Synthetic Metals 103 (1999) 2555−2558

Optical Properties of Single-Wall Carbon Nanotubesa,*H. Kataura
a

a

b

c

c

c

Department of Physics, Faculty of Science, Tokyo Metropolitan University, 1-1 Minami- Ohsawa, Hachioji, Tokyo 192-0397, Japanbca, Y. Kumazawa , Y. Maniwa , I. Umezu , S. Suzuki , Y. Ohtsuka and Y. Achiba

Department of Applied Physics, Faculty of Science, Konan University, 8-9-1 Okamoto Higashinadaku, Kobe 658-8501, Japan

Department of Chemistry, Faculty of Science, Tokyo Metropolitan University, 1-1 Minami- Ohsawa, Hachioji, Tokyo 192-0397, Japan

Abstract
Four kinds of single-wall carbon nanotubes (SWNTs) with different diameter distribution have been synthesized and opticalabsorption spectra have been measured. Three large absorption bands due to the optical transitions between spike-like density of states,
characteristics of SWNTs, were observed from infrared to visible region. Comparing with the calculated energy band, it has beenconcluded that the first and the second lowest absorption bands are due to the optical transitions between spikes in semiconductor phases
and the third one is due to that in metallic phases. Absorption Peaks sensitively shifted to higher energy side with decreasing tube
diameters as the band calculation predicted. Resonance Raman spectra were also measured using various laser lines. When the excitation
is in an energy region corresponding to the absorption band of metallic phase, spectra have shown Breit-Wigner-Fano line shape, which isa sign of metallic phase. Using these results, we can easily characterize SWNTs from the optical absorption spectra without Raman
measurements and transmission electron microscope observations.
Keywords: Infrared and Raman spectroscopy, UV-Vis-NIR absorption, Photothermal deflection spectroscopy, Graphite and related
compounds

1. Introduction
From the discovery of the single-wall carbon nanotube(SWNT) by Iijima and Ichihashi [1], many investigators havestudied this new form of carbon to clarify its attractive physicalproperties aiming for a development of future applications. [2]Theoretical works indicated that SWNT has characteristic
electronic structure due to a low dimensionality, such as spike
like density of states due to one-dimensional van Hove singularity.
[3,4] Within a zone-folding scheme, one third of all the SWNTs
are metallic and always have wider first energy gaps between
spikes than semiconducting ones with almost the same diameters.
Indeed, very recently, Wildöer et al. have directly observed
electronic density of states of individual SWNTs by scanningtunneling spectroscopy and have shown a good agreement withthe tight-binding zone-folding calculation. [5] On the other hand,
Rao et al. have shown resonance Raman spectra of SWNTs for awide energy region. [6] Very sharp resonant feature shows that
optical transitions between spikes of density of states seem toenhance the Raman intensity. Thus, it is very interesting tomeasure optical absorption spectra of the SWNTs. Opticaltransition between spikes will be observed and different energy
gap values in metallic and semiconducting SWNTs will be seen.
Technologies to synthesize SWNTs have greatly advanced todate. Both a double laser vaporization method using Ni/Co
catalyst [7] and an electric arc method using Ni/Y catalyst [8] can
synthesize very high concentration of SWNTs in a soot product.
*E-mail address: kataura@phys.metro-u.ac.jp.

Diameter control technique has also been advanced. For example,
very thin SWNTs could be synthesized by laser vaporization of
Rh/Pd catalyzed graphite rod. [9]In this report, the optical absorption spectra of SWNTs withvarious diameter distributions will be shown. For an assignmentof the spectra, π band of SWNT was calculated by tight-bindingzone-folding method. Further, resonant Raman spectra for a wide
excitation energy region will be shown.

2. Experimental
SWNTs were prepared by both laser vaporization and electricarc methods. Details of procedure of the laser vaporization
method have been published previously, [10] and the electric arc
method is quite conventional one. In the laser vaporization
method, the second harmonic Nd:YAG laser pulse is focused on
the metal catalysed carbon rod settled in a quartz tube which washeated to 1200 °C by electric furnace and was filled 500 Torr Ar
gas. Laser-vaporized carbon and catalyst finally became sootcontaining SWNTs and nanoparticles of the catalysts. In thismethod, we can control a diameter distribution of SWNTs
changing a temperature of the furnace. On the other hand, theelectric arc method has a simple procedure. DC arc between
catalyzed carbon anode and pure carbon cathode produced
SWNTs in 500Torr He. We can also control diameters of SWNTs
with changing the pressure of He gas. Used catalysts forformation of SWNTs are NiY (4.2-1 at.%), NiCo (1.2 at.%), Ni

H. Kataura et al. / Synthetic Metals 103 (1999) 2555 − 2558

2556

1
In ten sity (a rb. units)

Phototherm al deflection signal (arb. unit)

