論文 / 著書情報
Article / Book Information
題目(和文)
Title(English)

CVD Growth of Single-Walled Carbon Nanotubes and their Anisotropic
Optical Properties

著者(和文)

村上陽一

Author(English)

Yoichi Murakami

出典(和文)

学位:博士(工学),学位授与機関:東京大学大学院工学系研究科,
報告番号:,
授与年月日:2005年3月24日,
学位の種別:課程博士,
審査員:

Citation(English)

Degree:Doctor (Engineering),
Conferring organization: The University of Tokyo,
Report number:,Conferred date:2005/3/24,
Degree Type:Course doctor,
Examiner:

学位種別(和文)

博士論文

Type(English)

Doctoral Thesis

Powered by T2R2 (Science Tokyo Research Repository)

CVD Growth of Single-Walled Carbon Nanotubes
and their Anisotropic Optical Properties
byYoichi Murakami

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF ENGINEERING

Department of Mechanical Engineering
The University of Tokyo
December 2004

CVD Growth of Single-Walled Carbon Nanotubes
and their Anisotropic Optical Properties
by Yoichi Murakami

Approved, Thesis Committee:__________________________________________
Shigeo Maruyama, Thesis advisor and Chairman
Professor of Mechanical Engineering,
The University of Tokyo__________________________________________
Yoichiro Matsumoto
Professor of Mechanical Engineering,
The University of Tokyo__________________________________________Yuichi Ikuhara
Professor of Materials Engineering,
The University of Tokyo__________________________________________
Atsumu Tezaki
Associate Professor of MechanicalEngineering, The University of Tokyo__________________________________________
Tatsuya Okubo
Associate Professor of Chemical System
Engineering, The University of Tokyo__________________________________________
Shinji Yamashita
Associate Professor of Electronics Engineering,
The University of Tokyo

Table of Contents
Chapter 1:
1.1
1.2

Introduction

Introduction and overview of the thesis
Structural representation of SWNTs

1
2
5

References for Chapter 1

Chapter 2:
2.1

2.2

2.3

CVD growth of SWNTs and their analyses

Characteristics of SWNT growth from zeolite-supported catalysts
2.1.1

Research background

2.1.2

Catalyst preparation and experimental procedure

2.1.3

Definition of SWNT yield

2.1.4
2.1.5

Effect of CVD time and reduction of catalyst on SWNT yield
Microscopic analyses of obtained SWNTs on zeolite support

2.1.6

Effect of catalyst metal selection on growth of SWNTs

2.1.7

Summary

Catalyzed growth of SWNTs from mesoporous silica thin films
2.2.1

Research background and motivation

2.2.2

Preparations and experiments

2.2.3

Results and discussions

2.2.4

Summary of SWNT growth from MPS thin films

Development of techniques for direct synthesis of SWNTs on solid
flat substrates
2.3.1

Research background and motivation

2.3.2
2.3.3

Development of dip-coat catalyst supporting method
Direct synthesis of SWNTs on Si and quartz substrates

2.3.4

2.3.3.1

Experimental procedure

2.3.3.2

Resonant Raman scattering analysis

2.3.3.3

Microscopic analysis

2.3.3.4

Discussions

15
16

30

38

Summary of direct growth of SWNTs on flat substrates

i

2.4

Morphology and chemical state analysis of Co-Mo catalysts
supported on substrates by TEM and XPS analyses
2.4.1

Questions to be resolved for dip-coat supported Co-Mo catalysts

2.4.2

Methods for catalyst characterization

2.4.3

2.4.2.1

TEM observation and its sample preparation

2.4.2.2

Procedure for XPS measurement

60

Results of TEM and XPS analyses
2.4.3.1

Morphology of calcined and reduced Co-Mo catalyst

2.4.3.2

Chemical state of calcined and reduced Co-Mo catalysts analyzed
by XPS

2.4.3.3

2.4.4

2.5

Mechanism and formation process of Co-Mo catalyst

Summary of formation process and role of Co-Mo catalyst

Summary of Chapter 2

70

Acknowledgements for Chapter 2
References for Chapter 2

Chapter 3:
3.1
3.2
3.3
3.4

3.5
3.6

3.7

Growth of vertically aligned SWNT films on substrates
and their formation process

Research background and motivation
Experimental and analysis procedures
Effect of CVD chamber vacuum on SWNT growth
Microscopic and optical analyses
3.4.1

Morphological investigations by FE-SEM and HR-TEM

3.4.2

Resonant Raman scattering analysis

Discussion of vertical alignment formation in SWNTs
Transient investigations and modeling of growth process of verticallyaligned SWNT films
3.6.1

Growth and formation process of vertically aligned SWNT film

3.6.2

In situ measurement of growth process of vertically aligned

3.6.3

SWNT film
Formulation for growth process of vertically aligned SWNT film

Summary of Chapter 3

Acknowledgements for Chapter 3
References for Chapter 3
ii

79
80
81
82
84

90
92

107

Chapter 4:
4.1

Anisotropic optical properties of SWNTs and their
optical applications

Determination of optical anisotropy of the vertically aligned
SWNT film and optical absorption cross-section of SWNTs
4.1.1

Research background for polarized optical properties of SWNTs

4.1.2
4.1.3

Experimental and optical measurement setup
Dependence of optical absorption spectrum on SWNT morphology

4.1.4

Polarized optical absorption of vertically aligned SWNT film

4.1.5

Anisotropic optical properties of graphite

4.1.6

Modeling and formulation of multi-dipole optical absorptionof SWNTs
4.1.6.1

Transition probability

4.1.6.2

Optical absorption by dipole transition moment

4.1.6.3

Formulation for multiple dipole absorption by vertically

111
112

aligned SWNTs

4.1.7

Determination of optical anisotropy and bare optical absorption
cross-section of SWNTs

4.1.8

4.2

Summary of anisotropy optical properties of SWNTs

Polarization dependence of Raman scattering characteristics fromvertically aligned SWNT film
4.2.1

Introduction - Role of Raman scattering in SWNT analysis

4.2.2
4.2.3

Raman scattering measurement
Experimental results and analyses

4.2.4

4.2.3.1

Raman spectrum dependence on laser polarization

4.2.3.2

RBM peak behavior by molecular adsorption

4.2.3.3

RBM peak dependence on laser intensity

131

Discussion and interpretation of obtained data
4.2.4.1

Interpretation of data based on ∆µ = ±1 transition bycross-polarized light

4.2.4.2

4.2.5

4.3

Another possibility of interpreting the data

Summary of polarization dependence of Raman scattering

Optical applications of SWNT film directly synthesizedon solid surfaces
4.3.1

154

Motivation and research background
iii

4.4

4.3.2

Experimental setup

4.3.3
4.3.4

Principles of mode-locked ring fiber laser
Results and summary

Summary of Chapter 4160

Acknowledgements for Chapter 4
References for Chapter 4

Chapter 5:

Summary

Appendix:

Perturbated Hamiltonian for one-photon process

Acknowledgements
List of publications

iv

167

Chapter 1:
Introduction

1.1 Introduction and overview of the thesis
Single-walled carbon nanotubes (SWNTs) are a new group of carbon materials
possessing one-dimensional cylindrical geometry that is formed by rolling a sp2-bonded
graphene sheet. Immediately after its landmark discovery and structure determination in
1993 by Iijima and Ichihashi [1], theoretical studies on SWNTs commenced; these revealed
several distinctive physical properties of SWNTs, such as their unique electronic density ofstates (eDOS) and metal-semiconducting distinction that is solely dependent on theirchirality [2].
Experimental studies on SWNTs became possible after the establishment of production
methods in the late 1990s, such as laser-furnace (1996) [3], arc-discharge (1997) [4], andcatalytic CVD methods with supported catalysts (1996) [5] and floated catalysts (1998)[6,7]. These methods are intended for use in the mass synthesis of SWNTs in which the
SWNTs are obtained as soot adhered on the wall of the production chambers. Since theas-obtained soot contains amorphous carbons, multi-shelled graphites, fullerenes, and/or
catalyst metal particles as impurities, a purification process [8–11] is generally required
prior to its use. Although the SWNTs produced by these methods usually necessitates sucha purification process, these production methods are firmly established at present. In
particular, the HiPco method (1999) [12] that utilizes the disproportionation reaction of CO
gas is now regarded as a commercially feasible method for the mass production of SWNTs.
At the same time, the CVD method with a supported catalyst is currently being intensively
studied as a promising technique. The alcohol CCVD method (2002) [13], which is used inthis thesis, is one of such technique and can produce high-quality SWNTs that are almost
free from the aforementioned impurities even in the as-synthesized state.
With the establishment of production methods of SWNTs, experimental studies for
specific applications have become active and many innovative applications have beenstudied and proposed [14], such as one-dimensional (1D) quantum wire [15], field effecttransistor (FET) [16–19], cold cathodes for electron emitters [20,21], chemical sensors[22,23], probe tips for atomic force microscopes (AFM) [24–26], saturable opticalabsorbers for ultrafast all-optic switches [27–29], and nano-sized infrared detectors/emitters[30,31]. In any application, the 1D geometry, nanoscale size, and the physical/chemical
properties of SWNTs are of great importance.
However, in order to completely achieve such innovative applications, the following
problems should be resolved:
2

Chapter 1  Introduction

1)
2)

Direct growth of SWNTs on Si or other flat substrates.
Elucidation of the function of the catalyst that is optimal for the growth of SWNTs
and construction of guidelines for the selection of a catalyst.

3)Morphologically aligned growth of SWNTs on Si or other flat substrates.

4)
5)

Elucidation of anisotropic optical properties of SWNTs toward light polarization.
Separation of bulk-synthesized SWNTs based on metallic/semiconducting
distinction, or ideally, their chirality.

6)

Selective growth of SWNTs as either metallic or semiconducting SWNTs, or ideally,chirality-specific growth.

A brief overview of these topics follows. Regarding problem 1, a SWNT-based FET has
often been fabricated from bulk-produced SWNTs dispersed and spun coated on Si/SiO2
substrates [15–19]. However, the yield of electrical devices fabricated by this method is
considerably low because favorably isolated SWNTs on Si have to be found by atomic
force microscopy (AFM) prior to the device fabrication. Kong et al. [32] demonstrated forthe first time that SWNTs could be grown on Si substrates by CVD. However, the SWNTs
in that study were indirectly grown on the surface of the Si substrate, that is, the SWNTs
were grown from Fe-Mo catalyst mixed with patterned alumina islands [32]. These
supporting islands (3 × 3 µm2) are not essential for the functioning of the device; therefore,
it is desireble to eliminate them in order to enable high-density fabrication of the devices. A
method of growing SWNTs directly on the surface of the Si/SiO2 substrate is developed in
Section 2.3, in which the catalyst metal is directly supported on the Si/SiO2 surface without
using an intermediate supporting layer.
Regarding problem 2, several types of catalysts, either monometallic or bimetallic, havebeen proposed for the growth of SWNTs. Empirically, it is known that a bimetallic catalyst
such as Fe-Mo [32–36], Fe-Co [13,37], or Co-Mo [38–40] is more effective than amonometallic catalyst in enhancing the growth of SWNTs. Section 2.1 discusses the effectof the Fe-Co catalyst in terms of a thermo-gravimetric analysis (TGA) and thermodynamic
properties of catalytic metals. In section 2.4, the role of the Co-Mo catalyst on Si/SiO2
surface is elucidated, and a new model for catalyst dispersion is proposed, which isdifferent from the previously proposed model for the Co-Mo system [39,40].
Regarding problem 3, significant effort was devoted to the morphologically controlled
growth of SWNTs on solid surfaces. The vertical growth of multi-walled carbon nanotubes
3

(MWNTs) on a flat substrate has been successfully achieved [41–43]; however, when
SWNTs are concerned, they have only been aligned parallel to the substrate surface [44-46].
Since it is well known that the transport properties of SWNTs are superior to those of
MWNTs [14], the achievement of vertically aligned growth of SWNTs on flat substrates
would accelerate their application as a cold cathode for electron emission electrodes. In
Chapter 3, a new method, which is easy and reproducible, is developed for the vertical
growth of SWNTs uniformly over the quartz substrate, and the growth process andmechanism are investigated in detail.
Regarding problem 4, SWNTs are also considered as a promising material for opticaldevices [27–29]. Since a SWNT has a 1D shape, its optical properties are expected to
exhibit anisotropy toward light polarization with respect to the axis of SWNTs. However, it
should be noted that the fundamental anisotropic optical properties of SWNTs have not yet
been elucidated to a great extent. This is partly because it is difficult to prepare awell-aligned SWNT film that exhibits sufficient light absorption. Using the verticallyaligned SWNT film developed in Chapter 3, the anisotropic optical absorption properties
and Raman scattering characteristics are elucidated in Chapter 4.
Problem 5 is presently being resolved for metallic/semiconducting separation [47,48].
Regarding problem 6, the preferential growth of semiconducting SWNTs was recently
reported [49] although chirality-specific growth, an important target for the future, has not
yet been achieved.
The scope and originality of this thesis are related to the resolutions of problems 1–4.
Although all of these have originally been investigated and resolved in this thesis, the mostimportant originalities of this thesis lie in the resolutions of problems 3 and 4. In Chapter 2,
a new method for the direct growth of SWNTs on Si and quartz substrates is presented,
extensively analyzed, and discussed with respect to problems 1 and 2. In Chapter 3, highdensity, vertically aligned growth of SWNTs on the substrates—with respect to problem
3—is achieved, and a mechanism for vertical growth is investigated and modeled. In
Chapter 4, using a vertically aligned SWNT film grown on quartz substrates, thepolarization-dependent optical absorption property of SWNTs—with respect to problem
4—is elucidated. Finally, the contents of the thesis are summarized in Chapter 5.
A detailed introduction and background for each topic accompanies the beginning of therespective section or chapter.

4

Chapter 1  Introduction

1.2 Structural representation of SWNTs
The structure of the sp2 carbon network of a two-dimentional (2D) graphene sheet isschematically presented as a hexagonal lattice in Fig. 1-1a. The shadowed rhombus
indicates a unit cell of the graphene, which contains two non-equivalent C atoms. The
distance between neighboring atoms ac-c is 1.42 Å, and vectors a1 and a2 represent the unit
vectors of the cell. The Brillouin zone of the graphene is denoted in Fig. 1-1b as ashadowed hexagon, and vectors b1 and b2 are the reciprocal vectors. These are expressed as
 3
 3 aa
a1 = 
a ,  , a 2 = a , - 
2
2
 2
 2

(1)

and
 2π
 2π 2π 
2π b1 = 
(2),, , b2 = 
a 
 3a
 3a a 
based on the x-y and kx-ky coordinates, respectively, as shown in Fig. 1-1. In these equations,the lattice constant of the 2D graphene is defined as a ≡ |a1| = |a2| = 1.42 Å × 31/2 = 2.46 Å.
By convention, high symmetry points at the center, corner, and the midpoint of theneighboring corners of the Brillouin zone are denoted as Γ, M, and K points, respectively.
The unit cell of SWNTs is enlarged when compared to that of the graphene due to thelower symmetry of SWNTs. Figure 1-2 shows an unrolled hexagonal lattice of a SWNT, inwhich the unit cell of a certain type of SWNT is indicated as a shadowed area. The vectors
Ch and T that connect two crystallographically equivalent sites in the circumferential andaxial directions of SWNTs, respectively, are also shown. These vectors are termed thechiral vector and the translational vector, respectively, as further explained below.

a

b

y

Γ

ky

a1
x

b1

a2

kx

K
M

b2

ac-c

Fig. 1-1. (a) Unit cell and (b) Brillouin zone of 2D graphite represented as the shadowed rhombus andhexagon, respectively. ai and bi (i = 1, 2) are unit vectors and reciprocal lattice vectors, respectively.
The high-symmetric points in the 2D Brillouin zone conventionally called Γ, K, and M point, are also
shown.

5

The chiral vector Ch is expressed in terms of real-space unit vectors a1 and a2 and two
integers n and m (0 ≤ m ≤ n) as
C h = na1 + ma 2 ≡ (n, m)(3)

The type of SWNT is completely specified by the two integers (n, m) through the definition
given in Eq. 3. Since the length of Ch indicates the circumferential length of the SWNT, thediameter of the SWNT, dt, is expressed as
dt =

Ch

π

=

Ch ⋅ Chπ=

a n 2 + m 2 + nm

(4)πHere, a ≡ |a1| = |a2| = 1.44 Å × 31/2 = 2.49 Å is the lattice constant of the honeycomb latticeof the SWNT. A slightly greater C–C bond length in SWNTs compared to that in thegraphene (1.42 Å) should be noted.
The angle formed by Ch and a1 is termed chiral vector θ, and its value is 0 ≤ θ ≤ 30° due
to the hexagonal symmetry of the honeycomb lattice; specifically, it is expressed asC ⋅a2n + m(5)cosθ = h 1 =2
C h a1 2 n + m 2 + nm
The translational vector T is defined as the unit vector of a 1D SWNT, which is parallelto the SWNT axis. From the relationship Ch⋅T = 0,(n, m) = (4, 2)

Axial direction

y

x

T
θ

a1

Ch

Circumferential
direction

a2

Fig. 1-2. Unrolled hexagonal lattice of a SWNT. The chiral vector Ch and translational vector T are
presented for the case of Ch = 4a1 + 2a2 SWNT. Its unit cell is denoted as shadowed area in which N= 28 hexagons are contained. The angle between a1 and Ch gives the chiral angle θ (0 ≤ θ ≤ 30°).

6

Chapter 1  Introduction

T = t1a1 + t 2 a 2 ≡ (t1 , t 2 ),t1 =2m + n2n + m, t2 = −
dR
dR

(6)

where dR is the greatest common divisor (gcd) of (2m + n) and (2n + m). Using the above
defined dR, the number of hexagons in the unit cell of a SWNT N is expressed as
N=

Ch ×T
a1 × a 2=(

2 n 2 + m 2 + nm
dR

)

(7)

Therefore, there are 2N carbon atoms in the unit cell of a SWNT. For example, (n, m) = (4,2) SWNT shown in Fig. 1-2 has 28 hexagons in the unit cell.
Since the unit cell of a SWNT is 2D and specified by the orthogonal lattice vectors Ch
and T, as shown in Fig. 1-2, the reciprocal lattice vectors corresponding to thecircumferential direction K1 and the axial direction K2 are defined such that the following
relationships are satisfied:C h ⋅ K 1 = T ⋅ K 2 = 2π , C h ⋅ K 2 = T ⋅ K 1 = 0(8)Solving these relations using Eqs. 6 and 7, K1 and K2 are expressed as

K1 =1(− t 2 b1 + t1b2 )
N

(9)

K2 =

1
(mb1 − nb2 )N(10)

Figure 1-3 shows the reciprocal lattice vectors K1 and K2 for (n, m) = (4, 2) SWNT. The
first Brillouin zone of the SWNT is expressed as a line segment W-W’ as shown in Fig.
1-3a. Therefore, N line segments µK1 (µ = 1, ⋅⋅⋅, N – 1) give rise to N discrete wave vectors,
which originate from the quantized wave vector in the direction of Ch due to the periodic
boundary condition imposed in this direction.
The electronic structure of a SWNT can be obtained from that of 2D graphite. When theenergy dispersion relation of 2D graphite is denoted as Eg, 2D, N pairs of 1D energy
dispersion relation Eµ(k) are expressed as
 K

π
π
E µ (k ) = E g , 2D  k 2 + µK 1  , ( µ = 0,⋅ ⋅ ⋅, N − 1, and −
<k< )
T
T
 K2


(11)

Here, k denotes the wave number along the SWNT axis. If these energy dispersion curves
are collected (or folded) into the first Brillouin zone of the 2D graphite by translating themusing multiples of K1 and K2, Fig. 1-3a is equivalently expressed as Fig. 1-3b in the reducedzone scheme. This expression shows that the wave vectors possible in the case of SWNTs
7

are limited from the case of 2D graphite. The line indicating the possible wave vector
shown in Fig. 1-3b will hereafter be referred to as “cutting line”.
Such a quantized wave vector of SWNTs causes a sharp divergence in their eDOS,
termed “van Hove singularities,” that is characteristic of 1D materials. Figure 1-4 shows theeDOS of (n, m) = (4, 2) SWNT calculated by the tight-binding method with parameters γ0 =2.9 eV, s = 0, and ac–c = 0.144 nm. Since it is obvious that the cutting line of this
SWNT—described by Eq. 11—does not pass the K-point, in which the valence andconduction bands meet in the case of 2D graphite, the (n, m) = (4, 2) SWNT issemiconducting in which eDOS is absent at the Fermi level. On the other hand, when theab(n, m) = (4, 2)

b1
W
W’

K2

Γ

K2
K1

K1

b2

Fig. 1-3. (a) Brillouin zone of a SWNT represented by the line segment W-W’ for the case of (n, m) =(4, 2) SWNT, and (b) its equivalent representation displayed by the reduced-zone scheme. The
vectors K1 and K2 are reciprocal lattice vectors correspond to Ch and T, respectively.

4(n, m) = (4, 2)

Energy (eV)

2

0

–2

–4

http://www.photon.t.u-tokyo.ac.jp/~maruyama/kataura/1D_DOS.html

Fig. 1-4. (a) 3D Brillouin zone of graphite and cutting lines for (n, m) = (4, 2) SWNT. (b) eDOS of(n, m) = (4, 2) SWNT calculated by tight-binding method with γ0 = 2.9 eV, s = 0, and ac-c = 0.144 Å.

8Chapter 1  Introduction

cutting line passes the K-point in the case of e.g. (n, m) = (5, 2) SWNT, the SWNT ismetallic in which eDOS is at the Fermi level. In general, mod(n – m) = 0 SWNTs aremetallic and mod(n – m, 3) ≠ 0 SWNTs are semiconducting. One of the most importantcharacteristics of SWNTs is that the difference of metallic/semiconducting transport
properties is determined solely by the chirality.
Figure 1-5 shows the chiral mapping of (n, m) SWNTs that are either metallic (opencircles) or semiconducting (solid circles). Any chirality is specified either by two integers(n, m) or equivalently, a combination of diameter d and chiral angle θ, as schematized inthis figure. Among these, the SWNTs with m = 0 (i.e., θ = 0°) and n = m (i.e., θ = 30°)
chirality are termed “zig-zag” and “armchair” types, respectively. This is because the edgesof their tubes look like a zigzag and an armchair, as shown in Fig. 1-6a and 1-6b,
respectively. The SWNTs that do not belong to either of these types are the “chiral” type,as shown in Fig. 1-6c.
The fundamental characteristics, structure, and notational system presented in this section
will be used in subsequent chapters, in which specific topics are studied in detail.

9zig-zag
(0,0)

(1,0)

(2,0)

(1,1)

(3,0)

(2,1)

(4,0)

(3,1)

(2,2)

(5,0)

(4,1)

(3,2)

armchair

(5,1)

(4,2)

(3,3)

(6,0)

(7,0)

(6,1)

(5,2)

(4,3)

(4,4)

(7,1)

(6,2)

(5,3)

(8,0)

(5,4)

(8,1)

(7,2)

(6,3)

θ

(8,4)

d

(7,5)

(6,6)

: Metallic

(9,2)

(8,3)

(7,4)

(6,5)

(10,0)

(9,1)

(8,2)

(7,3)

(6,4)

(5,5)

(9,0)

π

(7,6)

6

: Semiconducting

Fig. 1-5. The (n, m) of SWNTs that are metallic (open circles) and semiconducting (solid circles),respectively, denoted on the map of chiral vectors (n, m). Any chirality is specified either by two
integers (n, m) or, equivalently, a combination of diameter d and chiral angle θ.

a Zig-zag typeb

Armchair typea1

a1

(n, m) = (10, 0)(θ = 0°, d = 0.794 nm)(n, m) = (8, 8)(θ = 30°, d = 1.1 nm)

c

Chiral typea1

(n, m) = (10, 5)(θ = 19.1°, d = 1.05 nm)

Fig. 1-6. Structure of (a) zig-zag type, (b) armchair type, and (c) chiral type SWNTs represented by(n, m) =(10, 0), (8, 8), and (10, 5) tubes.

10Chapter 1  Introduction

References for Chapter 1
1.

S. Iijima, T. Ichihashi, Nature 363 (1993) 603.

2.

R. Saito, G. Dresselhaus, M.S. Dresselhaus, Physical Properties of Carbon Nanotubes,
Imperial College Press, London, 1998.

3.

A. Thess, R. Lee, P. Nikolaev, H. Dai, P. Petit, J. Robert, C. Xu, Y.H. Lee, S.G. Kim, A.G.
Rinzler, D.T. Colbert, G.E. Scuseria, D. Tománek, J.E. Fischer, R.E. Smalley, Science 273(1996) 483.

4.

C. Journet, W. K. Maser, P. Bernier, A. Loiseau, M. L. de la Chapelle, S. Lefrant, P. Deniard,
R. Lee, J. E. Fisher, Nature 388 (1997) 756.

5.

H. Dai, A. G. Rinzler, P. Nikolaev, A. Thess, D. T. Colbert, R. E. Smalley, Chem. Phys. Lett.
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6.

B.C. Satishkumar, A. Govindaraj, R. Sen, C.N.R. Rao, Chem. Phys. Lett. 293 (1998) 47.

7.

H.M. Cheng, F. Li, G. Su, H.Y. Pan, L.L. He, X. Sun, M.S. Dresselhaus, Appl. Phys. Lett. 72(1998) 3282.

8.

K.B. Shelimov, R.O. Esenaliev, A.G. Rinzler, C.B. Huffman, R.E. Smalley, Chem. Phys. Lett.
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9.

A.G. Rinzler, J. Liu, H. Dai, P. Nikolaev, C.B. Huffman, F.J. Rodriguez-Macias, P.J. Boul,
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10. P. Hou, C. Liu, Y. Tong, S. Xu, M. Liu, H. Cheng, J. Mater. Res. 16 (2001) 2526.
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13

14

Chapter 2:
CVD growth of SWNTs and their analyses

2.1 Characteristics of SWNT growth from zeolite-supported catalysts
2.1.1 Research backgroundTo date, the unique physical properties of SWNTs have suggested several novel
applications [1] that would not be possible to achieve with conventional materials; further,
there is much scope to realize such inventions using SWNTs. Therefore, a low-cost
synthesis technique of high-quality SWNTs is currently a pressing necessity.
In addition to the initial laser-furnace [2] and arc-discharge [3] techniques, a variety ofstudies have been reported [4–13] using the chemical vapor deposition (CVD) techniquethat is suitable for mass production. Several types of carbon sources, support materials, andsynthesis conditions have so far been tested, but the best approach has not yet been attained.
Toward this goal, our group reported [14] that SWNTs with remarkable purity weresynthesized at a temperature as low as 600°C using alcohol (ethanol and methanol). Further
merits of using alcohol lie in its harmlessness, low cost, and easy-handling properties.
There have been no reports that support the validity of the SWNT yield using asimultaneous combination of Raman, TGA, and transmission electron microscopy (TEM),
other than a report by Alvarez et al. [11], in which MWNTs coexisted as a byproduct.
Furthermore, in a majority of the reports, the characteristics of the reported highest yield
were not presented. It is the author’s belief that a comprehensive discussion should be maderegarding the definition of SWNTs yield, with an clear notation of the upper yield limit forpractical quality. In this section, the effects of CVD reaction time and pre-reduction of
catalytic metal on the quality and yield of synthesized SWNTs are investigated in order todiscuss the feasibility of using our alcohol CCVD method for mass production.

2.1.2 Catalyst preparation and experimental procedure
The catalyst powder mentioned in this section is prepared as follows: Cobalt acetate(CH3CO2)2Co-4H2O and iron acetate (CH3CO2)2Fe were dissolved in ethanol along with
Y-type zeolite powder (TOSOH Corp. HSZ-390HUA, over 99% SiO2) so that the weight
concentration of each metal species over the total catalyst powder (i.e., zeolite + metal) is
2.5 wt%. Their typical amounts are 108.4 mg (Co acetate), 81.1 mg (Fe acetate), 20 ml(ethanol), and 1 g (zeolite powder). The mixture was sonicated for 1 h in a beakersubmerged in a bath-type sonicator; subsequently, it was placed in a furnace maintained at
80°C for 1 h for evaporation of the ethanol. Sonication and evaporation were alternatively
repeated until the contents of the beaker dried uniformly. The resultant white-yellow
16Chapter 2  CVD growth of SWNTs and their analyses

powder was ground into fine powder by a mortar and stored for future use in a furnace at atemperature of 80°C. This procedure was developed based on the procedure originallypresented in Refs. 15 and 16.
Figure 2-1 shows a schematic of the CVD apparatus used in Sections 2.1 and 2.2. For the
CVD procedure, 30–50 mg of the catalytic powder was sparsely mounted on a quartz boat,
and the boat was then is placed at the center of a quartz tube (26 mm inner diameter, 1 m
length). As shown in Fig. 2-1, a 30-cm central portion of the quartz tube was heated in anelectric furnace with an Ar flow of approximately 300 sccm, so that the pressure inside thetube could be maintained at 300 Torr by operating only the “needle valve.” After thereaction temperature was achieved typically within 30 min, the supply of Ar was stopped
and the quartz tube was evacuated by opening the “valve,” as shown in Fig. 2-1.
Subsequently, ethanol vapor was introduced keeping the pressure at just before entrance ofthe quartz tube constant as measured by the “pressure manometer.” Finally, the ethanol
supply was stopped and the furnace was turned off before returning the system to room
temperature with an Ar flow of 100 sccm. In some experiments, instead of pure Ar, Ar
containing 3% of hydrogen (referred to as “Ar/H2”) was used for the reduction purpose.
As-prepared blackened powder was characterized by TGA, Raman spectroscopy, andTEM. TGA was performed using Seiko Instruments Inc. Exter 6000 and TG/DTA 6300
under a heating rate of 5 °C/min with an Ar flow of 100 sccm. In every TGA measurement,a sample weighing 10 ± 1 mg was used in order to reduce the TG error to below 1%, andthe temperature was maintained at 100°C for 2 h prior to the start of the measurement inorder to ensure reproducibility. Raman measurement was conducted using Chromex 501iskPa

Needle valve

Pressure
manometer

Mass-flow
controller

Valve

Rotary pump

Ar
orElectric furnace

Ar/H2

Bellows valve
Quartz tube
Quartz boat
Glass flask

Pa

Pirani gauge: 1/4” Flexible tube

: SUS 1/4” pipe

Fig. 2-1. Schematic description of CVD apparatus used in Section 2.1 and 2.2.

17

and Andor Technology DV401-FI as the spectrometer and CCD system, respectively, alongwith an optical system, Seki Technotron Corp. STR250. A laser wavelength of 488 nm wasused in all the measurements.

2.1.3 Definition of SWNT yield
Recent findings by TG or temperature-programmed oxidation (TPO) analyses[9,11,17–21] are utilized to estimate the SWNT yield. The burning temperature of SWNTs
is greatly influenced by the condition of the SWNTs specimen; therefore, caution must be
exercised in comparing these results. It is remarkable that when catalytic metal particles are
mixed with SWNTs, the decomposition temperature is somewhat lower than that of
purified SWNTs [17–20]. At least, the burning temperatures of purified and annealed
SWNTs produced by the laser furnace method [2,18] or the HiPco method [7,19,20] are in
the same temperature range of 500–700°C.
Since amorphous carbon decomposes at approximately 300–500°C [9,11,17], which islower than the decomposition temperature of SWNTs, its existence is readily recognizedfrom the TG or TPO curves. However, when graphitized carbon products such as MWNTs
coexist with SWNTs, it becomes considerably difficult to specify the amount of SWNTs
using only the TGA or TPO curves. As pointed out by Alvarez et al. [11], this is because acertain type of well-graphitized product burns at slightly higher temperature range thatoverlaps the range of SWNTs. As a method for estimating the amount of each constituent,
Alvarez et al. [11] decomposed their TPO curves into several Gaussian-Lorentziancomponents and attempted to estimate the amount of each carbon species, including
amorphous carbons and MWNTs. However, this method has large scope for freedom in the
choice of fitting parameters; hence, although physically effective, it may not be the mosteffective method for accurate yield estimation.
Therefore, the most appropriate method is to perform the estimation on a specimen that
contains negligible amounts of amorphous carbon and MWNTs, for which
Gaussian-Lorentzian decomposition is not required. The absence of amorphous carbon and
MWNTs can be confirmed by TGA and TEM, respectively. The yield of SWNTs in thisstudy is defined as the ratio of the weight loss between 500 and 700°C to the weight thatremained at 1000°C; both are measured by TGA. In other words, the yield is a
representative ratio of the weight of SWNTs to that of the catalytic powder.

18

Chapter 2  CVD growth of SWNTs and their analyses

2.1.4 Effect of CVD time and reduction of catalyst on SWNT yield
Figure 2-2a shows the TG and DTG curves of the as-prepared powders for several CVD
reaction times when Ar was used during the heating of the electric furnace. The reaction
temperature and pressure were 800°C and 10 Torr, respectively. For these conditions, thistemperature was confirmed to be optimal (i.e., achieving minimum impurities) by Raman
and TEM analyses. In our previous report [14], SWNTs with sufficiently highquality/purity were synthesized even at 650°C; however, this was possible because thepressure was much lower (2–5 Torr) than that in the present study in which the conditions
for the highest yield are discussed. A slight weight gain at approximately 250°C is due tothe oxidation of catalytic metals [19,20], and the following weight loss up to 500°C is dueto the burning of amorphous carbons. The weight loss between 500 and 700°C was
attributed to the burning of SWNTs, which strongly depends on the CVD reaction time. It
should be noted that the burning temperature of the current SWNTs is equal to that of
purified and annealed SWNTs that are synthesized by the laser-furnace [18] and HiPco[19,20] methods, indicating that the sidewalls of the SWNTs in this study are of goodquality and are devoid of metal particles. The gradual shift of the DTG peaks toward ahigher temperature is attributed to the increase in the diameter of SWNTs or thickening of
the bundles. In the 300-min case, this shift is partially due to the formation of MWNTs.
TEM observations displayed no multi-layered carbons such as MWNTs in the 120-min case,while a small amount of MWNTs was observed in the 300-min case (data not shown).

a80

2, 10, 30, 60, 120, and
300 min in the directionof arrows.

1
0
0

b

10 min (850°C)

90
TG, %

90

70
2
DTG, %/min

100

DTG, %/min

TG, %

100

500
Temperature, °C

1000

10 min (800°C)

80

60 min (850°C)

70
2

120 min (850°C)

120 min (850°C)

100

60 min (850°C)
10 min (850°C)

10 min (800°C)

500
Temperature, °C

1000

Fig. 2-2. TG/DTG curves when (a) Ar and (b) Ar/H2 were used during the heat-up of the electric
furnace. The ethanol pressure during CVD reaction was 10 Torr in all cases. The reaction
temperature in panel (a) was 800°C for all cases.

19

A series of experiments were carried out using Ar/H2, and their TG and DTG results arepresented in Fig. 2-2b. The ethanol pressure during the reaction was 10 Torr. For acomparison with the curves in Fig. 2-2a, the first experiment was conducted under theconditions of 800°C and 10 min. The TG curve in the case of Ar/H2 (dashed line) exhibits agreater total carbon yield than in the case of Ar (Fig. 2-2a). This increase is thought to arise
from the additional reduction of catalytic metals that would otherwise be reduced by carbon
atoms at a lower speed. A side effect, i.e., a simultaneous increase of amorphous carbon,
can be suppressed by employing a higher reaction temperature. The solid lines in Fig. 2-2b
represent the TG/DTG curves of SWNTs synthesized at 850°C, showing that the amount ofamorphous carbon was suppressed to the same extent as that in Fig. 2-2a. It is noted that
this comparison implies not only that Ar/H2 enhances the yield of SWNTs but also that Ar
lowers the reaction temperature, which can be an important controllable parameter in the
production of SWNTs.
Figure 2-3 shows the Raman spectra corresponding to Fig. 2-2b. Detailed interpretationsof the Raman spectra are presented in elsewhere [22]. The decrease in the D-band
magnitude from “10 min at 800°C” to “10 min at 850°C” coincides with the observation in
Fig. 2-2b. Although the magnitudes of the D band gradually increased with the reaction
time, they retained sufficiently good quality, according to the TEM observations. Since the
TGA results indicate a negligible amount of amorphous carbon compared with SWNTs
2

Diameter (nm)
1 0.9

0.8

Intensity(arb.units)

10 min (800°C)

10 min (800°C)
10 min (850°C)

10 min (850°C)
60 min (850°C)

60 min (850°C)
120 min (850°C)

120 min (850°C)

100

200

300
–1

Raman Shift (cm )

0

500

1000

1500
–1

Raman Shift (cm )Fig. 2-3. Raman spectra corresponding to Fig. 2-2b taken with 488 nm laser light. The left panel
is a magnification of the low-frequency area of the right. The gas used in the heating-up of theelectric furnace and the ethanol pressure during CVD reaction were Ar/H2 and 10 Torr,
respectively.

