Substrate Vout Shear displacement Vertical displacement ILmin Charge density
(V) (nm) (nm) (dB) (µC cm−2)
36◦-YX LiTaO3 1.5 0.12 0.01 -27.1 200
41◦-YX LiNbO3 4.8 0.29 0.07 -15.6 250
90◦-AT quartz 0.031 0.010 5.8×10−5 -37.8 20
90◦-ST quartz 0.030 0.012 4.3×10−5 -38.4 19.5
Table 2.3: Maximum values of output voltage, shear displacement, vertical displacement, charge density, and minimum insertion loss obtained for SH-SAW delay line device considering different substrates.
0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 -300
-250 -200 -150 -100 -50 0 50 100 150 200 250 300
Electrostaticchargedensity(C/m
2 )
x ( m) 36-YX LiTaO
3
41-YX LiNbO 3
(a)
0 6 12 18 24 30 36 42 48 54 60 66 72 78 84 -25
-20 -15 -10 -5 0 5 10 15 20 25
0 0
0 0
+1 +1 +1
+1
0
Electrostaticchargedensity(C/m
2 )
x ( m)
35.25-AT Quartz 42.75-ST Quartz
+1
(b)
Figure 2.23: Variation in electrostatic charge density with device length for (a) 36◦-YX LiTaO3 and 41◦-YX LiNbO3 and, (b) 90◦-AT quartz and 90◦-ST quartz.
2.6.4 Insertion loss
The input IDT is excited with a unit impulse input of 1.5 ns duration. Fig. 2.24ashows the impulse response of the device. The electromagnetic feed-through effect seen at the beginning of the impulse response is about 100 times less than the applied unit impulse signal. The feed- through can be further reduced if device length is increased, but it would enhance the number of elements required for meshing, thus increasing the time and memory usage. The frequency response of the delay line was obtained by taking the Fourier transform of the impulse response voltage at the output IDT and is shown in Fig. 2.24b. Since the time response simulation contained a limited number of data points, the frequency response signal was improved by zero padding the output voltage signal [127]. The 41◦-YX LiNbO3 substrate gives a minimumILof -15.6 dB while 36◦-YX LiTaO3 provides a minimumILof -27.1 dB. In comparison, the ST/AT quartz because of their poor K2, gives largeILof about -38 dB. The obtained results of ILof SH-SAW device is consistent with results reported in [147], [148]
2.7. Summary
0 5 10 15 20 25 30 35 40 45 50
-0.05 -0.04 -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 0.04 0.05
Voltage(V)
t (ns)
(a)
100 150 200 250 300 350 400 450 500 550 600 -70
-65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10
Insertionloss(dB)
f (MHz) 41-YX LiNbO
3
36-YX LiTaO 3
90-AT quartz
90-ST quartz
(b)
Figure 2.24: (a) Impulse response of 36◦-YX LiTaO3 SH-SAW delay line. (b) Comparison of insertion loss of SH-SAW delay line devices considering different substrates.
model and P-matrix based COM model is presented. Assuming loss-less non-reflective transduc- ers, SAW delay line, resonant cavity, and one and two port resonators were modeled using the useful P-matrix based approach. It helps to calculate the frequency response and admittance characteristics of the device by designing an appropriate number of IDT finger pairs and re- flector gratings. The chapter also presented a brief outline of FEM based simulation technique describing the basic principle, limitations, approximations and boundary conditions used for simulation of the structure.
FE simulation of SH-SAW resonator and delay line was performed using COMSOL Multi- physics software by applying appropriate boundary conditions and Euler angles to the simulation geometry. The rotation of a Y-cut LiTaO3 crystal by an angle θ about the crystallographic X axis is investigated using FE simulation. The Leaky SAW has high coupling coefficient than the non-leaky SAW. Leaky SAW at θ = 36◦ takes the form of a near perfect shear horizontal surface wave which gets transformed to a Rayleigh type wave atθ = 125◦. Eigenmode analysis of SH-SAW resonator based on 36◦-YX LiTaO3, 41◦-YX LiNbO3, 90◦-AT quartz, and 90◦-ST quartz was performed to calculate surface velocities, coupling coefficient, and TCF of the device.
