university of california santa barbara design, fabrication, …memsucsb/research/dissertatio… ·...
TRANSCRIPT
UNIVERSITY OF CALIFORNIA
Santa Barbara
Design, Fabrication, and Characterization of Beam - Supported Aluminum Nitride
Thin Film Bulk Acoustic Resonators
A Dissertation submitted in partial satisfaction of the
requirements for the degree Doctor of Philosophy
in Mechanical Engineering
by
Lori Ann Callaghan
Committee in charge:
Professor Noel C. MacDonald, Chair
Professor Glenn E. Beltz
Professor David R. Clarke
Professor Kimberly L. Turner
September 2005
The dissertation of Lori Ann Callaghan is approved.
____________________________________________ Glenn E. Beltz
____________________________________________ David R. Clarke
____________________________________________ Kimberly L. Turner
____________________________________________ Noel C. MacDonald, Committee Chair
July 2005
iii
Design, Fabrication, and Characterization of Beam - Supported Aluminum Nitride
Thin Film Bulk Acoustic Resonators
Copyright © 2005
by
Lori Ann Callaghan
iv
ACKNOWLEDGEMENTS
This section, the acknowledgements of the people whom without the work
covered in the dissertation would not have been possible, has been the most difficult
to write. I have started this section several times only to write an incomplete
paragraph. It is not that I am unappreciative of the guidance and support I have
received but that this section is essentially saying goodbye to people that made my
five years at UCSB richer. The relationships that I have forged with others in the
UCSB community have been the most fulfilling part of my graduate school
experience. The stress of my project manifested itself in headaches and back
problems. The people I interacted with gave me memories that I will cherish and
take with me when I move away from Santa Barbara next month.
First, I want to thank the one person that is leaving Santa Barbara with me, my
husband Dave Andeen. I would not have survived the ups and downs of graduate
school without him. He did everything from providing emotional support over the
years to helping me edit my dissertation. The future is ours, honey.
There is a group of graduate students that provided me with camaraderie and
insight into my project. This project would not have been possible without Vanni
Lughi successfully sputtering AlN on silicon. Micheal Requa introduced me to the
VNA and taught me how to use ADS software to manipulate scattering parameter
data, which was essential to this project. Vanni and Mike were also always available
to brainstorm solutions when my project ran into one of its many snags. Thank you
to the past and present students of the MacDonald Research Group, Alok Paranjpye,
v
David Follman, Adam Pyzyna, Zuruzi Abu Samah, Garrett Cole, Marco Aimi, Seth
Boeshore, Yanting Zhang, Anton Riley, Emily Parker, Justin Bellante, Changsong
Ding, Adam Monkowski, Trent Huang, Marcus Ward, and our esteemed postdoc
Masa Rao. The MacDonald Research Group is superior in helping each other find
our ways through the chaos of graduate school. Special thanks to Follman and Alok
who remember the confusion at the beginning, to Emily for providing
encouragement at the end, and Garrett who was always interested in my work and
contributed indispensable advice and insight. Finally, I would like to acknowledge
Hongtao Xu for performing the first scattering parameter measurements on the
FBARs.
Thank you to the faculty and staff at UCSB for providing me with the tools and
facilities needed to complete this work. I want to acknowledge my advisor, Noel
MacDonald, who gave me the opportunity to work with FBARs and on the MINT
grant. A special thank you to Dave Bothman for constructing the MEMS cleanroom
and ESB lab, which is where I spent many hours. He was also a fantastic resource
for knowing how to accomplish tasks in the UCSB environment. The UCSB
Nanofabrication Facility was where I spent years developing my fabrication
processes. Thank you to the Nanofab staff, especially Brian, Bob, and Don, for
providing processing advice, maintaining the tools, and making the cleanroom as
pleasant of an environment as it could be. Thank you to the UCLA Nanoelectronics
Research facility where I did my backside lithography. Thank you to Andrew
Cleland for testing a device in his vacuum chamber. I would like also to
acknowledge and thank my dissertation committee, Kimberly Turner, Glenn Beltz,
vi
and David Clarke, each of whom in different ways provided insight and aid toward
completion of my project and dissertation. And of course, an acknowledgment to
DARPA for sponsoring this work.
I would not have completed grad school without the UCSB Masters Swim Team.
No matter how bad my research was on a given day, swimming always made the day
better. Thank you to my coaches Jeremy, Suzy, John, Brandi, Andy, and Jane for
pushing my performance at workout. And the Swim Team Group at Joes – its been
too fun.
Thank you to the many friends I have met at UCSB. I will miss you.
And finally, thank you to my parents, Jim and JoAnne Callaghan, who have
always been supportive throughout my life.
vii
I dedicate this dissertation to my husband, Dave.
viii
VITA OF Lori Ann Callaghan June 2005
EDUCATION
Doctor of Philosophy in Mechanical Engineering, University of California, Santa Barbara, June 2005 (expected)
Master of Science in Mechanical Engineering, University of California, Santa Barbara, September 2004
Bachelor of Science in Mechanical Engineering, Massachusetts Institute of Technology, June 1996
PROFESSIONAL EMPLOYMENT
1996-2000: Mechanical Engineer, Applied Materials, Santa Clara, CA
PUBLICATIONS, CONFERENCES, AND PATENTS
L. A. Callaghan, V. Lughi, N. C. MacDonald, and D. R. Clarke, “Beam-Supported AlN Thin Film Bulk Acoustic Resonators,” to be published
L. A. Callaghan, V. Lughi, M. V. Requa, D. R. Clarke, N. C. MacDonald, K. L. Turner, "Comparison of Suspended versus Clamped Aluminum Nitride Acoustic Resonators," presented at the Spring Meeting of the Materials Research Society, San Francisco, March 28th - April 1st (2005), Presentation J5.1.
L. A. Callaghan, V. Lughi, M. V. Requa, N. C. MacDonald, D. R. Clarke, and K. L. Turner, "Fabrication and testing of beam supported AlN FBARs," proceedings of the 2004 IEEE Ultrasonics, Ferroelectrics, and Frequency Control 50th Anniversary Joint Conference, pp. 18-21
L. A. Scudder, L. Washington, L. A. Callaghan, B. M. Curelop, “Wafer carrier,” U. S. Patent 6,544,033, April 8, 2003
L. A. Callaghan, R. N. Anderson, and D. K. Carlson, “Silicon carbide sleeve for substrate support assembly,” U. S. Patent 6,315,833, November 13, 2001
ix
ABSTRACT
Design, Fabrication, and Characterization of Beam - Supported Aluminum Nitride
Thin Film Bulk Acoustic Resonators
by
Lori Ann Callaghan
Micro-mechanical filters comprised of bulk acoustic resonators are being
fabricated and studied as a solution to the demands for low power consumption, high
functionality devices in the telecommunication industry. A novel, suspended thin
Film Bulk Acoustic wave Resonator (SFBAR) has been fabricated using an
aluminum nitride film sputtered directly on a <100> silicon substrate. The
suspended membrane design uses thin beams to support, as well as electrically
connect, the resonator. The SFBAR has been fabricated by combining both thin film
processing and bulk silicon micro machining. The AlN was etched in an Inductively
Coupled Plasma (ICP) chlorine etch, using titanium dioxide as the masking material.
A silicon Deep Reactive Ion Etch (DRIE) was used to create an open ended air
cavity with a novel circular shape. A representative resonator, designated here as
sample W9HS8 resonator 10018, was characterized with a Quality Factor values at
resonance and anti-resonance of 68 and 151, respectively. The sample also has an
x
effective electromechanical coupling coefficient of 4.6% and is free of spurious
resonances. The response of the resonator was representative of the majority of the
resonators tested. The Quality Factor and the effective electromechanical coupling
coefficient were characterized as a function of the number and the length of the
support beams. The length of the support beams was found not to have any effect on
the quality factor at resonance or the effective electromechanical coupling factor.
However, longer support beams do facilitate better frequency pair response. Device
performance varied with the number of support beams: 70% of the resonators tested
show a higher Figure of Merit with eight support beams than with four support
beams. A Butterworth–Van Dyke (BVD) lumped element circuit model was used to
simulate the response of the SFBAR. The results from the BVD simulation match
the experimental data and provide insight into the response of the SFBARs.
xi
TABLE OF CONTENTS
Chapter 1 Introduction ......................................................................................1
Chapter 2 Background ......................................................................................8
2.1 Through-Thickness Piezoelectric Propagation ........................................8
2.2 Aluminum Nitride Properties .................................................................14
2.3 Structural versus Acoustic Resonance ...................................................15
2.4 Multi-Resonator Filter............................................................................15
2.5 Summary ................................................................................................19
Chapter 3 Resonator and Mask Design...........................................................20
3.1 Resonator Design ...................................................................................20
3.2 Mask Set.................................................................................................27
3.2.1 Mask Set Layout ............................................................................28
3.2.2 Backside Mask ...............................................................................32
3.3 Summary ................................................................................................33
Chapter 4 Fabrication......................................................................................36
4.1 Fabrication Overview.............................................................................38
4.2 AlN Processing.......................................................................................47
4.3 Silicon Deep Reactive Ion Etch (Si DRIE) ............................................54
4.3.1 Front side Silicon Etch ...................................................................55
4.3.2 Air Cavity Etch ..............................................................................57
4.4 Summary ................................................................................................58
xii
Chapter 5 Testing and Characterization .........................................................60
5.1 Data Collection.......................................................................................60
5.2 Resonator Characterization Factors .......................................................64
5.2.1 Quality Factor.................................................................................65
5.2.2 Effective Electromechanical Coupling Coefficient .......................69
5.2.3 Figure of Merit ...............................................................................71
5.2.4 Spurious Resonances......................................................................73
5.3 One-Dimensional Frequency Model ......................................................78
5.4 Three-by-Three Array ............................................................................82
5.5 Summary ................................................................................................84
Chapter 6 Performance Analysis ....................................................................86
6.1 Silicon ....................................................................................................86
6.2 Vacuum Test ..........................................................................................88
6.3 Support Beam Characterization .............................................................92
6.3.1 Support Beam Length ....................................................................92
6.3.2 Number of Support Beams.............................................................96
6.4 The Quality Factor as a Function of the Effective
Electromechanical Coupling Coefficient ...............................................................98
6.5 Metal Electrodes...................................................................................100
6.6 Summary ..............................................................................................107
Chapter 7 Analysis Using the Butterworth-Van Dyke Circuit Model..........109
7.1 Quality Factor of the Butterworth – Van Dyke Circuit .......................110
xiii
7.2 Computer Simulation of the BVD Circuit Response ...........................117
7.3 Optimization of Beam-Supported Design Using the BVD
Simulation ............................................................................................................124
7.3.1 Electrode Optimization ................................................................125
7.3.2 Optimization Recommendations ..................................................129
7.4 Summary ..............................................................................................129
Chapter 8 Interactions between FBARs Sharing a Substrate .......................131
8.1 Interaction between Two Unconnected Devices..................................132
8.2 FBARs Connected in Parallel ..............................................................134
8.3 Summary ..............................................................................................140
Chapter 9 Conclusions and Future Directions ..............................................142
9.1 Conclusions ..........................................................................................142
9.2 Future Directions..................................................................................146
References ..........................................................................................................149
Appendix A ........................................................................................................156
Appendix B ........................................................................................................166
xiv
LIST OF FIGURES
Figure 1.1. (a) Schematic of the cross section of a Bragg Reflector and (b) the
scanning electron microscopy image composed of Mo electrode and AlN
piezoelectric films from Lee et al. [10]................................................................. 2
Figure 1.2. Cross section of :(a) ZnO FBAR and (b) PZT FBAR. Both are
examples of membrane resonators from Su et al. [6]............................................ 3
Figure 1.3. Four-by-four array of previous generation of FBARs............................... 5
Figure 1.4. SEM image of beam-supported FBAR...................................................... 6
Figure 2.1. Common piezoelectric modes of propagation ......................................... 10
Figure 2.2. Schematic of a ladder filter [11] .............................................................. 16
Figure 2.3. Figure from Loebl et al. [13] illustrating a single section bulk
acoustic wave filter consisting of one series and one parallel resonator.
Right: Electric impedance of series and parallel resonator. The bottom curve
shows the transmitted signal S21 revealing a band-pass filter characteristic....... 17
Figure 2.4. Generic two-port network with incident and emergent waves ................. 18
Figure 3.1. Schematic of SFBAR cross-section......................................................... 22
Figure 3.2. SEM image of beam -supported FBAR with 300 µm long beams .......... 23
Figure 3.3. SEM image of an FBAR with circumference solidly clamped to
substrate............................................................................................................... 24
Figure 3.4. SEM image of the Ground Signal Ground probe pads of a FBAR
with beam supports 50 µm long .......................................................................... 26
xv
Figure 3.5. Top metal electrode and transmission line highlighted in SEM image
due to AlN dielectric charging ............................................................................ 27
Figure 3.6. Schematic of cross-section of support beam with transmission line ....... 27
Figure 3.7: Complete set of four photolithography masks superimposed upon
each other, each in a different color, in order to show the complete layout of
resonators per stepper die.................................................................................... 29
Figure 3.8. Photolithography mask used to pattern AlN film.................................... 30
Figure 3.9. Photolithography mask used to pattern front side SiO2........................... 224H31
73HFigure 3.10. Photolithography mask used for the front side silicon etch and top
metal electrode liftoff step................................................................................... 225H32
74HFigure 3.11. Twelve die pattern for backside contact mask as would be place on a
four inch wafer .................................................................................................... 226H34
75HFigure 3.12. Backside contact mask pattern............................................................... 227H35
76HFigure 4.1. Optical microscope image of cracked AlN thin film after the substrate
release.................................................................................................................. 228H37
77HFigure 4.2. Normalized thickness variation of AlN across silicon wafer for
different values of Bipolar power. Bipolar refers to the arbitrary value that
determines the amount of material sputtered from each of the two targets in
the sputtering chamber [35]................................................................................. 229H38
78HFigure 4.3. Illustration of front and back side of double sided polished silicon
wafer with a sputtered AlN film on the front side............................................... 230H39
79HFigure 4.4. Illustration of deposition of TiOB2B
process step ........................................ 231H40
80HFigure 4.5. Illustration of resonator pattern in the TiOB2B
mask material ..................... 232H41
xvi
81HFigure 4.6. Illustration of resonator pattern in AlN film............................................ 233H41
82HFigure 4.7. Illustration of PECVD SiO B2B
on the front and back of wafer ................... 234H42
83HFigure 4.8. Illustration of the patterned front side electrical isolation SiOB2B
and
backside air cavity SiOB2B
masking material.......................................................... 235H44
84HFigure 4.9. Illustration of exposed silicon during front side DRIE............................ 236H45
85HFigure 4.10. Illustration of top electrode lift-off step ................................................ 237H46
86HFigure 4.11. Illustration of backside air cavity etch................................................... 238H46
87HFigure 4.12. Illustration of evaporation of backside electrode .................................. 239H47
88HFigure 4.13. SEM image of a resonator surrounded by a rough silicon substrate
after the AlN etch and before TiOB2B
mask removal.............................................. 240H50
89HFigure 4.14. SEM image of AlN particles leftover after AlN etch ............................ 241H51
90HFigure 4.15. Digital image of the endpoint detector monitor screen displaying the
plot of the laser interferometery response from an AlN etch. The decreasing
amplitude of the sine wave is indicative of a material that has a slower etch
rate than its substrate. .......................................................................................... 242H52
91HFigure 4.16. Dektak topology scan of AlN etch for wafer W9H ............................... 243H54
92HFigure 4.17. SEM images of remaining silicon substrate on an AlN support beam
(a) front view and (b) air cavity view. The surface beneath the beam in b) is
the sample holder ................................................................................................ 244H56
93HFigure 4.18. Sample mounted on 4-inch carrier wafer in preparation for air cavity
etch ...................................................................................................................... 245H57
94HFigure 4.19. SEM image of the air cavity of a 300 µm support beam resonator ....... 246H59
95HFigure 5.1. Photograph of RF probe station test setup............................................... 247H62
xvii
96HFigure 5.2. Smith Chart plot of SB11B
response from 500 MHz to 6 GHz of sample
W9HS8 resonator 10018 ..................................................................................... 248H63
97HFigure 5.3. ADS design interface and simulation model used to read collected
data into the ADS platform ................................................................................. 249H64
98HFigure 5.4. Smith Chart plot of SB11B
response from 1-2 GHz of sample W9HS8
resonator 10018................................................................................................... 250H66
99HFigure 5.5. Magnitude and phase angle plots of input impedance of sample
W9HS8 resonator 10018 ..................................................................................... 251H68
100HFigure 5.6. Polynomial equation fitted to phase angle data generated by Matlab P®P
code ..................................................................................................................... 252H69
101HFigure 5.7. Butterworth – Van Dyke equivalent circuit............................................. 253H73
102HFigure 5.8. Smith Chart plot for a resonator that exhibited a spurious resonance at
the fundamental frequency .................................................................................. 254H74
103HFigure 5.9. Smith Chart plot illustrating the conductive and inductive areas of the
reactance.............................................................................................................. 255H75
104HFigure 5.10. Smith Chart plots from resonators that showed spurious resonances
as ripples. (a) Resonator W3KS7 5023 (b) W3KS7 10012................................. 256H76
105HFigure 5.11. Agilent Technologies FBAR exhibiting Lamb wave excitation at
lower frequencies [3]........................................................................................... 257H77
106HFigure 5.12. Mason model equivalent circuit ............................................................ 258H79
107HFigure 5.13. Comparison of the one-dimensional frequency model to the RMS of
the resonators’ measured parallel frequencies per sample; all data points are
for the fundamental acoustic frequency except where noted. ............................. 259H81
xviii
108HFigure 5.14. Three-by three 2000 µm pitch array of 100 µm long beam support
resonators with their corresponding resonant frequency, quality factor at
resonance, and 2effk listed ..................................................................................... 260H83
109HFigure 5.15. Three-by three 1000 µm pitch array of solidly clamped resonators
with their corresponding resonant frequency, quality factor at resonance, and
2effk listed ............................................................................................................. 261H84
110HFigure 6.1. Figure of Merit of the Fundamental response of a FBAR structure, as
illustrated in Rosenbaum [2]. As the thickness ratio between the silicon
substrate and the ZnO piezoelectric increases, the device performance
rapidly decreases. ................................................................................................ 262H88
111HFigure 6.2. Smith Chart plots of the fundamental frequency SB11B
parameter
response measured from 1-1.999375 GHz (a) at atmospheric pressure and (b)
comparing 0.1 Torr and 0.35 mTorr to atmospheric pressure............................. 263H90
112HFigure 6.3. The magnitude and phase of the input impedance at atmospheric
pressure, 0.1 mTorr and 0.35 mTorr ................................................................... 264H91
113HFigure 6.4. Quality factor at resonance versus support beam length for individual
resonators ............................................................................................................ 265H93
114HFigure 6.5. Effective electromechanical coupling coefficient versus beam length
for individual resonators ..................................................................................... 266H94
115HFigure 6.6. The Figure of Merit at anti-resonance versus support beam length for
individual resonators ........................................................................................... 267H95
xix
116HFigure 6.7. SEM image of resonator after 4 support beams were cut off using a
focused ion beam................................................................................................. 268H97
117HFigure 6.8. The percent change in the FOM at resonance and anti-resonance per
individual resonator after the removal of four support beams. Trend lines
indicated the average change. ............................................................................. 269H98
118HFigure 6.9. Quality factor as a function of the effective electromechanical
coupling coefficient........................................................................................... 270H100
119HFigure 6.10. Quality factor plotted against beam length for three different
electrode configurations .................................................................................... 271H103
120HFigure 6.11. The effective electromechanical coupling coefficient plotted against
beam length in terms of electrode configuration............................................... 272H105
121HFigure 6.12. Effective Electromechanical coupling coefficient as a function of the
thickness as presented by TFR Technologies[62]............................................. 273H106
122HFigure 7.1. Butterworth–Van Dyke equivalent circuit............................................. 274H110
123HFigure 7.2. Butterworth–Van Dyke equivalent circuit with variable tuning
capacitor in parallel ........................................................................................... 275H110
124HFigure 7.3. Magnitude of ZBinB
for sample W9HS8 resonator 10018.......................... 276H114
125HFigure 7.4. Butterworth–Van Dyke equivalent circuit at off-resonant frequencies. 277H115
126HFigure 7.5. Comparative plots of the RMS of the Q and the BVD Q of the
resonators for each sample ................................................................................ 278H117
127HFigure 7.6. BVD circuit constructed in ADS simulation window ........................... 279H118
xx
128HFigure 7.7. BVD circuit simulation compared to the experimental data collected
from sample W9HS8 resonator 10018 (a) reflection coefficient Smith Chart
plot (b) input impedance [dB] (c) phase of input impedance............................ 280H121
129HFigure 7.8. BVD model output plots with various RBmB
values: (a) reflection
coefficient Smith Chart plot (b) input impedance [dB] (c) phase of input
impedance.......................................................................................................... 281H122
130HFigure 7.9. BVD model output plots with various RBtB
values: (a) reflection
coefficient Smith Chart plot (b) input impedance [dB] (c) phase of input
impedance.......................................................................................................... 282H123
131HFigure 7.10. The motional resistance plotted against beam length for FBARs that
exhibited a frequency pair ................................................................................. 283H125
132HFigure 7.11. The transmission line resistance as plotted function of beam length
for different electrode configurations. The trends lines are the relationship
between the resistance and the dimensions of the transmission line,
eR L A ........................................................................................................ 284H127
133HFigure 7.12. The motional resistance plotted as a function of beam length for
different electrode configurations. .................................................................... 285H128
134HFigure 8.1. ADS design interface and simulation model used to read collected
data from two port device into the ADS platform............................................. 286H132
135HFigure 8.2. Smith Chart plot of the reflection coefficients of resonator 10014
before and after the substrate coupling test....................................................... 287H133
xxi
136HFigure 8.3. SEM image of two FBARs connected by transmission line supported
on an AlN beam................................................................................................. 288H135
137HFigure 8.4. Schematic of two FBARs connected in parallel .................................... 289H136
138HFigure 8.5. Reflection and transmission responses of sample W3KS6 10017 to
10014................................................................................................................. 290H137
139HFigure 8.6. SEM image of backside of sample W3KS2 with the wall in between
the air cavities etched during the deep silicon etch........................................... 291H138
140HFigure 8.7. SEM image of connecting beam after silicon support was removed
with a FIB.......................................................................................................... 292H139
141HFigure 8.8. Scattering parameter responses of connected FBARs before and after
the silicon was removed from the connecting beam ......................................... 293H140
xxii
LIST OF TABLES
142HTable 2.1. Material properties of candidate piezoelectric materials for FBARs........ 294H15
143HTable 4.1. Panasonic ICP Etch conditions and results for AlN etch.......................... 295H53
144HTable 5.1. Acoustic velocity values ........................................................................... 296H82
145HTable 5.2. Summary of the characterization of sample W9HS8 resonator 10018..... 297H85
146HTable 6.1. The Quality Factor of a resonator at different pressures........................... 298H89
147HTable 6.2. The percentage of tested resonators that exhibited a frequency pair as
correlated to support beam length ....................................................................... 299H96
148HTable 6.3. Electrode configurations materials and thicknesses ............................... 300H101
149HTable 7.1. Resonant properties of sample W9HS8 resonator 10018 ....................... 301H116
150HTable 7.2. Average transmission line resistance of each electrode configuration ... 302H119
151HTable 7.3. Values used in BVD circuit model simulation........................................ 303H119
1
Chapter 1 Introduction
As the wireless telecommunication industry continues to grow, the demand for
devices with both low power consumption and high functionality is fueling the
industry. In response, micromechanical ladder filters that use micron-scale, thin film
resonators are replacing the solid state and Surface Acoustic Wave (SAW) filters in
cell phones [1-3]. The acoustic resonators, often referred to as thin Film Bulk
Acoustic wave Resonators (FBARs), have shown to have improved power handling
and thermal characteristics compared to SAW devices without the limited frequency
range [3-6]. The basic structure of a FBAR is a piezoelectric thin film sandwiched
between metal electrodes. The piezoelectric film resonates in the thickness direction
at a specific frequency in the Ultra High Frequency (UHF) regime (300 MHz –
3GHz). The frequency is dependent on device geometry and material properties.
