67 3.3 Displacement profile of single-gate resonator at resonance frequency. a) Total displacement profile, (b) x-displacement profile and, (c) y-displacement profile. 3.9 2D geometry of single-port SAW resonator with NCIDT used in simulation to study the effect of bearing substrate thickness.
Surface acoustic waves – A brief introduction
The electromagnetic field associated with the Rayleigh wave moves in the direction of wave propagation, and the energy of the wave is confined close to the surface. FPM is similar to the Rayleigh wave, but the wave speed depends on the thickness and material of the plate.
Generation of surface acoustic waves - The IDT
The resonance frequency or synchronous frequency f0 is related to the height p of the IDT fingers and the SAW phase velocity v as given in equation (1) and equation (2). The bandwidth of the SAW device is determined by the number of IDT finger pairs.
SAW devices - Basic configurations
A single-gate SAW resonator can also be made using a large number of IDT fingers without reflectors as shown in Figure 1.3 (c). In the case of two-port resonators, two sets of reflectors are fabricated on the outer sides of two bidirectional IDTs as shown in Figure 1.3 (d).
Problem definition
In conventional SAW devices, the metallic IDTs fabricated on a piezo substrate cause the secondary effects such as reemission, bulk wave generation, diffraction, phase velocity variations, reflections, and electromagnetic coupling [4]. These effects in conventional SAW devices are discussed and verified by simulations based on the finite element simulation method (FEM) using COMSOL Multiphysics [14] in Chapter 2.
Literature reports - Electric field coupled SAW devices
Scope of the thesis
Study and simulation of conventional SAW devices such as IDT single-gate infinite-finger SAW resonator and SAW delay device to verify secondary effects using FEM-based COMSOL Multiphysics. Study and simulation of proposed SAW devices with electric field-coupled bond pads and comparison with conventional SAW devices.
Thesis organization
Experimental validation of the proposed SAW devices with NCIDT and an experiment to study non-ideal conditions such as separation effects, tilt effects and orientation effects. The results are compared with simulation results on the proposed SAW devices under ideal conditions.
Discrete source or delta function method
Brief descriptions of the modeling techniques used for SAW devices are given in the following sections. Note: The solid line shows the spatial distribution with N = and the dashed line the deviation in the spatial distribution for N = 2.
Impulse response method
Piezoelectric permittivity method
Equivalent circuit model
In this model, is expressed as 2f f0, where f is the frequency of the applied input potential and f0 is the resonance frequency and is the periodic section angle. If the generator IDT and receiver IDT of the SAW device match completely, the Y parameters of the 3-port network using the equivalent circuit of a period of an IDT can be expressed as
Coupling of mode (COM) model
In the above equations T = π and B = π/2 are grid and potential phase offsets respectively, and ω =2πf is the angular frequency. The admittance or P33 can be calculated from simulations and is the most useful parameter in device design.
Solution of SAW
- Elasticity in piezoelectric materials
- Piezoelectricity and constitutive equations
- Equation of motion
- Solution of surface wave in piezoelectric media
Piezoelectricity is a Greek word that means 'electricity through pressure'. The external force applied to piezoelectric material results in the generation of an electric field at the surface of the material. Before an external force is applied to the piezoelectric material, the gravitational centers of positive and negative charges of each molecule of the piezoelectric material coincide.
Finite element method (FEM)
Input and output information in FEM
The elements created in the geometry can be in the form of triangle, square, quadrilateral or brick, depending on the dimensionality. More details of the software can be found in the user guide of the software [15].
Finite element simulation of SAW devices
From Figure 4.4 (a) and (b), the ratio of the corresponding conductance peaks shows that the excitation efficiency in the SAW resonator with the electric field-coupled bond pads is about 2 orders of magnitude lower than that of the conventional SAW resonator. It can be seen from Figure 6.2 that the measured resonant frequency of the fabricated device is around 66.3 MHz and has an input return loss of -100.6 dB.
Simulation for meshes optimization and free surface SAW
Simulation of conventional one-port SAW resonator based on FEM in
Simulation methodology
A conventional one-port SAW resonator with an infinite number of IDT fingers on a piezo substrate is considered for the simulation. 2D geometry of a periodic segment of the resonator considered for the simulation is shown in Figure 2.14.
Results and discussions
The resonant frequency of the free surface f0 calculated from the eigenmode analysis of the piezo substrate is 217.3696 MHz. The quality factor Qr at the resonant frequency of conventional SAW resonators is calculated from Figure 2.16(b).
