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Surface acoustic wave waveguides for signal processing at radio frequencies
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Surface acoustic wave waveguides for signal processing at radio frequencies
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Content
SURFACEACOUSTICWAVEWAVEGUIDESFORSIGNAL
PROCESSINGATRADIOFREQUENCIES
by
Masashi Yamagata
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulllment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
August 2022
Copyright 2022 Masashi Yamagata
Dedication
To my dad, my mom, my sister, and my dearest Cindy.
ii
Acknowledgements
No man is an island - John Donne
Achievements and goals are attained with the help and support of those around us. This
Ph.D. would not have been possible without the support and encouragement from many
people.
I would like to rst thank my family, starting with my parents, Yuichi and Yasue Yam-
agata, for their unconditional love and support. Their hard work and many sacrices have
led to my success and many opportunities that were aorded to me. I wish I could have
nished my studies for my dad to see and thank him in person for all his love, support, and
encouragement. I would also like to thank my sister, Ryoko, and her husband Bruce for their
unconditional love, support, patience, and occasional banter throughout my Ph.D. as well.
I would like to thank my advisor, Prof. Hossein Hashemi, who has guided me through
my Ph.D. study. His support, feedback and encouragement have allowed me to work on a
subject matter that I had no knowledge of when I rst started except that it existed.
I would like to thank my dissertation committee members Prof. Eun Sok Kim, Prof.
Mike Shuo-Wei Chen, Prof. Constantine Sideris, and Prof. Jayakanth Ravichandran for
their support and invaluable contribution towards my academic progress. I am grateful for
their time and eorts, as well as their invaluable feedback that helped enrich my work. I
would like to thank Prof. Han Wang and Prof. Eva Kanso as well, both of whom served
on my qualifying exam committee, for their invaluable contributions toward my academic
progress. I would also like to thank Prof. Choma, who unfortunately passed away in 2014,
who encouraged me to pursue a graduate degree and started my journey as a researcher.
iii
I would like to thank the many EE sta members for all of their help and support. Thank
you so much Diane Demetras, Kim Reid, Jenny Lin, Sunny Bhalla, Elizabeth Castaneda,
and Lauren Villarreal.
I would like to thank the many group members that I have come across throughout
my Ph.D. studies: Dr. John Roderick, Kenneth Newton, Prof. Harish Krishnaswamy, Dr.
Ankush Goel, Prof. Ta-Shun Chu, Dr. Zahra Safarian, Prof. Firooz A
atouni, Dr. Alireza
Imani, Dr. Kunal Datta, Dr. Run Chen, Dr. Sushil Subramanian, Dr. Hooman Abediasl,
Dr. Hongrui Wang, Dr. Marcelo Segura, Dr. Behnam Analui, Sam Mandegaran, Dr. Fate-
meh Rezaeifer, Chenliang Du, Tim Mercer, Dr. Aria Samiei, Samer Idres, Vinay Chenna, Dr.
SungWon Chung, Makoto Nakai, Prof. Keisuke Kondo, and Yongwei Ni. I would also like
to thank Prof. Mike Chen and his group members for their support and encouragement as
well. I would like to especially thank Rezwan Rasul, who I have had the honor and privilege
of sharing an oce with. I would also like to thank Dr. Shiyu Su, Dr. Aoyang Zhang, Dr.
Cheng-Ru Ho, Prof. Jaewon Nam, Dr. Mohsen Hassanpourghadi, Mostafa Ayesh, Qiaochu
Zhang, Juzheng Liu, and Ce Yang. I would also like to thank Michella Rustom from Prof.
Sideris' lab. The completion of this work was possible because of all of you. I will forever
treasure all of your support, encouragement, and friendship.
I do not advise doing so but I have been working on my Ph.D. while continuing to work
in the industry as well. It is dicult to do both, but I was able to do so with the help,
support, and encouragement from my manager and co-workers. I would like to thank rst
and foremost, my manager Dr. Shahrzad Tadjpour for her help, support, and understanding
as I worked on completing my Ph.D. work. I would also like to thank Dr. Ark Wong, Dr.
Run Wang, Dr. Cem Cakir, Jina Jun, Hamid Firouzkouhi, Ramesh, Eric Shim, Krishna
Shivaram, Grace Mao, and Richard Alexander for their support, encouragement, and banter
throughout my Ph.D. journey.
Ph.D. work is dicult on its own but when your body is not right, it makes it an even
harder task to complete. I would like to thank Dr. Julie and her sta for working with me
iv
the past few years in getting my health back on track to be able to make the nal push to
nish my Ph.D. work.
Lastly, and most importantly, I would like to thank my girlfriend Cindy Chun for every-
thing. I would not have been able to complete this work without her support, encouragement,
and patience.
v
Table of Contents
Dedication ii
Acknowledgements iii
List of Tables viii
List of Figures ix
Abstract xix
Chapter 1: Introduction 1
1.1 Brief History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Interdigital Transducers . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Filters and Resonators . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1.3 Waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.1.4 Active SAW Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.1.5 mm-Waves and SAW Integration . . . . . . . . . . . . . . . . . . . . 17
1.2 Dissertation Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Chapter 2: Background 21
2.1 Physics of Surface Acoustic Waves . . . . . . . . . . . . . . . . . . . . . . . . 22
2.1.1 1-D Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.1.2 3-D Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2 Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3 Interdigital Transducers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4 SAW Filter Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Chapter 3: SAW Waveguides 36
3.1 Concepts of SAW Waveguiding . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.1.1 Straight Waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.1.2 Waveguide Bends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.1.3 Waveguide Taper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.1.4 Multistrip Coupler . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.1.5 Coupled Waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
vi
3.2 Beam Steering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.3 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.4 Measurements and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Chapter 4: SAW Phase Shifters 90
4.1 Thermal Phase Shifter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.2 Electroacoustic Phase Shifter . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.2.1 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.3 Measurements and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.3.1 Thermal Phase Shifter . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.3.2 Electroacoustic Phase Shifter . . . . . . . . . . . . . . . . . . . . . . 100
4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Chapter 5: Case Study 103
5.1 Interference Cancellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.2 SAW Phased Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5.2.1 Implementation and Measurement Results . . . . . . . . . . . . . . . 112
5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Chapter 6: Conclusion and Recommendations For Future Work 118
6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.2 Future Research Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
References 122
Appendix A: Tensor Notation 130
Appendix B: COMSOL Multiphysics 133
B.1 2-D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
B.1.1 Eigenfrequency Simulation . . . . . . . . . . . . . . . . . . . 135
B.1.2 Frequency Domain Simulation . . . . . . . . . . . . . . . . . 146
B.1.3 Time Dependent Simulation . . . . . . . . . . . . . . . . . . 157
B.1.4 Perfectly Matched Layer . . . . . . . . . . . . . . . . . . . . 161
B.2 3-D simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
vii
List of Tables
2.1 SAW Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.1 Overlay Metal Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2 Calculated Coupling Length of Waveguide Coupler . . . . . . . . . . . . . . 52
3.3 Peak S
21
for Straight Delay Lines Without Metal Overlay for = 6.56 um . 66
3.4 Simulated and Measured Loss Breakdown for Straight and Bent Waveguides 78
3.5 Peak S
21
for Multistrip Couplers . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.6 Peak S
21
, S
31
, and S
41
for Family of Fabricated Waveguide Couplers . . . . . 84
viii
List of Figures
1.1 Propagation of (a) Rayleigh wave and (b) Love wave. . . . . . . . . . . . . . 2
1.2 2-port system showing a simple interdigital transducer used for generating
and detecting surface acoustic waves. . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Examples of SAW IDT structures with (a) single electrode IDT, (b) double
electrode IDT, (c)
oating electrode IDT, (d) single-phase unidirectional IDT
(SPUIDT), and (e) focused IDT. . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 (a) Desired impulse response and (b) IDT electrode patterning to achieve
impulse response [7]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 (a) A binary phase shift keying (BPSK) coded SAW and (b) a withdrawal
weighted IDT, where dotted shapes indicate electrodes that were removed [7]. 6
1.6 A slanted down-chirp lter [7]. . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.7 An example of a (a) one-port resonator and its (b) equivalent electrical circuit
[15]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.8 An example of a (a) two-port resonator and its (b) equivalent electrical circuit
[16]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.9 A two-port SAW lter employing a multistrip coupler to transfer the SAW
from the top track to the bottom track, eliminating the undesirable bulk wave. 9
1.10 A three IDT SAW device with reduced triple-transit eect. . . . . . . . . . . 10
1.11 A schematic of a ladder-type lter employing SAW resonators. . . . . . . . . 10
1.12 A schematic of a double mode SAW (DMS) lter. . . . . . . . . . . . . . . . 11
1.13 Examples of acoustic waveguides. (a) and (b) are examples of overlay waveg-
uides, (c) is a ridge waveguide, which falls under what are known as topo-
graphic waveguides, and (d) is an example of either a cladded waveguide or
in-diused/ion-implanted waveguide. . . . . . . . . . . . . . . . . . . . . . . 13
1.14 Directional coupler using (a) coupled waveguides [23] and (b) multistrip cou-
plers [14]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
ix
1.15 A surface acoustic wave waveguide using periodic gratings [34]. . . . . . . . . 14
1.16 Top view of a phononic crystal SAW waveguide. . . . . . . . . . . . . . . . . 15
1.17 Examples of active SAW devices: (a) SAW phase shifter and (b) SAW amplier. 16
1.18 An illustrative schematic of a radio-frequency front-end module supporting
multiple frequency bands. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1 1-D displacement of a particle. . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2 1-D illustration of stress applied on a particle. . . . . . . . . . . . . . . . . . 24
2.3 Propagating surface acoustic wave with axes. . . . . . . . . . . . . . . . . . . 27
2.4 Beam steering eect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.5 Single electrode IDT on a piezoelectric substrate. . . . . . . . . . . . . . . . 30
2.6 (a) Dimensional setup for an IDT eigenfrequency simulation in COMSOL.
(b) Eigenfrequency simulation result showing the symmetric (left) and anti-
symmetric (right) SAW modes. . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.7 Normalized transducer response for IDT nger pairs of 1, 10, and 100. . . . . 31
2.8 Equivalent circuit of the IDT. . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.9 (a) Interdigitated interdigital SAW lter, (b) double mode surface acoustic
wave lter, and (c) ladder-type SAW lter made with SAW resonators. . . . 34
3.1 Examples of acoustic waveguides. (a) and (b) are examples of overlay waveg-
uides, (c) is a ridge waveguide, which falls under what are known as topo-
graphic waveguides, and (d) is an example of either a cladded waveguide or
in-diused/ion-implanted waveguide. . . . . . . . . . . . . . . . . . . . . . . 37
3.2 SAW velocity and corresponding refractive index for aluminum, tungsten and
gold overlay waveguides with = 6.56 m. . . . . . . . . . . . . . . . . . . . 39
3.3 SAW waveguide dispersion curves using gold metallization. The blue curve
represents the Rayleigh wave while the black curves represent higher order
modes. The wavelength used for the analysis is 6.56 m with 100 nm gold
thickness and waveguide widths of (a) 3m, (b) 6m, (c) 12m, and (d) 24
m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4 (a) Simulation setup for computing waveguide connement with (b) simulation
results for aluminum, tungsten, and gold for the waveguide overlay material. 41
3.5 3D COMSOL eigenfrequency simulation result for 128
o
YX LiNbO
3
with 100
nm gold IDT electrodes and = 6.56 m. . . . . . . . . . . . . . . . . . . . 41
3.6 Plot of IDT electrode pair capacitance vs. aperture width. . . . . . . . . . . 43
x
3.7 Plot of IDT resistance vs. aperture width. . . . . . . . . . . . . . . . . . . . 43
3.8 (a) 3D COMSOL drawing of IDT with = 6.56 m, aperture width = 100
m, and 24 100 nm thick gold electrode pairs and the (b) corresponding S11
simulation result. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.9 (a) Diagram of an electrode width controlled single-phase unidirectional IDT.
(b) A 2D COMSOL frequency domain simulation result of the EWC IDT,
showing the loss of the forward and backward propagating wave. . . . . . . . 44
3.10 Return loss simulation result for an EWC IDT with 32 periods, 130m aper-
ture width, and 100 nm thick gold on 128
o
YX LiNbO
3
. . . . . . . . . . . . . 45
3.11 A simplied 2D simulation setup for estimating straight waveguide loss. . . . 45
3.12 Simulation setup for analyzing waveguide bend with waveguide width = 6 m. 46
3.13 Total displacement simulation result for 180
o
bend for waveguide width = 6
m and bend radius of 200 m. . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.14 Simulation result for 180
o
bend for = 6 m and waveguide width = 6 m. 47
3.15 (a) Waveguide taper simulation setup mating an aperture width of w
IDT
on
to w
wg
, corresponding to the IDT aperture widths and waveguide aperture
widths, respectively. (b) Simulated loss for w
IDT
of 100 m and w
wg
of 6 m
over taper length of L
t
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.16 Schematic diagram of a multistrip coupler. . . . . . . . . . . . . . . . . . . . 49
3.17 SAW decomposed into even and odd modes in a multistrip coupler. . . . . . 50
3.18 SAW eigenfrequency (a) setup and (b) mode shape for a 500 nm thick alu-
minum plate on 128
o
Y-cut LiNbO
3
with = 50 m. . . . . . . . . . . . . . 51
3.19 SAW eigenfrequency (a) setup and (b) mode shape for a 500 nm thick alu-
minum strips on 128
o
Y-cut LiNbO
3
with = 50 m. . . . . . . . . . . . . . 51
3.20 Simulation result for 90
o
bend for = 6.56 m and waveguide width = 6 m. 52
3.21 Waveguide coupler simulation setup. . . . . . . . . . . . . . . . . . . . . . . 53
3.22 Waveguide coupler displacements for waveguide and coupled waveguide for a
gap = 1 m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.23 Waveguide coupler displacements for waveguide and coupled waveguide for a
gap = 2 m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.24 Waveguide coupler displacements for waveguide and coupled waveguide for a
gap = 3 m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.25 Slowness curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
xi
3.26 Simulated slowness curve for a 6 m wavelength IDT with 100 nm thick gold
for (a) 128
o
Y-cut LiNbO
3
and (b) X-cut LiNbO
3
. . . . . . . . . . . . . . . . 57
3.27 Simulated dispersion curves for waveguides with an aperture width of (a) 6
m and (b) 12 m for y-propagating SAWs on X-cut LiNbO
3
. . . . . . . . . 58
3.28 (a) COMSOL simulation setup showing the waveguide structure on an X-cut
LiNbO
3
substrate. (b) Total displacement simulation result for a SAW at 588
MHz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.29 Diagram of the straight test structure with one structure (a) without any met-
allization and (b) with waveguiding structure between the input and output
IDTs. m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.30 Microscope image of the straight test structure with waveguide metallization. 61
3.31 S11 and S21 measurement results for straight test structures with no waveg-
uide for L
wg
of 1 mm (blue) and 2 mm (red). . . . . . . . . . . . . . . . . . . 62
3.32 S11 and S21 measurement results for straight waveguide test structures with
100 nm thick gold waveguides and L
wg
of 1 mm (blue) and 2 mm (red). . . . 62
3.33 Diagram of the straight test structure with one structure (a) without any met-
allization and (b) with waveguiding structure between the input and output
IDTs. m. Re
ectors were added behind the IDTs to make the IDTs more
unidirectional. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.34 Microscope image of straight waveguide with aperture width w
2
= 6 m and
length L
2
= 1 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
3.35 S
11
measurement results for aluminum (blue), tungsten (red), and gold (black)
metallization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.36 S
21
measurement results for (a) aluminum, (b) tungsten, and (c) gold met-
allizations. The columns are divided into waveguide widths, with the left
column showing results for 6 m waveguide widths, the center column show-
ing results for 12m waveguide widths, and the right column showing results
for 24 m waveguide widths. The colors in each plot represent the dierent
waveguide lengths of 1 mm (blue), 2 mm (red), and 4 mm (green). . . . . . . 65
3.37 Peak S
21
and group delay measurement results for (a) aluminum, (b) tungsten,
and (c) gold metallizations for the three dierent waveguide lengths. The
columns are divided into waveguide widths, with the left column showing
results for 6 m waveguide widths, the center column showing results for
12 m waveguide widths, and the right column showing results for 24 m
waveguide widths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
xii
3.38 Straight delay line insertion loss comparison for 100 nm thick aluminum IDTs
on 128
o
YX LiNbO
3
without metal overlay. The results compare simulated
results for IDTs without re
ectors (blue) and IDTs with re
ectors with mea-
sured results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.39 Straight delay line insertion loss comparison for 100 nm thick tungsten IDTs
on 128
o
YX LiNbO
3
without metal overlay. The results compare simulated
results for IDTs without re
ectors (blue) and IDTs with re
ectors with mea-
sured results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.40 Straight delay line insertion loss comparison for 100 nm thick gold IDTs on
128
o
YX LiNbO
3
without metal overlay. The results compare simulated results
for IDTs without re
ectors (blue) and IDTs with re
ectors with measured
results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.41 Close-in plot of a 2D COMSOL simulation, indicating the re
ector-IDT bound-
ary and IDT-free LiNbO
3
boundary (top). The Y-displacement at 561 MHz
(middle) and 566 MHz (bottom) are shown. The Y-displacement at 561 MHz
indicates a resonance occurring between the re
ector and IDT with very little
of the SAW propagating towards the output while the Y-displacement at 566
MHz shows the SAW propagating towards the output. . . . . . . . . . . . . 68
3.42 2D COMSOL loss simulation result for diering re
ector nger pitch. . . . . 69
3.43 Waveguide S-bend test structure. . . . . . . . . . . . . . . . . . . . . . . . . 69
3.44 Microscope image of an s-bend waveguide structure with a width of 6m and
bending radius of 400 m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.45 S
21
magnitude response for s-bend test structures for waveguide width of 6
m using for (a) aluminum, (b) tungsten, and (c) gold metallizations. Each
plot shows the measurement results for bending radii of 100 m (blue), 200
m (red), and 400 m (black). (d) shows the peak S
21
across the dierent
radii for the three metallizations. . . . . . . . . . . . . . . . . . . . . . . . . 71
3.46 S
21
magnitude response for s-bend test structures for waveguide width of 12
m using for (a) aluminum, (b) tungsten, and (c) gold metallizations. Each
plot shows the measurement results for bending radii of 100 m (blue), 200
m (red), and 400 m (black). (d) shows the peak S
21
across the dierent
radii for the three metallizations. . . . . . . . . . . . . . . . . . . . . . . . . 71
3.47 S
21
magnitude response for s-bend test structures for waveguide width of 24
m using for (a) aluminum, (b) tungsten, and (c) gold metallizations. Each
plot shows the measurement results for bending radii of 100 m (blue), 200
m (red), and 400 m (black). (d) shows the peak S
21
across the dierent
radii for the three metallizations. . . . . . . . . . . . . . . . . . . . . . . . . 72
xiii
3.48 S
21
magnitude response for s-bend test structure without waveguiding metal-
lization for gold and bending radii of 100 m (blue), 200 m (red) and 400
m (black). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.49 Waveguide U-bend test structure. . . . . . . . . . . . . . . . . . . . . . . . . 73
3.50 Microscope image of the U-bend structures for outer bend radius of 200 m. 74
3.51 S21 magnitude plots for U-bend test structures. The plots of (a) are for a
bending radius of 100 m, (b) for a bending radius of 200 m, and (c) for a
bending radius of 400 m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.52 Microscope image of the U-bend structure without waveguide metallization
for outer bend radius of100 m. . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.53 S21 magnitude plots for U-bend test structures without 180
o
bend metalliza-
tion for equivalent bend radii of 100 m, 200 m, and 400 m. . . . . . . . . 75
3.54 S
21
measurement results for 6 m wavelength for (left) waveguide lengths of
1 mm, 2 mm, and 4 mm. The peak S
21
vs. waveguide length is also plotted
along with a linear t line (right). . . . . . . . . . . . . . . . . . . . . . . . . 76
3.55 S
21
measurement results for 6m wavelength for (left) straight test structure
without an overlay metallization of equivalent waveguide lengths of 1 mm, 2
mm, and 4 mm. The peak S
21
vs. waveguide length is also plotted along with
a linear t line (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.56 Die microphotograph for (a) back-to-back IDT test structure and (b) back-
to-back IDT-taper structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.57 S
21
measurement results for back-to-back IDT test structure (blue) and back-
to-back IDT-taper structure (red). . . . . . . . . . . . . . . . . . . . . . . . . 77
3.58 Loss breakdown for a (left) straight waveguide and (right) 180
o
waveguide
bend for 6 m wavelength and waveguide width of 6 m. . . . . . . . . . . . 78
3.59 Microphotograph of a multistrip coupler, outlining the re
ector, and IDT of
port 1 along with the MSC strips. . . . . . . . . . . . . . . . . . . . . . . . . 79
3.60 S
21
and S
41
magnitude plots for multistrip coupler with transfer length of 90
m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.61 S
21
and S
41
magnitude plots for multistrip coupler with transfer length of 100
m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
3.62 S
21
and S
41
magnitude plots for multistrip coupler with transfer length of 110
m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.63 S
21
and S
41
magnitude plots for multistrip coupler with transfer length of 140
m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
xiv
3.64 S
21
and S
41
magnitude plots for multistrip coupler with transfer length of 150
m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.65 S
21
and S
41
magnitude plots for multistrip coupler with transfer length of 160
m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.66 Diagram for a SAW waveguide coupler. . . . . . . . . . . . . . . . . . . . . . 82
3.67 Microscope image of a waveguide coupler. . . . . . . . . . . . . . . . . . . . 82
3.68 S21 magnitude measurement results for waveguide coupler test structure for
coupling lengths of (a) 57 m, (b) 123 m, and (c) 190 m. . . . . . . . . . 83
3.69 Two structures used to measure diraction and beam steering of SAW. The
IDTs on the right are spaced by about 308.5 m. The top structure has an
output IDT, B4, that is directly across from the input IDT, A. The bottom
structure has IDTs, labeled as Cx, that are oset by about 154m, lling the
gaps in between the IDTs labeled as Bx in the top structure. . . . . . . . . . 85
3.70 Microscope image of one of the test structures used to measure diraction and
beam steering of the SAW. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.71 Insertion loss measurement results for the diraction/beam steering structure
shown in Fig. 3.69 for the structure fabricated on 128
o
Y-cut LiNbO
3
with an
X-propagating SAW. The noted values are the minimum insertion loss values
for the respective curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
3.72 Insertion loss measurement results for the diraction/beam steering structure
shown in Fig. 3.69 for the structure fabricated on X-cut LiNbO
3
with a Y-
propagating SAW. The noted values are the minimum insertion loss values for
the respective curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
3.73 S
21
for a straight XY LiNbO
3
structure without waveguides (blue), with 6m
wide waveguide (red), and with 12 m waveguide (black). . . . . . . . . . . . 88
3.74 S
21
for a XY LiNbO
3
U-bend structure for a waveguide width of (a) 6m and
(b) 12 m for bending radii of 100 m, 200 m, and 400 m. . . . . . . . . . 88
3.75 S
21
for a XY LiNbO
3
U-bend structure for a waveguide width of 12 m and
bend radius of 400m for a structure with (blue) and without (red) waveguide
overlay metallization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.1 Plot of phase shifter length vs. temperature change. . . . . . . . . . . . . . . 92
4.2 SAW thermal phase shifter sharing heating element with multiple segments
of the phase shifter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
xv
4.3 (a) Diagram of a Mach-Zehnder interferometer (MZI) with a phase shifter as
the device-under-test (DUT). (b) Conceptual diagram of the phase shifter test
structure in an MZI. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.4 Meandered resistor designed for the heater of the thermal phase shifter. . . . 94
4.5 Cross-section of a SAW delay line with electrodes used to control the electric
eld for phase shifting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.6 Cross-section of a SAW phase shifter on Y-cut LiNbO
3
-on-silicon with elec-
trodes used to control the electric eld for phase shifting. . . . . . . . . . . . 97
4.7 Calculated shift in phase versus waveguide bias voltage for silicon resistivities
of 2,200
-cm, 22,000
-cm, and 44,000
-cm and phase shifter length of 6.39
mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.8 Die microphotograph of the Mach-Zehnder interferometer test structure for
testing the SAW thermal phase shifter. . . . . . . . . . . . . . . . . . . . . . 99
4.9 Measured S
21
of the MZI test structure versus dissipated power. . . . . . . . 100
4.10 Microphotograph of the electroacoustic phase shifter. . . . . . . . . . . . . . 101
4.11 (a) S
21
magnitude result and (b) measured phase shifts for the straight SAW
phase shifter (blue) and 180
o
waveguide bend (red) at 609 MHz. . . . . . . . 101
5.1 A simple diagram of a time division duplexed system (left) as well as a diagram
depicting the transmit (Tx) and receive (Rx) paths operate at dierent times
(right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.2 A simple diagram of a frequency division duplexed system (left) as well as
a diagram depicting the transmit (Tx) and receive (Rx) paths operating at
dierent frequencies (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.3 (a) Ideal two-tone signal spectrum out from the transmitter and (b) actual
transmitted spectrum with increased noise and signal harmonics. . . . . . . . 106
5.4 Illustrative example of self-interference signal level and required ADC dynamic
range to cancel self-interference signal. . . . . . . . . . . . . . . . . . . . . . 106
5.5 A simple diagram of a system employing self-interference cancellation using
(a) two separate antennas for the transmitter and the receiver and (b) using
a single shared antenna by using a circulator. . . . . . . . . . . . . . . . . . 107
5.6 Conceptual diagram of a 4-element antenna array receiver. . . . . . . . . . . 109
5.7 Plot of a 4-element array pattern for dierent beam-steering angles. . . . . . 109
5.8 N-element antenna array with incoming wavefront. . . . . . . . . . . . . . . 111
xvi
5.9 n-element array receiver with coherent signal summation and uncorrelated
noise, improving output SNR. . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.10 A couple of the design considerations of a phased array are the antenna spac-
ings and the number of elements to use. . . . . . . . . . . . . . . . . . . . . 113
5.11 4-element array pattern for antenna spacings of =4 (blue), =2 (red), and
(black). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.12 Array pattern for 2, 4, 8, and 16 antenna elements. . . . . . . . . . . . . . . 113
5.13 Die microphotograph of 4-element electroacoustic SAW phased array. . . . . 114
5.14 (a) S
11
measurement results for the four elements of the SAW phased array.