Zinc oxide and aluminum nitride films are good candidates for this application due
to their high acoustic velocities and electromechanical coupling constants [6-9]. The
piezoelectric sandwich is supported by two methods. The first device type is
referred to as a Bragg Reflector and consists of an acoustic mirror of alternating low
and high acoustic impedance materials underneath the piezoelectric film and the
metal electrodes. 304HFigure 1.1 X is a schematic of the Bragg Reflector from Lee et al.
[10]. The second device type is a thin film membrane. The membrane is supported
by a thin structural layer underneath the bottom electrode. The entire structure is
suspended over an air cavity [2, 11-13]. AXn example of a membrane style resonator
from Su et al. [6] is shown in X305HFigure 1.2X.
2
Figure 1.1. (a) Schematic of the cross section of a Bragg Reflector and (b) the
scanning electron microscopy image composed of Mo electrode and AlN
piezoelectric films from Lee et al. [10]
3
Figure 1.2. Cross section of :(a) ZnO FBAR and (b) PZT FBAR. Both are
examples of membrane resonators from Su et al. [6]
The research outlined in this dissertation was funded by DARPA; the UCSB
project was entitled MINT, Mechanical Integration for Networked
Telecommunications [14]. One of the primary research goals was to sputter higher
quality AlN films directly on a <100> silicon wafer. This objective was researched
by Vanni Lughi, a Ph.D. candidate at UCSB. The intention was that the silicon
4
crystalline structure would help produce better films than the previously standard
practice of sputtering on the bottom metal electrode of the FBAR [15].
Following deposition, the AlN films were used to produce the beam-supported
FBARs. This dissertation covers the design, fabrication and characterization of
these devices. Earlier, non beam-supported FBAR designs were fabricated. These
FBARs did not produce strong piezoelectric responses. The older resonators, as
shown in X306HFigure 1.3, were square, and the entire perimeter of the device was
clamped to the substrate. The transmission lines were long and generated resistive
losses. These devices will not be discussed, but their failure to produce a strong
response provided insight into the design of the beam-supported FBAR. However,
the micro-fabrication techniques that were developed were used to fabricate
subsequent resonators. The beam-Supported thin Film Bulk Acoustic wave
Resonator (SFBAR), as pictured in X307HFigure 1.4, is a novel design that consists of a
thin film membrane suspended over a circular, open ended air cavity without a
structural support layer. The thin membrane is connected to the substrate by AlN
support beams. The purpose of the SFBAR design was to characterize the
performance of a resonator when isolated from the substrate, as opposed to being
clamped to the substrate by its entire perimeter.. Free standing membranes [16] and
beam-supported resonators [17] have been fabricated using a selective silicon wet
etched to form the air cavity. We, however, use a MEMS-based, bulk silicon Deep
Reactive Ion Etch (DRIE) process to form the air cavity using a PlasmaTherm etcher
and the Bosch etch processTM. The Bosch process allows the air cavity to be
5
circular, since the cavity size and shape are not limited by an orientation-dependent
wet etch [18].
Figure 1.3. Four-by-four array of previous generation of FBARs
The SFBARs were evaluated and characterized using general resonator
performance parameters, including quality factor (Q), effective electromechanical
coupling coefficient ( 2effk ), and the presence of spurious resonances. The largest
measured 2effk value obtained is 6.3%, which is close to the theoretical maximum of
6.5% [8]. The largest Q at resonance is 145 at 2.3 GHz. This value for Q is quite
low compared to commercial products [3, 12] and other air-backed free standing
FBARs [16], but, is an improvement over a previous beam suspended design, which
G-S-G Contact Pads
Clamped Resonator
Transmission Line
6
published a quality factor of 91.7 and a 2effk of 2.4% at 17 MHz [17]. Though the
Quality Factors are not high, the focus of this work is not to raise the values. Instead
elements of the SFBARs design such as the beam length are evaluated in terms of
how they affect the Q. Despite having low quality factors, the beam-supported
FBARs have smooth Smith Chart plots and do not appear to be plagued by Lateral
standing Lamb waves, which are a common energy loss mechanism in FBARs [3,
19].
Figure 1.4. SEM image of beam-supported FBAR
This document is organized with the subsequent chapter briefly outlining the
background of the project. In Chapter 3 the design and fabrication of the beam-
7
supported FBAR is detailed. An explanation of the factors used to characterize the
SFBARs follows in Chapter 4. Using the characterization factors, Chapter 5
discusses trends in relation to the support beams and the electrodes. The
Butterworth-Van Dyke circuit is then used to model the beam-supported FBAR
behavior in Chapter 7. In Chapter 8, the interaction between SFBARs sharing the
same substrate is addressed. Finally, Chapter 9 contains the conclusion and possible
future directions are discussed.
8
Chapter 2 Background
This chapter covers an array of scientific concepts applicable to beam-supported
FBARs. First, the mode of through-thickness piezoelectric activation is defined and
discussed. Next, the reasons behind the material choice of AlN are outlined.
Common misconceptions about the difference between the structural and acoustic
natural frequencies, and the resulting purpose of support beams, are also resolved.
Finally, the scattering matrix, which is used to characterize the FBARs is defined,
and we explain how the matrix applies to single and two port devices is explained.
2.1 Through-Thickness Piezoelectric Propagation
The beam-supported FBARs, along with most of the devices referenced in this
dissertation, are piezoelectrically activated by the through-thickness or thickness-
extension mode. As illustrated by Johnson [20] and redrawn in X308HFigure 2.1X, the
electric field and the relevant mechanical response of the material (in particular,
displacements) are only in the thickness direction, hereafter referred to as the 3-
direction. This response occurs because the 1-direction and 2-direction
characteristic dimensions are orders of magnitude larger than the thickness and,
therefore, the resulting transverse motion is negligible [2, 21, 22]. A through-
thickness device was designed for this project because of its simplicity compared to
other modes of propagation illustrated in X309HFigure 2.1X. The natural frequency of a
through-thickness resonator is given by the equation 2af v d where f [GHz] is the
frequency, va [km/s] is the acoustic velocity, and d [µm] is the film thickness since
9
the piezoelectric activation has only one degree of freedom [23]. This is detailed
later in the dissertation.
10
Figure 2.1. Common piezoelectric modes of propagation
Length- Extension Bar with Transverse Bias and Excitation
Polarizatio
Electric field excitation
Particle motion and propagation
3
2
1
Thickness-Extension Disk and Plate
1 1
3
2
3
2
Polarizatio ExcitationParticle motion and propagation
Thickness-Shear Mode Plates
Polarizatio
Motion
Excitation and propagation
Excitation Motion
Polarization and propagation
33
11
2
2
11
The simplicity of a through-thickness resonator can be shown with the
piezoelectric propagation matrix algebra, which is explored in detail in Chapter 4 of
Rosenbaum [2]. The stress (T) of the piezoelectric film can be equated to an electric
field (E) and a strain (S) through:
E
K Kk k KJ JT e E c S (2.1)
where TK, EK, and SK represent components of the stress tensor, electric field, and
strain, respectively (K takes on values 1-6 0F
1); eKk represent components of the
piezoelectric stress tensor (the range for K is 1-6, and the range for k is 1-3;
visualized as a 3×6 matrix); and E
KJc represent the components of the compliance
tensor measure at constant electric field (The range of K and J are 1-6; visualized as
a 6×6 matrix). The dimensions of eKk are Cm-2 and the dimensions of E
KJc are Nm-2.
Where a subscript is repeated, a summation is assumed. For example,
3 31 1 32 2 33 3 31 1 32 2 33 3 34 4
35 5 36 6
E E E E
E E
T e E e E e E c S c S c S c S
c S c S (2.2)
AlN is a wurtzite structure with a piezoelectric stress components [24]:
1 T1 is equivalent to T11, T2 is equivalent to T22, T3 is equivalent to T33, T4 is equivalent to T23, T5 is equivalent to T13, and T6 is equivalent to T12.
12
0 0 0 0 0.48 0
0 0 0 0 0 0
0.58 0 1.55 0 0 0Kke
Therefore, if the electric field is only imposed in the 3-direction, only the e33 B
component contributes to the piezoelectric activation (see Eq. (2.2)). This is
analogous to the dB33 B propagation because E
Kk KJ Jke c d . It should be noted that the
largest piezoelectric constant of AlN is along the c-axis. The AlN sputtered on
silicon is c-axis oriented. Therefore, through-thickness propagation utilizes the
largest piezoelectric constant of the material.
The piezoelectric coupling constant (K) and the electromechanical coupling
constant (k Bt B) are often used to characterize a resonator rather than the piezoelectric
constants of the material. These constants are derived from the acoustic velocity (
v Ba B) and the phenomena that a piezoelectric crystal stiffens when exposed to an
electric field which then alters the acoustic velocity. For a given propagation
direction l̂ , the scalar quantity of the stiffened acoustic velocity (v Ba B’) is defined:
2'
E S
a
c ev (2.3)
where P
SP is the permittivity measured at a constant strain. (The Christoffel matrix
can be used to find the scalar quantities of e and cE along a particular propagation
direction [2].) Eq. (2.3) rewritten in term of the unstiffened acoustic velocity is:
13
E
a
cv (2.4)
1 2' 21a av v K (2.5)
Where
22
E S
eK
c (2.6)
and the electromechanical coupling constant is defined:
22
21t
Kk
K (2.7)
For a through-thickness device with a propagation direction in the 33-direction, the
piezoelectric coupling constant reduces to:
22 3333
33E S
eK
c, (2.8)
14
which demonstrates that through-thickness propagation simplifies the materials
constants that apply to the device.
2.2 Aluminum Nitride Properties
As mentioned in the introduction, ZnO and AlN are common materials for FBAR
applications. Resonators have also been fabricated using PbZr B1-x BTi Bx BOB3 B (PZT) as the
piezoelectric layer [25]. PZT has a high mechanical coupling constant (see X310HTable
2.1) X but it has a low acoustic velocity. In addition, it has fabrication process
limitations that include incompatiblity with silicon microfabrication [6].
Consequently, sputtered AlN and ZnO are more commonly used as the piezoelectric
film in FBARs. Though ZnO has a higher 2tk than AlN, AlN has other advantages
over ZnO. While compatible with silicon semiconductor process technology, AlN
also has a large band gap and high resistivity. In contrast, ZnO is a semiconductor
making highly resistive ZnO difficult to obtain [8]. AlN also has a high acoustic
velocity which is advantageous because, in general, materials with a high acoustic
velocity tend to have high Q-factors and low absorption coefficients ( ) [2].
Absorption is the imaginary part of the complex propagation constant.
15
Table 2.1. Material properties of candidate piezoelectric materials for FBARs
MaterialAlN
[7-9, 24, 26, 27]ZnO
[2, 6, 8] PZT
[6, 8, 28, 29] Piezoelectric stress
constant, e B33 B [C mP
-2P]
1.55 1.32 940…1600
DielectricPermittivity, B33 B
11 11 300….1300
Electromechanical coupling constant, 2
tk6.5% 7.4% 20%
Acoustic velocity, v Ba B
[m sP
-1P]
11,000 6340 4500
Bandgap [eV] 6.2 3.0 3
2.3 Structural versus Acoustic Resonance
A common misconception about FBARs is how they resonate. They do not
vibrate at their structural natural frequency, which is in the kilohertz regime. Rather,
they resonate at their acoustic natural frequency, which is in the ultra high frequency
regime. Because the structural natural frequency is orders of magnitude less than the
acoustic natural frequency, it makes no contribution to the resonance of the FBAR.
Within this misconception, the beams can be viewed as MEMS-like springs that give
the structure more flexibility. The role of the beams is simply to isolate the
piezoelectically activated material from the substrate. In addition, the beams
themselves are not piezoelectrically activated.
2.4 Multi-Resonator Filter
An acoustic resonator is the basic component in a UHF filter. In a ladder filter,
the resonators are arranged in series and parallel, each with respect to the input and
16
output, as illustrated by Aigner [11] and reprinted in X311HFigure 2.2. The parallel
resonators are shifted downward in frequency by approximately half the width of the
pass band [11]. Loebl et al. both illustrate and explain why the parallel filters are
shifted in frequency [13]. The illustration is reprinted in X312HFigure 2.3X, which shows
how the responses of a resonator in series and another in parallel are additive to
produce a band pass filter. Loebl et al. explain that when the resonance frequency
f Br_s B of the series resonator equals the anti-resonance frequency f Ba_p B of the parallel
resonator, a maximum signal is transmitted from input to output. At the anti-
resonance frequency f Ba_s B of the series resonator filter, transmission is blocked. At the
resonance frequency of the parallel resonator f Br_p B the filter input is connected to
ground so that the bulk acoustic resonator filter also blocks signal transmission at
this frequency [13].
Figure 2.2. Schematic of a ladder filter [11]
17
Figure 2.3. Figure from Loebl et al. [13] illustrating a single section bulk
acoustic wave filter consisting of one series and one parallel resonator. Right:
Electric impedance of series and parallel resonator. The bottom curve shows
the transmitted signal S21 revealing a band-pass filter characteristic.
A filter and its component resonators are two port devices. If the filter or a
particular resonator is modeled as a black box all the properties of the impedance
can be described by the scattering matrix (S). Using the incident and emergent
waves illustrated in X313HFigure 2.4 X, Sij can be defined as [30]:
1 11 1 12 2
2 21 1 22 2
b S a S a
b S a S a
where:
SB11 B is the port-1 reflection coefficient
18
SB22 B is the port-2 reflection coefficient
SB21 B is the forward transmission coefficient
SB12 B is the reverse transmission coefficient.
The scattering parameters along with the characteristic impedance (ZBo B) of the
network can be used to calculate the impedance of the device.
Acoustic
Device Port-1 Port-2
a1
b1
a2
b2
Figure 2.4. Generic two-port network with incident and emergent waves
In order to simply the characterization of the FBAR and reduce the number of
applicable S parameters, the beam-supported FBARs were single port devices. This
reduces the S parameter expression to:
11 1 1S b a .
Because of the simplicity of the one-port device, bulk acoustic resonators are
generally characterized as such and the factors used to characterize a resonator are
based off the SB11 B parameter. Filters are characterized by their bandwidth and
19
insertion loss, which is determined by the S B21 B parameter. These are not applicable to
single port devices.
2.5 Summary
The basic concepts concerning the beam-supported FBARs were mentioned in
this chapter. The mechanical propagation and the electrical excitation are both in the
3-direction for a through-thickness resonator. The properties of the AlN were also
discussed; its high acoustic velocity and compatibility with silicon micro fabrication
make AlN a good choice for the piezoelectric material. Common misconceptions
regarding structural and acoustic natural frequencies and the role of the support
beams were discussed. Finally, this dissertation is focused on the fabrication and
characterization of AlN acoustic resonators, but it is important to note that the
resonator is for ultimate integration into a filter.
