Design and simulation of Bulk acoustic wave MEMS resonator

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International Journal of Exploring Emerging Trends in Engineering (IJEETE)

Vol. 01, Issue 01, Sept, 2014 WWW.IJEETE.COM

All Rights Reserved 2014 IJEETE Page 14

Design and simulation of Bulk acoustic wave MEMS resonator

1Wahengbam Kanan Kumar,

2Anuj Goel

1M.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 Surfaceacoustic 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 andpiezoelectric material is the prime focus for

studying the basic variation in series resonanceand 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-varyingdeformations or vibrations within a given

material medium. In case of solid, it is the result

of deformation of the material. Deformationoccurs when atoms within the material movefrom 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 inan arbitrary solid body- the equilibrium state is

shown by solid dots and the deformed state is

shown by circles [16].

Figure 1:Equilibrium and deformed states of particles in a

solid body

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 thedirection 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 casethe particles vibrate in a plane normal to the

direction of propagation. However due toboundary restrictions on the propagationmedium, 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 ofmethods such as mechanical impact, pulsed

thermal energy, and inverse piezoelectric effect.Acoustic devices are employed in manufacturing

transducer which can be broadly classified intotwo groups: surface acoustic wave (SAW) and

bulk acoustic wave (BAW) devices.

Piezoelectric crystals play crucial role in the

communication and electronics industry in areas


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like filters, precision timers and frequency

control in oscillator circuits. This effect is

demonstrated in the Figure 3. Material tends to

get deformed due to the applied potential acrossits two surfaces. This is due to coupling of linear

elasticity and electrostatic charge. Hookes law

for elasticity may be written as :

S = s.T (1)

D = .T (2)

Piezoelectric materials combine the above two

equation into one coupled equation:

S = sE.T + dt.E (3)

D = d.T + T.E (4)

Where, S=strain, s=compliance, T=stress,

D=charge density, =permittivity, E=electricfield, d=coupling matrix, T=relative

permittivity, sE=compliance matrix.

II. SENSOR STRUCTURE

Surface acoustic wave (SAW) device

SAW devices make use of mechanical wave thatpropagates along the surface of a piezoelectric

material and whose amplitude decreases

exponentially with depth of the material. They

are mostly employed in electronic devices suchas sensors, actuators, oscillators and filters.

[9][13]. The SAW uses two metal comb-shaped

electrodes placed on a piezoelectric substrate. Anelectric potential V applied to the electrodes

creates dynamic strains in the piezoelectric

substrate, which launches elastic waves. Thesewaves 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 theelastic wavelength R [9]-[13]:d = R/2 (5)The associated frequency is known as

synchronous frequency, f0

f0= VR/ R (6)

At this frequency, the transducer efficiency in

converting electrical energy to acoustical, or vice

versa, is maximised.

Figure 3: Finger-spacings and their role in the

determination of the acoustic wavelength [16]

The simplest SAW device is the non-dispersivedelay 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 thereceiving transducer converts the surface wave to

an electrical signal.

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 alongwith 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 andthe 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. Athick silicon layer is etched as the bottom layer

and a potential drop is applied in between the

two electrodes and the admittance in thepiezoelectric layer is calculated. The bottom

electrode is made the ground layer.


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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 forcewith 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 iswritten as:

(8)

Where Iel is a unity vector at positions

corresponding to those electrical DOFs for anelectrode.

Figure 5: Equivalent Butterworth Van Dyke lumped

element equivalent circuit of BAW resonator [6]

Considering the BVD model [6] shown in thefigure 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, planarfrequency coincides with the series resonance

frequency, fs. At higher resonance, another

impedance minimum (i.e the axial resonance

frequency) is encountered. The thickness modefrequency constant, NT, is related to the

thickness of the ceramic element, h by [17]:

NT= fs h (10)

III. SIMULATED RESULTS

Figure 6: Bulk acoustic wave resonator used in this paper

A pictorial representation of the modelled BAW

resonator is displayed in the figure above. Allsimulations are performed in COMSOL

Multiphysics 4.3 environment. It is a finiteelement analysis; solver and simulation software

packaged for various physics and engineering

applications, especially coupled phenomena, or

Multiphysics. In addition it also enables user toenter coupled systems of partial differential

equations (PDEs). It also offers extensive

interface to MATLAB and its toolboxes for avariety of pre-processing and post processing

applications [18][19]. All the geometricalmeasurements 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 bottomlayer is the silicon substrate layer on top which is

a thin metal layer serving as the ground

electrode. A thin piezoelectric layer issandwiched between two metal layers. It may be

noted that the top metal serves as the positiveelectrode 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 increasedin the second reading. The physical deformation

along with the admittance, Eigen frequency and


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series resonant frequency of the device body are

tabled in accordance with the simulated results as

shown below. Four different piezoelectricmaterials are used for each simulation Zinc

Oxide, PZT 5H, LiNbO3, Barium titanate.

Reading I: Thickness (m) 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

Piezoele

ctric

material

(PZD)

Thickness(m)Defo

rmation

n(n

m)

Re

son

antfre

q

(Mhz)

|Admitta

nce|PZDMetal

Sili

con

ZnO 9.6

0.26.9 1.03 22

1

100

PZT 5H 9.6 0.26.9 61.1

239.9

102.5

Lithium

niobate9.6 0.2 6.9 2.46 16

5

10-1

Bariumtitanate

9.6 0.26.9 3.8

199.5

100.5

Reading II: Thickness (m) of : PZD = 3,

Metal= 0.4, Silicon = 1.6, top metal = Al, bottommetal = Mb


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Figure 8: Admittance, Eigen frequency and

series resonance frequency with LiNbO3as PZD

Table 2: Result 2

IV. CONCLUSION

The simulated model has the capability to sustain

different types of oscillations, where the lowest

and highest series resonant frequencies werefound 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 7and figure 8 shows the deformation in surfacewith 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. Theadmittance plot in each reading is used to

determine the resonant and anti-resonantfrequency. It may also be observed that theabsolute value of admittance is highest in PZT

5H, i.e. of the order of 103.

REFERENCES

[1]Tapani Makkonen, Antti Holappa, Juha Ella,

and Martti M. Salomaa,Finite element

simulations of Thin-Film Composite BAWResonators, IEEE Trans. On Ultrason,

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[2]H.Satoh, H.Suzuki, C. Takahashi, C.

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Piezoelectri

c material

(PZD)

Thickness(m)Defor

matio

n

(nm)

Reso

nant

freq

(Mhz

)

|Adm

ittanc

e| (S)PZ

DMetal

Sili

con

ZnO3

0.4 1.6

3

630.2

101

PZT 5H 3 0.41.6 4.3 977.5

>103.3

0

Lithium

niobate3 0.4

1.6 3.704 684101

Barium

titanate3 0.4

1.6 9.11 558.3101.7


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AUTHORS BIBLOGRAPHY

Wahengbam Kanan Kumarwas born in Manipur, India in

1991. Presently he is pursuingM.Tech in VLSI Design at

Maharishi Markandeshwar

University. After completingB.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 inHaryana, 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.

Design and simulation of Bulk acoustic wave MEMS resonator

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