(b) S
21
measurement results for the four elements of the SAW phased array
with electroacoustic phase shifter biased at 60 V. . . . . . . . . . . . . . . . 115
5.15 (a) S
21
measurement results at 604 MHz and (b) corresponding phase shifts
for the four elements of the SAW phased array over bias voltage. vb5 is biased
at 30 V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
5.16 (a) Phased array measurement setup for Rx mode. (b) Outdoor measure-
ment setup with array antennas spaced at=2 for SAW phased array receiver
measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.17 Received phased array pattern for four dierent settings. . . . . . . . . . . . 117
1 New page menu in COMSOL Multiphysics. . . . . . . . . . . . . . . . . . . . 134
2 Spatial dimension menu in COMSOL Multiphysics. . . . . . . . . . . . . . . 134
3 Physics menu in COMSOL Multiphysics. . . . . . . . . . . . . . . . . . . . . 135
4 Eigenfrequency study selection in COMSOL Multiphysics. . . . . . . . . . . 138
5 Eigenfrequency simulation interface in COMSOL Multiphysics. . . . . . . . . 138
6 Dening coordinate system in COMSOL Multiphysics. . . . . . . . . . . . . 139
7 Settings for 128
o
rotated system in COMSOL Multiphysics. . . . . . . . . . . 139
8 Dening parameters or variables in COMSOL Multiphysics. . . . . . . . . . 140
9 2-D geometry for eigenfrequency simulation of IDT ngers on LiNbO
3
sub-
strate with the settings for the substrate (left), rst IDT nger (middle), and
the second IDT nger along with the simulation geometry (right). . . . . . . 141
10 Add lithium niobate to the model. . . . . . . . . . . . . . . . . . . . . . . . . 142
11 Dene gold as a material for the model. . . . . . . . . . . . . . . . . . . . . . 143
12 Periodic boundary condition dened for the model. . . . . . . . . . . . . . . 144
xvii
13 Ground boundary condition dened for the model. . . . . . . . . . . . . . . . 145
14 Dening the mesh (a) type and (b) element size for the model. . . . . . . . . 146
15 Eigenfrequency simulation settings. . . . . . . . . . . . . . . . . . . . . . . . 147
16 Eigenfrequency mode shape color setting. . . . . . . . . . . . . . . . . . . . . 148
17 Eigenfrequency mode shape color setting. . . . . . . . . . . . . . . . . . . . . 149
18 Initial parameters used for a frequency domain simulation. . . . . . . . . . . 152
19 Ground and signal electrodes of input IDT. . . . . . . . . . . . . . . . . . . . 153
20 Array settings for input IDT electrodes. . . . . . . . . . . . . . . . . . . . . 154
21 Signal electrode setting for output IDT. . . . . . . . . . . . . . . . . . . . . . 154
22 Creating a selection group for ground electrodes. . . . . . . . . . . . . . . . . 155
23 Changing the out-of-plane thickness of the model. . . . . . . . . . . . . . . . 158
24 Changing the \Electrostatics" settings for S-parameter simulation. . . . . . . 158
25 Parametric sweep settings for S-parameter simulation. . . . . . . . . . . . . . 159
26 The \Layers" option from the \Settings" menu for the substrate. . . . . . . . 161
27 Input the PML thickness and select the regions of the geometry to dene as
PML. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
28 After building the geometry, the rectangle will be divided into the regions
dened in the previous step. Then select the \Perfectly Matched Layer" option
to dene the regions as PML. . . . . . . . . . . . . . . . . . . . . . . . . . . 162
29 Select the regions to dene as PML. . . . . . . . . . . . . . . . . . . . . . . . 163
30 Add and dene material for the geometry. . . . . . . . . . . . . . . . . . . . 163
31 De-select the PML regions from being piezoelectric in the \Solid Mechanics"
physics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
32 De-select the PML regions from being piezoelectric in the \Electrostatics"
physics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
xviii
Abstract
Waveguides are used for the processing of optical and mm-wave signals. They can provide a
high-dynamic range analog signal processor in a compact form factor. However, the use of
waveguides for the analog signal processing of radio frequency (RF) signals has been dicult
to implement due to the impractically large size of waveguides at these frequencies. The size
of the waveguide is inversely proportional to the speed of that the signal propagates, which
is very large for electromagnetic (EM) waves. Thus, the use of waveguides has eluded radio
frequencies. In contrast, acoustic velocities are many orders of magnitude lower than the
speed of light at which EM waves propagate, providing a means of designing waveguides at
the relatively low frequencies RF signals occupy.
Acoustic devices are currently found in most RF devices. They are found mainly as lter-
ing elements of modern RF front-ends. In this thesis, the use of acoustic waves, specically
surface acoustic waves (SAW), is explored for going beyond ltering and expanding into fur-
ther signal processing of RF signals. This will be made possible through the use of lithium
niobate, which is a piezoelectric material that greatly simplies the generation of surface
acoustic waves. Guiding of SAWs through straight waveguides and waveguide bends will be
investigated. The investigation will look at a few metals used for designing the waveguide
as well as a brief study in the crystal cut of the lithium niobate and how it can aect the
waveguiding of SAWs. This is due to the anisotropic nature of lithium niobate, making it
have dierent properties depending on the crystal cut and direction of propagation of the
SAW.
Finally, the electroacoustic eect will be studied for its ability to change the stiness of
xix
the lithium niobate. This change in stiness causes a change in the acoustic velocity of the
propagating SAW, and this change in velocity will be used to design a SAW phase shifter.
The modulation of the acoustic velocity can also be obtained through the modulation of the
temperature of the waveguide as well. However, this method runs counter to current SAW
devices which have high temperature stability requirements while burning a considerable
amount of power. On the other hand, electroacoustic phase shifter operates like a capacitor
and therefore, does not consume power while providing the necessary phase shifts. The elec-
troacoustic eect will be demonstrated using a thin lithium niobate wafer bonded to a high
resistivity p-type silicon substrate. The modulation of the surface charges in the silicon will
be used to modulate the velocity of the SAW. This electroacoustic phase shifter will then
be implemented into a 4-element phased array, demonstrating the signal processing of RF
signals using SAW waveguides.
xx
Chapter 1
Introduction
1.1 Brief History
The study of acoustics, or sound waves, can be found throughout history generally in the
form of music such as in the study of vibrating strings by Pythagoras in the sixth century
B.C., Galileo, or Bernoulli [1]. However, it wasn't until 1701 that the word \acoustics" was
used to describe the science of sound. In 1885, Lord Rayleigh demonstrated the existence
of the basic type of surface acoustic wave, which is now known as the Rayleigh wave [2].
Lord Rayleigh was interested in the seismic movement and showed that a slow surface wave
existed that followed the bulk longitudinal and transverse waves generated by earthquakes.
In 1911, Augustus Edward Hough Love published his study on shear surface waves, which is
a surface wave with a motion that is perpendicular to the sagittal plane, as opposed to the
Rayleigh wave in which the particles move in the sagittal plane. This shear surface wave is
known as the Love wave. The propagation of the two waves is shown in Fig. 1.1.
In 1915, transducers for submarine sonars were developed using the piezoelectric eect
of quartz to generate the acoustic waves in the sea [3]. The development of acoustic devices
continued with the use of piezoelectric materials to design stable oscillators around 1920.
Surface waves were also used for non-destructive testing of metals [4]. The wars contributed
to the interest of surface acoustic waves (SAW) for radar applications, where SAWs were
used to create long delay lines for pulse compression devices [2] [5].
1
Figure 1.1: Propagation of (a) Rayleigh wave and (b) Love wave.
1.1.1 Interdigital Transducers
The transduction of SAWs was generally performed by generating bulk waves using piezo-
electric plates and then converting the bulk waves into surface waves. However, a major
breakthrough for SAW devices came in 1965 with the demonstration of the interdigital
transducer that greatly simplied the generation and detection of surface acoustic waves on
a piezoelectric substrate [3]. The concept of the IDT was proposed a couple of years earlier
in 1963 by both Rowen and Mortley but the realization of the IDT was experimentally shown
in 1965 by White and Volmer [2]. A two-port system depicting the transduction of electrical
signals to a SAW and vice-versa is shown in Fig. 1.2. The interdigital transducer, or IDT, is
a patterned metallic thin lm that is deposited on the surface of a piezoelectric substrate and
can directly generate a surface wave from an electrical signal and likewise, detect a surface
wave and convert it to an electrical signal.
2
Figure 1.2: 2-port system showing a simple interdigital transducer used for generating and
detecting surface acoustic waves.
In September of 1968, a SAW lter using delay lines and the periodic electrode IDT was
demonstrated for 100 MHz operation having 10 dB of insertion loss [6]. However, it was
found that 6 dB out of the 10 dB insertion loss was from the bidirectional nature of the
IDTs. The symmetry of the IDT, shown in Fig. 1.3(a), launches waves in both directions.
Eort into understanding and improving the IDT performance ensued. The double electrode
IDT, shown in Fig. 1.3(b) and
oating electrode IDT, shown in Fig. 1.3(c), were introduced
in 1972 [2] [7], which eliminated the triple-transit eect, which is a detrimental eect caused
by unwanted re
ected waves reaching the output IDT after three transits [3]. This triple-
transit eect was eliminated by the cancellation of the re
ected waves caused by the IDT
electrodes. However, due to the symmetric nature of the double IDT, it still launched SAWs
in both directions. In order to address this, eort was placed on making the IDT more
directional. One way was to place a re
ector behind the IDT, re
ecting the SAW back
towards the desired propagation direction [8]. Another work looked at driving the ngers of
the IDT with dierent phases to increase the directionality of the IDT while suppressing triple
transit eects [9]. Single phase unidirectional IDTs (SPUIDT) have also been demonstrated,
with an example of a SPUIDT shown in Fig. 1.3(d) [10] [11]. Eort has also been exercised
in the design of focused IDTs, shown in Fig. 1.3(e) [12] [13]. The focused IDT is combines
the IDT with a taper region that may be necessary if the propagation channel of interest
3
is narrower than the aperture width of the IDT itself. Due to the anisotropic nature of the
piezoelectric substrate, the ngers of the IDT are shaped according to the group velocity
prole of the SAW propagating in the substrate.
Figure 1.3: Examples of SAW IDT structures with (a) single electrode IDT, (b) double
electrode IDT, (c)
oating electrode IDT, (d) single-phase unidirectional IDT (SPUIDT), and (e)
focused IDT.
Also during this time period, signal processing through the patterning of IDT electrodes
was being introduced as well. In 1969, Tancrell introduced the concept of apodization [7],
which is the varying of the overlapping of IDT electrodes along the length of the transducer
[3]. An example of a desired impulse response and the corresponding apodized IDT to achieve
the desired impulse response is shown in Fig. 1.4. Other signal processing techniques such
as phase coding by using weighting techniques on IDT electrodes (Fig. 1.5(a)), passband
shaping and sidelobe control through withdrawal weighting followed (Fig. 1.5(b)). Tancrell
4
also introduced the concept of a chirp device as well, with SAW chirp devices following, such
as the slant-dispersive IDT shown in Fig. 1.6.
Figure 1.4: (a) Desired impulse response and (b) IDT electrode patterning to achieve impulse
response [7].
1.1.2 Filters and Resonators
As the development of SAW IDTs progressed, eort in the design of acoustic lters were also
being developed. A Kallman non-recursive transversal lter became a possibility when it was
found that a SAW could be electrically tapped out at arbitrary points along its propagation
path [6]. These taps could then be summed to form the lter. Commercial interest in SAW
lters came in 1970 with the use of lithium niobate to provide channel selectivity in color TV
sets. As mentioned earlier, the military also showed interest in SAW lters and devices for
pulse-compression radar systems and for spread spectrum communication systems. The use
of gratings with a half-wavelength pitch created a good SAW re
ector that could enhance
5
Figure 1.5: (a) A binary phase shift keying (BPSK) coded SAW and (b) a withdrawal weighted
IDT, where dotted shapes indicate electrodes that were removed [7].
the SAW lter performance with the proper design. A single strip has weak re
ectivity but
by arraying multiple grating strips, good re
ectivity was obtained. This also led to more
ecient SAW resonator designs for use in things like oscillators as well. Examples of 1-
port and 2-port resonators and their equivalent electrical circuits are shown in Fig. 1.7 and
1.8, respectively. The introduction of multistrip couplers, which is an array of unconnected
electrodes that are placed parallel to the SAW wavefronts, in 1971 by Marshall and Paige
allowed bandpass lters to be designed while eliminating unwanted bulk waves from being
transferred from the input to the output [14]. The multistrip coupler or MSC, shown in Fig.
1.9, acted like a directional coupler that allowed a SAW propagating on one track to transfer
to another track without transferring the bulk wave component.
In 1972, a three-transducer device was demonstrated by M.F. Lewis and is shown in Fig.
1.10 [17]. In the proposed device, when the output IDT was tuned and matched at the
6
Figure 1.6: A slanted down-chirp lter [7].
Figure 1.7: An example of a (a) one-port resonator and its (b) equivalent electrical circuit [15].
center frequency, the two SAWs approaching from opposite directions from the two input
IDTs were completely absorbed by the output IDT, thus reducing the insertion loss by 3 dB.
He further proposed that interdigitating more input and output IDTs, which he called the
interdigitated interdigital transducer, or IIDT, which he demonstrated as a bandpass lter
with a center frequency of 100 MHz and an insertion loss of 2 dB 10 years later [18]. A
disadvantage of the IIDT cited in the paper is the increased length of the device. However,
it is argued that the overall area is not signicantly increased as the longer length is oset
by the reduced aperture width.
In 1974, the idea of using SAW resonators in a ladder-type lter was published [19].
Ladder-type lters, shown in Fig. 1.11, are not new as they were patented in 1927 using
crystal resonators. An implementation of a ladder-type lter using SAW resonators was
published in 1988 that showed insertion loss down to 1 dB at 800 MHz [20].
7
Figure 1.8: An example of a (a) two-port resonator and its (b) equivalent electrical circuit [16].
8
Figure 1.9: A two-port SAW lter employing a multistrip coupler to transfer the SAW from the
top track to the bottom track, eliminating the undesirable bulk wave.
9
Figure 1.10: A three IDT SAW device with reduced triple-transit eect.
Figure 1.11: A schematic of a ladder-type lter employing SAW resonators.
In 1992, a double mode SAW (DMS) lter was presented that achieved low loss over
a wide bandwidth [21]. A simple DMS lter is shown in Fig. 1.12, presenting the inline
arrangement of input and output IDTs sandwiched between re
ectors. The DMS lter
operates by coupling two dierent longitudinal acoustic modes that are supported by the
structure and is able to function as a balun and also perform impedance transformations as
well [22].
High volume fabrication and use of SAW lters began with IF lters for televisions [22].
The SAW lters were compact compared to LC lters, and they did not require manual
10
Figure 1.12: A schematic of a double mode SAW (DMS) lter.
adjustment of the frequency response. As the IDT evolved and the losses reduced with single
phase unidirectional IDTs, IF lters found their way into GSM cellular phones. However,
with the shift of homodyne or low IF receivers, the need for IF lters diminished. However,
improvement in the loss performance of SAW lters with the use of DMS lters and ladder
type lters allowed the use of SAW lters as RF lters. The DMS lters and ladder lters
are the two lter techniques used for implementing RF lters for cellular phones.
1.1.3 Waveguides
Interest in microwave concepts applied to SAW devices garnered attention as well. The
small acoustic wave velocity was attractive in the conceptual possibility to reduce the size
of passive microwave structures that occupied the majority of the area in microwave circuits
[23]. The realization of the IDT helped spur interest in microwave acoustic waveguides
as the generation and detection of SAWs were an obstacle until then. Examples of SAW
waveguides are shown in Fig. 1.13 [23] [24] [25]. The waveguides in Fig. 1.13(a) and (b)
are known as overlay waveguides where a material is put on top of the substrate to conne
the acoustic wave. The slow region, in which a SAW will be conned, in the waveguide of
Fig. 1.13(a) can be performed by overlaying a material with a slower SAW velocity than
a wave propagating in the substrate, by electrical shorting by use of a metal, or by mass
loading where a heavy material is overlaid to slow the movement of particles under the heavy
11
material and thus, producing a slow velocity region. An example of an overlay type SAW
waveguide was experimentally veried using a thin gold strip that was deposited on a fused
quartz substrate [26]. The tested waveguide was a spiral and a dierential loss of 0.03 dB/s
was measured. On the other hand, the slow region in Fig. 1.13(b), also known as a slot
waveguide [25], is created by overlaying the outer regions, or the cladding region, with a
material that has a faster SAW velocity than the SAW velocity in the substrate alone. This
makes the outer regions faster than the center region, conning the SAW in the slow center
region. An example of a slot waveguide was published in 1974 using SiO
x
lms deposited
on (001) cut (110) propagating Bi
12
GeO
20
substrates [27]. This was a straight waveguide
comparison between a slot waveguide and a dispersionless reference delay line. However,
the focus was on dispersion and so accurate measurements of the loss between the slot
waveguide and reference delay line were not measured. A straight slot waveguide was more
recently designed and demonstrated using silicon nitride (Si
3
N
4
) on X-cut lithium niobate
as well [28]. While both types of overlay waveguides exhibit waveguiding, it seems like the
overlay waveguide of Fig. 1.13(a) maybe more dispersive than the slot waveguide of Fig.
1.13(b). The ridge waveguide in Fig. 1.13(c) connes the SAW, in the lateral directions,
in the ridge as surface waves cannot propagate in air. A ridge waveguide using ZnO to
generate SAWs on silicon was published in 2014. An S
21
of slightly more than -40 dB was
obtained at around 920 MHz [29]. It is of note that a cladding material other than air can be
utilized and if so, it is important to use a material with a faster SAW velocity than the SAW
velocity of the substrate alone. In this instance, the waveguide becomes more of the type
shown in Fig. 1.13(d). This type of waveguide can be produced by sandwiching a slow SAW
velocity material with a faster material, conning the SAW in the center region. It can also
be created by diusion or ion-implantation to make the slow center region surrounded by a
faster cladding region. One demonstration of using ion implantation to slow the SAW velocity
was performed in 1975 using lithium niobate [30]. The reduction in the SAW velocity was
mainly attributed to the reduction of the eective electromechanical coupling coecient. In
12
terms of fabrication of the waveguides, the waveguide in Fig. 1.13(a) does have an advantage
in that it can be fabricated with only 1 mask layer if the overlay material uses the same metal
and thickness as is used for the IDT design.
Figure 1.13: Examples of acoustic waveguides. (a) and (b) are examples of overlay waveguides,
(c) is a ridge waveguide, which falls under what are known as topographic waveguides, and (d) is
an example of either a cladded waveguide or in-diused/ion-implanted waveguide.
Along with waveguides, directional couplers were also explored for microwave SAW de-
vices. In 1967, a coupled waveguide based directional coupler, shown in Fig. 1.14(a), was
presented [23]. The waveguide was created by cutting two slots into the substrate, essentially
creating an air barrier that conned the SAW between the slots. An uncut region between
two such waveguides allowed the SAW to couple to the other waveguide, creating a direc-
tional coupler. In 1971, a directional coupler using periodic array of metallic grating strips
called a multistrip coupler, shown in Fig. 1.14(b), was demonstrated [14]. It is important
to note that the periodicity of the multistrip coupler must not be equal to the periodicity
of the IDT used to generate the SAW. This is to avoid the Bragg condition in which the
metal grating strips cause very strong re
ections in the frequency of interest [31] [32]. Some
grating periodicities that have been used are /4 [33] and 3/8 [34]. The multistrip coupler
was demonstrated again in 2000, along with a metallic grating-based waveguide as shown
13
in Fig. 1.15 [34]. Again, it is important that the metallic gratings of the waveguide do
not match the periodicity of the IDT so as to avoid the waveguide behaving as a re
ector.
The multistrip coupler was also demonstrated as a directional coupler for Lamb waves as
well [33].
Figure 1.14: Directional coupler using (a) coupled waveguides [23] and (b) multistrip
couplers [14].
Figure 1.15: A surface acoustic wave waveguide using periodic gratings [34].
Recent years have seen the continued exploration of guiding of surface acoustic waves. In
2014, a ridge waveguide was demonstrated for a gigahertz frequency SAW ring lter [29]. In
this work, the SAW was generated using a ZnO piezoelectric layer, and then transferred the
SAW onto germanium ridge waveguides on a silicon substrate. Periodic structures, known
as phononic crystals, that were studied in the 1960s [35], has also drawn interest once again
14
for guiding surface waves, guiding surface waves through tight bends, and for the design of
compact re
ectors [36] [37] [38]. An example of the top view of a phononic crystal waveguide
is shown in Fig. 1.16, where the periodic structures are used to create bandgaps that can be
designed to block the propagation of surface acoustic waves. They can thus be patterned in
such a way as to create openings for SAWs to pass while creating walls to conne the wave
to the openings. The patterns can be made by the addition or removal of material on the
substrate.
Figure 1.16: Top view of a phononic crystal SAW waveguide.
1.1.4 Active SAW Devices
While much of the work centers around passive SAW devices, it is of interest that active
SAW devices were explored as well. It was found that the interaction of an acoustic wave
with drifting carriers in a semiconductor in close proximity to the piezoelectric substrate
propagating the SAW, can amplify the acoustic wave, as well change the acoustic wave
velocity. This change in acoustic wave velocity can be used to design tunable SAW phase
shifters and resonators [39] [40] [41]. An example of a SAW phase shifter is shown in Fig.
1.17(a), but the phase shifter can be designed with dierent placements of the semiconductor
material. For example, here, it is designed with the piezoelectric layer bonded on top of
15
Figure 1.17: Examples of active SAW devices: (a) SAW phase shifter and (b) SAW amplier.
the semiconductor, but it can also be designed with the semiconductor layer on top of
the piezoelectric substrate as well. In the latter conguration, however, a dielectric layer
is usually placed in between the semiconducting layer and piezoelectric substrate as the
semiconductor can behave as an electrical shorting element on the surface of the piezoelectric
substrate where the SAW is propagating, aecting its performance.
An example of a SAW amplier is also shown in Fig. 1.17(b). The propagating SAW
under the semiconductor generates an evanescent eld that interacts with the drifting carriers
from the applied voltage [42]. If the charges are traveling slower than the SAW, energy
is taken from the SAW by the charges to bring them closer to the SAW velocity, thus
attenuating the SAW [43]. However, if the drift carriers are traveling at a higher velocity
than the SAW, some of its kinetic energy is transferred to the SAW, thus amplifying the
wave. While SAW amplication has been explored from the 1960s, they were not practical
due to the high power consumption and operating voltages required to operate them [44].
However, with technological advancements, practical acousto-electric devices that require a
thin semiconducting layer, low doping, high mobility, and low density of trap states have
become possible.
16
1.1.5 mm-Waves and SAW Integration
Eort is also used in pushing acoustic lters to the mm-waves to support 5G mobile com-
munications. The use of dierent piezoelectric materials such as ZnO based transducers on
silicon, or layered structures of AlN/diamond/Si or AlScN/diamond/Si, which have larger
SAW velocities [45] [46] [47], or using techniques that allow ne transducer nger widths of
35 nm [48] have pushed SAW transducer operation into the mm-wave frequencies. There
is also work towards a single-chip, all acoustic radiofrequency (RF) signal processor using
the interaction of the SAW with a semiconductor for amplication and phase shifting, and
reverse multistrip couplers to design a circulator [49].
While discussion of the study of materials used for SAW devices has not been mentioned
so far, it is important to mention the importance of the eort that went into exploring the
optimal materials to use to improve the SAW performance. The IF lters for TV were ini-
tially fabricated on ceramic substrates, ZnO on glass, single crystal X-112Y LiTa
3
, and single
crystal 128
o
Y-X LiNbO
3
. Each substrate had diering properties, but none really stood
out to be the optimal material. For example, ZnO was the most cost eective and easier to
fabricate material while LiTaO
3
had the smaller temperature coecient of frequency (TCF)
and LiNbO
3
had the higher piezoelectric coupling factor. At the end, LiNbO
3
prevailed as
the substrate for TV IF lters. Study in achieving better temperature stability was also
on-going as well. In 1974, it was found that a thin SiO
2
layer on the YZ LiNbO
3
and
YZ LiTaO
3
could bring the rst order temperature coecient of time delay to zero. Other
works showed thin SiO
2
layers improving the temperature stability of SAW devices on other
LiNbO
3
and LiTaO
3
cuts as well. In 1996, direct bonding of a piezoelectric substrate to a
glass wafer showed the TCF reducing as well. Along with temperature performance, other
works showed improvement in re
ector performance and reduction of spurious modes with
dierences in the electrode metal thicknesses. Material investigations also played a large role
in improving SAW performances and is an active area of research for pushing SAW devices
to higher frequencies and/or to new applications.
17
1.2 Dissertation Outline
Surface acoustic wave devices have been a staple in communication systems and are known
for their low loss and high quality factor ltering capabilities [50]. They can be found
as highly selective lter components and duplexers in radio-frequency front-end modules
(RFFE) [22]. An illustrative RFFE employing frequency division duplexing and supporting
several dierent bands is shown in Fig. 1.18. The small form factor of SAW devices is due
to the relatively small wave velocity of acoustic waves compared to electromagnetic waves.
For example, in lithium niobate, the SAW velocity for a 128
o
Y-cut x-propagating wave is
about 3979 m/s [3]. As will be shown in later chapters, the wavelength of a signal at 600
MHz is about 6 m. In comparison, an RF signal propagating in free space will travel at
the speed of light at approximately 2.998x10
8
m/s and will have a wavelength of about 0.5
m. Due to the dierence in wave velocity, the wavelength of a SAW device is many orders of
magnitude smaller than its electromagnetic wave counterpart. The small form factor is what
allows banks of acoustic lters to be used in mobile devices to support the large number of
frequency bands used today. And while SAW devices are generally considered as lters for
communication systems and devices, they are also nding use in a wide range of applications
from micro
uidics, sensors, cell manipulation and quantum acoustics [51].
