Investigation of carbon nanotube properties and applications at microwave and THz frequenciesкод для вставкиСкачать
INVESTIGATION OF CARBON NANOTUBE PROPERTIES AND APPLICATIONS AT MICROWAVE AND THZ FREQUENCIES by Lu Wang ______________________ A Dissertation Submitted to the Faculty of the DEPARTMENT OF PHYSICS In Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY IN PHYSICS at the UNIVERSITY OF ARIZONA 2010 UMI Number: 3404686 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. UMI 3404686 Copyright 2010 by ProQuest LLC. All rights reserved. This edition of the work is protected against unauthorized copying under Title 17, United States Code. ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI 48106-1346 2 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE As members of the Dissertation Committee, we certify that we have read the dissertation prepared by Lu Wang entitled Investigation of Carbon Nanotube Properties and Applications at Microwave and THz Frequencies and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy. _______________________________________________________________________ Date: 01/21/2010 Hao Xin, Ph. D. _______________________________________________________________________ Date: 01/21/2010 Ke Chiang Hsieh, Ph. D. _______________________________________________________________________ Date: 01/21/2010 Brian Leroy, Ph. D. _______________________________________________________________________ Date: 01/21/2010 Fulvio Melia, Ph. D. _______________________________________________________________________ Date: 01/21/2010 Michael Shupe, Ph. D. Final approval and acceptance of this dissertation is contingent upon the candidate’s submission of the final copies of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement. ________________________________________________ Date: 01/21/2010 Dissertation Director: Hao Xin, Ph. D. 3 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED: _____Lu Wang________ 4 ACKNOWLEDGEMENT I would like to thank my advisor Dr. Hao Xin for his guidance, advice, insight, and support throughout this dissertation work, which have been crucial to the success of the work. I am very grateful to have the opportunity working with him. I would also like to thank all the dissertation committee members for reading the dissertation and all the support they offered. I owe many thanks to Ziran Wu for his great effort on THz measurements, to Binh Duong and Dr. Supapan Seraphin of Material Science and Engineering Department for their wonderful collaborations in carbon nanotube growth and characterizations, to Dr. Liwei Chen at Suzhou Institute of Nano-Tech and Nano-Bionics in China and Yao Xiong at Ohio University for their wonderful collaborations in the carbon nanotube purification project, to Jiamin Xue, Dr. Yitian Peng, and Tremaine Powell for their assistance on equipment operation, to Dr. Olli Nordman and Dr. Brooke Beam for their technical support, to TC Chen for the helpful discussion, and to Dr. Bowden from Arizona Cancer Center for offering us the access to their probe sonicator. I also wish to thank all the members in the mmW Antennas and Circuits group. I am forever indebted to my mother Zhuying Wang, my grandma Guirong Zhang, and the rest of my family for the constant love they have been giving to me over the course of my life. Without their support, this work would not have been possible. I am also deeply grateful for the understanding and encouragement from my dear friends Marten, Jon, Keqian, Pick Chung, David, Hua, Chuan, and all other ISFers. 5 TABLE OF CONTENTS LIST OF FIGURES ............................................................................................................ 7 LIST OF TABLES ............................................................................................................ 12 ABSTRACT ...................................................................................................................... 13 CHAPTER 1. INTRODUCTION ............................................................................ 15 1.1. BACKGROUND........................................................................................................ 15 1.1.1. Basic Background ........................................................................................ 15 1.1.2. Applications ................................................................................................. 23 1.2. MOTIVATION.......................................................................................................... 25 1.3. DISSERTATION ORGANIZATION .............................................................................. 29 CHAPTER 2. CVD GROWTH OF CARON NANOTUBE .................................... 32 2.1. CVD PROCESS OF CARBON NANOTUBE GROWTH.................................................. 32 2.2. EXPERIMENTAL PROCEDURE .................................................................................. 35 2.2.1. Catalyst Preparation ..................................................................................... 35 22.214.171.124. Plain Catalyst Preparation ................................................................. 35 126.96.36.199. Patterned Catalyst Preparation .......................................................... 36 2.2.2. Growth Conditions ....................................................................................... 38 2.3. MICROSCOPIC CHARACTERIZATION OF GROWN CNTS .......................................... 39 2.3.1. Introduction to CNT Characterization Methods .......................................... 39 2.3.2. Instruments for CNT Characterization......................................................... 40 2.3.3. Background of Raman Spectroscopy ........................................................... 41 188.8.131.52. RBM .................................................................................................... 43 184.108.40.206. G-band ................................................................................................ 44 2.4. RESULTS AND DISCUSSION..................................................................................... 45 2.4.1. Effects of Substrates .................................................................................... 45 2.4.2. Effect of Methane Flow ............................................................................... 47 2.5. CONCLUSION.......................................................................................................... 53 CHAPTER 3. POTENTIAL MICROWAVE-INDUCED SWNT SEPARATION TECHNIQUE ........................................................................................................... 55 3.1. MOTIVATION.......................................................................................................... 55 3.2. POTENTIAL SELECTIVE BREAKDOWN SCHEME ...................................................... 57 3.3. SAMPLE PREPARATION .......................................................................................... 59 3.4. EXPERIMENTAL SETUP ........................................................................................... 61 3.5. RESULTS AND DISCUSSION..................................................................................... 62 3.5.1. THz Power Transmission Measurement ...................................................... 63 3.5.2. Raman Spectroscopy Analysis..................................................................... 67 3.5.3. Discussion on Possible Underlying Physics of the Observed Effects ......... 77 3.6. CONCLUSION AND FUTURE WORK ......................................................................... 78 6 TABLE OF CONTENTS - Continued CHAPTER 4. MICROWAVE (8-50 GHZ) CHARACTERIZATION OF MWNT PAPERS ........................................................................................................... 82 4.1. INTRODUCTION ...................................................................................................... 82 4.2. MULTI-WALLED CARBON NANOTUBE PAPER SAMPLE .......................................... 87 4.3. EXPERIMENTAL SETUP AND MEASURED S-PARAMETER DATA .............................. 87 4.4. COMPLEX PERMITTIVITY AND PERMEABILITY EXTRACTION .................................. 90 4.4.1. Scattering Parameters................................................................................... 90 4.4.2. Nicolson-Ross-Weir Method ....................................................................... 92 4.4.3. Extracted Complex Permittivity and Permeability ...................................... 96 4.5. EXTRACTION VERIFICATION BY FINITE-ELEMENT SIMULATION ............................ 98 4.6. SYSTEMATIC ERROR ANALYSIS OF THE CHARACTERIZATION METHOD ............... 100 4.7. INTRINSIC PROPERTIES OF MWNTS..................................................................... 104 4.8. CONCLUSION........................................................................................................ 106 CHAPTER 5. THZ CHARACTERIZATION OF MWNT PAPER  .............. 108 5.1. MOTIVATION........................................................................................................ 108 5.2. SAMPLE AND EXPERIMENTAL SETUP ................................................................... 109 5.3. MEASURED REFLECTION AND TRANSMISSION DATA IN TIME DOMAIN AND FREQUENCY DOMAIN .................................................................................................... 111 5.4. MATERIAL PROPERTY EXTRACTION .................................................................... 113 5.5. DRUDE-LORENTZ MODEL FITTING OF EXTRACTED PERMITTIVITY ...................... 119 5.6. DISCUSSION ......................................................................................................... 120 5.7. CONCLUSION........................................................................................................ 123 CHAPTER 6. INDIVIDUAL CARBON NANOTUBE CHARACTERIZATION ................................................................................................ 125 6.1. INTRODUCTION .................................................................................................... 125 6.2. TEST FIXTURE DESIGN ......................................................................................... 128 6.2.1. RF model of CNT ...................................................................................... 128 6.2.2. Impact of Port Impedance and Parasitics on CNT Measurement .............. 132 6.2.3. Designs of CNT Test Fixtures ................................................................... 139 6.3. RF CALIBRATION ALGORITHM ............................................................................ 148 6.4. MICRO-CIRCUIT FABRICATION ............................................................................ 156 6.4.1. Grids Fabrication ....................................................................................... 157 6.4.2. CNT Dispersion, Deposition and Localization .......................................... 160 6.4.3. Testing Circuit Fabrication ........................................................................ 161 6.5. CONCLUSION........................................................................................................ 163 CHAPTER 7. CONCLUSION AND FUTURE WORKS ..................................... 165 APPENDIX: PERMISSIONS......................................................................................... 172 REFERENCES ............................................................................................................... 184 7 LIST OF FIGURES Figure 1-1. The structures of carbon nanotubes. (a) The definition of the chiral vector Ch on the honeycomb lattice of carbon atoms of a graphene sheet; and the schematic models of (b) an armchair carbon nanotube; (c) a zigzag carbon nanotube; (d) a chiral carbon nanotube. ........................................................................................................................... 18 Figure 1-2. Electronic properties of SWNT species predicted by the tight binding model. Reprinted with permission from . Copyright (1992), American Institute of Physics. . 18 Figure 1-3. Calculated density of states for (a) (10, 0) zigzag SWNT, and (b) (9, 0) zigzag SWNT. The dotted lines are the density of states for graphene. The sharp peaks are vHs singularities. Reprinted with permission from . Copyright (1992), American Institute of Physics. ......................................................................................................................... 19 Figure 1-4. Transmission line model for a SWNT  .................................................... 22 Figure 1-5. Schematic of a top-gated CNT-FET. Reprinted with permission from . Copyright (2001), the American Physical Society. .......................................................... 24 Figure 2-1. (a) Schematic and (b) photo of the in-house CVD system............................. 33 Figure 2-2. Patterned catalyst is prepared using standard electron beam lithography procedure. (a) PMMA spin coating; (b) Patterned electron beam exposure; (c) Develop; (d) Catalyst deposition; (d) Lift off. .................................................................................. 37 Figure 2-3. CNTs grown on patterned catalyst. SEM images of (a) a patterned array, and CNTs grown on a single 4 µm x 4 µm square on (b) a Si substrate, and (c) a quartz substrate. ........................................................................................................................... 38 Figure 2-4. (a) Raman spectra of isolated SWNTs (metallic and semiconducting); (b) Gband feature of a highly oriented pyrolytic graphite (HOPG), a semiconducting SWNT and a metallic SWNT; (c) RBM and G-band spectra of SWNT species (15, 8), (17, 3), and (15, 2). Reprinted with permission from . Copyright (2005), Elsevier. .............. 41 Figure 2-5. Calculated energy separation between vHs singularities Eii (i denotes for ith vHs singulary) vs. SWNT diameters (Kataura plot). Stars (MOD0): metallic. Open (MOD1) and filled (MOD2) circles: semiconducting. MOD denotes for the reminder of 2n+m divided by 3. Reprinted with permission from . Copyright (2005), Elsevier... 42 Figure 2-6. SEM image of CNTs on Si substrate at methane flow rate of (a) 300 cc/min, (b) 500 cc/min, (c) 600 cc/min, and (d) 700 cc/min; and on quartz substrate at methane flow rate of (e) 300 cc/min, (f) 500 cc/min, (g) 600 cc/min, and (h) 700 cc/min. ............ 46 Figure 2-7. TEM image of (a) bundles of DWNTs, (b) individual and bundled SWNTs, and (c) MWNTs. ............................................................................................................... 48 Figure 2-8. (a) SEM image and (b) Raman spectra of CNTs grown on a Si substrate with the CH4 flow rate at 700 cc/min........................................................................................ 49 Figure 2-9. Raman spectra (collected at 5 different positions) of CNTs grown on a Si substrate with the CH4 flow rate at (a) 300 cc/min and (b) 600 cc/min............................ 51 8 LIST OF FIGURES - Continued Figure 2-10. Raman spectrum of CNTs grown on a quartz substrate. “*” denotes the Raman signal of the quartz substrate. ............................................................................... 53 Figure 3-1. Estimation of electromagnetic-wave-induced current density in an infinitely long cylinder. .................................................................................................................... 59 Figure 3-2. Microwave-induced selective breakdown scheme. ........................................ 59 Figure 3-3. (a) AFM image, (b) SEM image, and (c) photo of HiPCO SWNT thin film samples.............................................................................................................................. 60 Figure 3-4. Setup for the microwave irradiation experiment. ........................................... 62 Figure 3-5. Medium interface of SWNT film samples. .................................................... 63 Figure 3-6. (a) THz transmission spectra, and (b) extracted surface conductivity of a HiPCO SWNT thin film on quartz before and after microwave irradiation of various time (up to 2430 seconds). (c) Surface conductivity (at 200 GHz, 400 GHz and 600 GHz) decreases as a function of irradiation time. ....................................................................... 65 Figure 3-7. Raman RBM band and G band spectra of HiPCO SWNT thin films on glass substrates before (solid curves) and after (dashed curves) microwave irradiation. (a) and (b) are obtained with 514-nm laser excitation; (c) and (d) are obtained with 532-nm laser excitation. .......................................................................................................................... 68 Figure 3-8. Kataura plots obtained (a) experimentally in , and (b) theoretically in . They are utilized to identify the species in the measured RBM spectra. The labeled values of 2n+m denote the SWNT electrical property. If 2n+m=3q (q=1, 2, 3…), the species are metallic; otherwise, the species are semiconducting. The solid rectangular boxes are corresponding to the 514-nm laser energy (±0.1 eV) and the dashed rectangular boxes are corresponding to the 532-nm laser energy (±0.1 eV). (a) Reprinted with permission from . Copyright (2005), Elsevier. (b) Reprinted with permission from . Copyright (2005), the American Physical Society............................................................................. 71 Figure 3-9. Raman RBM band and G band spectra of CoMoCat SWNT thin films on glass substrates before (solid curves) and after (dashed curves) microwave irradiation. (a) and (b) are obtained with 514-nm laser excitation; (c) and (d) are obtained with 532-nm laser excitation. ................................................................................................................. 76 Figure 3-10. (a) Optical microscopic image of the labeling system fabricated with PMMA; (b) AFM image of isolated HiPCO SWNTs ..................................................................... 80 Figure 3-11. Cylindrical resonator .................................................................................... 81 Figure 3-12. A gap-coupled λ/2 planar resonator achieving electric fields higher than 106 V/m at the gaps. (a) Top view; (b) Electric field magnitude on the substrate surface simulated with HFSS. ....................................................................................................... 81 Figure 4-1. Electromagnetic spectrum .............................................................................. 83 Figure 4-2. Illustration of microwave characterization method of a CNT ensemble. ...... 84 Figure 4-3. A 1-inch-diameter multi-walled carbon nanotube paper photo (left) and a 3.8µm × 2.8-µm SEM image (right) (From ). ............................................................... 87 9 LIST OF FIGURES - Continued Figure 4-4. (a) MWNT paper is sandwiched in between two waveguides. (b) The VNA experimental setup. ........................................................................................................... 88 Figure 4-5. Measured (circles) and simulated (solid lines) reflection and transmission coefficients (magnitude and phase) of a MWNT paper. The S-parameters are not continuous due to different waveguide port impedances. The simulated curves are obtained from HFSS simulation for the purpose of algorithm verification (Section 4.5). 90 Figure 4-6. (a) Voltage waves at the interfaces of a 2-port network; (b) Reference planes in the waveguide measurement. ........................................................................................ 92 Figure 4-7. Extracted real part of the index of refraction with different choices of m. .... 96 Figure 4-8. The effective medium properties of the nanotube paper extracted from the measured S-parameters: (a) ε’, (b) ε”, (c) μ’ and (d) μ”. The circled lines are the extracted values and the regions above and below them are the error bars. ..................... 97 Figure 4-9. Extracted complex index of refraction and conductivity of the nanotube paper. ........................................................................................................................................... 98 Figure 4-10. The HFSS simulation model to verify the extracted material properties. The boundaries of the waveguides and the edges of the sample slab sandwiched in the middle are set to be PEC here. ...................................................................................................... 99 Figure 4-11. Real (ε’MWNT) and imaginary (ε”MWNT) parts of the relative intrinsic permittivity of a single multi-walled carbon nanotube (MWNT) computed using the effective medium theory. ................................................................................................ 106 Figure 5-1. (a) THz-TDS transmission characterization setup; (b) THz-TDS reflection characterization setup. The incident E field is S-polarized in both measurements. ...... 110 Figure 5-2. THz-TDS measurement results of (a) the reflection pulses of the reference (dashed line) and a MWNT paper (solid line); (b) the transmission pulses of the reference (dashed line) and the MWNT paper (solid line); (c) Fourier transformed frequency domain signals: transmission reference (dash-dotted line), sample transmission (dotted line), and sample reflection (solid line), noise floor (dotted line). ................................. 112 Figure 5-3. Extracted index of refraction (dots connected with line): real part n’ (a) and imaginary part n” (b). VNA measurement results from 8 to 50 GHz are also plotted (open circles). .................................................................................................................. 116 Figure 5-4. Extracted complex permittivity and permeability: (a) µ’, (b) µ”, (c) ε’, and (d) ε”. VNA (open diamonds, from 8 to 50 GHz) and THz-TDS (open triangles, from 50 to 370 GHz) results are plotted together. The extracted real and imaginary parts of the permittivity are also fitted by a Drude-Lorentz model (solid lines in (c) and (d)). ........ 118 Figure 5-5. Field magnitude loss factor after one round trip internal reflection, calculated from the extracted MWNT paper parameters. ............................................... 122 Figure 6-1. Demonstration of the impedance mismatch and parasitic effects on highimpedance device characterization. (a) Without matching networks. Parasitic capacitance = 5 fF. (b) With input matching network (IMN) and output matching network (OMN). Parasitic capacitance = 0.05 fF. ...................................................................................... 128 10 LIST OF FIGURES - Continued Figure 6-2. Transmission line model of a metallic SWNT. (a) Geometry of a SWNT in presence of a ground plane; (b) A single-channel transmission line model; (c) A transmission line model for interacting electrons in a SWNT with four conducting channel; (d) The equivalent transmission line model for the common mode. LM is neglected in (c) and (d). ........................................................................................... 130 Figure 6-3. Equivalent circuit model of a SWNT. .......................................................... 132 Figure 6-4. (a) Coplanar waveguide; (b) GSG RF probe configuration; (c) Top view of a CPW test fixture with an individual CNT at the center with two ends buried underneath the electrodes. ................................................................................................................. 134 Figure 6-5. Equivalent circuit of the parasitics. .............................................................. 135 Figure 6-6. Schematics for S-parameter simulations (a) without and (b) with a CNT across the center gap. ...................................................................................................... 135 Figure 6-7. Simulated S-parameters without (solid lines) and with (triangles) a CNT across the center gap. No impedance matching is provided. (a) S11 magnitude in dB; (b) S21 magnitude in dB; (c) S11 phase in degree; (d) S21 phase in degree. ........................... 137 Figure 6-8. Simulated S-parameters without (solid lines) and with (triangles) a CNT across the center gap. Impedance is matched from 50 Ω to 20 kΩ. (a) S11 magnitude in dB; (b) S21 magnitude in dB; (c) S11 phase in degree; (d) S21 phase in degree. ..................... 139 Figure 6-9. Schematic of a tapered transmission line matching network. ...................... 140 Figure 6-10. Layout of the tapered transmission line test fixture (unit: μm) .................. 142 Figure 6-11. Port setting for ADS Momentum ............................................................... 142 Figure 6-12. Schematics for S-parameter simulations (a) without and (b) with a CNT equivalent circuit model across the center gap of the designed tapered-line test fixture. ......................................................................................................................................... 143 Figure 6-13. Simulated S-parameters without (solid lines) and with (triangles) a 1-μm CNT across the center gap for the designed tapered line test fixture. (a) S11 magnitude in dB; (b) S21 magnitude in dB; (c) S11 phase in degree; (d) S21 phase in degree. .............. 144 Figure 6-14. Simulated S-parameters without (solid lines) and with (triangles) a 2-μm CNT across the center gap for the designed tapered line test fixture. (a) S11 magnitude in dB; (b) S21 magnitude in dB; (c) S11 phase in degree; (d) S21 phase in degree. .............. 145 Figure 6-15. An arbitrary step-line test fixture (unit: μm) .............................................. 146 Figure 6-16. Simulated S-parameters without (solid lines) and with (triangles) a 1-μm CNT across the center gap for the arbitrary step-line test fixture. (a) S11 magnitude in dB; (b) S21 magnitude in dB; (c) S11 phase in degree; (d) S21 phase in degree. ..................... 147 Figure 6-17. The zoom-in layout of the linear tapered design with a 5 μm x 5 μm pad added at the center. ......................................................................................................... 148 Figure 6-18. Simulated S-parameters without (solid lines) and with (triangles) a 2-μm CNT across the center gap for the modified linear tapered test fixture. (a) S11 magnitude in dB; (b) S21 magnitude in dB; (c) S11 phase in degree; (d) S21 phase in degree. .......... 148 Figure 6-19. Equivalent circuit of the parasitics of a test fixture.................................... 150 11 LIST OF FIGURES - Continued Figure 6-20. Extraction z1 and z2 from the through and two isolated open standards (left and right). ........................................................................................................................ 150 Figure 6-21. Simulated S-parameters of the open standard (solid), through standard (triangles), and the test fixture with a 1-μm CNT across the center gap (circles) for the designed tapered line test fixture. (a) S11 magnitude in dB; (b) S21 magnitude in dB; (c) S11 phase in degree; (d) S21 phase in degree.................................................................... 153 Figure 6-22. Comparison between the extracted CNT S-parameters with the theoretical model............................................................................................................................... 154 Figure 6-23. Illustration of CNT testing circuit fabrication. (a) Fabricated grids; (b) Deposit and locate tubes; (c) Fabricate the testing circuit across the tube by applying the alignment technique ........................................................................................................ 