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Baylis, Samuel Andrew.
Tunable patch antenna using semiconductor and nano-scale Barium Strontium Titanate varactors
h [electronic resource] /
by Samuel Andrew Baylis.
[Tampa, Fla.] :
b University of South Florida,
ABSTRACT: Patch antennas are fundamental elements in many microwave communications systems. However, patch antennas receive/transmit signals over a very narrow bandwidth (typically a maximum of 3% bandwidth). Design modifications directed toward bandwidth expansion generally yield 10% to 40% bandwidth. The series varactor tuned patch antenna configuration was the bandwidth enhancement method explored in this research; this configuration is implemented by dividing a patch antenna into multiple sections and placing varactors across the resultant gaps. In addition to yielding a large bandwidth, the configuration has a number of ancillary benefits, including straightforward integration and design flexibility. Through the research represented by this work, the properties of the series varactor tuned patch antenna, herein referred to as the Fragmented Patch Antenna (or FPA), were explored and optimized. As a result, an innovative patch antenna was produced that yielded 63.4% frequency tuning bandwidth and covered a frequency range between 2.8 and 5.4 GHz. The wide bandwidth was achieved through a detailed parametric study. The products of this study were the discovery of multiple tuning resonances that were used to expand the tuning bandwidth and the understanding/documentation of the significance of specific antenna dimensions. Measurement results were obtained through the fabrication of a prototype antenna using semiconductor varactors. In the second research phase, the construction of capacitors using the tunable permittivity material Barium Strontium Titanate (BST) was investigated. Using this material in conjunction with nano-fabrication techniques, varactors were developed that had good estimated performance characteristics and were considered appropriate for integration into adaptive microwave circuitry, such as the tunable antenna system. The varactors were constructed by using Focused Ion Beam (FIB) milling to create a nano-scale capacitive gap in a transmission line. A combination of end-point current detection (EPD) and cross-section scanning electron (SEM) and ion beam (FIB) microscope images were used to optimize the milling procedure. The future extensions of this work include the integration of the BST varactors with the antenna design; the configuration of the developed BST varactors lends itself to a straightforward integration with the FPA antenna.
Thesis (M.S.)--University of South Florida, 2007.
Includes bibliographical references.
Text (Electronic thesis) in PDF format.
System requirements: World Wide Web browser and PDF reader.
Mode of access: World Wide Web.
Title from PDF of title page.
Document formatted into pages; contains 123 pages.
Advisor: Thomas M. Weller, Ph.D.
Focused ion beam milling.
End point detection.
End point monitor.
x Electrical Engineering
t USF Electronic Theses and Dissertations.
Tunable Patch Antenna Using Semiconductor and Nano-Scale Barium Strontium Titanate Varactors by Samuel Andrew Baylis A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering Department of Electrical Engineering College of Engineering University of South Florida Major Professor: Thomas M. Weller, Ph.D. Lawrence P. Dunleavy, Ph.D. Ashok Kumar, Ph.D. Date of Approval: March 23, 2007 Keywords: BST, focused ion beam milling, end point detection, end point monitor, EPD, thin-film, ferroelectric, parael ectric, tunable, frequency ag ile, frequency adaptive, nonlinear, microstrip, broadband, varactor Copyright 2007, Samuel Andrew Baylis
Dedication This thesis is dedicated to Jesus, th e Christ. He is my Lord and Savior, and without Him, nothing I do can have any lasting value. It is true for me as it says in Psalm 40:1-3, Â“I waite d patiently for the LORD; and He inclined unto me, and heard my cry. He brought me up also out of a horrible pit, out of the miry clay, and set my feet upon a rock, and established my goings. And He hath put a new song in my mouth, even praise unto our God.Â”
Acknowledgements This project could not have been completed without the a ssistance and support of many talented people. I am grateful fo r their contributions and friendship. I would like to thank first and fore most the guidance of my advisor Dr. Thomas Weller. I owe a significant portion of my pr ofessional development to Dr. Weller, and I am most grateful. Thanks to my committee members Dr. Dunleavy and Dr. Kumar. Thanks to Dr. Kumar and his research team for guidance rela ting to the materials side of this work. Thanks to Dr. Dunleavy for his suppor t throughout my career and funding through Modelithics during my u ndergraduate years. I also thank the following present and fo rmer graduate students of Dr. Weller and Dr. Dunleavy for their friendship and assistance. To Alberto Rodriquez, Bojana Zivanovic, Sergio Melais (my undergraduate wireless lab instructor and friend) Suzette Presas, Lee Le, Henrry La Rosa, Diana Aristizabal, Quenton Bonds, Tony Price, Evelyn Benabe, Saravana Natarajan, Srinat h Balachandran, Tom Ricard, Rick Connick, Byoungyong Lee, John Daniel, Jason Boh, and Ahmad Aljesira wi, you will always be special to me. Thanks to Rick Connick and the staff of Modelithics for their support and flexibility in allowing me to use ModelithicsÂ’ measurement lab to conduct experiments from time to time. Thanks to Dr. Yusuf Emirov of NN RC (Nanomaterials and Nanomanufacturing Research Center) for his help with USFÂ’s FI B system. I would additionally like to thank Ben Rossie of the Center for Ocean Technol ogy Research at USF for his invaluable
contributions to the FIB portion of this work. Thanks to Dr. Rudy Schlaf for his contributions to the FIB methodology. Thanks to Venkat Gurumurthy of the A dvanced Materials Resear ch team for his help on various aspects of the project and for his friendship. I appreciate the contributions of Evelyn Benabe and Suzette Presas for work relating to the mode ling of the BST and semiconductor varactors, respectively. Thanks to Dr. Thomas Ketterl of the Center for Ocean Technology Research at USF for the use of his work and his continued assistance on this project. Thanks to Sriraj Manavalan for orienting me to this project. Thanks to Dr. Jim Culver, Dr. Balaji Lakshminarayanan, Srinath Balachandran, and, most of all, Saravana P. Natarajan for teac hing me the art of fabrication. Thanks to all of my friends at Idlewild Baptist Church for your friendship and support. Thanks to my family. Particularly, my dad, Dr. Charles Baylis, for his guidance, support, and friendship; specifi cally, I would like to thank hi m for leading me to Jesus and teaching me the Bible. I would like to thank my mother, Sharon Baylis, especially for her loving support and for her tireless a nd patient manner of teaching me at home from the 2nd grade through high school. I would also like to thank my brother Charlie Baylis and my sister Leanna Baylis for their support and friendship. Thanks to my grandparents Robert and Harriett Smith and Al bert and Eleanor Baylis for their support and many prayers. Thanks to Northrop Grumman-Xetron Corporation and Dr. James Culver for their funding of the tunable antenna project and to the National Science Foundation for their funding of the BST varactor development. Th is material is based upon work supported by the National Science Foundation under Grant No. 0601536.
i Table of Contents List of Tables iv List of Figures v Abstract ix Chapter 1: Introduction 1 1.1 Project Discussion 1 1.2 Project Background 3 1.2.1 Alternative Tuning Methods 3 1.2.2 Proposed Method 5 1.2.3 Varactor Technologies 5 1.3 Thesis Overview 7 Chapter 2: Antenna Development 9 2.1 Introduction to Basic Antenna Theory 9 2.1.1 Antenna Electromagnetics 9 2.1.2 Patch Antennas 10 2.1.3 Mechanics of Frequency-Tunable Antennas 13 2.2 Fragmented Patch Antenna Introduction 14 2.3 FPA Analysis and Op timization Techniques 16 2.4 Optimization and Design 22 2.4.1 Substrate Choice 23 2.4.2 Optimal Capacitance Region 25 2.4.3 Number of Sections 26 2.4.4 Section Length Scaling 29 2.4.5 Capacitance Scaling 30 2.4.6 Varactors Per Gap 30 2.4.7 Section Width 32 3.4.8 Matching Techniques 34 3.4.9 Comparison of Three Configurations 36 2.4.10 Parametric Summary and Conclusions 38 2.5 FPA Construction 40 2.6 Chapter Summary 41
ii Chapter 3: Antenna Performance 42 3.1 Antenna Simulation Characterization 42 3.1.1 Radiation Pattern Simulation 42 3.1.2 Semiconductor Varactor Characterization and Modeling 47 3.1.3 Hybrid Simulation Using Semiconductor Varactor Models 50 3.1.4 Simulation Analysis Conclusion 51 3.2 Antenna Measurement Analysis 52 3.2.1 S-Parameter Measurement and Analysis 52 3.2.2 Radiation Pattern Measurement and Analysis 54 3.3 Chapter Summary 57 Chapter 4: Varactor Development and Characterization 59 4.1 Introduction to BST Devices 59 4.1.1 BST Material Properties Summary 60 4.1.2 BST Varactor Configurations Summary 66 4.2 Series Gap Capacitor Design 68 4.2.1 Design Overview 68 4.2.2 Design Method 69 4.2.3 Substrate Choice 71 4.2.4 Film Composition and Thickness 71 4.2.5 Design Summary 73 4.3 Device Fabrication 73 4.3.1 BST Deposition 73 4.3.2 Photolithography and Etching 75 4.3.3 Focused Ion Beam Milling Introduction 78 4.3.4 Focused Ion Beam Milling Methodology 81 4.3.5 Depth Optimization Experiments Using End Point Detection 87 4.3.6 Discussion and Summary of Milling Procedures 93 4.4 Device Characterization 95 4.4.1 Measurement Setup and Device Properties 95 4.4.2 Calibration 97 4.4.3 Measurement and Characterization 98 4.4.4 Summary 102 4.5 Chapter Summary 103 Chapter 5: Summary and Conclusions 105 5.1 Summary of Findings 106 5.1.1 Tunable Antenna Using Semiconductor Varactors 106 5.1.2 Barium Strontium Titana te Nano-Scale Varactors 108 5.2 Recommendation for Future Work 108 5.2.1 Advanced BST Varactor Fa brication and Characterization 109 5.2.2 Integrated Fragmented Patch Antenna 109 5.2.3 Non-Linear Transmission Lines 110 5.3 Overall Conclusion 111
iii References 112 Appendices 117 Appendix A: MathCAD Transmission Line Phase Analysis 118 Appendix B: BST Series Ga p Capacitor Process Flow 122
iv List of Tables Table 2-1. Summary of FPA performance specifications and associated design parameters. 17 Table 2-2. Summary of the tuna bility simulation results for configurations #1-#3. 37 Table 3-1. Extracted lumped element circuit parameters. 50 Table 3-2. Maximum received power leve ls (relative to the transmit power) for each radiation pattern. 56 Table 4-1. Summary of sample groups. 70 Table 4-2. Device design summary. 73 Table 4-3. BST sputter-deposition parameters. 74 Table 4-4. Milling parameter summary. 81 Table 4-5. TRL calibration delay lin e lengths and CPW dimensions. 97 Table 4-6. Extracted Cs values over frequency. 102
v List of Figures Figure 2-1. Simple probe-fed patch antenna schematic. 10 Figure 2-2. Voltage vs. position MathCAD plot at several instances in time for the TM10 mode. 12 Figure 2-3. Current vs. position MathCAD plot at several instances in time for the TM10 mode. 12 Figure 2-4. Basic probe-fed series-t uned patch antenna schematic. 14 Figure 2-5. Smith Chart illustration of series varactor tuning. 16 Figure 2-6. ADS schematic for hybrid EM simulation using ideal capacitors. 19 Figure 2-7. Concept drawing of the integrated capac itor technique. 20 Figure 2-8. FPA design cycle chart. 21 Figure 2-9. Final FPA schematic. 22 Figure 2-10. Simulated S11 (dB) of 25 (circl es) and 59 mil (straight) substrates at two capacitance values. 24 Figure 2-11. Optimal capacitance region plot. 26 Figure 2-12. S11 phase plot of a two line configuration (circles) and a three line configuration (straight) at minimum capacitance (0.7 pF). 27 Figure 2-13. S11 phase plot of a two line configuration (circles) and a three line configuration (straight) at ma ximum capacitance (2.1 pF). 27 Figure 2-14. S11 phase plot of a three lin e configuration (circl es) and a four line configuration (straight) at minimum capacitance (0.7 pF). 28 Figure 2-15. S11 phase plot of a four line configuration at minimum (circles) 0.7 pF capacitance and maximum 2.1 pF capacitance (straight). 29
vi Figure 2-16. Hybrid S11 simulation comparison between an FPA with one varactor per gap (solid) and two varactors per gap (circles). 32 Figure 2-17. Simulated return loss at C= 1 pF for an FPA with approximately 90 degree width (thin black) and an FPA with approximately 180 degree width (thick black). 33 Figure 2-18. Configuratio n #1 schematic drawing. 36 Figure 2-19. Configuratio n #2 schematic drawing. 37 Figure 2-20. Configuratio n #3 schematic drawing. 37 Figure 2-21. Final FPA design. 41 Figure 3-1. Momentum layout for th e integrated capacitor simulation of configuration #3. 43 Figure 3-2. Momentum coordinate system. 44 Figure 3-3. Co-polarized H and E pl ane simulated radiation pattern measurements. 45 Figure 3-4. Cross polarized E and H pl ane simulated radiation patterns. 46 Figure 3-5. Measured S21 (left) and S 11 (right) parameters for the varactor diode at five bias voltages. 48 Figure 3-6. Effective capacitance (left) and Q factor (right) vs. bias voltage at 3 GHz. 49 Figure 3-7. Lumped element equiva lent varactor diode circuit. 49 Figure 3-8. Hybrid simulated S11 of th e antenna using modeled varactors. 50 Figure 3-9. FPA bias scheme. 52 Figure 3-10. Measured FPA S11 at five bias voltages. 53 Figure 3-11. Measured (dashed) and simu lated (solid) S11 vs. frequency at the 5 volt bias condition. 53 Figure 3-12. Illustration of the measurement axis definitions of the antenna. 55
vii Figure 3-13. Measured 5 volt co-pol arized and crosspolarized FPA radiation patterns. 56 Figure 4-1. Perovskite family cubic molecular structure. 62 Figure 4-2. Typical ferroelectric permittivity vs. applied voltage curve. 64 Figure 4-3. Typical parallel plat e varactor con cept drawing. 66 Figure 4-4. Typical interdigital varact or configuration concept drawing. 67 Figure 4-5. FIB milled BST Series Gap Capacitor configuration. 69 Figure 4-6. Series gap capacitor sample device map. 70 Figure 4-7. XRD spectrum pl ots from sample #2. 74 Figure 4-8. Photolithographic process illust ration for the series gap capacitor. 75 Figure 4-9. Finished series gap capacitor signal line showing misaligned BST region. 76 Figure 4-10. Illustration of the Focused Ion Beam milling system. 79 Figure 4-11. Illustration of beam ra ster scanning and the relationship between pitch and percent overlap. 80 Figure 4-12. Top down schematic view of the cross-sectional depth experiment. 83 Figure 4-13. Top-down SEM image of the cro ss-sectional destructive test setup. 83 Figure 4-14. Cross-sectional ion-beam image of a FIB milled slit in the signal line. 84 Figure 4-15. EPD process illustration. 86 Figure 4-16. Sample EPD graph showing milling time vs. absorbed current. 87 Figure 4-17. Top down SEM image of test lines and cross sectional viewing region. 89 Figure 4-18. EPD data graphs for lines 4-7. 89 Figure 4-19. Cross sectional ion-beam images of lines 7 and 6 (left), and lines 5 and 4 (right). 91
viii Figure 4-20. SEM image comparing two tren ches with a 0% overlap setting (left) and a 50% overlap setting (right). 93 Figure 4-21. EPD region analysis summary. 95 Figure 4-22. SEM image of sample #4, device 12. 96 Figure 4-23. Device 12 endpoint detection graph. 96 Figure 4-24. S21 TRL data for sample #4, device 12. 99 Figure 4-25. S11 TRL measurement data for sample #4, device 12. 99 Figure 4-26. S21 and S11 SOLT measurem ent data for sample #4, device 12. 100 Figure 4-27. Measured S11 phase data from sample #4, device 12. 100 Figure 4-28. Equivalent 2-port admittance pi network. 101 Figure 4-29. Extracted series capacita nce vs. frequency at bias voltages 0 and 25 volts. 102 Figure 5-1. Completed Fragme nted Patch Antenna using semiconductor varactors. 106 Figure 5-2. Concept drawing of the integrated FPA design. 110 Figure A-1. Array plot1 vs. capacitance and frequency. 121
ix Tunable Patch Antenna Using Semiconductor and Nano-Scale Barium Strontium Titanate Varactors Samuel Andrew Baylis ABSTRACT Patch antennas are fundamental el ements in many microwave communications systems. However, patch antennas receive/tran smit signals over a ve ry narrow bandwidth (typically a maximum of 3% bandwidth). Design modifications directed toward bandwidth expansion generally yield 10% to 40% bandwidth. The series varactor tuned patc h antenna configurati on was the bandwidth enhancement method explored in this resear ch; this configuration is implemented by dividing a patch antenna into multiple sections and placing varactors across the resultant gaps. In addition to yielding a large bandw idth, the configuration has a number of ancillary benefits, including straightforwar d integration and design flexibility. Through the research represented by this work, the pr operties of the series varactor tuned patch antenna, herein referred to as the Fragmented Patch Antenna (or FPA), were explored and optimized. As a result, an innovative patc h antenna was produced that yielded 63.4% frequency tuning bandwidth and covered a frequency range between 2.8 and 5.4 GHz. The wide bandwidth was achieved thr ough a detailed parametric study. The products of this study were the discovery of multiple tuning resonances that were used to expand the tuning bandwidth and the understanding/doc umentation of the signi ficance of specific antenna dimensions.
x Measurement results were obtained th rough the fabrication of a prototype antenna using semiconductor varactors. In the second research phase, the construction of capacitors using the tunable permittivity material Barium Strontium Tita nate (BST) was investigated. Using this material in conjunction with nano-fabrication techniques, va ractors were developed that had good estimated performance characteristic s and were considered appropriate for integration into adaptive microwave circui try, such as the tunable antenna system. The varactors were constructed by us ing Focused Ion Beam (F IB) milling to create a nano-scale capacitive gap in a transmission line. A combination of end-point current detection (EPD) and cross-section sca nning electron (SEM) and ion beam (FIB) microscope images were used to optimize the milling procedure. The future extensions of this work in clude the integration of the BST varactors with the antenna design; the configuration of th e developed BST varactors lends itself to a straightforward integrati on with the FPA antenna.