20
Chapter 3 Resonator and Mask Design
The resonator geometry and the photolithography mask set used to pattern the
wafer were designed concurrently. It was necessary to envision the three-
dimensional resonator in terms of the two-dimensional masks and the planar
fabrication processes that would be used to fabricate the resonator. The mask
determined both the size and shape of the features and also the order of the
fabrication processing steps. In this section the device geometry is discussed and the
mask set is described in detail.
Key issues in the resonator design included electrode material, active layer
geometry, and proper isolation of the components. The four necessary masks were
designed to accommodate the design criteria as well as certain hardware and
laboratory limitations in the fabrication process.
3.1 Resonator Design
The proposed innovations for the resonators were to use AlN directly sputtered
on <100> Si wafers and to explore novel geometries to address spurious frequency
modes. In typical FBAR fabrication sequences, the piezoelectric layer is sputtered
on top of a “bottom-metal electrode”. Here the AlN was sputtered first on <100>
silicon in order to produce a higher quality film, leaving the electrode to be
integrated later in the process. There was an original plan to use a thin layer of a
highly conductive silicon substrate as the bottom electrode. Unfortunately, the
silicon damped out the resonant frequency response, but the design allowed for
21
metal to be evaporated on to the backside of the resonator at the end of the
fabrication sequence. The design could not be dependent on the thickness of the
AlN, because the fabrication of the devices was done concurrently with the material
development. Consequently, the film thickness ranged from wafer to wafer, between
1.6-3.0 µm, and whatever was available was used in the fabrication. The majority of
acoustic resonators are fabricated using all thin film deposition techniques. The
SFBAR process flow incorporated bulk silicon fabrication, which facilitates MEMS
component integration for future designs and allows for non crystalline oriented
shapes to be etched in the silicon. Lastly, the spurious modes caused by lateral
acoustic waves and the other damping originating from the substrate were addressed
by reducing the area of the FBAR that was clamped to the substrate with support
beams.
The single port resonator consists of a sputtered AlN layer sandwiched between
a top and bottom metal electrode. Gold and aluminum are used as electrode
materials. There is no silicon substrate supporting the membrane underneath the
piezoelectric activated portion of the AlN film. Below the bottom electrode is an air
cavity, as shown in X314HFigure 3.1 X.
22
AlN
Metal Electrodes
Air Cavity
Silicon Silicon
Figure 3.1. Schematic of SFBAR cross-section
The activated part of the AlN is a 300 µm diameter circle which is connected to
the substrate with AlN support beams. The beams, with the exception of the one that
supports the transmission line, do not have top metal electrodes, and, therefore,
cannot be piezoelectrically activated. Beam lengths of 10, 50, 100 and 300 µm were
fabricated and tested. A resonator with 300 µm long support beams is shown in
X315HFigure 3.2X. Resonators with no springs, thereby fixed continuously to the substrate
around their circumference, were fabricated as a control device, as shown in X316HFigure
3.3X. These resonators did not sit on a solid silicon substrate but are thin membranes,
like their beam-supported counterparts.
A 300 µm diameter was chosen as the standard dimension for the activated
region based on through wafer etches. The DRIE reactor consistently etched a
cavity with a diameter of 300µm cleanly through the entire 500 µm thickness of a
four inch wafer. The floor of the cavities with length scales of 100 and 200 µm
would often be covered with spikes of silicon or “grass” [31]. Because the smallest
23
device had no springs, the air cavity was the same size as the activated region.
Therefore, 300 µm was chosen as the standard diameter for the mask.
300 µm diameter activated
membrane
300 µm length
support beam x8
Figure 3.2. SEM image of beam -supported FBAR with 300 µm long beams
24
300 µm
Figure 3.3. SEM image of an FBAR with circumference solidly clamped to
substrate
Probe pads with a Ground Signal Ground (G S G) configuration were
integrated into the design for testing. A silicon dioxide layer isolates the signal pad
from the conductive silicon substrate; the metal ground pads are in direct contact
with the silicon substrate, as labeled in X317HFigure 3.4X. The electrodes on the fabricated
resonators consist either of entirely aluminum or a stack of metals in which
aluminum is the bottom layer. It was necessary to use aluminum as the bottom layer
because it was found experimentally that it had superior adhesion to the AlN over
other commonly used metals in micro-fabrication. In order to ensure good contact
formation, the aluminum was annealed to the silicon during the fabrication process
[32]. Highly conductive silicon wafers with a resistance specification between 0.005
25
- 0.02 Ohm-cm were used to ensure a continuous electrical connection of the ground
plane between the metal probe pads and the metal bottom electrode of the FBAR.
The maximum thickness of the SiOB2 B isolation layer was constrained by the Cascade
Microtech RF probes (P/N I40-A-GSG-150) used for testing. During testing, the
probes may not be separated vertically by more than 0.5 µm. Therefore, the oxide
could not be thicker than 0.5 µm in order to keep the pads close enough to
accommodate the vertical pitch of the probes. Using the RF probes in conjunction
with the metal probe pads eliminated the need for wire bonding and the associated
resistance of the leads.
The top circular electrode of the SFBAR is connected to the signal pad by a thin
transmission line that rests on one beam. Due to the charging of the AlN, the SEM
image in X318HFigure 3.5 X clearly shows the transmission line. The beam width for all the
devices is 24 µm with a transmission line width of 4.3 µm. These dimensions ensure
that the electric field does not terminate on the sides of the beam, which requires that
the distance from the edge of the beam to the edge of the transmission line is greater
than twice the width of the transmission line, see X319HFigure 3.6X [33].
26
SiO2
Isolation
GroundPad
GroundPad
Signal
Pad
Figure 3.4. SEM image of the Ground Signal Ground probe pads of a FBAR
with beam supports 50 µm long
27
Transmission
Line
Figure 3.5. Top metal electrode and transmission line highlighted in SEM
image due to AlN dielectric charging
AlN Beam
T Tw
Bottom electrode
Microstrip Transmission line
T/w>2 ensures no fringing
electrical fields
Figure 3.6. Schematic of cross-section of support beam with transmission line
3.2 Mask Set
The device is patterned using a set of four masks. The three masks used on the
front side of the wafer were designed for processing on the GCA 6300 I-Line Wafer
28
Stepper in the UCSB Nanofabrication Facility. The first mask patterned the AlN
film, the second patterned the front side SiO B2 B, and the third mask is used for two
separate lithography steps. The third mask patterned negative photoresist for the
front side silicon etch, and it patterned positive photoresist for the lift-off step for the
front side metal electrode. The fourth mask is used on the backside of the wafer to
pattern the holes for the air cavity etch. Because the UCSB stepper does not have
the capability to align front side features to the backside of a wafer, the fourth mask
was a contact mask used in conjunction with the Suss Microtec MA 6 mask aligner
in the Nanoelectronics Research Facility at UCLA
3.2.1 Mask Set Layout
The mask set was created by drawing the layout for one die (1.5 mm x 1.5 mm)
using AutoCad 2000 drafting software [34]. X320HFigure 3.7X illustrates the mask layout
with each mask depicted in a different color. The turquoise layer is the AlN mask,
the green layer is the SiOB2 B mask, the pink layer is the top electrode lift-off mask, and
the blue layer is the backside air cavity pattern. The air cavity holes were centered
underneath the resonators and were 30 µm smaller in diameter to leave a 15 µm shelf
to support and attach the AlN beams to the silicon substrate.
Resonators of the same support beam length were arranged in three-by-three
arrays. The arrays had pitches, the distance between the center points of two
resonators, of 500 µm, 1000 µm , or 2000 µm. Devices with only transmission lines
and no top electrode were included on the masks as test features so that the
impedance of the transmission lines could be measured. The front side stepper
29
masks were produced from this layout by simply increasing the feature sizes five
times. Each mask is shown individually in X321HFigure 3.8X, X322HFigure 3.9X, and X323HFigure 3.10.
Figure 3.7: Complete set of four photolithography masks superimposed upon
each other, each in a different color, in order to show the complete layout of
resonators per stepper die
30
Figure 3.8. Photolithography mask used to pattern AlN film
31
Figure 3.9. Photolithography mask used to pattern front side SiO B2
32
Figure 3.10. Photolithography mask used for the front side silicon etch and top
metal electrode liftoff step
3.2.2 Backside Mask
As already mentioned, the backside air cavity etch mask was designed for
contact lithography. Therefore, instead of individual dies being stepped and
exposed, the entire wafer is exposed and patterned at once. In order for all the
features on the backside mask to align to the features on the front side, the die
33
stepping pattern of the front side masks had to be predetermined and integrated into
the backside mask. As illustrated in X324HFigure 3.11X, the twelve die pattern was drawn
on the outline of a four inch wafer. The backside layer of the four mask layer was
then mirrored around the y-axis centerline and placed in each of the twelve dies, as
shown in X325HFigure 3.12X.
3.3 Summary
The following chapter describes the detail fabrication flow and shows how the
masks are used to build the resonators. The constraint that the thickness of the AlN
is variable and deposited directly on the silicon was addressed in the resonator
design. The circular air cavities took advantage of the bulk silicon micromachining
process. Finally, the design incorporated support beams to look at how the substrate
affects damping and spurious modes.
34
Figure 3.11. Twelve die pattern for backside contact mask as would be place on
a four inch wafer
35
Figure 3.12. Backside contact mask pattern
36
Chapter 4 Fabrication
The majority of the resonator fabrication was done in the UCSB Nanofabrication
Facility with the backside photolithography performed at the UCLA Nanoelectronics
Research Facility and the wafer cleaning in the UCSB MEMS cleanroom. This
section outlines the process steps developed to build the resonators and presents the
more critical procedures in detail. These critical processes include etching of the
AlN and the deep silicon etching of the air cavity. A comprehensive outline of each
recipe is in Appendix A.
As mentioned in previous sections, the resonators are fabricated from a <100>
silicon wafer with textured AlN sputtered directly on the silicon. The AlN films
were highly oriented in the c-axis direction but were not oriented in plane. The AlN
material deposition and characterization was done by a fellow Ph.D. candidate,
Vanni Lughi, using an AC reactive sputter chamber on a Sputtered Film, Inc.
Endeavor 8600 sputter tool. His advancements in sputtering AlN made this
fabrication process possible. Most importantly, Vanni developed methods to control
the stress, resulting in films with a tensile stress of 100-300 MPa [15]. This ensured
that the AlN thin film did not crack when released from the substrate, as opposed to
the older film shown in X326HFigure 4.1X that cracked upon release. Unfortunately, the
ability to control the thickness uniformity across a single wafer was much more
difficult to achieve. Upon visual inspection, at least ten different color rings, each
corresponding to a different thickness reflecting a different wavelength of light,
would be visible on an individual wafer. This added complexity to the etching of the
37
AlN film. 327HFigure 4.2 is a plot of the normalized AlN film thickness as a function of
the distance from the center of the wafer. Normalized thickness is equal to film
thickness divided by the film thickness at the wafer’s center. Bipolar power, as
shown in 328HFigure 4.2, is a growth parameter in the sputtering process the effects of
which will be published by Lughi et al. [35]. The plot shows both significant
variation in film thickness and a non-linear relationship between Bipolar power and
film thickness.
Figure 4.1. Optical microscope image of cracked AlN thin film after the
substrate release
38
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
0 10 20 30 40 50
Bipolar 0
Bipolar 10
Bipolar 15
No
rma
lize
d T
hic
kn
ess
Distance form center [mm]
Figure 4.2. Normalized thickness variation of AlN across silicon wafer for
different values of Bipolar power. Bipolar refers to the arbitrary value that
determines the amount of material sputtered from each of the two targets in the
sputtering chamber [35]
4.1 Fabrication Overview
Processing Steps
1. Sputter AlN on a <100> silicon double sided polished wafer, as
illustrated by X329HFigure 4.3X. The wafer was polished on both sides to
facilitate an air cavity etch free of silicon grass.
39
Back side Front side
ALN film Silicon
Substrate
Figure 4.3. Illustration of front and back side of double sided polished silicon
wafer with a sputtered AlN film on the front side
2. Deposit a 1.3 µm thick titanium dioxide film on top of the AlN
film by DC reactive sputtering, as illustrated by 330HFigure 4.4X. TiOB2 B
was the masking material for the AlN etch.
40
Back side Front side
TiO2
Figure 4.4. Illustration of deposition of TiO B2 B process step
3. Spin AZ P
®P 4330-RS photoresist (3 µm thick) on the TiOB2 B. Using
the AlN resonator mask ( X331HFigure 3.8X), expose in the UCSB stepper,
hard bake, and then develop.
4. Etch the TiOB2 B in the Panasonic Inductively Coupled Plasma (ICP)
tool with a CHFB3 B plasma, as illustrated by X332HFigure 4.5X.
41
Back side Front side
TiO2
AlN
Figure 4.5. Illustration of resonator pattern in the TiO B2 B mask material
5. Etch AlN in Panasonic ICP with a chlorine plasma, as illustrated
by X333HFigure 4.6 X.
Back side Front side
AlN
Si
Figure 4.6. Illustration of resonator pattern in AlN film
42
6. Strip the TiOB2 B mask with a dip in a 49% hydrofluoric acid bath
diluted 20:1 with deionized water.
7. Deposit a 0.5 µm film of PECVD SiOB2 B on the front side of the
wafer and 2 µm film on the backside, as illustrated by X334HFigure 4.7X.
The front side oxide provided the electrical isolation for the
device. The backside oxide was the masking material for the air
cavity etch.
Back side Front side
SiO2
SiO2
Figure 4.7. Illustration of PECVD SiO B2 B on the front and back of wafer
8. Spin AZ P
®P 5214 photoresist on the back of the wafer. Expose the
resist using the Hard Contact mode of the UCLA Suss M6 contact
aligner with the backside contact mask ( X335HFigure 3.12X). Then bake
and flood expose, which cross-links the photoresist and converts
43
the polymer to a negative photoresist. Develop in MF701. The
AlN was protected by the SiO B2 B so it was not etched by the MF701
9. To harden the photoresist and to make the photoresist more
resistant to the SiOB2 B etch chemistries, store wafer for 24 hours and
then bake for 20 minutes at 120 degrees [36].
10. Etch backside SiOB2 Bin the Panasonic ICP with a CHFB3 B plasma, as
illustrated by X336HFigure 4.8X.
11. Solvent clean wafer.
12. Spin AZ P
®P 4110 photoresist (1.2 µm thick) on the front SiOB2 B.
Using the SiOB2 B mask ( X337HFigure 3.9X), expose in the UCSB stepper
and develop.
13. Etch front side SiOB2 Bin the Panasonic ICP with a CHFB3 B plasma, as
illustrated by X338HFigure 4.8X.
44
Back side Front side
Figure 4.8. Illustration of the patterned front side electrical isolation SiOB2 B and
backside air cavity SiO B2 B masking material
14. Solvent clean wafer
15. Spin AZ P
®P 5214 photoresist (1 µm thick) on the front side of
wafer. Using the liftoff mask ( X339HFigure 3.10X), expose in the UCSB
stepper, hard bake, flood expose, and then develop.
16. Etch exposed silicon in between AlN beams for 1 minute in
DRIE, as illustrated by X340HFigure 4.9X.
45
Back side Front side
Exposed
Silicon
Figure 4.9. Illustration of exposed silicon during front side DRIE.
17. Clean wafer with solvent and OB2 B plasma.
18. Spin AZ P
®P 4110 photoresist (1.2 µm thick) on the front side of
wafer. Using the liftoff mask ( X341HFigure 3.10X), expose in the UCSB
stepper, soak in toluene to facilitate liftoff [37], and then develop.
19. Evaporate metal on front side with the CHA Multi-Wafer
evaporator.
20. Lift-off resist and metal with acetone, as illustrated by X342HFigure
4.10X.
46
Back side Front side
Figure 4.10. Illustration of top electrode lift-off step
21. Etch air cavity from the backside of sample with the Si DRIE,
illustrated by X343HFigure 4.11X.
Back side Front side
Figure 4.11. Illustration of backside air cavity etch
47
22. Solvent clean sample.
23. Evaporate metal on backside side with the CHA Multi-Wafer
evaporator, as illustrated by X344HFigure 4.12X.
Back side Front side
Figure 4.12. Illustration of evaporation of backside electrode
24. Anneal aluminum to silicon with a forming gas at 465° C for 30
seconds [32].
4.2 AlN Processing
AlN is a fairly inert material with low etch rates compared to other group-III
nitrides. AlN is typically etched in chlorine-based plasmas [38-40]. The early stages
of the process development for the AlN etch was done using thinner films, less than
2 µm, and a 3 µm photoresist mask. All the etches were done in a PlasmaTherm
Reactive Ion Etch Load-Locked, Chlorine-Based System, which had a maximum
48
power of 200 Watts [31]. This was less than ideal, since earlier studies on III-V
nitride etching had shown that using an ICP reactor was preferable over a RIE
reactor and that higher powers helped reduce the sidewall slope [41]. Therefore,
when the Panasonic Inductively Coupled Plasma Etcher Model E640 became
available in the UCSB Nanofab, all further AlN processing was done in the
Panasonic ICP. One important note, despite AlN’s inertness, it does etch in most
photoresist developers and KOH solutions. Therefore, a developer designed to be
used with aluminum, such as AZ P
®P DEV, diluted 1:1 with DI water, must be used as
the developer when AlN is exposed to the solution.
Etching AlN with a ICP reactor required a masking material other than
photoresist because the higher power reduces the selectivity between the photoresist
and the AlN. The need for a more inert mask was compounded because thicker AlN
films were being produced due to modifications in the growth process. The new
mask was 1.3 µm of titanium dioxide sputtered in the DC reactor chamber of the
Sputtered Films, Inc. Endeavor 8600. TiOB2 B was originally used as an etch mask for
AlN because of its high selectivity in chlorine plasmas when etching titanium [42].
Because the TiOB2 B was sputtered in a DC reactor rather than an AC reactor, the
quality of the TiOB2 B varied greatly from film to film. Therefore, no consistent
selectivity rate between the AlN and TiO B2 B could be determined. However, the 1.3
µm thick mask withstood etches of 3 µm AlN films. The TiO B2 B was removed after
the AlN etch with a 20:1 diluted 49 % hydrofluoric acid dip. It is important to note
that buffered HF should not be used because the ammonia fluoride will attack the
AlN.
49
Three main factors used to qualify the AlN etch on the Panasonic ICP were etch
rate, perpendicularity of the sidewalls, and the roughness of the exposed silicon
substrate. The exposed silicon is rough because the silicon has a faster etch rate than
AlN in a chlorine plasma. When the silicon substrate became exposed, the AlN
acted as point masks for the silicon, as shown in 345HFigure 4.13 and 346HFigure 4.14. This
behavior was observed on samples etched using a laser interferometer endpoint
detector. The typical endpoint response is a step. The sine wave response, in X347HFigure
4.15X, shows a slow decrease in amplitude despite the observation that the AlN had
been completely etched. This is indicative of an etch where the material to be etched
has a slower etch rate than its substrate.
50
Figure 4.13. SEM image of a resonator surrounded by a rough silicon substrate
after the AlN etch and before TiO B2 B mask removal
51
TiO2 Mask
Exposed AlNsidewalls
AlN Particles
Figure 4.14. SEM image of AlN particles leftover after AlN etch
52
Figure 4.15. Digital image of the endpoint detector monitor screen displaying
the plot of the laser interferometery response from an AlN etch. The
decreasing amplitude of the sine wave is indicative of a material that has a
slower etch rate than its substrate.
