic
wave which propagates in an infinite
homogenous medium. It is further of two types:
Longitudinal and shear waves, depending on the
direction of propagation and polarization of the
vibrating atoms within the propagating medium.
In the former, the particles vibrate in the
direction of propagation, while in the latter case
the particles vibrate in a plane normal to the
direction of propagation. However due to
boundary restrictions on the propagation
medium, it is no longer an infinite medium and
consequently the nature of the wave changes. A
graphical representation of the shear wave
propagation is presented in the Figure 2 below.
An acoustic wave can be described in terms of
both its propagation and polarization directions.
Figure 2: Acoustic shear waves in a cubic crystal medium
[16]
Acoustic wave can be induced by a variety of
methods such as mechanical impact, pulsed
thermal energy, and inverse piezoelectric effect.
Acoustic devices are employed in manufacturing
transducer which can be broadly classified into
two groups: surface acoustic wave (SAW) and
bulk acoustic wave (BAW) devices.
Figure 1: Equilibrium and deformed states of particles in a
solid body
Piezoelectric crystals play crucial role in the
communication and electronics industry in areas
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International Journal of Exploring Emerging Trends in Engineering (IJEETE)
Vol. 01, Issue 01, Sept, 2014 WWW.IJEETE.COM
like filters, precision timers and frequency
At this frequency, the transducer efficiency in
control in oscillator circuits. This effect is
converting electrical energy to acoustical, or vice
demonstrated in the Figure 3. Material tends to
versa, is maximised.
get deformed due to the applied potential across
its two surfaces. This is due to coupling of linear
elasticity and electrostatic charge. Hooke’s law
for elasticity may be written as :
S = s.T
D = ε.T
(1)
(2)
Piezoelectric materials combine the above two
equation into one coupled equation:
S = sE.T + dt.E
(3)
D = d.T + εT.E
(4)
Where, S=strain, s=compliance, T=stress,
D=charge density, ε=permittivity, E=electric
field,
d=coupling
matrix,
εT=relative
permittivity, sE=compliance matrix.
Figure 3: Finger-spacings and their role in the
determination of the acoustic wavelength [16]
The simplest SAW device is the non-dispersive
delay line depicted in Figure 4. One IDT is
connected to an electrical source and the other to
a detector. The source IDT sets up an electric
field in the substrate that launches a SAW by
means of the piezoelectric effect, and the
receiving transducer converts the surface wave to
an electrical signal.
II. SENSOR STRUCTURE
Surface acoustic wave (SAW) device
SAW devices make use of mechanical wave that
propagates along the surface of a piezoelectric
material and whose amplitude decreases
exponentially with depth of the material. They
are mostly employed in electronic devices such
as sensors, actuators, oscillators and filters.
[9][13]. The SAW uses two metal comb-shaped
electrodes placed on a piezoelectric substrate. An
electric potential V applied to the electrodes
creates dynamic strains in the piezoelectric
substrate, which launches elastic waves. These
waves contain the Rayleigh waves that run
perpendicular to the electrodes with a velocity.
To ensure constructive interference and in-phase
stress, the distance ‘d’ between two
neighbouring fingers should be equal to half the
elastic wavelength λR [9]-[13]:
d = λR/2
(5)
The associated frequency is known as
synchronous frequency, f0
f0 = VR/ λR
(6)
Figure 4: Schematic of a SAW device with IDTs
metallised onto the surface [16]
Bulk acoustic wave (BAW) device:
Bulk acoustic wave promises frequency in GHz
range when integrated with RF circuits along
with small size resonator and filters [1-5][7][8].
The resonator is of thin film [1],[3],[8] type in
which the substrate is etched away on the back
side. The natural frequency of the material and
the thickness are used as design parameters to
obtain the desired operating frequency. It is
modelled by sandwiching a piezoelectric layer in
between two electrodes as shown in Figue 5. A
thick silicon layer is etched as the bottom layer
and a potential drop is applied in between the
two electrodes and the admittance in the
piezoelectric layer is calculated. The bottom
electrode is made the ground layer.
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International Journal of Exploring Emerging Trends in Engineering (IJEETE)
Vol. 01, Issue 01, Sept, 2014 WWW.IJEETE.COM
III. SIMULATED RESULTS
The admittance Y is obtained by dividing total
charge Q on an electrode by the amplitude of the
driving voltage [1]:
(7)
The total charge on electrode is calculated as the
sum of the nodal charges. If FF is the nodal force
with a constant displacement and QQ is the nodal
charge with a fixed potential, the total charge on
an electrode can be computed by taking
summation of all the nodal charges which is
written as:
(8)
Where Iel is a unity vector at positions
corresponding to those electrical DOFs for an
electrode.