1 Chapter 1: Introduction 1.1 Project Discussion The purpose of this work is to descri be the development of a frequency tunable patch antenna using Barium Strontium Titanate (or BST) varactors. Patch antennas are important to microwave system design, but th eir primary shortcoming is that they are bandwidth limited. This work develops an antenn a that operates on the same principles as a patch antenna, but is able to adjust its center receive/tran smit frequency in response to a changing control voltage input thereby expanding the operational bandwidth. The tuning mechanism that causes the antenna frequency sh ift is tunable capacitance. Such methods often create complicated res onance-mode structures which are not well understood or documented. For this reason, this work include s the parametric study of selected antenna properties to assist in the fundamental unde rstanding of similar antenna systems. The design goal was to realize antenna freque ncy tunability between 2.45 and 5 GHz. BST is a ferroelectric/paraelectric material that has a tunable relative electrical permittivity and exhibits low loss performance at microwave frequencies. The discovery of this material has opened the door to a wide horizon of new microwave components that are able to dynamically adapt their electri cal properties to adjust to changing systemic or demand-related needs.
2 Currently, researchers are inve stigating ways to make BST devices more tunable, more easily constructed, and lower loss. The research methodology of this work was to first develop a working patch antenna configuration that would use the available cap acitance tunability with optimal efficiency. This goal was achieved through a combination of mathematical analysis, advanced circuit and full-wave simulation, and finally the use of antenna prototyping using packaged semiconductor varactors. Then after a work ing antenna design was achieved, the work focused on the development of high performanc e BST varactors; that is, varactors with high capacitance tunability and good loss perf ormance. This goal was achieved through the nano-fabrication of capacitors using focused ion beam milling. While an integrated device was not physically realized, a wo rking antenna system was created using semiconductor varactors, a working BST varactor design was created that exhibited good estimated performance, and repeatable varactor fabrication techniques were developed. A summary of the methodology descri bed above is compiled into the following chronological project objective list: Explore, through simulation and measuremen t, the possibility of dividing patch antennas into multiple sections and connect ing the sections using varactor diodes. Utilize software simulation tools to optimi ze antenna parameters to develop such an antenna that is maximally frequency tunable. Fabricate a prototype antenna using semiconductor varactors. Simulate the antenna as accurately as possible. Measure the S-parameters and the radiation patterns of the fabricated antenna and compare the results with the simulation. Explore the possibility of using Focuse d Ion Beam milling (FIB) to construct tunable capacitors using (Ba,Sr)TiO3 thin films. Fabricate and measure a t unable BST-based varactor.
3 The plan above, along with associated hypothesis, experiments, data, and conclusions, is representative of the research that will be described in the following pages of this thesis. 1.2 Project Background Patch antennas, with widely availa ble well-documented designs, straightforward system integration, conformability, and a low-profile, are often a convenient choice for system designers. Microstrip patch antenna s are found in diverse applications from avionics to satellite radio to radar to biom edical systems . However, patch antennas are limited by narrow bandwidth (about 3%), an d this often disqualifies patch antennas for otherwise suitable applica tions. Many solutions have been contrived with the purpose of expanding the bandwidth of patch antenna s [1-6]; while these solutions are all beneficial in some way, they usually either complicate the fabrication and/or only achieve minimal bandwidth expansion. Some tunable pa tch antenna schemes are described in the section below. 1.2.1 Alternative Tuning Methods The first approach is discrete element tuning. Discrete element tuning uses a large array of patch antennas with different center frequencies . A switching network turns the patch elements on or off depending on the system demands. This method can be thought of as a pipe organ, in that it contai ns different antennas of different resonant lengths to produce the desired result. While this type of system has potentially unlimited tunability, it is not continuously tunable. The designer must choose between antenna
4 system size and bandwidth. MEMS switches ar e often used to dynamically control the array configuration . The second approach is adaptive substrate tuning. Adaptive substrate tuning uses a standard patch antenna mounted on a substrat e material with variable permittivity, such as BST . Some work has gone so far as to suspend the antenna above the substrate upon height-adjustable MEMS platforms [8-9]. In this way, the Â“thicknessÂ” of the air dielectric substrate may be varied by ad justing the height of the MEMS platform support(s). The difficulties with this ge neral method include low tuning ranges and radiation pattern distortion due to the presence of a high-permittivity substrate directly beneath the radiating surface (in the case of BST/ferroelectric tuning). The third method is to use shunt-mounted variable reactance tuning. Shunt-mounted variable reactance uses shunt-mounted reactiv e elements (most likel y capacitors) placed along the radiating edges of the antenna surface. This approach yields good tuning bandwidths, but makes fabrication more di fficult with the introduc tion of shunt ground plane connections (vias) in to the design. Tuning bandwidth s are usually around 25% for these designs . The final method is to use series-mounted variable reactance tuning. Series-mounted variable reactance tuning works by dividi ng a patch antenna into multiple parts and placing tunable reactive elements across the gaps . This approach may yield higher tunability (~40%) than the other methods with easier fabrication/integration and higher design flexibility.
5 1.2.2 Proposed Method The antenna tuning mechanism that was chosen for analysis in this work, was the series reactance (in this case, series capacitanc e) configuration, herein referred to as the Fragmented Patch Antenna, or FPA. On the surface, the immediate reason for selecting the FPA, without knowing any design/performan ce characteristics, was simpler, costeffective fabrication and/or monolithic integration. After some investigation into the workings of this configuration, it became appare nt that there was a marked increase in the level of design flexibility and potential for improvement through optimization. In particular, one feature of the design presente d in this work is multiple, tunable, and overlapping resonances; this pr operty allowed significant bandwidth expansion and is believed by the author to be unique to this design. Since the series mounted configura tion requires tunable cap acitance, there are a number of varactor technologi es that can be applied towa rd antenna tuning (or dynamic circuits in general). The following paragra phs give a brief summary of the available varactor technologies. 1.2.3 Varactor Technologies The first varactor tec hnology that is commonly employed is semiconductor diode varactors. Semiconductor diodes are based on a pn junction that has a more pronounced depletion region, resulting in an exaggerated junction capacitance . Driving the diode further into the reverse bias region results in a widening of the depl etion region which, in turn, results in a smaller capacitance. Varact or diodes have high tunability but low quality factors in the microwave operating region , .
6 The second varactor technology is MEMS varactors. Microelectronic mechanical system (MEMS) varactors are miniatur e mechanically-tuned capacitors. A common design for MEMS based varactors is the Â“air bridgeÂ” design  where a verticallymoveable rectangular piece of conducting materi al is suspended directly over another non-moving piece. A voltage delivered acro ss the conducting sections creates an electrostatic charge force that draws the plates together, crea ting an increase in capacitance. MEMS varactor s possess high quality factors, but generally lower capacitance tunability . Manufacturing comple xity and reliability problems  are also current problems for this approach. The final varactor type is tunable dielectric varactors. Tunable di electric varactors are based on dielectric films (most commonly BST) that have a field-dependent permittivity; that is, the value of the relative dielectric constant changes with an applied changing electric field; if the relative permittivity of the capacitor dielectric changes, then the capacitance value must also change. This type of varactor usually appears in of the two following configurations: the para llel plate configuration or the interdigital configuration [17-18]. Both the loss and the tunability of these devices are heavily process dependent, since the characteristics of the dielectric film largely depends on the film composition and deposition parameters. Between these three c hoices, the tunable dielectric (BST) method was chosen, since the technology offers potentially easy inte gration, better tunability (as compared to MEMS), good microwave loss performance, and hi gh design flexibility. It is important to note that semiconductor varactors were used in this project for the antenna system prototype.
7 Since the overarching goal of this pr oject was to achieve high frequency tunability, it followed that the most important capacito r parameter to be considered would be tunability. However, even though semiconductor di odes had the best tuna bility available, the input matching characteri stics of patch antennas ar e very narrow band, and for a given frequency range, there is only a sma ll corresponding capacitance range that yields efficient tunability; it was hypothesized and then subsequently shown that the extra amount of tunability provided by the varactor diodes over the BST va ractors would be of only minor value. Additionally, BST vara ctors have better microwave loss characteristics, similar tuning voltage range s, lower junction noi se, and comparable switching speed . The varactors described herein are simila r to the series gap capaci tor presented in  in that they are composed of a co-planar waveguide whose signal line has been severed perpendicular to the direction of signal travel. The gap was nano-machined using focused ion beam technology (FIB). The presence of this gap introduces a series capacitance into the line, and, in this sense, they ar e similar to other interdigital designs. The design, theory, and fabrication met hods of both the antenna and varactor systems will be expanded upon in the following chapters of this work. 1.3 Thesis Overview The purpose of this thesis is to describe in detail the development of a frequency tunable antenna system using both semiconductor va ractors and BST thin film varactors. The contribution of this thesis in th is respective research area is significant; the antenna developed in the pages of this work is the most highly fr equency tunable patch
8 antenna design known to date. Although the te chnology is not yet mature, the capacitance agile, thin-film capacitors developed were esti mated to exhibit tunability characteristics on par with only the best performing BST varactors ( i.e ., devices with tunability ratios greater than 3.5:1), and the unique design and nano-fabri cation methods render it a custom fit for integration into the FPA antenna system. In summary, the complete antenna system described in this work is a significant contribution because it represents a highly advanced and easily manufactured fr equency agile antenna system solution. Chapter 1 of this thesis gives an ove rall view of this work and its associated background, a defense of the re search methodology, a statement of the contributions of this work, and an overview of the enclosed chapters. Chapter 2 gives a full description of the antenna development process, involving a summary of the applicable th eory, a discussion of altern ative methods, mathematical modeling, electromagnetic simulation, optimi zation, and a final design description. Chapter 3 provides a description and an alysis of the antenna measurements along with comparisons to simulated data. Chapter 4 describes in detail the BST varactor theory, development and characterization. This includes a background study into alternative desi gn configurations, an overview FIB device design, a detailed repor t on fabrication methods and an analysis of measurement data. Chapter 5 summarizes the findings of this thesis, draws conclusions from the findings, and suggests research paths for future work.
9 Chapter 2: Antenna Development 2.1 Introduction to Basic Antenna Theory 2.1.1 Antenna Electromagnetics Fundamental electromagnetic th eory states that a stationa ry electric charge in free space produces a static electric field. For a posit ive charge situated in free space, electric field lines radiate out in a ra dial pattern from the charge. The electric field intensity E generated in a material by a charged pa rticle q at a give n observation point R is expressed by the equation (2-1) below, where R Âˆ is the unit vector pointing in the direction away from the charge and is the permittivity of the surrounding material . 24 Âˆ R q R E (2-1) If this charge is given a velocity v, then a moving (dynamic) E-field (electric) is created. Consequently, if a DC current is applied through the free space, then a dynamic electric field is generated. Any constant, but moving (in the case of DC current) E-field creates a static H-field (magne tic). If the velocity vector v changes over time, then the Hfield also becomes dynamic (the Biot-Savart la w) . Consequently if an alternating current is applied to the free space, then both dynamic electric and magnetic fields are generated.
10 This is the fundamental princi ple of all antenna radiation; electromagnetic radiation is due to time varying currents . If the alternating current is applied to a conductor (as in the case of ante nnas), then the situation becomes complicated due to various attractive and repulsive charges within the metal, but the fundamental principles do not ch ange. The consequence of this is that at the surface of the conductor, some E-field comp onents do not exist, but the effect of the time-varying current does exist in the form of the H-field. This H-field, will ultimately produce a dynamic E-field in the far field region . For this reason, field interaction very close to the antenna surface is difficult to predict in practice, and most antenna measurement schemes are designed to be conducted in the far-field . 2.1.2 Patch Antennas A patch antenna is a flat piece of conduc tive material (usually situated above a ground plane) whose geometrica l shape and dimensions determine the antenna radiation characteristics. The most common form of this antenna is the recta ngular patch antenna, shown in Figure 2-1 below. Figure 2-1. Sim ple probe-fed patch antenna schematic.
11 Patch antennas are classified genera lly as standing wave antennas (as opposed to traveling wave antennas) that are based on cu rrent sourced fields (a s opposed to aperture antennas, such as a horn). A resonant standi ng wave forms when an incident wave on the antenna surface interferes with the reflected wave (reflec ted from the antenna conductor boundary), form a wave with large maxima and minima that are static with respect to position along the antenna surface . The boundary condition along the edge of th e antenna that is opposit e the feed-point is an open circuit condition; therefore, the total voltage is forced to be a maximum at this point and the current is forced to zero. Since impedances repeat along a transmission line every wavelength, for n ) 2 / 1 ( long surfaces (where n=1, 2, 3, 4Â…), the leading edge of the antenna is an identical open circuit condition. Theref ore, for wavelength resonance, the input impedance is large at the leading edge of the antenna (voltage divided by current is infinity) a nd is zero at the center of th e antenna. For this reason, the excitation point is placed between the leadi ng edge and the center of the antenna where the input impedance is 50 ohms (see Figure 2-1). If a standing wave with a length of n/2 wavelengths exists along the length of the surface, then it is said that th e antenna is operating in the TMn0 mode. For a standing wave distribution across the width, the notation is TM0n. It is possible for both standing wave distributions to occur at once, although it is typically undesirable for efficiency and pattern purposes . Radiation patterns ar e heavily dependent on operational modes. The voltage and current standing wave dist ributions are shown for the fundamental TM10 mode in Figures 2-2 and 2-3 belo w. These plots were generated by MathCAD
12 Figure 2-2. Voltage vs. positi on MathCAD plot at several instances in time for the TM10 mode. Figure 2-3. Current vs. positi on MathCAD plot at several instances in time for the TM10 mode. Because of the strict resonant co nditions of the rectangular patch antenna, many solutions have been developed to expand the bandwidth of these antennas [1-6].
13 One of these approaches is to modify the basic rectangular desi gn to allow frequency tunability. 2.1.3 Mechanics of Frequency-Tunable Antennas There are three common methods for tuning patch antennas. These methods are (a) shunt varactor tuning, (b) dynamic substrate tuning, and (c), the focus of this thesis, series varactor tuning. Shunt varactor tuning, as presented in  and describe d in the introduction section of this work, operates by modifying the boundary condition at the radiating edges of a standard patch antenna. If the varactors are no t attached, then an open circuit appears at the end of the surface. If the var actor (or varactors) is attached to the edge of the surface, the loading at the end of the transmission lin e would be altered from the previous open circuit condition; ther e would be a new frequency that would satisfy the standing wave resonance criterion. Dynamic substrate tuning works simply by changing the permittivity of the substrate sandwiched between the ground plane and the top radiating surface. When the permittivity changes, the electrical length of the transmission line also changes; this change in electrical length is accompanied by a resultant change in resonant frequency. Series varactor tuning works by alteri ng the electrical length of the radiating surface through varactors mounted in seri es along the signal path on th e radiating surface. This is the tuning mechanism employed by the antenna design described by this work; a full explanation of the operating prin ciples is provided in the following section. The specific design is herein referred to as th e Fragmented Patch Antenna, or FPA.