Simulation of conventional one-port SAW resonator based on FEM in
At resonant frequency the displacement is maximum between the fingers of the resonator, while at anti-resonant frequency the displacement is maximum at the center of the finger, as shown in section 2.8. Displacement profiles at resonant frequency 212.119 MHz, (a) Total displacement profile, (b) x displacement profile with distorted shape, (c) y displacement profile with distorted shape.
Simulation of a conventional SAW delay line
Simulation methodology
Results and discussions
Secondary effects of IDT fabricated on piezo-substrate
Simulation to study the mass loading effects of IDT
The normalized SAW phase velocity as a function of MR for various values of electrode thickness is shown in Figure 2.22 (b). The normalized SAW phase velocity as a function of MR for massless IDT SAW resonator is given in Figure 2.22 (b).
Simulation to study the electrical loading effects of IDT
From Figure 2.16 (b) and Figure 3.4 (b), the ratio of the corresponding conductance peaks shows that the excitation efficiency in NCIDT resonator is about 4 orders lower than conventional resonator. Coquin, “Determination of elastic and piezoelectric constants for crystals in class (3M),” The Journal of the Acoustical Society of America, vol.
Simulation to study the SAW generation
Summary
SAW devices with coupled electric field pads are presented in Chapter 4 and SAW devices with NCIDT are studied in this chapter. Sensor simulations using the proposed and conventional SAW devices are performed and their sensitivities are compared.
SAW devices with NCIDT – Theory and operation
We analyzed SAW devices with NCIDT by conducting rigorous simulations and experiments, and concluded that the proposed configuration has potential applications in the areas of signal processing and communications, where frequency accuracy is crucial. The simulation of the proposed SAW devices with NCIDT by FEM using COMSOL Multiphysics is described below.
Simulation of one port SAW resonator with NCIDT based on FEM in
Structure of one port SAW resonator with NCIDT
Simulation methodology
The eigenmode analysis is performed to calculate the resonant frequency of the NCIDT SAW resonator. Nevertheless, the resonant frequency of the NCIDT SAW resonator is remarkably close to the resonant frequency of the free surface.
Results and discussions
Simulation of one port SAW resonator with NCIDT based on FEM in
Simulation methodology
The dimensions used for the simulation are as follows: NCIDT finger width (d) 1 µm, electrode spacing (p) 2 µm, depth of the piezo substrate 10λ in –x3 direction, thickness of the electrode finger (he)0.2 µm, retaining substrate thickness (hh) shortened to 7 µm in x3 direction. It is assumed that the upper surface of the substrate is stress-free, the lower surface is fixed in position.
Results and discussions
To analyze the propagation of SAW across the delay line, transient analysis is performed using direct solver SPOOLES available in COMSOL Multiphysics [15] for 15 ns with a time interval of 0.1 ns, and the displacements and potential at the receiver electrode are recorded.
Different aspects of NCIDT SAW devices
Effect of properties of the holding substrate on SAW phase
It is observed that the SAW phase velocity decreases as the thickness of the retaining substrate increases. The SAW phase velocity and resonance frequency with and without retaining substrate are shown in Table 3.6.
Effect of air gap on SAW phase velocity
The electromechanical coupling coefficient K2 of the NCIDT SAW device for various values of air gap between NCIDT and piezo substrate is calculated. The reflection coefficient per period of the NCIDT SAW resonator is calculated for various values of air gap between NCIDT and piezo substrate.
Secondary effects in NCIDT SAW devices
Mass loading effects of NCIDT in NCIDT SAW devices
With respect to the free-surface SAW phase velocity, the velocity change is the largest (2.2%) in a conventional SAW resonator for a maximum MR of 0.9. A more detailed discussion of the electrical loading in the NCIDT SAW resonator is given in the next section.
Electrical loading effects of NCIDT in NCIDT SAW device
Figure 3.19 shows that the surface electric field under the IDT fingers in a conventional SAW resonator is short-circuited by the metal IDT fingers. In NCIDT SAW resonators, the x-component of the electric field at the surface is almost unchanged due to the air gap.
BAW generation in NCIDT SAW devices
SAW sensors
SAW sensor with direct mass load
The dimensions used for 2D simulation are as follows: NCIDT finger width (d) 1 µm, electrode spacing (p) 2 µm, electrode finger thickness (he) 0.2 µm, thickness of silicon holding substrate (hSi) truncated to 4 µm in x3 direction, and depth of the piezo substrate 10λ in – x3 direction. The material constants for piezo substrate are as used in Section 2.10 and are also given in Appendix C.