156 Figure 6-24. Illustration of a typical EBL fabrication process. ...................................... 158 Figure 6-25. The grid coordinate pattern (a) Overview (not to scale); (b) An AFM image of our grids ...................................................................................................................... 159 Figure 6-26. (a) SEM image of the CNTs deposited on a Si substrate with 0.75 ml dispersed CNT solution; (b) AFM image of the CNTs deposited on a quartz substrate with 0.45 ml dispersed CNT solution. ............................................................................ 161 Figure 6-27. Optical microscopic image of a fabricated testing fixture by following the described procedure. ....................................................................................................... 163 12 LIST OF TABLES Table 3-1. Possible species assignment for HiPCO .......................................................... 72 Table 3-2. Possible species assignment for CoMoCat ...................................................... 73 Table 3-3. Comparison of the calculated M11-to-S33 ratios before and after microwave irradiation for the HiPCO film sample.............................................................................. 74 Table 4-1. Summary of Reported Carbon Nanotube Paper Measurements ...................... 85 Table 4-2. Uncertainties of S-parameters ....................................................................... 101 Table 5-1. Fitting Parameters for Drude Lorentz Model ................................................ 120 Table 6-1. A 50-Ω CPW geometries and the associated parasitics ................................ 134 Table 6-2. Fitted equivalent circuit component values ................................................... 156 13 ABSTRACT This dissertation presents research on synthesis, high-power microwave postsynthetic purification and high frequency characterization of Carbon Nanotubes (CNT). First, CNTs are synthesized using a Chemical Vapor Deposition system. The impact of substrate and methane flow rate on CNT growth is studied using Scanning Electron Microscopy, Transmission Electron Microscopy and Raman microscopy. Second, the microwave irradiation effects on purified HiPCO and CoMoCat Single-Walled CNT thin films are investigated. The measured drastic THz power transmission increase (>10 times) indicates a significant metallic content reduction after the irradiation. The Raman spectra also confirm the metallic-to-semiconducting ratio of Raman-active CNTs decreases by up to 33.3%. The observed microwave-induced effects may potentially lead to a convenient scheme for CNT demetalization. Third, Multi-Walled CNT papers are characterized from 8 to 50 GHz by rectangular waveguide measurements using a vector network analyzer. A rigorous algorithm is developed to extract the samples’ effective complex permittivity and permeability from the measured S-parameters. Unlike other reported work, this method does not impose the unity permeability assumption. The algorithm is verified by finite-element simulations and the uncertainties for the characterization method are analyzed. The effective medium theory is then applied to obtain the intrinsic CNT properties. Furthermore, Terahertz Time-Domain Spectroscopy is used to characterize the samples from 50 to 370 GHz. Both transmission and reflection experiments are 14 performed to simultaneously extract the permittivity and permeability. The extracted permittivity is fitted with a Drude-Lorentz model from 8 to 370 GHz. Finally, individual CNT characterizations at microwave frequency are studied. The impacts from impedance mismatching and parasitics on measurement sensitivity are systematically studied, revealing that the parasitic effect is possibly dominant above 10 GHz. A tapered coplanar waveguide test fixture is designed using Advanced Design System (ADS) to improve the impedance mismatching and minimize the test fixture parasitics, therefore optimize the measurement sensitivity. A de-embedding procedure to obtain the CNT’s intrinsic electrical properties is presented and demonstrated with ADS simulations. In addition, the test fixture fabrication process is discussed, which is an ongoing research work. At the end, the conclusions of this dissertation are drawn and possible future works are discussed. 15 CHAPTER 1. INTRODUCTION Since being discovered in 1991 by Iijima at NEC laboratory , carbon nanotubes have stimulated extensive research interests in virtue of their unique mechanical, electrical, and field emission properties. In this chapter, a brief review of carbon nanotubes, including their structure, electrical properties and potential applications, will be presented. Then the motivation of this work will be discussed followed by the dissertation organization. 1.1. Background 1.1.1. Basic Background Carbon nanotubes are seamless tubular nanostructures formed from graphene sheets. A carbon nanotube may be single-walled if the tube has only one-atom-thick layer, or multi-walled if the tube consists of more than one layer of graphene sheets. Single-walled carbon nanotubes (SWNT) have remarkable electronic properties. Depending on its geometrical characteristics including diameter and chirality, a SWNT can be either metallic or semiconducting, which was theoretically predicted in 1992  and experimentally confirmed in 1998 . The structure of any SWNT can be represented by the chiral vector Ch = na1+ ma2 to denote its circumference and the 1-D translation vector T, as shown in Figure 1-1 (a), where Ch connects two crystallographically equivalent sites on the honey comb lattice of a graphene sheet, a1 and 16 a2 are the unit vectors of the lattice, and T is determined by connecting point O and the first lattice point that the normal of Ch meets. The unit cell of the 1-D lattice is defined by Ch and T. Each pair of (n, m) uniquely identifies one nanotube species. Based on the specific combinations of the integer pair, SWNTs are classified into three categories . When n = m, the nanotubes are called armchair nanotubes as indicated by the shape of the circumference as shown in Figure 1-1 (b). All nanotubes of this type are metallic. When m = 0, zigzag nanotubes are obtained as shown in Figure 1-1 (c). All the other species are called chiral nanotubes (Figure 1-1 (d)). Shown in Figure 1-1(a), the chiral angle θ of each species is defined with reference to the chiral vector of zigzag nanotubes. With (n, m) being specified, the diameter and chiral angle of a SWNT are determined by  dt = 3a n 2 + m 2 + nm (1.1) θ = sin −1 ( 3m / (2 n 2 + m 2 + nm )) (1.2) π where a = 0.142 nm is the Carbon-Carbon bond length. Due to the unique band structure of an isolated graphene sheet, the electronic properties of a SWNT appear to be very sensitive to its geometric characteristics. Calculated with the tight binding model, a graphene sheet is a semiconductor with a zero band gap. Its bonding and anti-bonding π bands are degenerate at the K point in the Brillouin zone . When a graphene sheet is rolled up to form a carbon nanotube, the periodic boundary conditions are imposed that only a certain group of k vectors are allowed. If the allowed k vectors include the degenerate point K, the formed carbon nanotube is likely to be metallic. Therefore, when (n, m) satisfies the condition of 17 n – m = 3q (q is an integer), (1.3) which is obtained by applying the boundary condition to the k vector at the degenerate K point , the species are metallic. Therefore, as shown in Figure 1-2, about 1/3 of SWNT species are metallic, and the rest of them are semiconducting. From Eq. (1.3), all armchair SWNTs are metallic. Strictly speaking, the band gaps for the species with n - m = 3q (q≠0) are not exactly zero, but very tiny. This is due to the SWNT’s curvature effects . However, this effect can be neglected especially when the diameters of the tubes are large since the band gap is inversely proportional to the tube diameter . Figure 1-3 shows examples of the calculated density of states of a metallic and a semiconducting zigzag SWNT. One can see that the metallic tube has a non-zero DOS at the Fermi level, while the semiconducting tube has a zero DOS. The sharp peaks in DOS are van Hove singularities (vHs), which are very important features. The transition of electrons between the vHs coupled with SWNT’s transverse acoustic vibrational modes leads to Raman radial breathing mode (RBM) and will be discussed in more details in Chapter 2. 18 (c) (a) O (d) θ (b) Figure 1-1. The structures of carbon nanotubes. (a) The definition of the chiral vector Ch on the honeycomb lattice of carbon atoms of a graphene sheet; and the schematic models of (b) an armchair carbon nanotube; (c) a zigzag carbon nanotube; (d) a chiral carbon nanotube. Figure 1-2. Electronic properties of SWNT species predicted by the tight binding model. Reprinted with permission from . Copyright (1992), American Institute of Physics. 19 Figure 1-3. Calculated density of states for (a) (10, 0) zigzag SWNT, and (b) (9, 0) zigzag SWNT. The dotted lines are the density of states for graphene. The sharp peaks are vHs singularities. Reprinted with permission from . Copyright (1992), American Institute of Physics. Defects or deformations on a carbon nanotube may affect its electronic properties to different extents. For example, a pentagon-heptagon defect or a bend in a tube would not affect the conductance dramatically [8, 9]. However, a twisting may introduce a band gap for an armchair metallic tube . In addition, the inter-tube interaction in a nanotube bundle can possibly lead to a pseudo band gap due to the broken-symmetry . A carbon nanotube is considered as a prototype 1-D system, in which the interacting electrons are known as a Luttinger Liquid (LL). The electron transport in 20 SWNTs shows fascinating phenomena. Ballistic conduction is observed in metallic SWNTs with nearly transparent electrical contact , which indicates a scattering-free transport and no heat is dissipated. The measured conductance is 2G0=4e2/h (G0: quantum conductance) due to the existence of two conduction channels. However, with high-resistance (larger than the quantum resistance) contacts, Coulomb Blockade behavior appears, that is, the blocking of current is observed before the bias voltage is high enough to provide the required charging energy (EC) to add a single electron to a nanotube. This effect dominates at low temperature (kT < EC) . At high temperature, Luttinger Liquid behavior of nanotubes manifests due to the tunneling effect from 3-D electrodes to a 1-D carbon nanotube. Different from the tunneling into a Fermi Liquid, which is energy-independent, the tunneling amplitude of an electron into a 1-D Luttinger Liquid follows a power law in the electron energy. As a result, the conductance shows a power law dependence on temperature (at low bias, eV << kT) or on bias voltage (at high bias eV >> kT) . Therefore, the electron transport in a SWNT is highly dependent on the tube-electrode contact properties. The ballistic transport of metallic SWNTs leads to a mean free path of at least 1µm. However, for semiconducting SWNTs, the mean free path is around three orders of magnitude shorter . Multi-walled carbon nanotube (MWNT), as mentioned earlier, have several layers coaxially arranged with an interlayer spacing of around 0.34 nm . Due to the complexity of the structure and different interaction among the layers, the band structure of MWNTs may be modified significantly. However, since the electrodes only have contact with the outmost layer, the electron transport is to a great extent confined to the 21 outmost layer. Most of the MWNTs produced by arc-discharge process have the outer diameter on the order of 20 nm . Even for a semiconducting SWNT with this diameter, the resulting band gap is small (around 44 meV) . If the outer layer is semiconducting with large band gap and the electrons need to penetrate through until reaching the first layer of metallic tube, a large contact resistance will be expected. However, experimentally, high-resistance contacts are found to be rare (~10%) . Ballistic transport is observed in MWNT as well by applying a liquid metal contact . This 1-D system of interacting electrons (Luttinger Liquid) has not only been explored at DC, but also stimulated many research interests at high frequencies. A transmission line model of a SWNT was first proposed by Bockrath  and also presented by P. J. Burke in 2002 . Considering a SWNT with a diameter d placed a distance h from the ground plane, this typical transmission line configuration can be modeled with the circuit model shown in Figure 1-4 if only considering one conduction channel. In this model, CE is the electrostatic capacitance; CQ is the quantum capacitance, which counts for the energy needed to add an extra electron to a 1-D system; LM is the magnetic inductance; LK is the kinetic inductance, which is calculated from the energy increase of the system to generate a finite current and has a much higher (4 orders of magnitude) value than LM for a SWNT. If only taking CQ into consideration, the model is essentially describing a 1-D system with no electron interactions. The phase velocity of such a transmission line is equal to the Fermi velocity (vF) of a carbon nanotube. If taking CE into account, the electron-electron interaction is included and the wave velocity is higher than vF. The ratio between these two wave velocities is defined as the g factor, 22 which has a value smaller than 1 and is an indicator of electron interaction strength. From a finite-length transmission line measurement with 1-D plasmons excited by a microwave signal generator, the g factor can be characterized . Since a SWNT has two conduction channels and each of them includes spin up and spin down, the complete model has four transmission lines in parallel with interactions with each other. If the damping due to the electron scattering in the tube and the imperfect grounding are counted, additional distributed resistance should be included in the model. LM LK CQ CE Figure 1-4. Transmission line model for a SWNT  In addition to their remarkable electronic properties, carbon nanotubes are also found to be one of the strongest materials. Their Young’s modulus is found to be ~1.5 TPa, which is comparable to that of diamond, and about one order higher than that of steel or tungsten . Their nano-scale radius of curvature, excellent electrical conductivity together with the merit of mechanical stiffness, also makes CNTs good field emitters . 23 1.1.2. Applications In virtue of their unique mechanical, electrical and field emission properties, various applications of carbon nanotubes have been proposed, such as field emission displays , microscope tips , fuel cells  and many nano-electronic applications . The extremely small diameter and high carrier mobility of CNTs suggest their great potential in nano-electronic devices such as CNT field effect transistors (FET) , nanoantennas , and nano-interconnects , etc. CNT-FETs exhibit many notable qualities and appear to be very competitive among future transistor technologies. Compared to Si metal–oxide–semiconductor fieldeffect transistors (MOSFET), CNT-FETs show higher transconductance and higher drive current capabilities by about four times . The great performance of CNT-FETs is usually obtained by fabricating Ti electrodes as the top contacts followed by thermal annealing process, which leads to the formation of TiC to reduce the contact resistance dramatically and provide a very good coupling between the CNT and electrodes . Although most of the early reported CNT-FETs are back-gated, it has been found that the transconductance of FETs can be dramatically improved (~ 10 times) with a top-gated configuration as shown in Figure 1-5. The threshold voltage is lowered by one order in magnitude as well . It is interesting that CNT-FETs are actually ambipolar even though they were believed to be p-type initially . Since the adsorbed O2 can affect the Schottky barriers at the contacts and cause Fermi level pinning near the valence band maximum, CNT-FETs prepared in air always appear to be p-type. Annealing the device in vacuum can turn it into n-type eventually via ambipolar intermediate states . To 24 optimize device performance, CNT arrays can be used instead of single tube. However, screening effect from neighbor tubes may reduce the current per CNT . Figure 1-5. Schematic of a top-gated CNT-FET. Reprinted with permission from . Copyright (2001), the American Physical Society. CNTs are also considered as a candidate for nano-interconnects in very-largescale integration (VLSI) circuits, which may address the imminent challenges that copper interconnects face. The surface and grain boundary scattering in copper traces with lateral dimensions below 40 nm lead to a rapid resistivity increase. The remarkable electrical properties, and great power and thermal performance of CNTs stimulated much research effort on CNT electromagnetic modeling, integration processing and contact resistance reducing . Recently, many microwave (3x108 Hz to 3x1011 Hz) and THz (3x1011 Hz to 3x1012 Hz) applications have been suggested as well . Nougaret et al. demonstrated a back-gated CNT-FET using highly purified semiconducting SWNTs with current gain cut-off frequency fT up to 80 GHz . Ideally, a much higher cutoff frequency up to 8 THz may even be achieved when parasitics are negligible . Sazonova et al. demonstrated a tunable CNT electromechanical resonator in RF mixer configuration . 25 Hanson calculated the CNT dipole antenna characteristics via a semi-classical approach, which is valid through THz frequencies . Since the wave velocity in CNT is about 100 times smaller than the free-space wavelength [19, 25], a CNT antenna may resonate at much lower frequency compared to a copper wire with the same dimensions. For instance, according to the semi-classical model, a 10-µm long armchair (m = 40) SWNT dipole antenna would resonate at 160 GHz while a 10-µm copper dipole is expected to resonate at 7500 GHz. This theoretically predicted 1-D Plasmon resonance cuts off below the relaxation frequency (~53 GHz). However, the efficiency of this nano-antenna is very low due to its high ohmic loss. Recently, it was reported that the CNT antenna efficiency can be improved dramatically by using bundles instead . 1.2. Motivation Although tremendous research effort has been invested in the CNT research at DC, low frequencies, and optical frequencies, over the microwave and THz regime, carbon nanotubes’ electrical properties have not yet been well studied. This frequency range is also often referred to as the radio frequency (RF), which is a more general term and covers the frequencies from 3x102 Hz to 3x1012 Hz. Numerous military and commercial applications are located in this portion of spectrum, such as radio communications, radar system, Global Positioning Satellite (GPS), wireless communications, etc. The remarkable electrical properties of CNTs make them very attractive for RF applications 26 as discussed previously. To advance the development in this field, the RF characterization of CNTs is indispensible. The most intuitive method to study the microwave properties of carbon nanotubes is to characterize individual tubes. However, it is very challenging to conduct this kind of measurements due to nanotubes’ high intrinsic impedance (~10 KΩ to MΩ), which is incompatible with typical 50-Ω microwave testing equipment. As a result, most of the signal is reflected, thus the transmitted signal is buried under the noise floor, leading to a large measurement uncertainty. For instance, the value of the transmission coefficient when measuring a 100-KΩ device is expected to be -60 dB (0.001), the associated systematic uncertainty of the phase measurement at this signal level could be as large as ±10.8° at 2 GHz , which may lead to a significant error in CNT property extraction. In addition, at microwave frequencies, parasitics of testing structures often dominate over the intrinsic properties of carbon-nanotube devices under test . Assuming a small parasitic capacitance of 5 fF (5x10-15 F) exists across the input and output of the test fixture, the difference in the reflection and transmission coefficients at 2 GHz for a 100KΩ device and a 200-KΩ device are only 0.0005 and 0.00006 respectively. These differences are too small to detect, therefore it is impossible to extract the device property from the measurement. To overcome these difficulties, appropriate impedance matching can be applied to address the high impedance issue. For instance, if the 50-Ω port impedance is matched up to 10 kΩ, the transmission coefficient from the 100-kΩ device would be raised up to -15.6 dB corresponding to a smaller estimated systematic phase uncertainty of ±5.6° . Therefore, the accuracy of CNT property extraction is 27 improved. In addition, at this signal level, the difference in the reflection and transmission coefficients at 2 GHz for a 100-KΩ and a 200-KΩ device are much larger (0.23 and 0.59) making the device characterization possible. At the same time, the parasitics can be reduced by employing well designed narrow electrodes for CNT testing. Furthermore, de-embedding techniques need to be applied to calibrate the parasitic impact out and obtain the intrinsic CNT properties. However, individual nanotube characterization requires complicated microelectrode fabrication with accurate alignment, which is not trivial to achieve. To avoid the difficulty in fabrication, an alternative approach is to characterize a large ensemble of nanotubes, for example, a coplanar waveguide (CPW) filled with carbon nanotubes , carbon-nanotube films -, or arrays, to obtain the relevant material properties. When a microwave signal or a THz pulse impinges upon a nanotube assembly, at the interface, part of the signal is reflected and part of it is transmitted. The magnitude and phase of the reflection and transmission depend on the sample’s electrical properties and can be measured and used to extract the complex permittivity and permeability of the assembly. To obtain the intrinsic material properties, effective medium theories can be applied to remove the impact from the air in the sample. Since the measured responses from an assembly are collective signals from a huge number of carbon nanotubes, it is much larger than that of a single nanotube, thus dramatically alleviating the measurement challenges. Numerous applications of carbon nanotubes have been proposed and demonstrated as discussed in the previous section. However, most of these applications 28 preferably require nanotubes to be either purely semiconducting, or purely metallic. The heterogeneity of as-synthesized carbon nanotubes, which are always mixtures of both metallic and semiconducting species, has therefore become one of the biggest obstacles for CNTs to enter nano-scale integrated circuits. Thus far, several methods for separation of metallic and semiconducting nanotubes have been reported, based on their differences in electric conductivity, chemical reactivity, dielectric response, affinity with surfactants, density, etc. [33-35]. Nevertheless, none of the reported methods are complete solutions for applications in nano-electronics. For example, the reported selective electrical destruction method  by applying a DC current is fairly reliable but it is a serial process that requires microelectrode fabrication and sequential manipulation of each individual device, thus has limited throughput. To simplify the selective electrical destruction scheme, electromagnetic waves can be considered as an alternative to DC excitation so that the electrode fabrication and CNT-electrode contacts are no longer necessary. Due to the significant conductivity difference between metallic and semiconducting carbon nanotubes, as the electric field increase, the induced current on metallic tubes may reach the breakdown threshold much earlier while the semiconducting tubes stay intact. This might be a potential convenient scheme for microwave-induced selective breakdown of metallic nanotubes so that pure semiconducting tubes can be obtained for realizing large-scale integrated circuits. 29 1.3. Dissertation Organization The work presented in this dissertation will discuss the investigation of synthesis, potential microwave-induced post-synthetic purification and high frequency characterization of CNTs. The dissertation is organized as the followings. Chapter 2 presents the chemical vapor deposition (CVD) growth of carbon nanotube. The impact of different substrates (Si versus Quartz) and feed stock gas flow rates on CNT growth will be discussed. This is a collaborative project with Dr. Supapan Seraphin. The plain and patterned catalyst on different substrates for CNT growth is prepared by the dissertation author. The CVD experiment, and CNT characterizations and analysis are carried out by Binh Duong. The manuscript submitted to Carbon is first authored by Binh Duong. Chapter 3 describes the potential microwave-induced selective breakdown scheme. SWNT thin films are prepared from HiPCO and CoMoCat samples. The microwave irradiation effects on the films are studied by THz power transmission measurement, and Raman spectroscopy. The metallic content changes are examined both qualitatively and quantitatively. This is a collaborative project. The microwave irradiation experiments, electric field measurement, theoretical study of the induced currents on nanotubes, and the spectra analysis are performed by the dissertation author. The manuscript of this work is first authored by the dissertation author. Chapter 4 proposes a convenient characterization method for MWNT papers at microwave frequencies. A vector network analyzer (VNA) is used to measure the Sparameters of MWNT papers from 8 to 50 GHz with rectangular waveguides as test 30 fixtures. The algorithm is developed based on the Nicolson-Ross-Weir (NRW) approach to extract the material’s complex permittivity and permeability from the measured Sparameters. Numerical simulation using Ansoft HFSS  is performed to verify the extraction algorithm. The error associated with this characterization method is analyzed. The Brugmann effective medium theory is applied to remove the impact from air and extract intrinsic MWNT permittivity. Chapter 5 reports a time-domain characterization method at THz frequencies for MWNT papers. Two different configurations of THz time-domain spectroscopy system are employed to measure both the transmitted and reflected pulses from the samples. The frequency-domain spectra are obtained by applying Fourier Transformation. The algorithm to simultaneously extract the complex permittivity and permeability is developed. The extracted permittivity is consistent with VNA results at microwave frequency and fitted by a Drude-Lorentz model. This is a collaborative project between Ziran Wu and the dissertation author. The VNA results are measured and analyzed by the dissertation author. The Matlab code for the Drude-Lorentz model fitting and intrinsic MWNT permittivity extraction using the effective medium theory are developed or performed by the dissertation author as well. The publications on this work,  and , are first authored by the dissertation author and Ziran Wu, respectively. Chapter 6 presents the high frequency characterization methodology of an individual CNT. First, a systematic study of the impedance mismatching and parasitic effects in individual CNT characterization at microwave frequencies is presented. Then a tapered Coplanar Waveguide (CPW) test fixture is designed using ADS Momentum  31 to optimize the measurement sensitivity. A RF de-embedding algorithm to extract the intrinsic CNT properties is presented and demonstrated with ADS simulations. At the end, the Electron Beam Lithography (EBL) fabrication procedures for CNT testing circuits are described. Finally, the conclusions and future works are discussed in Chapter 7. 