14 2.2 Fragmented Patch Antenna Introduction The Fragmented Patch Antenna is a variati on of the series vara ctor tuned topology, which is illustrated in basic form below in Figure 2-4. The first known version of this topology was documented by Fayyaz et. al. ; here, a probe-fed standard patch antenna was broken into two equal parts and si x varactor diodes we re placed across the gap in the middle. This design yielded a 42% frequency bandwidth (tunable between 1.5 and 2.3 GHz) with a capacitance tuning rati o of approximately 15:1. The theoretical reason for why the capacitors cause a fr equency shift is straightforward. Figure 2-4. Basic probe-fed series -tuned patch antenna schematic. As discussed in Section 2.1.2, patch antennas are stand ing wave antennas; this means that they have maximum return loss at wavelength resonant points. For an antenna without the diodes in-line, the electrical length is strictly prop ortional to the physical length of the radiating surface. When the su rface is sectioned and capacitors are placed in-line, the electrical length is dependen t upon both the physical length of the conductor and the reactance of the capacitors.
15 To understand this concept mathemati cally, consider a series combination of a variable capacitor and an open circuited transmission line. The input impedance of an open circuited transmission line is given by eqn. (2-2). ) 2 cot( c length line f iZ Zo inLine (2-2) When this result and the impedance of the cap acitor are added in series, the result is given by (2-3). C f i c length line f iZ Zo in* 2 ) 2 cot( (2-3) The reflection coefficient ( or S11) is given by (2-4). 0 0Z Z Z Zin in (2-4) From eqs. (2-2) and (2-3), it is evid ent that a change in capacitance in (2-3) would cause a change in the phase of S11, the re flection coefficient. Since there is a phase change caused by the capacitor, the transm ission line appears elec trically longer or shorter depending on whether the capacitance is increased or decreased, respectively. This concept is graphically depicted on a Smith chart in Figure 2-5 below.
16 Figure 2-5. Smith Chart illustration of series varactor tuning. In the first case from Figure 2-5, th e case of the transmission line without a series varactor, the presence of the transmissi on line rotates the angle of the reflection coefficient toward the generator by approxi mately 45 degrees. For the second case, a varactor that tunes between .1 and 5 pF is inserted into the line; the presence of the varactor moves the angle back toward the open circuit condition, thereby making the transmission line appear shor ter by an amount dependent upon the value of the capacitor. This is the operating principle of the seri es varactor tuned pa tch antenna topology. 2.3 FPA Analysis and Op timization Techniques For a multi-section FPA, the basic theory presented in Section 2.2 can be applied in multiple ways and thus there is significant room for optimization of the antenna design parameters (e.g., number of sections, number of varactors per gap, etc. ). At the outset of
17 this project, one major question was whethe r there existed an optimal combination of these parameters that would produce a design that would possess both high tunability and good return loss. To find the answer to th is question, an optimization study was conducted and it was found that these parame ters had widely varied effects on the antenna performance. While documentation of the optimization procedure is given in section 3.4, a summary of the antenna parame ters with their associated performance is shown in Table 2-1. Table 2-1. Summary of FPA performan ce specifications and associated design parameters. Parameter Affected Performance Specification substrate height return loss, efficiency, instantaneous bandwidth, radiation patterns # of sections number of tunable resonances size of sections relative position of tunable resonances capacitance scaling eliminates secondary tunable resonances varactors per gap no observed major effect, minor radiation pattern variation section width return loss gap width return loss inset length return loss, matching distribution over bandwidth The optimization was conducted through an iterative process us ing a combination of mathematical analysis, transmission line modeling, and full wave structure simulations. These methods of antenna performance predic tion can be grouped into the following two general groups: transmission line modeling (ideal and non-ideal) and full-wave EM simulation. Ideal transmission line modeling im plies the use of phase and impedance data only, while non-ideal transmission line modeli ng denotes the use of substrate and limited electromagnetic calculations (relating to micr ostrip line characteristics) in addition to phase and impedance data. The first type of transmission lin e modeling was using Mathsoft MathCAD to characterize the FPA in terms of transmission line theory. MathCAD was used to provide
18 a graphical phase vs. frequency analysis of both the tunable bandwidth and the instantaneous bandwidth of a given transmission line confi guration. This algorithm was constructed by T. Weller1 and is shown in detail with explanatory comments written by the author in Appendix A. Ideal capacitors were assumed for all MathCAD analysis. The second type of transmi ssion line modeling was using Agilent Advanced Design System (or ADS ) to perform a cross-validation of the MathCAD analysis (ideal transmission line analysis) and perform transmission line phase simulations using nonideal micro-strip transmission lines. Ideal capacitors were used for all ADS simulations. There were two types of full wave EM simulation: the hybrid technique and the integrated capacitor technique. Both types utilized the software program Agilent Momentum The first method (hybrid) was to electromagnetically simulate the radiating sections of the FPA independently from th e capacitors. The capacitors were replaced by excitation ports at the contact points of the bridging capacitors. The simulation of this scheme produced a [(n*2)-1] port (one input port, n-2 capacitor contact point ports, where n is the number of sections) data file. This file was then inserted into an ADS schematic and either ideal capacitors or modeled capacitors were connected across their associated ports. The associated ADS schematic is shown in Figure 2-6. 1 T. Weller, PhD., Professor, University of South Florida
19 Figure 2-6. ADS schematic for hybrid EM simulation using ideal capacitors. This configuration is for a three section, one varactor per gap configuration. The second approach (integrated capaci tor) was to electromagnetically simulate an integrated version of the antenna using Momentum ; this simulation was accomplished by fashioning parallel plate capacitor structures to fit between the gaps in the radiating surface. The capacitors were constructed by placing two 100 um by 100 um conductive squares in direct overlap of one another 2 um apart with an infinite (in the horizontal plane) dielectric layer sandwiched between. Th is layer was defined to have a relative dielectric constant value between 4 and 12, depending on which bias state was desired (this setup emulated a variable capacitor topology based on a tunable dielectric film). The integrated capacitor technique is illustrated in Figure 2-7.
20 Figure 2-7. Concept drawing of the integrated capacito r technique. This drawing assumes a three section, one va ractor per gap design. The hybrid simulation method produced results that most closely predicted the measured S-parameter response, since it allo ws for the introducti on of lumped element varactor modeling (as described in Chapter 3). The drawback of this approach is that it does not allow for radiation pattern simulation. The integrated capacitor technique, while having limited ability to effectively model the varactors, allows for approximate radiation pattern simulation.
21 Figure 2-8. FPA design cycle ch art. These simulation/analysis techniques we re used in conjunction with the development flow chart shown in Figure 2-8. Once the FPA concept was conceived, analysis was conducted to gather optimization informati on; the optimization process examined the parameters summarized in Table 2-1 above and analyzed in Section 2.4. From this analysis, three primary configur ations were chosen for full-wave simulation. From these three configurations, the best alternative was chosen for fabrication and measurement. The outcome of the design analysis wa s an inset-fed series-tuned patch antenna having three sections of equal width and length, us ing only one varactor across each gap (see
22 Figure 2-9). Figure 2-9 shows the final schema tic for the FPA; a full development of this design is given in Section 2.4 with a para metric summary in 2.4.10, a final design summary in Sections 2.4.10 and 2.5, hybrid simulation results in Section 3.1.3, and measurement results in Sections 3.2.1 and 3.2.2. Figure 2-9. Final FPA schematic. 2.4 Optimization and Design This section describes the optimization an alysis of the critical antenna parameters; this analysis resulted in a deeper understanding of the mechanics of the FPA and lead in part to the final design choice. The final design (and its related measurement data) is the result of only one design cycle; therefore the possibi lity remains that there is significant room for improvement. The parametric study of this Section 2.4 is a representation of the aggregate knowledge accumulated throughout the entire design cycle; therefore, aspects of theory and design principles that were not applied to the final design are noted where appropriate.
23 2.4.1 Substrate Choice Substrate choice largely affect s radiation efficiency/pattern s, antenna dimensions, and instantaneous bandwidth. Typically, since patch antennas are intended to launch EM waves directly into the space above the radia ting surface, substrate dielectric constants are kept as low as possible. Alternately, transmission lines work better with higher dielectric constants, since th e purpose of a line is to create guided waves between the metallization and the substrate . However, for inset-fed designs the substrate must support a feed transmission line and an antenna so the final permittivity value must be a compromise. The thickness of the substrate determines the instantaneous bandwidth of the resonance and the percentage of the input ex citation energy that is converted to surface waves as opposed to radiated energy (an in crease of surface waves lowers the radiation efficiency). When the thickness of the s ubstrate increases, the surface waves and the instantaneous bandwidth increase; as a result the bandwidth increases but at the expense of radiation efficiency. When the substrate height h falls within the region given by eq. (2-5) below, the power loss due to surface wave s is considered to be negligible . rh 2 3 .0 (2-5) A more fundamental aspect of substrat e choice is antenna dimensions; for a given set of dimensions, a modification of the substrat e depth and/or relative permittivity will slightly change the resonant frequency of the antenna. This is because an increase in the depth of the substrate increases the size of the fringing fields which consequently increases the effective length of the antenna surfa ce (decreasing the resonant frequency).
24 Figure 2-10 illustrates the effect that s ubstrate thickness can have on return loss characteristics. Notice the change in return loss magnitude and the relative position of the resonances; the 59 mil substrate exhibits a la rger instantaneous bandwidth, as expected. The simulations were conducted using the integrated capacito r technique (with an ideal capacitor) and a two section/one va ractor, inset fed patch antenna. Figure 2-10. Sim ulated S11 (dB) of 25 (circles ) and 59 mil (straight) substrates at two capacitance values. The top graph represents data obtained with a capacitance value of 0.7 pF, while the bottom graph represents data obtained with a capacitance value of 2.1 pF. The substrate material was FR4 with a relative permittivity of 4.3. After a substrate study using integrat ed capacitor EM simulations, it was determined that a 59 mil substrate with a relative permittiv ity of 4.3 should be used. Simulations at a dielectric constant value of 9.6 indicated that the return loss was much greater for a 77
25 mil substrate than for a 25 mil substrate. At th is stage in the design cycle, it was expected that antenna varactor integr ation would be done on a silic on or sapphire substrate (thus, the 9.6 dielectric constant value), which would be mounted on a FR4 platform. For the prototype antenna, fabrication wa s performed directly on FR4. For an antenna tunable between 2.5 and 5 GHz, the frequency region between 4.7 and 5 GHz violates the condition set by (2-5), and th us antenna efficiency is expected to be low in this region for an antenna mounted on 59 mil FR4. This is a largely unexplored area for improvement in future design generations. 2.4.2 Optimal Capacitance Region There exists a capacitance tuning range wh ere the ability to make a percent change in the transmission phase along the FPA is maximized. Below a certain capacitance value the capacitor reactance becomes so large that further increases have a diminishing effect, and a similar result occurs for large capacitance values. The optimal solution is center frequency-dependent and must also take into consid eration the upper and lower capacitance limits of the varactor device. Fo r a three section, two capacitor design, the low end of this range was determined through simulation to be between 0.3 and 1 pF, as shown in Figure 2-11, where the assumed tuning range of the varactors was 8.7:1 and the intended frequency range was ~2-5 GHz. Fo r these results the tunable bandwidth was defined as the frequency range over which the input reflection coefficient phase could be held at 0 using the ADS non-ideal transmissi on line model (described in Section 2.3).
26 Figure 2-11. Optimal capacitance region pl ot. Graph shows the tunable percent bandwidth vs. starting capacito r values. Plot assumes 8.7: 1 varactor tuning ratio. As a result of this study, the low capaci tance value for the final design was chosen to be 0.6-0.7 pF. 2.4.3 Number of Sections In this section, the eff ect of increasing the number of sections beyond two is examined. The method of analysis for this parameter was ideal and non-ideal transmission line simulations as defined in Section 2.3. The test procedure was conducted by de signing the section lengths so that, when the capacitors were set to 0.7 pF (as determined by Section 2.4.2), the 1st resonant frequency 0-degree phase crossing was located at 5 GHz, regardless of the number of sections used. The first test was to determine wh ether a three section design would yield more tunability than a comparable two section desi gn. In a direct comparison between the nonideal simulations, it was determined that a design with three equal line sections would provide more tunability than an equi valent design using two line sections.
27 Figure 2-12. S11 phase plot of a two line configuration (circles) and a th ree line configuration (straight) at minimum capacitance (0.7 pF). Figure 2-13. S11 phase plot of a two line configuration (circles) and a three line configuration (straight) at maximum capacitance (2.1 pF). It can be seen from Figures 2-12 and 2-13 that the three segment design has a greater tuning range than that of the two segment design. The other point that should not be overlooked from these graphs is that both th e first and second resonances of the three section design were tunable.
28 For the two section design, only the fi rst resonant point was tunable and the second one was static with respect to capacitan ce. The multiple resonance effect was only observed for the non-ideal phase simulation. The second test was to determine whether a four section design would increase the number of tunable resonant points and/or cause the poi nts to overlap. The same simulation procedure was conducte d as with the first test. Figure 2-14. S11 phase plot of a three line configu ration (circles) and a four line configuration (straight) at minimum capacitance (0.7 pF). From Figure 2-14, the four line configur ation yielded slightly greater tunability and produced more resonant points at frequenc ies below 10 GHz than did the three line configuration. From Figure 2-15, these tunable resonant point s all, with the exception of resonance #4 (from left), shift with the cha nge in capacitance. Also, the #2 resonance of the 2.1 pF capacitance state overlaps th e #1 resonance of the 0.7 pF state.
29 Figure 2-15. S11 phase plot of a four line configuration at minimum (circles) 0.7 pF capacitance and maximum 2.1 pF capacitance (straight). In summary, more than two sections ma y be used with great advantage. First, three sections are better than tw o and four is better than three in terms of 1st resonance tunability. Second, using more than two s ections increases the number of tunable resonances that are available. 2.4.4 Section Length Scaling The variation of individual section le ngths has been shown through non-ideal transmission line phase simulation to alter the position of individual tunable resonances with respect to one another. This design as pect can be used to tailor the antennaÂ’s response to the needs of the specific applic ation. The final design did not incorporate section length scaling; this was because th e two tunable resonances overlapped after the first design cycle.
30 2.4.5 Capacitance Scaling Capacitance scaling is the use of two di fferent size capacitors w ith different associated tuning ranges in a single desi gn to alter the loading characteristics of the antenna. For instance, this concept might be implemented by using a C1 range of 0.7 to 2.1 pF, while using a C2 range of 0.1 to 0.3 pF. Intuitively, such a scheme would have a significant affect on the resonance modes of the antenna For a given frequency, the discontinuity between the first and second sect ions would appear more transp arent to the incident wave than would the discontinuity between the second and thir d sections. Also, since the overall capacitance would be smaller, each line section would have to be made longer to compensate. From non-ideal phase simulations, it was determined that the tuning range of such a configuration was comparable to that of a configuration with equal capacitance and shorter, equal line lengths. 2.4.6 Varactors Per Gap Among the possible effects of placing mo re than one varactor across each gap could be a radiation pattern change, a change in tunability, and/or a change in return-loss characteristics in the form of either instantaneous bandwidth or maximum return loss. Based on the work described in  using multiple varactors along the radiating edges of shunt-varactor tuned designs results in higher equivalent varactor quality factors and higher field uniformity, which in turn resu lts in higher antenna gain and less-erratic radiation patterns, respectively. The unif ormity benefits are manifest both in instantaneous field uniformity and overall fiel d uniformity across the tuning range. Since
31 the desired resonant mode only operates in th e vicinity of the s hunt varactor(s), the boundary imposed voltage maximums and/or minimums are heavily localized at the connection point(s). Therefore radiation properties are non-u niform along the radiating boundaries of the antenna. In terms of an FPA configuration operating in the TM10 mode, the dynamics are hypothesized to be slightly diffe rent, since the current distribu tion is tied to the varactor connection points at multiple points in the interior of the antenna where the current is the greatest. The voltage is expected to distribut e across the width of the antenna and remain largely unaffected by the varactor discontin uities. Furthermore the boundary condition at the far edge of the antenna would be enforced along the entire width. The effect of adding a second varact or across each gap was examined through both hybrid (for return loss) and integrated capaci tor (for radiation patterns) simulations. For both the hybrid and the integrat ed capacitor simulations a th ree section FPA and 0.7 to 2.1 pF capacitors were used. From Figure 2-16, there were small cha nges in the return loss characteristics at high frequency and no significant change in tunabili ty for the two varactor per gap design. The high frequency response of the one-varacto r per gap design was more resonant. One hypothetical explanation was that the resonances were occuri ng as a result of resonant modes occurring across the lengths or widths of individual secti ons. The two varactor case most likely destroyed these resona nces because the boundary condition was enforced more broadly across the varactor loaded edges, thereby discouraging higherorder modes. If high frequency resonance is also a desired performance feature, then adding more varactors could destroy this affect.
