A model is developed to map the variation of sensitivity of a surface acoustic wave (SAW) resonator sensor over its surface, in order to find the region with maximum sensitivity. The model is based on a combined coupling of modes (COM) and periodic Green&#039;s function analysis. In order to extend the analysis to layered media, a new efficient technique is introduced to account for the mechanical interactions with buried electrodes. Using this technique the sensitivity calculations are found to be in good agreement with measurements. It is also shown that whilst changes in other parameters influence the sensitivity, it is the velocity change which most strongly determines the overall frequency change

Kalantar-Zadeh, K

Powell, D

Wlodarski, W

RMIT Research Repository

Optimum Sensitive Area of Surface Acoustic Wave
Resonator Chemical and Bio-Sensors
David A. Powell, Kourosh Kalantar-zadeh, and Wojtek Wlodarski
Sensor Technology Group, School of Electrical and Computer Engineering
RMIT University City Campus, Melbourne, VIC 3001, AUSTRALIA
email: david.powell@ieee.org
Abstract— A model is developed to map the variation
of sensitivity of a Surface Acoustic Wave (SAW) resonator
sensor over its surface, in order to find the region with
maximum sensitivity. The model is based on a combined
Coupling of Modes (COM) and periodic Green’s function
analysis. In order to extend the analysis to layered media,
a new efficient technique is introduced to account for the
mechanical interactions with buried electrodes. Using this
technique the sensitivity calculations are found to be in
good agreement with measurements. It is also shown that
whilst changes in other parameters influence the sensitivity,
it is the velocity change which most strongly determines
the overall frequency change.
I. INTRODUCTION
SAW sensors based on shear-horizontal (SH) waves
are well established devices for studying the properties
of liquids, and chemical or biological reactions occurring
within a liquid environment. Compared to SAW devices
based on a delay-line configuration, resonator structures
offer higher frequency stability for a given device size,
due to the multiple reflections increasing the group delay.
Figure 1 shows a schematic representation of a 2-port
resonator SAW structure (not to scale). Regions B-C and
D-E represent the input and output interdigital transduc-
ers which are connected to the external circuit. Regions
A-B and E-F are short-circuited electrode gratings of the
same period as the IDTs. These gratings serve to reflect
acoustic energy and create a resonant cavity. Region C-D
is a grating with a different period to that of the IDTs.
Its purpose is to trap the SH wave towards the surface
without causing significant reflection.
SAW transducer sensitivity has been investigated by
both theoretical and experimental means (e.g. [1]). How-
ever, in most cases it is assumed that the device in-
teraction with the analyte is uniform over the surface.
In applications such as bio-sensing, this assumption
is not well grounded. Using such a model it is not
possible to conclude which part of the device is most
F
y
x
A B DC E
Fig. 1. Layout of 2-port resonator SAW sensor in (x, y)-plane
sensitive to surface perturbations. It has previously been
shown that for SAW delay lines with electrodes exposed
to the analyte, sensitivity varies significantly over the
device surface [2]. For resonator type SAW devices
even stronger sensitivity variation is expected, since
acoustic energy decays exponentially into the reflective
gratings. Thus it is necessary to investigate the effect of
inhomogeneous mass-loading, in order to find the region
of the SAW device where sensitivity is highest.
This is particularly important in cases where only a
small quantity of selective material is available, so that
it can be placed on the most sensitive region of the SAW
device. Similar considerations also apply when a limited
amount of analyte is available.
II. MEASUREMENTS
The 2-port resonator sensors were fabricated on a
36◦-YX LiTaO3 substrate. Gold electrodes of 0.1µm
thickness were patterned, and the period of the IDT elec-
trodes was 20µm. A small spacing adjustment is made at
point D to ensure a single resonant frequency with high
quality factor (Q). A 0.4µm layer of SiO2 was deposited
on the device surface using RF magnetron sputtering, in
order to protect the electrodes. The resultant devices had
resonant frequencies in the range of 205-206MHz.
Sensitivity measurements were performed by placing
the SAW devices within the oscillator circuit before and
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after the addition of a perturbing mass, and measuring
the change in oscillation frequency. The system was
designed to ensure that the pressure placed on the
SAW device by measurement probes was repeatable.
The added mass was AZ1512E photo-resist, of thickness
0.6µm. This relatively thick layer was chosen to ensure
that a strong response was observed. Because the photo-
resist is a soft material the response should be mainly
attributable to its mass, although some viscosity influ-
ence would also be expected. Each measurement was
repeated simultaneously on 5 different devices, which
were fabricated in the same batch.