32 CHAPTER 2. CVD GROWTH OF CARON NANOTUBE In this chapter, synthesis of CNTs using an in-house Chemical Vapor Deposition (CVD) system will be presented . CNTs are grown on silicon and quartz substrates using CVD process at 900°C with methane as carbon source. Synthesized CNTs are characterized by Scanning Electron Microscope (SEM), Raman spectroscopy, and Tunneling Electron Microscope (TEM). The effects of growth conditions such as substrates and methane flow rates on the distribution, morphology, internal structure and electrical properties of the nanotubes are investigated. The possible growth mechanisms are also explored. 2.1. CVD Process of Carbon Nanotube Growth Since Iijima’s observation of MWNTs at NEC Laboratory in 1991 , significant research efforts have been carried out to develop various CNT growth methods such as arc discharge , laser ablation , and chemical vapor deposition . Among these methods, chemical vapor deposition becomes commonly used due to its diameter controllability, high yield, and its ability to easily scale up to industrial production. One of the major drawbacks of this technique is that it may produce a mixture of different types of nanotubes with various sizes among many forms of carbon clusters and amorphous . Recently, different techniques have also been applied to improve the CVD process, such as the plasma enhanced CVD , High pressure CO process 33 (HiPCO) , CoMoCat process , etc., to improve the yield and controllability of CVD growth. In CVD process, an energy source is provided to first disassociate hydrocarbon molecules into active atomic carbons. The decomposed carbon atoms dissolve and diffuse into the catalyst nano-particles on the substrate and further precipitate into tubular solid structure. Shown in Figure 2-1 are a schematic and a photo of our in-house CVD system. The furnace provides the required energy source. Three types of gases are fed with controlled flow rates, among which methane is the carbon-source gas, while argon and hydrogen function are process gases. Hood Furnace Quartz Tube Flowmeter H2O (a) Flowmeter Controller Ar CH4 H2 (b) Figure 2-1. (a) Schematic and (b) photo of the in-house CVD system. There are several key parameters controlling the CNT growth process including hydrocarbon source, catalysts, growth temperature and time. It is obvious that the 34 morphology, structure, properties and type of the nanotubes are highly dependent on the hydrocarbon feedstock. Extensive studies have been reported on the role and impact of different carbon precursors on the nanotubes. Methane is found to be a great candidate to form high-purity SWNTs. Kong et al. reported on the synthesis of abundant individual SWNTs and their bundles at 900oC using methane (CH4) as carbon precursor and found almost no amorphous carbon coating around the grown CNTs . The massspectrometry study of methane under high temperature CVD growth (900oC) carried out by Franklin et al. revealed that when the decomposition of methane occurs, it does not interact with other decomposed species and undergoes the least self-pyrolysis at high temperature . The systematic study of the effect of hydrocarbon sources (methane, hexane, cyclohexane, benzene, naphthalene and anthracene) on the CNT formation in CVD process between 500-850oC reported by Li et al.  also found that methane was more chemically stable and more favorable to form high-purity SWNTs, compared to the other sources. Therefore, the tubes grown using methane source are usually of higher quality. Although many studies have shown the advantages of using methane as hydrocarbon source in CVD growth of CNTs, there is limited systematic detailed study on the effects of methane flow rate on the growth of the nanotubes in the temperature range of 900oC. Investigating the CNTs products by varying the amount of methane is thus crucial towards a better understanding of the formation and properties of nanotubes grown in the CVD process. More importantly, our ultimate goal in this study is to understand the properties of CNTs in the microwave frequency range for electronic 35 devices. For microwave testing purpose, quartz substrate is usually used due to its low loss. Although numerous studies performed on nanotubes grown on Si substrates, limited works have been reported on nanotubes grown on quartz substrate. A substrate is one of the most important aspects that can alter the unique properties of CNTs. Hence, in this chapter, CNTs grown on quartz substrates are studied in comparison to those grown on silicon substrates. 2.2. Experimental Procedure 2.2.1. Catalyst Preparation The catalyst solution is prepared by mixing 30 mg of aluminum oxide, Al2O3 (Degussa, aluminum oxide C, average particle size 14 nm), 40 mg of iron (III) nitrate nonahydrate, Fe(NO3)3·9H2O (Sigma-Aldrich) and 10 mg of Bis(acetylacetonato)dioxomolybdenum (VI) (MoO2acac2, Aldrich) in 30 ml of methanol. The solution is then thoroughly stirred for 24 hours and sonicated for at least one hour before the deposition onto the substrate. 220.127.116.11. Plain Catalyst Preparation Two types of substrates, quartz and silicon, are investigated. The silicon substrates are used without any process to remove the native oxide. Substrates are first bath sonicated in deionized water, acetone and isopropyl alcohol (IPA) to remove any contamination on the surface. A drop of the prepared catalyst suspension is deposited on each substrate. Then, the methanol in the suspension is removed by blow-drying the 36 substrates with nitrogen gas. After that, the substrates are baked on a hot plate at 150oC for 5 minutes. For the following parametric study of CNT growth, only plain catalyst is used for simplicity. 18.104.22.168. Patterned Catalyst Preparation To grow CNTs at specific positions, catalyst needs to be patterned. This may lead to a possibility of directly assembling CNTs across the pre-fabricated electrodes through CVD growth process, which would be advantageous for mass production of CNT-based circuits. The catalyst can be patterned using standard electron beam lithography (EBL) procedure. As shown in Figure 2-2, to fabricate a catalyst pattern, a bilayer of polymethyl methacrylate (PMMA) (PMMA 495 / PMMA 950) is first spin coated on the substrate sequentially and soft baked for 3 minutes after the deposition of each layer (Figure 2-2 (a)). The purpose of using the bilayer is to create an undercut to help the later metal lift off process. Then a nanometer pattern generation system (NPGS) incorporated on a commercial scanning electron microscope (SEM) is employed to write desired patterns on the substrate (Figure 2-2 (b)). The digitized areas under electron beam exposure become solvable in the mixture of Methyl isobutyl ketone (MIBK) and IPA (MIBK : IPA = 1:3) and are easily removed during the develop process ((Figure 2-2 (c)). The prepared catalyst solution is then deposited on the top and baked for 5 minutes (Figure 2-2 (d)). At last, the substrate is dipped into acetone solvent to remove the un-digitized areas, leaving the desired catalyst patterns (Figure 2-2 (e)). The SEM image of a fabricated array pattern 37 is shown in Figure 2-3 (a). The carbon nanotubes grown at a 4 μm x 4 μm catalyst island for a Si substrate and a quartz substrate are shown in Figure 2-3 (b) and (c), respectively. PMMA 950 PMMA 495 (a) Substrate e‐ e‐ e‐ e‐ e‐ (b) Substrate (c) Substrate (d) Substrate Catalyst (e) Substrate Figure 2-2. Patterned catalyst is prepared using standard electron beam lithography procedure. (a) PMMA spin coating; (b) Patterned electron beam exposure; (c) Develop; (d) Catalyst deposition; (d) Lift off. 38 Figure 2-3. CNTs grown on patterned catalyst. SEM images of (a) a patterned array, and CNTs grown on a single 4 µm x 4 µm square on (b) a Si substrate, and (c) a quartz substrate. 2.2.2. Growth Conditions To grow carbon nanotubes, the substrates are loaded into a 1-inch diameter quartz tube furnace (Lindberg blue). Argon gas is passed through the tube at the rate of 730 standard cubic centimeters per minute (cc/min) while the furnace is heated up from room temperature to 900°C. As the furnace temperature reaches 900°C, the process gas (H2) and the carbon feedstock gas (CH4) are passed through the tube. The flow rate of hydrogen is fixed at 240 cc/min, while the flow rate of carbon feedstock methane is varied with four different values (300, 500, 600 and 700 cc/min). The growth time is held constant for 15 minutes. Afterwards, as the furnace is cooled down, Ar is flown through at a rate of 730 cc/min to avoid contamination and to prevent produced CNTs from burning. The samples are taken out of the furnace for characterization after the temperature drops below 100°C. 39 2.3. Microscopic Characterization of Grown CNTs 2.3.1. Introduction to CNT Characterization Methods There are several well-known methods to characterize CNTs, including transmission electron microscopy (TEM), scanning electron microscope (SEM), atomic force spectroscopy (AFM), Raman spectroscopy analysis, and scanning tunneling microscopy (STM), etc. Each method provides different perspectives on the properties of CNTs. TEM is capable of imaging at very high resolution and provides the information on the internal structure of the CNTs. However, it is limited by the requirement on the specimen, which has to be ultra thin. SEM is compatible with various types of samples and provides good information on the morphology of CNT samples . But the SEM resolution is relatively low to identify the detailed structure of the tubes. AFM has a higher resolution than that of SEM and can provide the diameter information of CNTs. However, one of its drawbacks is the long image acquisition time. Raman spectroscopy, on the other hand, has many merits on CNT characterization. It has more flexibility on the forms of sample, at the same time, it can reveal the structural and the electrical properties of CNTs, such as species information, stress/strain state, crystal symmetry, quality of crystal as well as metallic/semiconducting state of the sample [55, 56]. However, the information is obtained from a less straightforward way and needs to be extracted from the measured spectra. Among these methods, STM has the highest resolution and is capable of revealing the atomic structure of a CNT . 40 2.3.2. Instruments for CNT Characterization In this work, the grown CNTs are characterized via TEM, SEM and Raman spectroscopy. In addition, the state-of-art instrument available at University of Arizona  combines SEM and Raman spectrometers, enabling us to observe the morphology of CNTs and identify their structural and electrical properties simultaneously. Field emission SEM (Hitachi, FESEM, S-4800) is first employed to obtain highresolution images of the morphology, density, and distribution of CNT samples. Then the sample is transferred to a variable pressure SEM (Hitachi, S-3400N) equipped with energy dispersive X-ray spectrometer (EDS) and Raman spectrometer (Renishaw structural and chemical analyzer (SCA)) to acquire Raman spectra while monitoring the morphology of the CNTs. The 50-mW laser of the SCA has a wavelength of 514 nm (energy of 2.41 eV), and a beam diameter of ~ 1 µm. To ensure the same physical locations on the sample are characterized for the two SEMs, the coordinates of the characterized areas are recorded. The samples are also imaged with TEM (Hitachi, H8100) to obtain their internal structure information. The sample for TEM is prepared by the following procedure. First, the grown CNT soot is bath-sonicated in Isopropyl alcohol (IPA) for 15 minutes. Then 0.05 ~ 0.1 ml of the solution is dropped on a copper TEM grid. The grid is air dried for at least 24 hours before being used in the TEM. 41 (a) (b) (c) Figure 2-4. (a) Raman spectra of isolated SWNTs (metallic and semiconducting); (b) G-band feature of a highly oriented pyrolytic graphite (HOPG), a semiconducting SWNT and a metallic SWNT; (c) RBM and G-band spectra of SWNT species (15, 8), (17, 3), and (15, 2). Reprinted with permission from . Copyright (2005), Elsevier. 2.3.3. Background of Raman Spectroscopy Raman spectrum of a CNT results from the coupling between the electrons and the phonons from the vibrational modes in the 1-D system. As discussed in Chapter 1, the unique electronic states of CNTs are highly dependent on their geometrical structures. Therefore, the resulting Raman effects also reflect the CNT diameter and chirality information, thus can be used to probe the structural and electrical properties of CNTs. 42 Due to the special symmetries of CNTs, only a few vibrational modes are Raman-active . Shown in Figure 2-4 (a) are typical Raman spectra observed for SWNTs , where the peaks at low frequencies / long wavelengths (Figure 2-4 (c)) are the well-known Radial Breathing modes (RBM) resulting from the in-phase radial displacement (A1g symmetry); the features at 1500~1605 cm-1 are referred to as the tangential G-band, which are derived from graphite-like in-plane modes; the peaks around 1350 cm-1 (Dband) and its second harmonic at around 2700 cm-1 (G’ band) are defect-induced and highly dispersive . Figure 2-5. Calculated energy separation between vHs singularities Eii (i denotes for ith vHs singulary) vs. SWNT diameters (Kataura plot). Stars (MOD0): metallic. Open (MOD1) and filled (MOD2) circles: semiconducting. MOD denotes for the reminder of 2n+m divided by 3. Reprinted with permission from . Copyright (2005), Elsevier. 43 22.214.171.124. RBM For the radial breathing modes, the Raman frequency is found inversely proportional to the tube diameter and can be calculated with the following formula for nanotubes with diameters smaller than 1.4 nm . ωRBM = (219 ± 3) / dt + (15 m 3) (2.1) (There are also other different formulas reported with slight variations in the coefficients .) In addition, due to the trigonal warping effect, the electronic energy levels of SWNTs not only have strong dependence on the tube diameters, but also have weak dependence on the tube chiralities . Therefore, each SWNT (n, m) has a unique set of van Hove singularities (vHs) in the density of state (Figure 1-3). This enables us to identify different SWNT species given the inter-band transition energy and the nanotube diameter, which is directly related to the Raman frequency shift. Shown in Figure 2-5 is a Kataura plot  which maps SWNT species with their inter-band transition energies and diameters. The species are divided into different groups on the plot. For instance, E11S represents a semiconducting group with their transition energy between the first pair of vHs plotted. Note that when the laser excitation energy is in resonance with the transition energy between two vHs singularities, the Raman scattering cross-section becomes very large and a strong signal enhancement can be achieved. Therefore it is possible to observe Raman features from an isolated CNT . For bulky samples in which tubes are formed in bundles, species identification may still be valid. However, due to the intertube interaction, the RBM frequencies are up shifted by 7-10% for tubes with diameters 44 less than 1.5 nm . However, for SWNTs with diameters greater than 3 nm, it has been shown that RBM peaks become too broad to be observed experimentally . While Raman spectroscopy has been extensively utilized in the investigation of SWNT properties, not many Raman features from MWNTs are reported due to the large inner diameters of the grown tubes. Zhao et. al.  reported Raman spectroscopy of MWNTs produced from the arc discharge method. It is believed that the observed RBM band are mainly from the inner most layer of the MWNTs since the outer layers have diameters too large to stimulate Raman signal within the observable frequency ranges. In addition, the RBM frequencies are up shifted as well by ~ 5% due to the interlayer interactions . For double-walled carbon nanotubes (DWNT), however, both layers may contribute to the RBM response. Recently, Villalpando-Paez  reported Raman spectroscopy study on isolated DWNTs, which clearly demonstrated the RBM peaks from both layers. 126.96.36.199. G-band Unlike the RBM mode, the G-band Raman frequencies are not dependent on the tube diameter or chirality. However, the line shape of this band provides information on whether a tube is semiconducting or metallic . As shown in Figure 2-4 (b), the Gband feature of a CNT has two peaks in contrast to the single-peak feature for highly orientated pyrolytic graphite (HOPG). The lower-frequency component at ωG− is associated with the vibrations along the circumference direction. The higher-frequency component at ωG+ is associated with the vibrations along the CNT axial direction. For a 45 semiconducting tube, both peaks have Lorentzian shapes. For a metallic tube, G+ peak has a Lorentzian shape as well, but G- peak exhibits a broad Breit-Wigner-Fano line shape. 2.4. Results and Discussion 2.4.1. Effects of Substrates The SEM images of carbon nanotubes grown on Si and quartz substrates at different flow rates of methane (300 cc/min, 500 cc/min, 600 cc/min, and 700 cc/min) are shown in Figure 2-6. It is obvious that the catalysts are distributed differently on these two substrates. They are dispersed uniformly on the Si substrate but tend to form big islands on the quartz substrate. This is caused by the different surface properties of the two substrates. A silicon substrate with a thin native oxide layer of about 0.1 - 0.2 nm has a hydrophobic surface, in contrast to the quartz substrate which has a hydrophilic surface. When a drop of catalysts is placed on a Si substrate, it would divide into many tiny spherical droplets to minimize contacts, which results in the well-dispersed catalysts on Si substrates. Quartz, on the other hand, is highly hydrophilic. Therefore, as a drop of catalyst solution is placed on the substrate, it tends to maximize the contact with the surface and leads to catalyst clusters on the substrate. In addition, the tubes grown on the Si substrate are longer and connected from one catalyst cluster to others as showed in Figure 2-6 (a)-(d). The tubes grown on the quartz substrate are relatively shorter and tend to be entangled around the big catalyst islands with fewer connections with neighboring catalyst islands as shown in Figure 2-6 46 (e)-(h). SEM analysis shows the lengths of most CNTs grown on quartz substrate are in the ranges of 4-10 μm, while the lengths of CNTs on Si substrate are about 15-20 μm. The diameters of the visible tube features on both types of substrates are about 20 nm, which are believed mainly CNT bundles. (a) (b) (c) (d) (e) (f) (g) (h) Figure 2-6. SEM image of CNTs on Si substrate at methane flow rate of (a) 300 cc/min, (b) 500 cc/min, (c) 600 cc/min, and (d) 700 cc/min; and on quartz substrate at methane flow rate of (e) 300 cc/min, (f) 500 cc/min, (g) 600 cc/min, and (h) 700 cc/min. Since a quartz substrate has very low microwave loss and is one of the good candidates for our CNT circuit study at microwave frequency (will be discussed in Chapter 6), this observation provides very important guideline for our CNT testing circuit 47 fabrication procedure optimization in terms of both catalyst pattern design and substrate selections for different application purposes. 2.4.2. Effect of Methane Flow From the SEM images shown in Figure 2-6, one can see that the tube density becomes higher as the flow rate of methane increases from 300 to 700 cc/min. This is because the carbon decomposition rate increases with the higher methane flow rate. In fact, it is found that the methane flow rate also has other significant effect on the nanotube properties. From the TEM analysis, numerous bundles of double-walled nanotubes are observed. The individual tube has a diameter ranging from 1.2 to 2.8 nm (Figure 2-7(a)). Besides bundles of DWNTs, other forms of tubes including SWNTs (Figure 2-7 (b)) and MWNTs (Figure 2-7 (c)) are occasionally observed. At the low flow rate of 300 cc/min CH4, abundant MWNTs and defective multi-walled structures with diameters of about 315 nm are found. As the flow rate of methane increases to 500 cc/min, bundles of DWNTs and many tubular structures such as carbon ribbons and carbon spherical beads are observed. When the flow rate of methane is set at 600 cc/min, majority of CNTs are double-walled. As the methane flow rate increases to 700 cc/min, numerous DWNTs mixed with SWNTs are observed, and most of the nanotubes are without amorphous coating. 48 (a) (b) (c) Figure 2-7. TEM image of (a) bundles of DWNTs, (b) individual and bundled SWNTs, and (c) MWNTs. To further investigate the diameter and electrical properties of the grown tubes, Raman spectra are collected on ten random positions on each sample. Figure 2-8 (a) shows a SEM image of CNTs grown at a methane flow rate of 700 cc/min on a Si substrate. The corresponding Raman spectrum, which is collected at the center of the SEM image with a laser beam diameter of about 1 µm, is shown in Figure 2-8 (b). Note that the peak at 520 cm-1 is the Raman response from the Si substrate. It is found that the RBM (100 cm-1 - 250 cm-1) features are present in seven out of the ten spots for this sample. The same statistics is obtained for the 500 cc/min methane flow rate samples. This is in contrast to the spectra obtained for the 600 cc/min and the 700 cc/min flow rates samples where nine out of ten spots contain the RBM peaks. This indicates that the samples grown at 600 cc/min and 700 cc/min flow rates contain higher density of CNTs with small inner diameters. The observation is in good agreement with the TEM analysis, 49 showing that at lower methane flow rate, more MWNTs with large inner diameter are produced , while at higher methane flow rate more DWNTs and SWNTs are formed. (a) (b) Figure 2-8. (a) SEM image and (b) Raman spectra of CNTs grown on a Si substrate with the CH4 flow rate at 700 cc/min. Figure 2-9 (a) shows Raman spectra of five selected spots on the sample prepared at a CH4 flow rate of 300 cc/min on a Si substrate. The tube diameters, dt, can be calculated from the RBM frequency, ωRBM, using the formula dt = A/ωRBM where A is a constant. Multiple values of “A” have been reported and the average value of A = 234 cm1 ·nm is used here . The diameters of the produced tubes are found to be in the range between 1.07 nm and 1.86 nm with 7 ~ 10% uncertainty . It is worth to point out that the diameter range identified here could be possibly from the diameter of a SWNT, the inner diameter of a MWNT, and the inner or outer diameter of a DWNT. As discussed previously, the electronic properties of nanotubes can be extracted from the RBM frequencies given the laser excitation energy. Li et al. reported that with 50 the laser energy of 2.41eV, the RBM peaks of metallic tubes are located at 126 cm-1 and between 235 cm-1 and 265 cm-1 while semiconducting tubes have RBM peaks from 135 to 185 cm-1 . As shown in Figure 2-9 (a), the measured Raman RBM peaks of the CNTs grown at a methane flow rate of 300 cc/min locate at around 125 cm-1, 170 cm-1, and 225 cm-1, suggesting that the produced RBM-active nanotubes at this flow rate are a mixture of both metallic and semiconducting tubes. At the same time, the frequent absence of RBM features indicates that more tubes with large diameters (most likely MWNTs) are also produced. In contrast, more RBM peaks of the nanotubes produced at the flow rates of 500 cc/min, 600 cc/min and 700 cc/min are located between 150 and 210 cm-1, suggesting that more of the observed RBM-active tubes are semiconducting. Especially, at the rate of 600 cc/min, more tubes have smaller diameters are produced and most of the observed RBM peaks are from semiconducting tubes (Figure 2-9 (b)). These observations are consistent with the TEM analysis. Additionally, the intensity of the RBM peaks for the 600 cc/min and 700 cc/min flow rates samples are 3 - 20 times higher than the peaks for other samples (up to ~ 10000 counts vs. 500 – 3000 counts). The presence of more DWNTs, in the 600 cc/min and 700 cc/min samples rather than largediameter MWNTs, which are mostly likely Raman inactive, is believed to be the main reason for this observation. 51 100 200 1300 1400 1500 1600 1700 1800 200 1300 1400 1500 1600 1700 1800 (a) 100 Raman shift (cm-1) 100 200 1300 1400 1500 1600 1700 1800 200 1300 1400 1500 1600 1700 1800 (b) 100 -1 Raman shift (cm ) Figure 2-9. Raman spectra (collected at 5 different positions) of CNTs grown on a Si substrate with the CH4 flow rate at (a) 300 cc/min and (b) 600 cc/min. 52 During the Raman spectra study, it is also found that the intensity of the Raman spectra for CNTs grown on quartz substrates is much lower (shown in Figure 2-10) and not as informative as that of tubes grown on Si substrates because the quartz substrates interact strongly with the laser beam and interfere with the RBM mode. In addition, the defect information of the CNTs grown on different substrates is also revealed. As discussed previously, the D-band features between 1200 and 1350 cm-1 indicates the presence of defects in the tube structure. A high ratio of the peak intensity of D-band and G-band usually would indicate the presence of amorphous carbon . The D/G ratio of the CNTs grown on Si is found between 0.01 and 0.15, which is relatively low compared to that of quartz (0.8-0.89). It indicates that the tubes grown on silicon are more crystalline than those on the quartz. This may be another important factor to consider for potential mass production of CNT-based circuits for microwave applications by assembling CNTs across the pre-fabricated electrodes through CVD growth process with pattern catalyst. 53 2500 2000 Counts 1500 1000 500 0 500 1000 1500 2000 2500 3000 -1 Raman shift (cm ) Figure 2-10. Raman spectrum of CNTs grown on a quartz substrate. “*” denotes the Raman signal of the quartz substrate. 2.5. Conclusion Carbon nanotubes are synthesized using the CVD process. The grown CNTs are characterized by SEM, TEM, and Raman spectroscopy. The effects of substrate and feedstock gas (methane) flow rate are investigated. It is found that the tubes grown on quartz substrates appear to be shorter, less evenly distributed, and less crystalline compared to those grown on Si substrates. These observations provide very useful guidelines for future CNT-based circuit fabrication procedure optimization in terms of both catalyst pattern design and substrate selections for microwave applications. In addition, it is found that the CNT growth is highly dependent on the methane flow rate. At low flow rates, more large-diameter MWNTs are produced. As the methane flow rate 54 increases, more DWNTs or SWNTs are produced rather than large-diameter MWNTs. These observations lead to a better understanding of the CNT synthetic control using our CVD system and provide valuable information to provide specific types of CNTs for the purpose of microwave characterization. 