32 Figure 2-16. Hybrid S11 sim ulation comparis on between an FPA with one varactor per gap (solid) and two varactor s per gap (circles). The fi rst graph (left) shows the relationship between the two configurations at maximum capacitance (2.1 pF) and the second graph (right) shows the same relati onship at minimum capacitance (.7 pF). From the simulated radiation patterns, it was observed that th e two varactors per gap case had higher H-plane levels at the second resonance. This c ould have been an affect of broader current distribution acr oss the width of the antenna. In summary, while multiple varactors per gap is not detrimental to antenna performance, based on these experiments th ere is no outstanding be nefit to using two over oneother than slightly improved radiatio n characteristics. However, if more than two are used, the benefits that do exist could be augmented. Using one varactor across the gap also encourages additional resonance m odes, thereby increasing the high-frequency response. Placing more varactors across the ga p lowers the optimal capacitance range (for individual varactors), and may or may not be feasible, depending on design constraints. For the prototype design in this work, one varactor per gap was used. 2.4.7 Section Width The width of a patch antenna generally im pacts antenna resonant frequency, input impedance, instantaneous bandwidth, efficien cy, and directivity [ 23]. The theoretical
33 motivation for increasing width of a patch antenna is to maximize radiation by increasing the size of the radiating edges along the width. Additionally, the resonance mode structure is highly dependent upon the length to width ratio and the relative location of the feedpoint . The width of a conventi onal patch antenna is given by (3-5) . 1 2 2 rrf c W (2-6) However, it was found through simulation that, for a 4.4 GHz center frequency, an arbitrarily chosen wavelengt h width provided better return loss at the two bands of interest (for a standard inse t length) than did the width dictated by (2-6). Figure 2-17 shows the two width configurations for a three section design with C=1 pF. Figure 2-17. Sim ulated return loss at C=1 pF for an FPA with approximately 90 degree width (thin black) and an FPA with approximately 180 degree width (thick black). In summary, it is reasonable to conc lude that standard design equations for patch antennas do not necessarily apply in the fragme nted antenna case. It is possible, however, that the input matching characteristics and th e mode structure cha nge considerably upon an increase in width; a change in either of these two parameters would create new
34 matching conditions, and the same input matchi ng scheme was used for both cases in this test. For the final design, a wavelength width at 4.5 GHz was used. Antenna width optimization is considered to be an area where further improvement is possible. 2.4.8 Matching Techniques There are two predominate methods for deliv ering signal to a pa tch antenna surface: probe feeding and inset feedi ng. The feed point on the antenna surface determines the excitation point, and the location of this poi nt determines the input impedance of the antenna. In probe-fed designs, the signal is fed from the bottom of the antenna through a via hole. This method of feeding is adva ntageous because the feed can be placed anywhere on the surface, which makes input match optimization and feed-based resonant mode control techniques very straightforward and flexible ; on the downside, the via hole adds inductance, causes a discontinuity in the ground plane , and is difficult to implement in practice . With a microstrip inset feed, there is the possibility that the wide feedline or the discontinuities at the transmission line/antenna interface could radiate and disturb the radi ation patterns by increasing si de-lobe and cross-polarized power levels , . However, the inset feed naturally lends itself to easier integration, and was therefore used for this design. The design parameters of the inset length and matching networks were determined and valid ated based on a three line FPA with equal section lengths and capacitance; ADS and the Momentum hybrid simulation method were used for all experiments in this section.
35 The two primary parameters of interest for inset feed design are inset length and gap width. The inset length is the distance betw een the excitation point and the leading edge of the antenna. The gap width is the sp ace on either side of the inset line. The inset length was first calculated fr om the design equations presented in , and was approximated by 1/3 of the length of a wavelength 4.5 GHz transmission line (6.08 mm). This approximated length was ve rified through a comparison of results for different inset lengths and was found to provide the best input match over the full operational bandwidth. The gap width was found through simulatio n to affect the return loss; in general, narrower gaps produce higher return loss . It was experimentally determined that lowering the gap width from 0.7 mm to 0.3 mm increased the return loss at 4.5 GHz by 5 dB. Although the 0.3 mm gap width was used for the final design, this was a conservative choice, and it was shown through simulation th at smaller gap widths may produce better results over narrow frequency bands. For a wide-bandwidth antenna, it is n ecessary to provide an input match over a wide range of frequencies. Therefore, simulations were conducted to disc over whether it was possible to achieve a broader band match than possible with a standard inset feed. The two primary methods examined were to modify the existing inset feed length to provide a match at both frequencies and/or to use an external tunable matching network. The first experiment was to determine th e effect of using two di fferent inset lengths on the top of the inset and the bottom of the inset. The top inset length was 6.4 mm, designed to match at 4.7 GHz; the bottom inse t length was 5.8 mm, designed to match at 4.7 GHz. Although this design f eature was not included in th e final design, the test
36 indicated that there is a possibility that th e simultaneous use of di fferent inset lengths may match the antenna at two resonance ranges. The second approach was to use an external matching network. Through Momentum hybrid simulation and measurement, it was dete rmined that a series LC matching network with fixed inductance and vari able capacitance (using a varactor) could serve to improve the return loss at one of the resonance ranges, but not both. 2.4.9 Comparison of Three Configurations For the purpose of direct simu lation comparison, three prototypical FPA configurations were designed from the para metric study above. These configurations were analyzed using MathCAD transmission lin e analysis from the algorithm developed fully in Appendix A, ideal and non-ideal tr ansmission line simula tion in ADS, and full wave simulation with the Momentum hybrid technique. The confi gurations are referred to herein as Configurations #1-#3 and are shown in the schematic drawings of Figures 2-16 thru 2-18 below. For all conf igurations, gap_w = .3 mm and inset_w=2.9 mm. Inset_L= 7mm, antenna width w=10.3 mm for Confi guration #2 and inset_L=6.08 mm, antenna width w= 9 mm for Configurations #1 and #3. Figure 2-18. Configuration #1 schematic drawing.
37 Figure 2-19. Configuration #2 schematic drawing. Figure 2-20. Configuration #3 schematic drawing. A summary of the tunability percentage s for each configurati on for a given analysis method is given below in Table 2-2. Table 2-2. Summary of the tunability simulation results for configurations #1-#3. MathCAD ADS Ideal Tunable Range % Bandwidth Tunable Range % Bandwidth Configuration #1 4.375-5 GH z 13.33% 4.4 5 GHz 12.80% Configuration #2 4-5 GHz 22% 4-5 GHz 22% Configuration #3 4-5 GHz 22% 4-5 GHz 22% ADS Non-Ideal Momentum Electromagnetic Tunable Range % Bandwidth Tunable Range % Bandwidth Configuration #1 4.2-5 GHz 17.39% 4.1-4.6 GHz 11.50% Configuration #2 4-5 GHz 22% 3.8-4.5 GHz 17% Configuration #3 3.8-5 GHz 25.80% 3.6-4.5 GHz 22% Table 2-2 indicates that Configuration #1 exhibited the lo west tunability as expected from the parametric study. In addition, the S-parameters for Configuration #2 showed that this configuration only exhibited one tunable resonance in the frequency band of
38 interest. This result was not expected from the ADS phase simulations; it was hypothesized that the other tunable resonance was not present due to an input impedance mismatch. Configuration #3 was selected for the final design. 2.4.10 Parametric Summary and Conclusions The findings from the optimization analysis and the literature search are summarized in the following eight points below. First, the substrate must be chosen to maximize antenna radi ation while discouraging the entrapment of waves between the ground plane and the top surface of the substrate (surface waves). 59 mil FR4 was chosen was chosen for the final design. For this substrate and a frequency range between 2. 5 and 5 GHz, the upper 12% of the bandwidth is expected to exhibit an incr eased level of surface waves. Second, there is an optimal capacitan ce region that most e fficiently converts the capacitance tuning range into frequency t uning. For an antenna with a maximum frequency of 5 GHz (first resonance) and a varactor having an 8. 7:1 tuning range, the lowest value of capacitance should be between 0.2 and 0.8 pF. Third, using more sections than two expands the per-resonant point tuning bandwidth of the antenna. Additionally, using more th an two sections creates multiple tunable resonances, and if these resonances overl ap, then the overall tuning bandwidth is expanded. Fourth, if the lengths of individual sections are modified then the relative position of individual resonances can be shifted.
39 Fifth, using different capacitance values for the first ga p and the second gap for a three line configuration has similar tuning perf ormance to a configuration with equal capacitance values. However, using the scal ed capacitance design of Configuration #2 will eliminate the dual-band tuning benefits of the three line design. Sixth, using multiple varactors per gap results in higher H-plane levels in simulated radiation patterns for a thr ee section and equal capacitan ce configuration. Using one varactor per gap encourages high frequenc y resonance modes that are suppressed by multiple varactors. There were no pronounced bene fits of using more than one varactor in terms of tunability or return loss. Seventh, the appropri ate antenna width is largely unknow n for the FPA configuration. For standard patch ante nnas operating in a TMX0 mode, using wider widths encourages stronger radiation from the increased antenna surface area. Hybrid simulations of a three line FPA configuration showed that a narrowe r width produced better return loss than a width calculated from standard patch antenna design equations. Eighth, using an inset feed over other f eeding methods is considered to be better since it is more suitable for monolithic integration. Smaller gap widths generally result in better return loss. Using unequal gap lengths may allow matching for both bands of a dual band antenna. For a dual band antenna, a series LC matching networ k with a tunable capacitance may be designed to increase the re turn loss of one res onance range at the expense of the return loss of the other resonance range.
40 From the results of the parametr ic study and the comparison between the three configurations, it was determin ed that Configuration #3 (as presented in Section 3.4.9) should be the final design. The design featur ed three equal secti on lengths with equal capacitor ranges across each gap. 2.5 FPA Construction The simulated and measured results pr esented herein were ba sed on the Configuration #3 design constructed on 59 mil thick FR4 board ( r=4.3) with a back ground plane which covered both the entire radiating surface and the feedline structure. The antenna dimensions were inset_L=6 mm, inse t_W=2.9 mm (50 ohms), gap_W=0.3mm, L1=L2=L3=10 mm, and w=9mm. The antenna wa s interfaced to coaxial cable via a 51 mm long, 50 ohm feedline and a board-mounted coaxial SMA connector. The varactor diodes used in this design were Metelics MSV34,067-0805 (0805 surface mount package) that had a measured 3 GHz tuning range between 0.6 pF at 17.5 Volts and 5.66 pF at 0 volts bias. Bias was supplied to each antenna section through a 10k-ohm resistor. The final design is shown below in Figure 2-20.
41 Figure 2-21. Final FPA design. The 51 mm feedline connects to the inset length. 2.6 Chapter Summary Through the design process outlined and deta iled in this chapte r, a patch antenna design was developed whose performance was e xpected to include tunability inside the range between 2.45 and 5 GHz with good re turn loss and acceptable radiation characteristics. Although all three of the configurations that were evaluated were considered to be viable options Configuration #3 was determined to be the most suited to fulfill the stated expectations. In the sections of Chapter 3, the performance of Configuration #3 is presented thr ough simulation and measurement.
42 Chapter 3: Antenna Performance The following sections were intended to assist in the understanding of the operational characteristics of the Fragmented Patch Ante nna (FPA) through varact or characterization, S-parameter simulation/measurement, and ra diation pattern simulation/measurement. 3.1 Antenna Simulation Characterization 3.1.1 Radiation Pattern Simulation Radiation pattern simulations were c onducted using the integrat ed capacitor technique in Momentum as described in Chapter 2. The pa rallel capacitor plates were sized in conjunction with the dielectric film permittivity to yield capacitance values similar to that of the 5 volt bias condition of the varactor diodes, which wa s the bias condition used to obtain the measured radiation patterns. The first resonance occurred at 3.21 GHz, and the second resonance occurred at 4.85 GHz. Th e simulated return loss of the second resonance was much higher than that of the first resonance. The effects of the 51 mm feedline were not included in the simulated radiation pattern analysis. An image from the simulation window in Momentum for this simulation scheme is given in Figure 3-1.
43 Figure 3-1. Mom entum layout for the integrat ed capacitor simulation of configuration #3. Dimensions are in mm. For the antenna configuration shown in Figure 3-1, the =0 axis was defined in Momentum to be perpendicular to the top f ace of the antenna (broadside) and the =0 direction was defined to be in the direction of the feedline. The reference coordinate system is given in Figure 3-2. The Eand Hplanes were parallel a nd perpendicular to the feedline, respectively. The polarization of th e antenna was aligned with the feedline. The coordinates and express the location of the ob servation point. For H-plane measurements, was held at 90 degrees while was rotated 360 degrees. For E-plane measurements, was held at 0 degrees while was rotated. The radiation patterns are plots of the radiation levels at each degree of for the given value of (this value is constant for the desired measurement plane).
44 Figure 3-2. Mom entum coordinate system.
45 Figure 3-3 shows the co-polarized E a nd H plane simulated radiation patterns of the FPA Configuration #3. The cross polarized H an d E plane radiation patterns are given in Figure 3-4 Figure 3-3. Co-polarized H and E plane si m ulated radiation pattern measurements.
46 Figure 3-4. Cross polarized E and H plane sim ulated radiation patterns. An important aspect of these simulated radiation patterns is the characteristics of the second resonance. In the H-plane, while there are no co-polarized radiation levels for the second resonance, there is some cross polari zed radiation. In the E-plane there is both cross and co-polarized radiation. When tw o varactors were placed across the gap, a marked increase was observed in the co-polar ized H plane radiation level at the second resonance.
47 Additionally, the array-like lobed performance of the E plane 2nd resonance was roughly characteristic of patc h antennas operating in highe r-order resonance modes, particularly the TM02 mode . However, the 1st resonance radiation patterns were highly characteristic of conventiona l patch antennas operating in the TM10 mode. The abnormalities in the 2nd resonance modes can likely be explained by surface waves and substrate loss. Simulated antenna efficiency was 35% at first resonance and 15% at second resonance. Inefficiency is, by definition, either due to input mismatch, surface waves, or dissipated energy in the conductor or the substrate. When the loss tangent of the substrate was ignored, effici ency improved to 100% and 55% at the first and second resonances, respectively. This i ndicated that no surface waves were present for the first resonance, and the inefficiency was due strictly to substrate loss. At the second resonance, the loss of efficiency was due in part to substrate loss, but the rest was related to surface waves. For a 59 mil substr ate, the 4.85 GHz resonance was calculated to be highly subject to surface wave propaga tion , and since the simulated return loss was much higher and the simulated efficiency was much lower for this resonance, these results can be explained by loss of radiation to surface waves. 3.1.2 Semiconductor Varactor Characterization and Modeling The analysis of the varactor performance is important to the understanding of the FPA behavior. Modeling of th e Metelics MSV34-067,0805 va ractors was completed2 based on S-parameter measurements and RF impedance data. 2 Modeling work was performed by Suzette Presas, University of South Florida
48 This section presents performance data from the direct measurement of the devices and provides an explanation of the modeling mechanism. The S-parameter and impedance measurements were made using an Anritsu 37397C Lightning network analyzer and an Agilent 4287A LCR Meter, respectively. Reverse voltage bias was applied to the diodes from a bi as voltage supply via in ternal bias tees in the Lightning VNA for the S-parameter meas urements and through a Picosecond Labs 5542-203 bias tee for the impedance analyzer measurements. Figure 3-5 below shows the measured S11 and S21 performance of the vara ctor diode for bias voltages 0, 1, 5, 11, and 17.5 volts. Figure 3-5. Measured S 21 (left) and S11 (right) parameters for the varactor diode at five bias voltages. The top curve on the S21 gra ph and the lowest curve on the S11 graph are the 0-bias plots. Bias voltages were 0, 1, 5, 11, and 17.5 volts.