Figure 2 shows the results of the measurement, along
with calculated values which will be discussed in Sec-
tion III. The horizontal axis of the graph gives the
location along the x-axis as shown in Fig. 1, with the
corresponding points A through F being marked out.
Each circle marked on the graph represents a simulated
mass sensitivity value. The corresponding horizontal line
represents the region over which the additional mass
has been deposited or modelled. The nearby crosses
represent the measured values of sensitivity. In all cases
the mass has been deposited over the complete width of
the device in the y-direction.
III. MODEL
The model is based on the formulation of a spectral
domain Green’s function G(s1), which describes the
acoustic wave properties of the substrate and guid-
ing layer. Since the devices have a large number of
electrodes, a periodic Green’s function Gp(x) is used
to reduce computation time. Using this function, the
harmonic admittance of an infinite electrode array can be
calculated using the Boundary Element Method (BEM).
A fitting procedure [3] is used to derive Coupling of
Modes (COM) parameters from this admittance curve.
The COM model has parameters for propagation veloc-
ity v, reflection κ, transduction α, capacitance C and
attenuation γ.
This approach is advantageous because it combines
the speed and simplicity of the COM model with the
accuracy of the rigourous BEM solution. The application
of this model to layered SAW resonators operating in
liquid media was previously reported by the authors [4].
The COM parameters are used to derive a P-matrix
for each electrode pair in the device, and this P-matrix
can be calculated for the cases with and without mass-
loading, thus allowing mass sensitivity to be calculated
along the length (x) of the device. Variation of the mass
sensitivity across the width (y) of the device has been
neglected in this model. This effect can be assumed to
be insignificant since the device geometry is constant
across its width, which is much greater than the acoustic
wavelength.
Using the P-matrix model, the complete 2-port pa-
rameters of the SAW device can be calculated and the
resonant frequency determined. The shift in this resonant
frequency, divided by the mass which causes the shift
is considered as a measure for the device sensitivity.
The model shows how a local change in mass loading
at a region on the device surface affects the resonant
frequency of the device.
A. Mechanically Thin Electrodes
Provided the electrodes are of negligible thickness
compared with the acoustic wavelength, and are made
from a light material, their mechanical properties do not
need to be taken into account and they can be considered
as being infinitely thin. This assumption greatly simpli-
fies the analysis, and speeds up the computation. Figure
2 shows the theoretical and measured sensitivity of our
test device based on this assumption. It can be seen that,
as expected, the sensitivity is greatest at the centre of
the device. The region B-E will be denoted the optimum
region, although this region is arbitrarily selected, and
may be chosen differently for another device geometry.
This region accounts for the majority of the total device
response.
−1.5 −1 −0.5 0 0.5 1 1.5
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se
n
si
tiv
ity
 (H
z/n
g)
x position (mm)
A B C D E F
Fig. 2. Sensitivity with thin electrodes
The agreement in shape is quite good, however the
measured sensitivity is more confined to the centre than
the model predicts, and the average sensitivity over the
complete device is also greater. This disagreement can be
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attributed to the relatively heavy electrodes which were
not included in the model. The heavy electrodes enhance
the acoustic reflection, thus confining the acoustic energy
to the centre of the device. They also trap acoustic energy
to the surface, thus further increasing the average mass
sensitivity of the device.
B. Mechanically Thick Electrodes
The results of Section III-A indicate that mechanical
electrode interactions have a significant influence on the
performance of our device. Typically the Finite Element
Method (FEM) is used to account for such interactions,
however FEM becomes cumbersome in the case of elec-
trodes embedded within layered media [5]. In this paper
we utilise a simpler technique based on the formulation
of a matrix eigen-operator [6]. Briefly, the piezoelectric
equations are manipulated into the following form:
[
L11(x) L12(x)
L21(x) L22(x)
]
τ =
∂
∂z
τ , (1)
where τ =
[
u ϕ T Dz
]
T
are the mechanical
displacement, voltage, z-components of stress and z-
component of electric flux respectively. The device con-
figuration to be modelled is shown in Fig. 3.
z
x
z=z
z=z
Guiding Layer
(i)
(ii)
(iii)
Guiding Layer
Substrate
p 1
2Electrode Electrode
Fig. 3. Cross-section of electrode configuration in (x,z) plane
Regions (i) and (iii) are accounted for using the ex-
isting Green’s function, and for simplicity it is assumed
that the charge is located only at z = z1. The new model
is required for region (ii), where there are 2 different sets
of material constants, alternating periodically. To allow
a numerical solution of (1), the material constants (or