20

Chapter 2  CVD growth of SWNTs and their analyses

even for longer-CVD-time cases, the D band increase in this case may partly be ascribed tothe double resonance effect by SWNTs with defects. The left panel displays the radial
breathing mode (RBM) of SWNTs, from which the diameter distribution of SWNTs can be
estimated using the relationship “d (nm) = 248/ν (cm-1)” [23,24], where d is the diameter of
a SWNT and ν is the Raman shift. The observed increases in the diameter with CVD
reaction time are partly because larger catalytic particles, which would produce SWNTs
with larger diameter, require a longer time until they are activated and saturated with C
atoms. As the reaction time increases, SWNTs begin to grow from larger catalyst particles,
and at 300 min (shown in Fig. 2-2a), catalytic particles that are large enough to produce
MWNTs are finally activated. Since it is more difficult to properly anneal SWNTs grownfrom larger catalyst particles at the moment of separation from the catalyst [5], these
SWNTs are considered to possess a greater amount of defects. The above reasons serve to
explain the increase in the D-band magnitude with CVD time that is observed in Fig. 2-3.
Figure 2-4 shows the time sequence plots of the SWNT yields. The error arising fromTG was ± 0.5%. The definition of the SWNT yield is not strictly applicable for the 300-min
case in which MWNTs were observed. This figure also displays the enhanced yield in the

SWNT yield (500 – 700°C), wt%

case of “850°C, 10 Torr, Ar/H2” compared with that of “800°C, 10 Torr, Ar”.

850°C, 10 Torr, Ar/H2

40

800°C, 10 Torr, Ar

20

800°C, 5 Torr, Ar

0
0

100

200

300

CVD time, minFig. 2-4. Time progresses of SWNT yields for the conditions of ‘850°C, 10 Torr, Ar/H2’ (circle),‘800°C, 10 Torr, Ar’ (square), and ‘800°C, 5 Torr, Ar’ (diamond), for the temperature, pressure,and gas used in the heating-up of the electric furnace, respectively. A straight line for eachcondition denotes a least-squares fit. Note that a small amount of multi-layered carbon products
were observed in cases of 300 minutes.

21

2.1.5 Microscopic analyses of obtained SWNTs on zeolite support
The quality of the above-described SWNTs was investigated by TEM. The as-grownsample was sonicated in methanol for 5 min and the solution was dropped onto a TEM grid.
Figure 2-5 presents a few representative TEM images. In the context of the simultaneousachievement of yield and quality, “850°C, 10 Torr, 60 min, Ar/H2” (Fig. 2-5a) was the best
among the tested cases. The quality of the “850°C, 10 Torr, 120 min, Ar/H2” case wasalmost the same (Fig. 2-5b) but these SWNTs had thicker bundles, and that of the “10 Torr,
60 min, Ar” case followed them. In this study, therefore, the practical limit of the reaction
time in order to assure sufficient quality/purity of the product is 120 min, in which a SWNT
yield 40% relative to the weight of the zeolite support powder with Fe-Co catalyst wasachieved. This corresponds to a yield of more than 800% over the weight of the catalytic
metal since the total metallic weight in the catalytic powder was 5%. The “as-grown” highquality of our SWNTs is evident when the TEM images (Fig. 2-5) are compared with thosepresented in previous reports, for example [7–11,13,19]. The choice of ethanol for the
carbon feedstock appears to be a crucial factor.
Figure 2-6 shows FE-SEM micrographs for the as-grown stage of the “850°C, 10 Torr,
60 min, Ar/H2” SWNTs obtained at different magnifications. The low-magnification image
reveals that zeolite powder particles of several hundreds of nanometers were bound to eachother by web-like SWNT bundles. The surface of the zeolite powder was densely covered
with SWNT bundles whose typical thickness is 10–20 nm. Thinner bundles of ~10 nm wereobserved at the highest magnification particularly near the surface of the zeolite particle,
and the thickness of the bundles appears to increase toward the zeolite surface. At theoutermost surface, where the bending stiffness of the thickened bundles exceeded the vander Waals attraction force from the surface of zeolite, the bundles finally depart into space.
It should be noted that the surfaces of the SWNT bundles are smooth and no contamination
is observed on them; this also verifies the high quality of the pure SWNTs grown by the
proposed method.

22

Chapter 2  CVD growth of SWNTs and their analyses

Fig. 2-5. TEM images for ‘as-grown’ SWNTs synthesized at the conditions of (a) ‘850°C, 10
Torr, 60 min, Ar/H2’, and (b) ‘850°C, 10 Torr, 120 min, Ar/H2’, for the temperature, pressure,time, and gas used during the heat-up of the electric furnace, respectively. Note the high purity of
SWNTs without contaminants such as metallic particles, amorphous carbons, or MWNTs.

23

Fig. 2-6. FE-SEM micrographs for the ‘850°C, 10 Torr, 60 min, Ar/H2’ SWNTs in ‘as-grown’ state
on zeolite support powder, taken at several different magnifications. The same sample has been
investigated and presented in Figs. 2-2 - 2-5.

24Chapter 2  CVD growth of SWNTs and their analyses

2.1.6 Effect of catalyst metal selection on growth of SWNTs
Previous experiments have used a catalyst prepared by an impregnation of Fe and Co
acetates into Y-type zeolite powder, as described in Section 2.1.2. The use of Fe-Co
catalyst leads to a high yield of the SWNTs, as seen in Fig. 2-4. This subsection
investigates the effect of different catalyst metals on the growth of SWNTs on SiO2
supports. Mo, Fe, Co, and Ni, in particular, are examined because they are often used andare thought to be suitable as catalysts for SWNT growth. They are d-orbital transition
metals known to have strong catalyst activity in general [25].
Figure 2-7 shows the Raman spectra, measured with 488-nm laser light, of SWNTs
grown using different catalyst metals supported by the impregnation of their metallic
acetates into Y-type zeolite powder. In all the cases, the weight% of metal over the support
was set as 5 wt%. The CVD experiments were performed under the same conditions: 800°C,
5 Torr, and 10 min for reaction temperature, ethanol pressure, and reaction time,
respectively, with the use of Ar while heating up the electric furnace. The output powders
appeared to be colored almost white (Mo), gray (Fe, Ni), and black (Co), and they are
investigated later in greater quantitative detail. With the exception of Mo (Fig. 2-7a), theRaman spectra obtained with a high G/D ratio at ~1593 cm-1 and a clear indication of RBM
Diameter (nm)2

1 0.9 0.8

0.7

CVD: 800°C, 5 Torr, 10 min
Raman: 488 nm, x10

Intensity (arb.units)(a) Mo 5 wt%(b) Fe 5 wt%(b) Fe 5 wt%(c) Co 5 wt%(c) Co 5 wt%(d) Ni 5 wt%

100(a) Mo 5 wt%

200

300
–1

Raman Shift (cm )(d) Ni 5 wt%

400 1000

1200
1400
1600
–1
Raman Shift (cm )Fig. 2-7. Raman scattering spectra measured with 488 nm laser light from SWNTs grown from (a)Mo, (b) Fe, (c) Co, or (d) Ni catalyst supported on USY-zeolite powder through impregnation of theiracetates as described in Section 2.1.2. The metallic concentration over the support powder is 5 wt%
for all cases..

25

in lower frequency region are identified as those of SWNTs. It is evident that the diameterof the produced SWNT increases in the order of Fe < Co < Ni, indicating that the diameterof the metal particles formed on the SiO2 support also varied in the same order.
This experimental observation can be explained in terms of the thermodynamic
properties of metals, according to the methodology originally proposed by Hu et al. [26]used for explaining the morphologies of sputtered metals on TiO2 substrates. Table 2-1 lists
several thermodynamic properties of the metals employed in Fig. 2-7. ∆Hf°oxide and∆Hf°sublimation denote the heat of formation of metal oxide per mole of the metal and the heatof sublimation of the metal, respectively, both at standard state, cited from Ref. 27. The
former assumes the oxidized state shown in the table and the latter is the so-called cohesiveenergy that well correlates with the melting point of the metal. An alternative property of∆Hf°sublimation, experimentally measured surface energy γ cited from Ref. 28, is also shownin Table 2-1.
These thermodynamic properties are reflected in the behavior of the metals supported on
the oxidized surface provided there are no significant changes in the chemical states at theelevated temperature (~800°C) at which CVD is performed. Since ∆Hf°sublimation (or γ)
represents the affinity of metals with themselves and ∆Hf°oxide represents that of metals withoxygen, these ratios should provide a measure of the degree of wetting of the metal on the
SiO2 support. The last two rows of Table 2-1 show these ratios, and the agreement of theirtendency with the experimental observation in Fig. 2-7 is excellent. Other studies have also
reported these tendencies in the catalyst for SWNT growth. For example, the SEM
Table 2-1. Thermodynamic properties of Fe, Co, Ni, and Mo.
Element

Mo

Fe

Co

Ni

Atomic number [-]

42

26

27

28

Melting point [K]

2895

1811

1770

1728

Oxidized state

MoO3

Fe2O3

Co3O4

Ni2O3

∆Hf°oxide [kJ/mol](oxide per mol of metal)-745.58-412.40-297.26-244.92∆Hf°sublimation [kJ/mol](cohesive energy of metal)

658.58416.59424.96427.95γ × 10 [kJ/m ](surface energy of metal)

3.00

2.48

2.55

2.45

-∆Hf°sublimation / ∆Hf°oxide [-]

0.883

1.01

1.43

1.75

4.02

6.00

8.58

10.0

3

2

6

2

-γ/ ∆Hf°oxide × 10 [mol/m ]← highly wet on SiO2

26

highly agglomerated on SiO2 →Chapter 2  CVD growth of SWNTs and their analyses

micrograph of the Si substrate after C2H2 molecular beam epitaxy (MBE) growth of carbon
nanotubes at 750°C from vacuum-deposited Ni catalyst layer (thickness 5 nm) reveals
significant agglomeration of Ni metal, as large as ~50 nm in diameter [29]. Even at a
reduced amount (~1 nm) of deposited Ni, the catalyst agglomerates into ~10 nm particles,
resulting in the growth of only MWNTs. Since Ni has often been used for growing
vertically aligned MWNTs on a flat substrate [30,31], such an empirical choice of catalyst
could be quantitatively explained using the method shown in Table 2-1.
Figure 2-8 shows the TGA curves of SWNT-grown zeolite powders that were examined
in Fig. 2-7 along with that of our standard Fe-Co (2.5 wt% each) catalyst used in Figs. 2-2
to 2-6. Once again, all the CVD experiments were performed at 800°C, 5 Torr, and 10 min.
For monometallic catalyst, it is recognized that Co yields the largest amount of SWNTs,
while Ni and Fe yield a lower amount. TGA was not performed on the sample with Mo
catalyst examined in Fig. 2-7 because virtually no production of SWNT was confirmed by
the result of Raman scattering analysis. This result indicates the existence of an optimum
point in the choice of catalyst. Based on the current discussion, it is reasoned that Fe and Ni
produce a lower amount of SWNTs because they exhibit excess wetting and agglomerating
CVD: 800°C, 5 Torr, 10 min

TG, %

100

: Fe 5 wt%

95: Co 5 wt%: Ni 5 wt%

DTG, %/min: Fe/Co 2.5 wt% each

0
0.2

500

1000

0.1
0

–0.1
0

SWNT

500
Temperature (°C)

1000

Fig. 2-8. TG and DTG curves measured from as-prepared SWNTs grown from Fe, Co, Ni, andFe/Co catalyst supported on Y-type zeolite powder. The metallic concentration over the support
powder is 5 wt% for all cases. The elevating speed of temperature and flow rate of air during TG
measurements were 5 °C/min and 100 sccm, respectively.

27

on the SiO2 support, respectively. On the other hand, Co exhibits the best performance
among these because the wettability is moderate; hence, particle formation is appropriate
for the efficient growth of SWNTs.
As shown in Fig. 2-8 with a solid curve, the yield of SWNTs can be further enhanced by
the use of a bimetallic Fe-Co catalyst. Several studies have demonstrated the effectivenessof the use of bimetallic catalysts; this will be investigated and discussed in depth in Section
2.3 and 2.4. The effect of bimetals on the surface of the SiO2 support is considered to be as
follows: The metal with higher wettability to SiO2 (such as Fe or Mo) comes closer to the
SiO2 surface and stabilizes the other metal species (such as Co or Ni) that works as themain catalyst for the SWNT growth. Thus, the main catalyst (i.e., Co or Ni) is dispersed
and even protected from deactivation due to a chemical reaction with SiO2 (e.g., oxidationor silicidation) by the underlying wetting metal (i.e., Fe or Mo) that serves as a sacrificing
layer. It should be noted that this discussion (i.e., the effectiveness of bimetal) is limited tothe case of the supported catalyst used for the growth of SWNTs. In the case of a floatedcatalyst, in which the wettability of the metal to the support is irrelevant, many studies havedemonstrated that monometallic Fe serves as an excellent catalyst for SWNTs such as in
the HiPco process [4,7].
Finally, for subsection 2.1.6, Fig. 2-9 shows a phase diagram for the Fe-Co alloy system,
cited from Ref. 29. Since both metals do not form a eutectic compound, they can work
respectively, as described above.

Fig. 2-9. Phase diagram for Fe-Co alloy system cited from Ref. 29.

28

Chapter 2  CVD growth of SWNTs and their analyses

2.1.7 Summary
In Section 2.1, the growth of SWNTs by the alcohol CCVD method was investigated andcharacterized by means of Raman scattering and TG analyses. The bimetallic Fe-Co
catalyst supported through the impregnation of its acetate solution into Y-type zeolite
powder is effective and feasible for the bulk production of SWNTs. The effect of reduction
on the yield and diameter of the resultant SWNTs was elucidated through the comparative
experiments. The reduction of the catalyst prior to the CVD reaction was shown to beeffective in enhancing the growth of SWNTs.
The definition of SWNT yield has been clearly described in this study based on theappropriate interpretation of TGA results with a support by TEM observations. It has been
demonstrated that a yield of SWNTs greater than 40% with sufficiently high quality can beachieved from ethanol within a CVD time of 120 min; thus, the feasibility of the proposed
method toward mass production was confirmed. The reduction of the catalytic metal, whichleads to an effective enhancement of the yield, plays an important role in the synthesis of
SWNTs. Finally, the effect of the choice of catalyst metal on the growth of SWNTs wasinvestigated in terms of the thermodynamic properties of the metal catalysts Fe, Co, Ni, and
Mo. It was clarified that the ratio ∆Hf°sublimation/∆Hf°oxide (or γ/∆Hf°oxide) explains theobserved difference in the growth of SWNTs from different monometallic catalysts; further,
it provides a theory-based index for the choice of catalyst for SWNT growth. The effect of
the bimetallic catalyst was also explained in this discussion. Further detailed investigations
and discussions will be presented later in Section 2.3 and 2.4.

29

2.2 Catalyzed growth of SWNTs from mesoporous silica thin films
2.2.1 Research background and motivation
So far, several studies [30-33] have been reported to synthesize carbon nanotubes
directly on silicon wafer as a preliminary step for incorporating them into electronic circuits.
However, this approach has resulted in the occasional production of multi-walled nanotubes(MWNTs) [31-33] due to a sintering of deposited/sputtered catalytic metals, which can becaused by their higher CVD temperature (typically 900°C) and almost perfect flatness of Si
surface. From this concern, mesoporous silica (MPS) could be an ideal material forachieving well-regularized synthesis of carbon nanotubes with an expected effect ofpreventing sintering of catalytic metals.
To date, several attempts have been made to synthesize carbon nanotubes using MPS asa catalytic support [34-41]. Powders of various types of MPS were employed for mass
production [34,37,38], but they all have resulted in MWNTs. Among them, Okamoto et al.
[38] have reported growth of some amount of SWNTs in addition to MWNTs. Films of
MPS were sometimes formed on solid substrates [35, 36, 39-41], but their major products
were MWNTs and no successful synthesis of SWNTs has yet been reported. Although thegrowth of SWNTs was insisted by Huang et al. [41], no experimental evidence has been
given by the authors concerning whether the grown nanotubes were SWNTs or MWNTs.
In this section, a new methodology of synthesizing high-quality SWNTs is proposed
employing a 3-dimensional (3D) MPS thin film with accessible pores on the surface, which
has near-“SBA-16” cubic structure. The method of metal loading differs from any of thepast reports [35,36,39-41], where the catalytic metal was pre-mixed in the stage of silica
formation. By this, the ability of MPS thin film to support of catalyst for the growth of
SWNTs are demonstrated and the role of MPS layer are discussed in order to solve
aforementioned problems in the selective growth of SWNTs on flat substrates.

2.2.2 Preparations and experiments
A thin film of 3D MPS was coated on a Si substrate based on the procedure developedby Yamakita [42], which had been established from the original recipe shown by Zhao et al.
[43] for the fabrication of SBA-16 type MPS. First, TEOS (tetra-ethyl-ortho-silicate),ethanol, H2O, and HCl were mixed and stirred for 1 h at 65 °C to form a sol-gel solution.
This solution was mixed with an ethanol solution of amphiphilic triblock copolymer[(C2H2O)106 - (C3H4O)70 - (C2H2O)106] (BASF, F127) and stirred for another 2 h at room30

Chapter 2  CVD growth of SWNTs and their analyses

temperature. The self-assembled polymers served as a structure-directing agent (SDA) in
the formation of mesopores. The overall composition of prepared mixture was fixed to{TEOS : H2O : HCl : Ethanol : polymer = 1 : 9.2 : 0.021 : 40 : 7.2 × 10-3} in molar ratio[42]. The solution thus prepared was mounted on a piece of Si substrate (2 cm × 2 cm) by
the dip-coating method at a constant pull-up rate of 6 cm/min. After the coating, the piece
was dried in air at 80°C overnight and calcinated in air at 500°C for 4 h to remove thepolymers, by which an MPS thin film with a typical thickness of 50 nm was formed [42].
Subsequently, catalytic metal was loaded on the MPS-coated Si substrate (referred to as“MPS/Si substrate”). Iron acetate (CH3CO2)2Fe and cobalt acetate (CH3CO2)2Co-4H2O
were dissolved in ethanol (typically 20 ml) to form a metal acetate solution so that theweight concentration of both metals were made equal, either 0.01 wt % or 0.001 wt % inthis report. The MPS/Si piece was placed on the bottom of a beaker containing the metal
acetate solution and was then transferred into a desiccator for evacuation by a rotary pumpfor 1 h. It is crucial to set the initial solution level below 10 mm to avoid sudden boiling
during the evacuation. With this process, air remaining inside the mesoporous film was
replaced with the solution. The piece's surface was washed immediately after drawn-out
from the solution with ethanol by two different procedures, as described in a later section.
The metal-loaded MPS/Si piece was heated up to about 400 °C in the flow of He/O2 (5 %O2) to remove organic residues and to form oxidized bimetallic particles inside (or partly on
the surface) of the thin film. As reference experiments, silica-coated Si substrates (referred
to as “Silica/Si substrate”) without mesoporous structure were employed to examine therole of the mesopores. This silica/Si piece was fabricated by identical procedures for the
metal loading process but without addition of the polymers.
The subsequent CVD procedure and employed CVD apparatus are the same as thosepresented in subsection 2.1.2. The reaction temperature, time, and ethanol vapor pressure
employed in this study are 750°C, 10 min, and 10 Torr, respectively. The gas used whileheating up and cooling down of the electric furnace is Ar/H2 (3 % H2). Thereby synthesized
SWNTs are characterized with FE-SEM observation (HITACHI, S-900) and Raman
spectroscopic analysis (CHROMEX 501is and ANDOR DV401-FI for the spectrometer and
CCD system, respectively). Laser wavelength of 488 nm is used for all Raman
measurements.

31

2.2.3 Results and discussions
Figure 2-10 presents a FE-SEM image of the MPS/Si surface before catalytic metal was
loaded. Platinum film with a thickness of less than 0.5 nm (measured by a quartz crystal
microbalance) was sputtered on the surface to enhance the visibility, and the observation
was performed at 6 kV, where no charge-up occurred. The dark circular apertures
correspond to the mesopores formed in the silica framework. The inset reveals that themesopores were periodically located with an approximate interval of 15 nm.
Figure 2-11 shows the pore size distribution of this MPS film determined by theAbsorption, cc / (nm g)

Fig. 2-10. FE-SEM image of platinum-sputtered MPS/Si surface before loading of catalytic metal.
taken by Hitachi S-900 at 6 kV. The dark apertures are the mesopores formed in silica framework.

0.01

0
2

3

4

5 6 7 8 910

20Pore diameter, nm

Fig. 2-11. Pore size distribution of current MPS thin film calculated using the BJH analysis.

32

Chapter 2  CVD growth of SWNTs and their analyses

Barrett-Joyner-Halenda analysis using the MPS films coated on glass substrates in the N2
absorption/desorption measurement. A sharp peak at 6 nm corresponds to the mesopores,
and a less remarkable peak around 2.6 nm is ascribed to the diameter of connecting holes
between the pores (refer to Ref. 44 for 3D schematic of SBA-16 type MPS).
Figure 2-12 shows FE-SEM images of the MPS/Si surfaces after the CVD reaction withseveral magnifications. The metallic concentrations of the acetate solution used in Figs.
2-12a and 2-12b were 0.01wt% and 0.001 wt%, respectively. In both cases, the substratesurface was rinsed with ethanol immediately after the metal loading for about 3 s. The
bright lines represent the bundles of SWNTs, which look somewhat blurred and thicker
than actual: This is due to a change in the local emission property of secondary electrons,
often observed for the SWNTs grown on Silica/Si surface [45]. The SWNTs in Fig. 2-12a
look sparser and less uniform than those in Fig. 2-12b. Notably, metal particles larger than
10 nm (bright dots) are densely inhabited on the MPS surface, where some of them seem tohave sintered. These particles are seen to ‘clog’ the mesopores beneath them, which might
be a partial reason for such sparser population of SWNTs.
In contrast, SWNTs shown in Fig. 2-12b look more densely and uniformly populated andabFig. 2-12. FE-SEM micrographs of MPS/Si surface after the CVD reaction when the metallic
concentration in the solution used in the metal loading process was (a) 0.01 wt% and (b) 0.001 wt%,
measured by Hitachi S-900 at 10 kV. The employed washing treatment was a light rinsing in ethanol.
Horizontal lines denote 100 nm.

33

very few metal particles are found on the surface. Then it is reasonably speculated that acertain amount of SWNTs were grown from inside of the MPS thin film. Anothernoticeable difference lies in the visibility of the surface: The surface structure is hardly
recognizable in Fig. 2-12a, while in Fig. 2-12b the fine structure of the MPS surface isclearly observed. Note that these two substrates were treated in the same batch in theprocesses of preparation, metal loading, CVD, and SEM observation. Usually, the surfaceof MPS cannot be observed without sputtering of metal particles, as exemplified in Fig.
2-10. This improved visibility was caused by a uniform coverage of its surface with
SWNTs, which can act as an excellent conductor.
In order to examine the function of the MPS layer, SWNTs synthesized on the MPS/Si
were compared with those on the Silica/Si substrate at a fixed metallic concentration of
0.001 wt%. Figure 2-13 presents Raman spectra of the SWNTs synthesized on the MPS/Si
and Silica/Si substrates measured with 488 nm laser light, and for each substrate two types
of washing treatment were employed: The first method is that employed in Fig. 2-12, or arinse of the surface with ethanol for about 3 s (denoted as ‘lightly rinsed’). The othermethod is a soak of the substrate into ethanol (typically 20 ml) for 10 minutes before it was
drawn out from the ethanol and dried in air (denoted as ’10 min soaked’). In each case,
spectra were measured at five different locations chosen randomly, and they were
Diameter (nm)
1

0.9

0.8

*

*

Lightly rinsed* : Si+ : System

Intensity (arb. units)+
MPS/SiLightly rinsed+

10 min soaked

MPS/Si*MPS/SiMPS/Si10 min soaked

Lightly rinsed

Silica/Si

Silica/Si

10 min soaked
Silica/Si

Silica/Si

200

300
–1

Raman Shift (cm )0500Lightly rinsed

10 min soaked

1000

1500
–1

Raman Shift (cm )Fig. 2-13. Raman spectra of MPS/Si and Silica/Si substrates after the synthesis of SWNTs measured
with 488 nm laser light. The metallic concentration during the metal loading process was 0.001 wt%
for all cases. For each substrate, two types of washing treatment noted in text were employed.

34

Chapter 2  CVD growth of SWNTs and their analyses

arithmetically averaged. All spectra were normalized by the height of the silicon-derived
peak around 960 cm-1. The interpretation of the Raman spectra of SWNTs is presented inelsewhere [22].
The right panel of Fig. 2-13 shows a high-frequency area, where the magnitude of the
G-band around 1590 cm-1 relative to the Si peak at 960 cm-1 approximates the amount ofsynthesized SWNTs. When the ‘lightly rinsed’ washing treatment was employed, no
significant difference in the G-band magnitude was observed between MPS/Si and Silica/Si
cases. However, the difference became much clearer when they were treated with ’10 min
soaked’ washing: No significant change in the G-band magnitude was observed in MPS/Si,
while the magnitude in Silica/Si drastically decreased as expected. This indicates that the
MPS layer serves as an efficient capacitor for catalytic metals, supporting our idea thatmany of SWNTs were grown from the metals inside of the mesopores.
A peak around 1350 cm-1 called the D-band represents the extent of disorder in the sp2
arrangement of carbon atoms, from which the quality of SWNTs were estimated.
Interestingly, in the case of MPS/Si the ‘10 min soaking’ treatment has enhanced thequality of SWNTs. Furthermore, the standard deviation of the G-band intensities among thefive measurements in the ‘lightly rinsed’ case was over 50 %, whereas that in the ’10 min
soaked’ case was only 8 %, indicating that the soaking process has improved the uniformityof the catalytic distribution. As we speculate, the metals on the surface are also reduced
through the ’10 min soaked’ process, but a more detailed analysis is essential for further
discussion. The lower Raman spectra are magnified in the left panel of Fig. 2-13,
presenting the radial breathing mode (RBM) peaks that identify SWNTs. The diameter
distribution of SWNTs is estimated using “d (nm) = 248 / ν cm-1” [23,24] where d is the
SWNT diameter and ν is Raman shift. The SWNTs synthesized on MPS/Si have diameters
around 0.9 - 1.5 nm.

35

Figure 2-14 shows FE-SEM images of the above discussed MPS/Si substrate with ’10
min soaked’ treatment, taken from tilted angles so that their broken cross-sections can be
included. The cross-section exhibits a three-layered structure of this MPS/Si substrate: The
MPS top layer has an approximate thickness of 50 nm, and the SiO2 layer with a thicknessof 100 nm is seen below it. In the base is the Si substrate that looks darkened. The upper
picture reveals that most of the SWNT bundles are adhered to the MPS surface to form a
uniform, web-like network of SWNTs. The lower picture with larger magnification shows
the fine structure of MPS beneath the SWNTs. No remarkable difference in the form ofsynthesized SWNTs from the case of ‘Lightly rinsed’ is observed in the FE-SEM
observation. Some of the SWNT bundles are observed to detach from the surface, but they
eventually collide with the surface again due to the flexibility of SWNTs and are capturedby the van der Waals attraction of silica frameworks.

Fig. 2-14. FE-SEM micrographs of MPS/Si substrate after the synthesis of SWNTs taken from atilted angle taken by Hitachi S-900 at 8 kV. The metallic concentration during the metal loading
process was 0.001 wt%, and the substrate was subsequently soaked in ethanol for 10 min.

36

Chapter 2  CVD growth of SWNTs and their analyses

With further FE-SEM observation of the broken cross-section with higher magnification,
we have occasionally observed metal particles embedded in the MPS layer from which
SWNTs were extended. These images support our idea regarding the role of the MPS layer;
however, they are not sufficiently convincing for a clearer discussion on the morphology of
SWNTs and the metallic particles located inside or on the surface of the MPS layer. A
further detailed study is needed for their characterization by the use of e.g. a cross-sectional
HR-TEM analysis [46].

2.2.4 Summary of the SWNT growth from MPS thin films
High-quality SWNTs have been synthesized on 3D MPS thin film and its function has
been elucidated through a reference experiment with Silica/Si substrate. The MPS layer
provides an additional volumetric capacity for holding catalytic metals inside it, and aphysical potential for prevention of sintering. The present CVD process at relatively low
temperature contributes to the prevention of metallic sintering at the same time to thepreservation of the MPS structure. This study has suggested a possibility of growing
SWNTs regularly in well-defined intervals by utilizing the periodic structure of MPS.

37

2.3 Development of techniques for direct synthesis of SWNTs on solid flat
substrates
2.3.1 Research background and motivation
When the fabrication of SWNT-based devices is attempted, an appropriate incorporationof SWNTs into silicon or other material-based systems is essential. Thus far, several studies
have been reported in which carbon nanotubes were synthesized on the substrates by
various methods. Kong et al. [47] and Franklin et al. [30] spun coated their Fe-Mo catalyst
with alumina support particles to form patterned catalytic islands on Si surfaces andsynthesized small amounts of SWNTs. Cassell et al. mounted mesoporous alumina/silica on
Si substrates to support their Fe-Mo catalyst and produced SWNTs [48].
In other studies, mesoporous silica was coated as a supporter on a Si substrate in the formof a thin film, leading to the production of MWNTs [35,36,40] or SWNTs [49]. However,such supporting material is often undesirable because it is an additional material notessential for the functioning of the devices. A way to circumvent the use of the support
material was proposed by Li et al. [50], in which ferritin protein was utilized for sparsely
located iron nanoparticles on a flat SiO2 substrate to synthesize SWNTs. Homma et al. [51]dispersed commercially available Fe or Fe2O3 nanoparticles in ethanol and loaded them
onto an Si substrate. They produced thin carbon nanotubes including SWNTs at 950°C
using Fe2O3 as the catalyst; however, the selectivity to SWNTs is unknown.
The above-mentioned studies [30,35,36,40,47–51] made use of liquid-based approaches
for catalyst preparation; however, in some cases, catalytic metals were mounted on
substrates using dry processes such as sputtering or vacuum vapor deposition [32,33,52–55].
Although the selective synthesis of SWNTs on a flat Si surface was recently reported [55],this method usually accompanies agglomerated catalyst metals with larger diameters (i.e.,
greater than 5 nm) that can result in an undesirable production of MWNTs. For example,
the dominant products in the studies by Nerushev et al. [32] and Yoon et al. [33] were
MWNTs although SWNTs were also reportedly produced; in both reports, agglomerationsof metals were clearly observed in the SEM micrographs. Delzeit et al. [52] synthesized
SWNTs with relatively high quality and selectivity by pre-depositing 20 nm of an Al
underlayer on a Si surface before depositing 1 nm of Fe-Mo catalyst; however, due to an
agglomeration of Al, such an underlayer resulted in significant surface roughness. A similar
procedure was performed by Zhang et al. [53], in which SWNTs were grown from Ni
38

Chapter 2  CVD growth of SWNTs and their analyses

Catalyst dispersed by the Al layer; however, this method also accompanies serious
agglomeration of Al in the order of several tens of nanometers. Further, although SWNTs
were not produced in the case of a Si substrate, Hongo et al. [54] sputtered Fe on the A-faceof a sapphire crystal and synthesized a relatively abundant amount of SWNTs at a CVD
temperature of 800°C.
In other reports, SWNTs were incorporated on a catalyst-patterned substrate as afield-emission transistor (FET) [56,57], in a manner different from the conventional methodof post-dispersion of bulk-produced SWNTs [58]. In their prototypes, a very small quantity(one or a few) of SWNTs were grown from catalytic islands having much larger
dimensions (3 µm [56] and 100 µm [57]), indicating that there were very few active sites
and most catalyst areas did not participate. However, it is desirable to increase the area
efficiency of the catalyst in order to improve the concentration of FET-device density.
In the beginning of this section, a new catalyst supporting method was presented that
achieves the direct growth of high-quality SWNTs on the surface of flat substrates. Thismethod does not necessitate any intermediate supporting material such as theaforementioned oxide porous materials or Al deposition layers, which often result inundesirable roughness of the substrate surface after CVD. It was elucidated that the
proposed liquid-based technique, employing Co-Mo bimetallic catalyst, excels incontrolling the amount of supported metals, resulting in a fine monodispersion of Co
particles with diameters ranging from 1–2 nm. The advantages and details of the proposed
catalyst supporting technique will be discussed.

39

2.3.2 Development of dip-coat catalyst supporting method
In the first step, molybdenum acetate (CH3COOH)2 Mo and cobalt acetate (CH3COOH)2
Co-4H2O are dissolved in ethanol by sonication for 2 h in order that the concentration ofeach metallic species over the weight of the solution is 0.01 wt%. Their typical amounts are
as follows: ethanol: 40 g, Co-acetate: 16.9 mg, and Mo acetate: 8.92 mg. An n-type Si
wafer with (001)-surface (Nilaco Corp., SI-500452) and a fused quartz with both sides
optically polished (Fujitok Corp., #19983) were employed as the substrates. Both substrates
had a thickness of 0.5 mm. The silicon substrate was cut into a strip of approximately 7 mm
× 20 mm, while a strip of size 25 mm × 25 mm was used for the quartz substrate. A larger
dimension was chosen in the case of quartz for the optical measurement described asfollows. These substrates are held by a small clip with a stabilizing weight and a nylon
fishing line. The substrate piece is then submerged into the prepared metallic acetate
solution for 10 min, with its top 5 mm remaining above the solution level to prevent the clip
from coming into contact with the solution. The piece is then withdrawn from the solution
at a constant speed of 4 cm/min. The surface of the substrate is rapidly dried at several
millimeters above the liquid-contact level immediately after withdrawal from the solution.
As soon as this process is complete, the piece is placed in a furnace in air maintained at
600a

Co acetate(II), 4H2O

80

400

60
200

40
0

100
600

b

Mo acetate(II), dimer

80

400

60
200
40
0

50
Time, minTemperature, °C

Weight, %100

50

Temperature, °C

Weight, %

100

100

Fig. 2-15. TG (left ordinate) and temperature (right ordinate) curves measured for (a) (CH3COOH)2
Co-4H2O and (b) (CH3COOH)2 Mo measured. Measurement was performed with Seiko Instruments
Inc. Exter 6000 and TG/DTA 6300, at a heating rate of 5 °C/min with 100 sccm flow of air.

40

Chapter 2  CVD growth of SWNTs and their analyses

400°C for 5 min to decompose acetic or any organic residue in order to form an oxide ofbimetallic Co-Mo catalyst. As shown in Fig. 2-15, the decomposition of these metallic
acetates below 400°C was confirmed by TGA.

2.3.3 Direct synthesis of SWNTs on Si and quartz substrates
2.3.3.1 Experimental procedure
Figure 2-16 shows the CVD apparatus used in this section and later in Chapter 3. A pieceof substrate on which the catalyst was supported is placed at the center of a quartz tube witha length of 1 m and an inner diameter of 26 mm. When the substrate piece is small, a quartz
boat is used to mount it. The quartz tube was set inside an annular electric furnace (60 cm
in length) and heated with 300 sccm of Ar/H2 (3% H2) typically at 300 Torr, adjusted byoperating only the “bellows needle valve” shown in Fig. 2-16. When the desired
temperature is attained, the supply of Ar/H2 is stopped and inside the quartz tube is brought
to vacuum by opening the “valve” shown in Fig. 2-16. Subsequently, ethanol vapor is
supplied so that the pressure just before the entrance of the quartz tube, monitored by the“pressure manometer” shown in Fig. 2-16, is maintained at 10 Torr. After the CVD reaction,
the electric furnace is turned off and cooled to room temperature with an Ar/H2 flow of 100
sccm. Hydrogen is used for reducing the catalyst in order to retrieve its catalytic function;
its effects were confirmed in Section 2.1 and will be discussed below.
The synthesized SWNTs are characterized with FE-SEM (Hitachi, S-900) andmicro-Raman scattering measurement using an optical system (Seki Technotron STR250)
comprising a spectrometer (Chromex 501is) and a CCD system (Andor DV401-FI). All

kPa

Bellows
needle valve

Pressure
manometer

Mass-flow
controller

Oil-free pump
(ULVAC DVS-321)

Ar/H2

Valve

Foreline
trapElectric furnace

Bellows valve
Quartz tube
Substrate
Glass flask

Pa

Pirani gauge: SUS 1/4” pipe

Fig. 2-16. Schematic of CVD apparatus used in Section 2.3 and Chapter 3 for the direct synthesis of
SWNTs on flat substrates.