49 Figure 3-6. Effective capacitance (left) and Q factor (right) vs. bias voltage at 3 GHz. The m easured Q and effective capacitan ce over bias voltage is shown in Figure 3-6 for 3 GHz; this data was obtained from th e impedance analyzer measurements. From the S-parameter measurement graph of Figure 3-5, resonance occurred around 5.5 GHz at 0 volts bias. Figure 3-6 above indicates that the capacitor tuned from approximately .6 pF to 5.66 pF as measured at 3 GHz. The lumped element equivalent circu it used to model the measured performance is shown in Figure 3-7. Figure 3-7. Lumped element equiva lent varactor diode circuit.
50 The series capacitance and inductance shown in Figure 3-7 were extracted from the impedance analyzer measurements; the values of Ls and Cs were obtained from the series inductance and capacitance data and the effective series resistance equation block was curve-fit from the series resistance measurem ents. Table 3-1 gives th e equivalent circuit parameters for each bias point. Table 3-1. Extracted lumped element circuit parameters. Bias Voltage Cs (pF) Ls (nH) a b 0 1.195 11.7941.328e-5 1 1.362 11.61113.541e-6 5 0.854 11.40312.039e-6 11 0.637 12.411-1.11e-5 17.5 0.549 11.01216.926-6 3.1.3 Hybrid Simulation Using Semiconductor Varactor Models The antenna design was simulated usi ng the measured data and the models produced from the varactor characterization outlined in Section 3.1.2. The S-parameter simulation data of the antenna using the varactor models is shown below in Figure 3-8. Figure 3-8. Hybrid sim ulated S11 of the antenna using modeled varactors.
51 As desired, the upper resonance range of the 0 bias condition overlapped with the lower resonance of the 17.5 volt bias condi tion. The overlapping resonance was caused by the 1 nH parasitic inductance present in the varactor diodes; at frequencies approaching the varactor resonance, the cap acitance increased causing an upward shift in electrical length, which cause d the center frequencies of the upper resonance points to decrease. 3.1.4 Simulation Analysis Conclusion The preceding sections gave a brief an alysis of antenna simula tion using a variety of techniques, including integrated capacitor radi ation pattern simulation and return loss simulation using varactor diode models. The ra diation patterns indicate d that the radiation patterns for the 1st resonance were similar to those of a standard patch antenna, but that the 2nd resonance radiation patterns were non-id eal, indicated by the low co-polarized Hplane levels and the high ine fficiency. This distortion at 2nd resonance was hypothesized to be a result of surface waves propagating at the higher frequency and/or higher order mode propagation causing the lobes in th e co-polarized E-plane measurements. The simulated S-parameters, obtained from the use of equivalent varactor circuits and the hybrid simulation technique in ADS/Momentum indicated that the design configuration possessed a wide tuning range with the expected overlapping dual-band operation characteristic.
52 3.2 Antenna Measurement Analysis 3.2.1 S-parameter Measurement and Analysis S-parameter measurements of the fr agmented patch antenna were made using an Agilent 8753D network analyzer; an SO LT calibration was performed to set the measurement reference planes at the coaxia l port of the antenna. An Agilent 3620A DC supply was used to deliver bias to the antenna via the 10 k-oh m resistive bias lines. The antenna was biased as shown in Figure 3-9. Figure 3-9. FPA bias scheme. The varactor diodes were bonded to the antenna surface so that the cathodes rested on the central section of the antenna. In this way, a common positive voltage applied to the outer sections would re verse bias the two varactors simultaneously. The measured S11 data for the FPA antenna at bias voltages 0, 1, 5, 11, and 17.5 volts are shown below in Figure 3-10.
53 Figure 3-10. Measured F PA S11 at five bias voltages. From the measured S11 data and the si mulated data presented in Section 3.1.3, there was a strong correlation between the measured results and the simulated results obtained with the varactor diode model. A comparison of the simulated vs. measurement data is given in Figure 3-11 at the 5 volt bias c ondition. All other bias conditions exhibited similar modeled vs. measured correlations. Figure 3-11. Measured (dashed) and simulated (solid) S11 vs. frequency at the 5 volt bias condition.
54 The 10 dB total operational bandwidth of this antenna was approximately 63.4%, with an instantaneous 10 dB bandwidth of 200 MHz at 2.8 GHz (7%). The instantaneous bandwidth was attributed to the thick substrat e and the wide total bandwidth was afforded by the dual-band resonant characteristic. The overlapping dual resonances were caused by parasitic inductance in the varactor diodes (as not ed in Section 3.1.3). A comparison between simulation with ideal varactors and with and without the 51 mm feedline indicated that the cause of the out-of-band return loss levels was primarily related to substrat e/radiation losses along the feedline. In summary, the return loss/tuning pe rformance of this antenna met and exceeded the expectations that were formed after the system atic design process analysis of Chapter 2. 3.2.2 Radiation Pattern Measurement and Analysis The FPA radiation pattern measurem ents were made by placing a transmit antenna and a receive antenna (the DUT) inside an anechoic chamber whose walls were covered with microwave absorber structures. The tran smit antenna remained stationary while the receive antenna rotated on th e specified axis through 360 degrees. The instantaneous position of the receive antenna was denoted by th e angle of a vector perpendicular to the broadside face of the antenna, relative to th e 0 degree angle which was defined as the orientation at which the DUT antennaÂ’s face was aligned with the face of the transmit antenna. Measurements were rotated about th e following two axis: fi rst, a rotation about the axis parallel to and in the plane of the feedline (H-plane measurements) and second, a rotation about the axis perpendicular to a nd in the plane of th e feedline (E-plane measurements). This scheme is illustrated in Figure 3-12.
55 Figure 3-12. Illustration of the measurement axis definitions of the antenna. At intervals of two degrees of rotation, the power received by the DUT antenna was measured by an Agilent 8753D VNA and plo tted using specialized software (Diamond Engineering Antenna Measurement Studio ). For the measurement data shown herein, the antenna was biased at 5 volts using an Agilent 3620A DC power supply (see Section 3.2.1 for the biasing scheme). Measurements were made at each resona nt point in the co-polar and cross-polar E and H directions. The polarizati on of the antenna was define d to be along the feedline. At the 5 volt bias condition, the fi rst resonance was at 3.6 GHz and the second resonance was at 4.92 GHz (see Figure 3-11) The measured 5 volt antenna radiation plots are shown below in Figure 3-13. The va lue of at each degree point was normalized to the maximum value for the respective co -polar plot. The maximum received power levels in dB (relative to the input/tran smit power) are summarized in Table 3-2.
56 Figure 3-13. Measured 5 volt co -polarized and cross-polari zed FPA radiation patterns. Table 3-2. Maxim um received power levels (relative to the tran smit power) for each radiation pattern. Resonance #1 Resonance #2 Pattern Level (dB) Pattern Level (dB) Co-pol H -40.7Co-pol H -42.59 X-pol H -55.04X-pol H -50.314 Co-pol E -36.95Co-pol E -37.99 X-pol E -52.69X-pol E -49.42 The performance of the antenna at 1st resonance was highly typi cal of patch antennas operating in the fundamental TM10 mode. The performance at 2nd resonance was consistent with documented patch antenna performance in the TM30 mode . TM30 modes are typically characterized by a broads ide circular pattern in the H-plane and a three lobed broadside pattern in the E-plan e . Surface waves were expected to be
57 present at resonances above 4.7 GHz (s ee Chapter 2), and were likely partially responsible for any minor deviation of the radiatio n patterns from the documented standard patch antenna patterns. Radiation pattern measurements were conducted for several bias points, and from these measurements it was observed that the ra diation patterns retained their basic shape over the voltage tuning range. Therefore, it fo llows that the pattern shapes were mode dependent not frequency dependent. In general, while room for improvement remains, the measured radiation patterns were considered to be explainable and useful in standard patch antenna applications. 3.3 Chapter Summary The preceding sections detail the si mulation and measurement analysis of the FPA Configuration #3. The simulated S-parameters and radiation pattern s were useful in predicting the measured perfor mance of the FPA design. From the S-parameter measurements it was found that th e two resonance points overlapped at high and low bi as, thereby expanding the operation bandwidth of the antenna. The measured operational bandwidth was 63.4%. From the simulated radiation patterns, it was found that the loss and the dielectric properties (permittivity, thickness) of the FR4 substrate caused high inefficiency at the second resonance point. Cross polarization leve ls were highest for the second resonance. From the measured radiation patterns, the H-plane co-polarized levels at the second resonance were improved, the pa tch antenna exhibited roughly TM30 performance at the second resonance, and the radiation patterns at first resonance were similar to the
58 simulated values, except the cross-polarized levels were higher. Any deviation from standard TM10 and TM30 radiation patterns were attrib uted to substrate effects ( e.g ., surface waves), feedline radiation, or general disruptions caused by the surface discontinuities. Possible areas of improvement are substrate choice and surface width design. In addition, the use of more sections is a promising method of increasing the bandwidth further. The author considers that, based on the measured performance, such an antenna design is a viable option in applicatio ns where tunable antennas are needed.
59 Chapter 4: Varactor Development and Characterization 4.1 Introduction to BST Devices Whenever conditions change in either a ci rcuit itself or the applic ation of a circuit, the need arises to somehow dynamically adjust circuit parameters to accommodate the changing demand. If the circuit cannot adapt itself to the new conditions, device performance will suffer or fail completely; th e benefits of dynamic circuitry are many, which may include, smaller size, increased si gnal strength, low costs, and increased energy savings , . In addition to ot her technologies, Barium Strontium Titanate (BST), or (Bax, Srx-1)TiO3, has been examined for this use for over 30 years  and in increasing measure in recent years , . BST is a family of ferroelectric/paraelectric materials whose associated dielectric consta nt(s) are tunable with applied voltage. This field-dependent permittivity ma kes BST an attractive choice for microwave devices, since dielectric propertie s are often critical aspects of such electrically-large systems. Dynamic phase shifters, filters, matching networks, and antennas are all among the devices that have been re-designe d to work successfully with BST.
60 Typically, the fundamental tunable co mponents in these devices are varactors (or tunable capacitors) , since capacitance is di rectly related to dielectric permittivity and changing capacitance results in a changing capac itive phase shift, which is useful in many of these devices. For this work, the principle concern of the varactor design process was to develop varactors that were suited for integration in to the tunable antenna design described in Chapters 3 and 4. This dictates that the va ractors must be low loss and highly tunable. They also need to possess low capacitance values in the range of 0.1 to 5 pF. The following sections will give a highlevel explanation of the theory, a description of the development/implementation process, and a brief discussion of the measured performance. 4.1.1 BST Materi al Properties Summary BST is a high-permittivity dielectri c material that has complex properties and mechanisms. The purpose of this section (4.1.1 ) is to provide a highlevel explanation of the dielectric, tunability, and loss mechanisms of BST materials, since these properties directly relate to the basic performance of varactors in antenna systems. The author recommends Damjanovic et. al.  for a detailed explana tion of the relevant material principles. Dielectric materials are characterized by a tendency to form electric dipoles in response to the presence of an electric field . The degree to which the structures in the film are Â“willingÂ” to form these dipol es (to be polarized, in other words), is characterized by the electroni c polarizability constant e ( is general polarizability, e is
61 the polarizability of a neutral atom), which is directly proportional to the magnitude of the relative permittivity, or r , ; the electronic polar izability and the relative permittivity are related through equation (4-1), where N is the number of molecules per unit volume and 0 is the permittivity of free space. 01 e rN (4-1) The relative permittivity is defined as the ratio of charge stored on two parallel conductive plates with the di electric between, over the ch arge stored without the dielectric between. This value, mu ltiplied by the permittivity of free space, 0, comprises the real part of the complex permittivity, or Â’. The imaginary part, Â’Â’, is directly proportional to the loss tangent (tan ) of the material. The real permittivity and the loss tangent are often used to express the char acter of a microwave material . The molecular structure and mechanics of the material determines these two important electrical parameters. BST is a perovskite structure, and this family of materials is identified by the chemical form ABO3 , , . The simple cubic3 prototypical structure of this material is shown in Figure 4-1. 3 Symmetric cubic structures form in the paraelectric phase only 
62 Figure 4-1. Perovskite family cubic molecular structure. The ABO3 molecule is typically drawn with the B (Ti) molecule at the center position and the A (Ba, Sr) molecules holding the corn ers ,  as in Figure 4-1, but an alternate configuration is pres ented in , where the A molecules hold the corners and the unit cell is centered on the B molecule Both configurations are equivalent. When an external electric field is applied to the ABO3 structure, the molecular structure deforms (the B molecule shifts pos ition) and the polarization is increased, which alters the relative permittivity  by lowering the polarizability constant The application of this field and the resultant stretching causes the si ze of the lattice to increase. To compensate, regions form within the lattice that are of various uniform polarizations; these organizations of polarizations are referred to as domains and facilitate the overall lowering of energy within the latt ice , . The sum total polarization, composed of the individual dipoles in the lattice, is aligned with the applied field .
63 The dynamics of these domains in response to applied fields contribut e to the dielectric properties as much or nearly as much as does the individual mo lecular response . When domain boundaries, known as walls are free to move with a change in field strength, the polarizability (and therefore the permittivity) is increased. Practically, this is illustrated by the following scenario; as external large signal DC field strength increases, the domain boundaries (known as walls) continue to adjust and form until saturation is reached . At this point, any incoming sm all-signal AC would only affect the direction of atomic polarization, not the location of th e domains, since they are now saturated. If the large signal DC bias is removed, th en any incoming AC si gnal would additionally move the domain walls freely back and forth a nd/or freely create domains as the signal voltage would alternate around 0 volts . The decreasing domain wall mobility with increasing field strength results in the bell -shaped permittivity/loss tangent vs. voltage curve. There are two primary loss mechanisms that result from this model. First, movement of domain walls uses energy, and therefore AC signal loss is increased at 0 volts. Second, regardless of the large signal voltage, small signal voltages cause alternating molecular/atomic polar directions; switchi ng directions also requires energy, and therefore there is an inherent loss that is directly proporti onal to the polarizability in any dielectric , . An illustration of the permittivity vs. bias voltage curve is given in Figure 4-2.
64 Figure 4-2. Typical ferroelectric permittivity vs. applied voltage curve. Domain formation is not only seen upon th e application of an ex ternal field, but the effect may also be seen over temperature, particularly as it relates to the Curie temperature. The Curie temperature (Tc) is the temperature at which the film undergoes a transition between the ferroelectr ic state (below Tc) and the paraelectric state (above Tc). For microwave devices, the ambient temperature shou ld be above the Curie point, so that the film will operate in the paraelectric phase. In the ferroelectric state, the molecule s in the film are asymmetric and are therefore polarized regardless of whether there is an external applied field or not (spontaneous polarization) ,  ; as noted above, this mech anism also causes the formation of domains within the lattice (as do external electric fiel ds) because of the spontaneous polarization. In the paraelectric phase, th e material has no natural polarization and assumes the symmetric cubic structure shown in Figure 4-1. The primary consequence is
65 that a ferroelectric film will maintain its stre tched shape after the external field has been removed (known as hysterisis); a paraelectric film will return to its natural unit cell structure. In summary, the primary differe nce between a ferroelectric film and a paraelectric film is that for a ferroelectric film, domains and polari zation exist without an applied field, and, for an ideal paraelectric film, domain s and polarizations exist only with an applied field , . The chemical notation for BST is given as (Bax, Srx-1)TiO3, where x is less than or equal to 1. BaTiO3 (x=1) also works well as a tunabl e dielectric material, and for many years was the primary material for this use, but the Curie temperature for this formulation is roughly 110C-130C ,  which can vary widely depending on whether the film is bulk or thin. Consequently, BaTiO3 is not suitable for use for most microwave system applications where switching between permittivity states must be based on a direct relationship between bias voltage and permittivity. For this reason, Strontium (Sr) is included in BST; the addition of Sr lowe rs the Curie temperature significantly ,  so that the formulation is paraelectric at typical room/device operating temperatures.
66 4.1.2 BST Varactor Configurations Summary While there are many variations, there are two primary BST thin-film varactor configurations: parallel plate and interdigital. The parallel plate varactor , , [1 3],  is often used to characterize BST films since the application of the standard capacitance equation is straightforward for this configuration. Therefore, it is easy to extract the relative permittivity of the film once the capacitance is known. These capacitors typically take on a vari ation similar to that shown in Figure 4-3. Figure 4-3. Typical parallel plat e varactor concep t drawing. From Figure 4-3, it is evident that the field lines w ill originate from the signal line, penetrate the BST and into the bottom electrode in the immediate area of the signal line.