The roughness of the silicon was observed qualitatively through its color and
sheen. A substrate black in color would represent roughly etched Si surface while a
shiny reflective surface would mean little or no surface damage. Four etch
conditions listed in X348HTable 4.1X were tried. Argon flow was varied to reduce the
sputtering of the silicon substrate and the power and bias were varied to boost the
53
etch rate. The etch rates were determined using the Filmetrics White Light
Reflectometer to measure the film thickness. The Dektak II Profilometer was used to
determine the etch topology. X349HFigure 4.16X is a Dektak scan of the topology of a
sample that had been etched for 5 minutes and 45 seconds with Recipe 4, which was
selected for its high etch rate and minimal damage to the Si surface.
Table 4.1. Panasonic ICP Etch conditions and results for AlN etch
Recipe 1 Recipe 2 Recipe 3 Recipe 4
ChlorineFlow [sccm]
30 30 30 30
Argon Flow [sccm]
20 10 5 5
Power [W] 400 400 400 600
Bias [W] 100 100 100 150
SiliconAppearance
Black White SilveryWhite
Silvery
Etch Rate [nm/min]
133 - 121 300
As can be seen on the Dektak plot in X350HFigure 4.16X, the silicon substrate is not
smooth. The SEM images show a wafer after the AlN is etched but before the TiOB2 B
is removed. The silicon substrate was littered with AlN particles that were not
cleared. These particles are the measured roughness in the DekTak plot, and the
particles act as point masks if the process is continued. Instead, the AlN particles
were not removed and the processing of the wafer continued. A possible solution to
removing these AlN particles is to quickly dip the wafer in a photoresist developer
54
which would etch the AlN but not the silicon. Since the particles would be attacked
from all sides they might be able to be removed before the dimensions of the larger
AlN features were affected or this wet etch could be designed into the dimensions of
the mask layout. Unfortunately, this developer etch was not tested because, at the
time the idea was conceived, wafers with high quality AlN films were not available
due to oxygen contamination in the deposition chamber.
Figure 4.16. Dektak topology scan of AlN etch for wafer W9H
4.3 Silicon Deep Reactive Ion Etch (Si DRIE)
The silicon DRIE reactor was used for both the front side and backside silicon
etch. The reactor switches between etching the silicon with a SF6 plasma and
protecting the already etched sidewalls with the polymer C4F8. This process etches
55
straight, smoothly scalloped, walls into silicon without a crystalline orientation
preference [18].
4.3.1 Front side Silicon Etch
As mentioned in the process flow, the front side DRIE etched the exposed silicon
between the AlN beams, as shown in X351HFigure 4.9. This etch was one minute long and
removed approximately 2 µm of silicon. In the interest of cost, as outlined in
Section X352H4.1X, the photoresist for the front side silicon etch was patterned using the
electrode lift-off mask ( X353HFigure 3.12). This left the AlN beams exposed. Therefore,
even though the DRIE is typically used for deep silicon etches, AlN’s inertness to
SFB6 B made the DRIE the best candidate for the front side silicon etch.
The removal of silicon between the AlN support beams enabled a more uniform
release during the air cavity etch, counteracting the DRIE reactor’s tendency to etch
slower near the side walls. It also ensured that the bottom electrode, in the last step
of the process, had an adequate amount of silicon remaining on the support beams
for annealing and, therefore, the device had good contact formation. Images of the
remaining silicon from the front side and through the air cavity are shown in X354HFigure
4.17. Note the roughness of the surface next to the AlN beam in 355HFigure 4.17 (a).
This roughness is a result of the AlN etch, as discussed in Section 4.2 and shown in
356HFigure 4.14.
56
(a)
(b)
Silicon
AlN Beam
AlN Beam
Remaining Silicon
Figure 4.17. SEM images of remaining silicon substrate on an AlN support
beam (a) front view and (b) air cavity view. The surface beneath the beam in b)
is the sample holder
57
4.3.2 Air Cavity Etch
The air cavity etch was the first step of the process that could not be performed
on the 4-inch wafer sample. Though the DRIE reactor is configured for four-inch
wafers, the loading across the wafer was extremely pronounced for a 500 µm deep,
through-wafer etch. It was not possible to successfully etch both the dies located in
the center and the edges of the wafers. Instead, an individual die was mounted along
its edges with 3M P
™P Thermally Conductive Adhesive Transfer Tape 9890 to a carrier
wafer, as shown in X357HFigure 4.18X. The sample was easily removed from the carrier by
soaking it in acetone.
Figure 4.18. Sample mounted on 4-inch carrier wafer in preparation for air
cavity etch
58
The DRIE reactor’s etch rates were not consistent because of instabilities of the
power supply. They ranged from 2.2-3.2 µm/minute for the largest air cavities. The
variation in etch rates made it necessary to closely monitor each etch. The bulk of
the substrate would be etched in a three hour session. After the three hour etch, the
300 µm long, support beam resonators would usually just start showing. At this
point the sample would be etched for time durations ranging from 1 to 15 minutes
and then inspected with an optical microscope to determine the time interval of the
next etch. Determining the duration of the next etch was based on the appearance of
the Si and the performance of the DRIE reactor on that given day. The resulting air
cavity with smooth walls and no silicon debris is shown in X358HFigure 4.19X
4.4 Summary
The fabrication of the beam-supported FBARs used both thin film deposition and
bulk silicon MEMS fabrication techniques. The AlN was etched in the Panasonic
ICP with a chlorine plasma and was optimized with an etch rate of 300 nm/min and
minimal silicon substrate damage. The silicon DRIE reactor was used for both the
front and backside silicon etches. The front side silicon etch ensured that there was
silicon left supporting the beams and the backside electrode would anneal to the
silicon. The silicon DRIE of the backside produced air cavities with smooth
sidewalls. The circular shape was novel and demonstrated that any shape can be
processed without being limited by the crystal orientation of the silicon.
59
Figure 4.19. SEM image of the air cavity of a 300 µm support beam resonator
60
Chapter 5 Testing and Characterization
This chapter covers how the responses of the resonators were measured and how
the data was collected. The Figure of Merit values used to characterize the
performance of the resonators are introduced. The evaluation of the Quality Factor
and the effective electromechanical coupling coefficient is also described. A
representative resonator, sample W9HS8 resonator 10018, is used throughout this
section to demonstrate the analysis. The AlN film thickness of sample W9HS8
resonator 10018 is 1.7 µm with a top metal electrode primarily of gold and a bottom
aluminum electrode with thicknesses of 330 nm and 700 nm, respectively. The
different electrode thicknesses are meant to compensate for the difference between
acoustic velocities of aluminum and gold. The support beams of the resonator are
100 µm long.
5.1 Data Collection
The reflection coefficient (SB11 B) response of the single port acoustic resonator was
measured with a HP 8753C voltage network analyzer (VNA) in conjunction with
Wincal P
TMP Calibration Software [43]. The VNA delivers waveforms of a specified
frequency range into the device and measures the reflected power. The power
dissipated is the acoustic load and is dependent on the reflection coefficient [30].
All testing done was done with 0 dB output power level.
61
The test setup consisted of the VNA and a Cascade Microtech G-S-G RF probe
joined by a RF cable with 3.5 mm connectors 1F
2.FPT All the components had a
characteristic impedance (ZBo B) of 50 . The probe was supported and manipulated
with a probe station designed for RF measurements. X359HFigure 5.1X is a photograph of
the test setup. Before any resonator response data was collected, the three tips of the
RF probe were planarized in the z-direction and the system was calibrated for the
frequency span to be tested.
The measurements were done by first collecting the SB11 B data across a large
frequency sweep from 500 MHz to 6 GHz TPF2F
3 with a frequency step of 3,437,500 Hz.
For example, X360HFigure 5.2 X is a Smith Chart plot of the SB11 B parameter response from the
resonator which showed a fundamental acoustic resonance at 1.342 GHz and lesser
responses at the 2 P
ndP and 3 P
rdP harmonics. A second frequency sweep was performed
over a smaller range around the fundamental frequency. Note that a Smith Chart is a
graphical tool used to analyze and design transmission lines. A Smith Chart is
comprised of two intersecting families of circles; one to plot the real component of
the reflection coefficient and one to plot the imaginary component for each
frequency step value. The Smith Chart will be further explained in later in this
chapter.
TP
2PT 3.5 mm connectors are rated up to 20 GHz.
TP
3PT The frequency range of the HP 8753 is 300 kHz 3 GHz or 3 MHz 6 GHz with
the doubler on.
62
Figure 5.1. Photograph of RF probe station test setup
63
freq (500.0MHz to 6.000GHz)
S1
1
fs=1.342 GHz
2nd
Harmonic
3rd
Harmonic
Figure 5.2. Smith Chart plot of SB11 B response from 500 MHz to 6 GHz of sample
W9HS8 resonator 10018
Using the characteristic impedance of the RF test components and the reflection
coefficient, the input impedance (ZBin B) of the FBAR can be obtained from the
equation [44, 45]:
11
11
150
1in
SZ
S. (5.1)
The collected data was manipulated using Advanced Design System (ADS) by
Agilent Technologies [46]. ADS is a software program that provides a platform to
64
simulate, design, and manipulate collected data for RF systems. The ADS design
interface and the model that was built to read the collected SB11 B data into the ADS
system is shown in X361HFigure 5.3 X. The ADS platform made it possible to easily convert
and plot ZBin B and SB11 B in different formats, such as their imaginary and real parts.
VNA and
probe
Collected
Date file
Data
Parameters
Figure 5.3. ADS design interface and simulation model used to read collected
data into the ADS platform
5.2 Resonator Characterization Factors
The factors covered in this section were calculated or observed directly from the
collected data and the resulting input impedance. The key calculated values are the
65
quality factor at resonance and anti-resonance and the effective electromechanical
coupling coefficient. The response was also examined qualitatively by observing if
spurious modes were present.
5.2.1 Quality Factor
The Quality Factor (Q) of an FBAR, which quantifies the dissipation of the
stored energy per cycle, is measured at resonance and anti-resonance. Resonance
occurs when the input impedance is at a minimum and anti-resonance occurs when it
is at a maximum. The response of a through-thickness acoustic resonator is similar
to that of a multi-pole resonant circuit. A multi-pole resonant circuit combines the
components of a series resonant circuit and a parallel resonant circuit. A series
resonant circuit allows a maximum current flow at resonant frequency, whereas a
parallel resonant circuit allows a minimum at resonance [47]. Therefore, the
resonant frequency and the anti-resonant frequency are often referred to as the series
frequency (f Bs B) and the parallel frequency (f Bp B), respectively [21]. Together they are
referred to as a frequency pair. At these frequencies the response is completely real
and does not have an imaginary component. Specifically, the input impedance may
be written as [2]:
inZ R jX ; (5.2)
66
and at resonance and anti-resonance frequencies, 0X . On a Smith Chart plot
the frequency pair corresponds to where the data crosses the x-axis. X362HFigure 5.4X
highlights a frequency pair on a Smith Chart plot with a frequency span between 1-2
GHz and frequency step of 625 kHz; this is the sample W9HS8 resonator 10018,
shown in X363HFigure 5.2 X.
freq (1.000GHz to 2.000GHz)
S1
1
fs=1.342 GHz fp=1.368 GHZ
Figure 5.4. Smith Chart plot of SB11 B response from 1-2 GHz of sample W9HS8
resonator 10018
The equation used to find the Q of the resonators is:
67
,,
,2
s p
s p
s p
f f
f dZQ
df (5.3)
where Z is the phase angle of the input impedance. Eq. (5.3) is algebraically
equivalent to 2 1s sQ f f f where f B1 B and f B2 B are the frequencies at which the
magnitude of the input impedance is 1 2 of its value at resonance or anti-
resonance. The input impedance magnitude and phase angle are plotted for the
sample W9HS8 resonator 10018 in X364HFigure 5.5X. Note that the resonance and anti-
resonance occur when the phase angle crosses zero.
68
1.2E9 1.4E9 1.6E9 1.8E91.0E9 2.0E9
25
35
45
15
55
-1.0
-0.5
0.0
0.5
-1.5
1.0
Frequency [GHz]
Z [dB
]
Phase A
ngle
of Z
[rad]
fs fp
Figure 5.5. Magnitude and phase angle plots of input impedance of sample
W9HS8 resonator 10018
The slope of the phase angle was found using both ADS and MatlabP
®P by The
Mathworks, Inc. [48]. ADS converted the collected data from its real and imaginary
values to its magnitude and phase angle in radians. The phase angle values near the
resonant or anti-resonant frequency were entered into a Matlab P
®P code that fits a
polynomial to the data, finds the derivative, and solves for the Q. The code is
presented in Appendix B. X365HFigure 5.6X shows an example of a graph produced by the
MatlabP
®P code for sample W9HS8 resonator 10018. The circles denote the actual
data points and the fitted polynomial is shown by the red dashes. The QBs B and the QBp B
for sample W9HS8 resonator 10018 are 86 and 151, respectively. These values are
69
representative of the quality factors of the tested support beam FBARs. The highest
Q achieved at resonance in the devices was 145 at 2.3 GHz. This value for Q is
quite low compared to commercial products [3, 12] and other air-backed free
standing FBARs [16], but the increase in Q is an improvement over the previous
beam suspended design [17].
1.332 1.334 1.336 1.338 1.34 1.342 1.344 1.346 1.348 1.35
x 109
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
freq, Hz
Z p
hase d
eg
Phase Angle Polynomial Fit
4 3
2
6.39 30 3.49 20
7.13 11 6.48 2 2.21 7
Z E f E f
E f E f E
Figure 5.6. Polynomial equation fitted to phase angle data generated by
MatlabP
®P code
5.2.2 Effective Electromechanical Coupling Coefficient
The effective electromechanical coupling coefficient ( 2effk ) is defined as [49, 50]:
70
22
2( )
4s
eff p s
p
fk f f
f. (5.4)
Eq. (5.4) is an approximation for the electromechanical coupling constant ( 2tk ) that
is applicable when 2tk is small [51]. The 2
effk is a relative measure between the
series and parallel frequencies that depend on both the material properties and the
resonator geometry [21]. This is an important measure because it is directly
correlated to the bandwidth of the filter.
The electromechanical coupling constant is a measure of material properties and
is defined as a scalar quantity for a given propagation direction as [2]:
22
21t
Kk
K (5.5)
and when the propagation is in the 33-direction:
22 3333 2
33S
eK
c (5.6)
where e refers to the piezoelectric stress component, Ec is the compliance
component at a constant electric field, and S is the permittivity at constant strain.
71
The definition of K is derived from the stiffened acoustic velocity as shown in
X366HChapter 2. The 2effk of the sample W9HS8 resonator 10018 is 4.6%, but values as
high as 6.3% have been measured for the SFBARs, shown in X367HFigure 6.5X, which is
close to the bulk AlN theoretical maximum of 6.5% [8].
Research groups have been trying to correlate the measured 2effk to the 2
tk .
Zhang et al. [52], using the Mason Model [53], correlated the 2effk to the 2
tk , but the
model is limited to FBAR’s with electrodes that are 10% or less than the thickness of
the piezoelectric film. Lee et al. [10] constructed a model that solved for the 2tk with
measured values while taking into account of the acoustic impedance of the
electrodes, but they did not correlate the results to experimental data.
5.2.3 Figure of Merit
A Figure of Merit (FOM) is a common way for resonators to be characterized
and compared. The IEEE Standard for piezoelectric vibrators [54] defines the FOM
using the terms of the Butterworth – Van Dyke equivalent circuit model, as shown in
368HFigure 5.7. (The Butterworth – Van Dyke circuit is described and explored further
in Chapter 7.) The FOM is inversely proportional to the motional resistance, Rm, and
the parallel plate capacitance, Co:
0
1 m
s o m
CFOM Q
C R C (5.7)
72
where s is the radial resonant frequency and Cm is the motional capacitance. Q is
the quality factor of the circuit and is defined as:
1s m
m s m m
LQ
R C R. (5.8)
where Lm is the motional inductance. The explanation for the FOM given in the
IEEE Standard on Piezoelectricity [21] states that the FOM for a resonator is defined
in terms of 2effk and Q as follows:
2 21eff effFOM k Q k (5.9)
When effk is small, the FOM reduces to:
2effFOM Q k . (5.10)
Eq (5.10) can shown to be the equivalent to Eq. (5.7) using the IEEE Standard
definition [54]:
2 2
2
p s m
s o
f f C
f C (5.11)
73
The advantage of the FOM is that it can be directly correlated to the insertion
loss of the ensuing filter [1]. Agilent Technologies has found direct ties between the
FOM of the resonator and the roll-off and insertion loss of the filter[55].
The FOMs at resonance and anti-resonance for sample W9HS8 resonator 10018
are 4.0 and 6.9, respectively. These values are low compared to the reported values
from industry, which are as high as 100 [1, 3]. .
Zin
Lm
Rm
Cm
Co
Figure 5.7. Butterworth – Van Dyke equivalent circuit
5.2.4 Spurious Resonances
Any resonance that does not exhibit a frequency pair can be deemed a spurious
resonance or mode. Two varieties of spurious resonances are discussed in this
dissertation. One type of spurious resonance observed in our fabricated and tested
FBARs is a resonance at the bulk acoustic natural frequency instead of a frequency
pair. The data plotted on the Smith Chart in X369HFigure 5.2 has a frequency pair at the
fundamental frequency, but the two other circles on the plot -- not crossing the real
axis -- are spurious resonances at the 2nd and 3rd harmonics. Some other resonators
74
do not have a frequency pair at the fundamental frequency, but only a spurious
resonance, as shown in 370HFigure 5.8. A non-frequency pair response is not desirable
for filter applications. A non-frequency pair response exists entirely below the x-
axis of the Smith Chart plot which is where the reactance of the response is in the
conductive regime, as illustrated in 371HFigure 5.9. This is not desirable because a filter
needs to act as an RF choke or inductor and trap the electromagnetic wave. Hence,
to be in the desired inductive regime, the response needs to cross the x-axis and enter
the top half of the Chart Plot, creating a frequency pair response. Trends observed
with respect to when a frequency pair occurred in the beam-supported FBARs are
discussed in the next chapter.
freq (500.0MHz to 6.000GHz)
S1
1
Figure 5.8. Smith Chart plot for a resonator that exhibited a spurious
resonance at the fundamental frequency
75
Conductive
Regime
Inductive
Regime
Figure 5.9. Smith Chart plot illustrating the conductive and inductive areas
of the reactance
Ripples on the Smith Chart plots are the other variety of observed spurious
resonances, as shown in X372HFigure 5.10. The ripples are small responses at frequency
intervals that do not align to the acoustic resonant harmonics of the device. The
ripples dissipate energy and are deemed undesirable. One of their sources is higher
order lateral standing Lamb waves [3, 19]. Lamb waves have both shear and
longitudinal components and, therefore, excite particle displacement both in and out
of plane of the membrane. In the case of the through-thickness mode, waves
propagating in-plane occur in a structure with finite lateral dimensions [56]. 373HFigure
5.11, taken from from Ruby et al. (2001) [3], show the Lamb wave ripples that had
76
plagued Agilent Technologies FBARs. These have been reduced by modifying the
geometry of the FBAR [57]
freq (2.000GHz to 2.500GHz)
S1
1
freq (2.000GHz to 2.500GHz)
S1
1(a) (b)
Spurious
ripples
Figure 5.10. Smith Chart plots from resonators that showed spurious
resonances as ripples. (a) Resonator W3KS7 5023 (b) W3KS7 10012
77
Figure 5.11. Agilent Technologies FBAR exhibiting Lamb wave excitation
at lower frequencies [3]
Most of the tested resonators, including the resonators solidly clamped around
their entire perimeter, do not display the ripples shown in X374HFigure 5.10 X The presence
of ripples on some of the devices could not be correlated to beam length or silicon
debris remaining after the air cavity etch. The ripples did not occur on any of the
samples with gold as the electrode material. Further study is needed to confirm if
and why the gold damped spurious resonances. One possibility is that the lower
acoustic velocity of Au results in Lamb waves of lower acoustic velocity. These
78
Lamb waves may be of a lower velocity than the measured range of 500 MHz to 6
GHz. Another possibility is that the Al, which was observed to be less resistant to
the fabrication process than the Au, resulted in responses with spurious ripples due
to its rougher surface. Another feature of the beam-supported FBAR design that
could affect the damping of spurious resonances is the circular shape of the air
cavity. Altering the shape of the cavity either experimentally or with a simulation
would provide insight.