41

Raman spectra presented in this section are an arithmetic average of the measurements at
10 randomly chosen locations on the substrate. The VIS-NIR absorption spectra aremeasured using Hitachi U-4000.
2.3.3.2 Resonant Raman scattering analysis
Figure 2-17 shows the Raman spectra of SWNTs directly grown on Si and quartz
substrates measured with 488-nm laser light. The CVD reaction time was 10 and 60 min for
Si and quartz, respectively. As for the Si substrates, the spectra for several CVD
temperatures are presented. The amount of synthesized SWNTs was quantitatively
compared using a height ratio of the G-band to Si-derived peak at 518 cm-1, which was
determined to be 0.07, 0.23, 5.2, and 1.5 for the temperatures of 650, 750, 800, and 850°C,
respectively. No SWNTs were synthesized at 900°C (data not shown). Therefore, theoptimum temperature for maximizing the amount of SWNTs in this study is 800°C. The
decrease in the amount beyond 850°C is considered to arise from the formation of silicide,
as demonstrated by Arcos et al. [59] with their Fe catalyst. It should be noted that the
optimum synthesis temperature may be affected by the thickness of a natural oxidation
488 nm*+* : Si+ : System

Intensity(arb.units)* Si, 850 °C

Si, 800 °C

Si, 750 °C*

Si, 650 °C

Quartz, 800 °C

0

500

1000

1500
–1

Raman Shift (cm )Fig. 2-17. Raman spectra of SWNTs synthesized on silicon and quartz substrates at various CVD
temperatures measured by 488 nm laser light.

42

Chapter 2  CVD growth of SWNTs and their analyses

layer on the surface of the employed Si wafer, which, as described later, is typically in therange of 0.5 to 3 nm. Several Si wafers purchased from different manufacturers were tested
and the optimum temperature of certain Si wafers was found to be 750°C. At any
temperature, sufficiently high-quality SWNTs were confirmed from their high G/D ratio(e.g., 30 at 800°C). The RBM peaks were observed at all the temperatures. It should be
noted that the synthesis of SWNTs on the Si substrate at a temperature of 650°C is by far
the lower than the previous reports [30,32,33,47,48,50–52], in which a temperature of
900–1000°C was required for the growth of SWNTs. The spectrum of SWNTs synthesizedon a quartz substrate at 800°C indicates high quality (G/D ratio > 25) despite a relatively
long CVD exposure of 60 min.
Figure 2-18 shows the RBM spectra of SWNTs directly grown on Si and quartz
substrates at 800°C at three different excitation wavelengths—488, 514.5, and 633 nm. For
the purpose of comparison, the RBM spectrum of HiPco SWNTs [7,60] (batch #:HPR113.4) supplied by Rice University is also included in Fig. 2-18. The CVD reaction
time was 10 and 60 min for Si and quartz, respectively. At the top of the figure, the Katauraplot [61] calculated with the parameters γ0 = 2.9 eV and ac–c = 0.144 nm [23,24] isexhibited along with the horizontal lines corresponding to the energies of the employedlaser lights. The diameter of the SWNTs d was estimated from the RBM Raman shift νusing the relationship “d (nm) = 248/ν (cm-1)” [23,24]. The locations of the measured
Raman peaks closely match the prediction by the Kataura plot, and a diameter distribution
in the range of 1.1–1.7 nm was observed.

43

0.8

2.6

488 nm514.5 nm

2.4
2.2
2

633 nm1.8
Si, 488 nm

Intensity (arb.units)

Energy Separation (eV)Nanotube Diameter (nm)10.9Quartz, 488 nm
HiPco, 488 nm
Si, 514.5 nm
Quartz, 514.5 nm

Si, 633 nm
Quartz, 633 nm

150

200
250
–1
Raman Shift (cm )300

Fig. 2-18. RBM spectra of SWNTs grown at 800°C on the surface of Si and quartz substrates
corresponding to Fig. 2-17, measured by 488, 514.5, and 633 nm excitations. ‘HiPco’ is thereference spectrum of a pristine HiPco sample measured by 488 nm excitation. The Kataura plot
for the corresponding range is attached on the top, where solid and open circles denotesemiconducting and metallic SWNTs, respectively.

44

Chapter 2  CVD growth of SWNTs and their analyses

2.3.3.3 Microscopic analysis
Figures 2-19a and 2-19b show the FE-SEM micrographs of SWNTs directly grown on
the Si and quartz substrates, respectively, at 800°C, which correspond to the Raman spectra
shown in Figs. 2-17 and 2-18. The dark background area of Fig. 2-19a represents thesurface of the Si substrate on which a uniform layer of web-like SWNT bundles is observed.
Figure 2-19b shows an image acquired at a tilted angle including a broken cross section of
the quartz substrate. A film of SWNTs with a thickness of a few hundred nanometers isobserved to be formed on the surface. In both micrographs, the observed strings are SWNT
bundles.

abFig. 2-19. FE-SEM micrographs of SWNTs synthesized on (a) silicon substrate taken from top
and (b) quartz substrate taken from slanted angle, taken by Hitachi S-900 at 7 kV. Both samples
correspond to those presented in Fig. 2-18.

45

Figure 2-20 shows images of an identical SWNT-grown quartz substrate acquired at
different magnifications. Figure 2-20a is a picture showing the change in appearance of thesubstrate from before CVD (left) to after CVD (right). After CVD, a film of SWNTs hasgrown uniformly over the region in which the catalyst was dip coated. Figure 2-20b shows
an optical microscope image observed at a scratched region of the film from which theuniformity of the film is recognized. Figures 2-20c and 2-20d show magnified images,
×20K and ×50K, respectively, of the scratched area acquired by a Hitachi FE-SEM S-900 at
7 kV. These images confirm that SWNTs are randomly oriented on the surface of substrate.
The film observed in Figs. 2-20c and 2-20d was locally scratched and peeled off for the

a

b

10 mm

20 µm

c

d

500 nm

(Optical microscope, x50)

200 nmFig. 2-20. Observations on the same SWNT-grown quartz substrate at various magnifications. (a) A
picture of the substrate before (left) and after CVD (right). (b) An optical microscope image ofscratched site of the film. (c, d) Magnified images on the scratched area observed by Hitachi FE-SEM
S-900 at 7 kV in different magnifications. The film is scratched and partially peeled off for the
purpose of investigating morphology of the film as well as the substrate surface after CVD.

46

Chapter 2  CVD growth of SWNTs and their analyses

purpose of investigating the morphology of the film and the surface of the substrate. No
particular agglomerated metals were observed on the exposed surface of the substrate.
For a further detailed investigation of the morphological state of the substrate surface
after CVD, FE-SEM observations by Hitachi S-5200 at 2 kV were performed on a quartz
substrate on which SWNTs were sparsely grown. Figure 2-21a shows the micrographobtained from the top of the substrate, in which the surface of the substrate is observed
beneath the randomly oriented SWNT bundles. Although agglomerated metallic particles

a

c

b

100 nm50 nm

Fig. 2-21. Observations on a quartz substrate on which SWNTs were sparsely grown by Hitachi
FE-SEM S-5200 at 2 kV from (a) top of the substrate in ×50k and (b, c) side of the substrate at
fractured edge of the substrate in ×200k and in ×350k, respectively.

47

are locally observed as bright dots in a few locations, no metal agglomerates wererecognized in major part of the surface. The occasional presence of agglomerated metals
could be due to an imperfection in the surface cleanness that arose during the dip-coatprocess. Figures 2-21b and 2-21c are micrographs obtained at the fractured edge of thesubstrate at higher magnifications, ×200 K and ×350 K, respectively. These figures provide
strong evidence that the proposed catalyst supporting method is virtually devoid of metal
agglomerates, in contrast to the previously reported methods [32,33,52–57]. This smoothsurface (i.e., devoid of agglomerated metals on the surface) is considered to beadvantageous for various device applications because, in general, agglomerated metals do
not contribute to the functioning of devices.
Figure 2-22 shows a TEM image of the SWNTs investigated in Fig. 2-20. A TEM
micro-grid was directly rubbed against the blackened quartz surface in order to observe theas-grown state of the SWNTs. An edge of a SWNT drapery was observed to assure thetransmittance of the electron beam. Figure 2-22 reveals that the synthesized SWNTs
possess a fine quality that is free from any type of metal particles, amorphous carbon, andmulti-walled nanotubes.
In order to clarify the morphologies of SWNTs and the catalyst, cross-sectional TEM(X-TEM) analysis was performed. The sample for the X-TEM observation was prepared byplacing the two pieces of Si(001) substrate—on which SWNT were randomlygrown—facing each other, so that the structure is “Si/SWNT/glue/SWNT/Si”; the30 nmFig. 2-22. TEM image of an edge of a SWNT drapery by JEOL 2000EX at 120 kV. A TEM grid was
directly rubbed onto the substrate in order to observe as-grown state of the SWNTs.

48

Chapter 2  CVD growth of SWNTs and their analyses

sandwiched structure was subsequently sliced and thinned from its side.
Figure 2-23 presents the X-TEM images observed at the surface of the Si substrate.
Despite the lower contrast due to the SWNTs embedded in glue, several SWNTs wereclearly observed on the Si(001) substrate. At the top of the surface, an approximately 2-nm

Fig. 2-23. X-TEM images of SWNTs directly grown on Si(001) surface viewed from [110] directionof Si. A native SiO2 layer with a thickness of approximately 2 nm is seen on the top surface of thesubstrate.

49

thick native SiO2 layer is observed. In the middle panel, some of the observed SWNTs areindicated with their estimated diameters whose range agrees with the diameters measured inFig. 2-22. Several dark circles with diameters similar to those of SWNTs are sparsely
observed, and these are believed to be metallic catalysts. Their lattice planes were notrecognized from the image. The lowermost panel shows a magnified image in which thecross sections of two SWNTs that extend perpendicular to the page are observed. The
ordering of Si atoms in the substrate is also observed, and the hexagonal alignment of
atoms indicates that the direction of electron transmission is the [110] direction. Figure
2-24 presents a schematic description of Si atomic ordering in this X-TEM observation.

[111]

d{111} = 0.314 nm
[001]

[110]

Fig. 2-24. Schematic representation of the cross-sectional view of Si(001) substrate exhibited in Fig.
2-23. Spheres and orange circles denote Si atoms and Bravais lattice points of the crystal,respectively, viewed from [ 1 1 0] direction. Pink spheres correspond to Si atoms at eight corners of
FCC Bravais lattice. Inter-plane distance for [111] direction is presented as d{111}.

50

Chapter 2  CVD growth of SWNTs and their analyses

2.3.3.4 Discussions
a. Effect of catalyst reduction
Prior to the CVD reaction, H2 gas is supplied during the heating of the electric furnace forthe purpose of catalyst reduction. Since the catalyst is oxidized before the CVD andtherefore has less activity, it should be reduced prior to the reaction. It was confirmed in
Section 2.1 that the amount of SWNTs is low when the catalyst is not reduced prior to the
CVD reaction. This situation also occurs in the case of a flat substrate. Figure 2-25 shows
the Raman spectra measured with a 488-nm laser light from the surface of the Si substrate
after CVD at 750°C. Figure 2-25a shows the spectrum when Ar/H2 (3% H2) is supplied
during the heating of the electric furnace, and Fig. 2-25b shows the spectrum when Ar is
supplied instead of Ar/H2. The intensity of the G-band shown in Fig. 2-25a isapproximately 40 times larger than that shown in Fig. 2-25b. This demonstrates that theamount of SWNTs on the Si surface can be significantly enhanced by using H2 to reducethe catalyst prior to the CVD reaction.

Intensity (arb. units)

x 25

1200

1400

1600

1800
–1

Raman Shift (cm )(a) w/ H2(b) w/o H2

0

500

1000

1500
–1

Raman Shift (cm )Fig. 2-25. Raman spectra taken by 488 nm of SWNTs synthesized on Si surface when (a) Ar/H2 (3 %H2) or (b) Ar was flowed during heat-up of the electric furnace. CVD was performed at 750ºC for (a)10 min and (b) 30 min. Inset magnifies G-band in the case of (b). CVD times for Si and quartz are 10
min and 1 h, respectively. Spectral magnitudes are normalized by the height of Si peak at 520 cm-1.

51

b. Effect of bimetallic catalyst
In this study, bimetallic Co-Mo catalyst is employed for the synthesis of SWNTs on flat
substrates. To date, several types of bimetallic catalysts such as Fe-Co [14,62], Co-Mo[9,11], and Fe-Mo [5,10,63,64] have been used for the mass synthesis of SWNTs byimpregnating them into porous support powders (e.g., silica, alumina, or MgO). Some ofthese studies [9,11,63,64] discussed the effect of bimetals on the growth of SWNTs.
Figure 2-26 shows Raman scattering spectra of SWNTs grown from different catalysts onquartz substrates measured with 488-nm laser light. In all the cases, CVD was performedfor 1 h at 800°C. The CVD experiment and Raman scattering measurement shown in Fig.
2-26a to 2-26d were performed in the same batch to ensure comparability. Figure 2-26ashows the Raman spectrum of SWNTs grown from a standard acetic Co-Mo catalyst (0.01
wt% each), which results in the strongest Raman intensity of all the cases.
Figure 2-26b shows a spectrum of SWNTs grown from a bimetallic catalyst ofmolybdenum acetate and cobalt nitrate, Co(NO3)2-6H2O. The condition of Fig. 2-26b is

2

Diameter (nm)
1 0.9 0.8
488 nmIntensity (arb.units)

(a)
(a)
(b)

x4

*
(c)

x25

(d)

x25

*

100

200

300
–1

Raman Shift (cm )

1000

(b)

x4

(c)

x25

(d)

x25

1200

1400

1600
–1

Raman Shift (cm )Fig. 2-26. Raman spectra (taken by 488 nm) of SWNTs generated on quartz substrates from various
catalysts, (a) Co acetate and Mo acetate 0.01 wt% each, (b) Co nitrate and Mo acetate 0.01 wt% each,(c) Co acetate 0.02 wt%, and (d) Mo acetate 0.02 wt%. The weight concentration here is defined as
the ratio of metallic weight in salt to total solution weight used for the dip-coating process (seeexperimental section). The right panel shows G-band while left panel exhibits RBM. The asterisk at
220 cm-1 denotes the background noise of our measurement system.

52

Chapter 2  CVD growth of SWNTs and their analyses

seemingly similar to the case of Fig. 2-26a; however, the amount of SWNTs in the former
is appreciably lower than that in the latter. This difference may be explained by the study
conducted by Sun et al. [65] who prepared cobalt catalysts by impregnating a mixture ofcobalt (II) nitrate and cobalt (II) acetate salts onto silica gel powder. They tested various
nitrate/acetate ratios from 1:0 (all nitrate) to 0:1 (all acetate) and demonstrated that only
when acetate was solely used, the fine dispersion of Co particles of approximately 2 nm indiameter was obtained; however, when nitrate was used, the resultant Co particles becameas large as 10 nm in diameter. They reported that this was caused by a strong interaction
between the metal acetate and the SiO2 support [65]. Although the structure of SiO2 in Ref.
33 is different from that in the present study, the lower catalytic activity observed in Fig.
2-26b compared with that observed in Fig. 2-26a may be caused by the weaker interaction
between Co and the SiO2 surface.
Figure 2-26c shows a spectrum of SWNTs grown from 0.02 wt% Co catalyst, in which
the observed intensity of the G-band is much lower (1/25 of Fig. 2-26a). Furthermore, when
0.02 wt% Mo catalyst was employed, no signals of SWNTs were detected, as shown in Fig.
2-26d, indicating that monometallic Mo is inactive as a catalyst for SWNTs. Our
observation here agrees with the results obtained by Alvarez et al. [11] who discussed therole of Mo in the stabilization of Co. The result in Fig. 2-26 shows clearly that the
combination of Co and Mo acetates provides the best result among the tested cases.
c. Merits and application of current techniqueSince the production of SWNTs requires an active catalyst with a size comparable to thediameter of a SWNT (i.e., a few nanometers [4]), it is very important to mount small
amounts of catalytic metals on the surface and, at the same time, to prevent them fromagglomerating into large particles even under the high temperature of the CVD reaction. An
obvious merit of our dip-coating technique is the ease with which extremely small amountsof bimetallic catalyst can be loaded on the surface; this is partly because the concentrationof catalyst solution can accurately be adjusted merely by diluting.
Figure 2-27 presents a plan-view HR-TEM image of the quartz substrate heated to
800°C with an Ar/H2 flow of 300 sccm without the subsequent CVD reaction. It is revealed
that the Co catalyst particles (observed as black circles) are finely monodispersed over thesubstrate with approximate diameters of 1–2 nm without producing agglomerated metals
even after heating under the Ar/H2 reductive atmosphere [65]. This good dispersion ispartially explained by the strong chemical interaction between metal acetate and the SiO2
53

2 nm

10 nm

Fig. 2-27. Plan-view HR-TEM image of the quartz substrate surface after reduction by heated up to
800°C without undergoing CVD reaction. Catalyst particles are seen as black circles and are finely
mono-dispersed on the surface. Inset magnifies a typical image of the catalyst particle.

base, as stated above. The mechanism of finely dispersed Co-catalyst formation and therole of Mo will be investigated and discussed in detail in Section 2.4. Such chemicalinteractions would not occur when the catalyst is loaded by conventional sputtering or
vacuum vapor deposition method.
The lowering of CVD temperature is also an important factor because a high temperatureaccelerates the chemical reaction between the catalyst metal and silicon to create inactive
metallic silicide [51,59] and an agglomeration of catalysts. The alcohol CCVD method issuperior, as demonstrated in Fig. 2-17 as well as in previous reports [14,49,62], in
producing relatively high-quality SWNTs at lower temperatures. This low-temperatureprocess is beneficial to our direct synthesis technique because conventionally used support
materials are not required in our method.
To the best of the author’s knowledge, this is the first study to directly synthesize visually
recognizable amounts of SWNTs on the surface of a quartz substrate. It has recently beenreported [66,67] that SWNTs exhibit excellent bleached absorption properties due to theirstrong third-order optical nonlinearity (χ(3)) along with an absorption of approximately 1.55
µm light that is used in optical telecommunication. These characteristics have motivatedattempts to apply SWNTs in optical switching [66,67] and mode-locked lasers.

54

Chapter 2  CVD growth of SWNTs and their analyses

Figure 2-28 shows an optical absorption spectrum of SWNTs directly grown on thequartz surface. As a reference, Fig. 2-28 also shows the spectrum of SWNTs synthesized by
the alcohol CCVD method on zeolite support using Fe-Co catalyst (refer to Section 2.1),
which was suspended in 1 wt% SDS-added D2O after strong sonication, centrifugation, anddecantation of its supernatant, based on the procedure reported in Ref. 68. In the spectrum
shown in Fig. 2-28a, several broad peaks can be observed and this broadening is due to thebundling of SWNTs [69]. Sharper peaks are observed when the SWNT bundles are
removed by centrifugation (Fig. 2-28b). The difference in the locations of the peaks
between Figs. 2-28a and 2-28b arises due to the difference in the bandgap of the contained
SWNTs (i.e., difference in chirality). Further, the spectrum of Fig. 2-28a is considered to be
red-shifted due to the effect of bundling. There are a few recognizable groups of peaks inthe spectra. The peaks at approximately 1450 nm in Fig. 2-28a are derived from thefirst-energy gaps of semiconducting tubes ES11, and the peaks at approximately 800 nm arederived from the second-energy gaps ES22 [69]. These results suggest the possibility ofapplying our sample to the aforementioned optical applications, which will be demonstrated
in detail at the end of Chapter 4.
0.4(a) On quartz, as–grown.

0.08

S

S

E 22

0.3

E 11

0.06

AbsorbanceAbsorbance

0.1

0.2
(b) On zeolite, dispersed andcentrifuged.

0.04

500

1000

1500

Wave length (nm)Fig. 2-28. Optical absorption spectra of (a) SWNTs synthesized directly on the surface of quartz, and(b) those synthesized on zeolite support using Fe/Co catalyst as a reference. The spectrum in the caseof (b) was measured by dispersing the specimen in 1 wt% SDS-added D2O solution followed by astrong sonication, centrifugation, and decantation of its supernatant based on the procedure in Ref. 68.

55

d. Applicability of current technique to Si/SiO2 microstructures
Although the conventional vacuum vapor deposition technique has an important
advantage of being a dry process in which cleanness is easier to maintain than in the wet
process, the catalyst metal is mounted only on the side facing the linearly incoming metallic
vapor flux. Furthermore, such a vacuum process is not only expensive but also involves adifficulty in uniformly loading the catalyst onto a large surface area due to the limited sizeof the available vacuum chamber. On the other hand, the proposed liquid-based dip-coatprocess is not subject to such a limitation; further, by this method, the catalyst can beloaded even onto the surfaces of infinitely long fibers or strips at a considerably lower cost.
An additional merit of the dip-coat method is its applicability to solid surfaces that havecomplexsurfacegeometry,suchasmicrostructuresfabricatedbymicro-electro-mechanical-system (MEMS) processes. Due to the nature of the dip-coat
method, it is possible to load the catalyst even onto a surface with complex geometry atwhich the metallic vapor flux does not reach, such as the inner walls of concentricallyhollow optical fibers. The feasibility of the proposed technique toward MEMS structures isgoing to be presented here. It should be noted that such an incorporation of SWNTs into
MEMS structures is an important fundamental technology that connects micro and nanoregimes.
Figure 2-29 shows the FE-SEM images for several examples of direct incorporation of
SWNTs on Si microstructures. Figure 2-29a shows the surface of the Si substrate on whicha trigonal array of cylindrical pillars was fabricated. The diameter and height of the pillar
were 2 µm and ~7 µm, respectively. The catalyst was supported on the substrate by the dip
coating of 0.01 wt% Co-Mo acetate solution, as described in Section 2.3.2. The ACCVD
was performed at a reaction temperature and ethanol vapor pressure of 750°C and 10 Torr,
respectively. It was frequently observed (approximately 30% of the pillar intervals) that
SWNTs, either bundled or isolated, were bridged between the top surfaces of neighboring
pillars, as shown in Fig. 2-29a. SWNTs were also observed on the bottom surface of thesubstrate and the side surface of the pillar; however, they grew along the surface andtherefore do not depart from it. This may be explained that only SWNTs on the top surfaceof the pillar had the opportunity to overcome the van der Waals attractive force from thesurface at the circular edge of the pillar.
Figure 2-29b shows the FE-SEM image of the bridged SWNT between the tips of theinterfacing Si cantilevers at intervals of 5 µm. The CVD conditions were identical to thosein the case of Fig. 2-29a. These cantilevers were fabricated in the same Si piece, as shown
56

Chapter 2  CVD growth of SWNTs and their analyses

in the inset, over a penetrated hole manufactured in the substrate. Such a SWNT suspendedin space should be useful for several optical investigations of SWNTs, such as a moreaccurate measurement of polarized Raman scattering of SWNTs under reduced
environmental effects. The reproducibility of this suspension is considerably high, and thus
far, the bridging has been observed in all the trials (5 out of 5 pieces).
Figure 2-29c shows the growth of SWNTs on the surface of a quartz grating. It should be
noted that the SWNTs were selectively grown in the shallow grooves of the grating. Thiscan be explained by the fact that the Co-Mo acetate solution used in the dip-coat process
was selectively trapped inside the grooves due to the capillary force exerted on the liquid.
On the other hand, Fig. 2-29d shows SWNTs that are grown preferentially on the top
surface of the Si/SiO2 substrate on which deep grooves were fabricated. In this case, it ispossible that the high aspect ratio of the groove cross section prevented the residual air inthe deep grooves from being replaced with the Co-Mo solution. The examples shown in
Figs. 2-29c and 2-29d indicate the possibility that the SWNT growth can be spatiallycontrolled by exploiting the difference in the wettability of microstructures. It should be
noted that all the surfaces presented in Fig. 2-29 are sufficiently clean and devoid of
agglomerated catalyst metals that could have caused roughness of the surface after CVD.

57

Fig. 2-29. FE-SEM images for several examples of direct growth of SWNTs in Si/SiO2
microstructures from Co-Mo catalyst supported by the dip-coat technique. SWNTs were directly
synthesized on (a) arrays of cylindrical Si pillar, (b) interfacing cantilevers fabricated over a hole
penetrating the Si substrate, (c) inside nano-grooves of a quartz grating plane, and (d) top surface of
Si/SiO2 substrates on which deep grooves were fabricated. See text for details.

58

Chapter 2  CVD growth of SWNTs and their analyses

2.3.4 Summary of direct growth of SWNTs on flat substrates
This section presented a new method of synthesizing SWNTs with sufficient quality
directly on the surface of Si and quartz substrates. It was observed that the Co-Mo catalyst
supported by the proposed method combined with the alcohol CCVD method produces
SWNTs with high quality and selectivity directly on the flat Si/SiO2 surface. It wasdemonstrated that intermediate support materials such as oxide porous materials or Al
deposition layers are unnecessary for the growth of SWNTs on the Si/SiO2 surface,differently from conventional understandings.
The proposed dip-coat technique with Co-Mo bimetallic catalyst was observed to excel incontrolling the amount of supported metals and can yield finely monodispersed Co particles
with a diameter range of 1–2 nm. The SWNTs were synthesized directly on the Si surface
even at a temperature of 650°C, which is much lower than previously reported temperaturesof 800–1000°C. On the quartz surface, an abundant amount of SWNTs were produced tothe extent that the surface was blackened with SWNTs. It was demonstrated that the
proposed technique is applicable to the direct incorporation of SWNTs into Si-based
MEMS structures.
The proposed dip-coating method is an easy and cost-effective approach that is suitable
for mounting small amounts of catalysts on the surface. The strong interaction between
metal acetate and the SiO2 base may aid the fine dispersion of the catalyst, which isdifficult to achieve by conventional sputtering and deposition techniques. Further
elucidation of the Co-Mo catalyst formation process is presented in Section 2.4.

59

2.4 Morphology and chemical state analysis of Co-Mo catalysts supported
on substrates by TEM and XPS analyses
2.4.1 Questions to be resolved for dip-coat supported Co-Mo catalysts
In Section 2.3.3, it has been presented that the catalyst supported by the dip-coating ofbimetallic Co-Mo acetates on Si/SiO2 substrates yield high quality SWNTs without
generating agglomerated metals on the substrate. However, the mechanism concerning thehigh activity and selectivity of Co-Mo catalysts in the growth of SWNTs has not been fully
clarified at that time. As clarified in Section 2.3.3, the catalytic performances in the SWNT
growth have the order of {Co-Mo acetates > Co (nitrates)-Mo (acetates) >> Co acetates >>Mo acetates}. Although this result is supporting an inference that Co species are stabilized
by Co-molybdate at an optimum Co/Mo ratio and that Mo carbides release active carbon tocatalytic Co particles from which SWNTs selectively grow during the CVD reaction[11,70-72], the detailed correlation between the morphology and the chemical state of
Co-Mo catalysts during their preparation and activation has not been verified so far. The
effect of Mo in bimetallic catalysts on the growth of SWNTs should also be clarified.
In this Chapter, to resolve these questions, Co-Mo catalysts are prepared on quartz
substrates from metal acetate solutions using a procedure of dip coating, followed bycalcination and reduction, instead of using single crystals or porous materials as catalyst
support. This allows one to quantitatively characterize the catalyst morphology usingtransmission electron microscopy (TEM), and the chemical state of metal species using
X-ray photoelectron spectroscopy (XPS). Based on evidences discovered from a series ofmeasurements, a model is then developed to understand why Co-Mo catalysts preparedwith the above method show high selectivity and activity for the growth of high-purity
SWNTs densely and vertically aligned on quartz substrates during the alcohol CCVD
process.

2.4.2 Methods for catalyst characterization
2.4.2.1 TEM observation and its sample preparation
The morphology of Co-Mo catalysts after calcination and after reduction is characterizedusing TEM. The samples for plan-view TEM observations are sputter-coated with a 10-nm
SiO2 layer to avoid structural variation during TEM observations. For the samples for
XTEM observations, two identical substrates are adhered to each other from the catalyst
60

Chapter 2  CVD growth of SWNTs and their analyses

side by using glue without depositing a SiO2 layer. The samples for plan-view TEM andXTEM observations have a sandwich structure of SiO2(quartz) / catalyst / SiO2(10nm) andSiO2(quartz) / catalyst / glue / catalyst / SiO2(quartz), respectively. Then, these substrates
are sliced and punched into circular discs with a diameter of 3 mm and a thickness of 2mm.
Finally, these discs are further thinned by conventional mechanical grinding, polishing,and dimpling, followed by Ar ion milling at an acceleration voltage 4 kV at an incidence
angle of 6° with a Gatan 691 Precision Ion Polishing System (PIPS). Plan-view TEM andXTEM observations are done using a JEOL JEM-4000EX at 400 kV and 2010F at 200 kV,
respectively. Because there is no crystalline orientation information from the fused quartz
substrates, no orientation adjustment during XTEM observations is performed to make theincident angle of electron beam parallel to the direction of quartz-glue interfaces.

2.4.2.2 Procedure for XPS measurement
The chemical states of the Co-Mo catalysts after calcination by heated at 400°C in air andafter reduction by heated up to 800°C in the flow of Ar/H2 (3% H2), as their details
described in Section 2.3, are characterized using XPS. The measurements are done using a
PHI 1600 X-ray photoelectron spectrometer equipped with an Mg Kα (1253.6 eV) source
operating at 300 W. To decrease the influence of oxidation and contamination for XPS
samples, these substrates are sealed in a plastic box filled with Ar gas as soon as they are
removed from the furnace or the CVD reactor, and then transferred to an analysis chamber(2.0×10-9 Torr) through a loading chamber (5.3 × 10-6 Torr) for XPS measurements. All
these procedures are finished in 30 min. Binding energies (BEs) are referenced to the C 1s
peak at 284.6 eV to compensate for the charging effect. The BE curves are fitted using amixed Gaussian/Lorentzian curve after subtracting the background using the Shirley
algorithm [73], in which spin-orbital-splitting intensities are fixed at their theoretical ratios.
The surface atomic ratios of the calcined and the reduced quartz substrates coated with
Co-Mo catalysts are estimated from peak intensities in the XPS spectra and atomic
sensitivity factors.

61

2.4.3 Results of TEM and XPS analyses
2.4.3.1 Morphology of calcined and reduced Co-Mo catalyst
First, it is mentioned that the reduced samples for TEM observations should beconsiderably oxidized even if the catalysts are in metallic state right after reduction due tothe following two reasons: 1) An oxide layer or a glue layer was coated on the catalysts; 2)More than two weeks was taken to prepare the TEM samples ready for observation.
Figure 2-30 shows plan-view TEM images of the calcined and the reduced Co-Mo
catalysts on the quartz substrates. For both samples for after calcination and after reduction
shown in Figs. 2-30a and 2-30d, respectively, well-dispersed nano-sized particles withdiameters of 1 - 2 nm can be observed. Figures 2-30b and 2-30e reveal that the Co-Mo
catalyst particles after reduction seemed to shrink to a smaller size, while remaining gooddispersion without agglomerating into larger ones. The number density of these uniformly

Fig. 2-30. Plan-view TEM images of (a) calcined and (d) reduced Co-Mo catalysts on quartz
substrates, and HR-TEM images of (b) (c) calcined and (e) (f) reduced Co-Mo catalysts. SAED
patterns are shown in the insets of (a) and (d).

62

Chapter 2  CVD growth of SWNTs and their analyses

distributed catalyst particles after reduction was estimated from the TEM images to be as
high as ~1.3 × 1017 m-2.
Selected area electron diffraction (SAED) patterns shown in the insets of Figs. 2-30a and2-30d, and high-resolution TEM (HR-TEM) images shown in Figs. 2-30b and 2-30e
revealed that most of the nano-sized catalyst particles were amorphous, and only some ofthem were crystalline. As indicated in Figs. 2-30c and 2-30f, these crystalline particles
exhibit lattice distances of 2.13 - 2.38 Å, which are approximately consistent with CoO(200) lattice constant (2.13 Å), but significantly differ from those of Co (111) (2.05 Å),
Co3O4 (311) (2.44 Å), MoO2 (110, 11 1 ) (3.41 Å), MoO3 (021) (3.26 Å), and CoMoO4 (002,220) (3.36 Å) lattices. Because Co:Mo = 1.6:1 in ethanol solutions, the amount of Co
species should be in excess on the substrates. Therefore, we conclude that most of thosenano-sized particles, whether crystalline or amorphous, might be mainly composed of CoO.
This conclusion is supported with the surface composition analysis using XPS, which isshown later in this section.
Figure 2-31 shows XTEM images of the reduced Co-Mo catalysts on the quartz
substrates. Because the incident angle of electron beam deviated from the parallel directionof quartz-glue interfaces, as shown in Fig. 2-31a, catalyst particles were seemingly locatedwithin a vertical range of ~ 10 nm. High-resolution XTEM images in Fig. 2-31b exhibitedthat these spherical- or elliptical-like particles with diameters of 1 - 2 nm were wellFig. 2-31. (a) XTEM and (b) HRXTEM images of reduced Co-Mo catalysts on quartz substrates.

63

dispersed without aggregation, which is consistent with corresponding plan-view images.
These results indicate that Co-Mo catalysts existed as well-dispersed nano-sized particles
on the quartz substrates just before the CVD reaction. This morphology should be closely
associated with the subsequent growth of densely and vertically aligned SWNTs, and themechanism for this dispersion is going to be investigated by XPS in the nest subsection.

2.4.3.2 Chemical state of calcined and reduced Co-Mo catalysts analyzed by XPS
Figure 2-32 shows BEs of C 1s, Si 2p, and O 1s levels for the calcined and the reduced
catalysts on the quartz substrates. As indicated in Figs. 2-32b and 2-32c, the BEs of Si 2p at
103.4 - 103.6 eV, and O 1s at 532.3 - 532.5 eV agree well with quartz references (Si:103.3 103.7 eV, O: 532.1 - 532.7 eV) [74,75]. This suggests that the BE shift due to the charging
effect has been corrected well with the C 1s BE as a reference. The spectra of C 1s and Si
2p indicate the absence of acetate residues (288.2 - 289.3 eV) [76,77], metal carbides(282.7 - 283.1 eV) [78,79], and metal silicides (99.1 - 99.6 eV) [80-82]. Moreover, thespectra of O 1s indicate the formation of metal oxide species (530.3 - 530.4 eV) [83].
Figure 2-33a shows BEs of Mo 3d levels for the calcined and the reduced catalysts on thequartz substrates. Both spectra exhibit a pair of spin-orbit BEs at 232.4 - 232.5 and 235.4 235.5 eV, whereas a pair of new spin-orbit BEs appeared at 229.0 and 232.0 eV only forthe reduced catalysts. The Mo 3d5/2 BE at 232.4 - 232.5 eV is attributed to Mo6+ in MoO3
(232.2 - 233.0 eV) [70,84-88] and/or non-stoichiometric Co molybdates, CoMoOx(232.1.232.3 eV for stoichiometric Co molybdates where x = 4) [70,87,88]. The new Mo
3d5/2 BE at 229.1 eV is attributed to Mo4+ in MoO2 (229.0 - 230.1 eV) [70,84-87]. These
results indicate that the decomposition of Mo acetates resulted in the formation of Mo6+ in

a

b

c

Fig. 2-32. XPS spectra of (a) C 1s, (b) Si 2p, and (c) O 1s levels for calcined and reduced Co-Mo
catalysts on quartz substrates.

64Chapter 2  CVD growth of SWNTs and their analysesabFig. 2-33. XPS spectra of (a) Mo 3d5/2 and 3d3/2, and (b) Co 2p3/2 and 2p1/2 levels for both calcined
and reduced Co-Mo catalysts supported on quartz substrates.

MoO3 and/or CoMoOx, and the reduction of calcined catalysts converted Mo oxide species
to MoOy (y ≤ 2) or even metallic Mo that was not detected due to its oxidization during exsitu XPS analyses.
Figure 2-33b shows BEs of Co 2p levels for the calcined and the reduced Co-Mo
catalysts on the quartz substrates. The reduced samples showed remarkable differencesfrom calcined ones in two aspects. One is the appearance of a new BE at 777.8 eV, which is
attributed to metallic Co (777.8 - 778.5 eV) [70,87,89,90]. The other is the decreased
distance between the 2p3/2 and 2p1/2 spin-orbit BEs by as large as 1.6 eV, while the 2p1/2 BEremained almost unchanged. This should result from the change in chemical state of Co
oxide species during reduction, rather than from the charging effect due to particle sizes[91] or layered structures [92] with different dielectric properties.
To clarify the above changes, the Co 2p3/2 BEs are decomposed and fitted as shown in
Fig. 2-34. The spectra for calcined and the reduced catalysts are composed of two 2p3/2
components at 780.9 - 781.0 eV and 783.3 - 783.5 eV, and two distinct shake-up satellites
at 786.9 - 787.0 eV and 790.2 - 790.6 eV. The two 2p3/2 BEs are attributed to Co2+ oxide
species based on these intense shake-up satellites 6.0- 6.5 eV higher than the primaryspin-orbit BEs [88,93]. The two 2p3/2 BEs at 780.9 - 781.0 eV and 783.3 - 783.5 eV are
further assigned to Co2+ in CoO and Co2+ in CoMoOx, respectively, due to their agreementwith CoO (780.0 - 780.7 eV) [70,89,90,94,95] and CoMoO4 (780.5 - 781.2) [87-89,96]
65

Fig. 2-34. XPS spectra of Co 2p3/2 levels for calcined and reduced Co-Mo catalysts on quartz
substrates.

references. The relatively large BE deviation of Co2+ in CoMoOx from Co2+ in CoMoO4
might result from the polarization effect or the non-stoichiometry when Co2+ ions areincorporated into highly oxidized MoO3 matrix [89,96,97]. The BE intensity ratio of Co2+
in CoMoOx to that in CoO increased from 1.3 to 2.6 after reduction, indicating that more
CoMoOx was formed at the expense of CoO and MoO3. This change leads to the seemingly
decreased distance between Co 2p3/2 and 2p1/2 BEs shown in Fig. 2-33b. Therefore, it isconcluded that the calcination of dip-coated substrates decomposed Co acetates into Cooxide species existing as CoO and CoMoOx, and the subsequent reduction resulted in theformation of metallic Co and more CoMoOx.
Table 2-2 shows the surface atomic ratios of the calcined and the reduced quartz
substrates coated with Co-Mo catalysts. The quantity of metals as low as less than 10% of
the total composition supports the approximate estimation in the experimental section thatthe quartz substrates might be covered with the metallic catalyst layers. The calcined andthe reduced samples had Co/Mo atomic ratios of 2.1 - 2.3, approximately consistent with66

Chapter 2  CVD growth of SWNTs and their analyses

Table 2-2. Surface composition of quartz substrates dip-coated with
Co-Mo catalysts after calcination and after reduction.
Co
Mo
Si
O

C

Calcined(atomic %)

5.1

2.2

27.9

59.7

5.1

Reduced(atomic %)

3.2

1.5

29.8

61.7

3.7

the initial ratio of 1.6 in metal acetate solutions, so that only excess Co species wereobserved in TEM images. It is noteworthy that the atomic ratios of Co and Mo to totalelements decreased by 63 % and 68 % after reduction, respectively, which could be
explained from the decrease in catalyst coverage, i.e., the decrease in catalyst particle size,as confirmed in TEM images.