55 CHAPTER 3. POTENTIAL MICROWAVE-INDUCED SWNT SEPARATION TECHNIQUE In this chapter, the microwave irradiation effects on purified HiPCO and CoMoCat single-walled carbon nanotube thin films are investigated . THz transmission measurements are carried out to provide a direct indication of the metallic content. The drastic transmission increase indicates a significant metallic content reduction after the irradiation. Two different laser excitations are applied for Raman spectroscopy to reveal the responses of different nanotube species. The Raman spectra for both HiPCO and CoMoCat thin films confirm the decrease of metallic carbon nanotube content. Possible physical mechanisms responsible for the observed phenomenon are discussed. The observed microwave-induced effects may potentially lead to a convenient scheme for demetalization of single-walled carbon nanotube mixtures. Future work to further investigate the exact underlying physical mechanism and to improve the selectivity of this method is also discussed. 3.1. Motivation As the integration density of integrated circuits continuously increases, carbon nanotubes have been considered as one of the potential candidates for nano-electronics for more than a decade in virtue of their remarkable electronic properties as discussed in Chapter 1. However, no wide-spread applications in electronics based on CNTs have been realized so far. One of the main bottlenecks is the co-existence of metallic and 56 semiconducting tubes from all the existing material growth methods. Even in the fast developing field of carbon nanotube thin film electronics, the presence of metallic tubes also deteriorates device performance such as causing small on/off ratio and sub-threshold slope . Various methods for separation of metallic and semiconducting SWNTs have been reported, based on their differences in electric conductivity, chemical reactivity, dielectric response, affinity with surfactants, density, etc. [33-35]. Nevertheless, none of those methods are complete solutions for applications in nano-electronics. For example, selective chemistry method often requires nanotubes to be functionalized and most of the reported work focuses on tubes with smaller diameters ; the reported dielectrophoresis method is able to achieve high-purity metallic SWNTs (~ 80%) but has limited throughput ; the reported selective electrical destruction method  by applying a dc current is fairly reliable to remove metallic tubes, but it is a serial process that requires microelectrode fabrication and sequential manipulation of each individual device, thus also has very limited throughput. To simplify the selective electrical destruction scheme, electromagnetic waves can be considered as an alternative to DC excitation so that the electrode fabrication and CNT-electrode contacts are no longer necessary. This might be a potential convenient scheme to selectively remove metallic nanotubes, which will be fast, efficient, and compatible with electronic processes. In addition, since the high conductivity of metallic nanotubes is along axial direction, the electromagnetic wave excitation is highly dependent on the polarization matching between the electric field and the tube orientations. Therefore, the orientation selection can also be realized. 57 In previous publications, microwave irradiation has been employed to remove catalytic particles in SWNTs by significantly raising the local temperature of catalyst particles to oxidize the carbon coating . However, the microwave-induced effects on purified SWNT samples have not been well studied [71-73]. The microwave-induced effects on as-produced SWNT powder were reported by Song et al. . Quantitative analyses of the microwave irradiation effect on HiPCO SWNTs were reported by Priya and Byrne using optical absorption and Raman spectroscopy with 633-nm laser excitation . In this work, we investigate the microwave irradiation effects on both purified HiPCO and CoMoCat SWNT thin film samples using time domain THz transmission spectroscopy as a convenient and direct measure of metallic content. In addition, Raman spectra are measured with both 514-nm and 532-nm laser excitations, which provides more information of the SWNT population before and after microwave irradiation as different SWNT species are in resonance with different laser excitation energies. At last, possible physical mechanism behind this selective destruction scheme and future experiments for identifying the exact underlying physics of the observed phenomenon are discussed. 3.2. Potential Selective Breakdown Scheme When a microwave signal impinges on SWNTs, currents are induced on the tubes. If simply approximating a nanotube as an infinitely long solid cylinder with a conductivity σ (Figure 3-1), the excited electrical field on the tube can be analytically calculated by 58 Ezt = E0 Hϕt = ∞ ∑aJ n =−∞ k2 E0 jωμ2 n n (k2 ρ )e jnϕ ∞ ∑ a J ′ ( k ρ )e n =−∞ n an = −(− j ) − n e − jnϕ i n jnϕ 2 (3.1) μ2 k1[ J n′ (k1a ) H n(2) (k1a) − J n (k1a) H n(2)′ (k1a )] μ2 k1 J n (k2 a) H n(2)′ (k1a) − μ1k2 J n′ (k2 a ) H n(2) (k1a)] where E0 is the incident electric field magnitude; k1, k2, μ1, and μ2 are the wave vectors and medium permeability in air and in the conductor respectively; a is the radius of the cylinder; ω is the radian frequency; Jn and Kn are the nth order Bessel and Hankel functions. When a is on the order of nm, and the frequency is on the order of GHz (109), the excited electric field inside the cylinder is almost equal to E0 (different by less than 0.2%) and does not show any angular dependence. Therefore, the induced current on the cylinder is proportional to σ and the incident electric field. The Ansoft High Frequency Structure Simulator (HFSS) enables us to confirm the analytical result by numerical simulations. For a cylinder with a finite length, the scattering at the cylinder is much more complicated and the induced current on the cylinder may be lower than that of an infinite long tube. Moreover, an actual nanotube is a hollow structure instead of a solid cylinder and the scattering mechanism may be even more complicated. However, as the induced current is confined in an even smaller space (on the surface) for a hollow structure, the current density is expected to be higher than that in the solid cylinder case. Since the conductivity of semi-conducting tubes is much lower than that of metallic tubes (~ 105 times smaller for tubes with small diameters) , when the electric field is high enough (believed to be well above 105 V/m), the induced current density on metallic tubes may reach the breakdown threshold of ~ 1013 A/m2 while semiconducting tubes 59 stay intact . This may lead to a convenient scheme for microwave-induced selective breakdown of metallic nanotubes (Figure 3-2). Figure 3-1. Estimation of electromagnetic-wave-induced current density in an infinitely long cylinder. v E 0 v k v v J =σ E M: break down EM wave Induce current S: stay intact Figure 3-2. Microwave-induced selective breakdown scheme. 3.3. Sample Preparation The SWNT thin films studied are prepared with HiPCO SWNTs (produced by high-pressure CO conversion process, Carbon Nanotechnologies, Inc., Houston, TX) and CoMoCat SWNTs (produced by the cobalt-molybdenum catalyst based process, Southwest Nanotechnologies, Norman, OK) using the previously published vacuumfiltration method . SWNT powder is first dispersed in 1 wt % of sodium dodecyl 60 sulfate (SDS) (C12H25SO4Na) solution via ultra-sonication treatment, and centrifuged at 25000 G for 2 hours to remove catalyst particles. Then, the SWNT suspension is filtrated through 200 nm Millipore polycarbonate membrane. A layer of SWNT thin film is formed on the membrane and the SDS is washed away by excessive de-ionized water. The filtration membrane is then transferred onto a glass or quartz substrate (both glass and quartz are mostly transparent to microwave radiation), and immersed in chloroform bath for 6 hours to remove the membrane. Resulting SWNT thin film samples on substrates are dried at 75ºC for 3 hours. Atomic force micrograph (AFM) and scanning electron micrograph (SEM) (Figure 3-3) show that the thin films consist of entangled SWNTs without catalyst particles and the film thickness is about 30 nm (determined by AFM). (c) Figure 3-3. (a) AFM image, (b) SEM image, and (c) photo of HiPCO SWNT thin film samples. 61 3.4. Experimental Setup SWNT thin film samples are then irradiated in a commercial microwave oven (2.45 GHz, 1100 W). The sample position is fixed next to the power-feeding waveguide, where the highest microwave field strength occurs (Figure 3-4). The power level of the oven is set to be 100%, at which the electric field strength at the sample position is approximately 4400 V/m, which is estimated by measuring the temperature increase of a small volume of water (~ 3 ml) heated over certain period of time. Quantitatively, the absorbed power by a lossy dielectric under electromagnetic wave irradiation is give by Eq. (3.1) . Therefore, the electric field can be estimated by Eq. (3.2), where t is the heating time, ω = 2π x 2.45x109 rad/s is the radian frequency, ε” is the imaginary part of the relative permittivity, ε0 is the permittivity of free space, C = 4.2 J/g·°C is the specific heat of water, ρ = 1·103 kg/m3 is the density of water, and V is the volume of water. Generally, ε” depends on both temperature and frequency. At 2.45 GHz and 40°C, the value of ε” is around 6.2 . At position 1 and position 2 as labeled in Figure 3-4, the measured water temperature increases within 5 seconds are 20.6°C and 10.4°C, respectively, corresponding to the electric field magnitudes of 4400 V/m and 3100 V/m. Therefore, the samples are set at position 2 upstanding to match the electric field polarization from the feeding rectangular waveguide to the best extent. P = ωε ′′ε 0 E 2V t ⋅ ωε ′′ε 0 E 2V = C ρV (ΔT ) (3.1) (3.2) 62 Microwave oven Film sample 2 1 Feeding waveguide holder Figure 3-4. Setup for the microwave irradiation experiment. Under the microwave irradiation in the oven, the samples heat up in just a few seconds and the glass substrates (0.17 mm thick) carrying SWNT thin films often break into pieces due to excessive heat generated, while the same bare glass substrates do not break in control experiments at all. Interestingly, it is consistently observed that the glass substrates covered with HiPCO SWNT thin films (28 ± 6% metallic contents ) break faster than the glass substrates covered with CoMoCat SWNT thin films with less metallic content (14 ± 5% metallic contents ). This simple observation is supporting evidence that the generated heat is from the induced currents on metallic SWNTs. 3.5. Results and Discussion The THz power transmission spectra of the SWNT film samples before and after microwave irradiations are measured with a photoconductive THz Time Domain Spectrometer (TDS) system from Picometrix Inc. . The films are also characterized by Raman spectra measurements taken with both 514 nm (Renishaw’s structural and 63 chemical analyser) and 532 nm laser excitations (alpha300 S Raman spectral imaging microscope, WItec Instruments Corp., Ulm, Germany). 1 Air SWNT thin film 3.5.1. THz Power Transmission Measurement 2 Substrate Figure 3-5. Medium interface of SWNT film samples. To study the changes of SWNT thin films after microwave irradiation, THz transmission response of HiPCO SWNT thin film samples deposited on glasses and quartz substrates are measured before and after various microwave irradiation time using a THz Time Domain Spectrometer (THz-TDS) . A THz pulse is generated and passing through the sample under test and detected in time domain (the THz-TDS system will be discussed in more details in Chapter 5). The measured transmission is then Fourier transformed into frequency domain. The composition of the sample can be examined from the transmission measurement. For instance, if the sample is composed of pure metallic tubes, it behaves like a thin metal sheet, thus most of the signal is reflected and the transmission would be low. On the contrary, if the sample contains pure semiconducting tubes, it behaves more like a thin dielectric slab and a much higher transmission would be obtained. Therefore, increase of measured transmission would 64 indicate decrease of metallic content in the sample. More quantitatively, the surface conductivity of the SWNT thin films can be calculated from the measured transmission responses since the film thickness (~ nm) is much less than the wavelength at THz frequencies (~ mm) and can be treated as a surface boundary condition. As illustrated in Figure 3-5, at the air-film interface, the reflection coefficient r and transmission coefficient t can be written as [105, 115] r= Y− − σ s Y+ + σ s (3.3) t= 2Y1 Y+ + σ s (3.4), where σ s is surface conductivity of the thin film; Y+ and Y− are functions of Z1, Z2 and Z0, which are corresponding to the wave impedances in medium 1 (air), medium 2 (substrate) and free space; n1 and n2 are the indices of refraction in air and substrate, respectively. Y± = Y1 ± Y2 Y1,2 = n 1 = 1,2 Z1,2 Z 0 (3.5) (3.6) Now, if taking multiple reflections (FP) into consideration, the transmission coefficient can be derived as a function of σ s . T= N 4 X ⋅ nsub n −1 exp(−i (nsub − 1)k0 d sub ) ⋅ ∑ (exp(−2insub k0 d sub ) sub (2nsub X − 1)) FP (3.7) nsub + 1 nsub + 1 FP = 0 X −1 = 1 + nsub + σ s Z 0 (3.8) 65 Here, nsub and dsub denote the index of refraction and thickness of the substrate, and k0 is the wave number in free space. Therefore, the surface conductivity of a film, σ s , can be Power Transmittance (dB) numerically solved from the measured transmission coefficient. 0 (a) -5 -10 -15 -20 -25 -30 150 -1 σS (Siemens) 10 300 450 Frequency (GHz) 600 750 (b) -2 10 -3 10 after 2430 s after 420 s after 180 s after 35 s after 15 s original -4 10 -5 10 -6 10 -1 10 σS (Siemens) after 2430 s after 420 s after 180 s after 35 s after 15 s original 150 300 450 600 Frequency (GHz) 600 GHz 750 (c) 400 GHz -2 10 -3 10 0 200 GHz 500 1000 1500 2000 Accumulated Irradiation Time (s) 2500 Figure 3-6. (a) THz transmission spectra, and (b) extracted surface conductivity of a HiPCO SWNT thin film on quartz before and after microwave irradiation of various time (up to 2430 seconds). (c) Surface conductivity (at 200 GHz, 400 GHz and 600 GHz) decreases as a function of irradiation time. 66 Shown in Figure 3-6 (a) are the THz transmission spectra of a HiPCO SWNT thin film deposited on a quartz substrate after a sequence of microwave irradiation processes. One can see that the transmitted power increases dramatically by up to 10 times after microwave irradiation. Accordingly, the numerically solved surface conductivity, plotted in Figure 3-6 (b), decreases by 10 times or more, indicating a significant metallic content reduction from the irradiation process. It is worth noting that the surface conductivity drops more significantly during the first 180 seconds of irradiation as shown in Figure 3-6 (c). Afterwards, the conductivity reduction appears to be much slower, which is due to the limited metallic content in the film. That is, for the metallic tubes experiencing an electric field above their damage threshold (either induced by high current or excessive heat), after certain irradiation time period, the damage has already been done and a saturation state is approached. Therefore, additional irradiation time would not significantly introduce more metallic tube breakdown and increase the THz power transmission. This THz characterization method can be conveniently applied to extract the complex permittivity and permeability as well [79, 80], which will be presented in more details in Chapter 5. Compared to the traditional four-point DC conductivity measurement, this method is much more reliable since it does not require any contact on the samples. This advantage is prominent especially for the film samples with delicate morphology. Different contacts can change the surface morphology differently and are found introducing large uncertainties. For CoMoCat thin film samples, similar but smaller THz transmission increase is observed after microwave irradiation, which is expected since CoMoCat samples contain less metallic content. 67 3.5.2. Raman Spectroscopy Analysis Raman spectroscopy studies also support the notion of decreased metallic content after microwave irradiation. Shown in Figure 3-7 are the Raman radial breathing modes (RBM) and G band features of a HiPCO thin film obtained with 514-nm and 532-nm laser excitations. Each spectrum is averaged over several different spots on the thin film sample. 68 Intensity (a. u.) 2500 S33 2000 (a) M11 After 1500 Before 1000 500 0 100 200 300 400 -1 Raman Shift (cm ) Intensity (a. u.) 12000 (b) After 8000 Before G band 4000 D band 0 1300 1500 1700 -1 Raman Shift (cm ) Intensity (a. u.) 5000 S33 4000 After 3000 Before 2000 1000 0 100 200 300 Raman Shift (cm ) (d) After 20000 10000 0 400 -1 30000 Intensity (a. u.) (c) M11 Before G band D band 1300 1500 1700 -1 Raman Shift (cm ) Figure 3-7. Raman RBM band and G band spectra of HiPCO SWNT thin films on glass substrates before (solid curves) and after (dashed curves) microwave irradiation. (a) and (b) are obtained with 514-nm laser excitation; (c) and (d) are obtained with 532-nm laser excitation. 69 As discussed in Chapter 2, from the Kataura plot, the SWNT species corresponding to the RBM peak frequencies may be identified given the laser excitation energies. There might be ambiguities, but it can in principle be eliminated by using multiple laser excitations. The Kataura plots shown in Figure 3-8 are utilized to identify the species from our RBM spectra. The Kataura plot in Figure 3-8 (a) is obtained experimentally and reported to identify the SWNT species in HiPCO samples , and the Kataura plot in Figure 3-8 (b) is obtained theoretically based on the extended tight binding model and reported to identify the SWNT species in CoMoCat samples . The 514-nm laser excitation corresponds to inter-band transition energy of 2.41 eV, and the 532-nm laser excitation corresponds to inter-band transition energy of 2.34 eV. An experimental uncertainty of ±0.1 eV on the laser excitation energies is allowed, which is denoted by the rectangular windows in Figure 3-8. The possible observed species from our RBM spectra are listed in Table 3-1 and Table 3-2. Therefore, the RBM spectra shown in Figure 3-7 (a) and (c) are separated into the M11 region (215 cm-1 ~ 290 cm-1), for which the excitation laser is in resonance with the first van Hove singularity (vHs) transition of metallic tubes in the diameter range of 0.8 1.1 nm, and the S33 region (160 cm-1 ~ 215 cm-1), for which the excitation laser is in resonance with the third vHs transition of semiconducting tubes in the diameter range of 1.1 - 1.5 nm, according to the Kataura plot [35, 56, 61, 81]. The spectral features in the M11 region are significantly lowered after irradiation while the decrease is much less significant in the S33 region. To compare the changes of metallic tubes relative to the 70 changes of semiconducting tubes from the RBM spectra, the M11-to-S33 ratios are calculated by integrating the spectral area within each region . As shown in Table 3-3, this ratio is reduced by 16.5% and 33.3% for the 514-nm and the 532-nm laser excitations, respectively. It is worth pointing out that the decrease of the metallic-to-semiconducting (M/S) ratios calculated here does not represent the decrease of the M/S ratios for the entire population of the SWNT thin film sample, as Raman spectra only reflect information of SWNTs that are in resonance with the excitation laser. In fact, the decrease of metallic spectral features is different for the two excitation lasers. Nevertheless, a clear trend of demetalization is observed in both cases. Furthermore, it can be seen from Figure 3-7 (b) and (d) that the G- band (1460 cm-1 ~ 1560 cm-1) in the G band region becomes slightly narrower after irradiation, indicating the decrease of metallic content , which is consistent with the THz transmission measurements and the RBM band analyses. 71 (a) 2.41ev,514nm 2.34ev, 532nm c c (b) 2.41ev,514nm 2.34ev,532nm ωRBM (cm‐1) Figure 3-8. Kataura plots obtained (a) experimentally in , and (b) theoretically in . They are utilized to identify the species in the measured RBM spectra. The labeled values of 2n+m denote the SWNT electrical property. If 2n+m=3q (q=1, 2, 3…), the species are metallic; otherwise, the species are semiconducting. The solid rectangular boxes are corresponding to the 514-nm laser energy (±0.1 eV) and the dashed rectangular boxes are corresponding to the 532-nm laser energy (±0.1 eV). (a) Reprinted with permission from . Copyright (2005), Elsevier. (b) Reprinted with permission from . Copyright (2005), the American Physical Society. 72 Table 3-1. Possible species assignment for HiPCO Excitation Semiconducting Raman Shift (n, m) or Metallic (cm-1) 185 (13,6) s 205 (13,3) s 216 (11,5) m 226 (9,6) m 243 (7,7) m 258 (8,5) m 264 (9,3) m 182 (13,6) s 200 (12,5) s 228 (9,6) m 240 (10,4) m 248 (7,7) m 273 (9,3) m 280 (10,1) m 2.41 eV (514 nm) HiPCO 2.34 eV (532 nm) 73 Table 3-2. Possible species assignment for CoMoCat Excitation Semiconducting Raman Shift (n, m) -1 or Metallic (cm ) 186 (14,4) s 208 (14,1) s 248 (7,7) m 262 (8,5) m 272 (9,3) m 290 (9,2) s 320 (8,2) m 310 (6,5) s 236 (10,4) s 245 (9,6) s 2.34 eV 280 (10,1) m (532 nm) 300 (10,0) m 320 (8,2) m 310 (6,5) s 2.41 eV (514 nm) CoMoCat 74 Table 3-3. Comparison of the calculated M11-to-S33 ratios before and after microwave irradiation for the HiPCO film sample Laser excitation 514 nm 532 nm M/S ratio (before) 1.93 1.74 M/S ratio (After) 1.61 1.16 M/S ratio decrease (%) 16.5% 33.3% Similar Raman spectroscopy results are observed for the CoMoCat samples, as shown in Figure 3-9. The spectral features in the M11 region are obviously lowered after irradiation, although the peak reduction at around 280 cm-1 with the 532-nm laser excitation is less evident. A slight G band line width narrowing is observed as well. The difference in chiral (n, m) species distribution between the CoMoCat SWNTs and the HiPCO SWNTs is manifested in Raman spectral region of 290 - 330 cm-1, which corresponds to the RBM region of small diameter (< 0.8 nm) SWNTs. A significant decrease of Raman signal is observed at the peak around 310 cm-1 in both Figure 3-9 (a) and (c), which is possibly from either semiconducting tubes (6, 5), or from metallic tubes (8, 2), or from both species [61, 81]. Therefore, for the tubes with diameters smaller than 0.8 nm in CoMoCat samples, from the Raman spectra alone, it is not definitive whether the microwave-induced content reduction only occurs to metallic tubes or it occurs to semiconducting tubes as well. However, in Figure 3-9 (a), the peak center is found shifted to a lower frequency after the microwave irradiation. Since (6, 5) and (8, 2) are 75 corresponding to the Raman frequencies of 310 cm-1 and 320 cm-1 respectively, the peak shift may be an indication that (8, 2) tubes are significantly damaged and the relative concentration of (6, 5) species is enhanced after microwave irradiation. 76 Intensity (a. u.) 1500 S33 (a) M11 After 1000 Before 500 0 100 200 300 400 -1 Raman Shift (cm ) Intensity (a. u.) 15000 (b) After 10000 5000 0 G band Before D band 1300 1500 1700 -1 Raman Shift (cm ) Intensity (a. u.) 5000 S33 4000 (c) M11 After Before 3000 2000 1000 0 100 200 300 400 -1 Raman Shift (cm ) Intensity (a. u.) 20000 15000 (d) After Before G band 10000 D band 5000 0 1300 1500 1700 -1 Raman Shift (cm ) Figure 3-9. Raman RBM band and G band spectra of CoMoCat SWNT thin films on glass substrates before (solid curves) and after (dashed curves) microwave irradiation. (a) and (b) are obtained with 514-nm laser excitation; (c) and (d) are obtained with 532-nm laser excitation. 77 3.5.3. Discussion on Possible Underlying Physics of the Observed Effects In summary, microwave irradiation appears to be an effective method for demetalization of SWNT mixtures. The high-power electromagnetic field induces strong currents on metallic tubes as suggested in Section 3.2. The induced currents produce excessive heat and cause significant local temperature rises, which explain the breaking of the glass substrates and account for the reason why HiPCO samples break faster than CoMoCat samples do. Although the estimated external field of 4400 V/m is well below the threshold of current induced breakdown mechanism , the actual field experienced by the metallic tubes could be much higher because of field enhancement in bundled and entangled nanotube configuration. The observed metallic SWNT damage may be heatinduced, or current-induced, or a combination of both mechanisms . Since SWNTs (metallic and semiconducting) are entangled in the films as shown in Figure 3-3, the microwave induced excessive heat can influence the semiconducting tubes in proximity and may lead to the destruction of some of them as well, especially for the tubes with smaller diameters as they have higher curvature and are more prone to oxidation under the same microwave power. This could be one of the factors causing the decrease of the RBM peak at around 310 cm-1 in the Raman spectra shown in Figure 3-9 (a) and (c). Therefore, for this proposed technique, better selectivity would be achieved if CNT samples are in a sparse or isolated form, which is often the case for CNT-based nanoscale circuits. While it is clear that metallic transport behavior is reduced after microwave irradiation, as represented in both THz transmission measurement and Raman RBM 78 spectra, what chemically happen to the metallic and semiconducting tubes in the thin film stays unrevealed. The following physical scenarios are plausible. Metallic tubes could be evaporated as suggested in some electrical breakdown schemes, or merely lose their metallic properties while keeping physical form of hollow tubes as in some chemical functionalization schemes. To provide a definite answer to this question, the collective characterization methods used in this chapter on entangled CNTs are no longer adequate. Therefore, further microscopic study on isolated CNTs needs to be carried out in the future to investigate the exact underlying mechanism. 