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Investigation of carbon nanotube properties and applications at microwave and THz frequencies

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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
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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 2.2.1.1. Plain Catalyst Preparation ................................................................. 35 2.2.1.2. 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 2.3.3.1. RBM .................................................................................................... 43 2.3.3.2. 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 [79] .............. 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 [6]. 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 [6]. Copyright (1992), American Institute
of Physics. ......................................................................................................................... 19 Figure 1-4. Transmission line model for a SWNT [19] .................................................... 22 Figure 1-5. Schematic of a top-gated CNT-FET. Reprinted with permission from [29].
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 [60]. 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 [60]. 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 [60], and (b) theoretically in [81].
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
[60]. Copyright (2005), Elsevier. (b) Reprinted with permission from [81]. 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 [104]). ............................................................... 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). [19]........................................................................................... 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 [1], 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 [2]
and experimentally confirmed in 1998 [3]. 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 [4].
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 [4]
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 [2]. 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 [6], 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 [2]. 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 [4].
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 [6]. 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 [6]. 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 [10]. In addition, the inter-tube interaction in a
nanotube bundle can possibly lead to a pseudo band gap due to the broken-symmetry [11].
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 [12], 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) [13]. 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) [14]. 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 [18].
Multi-walled carbon nanotube (MWNT), as mentioned earlier, have several layers
coaxially arranged with an interlayer spacing of around 0.34 nm [4]. 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 [4]. Even for a semiconducting SWNT with this diameter,
the resulting band gap is small (around 44 meV) [4]. 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%) [15]. Ballistic
transport is observed in MWNT as well by applying a liquid metal contact [16].
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 [18] and also
presented by P. J. Burke in 2002 [19]. 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 [18]. 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 [19]
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 [17]. Their nano-scale radius of curvature, excellent electrical
conductivity together with the merit of mechanical stiffness, also makes CNTs good field
emitters [20].
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 [21], microscope tips [22], fuel cells [23] and many nano-electronic applications
[24]. 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) [24], nanoantennas [25], and nano-interconnects [26], 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 [24]. 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 [28].
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 [29]. It is interesting that CNT-FETs are actually ambipolar even
though they were believed to be p-type initially [28]. 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 [30]. 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 [31].
Figure 1-5. Schematic of a top-gated CNT-FET. Reprinted with permission from
[29]. 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 [26].
Recently, many microwave (3x108 Hz to 3x1011 Hz) and THz (3x1011 Hz to
3x1012 Hz) applications have been suggested as well [85]. 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 [32]. Ideally, a much higher cutoff frequency up to 8
THz may even be achieved when parasitics are negligible [83]. Sazonova et al.
demonstrated a tunable CNT electromechanical resonator in RF mixer configuration [84].
25
Hanson calculated the CNT dipole antenna characteristics via a semi-classical approach,
which is valid through THz frequencies [25]. 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 [27].
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 [69], 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 [36]. 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° [69]. 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 [37], carbon-nanotube films [38]-[42], 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 [34] 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 [43] 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, [79] and [80],
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 [44]
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 [68]. 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 [1], significant
research efforts have been carried out to develop various CNT growth methods such as
arc discharge [45], laser ablation [46], and chemical vapor deposition [47]. 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 [48]. Recently, different techniques have also been applied to improve the
CVD process, such as the plasma enhanced CVD [49], High pressure CO process
33
(HiPCO) [50], CoMoCat process [51], 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 [48]. 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 [52]. 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. [53] 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.
2.2.1.1. 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.
2.2.1.2. 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 [54]. 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 [57].
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
[58] 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 [60].
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
[59]. Shown in Figure 2-4 (a) are typical Raman spectra observed for SWNTs [60], 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 [56].
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 [60]. Copyright
(2005), Elsevier.
43
2.3.3.1. 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 [61].
ωRBM = (219 ± 3) / dt + (15 m 3)
(2.1)
(There are also other different formulas reported with slight variations in the coefficients
[62].) 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 [56]. 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 [63] 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 [61]. 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 [59]. However, for SWNTs with diameters greater than 3 nm, it has been
shown that RBM peaks become too broad to be observed experimentally [61].
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. [64] 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 [4]. For double-walled carbon nanotubes (DWNT), however, both layers may
contribute to the RBM response. Recently, Villalpando-Paez [65] reported Raman
spectroscopy study on isolated DWNTs, which clearly demonstrated the RBM peaks
from both layers.
2.3.3.2. 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 [56]. 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 [64], 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 [62]. 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 [62]. 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 [66]. 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 [67]. 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 [116]. 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 [32]. 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 [33]; the reported
dielectrophoresis method is able to achieve high-purity metallic SWNTs (~ 80%) but has
limited throughput [35]; the reported selective electrical destruction method [34] 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 [70]. 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. [72]. 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
[73]. 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) [74], 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 [34]. 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 [75]. 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) [76]. 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 [77]. 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 [78]) break
faster than the glass substrates covered with CoMoCat SWNT thin films with less
metallic content (14 ± 5% metallic contents [78]). 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. [79]. 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) [79]. 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 [60], 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 [81]. 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 [35]. 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 [75], 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 [60], and (b) theoretically
in [81]. 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 [60]. Copyright (2005), Elsevier. (b) Reprinted
with permission from [81]. 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 [34], 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 [34]. 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) [78] 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 [82].
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 [106]. 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) [43] 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 [84],
CNT antennas [25], and high-performance CNT radar-absorbent material, etc. [85].
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 [36], 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 [37], 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
[38]
[39]
[40],[41]
[42]
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. [104]. 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 [104]).
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 [86]
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 [87][89]
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 [90]. 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 [89]. 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 [90]-[93]. 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 [94]-[96].
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 [79]
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 [101]. 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. [104] 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 [105].
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 [106]. 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 [106] 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
[106]. 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
[107] was applied and a reasonable fitting was obtained in [108] 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 [39],
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 [103], 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
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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 [106]. 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
[32], CNT antennas resonant in the THz regime ([25, 27]), and CNT transmission lines
[19], 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 [18] and also
presented by P. J. Burke in 2002 [19]. 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. [36], 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 [36], 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 [19]. The theoretical model of such a transmission line (Figure 6-2 (b)) presented by
129
Bockrath [18] and Burke [19] 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 [18]. 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) [19]. 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). [19]
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 [25] 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 [111] based on the theoretically predicted frequency-dependent CNT
conductivity [25]. 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 [86]. 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 [44]. 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 [69]. 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 [86]. 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 [86]. 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 [114]. 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 [36], 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 [86].
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 [86]. 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
[113].
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
[12]. 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. Furthermore, by taking this
approach, the CVD growth conditions, such as feedstock gas flow rate and temperature,
can be correlated to the RF characterization, which will provide valuable statistical data
on the RF properties of CVD-grown CNTs.
At last, all the characterization presented in this dissertation assumes a zero gate
bias, which may be sufficient for the study of metallic nanotubes. In the longer term, a
top-gated bias may also be added to study the semiconducting carbon nanotube properties
at RF frequency. In addition, to accurately characterize individual CNTs at higher
frequencies (> 30GHz), a four-port parasitic de-embedding methodology should be
171
applied instead so that no lumped-component approximation is needed to describe the
parasitics and its distributed nature of will be considered.
172
APPENDIX: PERMISSIONS
173
174
175
176
177
178
179
180
181
182
183
184
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