672.4.3.3 Mechanism and formation process of Co-Mo catalyst
Based on the above results, a model was deduced for the evolution in morphology andchemical state of Co-Mo catalysts on the quartz substrates during calcination and reduction
as illustrated in Fig. 2-35. It is assumed that a layer of bimetallic acetate film (Co:Mo =1.6:1 in atomic ratio) is formed on the quartz substrates after the dip coating from dilutemetal acetate solutions. After calcination in air at 400°C, metal acetates are decomposed
into CoO, CoMoOx (x = 4 for stoichiometric Co molybdates), and MoO3, which exist as
well-dispersed nano-sized particles. After reduction in Ar/H2 up to 800°C, existing
CoMoOx remains unchanged, whereas CoO and MoO3 are reduced into Co and MoOy (y ≤2), and more CoMoOx are formed at the expense of Co and MoO3. During this process, nodistinct agglomeration occurs although catalyst particles partially de-wet into smaller sized
ones. Finally, SWNTs start to grow from the metallic Co particles that have comparable
diameter to that of SWNTs, at the time ethanol vapor is supplied over the catalyst.
Furthermore, it is deduced that even if Mo and Co species uniformly coexist on SiO2
surfaces during calcination, Mo preferentially promotes the formation of metal oxides at
catalyst/SiO2 interfaces, because Mo has a stronger affinity to oxygen than Co [26].
Because of Co:Mo = 1.6:1 in atomic ratio, the excess Co easily diffuses into MoO3 [96] andforms CoMoOx underlayers/boundaries, whereas the residue Co exists as CoO particles
either located on CoMoOx underlayers or attached to CoMoOx boundaries.

(a) After calcination

CoO(b) After reduction
CoMoOxCoMoOxMoO3

CoMoOxMoOy
Co

and/orCoO

MoO3

Reduction
up to 800°C

CoMoOxand/orCo

MoOy

Fig. 2-35. Chemical state and morphology of Co-Mo catalysts on quartz substrates after (a)calcination and (b) reduction.

68

Chapter 2  CVD growth of SWNTs and their analyses

The formation of well-dispersed nano-sized catalyst particles during calcination is
attributed mainly to the decomposition of metal acetates on oxide substrates. It is suggested
that the strong coordination of carboxylic groups with metal ions mediates thedecomposition of metal acetates to prevent the formation of large particles [65,98], as was
discussed in Section 2.3. As a result, compared with metal nitrates, metal acetates form
better-dispersed nano-sized particles during calcination [65,98], thereby accounting fortheir best performance for the growth of SWNTs.
As the temperature rises from R.T. during reduction, CoO and MoO3 under the flow of
Ar/H2 start to be reduced into metallic Co and MoOy, respectively, whereas CoMoOx
remains unchanged due to their extreme stability against reduction [99,100]. These metallic
Co was detected in XPS analyses under particular protection from exposure to oxygen,
whereas only metal oxides were confirmed in TEM observations. In addition, the decreased
CoO intensity and the increased CoMoOx intensity support the following deduction. The
firstly reduced metallic Co reacts with MoO3/MoOy until Mo oxides are depleted to form
CoMoOx, and the residue Co remains metallic and works as a catalyst. That is, theformation of metallic Co possibly competes with that of Co molybdates, and finallybecomes dominant.
The stable existence of well-dispersed nano-sized Co particles during reduction is
attributed to the immobilization effect of CoMoOx underlayers. Although metallic Co
particles vigorously migrate on SiO2 surfaces [90], they should be easily trapped on
CoMoOx underlayers, owing to the strong interactions between MoO3 and metallic Co [96].
The decreased size and the spherical- or elliptical-like shape of catalyst particles after
reduction, which were observed in plan-view TEM and XTEM images, suggest thatmetallic Co might de-wet on quartz substrates. This deduction was confirmed by thedecreased metal/substrate atomic ratio after reduction indicated by XPS analyses [90].
Although these metallic Co particles de-wet partially on CoMoOx, their interfacialinteractions are strong enough to limit their mobility and prevent them from agglomerating
into large particles. Therefore, it is concluded that the role of Mo in bimetallic Co-Mo
catalysts is to stabilize well-dispersed nano-sized metallic Co particles from agglomeration.
Without Mo [90,91] or CoMoOx [71,88], the catalyst selectivity for the growth of SWNTs
decreases or even disappears due to the agglomeration of Co particles.

692.4.4 Summary of formation process and role of Co-Mo catalyst
High-purity SWNTs with diameters of 1.2 nm were grown densely (~1.0 × 1017 m-2) andvertically on the quartz substrates where bimetallic Co-Mo catalysts with a stoichiometry of~1.6 were dip-coated from metal acetate solutions, followed by calcination and reduction.
HRTEM and XPS studies on the morphology and chemical state of the calcined and the
reduced catalysts provided critical evidence for their catalytic mechanism.
The results show that calcination in air at 400°C decomposes metal acetates into metaloxide species composed of CoO, MoO3 and CoMoOx (x = 4 for stoichiometric Co
molybdates), which exist as well-dispersed nano-sized particles possibly due to themediation of strong coordination of carboxylic groups with metal ions during the acetate
decomposition. The excess CoO might be either located on or attached to CoMoOx
underlayers/boundaries. After reduction in Ar/H2 up to 800 °C, metallic Co, MoOy (y ≈ 2)
and more CoMoOx are formed at the expense of CoO and MoO3. The strong interactions
between metallic Co and CoMoOx underlayers prevent these well-dispersed (~1.3 × 1017m-2) nano-sized (1 - 2 nm) catalyst particles against agglomerating into larger ones.
The good dispersion of nano-sized catalyst particles due to the acetate decomposition,
their stability against agglomeration due to the interactions between Co and CoMoOx, theirhigh activity due to the continuous supply of H2 throughout the CVD reaction, and the insitu purification of growing SWNTs due to the oxygen radicals generated from the ethanol
decomposition lead to the highly selective growth of high-purity SWNTs densely andvertically aligned on the quartz substrates.

2.5 Summary of Chapter 2This chapter presented a comprehensive discussion of several important problems withregard to the research and application of SWNTs, such as developing methods forsupporting the catalyst, growing SWNTs on solid flat surfaces, and elucidating the role andformation process of the catalyst.
In Section 2.1, the yield of SWNTs grown from Fe-Co catalyst supported on USY-typezeolite was systematically investigated in order to examine the feasibility of the alcohol
CCVD method toward mass production. It was determined that the yield could be enhanced
by reducing the catalyst prior to the CVD reaction. Furthermore, the wettability of Fe, Co,
Ni, and Mo catalysts on the SiO2 support was investigated. The resultant diameters of the
SWNTs were attributed to the magnitude of ∆Hf°sublimate/∆Hf°oxide, which may provide
70Chapter 2  CVD growth of SWNTs and their analyses

useful guidelines for the choice of either a monometallic or bimetallic catalyst on SiO2
supports.
Section 2.2 reported the development of a new technique for the catalyzed growth of
SWNTs utilizing MPS thin film on Si substrate. The role of mesopores for supporting thecatalyst was demonstrated from the reference experiments using a silica thin film without
mesopores.
Section 2.3 reported the development of the dip-coat catalyst supporting method for the
direct support of a small amount of catalyst on the flat substrate. It was determined thatwhen cobalt and molybdenum acetates were used, the monodispersed Co particles withdiameters of 1–2 nm were densely supported on the SiO2 surface without agglomerationeven at 800°C.
In Section 2.4, the underlying mechanism for the successful dispersion of Co wasinvestigated by TEM and XPS. It was elucidated that the CoMoOx (x ≤ 4) compound wasformed on the SiO2 surface and this layer aided in stabilizing the excess Co particles andpreventing their agglomeration into larger particles.
The information and methods presented in this chapter will be used in Chapters 3 and 4
for the morphologically controlled growth of SWNTs and elucidation of their anisotropic
optical properties.

Acknowledgments for Section 2.1
The author expresses gratitude to Mr. H. Tsunakawa, Mr. T. Ito, and Mr. Y. Kakegawa for theirkind assistance in obtaining the TEM observations shown in Fig. 2-5 and Prof. T. Okubo and Mr. T.
Sugawara at The University of Tokyo for the use of FE-SEM S-900, the observations from which
are shown in Fig. 2-6. A part of this section has been published in Chemical Physics Letters, vol.
374, pp. 53–58, 2003 by Y. Murakami, S. Chiashi, Y. Miyauchi, and S. Maruyama.

Acknowledgments for Section 2.2
The author would like to thank Prof. T. Okubo at The University of Tokyo and Mr. S. Yamakita at
Sony Corp. for valuable collaboration and discussions on the investigation of catalyzed growth of
SWNTs from MPS pores, presented in Section 2.2. This work has been published in Chemical
Physics Letters, vol. 375, pp. 393–398, 2003 by Y. Murakami, S. Yamakita, T. Okubo, and S.
Maruyama.

71

Acknowledgments for Section 2.3
The author would like to express gratitude to Prof. T. Okubo and Mr. T. Sugawara at The
University of Tokyo for the use of FE-SEM S-900, the observations from which are shown in Figs.
2-19 and 2-20; Mr. S. Watanabe, Ms. M. Nakagawa, and Mr. R. Tamochi at Hitachi Science
Systems, Ltd. and K. Shibata at Hitachi High-Technology Corp. for their observations by FE-SEM
S-5200 shown in Fig. 2-21; Mr. H. Tsunakawa at The University of Tokyo for his assistance inobtaining the TEM observation shown in Fig. 2-22; Prof. Y. Ikuhara at The University of Tokyo for
the X-TEM measurement of a SWNT-grown Si substrate shown in Fig. 2-23; Dr. M. Hu and Prof. T.
Okubo at The University of Tokyo for the HR-TEM observation of the catalyst on the surface of thequartz substrate shown in Fig. 2-27; Prof. R. E. Smalley at Rice University for supplying the HiPco
sample corresponding to Fig. 2-28; and Profs. K. Hoshino and S. Yamashita at The University ofTokyo for supplying MEMS-processed substrates presented in Fig. 2-29. A part of this section has
been published in Chemical Physics Letters, vol. 377, pp. 49–54, 2003 by Y. Murakami, Y.
Miyauchi, S. Chiashi, and S. Maruyama and in Japanese Journal of Applied Physics, vol. 43, pp.
1221–1226, 2003 by Y. Murakami, S. Chiashi, Y. Miyauchi, and S. Maruyama.

Acknowledgments for Section 2.4
All the HR-TEM and XPS measurements presented in this section were performed by Dr. M. Hu
and Prof. T. Okubo in the Department of Chemical System Engineering, The University of Tokyo.
The author thanks them for their valuable assistance and discussions on the morphology andchemical state of the catalyst used for SWNT growth. The contents of this chapter have been
published in Journal of Catalysis, vol. 225, pp. 230–239, 2004 by M. Hu, Y. Murakami, M. Ogura,
S. Maruyama, and T. Okubo.

72

Chapter 2  CVD growth of SWNTs and their analyses

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76

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78

Chapter 3:
Growth of vertically aligned SWNT films on
substrates and their formation process3.1 Research background and motivation
The possibility of conducting experimental studies on SWNTs greatly increased after thedevelopment of selective production by the laser furnace method [1] and more scalable
CVD techniques such as the HiPco method [2]. In addition to the bulk synthesis of SWNTs,
controlled positioning of carbon nanotubes on a substrate is considerably important for
many applications such as field emission transistor (FET) [3–5], chemical sensors [6,7],
and optical devices for telecommunications [8–10]. Although the vertically aligned growthof MWNTs on flat substrates has been reported [11,12], that of SWNTs has not beenreported. In the case of SWNTs, only an alignment that is parallel to the substrate plane has
been achieved by the application of a strong electric or magnetic field [13–15]. To date,
several innovative applications using vertically aligned MWNT films such as a fieldemission source [11] or a toxic gas sensor [16] have been reported. However, using SWNTs
instead of MWNTs for these applications is desirable because the former have several
superior electrical/mechanical properties in addition to structural perfection.
This chapter reports the achievement, for the first time, of vertically aligned growth of
SWNTs on a flat substrate with the CVD process. Initially, the morphology and quality of
the aligned SWNTs are investigated by FE-SEM, HR-TEM, and resonant Raman scattering(RRS) analysis. This chapter also shows that the RRS spectra of vertically aligned SWNTs
exhibit a characteristic spectral shape that originates due to their aligned morphology.
Finally, the growth and alignment formation processes of the vertically aligned SWNT filmwith respect to CVD reaction time is investigated by optical absorption and FE-SEM
observations. A model for the growth process of the vertically aligned SWNT film isformulated based on the measured optical absorption characteristics, using which thegrowth of the aligned SWNT film will be discussed.

80

Chapter 3  Growth of vertically aligned SWNT films on substrates
and their formation process

3.2 Experimental and analysis procedures
The catalyst preparation procedure and the CVD process are essentially the same as thosepresented in Section 2.3. After an as-delivered quartz substrate with both sides opticallypolished (Fujitok #19983, 25 × 25 × 0.5 mm) is baked for 5 min in air at 500°C, bimetallic
Co-Mo catalyst is supported on the substrate by dip coating its acetate solution.
Subsequently, the substrate is heated in air at 400°C to decompose these acetates into metaloxides, which are reduced in the CVD chamber during the heating of an electric furnacewith an Ar/H2 (3% H2) flow of 300 sccm; this is done so that the catalytic activity is
retrieved. When the SWNT growth temperature is attained in the electric furnace, thesupply of Ar/H2 gas can be cut off or the gas flow can be continued during the CVD
reaction. The effect of the Ar/H2 gas flow during the CVD reaction will be investigated in
the next section.
All the CVD experiments in this chapter were performed at 800°C under an ethanol
vapor pressure of 10 Torr for 10 min, unless specified otherwise. The Ar/H2 gas is supplied
only during the heating stage and is cut off during the CVD reaction, unless specified
otherwise. The flow rate of the Ar/H2 gas during the heating stage is 300 sccm under apressure of 300 Torr. If Ar/H2 is supplied during the CVD reaction, the flow rate remains at
300 sccm but the partial pressure is lowered to 7 Torr. To ensure reproducibility, thebackground pressure of the CVD chamber should be less than 2 × 10-2 Torr. The schematicof the CVD apparatus is presented in Fig. 2-15.
In order to obtain the microscopic characterizations of the SWNTs, an FE-SEM
observation was performed with a Hitachi S-900 at 4 KV, a Hitachi S-4700 at 1 kV, or a
Hitachi S-5200 at 2 kV. The HR-TEM observations were performed with a JEOL 2000EX
at 120 kV.
For obtaining Raman scattering measurements, a micro-Raman setup (Seki Technotron
STR-250) comprising an optical microscope (Olympus BX51), a spectrometer (Chromex
501is), and a CCD (Andor DV401-FI) was used. The measurements were conducted in thebackscattering configuration with an incident laser power of 0.3–1.0 mW, a 50× objective
lens, and a laser spot diameter of approximately 3–5 µm. Linearly polarized 488- (2.54 eV)and 514.5-nm (2.41 eV) laser lights were used. The scattered light was collected into themicroscope, passed through a depolarizer, and finally, guided to the spectrometer.

813.3 Effect of CVD chamber vacuum on SWNT growthFirst, it should be mentioned that the morphology and the growth speed of SWNTs
largely depend on the cleanness of the CVD chamber just before the CVD process begins.
Namely, the speed of vacuum deterioration by de-gas generation from the chamber wall,measured by a pilani gauge with the valve to the vacuum pump closed, is an importantfactor that controls the growth. Figure 3-1 shows the optical absorbance spectra of samples
prepared at different de-gassing speeds Vde-gas° [cm3/sec] expressed in the equivalent speed
at standard state (1 atm, 0°C). The volume of our CVD chamber is approximately 1000 cm3.
The resulting morphology (i.e., random or vertically aligned) are denoted for each spectrum
and the magnitude of absorbance is a measure of the amount of SWNTs grown on thesubstrate. The morphology was random when the de-gas generation speed was high, asshown in Fig. 3-1(iii). On the other hand, when the de-gas generation was suppressed,
SWNT growth increased and this lead to a vertical alignment of SWNTs, as shown in Fig.
3-1(i) or 3-1(ii). This result clearly reveals that de-gas generated from the CVD chamber
wall poisoned the catalyst and thus lowered its activity. Hence, greater chamber cleanness
1.5o(1): Flowing Ar/H2, vertically alignedo–5(Vde–gas = 4.60 x 10 cc/sec)a(Vde–gas = Equivalent speed of de–gas generation
under the standard condition i.e. at 0°C, 1 atm.)

Absorbance1(3): EtOH only, vertically alignedo–5(Vde–gas = 7.67 x 10 cc/sec)(i)(ii): EtOH only, vertically alignedo–5(Vde–gas = 7.67 x 10 cc/sec)b(2): EtOH only, vertically alignedo–5(Vde–gas = 5.75 x 10 cc/sec)(i): EtOH only, vertically alignedo–5(Vde–gas = 5.75 x 10 cc/sec)(2)(4): Flowing Ar/H2, vertically aligned–5o(Vde–gas = 15.3 x 10 cc/sec)(iii): EtOH only, random–5o(Vde–gas = 51.1 x 10 cc/sec)(5): EtOH only, randomo–5(Vde–gas = 51.1 x 10 cc/sec)

(ii)

0.5

(3)
(1)
(4)

(iii)

0
0

1

2
Energy (eV)

3

(5)

0

1

2
Energy (eV)3Fig. 3-1. (a) Optical absorption spectrum of SWNT films grown on quartz substrates either with
(2,3,5) or without (1,4) flowing Ar/H2 during CVD reaction. The Arabic number denotes order ofcleanness of the CVD chamber. To each spectrum, the morphology of SWNT film (vertically aligned
or random) and the de-gas generation speed Vde-gas° [cm3/sec] (see text for definition) is presented. (b)Selected presentation for the spectra measured from SWNT film grown without Ar/H2 flow from thecase of (a). To each spectrum (i-iii), the morphology of SWNT film and the vacuum deterioration
speed is denoted.

82

Chapter 3  Growth of vertically aligned SWNT films on substrates
and their formation process
is necessary for a higher degree of catalyst activity that is consequently required for thevertical alignment of SWNTs, as discussed below.
In Fig. 3-1b, the optical absorption spectra of SWNT films grown with a flow of Ar/H2
during the CVD reaction are compared with those without a flow of Ar/H2 (shown in Fig.
3-1a). The numbers in parentheses denote the order of chamber cleanness in these fiveexperiments. When the cleanness is low, the flow of Ar/H2 is thought to enhance theactivity of the catalyst, presumably because H2 acts as an anti-oxidation agent for
de-gassing contaminations. However, when the chamber cleanness is high, the existence of
H2 decelerates the growth of SWNTs. This may be due to the fact that the strong adsorptionof H2 on the surface of transition metals [17] can reduce the active surface area of thecatalyst.
The “vacuum deterioration” shown in Fig. 3-1 is considered to be caused by thegeneration of de-gases from the chamber wall and not by a leak in the chamber. This isbecause at this vacuum level, the deterioration speed can be lowered by evacuating thechamber with flowing several tens of sccm of Ar/H2 for a few hours. We consistently usedan oil-free pump (ULVAC DVS-321) for evacuation; this is because vertically aligned
SWNT growth has not been achieved using an ordinary oil pump, presumably due tocatalyst poisoning by the diffusion of oil-derived molecules into the CVD chamber.

83

3.4 Microscopic and optical analyses
3.4.1 Morphological investigations by FE-SEM and HR-TEM
Figure 3-2 shows cross-sectional images of the vertically aligned SWNT film grown on aquartz substrate acquired by a Hitachi FE-SEM S-900 at 4 kV at a tilted (upper row) andhorizontal direction (lower row). The vertical alignment of SWNTs with an approximate
height of 6 µm is observed along with their spatial uniformity. Typically, the film is
optically uniform over the entire area of the substrate both in terms of appearance and theresults of reflectance interferometry (data not shown). This alignment is believed to arise
from the significantly high density of the SWNTs, as discussed below.

Fig. 3-2. Cross-sectional image of vertically aligned SWNT film with approximate thickness of 5 µm
grown on a quartz substrate. The images were taken at fractured edge of the substrate by Hitachi
FE-SEM S-900 at 4 kV, from tilted (upper row) and horizontal direction for the substrate (lower
row).

84

Chapter 3  Growth of vertically aligned SWNT films on substrates
and their formation process
Figure 3-3 shows higher magnification images of the vertically aligned film with anapproximate thickness of 2 µm acquired by a Hitachi FE-SEM S-5200 at 2 kV for (a) theentire cross section, (b) the upper part of the film, (c) the mid cross section, and (d) thelower part of the film. Images (a), (b), and (d) are acquired at a 30° tilted angle from thehorizon, and (c) is acquired from the horizontal direction. In the magnified image shown in
Fig. 3-3c, most of the SWNTs are bundled and their typical diameter is ~15 nm. The degreeof alignment as well as optical anisotropy in the film will be investigated and discussed in
Section 4.1.
Figure 3-3d shows the morphology of the bottom of the SWNT film and clearly reveals
that thinner bundles, with diameters of ~4 nm just above the substrate surface, coalesce into
thicker bundles as the SWNTs grow away from the substrate. Furthermore, as shown in Fig.
3-3(d), it appears as though the roots of the SWNTs are pulled upward, presumably by an

Fig. 3-3. High-magnification images of vertically aligned SWNT film with approximate thickness of
2 µm grown on a quartz substrate, for (a) whole cross-section, (b) upper part of the film, (c) mid
cross-section, and (d) lower part of the film. The images were taken at fractured edge of the substrate
by Hitachi FE-SEM S-5200 at 2 kV. Images (a, b, d) are taken from 30° from the substrate plane and(c) is taken from horizontal direction to the substrate.

85

internal frictional force among the SWNT bundles. This internal force is considered tooriginate from the difference in the catalyst activity at a later stage of the growth where theactivity begins to deteriorate (refer to Section 3.6 for details). This is because a differencein catalyst activity can cause a difference in the extending speed depending on the SWNT
bundle. Further, it should be noted that on the surface of the quartz substrate, aggregatedmetal particles that would be observed if the diameter exceeded 2–3 nm by FE-SEM
S-5200 were not observed. This result is consistent with the HR-TEM image of thesubstrate surface shown in Section 2.4.
Figure 3-4 shows the HR-TEM image of the vertically aligned SWNT film. The film was
weakly sonicated in methanol for 5–10 s and dropped onto a TEM microgrid. Observations
were performed on the film fragments that retained their alignment to a large extent. Twotypes of film edges were observed. One is shown in Fig. 3-4a in which the degree ofalignment is relatively high and almost no metallic particles were found among the SWNTs.

Fig. 3-4. HR-TEM images of a fragment of a vertically aligned SWNT film deposited on a TEM grid
after a weak sonication in methanol for 5 - 10 s, taken by JEOL 2000EX at 120 kV. Images are those
presumably correspond to (a) the upper side of the film and (b-d) lower side of the film, as observed
by FE-SEM in Fig. 3-3. Panels (c, d) are the magnification from the edge observed in the panel (b).

86

Chapter 3  Growth of vertically aligned SWNT films on substrates
and their formation process
The other type is shown in Fig. 3-4b, in which abundant particles were found among the
SWNTs and the degree of alignment is less than that shown in Fig. 3-4a. Figure 3-4c and d
are magnifications of the film fragment edge shown in Fig. 3-4b. These images revealed
metallic particles with diameters of 2–3 nm, and they are considered to be cobalt carbide(Co2C). However, a determination of the elemental composition of the particle using anexperimental investigation technique such as EELS analysis is necessary for further
discussion.
Figure 3-5 shows another HR-TEM image of the vertically aligned SWNT film. In thiscase, however, the film was directly rubbed onto a TEM microgrid (i.e., the film had notundergone dispersion in solvent) in order to precisely investigate the morphology andquality of the SWNTs. This observation was conducted in a manner similar for the caseshown in Fig. 3-4 but at a higher magnification; the film fragment that retained alignment
was found and investigated. Figure 3-5a shows the upper edge of the observed film

Fig. 3-5. HR-TEM images of a fragment of the vertically aligned SWNT film directly rubbed against
a TEM grid, taken by JEOL 2000EX at 120 kV. Images are (a-c) Images are those presumably
corresponds to (a-c) the top side of the film taken at various magnification, and (d) lower side of thefilm in which metal particles are observed among SWNTs.

87

fragment at a lower magnification, and the entire image of the film fragment is indicated in
the inset. The morphology observed in Fig. 3-5a coincides with that of the upper side of thefilm observed by FE-SEM shown in Fig. 3-3b. Figure 3-5b is a magnification of the upperedge of Fig. 3-5a, where closed and empty SWNT ends are occasionally observed; these arefurther magnified in Fig. 3-5c. Similar to the case of Fig. 3-4, two types of edges in the film
fragments were confirmed in the observation shown in Fig. 3-5, and one of these is shownin Fig. 3-5a, b, and c. The other type of edge is shown in Fig. 3-5d and is considered to be apeeled interface between the film and the substrate where the darkened area toward theright is the film, which is oriented perpendicular to the page. Particles with diameters of
2–3 nm are observed among the entangled SWNTs, as shown in Figs. 3-4c and 3-4d; these
are considered to be Co2C.
From the HR-TEM observations shown in Figs. 3-4 and 3-5, the growth of the SWNT
film in the present study is ascribed to the base growth from the catalyst particles thatremain on the substrate. These images, especially those observed for the film that did notundergo dispersion in the solvent, as shown in Fig. 3-5, indicate that each SWNT issufficiently clean, i.e., virtually free from amorphous carbon and other impurities on the
SWNT wall. No MWNTs were observed in repeated TEM observations whereas several
double-walled carbon nanotubes (DWNTs) were found; however, their population is
negligible compared with that of SWNTs. By measuring the diameter of more than 50
SWNTs, the diameter of the specimen was determined to be in the range of 0.8–3.0 nm
with an average diameter dav of ~1.9 nm and a standard deviation σ of ~0.4 nm. This
diameter is larger when compared with that of typical CVD-grown SWNTs; in addition, thediameter distribution is broader.

3.4.2 Resonant Raman scattering analysis
In order to spectroscopically investigate the quality of the sample, Raman scattering
measurement was performed on the vertically aligned (Fig. 3-6a, c) and the randomly
oriented SWNT films (Fig. 3-6b, d) using 488- and 514.5-nm laser lights. The tangential
modes of the 488-nm laser light including the D-band (~1350 cm-1) and the G-band (~1593cm-1) are shown in the right panel. In all the measurements, the laser is incident
perpendicular to the substrate, i.e., from the top of the film. The ratio of G- to D-bands is
sufficiently high (25–35); therefore, the quality of the current sample is confirmed to be
sufficiently high even in the pristine state.

88Chapter 3  Growth of vertically aligned SWNT films on substrates
and their formation process
Diameter (nm)
1 0.9

2

0.8

*

Intensity (arb.units)*(a) Vertically aligned: 488 nm(b) Random: 488 nm*(a) Vertically aligned: 488 nm*(c) Vertically aligned: 514.5 nm(b) Random: 488 nm(d) Random: 514.5 nm

100

200

300
–1

Raman Shift (cm )

1200

1400

1600
–1

Raman Shift (cm )Fig. 3-6. Raman scattrering spectrum of (a, c) vertically aligned and (b, d) random SWNT film grownon quartz substrates measured with normal laser incidence to the substrate. The low frequency RBM
is shown for both 488 and 514.5 nm in the left panel and higher frequency tangential modes areshown for 488 nm in the right panel. Asterisk denotes the RBM peak observed only when veritcallyaligned SWNT is measured with perpendicularly polarized light to SWNT axis.

The difference in the spectra of “aligned” and “random” cases is partially due to thedifference in the diameter distributions (dav of the latter is ~1.3 nm, thinner than the former).
However, it should be noted that the RBM peaks marked with “*” in the left panel arecharacteristically observed in vertically aligned SWNT films when the polarization
direction of the incident light is perpendicular to the direction of SWNT alignment [18],which is investigated in detail in Section 4.2. These characteristic RBM peaks aresuppressed when the alignment is mechanically disturbed, for example, by a tip of tweezers.
Section 4.2 will discuss that these characteristic peaks can be explained by the resonance of∆µ = ±1 excitation (µ denotes the cutting line index of the 2D Brillouin zone of graphite[19]) caused by the absorption of cross-polarized light [20,21]. Since the RBM peaks in 488
and 514.5 nm are highly sensitive to morphology, vertical alignment can be recognized by
Raman scattering measurement without resorting to cross-sectional FE-SEM observation as
was done for the case shown in Fig. 3-2. However, since the RBM spectral shape of
SWNTs is highly affected by their physical and chemical environment in addition to theincident laser power [18], as shown in Section 4.2, a more stable and reproducible method
for evaluating the morphology is required. Further, in Section 4.1, it will be shown that89

optical absorption spectroscopy, which is generally simpler than Raman scattering
measurement, is a strong tool for distinguishing or even quantitatively evaluating themorphology of SWNTs.

3.5 Discussion of vertical alignment formation in SWNTs
The differences in the growth amount and diameter distribution between the verticallyaligned SWNT films and the randomly oriented films provide important insights into thereason that SWNTs could grow vertically from the substrate. An exceedingly higher
amount of grown SWNTs in the case of vertical alignment was clarified by both FE-SEM
observations (Figs. 3-2 and 3-3) and the difference in the magnitude of optical absorbance(Fig. 3-1). The increased average diameter and broader diameter distribution in thevertically grown SWNT film was demonstrated by both HR-TEM observation (Figs. 3-4
and 3-5) and Raman scattering analysis (Fig. 3-6).
The vertical alignment is considered to arise from the higher growth density of SWNTs,
due to which the SWNTs grow into thicker and hence more mechanically rigid bundles by
coalescing with each other as the growth proceeds, as shown in Fig. 3-3d. Consequently,
those bundles are only able to grow away from the substrate because of physicalinterferences with the neighboring bundles.
Based on the foregoing investigations, it is deduced that the high amount of growthrequired for the vertical alignment of SWNTs is caused by the simultaneous achievement of1) dense monodispersion of 1–2 nm Co catalyst particles supported by the dip-coat process
and 2) high degree of activation of the catalyst as a result of improving the cleanness of the
CVD chamber, which leads to the dense growth of SWNTs. The fine dispersion of thecatalyst arises from the use of bimetallic Co-Mo acetate solution and the resulting catalyst
stabilization by the CoMoOx layer, as discussed in Section 2.4. Hence, it is concluded thatthe augmentation and maintenance of catalyst activity by enhancing the chamber cleanness
is essential for the alignment to enhance the catalyst activity. The increase in the diameter
distribution observed in the unaligned case presented in Section 2.3 supports thisconclusion.
Finally, in this section, the area densities of the catalyst particles and SWNTs are
estimated and compared in order to evaluate the efficiency in the use of the catalyst. The
catalyst density is directly obtained from the TEM image (Fig. 2-30), and it is90

Chapter 3  Growth of vertically aligned SWNT films on substrates
and their formation process
approximately 1.3 × 1017 [m-2]. The approximate mass density of the film was estimated tobe ~3.5 × 10-2 [g/cm3] by comparing the weight of the substrate measured by a precisionelectric microbalance before and after removing the film from the substrate. Then thenumber density of SWNTs is calculated, assuming the SWNTs are (n, m) = (14, 14) tubes
with diameter of 1.93 nm, to be ~0.85 × 1016 [m-2]. This is approximately one-order lower
density compared to that of the catalyst particles.

913.6 Transient investigations and modeling of growth process of verticallyaligned SWNT films
3.6.1 Growth and formation process of vertically aligned SWNT film
A series of CVD experiments was performed for different CVD reaction times of 15, 30,
60, 180, 600, 1800, and 6000 s in order to investigate the growth process of the verticallyaligned SWNTs. All the CVD conditions except the CVD reaction time were set to be thesame in order to ensure inter-comparability. The speed of vacuum deterioration shown in
Fig. 3-1 is also set to be the same: “2 → 5 Pa = 8 ± 1 min.” In this series of experiments,
the reaction temperature and ethanol pressure were selected as 800°C and 10 Torr,
respectively, which are the standard CVD conditions used in this study. Figure 3-7 shows across-sectional FE-SEM image of the SWNT film from 15 to 600 s. The SWNT film is a
mixture of random in the upper portion and weakly aligned in the lower portion at the timeof 15 s, from which the alignment is gradually established as the reaction time proceeds. It
should be noted that SWNTs are grown on the both sides of the substrate, and hence, the
FE-SEM images in Fig 3-7 only show a half of the total thickness.

Fig. 3-7. Time-progressive growth observation of the vertically aligned SWNT film on quartz
substrates by Hitachi FE-SEM S-4700 at 1 kV. The SWNT flim was grown on quartz substrates atvarious CVD reaction times, 15, 30, 60, 180, and 600 s. CVD reaction temperature and ethanolpressure were 800°C and 10 Torr, respectively.

92

Chapter 3  Growth of vertically aligned SWNT films on substrates
and their formation process

Absorbance at 488 nm

0.5

5(488 nm)

200

400

600

0

10

b

(SEM)

10

1

10

0

(488 nm)

–1

10

1

10

CVD time (sec)

2

3

10
10
CVD time (sec)Thickness measured by SEM ( µm)(SEM)

Thickness measured by SEM ( µm)

a

0
0

0

10

Absorbance at 488 nm

1

4

10

Fig. 3-8. Changes of optical absorbance at 488 nm (left ordinate) along with total film thickness
measured by FE-SEM (right ordinate) plotted against CVD time taken in abscissa, represented by (a)linear scale for 15 - 600 s, or (b) logarithmic scale for 15 - 6000 s. The absorbance was measured
with perpendicularly incident light to the substrate represented as square (□). Film thickness wasmeasured by FE-SEM at several locations as each denoted by crosses (×), and the diamond (◊)
denotes their averaged value.

Figure 3-8 shows the changes of the optical absorbance at 488 nm (left ordinate) and thetotal film thickness measured by FE-SEM (right ordinate) plotted against the CVD time in
the abscissa. The absorbance was measured with a 488-nm light incident perpendicular tothe substrate, which is represented as a square (□) in the figure. The measurements of thefilm thickness by FE-SEM were performed in multiple locations on the same sample, which
are denoted by crosses (×); the diamond (◊) denotes their averaged value. While Fig. 3-8ashows the linear plots for 15–600 s corresponding to Fig. 3-7, Fig. 3-8b shows all the plots
for 15–6000 s on a logarithmic scale. It should be noted that after 600 s, the growth
eventually ceases; moreover, a slight decrease in the thickness is observed after 1800 s.
This growth cessation is attributed to the loss of catalytic activity due to the imperfectvacuum in the chamber; this is because the final thickness of the film is directly dependent
on the degree of vacuum, as confirmed in Fig. 3-1. The process for this growth cessation isquantitatively formulated and discussed in the following subsection. Since the current
SWNT films are grown directly on quartz substrates, the morphology of these films can beconveniently probed by optical absorption measurements.
Figure 3-9 shows the ratio between the absorbance at 488 nm and the film thickness
measured by FE-SEM (i.e., absorbance of the film per unit thickness), plotted against the
CVD reaction time in the abscissa. This figure indicates a monotonous decrease of the93(Abs. at 488 nm) / (Thickness measured by SEM)

–1

Absorbance per thickness ( µm )

0.3

0.2

15 sec30 sec

0.1
0.09
0.08

10 min

1 min

30 min
100 min

3 min

0.07
10

1

2

10
10
CVD time (sec)

3

10

4

Fig. 3-9. Relationship between optical absorbance at 488 nm per unit film thickness an CVD reaction
time, which is calculated from the result shown in Fig. 3-8b.