3.6. Conclusion and Future Work To conclude, the effects of microwave irradiation on both HiPCO and CoMoCat SWNT thin films without interferences from catalyst particles are studied. A significant THz transmission increase is observed after microwave irradiation, which indicates a significant decrease in metallic tube content. The Raman RBM spectra also confirm the metallic-to-semiconducting ratio decrease in the SWNT thin films after the irradiation. The observed effects may lead to a convenient and effective microwave-induced demetalization scheme of SWNT mixtures. Further work to understand the exact underlying physical mechanism of the observed phenomenon and to increase the selectivity of this purification method is currently under investigation. As discussed previously, to understand what physically happens to the metallic tube under high-power microwave irradiation, the characterization of collective and entangled SWNT film is no longer adequate. Therefore, 79 isolated tubes under a high microwave EM fields need to be investigated. The isolated tubes can be labeled with their electrical properties being pre-identified by various techniques such as electrical force microscopy (EFM)  so that each tube can be identified by its location, morphology and electrical properties before and after being exposed under high electromagnetic field. Whether metallic tubes are completely oxidized or only losing their electrical properties can be manifested. Shown in Figure 3-10 (a) is one of our fabricated labeling grids, with which one can go back to the exact position and monitor each isolated tube dispersed on the substrate. An AFM image of the isolated HiPCO SWNTs within an 8 µm x 8 µm area is shown in Figure 3-10 (b). The tubes are exposed under microwave oven irradiation for up to 5 minutes and investigated under an AFM (Dimension 3100). No evident physical form change is observed. It is likely that the field strength in a commercial microwave oven is not high enough so that it fails to reach the breakdown threshold in absence of the field enhancement effect from entangled CNTs. To boost up the electromagnetic field that can be applied to isolated tubes, two possible means are proposed. The first method is to build a cylindrical resonator with a loop configuration coupled to coaxial input and output (Figure 3-11). The adjustable loop feeding can be used to realize critical coupling to achieve maximum power density . This method is a convenient once for all approach and can be repeatedly applied to multiple samples, but requires a very high input power (~ kW). The second approach uses a gap-coupled planar resonator (Figure 3-12). The benefit of this approach is that the electric field at the gap can easily reach very high magnitude (~106 V/m) with much 80 lower power (~ 1 W) input due to the small size of the resonator, which has been confirmed by HFSS simulation. In contrast to a commercial microwave oven, the designed resonators can achieve much higher electric fields with more uniform directions. With the assistance of an AFM and an EFM, the use of the designed resonators to study isolated CNTs not only can enable a clear understanding of the underlying physical mechanism of this potential microwave-induced metallic CNT breakdown scheme, but also can possibly implement the orientation selection in metallic CNTs. Important parameters such as the minimum electric field strength, oxygen content, frequency dependence, etc., can all be studied in a systematic manner. μm (a) (b) 60 μm μm Figure 3-10. (a) Optical microscopic image of the labeling system fabricated with PMMA; (b) AFM image of isolated HiPCO SWNTs 81 (a) (b) 50‐Ω 50‐Ω Coaxial feeding Coaxial feeding TM010 excitation TM010 excitation Figure 3-11. Cylindrical resonator (a) (b) Gap coupling Figure 3-12. A gap-coupled λ/2 planar resonator achieving electric fields higher than 106 V/m at the gaps. (a) Top view; (b) Electric field magnitude on the substrate surface simulated with HFSS. 82 CHAPTER 4. MICROWAVE (8-50 GHZ) CHARACTERIZATION OF MWNT PAPERS In this chapter, microwave (8-50 GHz) characterization of multi-walled carbon nanotube (MWNT) papers using rectangular waveguides will be presented . An algorithm based on the Nicolson-Ross-Weir approach is developed to extract the complex permittivity and permeability. Verification of the algorithm is accomplished by HFSS (High Frequency Structure Simulator of ANSOFT)  finite-element simulation. Based on the VNA systematic uncertainties, we perform error analysis of the extracted complex permittivity and permeability. Finally, the effective medium theory is applied to remove the effect of air in the sample and obtain the more intrinsic characteristics of the multiwalled carbon nanotubes. 4.1. Introduction Microwave regime usually refers to frequencies between 300 MHz (3x106 Hz) and 300 GHz (3x109 Hz) (Figure 4-1). Major applications in microwave engineering have been intensively developed since World War II, ranging from military Radar systems to global positioning systems (GPS) and commercial wireless communication systems, etc. This field has been kept very dynamic and vibrant due to constant new application demands and available new technologies. For example, the advancement in semiconductor technologies (III-V devices in the 70’s, and nano-scale silicon based devices currently), discovery of superconductors, especially the high temperature 83 superconductors in the 80’s, and micro-electric-mechanical systems (MEMS) have all generated tremendous amount of research interests in new areas of microwave engineering. It is possible that carbon nanotubes, with their remarkable electrical, mechanical and thermal properties, may also have great potential in microwave applications, such as CNT-FET with very high cut-off frequency (possibly up to THz [32, 83]), CNT-based electro-mechanical systems (NEMS) in GHz frequency range , CNT antennas , and high-performance CNT radar-absorbent material, etc. . Frequency (Hz) 3x105 3x108 1 10‐1 10‐2 10‐3 10‐4 10‐5 Visible Light Microwaves Infrared 101 3x109 3x1010 3x1011 3x1012 3x1013 3x1014 Far Infrared 102 3x107 FM broadcast radio VHF TV Short wave radio AM broadcast radio Long wave radio 103 3x106 10‐6 Wavelength (m) Figure 4-1. Electromagnetic spectrum As discussed in Chapter 1, although numerous electronic transport measurements of carbon nanotubes are carried out at DC, low frequencies, and optical frequencies, over the microwave regime, carbon nanotubes’ electrical properties have not yet been well studied. The biggest challenges to directly study individual carbon nanotubes in this frequency range include significant impedance mismatching between nanotubes (~ 10 KΩ to MΩ) and conventional microwave testing systems (50Ω), dominant parasitics 84 response from testing structures over the intrinsic properties of carbon-nanotube devices under test , and difficulties in device fabrication. An alternative approach is to characterize a large ensemble of nanotubes, for example, a coplanar waveguide (CPW) filled with carbon nanotubes , carbon-nanotube films [38-42] or arrays, to obtain the relevant material properties. As illustrated in Figure 4-2, when a microwave signal impinges upon a nanotube ensemble, at the interface, part of the signal is reflected and part of it is transmitted. The magnitude and phase of the reflection and transmission coefficients depend on the sample’s collective properties and can be measured easily and used to extract the complex permittivity and permeability of the sample. Figure 4-2. Illustration of microwave characterization method of a CNT ensemble. 85 Table 4-1. Summary of Reported Carbon Nanotube Paper Measurements Reference   ,  Sample Unspecified CNT film SWNT mat SWNT film SWNT film Method Ellipsometry FT-IR TDS MVNA Frequency Range 362-1256 THz 0.45-150 THz 0.2- 2.0 THz 10-500 GHz Measured Signal Reflection Reflection Transmission Transmission Error ------Analysis CNT: Carbon nanotube; SWNT: Single-walled carbon nanotube; FT-IR: Fourier transform infrared spectrometer; TDS: Time domain spectroscopy; MVNA: Millimeter-wave network analyzer With error bars There have been several reports of CNT ensemble characterizations at high frequencies, some of them are shown in Table 4-1. However, most of the experiments reported so far measure only the reflection or only the transmission, while losing the other half of the information. As a result, the magnetic properties (permeability) cannot be extracted and the assumption of unity permeability has to be made to extract the permittivity. In addition, the error analysis of the measurement techniques is often omitted, thus, it is difficult to estimate the accuracy of the results and to evaluate their sensitivities to each measured quantity, thereafter to improve the methodology as much as possible. 86 In this work, we characterize multi-walled carbon nanotube papers using a vector network analyzer (Agilent PNA-E8361A) with rectangular waveguides as test fixtures. The vector network analyzer (VNA) measures both the magnitudes and phases of the reflection (S11) and transmission (S21) coefficients, which are referred to as S-parameters. The sample is treated as an effective medium with a known thickness and the Sparameters of this two-port network can be analytically derived as a function of the complex permittivity (ε = ε’ – i ε”) and permeability (μ = μ’ – i μ”) of the sample, where the imaginary parts represent the material loss. Thus, ε and μ can be solved from the measured S-parameters. Compared with other methods, one advantage of the nanotube paper measurement is the simplicity of the experimental setup. In addition, since four measured parameters (magnitude and phase of S11 and S21) are available for the extraction, no presumption of μ = 1 needs to be imposed. The method developed here can be used for other materials as long as the sample is lossy enough that the leakage from the edges of the waveguides may be negligible. The error analysis of the extraction method is then performed. Our results indicate that the imaginary part of the permittivity, ε”, carries the smallest systematic error among all four parameters (ε’, ε”, μ’, and μ”) and provides useful guidelines for future improvement in material characterization accuracy with this method. For instance, it is possible to utilize the more reliable ε” over a wide frequency range and apply the Kramers-Kronig relation to obtain ε’ more accurately, resulting in more accurate extraction of μ’ and μ” as well. 87 4.2. Multi-Walled Carbon Nanotube Paper Sample The sample used in our experiment is a sheet form of multi-walled carbon nanotubes with a thickness of 89 μm (~ 3.5 mil), made by NanoLab Inc. . To prepare the sample, nanotubes are suspended in a fluid and then filtered onto a membrane support. After drying, the paper is removed from the support, leaving a free-standing nanotube paper. A picture of the sample and its scanning electron micrograph (SEM) are shown in Figure 4-3, in which one can see that the carbon nanotubes are randomly oriented and entangled to form the paper. Figure 4-3. A 1-inch-diameter multi-walled carbon nanotube paper photo (left) and a 3.8-µm × 2.8-µm SEM image (right) (From ). 4.3. Experimental Setup and Measured S-parameter Data To measure the S-parameters of the nanotube paper, two rectangular waveguides are used to sandwich the paper in between so that it is perpendicular to the direction of the electromagnetic wave propagation. The waveguides are then connected to the two ports of an Agilent E8361A vector network analyzer via coaxial cables. The actual experimental setup is shown in Figure 4-4. Before measurement, two-port waveguide calibration is performed using the Agilent waveguide cal kits (X11644A, P11644A, 88 R11644A, and Q11644A) so that the reference planes of the measured S-parameters are exactly located at the two surfaces of the sample under test. The responses of the sample are measured at X-band (8 – 12 GHz), Ku-band (12 – 18 GHz), Ka-band (26 – 40 GHz), and Q-band (33 – 50 GHz), which requires four different waveguides WR-90 (900 mil x 400 mil), WR-62 (622 mil x 311 mil), WR-28 (280 mil x 140 mil), and WR-22 (224 mil x 112 mil) to be used respectively. Therefore, the measured S-parameters are based on different waveguide port impedances, which depend on both frequency and waveguide dimensions. Network Port 1 Analyzer Port 2 Waveguides (a) Network Port 2 Analyzer Port 1 Port 1 Nanotube MWNT paper Paper Port 2 (b) Figure 4-4. (a) MWNT paper is sandwiched in between two waveguides. (b) The VNA experimental setup. 89 Several MWNT paper samples are characterized. The measured S-parameters showed good repeatability. The data of one of the samples is plotted in Fig. 4-5 (circles). Since the K-band waveguides and cal kit are unavailable to us, there exist discontinuities in the plots from 18 to 26 GHz. From 33 to 40 GHz, there are two data points at each frequency since the frequency range is covered by both Ka-band and Q-band, which however have different reference impedances. We also rotate the sample orientation and measure the responses. The S-parameters before and after the rotation are almost identical, indicating that our nanotube samples are randomly aligned, as manifested in Figure 4-3. Consequently, it is reasonable to treat the nanotube paper as an isotropic effective medium for material property extraction. Note that if an anisotropic sample is used, such as a sample with aligned MWNTs, measurements with electric field along the tubes and perpendicular to the tubes can provide axial and transverse electrical properties of MWNTs, respectively. This will be studied in our future research effort. 90 Measured -28 Simulated -0.1 dB (S21) dB (S11) -0.2 -0.3 -0.4 -0.5 -30 -32 Measured 0 20 40 -34 60 Simulated 0 Frequency (GHz) Measured Simulated -177 -178 -179 -180 0 20 40 60 0 Phase (S21) (deg) Phase (S11) (deg) -176 20 Frequency (GHz) 40 Frequency (GHz) 60 Measured -10 Simulated -20 -30 -40 0 20 40 60 Frequency (GHz) Figure 4-5. Measured (circles) and simulated (solid lines) reflection and transmission coefficients (magnitude and phase) of a MWNT paper. The Sparameters are not continuous due to different waveguide port impedances. The simulated curves are obtained from HFSS simulation for the purpose of algorithm verification (Section 4.5). 4.4. Complex Permittivity and Permeability Extraction 4.4.1. Scattering Parameters Scattering parameters, also known as S-parameters or S-matrix, are widely used at microwave frequency to describe an arbitrary network, which is composed of interconnected electronic components. They can be directly measured with a vector network analyzer (Figure 4-4 (b)). For a 2-port network (Figure 4-6 (a)), the parameters are in relation to the incident and reflected voltage waves by  91 V S = | V − i ij + Vk+ = 0 , k ≠ j (i, j =1, 2) (4.1) j where the superscript “+” denotes the incident voltage waves at port 1 or 2, and “-” denotes the scattered voltage waves at port 1 or 2. From the definition, one can see that S11 and S22 are essentially the reflection coefficients of the network at port 1 and port 2 respectively, S21 is essentially the transmission coefficient from port 1 to port 2, and S12 is the transmission coefficient from port 2 to port 1. These four parameters form a matrix, which is referred to as the S-matrix. For a passive network, the S-matrix is symmetric and S21 = S12. For a symmetric network, S11 = S22 are equal to each other. Since S-parameters are related to the traveling incident and reflected voltage waves in both magnitude and phase, at microwave frequency, the reference planes at which the measurement is carried out need to be precisely defined. As described in Section 4.3, the reference planes of our measured MWNT paper response are located at two sides of the paper (Figure 4-6 (b)) after applying standard waveguide calibrations. Note that for waveguide measurements using Agilent VNAs, the port impedances corresponding to the measured S-parameters are set to be the waveguide impedance instead of 50 Ω. 92 (a) V1+ Port 1 − 1 V Port 2 V2+ V2− 2‐port network (b) Waveguide Waveguide 50Ω port 2 50Ω port 1 Reference planes Figure 4-6. (a) Voltage waves at the interfaces of a 2-port network; (b) Reference planes in the waveguide measurement. 4.4.2. Nicolson-Ross-Weir Method Now, if considering a 2-port network of a slab of the MWNT material with a finite thickness d, the attenuation and phase delay introduced by a single pass through the sample are described by the transmission term ξ =e − ikd = e − ik 0 εμ d (4.2) where ε = ε’ – i ε” is the relative permittivity, μ = μ’ – i μ” is the relative permeability, k0 is the free space wave number, and k is the wave number in the nanotube medium. Another material property as a function of ε and μ is the wave impedance of the nanotube paper (normalized to the waveguide characteristic impedance) 93 η′ = μ / ε ⋅η0 Z wg (4.3) where η0 is the free space wave impedance, and Zwg is the waveguide characteristic impedance, which is determined by the TE10 mode wave impedance and the dimensions of the waveguide, and given by Eq. (4.4). Z wg = k0η0 k02 − (π / a ) 2 ⋅ 2b a (4.4) where a and b are the longer and shorter side length of the waveguide cross section, respectively. With ξ and η’ being defined, the reflection coefficient (S11) and transmission coefficient (S21) can be derived and written as follows. S11 = (η ′2 − 1)(1 − ξ 2 ) (1 + η ′) 2 − (1 − η ′) 2 ξ 2 (4.5) S 21 = 4η ′ξ (1 + η ′) − (1 − η ′) 2 ξ 2 (4.6) 2 The Nicolson-Ross-Weir (NRW) approach introduces two composite terms  V1 = S 21 + S11 (4.7) V2 = S 21 − S11 (4.8) The appropriate combination of these two variables leads to a function only in terms of ξ 94 X = 1 + VV 1 2 V1 + V2 = 1+ ξ 2 2ξ (4.9) Therefore, with the measured S-parameters, the transmission term can be solved by ξ=X± X −1 2 (4.10) The proper sign in Eq. (4.10) should be selected to ensure the magnitude of ξ to be less than or equal to 1, thus producing the physically meaningful results. With ξ obtained, it can be simply derived that η’ as functions of ε and µ is determined by 1+ η′ = 1− ξ − V2 1 − ξ V2 ξ − V2 (4.11) 1 − ξ V2 In principle, with ξ and η’ determined, one should be able to solve ε and µ from Eqs. (4.2) and (4.3). However, there is still ambiguity to be clarified, which is caused by the multi-valued function ln(ξ). Since ξ is a complex number, the solution of Eq. (4.2) can be written as n= εμ = i k0 d ln(ξ ) = 1 k0 d [i ln | ξ | − (θ + 2 mπ )] (4.12), where n = n’- i n” is the complex index of refraction of the material, ө is the argument of the complex value ξ, and m can be any integer. Evidently, the imaginary part of n is uniquely determined. However, the real part of n has infinity number of possibilities. In this paper, the continuity of n’ in frequency is utilized to determine the 95 correct value of m . Since the free space wavelength at the lowest frequency 8 GHz (37.5 mm) is more than 400 times the thickness of the sample (~ 89 µm), the phase delay, k0n’d, at 8 GHz should be within ±π, otherwise the absolute value of n’ needs to be greater than 200, which is physically unlikely. From Figure 4-5, one can see that the S21 phase would become 0 if extrapolating the measured phase curve to zero frequency, which confirms that there is no phase wrapping in the frequency range of interest. Therefore, it is appropriate to take m = 0 at 8 GHz. As the frequency increases, the phase delay changes and may possibly exceed ±π at some frequency. To ensure the continuity of n’, a different value of m may be required. In order to validate the choice of m, the computed n’ with different values of m are plotted from 8 to 50 GHz in Figure 4-7. The absence of discontinuity indicates that the choice of m = 0 is valid over the entire frequency range of interest. After m is determined, μ can be simply calculated by applying multiplication between Eq. (4.3) and Eq. (4.12), and ε is calculated by substituting μ in Eq. (4.3). μ= η ′Z wg η0 k0 d [i ln | ξ | −θ ] (4.13) η0 μ 2 ε= η ′ Z wg 2 2 (4.14) 96 400 200 0 n′ -200 -400 m = -1 m=-1 m =0 m=0 -600 m m=1 =1 -800 -1000 m =2 m=2 5 10 15 20 25 30 35 40 45 50 Frequency (GHz) Figure 4-7. Extracted real part of the index of refraction with different choices of m. 4.4.3. Extracted Complex Permittivity and Permeability The extracted ε’, ε”, μ’ and μ” are plotted in Fig. 4-8 (the middle lines). The estimated error bars are also included, the details of which will be described in Section 4.6. The extracted ε’ from 8 to 50 GHz are between 700 and 250, and ε” are between 3400 and 350, corresponding to a conductivity of 1500-810 S/m (σ = ε”ε0ω), as shown in Figure 4-9 . The extracted μ” are about 0, and μ’ are negative with the absolute values smaller than 1.5, which is believed to be resulted from the large systematic errors as one can see that the error bars at many frequencies in Figure 4-8 (c) cross the μ’ = 0 line. (The calculation of systematic errors will be presented in Section 4.6.) The extinction coefficients n” are plotted in Figure 4-9 as well. 97 2000 1500 ε’ 1000 500 0 -5 0 0 0 10 20 30 40 50 40 50 40 50 40 50 F re q u e n c y (G H z ) (a) 4000 ε” 3000 2000 1000 0 0 10 20 30 F re q u e n c y (G H z ) (b) 2 μ’ 1 0 -1 -2 0 10 20 30 F re q u e n c y (G H z ) (c) 2 μ” 1 0 -1 -2 0 10 20 30 F re q u e n c y (G H z ) (d) Figure 4-8. The effective medium properties of the nanotube paper extracted from the measured S-parameters: (a) ε’, (b) ε”, (c) μ’ and (d) μ”. The circled lines are the extracted values and the regions above and below them are the error bars. 98 n′ 0 -20 -40 5 10 15 20 25 30 35 40 45 50 35 40 45 50 35 40 45 50 Frequency (GHz) n′′ 40 20 0 5 10 15 20 25 30 Frequency (GHz) σ (S/m) 2000 1000 0 5 10 15 20 25 30 Frequency (GHz) Figure 4-9. Extracted complex index of refraction and conductivity of the nanotube paper. 4.5. Extraction Verification by Finite-Element Simulation The algorithm discussed above for extraction neglects the leakage from the edges of the waveguides, since the MWNT samples are very thin (~ 89 µm) and lossy. To validate this assumption and verify our algorithm, a HFSS model is set up with the extracted frequency-dependant complex ε and μ assigned to a uniform thin slab of the same thickness as the measured nanotube paper. The slab is sandwiched in between two waveguides as shown in Figure 4-10. The excitations are defined on the top and bottom waveguide ports. The boundaries of the waveguides and the edges of the sample are first 99 set to be perfect electric conductor (PEC) to simulate the ideal case as assumed in the extraction. The simulated S-parameters are plotted together with the experimentally measured data in Figure 4-5 (solid curves). They match very well, which verifies our algorithm. The HFSS simulations are also performed with the waveguide flanges and radiation boundaries included, which would capture the leakage effects from the edges. Very little difference in S-parameters (less than 10% of the VNA systematic uncertainties shown in Table 4-2) is observed compared to the simulated results in the ideal closed waveguide case. Therefore, neglecting the leakage from the waveguide edges in the extraction algorithm is a valid assumption. This conclusion is also confirmed experimentally as good measurement repeatability is achieved for several samples with different sizes and shapes as long as the waveguide aperture is covered completely. E field direction Waveguide port 2 Waveguide port 1 88.9 µm slab assigned with extracted ε & µ (MWNT paper) Figure 4-10. The HFSS simulation model to verify the extracted material properties. The boundaries of the waveguides and the edges of the sample slab sandwiched in the middle are set to be PEC here. 100 4.6. Systematic Error Analysis of the Characterization Method When the transmission or reflection coefficient is close to unity, the extraction of the effective medium properties from the measured S-parameters can be challenging due to large uncertainties . As seen from Figure 4-5, for the waveguide characterization of the nanotube papers, the measured reflection coefficients S11 have magnitudes close to 0 dB, which may lead to large uncertainties. To better understand the systematic uncertainties in the extracted material properties, a rigorous error analysis based on the VNA uncertainties is performed. Assuming appropriate calibration scheme, intermediate frequency (IF) bandwidth, source power level, and number of averages, the VNA uncertainties for the magnitudes and phases of both S11 and S21 at different frequency bands and signal levels can be estimated. With our experimental settings, the uncertainties of S-parameters are summarized in Table 4-2. Although there are some variations on the S-parameter uncertainties at different frequency bands, they are not dramatically different from each other. The systematic errors of ε’, ε”, μ’ and μ” are calculated by the following equations: Δε ′ = ( ∂ε ′ ∂ε ′ ∂ε ′ ∂ε ′ Δ | S11 |)2 + ( Δ∠S11 )2 + ( Δ | S21 |)2 + ( Δ∠S21 )2 ∂ | S11 | ∂∠S11 ∂ | S21 | ∂∠S21 Δε ′′ = ( ∂ε ′′ ∂ε ′′ ∂ε ′′ ∂ε ′′ Δ | S11 |)2 + ( Δ∠S11 )2 + ( Δ | S21 |)2 + ( Δ∠S21 )2 ∂ | S11 | ∂∠S11 ∂ | S21 | ∂∠S21 Δμ ′ = ( ∂μ ′ ∂μ ′ ∂μ ′ ∂μ ′ Δ | S11 |)2 + ( Δ∠S11 )2 + ( Δ | S21 |)2 + ( Δ∠S21 )2 ∂ | S11 | ∂∠S11 ∂ | S21 | ∂∠S21 Δμ ′′ = ( ∂μ ′′ ∂μ ′′ ∂μ ′′ ∂μ ′′ Δ | S11 |)2 + ( Δ∠S11 )2 + ( Δ | S21 |)2 + ( Δ∠S21 )2 ∂ | S11 | ∂∠S11 ∂ | S21 | ∂∠S21 (4.15)-(4.18) 101 Table 4-2. Uncertainties of S-parameters Symbol X-band Ka-band Ku-band Q-band Δ|S11| Δ∠S11 (deg) Δ|S21| (dB) Δ∠S21 (deg) 0.0094 0.555 0.15 0.998 0.0094 0.553 0.141 0.94 0.0093 0.56 0.15 1.05 0.0094 0.558 0.154 1.076 The partial derivatives are computed numerically. For example, to calculate ∂ε'/∂|S11|, we evaluate ε’ with |S11| = |S11| + δ while all other parameters remain the same, and δ is a very small number, chosen to be 10-4 in our calculations. Then ∂ε'/∂|S11| is calculated by ∂ε ′ ∂ | S11 | = ε ′(| S11 | +δ ) − ε ′(| S11 |) δ (4.19) Other derivatives can be calculated in a similar fashion. The systematic errors of the complex permittivity and permeability are then evaluated at each frequency point and the corresponding error bars are plotted in Figure 4-8. Some of the systematic errors are rather large, especially for ε’, μ’ and μ” at lower frequencies. The imaginary part of the permittivity ε”, however, is relatively better compared to others, at less than +/-15% of error over the entire frequency range. In addition, these VNA uncertainties used (provided by Agilent) are the worst cases and may have caused overestimation of the errors, which explains why the measured statistical uncertainties in ε” seem to be much smaller than the estimated values. The experimental results of several different samples all have fairly close ε” (within +/-6.5% or less of variation across the entire frequency range, much better than the estimated error 102 bars). This makes sense intuitively because the multi-walled carbon nanotubes tend to be metallic, so that the frequency-dependent ε” dominates the microwave loss mechanisms and can be measured most reliably. However, the other material parameters are quite different for several different samples at low frequency range especially the X-band (8 to 12 GHz), consistent with the large estimated error bars (the data of other samples are not shown here). It is also found that the uncertainties associated with S11 have much larger impacts on the results than the uncertainties of S21. This is also understandable, as in our case, most of the incident power is reflected and the S11 magnitude is already very close to unity so that any change on material properties will cause much smaller relative differences on the reflection coefficient S11 than on the transmission coefficient S21. Conversely, if there is any error associated with S11 measurement, significant changes may be resulted on the extracted material properties whereas the impact of the measurement uncertainty in S21 will not be as significant. As mentioned above, the errors at lower frequencies are worse than those at higher frequencies, especially for ε’ and μ’, which at first glance is counter-intuitive as measurements at higher frequency normally have higher associated uncertainties. However, it can be understood by noticing the impact of phase uncertainties. Since the sample is very thin (~ 89 μm), its electrical length is very small compared to wavelengths at low frequencies. Thus, a small variation on the measured phases will cause a large difference on the material properties, especially for n’, ε’ and μ’, as indicated by Eqs. (4.12) - (4.14). At higher frequencies, the situation is quite improved as the wavelength decreases. However, since the loss is much less dependent on frequency, the uncertainties 103 of ε” and μ” are about the same over the entire frequency range. This is consistent with our experimental observation. At lower frequencies, especially at X-band, although the measured S-parameters for different samples are close to each other, the extracted ε’ and μ’ may vary dramatically, even swinging from negative values to positive values, whereas in most of the cases their error bars overlap. However, at Ka- and Q-bands, they are fairly close to each other. Besides the VNA uncertainties, other effects such as the gap between the two waveguides and the sample thickness variation (≤ 5 µm) are also possible error sources. Nevertheless, as discussed in Section 4-5, the HFSS simulations, when taking the waveguide flanges and radiation into account to capture the leakage from the gap, reveal that the differences in S-parameters compared with the ideal case are less than one tenth of the VNA uncertainties (shown in Table 4-2). Therefore, it is reasonable to neglect the leakage. On the other hand, the extraction using the thickness varied by 5 µm introduces about 5% of errors on all four effective media parameters, as expected. Since these errors contribute much less than the vector network analyzer uncertainties, they are not included in the error bars. As both the error analysis and the measured results show that the extracted ε” have good accuracy, it is logical to explore ways to improve the accuracy of the other extracted parameters using ε”. One common method is the Kramers-Kronig transformation -. The Kramers-Kronig relations show that either the real or imaginary component of the complex permittivity at any particular frequency can be constructed by knowing the other component over all frequencies. These relations have 104 been widely used in microwave and optical ranges to acquire material properties. However, to use the Kramers-Kronig relations, one component of the permittivity needs to be known over all frequencies, or at least over a very large frequency range, which is not the case here. Therefore, microwave characteristics of the nanotube papers need to be combined with THz or even optical properties to improve the accuracy of the ε’, μ’ and μ” by employing the Kramers-Kronig relations. 