Chapter 5 Experiment Results
5.2 One-port resonator
We evaluate the resonators by their electrical admittances. And the admittance is calculated from the measured S11 signal of the resonator as follows.
The admittance is the reciprocal of the impedance, 1 .
=
Y Z (5.1)
Where Y and Z represent the admittance and the impedance of the device, and the bold face means they are complex since the potential and the current can be not in phase.
And the S11 can be treated as the reflection coefficient from port 1 to the device, we have
for the impedance of port 1 is calibrated as (50 + j0) Ω. Therefore
11
The admittance has unit Ω-1, or Siemens (S). And the real part of the admittance is called the conductance (G) while the imaginary part is called the susceptance (B), or,
G jB.
Y= + (5.5)
Dozens of resonators were made, and the admittances of some of them are plotted from Fig 5.23 to Fig 5.25. The susceptance has a background slope which represents the static capacity of the IDT. The slope is significant relative to the resonance shows it had low electromechanical coupling. It is also found the susceptance is approximately pro-portional to the number of IDT pairs. The conductance has this trend also, but the peak of conductance is highly depends on the resonant performance and is with more uncer-tainty.
One of the most important factor to evaluate the performance of a resonator is its Q factor. Originally it is defined as the ratio of the stored energy to the dissipated energy in a half cycle. It can be estimated by the inverse of the fractional width between fre-quencies where the conductance becomes the half height of its peak [58]. The best Q factor obtained among these resonators is about 400, which is smaller than the simulat-ed result (1400). We found resonators with 20 rows of PC reflectors was not necessarily better than resonators with 15 or 10 rows PC since the reflection are all strong enough.
Instead a much more critical factor was the fabrication precision. The PC pattern with correction of the proximity effect (holes dimension near PC border were closer to the design) had much better response then that without the correction, although both of the
PCs reflected waves well, the optimized delay distance became different. And we have shown the delay distance influences the performance significantly (See Fig 3.13.). Also bias on the CVD SiO2 or aluminum electrodes thickness may change the optimized de-lay distance. And the alignment errors, directly altered the dede-lay distance, mattered. The most serious fabrication error was the size of the PC structure. From the SEM images of the PC holes Fig. 4.33 we found the fabricated holes had radii about 160 nm however they were designed to be 300 nm.
The material damping loss might decrease the Q. The damping of SiO2 was un-known but was sure larger than single crystals that usually used, especially in ultra-high frequency range.
And the ohmic loss existed because we observed that the conductance had a back-ground value, with a slope. Away from resonant the static capacity dominated which current existed in the IDT and ohmic loss showed for the resist of the metal. Of course at resonance the ohmic loss was even larger.
We also found that some resonators had split peaks on their conductance response which shows multiple resonances. Consider the resonator with Fabry-Perot model, there are infinite many resonant modes in the resonator cavity which their resonant frequency is proportional to the number of half wavelengths in the cavity (assuming non-dispersion). Although the modes are orthogonal to each other they may be non-orthogonal to the same excitation, thus they can be excited simultaneously. Espe-cially for a resonator designed with large number of half wavelengths inside its cavity, the neighboring modes are close in frequency and can be exited if there is some align-ment error.
Fig 5.1 VNA Agilent E5071C
Fig 5.2 Cascade Microtech probes with the platform
Fig 5.3 Impulse response of SFIT #2 on ST-cut quartz.
Fig 5.4 Original and gated signal in frequency domain.
Fig 5.5 Impulse response of SFIT #2 on 90°-rotated ST-cut quartz.
Fig 5.6 Original and gated signal of SFIT/90°-rotated ST-cut quartz in frequency domain.
Fig 5.7 Impulse response of SiO2/SFIT #1/90°-rotated ST-cut quartz
Fig 5.8 Original and gated signal of SiO2/SFIT #1/90°-rotated ST-cut quartz in fre-quency domain.
0.0 0.1 0.2 0.3 0.4 0.5
Fig 5.9 Impulse response of SiO2/SFIT #2/90°-rotated ST-cut quartz
800 1000 1200 1400 1600 1800
-110
Fig 5.10 Original and gated signal of SiO2/SFIT #2/90°-rotated ST-cut quartz in fre-quency domain.