67 The capacitive active region area is equal to the area of the si gnal line. The advantages of this configuration are straightforward mate rial properties extraction and low control voltages. The disadvantages are complicated fabrication, dominant electrode loss , and high capacitance values. The second type of varactor configurat ion is the interdigital design , , . Interdigital capacitors derive their name from the fact that the capacitor layout appears as several interlocking fingers, as shown in Figure 4-4. Figure 4-4. Typical interd igital varactor configur ation concept drawing. The field lines run between adjacent fingers, penetrating both the air on top and the dielectric thin-film material (BST) beneat h. Since the permittivity of the BST is significantly higher than that of the air, the e ffective dielectric constant will be closer to that of the BST, and the majority of the fields will concentrate in the thin-film dielectric. The advantage of the interdigital configuration is that it is easier to construct, since it requires only one metal layer. The disadvantage of the interdigital configurations is that they suffer from reduced tunability and high operating voltages, since the distance between the fingers is subject to phot olithographic restric tions , .
68 4.2 Series Gap Capacitor Design 4.2.1 Design Overview The chosen device confi guration (series gap capacitor) is similar to an interdigital capacitor in that the dielectri c lies beneath the conductive surface, and the capacitance is between a gap in the metal surface. However, the device cannot be strictly referred to as interdigital, since fingers are not necessarily included. Also, in the case of this design, the gap can be as small as 200 nm, and is not subject to stan dard photolithographic restrictions. A non-tunable version of this design (w ithout BST) was first presented by T. Ketterl et. al. . The design of  consisted of a co-planar waveguide structure whose signal line contained a capacitive series gap positioned perpendicular to the direction of signal travel. This slit, measuring between 200800 nm wide and 45 um long, introduced a series capacitance into the signal line. In the design of this work, the series gap was positioned above a ~150-200 nm f ilm of BST; the addition of the BST layer caused the design to be capacitance-tunable. Focused ion beam milling was used to pattern the series gap (refer to section 4.3.3 for an overview of FIB milling). The depth of this slit was critical, since the depth could only reach to the bottom of the conductive metal and not intrude into the BST layer; otherwise, tunabi lity would have been compromised. The high dielectric constant of the BST film (~300), ensu red that a high percen tage of the electric field would concentrate within the film belo w the slit, not the air on top and inside the gap. This configuration is illustrated in Figure 4-5 below.
69 Figure 4-5. FIB milled BST Series Gap Capacitor configuration. Capacitance values for this device w ithout BST underneath were reported by  to be between 8 and 11 fF. This translates into approximately .18 fF/um to .24 fF/um. With the introduction of the BST layer underneath the silt, this figure becomes dependent upon the material composition of the BST. Estimations for the capacitance/unit length after the addition of the BST were approximately .20 fF/um at high bias and .82 fF/um at 0 volt bias. 4.2.2 Design Method Four sample groups were fabricated for the purpose of experimenting with different parameters of the series gap capacitor design. Specifically BST pattern (confining the BST region to under the cut only or to the w hole wafer surface), cut depth, and substrate choice were all examined.
70 The effects of the substrate and film composition are summarized in Sections 4.2.3 and 4.2.4, whereas cut depth is addressed in Sections 4.3.4 through 4.3.6. Table 4-1 gives a summary of these sample groups. Table 4-1. Summary of sample groups. Substrate Experimental Parameter BST Pattern Sample Group #1 low resistivity Si general not patterned Sample Group #2 high resistivity Si cut depth determination not patterned Sample Group #3 high resistivity Si, MgO cut depth, BST pattern, substrate patterned Sample Group #4 high resistivity Si cut depth, milling parameters, resist stripping methods patterned All of the samples within a sample gr oup were fabricated iden tically, except for group #3 which contained devices parallel processe d on both Si and MgO, in order to cross compare substrate effects. Each sample within the sample group contained TRL calibration structures and 25 i ndividual devices. A device ma p is shown in Figure 4-6; devices are named DVxy (x=row, y=co lumn, DV is short for device). Figure 4-6. Series gap cap acitor sample device map.
71 4.2.3 Substrate Choice Deposition of BST directly onto silicon substrates is typi cally not considered to be an optimal solution, since there are crystallogr aphic mismatches between the BST and the silicon, a low permittivity oxide film may fo rm between the Si/BST interface during BST sputtering, and high-resistivity silicon may loose its resistivity when subjected to high temperature . Lattice mismatch may cause mechanical stress and reduced tunability due to the crystallographic structure of the resulting BST film . However, based on measurement resu lts from Samples #2-4, BST on Si does give good dielectric tunability and loss performan ce up to 65 GHz when high resistivity Si (3000-5000 ohm-cm) is used. Measurement of Sample #1 served to show that device performance is unacceptable on low-resistiv ity Si. Other substrate choices that are considered to be optimal are LaAlO3, MgO, and Al2O3 in both the polycrystalline (Alumina) and the single crystal states (Sapphi re) , , . It is expected that performance will increase significantly for films deposited on these substrates over films deposited on HR Si. Although a sample wa s fabricated on MgO (Sample #3), the FIB milling could not be carried out due to imaging problems that were mostly likely related to the resistivity of the MgO material. This prob lem is expected to be solved in the future by improving the grounding of the sample surface. 4.2.4 Film Composition and Thickness The two primary parameters that control the microwave response of BST films are film composition and thickness.
72 Thicker films generally have better t unability and higher diel ectric constants , . In addition, thicker f ilms require higher tuning voltage s. For this device design, capacitance values are much smaller than is needed for the antenna application, and tunability is a highly valued quantity, so thicker films are the preferred choice. Film composition determines film respons e and controls tunabil ity, loss, and the Curie temperature. The Sr content in the film has a direct effect on both the dielectric constant and the Curie temperature. Both the dielectric cons tant and the Curie temperature are inversely proportionally to the Sr content  The addition of Sr to BaTiO3 lowers the Curie temperature; it has been re ported ,  that Tc drops 3.4C for every percent increase in the Sr content of the BST fi lm. For a BST composition of (Ba.5, Sr.5)TiO3, the Curie temperature is approximately -50 C, which is adequate for tunabl e devices. Although the Ba/Sr=.5/.5 ratio was used for the devices in this work, further work may be done to optimize the film for this specific application. Studies  have shown that tunability and loss tangent is maximized when the device ope rating temperature is both above and near the Curie temperature. The Ti content, as expressed by the (Ba+Sr)/Ti ratio affect s dielectric loss and tunability. Higher ratios (lower Ti content) provide better tunability, while lower ratios (higher Ti content) give better loss charac teristics/quality factors , . The Ti content is controlled by oxygen concen tration during sputte r-deposition .
73 4.2.5 Design Summary The chosen varactor design is based on th e work presented in , and is expected to provide good tuning ratios, good loss performan ce, and straightforwar d integration into tunable antenna systems. The design paramete rs and their significance are summarized in Table 4-2. These parameters are largely de termined by fabrication process methodology, and this process is detailed in Section 3.3. Table 4-2. Device design summary. Parameter Related Performance Cut Depth and Width capacitance, tunability Film Thickness capacitance, r value range, bias voltage range Film Stoichiometry dielectric loss, tunability Substrate Properties quality factor, stru ctural integrity, frequency of operation Electrode Conductivity quality factor 4.3 Device Fabrication 4.3.1 BST Deposition Approximately 100-200 nm of BST was sputter-deposited onto high resistivity (30005000 ohm-cm) Si. The composition of the BST target was (Ba.5, Sr.5)TiO3. The parameters for BST deposition were adopted from Manavalan ; here, extensive research was done in order to optimize BST sputter-deposition for numerous substrates and deposition methods. The primary parame ters of consideration in BST sputtering were the argon/oxygen gas ratio and the proce ss temperature. Both of these parameters have an effect on film crystallinity, wh ile gas pressure additionally influences stoichiometry  and therefore the critical (Ba+Sr)/Ti ratio. Increasing the process temperature has been shown  to increas e the XRD peak intensities for many crystal orientations.
74 The sputter deposition proce ss parameters used for all devices in this work are summarized in Table 4-3 below. Table 4-3. BST sputter-deposition parameters. Parameter Setting RF Power (W) 150 Ar/O2 Ratio (%) 90/10 Total Pressure (mTorr) 25 Thickness (nm) 100-200 Temperature (C) 650 The XRD spectrum for Sample #2 is gi ven in Figure 4-7. The BST <110> and <200> orientation peaks are visible. The spectrum was obtained from a film deposited on a separate wafer alongside the de vice wafer of Sample #2. Figure 4-7. XRD spectrum pl ots from sample #2.
75 4.3.2 Photolithography and Etching The general photolithographic pr ocess for the construction of the series gap capacitor device described in Section 4.2.1 is gra phically summarized in Figure 4-8. The exhaustive process flow is pr ovided in Appendix B, and is summarized in the paragraphs below. Figure 4-8. Photolithographic process illust ration for the series gap capacitor. Between step 1 and step 2, the protective oxide layer was removed through a 10:1 BOE etch. In step 3, the BST was deposited by sputter deposition, as described in Section 4.3.1. The BST was then patterned by pos itive resist lithography and a second 10:1 BOE etch in step 4, followed by negative resist patterning and subsequent thermal deposition
76 of the top metal, Au, in step 5. In steps 6 and 7, PMMA (polymethal methalcrylate) was spun on to a thickness of ~2000 angstroms, and a thin layer of Cr was deposited on top. The PMMA served to support th e Cr and separate it from the Au for later removal. The Cr was necessary for FIB milling to provide a conductive top surface to assist in beam focusing (see Section 4.3.3) . In step 9, following the FIB milling in step 8, the PMMA and the Cr was removed by an acryl st rip. This process wa s developed largely by trial and error and by synthesizing the work sp ecifically presented in  and . A finished device is shown in Figure 4-9. Figure 4-9. Finished series gap capacitor signal line showing m isaligned BST region. There are three things which should be noted carefully when fabricating these devices. First, misalignment of the BST region is not as benign as it may seem. From Figure 4-9 it can be seen that the BST region is not comple tely covering the bottom side of the signal line; a small amount of the Au signal line is in direct contact with the Si. All devices fabricated in this manner broke down (that is DC current flowed freely across the gap) upon application of ~8 Volts DC. The hypothesi s was that the Si caused the premature breakdown for the following reason: whenev er the BST region is misaligned, the breakdown voltage of the device becomes subjec t to the breakdown volta ge of the Si if
77 the breakdown voltage is lower than that of the BST. The breakdown voltage of Si depends on doping concentration, an d is lower than that of BS T in some cases , . Due to low mask dimension tolerances, avoiding this effect is practically unavoidable for the entire 5 by 5 device field; nevertheless, devices with this level of mis-alignment should not be used. Second, trace amounts of photo-resist left after the positive resist step can have a terminally adverse effect on the devices dur ing the measurement phase. It is currently held by the author that trace amounts of resi dual positive resist left after the BST etch step can cause bubbling of the Au layers upon application of voltages above ~5 Volts. This effect was seen for Sample #3 and de stroyed the device by eroding the walls of the FIB milled gap. This effect was eliminated in subsequent samples by some or all of the following steps: thinner resist was used (Shipley 1813 instead of 1827), resist was removed by MicroChem 1165 photoresist strip, and/or any further residual resist was removed through an oxygen plasma etch for 2 minutes. The plasma etch should be avoided if possible, since it has been reported that RIE etches have damaged BST films and caused reductions in tunability . Third, it was observed that the io n beam interacts with the PMMA and makes it resistant to stripping. It was experimentally determ ined that using MicroChem Acryl strip was the most effective and non-destructiv e method employed in th is work to remove the PMMA after milling. However, there is currently no known effect of residual PMMA that is detrimental to device performance.
78 4.3.3 Focused Ion Beam Milling Introduction First developed in the 1970Â’s , Fo cused Ion Beam (FIB) Milling is an emerging means for manipulation of material structur es at the nano-scale. In an FIB system, material is sputtered from a target (the sample) by a beam of highly focused impinging Gallium ions; these ion beams can be as small as 5 nm meters in width (50 angstroms), and because of the small beam area, high-pr ecision micro-machining is possible. The beam can be directed to cut in highly comp lex patterns by data files and even picture files. Researchers are continuously finding new ways to apply this high-potential technology; in fact, one resear cher recently used focused ion beam milling to construct a nano-wire jungle gym on top of a human hair . Common applications include destructive device testing, modi fication, mask repair , sample preparation , and MEMS fabrication. The mechanics of a typical ion beam sy stem are similar to that of a scanning electron microscope, or SEM . In an SEM, an electron source scans an electron beam across the surface of the sample and a secondary el ectron detector receives the electrons coming off of the sample; the microscope generates an image from the incoming electrons. In an ion beam, a liquid metal ion source (LMIS) s upplies a stream of fo cused Ga+ ions by way of a complex lens-focusing system and finally through a thin tungsten needle . When the accelerated Ga+ ions strike the surface of the sample, secondary electrons, secondary ions, and neutral molecules are re moved from the surface . It should be noted that the term secondary refers to the pa rticles that are removed from the material as a result of the impinging beam. This pr ocess is illustrated in Figure 4-10.
79 Figure 4-10. Illustration of the Focused Ion Beam milling system. Instead of moving in a continuous scan, the beam makes a series of successive hits, analogous to making a line with a hole punch. These hits are sometimes referred to as pixels. The beam raster scans along the cut pa ttern until the desired depth is achieved. The raster scan process is la rgely controlled by the user, primarily through the following parameters: dwell time, z-size, % overlap/pi tch, and beam current. Dwell time is the length of time that the beam spends per pixe l, percent overlap/pitch is the degree to which each hit overlaps the pr eceding hit (also expressed by th e term pitchsee Figure 4-11), beam current is the strength of the ion beam (higher beam current results in faster milling and larger hit diameter ), and z-size is the desired cut depth.
80 The width of each pixel is also determin ed by focusing; this concept is intuitive, since if the beam is focused on a point 5 inches below the sample, then it follows that the beam incident on the sample surface will be wider than it would at the focus point. The raster scan pattern for a single pixel wide slit is illustrated in Figure 4-11. Figure 4-11. Illustration of beam raster s canning and the relationship between pitch and percent overlap. As the particles are re moved from the surface of the samp le, a current is generated in the sample that flows to ground. The magnitude of this current is di rectly proportional to the beam current and loosely related to the sput ter yield of the material being removed, so if the current flowing to ground (or abso rbed current) is measured, then a rough evaluation of sputtering yield ca n be obtained . This techni que is discussed in detail in Section 4.3.5, and is referred to as End Point Detection (EPD), or End Point Monitor (EPM). Focused Ion Beams can also be used to deposit certain metals, such as Pt . The simple explanation for this process is the following: the metal to be deposited is carried by various gases from the gas injector (see Fi gure 4-10) to the surface of the sample and the Ga+ ion beam forces the metal to th e surface in the desired pattern .
81 It is also necessary that the sample is coated with a thin layer (~50 angstroms) of conductive material to neutralize the sample surface. Otherwise, a strong charge will develop on the surface and will repel the ion b eam, resulting in poor beam focusing . Since for this application it was criti cal that the beam not enter the BST layer, a milling procedure was developed to stop the beam at the interface between the gold and the BST layers. 4.3.4 Focused Ion Beam Milling Methodology General FIB milling parameter settings ar e summarized in Table 4-4. The majority of these parameters were determined experime ntally and the experimental process is discussed in Section 4.3.5. Table 4-4. Milling parameter summary. Parameter Setting Effect Comments Z-size varied milling depth value dependent upon desired cut depth Dwell Time 1 usec unknown value used for all devices Overlap 0%, 50% trench roughness 50% was used to reduce residue inside trench Length ~60 um length of trench trench traversed entire width of signal line with excess for this length Beam Current .3, 3 nA milling time, spot size beam current must be increased to at least 3 nA for 50% overlapÂ—minimum system requirements may also vary depending on various milling conditions The primary difficulty with the FIB/BS T capacitor fabrication was the task of cutting a trench to a depth that completely cut th rough the metal and did not cut into the BST. For single layer compositions, the cut dept h (or z-size) for FIB milling is governed adequately by material-characterization data. When the user enters the desired cut depth (z-size), the software uses the characterizati on data to determine the optimal cutting time to achieve this depth, based on the user-specified milling parameters (e.g., % overlap,
82 dwell time, etc.). For multilayer devices, th is basic approach is largely invalid, since each different material has different propert ies, specifically density/sputter yield and stopping power . The following two methods were explor ed to determine the proper cut depth: method (a), cross-sectional metrology and method (b), end point current m onitor data. Although their use was not explored in this work, software such as SRIM and TRIM have been developed to model the ion-solid interactions for complex materials , and may also be useful for this application. The success of each cut was judged through a combination of passing DC current across the gap (to dete rmine whether the gold had been severed completely) and making RF measurements to de termine the tunability (and therefore the integrity) of the BST film. In the event that a cut comes just short of penetrating the Au layer, experiments have shown the remain ing metal can be removed by passing 30-50 mA of current through the semi-open slit. Method (a), cross sectional metrology, was accomplished by using the FIB to create several slits of different cut depths, deposit a thin strip of platinum perpendicular to the slits, and use the FIB to create a deep hol e that traversed each slit and dissected the platinum strip (see Figures 4-12 and 4-13). The purpose of the deep hole was to open a cross-sectional viewing area; th e floor of the hole was deepes t at the cross-sectional wall and sloped up toward the viewing location. The sloped floor was created to minimize milling time. The deposited Pt filled in th e slits so that the depth could be more accurately judged from th e cross-section view.