4.7. Intrinsic Properties of MWNTs Knowing the effective permittivity of the nanotube paper, which is a composite of randomly aligned multi-walled carbon nanotubes and air, the intrinsic permittivity of the nanotubes may be extracted by applying the effective medium theory. For a composite that contains a random mixture of materials A and B, the effective permittivity of the medium can be calculated by the following equations -. fa ε a − ε eff ε a + K ε eff + fb ε b − ε eff ε b + K ε eff =0 (4.20) where εa and εb are the complex permittivity of material A and material B, respectively, fa and fb are the volume fractions of each material, and K is the screening parameter of the particles and can be evaluated by K= 1− q q The Lorentz depolarization factor q can be calculated by (4.21) 105 q= 1 / a2 1 / a1 + 2 / a2 (4.22), which assumes the particles at the microscopic level are ellipsoids of rotation and a1, a2 are respectively the semi-axes parallel and perpendicular to the direction of the electromagnetic wave. This effective medium theory described by Eq. (4.20) is often referred to as the Bruggeman theory. For a single multi-walled carbon nanotube with a diameter of 20 nm and a length of 10 µm (based on the observation of individual nanotubes under SEM), the ratio of its length to diameter is much greater than 1 (~ 200). Although a nanotube is cylindrical, it is reasonable to treat it as an extremely stretched ellipsoid, which leads to the value of K being 501. Since the nanotube papers studied here has a density of 1.8 g/cm³ and the graphite density is 2.2 g/cm³, the volume fraction of nanotubes in the paper is estimated to be 0.818. Now if we consider the nanotubes are material A and the air is material B, the intrinsic permittivity of the carbon nanotubes can be found by Eq. (4.20), given the extracted permittivity of the nanotube paper (εeff) and εb = 1. The computed real and imaginary parts of the permittivity are plotted in Figure 4-11. Compared to the originally extracted permittivity, the intrinsic ε’ and ε” are both approximately increased by a factor of 1.2, which indicates that the conductivity is also increased by the same factor. One thing to point out is that this conductivity is much smaller than the reported 1-D DC conductivity along the axis of a multi-walled carbon nanotube, which is expected since the nanotubes in the paper form samples are randomly aligned and the conductivity along all different directions is averaged out. 106 1000 ε′ MWNT 800 600 400 200 5 10 15 20 25 30 35 40 45 50 35 40 45 50 Frequency (GHz) ε′′ MWNT 6000 4000 2000 0 5 10 15 20 25 30 Frequency (GHz) Figure 4-11. Real (ε’MWNT) and imaginary (ε”MWNT) parts of the relative intrinsic permittivity of a single multi-walled carbon nanotube (MWNT) computed using the effective medium theory. 4.8. Conclusion A simple broadband microwave characterization method for carbon nanotubes or similar type of thin and lossy material samples has been presented in this paper. To extract the microwave material properties, the S-parameters of the nanotube papers installed in between two waveguides are measured from 8 to 50 GHz. The complex permittivity and permeability of the nanotube papers are extracted from the S-parameters using the Nicolson-Ross-Weir approach. The uncertainties of the extraction method are analyzed and the understanding of the error sources provides the guidelines for future improvement of this characterization technique, such as applying the Kramers-Kronig relations to calculate the real part of the permittivity from the more reliably extracted 107 imaginary part of the permittivity. The method to extract the intrinsic characteristics of multi-walled carbon nanotubes by applying the effective medium theory is introduced, which provides valuable data for potential microwave applications involving multiwalled carbon nanotubes. 108 CHAPTER 5. THZ CHARACTERIZATION OF MWNT PAPER  A typical commercial VNA can only measure S-parameters up to 67 GHz. Some of them can be upgraded to 110 GHz. To characterize the Multi-walled carbon nanotube (MWNT) papers to higher frequencies such as the THz range, THz Time-Domain Spectroscopy (THz-TDS) is utilized instead. Both transmission and reflection experiments are performed in order to measure both the complex refractive index and the wave impedance. This method allows simultaneous extraction of both the permittivity ( ε = ε '− iε " ) and permeability ( μ = μ '− i μ " ) without any assumptions. Experimental results are obtained from 50 to 370 GHz and compared well with the microwave data (8 to 50 GHz) of the same sample measured using a vector network analyzer (VNA). The measured complex permittivity can be fitted with a Drude-Lorentz (D-L) model in the 8 to 370 GHz frequency range. 5.1. Motivation Although only occupying the frequency range from 3x1011 Hz to 3x1012 Hz in the electromagnetic spectrum (Figure 4-1), there have been many research interests stimulated in THz frequency regime in the past decade. Compared to the microwave regime, this portion of spectrum offers more bandwidth but is currently very much underutilized. Many applications have been proposed or realized in practice, including astronomic imaging, tissue imaging, tumor recognition, contraband detection, radar, communications, etc. [97-98]. Many potential applications of CNTs at THz frequency 109 have been reported as well, such as THz CNT-antenna, THz CNT-transistors, etc. [25, 27, 83, 100]. Therefore, it is very important to study the electrical properties of CNTs at THz frequencies. As discussed in the previous chapter, the electromagnetic properties of a material can be described by its complex relative permittivity, ε = ε’ – i ε”, and its complex relative permeability, µ = µ’ - i µ”, in which the imaginary parts represent losses. In order to characterize both the dielectric (ε) and magnetic (µ) behaviors of a MWNT paper, it is necessary to perform two independent measurements on the sample, for example, both the transmission and the reflection measurements . Most of the previously reported THz-TDS material characterizations, including previously reported CNTs characterizations [40, 41, 102, 103], involve only one measurement, either the transmission or the reflection. The complex permittivity ε is then extracted under the assumption that the sample under test is non-magnetic, or µ = 1, which is very probably invalid for CNTs. In this work, MWNT papers are measured in both the transmission and the reflection configurations, as shown in Figure 5-1. Therefore, with both magnitude and phase information of the transmission and reflection coefficients, the complex permittivity and permeability of the MWNT papers can be extracted simultaneously. 5.2. Sample and Experimental Setup The MWNT papers studied here are the same samples used for microwave measurement. They are provided by NanoLab Inc.  and the SEM image of the paper is shown in 110 Figure 4-2, which shows that MWNTs are randomly entangled to form the paper. The MWNT papers have a thickness of ~ 89 µm. Figure 5-1. (a) THz-TDS transmission characterization setup; (b) THz-TDS reflection characterization setup. The incident E field is S-polarized in both measurements. A photoconductive THz-TDS system from Picometrix Inc. is employed to characterize the MWNT papers. As shown in Figure 5-1, a THz pulse is generated by biased coplanar lines on a low-temperature-grown GaAs substrate, under the excitation of 111 a femtosecond laser. The detector is a 5-μm gap dipole antenna, which is also fabricated on a low-temperature-grown GaAs substrate. One part of the same femtosecond laser pulse is guided to the detector through an optical delay line as the gating signal for recording the received THz waveform. The sample under test is placed in the THz pulse beam path between the emitter and the detector. Both transmission (Figure 5-1 (a)) and reflection (Figure 5-1 (b)) responses can be measured with appropriate configurations. Because the measurement is coherent, both the magnitude and phase of the sample responses are obtained. The TDS used here has a bandwidth spanning from 50 GHz to 1.2 THz with high signal-noise-ratio in this frequency range . 5.3. Measured Reflection and Transmission Data in Time Domain and Frequency Domain In the normal incidence transmission configuration, the calibrated complex transmission coefficient is obtained by dividing the sample transmission spectrum with a reference spectrum taken without the sample in the beam path (as a lossless through reference). In the reflection configuration, the reference spectrum is obtained by placing a polished metal plate at the position of the sample (assumed to be a perfect reflector with a reflection coefficient of -1). The reflection spectrum of the MWNT paper is then calibrated by comparing the reference and sample spectra. Since the THz emitter and detector of the TDS cannot be co-located, the reflection measurement has an oblique incidence with an incidence angle of 26 ° . Collimating mirrors are applied in both configurations to confine the beam waist completely within the sample cross section area. 112 Multiple numbers of transmission and reflection measurements are performed and good repeatability of the measured spectra is observed. (a) (b) (c) Figure 5-2. THz-TDS measurement results of (a) the reflection pulses of the reference (dashed line) and a MWNT paper (solid line); (b) the transmission pulses of the reference (dashed line) and the MWNT paper (solid line); (c) Fourier transformed frequency domain signals: transmission reference (dash-dotted line), sample transmission (dotted line), and sample reflection (solid line), noise floor (dotted line). The measured time domain pulses of a MWNT sample and the references for both the reflection and transmission cases are shown in Figure 5-2 (a) and Figure 5-2 (b), respectively. Also plotted in Figure 5-2 (c) is the Fourier transformed frequency domain transmission reference (dashed line; for clarity, the reflection reference is not plotted since it is quite similar to the transmission reference), and the sample transmission (dotted line) and reflection (solid line) magnitudes. It can be observed that the reflected 113 signal dominates the transmitted signal at the interested frequency range, for example, the reflected signal strength is only slightly smaller than the approximately perfect reflector reference signal (Figure 5-2 (a)), while the transmitted signal strength is much smaller than the through reference signal (Figure 5-2 (b)). This is expected since the conductivity of MWNT papers measured at microwave frequency is quite high (~1500 S/m at 8 GHz). Because of the TDS bandwidth and the experiment noise level, the measured data of the 89-µm thick MWNT paper is only valid from about 50 to 370 GHz. The upper frequency is limited by the high transmission loss of the MWNT paper, that is, the transmission magnitude (Figure 5-2 (c), dash-dotted line) is buried beneath the experiment noise floor (Figure 5-2 (c), dotted line) beyond 370 GHz. 5.4. Material Property Extraction The calibrated and Fourier transformed reflection and transmission coefficients are used to extract the electromagnetic properties of the MWNT paper. The relative permittivity ε and the relative permeability µ are related to the sample complex refractive index n = ε ⋅ μ and the normalized wave impedance z = μ / ε . Assuming no internal Fabry-Perot type reflections within the sample (will be justified in Section 5.6), the normal-incidence transmission coefficient T0, and the oblique-incidence reflection coefficient R0 for the S-polarized incident wave read: T0 (n, z ) = 4z exp[2π i (1 − n) fd / c] ( z + 1) 2 (5.1) 114 sin 2 θ i n2 R0 (n, z ) = sin 2 θi z cos θi + 1 − n2 z cos θi − 1 − (5.2) where f is the frequency, d = 89 µm is the sample thickness, c is the speed of light, and θ i = 26°is the oblique incidence angle. As discussed previously, if the sample under test is non-magnetic (µ = 1), then both z and n are functions of ε only and either of the Eqs. (5.1) and (5.2) is sufficient to extract the material properties of the sample. For a sample thick enough compared to the input pulse width and with low loss, its TDS output signal would contain a series of pulses separated in time, corresponding to different orders of Fabry-Perot reflections. Due to the small thickness and high loss of the MWNT paper under test, these multiple reflection pulses are indistinguishable in the measured output time domain waveforms. However, in this case, the internal reflections are largely attenuated when propagating within the MWNT paper, thus having a small impact (a few percent) on the total transmission and reflection coefficients [101, 103]. For example, in the case of the normal incidence transmission, the transmission term T1 due to the first order Fabry-Perot reflection, can be expressed as: 2 ⎛ z −1 ⎞ T1 (n, z ) = T0 (n, z ) ⎜ ⎟ exp(−4π infd / c) ⎝ z +1⎠ (5.3) which will be much smaller than T0 if the sample is lossy enough. Therefore, the internal reflection contributions to the transmission and reflection coefficients are ignored and the two complex Eqs. (5.1) and (5.2) are used to extract the complex quantities n and z. Because the oblique-incidence for the reflection complicates Eq. (5.2) compared to the 115 normal-incidence case, Eqs. (5.1) and (5.2) cannot be solved analytically. Therefore numerical fittings are necessary to obtain n and z. The permittivity ε and permeability μ of the sample are then calculated by the following equations: ε= n n '− in " = z z '− iz " μ = n ⋅ z = (n '− in ")( z '− iz ") (5.4) (5.5) One issue that needs to be solved to accurately extract the material properties is related to the phase ambiguity of the transmission coefficient. From Eq. (5.1), the real part of the refractive index n = n’ – i n” can be written as: ⎡ ⎛ 4 z ⎞⎤ ⋅c ⎢ Phase(T0 ) − Phase ⎜ 2 ⎟⎥ ⎝ ( z + 1) ⎠ ⎦ ⎣ n ' = 1− 2π fd (5.6) Even though Eq. (5.6) is not directly used to calculate n ' , it clearly illustrates that a phase wrapping (or ambiguity) of 2mπ (m is any integer) in the numerator will lead to different values of n ' . In our numerical calculation, multiple branches of possible n ' solutions are obtained due to this phase ambiguity. Because the MWNT papers are very thin (89 µm), the m = 0 branch is presumed to be the physical solution. The appropriate selection of the correct branch is confirmed by comparing the obtained n’ with the previously characterized n ' of the same MWNT paper from 8 to 50 GHz using the VNA approach . The physical solution branch should maintain the continuity of the extracted n ' at 50 GHz. 116 Figure 5-3. Extracted index of refraction (dots connected with line): real part n’ (a) and imaginary part n” (b). VNA measurement results from 8 to 50 GHz are also plotted (open circles). The extracted real and imaginary parts of the refractive index of the MWNT sample (dotted line) are plotted from 50 to 370 GHz in Figure 5-3 (a) and Figure 5-3 (b), respectively. Error bars included in the plots are obtained statistically based on multiple measurements (most of them are very small, indicating good experimental repeatability). The microwave frequency results from 8 to 50 GHz (open circles) measured using a 117 VNA  are also included for comparison. From the plots, the real part of n increases from -25 at 8 GHz to 8 at 90 GHz, then eventually decreases to around 5 at 370 GHz. The imaginary part of n experiences a sharp drop from 38.5 to around 8 in the microwave region (8 GHz to 50 GHz), then slowly decreases to 5.8 from 50 GHz to 370 GHz. As shown in Figure 5-3, near the low frequency end, the indices of refraction measured with TDS fluctuate a bit. The real part n’ does not exactly overlap with the VNA measured values although the trends are continuous, while the imaginary part n” agrees better with the VNA results. One reason for this discrepancy is due to the small thickness of the MWNT paper such that a slight variance in the measured phase will cause significant change in the extracted index of refraction, especially for the real part . Another possible reason for the scattering of data at the low frequency end is the contribution from multiple internal reflections, which will be discussed more in Section 5.6. Nevertheless, the results from the VNA (microwave) and the THz-TDS match reasonably well, which validates the characterization techniques and the extraction algorithm used here. 118 Figure 5-4. Extracted complex permittivity and permeability: (a) µ’, (b) µ”, (c) ε’, and (d) ε”. VNA (open diamonds, from 8 to 50 GHz) and THz-TDS (open triangles, from 50 to 370 GHz) results are plotted together. The extracted real and imaginary parts of the permittivity are also fitted by a Drude-Lorentz model (solid lines in (c) and (d)). The complex permittivity ε and permeability µ are obtained from the numerically solved n and z using Eqs. (5.4) and (5.5). The extracted µ’, µ”, ε’ and ε” based on the THz-TDS results from 50 to 370 GHz are plotted (open triangles) in Figure 5-4 (a), (b), (c) and (d), respectively. The VNA results from 8 to 50 GHz are also included (open diamonds) for comparison. The measured µ’ varies from -1 to 1.8, and µ” varies from ~ 0 to 2.1, showing a weak magnetic response of the MWNT paper. This is consistent with the VNA measured microwave results. The measured ε’ decreases with frequency from 119 650 to 20, and ε” also decreases with frequency from 3400 to less than 10. A discontinuity is observed at 50 GHz between the THz-TDS and the VNA results for both ε’ and ε”. This is traced back to the discrepancy in n ' as discussed previously. Since there are more uncertainties associated with THz measurement around 50 GHz, the VNA results are believed more reliable in this range. 5.5. Drude-Lorentz Model Fitting of Extracted Permittivity In order to gain more physical insights into the extracted material properties and provide useful practical formula for future applications, different models have been tried to fit both the real and imaginary parts of the permittivity. Although the Drude model  was applied and a reasonable fitting was obtained in  for X-band, for the wider frequency range (8-370 GHz), it does not appear to be a good description of the nanotube paper. The simple Drude model does not fit ε’ and ε” curves simultaneously. Therefore, the Drude-Lorentz model is employed here instead, which combines the Drude term and localized Lorentzian absorptions. It can be described as ωp ω p1 2 ε = εc − ω (ω − jΓ ) 2 + −ω + jωΓ1 + ω1 2 2 (5.7) where only a single localized Lorentzian oscillation term is used. In Eq. (5.7), εc is a constant independent of frequency, ωp is the plasma frequency, Γ is the relaxation rate of electrons, ωp1 represents the oscillator strength, and ω1 and Γ1 are the center frequency and the spectral width of the resonance, respectively [39, 41]. With this model, ε’ and ε” can be simultaneously fitted at least qualitatively from 8 to 370 GHz, as shown in Figure 120 5-4 (c) and (d) together with the extracted permittivity results. The fitting is achieved by minimizing the difference between the extracted permittivity and Eq. (5.7). The two curves are fitted simultaneously with some accuracy sacrificed in ε” fitting to compensate the fitting of ε’. Since at lower frequencies, relatively high uncertainties are associated with the TDS results, the extracted ε’ and ε” from 50 to 80 GHz are not included during the fitting process. The resulting parameters are shown in Table 5-1. It is worth to point out that the Drude term plays a much more important role on fitting the curve of ε”compared to the Lorentz term does. On the other hand, the fitting of ε’ curve is sensitive to the parameters from both terms, especially to the values of ωp, ωp1 and ω1. Table 5-1. Fitting Parameters for Drude Lorentz Model εc * All parameters have the unit of rad/s except εc is unitless. ωp ωp1 ω1 Γ1 Γ 60 7.49x1012 6.46x1011 1.15x1014 4.2x1012 8.1x1013 Compared to the reported Drude-Lorentz fitting parameters for SWNT films , the plasma frequency ωp and the relaxation rate of electrons Γ found here for MWNT papers are 100 and 1000 times lower, respectively. The localized Lorentzian oscillation parameters, on the other hand, are roughly on the same order. 5.6. Discussion As described in the previous section and reported by , the total transmitted or reflected field measured in time domain is a vector summation of many fields with 121 different orders (0th, 1st, 2nd…). For instance, the mth order field is after m times internal reflections. The highest order number is determined by the truncation time in the measurement. The orders reaching the detector after the truncation time are not included in the time domain waveform. However, in the material parameters extraction algorithm, Fabry-Perot type multiple internal reflections are ignored based on the assumption that the loss in the material is high enough. In order to justify this assumption, the attenuation, or loss factor (for both the transmission and reflection measurements) due to one round trip of the internal reflections (for normal incidence) can be evaluated by Eq. (5.8). It is defined as the ratio of the electric field after one round-trip internal reflection to the field before the internal reflection. For an oblique incidence case, the attenuation is even higher for each round trip of internal reflection. ⎡⎛ z − 1 ⎞ 2 ⎤ LossFactor = mag ⎢⎜ ⎟ exp(−4π n " fd / c) ⎥ ⎢⎣⎝ z + 1 ⎠ ⎥⎦ (5.8) This loss factor for the normal incidence case is calculated using the extracted z and n” from 50 to 370 GHz and plotted in Figure 5-5. It can be observed that the multiple internal reflection effect is much smaller at high frequencies than at low frequencies. Beyond 100 GHz, because the loss factor stays below 4% and decreases with increasing frequency, the impact of Fabry-Perot internal reflections can be well ignored. However, from 50 to 60 GHz, the loss factor ranges from 0.1 to 0.15, which indicates that ignoring internal multiple reflections may lead to some inaccuracy in the extracted material parameters. As mentioned in the previous section, this contributes to the inconsistency observed between the VNA and the THz-TDS results. Therefore, compared to the 122 previously reported microwave VNA characterization method, which measures total reflection and transmission simultaneously in frequency domain and leads to an accurate solution of material properties, the THz-TDS method reported here is only accurate to the first-order approximation. However, it is evident that, for lossy CNT samples, the THzTDS characterization method is adequate to extract accurate material properties and provide valuable THz data especially above 100 GHz. Figure 5-5. Field magnitude loss factor after one round trip internal reflection, calculated from the extracted MWNT paper parameters. In the microwave frequency regime, the magnitudes and phases of both the reflection and transmission coefficients can typically be measured simultaneously in the format of the scattering parameters (S-parameters) by a VNA . In THz frequency 123 range, on the other hand, the reflection and transmission coefficients need to be measured separately. In this work, because both the reflection and transmission responses are measured by the THz-TDS, the complex permittivity and permeability can be extracted simultaneously without any assumption. Even though no strong magnetic response of the MWNT paper is observed, this method should still be more advantageous than just using the transmission or reflection measurement alone. It is found that the agreement between the index of refraction n obtained by the latter method and the microwave VNA results is significantly worse than that plotted in Figure 5-3. As presented in Chapter 4, since the MWNT samples studied can be considered as a composite made of a network of randomly oriented MWNTs and air, the effective medium theory can be applied to remove the impact of air and obtain the intrinsic properties of the MWNTs. Similar to what is presented in Chapter 4, by applying the Bruggeman theory, the extracted intrinsic permittivity increases by a factor of 1.2 after removing the effect of air. 5.7. Conclusion MWNT papers have been characterized by Terahertz Time-Domain Spectroscopy. Both transmission and reflection measurements are performed to simultaneously determine the complex permittivity and permeability of the sample. The extracted index of refraction, permittivity and permeability from 50 to 370 GHz are consistent with previously measured values from 8 to 50 GHz using a microwave vector network analyzer. A Drude-Lorentz model is applied to fit both the real and imaginary parts of 124 the permittivity from 8 to 370 GHz. The measured material properties provide valuable data for potential MWNT-based microwave and THz applications. 125 CHAPTER 6. INDIVIDUAL CARBON NANOTUBE CHARACTERIZATION In this chapter, studies on the RF-frequency characterization of individual carbon nanotube are presented. A systematic analysis of the impact of port impedance and parasitics on nanotube RF measurement is performed. Then a tapered line impedance matching approach is taken to improve the matching between the 50-Ω port impedance and the high impedance of a SWNT, at the same time reducing the parasitics. Several designs are proposed to increase the signal contrast between the responses with and without a nanotube across the test fixture. After that, a de-embedding algorithm is presented and demonstrated to obtain the intrinsic nanotube properties. At last, the ongoing work of the involved circuit fabrication process is discussed. 