The continued use of SAW devices, as well as the growing applications for SAW devices,
has drawn interest in the design of SAW devices to perform complex signal processing.
This dissertation investigates waveguiding of surface acoustic waves at radio frequencies,
borrowing many concepts from their electromagnetic counterparts, and examines the design
of several waveguide components, and ultimately, combining them to design an RF phase
array system using only SAW waveguides. Chapter 2 will introduce the mathematics that
govern surface acoustic waves, the wave equation, and nally, the principles of waveguiding of
surface waves. A discussion on the interdigital transducer will follow, along with a discussion
of some of the basic SAW lters.
Chapter 3 will discuss the design of basic SAW waveguide components. These components
18
Figure 1.18: An illustrative schematic of a radio-frequency front-end module supporting
multiple frequency bands.
19
include the interdigital transducer, which converts RF signals to surface acoustic waves,
straight waveguides, waveguide bends, and nally the waveguide coupler. The analyses
of the dierent components were performed using COMSOL Multiphysics. Prototypes of
the components were designed and fabricated on a 128
o
Y-cut lithium niobate (LiNbO
3
)
substrate and the measurements of these components will also be presented.
Chapter 4 will introduce active SAW devices, namely phase shifters, using both a thermal
method and also a charge-based method. While the thermal phase shifter was designed on
128
o
Y-cut LiNbO
3
, the charge-based method requires the use of a semiconductor as well.
This can be done by either using a semiconductor with piezoelectric properties or by bonding
a piezoelectric lm onto a semiconducting substrate. To maintain continuity with the designs
so far, the second method was adopted and wafers with a LiNbO
3
layer bonded to a silicon
wafer were used. Prototypes of both a thermal phase shifter and a charge-based phase shifter
were fabricated and measurement results are presented.
The nal chapter considers two case studies that demonstrate an all-acoustic system
performing complex signal processing of surface acoustic waves. The rst case study is a
design and demonstration of a 4-element phased array system operating in the acoustic
domain while the second case study looks at an all-acoustic RF interference cancellation.
While much work has been performed for this dissertation, it only provides a steppingstone
in opening up the full capabilities of waveguiding of surface acoustic waves. The dissertation
concludes with suggestions for future work in continuing to develop RF signal processing of
surface acoustic waves.
20
Chapter 2
Background
As the name suggests, surface acoustic waves travel along the surface of an elastic material,
which are materials that can undergo deformation but revert back to its original state after
the force causing the deformation is removed [52]. As a surface wave propagates, changes
in the relative positions of the atoms occur [3]. These changes are described in terms of
strains. Strain, in turn, creates stresses, which are the internal forces that are generated
by the strain experienced by the material. When a material undergoes some strain, this
generates stress. This generated stress will then produce a strain further down the material,
and this propagation of strains and stresses, creating an acoustic wave. Acoustic waves that
propagate along the surface of the material are known as surface acoustic waves, which is
the focus of this thesis. There are also waves that propagate freely inside the material as
well, which are known as bulk waves.
While the eld of surface acoustic waves is very mature, there is still much work in the
study of surface acoustic waves, whether it is pushing the devices to higher frequencies,
application to other elds, or expanding acoustic signal processing towards the holy grail
envisioned in the past of an all-acoustic chip. Technological advances have made what
once was impossible possible while ever expanding applications have made what once may
have been impractical practical and useful. The study of surface acoustic waves starts
with a mathematical formulation describing the motion and propagation of the wave, which
will be introduced in this chapter. The mathematical formulation will be followed by the
21
introduction of the interdigital transducer, which is the heart of surface acoustic wave devices
as this device greatly simplies the transduction of electrical signals to surface acoustic waves
and vice versa. Finally, the chapter concludes with a review of SAW lters which is the
dominant SAW device in use today.
2.1 Physics of Surface Acoustic Waves
Unfortunately, the notation used can be dierent between dierent textbooks used. For
the purposes of this thesis, strain will be represented by S, and stress by T [3] [53] [54]. To
simplify the discussion, the one-dimension case will rst be introduced for a non-piezoelectric
material, followed by the 3-dimensional case. Afterwards, the piezoelectric eect will be
introduced into the equations.
2.1.1 1-D Equation
In Fig. 2.1, a 1-D material extends in the +z direction. A particle in the material has an
equilibrium of x and after being displaced by an amount u, the particle's new position is x'
= x + u. Following the derivation found in [54], the rst order Taylor expansion component
of the displacement in a length L is found to be
u =
@u
@z
L =SL: (2.1)
The fractional displacement of the material
@u
@z
is dened as the strain.
The displacement of particles in a material is associated with force. The quantity of
force, force per unit area in 3-D, is known as stress, which as mentioned earlier is denoted
as T. The stress is positive if applied in the +z direction and is negative if applied in the -z
direction, as illustrated in Fig. 2.2. From Hooke's law, the stress is proportional to strain
through the elastic constant of the material, c,
22
Figure 2.1: 1-D displacement of a particle.
T =cS: (2.2)
If the stress and strain are a unit of time, the motion of the particles in the material
follows Newton's laws. The net translational force applied to the 1-D material in Fig. 2.2 is
L
@T
@z
, and Newton's second law is found to be
@T
@z
=m
0
@
2
u
@t
2
=m
0
u; (2.3)
where m' is the linear mass density. This is the 1-D equation of motion. For describing
motion, it is much more convenient to write the equation in terms of motion instead of
stress. Using equation 2.2 and that the fractional displacement,
@u
@z
, is the strain, the 1-D
equation of motion can be rewritten as:
c
@
2
u
@z
2
=m
0
@
2
u
@t
2
=m
0
u: (2.4)
2.1.2 3-D Equations
A similar formulation as the 1-d case will be used to arrive at the equation of motion for
the 3-d case. The Cartesian coordinate system will be used with x = (x, y, z) being the
position of a particle in the material and u = (u
x
, u
y
, u
z
) the displacement of the particle
23
Figure 2.2: 1-D illustration of stress applied on a particle.
from its equilibrium state. Similar to the 1-D case, u
x
, u
y
, and u
z
are generally a function
of the coordinates x, y, and z. As u represents the displacement of a particle, if x is the
equilibrium position of a particle, the new position of the particle will be x + u after being
displaced. Now, the strain at each point in the material is dened by [3]
S
ij
(x;y;z) =
1
2
(
@u
i
@j
+
@u
j
@i
); i;j =x;y;z: (2.5)
It is of note that equation 2.5 is an approximation of [54]
S
ij
(x;y;z) =
1
2
(
@u
i
@j
+
@u
j
@i
+
@u
k
@i
@u
k
@j
); i;j =x;y;z: (2.6)
However, for small displacements, the last term is small and is ignored. Another thing to
note is that strain is a second-rank tensor and is symmetrical such that
S
ij
=S
ji
(2.7)
Stress, which are the internal forces within the material, represented by T
ij
(x, y, z), is
also a second rank tensor and is also symmetric such that
T
ij
=T
ji
(2.8)
24
Similar to the 1-d case, the strains and stresses are proportional to each other through the
stiness tensor of the material, c
ijkl
, as:
T
ij
=
X
k
X
l
c
ijkl
S
kl
; i;j;k;l =x;y;z: (2.9)
It is of note that the stiness tensor subscripts are interchangeable as follows:
c
ijkl
=c
jikl
;c
ijkl
=c
ijlk
;andc
ijkl
=c
klij
: (2.10)
The forces on a face of a cube in the material is
+
2
T
ij
, and the equation of motion is
found to be:
@
2
u
i
@t
2
=
X
j
X
k
X
l
c
ijkl
@
2
u
k
@j@l
; i;j =x;y;z; (2.11)
where is the mass density of the material.
For piezoelectric materials, the stress component has a dependence on the electric eld
E. This dependence is added to equation 2.9 as:
T
ij
=
X
k
X
l
c
ijkl
S
kl
X
k
e
kij
E
k
; i;j;k;l =x;y;z: (2.12)
where e
kij
is the piezoelectric tensor that relates the elasticity of the material to the electric
eld. Similar to the stiness tensor, the piezoelectric tensor has symmetry such that
e
ijk
=e
ikj
(2.13)
Likewise, the electric displacement is determined by the electric eld and to the strain as
D
i
=
X
j
ij
E
j
+
X
j
X
k
e
ijk
S
jk
; i;j;k =x;y;z: (2.14)
25
ij
is the permittivity tensor of the piezoelectric material. Another form of equation 2.14
relates the electric displacement in terms of stress instead of the strain as
D
i
=
X
j
ij
E
j
+
X
j
X
k
d
ijk
T
jk
; i;j;k =x;y;z: (2.15)
Now for piezoelectric materials, the stiness tensor in equation 2.12 and the permittivity
tensor in equation 2.14 are actually expressed as c
E
ijkl
and
S
ij
, respectively. The superscript
\E" for the stiness tensor signies the coecients are under constant electric eld while
the \S" in the permittivity tensor signies the tensor is for constant stress. It is signicant
that the stiness tensor is for a constant electric eld as it signies that the stiness can be
modulated by changing the electric eld.
The electric eld can also be included in the equation of motion. However, instead of
using the electric eld directly, the equation of motion is often written in relation to the
electric potential, which is related to the electric eld as
E
i
=
@
@i
; i =x;y;z: (2.16)
Using equation 2.16, the equation of motion then becomes
@
2
u
i
@t
2
=
X
j
X
k
[e
kij
@
2
@j@k
+
X
l
c
ijkl
@
2
u
k
@j@l
]; i;j;k;l =x;y;z: (2.17)
The solution of the equation of motion takes the form
u =e
j(!tkx)
; (2.18)
where is a constant vector and k is the wave vector (k
x
, k
y
, k
z
) that gives the direction of
propagation, as shown in Fig. 2.3.
26
Figure 2.3: Propagating surface acoustic wave with axes.
Numerical methods are required to solve the equation of motion. In this work, nite
element method was employed through the use of COMSOL Multiphysics to study and
design surface acoustic wave waveguide structures.
2.2 Material Properties
Piezoelectric materials are anisotropic, which means that the properties of the material
change depending on its orientation and direction [3]. Single-crystal materials are generally
used for SAW devices as they can provide lower losses. Some important parameters when
considering the piezoelectric material for SAW devices are the wave velocities, piezoelectric
coupling, diraction, attenuation, and the level of undesirable bulk wave generation. While
not discussed in this work, temperature eects are also a very important parameter to
consider in order to meet temperature stability specications. Some crystals can provide good
loss performance while having poor temperature stability and vice versa. There are methods
to improve the temperature stability by layering material with the opposite temperature
coecients of the piezoelectric material to improve the temperature stability of the device
as well [55].
The piezoelectric coupling coecient is dened by a parameter K
2
and is a measure of
the eciency in which the piezoelectric material converts an electrical signal into mechanical
energy [53]. K
2
is given by
27
K
2
= 2
v
f
v
m
v
f
; (2.19)
where v
f
is the SAW velocity on a free surface while v
m
is the SAW velocity of a very thin
(mass-less) highly conducting metal lm. The idealized thin metal is to remove the mass
loading eect, which is the loading down and dampening of the SAW, reducing its velocity.
Diraction, which is the transverse spreading of the SAW as it propagates, is an eect
that is also experienced in optics as well. It is an undesirable eect as the insertion loss
of the SAW increases as the wave diverges outward. The eect is more pronounced in IDT
structures with narrow apertures. There is a distance from the IDT in which the wave roughly
maintains the aperture width while experiencing relatively little diractive eects [3] [53].
This is known as the near-eld. Beyond this distance, the diractive eects become more
pronounced. This region is known as the far-eld. Many SAW devices remain in the near-
eld and so experience relatively small diractive losses. Increasing the IDT aperture can
help minimize the losses experienced through diraction by extending the near-eld region
further out from the IDT. However, this increases the electrical conductive losses due to the
electrical signal having to propagate further in the thin, narrow lossy metal electrodes.
Another eect that increases the loss of the SAW is what is known as the beam steering
eect. Normally, one expects the SAW to propagate in the direction the IDT electrodes are
facing. However, depending on the anisotropic properties of the piezoelectric material, the
wave can propagate at an angle from the normal of the wavefront. This eect is known as
beam steering and is an eect that occurs in the near-eld region. As such, it is important
to orient the IDTs such that the wavefront normal is aligned along the symmetric axis of the
piezoelectric material so as not to experience any losses due to beam steering. The beam
steering eect is illustrated in Fig. 2.4.
28
Figure 2.4: Beam steering eect.
2.3 Interdigital Transducers
As mentioned in chapter 1, surface acoustic waves can be excited through the electrical
excitation of metal patterned on a piezoelectric substrate as shown in Fig. 2.5. The IDT
has been studied extensively since its introduction in 1965. The design of the IDT has many
degrees of freedom such as the electrode or nger width and height, electrode phase, electrode
position, and material choice like the metal used for the IDT as well as the piezoelectric
material [7]. The most basic is the single electrode IDT that was shown in Fig. 1.3a. The
pitch between two ngers or electrodes is half a wavelength, having an overall periodicity of
a wavelength.
An eigenfrequency simulation can be performed in COMSOL to visualize the mode shape
as well as to simulate the frequency of the SAW. Figure 2.6a shows a cut-out of the simulation
setup. The substrate will have a width equal to the wavelength of interest with periodic
boundary conditions applied on both the left and right boundaries. The IDT ngers for
a single electrode IDT has a width of a quarter-wavelength and pitch of half wavelength.
The wavelength, or periodicity of the IDT nger pair, determines the frequency of the SAW
through the inverse relationship
29
Figure 2.5: Single electrode IDT on a piezoelectric substrate.
f =
v
; (2.20)
where v is the velocity of the propagating SAW. It is of note that the nger width of
the IDT does not have to be a quarter wavelength and can be optimized to enhance its
performance, such as to minimize the harmonic response [53]. Likewise, the thickness of the
IDT nger can be optimized for impedance and mass-loading discontinuities.
In Fig. 2.6b, the SAW symmetric mode, or even mode, and anti-symmetric mode, or odd
mode, for a Rayleigh wave are shown. The two eigenfrequencies represent the stopband edges
of the SAW for an IDT with innite electrodes [56] [57]. This means that as the number of
electrodes increases, the bandwidth decreases, as seen in Fig. 2.7, where the shape of the
transducer frequency response is approximated by a sinc function [3].
The center frequency of the transduced SAW can be determined by
f
o
=
f
even
+f
odd
2
; (2.21)
where f
even
and f
odd
represent the even and odd mode eigenfrequencies, respectively. The
eigenfrequencies can be used to calculate the re
ectivity of an IDT electrode as
30
Figure 2.6: (a) Dimensional setup for an IDT eigenfrequency simulation in COMSOL. (b)
Eigenfrequency simulation result showing the symmetric (left) and anti-symmetric (right) SAW
modes.
Figure 2.7: Normalized transducer response for IDT nger pairs of 1, 10, and 100.
=
f
even
f
odd
f
even
+f
odd
: (2.22)
The re
ectivity of the electrode is an important parameter as each electrode, or nger, of
the IDT presents a discontinuity where re
ections occur. The re
ectivity of each electrode
is generally small but strong re
ections can be obtained with large numbers of electrodes.
When the number of electrodes, N, increase such that Njj >1, then strong re
ections
occur [3].
The IDT admittance can be modeled as
31
Y =G
a
(!) +jB
a
(!) +j!C
t
; (2.23)
where G
a
(!) is the conductance, B
a
(!) is the susceptance, and C
t
is the capacitance that
dominates the electrical admittance [3]. Figure 2.8 shows the equivalent circuit model of
the IDT showing the conductance, susceptance, and capacitance in parallel. At the center
frequency, the conductance is expressed as
G
a
(f
o
) = 8K
2
f
o
C
p
N
2
p
; (2.24)
where K
2
is the piezoelectric coupling coecient, C
p
is the capacitance of 1 periodic section
of the IDT, and N
p
is the number of periodic sections of the IDT [58]. The capacitance, C
t
,
is expressed as
C
t
=N
p
C
p
; (2.25)
and the IDT admittance at the center frequency is
Y (f
o
) =G
a
(f
o
) +j2f
o
C
T
: (2.26)
The admittance of the IDT can be used to improve the electrical matching of the IDT, and
thus reduce the insertion loss of the device as well [3].
2.4 SAW Filter Designs
As mentioned in chapter 1, SAW devices are widely known as front-end lters for radio-
frequency devices. In the early stages of the cellular era, lter structures known as interdigi-
tated interdigital transducer (IIDT) type lters, shown in Fig. 2.9(a), were mainly used [59].
Along with the IIDT SAW lter, double mode SAW (DMS) and ladder-type SAW lters
were also introduced and are shown in Fig. 2.9(b) and (c), respectively. The DMS lter
32
Figure 2.8: Equivalent circuit of the IDT.
couples two identical resonant modes in the longitudinal direction. The ladder-type SAW
lter utilizes SAW resonators arranged in series and parallel as shown in Fig. 2.9(c) and
generally exhibits the lowest loss, wider bandwidth, and better linearity among the three
types of lters. Table 2.1 tabulates a few of the SAW lters and their performances.
Table 2.1: SAW Filters
Reference Year Filter Type Freq. (GHz) Insertion Loss (dB) Piezoelectric Material
[60] 1993 IIDT 0.5 1.8 36
o
YX LiTaO
3
[61] 1995 IIDT 2 1.19 128
o
YX-LiNbO
3
[62] 1999 IIDT 0.9 2.3 LiNbO
3
[63] 1997 DMS 0.95 2.9 42
o
YX LiTaO
3
[64] 2000 DMS 0.29 < 3 64
o
YX LiNbO
3
[65] 2007 DMS 1.9 2.9 42
o
YX LiTaO
3
[66] 2015 DMS 0.3 3 42
o
YX LiTaO
3
[67] 1996 Ladder 0.9 1.2 36
o
YX LiTaO
3
[68] 1999 Ladder 3.15 1.7 LiTaO
3
[69] 2003 Ladder 0.94 - 0.958 < 0.5 128
o
YX LiNbO
3
[70] 2009 Ladder 2.4 < 1.5 LiTaO
3
[71] 2018 Ladder 3.5 < 1.7 50
o
YX LiTaO
3
[72] 2021 Ladder 1.281 0.8 15
o
YX LiNbO
3
/SiO
2
/Si
33
Figure 2.9: (a) Interdigitated interdigital SAW lter, (b) double mode surface acoustic wave
lter, and (c) ladder-type SAW lter made with SAW resonators.
34
2.5 Summary
This chapter brie
y covered the physics of surface acoustic waves, introducing the equation
of motion for SAWs. It then went on to discuss some of the eects that need to be considered
when determining the piezoelectric substrate to use. Generally, a high piezoelectric coupling
coecient is desirable to minimize loss. The anisotropy of the material must also be con-
sidered as the beam steering eect can have a detrimental eect on the performance of the
device as the wave propagates at an angle that is not normal to the face of the IDT. This can
increase the loss, or worse, have the SAW completely not intersect with the output IDT in
a two-port device. The chapter then discussed the interdigital transducer before concluding
with a summary of SAW lters.
35
Chapter 3
SAW Waveguides
While surface acoustic waves are widely used as RF lters, the relatively small wave velocities
make it possible to achieve a large delay in a relatively compact size. Generally, delay
lines have been fabricated as straight, un-guided gap between the input and output IDTs.
However, much larger delays can be achieved if SAWs can be guided and propagated through
bends without incurring large losses. These large delays can be used to process RF signals,
for example, in a phased array system. In this chapter, the general concepts of guiding SAWs
will be discussed.
3.1 Concepts of SAW Waveguiding
Similar to the IDTs, a SAW waveguide can have many shapes and forms. In the most general
sense, a SAW waveguide can be designed by adding material on to the piezoelectric substrate
or by removal of parts of the piezoelectric substrate. The dierent types of waveguides were
introduced in chapter 1 but shown again in Fig. 3.1. The waveguides in the gure fall into
overlay type waveguides where a material is added to the piezoelectric substrate to create the
connement region (Fig. 3.1 (a), (b), and (c) or topographic waveguides (Fig. 3.1(d) [25].
While the connement in the topographic waveguide in Fig. 3.1(c) [29] occurs as surface
acoustic waves cannot propagate in air, the overlay type waveguides work similarly to elec-
tromagnetic waveguides. The overlay type SAW waveguide in Fig. 3.1(a) can be designed by
36
Figure 3.1: Examples of acoustic waveguides. (a) and (b) are examples of overlay waveguides,
(c) is a ridge waveguide, which falls under what are known as topographic waveguides, and (d) is
an example of either a cladded waveguide or in-diused/ion-implanted waveguide.
either mass loading the connement region with a heavy material or by shorting the electric
eld through the use of a metal, creating a velocity dierential between the waveguide region
and the surrounding region [25] [26]. The waveguide region in eect will have a higher index
of refraction, and thus connes the SAW in the slow velocity region. On the other hand, in
the overlay waveguide of Fig. 3.1(b), a material that has a faster acoustic velocity compared
to the substrate is placed over the \cladding" region, or the region outside where waveg-
uiding should occur [27]. This creates a SAW velocity dierential by increasing the velocity
in the cladding region, thus creating a slow region as shown in the gure and conning the
SAW in the slow region.
The substrate material used for this study is a 128
o
Y-cut lithium niobate (LiNbO
3
)
with the main propagation direction being in the X-direction. The 128
o
YX-LiNbO
3
has a
relatively high piezoelectric coupling coecient as well as lower bulk wave generation [3]. A
SAW generated on 128
o
YX-LiNbO
3
also doesn't have any beam steering eects that can
have a detrimental eect on the performance of the propagating SAW. In order to keep the
fabrication simple and minimal, only one mask was used in this work. This limited the
37
structure to an overlay type waveguide structure such as shown in Fig. 3.1(a) or (b). It also
constrained the overlay material to be the same material and thickness as the IDT, limiting
the waveguide structure to the one shown in Fig. 3.1(a). Note that these constraints are
not necessary. With this limitation in mind, aluminum, tungsten, and gold were used as the
metallization materials in this investigation. Aluminum is a light metal with a mass density
of about 2,700 kg/m
3
while tungsten and gold are heavier metals with both having mass
densities around 19,300 kg/m
3
[73] [74] [75]. While tungsten and gold have similar mass
densities, the two dier in their electrical conductivities and stiness properties, with gold
being more electrically conductive having a smaller Young's modulus compared to tungsten.
These properties are summarized in Table 3.1. The eect of the SAW velocity between the
three metals were simulated using COMSOL Multiphysics and plotted in Fig. 3.2, alongside
the relative refractive index as well. As expected from the dierent mass densities, aluminum
only has a small eect on the SAW velocity, indicating that a waveguide designed using alu-
minum will most likely not conne the SAW well compared to waveguides using tungsten
or gold. Also from simulations, it seems like the dierence in the Young's modulus between
tungsten and gold plays a large role in gold showing a larger change in velocity with metal
thickness compared to tungsten. Taking into account the relative refractive index, and the
fabrication limits for resolving the IDT periodicity, a thickness of 100 nm was chosen for the
target frequency of 600 MHz.
Table 3.1: Overlay Metal Properties
a
Metal Aluminum (Al) Gold (Au) Tungsten (W)
Mass Density (kg/mm
3
) 2700 19320 19250
Young's Modulus (GPa) 68 77 400
Poisson's Ratio 0.36 0.42 0.28
Electrical Conductivity (S/m) 3.7x10
7
4.545x10
7
1.77x10
7
a
www.matweb.com
The width of the waveguide is determined by analyzing dispersion curves of the waveguide
structure. The dispersion curves for gold metallization for a few waveguide widths are shown
38
Figure 3.2: SAW velocity and corresponding refractive index for aluminum, tungsten and gold
overlay waveguides with = 6.56 m.
in Fig. 3.3. The blue curve represents the Rayleigh mode of interest while the black curves
represent higher order modes. The red line indicates the frequency of a Rayleigh wave
excited by an IDT with an aperture width of 100 m. For waveguides with a large aperture
width, the cut-o frequencies of higher order modes actually decrease, causing the modes
to concentrate together, making it possible for the excitation of these modes and increasing
the loss of the waveguide. From the dispersion curves, a waveguide with a width of 6 m
supports the Rayleigh wave while staying below the cut-o frequency of higher order modes
and is the design width chosen for the waveguides in this work.
A frequency domain simulation was performed to compute the connement of the waveg-
uide for dierent overlay materials of width 6 m and 100 nm thickness. As shown in Fig.
3.4(a), the strain energy was computed in the three monitors. The monitor is a 3D box in
the substrate with width and thickness of a wavelength and height equal to the aperture of
the waveguide. The ratio of the energy in the monitor under the waveguide over the energy
39
Figure 3.3: SAW waveguide dispersion curves using gold metallization. The blue curve represents
the Rayleigh wave while the black curves represent higher order modes. The wavelength used for
the analysis is 6.56 m with 100 nm gold thickness and waveguide widths of (a) 3 m, (b) 6 m,
(c) 12 m, and (d) 24 m.
over the three monitors is computed as the connement factor. As shown in Fig. 3.4(b),
gold has the best connement while aluminum has the worst connement among the three
metals.
A 3D eigenfrequency simulation was performed to analyze the SAW center frequency for
a single-electrode IDT structure with 100 nm thick gold electrodes on 128
o
YX LiNbO
3
.
The odd and even modes of the Raleigh wave and shown in Fig. 3.5. Using equation 2.21,
the center frequency is calculated to be 559 MHz. To compare the waveguiding properties
between aluminum and gold, designs with both aluminum and gold were fabricated.
Unfortunately, due to the size of the structures, it is not possible to simulate the en-
tire waveguide structure with the IDTs, waveguide taper, and the waveguide. Instead, the
structure is broken into smaller sections and analyzed separately. Equation 2.24 was used
to analyze the conductance, and hence the resistance at resonance, of the IDT. To minimize
40
Figure3.4: (a) Simulation setup for computing waveguide connement with (b) simulation results
for aluminum, tungsten, and gold for the waveguide overlay material.