83 Figure 4-12. Top down schem atic view of the cross-sectional depth experiment. Figure 4-13. Top-down SEM image of the crosssectional destructive test setup. This picture was taken from Sample #1, where the BST covered the entire surface of the wafer. After the structure of Figure 4-13 was milled, the sample was rotated in such a way that the wall of the deep hole that containe d the cross-sections of the cuts could be viewed.
84 When the microscope was oriented a nd zoomed correctly, the cross sections of each cut could be viewed with great detail as well as the individual layers of the multi-layer structure (see Figure 4-14). Figure 4-14. Cross-sectional ion-beam image of a FIB milled slit in the signal line. Note the pencil-like shape of the FIB cu t profile; the point of the tip is the focus point of the beam. The shape/slope of this cut pr ofile varies depending on beam focusing and layer thickness, and can cause the variation in cut width be tween the top of the cut and the bottom of the cut to be as much as 300%4. In Figure 4-14, it appears as though the cut penetrated the BST layer. As noted previously, the appropria te cut depth should reach the top of or slightly above the BST layer. U nder method (a), once the ideal depth has been determined, this value would be entered into the z-size parameter of the milling software and used for all devices on the sample. 4 Value was estimated by extrapolation and is subject to variation and error. Minimum beam spot size is generally ~5 nm.
85 This method is ineffective by itself to provide a means of repeat able cut depth, since the thickness of each individual layer (parti cularly the PMMA) varies between place to place on the wafer and between different sample s. However, when used in conjunction with the use of end-point curre nt detection data (EPD), it is an effective technique. Method (b) makes use of end-point curren t detection data to de termine in-situ the cut depth of the beam scan. This method was pr oven in experiments to be a repeatable method of determining cut depth both in this work and by Latif et. al . End-point detection monitors changes in sample curren t as material is removed from the sample surface. When particles are removed from the sa mple, they either are re-deposited on the sample surface or they disappear from the samp le altogether; in either case, neutralization current must flow from the sample to ground. The general equation for determining sample current based on particle remova l is given by (4-2) below , where Isample is the total current measured by a current me ter between the sample and ground, Ibeam is the ion beam current from the source, ISeis the current due to th e departure of secondary electrons (or other nega tive charges), and ISi+ is the current due to the departure of secondary positively charged ions. Si Se beam sampleI I I I (4-2) The sample current due to re-deposited particles is illustrated by Figure 4-15.
86 Figure 4-15. EPD process illustration. Refer to (4-2) for mathematical characterization. From Figure 4-15, the sample current flow is generated by ch arges appearing through re-deposition on the surface of the sample. The net surface charge is a result of secondary ions, secondary electrons, and Ga+ ions fr om the source. Based on Figure 4-15 and the model derived from (4-2), the sample curr ent should be directly proportional to the sputtering yield of the layer being milled at any instant in time. This is a true but simplistic view, since the sample current at one milling layer is also expected to be dependent upon certain ion-solid interactions such as backscattering and implantation  that may have occurred during the milli ng of preceding layers. Specifically, in the case of backscattering, when an incident ion strikes the surface of the sample, the energy
87 can either be returned to the incident ion (in the case of non-elastic interaction), causing backscattering and re-deposition or be transferred to the sample molecules (in the case of elastic interaction), causing secondary ion a nd electron generation. Upon arrival at the sample surface, the ion may also implant into the material, where its excursion into the material depends upon the stopping power of the material . To summarize, the relationship between sample current and material properties is complex and multifaceted. The author recommends  for a full treatment of this topic. Figure 4-16 shows a sample EPD graph for a C r-PMMA-Au-BST-Si structure. The graph contains multiple phases which are asso ciated with different materials in the multilayer structure. The depth of this cut extended well into the Si region. Figure 4-16. Sample EPD gra ph showing milling time vs. absorbed current. Numbers indicate different regions in the multilayer structure. 4.3.5 Depth Optimization Experiments Using End Point Detection Upon inspection of the graph in Figure 4-16, the initial hypothe sis considered region 1-3 to be the Cr layer, region 4 to be the PMMA region, region 5 to be the Au layer, and
88 region 6 to be the BST/Si areas. Region 7 is i nvalid since, this drop in current was created during beam shutoff. This hypothesis assume d a direct correlation between increased sample current and material conductivity. The first test on this hypothesis wa s to fabricate a device (Sample #2, device 22) where the beam shutoff time reached the maxi mum of phase 5. After milling, 15 volts DC was applied across the slit and some current flowed initia lly, but quickly went to zero within seconds. This indicated that some me tal was left, but was burned off with current; this would seem to corrobor ate the initial hypothesis. The second test on this hypothesis was to fabricate a set of sa mples with patterned BST regions (the BST region was confined to the area in the vicinity of the capacitive slit) and compare the EPD data with and without the BST region. Several lines were cut across the portion of the signal line lying di rectly over top the BST region and several lines were cut across the portion of the signal line lying directly over the Si substrate. Both the cross-sectional images and the EPD data were obtained for both types of lines. Figure 4-17 shows the top down view of these lines after milling. The edge of the BST region can be clearly seen; it appears as a ra ised section of metal. The EPD graphs for these lines are shown in Figure 4-18.
89 Figure 4-17. Top down SEM im age of test lines and cross se ctional viewing region. The edge of the BST region is indi cated with an arrow; lines 5-7 are located over the BST region and line 4 is locat ed outside the region. Figure 4-18. EPD data graphs for lines 4-7.
90 The relationship between the graph of 4 and the graph of 5 is of critical importance. From Figure 4-18, it is appare nt that the stopping time of line 4 lay outside of the BST region whereas the stopping time of line 5 was in side the region. Both lines were milled with a z-size setting of 3 um. Notice that region/phase 5 was missing from the graph of line 4. The conclusion from this finding was th at phase 5 must have resulted from the presence of a BST layer; this conclusion contradicts the initia l hypothesis. The new hypothesis was that phase 1 was the Cr, pha se 2 was the PMMA, phase 3 was the Au, phase 5 was related to the BS T layer, and phase 6 was asso ciated with the Si layer. However, there is insufficient evidence to sugge st that phase 5 direc tly indicates that the milling depth is at the BST during phase 5. La tif  suggests that the interpretation of the EPD data from insulators is not always straightforward, as it generally is with conductors. Possible explanations for the increase of sputtering yield in the vicinity of the BST layer could be (a) interaction between the Si and BST during the sputtering of the BST thin-film , (b) stray impurities lodged in the interf ace between the BST and the gold layers , and (c) accumulated Ga+ ions inside the BST film from previous elastic ion interactions in previously milled layers. The drop in sample current at phase 4 appears to representative of an interfa ce effect, most likely between Au and BST. From Figure 4-18, the stopping times of lines 6 and 7 were located inside the BST region. Line 6 clearly did not reach the bottom of the gold layer, and perhaps not even the PMMA layer. The EPD graph of line 6 shows that the milling stopped at the peak of phase 3. It is assumed that phase 3 is the Au layer, since phase 1 is most likely associated with the Cr layer.
91 Based on this comparison, the new hypothesis was that phase 3 was Au and phase 5 was BST. Under this method, it was assumed that the proper milling time for optimal cut depth would be in phase 4, and therefore li ne 7 was created; the EPD data for line 7 indicated that milling was terminated at th e end of phase 4 (see Figure 4-18). The cross sectional image for line 7 is shown below in Figure 4-19. The location of the BST layer can clearly be seen from Figur e 4-19 right, since the edge of the pattern is apparent on both the surface and the cross section. Figure 4-19. Cross sectional ion-beam images of lines 7 and 6 (lef t), and lines 5 and 4 (right). From Figure 4-19, although it is difficult to discern, the cut depth of line 7 did not penetrate the BST layer. The cut of line 5 either fully or partially penetrated the BST layer. DC measurement of a line with similar EPD data to that of line 7 indicated irreparable conductivity (the metal could not be removed through amperage) across the gap. An alternate theory that also agrees w ith the data is that the insulating materials (with the exception of Si) resulted in higher net sample current th an did the conductors. Under
92 this theory, the initial high sample current in phase 1 would have to be due to an ambient grown oxide on the surface of the Cr. This would make phase 2 the Cr, phase 3 the PMMA, phase 4 the Au, and phase 5 the BST. Since for both theories, phase 4 was supposed to correspond to the optimal stop time for milling, a theory was developed for why the gap remained conductive. Upon close examination of lines 4, 5, and 7 from Fi gure 4-19, the bottom surface of the trench appeared rough, with the topology varying signi ficantly over the length of the cut. The hypothesis was that this effect resulted from an interaction between beam focus depth and the 0% overlap setting. It was supposed that a 50 percent overlap would yield an overall cleaner cut, and thereby create a smoother tr ench floor yielding in turn better depth precision. Figure 4-20 gives a comparison be tween two lines with similar EPD (milling terminated in phase 4), but with different ove rlap settings. It shoul d be noted that the milling software required that a higher beam current be used for the 50% setting (3 nA).
93 Figure 4-20. SEM image comparing two trenches with a 0% overlap setting (left) and a 50% overlap setting (right). It is evident from Figure 4-20 that th e 50% overlap setting yiel ded both a cleaner and narrower cut. The general effect on the initial conductivity across the gap was that the cut depth (via milling time) could be moved slightly closer to phase 4 from phase 5 without causing irrepa rable shorting. 4.3.6 Discussion and Summary of Milling Procedures The following conclusions may be made from the results of Sections 4.3.4 and 4.3.5: First, ion beam excursion must be limited to the top of the BST layer. Single material characterization files are not applicable fo r depth control in mu ltilayer structures. Second, cross sectional metrology is ineffective by itself as a repeatable method of depth control. When used in combination wi th end-point detection data (EPD) it is a powerful means to examine th e quality of FIB trenches.
94 Third, EPD can be effectively used to determine in-situ the progress of the beam into the multilayer structure. EPD current may be lin ked loosely with material sputter yield, but ion scattering/re-deposition and implantation effects must all be considered. Different phases in the EPD data were identified and r oughly associated with different material layers in multilayer structur e. Through DC and RF measur ement, the optimal cut depth (as expressed by EPD data, not z-size) was determined. The % overlap setting mildly affected the optimal cut depth. Fourth, it is not known whether phase 5 was directly associated with the bulk of the BST layer. Fifth, the optimal cut depth was achiev ed when milling time reached the top of phase 5 for 0% overlap, and approximately halfwa y between phase 4 and 5 for 50% overlap. Following this guideline, working capacitors can be constructed on a generally consistent basis. The milling time regions and their re sults with respect to EPD phases are summarized in Figure 4-21.
95 Figure 4-21. EPD approximate region analys is summary. No experimental data was collected for phases 1 and 2. 4.4 Device Characterization 4.4.1 Measurement Setup and Device Properties S-parameter measurements of the series gap capacitors were made using an Anritsu 37397C Lightning network analyzer, an Ag ilent E3620A DC bias supply, NIST MultiCal software, and two GGB 150 micron pitch gr ound-signal-ground 67A -GSG-150-P probes. A 1.5k-ohm resistor was placed in the bias line to prevent high short-circuit current levels from damaging the probes or the bias tees. Sample #4, device 12 was chosen to be the object of the char acterization study, since it exhibited the best tunability and structur al integrity (i.e., lo w DC conductance across the gap/high breakdown voltage). A SEM image of this device is shown in Figure 4-22.
96 Figure 4-22. SEM im age of sample #4, device 12. The series gap in this device was cut using the 50% beam overlap setting and was cut at the far/top edge of the 50% optimal regi on extension area. DC measurements indicated that there was no trace of gold left after the m illing, so it was expected that some of, but a minimal amount of the BST was milled. The EPD graph for this device is shown below in Figure 4-23. Figure 4-23. Device 12 end-point detection graph.
97 4.4.2 Calibration Separate S-parameter measurements we re made using both TRL (thru-reflect-line) and probe-tip SOLT calibrations. The motivation for using the additional probe-tip calibration was to prevent an observed phase/impedance sh ift from occurring outside of the reference planes due to the application of bias acr oss the CPW line. The change in waveguide propagation due to the application of bias wa s experimentally related to Silicon-specific effects. While it was possible to perform sepa rate calibrations at each bias point, this approach necessarily forced one side of th e CPW line to a bias c ondition not included in the calibration (since during calib ration the waveguide had to be uniformly biased at all ports). The calibrated frequency range wa s 40 MHz to 65 GHz for the TRL calibration and 40MHz to 20 GHz for the probe-tip calibration. The TRL calibration wa s designed with five CPW dela y lines, a CPW 0-length THRU line, and a CPW 0-length open line. The delay line lengths along with the CPW dimensions are given in Table 4-5. Table 4-5. TRL calibration delay li ne lengths and CPW dimensions. Line # Length CPW Gap W Ground Plane W Signal Line W Delay 1 0.7 mm 27 um200 um45 um Delay 2 0.95 mm 27 um200 um45 um Delay 3 1.6 mm 27 um200 um45 um Delay 4 2.2 mm 27 um200 um45 um Delay 5 3.8 mm 27 um200 um45 um The TRL calibration using all four dela y lines was only successful when the standards were situated above a BST/Si structure. Calibration with all delay lines was not successful when the lines were placed direc tly on the HR Si substrate (in the case of Samples #3 and #4). The cause of this probl em is not known. Instead calibration was
98 performed using delay line #4, which gave ad equate phase coverage across the frequency range of interest. The probe-tip calibration was co nducted using a GGB CS-5 SOLT calibration substrate. 4.4.3 Measurement and Characterization The following two sets of measurement data are presented below: S-parameter data obtained to 65 GHz using a TR L calibration and S-paramete r data obtained to 20 GHz using a probe-tip calibration. Approximate seri es capacitance data wa s extracted from the TRL calibrated S-parameter data usi ng an equivalent pi network. Figure 4-24 below shows the S21 data obtained using a TRL calibration and at bias voltages 0, 1, 3, 5, 10, 15 and 25 volts. Figur e 4-25 shows the S11 data for this device obtained with a TRL calibration and taken over the same bias voltage range.
99 Figure 4-24. S21 TRL data for sam ple #4, devi ce 12. The top curve is for 0 volt bias and the bottom curve is for 25 volt bias. Figure 4-25. S11 TRL measurement data for sa mple #4, device 12. The top curve is for 25 volt bias and the bottom curve is for 0 volt bias. The low frequency positive S11 data for bias voltages 5, 10, and 25 volts were attributed to transmission lin e effects outside the reference planes due to the application of bias between the signal and the ground lines of the co-planar waveguide. For this reason, additional measurement data was obtai ned using a probe-tip SOLT calibration; in
100 this way, any bias-related performance ch anges would take place inside the reference planes of the calibration. Figure 4-26 below shows S21 and S11 over bias voltages 0, 1, 3, 5, 10, and 20 volts; these measurements were obtained using a probe-tip SOLT calibration to 20 GHz. Figure 4-26. S21 (left) and S 11 (right) SOLT m easurement data for sample #4, device 12. The top curve in the S21 data is 0 volt bias and the top curve in th e S11 data is 20 volt bias. The phase data obtained for both calib ration methods across the full bias range is shown in Figure 4-27. The phase difference between the calibration methods resulting from the narrower reference planes in the TRL calibration is apparent. Figure 4-27. Measured S11 phase data from sample #4, device 12. Both SOLT calibrated data and TRL calibrated data are shown.