(1)

(2)

(3)

(4)

Fig. 3-10. Schematic for the growth and alignment formation process of the SWNTs directly grownon quartz substrates.

absorbance per unit film thickness with CVD reaction time. As investigated in detail in
Section 4.1, the optical absorption cross section of SWNTs parallel to the axis is several
factors of magnitude greater than that perpendicular to the axis. Therefore, the result shownin Fig. 3-9 clearly indicates that the degree of alignment is largely improved within the first
3 min of the CVD reaction. At ~3 min, the alignment is almost established after which the94Chapter 3  Growth of vertically aligned SWNT films on substrates
and their formation process
optical nature of the film shows little variance, indicating the attainment of morphologicallysteady growth.
The FE-SEM observation confirmed that the morphology at a very early stage of thegrowth is quasi-2D along the substrate surface (shown in Fig. 3-18), as schematized in Fig.
3-10(1). The result shown in Fig 3-9 supports the following explanation of the growth
process: As discussed previously in Section 3.5, the progression of the growth leads to thecoalescence of SWNTs into bundles, as shown in Fig. 3-10(2). The entanglement andfriction due to the bundle formation gradually immobilize each SWNT; however, while inthis state, the carbon source reaches the catalyst located in the root of the SWNT. The highdensity of SWNTs, as well as the immobilization of an initial random layer, allows the
SWNTs to only grow away from the substrate, which eventually configurates the verticalalignment of bundled SWNTs.

3.6.2 In situ measurement of growth process of vertically aligned SWNT film
In order to conduct an in-depth investigation of the growth process, in situ monitoring of
the growth of the SWNT film was performed. As schematically described in Fig. 3-11, a
488-nm Ar+ laser light is guided into the CVD chamber through an aperture (φ = 5 mm)created in the wall of the annular electric furnace, so that the laser light passes
perpendicularly through the quartz substrate placed in the center of the chamber. The laser
light leaves the chamber through an aperture on the opposite side of the wall, and its
Controller

USB cable
PC

Laser light detector
Quartz substrate
Electric furnace
Gas flow

Quartz tube

Prism/Mirror

Ar+ Laser

Fig. 3-11. Schematic description of in situ growth monitoring system by a real-time measurement on
optical absorption of 488 nm laser light which is introduced into the CVD chamber.

95

intensity is measured by a laser light detector (Coherent, LM-2 VIS #33-0936-000)
combined with a computer-based data-logging system (Coherent, LaserPAD #1008557).
The attenuation in the laser intensity is used to calculate the absorbance of the sample forevery time instant of the CVD reaction.
Figure 3-12 shows the changes of the light absorbance at 488 nm measured with respect
to the CVD time for two different experiments, referred to as “A” and “B” in this section.
The fundamental difference between these experiments lies in the catalyst activity before
the CVD reaction, i.e., the chamber cleanness in “A” is higher than that in “B,” as theirdetailed CVD conditions described in the figures. As recognized in Fig. 3-12, experiment“B” resulted in a higher yield of SWNTs than “A”, and this is reflective of the difference inthe catalyst activity. In order to quantitatively explain the shapes of the transitional curves
shown in Fig. 3-12 (hereafter referred to as “growth curves”), several growth-limiting
models were initially tested, such as 1) diffusion limit imposed on the carbon-source
molecules that try to reach the catalyst as the film grows and 2) constant-speed
deterioration of catalyst activity due to the background pressure of impurity-gas species.
However, it appears that these models cannot quantitatively explain the shape of the growth
curve shown in Fig. 3-12. Another reasonable possibility is a growth limitation imposed by
the deterioration of catalyst activity caused by the decomposition of the carbon source
molecules themselves. This possibility will be investigated in the next subsection.
0.5

B

Absorbance

A

0.25

04/08/20 CVD–3

04/08/20 CVD–1

CoMo 0.01wt%, 800 °C, 10 Torr, 10 min

CoMo 0.01wt%, 800 °C, 10 Torr, 10 min

Ar/H2 300 sccm at 80 kPa, PPN(2–>5Pa)=40 min

Ar/H2 300 sccm at 40 kPa, PPN(2–>5Pa)=16 min

0
0

200

400

CVD time (sec)

600 0

200

400

600

CVD time (sec)Fig. 3-12. In situ measurements of optical absorbance of 488 nm laser light by catalyst supporting
quartz substrates for 10 min CVD processes. Two experiments ‘A’ and ‘B’ were performed at
different chamber cleanness, whose details are described in the figures.

96Chapter 3  Growth of vertically aligned SWNT films on substrates
and their formation process
3.6.3 Formulation for growth process of vertically aligned SWNT film
Catalyst activity η(t) [mol/m2s] is defined as the ability of catalyst within 1 m2 on thesubstrate to separate C atoms during unit time at time t. The initial catalyst activity isdenoted as η(0) = η0. The molar number of the C atoms that were separated as SWNTs attime t per 1 m2 is denoted as M(t) [mol/m2]. That is,dM = η
dt(1)Here, it is postulated that the deterioration of η per unit time is proportional to the molar
number of the separated C atoms within the unit time, and the proportionality constantlinking them is denoted as κ [s-1], which represents the time constant for catalyst
deactivation, or

−

dM
dη
=κ
= κη
dt
dt

(2)

η0
(1 − e −κt )κ

(3)Hence, M(t) is written as

M=
Further, active period τ [s] is defined asτ = κ −1

(4)
Under this postulation, the total molar number of the separated C atoms during the CVD
process is equal to η0τ, regardless of the CVD process.
The optical absorbance A is defined by the molar optical absorption cross section ε[m2/mol], the molar concentration of optical absorbent specie, [J] [mol/m3], and thethickness of the sample, l [m], asA = ε ⋅ [J ] ⋅ l(5)Since [J] is assumed to be constant along the thickness of the film, [J]·l [mol/m2] is equalto M(t) [mol/m2]. Further, since ε is considered to be a function of t until vertical alignmentis established (See Fig. 3-9), Eq. 5 can be rewritten as(6)
A(t ) = ε (t ) ⋅ M (t )The product ε [J] represents the absorbance per unit thickness of the film. If it is denoted ass(t), Eq. 5 can also be written as(7)
A(t ) = s (t ) ⋅ l (t )The experimentally measurable values are A(t) and s(t); therefore, ε(t), l(t), and M(t) shouldbe treated as unknowns

97

The molar concentration of the C atom per unit area per unit film thickness after theestablishment of the alignment, [J]∞, is estimated to be ~3.0 × 103 [mol/m3] (~3.5 × 10-2
[g/cm3]). This value is obtained by comparing the weight of the substrate measured by our
precision electric microbalance before and after removing the film from the substrate.
Using this value, the final thickness of the film, l∞ [m], at t → ∞ can be expressed asl ∞ ≈ 3.3 × 10 − 4

η0= 3.3 × 10 − 4 η 0τκ(8)Figure 3-13a, which is a partial presentation of Fig. 3-9 corresponding to below 10 min,indicates the absorbance at 488 nm per unit thickness of the film, s(t), vs. the CVD time tmeasured from a series of experiments performed under almost the same vacuum
deterioration speed of “2 → 5 Pa = 8 ± 1 min.” However, in general, the catalyst activity
and the growth speed are largely affected by the vacuum deterioration speed, as discussed
in Section 3.3. Therefore, Fig. 3-13a does not represent a universal process for thealignment formation. A universal process for the formation, in order to be independent ofboth η0 and κ, is obtained by expressing it as shown in Fig. 3-13b in which the absorbanceat 488 nm is indicated in the abscissa. This figure represents the absorbance per unit film
thickness at a specific absorbance, which would be universal if the SWNT film finallyachieves the morphologically steady state (i.e., the state in which the vertical alignment isestablished; refer to Fig. 3-9). From Fig. 3-13b, it can be recognized that the absorption per+5+5

15 sec30 sec

1

1 min
3 min

0
0

200

400
CVD time (sec)

10 min

600

–1

a

–1

Absorbance at 488 nm per thickness (m )2Absorbance at 488 nm per thickness (m )[×10 ][×10 ]

2b
15 sec30 sec

1

1 min
3 min

0
0

0.4
Absorbance at 488 nm

10 min0.8

Fig. 3-13. (a) Partial presentation of Fig. 3-9 for below 10 min and (b) that re-plotted for the
relationship between optical absorbance per thickness of the film and the absorbance at 488 nm.

98

Chapter 3  Growth of vertically aligned SWNT films on substrates
and their formation processunit film thickness s(A) decreases monotonically until A is ~0.3, and subsequently, a steadystate s(A)A→∞ ≡ s∞ ≈ 8.4 × 104 [m-1] is attained.
The plots in Figure 3-14 are identical to those in Fig. 3-13b but with the addition of two
functional lines described as follows. The morphology at t = 0 is considered to be random,and there exists a constant initial value s(0) = εrandom⋅[J]random corresponding to the initialstate. Two test cases, denoted as “Case 1” and “Case 2,” are introduced and indicated witha solid line and broken line, respectively, in Fig. 3-14. These lines represent two extreme
cases that are expected from the experimentally measured plots. and are chosen so that s(0)and s(∞) are exponentially related as


X
(9)
s ( A) = s ∞ 1 + exp{Y ( A − Z )} + 1Here X, Y, and Z are constants: X = 1.45, Y = 37.1, and Z = 0.123 for “Case 1” and X =3.03, Y = 22.0, and Z = 0.065 for “Case 2”. It is obvious that the functional form of Eq. 9
does not have any physical meaning, except that it is a reasonable expression connecting
two states s(0) and s(∞). However, the choice of such functional expression would be
irrelevant if the current model were to explain the measured phenomena regardless of thedifference between “Case 1” and “Case 2.”
+5

3

–1

Absorbance at 488 nm per thickness (m )[×10 ]
s(t) = ε x [J]Case 1

2

Case 2

1
Establishingalignment
ε = not const[J] = not const

00

Alignment established2

ε = 28.0 [m /mol]
33[J] = 3.0 x 10 [mol/m ]

0.4

0.8

Absorbance at 488 nm

Fig. 3-14. Re-presentation of Fig. 5-12b with two functional lines, ‘Case 1’ (solid line) and ‘Case 2’(dotted line), which are described by Eq. 9.

99

Prior to calculating M(t) from Eq. 6, ε(t) should be determined. In this study, it isreasonable to consider that although an optical absorption by van Hove singularities issuggested by the eDOS intensity of SWNTs, the optical absorption at 488 nm (2.54 eV) is
primarily due to the baseline extended from higher energy (~5 eV) absorption features
whose intensity is dependent on the molar number of the contained C atom. This will be
described in detail in Section 4.1.
Since s is a product of ε and [J], it is not possible to extract only ε from Fig. 3-14.
Although εt→∞ = 28.0 [m2/mol] is calculated from the measurement, εt→0 (= εA→0) has to be
calculated by some method. In the following paragraphs, a method of calculating ε(A) that
describes the initial growth stage of the SWNT film will be briefly presented.
First, Λ0 denotes the optical absorbance of linearly polarized light whose polarization isparallel to the SWNT axis by collinear transition dipole moments of ideally aligned (i.e., nophysical disturbance) SWNTs. Although transition dipoles exist perpendicular to the
SWNT axis as presented in Section 4.1, they are not considered here because of their
weaker strength. Further, the measured absorbance by normally (θ = 0) and tangentially (θ= 90°) incident p-polarized lights on the substrate are denoted as Λ’⊥ and Λ’||, respectively,
as schematized in Fig. 3-15.
Figure 3-16 presents the optical absorbance at 488, 633, and 1000 nm measured from thesample shown in Figs. 3-7 to 3-9 as “3 min” by changing the incident angle θ to thesubstrate. The absorbance in the ordinate is normalized by the cos-1θ increment of theLaser light (488 nm)

z

SWNTs

Ep

θ

x
SubstrateyFig. 3-15. Schematic drawing of p-polarized light incidence onto the vertically aligned SWNT film
on a quartz substrate at an angle of θ. Ep denotes electronic vector of the p-polarized light to thesubstrate.

100Chapter 3  Growth of vertically aligned SWNT films on substrates
and their formation process
light-path length, and each series of measured points fit well with the sin2θ curves. Λ’⊥corresponds to the absorbance at θ = 0 and Λ’|| corresponds to the extrapolated absorbanceat θ = 90°, using which the total absorbance Λ0 is expressed asΛ 0 = Λ '|| +2Λ ' ⊥(10)

The 3D-wise (Fig. 3-17a) and 2D-wise (Fig. 3-17b) initial morphologies are envisaged as
two extreme cases. In reality, the initial state lies somewhere in between these two cases. In
the following expressions, the parameters at the initial, 3 min, and steady state are denotedby the subscripts “t→0,” “t = 3min,” and “t→∞,” respectively. From Fig. 3-16, Λ’⊥,t=3minand Λ’||,t=3min are observed to be 0.39 and 1.00, respectively; the hypothetical absorbance ofthe film in 3D-wise and 2D-wise random morphology, Λrandom,3D,t=3min and Λrandom,2D,t=3min,respectively, at 3 min are expressed as
11
Λ random,3D,t =3 min = Λ 0,t =3 min = {Λ '||,t =3 min +2Λ ' ⊥ ,t =3 min } = 0.593
33
Λ random,2D,t =3 min =1
1
Λ 0,t =3 min = {Λ '||,t =3 min + Λ ' ⊥ ,t =3 min } = 0.89
2
2

(11)
(12)

Absorbance normalized by cos

Thickness = 2.1 µm x 2

1(04/03/13 800 °C 3 min)P–polarization

0.5
Blue: 488 nm
Red: 633 nm
Black: 1000 nm

0045
Tilt angle (deg)90Fig. 3-16. Dependence of optical absorbance at 488, 633 and 1000 nm measured for the sample shownin . Figs. 3-7 - 3-9 as “3 min”, on incident angle of the light θ to the substrate. Absorbance in ordinate
is normalized by cos-1θ increment of the light path length and each series of measured points are fittedwith sin2θ curves.

101

(a)

(b)

Fig. 3-17. Schematic descriptions of (a) 3D-wise and (b) 2D-wise random morphology of the
SWNT films grown on quartz substrates.

Since the morphology reaches its steady state at 3 min, the relationshipM t →0M t →0Λ random,3D,t =3 min< Λ ' ⊥ ,t →0 < Λ random,2D,t =3 min
M t =3 min
M t =3 min
is obtained. If this is divided by Λ’⊥,t=3min,MΛ ' ⊥ ,t →0 t =3 minΛ random,3D,t =3 minΛ random,2D,t =3 min
M t →0<<Λ ' ⊥ ,t =3 minΛ' ⊥ ,t =3 minΛ ' ⊥ ,t =3 min

M t =3 minΛ random,3D,t =3 minΛ random,2D,t =3 min
M t →0⇔<<Λ' ⊥ ,t =3 minε ⊥ ,t =3 min [ J ]t =3 min lt =3 minΛ ' ⊥ ,t =3 min

(13)

(14)

ε ⊥ ,t → 0 [ J ] t → 0 l t → 0(15)

Using the relationships ε⊥,t=3min = ε⊥,t→∞ and M = ε⋅[J], Eq. 15 is rewritten as

1.52 <ε ⊥ ,t → 0< 2.28ε ⊥ ,t → ∞(16)which represents the possible range of the ratios between ε⊥,t→0 and ε⊥,t→∞.

ε and [J] could not explicitly be distinguished in Fig. 3-14; however, if both parameters
are assumed to vary in a manner so as to maintain the ratio ε:[J] almost constant, Eqs. 9 and16 giveε ( A) = ε ⊥ ,t →∞ 1 +

X'exp{Y ( A − Z )} + 1

(17)
It should be noted that ε⊥,t→∞ is an experimentally measured constant (= 28.0 [m2/mol]) and
X’ is a constant determined solely from the experimentally obtained relation Eq. 16 asCase 1 : 0.525 < X ' < 1.29, Case2 : 0.644 < X ' < 1.59
(18)

102

Chapter 3  Growth of vertically aligned SWNT films on substrates
and their formation process
It should be repeated that the parameters Y and Z were provided in the context of Eq. 9 torepresent “Case 1” and “Case 2,” shown in Fig. 3-14. By substituting Eq. 17 into Eq. 6 andusing Eq. 3, the following expression is obtained.

 η0
X'
− κt
A = ε ∞ 1 +
 ⋅ κ 1− e exp{Y ( A − Z )} + 1

(

)

(19)

Here, ε⊥,t→∞ was rewritten as ε∞. This equation is implicit for A but explicit for t; this can besolved for t as





1 
A

t = − ln 1 −κ  η 0ε ∞ 

X'
1+

κ  exp{Y ( A − Z )} + 1 (20)

It should be reiterated that the parameters X’, Y, Z, and ε∞ are experimentally determinedparameters from either Fig. 3-14 or Fig. 3-16, not fitting parameters. Only η0 and κ, which
are physically evident as introduced in Eqs. 1 and 2, are used as the fitting variables to
explain the observed phenomena.
Figure 3-18 shows the growth curves calculated from Eq. 20 for “Case 1,” in which η0and κ were selected so that the calculated growth curve (dotted line) is the best match forthe measured curve (solid line) presented in Fig. 3-12 for both experiments “A” and “B.”{η0 = 7.58 × 10-5 [mol/m2s], κ = 6.49 × 10-3 [s-1] (⇔ τ = 154 [s])} and {η0 = 8.67 × 10-5[mol/m2s], κ = 5.64 × 10-3 [s-1] (⇔ τ = 177 [s])} were obtained for experiments “A” and“B,” respectively, that best fit the measured growth curves. The upper row (lower row) of
Fig. 3-18 corresponds to the assumption of 3D-wise (2D wise) morphology at the initial
growth stage, as schematized in Fig. 3-17. Importantly, when a 2D-wise initial morphology
is assumed, the current model overestimates the optical absorbance at the initial growthstage, while under the assumption of 3D-wise initial growth, the calculated growth curve
displays an excellent agreement with the measured curve.

103

0.5

A

2

η0 = 7.58E–5 [m /mol]–1

κ = 6.49E–3 [s ]B2

ε = 28.0 [m /mol]

Case 1

AbsorbanceCase 12

η0 = 8.67E–5 [m /mol]–1

κ = 5.64E–3 [s ]2

ε = 28.0 [m /mol]

0.25Black: ExperimentBlack: Experiment
Red: Calculation (Λτ=0 = Λ3D, random)

Red: Calculation (Λτ=0 = Λ3D, random)

04/08/20 CVD–1

04/08/20 CVD–3

CoMo 0.01wt%, 800 °C, 10 Torr, 10 min

CoMo 0.01wt%, 800 °C, 10 Torr, 10 min
Ar/H2 300 sccm at 80 kPa, PPN(2–>5Pa)=40 min

Ar/H2 300 sccm at 40 kPa, PPN(2–>5Pa)=16 min

0
0

200
400
CVD time (sec)

600 0

200
400
CVD time (sec)

600

0.5

A

2

η0 = 7.58E–5 [m /mol]–1

κ = 6.49E–3 [s ]B2

ε = 28.0 [m /mol]

Case 1

AbsorbanceCase 12

η0 = 8.67E–5 [m /mol]–1

κ = 5.64E–3 [s ]2

ε = 28.0 [m /mol]

0.25Black: Experiment
Green: Calculation (Λτ=0 = Λ2D, random)

Green: Calculation (Λτ=0 = Λ2D, random)

04/08/20 CVD–1

04/08/20 CVD–3

CoMo 0.01wt%, 800 °C, 10 Torr, 10 min

CoMo 0.01wt%, 800 °C, 10 Torr, 10 min

Ar/H2 300 sccm at 40 kPa, PPN(2–>5Pa)=16 min

00Black: Experiment

200
400
CVD time (sec)

600 0

Ar/H2 300 sccm at 80 kPa, PPN(2–>5Pa)=40 min

200
400
CVD time (sec)600

Fig. 3-18. Growth curves calculated from Eq. 20 for the experiments ‘A’ and ‘B’ in case of ‘Case 1’(dotted lines), along with the experimentally measured curves shown in Fig. 3-12 (solid lines). η0 andκ were chosen to be η0 = 7.58 × 10-5 [mol/ m2 s], κ = 6.49 × 10-3 [s-1] for experiment ‘A’, and η0 =8.67 × 10-5 [mol/ m2 s], κ = 5.64 × 10-3 [s-1] for experiment ‘B’. The upper row written in red (Thelower low written in green) corresponds to the assumption of 3D-wise (2D-wise) random morphology
at initial stage of the growth.

104

Chapter 3  Growth of vertically aligned SWNT films on substrates
and their formation process
0.5

A

2

η0 = 7.58E–5 [m /mol]B–1

κ = 6.49E–3 [s ]2

ε = 28.0 [m /mol]AbsorbanceCase 2

Case 22

η0 = 8.67E–5 [m /mol]–1

κ = 5.64E–3 [s ]2

ε = 28.0 [m /mol]

0.25Black: ExperimentBlack: ExperimentΛτ=0 = Λ3D, random)
Red: Calculation ((Λ00Red: Calculation (Λτ=0 = Λ3D, random)

04/08/20 CVD–1

04/08/20 CVD–3

CoMo 0.01wt%, 800 °C, 10 Torr, 10 min

CoMo 0.01wt%, 800 °C, 10 Torr, 10 min

Ar/H2 300 sccm at 40 kPa, PPN(2–>5Pa)=16 min

Ar/H2 300 sccm at 80 kPa, PPN(2–>5Pa)=40 min

600 0

200
400
CVD time (sec)200
400
CVD time (sec)

600

0.5

A

2

η0 = 7.58E–5 [m /mol]B–1

κ = 6.49E–3 [s ]2

ε = 28.0 [m /mol]AbsorbanceCase 2

Case 22

η0 = 8.67E–5 [m /mol]–1

κ = 5.64E–3 [s ]2

ε = 28.0 [m /mol]

0.25Black: Experiment
Green: Calculation (Λτ=0 = Λ2D, random)00Black: Experiment
Green: Calculation (Λτ=0 = Λ2D, random)

04/08/20 CVD–1

04/08/20 CVD–3

CoMo 0.01wt%, 800 °C, 10 Torr, 10 min

CoMo 0.01wt%, 800 °C, 10 Torr, 10 min

Ar/H2 300 sccm at 40 kPa, PPN(2–>5Pa)=16 min

Ar/H2 300 sccm at 80 kPa, PPN(2–>5Pa)=40 min

200
400
CVD time (sec)

600 0

200
400
CVD time (sec)600

Fig. 3-19. Growth curves calculated from Eq. 20 for the experiments ‘A’ and ‘B’ in case of ‘Case 2’(dotted lines), along with the experimentally measured curves shown in Fig. 3-12 (solid lines). η0 andκ are the same as those employed in the case of Fig. 3-18. Upper row, written in red (lower low
written in green) corresponds to the assumption of 3D-wise (2D wise) random morphology at initialstage of the growth, similarly to the case of Fig. 3-18.

Figure 3-19 shows the growth curves calculated from Eq. 20 for experiments “A” and“B” for “Case 2.” In the calculation, η0 and κ were the same as those used in Fig. 3-18.
Further, in this case, the calculated curve (dotted line) and the measured curve (solid line)
agree excellently in the case of 3D-wise initial morphology, while the calculated
absorbance exceeds the measured value at an earlier growth stage in the case of 2D initial105morphology. Two important conclusions are derived from the results shown in Figs. 3-18
and 3-19. First, the current model agrees well with the measured growth curve regardless ofthe two extreme assumptions “Case 1” and “Case 2” shown in Fig. 3-14. This implies that
this model has only two physically-clear variables η0 (initial catalyst activity) and κ(deactivation constant for catalyst) as the control parameters. Second, the initialmorphology is deduced to be rather close to 3D-wise randomness because this agrees wellwith the behavior of the measured absorbance at the initial growth stage.
This discussion on the initial morphology of the SWNT film is supported by the FE-SEM
observations shown in Fig. 3-20, which shows the morphology at a very early stage of thegrowth. This figure reveals that even when the thickness is ~30 nm, SWNTs and theirbundles start to stand up and grow away from the substrate, although the measured
absorbance A at this point is merely ~0.002. Even in the slightly developed case when thefilm thickness is ~150 nm, the morphology is clearly close to that of 3D wise and themeasured absorbance was only 0.07. Therefore, these FE-SEM observations support theidea that with the exception of the very early stage of the growth in which the opticalabsorbance is virtually negligible, the initial morphology in the context of this study can be
regarded as 3D-wise random, as indicated by Fig. 3-17a or 3-20. This indicates that theupper rows of Figs. 3-18 and 3-19 should be considered, in which the growth curves arewell explained by only the two physically clear parameters η0 and κ introduced in thepresent model.

≈ 150 nm≈ 30 nm

300 nm

300 nmFig. 3-20. Initial morphology of the SWNT films observed by Hitachi FE-SEM S-4700 at 1 kV. Filmthickness in the right and left panels are ~ 30 and ~ 150 nm whose optical absorbance at 488 nm are ~0.002 and 0.07, respectively.

106

Chapter 3  Growth of vertically aligned SWNT films on substrates
and their formation process
Using the current model, the final achievable absorbance A∞ and thickness l∞ that are
finally achieved are calculated from the expressions,

A∞ = ε ∞η0η1, l∞ = ε ∞ 0 ⋅κκ s (∞ )(21)

from Eq. 20. A∞ and l∞ for experiments “A” and “B” are then predicted from Eq. 21 to be
A∞ = 0.33, l ∞ = 3.85 [ µm] (experiment ' A' )A∞ = 0.43, l ∞ = 5.07 [ µm] (experiment ' B' )Since l∞ denotes the sum of the film thickness on both sides of the substrate, the thickness

per side would be 1.93 and 2.53 µm for experiments “A” and “B,” respectively.

3.7 Summary of Chapter 3This chapter demonstrated the possibility of growing vertically aligned SWNTs on flat
substrates under the optimized CVD condition by the alcohol CCVD method and the highly
monodispersed Co catalyst described in Chapter 2. It was observed that the cleanness of the
CVD chamber, which highly affects the speed of catalyst deactivation, is an importantfactor that controls the resultant morphology and the amount of SWNT growth. The
morphology and quality of the aligned SWNT film were investigated by FE-SEM,
HR-TEM, and Raman scattering analyses, from which the high selectivity and quality ofthe synthesized SWNTs were confirmed. The mechanism of vertical growth was discussed
in terms of both microscopic and optical absorption measurements. The SWNT film
developed in this study can be used in various applications and augments the possibility of
SWNT-based devices that have thus far been proposed using randomly oriented SWNTs
deposited on a substrate. This method is also suitable to obtain SWNTs with nearly
constant lengths defined by the thickness of the aligned SWNT film.
In order to further investigate the growth process of the aligned SWNT film, in situ
growth measurement was performed by monitoring the optical absorbance of the substratewith a laser detection system incorporated into the CVD apparatus. Growth models were
proposed and it was suggested that the growth curve was explained by two controlling
factors, initial catalyst activity η0 and deactivation constant for catalyst κ. This model
predicts that the total amount of SWNTs grown is determined by a single index η0/κ (=η0⋅τ) independent of the CVD process if the reaction temperature is the same, which shouldbe verified by further investigations. It was explained that the degree of the chamber

107

cleanness and that of catalyst reduction are strongly correlated to the resultant η0 and κ
values; however, their physical/chemical origins have not been elucidated in this chapter.
Investigations on the dependences of η0 and κ values on the reaction temperature andpressure would assist in elucidating these origins. In essence, “η0/κ” should be enhancedwith avoiding catalyst deactivation in order to achieve further thicker growth of thevertically aligned SWNT films.

Acknowledgements for Chapter 3
The author would like to thank Prof. T. Okubo and Mr. T. Sugawara at The Univ. Tokyo for theuse of FE-SEM Hitachi S-900 in Fig. 3-2, Mr. S. Watanabe, Ms. M. Nakagawa, Mr. R. Tamochi at
Hitachi Science Systems Ltd. and K. Shibata at Hitachi High-Technology Corp. for the observation
by FE-SEM Hitachi S-5200 in Fig. 3-3, Mr. H. Tsunakawa at The Univ. Tokyo for his assistancesin TEM observation in Figs. 3-4 and 3-5, Mr. T. Nishii at J-Power Co. Ltd. for the use of FE-SEM
Hitachi S-4700 in Figs. 3-7 and 3-20. Part of this Chapter has been published in Chemical Physics
Letters, vol. 385, pp. 298-303, 2004 by Y. Murakami, S. Chiashi, Y. Miyauchi, M. Hu, M. Ogura, T.
Okubo, and S. Maruyama.

References for Chapter 3
1.

A. Thess, R. Lee, P. Nikolaev, H. Dai, P. Petit, J. Robert, C. Xu, Y.H. Lee, S.G. Kim, A.G.
Rinzler, D.T. Colbert, G.E. Scuseria, D. Tománek, J.E. Fischer, R.E. Smalley, Science 273(1996) 483.

2.

M.J. Bronikowski, P.A. Willis, D.T. Colbert, K.A. Smith, R.E. Smalley, J. Vac. Sci. Technol.
A 19 (2001) 1800.

3.

P. Avouris, Chem. Phys. 281 (2002) 429.

4.

J.A. Misewich, R. Martel, P. Avouris, J.C. Tsang, S. Heinze, J. Tersoff, Science 300 (2003)
783.

5.

M. Freitag, Y. Martin, J.A. Misewich, R. Martel, P. Avouris, Nano Lett. 3 (2003) 1067.

6.

T. Someya, J. Small, P. Kim, C. Nuckolls, J.T. Yardley, Nano Lett. 3 (2003) 877.

108

Chapter 3  Growth of vertically aligned SWNT films on substrates
and their formation process
7.

J. Li, Y. Lu, Q. Ye, M. Cinke, J. Han, M. Meyyappan, Nano Lett. 3 (2003) 929.

8.

Y.C. Chen, N.R. Raravikar, L.S. Schadler, P.M. Ajayan, Y.P. Zhao, T.M. Lu, G.C. Wang, X.C.
Zhang, Appl. Phys. Lett. 81 (2002) 975.

9.

Y. Sakakibara, S. Tatsuura, H. Kataura, M. Tokumoto, Y. Achiba, Jpn. J. Appl. Phys. 42(2003) L494.

10. S. Yamashita, Y. Inoue, S. Maruyama, Y. Murakami, H. Yamaguchi, M. Jablonski, S.Y. Set,
Opt Lett. 29 (2004) 1581.
11. S. Fan, M.G. Chapline, N.R. Franklin, T.W. Tombler, A.M. Cassell, H. Dai, Science 283(1999) 512.
12. B.Q. Wei, R. Vajtai, Y. Jung, J. Ward, R. Zhang, G. Ramanath, P.M. Ajayan, Nature 416(2002) 495.
13. Y. Zhang, A. Chang, J. Cao, Q. Wang, W. Kim, Y. Li, N. Morris, E. Yenilmez, J. Kong, H.
Dai, Appl. Phys. Lett. 79 (2001) 3155.
14. E. Joselevich, C.M. Lieber, Nano Lett. 2 (2002) 1137.
15. J.E. Fischer, W. Zhou, J. Vavro, M.C. Llaguno, C. Guthy, R. Haggenmueller, M.J. Casavant,
D.E. Walters, R.E. Smalley, J. Appl. Phys. 93 (2003) 2157.
16. A. Modi, N. Koratkar, E. Lass, B. Wei, P.M. Ajayan, Nature 424 (2003) 171.
17. P.W. Atkins, Physical Chemistry 6th Ed., W.H. Freeman & Co., New York, 1997.
18. Y. Murakami, S. Chiashi, E. Einarsson, S. Maruyama, Phys. Rev. B in press.
19. R. Saito, G. Dresselhaus, M.S. Dresselhaus, Physical Properties of Carbon Nanotubes,
Imperial College Press, London, 1998.
20. H. Ajiki and T. Ando, Physica B 201 (1994) 349.
21. A. Grüneis, R. Saito, G.G. Samsonidze, T. Kimura, M.A. Pimenta, A. Jorio, A.G. Souza Filho,
G. Dresselhaus, M.S. Dresselhaus, Phys. Rev. B 67 (2003) 165402.

109

110

Chapter 4:
Anisotropic optical properties of SWNTs
and their optical applications

4.1 Determination of optical anisotropy of the vertically aligned SWNT
film and optical absorption cross-section of SWNTs
4.1.1 Research background for polarized optical properties of SWNTs
Single-walled carbon nanotubes (SWNTs) are a new group of carbon material possessing
one-dimensional cylindrical geometry formed by rolling-up an sp2-bonded graphene sheet[1]. Their 1D structure and nanoscale diameter give rise to quantization of wave vectors in
the circumferential direction, and strong divergences in the electronic density of states(eDOS) known as van Hove singularities (See Chapter 1), which formulate discrete energy
levels or “subbands” in the eDOS of SWNTs [2]. The energies of these subbands are solely
determined by the chirality of the SWNT, resulting in unique properties that make SWNTs
an important candidate for various electronic and optical applications [3-9]. In particular,
since the inter-subband gap energies correspond to infrared to visible light, and are roughly
tunable by the diameter, several innovative optical applications such as saturable absorbers
for all-optic telecommunication devices [5-7], ultra-small infrared photo-emitters [8] andphoto-detectors [9] have been recently proposed. The 1D shape of a SWNT would be moreadvantageous in polarization-sensitive optical devices, provided a sound understanding of
its anisotropic optical properties.
Despite the significant potential of SWNTs, there have been quite few experimental
studies on the fundamental optical absorption properties of SWNTs which can provide
confirmation of earlier theoretical works in the inter-subband [10] and higher energy
regions [11,12]. So far, measurements of the optical anisotropy of aligned SWNTs
embedded within a polymer matrix have been reported, [13,14] in addition to a recent
investigation of the anisotropic optical absorption cross-section by Islam et al. using
magnetically aligned SWNTs in gel [15]. However, all of these studies were limited to lessthan 3.5 eV mainly because of UV absorption of the employed polymers, hence no report
has presented polarized optical absorption properties of SWNTs for higher energy. The
elucidation of absorption properties in this region containing the π-plasmon around 5 eV, isurgent because they form the baselines in the inter-subband region that are of interest in
many optical measurements and applications.
In this Section, anisotropic optical absorption properties of SWNTs for the energy range
0.5 - 6 eV were investigated by polarized optical absorption measurements of the verticallyaligned SWNT film grown on an optically polished quartz substrate [16] shown in Chapter
3. In addition to inter-subband absorption below 3 eV, this study presents for the first time112

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications

the remarkable polarization dependence of absorption peaks at 4.5 eV and 5.25 eV.
Furthermore, the important relevance of these absorption peaks of SWNTs to the opticalproperties of graphite, which have not yet been fully elucidated, is revealed. In the end, amethod for determining a nematic order parameter for an aligned SWNT film by separating
the collinear absorption peak at 4.5 eV from other transition dipoles is introduced, followed
by determination the optical absorption cross-section of the SWNTs.

4.1.2 Experimental and optical measurement setup
A vertically aligned SWNT film is synthesized on both sides of a 25 × 25 × 0.5 mm
optically polished quartz substrate from dip-coat supported Co catalyst [16] using thealcohol CCVD method [17], as presented in previous Chapter 3. The film consists only of
SWNTs that are sufficiently clean, i.e. contain virtually no amorphous carbon and no
multi-walled carbon nanotubes, as confirmed by resonant Raman scattering (G/D ratio >25) [16] and high-resolution transmission electron microscopy (HR-TEM) [18]. Frommeasurements of diameters of more than 50 SWNTs by HR-TEM, it was confirmed that thediameter ranges between 0.8 and 3.0 nm with an average of ~ 2.0 nm and a standard
deviation of ~ 0.4 nm [18], which is a relatively broad diameter distribution. According tofurther FE-SEM observations, most SWNTs in the film form bundles with a typical
diameter of ~15 nm.
For optical absorption measurements, a UV-vis-NIR spectrophotometer (Shimadzu
UV-3150) with a rotating substrate holder (Shimadzu 206-22620-91) set behind a
UV-vis-NIR polarizer in the sample light path was used. The reference light path remained
blank. After baseline acquisition with both light paths blank, we scanned from 200 - 2500
nm at a specified incident angle (θ) and polarization toward the substrate (s or p). θ = 0 isdefined for normal incidence to the substrate. By convention, incident light is s-polarized(p-polarized) when its electric field vector is perpendicular (parallel) to the plane ofincidence. It was confirmed that the reflectance baseline of the bare quartz substrate for 0°< θ < 45° is quite exiguous, contributing to a measured absorbance of less than 0.03 for pand 0.06 for s-polarizations, although corrections for this contribution have been made in
the following results.