5.3 One-Dimensional Frequency Model
The parallel, or anti-resonant, frequency of a piezoelectric resonator that is only
activated in the through-thickness direction can be estimated by [23]:
2a
p
vf
d (5.12)
where v Ba B is the acoustic velocity of the material and d is the thickness. The
derivation of Eq. (5.12) originates from the Mason Model [53] definition of the input
impedance of a resonator. The Mason Model simulates a resonator as a transmission
line with each material layer having its own acoustic length. The Mason Model
equivalent circuit possesses two mechanical ports and one electrical port. A
transformer converts the energy from mechanical to electrical and vice versa. 375HFigure
5.12 is a Mason Model equivalent circuit from Rosenbaum [2].
79
Figure 5.12. Mason model equivalent circuit
Ignoring the effects of the electrodes, the input impedance derived from the Mason
Model is [2]:
1 tan1in t
o
Z kj C
(5.13)
where
2
kd. (5.14)
k is the complex propagation constant and defined as:
80
k j ; (5.15)
where is the phase constant and is the absorption. In an ideal resonator
2 ak f , therefore, substituting into Eq. (5.14)
2
a
f (5.16)
At the parallel frequency ZBin B= and, therefore, Bp B= /2. Substituting /2 for in Eq.
(5.16) results in Eq. (5.12).
When the effects of the electrodes are taken into consideration Eq. (5.12)
becomes:
1
1 2
1 22el AlN el
p
el AlN el
d d dNf
v v v. (5.17)
The film thickness for each layer should be the same for all the FBARs on the
same sample. Consequently, according to Eq. (5.17), their parallel frequencies
should all be the same. X376HFigure 5.13 X compares the one-dimensional frequency model
values to the root-mean-square (RMS) of the parallel frequencies of the resonators
on each sample. The acoustic velocity values used are listed in X377HTable 5.1X. The
thicknesses were determined with DekTak topology scans. The frequency model
81
predictions correlate with the collected data and, therefore, confirm that the
resonator is being excited in the thickness-extension mode. The small differences
between the model and the actual values are partially due to the variation of AlN
film thickness across a wafer making the individual AlN thickness of every resonator
difficult to determine.
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
W9HS2 W9HS3 W9HS4 W9HS5 W9HS8 W3KS2 W3kS6 W3KS3 W9HS10 W3KS7 W3KS4 W3KS5 W3KS8 W3KS6b W3KS11
RMS Experimental
1-D Model
Fre
qu
en
cy [
GH
z]
Sample
3rd
Harmonic
Figure 5.13. Comparison of the one-dimensional frequency model to the RMS
of the resonators’ measured parallel frequencies per sample; all data points are
for the fundamental acoustic frequency except where noted.
82
Table 5.1. Acoustic velocity values
MaterialAcoustic Velocity
[m/s]
AlN 11,000 [26]
Al 6350 [2]
Ni 6040 [58]
Au 3240 [58]
5.4 Three-by-Three Array
One of the goals of the MINT project was to fabricate a three-by-three array of
resonators each with different resonant frequency. Two arrays were produced where
every resonator exhibited a frequency pair. One array consists of 100 µm long
support beam resonators with a pitch, the distance between the center points of
neighboring resonators, of 2000 µm. The second array has solidly clamped
resonators with a 1000 µm pitch. X378HFigure 5.14 X and X379HFigure 5.15 X are illustrations of the
arrays with the resonant frequency, the quality factor at resonance, and the effective
electromechanical coupling coefficient listed next to the corresponding resonator.
83
fs=2.186 GHz Qs=30
2effk =5.8%
fs=2.193 GHzQs=30
2effk =5.4%
fs=2.163 GHzQs=30
2effk =5.8%
fs=2.195 GHz Qs=37
2effk =5.7%
fs=2.184 GHzQs=33
2effk =5.4%
fs=2.174 GHzQs=34
2effk =5.4%
fs=2.205 GHzQs=23
2effk =5.3%
fs=2.214 GHzQs=20
2effk =6.0%
fs=2.224 GHz Qs=30
2effk =5.7%
Figure 5.14. Three-by three 2000 µm pitch array of 100 µm long beam support
resonators with their corresponding resonant frequency, quality factor at
resonance, and 2effk listed
84
fs=2.446 GHz Qs=61
2effk =3.9%
fs=2.452 GHzQs=59
2effk =4.6%
fs=2.516 GHzQs=53
2effk =5.7%
fs=2.464 GHz Qs=51
2effk =3.8%
fs=2.469 GHzQs=43
2effk =4.5%
fs=2.479 GHzQs=68
2effk =5.5%
fs=2.532 GHzQs=112
2effk =3.8%
fs=2.479 GHzQs=89
2effk =4.4%
fs=2.453 GHz Qs=54
2effk =3.5%
Figure 5.15. Three-by three 1000 µm pitch array of solidly clamped resonators
with their corresponding resonant frequency, quality factor at resonance, and
2effk listed
5.5 Summary
The Figure of Merit, the Quality Factor at resonance and anti-resonance, the
effective electromechanical coupling coefficient, and the smoothness or lack of
spurious resonances are used to characterize sample W9HS8 resonator 10018. These
values are summarized in X380HTable 5.2X. Sample W9HS8 resonator 10018 was used as
an example because its performance is representative of the typical SFBAR. These
factors are also used to characterize how the beams affect the performance of the
85
device in the next chapter. The FBARs’ f Bp B values also agree with the through-
thickness one-dimensional frequency model predictions. Two three-by-three arrays
with each resonator with a distinct resonant frequency were also fabricated to meet
the MINT project requirements.
Table 5.2. Summary of the characterization of sample W9HS8 resonator 10018
Sample
ResonatorQBs B QBp B
2effk
FOM at
resonance
FOM at
anti-
resonance
Presence of
Spurious
Resonances
W9HS8 10018 86 151 4.6% 4.0 6.9 none
86
Chapter 6 Performance Analysis
The previous chapter discussed characterization of an individual resonator using
figures of merit, which include the quality factor, the effective electromechanical
coupling coefficient ( 2effk ), and the presence of spurious modes. In this chapter, a
number of variables in the processing and geometry of the device are examined as
they affect the various figures of merit. These variables include silicon as an
electrode, device performance in vacuum, and the length and number of beams. All
the resonators that exhibited frequency pairs are discussed in terms of their quality
factors and 2effk . The tested resonators that had a response that did not cross the real
axis of the Smith Chart are not included in the quality factor and 2effk studies. But,
in a separate study, they are compared to the resonators with a frequency pair
response in terms of beam length. Lastly, the influence of electrode material and
thickness on the device performance is characterized in terms of the quality factor
and 2effk .
The resonators originated from two wafers, 110503-1 and 030104-1. Wafers
110503-1 and 030104-1 were also referred to as W9H and W3K, and had average
AlN thicknesses of 1.7 µm and 2.0 µm, respectively
6.1 Silicon
The original design of the resonators used the silicon substrate as the bottom
electrode instead of a metal. The natural frequency was to be trimmed by
87
controlling the thickness of the silicon. For example, a thick layer of silicon would
support a thin film of AlN to lower the natural frequency. In addition, the AlN is
typically sputtered directly on the bottom metal electrode of an acoustic resonator,
so using the silicon substrate would eliminate the bottom electrode metal processing
steps later in the fabrication. Unfortunately, even a thin layer of silicon greatly
damped the device. Resonators with a silicon electrode that had a thickness about
the same as the piezoelectric film barely showed spurious resonances at the
harmonic spacing. The response was too damped to calculate a reliable and
accurate quality factor. Resonators with both silicon and a bottom metal electrode
had similar responses to those with only silicon.
These findings are consistent with the theory presented in Rosenbaum [2] which
states for the acoustic fundamental frequency that as the silicon thickness becomes
appreciable, the C ratio (Eq. 5.11) deteriorates, thereby, degrading the Figure of
Merit. 381HFigure 6.1 from Rosenbaum illustrates how the FOM declines as the
thickness ratio of the silicon substrate and the ZnO piezoelectric increases for
different resonator configurations.
88
Figure 6.1. Figure of Merit of the Fundamental response of a FBAR
structure, as illustrated in Rosenbaum [2]. As the thickness ratio between the
silicon substrate and the ZnO piezoelectric increases, the device performance
rapidly decreases.
6.2 Vacuum Test
The response of a resonator in vacuum was explored to determine if air
resistance was damping the resonators’ response or damping Lamb waves and other
spurious resonances. The S B11 B scattering parameter of sample W3KS4 resonator
5028 was measured at atmospheric pressure, 0.1 Torr, and 0.35 mTorr. The tests
were performed using the vacuum chamber in Andrew Cleland’s lab at UCSB with
the assistance of Prof. Cleland and Michael Requa, a Ph.D. student in mechanical
engineering at UCSB. The VNA was a HP 8753. The temperature was held
89
constant during the tests at 300 K. Sample W3KS4 resonator 5028 had an AlN
thickness of 2.0 µm and the aluminum top and bottom electrode thicknesses are 660
nm and 620 nm, respectively. The eight support beams were 50 µm long.
The sample was placed in a vacuum chamber and probed with a G-S-G
configuration as the chamber was pumped down. The resonator’s response was
tested between 1 – 1.999375 GHz with data taken every 625 kHz. The fundamental
frequency pair is the same at each pressure with a f Bs B of 1.461 GHz and f Bp B of 1.488
GHz, resulting in an 2effk of 4.3%. The Q slightly increases in vacuum as shown in
X382HTable 6.1X but not enough to consider air damping a major contributor to quality
factor loss.
Table 6.1. The Quality Factor of a resonator at different pressures
Pressure Quality Factor
Atmosphere 73.6
0.1 Torr 77.9
0.35 mTorr 79.0
The resonator is free of spurious resonances at atmospheric pressure as can be
seen in the smooth response plotted on the Smith Chart in X383HFigure 6.2 X. The response
of the resonator at 0.1 T and 0.35mT are equally smooth, showing that atmospheric
pressure does not damp out spurious responses. The Smith Chart plots in X384HFigure 6.2 X
also show that all the responses are virtually identical. The magnitude and phase
angles are plotted in X385HFigure 6.3 X. This is significant because FBARs are typically
90
packaged in vacuum and the open ended air cavity of this design could eliminate
that need.
(a)freq (1.000GHz to 1.999GHz)
S1
1
(b)
Atm
0.1 Torr
0.35 mTorr
freq (1.000GHz to 1.999GHz)
S1
1
Figure 6.2. Smith Chart plots of the fundamental frequency S B11 B parameter
response measured from 1-1.999375 GHz (a) at atmospheric pressure and (b)
comparing 0.1 Torr and 0.35 mTorr to atmospheric pressure
91
(a)
1.2 1.4 1.6 1.81.0 2.0
15
20
25
30
35
10
40
Frequency, GHz
Z [
dB
]
Atm
0.1 Torr
0.35 mTorr
(b)
1.2 1.4 1.6 1.81.0 2.0
-1.5
-1.0
-0.5
0.0
0.5
-2.0
1.0
freq, GHz
Ph
ase
of
Z [
rad
ian
s]
Atm
0.1 Torr
0.35 mTorr
Figure 6.3. The magnitude and phase of the input impedance at
atmospheric pressure, 0.1 mTorr and 0.35 mTorr
92
6.3 Support Beam Characterization
Two variables were explored in terms of the support beams; the beam length and
the number of support beams. The Q at resonance and anti-resonance, the 2effk , the
FOM, and the presence of spurious modes are used to characterize how the support
beams affected the resonator performance.
6.3.1 Support Beam Length
A trend is not observed for the quality factor at resonance or the 2effk as
compared to the beam length. There is a consistent spread of values across all beam
lengths, including the resonators without support beams and clamped around the
entire circumference. The Quality Factor at resonance and the 2effk of each resonator
is plotted versus its support beam length in X386HFigure 6.4 X and X387HFigure 6.5 X. The Figure of
Merit at resonance displays the same scatter. There is also a consistent scatter for
the FOM at anti-resonance for beams 100 µm long or less, but for the 300 µm beam
geometry the FOM values are only in the lower range, as shown in X388HFigure 6.6 X.
93
0
25
50
75
100
125
150
0 50 100 150 200 250 300
Qu
ality
Fa
cto
r at
Re
so
na
nc
e
Beam Length [µm]
Figure 6.4. Quality factor at resonance versus support beam length for
individual resonators
94
0%
1%
2%
3%
4%
5%
6%
7%
0 50 100 150 200 250 300
Eff
ecti
ve E
lectr
om
ech
an
ica
l C
ou
pli
ng
Co
eff
icie
nt
Beam length [µm]
Figure 6.5. Effective electromechanical coupling coefficient versus beam
length for individual resonators
95
0
5
10
15
20
25
30
0 50 100 150 200 250 300
FO
M a
t A
nti
-Re
so
na
nc
e
Beam Length [µm]
Figure 6.6. The Figure of Merit at anti-resonance versus support beam
length for individual resonators
The beam length does have an influence on whether the resonator exhibited a
frequency pair or just spurious resonances at the acoustic natural frequency. Two
hundred and twenty-five resonators were tested; all the resonators were visually
inspected with an optical and scanning electron microscope to ensure that the silicon
was cleanly etched and the electrodes did not exhibit any debonding or buckling.
These inspections provided the expectation that there were no structural differences
96
that would cause performance differences. As shown in X389HTable 6.2X, the percentage of
tested resonators exhibiting a frequency pair response increased with the length of
the beams. The longer beam length must reduce damping to facilitate a frequency
pair response. This is further explored using the Butterworth–Van Dyke circuit
model in the next chapter.
Table 6.2. The percentage of tested resonators that exhibited a frequency pair
as correlated to support beam length
Beam Length Frequency Pair %
No spring 45.6%
10 µm 56.3%
50 µm 60.4%
100 µm 77.4%
300 µm 83.3%
6.3.2 Number of Support Beams
The number of support beams was also considered as a factor affecting the
FOM. A resonator fabricated with eight beams would be tested, then, using a
focused ion beam, four of the beams would be removed leaving an evenly balanced
four support beam device, as shown in X390HFigure 6.7 X. That device is then tested and the
FOM compared to the original resonator. Devices of beam lengths 50, 100, and 300
µm were tested. Twenty-three resonators were tested with 16 resonators exhibiting
97
a decrease in FOM at resonance and 15 resonators showing a decrease at anti-
resonance, after the four beams were removed. The average percentage change in
the resonant and anti-resonant FOM is -12.6% and -13.6%, respectively, as shown
in X391HFigure 6.8.
Figure 6.7. SEM image of resonator after 4 support beams were cut off using a
focused ion beam
98
-100%
-80%
-60%
-40%
-20%
0%
20%
40%
60%
80%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Resonance
Anti- Resonance
Pe
rcen
tag
e C
han
ge i
n t
he F
OM
Resonator
Average Changes
Figure 6.8. The percent change in the FOM at resonance and anti-resonance
per individual resonator after the removal of four support beams. Trend lines
indicated the average change.
6.4 The Quality Factor as a Function of the Effective
Electromechanical Coupling Coefficient
The Q at resonance and anti-resonance for resonators are plotted as a function of
the 2effk in X392HFigure 6.9 X ; two trends emerge. The QBs B is independent of the 2
effk while
the QBp B increases as the 2effk increases. This is counter to the modeling results
99
concluded by Chen and Wang (2005) [51]. Chen and Wang defined 2effk as a
function of the mechanical quality factor of the piezoelectric film which is defined
as
'33"33
cQ
c (6.1)
where '33c and "
33c are the real and imaginary parts, respectively, of the elastic
stiffness of the film in the 33-direction. Their findings show that the 2effk should
decrease as the mechanical quality factor increases, contrary to our findings,
indicating that the Q of the resonators must be dominated by other factors and not
the mechanical quality factor of the AlN. In the next chapter, the Butterworth–Van
Dyke model provides insight into why the quality at anti-resonance increased with
the 2effk and the quality factor at resonance did not.
100
0
100
200
300
400
500
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
ResonanceAnti-Resonance
Qu
ali
ty F
acto
r
Effective Electromechanical Coupling Coefficient
Figure 6.9. Quality factor as a function of the effective electromechanical
coupling coefficient
6.5 Metal Electrodes
The performance of the FBARs fabricated with different electrode material
types and thicknesses is explored in terms of the quality factor, Q, and effective
electromechanical coupling coefficient, 2effk . Three electrode configurations were
tested using two AlN wafers. The configurations are listed in X393HTable 6.3. The
configurations of Electrode 1 and Electrode 2 are approximately quarter-wavelength
101
( /4) thick at the piezoelectric film resonance. Electrode 3 is a thinner electrode
with a thickness of 100 nm. This thickness was chosen because 100 nm is the
thinnest electrode pad that the RF probes could consistently probe without damage.
The top electrode of Electrode 1consisted of three metals. This was because it was
determined experimentally that evaporated Au does not adhere to AlN. Therefore,
Al was used as a sticking layer, nickel was used as a diffusion barrier [59], and the
majority of the electrode was Au.
Table 6.3. Electrode configurations materials and thicknesses
Configuration Wafer Top Electrode Bottom Electrode
Electrode 1 W9H Al: 20nm Ni: 40 nm
Au: 270 nm Al: 690 nm
Electrode 2 W3K Al: 660 nm Al: 600 nmX
Error! Bookmark not defined.X
Electrode 3 W3K Al: 100 nm Al: 100nm
Aluminum and gold are commonly used electrode metals [2, 60] for FBARs.
Molybdenum, with a relatively high acoustic velocity for a metal of 6250 ms-1 [58]
and good oxidation resistance, is also being used in research and commercial FBAR
applications [5, 10, 60, 61]. Molybdenum was not used as an electrode material for
this device because its high vapor pressure [58] makes it impractical to deposit by
evaporation and, therefore, it must be deposited by sputtering. Sputtering has good
sidewall coverage, but the beam-supported FBAR design relied on the line of site
102
deposition of evaporation to ensure that top and bottom electrodes were not
connected from the sides.
The simplest model of an FBAR states that the thinner the electrodes, the higher
the quality factor. The lower acoustic velocities of the metals correlate to a higher
absorption ( ) and lower quality factors. X394HFigure 6.10 X displays the resonators’
quality factors at resonance, for each of the three electrode configurations, plotted
versus beam length. Observation of this plot shows that there is another factor at
work. The thicker electrodes (configurations Electrode 1 and Electrode 2) have
higher quality factors than Electrode 3 at the longer beam lengths. Electrode 3,
however, has higher quality factors for the short beam and no beam configurations.
The collected data shows that the resistance of the transmission line from the probe
pads to the top electrode is greater for the thinner electrode. It is also higher for the
longer transmission lines associated with the longer beam length. Therefore, it can
be postulated that the transmission line resistance of the thinner configuration -
Electrode 3 - for the longer beam nullifies its performance advantage.