Quartz based devices suffer from low coupling coefficient but offer high phase velocities. 90◦-AT quartz provides the highest temperature stability. LiNbO3 substrate gives highest K2 but has the least temperature stability. The frequency response of SH-SAW resonators considering dif- ferent substrates was performed to study the mode shape and to calculate the total displacement and admittance of device. Simulations of SH-SAW delay line was carried out to investigate the wave propagation, time response and electrostatic charge density of the device. The insertion loss of SH-SAW delay line was calculated for different substrates and compared. LiNbO3 gives the lowest insertion loss followed by LiTaO3. Quartz because of low theirK2 values suffer from high insertion losses.
Chapter 3
Finite element analysis of Love wave devices
Every once in a while, a new technology, an old problem, and a big idea turn into an
innovation.
Dean Kamen
The Love wave (LW) devices were introduced in section 1.4.8. A LW device essentially consists of a guiding layer present on a substrate that generates SH-SAW. This chapter presents basic operation and principle of working of the LW device, analytical calculations of phase velocity, group velocity and mass sensitivity by solving the dispersion equation of LW, and 3D FE simulation of LW resonator to calculate mass sensitivity and coupling coefficient for the first two modes. Different guiding layers such as SiO2, gold, ZnO, SU-8, PMMA and polyimide are considered, and the results of FE simulation are compared with the analytically obtained values.
Selection of appropriate guiding layer is necessary for the proper design of LW device, and a comparison between different layers is presented. The frequency response of LW device along with depth displacement calculation for mode-0 and mode-1 is carried out. Comparison of SiO2 based LW device considering different substrates such as 36◦-YX LiTaO3, 41◦-YX LiNbO3, 90◦- AT quartz and 90◦-ST quartz is performed by calculating the variation inSf,K2 and TCF with the thickness of guiding layer. Lastly, 3D FE simulation of SiO2based LW delay line is performed to calculate the time response, mass sensitivity, and insertion loss. The mass sensitivity of delay line device is calculated by applying incremental surface mass density on the surface and noting the corresponding values of time and phase delays in the output voltage. The insertion loss of delay line is obtained by taking the FFT of the impulse response of the delay line device. The variation in minimum insertion loss of device with SiO2 and PMMA guiding layer thickness is also studied.
3.1 Love wave
LW is an elastic wave that propagates in a layered structure consisting of a substrate and a guiding layer on top of it. LW has pure shear horizontal vibrations with particle movement parallel to the surface and perpendicular to the wave propagation direction (perpendicular to the sagittal plane) [104]. The propagation of LW is possible only if the shear velocity in the layer is less than the shear velocity in the substrate. Thus, LW is a type of shear horizontally polarized wave that can be produced in an SSBW device or leaky SAW device when an overlayer with an acoustic shear velocity less that in bulk is deposited on the surface of the substrate [68]. The guiding layer slows down the propagating acoustic shear mode, thus decreasing the penetration depth and confining the energy of the wave in the layer.
The variation in the power flow of the fundamental LW mode as a function of the guiding layer thickness is shown in Fig. 3.1. LW device consists of a piezoelectric substrate with IDT fabricated on the surface. A guiding layer of thickness h is coated on top of the device. When the thickness of the guiding layer is much smaller than the wavelength (hλ), most of the wave energy is located in the piezoelectric substrate, and the LW propagates with a velocity close to the velocity in the substrate. When thicker layers are applied, with thickness still smaller than the wavelength (h < λ), the energy is concentrated in the overlayer, and the velocity of LW tends towards the velocity in the layer. At a certain thickness, the wave is maximally confined in the layer, with a large normalized wave amplitude (normalized to the total energy of the wave) at the surface [149], [150]. This thickness corresponds to the maximum mass sensitivity of the device. The guiding layer not only confines the wave energy to the surface and increases mass sensitivity but also serves to lower the insertion loss of the device. In addition, the guiding layer shields the metal electrodes from the liquid medium typically used for biosensing. SiO2, ZnO, gold and polymers are often used as guiding layer in LW sensors.
Piezoelectric substrates like 36◦-YX LiTaO3, 41◦-YX LiNbO3, 90◦- ST and AT quartz are some of the crystals that generate SH wave [9]. Quartz substrates generate pure SH wave, provide good temperature stability and high mass sensitivity, but they suffer from lowK2 and high insertion losses. LiNbO3 has high coupling coefficient but has poor thermal stability. 36◦- YX LiTaO3 provides better thermal stability than LiNbO3, sufficiently high K2 (higher than quartz but lower than LiNbO3), and lower insertion loss in comparison to quartz substrates [77], therefore it is often preferred for designing LW sensors.