Figure3.5: 3D COMSOL eigenfrequency simulation result for 128
o
YX LiNbO
3
with 100 nm gold
IDT electrodes and = 6.56 m.
41
external components, the IDT was designed to provide 50-
impedance matching so mea-
surements can be performed without an external impedance matching network. Equation
2.24 was modied such that
G
a
(f
o
) = 8K
2
f
o
WC
p
N
2
p
(3.1)
where W is the aperture width of the IDT and C
p
is the capacitance of an electrode pair per
unit aperture width of the IDT. A 2D simulation of the IDT, using the out-of-plane depth
parameter for the scaling of the IDT aperture width, was performed and the capacitance per
unit width of the electrode pair was calculated from the simulated admittance, as shown in
Fig. 3.6. Fig. 3.7 plots the number of nger pairs needed to achieve a resistance of 50
for
a given aperture width. For small aperture widths, the IDT requires a large number of nger
pairs in order to achieve a 50
resistance. As discussed in chapter 2, the SAW bandwidth
narrows as the number of IDT ngers increases. While the number of IDT nger pairs can be
reduced by using a large aperture width, increasing the aperture width beyond 100m or so
becomes less benecial as the rate of reduction in the number of nger pairs begins to taper
o. In this design, the aperture width of about 100 m has been chosen to allow a good 50
match. A 3D simulation was performed in COMSOL to simulate the S11 performance of
a 100 m wide, 24 electrode pair IDT having a wavelength of 6.56 m and using 100 nm
thick gold on 128
o
YX LiNbO
3
, with the simulation setup and S11 result shown in Fig. 3.8.
The S11 is better than -10 dB around the expected SAW center frequency.
While most of the designs used the single-electrode IDT, the initial design used an elec-
trode width controlled (EWC) IDT, which is a single-phase unidirectional IDT [76]. A
diagram of the EWC IDT is shown in Fig. 3.9(a). A simple 2D frequency domain of a
131 m aperture width, 32 period EWC IDT was simulated in COMSOL and the loss of
the forward and backward waves were measured using 24 period single-electrode IDTs. The
simulation result is shown in Fig. 3.9(b). At the center frequency of 559 MHz, the loss dif-
ference between the forward and backward wave is about 9.3 dB, showing the unidirectional
42
Figure 3.6: Plot of IDT electrode pair capacitance vs. aperture width.
Figure 3.7: Plot of IDT resistance vs. aperture width.
43
Figure 3.8: (a) 3D COMSOL drawing of IDT with = 6.56 m, aperture width = 100 m, and
24 100 nm thick gold electrode pairs and the (b) corresponding S11 simulation result.
Figure 3.9: (a) Diagram of an electrode width controlled single-phase unidirectional IDT. (b) A
2D COMSOL frequency domain simulation result of the EWC IDT, showing the loss of the forward
and backward propagating wave.
behavior of the IDT. The return loss of a 32 period EWC IDT with an aperture width of
about 130 m and 100 nm thick gold was simulated, and the result is shown in Fig. 3.10.
The simulation result shows a S
11
better than -10 dB.
3.1.1 Straight Waveguides
A 3D simulation was performed to estimate the loss of the waveguide. A simplied 2D
drawing of the setup is shown in g. 3.11. There is a perfectly matched layer (PML) on
all ve sides of the substrate in the actual 3D simulation. A spot frequency simulation was
44
Figure 3.10: Return loss simulation result for an EWC IDT with 32 periods, 130 m aperture
width, and 100 nm thick gold on 128
o
YX LiNbO
3
.
Figure 3.11: A simplied 2D simulation setup for estimating straight waveguide loss.
performed for aluminum, tungsten, and gold overlay metals for a SAW wavelength of 6.56
m, thickness of 100 nm, and with the monitors separated by 500 m. The estimated loss
for each metal is about 0.26 dB/mm, 0.51 dB/mm, and 0.4 dB/mm for aluminum, tungsten,
and gold, respectively. While aluminum waveguides have been shown to not conne the
SAW as well as tungsten or gold, it exerts less mass loading as well. Therefore, a SAW
propagating in an aluminum overlaid waveguide experiences less dampening, which exhibits
as less loss for straight waveguides [77].
45
Figure 3.12: Simulation setup for analyzing waveguide bend with waveguide width = 6 m.
3.1.2 Waveguide Bends
To understand the propagation properties of SAW waveguide bends, a series of COMSOL
simulations were conducted. Figure. 3.12 shows the setup for a 180
o
bend structure. The
monitors are 3D boxes in the piezoelectric substrate in which quantities such as the strain
energy can be measured at the input and output of the 180
o
bend. The loss is then computed
by taking the ratio of the strain energy between the input and output monitors. Figure 3.13
shows the displacement of the SAW propagating through a bend designed using a 100 nm
thick gold waveguide with a width of 6 m and bend radius of 200 m on a 128
o
Y-cut
LiNbO
3
. While most of the wave is conned in the waveguide, radiation loss is observed as
some of the wave can be seen propagating out of the waveguide, resulting in increased loss.
The displacement plot also indicates a possible mode conversion loss from the top straight
section to the beginning of the waveguide bend.
The loss of the bend for a SAW with a wavelength of 6 m, and a 100 nm thick gold
overlay was simulated for dierent bending radii, with the results plotted in Fig. 3.14. While
the simulation shows that a SAW can be guided through a waveguide bend, it also shows
that a fairly large bending radius is required in order to minimize the insertion loss.
46
Figure 3.13: Total displacement simulation result for 180
o
bend for waveguide width = 6m and
bend radius of 200 m.
Figure 3.14: Simulation result for 180
o
bend for = 6 m and waveguide width = 6 m.
47
3.1.3 Waveguide Taper
A waveguide taper is used to mate the wide aperture IDT to the narrower-width waveguide,
as shown in Fig. 3.15(a). A linear taper is simulated by using simplied IDTs at both ends
of the taper and measuring the power loss. The loss of the linear taper across dierent taper
lengths is plotted in 3.15(b). Based on the simulation results, the optimal taper length is
around 1 mm.
Figure 3.15: (a) Waveguide taper simulation setup mating an aperture width of w
IDT
on to
w
wg
, corresponding to the IDT aperture widths and waveguide aperture widths, respectively. (b)
Simulated loss for w
IDT
of 100 m and w
wg
of 6 m over taper length of L
t
.
3.1.4 Multistrip Coupler
A coupler is a useful device that can be used to either split a surface acoustic wave or to
combine surface acoustic waves together. One structure that can perform this function is
known as the multistrip coupler (MSC) [14] [78] [31] [34]. The multistrip coupler, shown in
Fig. 3.16, can transfer some or all of the SAW from track 1 to track 2 depending on the
transfer length, L
T
.
The operation of the multistrip coupler can be understood by the decomposition of the
in-coming SAW into a symmetric mode, or even mode, and an antisymmetric mode, or odd
mode [78] [33]. As the SAW propagates through the multistrip coupler, it produces potential
dierences on adjacent metal strips. This potential propagates down to the lower track to
launch a SAW in the lower half of the coupler. Now the even and odd modes propagate at
48
Figure 3.16: Schematic diagram of a multistrip coupler.
dierent velocities and as they propagate through the coupler, these two modes beat. At the
right coupling length, the beating of modes will cause the SAW in the top half of the coupler
to cancel and only leave the SAW propagating in the lower half of the coupler. Figure 3.17
illustrates this decomposition of modes for a multistrip coupler.
The transfer length, L
T
, for 100% coupling from track 1 to track 2 can be calculated
as [78]
L
T
=
K
2
(3.2)
where is the SAW wavelength and K
2
is the piezoelectric coupling coecient given in Eq.
2.19. The piezoelectric coupling coecient for 128
o
Y-cut LiNbO
3
with an X-propagating
SAW, or 128
o
YX LiNbO
3
, is found to be 5.4% [3]. Simulations using COMSOL show that
49
Figure 3.17: SAW decomposed into even and odd modes in a multistrip coupler.
this is for a metal plate, as shown in Fig. 3.18. A similar simulation for metal strips was
performed and the piezoelectric coupling coecient was found to be about 3.9%, as shown
in Fig. 3.19. For a wavelength of 6 m using 100 nm thick gold on 128
o
YX LiNbO
3
, and
using a K
2
value of 3.9%, the transfer length is calculated to be about 152m and therefore,
a 3-dB coupler would be about 78 m in length.
3.1.5 Coupled Waveguides
A structure that operates similarly to the multistrip coupler is the waveguide coupler. A
waveguide coupler is an important microwave structure and was studied for use with surface
acoustic waves. Similar to multistrip couplers, waveguide couplers can be used to split
and combine waves, with the coupling coecient depending on the length of the coupler
and the gap between the two waveguides [79]. The behavior of the waveguide coupler is
similar to the multistrip coupler in that the beating of the two modes eventually leads to
the SAW crossing over from one waveguide to the other. The coupling length was simulated
by nding the symmetric (even) and anti-symmetric (odd) modes of a coupler structure
50
Figure 3.18: SAW eigenfrequency (a) setup and (b) mode shape for a 500 nm thick aluminum
plate on 128
o
Y-cut LiNbO
3
with = 50 m.
Figure 3.19: SAW eigenfrequency (a) setup and (b) mode shape for a 500 nm thick aluminum
strips on 128
o
Y-cut LiNbO
3
with = 50 m.
51
Figure 3.20: Simulation result for 90
o
bend for = 6.56 m and waveguide width = 6 m.
using eigenfrequency simulations, as shown in Fig. 3.20. The relative refractive indices
were calculated based on the even and odd mode eigenfrequencies. The even and odd mode
refractive indices were then used to calculate the coupling length for 100% coupling of the
SAW from one waveguide to the other using
L
c
=
2n
; (3.3)
where n is the dierence between the relative refractive indices of the symmetric and anti-
symmetric modes. The results for a SAW centered near 600 MHz with a 100 nm gold overlay
are tabulated in Table 3.2.
Table 3.2: Calculated Coupling Length of Waveguide Coupler
gap (m) F
even
(MHz) F
odd
(MHz) n
even
n
odd
L
c
(m)
1 584.12 595.41 1.0997 1.0788 135.5
2 587.03 593.52 1.0942 1.0822 236.1
3 588.77 592.28 1.091 1.0845 436.9
52
Figure 3.21: Waveguide coupler simulation setup.
The computed coupling lengths in Table 3.2 are then further rened through a 3D fre-
quency domain simulation. A structure consisting of two waveguides separated by a gap
and excited by a small IDT, as shown in Fig. 3.21, is simulated in COMSOL. The aperture
width of the waveguides is 6 m and gaps of 1 m, 2 m, and 3 m have been simulated.
The displacement in the y-direction between the waveguide and the coupled waveguide for
the 3 gap widths are then plotted, as shown in Fig. 3.22 - 3.24. The dierence between the
displacement minimums between the waveguide to the coupled waveguide is then measured,
which is coupling length required for 100% coupling for the simulated gap. The coupling
lengths are close to the calculated coupling lengths using the even and odd eigenfrequencies
tabulated in Table 3.2.
53
Figure 3.22: Waveguide coupler displacements for waveguide and coupled waveguide for a gap =
1 m.
Figure 3.23: Waveguide coupler displacements for waveguide and coupled waveguide for a gap =
2 m.
54
Figure 3.24: Waveguide coupler displacements for waveguide and coupled waveguide for a gap =
3 m.
3.2 Beam Steering
In chapter 2, the eect of beam steering due to the anisotropy of piezoelectric materials
was introduced. The beam steering eect is an eect in which the SAW does not propagate
normal to the face of the IDT but instead, propagates at an angle. This eect can increase
the insertion loss of a two port SAW device as the SAW launched from the input IDT may
not completely intersect with the output IDT and, in long delay lines, the SAW may not be
received at all by the output IDT [77]. While SAW devices are designed to align properly
with the crystal propagation, it is also possible to use SAW waveguides to conne the wave
to propagate in the desired direction despite the beam steering eect.
The eect of beam steering can be analyzed by the slowness curve, which is the inverse
of the SAW velocity, as shown in Fig. 3.25 [3]. This is, in eect, plotting the wavevector of
the SAW as the wavevector is given by
k =
!
v
; (3.4)
55
Figure 3.25: Slowness curve.
where ! is the radial frequency and v is the phase velocity of the SAW. However, as the
direction of propagation aects material properties, the wavevector for anisotropic materials
can be re-written as
k() =
!
v()
; (3.5)
where is the propagation direction. The normal to the slowness curve is the direction of
propagation of the SAW. An approximation of the beam steering angle,
, which is the angle
relative to the normal of the wavefront or IDT ngers [53], can be calculated by
=atan(
1
v
dv
d
); (3.6)
where is the piezoelectric crystal orientation [3] [53].
The slowness curve was simulated in COMSOL for a 6 m wavelength IDT structure
with 100 nm thick gold for 128
o
Y-cut LiNbO
3
and X-cut LiNbO
3
, with the results shown in
Fig. 3.26(a) and 3.26(b), respectively. From a visual inspection, for a x-propagating SAW,
the normal looks to align with the x-axis for the 128
o
Y-cut LiNbO
3
while the normal for
56
Figure 3.26: Simulated slowness curve for a 6m wavelength IDT with 100 nm thick gold for (a)
128
o
Y-cut LiNbO
3
and (b) X-cut LiNbO
3
.
a y-propagating SAW on the X-cut LiNbO
3
looks to be at a very small angle away from
the y-axis. Using equation 3.6, a beam steering angle of about 0.68
o
is calculated for the
128
o
Y-cut LiNbO
3
for an x-propagating SAW while a beam steering angle of about 3.9
o
is
calculated for the y-propagating SAW on X-cut LiNbO
3
.
Dispersion curves for waveguides with an aperture width of 6 m and 12m were simu-
lated with the results plotted in Fig. 3.27. The cut-o frequency of the 6m wide waveguide
is about 580 MHz while the cut-o frequency for the 12 m wide waveguide is about 565
MHz. A 3D AC simulation was performed in COMSOL for a 6 m wide waveguide for a
y-propagating SAW on an un-rotated X-cut LiNbO
3
at 588 MHz, which is above the simu-
lated cut-o frequency of the waveguide, and the total displacement of the SAW is shown
in Fig. 3.28. The SAW is conned in the waveguide and shows that a SAW can be guided
despite the presence of the beam steering eect.
57
Figure 3.27: Simulated dispersion curves for waveguides with an aperture width of (a) 6 m and
(b) 12 m for y-propagating SAWs on X-cut LiNbO
3
.
Figure3.28: (a) COMSOL simulation setup showing the waveguide structure on an X-cut LiNbO
3
substrate. (b) Total displacement simulation result for a SAW at 588 MHz.
58
3.3 Fabrication
The fabrication of the SAW devices was performed through a lift-o process at the University
of Santa Barbara Nanofabrication Facility. The steps taken are as follows:
1 Solvent clean the wafer.
2 PEII O
2
plasma treatment (wafer surface dehydration): 300 mT/100W for 1 minute.
3 Spin-on LOL2000 underneath resist layer: 2.5 krpm for 40 seconds, spun to approxi-
mately 200 - 250 nm thickness.
4 Bake wafer directly on the hot-plate at 160
o
C for 5 minutes with 5
o
C/min. ramp-up
and ramp-down speeds, starting and ending at 50
o
C.
5 Spin-on UV6-0.8 top resist layer: 3 krpm for 30 seconds to approximately 800 nm
thickness.
6 Bake on the hot-plate at 135
o
C for 1.5 minutes with 5
o
C/min. ramp-up and ramp-down
speeds.
7 Expose on ASML PAS 5500/300 DUV Stepper at 20 mJ, 0 m focus oset.
8 Bake on the hot-plate at 135
o
C for 1.5 minutes with 5
o
C/min. ramp-up and ramp-down
speeds.
9 Develop in AZ300-MIF developer for 25 seconds.
10 PEII O
2
plasma descum: 300 mT/100W for 35 seconds.
11 E-beam evaporation: Ti/Al = 5 nm/100 nm, Ti/Au = 5 nm/100 nm, W = 100 nm
(no adhesion layer needed).
12 Lift-o in NMP solution cup inside of 80
o
C hot-water bath for 2 hours, then, in a fresh
NMP solution cup inside of ultrasonic bath at 70
o
C for 1 minute. Follow with acetone
and isopropanol soaking.
59
13 Spin-on UV-6 resist protective layer to approximately 800 nm thickness (thickness
non-critical).
14 Bake on the hot-plate at 135
o
C for 3 minutes with 5
o
C/min. ramp-up and ramp-down
speeds.
15 Dice wafer into chips.
16 Remove photoresist protection with acetone/isopropanol clean.
3.4 Measurements and Discussion
The SAW waveguides were fabricated on 128
o
Y-cut LiNbO
3
and were probed and measured
with a vector network analyzer (VNA) with no external matching network. A diagram of
the straight waveguide test structure is shown in Fig. 3.29. Fig. 3.29(a) is a structure
without any waveguides between the 2 IDT ports while Fig. 3.29(b) shows a structure
with the waveguiding structure. The dimensions of the two structures are similar with
L
1
being 25 m, L
T
being 1 mm, and L
wg
being 1 mm or 2 mm. The IDT is an EWC
type IDT with 32 periods and aperture width of 131 m. The metallization is gold with
a thickness of 100 nm and the propagation direction is in the x-direction. For all devices,
5 nm thick titanium is used as an adhesion layer. A die microphotograph of the straight
waveguide structure is shown in Fig. 3.30. The top structure is the test structure without
the waveguide metallization while the structure on the bottom has the straight waveguide
structure. The metal ring is a ground plane. The S
11
and S
21
measurements for the structure
without waveguides are shown in Fig. 3.31 while the S
11
and S
21
for the straight structure
with the waveguide structures are shown in Fig. 3.32. The measured center frequency is
about 553 MHz, which is close to the expected center frequency of 559 MHz. The S
21
for
the straight test structure without waveguides shows about 5 dB less loss compared to the
test structure with the waveguiding metallization. It is believed that the extra loss is due
60
Figure 3.29: Diagram of the straight test structure with one structure (a) without any metalliza-
tion and (b) with waveguiding structure between the input and output IDTs. m.
Figure 3.30: Microscope image of the straight test structure with waveguide metallization.
to the dampening of the SAW as it propagates through the metallized region. The S
11
for
the structure without waveguide metallization is better than the return loss for the guided
structure as well. The S
21
with the gold waveguide also looks to have spurious responses due
to bulk wave generation from the waveguide as well [80].
There was some concern that the ground plane shown in Fig. 3.30 could be aecting
the propagation of the SAW. Another fabrication was performed with the ground plane
removed. The wavelength was kept at 6.56 m. However, the IDT was changed to a single-
electrode IDT with re
ectors. The minimum electrode width and spacing of =8 of the
EWC IDT makes it dicult to fabricate at higher frequencies while the single-electrode IDT
will be easier to fabricate due to having a minimum electrode width and spacing of =4.
While other single-phase unidirectional IDT designs are available that have larger minimum
61
Figure 3.31: S11 and S21 measurement results for straight test structures with no waveguide for
L
wg
of 1 mm (blue) and 2 mm (red).
Figure 3.32: S11 and S21 measurement results for straight waveguide test structures with 100
nm thick gold waveguides and L
wg
of 1 mm (blue) and 2 mm (red).
62
Figure 3.33: Diagram of the straight test structure with one structure (a) without any metalliza-
tion and (b) with waveguiding structure between the input and output IDTs. m. Re
ectors were
added behind the IDTs to make the IDTs more unidirectional.
Figure 3.34: Microscope image of straight waveguide with aperture width w
2
= 6m and length
L
2
= 1 mm.
electrode widths and spacings than=8 [11], single-electrode IDTs with re
ectors were used
for the purposes of testing the waveguide designs, as shown in Fig. 3.33. A microscope image
of the structure is shown in Fig. 3.34. Single electrode IDTs were utilized with re
ectors
placed behind them to reduce the loss from the bidirectionality of the IDT. The IDT was
designed with 24 signal-ground nger pairs with an aperture width of 130 m to provide a
good match to 50
. A waveguide taper of length L
1
of 1 mm was used to interface the wide
aperture IDT to the narrower aperture of the waveguide [24]. The straight waveguides were
fabricated using aluminum, tungsten, and gold metallizations with a thickness of 100 nm.
The measured S
11
for the three metallizations is shown in Fig. 3.35. The measurement
results show that the S
11
is better than -10 dB for all three metallizations. The S
21
mea-
surement results for the three metallizations and for waveguide widths of 6 m, 12m, and
63
Figure 3.35: S
11
measurement results for aluminum (blue), tungsten (red), and gold (black)
metallization.
24 m are shown in Fig. 3.36. The peak S
21
values, as well as the measured group delay
at that frequency, for the dierent waveguide lengths and widths, are shown in Fig. 3.37.
As aluminum is lighter, it exhibits less of a dampening eect on the propagating SAW and
thus, results in a lower loss [77]. It is believed that the 24 m wide waveguide experience
excitation of higher order modes and therefore, does not have a good linear t for aluminum
and gold metallizations. Overall, the SAW waveguides demonstrate a low propagation loss
in the range of 2.1 - 6.3 dB/s. The low wave velocity of SAWs, along with its low loss char-
acteristic, make the propagation loss much smaller than the propagation loss of even silicon
photonic waveguides [81]. It is important to note that these measurements, by themselves,
do not prove the connement of wave in the waveguides as the SAW can easily reach from
one IDT to another one even without the metal-overlaid waveguides.
To understand the notches observed in the S
21
passband, delay lines without any metal
overlay to remove its eect were measured and compared with simulation results. Figures
3.38 - 3.40 plots the S
21
of a delay line without any metal overlay for IDTs fabricated with
a wavelength of 6.56 m and using 100 nm thick aluminum, tungsten, and gold on 128
o
YX LiNbO
3
, respectively. The input and output IDTs are separated by a distance of 3.123
mm for all three metals. The peak S
21
values are tabulated in Table 3.3 and show less loss
compared to the metal overlay guided waveguides. The waveguided structures incur addi-
tional losses due to dampening of the SAW due to the overlay metallization compared to the
64
Figure3.36: S
21
measurement results for (a) aluminum, (b) tungsten, and (c) gold metallizations.
The columns are divided into waveguide widths, with the left column showing results for 6 m
waveguide widths, the center column showing results for 12 m waveguide widths, and the right
column showing results for 24m waveguide widths. The colors in each plot represent the dierent
waveguide lengths of 1 mm (blue), 2 mm (red), and 4 mm (green).
Figure 3.37: Peak S
21
and group delay measurement results for (a) aluminum, (b) tungsten, and
(c) gold metallizations for the three dierent waveguide lengths. The columns are divided into
waveguide widths, with the left column showing results for 6 m waveguide widths, the center
column showing results for 12 m waveguide widths, and the right column showing results for 24
m waveguide widths.
65
unguided structures [77]. The measured results are compared with results from a COMSOL
2D simulation without any re
ectors (blue) and with re
ectors (red). The measured S
21
results show good agreement with the simulation results with re
ectors for all three metals.
The simulation result without re
ectors shows that the addition of the re
ectors introduces
the notches seen in the passband. Figure 3.41 shows the Y-displacement for a 2D simulation
for IDTs and re
ectors designed using 100 nm thick gold on 128
o
YX LiNbO
3
. The gure on
the top shows the close-in of the setup, showing the boundary between the re
ector and the
IDT, as well as the boundary between the IDT and the free LiNbO
3
region. The middle plot
shows the Y-displacement at 561 MHz, which corresponds to the rst passband notch seen in
Fig. 3.40, while the bottom plot shows the Y-displacement at 566 MHz, which is the part of
the passband where minimum insertion loss occurs in the simulation. The Y-displacement at
561 MHz indicates a resonance occurring between the re
ector and the IDT, with very little
of the wave propagating towards the output, corresponding to the notch occurring in the
passband in Fig. 3.40. The Y-displacement at 566 MHz shows the wave propagating freely
towards the output, and therefore, minimum loss incurred at this frequency. This resonance
at 561 MHz occurs due to the cancellation of the forward propagating wave by the re
ected
wave [82]. This re
ection occurs from both the input and output IDT-re
ector pairs. A way
to mitigate the notch occurring in the passband is to slightly oset the periodicity or pitch
(p) of the re
ector gratings so that it is dierent from the pitch of the IDT ngers. Figure
3.42 shows simulated loss for a two-port delay line without re
ectors paired with the IDTs,
with re
ectors with a pitch of =2 to match the pitch of the IDTs, and with pitches slightly
oset compared to the IDT. As can be seen from the plot, the notch due to the re
ectors
can be moved out of the passband by slightly osetting the pitch of the re
ector gratings.
Table 3.3: Peak S
21
for Straight Delay Lines Without Metal Overlay for = 6.56 um
Metal Aluminum (Al) Tungsten (W) Gold (Au)
S
21
(dB) -5.4 -8.6 -4.8
66
Figure 3.38: Straight delay line insertion loss comparison for 100 nm thick aluminum IDTs on
128
o
YX LiNbO
3
without metal overlay. The results compare simulated results for IDTs without
re
ectors (blue) and IDTs with re
ectors with measured results.
Figure 3.39: Straight delay line insertion loss comparison for 100 nm thick tungsten IDTs on
128
o
YX LiNbO
3
without metal overlay. The results compare simulated results for IDTs without
re
ectors (blue) and IDTs with re
ectors with measured results.
67
Figure 3.40: Straight delay line insertion loss comparison for 100 nm thick gold IDTs on 128
o
YX
LiNbO
3
without metal overlay. The results compare simulated results for IDTs without re
ectors
(blue) and IDTs with re
ectors with measured results.
Figure 3.41: Close-in plot of a 2D COMSOL simulation, indicating the re
ector-IDT boundary
and IDT-free LiNbO
3
boundary (top). The Y-displacement at 561 MHz (middle) and 566 MHz
(bottom) are shown. The Y-displacement at 561 MHz indicates a resonance occurring between
the re
ector and IDT with very little of the SAW propagating towards the output while the Y-
displacement at 566 MHz shows the SAW propagating towards the output.
