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Recently we reported experimental and simulation results on an increase in resonance frequency of a SAW resonator caused by mass loading of micropillars made of SU-8, attached normal to the surface of the resonator. We concluded that SAW resonator and the SU-8 micropillars in unison form a system of coupled resonators. We have now extended this work and performed a finite element method simulation to study the resonance frequency characteristics of the SAW-based coupled resonator. In this paper we report the effect of the resonance frequency of the micropillars on the resonance frequency of the system of coupled resonators, and observe the coupling of micropillar resonance and the propagating SAW as described in the well known Dybwad system of coupled resonators.

Surface acoustic wave (SAW) devices are widely used in sensor applications. The mass loading effect in SAW devices is one of the prime sensing principles in these types of sensors [_{0}) increases [_{0} of the system with pillars of different resonant frequency (_{r}) through finite element method (FEM) simulation. In this paper, we present the simulation results and discuss the coupled resonance between the SAW and the attached pillars with the help of Dybwad's explanation for systems of coupled resonators. Dybwad [_{0}). Dybwad [_{0} and this results in a decrease in resonance frequency of the coupled resonator, while a weakly bonded particle offers “elastic loading” to the quartz resonator when the resonance frequency of the particles is smaller than _{0} and results in an increase in the resonance frequency of the coupled resonator [

A one port SAW resonator consisting of a long interdigital transducer (IDT) with infinite number of fingers is considered for the simulation. The FEM model of piezoelectric material is explained in [_{R}_{L}_{2} direction to the boundaries Γ_{1} and Γ_{2}. The bottom surface is fixed. The geometry of the segment (_{2} direction (aperture) 43 μm, leading to an active area of 21.5 μm × 21.5 μm. Triangular mesh is applied to the upper part of the substrate with minimum mesh size of 1 μm and rest of the SAW resonator is meshed with square mesh with dimension in the order of 4 μm. Initially eigen frequency analysis of the SAW resonator is performed and the resonance frequency without pillars (_{0}∣_{h}_{= 0}) of the SAW resonator is found to be 39.52702 MHz. Later a suitable resonant micropillar (in the shape of a square prism) made of SU-8 material of 8.6 μm × 8.6 μm cross-section is placed in the active area of the substrate (see _{0}) of the SAW resonator is recorded. SU-8 is a negative photoresist hard polymer. The SU-8 material properties such as Young's modulus of 4.02 GPa, density of 1,190 Kg/m^{3}, and Poisson ratio of 0.22 are provided to the pillar in the simulation model. Further resonance frequency (_{r}

_{0}) of the SAW resonator for an increase in mass loading caused by SU-8 pillars of dimensions 8.6 μm × 8.6 μm × _{0} is calculated by subtracting _{0} from _{0}∣_{h}_{= 0}. It can be seen from the figure that as the pillar height is increased, the Δ_{0} decreases and reaches a minimum value of −1.8 MHz at _{o}_{o}_{0} from _{0}∣_{h}_{= 0}) for heights 12 μm < _{0} is negative (decrease in _{0} from _{0}∣_{h}_{= 0}) for heights 23. 4 μm < _{r}_{r}_{r}_{0} curves in _{r}_{0}∣_{h}_{= 0} the pillar offers negligible mass loading to the SAW device and resonance frequency shift tends to zero and reaches a positive value. This is a similar situation as reported in our earlier work [_{r}_{0}∣_{h}_{= 0} (that is _{r}_{0}∣_{h}_{= 0}), Δ_{o}_{r}_{0}∣ _{h}_{= 0} (that is _{r}_{0}∣_{h}_{= 0}), Δ_{o}_{x}_{3}) at the surface (_{3} = 0, see

Total displacements of SAW is calculated by equation,
_{1}, _{2}, and _{3} are the particle displacement in _{1}, _{2}, and _{3} directions (see _{x}_{3} at surface _{3} = 0 plane (see _{x}_{3} value at the pillar contact surface (the pillar footprint is indicated by a square geometry) is negative when the pillar offers inertial loading and positive when the pillar offers elastic loading. It should be noted that darker color indicates minimum stress value and lighter color indicates maximum stress value. For a typical case of inertial loading height of _{x}_{3} has a minimum value of −2.48 MPa, indicating a compressive stress at the pillar contact surface. On a contrary, for a typical case of elastic loading (_{x}_{3} value is at maximum of 1.79 MPa, indicating tensile stress at the pillar contact surface. It should be noted that the displacement profile of SAW resonator with SU-8 pillar of height _{s} profile for the case of SAW resonator without the pillar and SAW resonator with a pillar of _{s} is approximately zero. It can be seen also be seen from _{0} ∣_{h}_{= 23μm} is 16 Hz, which is a negligible resonance frequency shift. Thus one can conclude that at

The present work will be of interest to sensor community readers in designing highly sensitve SAW sensors using resonant structures as sensing medium. In our earlier study we observed that the sensitivity with the resonant pillars is at least 10 times that obtained by using a thin film as the sensing medium [_{0} per μm increase in _{r}_{0}∣_{h}_{=0}. Thus highly sensitive SAW sensors based on coupled resonance can be designed by choosing a sensing medium made of a resonant structure that has a resonance frequency close to the resonance frequency of the SAW resonator.

FEM simulation of a system of coupled resonators made of a SAW resonator and aspect ratio micropillars is performed and the resonance frequency characteristics of the coupled resonator are studied for different values of pillar resonance frequencies. The micropillars offer inertial loading to the SAW resonator when _{r}_{0}∣_{h}_{= 0} and elastic loading to the SAW resonator when _{r}_{0}∣_{h}_{= 0}. The resonance frequency characteristics observed in the simulation were in agreement with Dybwad's coupled resonance model. The SU-8 pillars used in the study can be replaced with a suitable sensing medium of resonant structures and can be used in sensing applications.

The authors thank the Monash University Sunway Campus, PSCT research strength 2011–2012 fund, Monash University Sunway Campus internal seed grant E-15-12, and Indian Institute of Technology Guwahati, India for supporting and publishing the work. The authors also acknowledge Indian Nanoelectronics User Program for providing facilities to conduct the experiments related to research in SAW based coupled resonators.

_{2}SAW gas sensor

(_{3} = 0).

Plot of simulated results: Height of pillar versus resonance frequency shift, and resonance frequency of the pillar. The width of the pillar considered is 8.3 μm. Note that the resonance frequency of the SAW resonator is 39 MHz.

Simulation results: Total displacement in the substrate for the SAW resonator with SU-8 pillars of height (_{3} is shown. In order to have a better visualization, the original deformation value is magnified 100 times and shown in the figure.

Simulation results: Normal stress _{x}_{3} at the SAW resonator surface (at _{3}= 0 plane, the entire top surface of the segment considered in the simulation is shown) obtained for different heights of pillar (

Plot of mass loading sensitivity versus resonance frequency of the pillar.