103
0
25
50
75
100
125
150
0 50 100 150 200 250 300
Electrode 1: 330 nm Au stack
Electrode 2: 660 nm Al
Electrode 3: 100 nm Al
Qu
ali
ty F
ac
tor
at
Re
so
na
nc
e
Beam Length [µm]
Figure 6.10. Quality factor plotted against beam length for three different
electrode configurations
Our data shows that the effective electromechanical coupling coefficient does
not seem to depend on electrode configuration (X395HFigure 6.11) X. X396HFigure 6.12 X was
presented at the 2001 IEEE Ultrasonics Symposium by Lakin et al. [62]. They
explained that the initial increase in 2effk , from an electrode thickness of zero, is due
to the improved match in the distribution of the acoustic standing wave to the linear
104
distribution of the applied electric potential. As the metal thickness increases, the
2effk begins to drop as more of the resonator volume becomes occupied by the non-
piezoelectric electrode material. The aluminum trend line in X397HFigure 6.12 X suggests
that the resonators with Electrode 3 with a ratio of 0.05 should report a larger 2effk
than Electrode 2 which had a ratio of 0.3. The data supports this conclusion for the
resonators with support beams 100 µm or less. The higher transmission line
resistance of the 300 µm support beams could be negatively affecting the 2effk along
with the Q. Unfortunately, a more comprehensive journal paper has not been
published with the details of the model or experimental results.
105
0%
0.01%
0.02%
0.03%
0.04%
0.05%
0.06%
0.07%
0 50 100 150 200 250 300
Electrode 1Electrode 2Electrode 3
Eff
ec
tiv
e E
lec
tro
mec
ha
nic
al C
ou
plin
g C
oe
ffic
ien
t
Beam Length [µm]
Figure 6.11. The effective electromechanical coupling coefficient plotted
against beam length in terms of electrode configuration
106
Figure 6.12. Effective Electromechanical coupling coefficient as a function of
the thickness as presented by TFR Technologies[62]
Lee et al. [10] constructed a model for a Bragg Reflector that uses the acoustic
impedance of the electrode material, along with resonant and anti-resonant
frequencies, to predict the 2tk . Similar to Lakin, they show that the 2
effk is higher for
smaller electrode to piezoelectric film thickness ratios. However, their findings
have another layer of complexity. For the electrode material molybdenum, as the
thickness increased the difference between 2effk and 2
tk increased. Therefore, a
higher 2effk , resulting in a larger bandwidth, can be achieved with thicker electrodes.
2effk values higher than the bulk theoretical maximum for AlN FBARs with
molybdenum electrodes have been measured [55]. The Lee et al. model predicts
107
that the increase for Al would not be as great as for molybdenum and tungsten, and
they postulate that it is due to the low acoustic impedance of Al. More experimental
work would need to be done to find the optimum thickness ratio that utilizes both
trends. Au would be interesting to study since the acoustic impedance of Au is
greater than Al.
6.6 Summary
In summary the following major points can be drawn from this chapter:
Tested resonators using silicon as the bottom electrode or having a thin
layer of the substrate in between the AlN and a bottom metal electrode,
barely produced a resonant response at the acoustic natural frequencies.
The quality factor at resonance only slightly decreases in vacuum
compared atmosphere. Air damping is not a factor in the performance of
the device due to the open air cavity.
The support beam length does not have an effect on the quality factor or
the 2effk of the resonators that exhibit a frequency pair in their response.
The longer the support beam length the higher the percentage of tested
resonators that exhibit a frequency pair response.
A majority of the resonators show a decrease in the FOM after four
support beams were milled off.
Resonators with a high 2effk also have a high QBp B values while the QBs B
values are consistently lower.
108
Resonators with thinner electrodes perform better than those with a
thicker electrode except for the resonators with 300 µm support beams
where the higher transmission line resistance dominates. The
optimization of the transmission line thickness is discussed in Chapter 7.
109
Chapter 7 Analysis Using the Butterworth-Van Dyke Circuit
Model
The two common methods of modeling an acoustic resonator are the Mason
Model [53] and the Butterworth-Van Dyke Circuit [2]. The Mason Model, as
described in Chapter 5, predicts the behavior of the resonator by treating it as a
transmission line. The Mason Model becomes complicated when the properties of
the electrodes are taken into account, and it can be difficult to use the model with
other components. The Butterworth-Van Dyke (BVD) equivalent circuit is a lumped
element model. X398HFigure 7.1 X is the BVD equivalent circuit where C Bo B is the parallel
plate capacitance and RBt B is the transmission line resistance. The piezoelectric
properties are modeled by the motional capacitance, the motional inductance, and
the motional resistance, CBmB, LBmB, and RBmB respectively. Other lumped electrical
components can be conveniently added to the model. For example, a possible future
project would be to add a tunable MEMS capacitor, CBv B, to the resonator to trim the
frequency of the resonator, as depicted in X399HFigure 7.2 X.
In this chapter the BVD circuit elements are used to calculate the quality factor
of the circuit and the results are compared to the Q derived from the slope of the
input impedance. Using ADS software, a BVD circuit is simulated and evaluated as
a model for the beam-supported FBAR. The simulation results are also used to lend
insight to the SFBAR behavior and the optimization of the beam-supported design.
110
Lm
Rm
Cm
Co
Zin
Rt
Figure 7.1. Butterworth–Van Dyke equivalent circuit
CvLm
Rm
Cm
Co
Zin
Rt
Figure 7.2. Butterworth–Van Dyke equivalent circuit with variable tuning
capacitor in parallel
7.1 Quality Factor of the Butterworth – Van Dyke Circuit
The BVD model is a multi-pole resonant circuit, combining the components of
both series and parallel circuits. As previously explained, a series resonant circuit
allows a maximum current flow at resonant frequency, whereas a parallel resonant
circuit allows a minimum at resonance. The combination of the two resonances
create a resonant response with a frequency pair [47]. The quality factor of the
111
circuit can be found using the components of the circuit in X400HFigure 7.1 X with the
following [10]:
m
t m
LQ
R R. (7.1)
Eq. (7.1) is equivalent to Eq. (5.3) with respect to the BVD Model. This can be
seen with the following short derivation which starts with the repeating Eq. (5.2),
which defines the input impedance in terms of its real and imaginary parts:
2 (2 )inZ R jX R f jX f (5.2)
The phase of the impedance is
1tanX
ZR
. (7.2)
Using the definition for the derivative of an inverse tangent:
1
2
1tan
1
d duu
dx u dx,
the slope of the input impedance can be derived:
112
2 2
1 1
1
dZ X dR dX
dx R df R dfX R. (7.3)
At resonance the reactance, X, is zero and the derivative reduces to:
1
sf
dZ dX
df R df. (7.4)
The circuit at resonance is essentially a series circuit and the reactance can be
written only in terms of the motional components:
12
2m
m
X fLfC
(7.5)
And
2
12
2m
m
dXL
df f C. (7.6)
Also, if there are no dissipative elements, at series resonance the input impedance is
zero, ZBin B=0, and the following relationship can be defined [2]:
113
2 1s
m mL C. (7.7)
Combining Eq. (5.3), Eq. (7.4), Eq. (7.6), and Eq. (7.7):
2 2
2s
s s m s m
t mf
f f L f LdZQ
df R R R.
Hence, since the quality factor equations are analogous, their resulting values for a
particular resonator should also be equal if the BVD circuit models the beam support
FBAR response.
In order to solve for Q using Eq. (7.1) it is necessary to solve for the lumped
elements in terms of measured values. Once again using the representative sample
W9HS8 resonator 10018, the input impedance at resonance is purely resistive and
therefore, inZ R . X401HFigure 7.3 X is a plot of the magnitude input impedance response
of sample W9HS8 resonator 10018 as a function of frequency, illustrating that at
resonance R=8.625 .
114
Resonancefreq=mag(Z)=8.6245
1.3425GHzResonancefreq=mag(Z)=8.6245
1.3425GHz
1.2 1.4 1.6 1.81.0 2.0
50
100
150
200
0
250
Freq [GHz]
Magnitude o
f Z
in [
ohm
s]
Resonance
Figure 7.3. Magnitude of ZBin B for sample W9HS8 resonator 10018
LBmB was solved for in terms of the measured value CBo B by combining Eq. (7.7) and
the following IEEE Piezoelectric Standard [54]:
2 2
2
p s m
s o
f f C
f C. (7.8)
The parallel plate capacitance can be calculated using:
o
AC
d (7.9)
115
Eq. (7.9) is the static capacitance and is a good estimate of the capacitance at high
frequency. Instead of using Eq. (7.9) to calculate CBo B which would produce the same
value for every resonator on a sample, the CBo B was calculated for each individual
resonator using a similar technique to Lee et al. [10]. At off-resonance, the BVD
model reduces to RBt B and CB0 B in series, as illustrate in X402HFigure 7.4 X. The reactance X( )
is only determined by the frequency and the parallel plate capacitance:
1
o
XC
(7.10)
Using Eq. (7.10), CBo B was calculated at four distinct off-resonant frequencies, two
before resonance and two after resonance, and averaged. For sample W9HS8
resonator 10018 the values used to calculate the BVD Q are listed in X403HTable 7.1X.
Co
Zin
Rt
Figure 7.4. Butterworth–Van Dyke equivalent circuit at off-resonant
frequencies
116
Table 7.1. Resonant properties of sample W9HS8 resonator 10018
ResonatorR
[ ]
CBo B
[pF]CBmB [pF]
LBmB
[nH]BVD Q QBs B
W9HS8 10018 8.625 3.974 0.154 91.5 89.5 86
The BVD Q (Eq. (7.1)) and the Q obtained directly from the collected data (Eq.
(5.3)) are very close, 89.5 and 86, respectively. The BVD Q and the Q at resonance
were compared for every resonator that exhibited a frequency pair. The BVD model
was not adequate for resonators with a 2effk less than 0.010. The closeness of the f Bs B
and the f Bp B values produces an unrealistically high LBmB and resulting BVD Q. The Q
values match reasonably well for resonators with higher coupling coefficients. The
RMS of the Q values of every resonator with a 2effk equal or above 0.010 for each
sample is charted in X404HFigure 7.5 X. The lines connecting the data in X405HFigure 7.5 X are there
only to aid in distinguishing the data points. Both 8 beam and 4 beam resonators are
included. The Quality Factors match fairly well showing that the BVD model is a
good model for predicting the Q of a resonator. Samples W3KS3 and W3KS6b had
the largest disparity between the BVD Q and the Q but they are not as statistically
significant as the other samples since they only contain two and one resonators,
respectively.
117
0
20
40
60
80
100
120
W9HS2 W9HS4 W9HS5 W9HS8 W3KS2 W3KS6 W3KS3W9HS10 W3KS7 W3KS4 W3KS5 W3KS8 W3KS6bW3KS11
BVD Q from Eq. (7.1)Q from Eq. (5.2)
Qu
ali
ty F
ac
tor
Sample
Figure 7.5. Comparative plots of the RMS of the Q and the BVD Q of the
resonators for each sample
7.2 Computer Simulation of the BVD Circuit Response
A BVD circuit model simulation was built in Agilent Advanced Design
Simulation (ADS) software, as shown in X406HFigure 7.6 X. Values for the transmission line
resistance, the parallel plate capacitance, and the motional inductance, motional
capacitance, and motional resistance were entered in the model along with a
frequency span and the theoretical response of the circuit was plotted and compared
to the measured SFBARs.
118
Figure 7.6. BVD circuit constructed in ADS simulation window
The parallel plate capacitance, the motional capacitance, and the motional
inductance were calculated using the resonant and anti-resonant frequencies, as
discussed in the last section, and therefore, they determine the resonance and anti-
resonance in the BVD simulation. The resistance (R) that was used to predict the
BVD Q is the sum of the transmission line resistance (RBt B) and the motional resistance
(RBmB). RBt B was measured at 6 GHz to ensure that the intrinsic resistance of the AlN
film would be negligible [16]. As expected the resonators with thinner transmission
lines have a higher resistance, as charted in X407HTable 7.2X. RBmB was determined by
subtracting the RBt B from R.
119
The BVD simulation circuit was run for the measured values for sample W9HS8
resonator 10018 and the model results compared to the experimental data. The
values used are listed in X408HTable 7.3X. A shown in X409HFigure 7.7 X, there is a good match
between the BVD simulation output and the experimental data near resonance.
Table 7.2. Average transmission line resistance of each electrode configuration
Electrode
Configuration
Electrode Material :
Approximate Thickness
Average
Resistance
Electrode 1 Al: 20nm/ Ni: 40 nm/ Au: 270 nm 5
Electrode 2 Al: 660 nm 3
Electrode 3 Al : 100 nm 12
Table 7.3. Values used in BVD circuit model simulation
Resonator
Simulated
CBo B
[pF]
CBmB
[pF]
LBmB
[nH]Measured
R [ ]
RBt
B[ ]
RBm
B[ ]
RBt B+RBmB
[ ]
W9HS8 10018 3.974 0.154 91.5 8.6 4.8 3.7 8.5
Trends are observed by varying the transmission line and motional resistances
separately. X410HFigure 7.8 X and X411HFigure 7.9 X show how the Smith Chart plots of the
scattering parameter and the magnitude and phase of the input impedance change
with respect to the RBmB and RBt B. RBmB determines the anti-resonance resistance while
both the RBmB and RBt B influence the resonant resistance. It can be concluded that a
smaller RBmB results in higher Qs at both resonance and anti-resonance and that a
smaller RBt B correlates to a higher Q at resonance. The BVD circuit simulation with
120
the highest RBmB did not produce a response that crossed the real axis of the Smith
Chart and, therefore, did not have a frequency pair response. It then can be surmised
from the data presented in previous chapters that the resonators with longer beams
were more likely to have a lower motional resistance since they were more likely to
exhibit a frequency pair. The model also accounts for why the Qs among the longer
beam SFBARs were low. The longer transmission line associated with the longer
support beams results in a higher resistance which produces a lower quality factor.
121
freq (1.000GHz to 2.000GHz)
S1
1
1.2 1.4 1.6 1.81.0 2.0
20
30
40
10
50
Frequency [GHz]
Z [
dB
]
1.2 1.4 1.6 1.81.0 2.0
-50
0
50
-100
100
Frequency [GHz]
Ph
ase
of
Z [
de
gre
es]
(c)
(a)
(b)
Simulation
Experimental
data
Figure 7.7. BVD circuit simulation compared to the experimental data
collected from sample W9HS8 resonator 10018 (a) reflection coefficient Smith
Chart plot (b) input impedance [dB] (c) phase of input impedance
122
freq (1.000GHz to 2.000GHz)
S1
1
1.3 1.41.2 1.5
20
30
40
50
10
60
Frequency [GHz]
Z [
dB
]
1.3 1.41.2 1.5
-50
0
50
-100
100
Frequency [GHz]
Ph
ase
of
Z [
de
gre
es]
Decreasing Rm
Decreasing Rm
Decreasing Rm
(c)
(a)
(b)
Figure 7.8. BVD model output plots with various RBmB values: (a) reflection
coefficient Smith Chart plot (b) input impedance [dB] (c) phase of input
impedance
123
freq (1.000GHz to 2.000GHz)
S1
1
1.3 1.41.2 1.5
20
30
40
10
50
Frequency [GHz]
Z [
dB
]
1.3 1.41.2 1.5
-50
0
50
-100
100
Frequency [GHz]
Ph
ase
of
Z [
de
gre
es]
Decreasing Rt
Decreasing Rt
Decreasing Rm
(c)
(a)
(b)
Figure 7.9. BVD model output plots with various RBt B values: (a) reflection
coefficient Smith Chart plot (b) input impedance [dB] (c) phase of input
impedance
124
7.3 Optimization of Beam-Supported Design Using the BVD
Simulation
Ideally, the Butterworth-Van Dyke circuit model should be used to optimize the
resonator beam length and the associated transmission line resistance. The observed
behavior -- that the percentage of resonators exhibiting a frequency pair response
increases as the beam length increases -- could lead to the hypothesis that longer
beams have a lower motional resistance. However, as shown in 412HFigure 7.10, a trend
between the motional resistance and beam length does not exist. There is perhaps a
trend between the motional resistance and beam length if the resonators not
exhibiting a frequency pair could be included. Unfortunately, the BVD model
cannot be applied to those resonators that did not exhibit a frequency pair. In order
to calculate the lumped element values from the measured data, the input impedance
must be completely real at resonance. Therefore, without a correlation between the
motional resistance and the beam length, the BVD simulation cannot be used to
optimize the beam length.
125
-20
0
20
40
60
80
0 50 100 150 200 250 300
Rm
[o
hm
s]
Beam Length [ m]
Figure 7.10. The motional resistance plotted against beam length for
FBARs that exhibited a frequency pair
7.3.1 Electrode Optimization
Another parameter that could be varied and optimized is the electrode and
transmission line thickness. The electrode thickness must be small for a low
motional resistance. In contrast, the transmission line thickness should be large for a
low transmission line resistance. However, the masks used to process the FBARs
126
limit the electrode and transmission line to being the same thickness. Hence, it
would be an ideal parameter to optimize.
Electrode Configuration (EC) 2 (~ 660 nm of Al) and EC 3 (100 nm Al) were
compared to establish trends. The data from EC 1 was not used because it consisted
of materials besides aluminum. The transmission line resistance behaved as
expected with higher resistances associated with EC 3 and the longer beam lengths,
as shown in 413HFigure 7.11. The trend lines plotted for each EC are based simply on the
relationship eR L A . The data fits the trend lines reasonably well with only the
300 µm long beam resonators inexplicably not following the trend line. It is
important to note that the solidly clamped resonators and the 10 µm long beam-
supported resonators have transmission lines of the same length.
127
0
5
10
15
20
25
30
35
0 50 100 150 200 250 300
Electrode 2Electrode 3
Rt [
oh
ms]
Beam Length [ m]
Figure 7.11. The transmission line resistance as plotted function of beam length
for different electrode configurations. The trends lines are the relationship
between the resistance and the dimensions of the transmission line, eR L A
In contrast to the transmission line resistance, the motional resistance does not
have a quantifiable relationship with the thickness of the electrodes. As shown in
414HFigure 7.12, the motional resistance was lower for the thinner electrode
configuration, except for the 300 µm long beam resonators, which, similar to the
128
transmission line resistance, did not follow the predicted pattern. Unfortunately,
results from only two different electrode thicknesses are not enough to quantitatively
model the motional resistance as a function of electrode thickness. In fact, Lee et al.
[10] test five different thickness of the electrode material molybdenum and only
determined that there was scatter and that the motional resistance does not linearly
depend on the thickness of the electrode. Therefore, the thickness of the electrodes
could not be optimized with the information available.
-10
0
10
20
30
40
0 50 100 150 200 250 300
Electrode 2Electrode 3
Rm
[o
hm
s]
Beam Length [ m]
Figure 7.12. The motional resistance plotted as a function of beam length
for different electrode configurations.
129
7.3.2 Optimization Recommendations
Unfortunately, as detailed in the previous section, it is not possible to quantify
the relationship between the motional resistance and beam length with the
information available. Moreover, it is not possible to optimize the electrode and
transmission line thickness because the relationship between the electrode thickness
and the motional resistance is not well understood. However, two recommendations
can be made based on the known data for the next generation of beam-supported
FBARs: First, the masks and process flow should be constructed so that the
electrodes and the transmission lines do not have to possess the same thickness.
This would allow the optimization of the electrode and transmission lines to be
independent. Secondly, the transmission line resistance is not as sensitive to the
change in length for a thicker transmission line. Therefore, the transmission line
should be kept thick and the beam length long, which would take advantage of the
higher frequency pair yields associated with the longer beams.
7.4 Summary
The Butterworth-Van Dyke circuit was used to model the beam-supported
FBARs due to its ease to integrate with other components. The BVD Q reasonably
matches the Q calculated from the slope of the input impedance. A BVD simulation
was constructed in ADS software platform. The results from the simulation matched
the measured data of sample W9HS8 sample 10018.