68
Figure 3.42: 2D COMSOL loss simulation result for diering re
ector nger pitch.
Figure 3.43: Waveguide S-bend test structure.
While the aluminum waveguide incurs the least loss for the straight waveguides, the
connement is less compared to the tungsten and gold waveguides. This is seen in the
measurement results of the waveguide bend structures, diagrammed in Fig. 3.43. The
waveguide bend test structure was fabricated using either aluminum, tungsten, or gold. The
same IDT and waveguide taper is used for the s-bend structure. The waveguide taper is
followed by a 500m straight section before going into the s-bend waveguide. Similar to the
straight waveguide, the waveguides are fabricated with either aluminum, tungsten, or gold
with a thickness of 100 nm. A die microphotograph of an s-bend structure is shown in Fig.
3.44.
69
Figure 3.44: Microscope image of an s-bend waveguide structure with a width of 6 m and
bending radius of 400 m.
The S
21
of the waveguide s-bend structures are plotted in Figs. 3.45 - 3.47. Fig. 3.45
shows the measured S
21
for a waveguide width of 6 m and bending radii of 100 m, 200
m, and 400m for aluminum, tungsten, and gold metallizations are shown in Fig. 3.45(a),
(b), and (c), respectively. Figure 3.45(d) plots the peak S
21
for all three metallizations.
The plot shows that the aluminum overlaid waveguide does not conne the SAW while
the best connement is seen in the gold overlaid waveguide. Similar results for waveguide
widths of 12 m and 24 m are plotted in Figs. 3.46 and 3.47, respectively. The waveguide
bends with radius of 12 m and 24 m also show that the aluminum overlaid waveguides
do not conne the SAW while it the gold overlaid waveguides conne the SAW. For 12
m widths, the tungsten overlaid waveguides also show connement. However, the loss of
the tungsten overlaid waveguides is higher overall compared to the gold overlaid waveguides.
While tungsten has a similar mass density as gold, it is believed that the stiness of tungsten
dampens the SAW more than gold, making it less suitable for SAW waveguiding.
Figure 3.48 shows the S
21
measurement result for an s-bend test structure fabricated
with gold and without the waveguiding element in between the two IDTs. As there is no
waveguiding element, the S
21
is lower than the S
21
measured in Figs. 3.45 - 3.47 for gold
metallization. However, it is of note that for a bend radius of 100 m, the S
21
is only about
7 dB lower than the s-bend S
21
with the gold waveguide metallization. This again seems to
indicate that perhaps the measurement of the s-bend test structure without the waveguide
70
Figure3.45: S
21
magnitude response for s-bend test structures for waveguide width of 6m using
for (a) aluminum, (b) tungsten, and (c) gold metallizations. Each plot shows the measurement
results for bending radii of 100 m (blue), 200 m (red), and 400 m (black). (d) shows the peak
S
21
across the dierent radii for the three metallizations.
Figure 3.46: S
21
magnitude response for s-bend test structures for waveguide width of 12 m
using for (a) aluminum, (b) tungsten, and (c) gold metallizations. Each plot shows the measurement
results for bending radii of 100 m (blue), 200 m (red), and 400 m (black). (d) shows the peak
S
21
across the dierent radii for the three metallizations.
71
Figure 3.47: S
21
magnitude response for s-bend test structures for waveguide width of 24 m
using for (a) aluminum, (b) tungsten, and (c) gold metallizations. Each plot shows the measurement
results for bending radii of 100 m (blue), 200 m (red), and 400 m (black). (d) shows the peak
S
21
across the dierent radii for the three metallizations.
metallization is measuring the diracting SAW. It also poses the question of whether the
SAW is actually being guided by the waveguide structure.
Figure 3.48: S
21
magnitude response for s-bend test structure without waveguiding metallization
for gold and bending radii of 100 m (blue), 200 m (red) and 400 m (black).
In order further validate the conning of the SAW by the waveguide, a 180
o
bend waveg-
uide structure, shown in Fig. 3.49 was fabricated and measured. A die microphotograph of
72
Figure 3.49: Waveguide U-bend test structure.
a 180
o
waveguide bend with outer bend radius of 200 m is shown in Fig. 3.50. The single
electrode IDTs for the 180
o
bend, or U-bend, was designed with = 6 m, aperture width
of 98.5 m, and 24 signal-ground nger pairs. Re
ectors were placed behind the IDTs to
minimize the loss from the bidirectionality of the IDTs and a 1 mm taper length is used to
interface the IDT and the waveguide. The design was fabricated using aluminum or gold
with a thickness of 100 nm. The measured insertion loss is shown in Fig. 3.51. The column
on the left shows plots for waveguide widths of 6 m and the column on the right shows
insertion loss results for waveguide widths of 12 m. The rows plot the insertion loss, from
top to bottom, for bending radii of 100 m, 200 m, and 400 m. The peak S
21
occurs at
around 606 MHz for the gold waveguides with peak S
21
values of -12.5 dB, -9.33 dB, -9.82
dB for bending radii of 100 m, 200 m, and 400 m, respectively. The S
21
measurements
of the U-bend show SAW connement for the gold waveguide but not for the aluminum
waveguide.
180
o
bend waveguides without the waveguides were also fabricated to further assess the
waveguiding of the SAW through the U-bend structure. A microphotograph of a structure
for an equivalent bend radius of 100 m is shown in Fig. 3.52. The S
21
of the U-bend test
73
Figure 3.50: Microscope image of the U-bend structures for outer bend radius of 200 m.
Figure 3.51: S21 magnitude plots for U-bend test structures. The plots of (a) are for a bending
radius of 100 m, (b) for a bending radius of 200 m, and (c) for a bending radius of 400 m.
74
Figure3.52: Microscope image of the U-bend structure without waveguide metallization for outer
bend radius of100 m.
Figure 3.53: S21 magnitude plots for U-bend test structures without 180
o
bend metallization for
equivalent bend radii of 100 m, 200 m, and 400 m.
structure without the bend metallization is shown in Fig. 3.53. Unlike for the s-bend test
structures, the S
21
dierence between the 100 m bending radius between having and not
having the waveguide metallization is about 26 dB, indicating that the waveguide is indeed
guiding the SAW through the 180
o
bend.
Straight waveguide structures with the new IDTs with a wavelength of 6 m were also
fabricated. The measured S
21
is plotted in Fig. 3.54(left) along with a plot of the peak S
21
vs.
waveguide length (right). Based on a linear t of the peak S
21
values, the straight waveguide
loss is calculated to be about -1.49 dB/mm. The same measurements were performed for a
similar test structure without the taper and waveguide regions and is plotted in Fig. 3.55.
75
Figure 3.54: S
21
measurement results for 6 m wavelength for (left) waveguide lengths of 1 mm,
2 mm, and 4 mm. The peak S
21
vs. waveguide length is also plotted along with a linear t line
(right).
Figure3.55: S
21
measurement results for 6m wavelength for (left) straight test structure without
an overlay metallization of equivalent waveguide lengths of 1 mm, 2 mm, and 4 mm. The peak S
21
vs. waveguide length is also plotted along with a linear t line (right).
The loss per length is also computed and is about -1.07 dB/mm, showing that an undamped,
non-metallized straight undergoes less loss per length.
Test structures of back-to-back IDTs and IDT-taper-taper-IDT structures were also fab-
ricated. The die microphotograph is shown in Fig. 3.56 and the S
21
for both structures are
plotted in Fig. 3.57. The peak S
21
of the back-to-back IDT structure is -2.21 dB while the
IDT-taper-taper-IDT structure is -6.77 dB. Based on the two measurements, the loss for a
re
ector-IDT is about 1.1 dB while the loss for a taper section is 2.3 dB. Table 3.4 compares
the simulated and measured IDT, taper, and waveguide losses.
The back-to-back IDT and IDT-taper structures allow for the estimation of the break-
down of the dierent components of the 6 m wide straight waveguide and 180
o
waveguide
76
Figure 3.56: Die microphotograph for (a) back-to-back IDT test structure and (b) back-to-back
IDT-taper structure.
Figure3.57: S
21
measurement results for back-to-back IDT test structure (blue) and back-to-back
IDT-taper structure (red).
77
Figure 3.58: Loss breakdown for a (left) straight waveguide and (right) 180
o
waveguide bend for
6 m wavelength and waveguide width of 6 m.
bend for a 6 m wavelength. The breakdowns are shown in g. 3.58. The losses are broken
down based on the IDT and taper losses measured from the two test structures. However,
it should be noted that the IDT impedances and associated losses between IDT-IDT and
IDT-taper interfaces are dierent and therefore, the losses are only estimates. It does show
the tapers are contributing the most losses, followed by the IDT themselves.
Table 3.4: Simulated and Measured Loss Breakdown for Straight and Bent Waveguides
Simulation (dB) Measurement (dB)
IDT -1.1 -2.2
Taper -5.38 -4.6
Straight, 1 mm -0.86 -1.5
Bend, 200 m -2.99 1.2
The device microphotograph of a multistrip coupler is shown in Fig. 3.59. The MSC
was fabricated for IDT wavelength of 6 m using 100 nm thick gold. The MSC strips have
periodicity of 3/8 and coupling lengths of 90m, 100m, and 110m were fabricated for
3-dB coupling while coupling lengths of 140 m, 150 m, and 160 m were fabricated for
100% coupling. The S
21
and S
41
magnitudes are plotted in Figs. 3.60 - 3.65. The peak S
21
and S
41
values for each length are also tabulated in Table 3.5. Based on the results, 3-dB
coupling occurs for a coupling length of about 100m while based on the devices fabricated,
100% coupling occurs for a coupling length of 160m. However, it is possible that the 100%
coupling length is longer than the fabricated 160 m in this work.
78
Figure 3.59: Microphotograph of a multistrip coupler, outlining the re
ector, and IDT of port 1
along with the MSC strips.
Figure 3.60: S
21
and S
41
magnitude plots for multistrip coupler with transfer length of 90 m.
Figure 3.61: S
21
and S
41
magnitude plots for multistrip coupler with transfer length of 100 m.
79
Figure 3.62: S
21
and S
41
magnitude plots for multistrip coupler with transfer length of 110 m.
Figure 3.63: S
21
and S
41
magnitude plots for multistrip coupler with transfer length of 140 m.
Figure 3.64: S
21
and S
41
magnitude plots for multistrip coupler with transfer length of 150 m.
80
Figure 3.65: S
21
and S
41
magnitude plots for multistrip coupler with transfer length of 160 m.
Table 3.5: Peak S
21
for Multistrip Couplers
Length S
21
(dB) S
41
(dB)
90 -4.5 -5.3
100 -4.6 -4.1
110 -5.6 -4.8
140 -7.8 -4.9
150 -9.7 -4.8
160 -10.5 -5.2
The diagram for the waveguide coupler is shown in Fig. 3.66. The IDT is designed with a
wavelength of 6m, an aperture width of 98.5m, and 24 electrode pairs. Gold metallization
is used with a thickness of 100 nm. A 1 mm taper length is used to interface the IDT to the
6 m wide waveguide. The gap between the coupled waveguides is 1 m. Fig. 3.68 shows
the insertion loss for the waveguide coupler for coupling lengths, L
c
of 57m (Fig. 3.68(a)),
123 m (Fig. 3.68(b)), and 190 m (Fig. 3.68(c)), representing 100% coupling to coupled
waveguide, 50% coupling between the two waveguides, and 100% coupling back to the main
waveguide, respectively. Of note is that the length dierence between having 100% of the
SAW in the coupled waveguide back to 100% of the SAW in the main waveguide is about
133 m, which matches the simulation results. In order to arrive at these plotted results,
a family of waveguide couplers with dierent lengths were fabricated and the peak S
21
, S
31
,
and S
41
are tabulated in Table 3.6. Compared to the multistrip coupler, the coupling length
81
Figure 3.66: Diagram for a SAW waveguide coupler.
Figure 3.67: Microscope image of a waveguide coupler.
for the waveguide coupler with 1m gap is shorter. However, one can argue that the overall
size of the multistrip coupler is smaller as the waveguide coupler uses bends and tapers,
making the overall device large in size.
In order to demonstrate the waveguiding of SAWs in the presence of beam steering,
waveguides were fabricated on an X-cut LiNbO
3
for a y-propagating wave. Based on calcu-
lations, the beam steering angle is about 3.9
o
. The structures in Fig. 3.69 were fabricated to
measure the diraction as well as the beam steering of a SAW. The top structure has output
IDTs, labeled as Bx, with B4 directly across from the input IDT, A, and with subsequent
IDTs spaced about 308.5 m above and below it. The bottom structure has the output
IDTs, labeled as Cx, oset from the center line by about 154m while maintaining the same
spacing of 308.5m from each other. The structure was fabricated on a 128
o
Y-cut LiNbO
3
82
Figure3.68: S21 magnitude measurement results for waveguide coupler test structure for coupling
lengths of (a) 57 m, (b) 123 m, and (c) 190 m.
83
Table 3.6: Peak S
21
, S
31
, and S
41
for Family of Fabricated Waveguide Couplers
Coupling Length (m) S
21
(dB) S
31
(dB) S
41
(dB)
57 -38.87 -36.05 -10.30
67 -33.03 -28.15 -10.76
77 -36.28 -22.95 -11.07
123 -19.22 -12.22 -12.73
133 -29.26 -12.64 -18.68
143 -21.74 -11.33 -16.07
190 -31.65 -9.84 -26.47
210 -28.15 -10.77 -23.03
220 -23.48 -10.88 -18.45
with an X-propagating SAW and a X-cut LiNbO
3
with a Y-propagating SAW, with the
measured insertion loss shown in Fig. 3.71 and Fig. 3.72, respectively. Fig. 3.71 shows that
for 128
o
Y-cut LiNbO
3
, much of the X-propagating SAW is going to the B4 IDT, with some
of the wave diracting to both C4 and C5 IDTs, indicating some diraction occurring and
that there seems to be a very slight beam steering angle, as the C5 IDT has slightly less loss
compared to the C4 IDT loss. On the other hand, Fig. 3.72 shows that the Y-propagating
SAW on the X-cut LiNbO
3
is beam steered to output IDT B3 and C4, with the loss being
less for the output IDT C4. A SAW steered toward C4 has a calculated beam steering angle
from the center line of about 2.8
o
. The resolution of the structures is coarse and so the
actual beam steering angle can be slightly larger or slightly smaller than 2.8
o
. However, the
measurements do show that the SAW is steered at an angle around 3
o
, which is in agreement
with the calculated angle.
Figure 3.73 shows the measured S
21
for a structure without waveguides, with a 6 m
wide waveguide, and a 12m wide waveguide. The structures are similar to the ones shown
in Fig. 3.33. For the waveguide structure, both the waveguide taper and waveguide are
1 mm in length. The IDT separation for the structure without waveguide metallization is
the same as the separation for the structure with waveguide metallization. In simulation,
for an IDT with a wavelength of 6 m and an aperture width of 100 m, the excited SAW
84
Figure 3.69: Two structures used to measure diraction and beam steering of SAW. The IDTs on
the right are spaced by about 308.5m. The top structure has an output IDT, B4, that is directly
across from the input IDT, A. The bottom structure has IDTs, labeled as Cx, that are oset by
about 154 m, lling the gaps in between the IDTs labeled as Bx in the top structure.
85
Figure 3.70: Microscope image of one of the test structures used to measure diraction and beam
steering of the SAW.
Figure3.71: Insertion loss measurement results for the diraction/beam steering structure shown
in Fig. 3.69 for the structure fabricated on 128
o
Y-cut LiNbO
3
with an X-propagating SAW. The
noted values are the minimum insertion loss values for the respective curves.
86
Figure3.72: Insertion loss measurement results for the diraction/beam steering structure shown
in Fig. 3.69 for the structure fabricated on X-cut LiNbO
3
with a Y-propagating SAW. The noted
values are the minimum insertion loss values for the respective curves
frequency is about 580 MHz, which is right around the simulated cut-o frequency for the
6 m waveguide. The measured S
21
shows that both the unguided SAW structure and the
6 m wide waveguide structure do not propagate the SAW well from the input IDT to the
output IDT. The unguided SAW is lost due to the beam steering eect while the 6 m wide
waveguide is operating close to the cut-o frequency of the SAW. However, SAW propagation
is supported in the 12 m wide waveguide and demonstrates that the SAW can be guided
even though the beam steering eect is present. The waveguide U-bend S
21
results for a
waveguide width of 6 m and 12 m are plotted in Fig. 3.74(a) and (b), respectively as
well. Again, it shows that the SAW does not propagate well in the 6 m waveguide while
connement and propagation is demonstrated for the 12 m waveguide.
87
Figure 3.73: S
21
for a straight XY LiNbO
3
structure without waveguides (blue), with 6 m wide
waveguide (red), and with 12 m waveguide (black).
Figure 3.74: S
21
for a XY LiNbO
3
U-bend structure for a waveguide width of (a) 6 m and (b)
12 m for bending radii of 100 m, 200 m, and 400 m.
Figure 3.75 shows the S
21
measurement result for a U-bend with a bending radius of 400
m and a waveguide width of 12 m along with the same U-bend structure without the
88
waveguide overlay metallization. The result clearly shows that the waveguide does indeed
conne that SAW even in the presence of the beam forming eect.
Figure 3.75: S
21
for a XY LiNbO
3
U-bend structure for a waveguide width of 12 m and bend
radius of 400 m for a structure with (blue) and without (red) waveguide overlay metallization.
3.5 Summary
This chapter went over the design process of the SAW waveguides. Straight waveguides,
waveguide bends, and coupled waveguides have been designed and demonstrated. Waveguide
tapers were used to interface the large aperture IDT to the narrower aperture waveguide.
It has also been demonstrated that SAWs can be guided even if the IDTs are not aligned
properly to the crystal propagation direction. The eect of metallization was also examined
with gold producing the best connement, compared to aluminum and tungsten. The SAW
devices were fabricated using the lift-o procedure.
89
Chapter 4
SAW Phase Shifters
While SAW waveguides allow for the design of microwave structures at radio frequencies, the
ability to manipulate the phase of the SAW will allow the design of SAW signal processors. By
modulating the SAW velocity slightly, a change in phase can be induced in the propagating
SAW, creating a SAW phase shifter. The SAW velocity can be modulated by a change
in temperature, or by changing the electric eld in the region the SAW is propagating.
The latter can be accomplished by the accumulation or depletion of charges in very close
proximity to the propagating SAW. A bonded lithium niobate on a semiconducting substrate
can be used to modulate the SAW velocity through electrical charges. In this chapter, an
example of a thermal phase shifter using just the gold metallization on 128
o
Y-cut LiNbO
3
will be introduced, followed by a charge-based, or electroacoustic, phase shifter using 128
o
Y-cut LiNbO
3
bonded on a silicon substrate.
4.1 Thermal Phase Shifter
As SAW devices are known for having very good temperature stability, it is not surprising
that a search for a thermal phase shifter is not very fruitful. For narrow band applications,
ST-quartz provides the best temperature stable properties for SAW devices [83]. However,
due to the low piezoelectric coupling coecient, eort has been put in to nd a material with
the desired properties of temperature stability and high piezoelectric coupling [84]. Until
90
that material is discovered, however, overlay materials such as SiO
2
are used to create a
temperature compensated composite material. Therefore, a thermal phase shifter will be an
undesirable device to have together with temperature sensitive devices. With that said, it
is easier to design a thermal phase shifter as only a heater needs to be added near the SAW
waveguide structures discussed in the previous chapter.
The temperature coecient for SAW velocity for an x-propagating SAW on 128
o
Y-cut
LiNbO
3
is -71.3 ppm/
o
C [85]. The temperature coecient does change depending on the
propagation direction, and temperature coecient for the SAW velocity for a z-propagating
SAW on the same 128
o
Y-cut LiNbO
3
is -86.3 ppm/
o
C. The length of the waveguide to
generate a 360
o
phase shift is calculated by using the equation
=
2L
dn
dT
T; (4.1)
where is the phase change, L is the device length, is the SAW wavelength,
dn
dT
is the
SAW velocity temperature coecient, and T is the change in temperature [86]. Using this
equation and the SAW velocity temperature coecient of -71.3 ppm/
o
C, the length of the
phase shifter was calculated, and the result is plotted in Fig. 4.1. In order to make the
thermal phase shifter have a short length, a large temperature change needs to be generated,
resulting in a high power consumption while a long length is required to reduce the power
consumption needed to create the temperature change. There are design choices that can
be made to create compact phase shifters with a long length by the use of multiple bends,
and power consumption can also be reduced by sharing the heating element with dierent
sections of the phase shifting device, as shown in Fig. 4.2.
Fig. 4.3 shows a diagram of a Mach-Zehnder interferometer (MZI) (Fig. 4.3(a)) and
a diagram of the thermal phase shifter test structure placed in the MZI (Fig. 4.3(b)).
The MZI is a structure that is seen in optical systems and operates on constructive and
destructive interference of a wave that is split into two branches and recombined after one
branch experiences a phase shift independent of the other branch [79]. If the recombined
91
Figure 4.1: Plot of phase shifter length vs. temperature change.
Figure 4.2: SAW thermal phase shifter sharing heating element with multiple segments of the
phase shifter.
92
Figure 4.3: (a) Diagram of a Mach-Zehnder interferometer (MZI) with a phase shifter as the
device-under-test (DUT). (b) Conceptual diagram of the phase shifter test structure in an MZI.
waves are in phase, the two waves will combine constructively and the amplitude will be
the largest. However, if the two waves are out-of-phase, they will combine destructively and
the amplitude will be lower. If the two waves are 180
o
out-of-phase, they will cancel each
other and the maximum loss will be experienced at the output of the MZI structure. The
constructive/destructive interference pattern was used to measure the SAW thermal phase
shifter.
Unfortunately, as only one mask layer is used for the fabrication, the metallization used
for the IDT and waveguide structures is gold, which is a good electrical conductor. To
increase the resistance so as to generate the necessary heat while not having the resistor to
burn due to electromigration, a meandered structure was adopted, as shown in Fig. 4.4.
The gold thickness is 100 nm, the width of the meandered line is 1 m, and the height of
the meandered line is 4 m. The overall length of the heater is 4 mm and the measured
resistance was about 2.1 k
.
93
Figure 4.4: Meandered resistor designed for the heater of the thermal phase shifter.
4.2 Electroacoustic Phase Shifter
While the thermal phase shifter can be used to modulate the phase of the SAW, it has two
disadvantages. One disadvantage mentioned earlier is that it requires the modulation of
the temperature of the propagation medium, which will aect the frequency stability of the
SAW against temperature. The other disadvantage is that the power consumption of the
phase shifter is very high. While the power consumption of the thermal phase shifter can be
reduced by sharing heating elements to heat both sides of the waveguides and perhaps using
another fabrication mask and depositing a dierent material for the resistor element, it will
still consume a non-negligible amount of power.
The other type of SAW phase shifter uses the property of piezoelectric stiening in
which the elastic stiness of the material can be modulated by the presence of free carriers
in a semiconductor in very close proximity to the propagating SAW [40] [87]. When a
SAW propagates in a piezoelectric material, it is accompanied by an electric eld [88]. The
additional potential energy from the electric eld makes the piezoelectric material behave as
if it is stier, causing the SAW velocity to increase. Modulating the electric eld can cause
changes to the SAW velocity, and thus, produce a phase shift.
Electroacoustic SAW phase shifters have been explored for many dierent materials. In
1971, a 30 k
-cm n-type silicon was pressed onto spacer rails of a Y-cut z-propagating
LiNbO
3
delay line [39]. The delay line that interacted with the silicon was about 8 mm for
94
Figure 4.5: Cross-section of a SAW delay line with electrodes used to control the electric eld for
phase shifting.
a SAW excited at 170 MHz. A phase shift of about 750
o
was achieved. However, due to the
thickness of the lithium niobate, a voltage of 900 V was needed to operate the device.
In 1977, a SAW phase shifter was demonstrated in which a silicon wafer was placed at
a height of 1000
A above a SAW on YZ LiNbO
3
[41]. A length of about 1 cm was used to
achieve a 180
o
phase shift with a voltage of 30 V. More recent examples have seen the use
of other types of materials. Semiconducting and piezoelectric ZnO layers grown on r-Al
2
O
3
were used to tune the acoustic velocity to achieve a 420
o
phase shift at a bias voltage of -18
V for Sezawa waves and 277.3
o
phase shift at a bias voltage at -18 V for Love waves [89].
As a change in the electric eld aects the stiness of the piezoelectric material, it
is possible to control the electric eld, and thus the phase shift of a propagating SAW,
without the semiconducting layer as well. A variable delay was created by sandwiching the
propagating region with bias and ground electrodes, as shown in Fig. 4.5 [90]. A SAW
propagating on 128
o
YX LiNbO
3
experienced a fractional time delay change greater than
9x10
4
for what appears to be a bias voltage in the kV range due to the thick LiNbO
3
.
In this work, a 128
o
Y-cut LiNbO
3
was bonded to a high resistivity silicon wafer. A
cross-section of the phase shifter is shown in Fig. 4.6. The LiNbO
3
is thinned to a thickness
of 5 m and bonded onto a 500 m thick high resistivity p-type silicon. A 100 nm thick
95
gold is used for the IDT and waveguides. The fractional change in the SAW velocity was
calculated using
v
R
v
= (
v
v
)
1
1
1
+
p
(4.2)
where
and are given by
=
2
tanh(h
1
) +
1
tanh(w)
2
+
1
tanh(h
1
)tanh(w)
(4.3)
=
1
+
2
tanh(h
1
)
1
tanh(h
1
) +
2
: (4.4)
v
v
is calculated from the piezoelectric coupling coecient using Eq. 2.19,
1
is the SiO
2
dielectric constant,
2
is the dielectric constant of silicon,
p
is the dielectric constant of
LiNbO
3
, h
1
is the SiO
2
thickness, is the SAW propagation constant, and w is the depletion
layer width in silicon [91]. The SiO
2
layer is assumed to be around 4 nm in thickness due
to the surface oxidation of the silicon [92]. In order to calculate the depletion layer width,
a simple 1D COMSOL simulation was performed to simulate the capacitance of a MOS
capacitor. For simplicity, the simulation is performed with just the 5 m thick LiNbO
3
as
the dielectric layer. The depletion layer width is then calculated using
w =
Si
C
(4.5)
where
Si
is the dielectric constant of silicon and C is the depletion layer capacitance [93].