their combinations which appear in L) are represented
by a truncated Fourier series. For example, density ρ is
represented as:
ρ(x) =
N∑
n=−N
ρne
j2pin/px (2)
The elements of τ are represented by a Fourier series
with an additional phase shift β:
τl(x, z) =
N∑
m=−N
τl,m(z)ej(2pim/p+β)x (3)
By substituting equations (3) and (2) into (1), an alge-
braic eigenvalue problem results. From the eigenvalues
and eigenvectors, a transmission matrix Φ can be devel-
oped, relating the field values at the top and bottom of
region (ii) in Fig. 3:
τm,k(z1) =
N∑
n=−N
8∑
k=1
Φmnklτn,l(z2) (4)
This can be regarded as a generalisation of Adler’s [7]
chain matrix technique for layered media, extended to
the case where the material constants are a function of
x. The new model will be presented in detail elsewhere.
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A B C D E F
Fig. 4. Sensitivity with thick electrodes
The mechanical electrode model was incorporated
into the periodic Green’s function analysis, and the
sensitivity was calculated as before. The result is shown
in Fig. 4. The sensitivity shows better agreement with
measurements in the case where complete device is mass
loaded, as does the sensitivity in the optimum region.
Because the SiO2 film is deposited conformably over a
surface covered with electrodes, the top surface of the
device has corrugations, which would also need to be
included in the model for improved accuracy.
C. Influence of Other Parameters
In order to test the relative importance of parameters
α, κ, C and γ in determining sensitivity, the sensitivity
was calculated with these parameters held constant, with
only v varying. The resulting sensitivity distribution is
shown in Fig. 5, being compared with the measured
values. It can be seen that the results do not differ greatly
from the full simulation, which indicates that in this case
the velocity change is predominant.
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−1.5 −1 −0.5 0 0.5 1 1.5
−12000
−10000
−8000
−6000
−4000
−2000
0
se
n
si
tiv
ity
 (H
z/n
g)
x position (mm)
A B C D E F
Fig. 5. Sensitivity considering only velocity change
IV. DISCUSSION
It is of interest to compare the sensitivity of the
complete device, the optimum region and of an idealised
infinite length IDT. The table below shows a comparison
of these sensitivity calculations. To compare with an
infinite IDT we must consider mass loading per unit area.
This shows that the optimum region accounts for 84%
of the complete device sensitivity. The sensitivity of the
device to homogeneous loading is closely related to the
sensitivity of the velocity and resonant frequency of an
infinite IDT. These parameters differ mostly because of
the sensitivity of the reflection coefficient [4].
Structure Sensitivity cm2/g
Infinite IDT v −96.4
Infinite IDT f −117.8
Complete Resonator −99.3
Optimum Region −83.5
The model suggests that for bio-sensing applications
with a limited quantity of available selective material,
to achieve maximum response, this material should only
be immobilised over the optimum region of the SAW
device. It must be stressed that there are other factors
which also need to be taken into account including mass
transport, optimum receptor concentration and whether
a flow-through or static cell has been used [8].
On the other hand, in situations such as environmental
gas monitoring, it is more reasonable to assume that
there is an unlimited quantity of analyte interacting with
the complete device surface. A comparison of delay
line and resonator structures has been made under these
assumptions, resulting in quite different conclusions [9].
Although mass sensitivity is investigated here the
mechanism for varying sensitivity across the device
surface is not specific to mass loading. The principal
is primarily the means by which the device structure
translates a local velocity change ∆v/v to an overall
change in the oscillation frequency of the device ∆f/f .
Thus similar results would be expected for sensors based
on changes in other parameters such as viscosity or
conductivity and for other types of SAW mode.
V. CONCLUSION
It was shown that a fixed quantity of analyte will
have a greater effect on the device response if it is
immobilised or adsorbed onto a small region at the centre
of the device. The authors propose to test this conclu-
sions using biological materials in a liquid environment,
to quantify the performance change when material is
immobilised only over the optimum region of the SAW.
ACKNOWLEDGEMENTS
The assistance of Professor Ali Reza Baghai-Wadji
in developing the model for electrodes buried within
layered media is gratefully acknowledged.
REFERENCES
[1] Z. Wang, J. D. N. Cheeke, and C. K. Jen, “Perturbation method
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[2] G. L. Harding, “Mass sensitivity of Love-mode acoustic sensors
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[3] J. Koskela, V. P. Plessky, and M. M. Salomaa, “SAW/LSAW
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[6] A. R. Baghai-Wadji, A Unified Approach for Construction
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Optimum sensitive area of surface acoustic wave resonator chemical and bio-sensors

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