UNIVERSITY OF CALIFORNIA Santa Barbara Design, Fabrication, …memsucsb/Research/dissertatio… ·...

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



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



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


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


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


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.


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.


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


44


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


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


Figure 4.10. Illustration of top electrode lift-off step

21. Etch air cavity from the backside of sample with the Si DRIE,



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.


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.


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]


S1

1


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


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


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


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


impedance

123


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


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.


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


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


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

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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


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



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:



Spin AZP

®P 5214 at 4000 rpm for 30 seconds for a

photoresist thickness of 1 m


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


Recipe: 123 SiOEtch – this is a cleanroom standard recipe designed

for high selectivity with photoresist

Power: 500 W

Bias: 400 W


Pressure: 1.0 Pa

Time: 11 minutes



diffusion pump oil.

Recipe 10: Pattern AZP

®P 4110 on Front Side SiO B2 B with SiO B2 B Mask


Steps:



Spin AZP





161

Develop in AZP


minutes

Rinse in DI

Recipe 11: Etch Front Side SiO B2


Recipe: 118 SIOVert – this is a cleanroom standard recipe designed

for straight sidewalls

Power: 900 W

Bias: 200 W


Pressure: 5.0 Pa

Time: 2.5 minutes



diffusion pump oil.


®P 5214 for Front Side Si Etch with Lift-Off Mask


Steps:



162

Spin AZP


photoresist thickness of 1 m



Bake for 60 seconds at 110º C

Flood Expose for 60 seconds

Develop in AZP


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


®P 4110 for Lift-Off with Lift-Off Mask


Steps:



Spin AZP





Soak in toluene for 5 minutes and blow dry

Develop in AZP


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

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-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

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% -- 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)

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%-- 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

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