The depletion width is used to calculate
v
R
v
using Eq. 4.2, which is then used to calculate
the expected phase shift using
= 360
o
(
v
R
v
)(
L
ps
) (4.6)
96
Figure4.6: Cross-section of a SAW phase shifter on Y-cut LiNbO
3
-on-silicon with electrodes used
to control the electric eld for phase shifting.
Figure 4.7: Calculated shift in phase versus waveguide bias voltage for silicon resistivities of 2,200
-cm, 22,000
-cm, and 44,000
-cm and phase shifter length of 6.39 mm.
where L
ps
is the length of the phase shifter and is the SAW wavelength [89]. Figure 4.7
shows the calculated phase shifts for silicon substrate resistivities of 2200
-cm, 22,000
-
cm, and 44,000
-cm and for a phase shifter length of 6.39 mm. The exact resistivity of the
silicon in the bonded wafer used in this work is unknown except that it is larger than 10,000
-cm. For the simulated resistivity ranges, the maximum phase shift can be around 330
o
to 470
o
. The plot also shows that a high resistivity silicon substrate is desirable as it would
allow the use of a lower bias voltage to achieve the large phase shift.
97
4.2.1 Fabrication
The fabrication of the electroacoustic SAW devices on LiNbO
3
-on-Si wafers was performed
through a lift-o process at the University of Santa Barbara Nanofabrication Facility similar
to the steps followed in the fabrication steps mentioned in chapter 3 with a few minor
modications for the baking process. The steps taken are as follows:
1 Solvent clean the wafer.
2 PEII O
2
plasma treatment (wafer surface dehydration): 300 mT/100W for 1 minute.
3 Spin-on LOL2000 underneath resist layer: 2.5 krpm for 40 seconds, spun to approxi-
mately 200 - 250 nm thickness.
4 Bake wafer directly on the hot-plate at 180
o
C for 5 minutes.
5 Spin-on UV6-0.8 top resist layer: 3 krpm for 30 seconds to approximately 800 nm
thickness.
6 Bake on the hot-plate at 135
o
C for 1.5 minutes.
7 Expose on ASML PAS 5500/300 DUV Stepper at 20 mJ, 0 m focus oset.
8 Post-exposure-bake (PEB) at 135
o
C for 1.5 minutes.
9 Develop in AZ300-MIF developer for 25 seconds.
10 PEII O
2
plasma descum: 300 mT/100W for 35 seconds.
11 E-beam evaporation: Ti/Al = 5 nm/100 nm, Ti/Au = 5 nm/100 nm, W = 100 nm
(no adhesion layer needed).
12 Lift-o in NMP solution cup inside of 80
o
C hot-water bath for 2 hours, then, in a
fresh NMP solution cup inside of ultrasonic bath at 70
o
C for 1 minute. Follow with
acetone and isopropanol soaking.
98
13 Spin-on UV-6 resist protective layer to approximately 800 nm thickness (thickness
non-critical).
14 Bake on the hot-plate at 135
o
C for 3 minutes.
15 Dice wafer into chips.
16 Remove photoresist protection with acetone/isopropanol clean.
4.3 Measurements and Discussion
4.3.1 Thermal Phase Shifter
The die microphotograph of the MZI test structure for the thermal phase shifter is shown in
Fig. 4.8. The length of the phase shifter is 4 mm. The measured S
21
of the MZI is shown in
Fig. 4.9. The plot shows that constructive and destructive interference occurring, indicating
that the phase shifter is working. The null-to-null behavior shows that about 322 mW of
power needs to be dissipated to generate a 2 phase shift.
Figure 4.8: Die microphotograph of the Mach-Zehnder interferometer test structure for testing
the SAW thermal phase shifter.
99
Figure 4.9: Measured S
21
of the MZI test structure versus dissipated power.
4.3.2 Electroacoustic Phase Shifter
A die microphotograph of the electroacoustic phase shifter is shown in Fig. 4.10. The
electroacoustic phase shifter was fabricated on a bonded 128
o
Y-cut LiNbO
3
-on-Si wafer using
5 nm thick titanium and 100 nm thick gold for metallization. Single electrode IDTs with
re
ectors were designed with a wavelength of 6 m. Two-port s-parameter measurements
were performed using a vector network analyzer (VNA) through direct RF probing. A DC
probe was used to bias the waveguide while the backside of the die was grounded. The
phase shifts were directly measured from the S
21
phase measurements. The length of the
phase shifter, which includes only one of the taper sections, is 6.39 mm. The measured S
21
magnitude and phase shifts at 612 MHz are shown as the blue curves in Fig. 4.11. The S
21
changes by almost 7 dB for the bias voltage range of 0 V to 70 V. Across the entire 70 V bias
voltage range, the phase changes by about 510
o
. Using Eqn. 4.6, the SAW velocity changes
by about 0.13% to achieve a phase shift of 510
o
. It is important to note that, unlike the
thermal phase shifter, the electroacoustic phase shifter does not consume static DC power
while demonstrating a large phase shift.
100
Figure 4.10: Microphotograph of the electroacoustic phase shifter.
Figure 4.11: (a) S
21
magnitude result and (b) measured phase shifts for the straight SAW phase
shifter (blue) and 180
o
waveguide bend (red) at 609 MHz.
A 180
o
waveguide bend structure, similar to the structure shown in Fig. 3.50 but with
a bend radius of 600 m, was also fabricated on a bonded 128
o
Y-cut LiNbO
3
-on-Si wafer.
The metallization used was 100 nm thick gold. The measured S
21
and phase shifts were
measured and plotted as the red curves in Fig. 4.11. The results demonstrate electroacoustic
waveguiding of a SAW through a bend structure as well. Both the straight waveguide and
180
o
waveguide bend show the loss increasing at higher bias voltages, with the waveguide
bend showing a much larger increase. This is due to the inversion of the surface charges in
the silicon behaving as a \short-circuit layer" to the propagating SAW [91].
4.4 Summary
This chapter discussed and demonstrated two dierent types of SAW phase shifters: thermal
phase shifter and electroacoustic phase shifter. The thermal phase shifter is heated through
the use of a resistor placed in close proximity to the SAW waveguide, with the tempera-
ture change causing a change in the SAW velocity, which manifested as a change in phase.
101
However, due to the poor thermal conductivity of lithium niobate, a large amount of DC
power was dissipated in order to produce a 2 phase shift. On the other hand, the elec-
troacoustic phase shifter did not consume DC power while producing phase shifts over 2.
The electroacoustic phase shifter was designed using a 5 m thick LiNbO
3
bonded onto a
silicon substrate. The depletion of the charges in the silicon surface at the bonded surface
modulated the stiness of the lithium niobate as well as removed a \short-circuit layer"
at the LiNbO
3
-Si interface, causing a modulation of the SAW velocity and thus, the phase
of the propagating SAW. Both a straight and bent electroacoustic SAW phase shifter were
demonstrated.
102
Chapter 5
Case Study
The previous chapters have introduced IDTs, waveguide tapers, straight waveguides, waveg-
uide bends, and SAW phase shifters. These constitute building blocks for ultimately building
a signal processing system. In this chapter, two example systems comprising of these build-
ing blocks will be discussed in the context of performing signal processing of radio frequency
(RF) signals.
5.1 Interference Cancellation
Wireless communication systems employ many techniques to improve performance and in-
crease capacity. One of the functions that are supported is allowing two-way communication,
also known as duplexing [94]. This is basically the ability to \talk" as well as "listen" on
the wireless device. One way to accomplish two-way communication is to employ time di-
vision duplexing (TDD). In TDD, transmitting and receiving messages occurs on the same
frequency but at dierent times, as shown in Fig. 5.1. A simple example of a TDD system
is in walkie-talkies in which a button is pushed to \talk" while it is released to \listen." In
this fashion, the transmission and reception of messages is done at dierent times, allowing
for two-way communication.
Another technique for enabling two-way communication is called frequency division du-
plexing (FDD). In FDD, transmission and reception occur on dierent frequencies. The
103
Figure 5.1: A simple diagram of a time division duplexed system (left) as well as a diagram
depicting the transmit (Tx) and receive (Rx) paths operate at dierent times (right).
Figure 5.2: A simple diagram of a frequency division duplexed system (left) as well as a diagram
depicting the transmit (Tx) and receive (Rx) paths operating at dierent frequencies (right).
use of dierent frequencies enables simultaneous transmission and reception to occur. A
conceptual diagram of an FDD system is shown in Fig. 5.2. With FDD systems, the trans-
mit and receive signals are isolated by a bandpass lter, allowing for simultaneous two-way
communication.
To improve spectral eciency, another technique that has garnered interest is what is
known as in-band full duplex operation (IBFD) [95]. In IBFD, transmission and reception
occur simultaneously at the same frequency. This potentially doubles the spectral eciency
of the system as instead of one frequency band being used for transmission and another being
used for reception, transmission and reception happens in the same frequency band, allowing
the other frequency band to be used by other users. However, simultaneously transmitting
and receiving using the same frequency band has a very detrimental eect known as self-
interference. Self-interference is the interference the transmitter causes to its own receiver as
the two share the same frequency of operation. To make matters worse, the received signal
will be weaker than the signal coming from its own transmitter as the signal would be coming
104
from a device located much further away than the transmitter. Also, the self-interference
can take many paths. One path is directly from the transmitter to the receiver. The other
paths can come from re
ected signals of the transmitted signal back to the receiver. As
the transmitter and receiver paths are operating on the same frequency, the self-interference
signals cannot be ltered without ltering the target frequency. The system can share the
antenna by employing a circulator, mitigating the direct self-interference path but will not
mitigate the eects from the re
ected self-interference.
While the self-interference cannot be ltered, it is possible to cancel it. Conceptually,
subtracting a copy of the transmitted signal, which becomes an interference signal for the re-
ceiver, from the received signal will cancel self-interference [95] [96]. The process seems quite
simple and straight forward as the transmitted signal should be known. However, there are
many hurdles that must be overcome in order to successfully apply self-interference cancella-
tion. The amount of suppression that must be achieved could be over 100 dB to completely
cancel the self-interference [96]. For example, WiFi signals are typically transmitted at 20
dBm average power and a receiver noise
oor around -90 dBm. That means that 110 dB
of suppression is required to bring the self-interference signal level down to the noise
oor.
One might consider performing the cancellation in the digital domain by rst passing the
received signal through an analog-to-digital converter (ADC) [95]. For the WiFi signal, if a
15 dB isolation is assumed between the transmitter and receiver, the self-interference signal
would be at 20 dBm - 15 dB = 5 dBm. That would mean the ADC would need a dynamic
range of 5 dBm - (-90 dBm) = 95 dB, which is almost 16 eective number of bits (ENOB).
The signal levels and required ADC dynamic range are illustrated in Fig. 5.4. This does not
take into account extra bits to budget for additional headroom as well as extra bits to make
sure the system is not quantization noise limited.
Also, ideally, the transmitted signal would be clean without any harmonic contents, as
shown in Fig. 5.3(a). However, the devices in the transmitter add noise to the signal-of-
interest while the non-linearity creates harmonic frequency content, as shown in Fig. 5.3(b).
105
Figure5.3: (a) Ideal two-tone signal spectrum out from the transmitter and (b) actual transmitted
spectrum with increased noise and signal harmonics.
Figure 5.4: Illustrative example of self-interference signal level and required ADC dynamic range
to cancel self-interference signal.
A self-interference cancellation must take into account for the added distortion to the desired
transmitted signal. An analog self-interference cancellation scheme that addresses these is-
sues is shown in Fig. 5.5. Figure 5.5(a) shows a transceiver that uses separate antennas
for the transmitter and the receiver while Fig. 5.5(b) employs a circulator to isolate the
transmitter and receiver while sharing a single antenna. While Fig. 5.5(b) uses a circulator,
it only provides a limited amount of isolation between the transmitter and receiver, while
also suering from re
ected self-interference signals as well. In both cases, a portion of the
transmitter signal is tapped o before the antenna, thereby capturing the transmitter noise
along with any harmonics that were generated. This signal is then delayed and attenuated
to the appropriate level in order to cancel the self-interference signal. Multiple delay and
attenuation paths can be implemented in order to cancel self-interference signals that arrive
from re
ections as well.
106
Figure 5.5: A simple diagram of a system employing self-interference cancellation using (a) two
separate antennas for the transmitter and the receiver and (b) using a single shared antenna by
using a circulator.
107
In chapter 4, the LiNbO
3
-on-Si SAW waveguide platform was shown to be able to provide
attenuation as well as a variable group delay. The group delay change can be varied to a
few nanoseconds, depending on the length of the waveguide. Unfortunately, the limited
bandwidth of the IDT makes it dicult to demonstrate self-interference cancellation. The
narrow bandwidth makes a phase shift a good approximation of group delay. Therefore,
even though the waveguide demonstrates varying group delay, it was not possible to come up
with a measurement setup to demonstrate self-interference cancellation based on the varying
group delay. So, while it is possible to use electroacoustic SAW waveguides to provide the
necessary attenuation and group delay to perform self-cancellation, it remains a conceptual
idea at the moment.
5.2 SAW Phased Array
Phased arrays are multiple antenna systems that are capable of beam forming and electron-
ically steering through changes in the relative phases of a transmitted or received signal of
each antenna element [97]. An RF phased array system using surface acoustic waves is an
intriguing application for the electroacoustic SAW phase shifters. Large phase shifts were
demonstrated for the LiNbO
3
-on-Si electroacoustic phase shifters in chapter 4. The phase
shifts were also obtained without burning any power, which makes a low power phased array
system a possibility. The concept of a SAW phased array is not new and has been mentioned
as a possible application for a tunable SAW delay line [90]. A SAW phased array employing
an array of IDTs that were oset from one another to provide a xed phase shift between
IDT elements was also demonstrated on PZT substrates [98]. However, it is believed that a
variable phase SAW phased array has yet to be demonstrated.
A simple diagram of a 4-element antenna array receiver is shown in Fig. 5.6. An inci-
dent wave is shown being received at an angle
in
to the normal of the antenna front. The
antenna of path 1 will receive the signal rst, followed by antenna 2 after some delay, and so
108
Figure 5.6: Conceptual diagram of a 4-element antenna array receiver.
Figure 5.7: Plot of a 4-element array pattern for dierent beam-steering angles.
forth. If the delay elements, signied by
x
, can compensate for the relative delays between
elements, the signal from each path will constructively sum and the signal can be recovered.
On the other hand, the signal will destructively sum if the delays do not compensate for
the relative delays between antenna elements. By using this capability of constructively and
destructively summing signals accordingly with the incident signal wavefront, a beam can
be formed. Figure 5.7 shows beam patterns for a 4-element antenna array for dierent delay
settings, illustrating the beamforming and steering.
The array pattern is obtained by calculating the array factor of an antenna array and
plotting the result in polar coordinates [99]. The array factor is obtained by assuming a
wavefront as shown in Fig. 5.8. The wavefront will reach the top antenna rst. It will have
109
to travel a distance
1
before it reaches the next antenna, and a distance
2
to reach the
third antenna, and so on. The extra distance the wavefront must travel is given by
m
=mkdcos() (5.1)
where m is the element number, starting from 0 at the top, and k is the wavenumber. The
array factor for an N element array is then
AF = 1 +e
jkdcos()+
+e
j[2kdcos()+]
+::: +e
j[(N1)kdcos()+]
; (5.2)
where is the phase dierence between dierent paths. Equation 5.2 can be simplied and
normalized to
AF =
1
N
sin(
N
2
0
)
sin(
1
2
0
)
(5.3)
where ' is
0
=kdcos() +: (5.4)
While a variable delay element will provide beam forming independent of the signal
frequency and bandwidth, many RF bands are only a small fraction of the center frequency
[97]. In such narrowband applications, the uniform delay can be approximated by a constant
phase shift. The variable SAW waveguides introduced in chapter 4 do perform as variable
group delay elements but due to the narrowband operation of the IDT, the device will behave
more like a variable phase shifter that can be used in narrowband phased array systems.
The benet of a phased array receiver can be explained using the n-element receiver
shown in Fig. 5.9 [100]. The input noise N
in
is assumed to be uncorrelated. In such a case,
the input signals add coherently as
110
Figure 5.8: N-element antenna array with incoming wavefront.
S
o
ut =n
2
G
1
G
2
S
in
(5.5)
while the total output noise becomes
N
out
=n(N
in
+N
1
)G
1
G
2
+N
2
G
2
: (5.6)
The array noise factor can then be expressed as
F =n
SNR
in
SNR
out
: (5.7)
Equation 5.7 shows that the sensitivity of an n-element receiver improves by 10log
10
(n)
compared to a single element receiver.
A couple of design choices for a phased array system is the spacing between the antenna
elements, d, and the number of elements to use in the array, N, as shown in Fig. 5.10. The
antenna elements of a phased array are usually spaced/2 apart [97] [100] [101]. Ideal array
patterns for antenna spacings of /4, /2, and are plotted in Fig. 5.11. As the spacing
111
Figure 5.9: n-element array receiver with coherent signal summation and uncorrelated noise,
improving output SNR.
between elements increases, the beam width is shown becoming narrower but with side-lobes
appearing. As a spacing equates to a 360
o
phase shift between elements, three beams are
actually formed as 0
o
, 90
o
, and -90
o
incident angles all coherently combine with 0
o
phase
shifts between elements. While /4 spacings between elements doesn't exhibit side-lobes,
the result neglects the eect of mutual coupling between antenna elements that aects the
performance of the phase array [102]. Also, it is important to maintain uncorrelated noise
sources for the 10log
10
(N) improvement in sensitivity [100]. Therefore,/2 antenna spacings
is a trade-o between the coupling of antenna elements, maintaining uncorrelated noise
sources, and side-lobe performance.
Figure 5.12 shows ideal array patterns for an array with 2, 4, 8, and 16 antenna elements.
The beam width becomes narrower and directed as the number of elements increases. While
side-lobes begin to appear from 4 elements, the level is much smaller compared to the main
lobe and becomes smaller as the number of elements increases.
5.2.1 Implementation and Measurement Results
To verify the functionality of the electroacoustic phase shifter, it was implemented in a 1D
4-element phased array. The array was fabricated on a 128
o
YX LiNbO
3
with a thickness
112
Figure 5.10: A couple of the design considerations of a phased array are the antenna spacings
and the number of elements to use.
Figure 5.11: 4-element array pattern for antenna spacings of=4 (blue),=2 (red), and (black).
Figure 5.12: Array pattern for 2, 4, 8, and 16 antenna elements.
113
Figure 5.13: Die microphotograph of 4-element electroacoustic SAW phased array.
of 5 m that was bonded on a 500 m thick high-resistivity p-type silicon substrate. A die
microphotograph of the device is shown in Fig. 5.13. The phase shifters for each element are
biased through vb1 - vb4. An extra bias pad is added for each element for redundancy. A
binary-tree acoustic waveguide combiner is used to coherently combine the signals from all
four paths. An additional DC voltage, vb5, is used to bias the waveguides in the combiner
to remove excess losses caused by the charges in the silicon surface under the combiner. The
die was mounted on a printed circuit board (PCB) using an electrically conductive epoxy
and gold wire bonds were used to wire bond the pads to the PCB.
The S
11
for each element, and the S
21
measurement results for each element with the
phase shifter biased at 60 V are shown in Fig. 5.14(a) and (b), respectively. As can be
seen from the result, the S
11
and S
21
of element 1 are signicantly dierent from the other
three elements. Unfortunately, it turns out that the IDT for element 1 shows some visible
damage. Therefore, the phased array can only operate as a 3-element phased array. Figure
5.15 shows the peak S
21
and corresponding phase shifts at 604 MHz for all four paths in the
114
Figure 5.14: (a) S
11
measurement results for the four elements of the SAW phased array. (b)
S
21
measurement results for the four elements of the SAW phased array with electroacoustic phase
shifter biased at 60 V.
Figure 5.15: (a) S
21
measurement results at 604 MHz and (b) corresponding phase shifts for the
four elements of the SAW phased array over bias voltage. vb5 is biased at 30 V.
SAW phased array structure. Figure 5.15(a) also shows the dierent performance between
element 1 and the other three elements. The three working elements show more than 400
o
of phase shifts across 60 V of bias voltage.
Due to the bidirectional nature of the structure, the 3-element phased array can operate
as either a transmitting phased array or as a receiving phased array. For the purpose of this
work, the structure was demonstrated as a receiving phased array. The measurement setup
to demonstrate the array is shown in g. 5.16(a). The transmitter uses a Hittite Microwave
HMC-T2220 DC-20 GHz signal generator connected directly to an L-COM ceiling mount
antenna. On the receive side, Abracon 5G sub-6GHz blade antennas, spaced 25 cm apart,
were used for the phased array. The antennas fed Mini-Circuits ZX60-V63+ high gain
115
Figure 5.16: (a) Phased array measurement setup for Rx mode. (b) Outdoor measurement setup
with array antennas spaced at =2 for SAW phased array receiver measurements.
wideband ampliers. The ampliers then drove the 3-element phased array. The output
of the phased array fed another ZX60-V63+ amplier before feeding an Agilent E4440B
spectrum analyzer. Unfortunately, as the anechoic chamber was not readily available, the
measurements were performed outside and therefore, the non-ideal eects from re
ections
were unavoidable. The outdoor phased array antenna measurement setup is shown in g.
5.16(b).
The transmitter (Tx) setup was kept xed while the makeshift receiver (Rx) antenna
stand was rotated around an axis. The Tx and Rx antennas were about 6 meters apart.
Figure 5.17 shows the antenna patterns that were measured from four dierent phased array
bias settings. Despite the presence of re
ections, the results show beamforming in four
dierent directions, demonstrating the operation of the SAW RF phased array.
5.3 Summary
This chapter discussed and demonstrated the use of the electroacoustic phase shifters dis-
cussed in chapter 4 for processing RF signals. An RF interference canceller was discussed,
and attempts were made to try to obtain meaning measurements for such an application.
116
Figure 5.17: Received phased array pattern for four dierent settings.
However, due to the narrow bandwidth of the device, the phase shifter could not be demon-
strated as a variable delay element as well, which is needed for a proper interference cancel-
lation system.
However, the electroacoustic phase shifters were able to be used in a passive, all-acoustic
phased array. The passive nature of the structure makes it a truly bidirectional phased array,
being able to operate as a transmitting phased array or as a receiving phased array. Outdoor
antenna measurements were performed with the phased array structure as a receiver, and
beamforming at dierent angles was demonstrated.
117
Chapter 6
Conclusion and Recommendations For Future Work
6.1 Conclusion
Acoustic wave devices are ubiquitous in RF and wireless systems, largely as front-end lters,
due to their compact size, low loss, and high selectivity. This thesis explored the design of
SAW waveguides and their use to realize more complex microwave signal processors. The
design of waveguide building blocks including straight waveguides, waveguide bends, and
waveguide couplers have been studied and demonstrated using 128
o
Y-cut LiNbO
3
. The
waveguides were designed by placing a thin overlay metal over the region of connement.
Due to the mass of the thin overlay metal, an eect known as \mass loading" created a slow
velocity region, conning the surface acoustic wave. The study explored the use of three
dierent metals: aluminum, tungsten, and gold. Mass loading eects are generally avoided
as it does dampen the propagating surface wave, increasing the loss. Thus, metals like
aluminum, which has a relatively small mass density, are used for SAW devices. However,
for waveguiding purposes, it was shown that a large mass loading eect is necessary to
conne the wave. Both tungsten and gold conned the SAW, with gold showing the best
performance in the SAW waveguides, while the aluminum waveguide was demonstrated to
not conne the wave.
The waveguide structures were then fabricated on a thin LiNbO
3
layer that was bonded
to a high resistivity silicon wafer. The addition of the silicon substrate made it possible to
118
design a waveguide based electroacoustic phase shifter, opening up the possibility to realize
more complex signal processing of microwave signals possible. As a proof-of-concept example,
an all-acoustic bidirectional phased array frontend was demonstrated.
6.2 Future Research Directions
Unfortunately, while waveguiding of surface acoustic waves through various waveguide struc-
tures were demonstrated, both the loss and size of the structures were much larger than
expected. The loss breakdown in chapter 3 showed that the waveguide tapers contributed
the most loss, followed by the IDTs. A possible optimization of the taper can look into min-
imizing the excitation of higher order modes or the mode conversion back to the Rayleigh
mode to minimize the loss. The use of unidirectional IDTs can help minimize the notch that
can be present with the use of re
ectors to provide a wide band frequency response. Also,
simulations seem to indicate that the impedance of the IDTs seem to change depending on
whether it is interfacing a taper, another IDT, or open LiNbO
3
surface. This impedance
mismatch can contribute to the IDT losses as well.
The overlay waveguides demonstrated in this work had excess loss due to the dampening
of the surface acoustic wave from the mass loading eect. Another type of overlay waveguide
places material on the region outside of the connement region, or the cladding region. This
would keep the guiding region free and reduce the loss. However, the material used for the
cladding region must have a surface acoustic wave velocity that is faster than that of the
piezoelectric material, which was 128
o
Y-cut LiNbO
3
in this work. This would create a faster
velocity region in the cladding region, conning the surface wave in the \slower" free region
in between the cladding region. It was not possible to explore this possibility as this work
focused on designing the SAW devices and waveguides with only one mask. However, the
material used in the cladding region probably should not mass load the region as it would
counter the eect of using a material with a faster surface wave velocity.
119
The waveguide bend displacement result in chapter 3 also seemed to indicate that there
is some mode conversion at the interface between a straight waveguide and waveguide bend.