6.1. Introduction Although various applications of CNTs have been proposed or demonstrated at high frequency, such as a CNT-FET with current gain cut-off frequency up to 80 GHz , CNT antennas resonant in the THz regime ([25, 27]), and CNT transmission lines , etc., the intrinsic properties of individual CNTs have not been well studied at microwave and THz frequencies. On the other hand, to further investigate CNTs’ potential in integrated circuits, an accurate model for the device is indispensable. Therefore, the high frequency characterization of individual tubes is critical to expedite the development of microwave and/or THz circuit applications of CNTs. The most well- 126 known theoretical model of a SWNT was first proposed by Bockrath  and also presented by P. J. Burke in 2002 . However, the experimental data for the verification of this model has been rarely reported [36, 109]. Most of the existing experiments are either at low frequencies (below MHz) or have too large uncertainties to be conclusive. For instance, in the individual CNT measurement reported by Plombon et. al. , the measured S-parameters could only be differentiated from the reference standard below 8 GHz and the signal level was very close to the noise floor, which might lead to large uncertainties in the extracted CNT equivalent circuit parameters. The quantum inductance associated with the 1-D Luttinger system as proposed in the model has not yet been explicitly verified. As discussed in the introduction chapter, the biggest challenges to conduct the individual tube measurements include the significant mismatch between nanotubes’ high intrinsic impedance (~10 KΩ to MΩ) and typical 50-Ω microwave testing systems, dominant parasitics of testing structures masking the CNT intrinsic properties at microwave frequencies , and difficulties in fabrication. A simple example to illustrate the mismatching between a high-resistance device and 50-Ω equipment as well as the parasitic effect at microwave frequency is shown in Figure 6-1 (a). It is assumed that there is a parasitic capacitance of 5 fF between the input and output ports, which is a typical value for a 50-Ω transmission line as will be shown later in this chapter. The resulting reflection (S11) and transmission (S21) coefficients are plotted in log-scale (dB) for a resistance of 100KΩ and 200KΩ from 1 to 50 GHz. Due to the significant mismatch, transmission is very small at lower frequencies. As frequency 127 increases, the parasitic coupling becomes strong thus the transmission increases. However, the small impedance of the parasitic compared to the highly resistive device masks both reflection and transmission differences when the resistance changes from 100 kΩ to 200 kΩ over the entire frequency range, causing the two sets of curves in Figure 6-1 (a) not differentiable from each other. In addition, as the signal level is very low and close to the noise floor, large uncertainties are associated with the measurement. Therefore, it is very challenging to accurately measure a high-impedance device, such as a CNT, in presence of both significant impedance mismatch and parasitics. Now if matching networks are applied at both the input and output to transform the port impedances from 50 Ω up to 10 kΩ, meanwhile the parasitic capacitance is reduced by two orders in magnitude, the resulting transmission coefficients are raised up by more than 25 dB at 1 GHz and become easily detectable (Figure 6-1 (b)). Furthermore, the differences in both the reflection and transmission coefficients between the 100-KΩ and 200-KΩ devices are well resolved over the entire frequency range. This example demonstrated that appropriate impedance matching and parasitic reduction must be performed in order to accurately characterize an individual CNT device. In this chapter, appropriate impedance matching techniques will be applied to optimize test fixture designs to achieve better measurement sensitivity and reduce the parasitics at the same time. In addition, a de-embedding procedure is developed to calibrate out the parasitics and obtain the intrinsic CNT properties. A fabrication process for CNT-based circuits using electron beam lithography (EBL) equipped with good alignment capability will also presented. 0 -10 -0.05 -20 -0.10 -30 200 KΩ 100 KΩ -0.15 -0.20 0 10 20 30 Frequency (GHz) (a) 50 Ω 40 -50 50 (b) -10 200 KΩ 100 KΩ R IMN -20 dB (S21) -1.0 50 Ω OMN 0.05 fF -15 dB (S11) 50 Ω Parasitic -40 0 -0.5 R 5 fF dB (S21) dB (S11) 128 Parasitic 50 Ω -1.5 -2.0 0 10 20 30 Frequency (GHz) 40 -25 50 10 kΩ 10 kΩ Figure 6-1. Demonstration of the impedance mismatch and parasitic effects on highimpedance device characterization. (a) Without matching networks. Parasitic capacitance = 5 fF. (b) With input matching network (IMN) and output matching network (OMN). Parasitic capacitance = 0.05 fF. 6.2. Test Fixture Design 6.2.1. RF model of CNT To design a test fixture with optimized performances for individual tube testing, an initial model of CNTs needs to be identified. It is well known that for a SWNT with ballistic transport, the dc resistance RCNT of the tube is 6.5 kΩ (1/(2G0), G0: quantum conductance) if two channels are counted. Besides that, for a metallic SWNT in the presence of a ground plane as shown in Figure 6-2 (a), it can be viewed as a transmission line . The theoretical model of such a transmission line (Figure 6-2 (b)) presented by 129 Bockrath  and Burke  is resulted from the Luttinger Liquid theory, which describes the interacting electrons in 1-D systems. The model includes the following four elements if assuming single conducting channel. The electrostatic capacitance CE between a nanotube and the ground is calculated by equating the capacitive energy to the stored electrostatic energy. It is related to the tube diameter d and the distance from the tube axis to the ground H (Eq. 6.1). It is believed that the electron-electron interaction effect can be included in CE. The quantum capacitance CQ is resulted from the energy needed to add an extra electron to a 1-D system. Unlike adding an electron in a classical electron gas, which costs no energy, in a quantum electron gas, one must add an electron to an available quantum state above the Fermi energy EF due to the Pauli principle. Therefore, the effective quantum capacitance can be calculated by equating the energy spacing in the 1-D system to the quantum capacitive energy. As displayed in Eq. 6.2, CQ is only related to the Fermi velocity of CNT (vF = 8·105 m/s). The magnetic inductance LM is simply calculated by setting the inductive energy equal to the stored magnetic energy and given by Eq. 6.3. The kinetic inductance LK is calculated from the energy increase of the system to generate a finite current, which can be established by taking some left-mover electrons and promoting them to be right-movers . The energy cost to generate a current of Δμ ⋅ G0 can be calculated by multiplying the promoted electron number N = eΔμ / 2δ by the energy added to each electron eΔμ / 2 , where eΔμ / 2 represents the Fermi energy level increase of the right movers, and δ = hvF 2π L is the energy level spacing in 1-D system. By equating the energy cost to the inductive energy, the kinetic inductance LK can be derived (Eq. 6.4). For a 1-D nanoscale system, LK is much higher 130 than LM (by four orders in magnitude). The estimated values of LK and CQ are 16 nH/μm and 100 aF/μm, respectively. Assuming a tube diameter of 2 nm and a tube-ground distance of 2 mm, the values of LM and CE are roughly 1 pH/μm and 50 aF/μm, respectively. Since a carbon nanotube has two conducting channels and electrons can be spin up or spin down, there are four channels which are interactive to each other as shown in Figure 6-2 (c) . Burke proved that there exist three spin modes (neutral) and one charge mode (common mode). For the scope of this work, only the charge mode is considered, for which all four channels have equal voltage. Then at RF, a CNT can be simplified to an equivalent transmission line model, as shown in Figure 6-2 (d). (a) (c) LK Spin up a LK C Q Spin up b d H LK Spin down a Spin down b CQ LK CQ CQ CE (b) (d) LM LK CQ CE LK/4 4CQ CE Figure 6-2. Transmission line model of a metallic SWNT. (a) Geometry of a SWNT in presence of a ground plane; (b) A single-channel transmission line model; (c) A transmission line model for interacting electrons in a SWNT with four conducting channel; (d) The equivalent transmission line model for the common mode. LM is neglected in (c) and (d).  131 To excite RF voltage waves along this SWNT transmission line is equivalent to collectively excite 1-D plasmons. With this proposed model, the plasmon velocity in the transmission line is proved to be on the order Fermi velocity, as shown in Eq. 6.5 [19, 86], which is two orders lower than the speed of light or the normal wave velocity in a macroscopic transmission line. Hanson  took a different approach to calculate the plasmon resonance by using the derived complex conductivity of a SWNT from Boltzmann’s equation under relaxation-time approximation and applying antenna theory. A Plasmon wavelength on the same order was reached ( v p ≈ 0.02c ). CE = 2πε −1 cosh (2 H / d ) (6.1) CQ = 2e 2 hvF (6.2) LM = μ h ln( ) 2π d (6.3) LK = vp = h 2e 2 vF 4CQ 1 4 1 + ( ) = vF 1 + Lk CQ CE CE (6.4) (6.5) In addition to the intrinsic equivalent circuit elements of a SWNT, the contact resistance RC between the nanotube under test and electrodes needs to be included in parallel with the coupling capacitance CC [36, 110]. Since the parasitic capacitances between the test fixture and the ground are most likely much higher than the electrostatic capacitance and quantum capacitance of a single tube, for the purpose of test fixture design, these two elements are omitted. Likewise, the magnetic inductance can be 132 ignored since the kinetic inductance dominates. Therefore, an individual SWNT can be modeled with the equivalent circuit shown in Figure 6-3. RC RCNT CC LK RC CC Figure 6-3. Equivalent circuit model of a SWNT. In the following sections, RCNT is taken to be 20LCNT kΩ; LK, 16LCNT nH; RC, 15LC kΩ; CC, 0.5LC fF. LCNT is the length of the CNT to be measured and LC is the length of the CNT in contact with the electrodes, which contributes to the contact resistance and the coupling capacitance. Both are in μm. It is worth to point out that there have also been reports of electromagnetic modeling of CNTs  based on the theoretically predicted frequency-dependent CNT conductivity . The modeling is carried out using commercially available EM simulation software based on method of moments (MoM) and finite element method (FEM), etc. However, the reliability of the modeling is depending on the accuracy of the conductivity and still limited by the immaturity of nano-scale simulations. 6.2.2. Impact of Port Impedance and Parasitics on CNT Measurement One of the most commonly used planar transmission lines at radio frequency (RF) is coplanar waveguide (CPW), as shown in Figure 6-4 (a). Compared to other well- 133 known transmission lines, such as microstrip line, stripline, and coplanar stripline, CPW has many advantages. First of all, its geometry is compatible with RF testing probes commonly used in semiconductor device characterization (Figure 6-4 (b)), thus no additional transition design is needed. Second, it works well up to very high frequency since no discontinuities in the ground plane is introduced when connecting the testing probes to a CPW. In addition, it has been very useful for fabricating active circuitry due to the close proximity between the center conductor and the ground . For the above reasons, CPW lines will be chosen for the rest of the study in this chapter. A CPW line has three metal traces on the top of a substrate with the groundsignal-ground (GSG) configuration. The center line is the signal line along which the electromagnetic wave is propagating in a quasi-Transverse Electro-Magnetic (TEM) mode. There are four design parameters to determine the characteristic impedance of the transmission line, including substrate dielectric constant εr and thickness h, center conductor width w, and the gap width between the center conductor and ground g. To reduce possible dielectric loss caused by the substrate, a low-loss material, quartz (tanδ = 0.0001), is chosen for the designs. In order to measure the RF response of a CNT, a gap of several microns is incorporated along the center line so that a CNT can be placed across it and underneath the electrodes as shown in Figure 6-4 (c). As mentioned in an earlier section, there are several factors which can dramatically affect the measurement accuracy of an individual nanotube, including the mismatching between the 50-Ω vector network analyzer (VNA) port impedance and the intrinsic SWNT impedance (~20 kΩ or higher) and test fixture parasitics. To study the 134 impact of these two factors, the parasitics from a typical CPW test fixtures are first determined. A 50-Ω CPW can be realized with the parameters listed in Table 6-1, which are calculated using ADS LineCalc tool. There are mainly two types of parasitic capacitance that can affect the measured response significantly. The first type of capacitance Cp is between the gap edges and the ground. The second type is the capacitance Cg across the center gap, where a nanotube under test will be placed. Shown in Figure 6-5 is the equivalent circuit of the center gap. These two capacitance values are determined by fitting the simulated S-parameters of the gap to the S-parameters of the equivalent circuit. For a 1-µm gap, the fitted values of Cp and Cg are tabulated in Table 6-1. Metal (a) (b) G S (c) CNT G Substrate Figure 6-4. (a) Coplanar waveguide; (b) GSG RF probe configuration; (c) Top view of a CPW test fixture with an individual CNT at the center with two ends buried underneath the electrodes. Table 6-1. A 50-Ω CPW geometries and the associated parasitics εr 3.78 h (μm) w (μm) g (μm) 350 80 8 Center gap Cp (fF) Cg(fF) (μm) 1 0.043 5.50 135 Cg CP CP Figure 6-5. Equivalent circuit of the parasitics. (a) Term Term1 Num=1 Z=50 Ohm C C2 C=Cp fF R R2 R=Rc kOhm (b) Term Term3 Num=3 Z=50 Ohm C C4 C=Cc fF C C8 C=Cp fF C C1 C=Cg fF L R L1 R1 R=Rcnt kOhm L=Lk nH R= C C6 C=Cg fF Term Term2 Num=2 Z=50 Ohm C C3 C=Cp fF R R3 R=Rc kOhm CNT C C5 C=Cc fF C C7 C=Cp fF Term Term4 Num=4 Z=50 Ohm Figure 6-6. Schematics for S-parameter simulations (a) without and (b) with a CNT across the center gap. With the parasitics identified, the reflection (S11) and transmission (S21) coefficients with and without a CNT can now be predicted by ADS simulation . First, 136 considering the case without any impedance matching, the CPW circuits are directly connected to the 50-Ω ports as shown in Figure 6-6. The simulated S11 has magnitude very close to 0 dB (100% reflection) and S21 has magnitude from -50 dB at 1 GHz to -16 dB at 50 GHz (Figure 6-7). This indicates that most of energy is reflected and not transmitted at lower frequencies. At higher frequencies, the contribution from the parasitic capacitance Cg increases the transmitted power. The existence of a CNT across the gap, which is represented by the equivalent circuit model discussed in the previous section, does not affect the transmission signal level much since the parasitic impact dominates. As discussed in Chapter 4, when the magnitude of S11 is close to 0 dB and the magnitude of S21 is very low, the uncertainties associated with the VNA measurement are high. At this signal level, the systematic uncertainty in the S11 magnitude could be as high as 0.1, and that in the S21 magnitude could be as high as 1.3 dB, provided by Agilent’s VNA uncertainty calculator . It is evident that the most of the signal differences (except the S21 phase) between the cases with and without a CNT are not measurable. Although these uncertainty data are obtained from two-port calibration with 1.85mm SMA connectors since the uncertainty data for on-wafer calibrations are not provided by Agilent, they are still expected to provide a guideline for first order estimations. It is worth to point out that the uncertainties provided here are based on the worse-case scenario therefore mostly likely are overestimated values. 137 (a) -10 dB (S21) -0.05 -0.10 -0.15 Phase (S11) (degree -0.20 0 (b) -20 -30 -40 -50 0 5 10 15 20 25 30 35 40 45 50 (c) Frequency (GHz) -2 -4 -6 -8 -10 0 5 10 15 20 25 30 35 40 45 50 Frequency (GHz) 0 Phase (S21) (degree dB (S11) 0.00 90 5 10 15 20 25 30 35 40 45 50 (d) Frequency (GHz) 80 70 60 0 5 10 15 20 25 30 35 40 45 50 Frequency (GHz) Figure 6-7. Simulated S-parameters without (solid lines) and with (triangles) a CNT across the center gap. No impedance matching is provided. (a) S11 magnitude in dB; (b) S21 magnitude in dB; (c) S11 phase in degree; (d) S21 phase in degree. Now, let us consider the case with an impedance matching from 50 Ω to 20 kΩ while keeping the same parasitics, the simulated S-parameter levels are improved dramatically as shown in Figure 6-8. This broadband impedance matching is an ideal case. In practice, the matching in a limited frequency band can be achieved by using two quarter-wavelength (λ/4) transformers in series, which are commonly used in microwave circuits. A λ/4 transformer with an impedance of Z transforms a load impedance Z0 to Z2/ Z0. First, a 10-Ω λ/4 line can be used to transform 50 Ω to 2 Ω. Then a 200-Ω line transforms the impedance from 2 Ω to 20 kΩ. However, a broadband matching to 20 kΩ 138 is not easy to achieve. The S11 magnitude appears to be lowered down to -18 dB, and the S21 magnitude is raised to -0.07 dB at around 10 GHz. With this signal level, the systematic uncertainty in S11 magnitude is about 0.07, and S21 magnitude uncertainty in dB is around 0.4 dB. Therefore, the systematic measurement uncertainties of Sparameters are lowered from the impedance matching. However, this impedance matching does not solve the problem completely. From Figure 6-8, one can see that the impedance matching is very helpful at lower frequencies. For example, at 1 GHz, the difference between the two cases (with and without a CNT) in S11 magnitude is ~ 2.5 dB, in S11 phase is ~ 20°, in S21 magnitude is ~ 1.2 dB, and in S21 phase is ~ 20°. These differences are clearly measurable. But when it is above 5 GHz, the improvements are degraded very fast and the two sets of curves completely overlap due to the impact from the parasitics. Therefore, it is indispensable to reduce the parasitics in order to characterize an individual CNT at high frequency. Nevertheless, at frequencies lower than 5 GHz, a narrow-band impedance transformer may be considered adequate to achieve distinguishable signal contrast. 139 (a) 0 -5 dB (S21) dB (S11) 0 -10 -15 -20 -2 -3 5 10 15 20 25 30 35 40 45 50 (c) Frequency (GHz) -40 -60 -80 -100 -120 0 5 10 15 20 25 30 35 40 45 50 Frequency (GHz) Phase (S21) (degree) Phase (S11) (degree) -20 -1 -4 0 (b) 40 30 20 10 0 -10 -20 0 5 10 15 20 25 30 35 40 45 50 (d) 0 Frequency (GHz) 5 10 15 20 25 30 35 40 45 50 Frequency (GHz) Figure 6-8. Simulated S-parameters without (solid lines) and with (triangles) a CNT across the center gap. Impedance is matched from 50 Ω to 20 kΩ. (a) S11 magnitude in dB; (b) S21 magnitude in dB; (c) S11 phase in degree; (d) S21 phase in degree. 6.2.3. Designs of CNT Test Fixtures As mentioned in the previous section, quarter-wavelength transformers are commonly used in microwave engineering for impedance matching from 50 Ω to any other real load impedance. However, it only works for a limited bandwidth. For broaderbandwidth applications, multi-section transformer can be used, which consists several equal-length sections of transmission lines to realize the transformation. Various types of the multi-section profile lead to different passband responses in the reflection coefficient measurement in frequency domain . As the number of the sections increases, a multi- 140 section transformer becomes a tapered transmission line. Similarly, different profiles of the taper, such as linear taper, exponential taper, and Klopfenstein taper, produce different passband characteristics . A typical tapered transmission line matching has the structure shown in Figure 6-9. The line impedance changes gradually from Z0 at z = 0 to ZL at z = L (L is the matching section length). ZL Z(z) Z0 z 0 L Figure 6-9. Schematic of a tapered transmission line matching network. There is a limitation for all of the above methods due to the fabrication restriction. Since only transmission lines within a range of impedances not requiring too large or too small dimensions can be physically manufactured, the matching directly from 50 Ω to 20 kΩ using only transmission lines is very difficult to implement. In addition, the design geometries at the two ends need to be compatible to the 150 µm ground-signal tip spacing of our GSG probe (Figure 6-4 (b)). In this work, a linear taper configuration is chosen for the test fixture design on a quartz substrate (εr = 3.78, tanδ = 0.0001). The maximum impedance used in the section is 185 Ω, which corresponds to a center line width (w) of 1 μm and a signal-ground gap width (g) of 16 μm (calculated by ADS LineClac tool). A 50-Ω transmission line has a 141 center line width of 27μm and a gap width of 3 μm. Between the edge (50-Ω) and the center (185-Ω) sections, the impedance is linearly increased from 50 Ω to 185 Ω. The corresponding geometries are also calculated by ADS LineCalc and confirmed by the HFSS port impedance simulations with 2g + w kept 33 μm. The layout file is generated using the ADS Momentum simulator, which requires finite number of points to be taken to form a curve. Therefore, the tapered line is composed of 14 equal-length sections as shown in Figure 6-10 with all the dimensions labeled on the figure. The ground lines are 195 μm by 1000 μm rectangles. The transformation is from the edge to the center, so the full test fixture is formed with the taper line and its mirror image facing each other. The center gap is 1 μm. The tapered line configuration not only provides an impedance matching, but also reduces the parasitic capacitance across the gap dramatically. As the center line width decreases, Cg is reduced to 0.508 fF, almost by 10 times compared to the Cg value in the 50-Ω transmission line case (Table 6-1). On the other hand, the value of Cp almost does not change at all (still around 0.043 fF). However, the value Cp is much smaller than that of Cg, therefore has much less impact on the S-parameters compared to Cg. The Cp and Cg values are determined by fitting the simulated Sparameters of the gap to the S-parameters of the equivalent circuit shown in Figure 6-5. 142 1 1.6 2.4 3.4 4.8 6.2 8.2 10.6 13 15.4 18.6 21 23.8 33 27 195 1000 Figure 6-10. Layout of the tapered transmission line test fixture (unit: μm) ground Port 1 ground ground Port 3 Port 4 Port 2 ground Figure 6-11. Port setting for ADS Momentum The designed test fixture is simulated using ADS Momentum simulator, which is based on the method of moments (MoM) algorithm . In addition to the two ports at the edges of the transmission line, there are two internal ports set on each side of the center gap (Figure 6-11). Therefore, after the ADS simulation, a 4-port S-parameter (.S4p) file is created. The response of the test fixture itself is obtained by leaving port 3 and port 4 open. The response with a CNT across is obtained by connecting port 3 and port 4 with the CNT equivalent circuit model discussed in Section 6.2.1. The ADS schematic and the simulated S-parameters are plotted in Figure 6-12 and Figure 6-13 respectively. One can 143 see that the signal contrast with and without a CNT at the center is dramatically improved over the entire frequency range of 1~55 GHz, especially for S21 in both magnitude and phase. Even at the highest simulated frequency (55 GHz), the difference in the magnitude of S21 is still about 3 dB. One thing worth to point out is that since a higher-order mode enters at 56 GHz for the 50-Ω transmission line at the edge sections, which is revealed in the HFSS multi-mode simulation, our study is only for the frequencies below 55 GHz. (a) Term Term1 Num=1 Z=50 Ohm 4 1 2 3 S4p file Ref Term Term2 Num=2 Z=50 Ohm S4P SNP3 File="Dst1_imp_linear_112309_intl.s4p" (b) R R3 R=15 kOhm C C2 C=.5 fF Term Term3 Num=3 Z=50 Ohm CNT L R L1 R1 R=20 kOhm L=16 nH R= 4 1 2 3 Ref R R4 R=15 kOhm C C1 C=.5 fF Term Term4 Num=4 Z=50 Ohm S4P SNP4 File="Dst1_imp_linear_112309_intl.s4p" Figure 6-12. Schematics for S-parameter simulations (a) without and (b) with a CNT equivalent circuit model across the center gap of the designed tapered-line test fixture. 144 (a) -0.05 dB (S21) dB (S11) 0.00 -0.10 -0.15 -0.20 -0.25 0 10 (c) 20 30 40 50 60 Frequency (GHz) -20 -40 -60 0 10 20 30 40 Frequency (GHz) 50 60 Phase (S21) (degree Phase (S11) (degree 0 -30 -40 -50 -60 -70 -80 -90 100 80 60 40 20 0 -20 (b) 0 10 (d) 0 20 30 40 50 60 50 60 Frequency (GHz) 10 20 30 40 Frequency (GHz) Figure 6-13. Simulated S-parameters without (solid lines) and with (triangles) a 1μm CNT across the center gap for the designed tapered line test fixture. (a) S11 magnitude in dB; (b) S21 magnitude in dB; (c) S11 phase in degree; (d) S21 phase in degree. The above simulation is assuming that the tube length across the gap is 1μm. If a 2-μm tube (RCNT = 40 kΩ and Lk = 32 nH) is used, the signal contrast in S21 magnitude is degraded as shown in Figure 6-14. However, the signal difference is still well resolved almost in the entire frequency range. The S21 magnitude difference at 40 GHz is 1.8dB, more than the systematic uncertainty (~1.3 dB). This is much better than the reported Sparameters in , which has S21 magnitude not differentiable above 8 GHz. An exponential tapered line is also designed, in which the impedance taper is exponential. The simulated S-parameters are very similar to those of the linear tapered 145 line in Figure 6-13. Besides the tapers in impedance, a linear taper in shape is also studied. The simulated S-parameters are slightly worse than those of the linear impedance-tapered line. These are expected since the center line used in this study is very narrow, different tapers appear very similar to each other. For a wider center line configuration, the difference caused by taper types is expected to be greater. (a) -40 dB (S21) -0.10 -0.15 Phase (S11) (degree) -0.20 0 -60 -70 -80 -90 0 10 20 30 40 50 -40 0 60 0 Frequency (GHz) (c) -20 -60 (b) -50 -0.05 Phase (S21) (degree dB (S11) 0.00 10 20 30 40 Frequency (GHz) 50 60 100 80 60 40 20 0 -20 10 30 40 50 60 50 60 Frequency (GHz) (d) 0 20 10 20 30 40 Frequency (GHz) Figure 6-14. Simulated S-parameters without (solid lines) and with (triangles) a 2μm CNT across the center gap for the designed tapered line test fixture. (a) S11 magnitude in dB; (b) S21 magnitude in dB; (c) S11 phase in degree; (d) S21 phase in degree. 146 A test fixture in step configuration shown in Figure 6-15 (designed by arbitrary tweaking of geometry) is also simulated and compared to the above designed tapered lines. Shown in Figure 6-16 are the simulated S-parameters. The signal contrast is worse and only well resolved up to around 35 GHz. 15 46 30 18 8 6 72 55 40 50 55 35 89 650 200 Figure 6-15. An arbitrary step-line test fixture (unit: μm) 147 (a) -0.02 -0.04 -0.06 -0.08 10 (c) 0 20 30 40 50 -50 -60 60 Frequency (GHz) -10 -20 -30 -40 0 10 20 30 40 Frequency (GHz) 50 60 Phase (S21) (degree Phase (S11) (degree -40 -70 0 (b) -30 dB (S21) dB (S11) 0.00 0 10 (d) 100 20 30 40 50 60 50 60 Frequency (GHz) 80 60 40 20 0 0 10 20 30 40 Frequency (GHz) Figure 6-16. Simulated S-parameters without (solid lines) and with (triangles) a 1μm CNT across the center gap for the arbitrary step-line test fixture. (a) S11 magnitude in dB; (b) S21 magnitude in dB; (c) S11 phase in degree; (d) S21 phase in degree. In circuit fabrication, many unexpected deviations can be introduced on the circuit geometries, which may possibly degrade the signal contrast compared to the simulation. In addition, to ensure a CNT across the center gap with the two ends underneath the electrodes, at least a 5-μm line width is needed with our fabrication facility. To study the fabrication tolerance, the linear tapered line design is modified by adding a 5 μm x 5 μm squares at the center (Figure 6-17), increasing the center gap size to 2 μm, and increasing the signal-ground gap to 10 μm. The simulated S-parameters still show good signal contrast up to 30 GHz (Figure 6-18). 