113

4.1.3 Dependence of optical absorption spectrum on SWNT morphology
In Section 4.2, the morphological dependence of the RRS spectrum from SWNTs will bepresented, using which the morphological difference between random and aligned films canbe discerned. However, as shown in Section 4.2.3, since the shape of the RBM spectra isremarkably affected by the physical and chemical environment of SWNTs and the power ofincident laser, a more reproducible method for morphological evaluation is required. The
following subsections will show that optical absorption spectroscopy, which is generally
simpler than Raman scattering measurement, is a strong tool for distinguishing or evenquantitatively evaluating the morphology of SWNTs.
Figure 4-1 shows the optical absorption spectra of the sample corresponding to Fig. 3-1
for 0.5–6 eV with an arbitrary ordinate. It should be noted that the difference in theabsorption at approximately 5 eV shows a strong dependence on the morphology of thesample. The results indicate that when the SWNTs are randomly grown on the substrate,
the peak at ~4.5 eV is dominant, and when they are vertically aligned, the peak at ~5.25 eV
becomes dominant. The spectrum (iv) in Fig. 4b was measured from the sample withconsiderable non-uniformity in which both random and aligned domains coexist, and both
two distinct peaks at ~4.5 and 5.25 eV are observed. This implies that the morphology of
SWNTs is indicated by the optical absorption spectrum at ~5 eV; this is investigated ingreater detail in the following subsections.
(i): Aligned, Λ3 eV = 0.82
o(Vde–gas =Absorbance (arb. unit)

5.75 x 10–53

cm /sec)(ii): Aligned, Λ3 eV = 0.42o(Vde–gas =7.67 x 10–53

cm /sec)(iv): Partially aligned,
Λ3 eV = 0.35(iii): Random, Λ3 eV = 0.08o(Vde–gas =51.1 x 10

05Energy (eV)–53

cm /sec)

10

Fig. 4-1. Absorption spectra for different SWNT film morphology in which the film is (i, ii) verticallyaligned, (iii) random, and (iv) partially aligned with spatial non-uniformity. Λ3 eV denotes absorbanceat 3 eV. In parenthesis denotes the de-gassing speed Vde-gas° that was defined in Section 3.3.

114

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications

4.1.4 Polarized optical absorption of vertically aligned SWNT film
Figure 4-2 shows polarized absorption spectra from the aligned SWNT film for s- andp-polarized light normalized by the cos-1θ increment of the light path length. The angle θ
was changed from 0° to 45° in increments of 7.5°. The SWNT film used for measurements
has a thickness of 2.1 µm per side, hence a total thickness of 4.2 µm. The examined
specimen is identical to that presented in the Fig. 5-7 as “180 sec”, and employed Figs. 3-7- 3-9. In the case of s-polarization, dominant absorption by non-collinear dipoles
perpendicular to the SWNT axis, and weaker collinear dipole absorption arising fromdisorder in the alignment, result in an absorption spectrum that is independent of θ. The
case of p-polarization, on the other hand, shows a clear anisotropy, reflecting a dominanceof absorption by collinear dipoles parallel to the SWNT axis. In the lower energy region (<3 eV), structure from resonant inter-subband absorption for ∆µ = 0 transitions (where µ
denotes the cutting-line index in the 2D Brillouin zone of graphite [2]) is observed asabsorption maxima. These peaks are the first (~0.64 eV) and second (~0.93 eV) subband
gaps in a semiconducting SWNT and the first gap (~1.45 eV) in a metallic SWNT, theenergies of which correspond to SWNTs with a diameter of ~ 1.9 nm [19].
Most noticeable is the polarization dependence of the peaks at 4.5 and 5.25 eV. Theseabsorption peaks have been observed in several studies of randomly oriented SWNT films
2a2

P–polarization

AbsorbanceAbsorbance

S–polarizationb

1
0°, 7.5°, 15°, 22.5°,
30°, 37.5°, 45°,0°, 7.5°, 15°, 22.5°,
30°, 37.5°, 45°1
SS E 22
E 11

M

E 11
4.5 eV 5.3 eV

0
0

2

4
Energy (eV)

6

0
0

2

4

6

Energy (eV)Fig. 4-2. Absorption spectra of 4.2 µm-thick (2.1 µm on one side) vertically aligned SWNT film
measured with (a) s- and (b) p-polarization toward the substrate. Incident angle of the light is varied
from the normal incidence θ = 0° to 45° at a step of 7.5° corresponding to the spectrum frombottom to top. All spectra are normalized by cos-1θ increment of the light path length. Perpendiculardotted lines indicate locations of inter-subband absorption of ES11, ES22, EM11, and of absorptions at
4.5 eV and 5.25 eV, from left to right.

115

[20-23] but considerable disagreements are found among the discussions. Kataura et al.
[20] attributed the peak at 4.5 eV to π-plasmon absorption observed in a purified SWNT
film while the 5.2 eV peak was only seen in the pristine sample containing amorphous
carbon. Pichler et al. [21] stated from their EELS measurements on purified SWNTs thatthe 5.2 eV peak observed at low electron momentum transfer was due to a π-plasmon along
the SWNT axis. Reed and Sarikaya, however, performed EELS on purified SWNTs in a
TEM [22], and showed that a peak at 4.2-4.5 eV was measured for ‘aloof’ incidence of theelectron beam, while the peak at ~5.2 eV was observed when the beam penetrated thecenter of an isolated SWNT. They explained these peaks as surface (4.2-4.5 eV) and bulk(~5.2 eV) π-plasmon excitations.

4.1.5 Anisotropic optical properties of graphite
Apart from SWNTs, it is known that absorption at ~4.5 eV is commonly observed ingraphitic materials [24-26]. It is known that the imaginary part of the dielectric function forgraphite in the direction perpendicular to the c-axis Im{ε⊥} has a maximum at 4.5 eV[27,28], whereas the maximum of the EELS function in the same direction Im{-ε⊥-1} isfound at ~ 7 eV as shown in Fig. 4-3 that is constructed based on the reflectivity data taken
by Venghaus [30] from EELS measurement on stripped pyrolytic graphite. In the direction
parallel to the c-axis, however, the optical properties of graphite have not yet been fully
elucidated because of difficulties in preparing good optical surfaces parallel to the c-axis[27,29]. Nonetheless, according to EELS data by Venghaus [30] measured from 2 - 18 eV
shown in Fig. 6-3, the maximum in Im{-ε||-1} appears at ~5.2 eV, and a broad maximum in
Im{ε||} at ~ 4.0 eV [27,28].

116

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications

Re{ε(ω)}4

Re{ε||}

0
Re{ε_|_}–4

12Im{ε(ω)}Im{ε_|_}

8

4

Im{ε||}

0
Im{–1/ε_|_}Im{–1/ε(ω)}

1.5

1

0.5

0
2

Im{–1/ε||}

4

6

8

Enrgy (eV)Fig. 4-3. Real (Re{ε}) and imaginary part of dielectric functions (Im{ε}), and EELS function(Im{-ε-1}) of graphite for the direction both parallel (||) and perpendicular (⊥) to the c-axis. This
figure was constructed based on the refractivity data presented in Handbooks of Optical Constants ofSolids II [27] whose original data were taken by H. Venghaus by EELS measurement on stripped
pyrolytic graphite at 60 keV [30].

From the fact that these two peaks are observed at almost the same positions regardless ofthe diameter and SWNT preparation method [18,20-23], it is reasonably deduced that theobserved peaks at 4.5 and 5.25 eV in Fig. 4-2 originate from the optical properties ofgraphite, and that they correspond to the maxima in Im{ε⊥} (parallel to SWNT axis) andIm{-ε||-1}(perpendicular to SWNT axis), respectively. We found that similar polarization
behavior of the absorption peaks at 4.5 and 5.25 eV in the present study are seen in Ref. 31,
117

in which a purified HiPco SWNT thin-film aligned on a glass plate was measured.
Although no explanation was given by the authors, their results are consistent with theabove discussion.
In a practical sense, the magnitude of these peaks at 4.5 and 5.25 eV can provide aquantitative and convenient index for evaluating the degree of SWNT alignment. However,more importantly, this optical relevance between SWNTs and graphite above theinter-subband region indicates the possibility of studying the optical properties of graphiteby studying SWNTs as arrays of graphene cylinders.

118

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications

4.1.6 Modeling and formulation of multi-dipole optical absorption of SWNTs
4.1.6.1 Transition probability
This subsection describes the formulation of anisotropic optical absorption by multiple
transition dipoles of SWNTs. The time-dependent Schrödinger equation for Hamiltonian H
is expressed asih∂Ψ (t )
= HΨ (t )∂t(1)

According to the time-dependent perturbation theory, the perturbed Hamiltonian H isexpressed as a summation of the unperturbed Hamiltonian H0 and the perturbation H’ as(2)
H = H0 + H'
In case there is no perturbation, the eigenvalue En and the eigenfunction Φn for H0 that are
related by
H 0 Φ n = En Φ n(3)
are assumed to be known. Then, the unperturbed Schrödinger equationih∂Ψ0 (t )= H 0 Ψ0 (t )∂t(4)

has its general solution as
 E 
(5)
Ψ0 (t ) = ∑ c n exp − i n t Φ n
h 

n =0
where cn denotes an arbitrary constant, and the exponential term is derived from thetime-evolution operator of the wave function. Since Φn forms a complete orthogonal basis,
Ψ(t) can be expanded in terms of Φn as
 E 
(6)
Ψ (t ) = ∑ c n (t ) exp − i n t Φ n
h 

n =0
Therefore, Ψ(t) is determined by calculating the time-dependent coefficient cn(t).
Substituting Eq. (6) into Eq. (1) and taking the inner product with Φf lead to iE f t  dc f
 E ih exp −= ∑ exp − i n t c n (t ) Φ f H ' Φ nh  dth n =0If the initial state of the system lies in one of the bases, Ψ(0) = Φi, that is,ci (0) = 1, c n (0) = 0 (n ≠ i )

(7)

(8)

Further, it is assumed that the state does not significantly deviate from the initial state
within the range of consideration, that is,ci (t ) ≈ 1, c n (t ) ≈ 0 (n ≠ i )

(9)

119

Then Eq. 7 for cf(t) can be rewritten asih

 i ( E f − Ei )t  Φ f H ' Φ n= exp
dt
h



dc f

(10)

and this can be solved asc f (t ) = Φ f H ' Φ n

1 − exp(iϖ fi t )hϖ fi

E f − Ei , ϖ fi ≡
h



(11)

Since cn(t) is an expansion coefficient for the wave function Ψ(t), as expressed in Eq. 6,
their squared values represent the possibility of obtaining the eigenvalue corresponding to
the basis Φn as indicated by an instance for H0,

 E 
 E 
*
Ψ H 0 Ψ = ∑∑ c n (t ) exp − i n t c m (t ) exp − i m t  Φ n H 0 Φ m
h 
h 


n m
 E − Em *= ∑∑ c n (t )c m (t ) exp − i nt  E mδ nm
h


n m

(12)

= ∑ c n (t ) E n
2n

Therefore, the probability of the transition Φi → Φf equals to |cf(t)|2 and this is obtained bysquaring Eq. (11) as

ϖ fi t 



2
sin
2
2
2


c f (t ) = Φ f H ' Φ n hϖ fi This relation is valid for the condition mentioned in Eq. 9.

2

(13)

4.1.6.2 Optical absorption by dipole transition moment
The perturbed Hamiltonian for the one-photon process H(1) (refer to Appendix) is writtenasH (1) ={he1
ik ⋅ r− ik ⋅ r*e j (e k ,γ ⋅ p j )a k ,γ + e j (e k ,γ ⋅ p j )a k ,γ∑∑m 2ε 0V j k ,γ ϖ k

}

(14)

where e, m, V, and ε0 denote the electric charge, mass of electron, volume of space, anddielectric function of vacuum, respectively. Vectors e, p, k, and r denote the unit vector forthe oscillatory direction of vector potential (which is parallel to the electronic potential
120

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications

vector E), momentum vector of electron, wave vector of electromagnetic wave, andposition vector in real space, respectively. Furthermore, γ (= 1 or 2), j (1 ≤ j ≤ N), ak, γ, andak, γ* denote the coordinate label perpendicular to k, index number of electron, annihilation
operator of photon, and creation operator of photon, respectively.
We define the initial and final state of the system as
Φ i = a n1 , n2 ,⋅ ⋅ ⋅, nk ,γ ,⋅ ⋅ ⋅ ,Φ f = b n1 , n2 ,⋅ ⋅ ⋅, nk ,γ ± 1,⋅ ⋅ ⋅(15)

where |a> and |b> denote the initial and final electronic state, respectively. Therefore, thematrix element for absorption of a photon by an electron in coordinate k, γ, is written asΦ f H (1) Φ i =ehik ⋅ rb ∑ e j (e k ,γ ⋅ p j ) a nk ,γ − 1 a k ,γ nk ,γm 2ε 0Vϖ kjnk ,γ heik ⋅r=b ∑ e j (e k ,γ ⋅ p j ) am 2ε 0Vϖ kj(16)Here, using the formula2

 sin x ∫−∞  x  dx = π∞(17)Equation 13 is rewritten with the assumption that |<Φf|H’|Φi>|2 is constant, as2

c f (t ) = Φ f H ' Φ n22πtδ (ϖ k − ϖ ab )
h2

(18)

which is known as Fermi’s golden rule. By substituting Eq. 15 into Eq. 18 with H’ = H(1),nk ,γ heik ⋅rc f (t ) =b ∑ e j (e k ,γ ⋅ p j ) am 2ε 0Vϖ k
j

2

2

2

⇔ c f (t ) ∝ be
ik ⋅r∑ e j (ek ,γ ⋅ p j ) am j2πtδ (ϖ k − ϖ ab )
h2
2

(19)

By taking the first term of the expansion (i.e., only dipole transition),1exp(ik ⋅ r j ) = 1 + ik ⋅ r j − (k ⋅ r j ) 2 + ⋅ ⋅ ⋅2(20)

and the relationship in an electronic system,b pj a =im( Eb − E a ) b r j a
h

(21)

121

the electronic dipole absorption is expressed from Eq. 19 as22

c f (t ) ∝ ( Eb − E a )2b e∑ (e k ,γ ⋅ r j ) a

(22)

j

Electronic dipole µ is introduced here asµ = −e∑ r j

(23)

j

with which the transition probability for Φi → Φf is expressed as22

c f (t ) ∝ ( E b − E a )2b ∑ (e k ,γ ⋅ µ) a

∝ µ⋅E

2

(24)

j

This equation indicates that the absorption probability is proportional to the square of µ⋅E.
4.1.6.3 Formulation for multiple dipole absorption by vertically aligned SWNTs
First, an x-y-z orthogonal coordinate is defined in which the z-axis is normal to thesubstrate and the light propagation vector k is within the y-z plane, as described in Fig. 4-4.
The angle between the k and the z-axis is denoted as θ (0 ≤ θ ≤ π/2). The orientation of the
SWNT axis vector l is described by ϕ (0 ≤ ϕ ≤ π/2) as the deviation angle of l from thez
Laser light (k)

ψ

p
s

ς

SWNT (l)

ϕ
θ

y

x

Fig. 4-4. Schematical representation of corrdinates (x, y, z) and angles (θ, ϕ, ψ, ζ) used in theformulation of multi-dipole optical absorption of polarized light propergaging in k by a SWNT withaxial vactor l.

122

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications
z-axis, and ψ (0 ≤ ψ ≤ 2π) is the rotational angle of a plane constructed by l and z-axes fromthe z-x plane. SWNT has assumed to have collinear dipole moment µ|| parallel to l, and thenon-collinear dipole moment µ⊥ perpendicular to l. The direction of µ⊥ is either radial ortangential to the SWNT circumference depending on the type of dipole considered. Sinceµ⊥ has all component around ζ (0 ≤ ζ ≤ 2π), the dipole located at the circumferential angle
ζ is expressed asµ ⊥ = µ ⊥(ζ =0) cos ζ + µ ⊥(ζ =π / 2 ) sin ζ(25)Here, µ||, µ⊥(ζ =0) and µ⊥(ζ =π/2) are written as
 − sin ϕ cosψ  sin ψ 
 cos ϕ cosψ 






µ|| = µ ||  sin ϕ sin ψ , µ ⊥(ζ =0 ) = µ ⊥  cosψ , µ ⊥(ζ =π / 2 ) = µ ⊥  − cos ϕ sin ψ 


 0 


cos ϕ
sin ϕ







(26)

and the electronic vectors for s- and p-polarization are given as Es = E(1 0 0)T and Ep = E(0cosθ sinθ)T, respectively.
The absorption of s-polarized light by the transition dipole perpendicular to the SWNT
axis is represented asΛS ⊥ (ϕ ,ψ , ζ ) = µ ⊥ ⋅ E s

2= µ ⊥ E 2 (sin 2 ψ cos 2 ζ + 2 cos ϕ cosψ sin ψ cos ζ sin ζ2+ cos 2 ϕ cos 2 ψ sin 2 ζ )(27)

Using the following relationshipsπ∫Λ (ϕ ,ψ ) = πS−⊥ΛS ⊥ (ϕ ,ψ , ζ )dζπ∫ π dζπ,∫ Λ (ϕ ,ψ )dψΛ (ϕ ) = π π∫ π dψ
S

−

⊥

S

⊥

(28)

−

−

S

Λ ⊥ is reduced toΛS ⊥ =1 2 2µ ⊥ E (1 + cos 2 ϕ )4(29)

In actual conditions, however, ϕ has a some distribution described by an unknown function
f(ϕ); then, the experimentally observed ΛS⊥’ is written asπ∫ f (ϕ ) ⋅ Λ (ϕ )dϕ = 1 µ E (1+ < cos ϕ >)
Λ '=
S

⊥

2
0

S

π

⊥

∫ f (ϕ )dϕ
2
0

2

4

⊥

2

2

(30)

123

On the other hand, absorption of s-polarized light by the transition dipole parallel to the
SWNT axis is represented as
ΛS || (ϕ ,ψ ) = µ|| ⋅ E s

2= µ || E 2 (sin 2 ϕ cos 2 ψ )2(31)

Similarly, using the relationships,π∫ Λ (ϕ ,ψ )dψΛ (ϕ ) = π π∫ π dψ
S

S

−

||

||

(32)

−

and then Λ ||(ϕ) is reduced toSΛS || (ϕ ) = µ|| ⋅ E S

2

=

1 2 2
µ || E sin 2 ϕ
2(33)

The experimentally observed ΛS⊥’ is written asπ∫ f (ϕ ) ⋅ Λ (ϕ )dϕ = 1 µ E < sin ϕ >
Λ '=
S

2
0

||

S

π

||

∫ f (ϕ )dϕ
2
0

2

2

2

2

(34)

||

Therefore, the absorbance of s-polarized light by whole dipoles measured by theexperiment ΛS’ isΛS ' =

11
Λ 0,|| < sin 2 ϕ > + Λ 0,⊥ (1+ < cos 2 ϕ >)
2
2

(35)

where µ||2 E2 ≡ Λ0,|| and µ⊥2 E2 ≡ 2 × Λ0,⊥ were defined. Since ΛS’ is function of only ϕ, it
provides a constant baseline regardless of θ.
The absorbance of p-polarized light by the transition dipole perpendicular to the SWNT
axis ΛP is written asΛP ⊥ (θ , ϕ ,ψ , ζ ) = µ ⊥ ⋅ E p

2= µ ⊥ E 2 (cosθ cosψ cos ζ − cosθ cos ϕ sin ψ sin ζ2+ sinθ sin ϕ sin ζ )

2

(36)

Similarly to the case of s-polarization (Eq. 28), the experimentally measured ΛP⊥’ isexpressed asΛP ⊥ ' (θ ) =

{

}

1 2 2
µ ⊥ E cos 2 θ (1+ < cos 2 ϕ >) + 2 sin 2 θ < sin 2 ϕ >4(37)Further, the absorbance of p-polarized light by the transition dipole parallel to the SWNT
axis ΛP is written as

124

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications

ΛP || ' (θ ) =1 2 2µ || E (cos 2 θ < sin 2 ϕ > +2 sin 2 θ < cos 2 ϕ >)4

(38)

Therefore, the absorbance of p-polarized light by whole dipoles measured by experiment
ΛP’ isΛP ' (θ ) =1
Λ 0,|| (cos 2 θ < sin 2 ϕ > +2 sin 2 θ < cos 2 ϕ >)2
1
+ Λ 0,⊥ cos 2 θ (1+ < cos 2 ϕ >) + 2 sin 2 θ < sin 2 ϕ >
2

{

}

(39)

In all, the experimentally measured values Λ’(θ=0) and Λ’(θ=π/2) are introduced using Eqs. 35
and 39 asΛ ' (θ =0 ) ≡ ΛP ' (0) = ΛS ' =1
1
Λ 0,|| < sin 2 ϕ > + Λ 0,⊥ (1+ < cos 2 ϕ >)
2
2

(40)

Λ ' (θ =π / 2 ) ≡ ΛP ' (π / 2) = Λ 0,|| < cos 2 ϕ > + Λ 0,⊥ < sin 2 ϕ >(41)

These Eqs. 40 and 41, of course, satisfy the requirement of total absorbance Λ0 as
Λ 0 ≡ 2 × Λ '(θ = 0 ) + Λ '(θ =π / 2 )= Λ 0, ⊥ (1+ < cos 2 ϕ >) + Λ 0, ⊥ < sin 2 ϕ > + Λ 0,|| < cos 2 ϕ > + Λ 0,|| < sin 2 ϕ >(42)= 2 × Λ 0, ⊥ + Λ 0,||
Therefore, the anisotropy α in the case of multiple dipole absorption is introduced in termsof Λ’(θ =0) and Λ’(θ =π/2) asα=Λ '(θ =π / 2 ) −Λ'(θ =0 )
Λ '(θ =π / 2 ) +2Λ '(θ =0 )=

Λ 0,|| − Λ 0,⊥
Λ 0,|| + 2Λ 0,⊥

⋅

(

)

1
3 < cos 2 ϕ > −1
2

(43)

4.1.7 Determination of optical anisotropy and bare optical absorption
cross-section of SWNTs
Figure 4-5a presents a portion of Fig. 4-2b as solid lines magnified for 0.5–3 eV. Since ateach energy point the absorbance increases well according to sin2θ, these spectra are
extrapolated into the absorbance at θ = 90° (Λ’(θ =π/2)), denoted by a dotted line. Figure 4-5b
shows α for 0.5–3 eV calculated using Eq. 43. In a lower energy region (< 2 eV), α
increases as the collinear absorption by the ∆µ = 0 inter-subband transition (ES11, ES22, andEM11) becomes dominant. In contrast, a lower value of α at a higher energy region is due to125

Absorbance1aΛ'(θ=π/2)

Λ'(θ=π/4)

0.5

Λ'(θ=0)Anisotropy , α

0
0.6

b

0.4
0.2
0
0

1

2

3

Energy (eV)Fig. 4-5. (a) Part of measured absorption spectra presentned in Fig. 4-2b for 0.3 - 3 eV byp-polarization from θ = 0° to 45° at a step of 7.5° (solid lines) and its extrapolation to the case of
θ = 90° (dashed line). (b) Calculated anisotropy α from Eq. 43.

the magnification of non-collinear dipoles that are perpendicular to the SWNT axis, whichis investigated in detail below, as well as due to the weakening of the ∆µ = 0 inter-subband
transition.
In order to determine the bare optical absorption cross section of SWNTs for bothparallel (σ||) and perpendicular (σ⊥) polarizations, one has to determine a nematic orderparameter S that is defined by

S=

(

)

1
3 < cos 2 ϕ > −1
2

(44)

In the present case, α cannot be substituted for S because α is rewritten asα=

σ || − σ ⊥⋅S < Sσ || + 2σ ⊥from Eq. 42 and using the Beer-Lambert law.
126

(45)

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications

In order to determine S, it is necessary to separate the dependence of the collinear dipole
on polarization from the entire spectra. As observed in Fig. 4-2b, the collinear absorption
peak at ~4.5 eV exhibits the clearest dependence on polarization. Hence, based on theobserved absorption maxima of either Im{ε} or Im{-ε-1} at ~2.8, 4.0, 4.4, and 5.2 eV fromthe reflectance measurement of a SWNT film by Lee et al. [32], Lorentzian curve fitting
was performed for 2.5–6.0 eV, as described below.
Figure 4-6 shows the decomposed spectra obtained by setting four peaks at 2.8, 4.0, 4.5,
and 5.3 ± 0.1 eV. Their widths were practically fixed at 4.0, 1.3, 0.98, and 1.72 ± 0.02 eV,
respectively. It was confirmed that the same peak positions and widths also decompose theabsorption spectra of other SWNTs with different diameters. Figure 4-6b is the Lorentzian
fitting for the absorption spectra of a randomly oriented SWNT film shown in Fig. 4-1(i)Absorbance

2

1

0
0
0.4
Absorbance

a

b

2

4

6

4

6

Energy (eV)

0.2

0
0

2

Energy (eV)Fig. 4-6. (a) Measured absorption spectra presetned in Fig. 4-2b from θ = 0° to 45° at a step of 7.5°
by p-polarization and their Lorentzian fitting with four curves. See text for peak locations andwidths. Arrows indicate the direction of change of each Lorentizan component from θ = 0° to 45°.
Dotted lines overlapping the measured spectrum repreesnts sum of these Lorentzian curves. (b)Lorentzian curve fitting performed to randomely oriented SWNT film corresponds to the spectrum(i) in Fig. 4-1 using the same peak position and widths.

127

that has a smaller diameter than the case of Fig. 4-6a. The spectra of Fig. 4-6b can also be
fitted well according to this scheme.
Figure 4-7a plots the change in each Lorentzian amplitude. The baseline of the
non-collinear peak at 5.25 eV may have some ambiguity because it is located at the borderof the measured range and could be affected by the collinear dipoles at a higher energy. The
plot for the peak at 4.5 eV is fitted with sin2θ, and S ≈ 0.75 and <ϕ> ≈ 24° are calculated
from Eqs. 11 and 13.
The molar absorption cross sections of this SWNT film sample, parallel to (η||) andperpendicular to (η⊥) the z-axis, are directly determined from Fig. 4-5a using the density of
C atoms in the current vertically aligned SWNT film, which is ~3.0 × 103 mol/m3 (3.5 ×
10-2 g/cm3) as estimated by SEM and TEM measurements. The molar cross section η was
defined in this study based on the definition of absorbance Λ = –log10T = η⋅n⋅l, where T, n,
and l are the optical transmission, molar concentration of C, and film thickness,
respectively. Therefore, the bare optical absorption cross section of the SWNTs parallel toAbsorbance2a

4.5 eV

5.3 eV1

2.8 eV
4.0 eV0030

θ (deg)60

90

2

σ (m /mole C)

b
200

σ||
100
σ_|_
0
0

4
6
Energy (eV)Fig. 4-7. (a) Dependence of each Lorentzian amplitude on the incident angle θ. Curves fitted by either
sin2θ or cos2θ are also shown. (b) Bare optical cross-sections parallel to (σ||) and perpendicular to (σ⊥)
the SWNT axis for 0.5 - 6 eV calculated using Eqs. 3, 4.

128

2

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications(σ||) and perpendicular to (σ⊥) the SWNT axis can be calculated by the relationships
derived from Eqs. 9, 10, and 13 as1
3

σ || = 2η ⊥ + η || +13σ ⊥ =  2η ⊥ + η|| −2(η || − η ⊥ )S
η|| − η ⊥ 
S




(46)

(47)

Figure 4-7b shows σ|| and σ⊥ for 0.5–6 eV. The ∆µ = 0 inter-subband absorption is seenclearly in σ|| as observed in Ref. 10. In the higher energy region (above 3 eV), σ|| attains amaximum (~30 m2/mole C) at 4.5 eV and σ⊥ attains its maximum (~10 m2/mole C) at 5.25
eV. It should be noted that even in the low energy region (<3 eV), there exists a small but
non-zero σ⊥, which is partly due to the extension of the Im{-ε||-1} π-plasmon at 5.25 eV into
the lower energy region. In addition, depolarization effects in a SWNT for cross-polarized
light, as shown by Ajiki and Ando [10], can be imperfect when SWNTs are bundled,leading to inter-subband absorption transitions where ∆µ = ±1 [33], as discussed in detaillater in Section 4.2. Therefore, the existence of multiple absorption dipoles, both paralleland perpendicular to the SWNTs axis, should be taken into account in opticalmeasurements, even for the inter-subband energy region.

4.1.8 Summary of anisotropy optical properties of SWNTs
In summary, the anisotropic optical absorption properties of SWNTs for 0.5–6 eV were
elucidated based on the polarized optical absorption measurements of a vertically aligned
SWNT film. This is the first study investigating the absorption features of SWNTs at 4.5
and 5.25 eV and their polarization dependence. In contrast to earlier theoretical studies[11,12], the positions of the absorption peaks near 5 eV including the π-plasmon did notdisperse depending on the incident polarization, diameter, and chirality of SWNTs. The
method of determining an order parameter for an aligned SWNT film was presented byextracting the collinear absorption element at 4.5 eV; then, the bare optical absorption crosssections for both parallel and perpendicular polarizations were determined up to 6 eV. It
was found that the tail of the non-collinear absorption peak at 5.25 eV appreciably
contribute to the σ⊥ in the inter-subband transition region (< 3 eV).
129

For practical purposes, the peaks at 4.5 and 5.25 eV provide convenient quantitativeindexes to evaluate the degree of alignment of SWNTs. Due to the fact that these peaks
were observed at almost the same positions regardless of the diameter and the sample
preparation method, they are attributed to the maxima in Im{ε⊥} (~4.5 eV) and Im{-ε||-1}(~5.25 eV) reflecting the optical properties of graphite. These results suggest an importantpossibility of investigating the unresolved optical properties of graphite in the direction
parallel to the c-axis by simple measurements of the optical absorption of aligned SWNT
films, as an array of graphene cylinders.

130Chapter 4  Anisotropic optical properties of SWNTs and their optical applications

4.2 Polarization dependence of Raman scattering characteristics fromvertically aligned SWNT film
4.2.1 Introduction − Role of Raman scattering in SWNT analysis
Resonant Raman scattering (RRS) spectroscopy has been an important tool to obtainstructural information including quality and diameter, as well as distinguishing between
metallic and semiconducting single-walled carbon nanotubes (SWNTs) [2,34]. In the radial
breathing mode (RBM) that appears in lower frequency region, the resonant nature ofelectronic transitions between van Hove singularities in the valence and conduction bands
has been utilized to experimentally probe for chiral distribution of SWNTs [19,35-37]. It
was demonstrated experimentally by Jorio and co-workers [38] that, from their RRS
measurements on G-band modes of isolated SWNTs, the possibility of ∆µ = ±1 transitions
should be taken into account in addition to the usual ∆µ = 0 transition (µ denotes the
cutting-line index [2,38]). Understanding the significance of the ∆µ = ±1 transition isimportant because it crucially affects the interpretation of RBM spectra needed for theassignment of chirality as well as the distinction between metallic and semiconducting
SWNTs based on the Kataura plot [20]. Theoretical work by Grüneis and co-workers [33]indicated that the ∆µ = ±1 transition is induced by absorption of light polarized across the
SWNT axis, and hence polarized Raman analysis should be effective to study this subject.
So far several studies employing polarized RRS on SWNTs, either bundled or isolated,have been reported [13,38-42]. While some of them focused solely on the G-band’s
intensity and structure by changing the polarization direction [38,39,41], a small number of
papers investigated the dependence of the RBM by the change of polarization. Hwang et al.
[13] and Duesberg et al. [40] performed polarized RRS experiments on nearly isolated
SWNTs on a glass plate and presumably bundled SWNTs aligned in a melt-spun PMMA
fiber, respectively, and showed that the scattering intensities of both RBM and G peaks are
maximized when the polarization of the light is parallel to the SWNT axis and aresuppressed when perpendicular. In both reports the change of only one isolated RBM peak
was presented at a fixed laser wavelength. Grüneis et al. [42] recently reported, from their
Raman measurement on randomly-oriented SWNT bundles, unexpected RBM peaks
between ES22 and EM11 (subscript number denotes serial number of van Hove singularities)
that apparently deviated from their tight-binding-based Kataura plot as well as from thedata based on photo-luminescence [43]. They reported that the unexpected RBM peaks
were an observation of ∆µ = ±1 excitations caused by the absorption by SWNTs of131

perpendicularly polarized light, because the dipole selection rules give different absorptionenergies for light with parallel and perpendicular polarization [33,42]. They discussed that,in contrast to isolated SWNTs, bundled SWNTs could absorb the cross-polarized light due
to an imperfection of the “depolarization effect” that was predicted by Ajiki and Ando [10].
Since all the RBM peaks measured from their randomly aligned and bundled SWNTs wereplotted [42] the peaks had not been unambiguously classified especially in the higher
energy region above EM11 on the Kataura plot, where the Eii plots start to broaden andoverlap each other [20].
In Chapter 3, a method to synthesize vertically aligned SWNT films directly on thesurface of quartz substrates [16] using the alcohol chemical vapor deposition (ACCVD)
method [17,44] has been developed. Since this SWNT film has a macroscopic thickness(approximately 5 µm) and is uniform over the substrate (25 × 25 mm2) [16,45], it is idealfor optical measurements including Raman scattering analysis. In this Section, it isdemonstrated that the spectral shape of the RBM from this aligned SWNT film exhibits aremarkable dependence on the relationship between the light polarization vector (e) and the
SWNT axis direction (l). The obtained spectra was analyzed quantitatively and it isconcluded that each specified peak falls clearly into one of two groups, where the peaks in
one group dominate for the case of e ⊥ l and the others dominate for e // l. The grouping of
RBM peaks is also observed by the difference in behavior toward an adsorption ofmolecules and a change in the incident laser power. These results evidence the e // l ande ⊥ l peaks are ∆µ = 0 and ∆µ = ±1 resonance, respectively. From the experimental
investigations performed in this report, both types of RBM peaks in a higher energy range(1.96 - 2.54 eV) that are often used in RRS analysis of SWNTs are unambiguously

distinguished, over wide range of tube diameter (0.8 - 1.8 nm).

4.2.2 Raman scattering measurement
When performing Raman scattering measurements a micro-Raman setup (SekiTechnotron, STR-250) composed of an optical microscope (Olympus, BX51), a
spectrometer (Chromex, 501is) and a CCD (Andor, DV401-FI) was used. Laser
wavelengths of 488 (2.54), 514.5 (2.41) and 633 nm (1.96 eV) were used. The
measurements were done in back-scattering configuration with an incident laser power of
0.2 - 0.5 mW with a spot size ≥ 5 µm at the sample surface and a 50× objective lens,unless otherwise stated. The energy density used in this study ( ≤ 2.5 × 103 W/cm2) is132

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications

chosen to be sufficiently low compared with that typically used in micro Raman
measurement on SWNTs (e.g. 1 × 106 W/cm-2 in Ref. 21), in order to avoid any unexpected
effects on Raman spectra caused by laser heating [47,48]. Specifically, we monitored thelocation of the G+ band (at approximately 1593 cm-1 at room temperature [48,49]) to makesure it did not descend below 1592 cm-1 (or above 100°C [48,49]) during the measurements.
The laser light incident on the sample was linearly polarized by a polarizer put in the pathof the laser light. Scattered light was collected back into the microscope, passing a half
mirror and then a depolarizer before entering the spectrometer. In some experiments (in Fig.
4) we placed a polarizer just before the depolarizer in order to check the spectral
dependence on the polarization of scattered light. Before every series of measurements the
spectrometer was calibrated with sulfur (153.8, 219.1 and 473.2 cm-1) and naphthalene(1382.2 and 1576.6 cm-1) characteristic peaks. All the Raman spectra shown in this Section
is an arithmetic average of more than 5 measurements within the same sample.