The bends were designed as simple circular sections but a more oval shape with a more grad-
ual transition to a bend may minimize this mode conversion loss, and possibly the radiation
loss as well. The waveguide bend itself should probably taper down to a narrower width to
account for the changing SAW velocity as it propagates around the bend. The waveguide is
most likely too wide as it makes a 90
o
bend, possibly exciting and supporting higher order
modes which are contributing to the loss. It is also worthwhile to explore phononic crystal
structures to create bandgaps for conning SAWs. They have been shown to bend SAWs in
a very compact manner, but the question remains whether phononic crystal structures can
be designed with low loss and a compact size while supporting commercial SAW fabrication
methods.
Another area to explore is pushing the operation of the waveguides to higher frequencies.
The frequency was limited to the lithography of the interdigital transducers and so simply
using better lithography would make the operation of the devices at higher frequencies pos-
sible. However, another possibility would be to explore higher order surface modes. The
operation of higher order modes, such as shear horizontal modes though, requires the use of
a thin propagating medium in order to not experience excess loss due to the excitation of
lower order modes. The exploration of surface acoustic wave devices on a bonded LiNbO
3
-
on-Si wafer would make it possible to explore higher order modes by using a thinner LiNbO
3
layer than was used in this work. With bonded layers, another possibility is to only use the
thin LiNbO
3
layer to excite the SAW and have the SAW propagate in a substrate with a
faster SAW velocity. Layered structures have been used to demonstrate SAW transduction
at 33.7 GHz [47].
Finally, the use of a bonded LiNbO
3
layer on a silicon wafer also opens up the possibility
of designing SAW ampliers as well. While SAW ampliers have been demonstrated in the
past, their inclusion would make the implementation of an all-acoustic microwave front-end
120
system possible. This is attractive as it would eliminate the need to switch in between elec-
trical and acoustic domains, as is done in current RF and wireless systems, and process RF
signals all in the acoustic domain.
121
References
[1] Thomas D. Rossing. Springer Handbook of Acoustics. Springer Science+Business
Media, New York, USA, 2007.
[2] David P. Morgan. History of saw devices. IEEE Proc. Intern. Freq. Contr. Symp.,
pages 439 { 460, May 1998.
[3] D. Morgan. Surface Acoustic Wave Filters with Applications to Electronic Communi-
cations and Signal Processing. Academic Press, Amsterdam, 2 edition, 2017.
[4] J. D. Ross, S. J. Kapuscienski, and K. B. Daniels. Variable delay lines using ultrasonic
surface waves. IRE National Convention, pages 118 { 120, 1958.
[5] Ian N. Court. Microwave acoustic devices for pulse compression lters. IEEE Microw.
Theory and Tech., MTT-17(11):968 { 986, November 1969.
[6] Jerey H. Collins. A short history of microwave acoustics. IEEE Trans. Microw.
Theory and Tech., MTT-32(9):1127 { 1140, September 1984.
[7] Donald C. Malocha. Evolution of the saw transducer for communication systems.
IEEE Proc. Ultrason. Symp., pages 302 { 310, August 2004.
[8] W. R. Smith, H. M. Gerard, J. H. Collins, T. M. Reeder, and H. J. Shaw. Design
of surface wave delay lines with interdigital transducers. IEEE Microw. Theory and
Tech., MTT-17(11):865 { 873, November 1969.
[9] C. S. Hartmann, W. S. Jones, and H. Vollers. Wideband unidirectional interdigital
surface wave transducers. IEEE Trans. Sonics and Ultrason., SU-19(3):378 { 381, July
1972.
[10] C. S. Hartmann, P. V. Wright, R.J. Kansy, and E. M. Garber. An analysis of saw
interdigital transducers with internal re
ectors and the application to the design of
single-phase unidirectional transducers. IEEE Proc. Ultrason. Symp., pages 40 { 45,
October 1982.
[11] S. L. Lehtonen, V. P. Plessky, C. S. Hartmann, and M. M. Salomaa. Spudt lters
for the 2.45 ghz ism band. IEEE Trans. Ultrason., Ferroelectr., and Freq. Control,
51(12):1697 { 1703, December 2004.
[12] M. S. Kharusi and G. W. Farnell. On diraction and focusing in anisotropic crystals.
Proc. IEEE, 69(8):945 { 956, August 1972.
122
[13] T.-T. Wu, H.-T. Tang, Y.-Y. Chen, and P.-L. Liu. Analysis and design of focused inter-
digital transducers. IEEE Trans. Ultrason, Ferroelectr, and Freq. Control, 52(8):1384
{ 1392, August 2005.
[14] F.G. Marshall and E.G.S Paige. Novel acoustic-surface-wave directional coupler with
diverse applications. Electronic Letters, 7(18):460 { 462, August 1971.
[15] W. Soluch. Scattering matrix approach to one-port saw resonators. IEEE Trans.
Ultrason., Ferroelectr., and Freq. Control, 47(6):1615 { 1618, November 2000.
[16] G. Gugliandolo, Z. Marinkovic, G. Campobello, G. Crupi, and N. Donato. On the
performance evaluation of commercial saw resonators by means of a direct and reliable
equivalent-circuit extraction. Micromachines, 2021, 12, 303.
[17] M. F. Lewis. Triple-transit suppression in surface-acoustic-wave devices. Electronics
Letters, 8(23):553 { 554, November 1972.
[18] M. Lewis. Saw lters employing interdigitated interdigital transducers, iidt. IEEE
Proc. Ultrason. Symp., pages 12 { 17, October 1982.
[19] S. C.-C. Tseng and G. W. Lynch. Saw planar network. IEEE Proc. Ultrason. Symp.,
pages 282 { 285, November 1974.
[20] M. Hikita, Y. Ishida, T. Tabuchi, and K. Kurosawa. Miniature saw antenna duplexer
for 800-mhz portable telephone used in cellular radio systems. IEEE Microw. Theory
and Tech., 36(6):1047 { 1056, June 1988.
[21] T. Morita, Y. Watanabe, M. Tanaka, and Y. Nakazawa. Wideband low loss double
mode saw lters. IEEE Proc. Ultrason. Symp., pages 95 { 104, October 1992.
[22] C. C. W. Ruppel. Acoustic wave lter technology - a review. IEEE Trans. Ultrason.,
Ferroelectr., and Freq. Control, 64(9):1390 { 1400, September 2017.
[23] E. A. Ash and D. Morgan. Realisation of microwave-circuit functions using acoustic
surface waves. Electronic Letters, 3:462 { 464, October 1967.
[24] E. A. Ash, R. M. De La Rue, and R. F. Humphryes. Microsound surface waveguides.
IEEE Microw. Theory and Tech., MTT-17:882 { 892, November 1969.
[25] A. A. Oliner. Waveguides for acoustic surface waves: A review. Proc. IEEE, 64:615 {
627, May 1976.
[26] L.R. Adkins and A.J. Hughes. Long delay lines employing surface acoustic wave guid-
ance. Journal of Applied Physics, 42(5):1819 { 1822, April 1971.
[27] L.A. Coldren and R.V. Schmidt. Acoustic surface wave slot waveguides on bi
12
geo
20
.
IEEE Trans. Sonics and Ultrasonics, SU-21(2):128 { 130, April 1974.
[28] L. Shao et al. Electrical control of surface acoustic waves. arXiv:2101.01626, January
2021.
123
[29] P. Boucher, S. Rauwerdink, A. Tahraoui, C. Wenger, Y. Yamamoto, and P.V. Santos.
Ring waveguides for gigahertz acoustic waves on silicon. Appl. Phys. Lett., 105, 2014.
[30] P. Hartemann. Acoustic-surface-wave velocity decrease produced by ion implantation
in lithium niobate. Appl. Phys. Lett., 27:263 { 265, September 1975.
[31] F. Graham Marshall, Cleland O. Newton, and Edward G. S. Paige. Surface acoustic
wave multistrip components and their applications. IEEE Trans. Microw. Theory and
Tech., MTT-21(4):216 { 225, April 1973.
[32] Ken-ya Hashimoto. Surface Acoustic Wave Devices in Telecommunications. Springer-
Verlag Berlin Heidelberg, New York, USA, 2000.
[33] R. Lu, Y. Yang, M.-H. Li, and S. Gong. Ghz low-loss acoustic rf couplers in lithium
niobate thin lm. IEEE Trans. Ultrason, Ferroelectr, and Freq. Control, 67(7):1448 {
1461, July 2020.
[34] J. Tsutsumi, T. Matsuda, O. Ikata, and Y. Satoh. A novel re
ector-lter using a saw
waveguide directional coupler. IEEE Trans. Ultrason., Ferroelectr., and Freq. Control,
47(5):1228 { 1234, September 2000.
[35] M. K. Miller. Acoustic wave motion along a periodic surface. The Journal of the
Acoustical Society of America, 36, November 1964.
[36] R. Lu, T. Manzaneque, Y. Yang, and S. Gong. Lithium niobate phononic crystals for
tailoring performance of rf laterally vibrating devices. IEEE Trans. Ultrason, Ferro-
electr, and Freq. Control, 65(6):934 { 944, June 2018.
[37] Jia-Hong Sun and Tsung-Tsong Wu. Propagation of surface acoustic waves through
sharply bent two-dimensional phononic crystal waveguides using a nite-dierence
time-domain method. Phys. Rev. B, 74:174305, November 2006.
[38] Zhangliang Xu and Yong J. Yuan. Implementation of guiding layers of surface acoustic
wave devices: A review. Biosensors and Bioelectronics, 99:500 { 512, 2018.
[39] B. E. Burke. An electronically variable surface acoustic wave phase shifter. IEEE
GMTT Intern. Microw. Symp. Dig., pages 56 {57, May 1971.
[40] P. S. Cross, W. H. Haydl, and R. S. Smith. Electronically variable surface-acoustic-
wave velocity and tunable SAW resonators. Appl. Phys. Lett., 28:1 { 3, January 1976.
[41] J. D. Crowley, J. F. Weller, and T. G. Giallorenzi. Acoustoelectric SAW phase shifter.
Appl. Phys. Lett., 31:558 { 560, November 1977.
[42] L. Hackett et al. High-gain leaky surface acoustic wave amplier in epitaxial InGaAs
on lithium niobate heterostructure. Appl. Phys. Lett., 114:1 { 5, June 2019.
[43] Z. Insepov et al. Surface acoustic wave amplication by direct current-voltage supplied
to graphene lm. Appl. Phys. Lett., 106:1 { 5, January 2015.
124
[44] A.M. Siddiqui et al. Comparison of amplication via the acousto-electric eect of
rayleigh and leaky-saw modes in a monolithic surface inp:ingaas/lithium niobate het-
erostructure. Ferroelectrics, 557:1:58 { 65, 2020.
[45] S. Buyukkose, B. Vratzov, D. Atac, J. van der Veen, P. V. Santos, and W. G. van der
Wiel. Ultrahigh-frequency surface acoustic wave transducers on ZnO/SiO2/si using
nanoimprint lithography. Nanotechnology, 23(31):315303, July 2012.
[46] L. Wang et al. Enhanced performance of 17.7 GHz SAW devices based on
AlN/diamond/Si layered structure with embedded nanotransducer. Appl. Phys. Lett.,
111:1 { 5, December 2017.
[47] L. Wang, S. Chen, J. Zhang, J. Zhou, C. Yang, Y. Chen, and H. Duan. High perfor-
mance 33.7 GHz surface acoustic wave nanotransducers based on AlScN/diamond/Si
layered structures. Appl. Phys. Lett., 113:1 { 4, August 2018.
[48] J. Zheng et al. 30 GHz surface acoustic wave transducers with extremely high mass
sensitivity. Appl. Phys. Lett., 116:1 { 5, March 2020.
[49] L. Hackett et al. Towards single-chip radiofrequency signal processing via acoustoelec-
tric electron-phonon interactions. Nature Communications, 12:1 { 11, May 2021.
[50] R. Aigner. Tunable lters? reality check. IEEE Microw. Mag., 16(7):82 { 88, August
2015.
[51] P. Delsing et al. The 2019 surface acoustic waves roadmap. J. Phys. D: Appl. Phys,
52(35), 2019.
[52] J.R. Barber. Elasticity. Spring Science + Business Media B.V., New York, 3 edition,
2010.
[53] C. K. Campbell. Surface Acoustic Wave Devices for Mobile and Wireless Communi-
cations. Academic Press, Inc., San Diego, CA, USA, 1998.
[54] Gordon S. Kino. Acoustic Waves: Devices, Imaging, And Analog Signal Processing.
Prentice Hall, Inc., New Jersey, corrected ed. edition, 2000.
[55] Ken ya Hashimoto et al. Recent development of temperature compensated saw devices.
Ultrasonics Symposium (IUS), 2011 IEEE International, pages 79 { 86, 2011.
[56] A. N. Darinskii, M. Weihnacht, and H. Schmidt. Surface acoustic wave scattering
from steps, grooves, and strips on piezoelectric substrates. IEEE Trans. Ultrason.,
Ferroelect., and Freq. Control, 57(9):2042 { 2050, September 2010.
[57] U.C. Kaletta and C. Wenger. Fem simulation of rayleigh waves for cmos compatible
saw devices based on aln/sio
2
/si(100). Ultrasonics, 54(1):294 { 295, 2014.
[58] U.C. Kaletta et al. Monolithic integrated saw lter based on aln for high-frequency
applications. Semicond. Sci. Technol., 28(6):1 { 7, May 2013.
125
[59] Y. Satoh, O. Ikata, T. Miyashita, and H. Ohmori. Rf saw lters. Intern. Symp.
Acoustic Wave Devices for Future Mobile Comm. Systems, pages 125 { 132, 2001.
[60] R. Weigel, B. Bader, G. Fischerauer, and P. Russer. Design and performance of wide-
band iidt-type saw lters with low loss and improved sidelobe suppression. IEEE
Intern. Microw. Symp. Digest, pages 1505 { 1508, June 1993.
[61] K. Yamanouchi and T. Terashima. 2 ghz range low loss iidt lters using narrow gap
idt structure and new cross-over techniques. IEEE Proc. Ultrason. Symp., pages 103
{ 106, November 1995.
[62] M. Koshino et al. Small-sized dual-band saw lters using
ip-chip bonding technology.
IEEE Proc. Ultrason. Symp., pages 341 { 346, October 1999.
[63] G. Endoh, M. Ueda, O. Kawachi, and Y. Fujiwara. High performance balanced type
saw lters in the range of 900mhz and 1.9ghz. IEEE Proc. Ultrason. Symp., pages 41
{ 44, October 1997.
[64] A. Loseu. Double-mode saw lters with improved selectivity. IEEE Proc. Ultrason.
Symp., pages 12 { 17, October 1982.
[65] S. Inoue, J. Tsutsumi, T. Matsuda, M. Ueda, O. Ikata, and Y. Satoh. Ultra-steep
cut-o double mode saw lter and its application to a pcs duplexer. IEEE Trans.
Ultrason., Ferroelectr., and Freq. Control, 54(9):1882 { 1887, September 2007.
[66] Doberstein Sergei. Balanced low-loss 2-idt double mode saw lter with narrowed pass-
band and improved selectivity. IEEE Joint Conf. of the IFCS and EFTF Proceedings,
2015.
[67] R. Weigel, K. Weigenthaler, R. Dill, and I. Schropp. A 900 mhz ladder-type saw lter
duplexer. IEEE Intern. Microw. Symp. Digest, pages 413 { 416, June 1996.
[68] A. Springer et al. Design and performance of a saw ladder-type lter at 3.15 ghz
using saw mass-production technology. IEEE Trans. Microw. Theory and Techn.,
47(12):2312 { 2316, December 1999.
[69] K. Ibata, K. Misu, K. Murai, K. Yamagata, and K. Yoshida. An m-derived ladder
high pass saw lter. IEEE Symp. Ultrason., pages 397 { 400, October 2003.
[70] V. Nogorodov et al. Compact low-loss 2.4ghz ism-band saw bandpass lter on the ltcc
substrate. Proc. Asia-Pacic Microw. Conf., pages 2072 { 2075, December 2009.
[71] Y. Takamine, T. Takai, H. Iwamoto, T. Nakao, and M. Koshino. A novel 3.5 ghz
low-loss bandpass lter using i.h.p saw resonators. Proc. Asia-Pacic Microw. Conf.,
pages 1342 { 1344, November 2018.
[72] R. Su et al. Wideband and low-loss surface acoustic wave lter based on 15
o
yx-
linbo
3
/sio
2
/si structure. IEEE Electron Device Letters, 42(3):438 { 441, March 2021.
126
[73] B. Lee, S. Lee, H. Lee, and H. Shin. Young's modulus measurement of aluminum thin
lm with cantilever structure. Proc. SPIE 4557, Micromachining and Microfabrication
Process Technology VII, (28 September 2001).
[74] F. Zhu, Z. Xie, and Z. Zhang. Phase control and Young's modulus of tungsten thin
lm prepared by dual ion beam sputtering deposition. AIP Advances, 8:1 { 7, March
2018.
[75] C. Birleanu et al. Temperature eect on the mechanical properties of gold nano lms
with dierent thickness. 2016 IOP Conf. Ser.: Mater. Sci. Eng., 147, 2016.
[76] Y. Shui, J.M. Lin, H. Wu, N. Wang, and H. Chen. Optimization of single-phase,
unidirectional transducers using three ngers per period. IEEE Trans. Ultrason., Fer-
roelectr., and Freq. Control, 49(12):1617 { 1621, December 2002.
[77] C. K. Campbell. Surface Acoustic Wave Devices and Their Signal Processing Appli-
cations. Academic Press, Inc., San Diego, CA, USA, 1989.
[78] F. Graham Marshall, Cleland O. Newton, and Edward G. S. Paige. Theory and design
of the surface acoustic wave multistrip coupler. IEEE Trans. Sonics and Ultrasonics,
SU-20(2):124 { 133, April 1973.
[79] L. Chrostowski and M. Hochberg. Silicon Photonics Design. Cambridge University
Press, United Kingdom, 2015.
[80] Ken ya Hashimoto and Masatsune Yamaguchi. Optimum leaky-saw cut of litao
3
for
minimised insertion loss devices. Ultrasonics Symposium (IUS), 1997 IEEE Interna-
tional, pages 245 { 254, 1997.
[81] Samer Idres and Hossein Hashemi. Optical binary switched delay line based on low
loss multimode waveguide. In Proc. Opt. Fiber Commun. Conf., pages 1 { 3, 2022.
[82] K. Hashimoto, T. Omori, and M. Yamaguchi. Design considerations on surface acoustic
wave resonators with signicant internal re
ection in interdigital transducers. IEEE
Trans. Ultrason., Ferroelectr., and Freq. Control, 51(11):1394 { 1403, 2004.
[83] C.S. Lam. A review of the recent development of temperature stable cuts of quartz for
saw applications. Intern. Symp. on Acoustic Wave Devices For Future Mobile Comm.
Sys., pages 1 { 8, March 2010.
[84] T.E. Parker and H. Wichansky. Temperature-compensated surface-acoustic-wave de-
vices with SiO
2
lm overlays. J. of Appl. Phys., 50:1360 { 1369, March 1979.
[85] Robert B. Ward. Temperature coecients of saw delay and velocity for y-cut and
rotated linbo
3
. IEEE Trans. Ultrason., Ferroelectr., and Freq. Control, 37(5):481 {
483, September 1990.
[86] N.C. Harris et al. Ecient, compact and low loss thermo-optic phase shifter in silicon.
Opt. Exp., 22, 2014.
127
[87] A. Wixforth, J. Scriba, M. Wassermeier, J. Kotthaus, G. Weimann, and W. Schlapp.
Surface acoustic waves on gaas/al
x
ga
1-x
as heterostructures. Phys. Rev. B, 40(11):7874
{ 7887, October 1989.
[88] Richard M. White. Surface elastic waves. Proc. IEEE, 58(8):1238 { 1276, August
1970.
[89] J. Zhu, Y. Chen, G. Saraf, N.W. Emanetoglu, and Y. Lu. Voltage tunable surface
acoustic wave phase shifter using semiconducting/piezoelectric ZnO dual layers grown
on r-Al
2
O
3
. Appl. Phys. Lett., 89:1 { 3, September 2006.
[90] S.G. Joshi and B.B. Dasgupta. Electronically variable suface acoustic wave time delay
using a biasing electric eld. Ultrasonics Symposium (IUS), 2011 IEEE International,
pages 319 { 323, 1981.
[91] Shuuji Urabe. Voltage controlled monolithic saw phase shifter and its application to
frequency variable oscillator. IEEE Trans. Sonics and Ultrason., SU-29(5):255 { 261,
September 1982.
[92] S. Zhang et al. Surface acoustic wave devices using lithium niobate on silicon carbide.
IEEE Trans. Microw. Theory and Techn., 68(9):3653 { 3666, September 2020.
[93] Ben G. Streetman and Sanjay Kumar Banerjee. Solid State Electronic Devices. Pear-
son Education Inc., New Jersey, USA, 2015.
[94] Behzad Razavi. RF Microelectronics. Pearson Education, Inc., New York, USA, 2
edition, 2012.
[95] A. Sabharwal, P. Schniter, D. Guo, D.W. Bliss, S. Rangarajan, and R. Wichman. In-
band full-duplex wireless: Challenges and opportunities. IEEE J. Sel. Areas Commun.,
32(9):1637 { 1652, September 2014.
[96] D. Bharadia, E. McMilin, and S. Katti. Full duplex radios. Proc. ACM SIGCOMM
Conf., pages 375 { 386, October 2013.
[97] H. Hashemi, X. Guan, A. Komijani, and A. Hajimiri. A 24-ghz sige phased-array re-
ceiver - lo phase-shifting approach. IEEE Trans. Microw. Theory and Tech., 53(2):614
{ 626, February 2005.
[98] C.S. Tsai and L.T. Nguyen. Scanning of surface acoustic wave phased array. Proc.
IEEE, 62:863 { 864, June 1974.
[99] Constantine A. Balanis. Antenna Theory. John Wiley & Sons, Inc., New Jersey, 4
edition, 2016.
[100] X. Guan, H. Hashemi, and A. Hajimiri. A fully integrated 24-ghz eight-element phased-
array receiver in silicon. IEEE J. of Solid-State Circuits, 39(12):2311 { 2320, December
2004.
128
[101] S. Chung, H. Abediasl, and H. Hashemi. A monolithically integrated large-scale optical
phased array in silicon-on-insulator cmos. IEEE J. of Solid-State Circuits, 53(1):275
{ 296, January 2018.
[102] H. Singh, H.I. Sneha, and R.M. Jha. Mutual coupling in phased arrays: A review.
Intern. J. of Ant. and Prop., pages 1 { 23, 2013.
[103] COMSOL Multiphysics, 2021.
129
Appendix A: Tensor Notation
While the stress, strain, elastic or stiness tensors, and piezoelectric tensors were introduced
in chapter 2, they are often notated in a reduced form, which will be discussed here [54].
Stress, denoted as T
ij
, has 6 components being T
xx
, T
xy
, T
xz
, T
yy
, T
yz
, and T
zz
. Recall that
T
xy
= T
yx
, T
yz
= T
zy
, and T
xz
= T
zx
. To simplify the notation, the 6 stress components
can be notated as:
T
xx
=T
1
; (1)
T
yy
=T
2
; (2)
T
zz
=T
3
; (3)
T
yz
=T
4
; (4)
T
zx
=T
5
; (5)
T
xy
=T
6
: (6)
Likewise, strain, denoted as S
ij
, also only has 6 components and can be notated as:
130
S
xx
=S
1
; (7)
S
yy
=S
2
; (8)
S
zz
=S
3
; (9)
S
yz
= 2S
4
; (10)
S
zx
= 2S
5
; (11)
S
xy
= 2S
6
: (12)
The elastic, or stiness, tensors and piezoelectric tensors can also be notated in reduced
forms as well. Recall that the stiness tensor is notated as c
ijkl
. This can be reduced to
c
mn
=c
ijkl
; m;n = 1; 2;:::; 6: (13)
where the subscript m is dened as
m =i fori =j
m = 9ij fori6=j; i;j = 1; 2; 3: (14)
and n is dened as
n =k fork =l
n = 9kl fork6=l; k;l = 1; 2; 3 [3]: (15)
Finally, the piezoelectric tensors, notated as e
kij
, can be reduced to
131
e
km
=e
kij
; k = 1; 2; 3; m = 1; 2;:::; 6: (16)
where m is related to i and j as shown in 14.
132
Appendix B: COMSOL Multiphysics
The COMSOL Multiphysics simulations used for this work have been the eigenfrequency
simulation, frequency domain simulation, and to a lesser extent, the time-dependent sim-
ulation. The eigenfrequency simulation is an analysis that shows the natural frequencies
of vibrations that are supported by the structure [103]. The results show the shape of the
supported vibrations, or modes, but cannot be used to determine the amplitude of the vi-
bration.
Figure 1 shows the COMSOL screen when starting a new page. Choose the \Model
Wizard" and it will help guide through the setup of choosing the dimensions (1-D, 2-D, etc),
the physics to include and the study or simulation type to perform. Additional physics and
studies can be added later or added in addition to the original simulation picked as well.
Once the \Model Wizard" is selected, the spatial dimension will need to be selected, as
shown in Fig. 2.
The next step after the spatial dimension is selected is to select the dierent physics to
include, as shown in Fig. 3. The \Piezoelectricity, solid" physics has been included in all the
simulations. This physics automatically adds the \Solid Mechanics" and \Electrostatics"
physics and couples them together. For some of the frequency domain and time domain
studies, the \Electrical Circuit" physics was added as well. This allows the inclusion of
circuit elements like voltage sources, resistors, voltage meters or current meters, and other
elements to be included to either drive or load the IDTs in the simulation. Once a physics
is selected, the \Add" button will become added and the selected physics should be visible
133
Figure 1: New page menu in COMSOL Multiphysics.
Figure 2: Spatial dimension menu in COMSOL Multiphysics.
134
Figure 3: Physics menu in COMSOL Multiphysics.
below in the \Add physics interfaces." Once the physics is added, the nal step will be to
add the study (simulation type).