Figure 5: Equivalent Butterworth Van Dyke lumped
element equivalent circuit of BAW resonator [6]
Considering the BVD model [6] shown in the
figure 5 admittance of the equivalent circuit is:
(9)
When an unrestrained piezoelectric ceramic
element is exposed to a high frequency
alternating field, an impedance minimum, planar
frequency coincides with the series resonance
frequency, fs. At higher resonance, another
impedance minimum (i.e the axial resonance
frequency) is encountered. The thickness mode
frequency constant, NT, is related to the
thickness of the ceramic element, h by [17]:
NT = fs h
(10)
Figure 6: Bulk acoustic wave resonator used in this paper
A pictorial representation of the modelled BAW
resonator is displayed in the figure above. All
simulations are performed in COMSOL
Multiphysics 4.3 environment. It is a finite
element analysis; solver and simulation software
packaged for various physics and engineering
applications, especially coupled phenomena, or
Multiphysics. In addition it also enables user to
enter coupled systems of partial differential
equations (PDEs). It also offers extensive
interface to MATLAB and its toolboxes for a
variety of pre-processing and post processing
applications [18][19]. All the geometrical
measurements were carried out using the MEMS
module present in the software tool.
The model consists of two thin film metal layers,
piezoelectric layer and a silicon substrate as
displayed graphically in Figure 6. The bottom
layer is the silicon substrate layer on top which is
a thin metal layer serving as the ground
electrode. A thin piezoelectric layer is
sandwiched between two metal layers. It may be
noted that the top metal serves as the positive
electrode while the bottom is the ground
electrode, a potential is applied between them.
The whole simulation is done by dividing the
readings into two broad categories – i.e.
thickness of the piezoelectric layer is increased
in the second reading. The physical deformation
along with the admittance, Eigen frequency and
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International Journal of Exploring Emerging Trends in Engineering (IJEETE)
Vol. 01, Issue 01, Sept, 2014 WWW.IJEETE.COM
series resonant frequency of the device body are
tabled in accordance with the simulated results as
shown below. Four different piezoelectric
materials are used for each simulation – Zinc
Oxide, PZT 5H, LiNbO3, Barium titanate.
Reading I: Thickness (µm) of: PZD = 9.6, Metal
(Al) = 0.2, Silicon = 6.9.
Figure 7: Admittance, Eigen frequency and series
resonance frequency with Zinc Oxide as PZD
Table 1: Result 1
Thickness(µm)
Piezoele
Sili
ctric
con
material
Met
PZD
(PZD)
al
ZnO
9.6 0.2
PZT 5H
9.6
0.2
Lithium
niobate
9.6
0.2
Barium
titanate
9.6
0.2
6.9
Defo
rmat
ion
n(n
m)
1.03
6.9
61.1
6.9
2.46
6.9
3.8
Re
son
ant |Ad
fre mitta
q
nce|
(M
hz)
22
1
23
9.9
16
5
19
9.5
100
102.5
10-1
100.5
Reading II: Thickness (µm) of : PZD = 3,
Metal= 0.4, Silicon = 1.6, top metal = Al, bottom
metal = Mb
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International Journal of Exploring Emerging Trends in Engineering (IJEETE)
Vol. 01, Issue 01, Sept, 2014 WWW.IJEETE.COM
Table 2: Result 2
Piezoelectri
c material
(PZD)
Thickness(µm)
Defor
matio
n
(nm)
Reso
nant
freq
(Mhz
)
PZ
D
Metal
Sili
con
ZnO
3
0.4
1.6
3
630.2
PZT 5H
3
0.4
1.6
4.3
977.5
3
0.4
1.6
3.704
684
3
0.4
1.6
9.11
558.3
Lithium
niobate
Barium
titanate
|Adm
ittanc
e| (S)
101
>103.3
0
101
101.7
IV. CONCLUSION
The simulated model has the capability to sustain
different types of oscillations, where the lowest
and highest series resonant frequencies were
found in Lithium niobate (165 MHz) and PZT
5H (977.5 MHz) respectively within the
investigated range of 100 MHz to 1 GHz. The
frequency response analysis shown in figure 7
and figure 8 shows the deformation in surface
with the change in frequency. The highest value
of deformation was observed when PZT 5H was
used as the PZD material, i.e. 61.1 nm. The
admittance plot in each reading is used to
determine the resonant and anti-resonant
frequency. It may also be observed that the
absolute value of admittance is highest in PZT
5H, i.e. of the order of 103.
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International Journal of Exploring Emerging Trends in Engineering (IJEETE)
Vol. 01, Issue 01, Sept, 2014 WWW.IJEETE.COM
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International Journal of Exploring Emerging Trends in Engineering (IJEETE)
Vol. 01, Issue 01, Sept, 2014 WWW.IJEETE.COM
AUTHOR’S BIBLOGRAPHY
Wahengbam Kanan Kumar
was born in Manipur, India in
1991. Presently he is pursuing
M.Tech in VLSI Design at
Maharishi
Markandeshwar
University. After completing
B.E. in 2012 he was a guest lecturer at NERIST
(Deemed University). His research interests
include SAW & BAW physics, MEMS based
design, Digital circuit design, Memory design,
Fuzzy logic, Neural network, Image processing.
Anuj Goel was born in
Haryana, India in 1983. He is
presently working as Assistant
Professor in ECE Department,
MMEC,
M.M.University,
India. His research interests
include MEMS Modelling, VLSI Design etc.
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