The simulation gave insight to trends observed in the previous chapter as listed:
130
The RBmB determines if there is a frequency pair response, so therefore, the
longer beams must correlate to a lower RBmB.
The Qs are still low among the FBARs with longer beams, therefore, the
higher transmission line resistance originating from the longer length
must be dominating the response.
It was observed that for resonators that have high a QBp B and a high 2effk the
QBs B is still low. Since the transmission line resistance only affects the
series resonance, the QBs B must be dominated by the transmission line
resistance.
Results indicate that a thinner electrode combined with a thicker
transmission line will produce a resonator with a higher Q. There was
not enough information to optimize the current design. A higher Q can
be achieved if the next generation resonator design makes the electrode
and transmission line thicknesses independent of each other.
131
Chapter 8 Interactions between FBARs Sharing a Substrate
All the FBARs on a wafer share the same substrate and, therefore, share the same
ground plane. In this chapter the interaction between two resonators on the same
substrate but not electrically connected is explored. The interaction between two
devices sharing the same signal and ground planes are also characterized to
determine the strength of the transmission between the FBARs.
Similar to the single port testing, the VNA and two G-S-G RF probes were used
to measure the scattering parameters. The reflection coefficient (SB11 B) and the
forward transmission coefficient (SB21 B) were analyzed using ADS software. The
model used to read the data into the ADS platform is shown in X415HFigure 8.1 X.
132
Figure 8.1. ADS design interface and simulation model used to read collected
data from two port device into the ADS platform
8.1 Interaction between Two Unconnected Devices
The possible interaction between two electrically unconnected resonators sharing
the same substrate was characterized by measuring the forward transmission
coefficient (SB21 B). The resonators 10014 and 10019, spaced 2.2 mm apart on sample
W9HS8, were simultaneously probed while the VNA sent power waves with a
frequency span between 500 MHz - 6 GHz into resonator 10014 and measured the
power transmission out of resonator 10019. The VNA, which has a minimum
detectable transmission of -2 dBm, was unable to detect a signal out of resonator
10019. Therefore, it can be assumed that the substrate does not significantly couple
133
the resonators. The piezoelectric movement of one resonator did not cause others to
propagate.
The result of the test described above was that it caused dielectric breakdown of
the AlN. As compared in X416HFigure 8.2 X, the Smith Chart plots of the reflection
coefficient of 10014 before and after the substrate coupling test show how the S B11 B
parameter response deteriorated after the test. Trying to detect a signal out of 10019,
the VNA sent higher and higher power levels into 10014, which eventually broke
down the dielectric. There was no change to the SB11 B parameter response of resonator
10019.
freq (500.0MHz to 6.000GHz)
S1
1
Before
After
Figure 8.2. Smith Chart plot of the reflection coefficients of resonator 10014
before and after the substrate coupling test
134
8.2 FBARs Connected in Parallel
Included among the fabricated resonators are FBARs that are connected together
electrically by a transmission line, as shown in X417HFigure 8.3 X. The microstrip
transmission line rests on a piezoelectric support beam that is shared by two FBARs.
The center of the beam is supported by silicon, which is part of the ground plane’s
electrical connection. Though there were two FBARs, this device was essentially a
two port resonator not a filter. A filter needs three or four FBARs to be electrically
connected in series and parallel at distinct resonant frequencies. If the piezoelectric
response of the transmission line connecting the 300 µm membranes is ignored, the
FBARs could be modeled as two devices in parallel, as shown in X418HFigure 8.4 X. But
two parallel devices still do not create a bandwidth response and, therefore, it would
not be appropriate to characterize the response as a filter. Instead to characterize a
two-port device, Su et al. [6] used a two port BVD circuit to define the Q at
resonance using measured values:
21 . 11 .
221 . 11 .
1 1
1
s
p Min Min
s
Min Mins
p
S SQ
S S (8.1)
135
Figure 8.3. SEM image of two FBARs connected by transmission line
supported on an AlN beam
Connection Beam
136
Figure 8.4. Schematic of two FBARs connected in parallel
Eq. (8.1) was derived assuming that the SB21 B and the SB11 B minimums were real
values, and therefore, the response had a frequency pair. Two sets of resonators
connected in parallel exhibit frequency pair responses, sample W3KS6 resonators
30017 to 30014 and sample W3KS6 resonators 30011 to 30012. Both responses are
small and there is significant scatter where SB21 B is at a minimum. X419HFigure 8.5 X shows
the Smith Chart plot, the magnitude of impedance, and the phase angle of the
impedance for the transmission and reflection responses of 30017 to 30014. As
shown by the phase response, there is too much noise and scatter to calculate the
transmission Q at resonance using the derivative of the phase of the input
impedance. The 2effk of this device is 0.007, which is beyond the point that the BVD
model adequately predicted the Q of the FBARs, therefore, Eq. (8.1) is also not
applicable.
137
freq (2.000GHz to 3.000GHz)
S
2.2 2.4 2.6 2.82.0 3.0
-40
-20
0
20
40
-60
60
freq, GHz
Z [
dB
]
2.2 2.4 2.6 2.82.0 3.0
-100
0
100
-200
200
freq, GHz
Ph
ase
Z [
de
gre
es]
c)
a)
b)
Reflection
Transmission
Figure 8.5. Reflection and transmission responses of sample W3KS6 10017 to
10014
Though the exact Q could not be calculated the data plots of the response show
qualitatively that the Q is small. A possible origin of the quality loss is the silicon
supporting the center of the AlN beam connecting the two membranes. By taking
advantage of a processing anomaly this was explored further. The silicon DRIE on
one sample, W3KS2, etched the sidewalls in between the cavities of the electrically
138
connected FBARS, as shown in X420HFigure 8.6 X. Using the Focused Ion Beam, the
remaining silicon on the connecting beam was removed and 100 nm Al was
evaporated and annealed in its place. Unfortunately, the process of removing the
silicon eroded the beam, as shown in X421HFigure 8.7 X The response of the connected
resonators degraded after the silicon removal, as compared in X422HFigure 8.8 X. The poor
response is most likely due to the deterioration of the beam and it is impossible to
determine if removing the silicon would have significantly improved the response.
Figure 8.6. SEM image of backside of sample W3KS2 with the wall in
between the air cavities etched during the deep silicon etch
139
Figure 8.7. SEM image of connecting beam after silicon support was
removed with a FIB
140
freq (1.000GHz to 2.000GHz)
S
S11 before S11 after S21 before S21 after
Figure 8.8. Scattering parameter responses of connected FBARs before and
after the silicon was removed from the connecting beam
8.3 Summary
The interaction between two FBARs sharing the same substrate was explored
with the similar techniques used to characterize the single port FBARs. There is no
interaction between resonators that share the same substrate but are not electrically
connected. The transmission and reflection scattering parameters were measured
and analyzed for a two port device which consisted of two resonators sharing the
same ground and signal planes. The responses are small with excessive scatter of
the data points making it impossible to calculate the Q of the transmission. A
reduction of the response is seen when the silicon was removed from underneath of
the connecting beam between two FBARs. This is most likely due to the
deterioration of the support beam that occurred during the silicon removal process
141
and not due to the removal of the silicon. Primarily, the FBARs did not transmit a
strong signal between each other. Once again, a less resistive transmission line
between the membranes would probably greatly improve the response.
142
Chapter 9 Conclusions and Future Directions
9.1 Conclusions
This dissertation examined the successful design, fabrication, and
characterization of a beam-supported FBAR. The geometric design of the FBAR
incorporated several basic scientific elements. The FBAR was designed to
piezoelectrically activate only in the through-thickness mode to simplify its
characterization and to take advantage of AlN’s larger e B33 B value. AlN was selected
as the piezoelectric film due to its compatibility with silicon micro fabrication
techniques and its high acoustic velocity which equate to a low material absorption.
The FBARs were single port devices for ease of characterization, but in practice, the
FBARs would be used in series and parallel in a two port filter configuration.
The resonator is a single port through –thickness device, consisting of a
piezoelectric film sandwiched between metal electrodes. The silicon substrate was
completely etched away leaving a free standing membrane. The membrane is
connected to the substrate with thin non-piezoelectrically activated AlN beams. The
beams were constructed to study the possible damping caused by clamping the entire
perimeter of a FBAR to the substrate. The FBAR was fabricated using a set of 4
masks and double-sided polished wafers that had AlN sputtered directly on the
silicon substrate. The AlN was sputtered directly on the <100> silicon wafers
instead of on the bottom metal electrode to take of advantage of the crystal structure
of the silicon substrate to produce a higher quality AlN film. The fabrication process
143
included 24 steps including five photolithography steps, which use both a stepper
and contact lithography. The AlN was etched in the Panasonic ICP with a chlorine
plasma with a resulting etch rate of 300 nm/min. Decreasing the Ar in the AlN etch
helped reduce the roughness of the exposed silicon substrate. TiOB2 B was used as a
hard mask for the AlN. The selectivity of TiO B2 relative to AlN, is higher in a
chlorine plasma thanB that of photoresist. In addition, TiO2 is easily removed with
diluted HF. The silicon DRIE was used to etch circular, smooth air cavities through
the entire thickness of a 4-inch wafer. The circular shape is possible because the
etch gas, SF B6 B, used in the DRIE reactor is able to etch silicon without a crystalline
orientation preference. This technology allows for any air cavity shape to be
explored.
The FBARs were characterized using their Quality Factor, the effective
electromechanical coupling coefficient, a Figure of Merit, and the presence of
spurious resonances. The FBAR was tested using RF rated probes and cables
connected to a voltage network analyzer that measured the reflection coefficient of
the devices. Agilent Technologies Advance Design software and The Mathworks,
Inc. MatlabP
®P were used to examine the measured data and calculate the Q and the
2effk of each device. A representative resonator, sample W9HS8 resonator 10018,
was used to demonstrate the analysis that was performed on every tested resonator
that exhibited a frequency pair in its response. Sample W9HS8 resonator 10018 has
Qs at resonance and anti-resonance of 86 and 151, respectively, and a 2effk of 4.6%.
Although, a 2effk of 6.3% was measured amongst the tested resonators. The
144
resonators that exhibited a frequency pair response are mostly free of spurious
resonances and they also follow the one-dimensional frequency model that predicts
the parallel frequency. To fulfill the MINT requirements, two three-by-three arrays
of working FBARs each with a distinct resonant frequency were fabricated and
characterized.
The FBARs as a collection did not have a strong response nor exhibited a
frequency pair if there was silicon underneath the piezoelectrically activated part of
the membrane. On the other hand, silicon remaining on the under side of the support
beams did not detract from the response of the device and facilitated the annealing of
the bottom metal electrode to the conductive silicon substrate. A SFBAR was also
tested in a vacuum chamber to compare responses at atmospheric pressure, 0.1 Torr
and 0.35 mTorr. The responses are nearly identical with the QBs B only slightly
increasing from 73.6 to 79.0 from atmosphere to 0.35 mTorr.
The FBARs were characterized in terms of how the support beam length and
number affected the Q and 2effk . Using the data from only the resonators that
exhibited a frequency pair, the Q and 2effk are not affected by the beam length. The
beam length did have an influence on whether the resonator exhibited a frequency
pair or not at the acoustic fundamental frequency. The percentage of resonators
exhibiting a frequency pair increased with the length of the support beams. The Q at
resonance and anti-resonance were also plotted against the 2effk for each resonator
that exhibited a frequency pair. The QBp B and the 2effk increase together while the QBs B
values are low for all resonators.
145
A thinner electrode produces higher figures of merit except for in the longer
support beam resonators where the higher transmission line resistance dominates the
resonator’s reflection coefficient response. It was indeterminable whether Au or Al
was a better electrode material. Al has a higher acoustic velocity but Au withstood
the fabrication process better. This is perhaps why the resonators with a Au
electrode to have quality factor and 2effk values in the same range as those with Al.
The Butterworth-Van Dyke circuit used lump circuit elements to model the
electrical and mechanical components of the acoustic resonator. The BVD Q values
reasonably match the Q values calculated from the slope of the input impedance. A
BVD simulation was constructed in ADS software platform which produced
reflection coefficient values that also matched the measured data around resonance.
The BVD circuit also lends insight into the behavior of the FBARs. In the BVD
model, the transmission line resistance contributes to the resistance at resonance.
The motional resistance contributes to the resistance at both resonance and anti-
resonance and determines if the response is strong enough to be a frequency pair.
Therefore, since the RBmB determines the generation of a frequency pair response and
longer beams are more likely to produce a frequency pair, longer beams must equate
to a lower motional resistance. Yet, for the FBARs that did exhibit a frequency
response, the Qs at resonance were still low among the FBARs with longer beams,
therefore, the higher transmission line resistance originating from the longer length
dominates the response. It was also observed that for resonators that had high a QBp B
146
and a high 2effk the QBs B was still low. Since the transmission line resistance only
affects the series resonance, the QBs B is dominated by the transmission line response.
There was no measured response between unconnected FBARs sharing the same
substrate and ground plane. Therefore, the substrate is not transmitting the
piezoelectric propagation from an activated resonator to an unactivated resonator.
Unfortunately, the transmission between two FBARs that share a signal and ground
plane is small. The largest energy loss is probably the resistance of the transmission
line connecting the resonators.
9.2 Future Directions
There are several future directions that this project could take. The quality
factors of the devices are quite low and the origins of the energy dissipation should
be explored. More studies could be performed on the beam geometry and the shape
of the air cavity to determine their optimum dimensions. Or, the geometry and
fabrication of the resonator can be modified to become a component of a filter.
To try to raise the quality factor of the FBAR as an open ended goal would be an
overwhelming task in a University setting. That is why even though the Q values of
my devices are quite low; I concentrated on a few factors such as beam geometry.
But I believe the two biggest quality losses are the roughness of the silicon substrate
and the electrodes. The rough silicon is reducing the Q even though its is not part of
the actual device [55]. A possible solution would be to sputter the AlN in the shape
of the resonator, using a lift-off technique. After the mask is removed the silicon
underneath would be smooth. The easiest way to reduce the resistance originating
147
from the electrodes would be to increase the width and thickness of the transmission
line. This would need to be done in conjunction with a study of changing the width
of the support beams since there are interdependent. Since the BVD model
explained observed behavior, it could be used in the future to isolate resistive
elements to further examine energy loss.
Further study of the geometry could focus on beam size or air cavity shape.
Changing the width of the support beams would help uncouple the support beams
from the shape of the circular shaped air cavity. Currently, we know that the
SFBAR design is robust to spurious resonances. However, the solidly clamped
resonators were not any more likely to have spurious ripples resonances than the
resonators with beams. There must be another aspect of the design that is inhibiting
the Lamb waves. The circular geometry is novel, and in depth modeling of lateral
waves in the circular geometry may provide some insight. The beams do lower the
motional resistance and varying the width of the beams along with the transmission
line thickness could provide insight.
Lastly, a filter could be constructed from the beam-supported FBARs but this
exposes the largest design flaw of the resonator. Since the AlN is sputtered directly
on the silicon substrate the SFBARs are not easily electrically isolated from each
other. When the AlN is sputtered on the bottom metal electrode the metal is already
patterned and a high resistive silicon substrate is used to electrically isolate the
individual SFBARs. Currently, all the beam-supported FBARs share a highly
conductive substrate as the ground plane. Possibly using a highly resistive substrate
148
and then ion implanting the areas of the substrate where the SFBARs are located
would isolate the SFBARs electrically.
In conclusion, an elegant working device was designed, fabricated, and
characterized. Hopefully, the knowledge gained will provide insight to readers of
this dissertation.
149
References
[1] K. M. Lakin, G. R. Kline, and K. T. McCarron, "High-Q Microwave Acoustic Resonators And Filters," IEEE Transactions on Microwave Theory and Techniques, vol. 41, pp. 2139-2146, 1993.
[2] J. F. Rosenbaum, Bulk Acoustic Wave Theory and Devices. Boston: Artech House, 1988
[3] R. C. Ruby, P. Bradley, Y. Oshmyansky, A. Chien, and J. D. Larson, III, "Thin film bulk wave acoustic resonators (FBAR) for wireless applications," presented at 2001 IEEE Ultrasonics Symposium, Piscataway, NJ, USA.
[4] S. Horwitz and C. Milton, "Application of film bulk acoustic resonators," presented at 1992 IEEE MTT-S International Microwave Symposium Digest, pp.165-8 vol.1. New York, NY, USA.
[5] J. D. Larson, III, R. C. Ruby, P. D. Bradley, J. Wen, S.-L. Kok, and A. Chien, "Power handling and temperature coefficient studies in FBAR duplexers for the 1900 MHz PCS band," presented at 2000 IEEE Ultrasonics Symposium. Proceedings. vol.1, 2000, pp.869-74. Piscataway, NJ, USA.
[6] Q.-X. Su, P. Kirby, E. Komuro, M. Imura, Q. Zhang, and R. Whatmore, "Thin-film bulk acoustic resonators and filters using ZnO and lead-zirconium-titanate thin films," IEEE Transactions on Microwave Theory & Techniques, vol. 49, pp. 769-78, 2001.
[7] J. G. Gualtieri, J. A. Kosinski, and A. Ballato, "Piezoelectric Materials For Acoustic-Wave Applications," IEEE Transactions on Ultrasonics Ferroelectrics And Frequency Control, vol. 41, pp. 53-59, 1994.
[8] S. Trolier-McKinstry and P. Muralt, "Thin film piezoelectrics for MEMS," Journal of Electroceramics, vol. 12, pp. 7-17, 2004.
[9] K. Tsubouchi, K. Sugai, and N. Mikoshiba, "High-frequency and low-dispersion SAW devices of AlN/Al/sub 2/O/sub 3/ and AlN/Si for signal
150
processing," presented at 1980 Ultrasonics Symposium Proceedings. IEEE. 1980, pp.446-50 vol.1. New York, NY, USA.
[10] S.-H. Lee, K. H. Yoon, and J.-K. Lee, "Influence of electrode configurations on the quality factor and piezoelectric coupling constant of solidly mounted bulk acoustic wave resonators," Journal of Applied Physics, vol. 92, pp. 4062-9, 2002.
[11] R. Aigner, "RF-MEMS filters manufactured on silicon: key facts about bulk-acoustic-wave technology," presented at 2003 Topical Meeting on Silicon Monolithic Integrated Circuits in RF Systems. IEEE. 2003, pp.157-61. Piscataway, NJ, USA.
[12] G. G. Fattinger, J. Kaitila, R. Aigner, and W. Nessler, "Thin film bulk acoustic wave devices for applications at 5.2 GHz," presented at 2003 IEEE Ultrasonics Symposium. IEEE. Part Vol.1, pp.174-7. Piscataway, NJ, USA.
[13] H. P. Loebl, C. Metzmacher, R. F. Milson, P. Lok, F. Van Straten, and A. Tuinhout, "RF bulk acoustic wave resonators and filters," Journal of Electroceramics, vol. 12, pp. 109-18, 2004.
[14] DARPA MTO.
[15] V. Lughi, et al., unpublished.
[16] H. Zhang and E. S. Kim, "Air-backed Al/ZnO/Al film bulk acoustic resonator without any support layer," presented at Proceedings of the 2002 IEEE International Frequency Control Symposium and PDA Exhibition pp.20-6. Piscataway, NJ, USA.
[17] H. H. Kim, B. K. Ju, Y. H. Lee, S. H. Lee, J. K. Lee, and S. W. Kim, "Fabrication of suspended thin film resonator for application of RF bandpass filter," Microelectronics & Reliability, vol. 44, pp. 237-43, 2004.