4.2.3 Experimental results and analyses
4.2.3.1 Raman spectrum dependence on laser polarization
Figure 4-8 shows an FE-SEM micrograph of the vertically aligned SWNTs taken fromthe side at the fractured edge of the substrate. The film thickness is around 5 µm andFig. 4-8. A cross-sectional FE-SEM image of a vertically aligned SWNT film at a fractured edge ofthe quartz substrate taken from tilted angle (top) and horizon (bottom)

133

Fig. 4-9. Schematical description of relationships between the laser propagation direction (k), the laser
polarization direction (e), and the SWNT axis direction (l) in the measurement.

aligned bundles of SWNTs are visible, which typically have diameter of approximately 15
nm as shown in Fig. 3-3. The overall density of SWNTs has been estimated to be ≈ 1.0 ×
1017 m-2 [16]. From TEM observations, it has been confirmed that no MWNTs are present,
and almost all SWNTs are clean i.e. free of amorphous carbon [18]. According to TEM
measurements this specimen has a diameter distribution ranging from d = 0.8 ~ 3.0 nm,
with an average diameter dav ≈ 1.9 nm and a standard deviation σ = 0.4 ~ 0.5 nm [18]. This
distribution is exceptionally broad compared to typical arc-discharge and laser-furnace(within ± 0.2 nm) [20], HiPco SWNTs (dav = 0.98 nm, σ = 0.2 nm) [50], and ACCVD
SWNTs grown on zeolite powder at 650°C [51], and therefore it is suitable for probing awide range of chiralities at the same time.
In the following, 4 different configurations of the laser propagation direction (k), the laser
polarization direction (e), and the SWNT axis direction (l) are employed as schematized inFig. 4-9. The “From top” configuration is k // l and e ⊥ l, where laser is incident
perpendicular to the substrate (or the SWNT film). In the “perpendicular” and “parallel”
configurations, the relationships are {k ⊥ l and e ⊥ l} and {k ⊥ l and e // l}, respectively, andin the “45°” configuration the angle between e and l is 45° while maintaining k ⊥ l. In thelatter 3 cases, the quartz substrate supporting the SWNT film was broken and stood on its
edge using adhesive tape in order to measure on the cross-section of the film.
Figure 4-10 shows RBM spectra taken in (i) from top, (ii) perpendicular, (iii) 45° and (iv)parallel configurations for 488, 514.5, and 633 nm laser wavelengths. On the top of eachpanel, corresponding diameter scale calculated by the formula ‘d (nm) = 248 / ν (cm-1)
134

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications[36]’ is presented. In the 488 nm case, the high frequency spectra including D and G bands
are also shown. All the RBM peaks were normalized by the height of G+ band at 1593 cm-1.
The G+ band was used for the normalization of the spectra assuming it represents resonance,
although it is known that the G+ peak as well as G- peak are composed of A1 and E1 modes
located very close (~ 2 cm-1) to each other [38]. At each wavelength, the spectra of cases (i)and (ii) (where e ⊥ l) show the same shape while that of case (iv) (where e // l) exhibits aremarkably different spectral shape. The spectra in case (iii) lie in the intermediate between(i) and (iv). It is obvious that some peaks are observed with certain intensities only in theFig. 4-10. RBM spectra measured by 488, 514.5, and 633 nm lasers for different incident
configurations (i - iv, see Fig. 4-9). G band spectra taken at 488 nm are also shown. The RBM spectra
were normalized by the corresponding G+ height and decomposed into Lorentzian curves bymaintaining the FWHM values within a spectrum. Asterisks denote the peaks dominantly observed inparallel polarization condition. The oscillatory line on the baseline denotes differential between
experimental spectrum and sum of Lorentzian curves.

135

e ⊥ l case and diminish in the e // l configuration, while the other group behaves oppositely.

This is especially remarkable for the 488 and 514.5 nm cases.
These spectra are decomposed into Lorentzian curves, keeping the full-width
half-maximum (FWHM) of the peaks within each spectra the same. For 633 nm we
employed the location of ES22 and EM11 peaks in 180 - 300 cm-1 presented by Strano [52]from the photoluminescence experiments: For the range below 180 cm-1, due to the absenceof data, we set peak locations so that the sum of the Lorentzian peaks consistently fits allcases. As for 488 and 514.5 nm, since no consistent set of data has been reported in thehigher energy region for ES33 and ES44, we performed decomposition using the least numberof peaks necessary for consistent fitting. We allowed ±1 cm-1 freedom to each peak’s
location based on the resolution of our Raman measurement system.
A slight downshift of G+ peak from 1593 to 1592 cm-1 is seen in the “parallel”
configuration due primarily to heating of the SWNTs by the laser, which is more significant
when e // l because light absorption is much enhanced [18]. It is noted that even when theincident laser intensity is further lowered (laser power of 0.1 mW with a spot size of ≈ 7 µm,
corresponding to ≈ 250 W/cm-2), the measured spectral shapes for (i) ~ (iv) are essentiallythe same as those shown in Fig. 4-10, with only a lowered signal-to-noise (S/N) ratio inthese cases. Therefore, the spectral changes depending on the measurement condition in Fig.
4-10 are not those induced by the laser heating.

136

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications

Fig. 4-11. RBM spectra taken at 488 nm with laser light incident (a) from side and (b) from top of thefilm. A polarizer was inserted in a scattering light path except the case denoted “-All”. The “X-Y”
description represents the polarization directions of incident and scattered light.

Figure 4-11 shows RBM spectra measured by polarized 488 nm light. To represent thepolarization of both incident and scattered light we employ the “X-Y” description often
used in polarized Raman studies [39-41]. A polarizer was inserted in the scattering light
path, as stated above, except the “-All” cases. In Fig. 4-11a “V” and “H” denotepolarization perpendicular and parallel to the SWNT axis, respectively. The intensity ratioof {V-V : V-H : H-H : H-V ≈ 40 : 15 : 100 : 15} at the G+ band indicates the cross-term“V-H” and “H-V” (either intrinsically or due to disorder in the SWNT alignment) is so
weak that the spectra of “V-all” and “H-all” are essentially the same as “V-V” and “H-H”.
Figure 4-11b shows the same measurement but the light is incident perpendicularly to thesubstrate in the “from top” configuration, which confirms that in the case of k || l thescattering spectra are independent of “X-Y” relation, as expected.
Figures 4-12a and 4-12b show the change of the height of selected Lorentzian peaks
shown in Fig. 4-10 divided by the G+ intensity among the “from top” - “45°” - “parallel”
conditions for 488 and 514.5 nm. The ordinate for each peak is normalized by the value inthe case of “from top”, to show the grouping behavior of the RBM peaks toward thepolarization. The collective peak at 185 cm-1 for 514.5 nm is decomposed into two adjacentpeaks of at 183 and 188 cm-1. Although some ambiguity remains in the quantitative
decomposition, the 188 cm-1 peak is recognized to be e // l peak based on Fig. 4-10. The
137

peaks apparently associated with the e // l configuration for 488 nm and 514.5 nm are {160and 203 cm-1} and {152 and 188 cm-1}, respectively. As for the 633 nm case, since nearlya From top 45°
42488 nmParallel
160 cm–1

203 cm

–1

2

–1

0

145 cm–1
180 cm–1
257 cm–1
242 cmNormalized peak intensity [–]Normalized peak intensity [–]20 ES22 and EM11 peaks are plotted by Strano [52] within 1.96 ± 0.1 eV in the 180 - 300
cm-1 range, it was difficult to unambiguously classify each peak into the either of the twogroups according to our decomposition method: however, at least the peaks observed at 148,
164, and 217 cm-1 should be the e // l peaks as identified in Fig. 4-10.

b From top

45°

Parallel

514.5 nm

152 cm–1

188 cm–1

1–1

259 cm–1
136 cm268 cm–1 234 cm

0

166 cm–1
225 cm–1–1

Fig. 4-12. The change in intensities of selected RBM peaks divided by the G+ band among “from top” “45°” - “parallel” conditions for (a) 488 and (b) 514.5 nm. The ordinate was normalized by the values of
the “from top” condition.

138

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications

4.2.3.2 RBM peak behavior by molecular adsorption
It should be noted that in the “from top” measurement, the e ⊥ l peaks can be suppressedby adsorbing a certain kind of molecules onto the SWNTs. The CVD chamber used for

SWNT growth (refer to Fig. 2-15) is evacuated by an oil-free pump (ULVAC, DVS-321).
However, if the specimen is placed in a chamber evacuated by ordinary oil pumps (e.g.,
ULVAC GVD-050, ALCATEL 2015I) in our laboratory, the spectrum shows the samechange as that observed in Fig. 4-10 from (i) to (iv). Figure 4-13 shows this change
measured in the “from top” condition with 488-nm light. The spectrum of an as-synthesized
sample (Fig. 4-13a) changes into that shown in Fig. 4-13b after evacuation for 1 h by the oilpump. This spectral change is reversible; this is because the spectrum of a different
molecule-adsorbed sample (Fig. 4-13c) prepared by the same method is readily recoveredby heating it at 200°C for 1 h in the CVD chamber evacuated by the oil-free pump (Fig.
4-13d). Although have not yet determined the adsorption molecule species and themicroscopic adsorption details, because of its relatively prompt recovery at low temperature(200°C), this easily reproducible result implies that this is a physisorption of someoil-derived molecules diffused from the oil pumps. A slight blue shift of the RBM
frequency (~3 cm-1) observed in Fig. 4-13b and c, which is thought to occur due to ahardening of the radial breathing motion of SWNTs by adhered molecules, agrees with thecurrent discussion.
Diameter (nm)
2

1

0.9

0.8

Intensity (arb.units)(a) As–synthesized(b) Evacuated by oil pump(c) Evacuated by oil pump(d) Evacuated by dry pumpfor 1 h at 200 °C

100(a) As–synthesized

200

–1

300

Raman Shift (cm )1200(b) Evacuated by oil pump

1400

1600

–1

Raman Shift (cm )Fig. 4-13. The change in RBM spectra measured in the “from top” condition by 488 nm light. Spectraare (a) the as-synthesized sample and (b) after evacuation by an oil-pump for 1h at 200°C. The
original spectrum of a different molecule-adsorbed sample (c) is recovered after heating it at 200°C
for 1 h in a CVD chamber evacuated by an oil-free pump (d). The spectra are normalized by theheight of the G+ peak. The right panel shows corresponding tangential mode spectra of (a) and (b).

139

The right panel of Fig. 4-13 shows a higher frequency region of the left panel and no
essential change between the tangential modes of Fig. 4-13a and b. However, since theintensity of the BWF peak [53] is weak before adsorption (Fig. 4-13a), we cannot perfectly
negate the possibility of chemisorption by judging the decrease of BWF, as observed by
Strano et al. [54]. Furthermore, it was confirmed that a mere wetting of the as-synthesized
random SWNT ropes grown on catalyst-supporting zeolite powder by methanol decreases
the peak at 180 cm-1 as measured by 488-nm light (results not shown), similarly to theobservation in Fig. 4-13. Therefore, it is certain that the adsorption of a particular molecule(presumably organic) diminishes the RBM peaks that were preferentially observed for e ⊥ l,while the peaks that are dominant in the e // l configuration are almost unaffected.
Further, a series of experiments were performed using optical absorption measurements
in order to support the above experimental results. First, the vertically aligned SWNT film
on a quartz substrate (whose Raman spectra are shown in Fig. 4-14a) was adsorbed by themolecules and its optical absorption spectrum was measured (Fig. 4-14b). The identicalspecimen was then returned to its original state by the method stated above, and the opticalabsorption spectrum was measured again (Fig. 4-14c). The effect of adsorption on optical

Intensity (arb.units)(a) As–synthesized

Absorbance

0.4(b) Adsorbed(c) Recovered

100

*

200
300
–1
Raman Shift (cm )

(c)

0.2

*
(b)

1000

2000

Wavelength [nm]Fig. 4-14. Optical absorption spectra of (b) an adsorbed sample and (c) the same sample after
recovery by heating in vacuum at 200°C for 1 h. In the inset are corresponding Raman spectra taken
at 488 nm in the “from top” configuration, along with (a) the original spectra before adsorption, towhich all spectra are normalized by the height of the G+ band. Asterisks indicate the switching
noise of the spectrophotometer.

140

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications

absorption is more significant in the low energy region, closer to Fermi level (EF), as
reported in Ref. 55. This observation is interpreted and discussed in a later subsection.
4.2.3.3 RBM peak dependence on laser intensity
The grouping behaviors in RBM peaks are observed in several experimental situations.

The most notable of these behaviors is the dependence of the RBM spectral shape on the
input laser power. Figure 4-15a shows the change in the RBM spectrum measured for the“from top” configuration with a 488-nm laser at an incident laser intensity ranging from0.75 to 2.42 mW, whose spectral change is reversible to the laser intensity. This change
exhibits an apparent similarity to that observed in Fig. 4-13 for molecular adsorption.
Figure 4-15b plots the height of each Lorentzian-decomposed peak normalized by the peak
at 0.75 mW (ordinate) against the input laser power (abscissa). While the intensities of the
160 and 203 cm-1 peaks for e // l absorption increase linearly with the laser power, the e⊥lpeaks seem insensitive to the laser power, as though they were photosaturated. Although
the mechanism of this insensitiveness is yet to be determined, this result indicates thecertainty of a recognizable difference in the electronic characteristics between the two typesof RBM peaks.
Figure 4-15a shows that some of the peaks red-shifteds due to the heating by the laser.
Figure 4-15c plots the relative shift of each RBM peak against that of the G+ band, bothfrom the case of 0.75 mW. While the e // l peaks exhibit a linear red shift of frequency as
Diameter (nm)Intensity (arb.units)a0.75 mW

1.51 mW

2.42 mW

100

200

4

0.8

300

–1

Raman Shift (cm )b–1

203 cm–1
160 cm2–1

145 cm–1
180 cm–1
257 cm–1
242 cmc–1

0.9

Shift of RBM peak [cm ]1Normalized peak intensity [ – ]

2

0

–2

–1

180 cm–1
257 cm–1
145 cm–1
243 cm160 cm–1–1

203 cm0012

Laser power [mW]

3

–6

–4

–2

–1

0

Shift of G–peak [cm ]Fig. 4-15. (a) Spectral change of RBM peaks by changing the laser power intensity from 0.75 to 2.42
mW, using 488 nm light in the “from top” configuration. The spectra were normalized by the G+ band.
(b) The intensity variance of each Lorentzian-decomposed RBM peak over the incident laser power.
Ordinate values were normalized by those in the case of 0.75 mW. (c) The relationship between thefrequency downshift of RBM peak and that of the G+ peak by heating of SWNTs, both from the case of
0.75 mW.

141

the temperature rises, the e ⊥ l peaks do not exhibit a noticeable shift. This is considered tobe caused by the difference in the manner of heating by the light incident on the e // l ande ⊥ l cases, because the light absorption of the former is several factors higher than the latter[18]. The observations in Fig. 4-15 are further explained in the following subsections.

4.2.4 Discussion and interpretation of obtained data
4.2.4.1 Interpretation of data based on ∆µ = ±1 transition by cross-polarized light
The reason of why only one group of RBM peaks survives in the course of molecularadsorption in Figs. 4-13 and 4-14 can be interpreted as follows. The peaks observed in the e// l configuration (corresponding to the ES33 and ES44 peaks with energies of 2.41 and 2.54eV) survive, because they were well lower than EF (i.e., approximately 1.21 and 1.27 eV
below EF, respectively) and hence almost uninfluenced by the charge-transfer effect [54]caused by molecular adsorption. On the other hand, the peaks observed in the e ⊥ lconfiguration diminish when adsorbed because they were close to EF and hence likely to be
subjected to the charge transfer. This proves that the e ⊥ l peaks obtained thus far have their
origin in ∆µ = ±1 resonance (such as EM12, ES12, ES24, etc.), which was predicted by Grüneis
et al. [33] who also observed a few peaks in the lower energy region between ES22 and EM11
from a measurement of randomly oriented SWNT ropes [42]. The reason for the differencein the excitation selection rule for optical absorption by SWNTs between parallel- andcross-polarized lights is briefly explained as follows. The transition probability isrepresented here as
W (k ) ∝ p ⋅ Ψ c (k ) ∇ Ψ v (k )

2

(48)

This is obtained by replacing p and ek,γ with ∇ and P, respectively, in Eq. 19 in Section 4.1
as
p = ih∇,P=e

ik ⋅ r j⋅ e k ,γ(49)

The absorption matrix element for k → k’ transition was given by Grüneis et al. [33] asN N i ( k − k ')⋅ R Bjjji ( k − k ')⋅ R Aj∗
Ψ c (k ) ∇ Ψ v (k ' ) ∝ ∑ e
U z (2π )v g − ∑ e
U z (2π )v g NN
j =1
 j =1


142

(50)

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications

Here, Uz (ϕ) denotes the rotational matrix around the z-axis by the degree of ϕ, and vg
denotes the transition dipole moment vector given by [33]3v g ∝ U y (−π / 6 + θ )∑ e ik '⋅bi bi

(51)

i =1

in which θ (0 ≤ θ ≤ 30°) denotes the chiral angle of the SWNT under consideration. The
atomic coordinate vectors (or symmetry vectors) RAj and RBj are defined as the position of
the jth atom with respect to the unit cell origin by translational vectors RA and RB, as
described in Fig. 4-16a for the case of (4, 2) SWNT. The red and blue circles in the figure
denote non-equivalent atoms in the unit cell of graphite. It is noted that RAj and RBj in Eq.
50 are periodic of N atoms, which are equal to the number of hexagons in the unit cell of
the SWNT. bi is a vector connecting an atom to its neighboring non-equivalent atom, as
schematized in Fig. 4-16b. Therefore, vg is constant when chirality is given.
a. When k - k’ = K (∆k = K)
Equation 50 can be rewritten asN N iK ⋅ R Bjj ∗iK ⋅ R A
Ψ c (k ) ∇ Ψ v (k ' ) ∝ ∑ e j U z (2π )v g − ∑ e j U z (2π )v g NN
j =1
 j =1


a

b

(52)

θ

T
1

b1

RA

b3 3
RB

2

b2

(1 ≤ i ≤ 3 )Ch
Fig. 4-16. (a) Schematic description of atomic coordinates represented by RAj and RBj (1 ≤ j ≤ N).
Red and Blue circles denote non-equivalent atoms in the unit cell of graphite. T and Ch denotetranslational and chiral vector of (4, 2) SWNT and the shadowed area denotes its unit cell. (b)Schematic for the vectors bi that connects neighboring non-equivalent atoms. θ (0 ≤ θ ≤ 30°) is
chiral angle of the SWNT.

143

Using the following relations,1(−t 2 b1 + t1b2 )N

R = pa1 + qa 2 ,K=

 3 1, a,
a1 = 
22


 3 1
,− aa 2 = 
2
2


(54)

 1  2π
 1
 2π
,1
, b2 = ,−1
b1 = 
 3  a 3
 a
R and K can be expressed as

(55)

1 
 1
2π  −
t2 +
t1 
K=
3
3 

aN 

− t 2 − t1a  3 p + 3q 
R = 
,2  p − q 

(53)

(56)

Therefore,
K ⋅R =

2π(t1q − t 2 p ) = 2π
NN

(Q t1q − t 2 p = 1)(57)

(1 ≤ j ≤ N , 0 ≤ ϕ j ≤ 2π )(58)

Since Rj = jR (1 ≤ j ≤ N),
K ⋅ R j = 2π

j
≡ϕj
N

Equation 52 can be written using this relationship asN N iϕ Biϕ A∗Ψ c (k ) ∇ Ψ v (k ' ) ∝ ∑ e j U z (ϕ Bj )v g − ∑ e j U z (ϕ jA )v g j =1
 j =1
(59)

When the first term of Eq. 12 and its real part are considered, this can be written as
cos ϕiϕ j
e U z (ϕ j )v g = ∑ cos ϕ j ⋅  sin ϕ
∑
j =1
j =1
 0
N

− sin ϕ

N

cos ϕ
0

0 vx  N vx cos 2 ϕ 
0 v y  = ∑ v y cos2 ϕ 
j =11  vz 
0



(60)

Here, the relationships
2π

2π

0

0

∫ cos ϕdϕ = ∫ sin ϕdϕ = 0,2π2π

∫ cos ϕdϕ =∫ sin ϕdϕ = π ≠ 0
0

2

2

0

(61)

were used. The second term of Eq. 12 is also calculated in a similar manner.
Equation 60 indicates that the ∆k = K transition is induced solely by the cross-polarized
light on the SWNT axis, and not by the light polarized parallel to the axis.

144

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications

b. When k - k’ = 0 (∆k = 0)
Similarly to the above case, Eq. 50 in this case can be rewritten as
N
N
j
j
∗
Ψ c (k ) ∇ Ψ v (k ' ) ∝ ∑ U z (2π )v g − ∑ U z (2π )v g NN
j =1
 j =1cos ϕ − sin ϕ 0 v x  N v x cos ϕ − v y sin ϕ   0 N= ∑  sin ϕ cos ϕ 0 v y  = ∑ v x sin ϕ + v y cos ϕ  =  0 
j =1
j =1
 0

  Nv z vz
01  v z (62)which means that ∆k = 0 transition is induced solely by the light polarized parallel to the
SWNT axis and not by the cross-polarized light on the axis.
c. When k - k’ = K0 (K0 ≠ 0, K0 ≠ K)
Using Eq. 56,

K0 ⋅ Rj =a2{ 3( p + q)k + ( p − q)k }≡ λ
0x

(63)

0y

Therefore,NΨ c (k ) ∇ Ψ v (k ' ) ∝ ∑ eiλU z (2π
j =1

j
)v g
N

vx cos ϕ cos λ − v y sin ϕ cos λ  0= ⋅ ⋅ ⋅ = ∑ vx sin ϕ cos λ + v y cosϕ cos λ  = 0
j =1 0vz cos λN(64)Here, the relationships
2π

2π

0

0

∫ cos ϕ cos λdϕ =∫ sin ϕ cos λdϕ = 0(λ ≠ ϕ )(65)

were used. Equation 64 indicates that no transition occurs if ∆k = K0 (K0 ≠ 0, K0 ≠ K). The
above results indicate that the selection rule for transition varies depending on thepolarization of the incident light. If the polarization is parallel to the axis, a ∆k = 0 (i.e., ∆µ= 0) transition occurs; however, if it is perpendicular to the axis, a quasi-nonvertical ∆k = K(i.e., ∆µ = ±1) transition occurs. The resonant energy is different in both cases, as
schematically shown in Fig. 4-17 for (8,7) and (10,10) SWNTs.

145

(8, 7)d = 1.03 nm(10, 10)d = 1.375 nm

3

4
3

ES24
2

EM12

2

EM22

ES44

z

1

∆k = K(∆µ = ±1)

1

EF1

∆k = 0(∆µ = 0)
y

2

1

x

3

SWNT

2

4

3

2.54 eV

Energy Separation (eV)Energy Separation (eV)Fig. 4-17. Schematic for ∆µ = 0 and ∆µ = ±1 transitions for the case of ∆E = 2.54 eV for (8,7) and(10,10) SWNTs. The DOS presented here were calculated by tight-binding method with parameters
γ0 = 2.9 eV, ac-c = 0.144 nm, and s = 0.129.

2.4

2.4

2.4

ES44

ES33

EM11

2

2

2

1.6

1.6

1.6

2.4

2.4

2.4

ES35 ES53
2

1.6
100

EM12 EM21
2

150

200

250
–1

Raman shift (cm )

1.6
100

ES24 ES42
2

150

200

250
–1

Raman shift (cm )

1.6
100

150
200
–1
Raman shift (cm )250

Fig. 4-18. The locations of several unambiguous e // l (∆µ = 0) peaks marked with circles and e ⊥ l(∆µ = ±1) with crosses on a Kataura plot calculated from tight-binding (solid symbols) andGW-method (open symbols). Panels in the upper row represent the plots for the ∆µ = 0 transition
while panels in the lower row correspond ∆µ = ±1.

146

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications

In Figure 4-18, several unambiguous e // l (i.e., ∆µ = 0) peaks are indicated in Fig. 4-18
by circles and e ⊥ l (i.e., ∆µ = ±1) peaks are indicated by crosses on a Kataura plot
calculated using the tight-binding (solid symbols) and GW methods [56] (open symbols).
The tight-binding DOS was calculated with γ0 = 2.9 eV, ac-c = 0.144 nm, and s = 0.129 [57].
It should be noted that these Kataura plots differ (especially for semiconducting SWNTs)from the plot based on fluorescence measurements [43]; however, it is still quantitatively
effective to discuss the transition energies of metallic as well as semiconducting SWNTs
for the higher energy regions (ES33 and ES44) where the availability of the data obtained byfluorescence measurements are fairly limited. The upper row of Fig. 4-18 shows the plots
for the ∆µ = 0 transition, while the lower row shows those for the ∆µ = ±1 transition. The
figure indicates that in both the ∆µ = 0 and ∆µ = ±1 transitions, the plotted points arepresent on the edge of the band distribution, i.e., near-zig-zag type SWNTs. This isconsistent with the experimental results obtained by Doorn et al. [37] who measured Raman
scattering from micelle-dispersed HiPco SWNTs and observed that the near-zig-zag typetubes have a stronger scattering intensity than the near-armchair type tubes. They also
showed that the scattering intensity from mod(n – m, 3) = 2 tubes in the ES22 transition is
one order higher than that from mod(n – m) = 1 tubes in the same transition; this result is inagreement with the theoretical prediction by Grüneis et al. [33]—the optical absorption
matrix element is higher along the K-M line than the K-Γ line. Therefore, strong scattering
would arise from the near-zig-zag type SWNTs in transitions ES11 and ES35 for mod(n – m,3) = 1 tubes and ES22 and ES24 for mod(n - m, 3) = 2 tubes. Based on the tight-binding and
GW-based Kataura plots in Fig. 4-18, intense ∆µ = ±1 peaks observed at 145 cm-1 for 2.54
eV and 136 cm-1 for 2.41 eV belong to either “EM12 (EM21)” or “ES35 (ES53),” and the peaks
at 180 cm-1 for 2.54 eV and 166 cm-1 for 2.41 eV belong to “EM12 (EM21).”4.2.4.2 Another possibility of interpreting the data
The results from Figs. 4-10 to 4-15 have been completely explained by the difference inthe selection rule between the cases of parallel- and cross-polarized light absorptions, i.e.,
the former results in ∆µ = 0 and the latter in ∆µ = ±1 photoexcitation of electrons, as
discussed in the previous subsection. Nevertheless, this subsection describes anotherpossibility of interpreting those data along with a series of experimental results presented asfollows. It is noted here that both the interpretations—the one in the current subsection and147

another that was discussed in Section 4.2.4.1—are self-consistent, and further
investigations are required to resolve them.
Figure 4-19 shows the Raman spectra obtained with a 488-nm laser light and from theside of the film so that the polarization of the incident light is perpendicular (red) andparallel (blue) to the SWNT axis, in addition to from the top (black), as schematicallyshown in Fig. 4-9. This is similar to the measurement shown in Fig. 4-10; however, using
finer diffraction grating in the measurement, the spectral resolution in Fig. 4-19 was twicethat shown in Fig. 4-10. Further, the ordinate is expressed in terms of the absolute CCD
count. Although these three spectra were measured consecutively under the same
conditions (e.g., laser power, laser spot size, CCD exposure, and other optical settings), therelativity in the ordinate is considered to be imperfect due to the nature of the micro-Raman
method.
Figure 4-19 shows that the prominent peak at 180 cm-1 in Fig. 4-10 is actuallycomposed of at least an isolated satellite peak at 174 cm-1 (FWHM of ~3 cm-1), a shoulder
at 178 cm-1, and the primary peak at 181 cm-1. In the result shown in Fig. 4-10, theLorentzian-fitted peaks at 145, 160, 180, and 203 cm-1 have a FWHM of ~11 cm-1. can be

1500

2

Diameter (nm)
1 0.9

0.8

488 nm, x50, 0.3 mW, 120sec x 3, grating=2400

Intensity (CCD count)

04/04/11 qrz, MoCo0.01wt%, 800C, 10Tr, 10min, ArH2

1000
Black: From top
Red: CS–Perpendicular
Blue: CS–Parallel

500

0
100

200

300
–1

Raman Shift (cm )Fig. 4-19. Raman spectra taken with 488 nm laser light from top of the film (black), and from side sothat polarization of incident light is perpendicular (red) and parallel (blue) to the SWNT axis as
schematized in Fig. 4-9. This is similar to the measurement shown in Fig. 4-10, however, spectral
resolution here was doubled from the case of Fig. 4-10 using finer diffraction grating in themeasurement. The ordinate is expressed in absolute CCD count and detailed measurement conditions
are written in the figure.

148

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications

interpreted as collective peaks of the “2n + m = const” family [58] that are located close toeach other in the Kataura plot. Furthermore, the peak at ~160 cm-1 is observed to split into
160 and 167 cm-1 spikes with a FWHM of ~3 cm-1, as shown in Fig. 4-19, whencross-polarized light is incident on the film (i.e., “from top” and “perpendicular”), while thesplit is not observed in the case of parallel-polarized light. Regarding the other peaks at 145
and 203 cm-1, the difference in splitting is not observed and they have larger FWHMs of ~9cm-1.
The reason for the presence of two types of FWHMs (i.e., ~3 cm-1 and ~9 cm-1) in a
spectrum can be interpreted by either of the following factors: the first is the difference
between the physical environment of bundled and isolated SWNTs. Isolated SWNTs are
considered to have small FWHMs—as low as 1.5 cm-1—as shown by Kataura et al. [59],while the bundled SWNTs have higher FWHMs due to augmented phonon scattering byneighboring SWNTs. The other factor is the increase in the inter-subband Eii slope in thelower Raman shift region in the “Raman shift” (abscissa) vs. “Energy” (ordinate) Katauraplot. That is, in the lower Raman shift region, the augmented density of RBM peaks along
the “Raman shift” axis may cause a coagulation of the peaks, thus leading to an apparent
increase in FWHMs.
Furthermore, it is known that bundling cause a slight red shift in resonant energy whencompared with the case of isolated SWNTs, as reported by O’Connell et al. [60]. Therefore,
the result shown in Fig. 4-10 along with that in Fig. 4-13 leads to another possible
interpretation: the group of dominant RBM peaks in the e⊥l configuration correspond to thescattering from the isolated SWNTs, and those in the e // l configuration correspond to thescattering from the bundled SWNTs. The slight difference in the resonant energies between
the isolated and bundled SWNTs can be reflected in the RBM spectra due to the following
morphological reasons: in the e⊥l configuration (refer to Fig. 4-9), the incident laser light
penetrates a greater depth in the SWNT film because it is relatively free from strong
collinear absorption (i.e., ∆µ = ±1) by the SWNT bundles (refer to Section 4.1). Therefore,
the light is scattered mainly by more isolated SWNTs that presumably reside randomly
among the aligned SWNT bundles. In the e // l configuration, on the other hand, theincident laser light could be dominantly absorbed and scattered by SWNT bundles within ashallower penetration depth, in which a smaller amount of light is scattered by the isolated
SWNTs.
This interpretation does not contradict the experimental observations presented in Figs.
4-13 to 4-15. In Fig. 4-13, the decrease of the e⊥l peaks caused by the molecule adsorption
149

is interpreted as the effect of adsorption being more significant for isolated SWNTs thanbundled SWNTs, due to the higher degree of surface exposure in the former. Accordingly,
the decrease in the optical absorbance in the lower energy region shown in Fig. 4-13 would
be caused mainly by the charge transfer from randomly residing isolated SWNTs due to theadsorption. The observation in Fig. 4-15c can be explained as follows: It is more difficult toheat isolated SWNTs due to their higher thermal conductivity—as confirmed by their small
FWHM value—compared with bundled SWNTs, in which phonon scattering is moresignificant. In essence, the result shown in Fig. 4-15c indicates an important possibility ofcalculating the thermal conductivity of SWNTs, which strongly depends on whether they
are isolated or bundled, by measuring the FWHM of the RBM spectrum. The result shownin Fig. 4-15b is not straightforward; however, it can be explained that isolated SWNTs are
more likely to be photo saturated than bundled SWNTs because the relaxation time of theformer (especially when they are semiconducting) is expected to be longer than the latter.
In order to further examine this interpretation, Raman scattering measurements were
performed on the non-aligned SWNTs grown from Co-Mo catalyst supported on zeolite
powder (refer to Section 2.1) using 488-nm laser light. Figure 4-20 shows the RBM spectra
measured from SWNTs that underwent 3 s (black) and 10 min (red) CVD reactions. In the
Diameter (nm)
2

1000

1

0.9

0.8

488 nm, x20, 0.3 mW, 120sec x 3, grating=2400
Black: 04/08/12 CoMo 0.45 mmol/g on zeolite
800 °C, 5 Torr, 3 sec, Ar/H2

Intensity (CCD count)Red:

04/07/22 CoMo 0.45 mmol/g on zeolite
800 °C, 8 Torr, 10 min, Ar/H2

500

0
100

200

300
–1

Raman Shift (cm )Fig. 4-20. RBM spectra taken with 488 nm laser light from randomly grown SWNTs on zeolite
support powder. CVD reaction times are 3 sec (Black) and 10 min (Red). Detailed measurement and
CVD conditions are written in the figure.

150

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications
case of the 3 s CVD, the most prominent peak is observed at ~180 cm-1, and the spectrum issimilar to that measured from the vertically aligned SWNT film with the e ⊥ l configuration(refer to Figs. 4-10 and 4-11). In the case of the 10-min CVD, however, several RBM
peaks—especially those below 180 cm-1—are reduced when compared with the 3-s case,and the thickening of SWNT bundles is considered to be responsible for this spectralchange. Therefore, if the thickening of bundles is responsible, it is considered that the peaks
at 180 and 145 cm-1 originate from isolated SWNTs and they decrease when SWNTs arebundled because of a slight red shift in the resonant condition.
Finally, Fig. 4-21 presents the RBM spectra measured from the “3 s” SWNTs grown on
zeolite powder that underwent different treatments: as-synthesized state (black),molecular-adsorbed state by evacuation with an oil-pump (red), and wetted with a few
drops of methanol and then dried at room temperature for several hours (blue). The figure
shows that despite the samples being identical, the RBM peaks in the lower frequency
region—especially those below 180 cm-1—exhibit remarkable reduction in both treatments.
In the case of adsorption with oil-derived molecules (red), the charge transfer due to the
Diameter (nm)
1000

2

1

0.9

0.8

488 nm, x20, 0.3 mW, 120sec x 3, grating=2400
04/08/12 CoMo 0.45 mmol/g on zeolite

Intensity (CCD count)

800 °C, 5 Torr, 3 sec, Ar/H2

Black: As–grown
Red: Oil adsorbed
Blue: Wet with MtOH

500

0
100

200

300
–1

Raman Shift (cm )Fig. 4-21. RBM spectra measured with 488 nm laser light from the “3 sec” SWNTs grown on zeolite
powder that underwent different treatment, as-synthesized state (Black), molecular-adsorbed state byevacuated with an oil-pump as Fig. 4-13 (Red), and wetted with a few drops of methanol and thendried in room temperature for several hours (Blue). Detailed measurement conditions are written in
the Figure.

151

adsorption is considered to be solely responsible for the spectral change, as observed in Fig.
4-13. The only difference between Figs. 4-21 and 4-13 is that the oil-adsorbed spectrum inthe former shows a reduction of the peak at 160 cm-1. This is unresolved and requires
further investigation; however, it may be explained that, in addition to isolated SWNTs,
SWNTs with larger diameter are considered to be more easily subject to the charge transfer
because of their weaker eDOS.
Further, when the treatment involves wetting with methanol (blue), the spectral change isconsidered to originate from both the charge transfer due to adsorption of methanol
molecules and a change in morphology (e.g., thickening of bundles) caused by surface
tension effect in the drying process. Complete elucidation of the mechanism responsible forthis RBM spectral change has not been attained yet, however at least, it is clear that theshape of the RBM spectrum should be regarded as being fairly sensitive to both thephysical and morphological environments of the considered SWNTs. Therefore, theconventional knowledge that the shape of the RBM spectrum represents the intrinsic
character (i.e., diameter distribution or metal/semiconducting ratio) of the SWNTs shouldbe altered for the characterization of SWNTs; this is because the spectrum is by and large
reflecting their extrinsic conditions, as proved by the results shown in this section.

4.2.5 Summary of polarization dependence of Raman scattering
Resonant Raman scattering from the vertically aligned SWNT films was investigated bychanging the polarization of the incident laser light with respect to the direction ofalignment. The shape of the RBM spectrum was observed to exhibit strong dependence on
the incident polarization. The RBM peaks were grouped into two types according to their
behavior: In one type, the peak intensity was strong when the light polarization wasperpendicular to the SWNT axis (e ⊥ l), while in the other type, the peak intensity wasstrong when the light polarization was parallel to the SWNT axis (e // l). The molecularadsorption experiment demonstrated that charge transfer between SWNTs and adsorbed
molecules was responsible for the subsequent change in the RBM spectrum.
In view of the changes observed in the RBM spectrum, two self-consistent interpretations
are proposed: In the first, the former group (e ⊥ l) originates from the ∆µ = ±1 transition
while the latter (e // l) corresponds to the ∆µ = 0 transition, which is consistent with earlier
theoretical predictions [10,33]. The considerable reduction of ∆µ = ±1 RBM peaks duringmolecular adsorption is supported by a charge transfer near the Fermi level, as elucidatedby optical absorption measurement. Some of the observed ∆µ = ±1 peaks at energies
152

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications

commonly used in RRS (2.41 and 2.54 eV) are unambiguously attributed to specific Ei,i±1
energy bands in the Kataura plot.
In the second interpretation, based on the fact that the resonant energy of bundled
SWNTs slightly differs (i.e., red shifted) from that of isolated SWNTs, the e ⊥ l RBM peaks
originate from isolated SWNTs whereas the e // l peaks originate from bundled SWNTs.
The coexistence of scatterings from isolated and bundled SWNTs in one RBM spectrum is
supported by the coexistence of two different FWHM values (i.e., ~3 cm-1 and ~9 cm-1).
The reason for the dependence of the dominant source of scattering (either isolated orbundled SWNTs) on the incident light polarization was explained in terms of themorphology of the vertically aligned film. This interpretation was also consistent withobservations in Figs. 4-13 to 4-15. Furthermore, the observation in Fig. 4-20 that the peaks
at ~145 and 180 cm-1 are prominently noticed from random SWNTs grown on zeolite
support powder for 3 s is also consistent with the proposed interpretation. However, inorder to decide the appropriate interpretation, further measurements with a higher
wavenumber resolution (<2 cm-1) are essential.
In this section, it was presented that the RBM spectra are not representing the intrinsic
character of the examined SWNTs (e.g., diameter distribution or metal/semiconducting
ratio) even with the use of several fixed laser excitation energies. Since the RBM spectra
are drastically affected by the extrinsic conditions of SWNTs, such as the morphology,
degree of bundling, and/or existence of molecular adsorption, considerable caution must be
paid when attempting to demonstrate the selective enrichment or removal of either thesemiconducting or metallic SWNTs based on RRS analysis. The apparent change of the
RBM spectral shape should be compensated by the use of continuous-energy laser light inorder to correctly distinguish whether the observed reduction in the RBM intensity is due tothe selective removal of specific type of SWNTs or this is due to the mere shift of resonant
energy caused by the change in the SWNT environment. Furthermore, a wavenumber
resolution of at least less than 2 cm-1 should be used in order to identify the physical state of
SWNTs, i.e., isolated or bundled.
In any interpretation, the RBM spectra can be varied even from a measurement from theidentical sample depending on the incident polarization and physical environment of the
SWNTs. Information on the nature of each RBM peak revealed in this section will aid inproviding a sounder characterization of SWNTs by RRS analysis.