0.0 0.1 0.2 0.3 0.4 0.5 -0.0004
-0.0002 0.0000 0.0002 0.0004
TimeHmsL S21HlinearscaleL
Fig 5.11 Impulse response of SFIT #1 with 10 rows of PC
800 1000 1200 1400 1600 1800
-120 -100 -80 -60 -40
FrequencyHMHzL S21HdBL
Fig 5.12 Frequency response of SFIT #1 with 10 rows of PC
0.0 0.1 0.2 0.3 0.4 0.5
Fig 5.13 Impulse response of SFIT #2 with 10 rows of PC
800 1000 1200 1400 1600 1800
-110
Fig 5.14 Frequency response of SFIT #2 with 10 rows of PC
0.0 0.1 0.2 0.3 0.4 0.5 -0.0004
-0.0002 0.0000 0.0002 0.0004
TimeHmsL S21HlinearscaleL
Fig 5.15 Impulse response of SFIT #1 with 15 rows of PC
800 1000 1200 1400 1600 1800
-120 -100 -80 -60 -40
FrequencyHMHzL S21HdBL
Fig 5.16 Frequency response of SFIT #1 with 15 rows of PC
0.0 0.1 0.2 0.3 0.4 0.5 -0.0004
-0.0002 0.0000 0.0002 0.0004
TimeHmsL S21HlinearscaleL
Fig 5.17 Impulse response of SFIT #2 with 15 rows of PC
800 1000 1200 1400 1600 1800
-120 -100 -80 -60 -40
FrequencyHMHzL S21HdBL
Fig 5.18 Frequency response of SFIT #2 with 15 rows of PC
0.0 0.1 0.2 0.3 0.4 0.5 -0.0004
-0.0002 0.0000 0.0002 0.0004
TimeHmsL S21HlinearscaleL
Fig 5.19 Impulse response of SFIT #1 with 20 rows of PC
800 1000 1200 1400 1600 1800
-120 -100 -80 -60 -40
FrequencyHMHzL S21HdBL
Fig 5.20 Frequency response of SFIT #1 with 20 rows of PC
0.0 0.1 0.2 0.3 0.4 0.5 -0.0004
-0.0002 0.0000 0.0002 0.0004
TimeHmsL S21HlinearscaleL
Fig 5.21 Impulse response of SFIT #2 with 20 rows of PC
800 1000 1200 1400 1600 1800
-120 -100 -80 -60 -40
FrequencyHMHzL S21HdBL
Fig 5.22 Frequency response of SFIT #2 with 20 rows of PC
Fig 5.23 Admittance signals of resonators containing 10.5 IDT pairs with (a) 10, (b) 15, (c) 20 rows PC as reflectors
(a)
(b)
(c)
Fig 5.24 Admittance signals of resonators containing 30.5 IDT pairs with (a) 10, (b) 15, (c) 20 rows PC as reflectors
(a)
(b)
(c)
Fig 5.25 Admittance signals of resonators containing 30.5 IDT pairs with (a) 10, (b) 15, (c) 20 rows PC as reflectors
(a)
(b)
(c)
Chapter 6
Conclusions and Future Works
6.1 Conclusions
In this thesis we present the methods analyzing acoustic waves in 2-dimensional phononic crystals. We investigate surface waves especially the Love wave propagating in the surface PC that has periodic structure modulations only near the free surface, strictly a quasi-2-D structure. And the anisotropy of the material are considered to cal-culate the complete band structure. We used a finite-depth model to calcal-culate the prop-agating eigenmodes, and proposed an explanation for the level repulsion between sur-face modes and plate modes. Also the region above the sound line used to be not dis-cussed in the literatures, were disdis-cussed. Degree of leakiness of the surface waves in the PC is therefore learned.
We analyzed a phononic SiO2 thin film/90°-rotated quartz substrate structure and expected a partial band gap for Love waves. The gap was later verified through the ex-periment. The reflection/transmission phenomenon of Love waves incident into the PC at the stop band frequency was investigated. Such phononic structure has excellent flection coefficient with little periods. A 1-port Love wave resonator base on the PC
re-flecting was designed and made. The method of designing the resonator is detailed in the thesis.
In the experiments we applied the advanced NEMS fabrication technology to fulfill the acoustic devices that operates in the GHz range. The experiments agreed with the theory.
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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