[18] F. Laermer and A. Schilp, "Method of anistropically etching silicon," U. S. Patent 5,501,893, March 26, 1996.
151
[19] J. Kaitila, M. Ylilammi, J. Ella, and R. Aigner, "Spurious resonance free bulk acoustic wave resonators," presented at 2003 IEEE Ultrasonics Symposium, Piscataway, NJ, USA.
[20] R. A. Johnson, Mechanical Filters in Electronics. New York: Wiley, 1983, p. 49.
[21] IEEE Standard on Piezoelectricity, IEEE Standard 176-1987, 1988
[22] V. M. Ristic, Principles of Acoustic Devices. New York: Wiley, 1983, p. 143.
[23] K. M. Lakin, "Modeling of thin film resonators and filters," presented at 1992 IEEE MTT-S International Microwave Symposium Digest, New York, NY, USA.
[24] X. L. Li, W. Q. Xu, H. Y. Jia, X. Wang, B. Zhao, B. F. Li, and Y. Ozaki, "Water-induced morphology changes in an ultrathin silver film studied by ultraviolet-visible, surface-enhanced Raman scattering spectroscopy and atomic force microscopy," Thin Solid Films, vol. 474, pp. 181-185, 2005.
[25] F. F. C. Duval, R. A. Dorey, R. W. Wright, Z. Huang, and R. W. Whatmore, "Fabrication and modeling of high-frequency PZT composite thick film membrance resonators," IEEE Transactions on Ultrasonics Ferroelectrics & Frequency Control, vol. 51, pp. 1255-61, 2004.
[26] S. P. Dodd, G. A. Saunders, M. Cankurtaran, and B. James, "Ultrasonic study of the elastic and nonlinear acoustic properties of ceramic aluminum nitride," Journal of Materials Science, vol. 36, pp. 723-9, 2001.
[27] J. H. Boo, S. B. Lee, Y. S. Kim, J. T. Park, K. S. Yu, and Y. Kim, "Growth of AlN and GaN thin films on Si(100) using new single molecular precursors by MOCVD method," Physica Status Solidi A-Applied Research, vol. 176, pp. 711-717, 1999.
[28] N. Ledermann, P. Muralt, J. Baborowski, S. Gentil, K. Mukati, M. Cantoni, A. Seifert, and N. Setter, "{100}-textured, piezoelectric Pb(Zr-x Ti1-x)O-3 thin films for MEMS: integration, deposition and properties," Sensors And Actuators A-Physical, vol. 105, pp. 162-170, 2003.
152
[29] S. B. Majumder, Y. N. Mohapatra, and D. C. Agrawal, "Optical and microstructural characterization of sol-gel derived cerium-doped PZT thin films," Journal Of Materials Science, vol. 32, pp. 2141-2150, 1997.
[30] M. T. Wauk and D. K. Winslow, "Determination of acoustic transducer conversion loss by impedance measurements," IEEE Transactions on Sonics and Ultrasonics, vol. SU16, pp. 86-88, 1969.
[31] L. Callaghan, "Techniques for Processing Aluminum Nitride Acoustic Resonators with Plate and Beam Geometries," M.S. Thesis, University of California, Santa Barbara, Santa Barbara, CA, USA, 2004.
[32] R. C. Jaeger, Introduction to Microelectronic Fabrication, Repr. with corrections May, 1993. ed. Reading, Mass.: Addison-Wesley Pub. Co., 1993, pp. 136-8.
[33] B. C. Wadell, Transmission Line Design Handbook. Boston: Artech House, 1991, p. 111.
[34] Autodesk, Inc., Autocad 2000, San Rafael, CA
[35] V. Lughi, et al., to be published.
[36] G. Cole (personal communication), 2004
[37] S. A. Campbell, The Science and Engineering of Microelectronic Fabrication, 2nd ed. New York: Oxford University Press, 2001, pp. 283-285.
[38] H. Cho, J. K. Kim, and S. J. Pearton, "Comparison of inductively coupled plasma chemistries for dry etching of group III-nitrides," Journal of Ceramic Processing Research, vol. 2, pp. 139-145, 2001.
[39] F. Engelmark, G. F. Iriarte, and I. V. Katardjiev, "Selective etching of AI/AIN structures for metallization of surface acoustic wave devices," Journal of Vacuum Science & Technology B, vol. 20, pp. 843-848, 2002.
153
[40] K. Zhu, V. Kuryatkov, B. Borisov, J. Yun, G. Kipshidze, S. A. Nikishin, H. Temkin, D. Aurongzeb, and M. Holtz, "Evolution of surface roughness of AlN and GaN induced by inductively coupled Cl-2/Ar plasma etching," Journal of Applied Physics, vol. 95, pp. 4635-4641, 2004.
[41] J. Lee, H. Cho, D. C. Hays, C. R. Abernathy, S. J. Pearton, R. J. Shul, G. A. Vawter, and J. Han, "Dry etching of GaN and related materials: Comparison of techniques," IEEE Journal of Selected Topics in Quantum Electronics,vol. 4, pp. 557-563, 1998.
[42] E. R. Parker, B. J. Thibeault, M. F. Aimi, M. P. Rao, and N. C. MacDonald, "Inductively coupled plasma etching of bulk titanium for MEMS applications," Journal of the Electrochemical Society, in press.
[43] Cascade Microtech, Wincal Calibration Software, Beaverton, OR
[44] K. M. Lakin and J. S. Wang, "Acoustic bulk wave composite resonators," Applied Physics Letters, vol. 38, pp. 125-7, 1981.
[45] F. T. Ulaby, Fundamentals of Applied Electromagnetics, 2004 Media ed. Upper Saddle River, NJ: Pearson, 2004, pp. 48-63.
[46] Agilent Technologies, Advanced Design System 2003A, Palo Alto, CA
[47] R. A. Bartkowiak, Electric Circuits. New York: Intext Educational Publishers, 1973, pp. 295-297.
[48] The Mathworks, Inc., Matlab, Natick, MA
[49] Q.-B. Zhou, Y.-K. Lu, and S.-Y. Zhang, "Extraction of electromechanical coupling coefficient of piezoelectric thin films deposited on substrates," Ultrasonics, vol. 39, pp. 377-382, 2001.
[50] Z. Wang, Y. Zhang, and J. D. N. Cheeke, "Characterization of electromechanical coupling coefficients of piezoelectric films using composite resonators," IEEE Transactions on Ultrasonics Ferroelectrics & Frequency Control, vol. 46, pp. 1327-30, 1999.
154
[51] Q. M. Chen and Q.-M. Wang, "The effective electromechanical coupling coefficient of piezoelectric thin-film resonators," Applied Physics Letters,vol. 86, 2005.
[52] Y. Zhang, Z. Wang, and J. D. N. Cheeke, "Resonant spectrum method to characterize piezoelectric films in composite resonators," IEEE Transactions on Ultrasonics Ferroelectrics & Frequency Control, vol. 50, pp. 321-33, 2003.
[53] E. K. Sittig, "Design and technology of piezoelectric transducers for frequencies above 100 MHz," in Physical Acoustics, vol. IX, W. P. Mason and R. N. Thurston, Eds. New York: Academic Press, 1972, pp. 221-275.
[54] Standard Definitions and Methods of Measurement for Piezoelectric Vibrators, IEEE Standard No. 177, 1966
[55] R. C. Ruby (personal communication), 2005
[56] T. Makkonen, T. Pensala, J. Vartiainen, J. V. Knuuttila, J. Kaitila, and M. M. Salomaa, "Estimating materials parameters in thin-film BAW resonators using measured dispersion curves," Ieee Transactions On Ultrasonics Ferroelectrics And Frequency Control, vol. 51, pp. 42-51, 2004.
[57] J. Larson, R. Ruby, and P. Bradley, "Method for reducing lateral modes in FBARs," U. S. Patent 6,215,375, March 30, 1999.
[58] D. R. Lide, "CRC handbook of chemistry and physics: a ready-reference book of chemical and phyical data," 77th ed. Boca Raton, FL: CRC Press, 1997, pp. various pagings.
[59] B. Jacobs, M. Kramer, E. J. Geluk, and F. Karouta, "Optimisation of the Ti/Al/Ni/Au ohmic contact on AlGaN/GaN FET structures," Journal of Crystal Growth, vol. 241, pp. 15-18, 2002.
[60] H.-C. Lee, J.-Y. Park, K.-H. Lee, and J.-U. Bu, "Preparation of highly textured Mo and AlN films using a Ti seed layer for integrated high-Q film bulk acoustic resonators," Journal of Vacuum Science & Technology B
155
Microelectronics & Nanometer Structures Processing Measurement & Phenomena, vol. 22, pp. 1127-33, 2004.
[61] K.-W. Tay, L. Wu, C.-L. Huang, and M.-S. Lin, "Growth of AlN thin film on Mo electrode for FBAR application," presented at 2003 IEEE Ultrasonics Symposium. Vol.2, pp.2024-7. Piscataway, NJ, USA.
[62] K. M. Lakin, J. Belsick, J. F. McDonald, and K. T. McCarron, "Improved bulk wave resonator coupling coefficient for wide bandwidth filters," presented at 2001 IEEE Ultrasonics Symposium. Proceedings. vol.1, 2001, pp.827-31. Piscataway, NJ, USA.
156
Appendix A
This appendix is an accumulation of the process recipes and flows. All tools
mentioned are located in the UCSB Nanofabrication Facility unless otherwise noted.
Recipes are listed in processing order but cleaning steps are not included.
URecipe 1: Sputter TiO UBU2 UB
Tool: Sputtered Films, Inc. Endeavor 8600
Chamber: DC chamber
SeasoningRecipe Name: Ti_20_2k_1000
SeasoningRecipe Power: 2000 Watts
SeasoningGas Flow: 20 sccm argon
Seasoning Time: 1000 seconds
Recipe name: TiO_20_10_23_45
Power: 2300 Watts
Gas Flow: 20 sccm argon, 10 sccm oxygen
Time: 4500 seconds
Film thickness: 1.3 µm
URecipe 2: Pattern AZUPU
®UPU 4330-RS on TiO UBU2 UBU with AlN Mask
Tool: GCA 6300 i-line Wafer Stepper
157
Steps:
Solvent clean and dehydrate wafer
Prepare surface with HMDS
Spin AZP
®P 4330-RS at 5000 rpm for 30 seconds for a
photoresist thickness of 3.2 m
Soft bake for 1 minute at 95º C
Expose 1.0 seconds with a focus offset of +10
Hard bake for 1 min at 105º C and cool
Develop in AZP
®P DEV diluted 1:1 with DI water for 8
minutes
Rinse in DI
URecipe 3: Etch TiO UBU2
Tool: Panasonic Inductively Coupled Plasma Etcher
Recipe: 123 SiOEtch – this is a cleanroom standard recipe designed
for high selectivity with photoresist
Power: 500 W
Bias: 400 W
Gas Flows: 40 sccm CHFB3 B
Pressure: 1.0 Pa
Time: 25 minutes
158
Note: The Panasonic ICP is designed for 150 mm wafers; therefore,
the four inch wafers were mounted to the 150 mm wafers with
diffusion pump oil.
URecipe 4: Etch AlN
Tool: Panasonic Inductively Coupled Plasma Etcher
Recipe 142 AlN
Power: 600 watts
Bias: 150 watts
Gas Flow: 30 sccm ClB2 B, 5 sccm Ar
Pressure: 4.0 Pa
Etch Rate: ~300 nm/min
Note: The Panasonic ICP is designed for 150 mm wafers; therefore,
the four inch wafers were mounted to the 150 mm wafers with
diffusion pump oil.
URecipe 5: Remove TiO UBU2 UB
Solvent clean wafer to ensure all diffusion pump oil and photoresist is are
removed. Dip wafer 49% hydrofluoric acid diluted 20:1 with DI water. Dip time
depends on the amount of TiOB2 B remaining. Average is 5 minutes
159
URecipe 6: Front and backside PECVD SiO UBU2 UB
To deposit front and back oxide both, the Unaxis High Density PECVD reactor
and the PECVD PlasmaTherm 790 for Oxides and Nitrides reactor were used. The
Nanofab’s standard recipes and calibrated deposition times for each tool were
implemented for the depositions.
Recipe 7: Backside Lithography
Tool: Suss Microtec MA 6 mask aligner
Steps:
Solvent clean and dehydrate wafer
Prepare surface with HMDS
Spin AZP
®P 5214 at 4000 rpm for 30 seconds for a
photoresist thickness of 1 m
Soft bake for 1 minute at 100º C
Expose 16 seconds in Hard Contact Mode
Hard bake for 2 minutes at 100º C
Flood expose for 120 seconds
Develop in MF701 for 45 seconds – this time is critical.
Do not exceed 45 seconds
Rinse in DI
Wait 24 hours and then bake for 20 minutes at 120º C.
160
Recipe 9: Etch Backside SiO B2
Tool: Panasonic Inductively Coupled Plasma Etcher
Recipe: 123 SiOEtch – this is a cleanroom standard recipe designed
for high selectivity with photoresist
Power: 500 W
Bias: 400 W
Gas Flows: 40 sccm CHFB3 B
Pressure: 1.0 Pa
Time: 11 minutes
Note: The Panasonic ICP is designed for 150 mm wafers; therefore,
the four inch wafers were mounted to the 150 mm wafers with
diffusion pump oil.
Recipe 10: Pattern AZP
®P 4110 on Front Side SiO B2 B with SiO B2 B Mask
Tool: GCA 6300 i-line Wafer Stepper
Steps:
Solvent clean and dehydrate wafer
Prepare surface with HMDS
Spin AZP
®P 4110 at 4000 rpm for 30 seconds for a
photoresist thickness of 1.3 m
Soft bake for 1 minute at 95º C
Expose 0.8 seconds with a focus offset of +6
161
Develop in AZP
®P DEV diluted 1:1 with DI water for 6
minutes
Rinse in DI
Recipe 11: Etch Front Side SiO B2
Tool: Panasonic Inductively Coupled Plasma Etcher
Recipe: 118 SIOVert – this is a cleanroom standard recipe designed
for straight sidewalls
Power: 900 W
Bias: 200 W
Gas Flows: 40 sccm CHFB3 B
Pressure: 5.0 Pa
Time: 2.5 minutes
Note: The Panasonic ICP is designed for 150 mm wafers; therefore,
the four inch wafers were mounted to the 150 mm wafers with
diffusion pump oil.
Recipe 12: Pattern AZP
®P 5214 for Front Side Si Etch with Lift-Off Mask
Tool: GCA 6300 i-line Wafer Stepper
Steps:
Solvent clean and dehydrate wafer
Prepare surface with HMDS
162
Spin AZP
®P 5214 at 4000 rpm for 30 seconds for a
photoresist thickness of 1 m
Soft bake for 1 minute at 95º C
Expose 0.3 seconds with a focus offset of +6
Bake for 60 seconds at 110º C
Flood Expose for 60 seconds
Develop in AZP
®P DEV diluted 1:1 with DI water for 40
seconds
Rinse in DI
Post-bake for 5 minutes at 110º C
Recipe 13: Etch Front Side Si
Tool: PlasmaTherm Silicon Deep Reactive Ion Etch
Recipe: CALL_L01
Etch loop time: 1 minute
Etch Loop Step Dep Etch A Etch B
Duration [sec.] 5.0 2.0 6.0
Pressure [mT] 23 23 23
CB4 BFB8 B [sccm] 70 0 0
SFB6 B [sccm] 40 50 100
Ar [sccm] 0 40 50
RF1 [W] 0 9 9
RF2 [W] 825 825 825
163
Recipe 13: Pattern AZP
®P 4110 for Lift-Off with Lift-Off Mask
Tool: GCA 6300 i-line Wafer Stepper
Steps:
Solvent clean and dehydrate wafer
Prepare surface with HMDS
Spin AZP
®P 4110 at 4000 rpm for 30 seconds for a
photoresist thickness of 1.3 m
Soft bake for 1 minute at 95º C
Expose 0.8 seconds with a focus offset of +6
Soak in toluene for 5 minutes and blow dry
Develop in AZP
®P DEV diluted 1:1 with DI water for 6
minutes
Rinse in DI
Recipe 14: Evaporate Top Metal Electrode
Tool: CHA, Industries SEC600 Multi-Wafer Evaporator
Metals used: Aluminum, nickel, and gold
Notes: When depositing Al keep the deposition rates low, 3 Å/sec.
Liftoff Soak in acetone, scrub and use spray bottles if necessary
164
Recipe 15: Etch Air Cavities
Tool: PlasmaTherm Silicon Deep Reactive Ion Etch
Recipe: CALL_L01
Etch loop time: 3 hours +
Etch Loop Step Dep Etch A Etch B
Duration [sec.] 5.0 2.0 6.0
Pressure [mT] 23 23 23
CB4 BFB8 B [sccm] 70 0 0
SFB6 B [sccm] 40 50 100
Ar [sccm] 0 40 50
RF1 [W] 0 9 9
RF2 [W] 825 825 825
Note: The wafer should be cleaved in to samples at this point.
Attach sample to carrier wafer with 3M P
™P Thermally
Conductive Adhesive Transfer Tape 9890
Recipe 16: Evaporate Bottom Metal Electrode
Tool: CHA, Industries SEC600 Multi-Wafer Evaporator
Metals used: Aluminum
Note: When depositing Al keep the deposition rates low, 3 Å/sec.
Recipe 17: Anneal Metal to Silicon
Tool: UCSB Nanofab Strip Annealer
Temperature: 465° C
165
Gases: Forming gas: NB2 B and HB2
Time: 30 seconds
166
Appendix B
Displayed below is the Matlab P
®P code written to solve for the quality factor by
finding the slope of the phase angle versus the frequency. This particular code has
values inputted for the sample W9HS8 resonator 10018 which is used as an example
throughout X423HChapter 5X.
% Create Polynomial for Phase Z vs. Freq and differentiated
%---- Read in File - remember to change for each data set
% for now type in%
ft=[1.333125E+09
1.333750E+09
1.334375E+09
1.335000E+09
1.335625E+09
1.336250E+09
1.336875E+09
1.337500E+09
1.338125E+09
1.338750E+09
1.339375E+09
1.340000E+09
167
1.340625E+09
1.341250E+09
1.341875E+09
1.342500E+09
1.343125E+09
1.343750E+09
1.344375E+09
1.345000E+09
1.345625E+09
1.346250E+09
1.346875E+09
1.347500E+09
1.348125E+09];
zt=[-1.02125
-0.98775
-0.95356
-0.91097
-0.86047
-0.80954
-0.73878
-0.65802
-0.56664
168
-0.47817
-0.40805
-0.32495
-0.23335
-0.14933
-0.05798
0.03381
0.12222
0.19604
0.26117
0.33228
0.41471
0.47990
0.52581
0.56215
0.60500];
% transpose
f=transpose(ft);
z=transpose(zt);
% -- type in resonant frequency in GHz
fr=1.342500E+09
169
% -- polynomial number--
n=4;
%--- polynomial --
p=polyfit(f,z,n);
%- plot data remember to change data
fi=linspace(1.333125E+09,1.348125E+09,300);
zi=polyval(p,fi);
figure
plot(f,z,'o',f,z,fi,zi,':')
xlabel('freq,GHz')
ylabel('Z phase deg')
title('Phase Angle Polynomial Fit')
%---differentiate---
pd=polyder(p);
%-- evaluate dir --
zd=polyval(pd, fi);
% - return number for resonant frequency -- need to type in
dzr=polyval(pd,fr)
170
%-- plot --
figure
plot(fi,zd)
xlabel('Freq, GHz')
ylabel('d(phase(z))/df')
title('Derivative of Polynomial Fit')
%-- Solve for Q
Q=fr*abs(dzr)/2