1534.3 Optical applications of SWNT film directly synthesized on solid
surfaces
4.3.1 Motivation and research background
Optical pulsed lasers are of great interest in many industrial and scientific fields.
Passively mode-locked fiber lasers are one of the best pulse sources currently available
because of their simplicity and ability to generate transform-limited optical pulses in thepicosecond and sub-picosecond regimes [61]. Since there is no necessity for expensive
modulators that are required in actively mode-locked lasers, passively mode-locked lasers
are cheaper as well as structurally simpler. Instead of the modulators, however, a passively
mode-locked laser requires a mode locker; this is a device whose response depends on theincident light intensity. The mode locker is usually a fast saturable absorber, such as asemiconductor-based [62] or fiber-based saturable absorber [63,64].
The semiconductor-based saturable absorbers, however, require complex and expensive
clean-room-based fabrication systems and processes. Furthermore, since thesemiconductor-based saturable absorber is a reflective device, its use is limited to certain
types of linear cavity topology. The fiber-based saturable absorber is simple but requires
long nonlinear fibers, typically longer than tens of meters, which makes the laser unstable
and lowers the repetition rate of the output light.
It was recently discovered that SWNTs exhibit excellent characteristics as saturable
absorbers due to their strong third-order non-linearity in electric susceptibility (χ(3)) andtheir ultrafast relaxation of excited electrons [35,36]. Moreover, the ES11 absorption
maxima of SWNTs is near the 1.55 µm wavelength band, as shown in Fig. 2-27, which isconsiderably advantageous for their application in optical telecommunication. Furthermore,
Set et al. recently proposed and demonstrated a saturable absorber incorporating a carbon
nanotube (SAINT) [67–70], which possesses several important properties, such as ultrafast
recovery time, polarization insensitivity, a theoretically high optical damage threshold,mechanical and environmental robustness, chemical stability, and the ability to operate intransmission, reflection, and bidirectional modes.
SAINTs were previously fabricated by the following process: SWNTs produced by thelaser-ablation method [71] were purified and dispersed in ethanol, which was then sprayedonto the surface of a quartz substrate to form a thin film of SWNTs. However, such a
process is laborious and the optical uniformity of the obtained film is low, in which lightscattering is not negligible due to the microscopic roughness of the film. In this section, it is154

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications

demonstrated that the SWNT film grown directly on quartz substrates developed in Section
2.3 can be employed as a new SAINT material. The mode-lock properties exhibited withthe proposed SAINT are investigated and described.

4.3.2 Experimental setup
A schematic of the mode-locked fiber ring laser is shown in Fig. 4-22. A very short (40cm) fluoride-based Er-doped fiber (EDF), backward pumped by a 980-nm laser diode (LD),is used as the laser gain medium. The use of fluoride-based EDF is advantageous becauseof its high gain coefficient [72]. Two optical isolators are inserted to prevent back reflectionin the cavity and to ensure unidirectional operation. The output light from the EDF is
launched through a fiber collimator and focused through an aspherical lens onto the SAINT,
which is directly synthesized on a quartz substrate. The spot size on the SAINT is ~10 µm.
The output light from the SAINT is collected and launched back into the fiber cavity via
another set of matching spherical lens and collimator. A 1-m-long dispersion-shifter fiber(DSF) was attached to each collimator, resulting in a total cavity length of 4.1 m. The
output of the laser is tapped through the 30% port of a fiber coupler, whereas the 70% port
is used to feed the output back into the cavity.

Fig. 4-22. Schematic description of mode-locked fiber laser with a SWNT film directly grown aquartz substrate used as a SAINT device. This figure is cited from Ref. 73.

155

4.3.3 Principles of mode-locked ring fiber laser
Pulsed light can be generated by a mode-locking method. The frequency in the resonantmode differs by integral multiples of c/2L, where c and L denote the speed of light and thelength of the resonator used, respectively. However, the phase of these “modes” fromwhich continuous wave (CW) light is produced is generally random. When the phase of allmodes is locked, a series of intense pulses is obtained by constructive interferences between
light packets. The formulation for the nth-mode wave with amplitude ε0 and frequency ωpropagating in a resonator of length L can be expressed as

ε n (t ) = ε 0 e iωt(66)

Using the relationship

ω=

2πc

λ

n
2L 
 nc  = 2π   Q λ =2Ln  2L  

= 2πc

(67)

Equation 66 is rewritten asε n (t ) = ε 0 expi ω 0 +πnc  

(68)
t 
L 

where ω0 denotes the angular frequency for the lowest mode. The superimposed wave
made up by summing N modes (n = 0, 1, ⋅⋅⋅, N – 1) of the mode-locked waves is written as
N −1

iπnct

ε (t ) = ∑ ε n (t ) = ε 0 e iω t ∑ e L
0

(69)

n =0

n

Further, using the relationshipN −1 iπnct
L

∑e

iπct

2 iπct=1+ e L + e L + ⋅⋅⋅n=0( N −1) iπct

sin( Nπct / 2 L)=
⋅ e 2Lsin(πct / 2 L)
Substituting Eq. 69 into Eq. 70,
( N − 1)πc   sin( Nπct / 2 L)
ε (t ) = ∑ ε n (t ) = ε 0 exp i ω 0 +t ⋅2 L   sin(πct / 2 L)
n


(70)

(71)

is obtained. Since the intensity of the output light, referred to as I, is proportional to thesquare of the magnitude of the wave, it is expressed as
I (t ) ∝ e ∗ e = ε 02

sin 2 ( Nπct / 2 L)
sin 2 (πct / 2 L)(72)

The functional shape is schematically expressed in Fig. 4-23. Equation 72 means that thepulse width shown in Fig. 4-23 decreases with an increase in the number of superposed156

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications

I
2L
c

t
Fig. 4-23. Schematic of intensity of mode-locked light I as a function of time t given by Eq. 72.

waves N, and the pulse frequency is given by 2L/c. The physical meaning of thisobservation can be described by Heisenberg’s uncertainty principle:(73)∆E ⋅ ∆t ≈ h or ∆ω ⋅ ∆t ≈ 2π

4.3.4 Results and summary
At a pump power of approximately 17 mW, the laser self-starts to mode lock andproduces single pulses in a round-trip time, as shown in Fig. 4-24a. Due to the use of very
short fluoride-based EDF, the fundamental repetition rate is 50.4 MHz, eight times higher
than that of the previous SAINT-based mode-locked fiber lasers [68–70]. The average
output optical power is ~–7 dBm (200 µW). The output spectrum in Fig. 4-24b shows thatthe 3-dB spectral width is ~3.0 nm. The second-harmonic generation autocorrelation trace
was measured with a two-photon absorption autocorrelator (Alnair APM-1000) and an
estimated FWHM of 0.9 ps. The resulting time-bandwidth product of 0.34 indicates that thepulses are transform limited. This fundamental mode-locked operation was reproducible
and stable for several hours in the laboratory. It was also observed that the laser could
produce multiple pulses in a round-trip time (multiple-pulse mode) by adjustment of
intracavity dispersion and polarization with the addition of several meters of SMFs and apolarization controller. When the SAINT is removed from the laser cavity, it is not possible
to mode lock the laser even with a high pump power. Direct synthesis of SWNTs was
performed on the fiber ends, as shown in the FE-SEM image and Raman scattering
spectrum in Figs. 4-25 and 4-26, respectively. However, the mode-locking operation withthis device was not stable, probably because of the terminal reflection at the fiber ends.

157

a

b

Fig. 4-24. (a) Pulse waveform and (b) spectrum of the output laser light. These figures were citedfrom Ref. 73.

In summary, the SWNT film grown directly on the surface of the quartz substratedeveloped in the previous section was demonstrated to serve as a new SAINT device for
optical applications. It was successfully applied to passively mode lock a fiber laser toproduce sub-picosecond pulses at a 50-MHz repetition rate.

158

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications

10 µm

200 nmFig. 4-25. FE-SEM image of SWNTs directly grown on the tip surface of an optical fiber whose
diameter is 0.1 mm. Right panel is partial magnification of the left.

Diameter (nm)Optical microscope image (×20)

Intensity (arb. units)

2100

1 0.9 0.8

200

300

500

1000

0.7

400

Fe/Co 0.01 wt%,
700°C, 10 Torr, 1 hflowing 300 sccm of Ar/H2
0

1500
–1

Raman Shift (cm )Fig. 4-26. Raman scattering spectra taken by 488 nm laser light from the SWNT film directly grownon the end of an optical fiber (diameter = 0.1 mm). The sample is the same as that presented in Fig.
4-25. The picture in the left is an optical microscope image (×20) of the top end of the optical fiber
after CVD.

159

4.4 Summary of Chapter 4
In this chapter, the fundamental optical properties and practical applications of SWNTs
were investigated and described using the SWNT films directly grown on quartz substrates.
In Section 4.1, the anisotropic optical absorption properties of SWNTs were elucidated
for a wide energy range of 0.5–6.0 eV. The optical absorption cross sections for bothparallel and perpendicular to the SWNT axis were determined. The peaks at 4.5 and 5.25
eV were discovered to correspond to the maximum of Im{ε⊥} (parallel to the SWNT axis)
and that of Im{-ε||-1} (perpendicular to the SWNT axis), respectively, originating from theoptical properties of graphite.
In Section 4.2, it was demonstrated that the shape of the RBM exhibited a strong
dependence on the polarization. The RBM peaks were grouped into two types according totheir behavior: In one type, the peak intensity was strong only for perpendicularpolarization (e ⊥ l), while in the other, the peak intensity was strong only for parallel
polarization (e // l). The RBM spectra can be varied even from a measurement from theidentical sample depending on the incident polarization and physical environment of
SWNTs. The knowledge on the nature of each RBM peak shown in this section will help
provide a sounder characterization of SWNT specimens by RRS analysis.
In Section 4.3, the randomly oriented SWNT film grown on the quartz substrate wasdemonstrated to serve as a SAINT device for optical applications at a 1.55-µm wavelength.
A passively mode-locked fiber laser was successfully fabricated to produce sub-picosecond
pulses at a 50-MHz repetition rate.

Acknowledgement for Chapter 4
The author cordially thanks Prof. S. Yamashita and Mr. Y. Inoue at The University of Tokyo and
Dr. S. Y. Set at Alnair Labs for their valuable collaboration and discussions on the mode-locked
fiber laser development presented in Section 4.3. The contents of Section 4.3 have been publishedin Optics Letters, vol. 29, pp. 1581–1583, 2004 by S. Yamashita, Y. Inoue, S. Maruyama, Y.
Murakami, H. Yamaguchi, M. Jablonski, and S.Y. Set. Thanks are also due to Dr. H. Kataura at the
National Institute of Advanced Industrial Science and Technology (AIST) for the discussion and Mr.
M. Oba for his assistance in constructing the Kataura plot shown in Fig. 4-18.

160

Chapter 4  Anisotropic optical properties of SWNTs and their optical applications

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165

166

Chapter 5:
Summary

Starting with the development and characterization of the growth of SWNTs, theunderlying mechanism and the direction for the choice of catalyst were investigated in
Chapter 2. The findings and conclusions obtained in Chapter 2 are as follows:
1) The yield of SWNTs was defined on the basis of TGA with a confirmedatory support
by TEM observations. The yield could be enhanced by the reduction of the catalyst
prior to the CVD reaction.
2) The observed difference in the wettability of Fe, Co, Ni, and Mo on SiO2 support andthe resultant diameter of the SWNTs were explained by the magnitude of the ratio∆Hf°sublimate/∆Hf°oxide. This provides a useful guidance for the choice of the catalyst on
SiO2 support.
3) A dip-coat catalyst supporting method was developed for the direct support of a small
amount of catalyst on the flat substrate. It was found that when cobalt andmolybdenum acetates were used, the monodispersed Co particles with a diameter of
1–2 nm were densely supported on the SiO2 surface without agglomeration even at
800°C.
4) The underlying mechanism for the successful dispersion of Co was investigated by
TEM and XPS. It was elucidated that the CoMoOx (x ≤ 4) compound was formed on
the SiO2 surface, and this layer was observed to stabilize the excess Co particles by
preventing them from agglomerating into larger particles.
The findings obtained in Chapter 3 are summarized below:
1) Vertically aligned growth of SWNTs on flat substrates was demonstrated for the firsttime to be possible under an optimum CVD condition. The cleanness of the chamber
is an important factor that controls the speed of catalyst deactivation during CVD.
Based on the HR-TEM analyses, it was confirmed that the growth is considered to be
the “root growth” and that the produced SWNTs possess high purity without
containing MWNT or amorphous carbons.

168

Chapter 5  Summary2) Growth and alignment formation processes were investigated in terms of FE-SEM
observations and optical absorption measurements using light incident normal to thesubstrate. Experimentally measured growth curves were explained by a proposedmodel in which the initial catalyst activity η0 and the deactivation constant κ describe
the entire growth process. The deterioration in the growth speed is considered to be an
accumulated loss of initial catalyst activity related to the decomposition of ethanol
molecules.
Chapter 4 presented several original findings that were obtained from optical measurementsof the vertically aligned SWNT film These are as follows:
1) Anisotropic optical absorption properties of SWNTs were elucidated for a wide
energy range of 0.5–6.0 eV. The optical absorption cross sections for both parallel andperpendicular to the SWNT axis were determined. The absorption peaks at 4.5 and5.25 eV were discovered to exhibit strong dependences on the light polarization.
2) The peaks at 4.5 and 5.25 eV correspond to the maximum of Im{ε⊥} parallel to the
SWNT axis and that of Im{-ε||-1} perpendicular to the axis, respectively, originatingfrom the optical properties of graphite. This optical relevance between SWNTs andgraphite implies the possibility of investigating unresolved optical properties ofgraphite in the direction parallel to the c-axis by measurements of the opticalabsorption of the aligned SWNT films.
3) The shape of the RBM spectrum was observed to exhibit a strong dependence on theincident light polarization. The RBM peaks were grouped into two types according totheir behavior: In one type, the peak intensity was strong only for perpendicularpolarization (e ⊥ l), while in the other type, the peak intensity was strong only forparallel polarization (e // l).
4) The RBM spectra can be varied even from a measurement from the identical sample
depending on the incident polarization and physical environment of SWNTs. The
knowledge on the nature of each RBM peak revealed in this section will aid inproviding a sounder characterization of SWNTs by RRS analysis.

1695) The SWNT film grown directly on the surface of the quartz substrate, which wasdeveloped in Section 2.3, was demonstrated to serve as a new SAINT device for
optical applications. It was successfully applied to passively mode lock a fiber laser toproduce sub-picosecond pulses at a 50-MHz repetition rate.

The author hopes that the findings presented in this thesis will contribute to the further
development of fundamental studies and applications of SWNTs.

170

Appendix:
Perturbated Hamiltonian for one-photon process

A.1 Description of electromagnetic wave by vector potential
Maxwell’s equation for electromagnetic waves propagating in vacuum is given by∂B= 0 , div B = 0∂t∂Drot H −
= 0 , div D = 0∂t

rot E +

(1)

With the relations D = ε0E and B = µ0H, Eq. 1 is rewritten as∂B∂E=0= 0 , rot B − ε 0 µ 0∂t∂t
div B = 0 , div E = 0

rot E +The vector potential A is introduced with the definition
B = rot A

(2)

(3)

that satisfies div B = 0. From Eqs. 2 and 3, E is expressed in terms of A as

E=−

∂A
∂t

(4)

The differential equation for A is then obtained by substituting Eqs 3 and 4 into Eq. 2 as

∇2 A −1 ∂2 A1= 0 , c == 3 × 108 m ⋅ s -1 22
ε 0 µ0
c ∂ t



(5)

Since A has a freedom in the magnitude of its baseline by the gradient of some scalar field∇ψ due to the relation ∇× (∇ψ) = 0, this freedom is conventionally eliminated by
employing so-called Coulomb gauge in which ∇2ψ is adjusted in order to set div A = 0.
The plane waves confined in a cube with edge length L (i.e. with volume V = L3) areconsidered. The wave numbers for x, y, and z direction kx, ky, and kz, respectively, arerepresented using integers nx, ny, and nz as
kx =

2π
2π
2π
nx , k y =ny , kz =
nz
L
L
L

(6)

in order to conform with the periodic boundary condition. Then, the plane-wave solution
for A is obtained in terms of wave number vector k (= [kx ky kz]T) and position vector r as

A(r , t ) = A0 e i ( k ⋅r −ϖt )(7)Furthermore, since the following relationship holds,
div A(r , t ) = ∇ ⋅ A = ik ⋅ A0 e i ( k ⋅r −ϖt ) = 0 ⇔ k ⋅ A = 0b(8)Appendix  Perturbated Hamiltonian for one-photon process

A is perpendicular to k. Using a unit vector e in the direction of A, Eq. 7 can be rewritten as

A(r , t ) = A0 e i ( k ⋅r −ϖt ) = eA0 e i ( k ⋅r −ϖt )(9)In order for A to be real number, Eq. 9 and its complex conjugate are added together as

{

}

(10)

ϖk = ck(11)

1∗
e k ,γ q k (t )e ik ⋅r + q k (t )e −ik ⋅rVwhere V-1/2 is a normalization constant. qk(t) is given as
A(r , t ) =qk (t ) = qk exp{− i (ϖ k t + δ k )},Both |qk| and δ are the parameters to be determined for the description of considered field.
Direction of e is projected on the orthogonal coordinates γ = 1 and γ = 2 that areperpendicular to the direction of propagation, as schematized in Fig. A-1. The generalsolution for A is expressed as a summation of all possible k and γ, as

A(r , t ) =

{

2
1
∗
e k ,γ q k ,γ (t )e ik ⋅r + q k ,γ (t )e −ik ⋅r∑∑
V k γ =1}

(12)

Similarly, E and B can be expressed using Eqs, 3, 4, and 12, asE (r , t ) =

{

2
1
∗
e k ,γ iϖ k q k ,γ (t )e ik ⋅r − q k ,γ (t )e −ik ⋅r∑∑
V k γ =1

}

(13)

γ=1
γ=2
ek,1
ek,2
direction of kek = ek,1 + ek,2Fig. A-1. Schematic for light propagation described by e and k. The coordinate γ = 1 and γ = 2
is perpendicular to the direction of wave propagation.

c

]{

[

2
1
∗
i k × e k ,γ q k ,γ (t )e ik ⋅r − q k ,γ (t )e −ik ⋅r∑∑
V k γ =1

B (r , t ) =

}

(14)

The behavior of A at the origin r = 0 is described as

{

}

2
2
1
1
∗
e
q
(
t
)
+
q
(
t
)
=
∑∑ k ,γ k ,γ∑∑ ek ,γ Qk ,γ (t )k ,γV k γ =1
V k γ =1

A(0, t ) =(15)

Here, Qk,γ(t) denotes amplitude of the (k, γ) component of A at the origin, given by

{

}

∗

Qk ,γ (t ) ≡ qk ,γ (t ) + qk ,γ (t ) = 2 qk ,γ cos(ϖ k t + δ k )(16)

and its time derivative Q& k ,γ (t ) is expressed as{}∗
Q& k ,γ (t ) = −iϖ k qk ,γ (t ) − qk ,γ (t )(17)Therefore, using Eqs. 13 and 14, qk,γ and qk,γ* are expressed as
i &1
q& k ,γ (t ) = Qk ,γ (t ) +Qk ,γ (t )
ϖk
2


(18)


1
i &
Qk ,γ (t )
Qk ,γ (t ) −
2
ϖk


(19)

∗
q& k ,γ (t ) =A.2 Description of photons
According to the electromagnetic theory, the energy density U of electromagnetic wave
is given by

U (r , t ) =1
1
1( D ⋅ E + B ⋅ H ) = (ε 0 E ⋅ E +B ⋅ B)
µ0
2
2

(20)

By substituting Eqs. 13 and 14 into Eq. 21, total energy of the electromagnetic wave H
inside the volume V (= L3) is expressed as
H = ∫∫∫Udr = ⋅ ⋅ ⋅ =(ϖ + c k ){q γ q γ + q γ q γ }
∑∑
2
γ

ε0

2

k

=1
2

2

= 2ε 0 ∑∑ϖ k q k ,γ q k ,γ
k

d

γ =1

∗

2

k

2

k,

∗

k,

∗

k,

k,

(21)

Appendix  Perturbated Hamiltonian for one-photon process

Then, substituting Eqs. 18 and 19 into Eq. 21,
H=

ε0

2

(Q& γ + ϖ Q γ )
∑∑
2
γ
k

=1

2

k,

2

k

2

(22)

k,

Comparing the equation for energy of 1-D harmonic oscillator(Energy of 1 - D harmonic oscillator) =m 2( x& + ϖ 2 x 2 )2(23)

and Eq. 22, it is derived that Qk,γ(t) represents a generalized coordinate and Pk,γ(t) given by
Pk ,γ = ε 0 Q& k ,γ(24)

represents a generalized momentum. Then, the Hamiltonian H can be represented in termsof generalized coordinate and generalized momentum is written as
2
1
1
2
2
2
(25)
H = ∑∑ (Pk ,γ + ε 0ϖ k Qk ,γ )2k γ =1 2ε 0
The momentum P has to be written as an operator in order to transform H into thequantum-mechanical form,
2

H = ∑∑ (−
k

γ =1

1
h2 ∂2
2
2
2
Pk ,γ + ε 0ϖ k Qk ,γ )2
2ε 0 ∂Qk ,γ2(26)

Now the problem is reduced to the basic quantum mechanics for case of 1-D harmonic
oscillator. Therefore, an eigenvalue for H in Eq. 26, which correspond to intrinsic energy E
is given by2
1
E = ∑∑ (nk ,γ + )hϖ k , (nk ,γ = 0, 1, 2, ⋅ ⋅⋅)2k γ =1(27)

The number of oscillator nk,γ is the number of photon whose energy is ħϖk. Furthermore,
the annihilation and creation operators ak,γ and ak,γ* are given from the analogy to the caseof 1-D harmonic oscillator asak ,γ =


2ε 0ϖ k 
2ε 0ϖ ki* Qk ,γ −Pk ,γ  =qk ,γε 0ϖ k
h 
h


(28)

a k ,γ =
2ε 0ϖ k i Qk ,γ +Pk ,γ  =ε 0ϖ k
h 


(29)

*

2ε 0ϖ kq k ,γhUsing Eqs. 28 and 29, Eq. 25 can be rewritten as

e

H=

2
1
*
*
∑∑ hϖ k (a k ,γ ak ,γ + ak ,γ a k ,γ )2 k γ =1(30)

Further, Using Eqs. 28 and 29, Eqs. 12, 13, and 14 are rewritten as

A(r ) =

{e
∑∑
2ε V
ϖ
γ
h

0

E (r ) =e k ,γ=1kik ⋅ ra k ,γ + e −ik ⋅r a k ,γe γ i ϖ {e
∑∑
2ε V
γ
2

h

0

B (r ) =

k

2

k

=1

ik ⋅ r

k

k,

2

0

k

=1

i

k,

}

a k ,γ − e −ik ⋅r a k ,γ

[k × e γ ] {e
∑∑
2ε V
ϖ
γ
h

*

ik ⋅ r(31)*}

a k ,γ − e −ik ⋅r a k ,γ

(32)

*

}

(33)

k

in terms of annihilation and creation operators ak,γ and ak,γ*. It is noted that time-dependent
term exp(-iεt/ ħ) is embedded in the wave function to which above operators couple, if
based on the Schrödinger’s representation.

A.3 Interaction between electron and electromagnetic wave
The force F exerted on a particle with charge q moving in electromagnetic field E and B
with the speed v is given by

F = e{E + (v × B )}(34)

which is called Lorentz force. Corresponding Newton’s equation of motion is written as
m&x& = eE x + e( y& B z − z&B y )m&y& = eE y + e( z&B x − x&B z )(35)

m&z& = eE z + e( x&B y − y& B x )E and B are given in terms of vector potential A in Eqs. 3 and 4, respectively, and using
these relations Eq. 35 is rewritten asfAppendix  Perturbated Hamiltonian for one-photon process

m&x& = −em&y& = −em&z& = −e∂Ax  ∂Ay ∂Ax   ∂Ax ∂Az  − z&+ e y& 
−
−

∂t
∂y   ∂z
∂x   ∂x  ∂A ∂Ay   ∂Ay ∂Ax  − x&−+ e z& z −∂y ∂z   ∂x∂t  ∂y∂Ay(36)

  ∂A ∂A  ∂A ∂Ay ∂Az+ e x&  x − z  − y&  z −∂t∂x ∂z   ∂z ∂yIn current case, Lagrangean has to be calculated firstly in order to determine Hamiltonianof the system. This is mainly because the force is dependent on the speed of the particle inthe case of Lorentz force in Eq. 34. Namely, momentum of the charged particle inelectromagnetic field is not simply given by [mass × velocity].
The Lagrangean L that satisfy the Lagrange’s equation of motiond  ∂L  ∂L=0
 −dt  ∂x&  ∂x

(37)

and, at the same time, Eq. 36 is found to beL=m 2( x& + y& 2 + z& 2 ) + e( x&Ax + y& Ay + z&Az )2(38)

Subsequently, the momentum of the particle in field A is obtained as∂L= mx& + eAx
∂x&
∂L
py =
= my& + eAy
∂y&

px =

pz =

(39)

∂L
= mz& + eAz∂z&Namely, an existence of an electromagnetic field A changes kinetic energy of the moving
particle as
1
2
pj
2m

→

1
( p j + eA)2
2m

(40)

Here, the subscript j denotes index number for the electron in the system. Therefore, thechange of Hamiltonian ∆H due to the existence of A is expressed as

 1( p j + eA(r j ))2  − ∑ 1 p j 2∆H = ∑  j 2mj  2m
e
e2
{
}
=
p
⋅
A
r
+
A
r
⋅
p
+
A 2 (r j )
(
)
(
)
∑
∑
j
j
j
j
2m j
2m j

(41)

g

Since pj = -iħ∇j in the quantum-mechanical expression,p j ⋅ A(r j ) = −ih{∇ j A(rj ) + A(rj ) ⋅ ∇ j } = −ihA(r j ) ⋅ ∇ j(42)

in which the relation div A = 0 was used, and hence, ∆H is expressed asee2∆H = ∑ A(r j ) ⋅ p j +A 2 (r j )
∑
m j
2m j

(43)

Let the first and second terms to be H(1) and H(2), respectively. The H(1) is expressed as
H (1) =

{

h
e
1
ik ⋅r
− ik ⋅ r*e j (e k ,γ ⋅ p j )a k ,γ + e j (e k ,γ ⋅ p j )a k ,γ∑∑m 2ε 0V j k ,γ ϖ k

}

(44)

This is a linear equation of ak,γ and ak,γ*, which means that the H(1) either increase or
decrease the number of photon by one through the one-photon process. On the other hand,the H(2) is a quadric equation of ak,γ and ak,γ* indicating that this Hamiltonian describes thetwo-photon process.

hAcknowledgements
During the course of this thesis, I have been privileged to receive the advice andassistance of many people. I would like to thank them all, but mentioning only a few isallowed here. First and foremost, I would like to express my sincere gratitude to mysupervisor, Prof. Shigeo Maruyama, for his continued advice and invaluable guidance
throughout the course of my research. I would also like to thank Prof. Tatsuya Okubo
and Dr. Minghui Hu for their many helps and discussions in the fulfillment of this thesis.
Without them, many important experimental facts and discussions regarding the role ofthe catalyst would not appear in this thesis. I would also like to acknowledge Prof.
Shinji Yamashita for the precious collaboration on the application of single-walledcarbon nanotubes to optical devices from which I fortunately could learn many things,
Prof. Yuichi Ikuhara for his brilliant cross-sectional TEM observation on the nanotubegrown substrates, and Prof. Kazunori Hoshino for his providing elaborated Si-based
microstructures. For precious advices and discussions on the thesis, I would like toexpress my gratitude to Prof. Yoichiro Matsumoto and Prof. Atsumu Tezaki. Thanks arealso gratefully extended to Dr. Hideo Tsunakawa for his kind and repeated assistancesin my TEM operations. Special thanks are owed to Mr. Mitsuru Inoue and Mr. Makoto
Watanabe who kindly supported me performing many affairs in the laboratory. I am
grateful to all my current and former lab-mates, with whom I have fortunately been
enjoying my research life here. Finally, I want to express my hearty gratitude to mywife, Asuka, for her kind support, encouragement, and patience throughout myfulfillment of the thesis research.

List of publicationsFirst Author Publications:
1. Y. Murakami and B. B. Mikić, “Parametric Optimization of Multichanneled Heat Sinks for
VLSI Chip Cooling,” IEEE Transactions on Components and Packaging Technologies, vol.
24, pp. 2-9, 2001.
2. Y. Murakami and B. B. Mikić, “Parametric Investigation of Viscous Dissipation Effects on
Optimized Air Cooling Microchanneled Heat Sinks,” Heat Transfer Engineering, vol. 24, pp.
53-62, 2003.
3. Y. Murakami, Y. Miyauchi, S. Chiashi, and S. Maruyama, “Characterization of SingleWalled Carbon Nanotubes Catalytically Synthesized from Alcohol,” Chemical Physics
Letters, vol. 374, pp. 53-58, 2003.
4. Y. Murakami, S. Yamakita, T. Okubo, and S. Maruyama, “Single-Walled Carbon Nanotubes
Catalytically Grown from Mesoporous Silica Thin Film,” Chemical Physics Letters, vol. 375,
pp. 393-398, 2003.
5. Y. Murakami, Y. Miyauchi, S. Chiashi, and S. Maruyama, “Direct Synthesis of High-Quality
Single-Walled Carbon Nanotubes on Silicon and Quartz substrates,” Chemical Physics
Letters, vol. 377, pp. 49-54, 2003.
6. Y. Murakami, S. Chiashi, Y. Miyauchi, and S. Maruyama, “Direct Synthesis of SingleWalled Carbon Nanotubes on Silicon and Quartz-Based Systems,” Japanese Journal ofApplied Physics, vol. 43, pp. 1221-1226, 2004.
7. Y. Murakami, S. Chiashi, Y. Miyauchi, M. Hu, M. Ogura, T. Okubo, and S. Maruyama,“Growth of Vertically Aligned Single-Walled Carbon Nanotube films on Quartz Substrates
and their Optical Anisotropy,” Chemical Physics Letters, vol. 385, pp. 298-303, 2004.
8. Y. Murakami, S. Chiashi, E. Einarsson, and S. Maruyama, “Polarization Dependence ofResonant Raman Scattering from Vertically Aligned Single-Walled Carbon Nanotube
Films,” Physical Review B, vol. 71, pp. 085403-1-085403-8, 2005.
9. Y. Murakami, E. Einarsson, T. Edamura, and S. Maruyama, “Polarization Dependence of
the Optical Absorption of Single-Walled Carbon Nanotubes," Physical Review Letters, inpress. vol. 94, pp. 087402-1-087402-4, 2005.

Co-Author Publications:
1. S. Maruyama, Y. Miyauchi, T. Edamura, Y. Igarashi, S. Chiashi, and Y. Murakami,“Synthesis of Single-Walled Carbon Nanotubes with Narrow Diameter-Distribution from
Fullerene,” Chemical Physics Letters, vol. 375, pp. 553-559, 2003.
2. S. Maruyama, Y. Miyauchi, Y. Murakami, and S. Chiashi, “Optical Characterization ofSingle-Walled Carbon Nanotubes Synthesized by Catalytic Decomposition of Alcohol,” New
Journal of Physics, vol. 5, pp. 149.1-149.12, 2003.
3. S. Chiashi, Y. Murakami, Y. Miyauchi, and S. Maruyama, “Cold Wall CVD Generation ofSingle-Walled Carbon Nanotubes and in situ Raman Scattering Measurement of the GrowthStage,”, Chemical Physics Letters, vol. 386, pp. 89-94, 2004.
4. Y. Miyauchi, S. Chiashi, Y. Murakami, Y. Hayashida, and S. Maruyama, “Fluorescence
Spectroscopy of Single-Walled Carbon Nanotubes Synthesized from Alcohol,” Chemical
Physics Letters, vol. 387, pp. 198-203, 2004.
5. S. Maruyama, Y. Murakami, Y. Miyauchi, and S. Chiashi, “Generation of Single-Walled
Carbon Nanotubes from Alcohol and Generation Mechanism by Molecular Dynamics
Simulations,” Journal of Nanoscience and Nanotechnology, vol. 4, pp. 360-367, 2004.
6. M. Hu, Y. Murakami, M. Ogura, S. Maruyama, and T. Okubo, “Morphology and Chemical
State of Co-Mo Catalysts for Growth of Single-Walled Carbon Nanotubes Vertically Alignedon Quartz Substrates,” Journal of Catalysis, vol. 225, pp. 230-239, 2004.
7. S. Yamashita, S. Maruyama, Y. Murakami, Y. Inoue, H. Yaguchi, M. Jablonski, and S. Y.
Set, “Saturable Absorbers Incorporating Carbon Nanotubes Directly Synthesized onto
Substrates/Fibers and their Applications to Mode-Locked Fiber Lasers,” Optics Letters, vol.
29, pp. 1581-1583, 2004.
8. H. Igarashi, H. Murakami, Y. Murakami, S. Maruyama, and N. Nakashima, “Purification andCharacterization of Zeolite-Supported Single-Walled Carbon Nanotubes CatalyticallySynthesized from Ethanol,” Chemical Physics Letters, vol. 392, pp. 529-532, 2004.
9. M. Kohno, T. Orii, M. Hirasawa, T. Seto, Y. Murakami, S. Chiashi, Y. Miyauchi, and S.
Maruyama, “Growth of Single-Walled Carbon Nanotubes from Size-Selected Catalytic
Metal Particles,” Applied Physics A, vol. 79, pp. 787-790, 2004.
10. Y. Ohno, Y. Kurokawa, T. Shimada, Y. Murakami, A. Sakai, T. Okazaki, S. Kishimoto, K.
Hiraga, S. Maruyama, H. Shinohara, and T. Mizutani, “Synthesis of Carbon Nanotube
Peapods Directly on Si Substrates,” Applied Physics Letters, vol. 86, pp. 023109-023111,
2005.

11. S. Maruyama, E. Einarsson, Y. Murakami, and T. Edamura, “Growth Process of Vertically
Aligned Single-Walled Carbon Nanotubes,” Chemical Physics Letters, vol. 403, pp. 320323, 2005.

International Conferences
1. Y. Murakami, Y. Miyauchi, S. Chiashi, and S. Maruyama, “Direct synthesis of high-purity
single-walled carbon nanotube mat on silicon and quartz substrates and their applications,”
International Conference on the Science and Application of Nanotubes 2003 (NT03), Seoul,
Korea, 2003.
2. Y. Murakami, S. Chiashi, Y. Miyauchi, and S. Maruyama, “Direct Synthesis of SingleWalled Carbon Nanotubes on Silicon and Quartz Based Sytems,” International Symposiumon Micro-Mechanical Engineering 2003 (ISMME 2003), Tsukuba, Japan, 2003.
3. Y. Murakami, S. Chiashi, Y. Miyauchi, M. Hu, M. Ogura, T. Okubo, and S. Maruyama,“Vertically Aligned Growth of SWNTs "Mat" on a Quartz Surface,” 227th American
Chemical Society National Meeting, Anaheim CA, USA, 2004.
4. Y. Murakami, T. Edamura, E. Einarsson, S. Chiashi, Y. Miyauchi, and S. Maruyama,“Thermal CVD Growth of Vertically Aligned Single-Walled Carbon Nanotube Films on
Substrates and their Optical/Microscopical Characterizations,” International Forum on Heat
Transfer 2004 (IFHT 2004), Kyoto, Japan, 2004.
5. Y. Murakami, E. Einarsson, T. Edamura, and S. Maruyama, “Anisotropic Optical
Absorption Properties of Single-Walled Carbon Nanotubes,” International Symposium on
Nanometer-scale Quantum Physics (nanoPHYS’05), Tokyo, Japan, 2005.