Chapter 6 Conclusions and Future Works
6.2 Future works
In the finite-depth model, we claimed that the degree of leakiness of a surface mode can be deduced by strength of coupling with the plate modes, however a quantita-tive estimation is lacking. This can be a next subject.
Resonator with stronger electromechanical coupling has more advantages in the applications, therefore quartz may be replaced by other piezoelectric materials such as lithium niobate or lithium tantalate. The possible applications of the Love wave resona-tors are filters in communications or sensors, especially for bio-sensors. SH-type SAWs are sensitive to the surface loadings and less leaky in liquids. And with the IDT pro-tected by chemical resistive and temperature stable material SiO2 it is suitable to operate in various sensing occasions. And with ultra-high operation frequency the sensitivity for mass loading is even higher.
Appendix Determination of the Elastic Stiffness of the PECVD SiO
2A.1 Background
As reported in the literatures [59]-[64], mechanical properties of SiO2 vary from different deposition methods such as CVD [59]-[61] or sputtering [62]-[64]. Even more, the properties of SiO2 films can also be altered via the deposition conditions. To have good matching between simulations and experiments, the mechanical properties of SiO2
film deposited by the certain machine with the conditions identical to the fabrications were measured before the devices were designed.
A.2 Methods
A method based on SAW propagation is proposed to estimate the two Lamé con-stants via the experiment data. By measuring the phase velocities of the Rayleigh wave and Love wave on the SiO2/quartz layered half space with a certain kh number, the two Lamé constants can be found.
First the SiO2 film is assumed to be homogeneous and isotropic, and has a density of 2200 kg/m3, for the density seems not affected by different deposition methods re-ported in the literatures. And then the SiO2 film is deposited on the ST-cut quartz, with IDT on the interface between SiO2 and quartz to generate SAWs. Given a wavelength defined by the pitch of the IDT, one can obtain the phase velocities of the excited SAWs by the frequency response of the IDT with the relation.
cp = f λ, (A.1)
where cp is the phase velocity, f is the responded frequency, and λ is the wavelength. In this experiment we used relatively thick SiO2 film (~4 µm; actually fabricated thickness:
3.72 ~ 4.00 µm) and long wavelength (15 µm and 25 µm), therefore the loading effect of the 100-nm-thick aluminum electrodes was ignored. Theoretically, the result of one experiment setup is enough to find the Lamé constants. But 2 sets with different kh number was done to confirm the correctness of these constants.
Some two-port, filter-like devices with two identical IDTs were made to find the responded frequency f, as shown in Fig. A1. With long enough delay lines between the IDTs, one can separate the triple transit echo (TTE) in the time domain impulse re-sponse. The IDT parameters are listed in Table A1.
As discussed in Section 2.3, a pure-SH Love wave can be generated on SiO2/90°-rotated ST-cut quartz. Since only shear strain exists in the SiO2 film, the Love wave properties depends on only the second Lamé constant µ (shear modulus), and are independent of the first Lamé constant λ. We made a plot of Love wave phase velocity vs. shear modulus with kh around 1.7, 1.0, by FEM simulation, comparing with the ex-periment result we obtained the shear modulus µ = 26 GPa (see Fig. A2, uppers).
The only unknown left to be determined is the first Lamé constant λ. It can be found by measuring the Rayleigh wave velocity. Since the IDT is decoupled with the Rayleigh wave on 90ST quartz direction, we made another set of IDT that is perpendic-ular to the previous one, i.e., on the ordinary ST-cut quartz. Then similarly a plot of Rayleigh wave phase velocity vs. the first Lamé constant λ was made by FEM simula-tion with kh around 1.7, 1.0 (knowing µ = 26 GPa), comparing with the experiment re-sult we obtained the first Lamé constant λ = 20 GPa (see Fig. A2, lowers).
A.3 Experiment Results
The impulse response (by inverse FT) and time-gated/original frequency responses of the IDT filters are shown in Fig. A3 ~ A8. We can see the shapes of the central lobes were not symmetric, and the envelopes time domain impulse responses were not per-fectly diamond-shaped. These were caused by the internal reflection in the IDTs. And it made the peak frequencies slightly shifted. However the edges of the central lobe (the notch frequencies) were not altered.1 So instead of taking the peak frequency, we took the average of the lobe edge frequencies as the responded frequency to calculate the phase velocity. It can also be found in the responses of split-finger 2121 type IDTs, the effect of internal reflection and the TTE were much smaller than the original IDTs for the period of the mechanical loading was orthogonal to the excited wave.
1 K. Hashimoto, Surface Acoustic Wave Devices in Telecommunications Modeling and Simulation, Ber-lin: Springer, 2000, pp. 206-209.
Table A1 IDT parameters for SiO
2 stiffness measurement# 1 # 2 # 3 # 4
Orientation ST-cut & 90°-rotated ST-cut quartz
Pitch 7.5 µm 7.5 µm 12.5 µm 12.5 µm
# of pairs 40.5 60.5 40.5 40.5
aperture 1500 µm 1500 µm 2500 µm 2500 µm
type normal normal normal “2121”
All the IDTs are made of 100-nm-thick aluminum and are covered with ~4-µm-thick PECVD SiO2
Fig. A1 A schematic drawing of the devices measuring SiO2 stiffness.
Fig. A2 Measured and simulated phase velocities of Love waves and Rayleigh waves vs. Lamé constants. In the lower two figures, the second Lamé constant µ was fixed 26 GPa
0 2 4 6 8 10
�0.0010
�0.0005 0.0000 0.0005 0.0010
Time Μs
S21 linearscale
310 320 330 340 350
120
100
80
60
40
Frequency MHz
S21 dB
Fig. A3 The response of the filter consisted of 2 IDTs of 60 pairs on 90ST quartz, wavelength = 15µm.
0 2 4 6 8 10
�0.0010
�0.0005 0.0000 0.0005 0.0010
Time Μs
S21 linearscale
180 190 200 210 220
100
80
60
40
Frequency MHz
S21 dB
Fig. A4 The response of the filter consisted of 2 IDTs of 40 pairs on 90ST quartz, wavelength = 25µm.
0 2 4 6 8 10
�0.0015
�0.0010
�0.0005 0.0000 0.0005 0.0010 0.0015
Time Μs
S21 linearscale
180 190 200 210 220
120
100
80
60
40
Frequency MHz
S21 dB
Fig. A5 The response of the filter consisted of 2 “2121” type IDTs of 40 pairs on 90ST quartz, wavelength = 25µm.
0 2 4 6 8 10
�0.003
�0.002
�0.001 0.000 0.001 0.002 0.003
Time Μs
S21 linearscale
190 200 210 220 230
100
80
60
40
Frequency MHz
S21 dB
Fig. A6 The response of the filter consisted of 2 IDTs of 60 pairs on ST cut quartz, wavelength = 15µm.
0 2 4 6 8 10 12 14
�0.0010
�0.0005 0.0000 0.0005 0.0010
Time Μs
S21 linearscale
100 110 120 130 140 150
120
100
80
60
40
Frequency MHz
S21 dB
Fig. A7 The response of the filter consisted of 2 IDTs of 40 pairs on ST cut quartz, wavelength = 25µm.
0 2 4 6 8 10
�0.0010
�0.0005 0.0000 0.0005 0.0010
Time Μs
S21 linearscale
100 110 120 130 140 150
100
80
60
40
Frequency MHz
S21 dB
Fig. A8 The response of the filter consisted of 2 “2121” type IDTs of 40 pairs on ST cut quartz, wavelength = 25µm.
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