SAW sensor with sensing film – Organic vapor sensors
The sensitivity is obtained from the resonance frequency shift for various concentrations of the organic vapors. The simulations are performed for various concentrations of the vapor and the resonance frequency is recorded.
Summary
The BAW shift in NCIDT SAW devices is found to be smaller than conventional SAW devices. This chapter deals with the study of the second type of proposed SAW devices, ie SAW devices with electric field-coupled coupling pads.
Simulation of one port SAW resonator with electric field coupled
Simulation methodology
The metal plates of the external electrodes can be fabricated on a suitable substrate such as Si and FR4. The metal plates of the external electrodes are placed in parallel with an air gap of 1 µm above the bonding pads fabricated on the piezo-substrate.
Results and discussions
From Table 4.3 it is observed that the harmonic admittance of the SAW resonator with electric field coupled bond pads is approximately 2 orders of magnitude lower than the conventional SAW resonator. The quality factor of the SAW resonator with electric field coupled bond pads is 744870.4 and is about 3% larger than that of the conventional SAW resonator.
Fabrication of SAW devices with NCIDT
Fabrication of NCIDT using UV photolithography process
In the proposed SAW device configuration, the NCIDT can be separated from the piezo-substrate surface. The tilt effect between the NCIDT and the piezo-substrate is analyzed by observing the change in the resonant frequency of the proposed SAW resonator.
Fabrication of NCIDT using LPKF PCB prototyping machine
Summary
NCIDTs for low frequency SAW devices are fabricated on copper clad FR4 sheets using LPKF PCB prototyping machine. The resonance frequency of SAW devices with NCIDT fabricated in Si and FR4 is measured by S11.
S 11 measurements of fabricated SAW resonator with NCIDT on Si
Measurements of resonance frequency, output electrical potential and other characteristics of SAW devices with NCIDT are performed using RF probe station (Cascade Microtech Summit 9000) and network analyzer (Agilent E8361A & Agilent 8753ES), signal generator (Agilent 33120A ) and the oscilloscope. (Yokogawa DL9040). The device response in terms of the log magnitude of S11 is shown in Figure 6.2.
S 11 measurement of fabricated SAW resonator with NCIDT fabricated
Measurement setup and results
Although the NCIDT is designed for SAW devices with delay lines, the following experiments for measuring the S11 parameter use only one port of the device. The NCIDT is held above the Y-Z cut LiNbO3 wafer, aligned with the direction of the cut wafer.
Non-ideal situations in the proposed SAW device
Effects of change in separation
Effects of tilt between NCIDT and piezo-substrate
Effects of orientation between NCIDT and piezo-substrate
Experiments on fabricated NCIDT SAW delay line device
The separation of 0.1 mm is achieved by placing pieces of OHP plate between the NCIDT and the piezo substrate as described in Section 6.3. From Figure 6.15, the maximum output potential occurs at the resonant frequency of 4.39188 MHz, and the plot shows the bandwidth of about 0.3 kHz.
Simulation of fabricated devices
Simulation methodology
As explained in Chapter 3, the optimized mesh density with triangular mesh is applied to the model. Eigenmode analysis is performed to find the resonant frequency of the NCIDT SAW resonator with a limited number of fingers.
Results and discussions
An infinite number of NCIDT fingers, as discussed in Chapter 3, can be modeled using periodic boundary conditions on both sides of the substrate to reduce computational cost.
Simulation of effect of separation
The edges of NCIDT electrodes fabricated on FR4 material are not perfectly smooth, as can be seen from the optical images shown in Figure 5.8. The resonant frequency of the device almost saturates after a spacing of 1 mm and the input return loss approaches 0 dB above 2 mm.
S 11 measurement of SAW device with electric field coupled bond
Measurement setup and results
Plots of resonance frequency versus separation for experiment and simulation are shown in Figures 6.17 and 6.18, respectively.
Demonstration of SAW sensor using NCIDT
From Figure 6.21 it is absorbed that the sensitivity of the proposed SAW sensor with NCIDT configuration is about 4 kHz/cP. The sensitivity of the proposed SAW sensor is at least 5 times the SAW sensor reported in [75].
Summary
For a 68 µm wavelength NCIDT used with LiNbO3 substrate, the resonant frequency of the fabricated device is around 66.3 MHz and has input return loss of –100.6 dB. The sensitivity of the proposed SAW sensor with NCIDT configurations of about 4 kHz/cP is observed.
Conclusions
The analysis of the first proposed SAW device with NCIDT is performed by simulation based on FEM. Mahdi, “Finite element method on mass loading effect for gallium phosphate surface acoustic wave resonators,” in Proceedings of the World Congress Engineering, vol.