148 5 um Figure 6-17. The zoom-in layout of the linear tapered design with a 5 μm x 5 μm pad added at the center. (a) -30 -0.05 dB (S21) dB (S11) 0.00 -0.10 -0.15 -50 -60 -80 10 (c) 0 20 30 40 50 60 Frequency (GHz) 10 20 30 40 Frequency (GHz) 50 60 Phase (S21) (degree 0 Phase (S11) (degree -40 -70 -0.20 0 -10 -20 -30 -40 -50 -60 (b) 100 0 10 (d) 20 30 40 50 60 50 60 Frequency (GHz) 80 60 40 20 0 0 10 20 30 40 Frequency (GHz) Figure 6-18. Simulated S-parameters without (solid lines) and with (triangles) a 2μm CNT across the center gap for the modified linear tapered test fixture. (a) S11 magnitude in dB; (b) S21 magnitude in dB; (c) S11 phase in degree; (d) S21 phase in degree. 6.3. RF Calibration Algorithm Although good signal contrast between a test fixture with and without a CNT may be obtained by the tapered transmission lines, to extract the intrinsic CNT properties, 149 additional calibration procedures are necessary. A 3-step de-embedding method [112, 113] is discussed here for removing the parasitics and obtaining the intrinsic nanotube properties as illustrated in Figure 6-19. This method is simple to implement and widely used in semiconductor device measurements. A test fixture’s parasitics can be equivalent to the circuit shown in Figure 6-19 (a). In this circuit, y1, y2 and y3 correspond to the capacitances to the grounds at the input and the output, and the coupling across the gap, respectively. It can be measured with an open standard with the device under test (DUT) absent. On the other hand, z1, z2 and z3 are the series parasitic inductance connected to the DUT and can be measured by a short standard. For the CNT testing configuration, since there is no contact between the CNT-DUT and the ground, z3 essentially does not exist. However, the long shorting trace from the signal line to the CPW ground traces in a short standard would introduce an unwanted inductance and should be avoided. Therefore, an alternate approach can be applied instead to extract z1 and z2 as illustrated in Figure 6-20. A through standard includes the parasitics of z1, z2, y1, and y2, where y1 and y2 can be subtracted by measuring two isolated open standards for both the left and right halves of the test fixture. 150 y3 (a) z2 z1 y1 y2 z3 (b) z2 z1 z3 (c) Figure 6-19. Equivalent circuit of the parasitics of a test fixture. z1 y1 z2 y2 ‐ Through y2 y1 ‐ Left Open = z1 z2 Right Open Figure 6-20. Extraction z1 and z2 from the through and two isolated open standards (left and right). 151 To perform the de-embedding, first, the measured S-parameters of the open standard and the total response from both the test fixture and the DUT are converted to the corresponding admittance matrix (Y-matrix) using the following formulas . Y11 = Y0 (1 − S11 )(1 + S22 ) + S12 S 21 (1 + S11 )(1 + S 22 ) − S12 S 21 (6.6) Y21 = Y0 −2S 21 (1 + S11 )(1 + S 22 ) − S12 S21 (6.7) For a reciprocal network, which is the case here, the Y-matrix is symmetric. The impact from the parasitic capacitance is eliminated by applying Y-matrix subtraction (Figure 6-19 (b)). ′ = YTOTAL − YOPEN (6.8) YDUT Second, the inductive parasitics are obtained by Eq. (6.9). As explained previously, the subtraction of the Y-matrices of the left-open and right-open standards from the Y-matrix of the through standard results in the Y-matrix of the inductive parasitics, the inverse of which is the corresponding impedance matrix (Z-matrix) Z IND . The intrinsic Z-matrix of the DUT is eventually obtained by subtracting ′ , which is the inverse of YDUT ′ . Z IND from Z DUT S = 11 Z IND = (YTHRU − YLO − YRO ) −1 (6.9) −1 ′ = Y ′DUT Z DUT (6.10) ′ − Z IND Z INT = Z DUT (6.11) ( Z − Z )( Z + Z ) − Z Z ( Z + Z )( Z + Z ) − Z Z 11 0 22 0 12 21 11 0 22 0 12 21 (6.12) 152 S = 21 2Z Z ( Z + Z )( Z + Z ) − Z Z 12 11 0 22 (6.13) 0 0 12 21 At last, the intrinsic S-parameters can be converted from the obtained Z-matrix using Eq. (6.12) and Eq. (6.13), where Y0 and Z0 in the formulas are the port admittance and impedance, respectively. The impedance of the CNT under test can also be obtained by the following formulas. Z CNT = |Z | Z 21 | Z |= Z11Z 22 − Z12 Z 21 (6.14) (6.15) The de-embedding procedure is applied to the linear impedance-tapered transmission line test fixture presented in the previous section. The open standard is simply the test fixture itself. The through standard connects the signal lines on the left and right sides by removing the center gap. The left-open and right-open standards are as illustrated in Figure 6-20. The S-parameters of the calibration standards are obtained from 2-port ADS Momentum simulations. And the S-parameters of the CNT on the test fixture are obtained in the same way as discussed previously by assuming a CNT equivalent circuit model. The simulated S-parameters are plotted together in Figure 6-21. Since both the magnitude and phase of S11 for the left- and right-open standards almost completely overlap with those for the open standard, they are not plotted in Figure 6-21. 153 0 (a) 0 (b) dB (S21) dB(S11) -20 -5 -10 -100 10 (c) 20 30 40 50 Frequency (GHz) 20 0 -20 -40 -60 0 10 20 30 40 Frequency (GHz) 50 0 60 Phase(S21) (degree) 0 Phase(S11) (degree) -60 -80 -15 40 -40 60 100 10 20 30 40 50 60 50 60 Frequency (GHz) (d) 50 0 -50 -100 -150 0 10 20 30 40 Frequency (GHz) Figure 6-21. Simulated S-parameters of the open standard (solid), through standard (triangles), and the test fixture with a 1-μm CNT across the center gap (circles) for the designed tapered line test fixture. (a) S11 magnitude in dB; (b) S21 magnitude in dB; (c) S11 phase in degree; (d) S21 phase in degree. 154 (a) -0.02 -40 S21, model S11, model S21, extracted S11, extracted -0.08 -0.10 0 Phase (S11) (degree) 0 (b) -0.02 20 40 Frequency (GHz) S21, model S11, model S21, extracted S11, extracted -0.04 -0.06 -60 60 30 20 10 -0.08 -0.10 0 20 40 Frequency (GHz) dB(S21) -50 -0.06 Phase (S21) (degree) dB(S11) -0.04 0 60 Figure 6-22. Comparison between the extracted CNT S-parameters with the theoretical model. After the de-embedding procedure, the extracted intrinsic S-parameters of the CNT are plotted together with the actual values directly simulated from the equivalent circuit model shown in Figure 6-12. As shown in Figure 6-22, both the magnitude and phase for the extracted S11 and S21 agree very well with the theoretical values below 20 155 GHz. At higher frequencies, relatively large discrepancies start to appear. This is expected, since the lumped element models are assumed for the parasitics in this deembedding method. The length of the designed test fixture (from the edge to the center gap) is 499.5 um, which is approximately corresponding to an electrical length of π/20 at 10 GHz. Therefore, the lumped-element parasitic models may be safely considered valid. However, as frequency increases, the electrical length increases and reaches π/7 at 30 GHz. The distributed effects of the parasitics can no longer be neglected. Therefore, for individual CNT characterization at frequencies higher than 30 GHz, a more sophisticated de-embedding algorithm becomes necessary and will be developed in our future work . Although with the some discrepancies at high frequencies, the extraction of the equivalent circuit components still leads to reasonable values. Shown in Table 6-2 are the circuit component values obtained from the curve fitting of the extracted intrinsic CNT Sparameters assuming the circuit model drawn in Figure 6-12. The fitting is accomplished by using the ADS optimization function which varies the circuit component values to match the target S-parameters over a wide frequency range. When fitting the Sparameters from 1 to 55 GHz, there are relatively large errors on the extracted equivalent circuit components especially on the kinetic inductance Lk. However, if only fitting the Sparameters from 1 to 20 GHz, fairly accurate equivalent circuit component values are obtained. Therefore, the developed de-embedding technique is successfully demonstrated for the RF characterization of individual CNTs with very good accuracy achieved up to 20 GHz. 156 Table 6-2. Fitted equivalent circuit component values Extracted (1~55 GHz) Extracted (1-20 GHz) Model Rcnt(kΩ) Lk (nH) Rc (kΩ) Cc (fF) 13.1 30.4 16.0 0.41 20.0 19.3 14.5 0.52 20 16 15 0.5 6.4. Micro-Circuit Fabrication (a) (b) Alignment markers (c) Testing circuit Figure 6-23. Illustration of CNT testing circuit fabrication. (a) Fabricated grids; (b) Deposit and locate tubes; (c) Fabricate the testing circuit across the tube by applying the alignment technique The testing circuits for CNTs can be fabricated using electron beam lithography (EBL) process with the following main steps. This procedure is also illustrated in Figure 6-23. 1. Fabricate grid coordinate system on a quartz substrate 2. Deposit CNTs on the substrate 157 3. Locate a CNT and record the coordinates using atomic force microscope (AFM). 4. Use the alignment function on a Nanometer Pattern Generation System (NPGS) to fabricate the test fixture at the appropriate position so that the tube will lie underneath and across the electrodes. 6.4.1. Grids Fabrication The grids are fabricated using standard EBL process. First, as shown in Figure 6-24, 495 C4 / 950 C4 bilayer of polymethyl methacrylate (PMMA) are spin-coated on the substrate sequentially and soft baked for 3 minutes after the deposition of each layer (Figure 6-24 (a)). The spinning speed and time for 495 PMMA is 500 rpm for 5 s followed by 3500 rpm for 30 s, and for 950 PMMA is 500 rpm for 5 s followed by 4000 rpm for 30 s. The purpose of using bilayer is to create an undercut to help the metal lift off process later. Then a NPGS system incorporated on a FEI scanning electron microscope (SEM) is employed to write the desired pattern on the substrate (Figure 6-24 (b)). Since quartz is not conductive, a 10-nm layer of Cr is sputtered on top of the PMMA layers to avoid the charging problem under the electron beam. The digitized areas under electron beam exposure become solvable in the mixture of Methyl isobutyl ketone (MIBK) and IPA (MIBK: IPA = 1:3) and are easily removed during the develop process (Figure 6-24 (c)). However, before applying MIBK/IPA, the Cr layer needs to be etched away by leaving the sample in Chrome Etchant (CEP-200) until the substrate appears to be transparent. After development, a 20-nm layer of Cr followed by 100-nm of Au are 158 deposited using electron beam evaporator (Figure 6-24 (d)). The Cr layer is used to assist the surface adhesion. To achieve a lower contact resistance, Ti can be used to replace Cr . After metal deposition, a lift-off process is applied by bath sonicating the sample in acetone solvent for several seconds to remove the un-digitized areas, leaving the desired pattern (Figure 6-24 (e)). The fabrication is processed in a class-1000 clean room. (a) Cr layer PMMA 950 PMMA 495 PMMA Coating Substrate e‐ (b) (c) Electron Beam Exposure e‐ e‐ e‐ e‐ Substrate Development Substrate (d) (e) Metal Deposition Substrate Metal Lift‐off Substrate Figure 6-24. Illustration of a typical EBL fabrication process. 159 (a) (b) Figure 6-25. The grid coordinate pattern (a) Overview (not to scale); (b) An AFM image of our grids The grid pattern has three sets of alignment markers as shown in Figure 6-25 (a). The outer most set has the marker size around 100 μm, and marker spacing on the order of 1000 μm. The intermediate layer has the marker size around 50 μm and marker spacing on the order of 500 μm. The inner most set has the marker size around 10 μm and marker spacing on the order of 150 μm. These three sets of markers will be used for a 3tier alignment later. The grid coordinate is located at the center. It can be a set of numbers or small features with distinct shapes. Figure 6-25 (b) shows an AFM image of our gird coordinate system, which is composed of square markers and triangle markers with the right-angled corner pointing at different directions. These grid markers are arranged in the way that any combination of four adjacent markers uniquely defines the coordinates of a square area. The size of the small grid markers is equal or less than 3μm x 3μm and the spacing is around 12 μm. The square area confined by any four adjacent markers is small enough that CNTs can be conveniently imaged under AFM (Dimension 3100). For the alignment purpose that will be discussed in detail in a later section, the positions where the grids are written needs to be recorded. This can be implemented by taking an 160 SEM image of a corner of the substrate, which can be easily identified and revisited later, and recording the relative coordinates from the corner to where the grids are written. The orientation is important too. Therefore the SEM image of the corner should include the sample edges for future reference. 6.4.2. CNT Dispersion, Deposition and Localization Carbon nanotubes are dispersed in sodium dodecyl sulfate (SDS) solution (1 wt. %) using a probe sonicator (Sonic & Materials) with the amplitude set to be 70. The solution is sonicated for 3 ~ 5 minutes. Then 0.1 ~ 0.8 ml solution is spin-coated on the substrate with fabricated grids. The spinning speed is set to be 3000 rpm. An SEM image of the deposited CNTs on a Si substrate is shown in Figure 6-26 (a) and an AFM image of the deposited CNTs on a quartz substrate with fabricated grids is shown in Figure 6-26 (b). The sample distribution density appears to be appropriate for the CNT testing circuit fabrication purpose. The position of the circled nanotube in Figure 6-26 (b) is conveniently recorded by simply taking an AFM image with all four adjacent marks included. 161 (a) (b) Figure 6-26. (a) SEM image of the CNTs deposited on a Si substrate with 0.75 ml dispersed CNT solution; (b) AFM image of the CNTs deposited on a quartz substrate with 0.45 ml dispersed CNT solution. 6.4.3. Testing Circuit Fabrication After a CNT is located, an AutoCAD file can be created accordingly for alignment. Since the position and the orientation of the CNT are determined, the testing circuit layout can be drawn such that the position of the center gap is located right at the position of the CNT center with appropriate orientation. In addition, at the positions where the alignment markers are located, corresponding windows are drawn for the purpose of alignment operations. Meanwhile, the same procedures presented in Section 6.4.1 need to be repeated for adding the PMMA and Cr layers on the surface of the sample before applying the second layer electron beam writing. To ensure the circuit to be fabricated at the right position, an alignment procedure must be performed. First, one needs to focus the electron beam at the accurate position of the corner recorded as described in Section 6.4.1. Then, since the relative coordinates of 162 the grid pattern center to the corner are recorded (Section 6.4.1), the substrate can be moved accordingly using the microcontroller so that the electron beam is located at the center of grid. This movement should be operated with the electron beam blanked to avoid undesired exposure. Now the windows at the alignment marker positions provide an open view to fine tune the sample position. As mentioned in Section 6.4.1, three sets of alignment markers are corresponding to a 3-tier alignment, which leads to the accuracy of the alignment to be better than 1 μm (~several hundred nanometers). Note that all the areas where the windows are located are exposed under the electron beam. After the alignment operation, the testing circuit is written on the substrate with electron beams. Since the position and orientation of the testing circuit relative to the grid is defined by the AutoCAD (computer aided design) software according to the position of the pre-located CNT, the written circuit should be located at such a position that the CNT is across the center gap of the circuit if an ideal alignment is fulfilled. The same development, metal deposition and liftoff procedures are applied to obtain the final circuit with the two ends of the CNT buried underneath the fabricated electrodes. An example of a fabricated testing circuit by following the alignment procedure is displayed in Figure 6-27. One can see that the grids are located at the center area and the fabricated CPW line is certain angle away from the horizontal direction, which is determined by the tube orientation. Unfortunately, the alignment of this circuit is off and the pre-located CNT is not underneath the electrodes and across the gap. Further research effort on the circuit fabrication is underway. 163 Signal Ground Grids Gap Ground Signal Alignment markers Figure 6-27. Optical microscopic image of a fabricated testing fixture by following the described procedure. 6.5. Conclusion In summary, RF-frequency characterization of individual carbon nanotube is investigated in this chapter. It is found that although the impedance matching from 50 Ω to 20 kΩ improves the signal level in the measurement, the existence of the parasitics still degrades the signal contrast badly at high frequencies between the cases with and without a CNT in the test fixture. A tapered line approach is taken to improve the impedance matching, at the same time reducing the parasitics. It is found that a good signal contrast is achieved up to 55 GHz. The fabrication tolerance study shows that this design is 164 compatible for real implementation. The performance of an arbitrary step-line is also studied. Furthermore, a de-embedding algorithm is presented and applied to obtain the intrinsic nanotube properties with the simulated S-parameters from ADS momentum assuming a theoretical CNT model. Fairly accurate equivalent circuit component values of the model can be extracted up to 20 GHz using this de-embedding technique. At last, the involved circuit fabrication process is presented in detail. 165 CHAPTER 7. CONCLUSION AND FUTURE WORKS With the increase in the integration density of IC circuits, carbon nanotubes are considered as a promising candidate for nano-electronics. However, their high frequency properties have yet been well studied. In addition, the heterogeneity of as-produced carbon nanotubes is also a major bottleneck that needs to be solved before wide-spread applications in electronics can be realized. The primary goal of this dissertation is to investigate the microwave and THz frequency properties of carbon nanotubes and explore a post-synthetic technique to improve the purity of the carbon nanotubes. First, Carbon nanotubes are synthesized using CVD process and characterized by SEM, TEM and Raman spectroscopy. The ultimate goal of this study is to provide a good understanding of the synthetic process control for the purpose of CNTs electronic devices fabrication for characterization in microwave frequency range. In virtue of their low loss in the interested frequency range, quartz substrates are often used for microwave testing purpose. However, limited work has been reported on CNT growth on quartz substrates. Our study of the substrate effects on CVD growth of CNTs reveals that the nanotubes grown on quartz substrates appear to be shorter (4-10 μm) and less evenly distributed compared to those grown on Si substrates (15 - 20 μm). In addition, the CNTs grown on Si substrates appear to be more crystalline than those on the quartz. This information provides very useful guidelines for future CNT-based circuit fabrication procedure optimization in terms of both catalyst pattern design and substrate selections for 166 microwave applications. Furthermore, the study on feedstock gas (methane) flow rate dependence reveals that more large-diameter MWNTs are produced at low flow rates. As the methane flow rate increases, more DWNTs or SWNTs are produced instead. This is also valuable synthetic control information to provide specific types of CNTs for the purpose of microwave characterization. Second, the effects of high-power microwave irradiation on both purified HiPCO and CoMoCat SWNT thin films without the impact from catalyst particles are studied to investigate the feasibility of a potential selective breakdown scheme based on the significant conductivity difference between metallic and semiconducting CNTs. The SWNT films before and after microwave irradiation are first characterized using a convenient non-contact THz transmission measurement. The observed significant THz transmission increase after the microwave irradiation indicates a significant decrease in the metallic tube content. The Raman RBM spectra also confirm that the metallic-tosemiconducting ratio decreases by up to 33.3% in the HiPCO SWNT thin films after the irradiation. The Raman spectra for CoMoCat also exhibit clear metallic tube reduction. From the observed effects, we conclude that high-power electromagnetic irradiation can induce damages on metallic tubes, at least causing them to lose their electronic properties. This may lead to a convenient and effective microwave-induced demetalization scheme of SWNT mixtures. Third, a broadband microwave characterization method using rectangular waveguides is developed to extract the complex permittivity and permeability of MWNT papers from 8 to 50 GHz, as an alternate approach to study the electrical and magnetic 167 properties of CNTs rather than characterizing an individual tube. The Nicolson-RossWeir method is taken to simultaneously extract the complex permittivity and permeability of the MWNT papers from the S-parameters measured using vector network analyzer, without imposing the assumption of μ = 1 like most of the literature reported. The algorithm is verified by numerical full-wave finite element simulation. Both real (ε’) and imaginary (ε”) parts of the extracted permittivity are found to have very high values, especially at lower frequencies. The extracted ε’ from 8 to 50 GHz are between 700 and 250, and ε” are between 3400 and 350, corresponding to a conductivity of 1500 - 810 S/m. The values of extracted μ’ and μ” are both very close to zero. The measured high loss at microwave frequencies indicates that MWNT papers may be a good radarabsorbent material (RAM). The detailed error analysis of the extraction method is also performed. It reveals that uncertainties in the extracted material parameters are higher at lower frequencies, and the imaginary part of permeability has the smallest uncertainties. The understanding of the systematic uncertainties provides a useful guideline for future improvement of this characterization technique, such as applying the Kramers-Kronig relations to obtain the real part of permittivity, which has much higher systematic uncertainties. In addition, Bruggeman effective medium theory is applied to remove the impact from air. The obtained intrinsic permittivity of the MWNTs is increased by a factor of 1.2. This convenient characterization method can be also applied to other thin and lossy material samples. The MWNT papers are also characterized up to THz frequency by the Terahertz Time-Domain Spectroscopy. Unlike most THz-TDS characterizations reported in 168 literature, both transmission and reflection measurements are performed to simultaneously determine the complex permittivity and permeability of the sample. The extracted index of refraction, permittivity and permeability from 50 to 370 GHz are consistent with previously measured values from 8 to 50 GHz using a microwave vector network analyzer. However, at THz frequencies, the extracted ε’ decreases to around 20 at 350 GHz, and ε” to around 10. On the other hand, μ’ and μ” both increase to around 2. A Drude-Lorentz model is applied to fit both the real and imaginary parts of the permittivity from 8 to 370 GHz. Similarly, the intrinsic ε’ and ε” of the MWNTs are increased by a factor of 1.2 by applying the Bruggeman effective medium theory to remove the impact from air. From the measured complex permittivity and permeability from 8 to 350 GHz, we conclude that an assembly of randomly aligned MWNTs does not exhibit significant magnetic response. However it has large dielectric constants and high loss at microwave frequencies. Both of them decrease rapidly at THz frequencies. The measured material properties provide valuable data for potential MWNT-based microwave and THz applications. At last, individual carbon nanotube characterization at microwave frequency is investigated. The impact of impedance matching and the parasitics on the S-parameters of an individual SWNT are studied. It is found that an impedance matching from 50 Ω to 20 kΩ improves the signal level. However, the existence of parasitics still degrades the signal contrast between the cases with and without a SWNT included in the test fixture at high frequencies. Therefore, we conclude that the parasitic impact on the measurement 169 sensitivity dominates at higher frequencies (> ~10GHz) compared to the impedance mismatching impact. The presented systematic study of individual SWNT characterizations at microwave frequencies provides important guidelines on test fixture designs. A tapered CPW line is then designed to improve the impedance matching, at the same time reducing the parasitics. Good signal contrast (with vs. without a SWNT) is demonstrated in our simulations up to 55 GHz, which surpasses the existing reported work. The fabrication tolerance study shows that this design can be realistically implemented. Furthermore, a three-step de-embedding algorithm to calibrate out the test fixture and obtain the intrinsic nanotube properties is presented. ADS software is utilized to simulate the implementation of the algorithm, which demonstrates a reasonable equivalent circuit model extraction of a SWNT with very good accuracy up to 20 GHz. At the same time, the limitation of the algorithm is also discussed. In the end, the developed circuit fabrication process for single nanotube testing circuits on nonconductive substrates is presented in detail. As potential extension of the works described in this dissertation, several areas should be very interesting for further study. First, although the selectivity in the presented potential microwave-induced breakdown scheme is demonstrated to some extent in the SWNT film experiment, the exact underlying physical mechanism behind it is yet clear. To observe closely the impact of high-power electromagnetic wave on a single nanotube, isolated tubes can be labeled and their electrical properties can be pre-identified by various techniques such as electrical force microscopy (EFM). After being exposed under high electromagnetic field, 170 each nanotube can be easily tracked using AFM or EFM on their morphology and electrical properties. Whether metallic tubes are completely oxidized / evaporated or just losing their electrical properties can be manifested with the microscopic investigation techniques. However, as discussed in Chapter 3, for this experiment, a much higher field strength would be necessary in order to excite the currents high enough to reach the breakdown threshold of metallic tubes. Two possible means (using cylindrical resonator or planar resonator) may be used to realize the required field levels as presented in Chapter 3. Second, the single tube testing circuit discussed in Chapter 6 has not been successfully fabricated due to the challenges in fabrication. Moreover, our current method of spin-coating the nanotubes dispersed in surfactant solution on a substrate usually produces tubes no longer than 6 µm. To ease the stringent alignment accuracy requirement, longer tubes are preferred. An alternative approach is to directly grow CNTs on a substrate with grid coordinate system fabricated. 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