101 Approximate series cap acitance values were extracted5 from the TRL calibrated Sparameter data using the equivalent pi network  shown in Figure 4-28. Figure 4-28. Equivalent 2-por t adm ittance pi network. The value of the series capacitance Cs was extracted from this circuit using ABCD parameters (calculated from S-parameter data ) and equations (4-3) and (4-4) , where Y3 is the complex series admittance of a two port network. B Y1 3 (4-3) )3Im(Y Cs (4-4) The result of (4-4) was plotted over a fr equency range between 40 MHz and 65 GHz at bias voltages 0 and 25 volts. These results are shown in Figure 4-29. The numerical results of the extraction are tabulated in Table 4-6. 5 Evelyn Benabe, University of South Florida
102 Figure 4-29. Extracted series capacitance (Cs) vs. frequency at bias voltages 0 and 25 volts. Table 4-6. Extracted Cs values over frequency. 1 GHz 3 GHz 5 GHz 10 GHz 20 GHz 60 GHz 0 Volts 84.7 fF 49.8 fF35.2 fF22.9 fF16.7 fF13.2 fF 25 Volts 6.4 fF 8.3 fF9.05 fF9.8 fF10.3 fF10.8 fF Ratio 13.2 18.104.22.168.2 4.4.4 Summary S-parameter data was taken at freq uencies between 40 MHz and 65 GHz. There were no resonant points observed acro ss this frequency range. TRL calibration caused slightly inaccurate measurement results since the applic ation of bias along th e line affected signal propagation and this effect occurred outside of the meas urement reference planes. A
103 probe-tip calibration was conduc ted to move the effect inside the reference planes. Approximate series capacitance values ranged from 6.4 fF to 84.7 fF and were heavily frequency dependent. 4.5 Chapter Summary BST devices are useful for microwave sy stems, such as the antenna developed in this work, that need to dynamically adjust ope rating parameters to conform to changing environments. The chapter above outlines the development of a device that has the potential to deliver high tunability, lo w loss, and planar integration. The permittivity characteristics of BST are governed by the changing molecular/lattice structure of the BST upon applied bias. This feature of the BST leads to bias-dependent permittivity and loss characteristics. Focused ion beam milling was used to create series gaps in the signal line of a coplanar waveguide. Significant experimental work was conducted to optimize the cut depth so that the integrity of the BST thin -film layer would not be compromised. Endpoint current detection proved to be a repeatable method to control the excursion of the beam into the multilayer structure. Measurements were conducted on a de vice that was fabricated using the end-point current method; approximate capacitance valu es (averaged over frequency) for this device ranged from 9 fF to 37 fF (~4:1 tuna bility). In general, devices with like EPD profiles had similar performan ce characteristics. This research lays the groundwork for future tunable devices and a deeper understanding of the performance of BST films as they relate to th e series gap capacitor
104 configuration. The constructe d configuration is appropriate for integration into the tunable antenna presented in this work, because the capacitance size can be tailored to the application by adjusting the series gap length, the design lends itself to planar integration and the devices are expected (analysis is not mature) to exhibit loss and tuning characteristics that are appropriate for antenna applications.
105 Chapter 5: Summary and Conclusions The overarching purpose of this pr oject was to realize a patch antenna whose operational bandwidth and ease of fabricati on exceeded that of other current design solutions. The antenna developed in the pages of this work fulfilled this purpose by delivering a wide operational bandwidth while maintaining straightforward integration and design. While not fundamental to the success of the design, the integrati on of the antenna with Barium Strontium Titanate varactors was cons idered to be a useful extension of the research. The varactors whose design methodol ogy and performance are described in the pages of this work are expected to in tegrate cleanly with the antenna without complicating fabrication or compromising perf ormance significantly. The possibility of integrating the BST with the antenna would simplify monolithic integration considerably, since the design of the varactor is plan ar, requiring only two photolithographic mask layers. The following section provides a high-le vel summary of the findi ngs reported in this work.
106 5.1 Summary of Findings 5.1.1 Tunable Antenna Using Semiconductor Varactors The following paragraphs are a summary of the main aspects of the antenna design process and results. Figure 5-1 shows the fi nished Fragmented Patch Antenna (FPA) with installed semiconductor varactors. Figure 5-1. Completed Fragmented Patch Antenna using semiconductor varactors. The antenna was developed through an optimization procedure. This procedure directly analyzed the parameters of the antenna including, the number of sections composing the radiating surface, the capacitanc e range of the varactors, the size of the sections, the width of the ante nna, and other design features. It was discovered through this procedur e that the antenna coul d be designed to have multiple overlapping resonant regions. This aspect could be exploited to produce an antenna with a tuning bandwidth that w ould be limited only by the input matching characteristics.
107 The outcome of the optimization pro cess was an antenna with three equal section lengths and widths, two equal capacitors (one for each gap), and an inset feed. Specific areas for improvement are antenna substrate, antenna width, the number of radiating sections, and input matching. The S-parameter and radiation patter n simulations indicated that the antenna was highly tunable, but that the ra diation patterns were significant ly altered by the modified patch antenna configuration. The S-paramete r measurements generally corroborated the simulated results. The simulated radiation patterns were largely distorted from typical patch antenna patterns due to the effects of surface waves and substrate loss. The measured radiation patterns indicated that the f undamental resonant mode of the antenna operated similarly to that of a standard patch antenna. The s econd resonance mode was loosely linked to a higher order patch antenna mode. The radiati on pattern measurements indicated that the radiation characteristics had retained enough pattern integr ity to make the antenna a viable solution. Because the antenna exhibited excellent tunability with usable radiation patterns, it is a recommended design configuration for situa tions where a wide bandwidth antenna is needed.
108 5.1.2 Barium Strontium Titanate Nano-Scale Varactors Focused Ion Beam milling is a micro-machining tool that can be effectively used to mill nano-scale structures on the surf ace of a wafer. Focused Ion Beam milling was used to create a capacitive series gap in the signal line of a co-planar waveguide structure situated over a thin layer of BST. End-point current detection was used to en sure that the beam did not cut into the critical BST layer, but still severed the conductive layer of the waveguide. A repeatable procedure was developed to accomplish this task accurately. Series capacitance data extracted from the measured S-parameter data indicated that the developed capacitors had good es timated tunability (~4:1) performance. The capacitance is fundamentally a function of the length of the slit. By varying the length of the slit, a custom capacitance value may be obtained. Specific areas for improvement are substrate choice, BST deposition optimization, beam cut width, and furt her ion-solid interaction modeling using software such as SRIM or TRIM. 5.2 Recommendation for Future Work The development of the antenna and the BST varactor provides a starting place for future research and development. Specifically, the advanced fabrication and characterization of the BST varactor, the integr ation of the BST varactor with the antenna and the development of non-linear transmission lines are three possible extensions of this research.
109 5.2.1 Advanced BST Varactor Fabrication and Characterization Since the performance of the BST series ga p capacitors is largely not understood, additional work is necessary to adequate ly model the device characteristics using equivalent circuit models. In addition, th e application of E-beam lithography to gap milling and the use of a protective layer of Silicon Carbide (SiC) over the BST as a method of FIB cut-depth control are r ecommended areas for future study. 5.2.2 Integrated Fragmented Patch Antenna The integration of the developed antenna and the BST varactor is straightforward. The following paragraphs summarize the proposed desi gn. This design is illustrated in Figure 5-2. An integrated FPA would be fabricated on a substrate appropriate for both BST growth and antenna performance (such as high resistivity Silicon, Sapphire, or Alumina). This substrate would be mounted on a base substrate containing a coaxialmicrostrip feed line transition. The micro-strip feedline would be wirebonded to the substrat e carrying the FPA and the varactors. The top substrate would be a conductive FPA pattern with the desired varactor locations situated over a thin layer of BST. Focused ion beam milling would be used to create slits in the antenna surface directly over the BST regions. The lengt h of the FIB cut would depend on the desired capacitance value.
110 Figure 5-2. Concept drawing of the integrated FP A design. 5.2.3 Non-Linear Transmission Lines The BST varactors can also be used effectively in non-linear transmission lines. Nonlinear transmission lines are used for pulse-shaping and square pulse re storation in digital communication systems . Nonlinear transmission lines consist of a transmission line loaded with variable shunt capacitance. With this configuration, a large signal propagating down the transmission line would bi as the varactors. Different portions of the signal would bias the vara ctors differently (each part of an AC signal has a different instantaneous magnitude) and would theref ore encounter a different capacitance. BST is a useful tool for this purpos e, since its capacitive volta ge relationship is nonlinear and symmetric and therefore can be ma nipulated through biasing to achieve the desired response. The nano-scale aspect of the varactors developed in this work yield low control voltages, which leads to a stronger non-linear response for low-level RF signals.
111 5.3 Overall Conclusion Both an effective antenna and a novel varact or solution have been developed. One of the most attractive aspects of the antenna conf iguration is its design flexibility. There are many parameters that are open to further opt imization and modification to meet specific design requirements. The varactor design and characterizat ion is still largely une xplored and immature. However, the groundwork for future has been laid through the fundamental research given both in this work and by Ketterl et. al.  through the provi sion of a repeatable fabrication process and the basic theory n ecessary for further performance analysis.
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118 Appendix A: MathCAD Transmi ssion Line Phase Analysis6 Z3 is the input impedance of the middle transmission line terminated in load impedance Z2, Z3L2C2 L3 f ()Zo Z2C2L3 f ()jZo tan2 f L2 c ZojZ2C2L3 f () tan2 f L2 c 6 Mathematical construction by T. Weller and comment s by S. Baylis, University of South Florida The three-section antenna is modeled as thr ee transmission line sections interconnected by ideal capacitors. The following equations (1) establish the refere nce impedance Zo, (2) the phase velocity c, and (3) the input impedance of the system. Note: If the phase velocity c is said to be 3*10^11, then the speed of light has been converted into mm/s and the relative dielectric constant of the substrate is assumed to be 1 (air dielectric). Zo50 c 31011 Z2 is the input impedance of the series combi nation of the 3rd transmission line section and the 2nd capacitor, Z1L3f ()j Zo cot2 f L3 c Starting from the side of the system furthest fr om the excitation point and working toward the input, Z1 is the input impedance of the 3rd ( numbered starting from excitation port side) transmission line section, Z2C2L3 f () 1 j2 f C2 1012 Z1L3f () and Z4 is the input impedance of the series comb ination of the 1st capacitor (the one closest to the excitation point) and impedance Z3. Z4C1L2 C2 L3 f () 1 j2 f C1 1012 Z3L2C2 L3 f ()
119 Appendix A: (Continued) Finally, the input impedance of t he whole system is the input im pedance of the transmission line closest to the excitation point terminated in load impedance Z4. ZinL1C1 L2 C2 L3 f ()Zo Z4C1L2 C2 L3 f ()jZo tan2 f L1 c ZojZ4C1L2 C2 L3 f () tan2 f L1 c The reflection coefficient (or S11) is calculated using the standard equation assuming port impedance to be equal to the characteristic impedance of the system S11L1C1 L2 C2 L3 f () ZinL1C1 L2 C2 L3 f ()Zo ZinL1C1 L2 C2 L3 f ()Zo We have now established the S-parameter/impedan ce characteristics of the system. The S11 equation will be called by other functions lower in the program. ----------------------------------------------------------------------------------------Below is a test to determine the electrical lengt h of a line at a given frequency and physical length Ltest. ----------------------------------------------------------------------------------------Ltest3 0 f2.510 9 1f ()2 f Ltest c 180 12.5109 90 1f ()90
120 Appendix A: (Continued) The objective of this section is to determine the tunable bandwidth for a given combination of frequency, capacitance range, and line lengths. It should be noted here that Fsteps prescribes the number of sampling points between the frequencies fmax and fmin. f represents the index value of the instantaneous frequency freq(f). Csteps prescribes the number of sampling points between the capacitances C1max and C1min. C represents the index value of the instantaneous capacitance cap1(C). C2 scale determines the value of C2 based on the present value of C1 (e.g., C2=C1*Cscale). The equations below set the range for the 1st capacitor (the one closest to the excitation port) and the definition of the instantaneous value for the first capacitor. C1max2. 1 C1min. 7 cap1C()C1min C1maxC1min Csteps C The array plot 1 is defined so that it calls the function S11 to fill its array positions. The array positions are defined by the index values of C and f. plot1Cf argS11L1cap1C () L2 cap1C()C2scale L3 freqf ()109 18 0 The array plot1 is modified so that if the value in any given position is less than 20, then it is changed to a '1'. If the value is otherwise then that position is filled with a '0'. plot1Cf 1plot1Cf 20 if 0otherwise fsteps2 0 Csteps2 0 C2scale1 fmax5. 7 fmin 3 L11 6 L21 6 L31 6 freqf()fmin fmaxfmin fsteps f f 0fsteps C 0Csteps
121 Appendix A: (Continued) BW is a figure of merit that describes the numbe r of times that a 1 appears in the plot1 matrix. BWCfplot1C f BW=36 Figure A-1. Array plot1 vs. capac itance and frequency. The x-axis is the scaled frequency range (fsteps), the y-axis is the scaled capaci tor value range (Csteps), and the z-value is 1 or 0 depending on whether there is a phase cr ossing or not (respectively) for the given value of Csteps and fsteps. plot1
122 Appendix B: BST Series Gap Capacitor Process Flow I. BST Deposition by Sputtering A. Chamber pump-down 1. Roughing pump-down to 10^-2 Torr. 2. Cryo pump-down to 10^-6 Torr B. BST Deposition 1. Clean Sample Acetone/Methanol 2. Set Deposition Conditions a. Substrate Temperature: 650 degrees Celsius b. RF Power: 150 W c. Total Pressure: 25 mTorr d. Ar/O2 Ratio: 90/10 (percentage) 3. Deposit to thickness of 100-150 nm II. BST Photolithography and Etch clean mask with Acetone/Methanol Rinse, N2 dry A. Static Dispense 1. Eye-drop HMDS (liberally cover entire sample) 2. Spin HMDS 3500 RPM, 30 seconds no ramp specified 3. Eye-drop positive photo resist SC1813 (thinner than SC1827, used formerly) 4. Spin PR 3000 RPM, 30 seconds no ramp specified 5. Soft bakeÂ—Hot Plate, 90 degrees Celsius, 90 seconds B. Exposure and Develop 1. First Exposure: Cover DUT area with black paper strip and expose calibration structure region only. 2. Expose 20 seconds. 3. Second Exposure: Use mask to expose BST region under the area covered by the exposure in step #1. 4. Expose, 20 sec 5. Develop in MF319 developer for 60 seconds 6. DI rinse/N2 dry 7. Microscope inspect image definition C. BST Etch 1. 10:1 BOE 8:00 2. DI water/N2 rinse 3. Microscope inspect image definition D. Photoresist Removal 1. 1165 strip; 80 deg Celsius for ~20 minutes 2. Oxygen O2 Plasma etch; ~2 minutes, 150 Watts
123 Appendix B: (Continued) III. Top Metal Negative Photolithography clean mask and sample with Acetone/Methanol Rinse, N2 dry A. Static Dispense 1. Eye-drop negative photo-resist 3000PY 2. Spin 3000 RPM, 3 second ramp, 40 seconds 3. Soft bakeÂ—Hot Plate, 155 degrees Celsius, 60 seconds 4. Begin cooling hot plate to 110 degrees B. Exposure and Develop 1. Align Mask with BST layer alignment CPW markings 2. Expose, 17 sec 3. Hard BakeÂ—Hot Plate, 110 degrees Celsius, 60 sec 4. Develop in RD6 developer for 28-30 seconds 5. DI rinse/N2 dry C. Microscope inspect image definition IV. Top Metal Deposition (Cr/Au 4000 angstroms)7 A. Chamber pump-down 1. Roughing pump-down to 75 mTorr cross-over pressure 2. Diffusion pump-down to 4 uT B. Thermal Evaporation Cr/Au to thickness of 50/4000 angstroms C. Chamber pump-down D. Photoresist removal 1. Liftoff in approximately 300 ml of Acetone until metal coated resist is gone (1 to 24 hours). See alternate steps below. 2. RR4 strip: ~20 minutes at 110 degrees Celsius follow with optional step #3. 3. Oxygen O2 Plasma etch: ~2 minutes V. PMMA (Polymethal methalcrylat e) Deposition (2000 angstroms) 1. Static Dispense HMDSÂ—liberally cover entire sample 2. Spin Dry HMDSÂ—3500 RPM, 30 seconds 3. Use 950 PMMA A4 Photoresist 4. Static Dispense: 3-4 drops, 10 seconds 5. Spin: 4000 RPM, high accell, 45 seconds 6. Bake: 180 degrees Celsius for 90 sec VI. Chrome Deposition (60 Angstroms) (ThermalÂ—same procedure as IV) VII. FIB Milling VIII. Removal of PMMA and Cr layers with MicroChem Acryl strip 7 T. Ketterl, University of South Florida