To summarize, the steps to create a new model are:
1. Create a new model.
2. Select \Model Wizard."
3. Select spatial dimension for model.
4. Select the physics to be used for the simulation.
B.1 2-D
B.1.1 Eigenfrequency Simulation
The steps to perform an \Eigenfrequency" simulation will be described in a little more detail
below but the basic steps to perform an \Eigenfrequency" simulation are:
1. Select \Eigenfrequency" for the study.
2. Dene the coordinate system (or rotate coordinate system).
135
3. Dene parameters (optional).
4. Create the geometry.
5. Add material properties and assign materials to the drawn geometries.
6. Select the geometry that should be piezoelectric under \Piezoelectric Material 1" for
\Solid Mechanics" physics and \Charge Conservation, Piezoelectric 1" for \Electro-
statics" physics.
7. Change the coordinate system for the simulation under \Piezoelectric Material 1" in
\Solid Mechanics" for the necessary rotation of the piezoelectric substrate.
8. Add periodic boundary conditions to the geometry for both \Solid Mechanics" and
\Electrostatics" physics.
9. Add \Fixed Constraint" to the bottom of the geometry (if warranted).
10. Add necessary boundary conditions for the electrodes (if warranted).
11. Set the mesh.
12. Set number of eigenfrequencies and the eigenfrequency to search around.
13. Run or \compute" simulation.
14. View results.
To perform an eigenfrequency simulation, select \Eigenfrequency" in the \Select Study"
box, as shown in Fig. 4. Once the selection is made, hit the \Done" button below. This will
bring up the interface shown in Fig. 5 where the structure to be simulated will be dened.
The \Units" that will be used for the simulation can be changed here. For example, the
default unit for length is in meters (m) but can be changed to m for convenience. Much of
setting up the simulation will be accomplished by selecting the dierent options available in
the \Model Builder" tab. Some of the available options can be found by selecting an item,
136
like \Geometry" and right clicking on it with the mouse.
The coordinate system must also be updated. The default coordinate system is cartesian
coordinates and in general, this coordinate system can be used. However, piezoelectric
materials are inherently anisotropic. Therefore, the system must be rotated for the particular
material cut that will be simulated. For the most part, 128
o
Y-cut LiNbO
3
was used for
the designs and so the setup will demonstrate simulations for 128
o
Y-cut LiNbO
3
with the
propagation direction generally in the x-direction unless otherwise stated. The coordinate
system can be modied by right clicking on \Denitions," go to \Coordinate Systems," and
selecting \Rotated System" from the menu. The menu is shown in Fig. 6 and this step is
the same for 3-D simulations as well. Note that this step will only dene the rotation of the
coordinate system. In a later step, this rotation must be selected to insure its use in the
simulation.
The \Rotated System" settings will show \In-plane rotation" as the input method. It
is easier to think in terms of general rotation angles using Euler angles and so the input
method should be changed to \General rotation." For a 128
o
rotation, the Euler angle is
calculated as
= 90
o
; (17)
where is the LiNbO
3
rotation angle [3]. For a 128
o
Y-cut LiNbO
3
, will be 128
o
and
will be 38
o
. The settings for \Rotated Systems" should look like Fig. 7.
This next step of dening parameters is not necessary but can help simplify dening
the geometry of the solution space. It can also help dene future geometries as well. \Pa-
rameters1" under \Global Denitions" is used to list variables and dene values for these
variables. These variables can later be used to dene the settings, geometries, etc. For
the rotation of the system, the rotation angle was explicitly dened but it can be dened
through a variable as well. Then, a sweep of this variable can be performed to study the
137
Figure 4: Eigenfrequency study selection in COMSOL Multiphysics.
Figure 5: Eigenfrequency simulation interface in COMSOL Multiphysics.
138
Figure 6: Dening coordinate system in COMSOL Multiphysics.
Figure 7: Settings for 128
o
rotated system in COMSOL Multiphysics.
139
Figure 8: Dening parameters or variables in COMSOL Multiphysics.
variables eect on performance or to optimize structures. For this particular simulation, the
parameters, or variables, are dened as shown in Fig. 8.
The geometry will now be dened using the dened parameters. Rectangles will be
added to the \Graphics" tab on the right by right clicking on \Geometry" and selecting
\Rectangle." The LiNbO
3
will be dened as shown in Fig. 9. The \Label" for each geometry
is by default named \Rectangle 1", \Rectangle 2" etc., but can be changed to better describe
the geometry being drawn. The IDT ngers are also drawn but may not be visible due to
the small thickness compared to the substrate. Also, parameters were used to dene some
of the geometry settings as well. This can make changing the sizes of the entire geometry
easier later, allow the sweeping of the geometry to see its sensitivity to the performance, or
for optimizing the design.
The next step is to add the dierent materials to be used for the simulation and then
assign the materials to the appropriate geometries. For this particular example, the materials
that will be added are LiNbO
3
for the substrate and gold for the electrodes. LiNbO
3
is a
material that is already available in COMSOL's material library, but gold is not and will
140
Figure 9: 2-D geometry for eigenfrequency simulation of IDT ngers on LiNbO
3
substrate with
the settings for the substrate (left), rst IDT nger (middle), and the second IDT nger along with
the simulation geometry (right).
need to be created.
To add LiNbO
3
to the model, right-click on \Materials" and select \Add Material from
Library." An \Add Material" tab will appear on the right. Under \Piezoelectric," \Lithium
Niobate" can be found. Right-click on \Lithium Niobate" and select the option \Add to
Component 1 (comp 1)" to add it to the model. It should now appear under \Materials" of
the model as shown in Fig. 10. Note that by default, all of the drawn geometries will be
listed under \Selection" for \Lithium Niobate." This is assigning all the drawn rectangles as
being lithium niobate. The electrodes can be removed from the list by selecting the electrode
geometries in the \Graphics" window, by selecting the geometry number under \Selection"
and hitting the \Remove from Selection" option just to the right of the \Selection" list, or
remove all geometries from the list by hitting the \Clear Selection" button, again found just
to the right of the \Selection" list, and adding just the substrate geometry in the \Graphics"
window.
To add gold into the materials list, right-click on \Materials" and select \Blank Material"
from the options. The label defaults as \Material 2" but can be changed to \Gold" to
help keep the model organized. Then, select the two electrodes, or any geometry that is
gold in the model. The two geometries should be added to the selection list for gold. At
141
Figure 10: Add lithium niobate to the model.
this point, the properties for gold can be input but rst de-selecting the electrodes from
being piezoelectric materials helps to simplify the required material properties to ll. In
order to do this, go to \Piezoelectric Material 1" under \Solid Mechanics" in the \Model
Builder." In the selection list for \Piezoelectric Material 1," all the drawn geometries will
be listed. Again, remove all geometries except for the LiNbO
3
substrate geometry. Also,
the rotated coordinate system can be applied to the LiNbO
3
by going to the \Coordinate
system" drop-down menu in the \Piezoelectric Material" tab and select \Rotated System
2 (sys2)," which was dened earlier. Next, go to \Charge Conservation, Piezoelectric 1"
under \Electrostatics" and remove all but the LiNbO
3
substrate geometry from the selection
list. By doing this under \Solid Mechanics" and \Electrostatics" physics, only the LiNbO
3
substrate geometry is assigned as being piezoelectric with a rotation to make it 128
o
. Due to
the orientation of the drawn structures with the y-axis being the vertical axis, it is the model
is for a 128
o
Y-cut with propagation direction in the x-direction. The material properties for
gold, such as the Young's modulus, Poisson's ratio, mass density, and relative permittivity,
can now be added as shown in Fig. 11.
142
Figure 11: Dene gold as a material for the model.
Once the materials are added and assigned to the geometries, the boundary conditions
can be added. For \Eigenfrequency" simulations, the drawn geometry will be dened as a
unit cell that periodically repeats by using the \Periodic Condition" boundary condition.
This boundary condition will be used for both the \Solid Mechanics" and \Electrostatics"
physics. To add the \Periodic Condition" boundary condition in \Solid Mechanics," right-
click on \Solid Mechanics" and under the \Connections" option, select \Periodic Condition."
In the \Periodic Condition" settings tab, the left and right sides of the LiNbO
3
substrate ge-
ometry will be selected, as shown in Fig. 12. The selected boundaries should be highlighted
and added to the selection list. If the electrodes were also on the edge of the structure, the
sides of the electrodes would also be selected to indicate that structure repeats by making the
solutions of the two sides (src and dst for source and destination boundaries) equal. To add
\Periodic Condition" under the \Electrostatics" physics, right=click on \Electrostatics" and
select \Periodic Condition." Then select the source (src) and destination (dst) boundaries
to dene the repeating unit cell to be simulated.
It is not necessary but the bottom of the LiNbO
3
geometry can be xed by right-clicking
on \Solid Mechanics," selecting the \Fixed Constraint" option, and adding the bottom
143
Figure 12: Periodic boundary condition dened for the model.
boundary to the selection list.
The electrodes can be assigned electrical boundary conditions like \Ground, Electrical
Potential, Floating Potential," etc. that is appropriate for the model to be simulated. For
this example, one of the electrodes will be assigned a \Ground" boundary condition while the
other electrode will be assigned with a \Electrical Potential" boundary condition. To assign
\Ground," right-click on \Electrostatics" and select the \Ground" option. Then, using the
\Select Box" tool, left mouse over one of the electrodes to add all four sides of the electrode
geometry to the selection list for the \Ground" boundary condition as shown in Fig. 13.
The process for the \Electrical Potential" boundary condition is similarly performed. A
static voltage can be assigned as the electrical potential value. The value does not aect the
solution.
The next step is to set the mesh. For this work, the \User-controlled mesh" option was
selected for the \Sequence type" under the mesh tab, as shown in Fig. 14(a). For size,
the \Element Size" was custom dened as shown in Fig. 14(b). For larger structures, the
maximum and minimum element sizes will need to be adjusted larger so as to reduce the
144
Figure 13: Ground boundary condition dened for the model.
compute memory required to solve the model. There are more advanced mesh settings that
can be useful in making the mesh more ecient that can be further explored as well.
Finally, the simulation settings need to be dened before running the simulation. The
general settings that need to be modied from the default are the \Desired number of eigen-
frequencies," and the \Search for eigenfrequencies around" options. The \Units" can be
modied as well but is not necessary. The settings for the study are shown in Fig. 15. Once
everything is set, the model can be saved (model can be saved at any point in the process)
and the simulation can be run by hitting the \Compute" button.
Once the simulation completes, the mode shapes will be automatically plotted, starting
from the lowest frequency mode. The dierent modes can be scrolled through to nd the
desired Rayleigh mode. The color scheme of the plotted mode shape can be changed as shown
in Fig. 16. The odd and even mode Rayleigh mode shape with corresponding eigenfrequency
is plotted in Fig. 17. For these plots, the \Rainbow" color scheme was used.
145
Figure 14: Dening the mesh (a) type and (b) element size for the model.
A similar simulation can be performed for 3-D models as well. The only dierence would
be that more sides and boundaries would have to be dened for the periodic boundary condi-
tion. In 3-D simulations, the Rayleigh modes for both the x-propagating and z-propagating
SAWs can be captured at once when simulating a 128
o
Y-cut LiNbO
3
substrate. The eigen-
frequency simulations can also be performed with a metal sheet instead of electrodes or
completely without any metallizations as well. The results from the un-metallized and met-
allized eigenfrequency simulations can be used to compute things like the relative refractive
indices or piezoelectric coupling coecients.
B.1.2 Frequency Domain Simulation
The steps to perform a \Frequency Domain" simulation is similar to setting up the \Eigen-
frequency" simulation. The basic steps are:
1. Select \Frequency Domain" for the study.
2. Dene the coordinate system (or rotate coordinate system).
146
Figure 15: Eigenfrequency simulation settings.
147
Figure 16: Eigenfrequency mode shape color setting.
148
Figure 17: Eigenfrequency mode shape color setting.
149
3. Dene parameters (optional).
4. Create the geometry.
5. Add material properties to the geometry.
6. Select the geometry that should be piezoelectric under \Piezoelectric Material 1" for
\Solid Mechanics" physics and \Charge Conservation, Piezoelectric 1" for \Electro-
statics" physics.
7. Change the coordinate system for the simulation under \Piezoelectric Material 1" in
\Solid Mechanics" for the necessary rotation of the piezoelectric substrate.
8. Add \Low-Re
ecting Boundary" under \Solid Mechanics" and add the appropriate
sides of the substrate to minimize re
ecting SAWs. A perfectly matched layer (PML)
can also be used but increases the geometry size slightly.
9. Add necessary boundary conditions for the electrodes.
(a) Add terminal for the excitation electrodes.
(b) Add ground for the ground electrodes.
(c) Add load or terminal for the output electrodes.
10. Add \Global Variable Probe" if needed.
11. Set the mesh.
12. Set number of frequency sweep parameters to simulate.
13. Run or \compute" simulation.
14. View results.
Much of the steps for setting up a \Frequency Domain" simulation is very similar with
setting up the \Eigenfrequency" simulation and so will not be repeated here. There are a few
150
dierences and simplications that can help in setting up the model and will be mentioned
here. The model that will be setup here will be for a 2-port simulation of back-to-back IDTs.
It is assumed that the steps not discussed here have all been taken care of to setup the model
for simulation.
The initial parameters used to draw the model is shown in Fig. 18. The model is for a
2-port IDT-to-IDT simulation. There is a wavelength gap from the edge of the substrate to
the IDTs and a 6 m gap between the two IDTs. Note that the width of the substrate is a
function of the number of electrode pairs used for each IDT and so the size of the model will
automatically adjust when the electrode number is changed. In Fig. 19, the two IDT ngers
for the input IDT has been drawn. The rst electrode is for the ground connection while the
second electrode will be assigned a terminal or source. The electrodes can easily be arrayed
to further increase the number of electrodes to include in the model. In order to array the
IDT electrodes, right-click on \Geometry" in the \Model Builder," go to \Transform" and
select \Array" from the options. Add the two electrodes in the selection list and update the
\Size" and \Displacement" parameters in the setting. The \Size" is the number of copies
of the electrode pairs to create, which will be set by the parameter n idt pairs, while the
\Displacement" is the pitch of the copies, which will be a wavelength. The array settings
and model are shown in Fig. 20. The process will be repeated for the output IDT, placing
a 6 m gap between the two IDTs. This can be accomplished as shown in Fig. 21. The
placement of the rst electrode of the output IDT is a function of the number of electrode
pairs in the IDT so that it will be automatically adjusted when the number of electrode pairs
parameter is changed.
The distance between the two IDTs can be measured using the \Measure" or ruler tool.
The tool can measure between objects, domains, boundaries or points. The selection option
can be changed by right-clicking in the \Graphics" window, going down to the \Geometric
Entity Level" and selecting one of the options. In this particular case, \Select Points" was
used and the points at the bottom of the input and output electrodes were selected. Then
151
Figure 18: Initial parameters used for a frequency domain simulation.
152
Figure 19: Ground and signal electrodes of input IDT.
153
Figure 20: Array settings for input IDT electrodes.
Figure 21: Signal electrode setting for output IDT.
154
Figure 22: Creating a selection group for ground electrodes.
the \Measure" button was pressed with the result appearing in the \Messages" box below.
This is a helpful tool as it is not easy to measure distances using the grid.
Once the model is drawn, a helpful step is to group the electrodes. This is done by
right-clicking on \Denitions," going to \Selections" and choosing the \Explicit" option.
Then, add the ground electrodes of both the input and output IDTs to the selection list as
shown in Fig. 22. Make sure that all sides of the electrodes are highlighted and not just
one edge. Change the \Output Entities" option to \Adjacent boundaries" and check the
\Interior boundaries" box as well. Repeat the same procedure, creating a separate selection
group for the input electrode and output electrode.
Before assigning boundary conditions, the out-of-plane thickness can be adjusted for both
the \Solid Mechanics" and \Electrostatics" physics. This parameter adjusts the dimension
out of the screen, or z-axis thickness in this case where x-axis is the horizontal axis while the
y-axis is the vertical axis. By default, this parameter is set to 1 meter but can be adjusted to
represent the aperture width of the IDT. The \Out-of-plane thickness" parameter is found
by selecting \Solid Mechanics" or \Electrostatics," as shown in Fig. 23. In the gure, the
parameter is explicitly set to 100 m but this value can also be parameterized as well.
155
Assigning of boundary conditions is done similarly as in the \Eigenfrequency" study
except that periodic boundary conditions will no longer be used. For the \Solid Mechan-
ics" boundary condition, \Low-Re
ecting Boundary" will be used for the sides and bottom
edges of the substrate. For \Electrostatics" boundary conditions, \Ground" and \Terminal"
boundary conditions will be used. For the ground boundary condition, the previously cre-
ated selection group can be used by using the drop-down menu under \Boundary Selection."
For the input and output IDTs, the \Terminal" boundary will be used. Again, for each
terminal, the drop-down menu selecting the appropriate group that was created earlier can
be selected. For \Frequency Domain" simulations, a couple of dierent simulations can be
performed. One is a S-parameter simulation while the other is a frequency or AC simulation.
The terminal settings for both simulations will be outlined below.
1. S-parameter Simulation
(a) Set \Terminal type" to \Terminated" for both the input and output terminals.
(b) By default, the reference impedance is 50
but can be adjusted by going to
\Electrostatics" and changing the \Reference impedance" parameter.
(c) Create a new parameter called portNum and give it a value of 1 under \Expres-
sion".
(d) Under \Electrostatics," check the \Use manual terminal sweep" box and change
the \Sweep parameter name" to portNum as shown in Fig. 24.
(e) Right-click on \Study 1" and add \Parametric Sweep." Add the \portNum" pa-
rameter and sweep it for values of 1 and 2 corresponding to the 2 terminal num-
bers. The settings are shown in Fig. 25.
(f) Set the frequency sweep values for \Step 1: Frequency Domain."
2. AC Simulation
(a) Set the input terminal type to \Circuit" and the output terminal type to \Charge."
156
(b) Create a \Global Variable Probe" for the output by right-clicking on \Denition,"
go to \Probes" and select \Global Variable Probe." Change the expression to
\es.V0 2", with the 2 representing the \Terminal Name" parameter of the output
terminal. If done correctly, the units and expression should automatically update
to \V" and \Terminal voltage."
(c) Right-click on \Electrical Circuit," go to \External Couplings" and select \Ex-
ternal I vs. U." Change the \n" node from 2 to 0, meaning it will be connected
to ground. Change \V" from \User dened" to \Terminal voltage (es/term1),"
representing the input terminal.
(d) Right-click on \Electrical Circuit" again and add a voltage source. Change \p"
from 3 to 1, connecting it to the input IDT, and \n" to 0. Change the source
type to \AC-source."
(e) Set the frequency sweep values for \Step 1: Frequency Domain."
For the AC simulation setup using the \Circuit" terminal type, more elements can be
connected, like a source resistance, current meters (ammeter), and volt meters and connecting
them together using the \Node names" of each device. Also, the output terminal can also
be a \Circuit" type as well and load resistances and other devices can be connected to the
output terminal too. For the output terminal, the \External I vs. U." parameter will be
\Terminal voltage (es/term2) to represent the second terminal.
B.1.3 Time Dependent Simulation
The steps to perform a \Time Dependent" simulation is similar to setting up an \Eigenfre-
quency" or \Frequency Domain" simulation. The basic steps are:
1. Select \Time Dependent" for the study.
2. Dene the coordinate system (or rotate coordinate system).
157
Figure 23: Changing the out-of-plane thickness of the model.
Figure 24: Changing the \Electrostatics" settings for S-parameter simulation.
158
Figure 25: Parametric sweep settings for S-parameter simulation.
159
3. Dene parameters (optional).
4. Create the geometry.
5. Add material properties to the geometry.
6. Select the geometry that should be piezoelectric under \Piezoelectric Material 1" for
\Solid Mechanics" physics and \Charge Conservation, Piezoelectric 1" for \Electro-
statics" physics.
7. Change the coordinate system for the simulation under \Piezoelectric Material 1" in
\Solid Mechanics" for the necessary rotation of the piezoelectric substrate.
8. Add \Low-Re
ecting Boundary" under \Solid Mechanics" and add the appropriate
sides of the substrate to minimize re
ecting SAWs. A perfectly matched layer (PML)
can also be used but increases the geometry size slightly.
9. Add necessary boundary conditions for the electrodes.
(a) Add terminal for the excitation electrodes.
(b) Add ground for the ground electrodes.
(c) Add load or terminal for the output electrodes.
10. Add \Global Variable Probe" if needed.
11. Set the mesh.
12. Set number of transient simulation parameters.
13. Run or \compute" simulation.
14. View results.
The setup for transient simulations is similar to \Eigenfrequency" or \Frequency Domain"
simulations and so will not be repeated here.
160
B.1.4 Perfectly Matched Layer
The steps to create a geometry to use a perfectly matched layer (PML) are listed below. It
will start with creating a new rectangle for the substrate and is as follows:
1. Once the rectangle for the substrate is drawn, select and expand the \Layers" option
from \Settings."
Figure 26: The \Layers" option from the \Settings" menu for the substrate.
2. Input the thickness for the PML and select the edges of the geometry that should be
selected as the PML. It is set as the wavelength parameter for this example.
161
Figure 27: Input the PML thickness and select the regions of the geometry to dene as PML.
3. Build the PML. Then, right click on \Denitions" from the \Model Builder" and select
the \Perfectly Matched Layer" option.
Figure 28: After building the geometry, the rectangle will be divided into the regions dened in
the previous step. Then select the \Perfectly Matched Layer" option to dene the regions as PML.
4. In the PML settings menu, select the regions that should be dened as PML in the
\Domain Selection."
162
Figure 29: Select the regions to dene as PML.
5. Add the material for the geometry. Lithium niobate is selected for this example. The
entire substrate, including the PML regions, are dened as the same material.
Figure 30: Add and dene material for the geometry.
6. Deselect the PML regions from \Piezoelectric Material 1" in \Solid Mechanics" in the
\Model Builder."
163
Figure 31: De-select the PML regions from being piezoelectric in the \Solid Mechanics" physics.
7. Deselect the PML regions from \Charge Conservation, Piezoelectric 1" in \Electro-
statics" in the \Model Builder."
Figure 32: De-select the PML regions from being piezoelectric in the \Electrostatics" physics.
8. The PML is set and the rest of the simulation setup can continue.
164
B.2 3-D simulation
The setup for 3-D simulations follows the setup for 2-D simulations with the added need to
apply boundary conditions on a 3-D geometry instead of a 2-D geometry. The other dierence
is the need to reduce or simplify the mesh to reduce the computing resource requirements,
such as the memory required to solve the model. Also, keep in mind that the time required
to solve a problem will increase as well and similar sized structures will not be able to be
simulated for 3-D models.
165
Abstract (if available)
Abstract
Waveguides are used for the processing of optical and mm-wave signals. They can provide a high-dynamic range analog signal processor in a compact form factor. However, the use of waveguides for the analog signal processing of radio frequency (RF) signals has been difficult to implement due to the impractically large size of waveguides at these frequencies. The size of the waveguide is inversely proportional to the speed that the signal propagates, which is very large for electromagnetic (EM) waves. Thus, the use of waveguides has eluded radio frequencies. In contrast, acoustic velocities are many orders of magnitude lower than the speed of light at which EM waves propagate, providing a means of designing waveguides at the relatively low frequencies RF signals occupy.
Acoustic devices are currently found in most RF devices. They are found mainly as filtering elements of modern RF front-ends. In this thesis, the use of acoustic waves, specifically surface acoustic waves (SAW), is explored for going beyond filtering and expanding into further signal processing of RF signals. This will be made possible through the use of lithium niobate, which is a piezoelectric material that greatly simplifies the generation of surface acoustic waves. Guiding of SAWs through straight waveguides and waveguide bends will be investigated. The investigation will look at a few metals used for designing the waveguide as well as a brief study in the crystal cut of the lithium niobate and how it can affect the waveguiding of SAWs. This is due to the anisotropic nature of lithium niobate, making it have different properties depending on the crystal cut and direction of propagation of the SAW.
Finally, the electroacoustic effect will be studied for its ability to change the stiffness of the lithium niobate. This change in stiffness causes a change in the acoustic velocity of the propagating SAW, and this change in velocity will be used to design a SAW phase shifter. The modulation of the acoustic velocity can also be obtained through the modulation of the temperature of the waveguide as well. However, this method runs counter to current SAW devices which have high temperature stability requirements while burning a considerable amount of power. On the other hand, electroacoustic phase shifter operates like a capacitor and therefore, does not consume power while providing the necessary phase shifts. The electroacoustic effect will be demonstrated using a thin lithium niobate wafer bonded to a high resistivity p-type silicon substrate. The modulation of the surface charges in the silicon will be used to modulate the velocity of the SAW. This electroacoustic phase shifter will then be implemented into a 4-element phased array, demonstrating the signal processing of RF signals using SAW waveguides.
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University of Southern California Dissertations and Theses
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Asset Metadata
Creator
Yamagata, Masashi
(author)
Core Title
Surface acoustic wave waveguides for signal processing at radio frequencies
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Electrical Engineering
Degree Conferral Date
2022-08
Publication Date
06/22/2022
Defense Date
05/04/2022
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
electroacoustic effect,lithium niobate,lithium niobate on silicon,OAI-PMH Harvest,phased array,radio frequency,surface acoustic wave,waveguides
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Hashemi, Hossein (
committee chair
), Chen, Shuo-Wei Mike (
committee member
), Kim, Eun Sok (
committee member
), Ravichandran, Jayakanth (
committee member
), Sideris, Constantine (
committee member
)
Creator Email
myamagat@usc.edu,myamagata.usc007@gmail.com
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-oUC111345525
Unique identifier
UC111345525
Legacy Identifier
etd-YamagataMa-10779
Document Type
Dissertation
Rights
Yamagata, Masashi
Type
texts
Source
20220623-usctheses-batch949
(batch),
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
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Repository Name
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Repository Location
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Repository Email
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Tags
electroacoustic effect
lithium niobate
lithium niobate on silicon
phased array
radio frequency
surface acoustic wave
waveguides