D =1.35 nm

PDS

0.6

0.4

P ristine

O ptical density

Purified

0.2

O ptical density (arb. units)

0.8

488nm
D =0.83 nm

N iY
N iC o
Ni
Rh Pd

120

160

200

240

280

-1

R am an shift [cm ]N iY (w eb)

N iC o(11 50C )N i(1 1 50 C )

0
0

1

2

3

4

5

6

R hP d(12 00C )Photon energy (eV )0.5(0.6 at.%) and RhPd (1.2 at.%), which have provided anotherdiameter distributions. In the case of NiY, web like SWNTs
obtained by electric arc could be easily purified by heating in air
at 350 °C for 30 minutes and by rinsing out metal particles inhydrochloric acid. Details will be described elsewhere.
Resonant Raman scattering was measured using 1 m double
monochromator, JOBIN YVON U-1000, and photo-multiplier,
HAMAMATSU PHOTONICS R943-02, with various laser
systems, Ar laser, Nd:YAG laser, dye laser and Ti-sapphire laser.
Since each laser has a different beam profile and a total sensitivityof measuring system changes with excitation wavelength, it isquite difficult to calibrate the relative intensity. To minimize theseeffects, in this paper, obtained Raman intensities were normalized
by integrated Raman intensity of a crystalline Si that was also
used as a standard of Raman shift.
A thin film of SWNTs was prepared by a painting method.
The soot containing SWNTs was dispersed in ethanol
homogeneously by supersonic waves, and was sprayed on aquartz plate using an airbrush with a hot air blow. The thickness
and uniformity of the film were controlled by eyes. Opticaltransmittance spectra were measured with HITACHI U-3500
spectrophotometer.
The optical absorption spectrum was measured also by
photothermal deflection spectroscopy (PDS) [11] for thermallypurified SWNTs fabricated by the electric arc method using theNiY catalyst. This technique measures heat which is produced
during relaxation of the electron hole pair generated by theabsorbed light. The PDS has advantages to measure scattering
materials since it measures optical absorption directly. In thismeasurement, carbon black was used as a black body reference.
Thus the spectrum reflects the difference in electronic states
between SWNTs and amorphous carbon.

1

1.5

2

2.5

3

3.5

P hoton energy (eV)Fig. 2. Optical absorption spectra of four kinds of SWNTs withdifferent diameter distributions. Background absorption due tothe π plasmon was subtracted. Inset shows Raman spectra of thebreathing mode, which provide a rough estimation of thediameter distribution. Electric arc method was used for NiY
catalyst and all the other samples were synthesized by laser
ablation method. Peaks at 0.55 and 0.9 eV are absorption by thequartz substrate.
3.5

3.0
(6,6)

G ap e nergies (eV )Fig.1. Optical absorption spectra of SWNTs. Solid curveshows optical density of SWNTs film on quartz plate fabricatedby electric arc method using NiY catalyst. Broken curve andDotted curve show optical density and PDS signal of purified
SWNTs (NiY), respectively. Due to the saturation of the PDS
signal, intensity decreased with increasing photon energy andmeasurements were restricted up to 3 eV.

2.5

M etal2.0(1 0,10)

1.5

S em iconducto r

1.0

0.5
R hP d
0.0
0.6

0.8

N iY

1

1.2

1.4

1.6

1.8

D iam e ter (n m )Fig. 3. Calculated gap energies between mirror-image spikes indensity of states for γ = 2.75 eV. Solid circles indicate themetallic SWNTs and open circles the semiconducting ones.
Double circles indicate the armchair-type SWNTs. Gap energies
for all the chiral indexes with larger diameter than (5,5) areplotted as a function of diameter. Arrows show diameter
distributions for the each catalyst. Two horizontal lines in eachcatalyst area show “metallic window” in which the opticaltransitions only by the metallic tubes would be observed.

H. Kataura et al. / Synthetic Metals 103 (1999) 2555 − 2558(a) N iY (thin)

3. Results and Discussion

2557
X 3

2.73 eV
2.66 eV1/ 2 3k x a   k y k  cos  + 4 cos 2  y E2 D = ± γ 1 + 4 cos







 2 
 2   2 .

(1)

2.54 eVR elative inten sity to c-Si (arb. un its)

2.50 eV

2.73 eV

2.41 eV
2.66 eV

2.06 eV

2.54 eV
2.02 eV
2.50 eV
2.41 eV
2.06 eV

2.02 eV
1.81 eV

1.81 eV

1.75 eV

1.75 eV

1.71 eV
1.66 eV
100

150

200

1.71 eV
1.66 eV

250 1400

1500
1600
-1
Ram an shift [cm ]-1

Ram an shift [cm ](b) Rh Pd

2.73 eV

1700

X 1/2

2.60 eV

2.73 eV

2.54 eV

2.60 eV
2.54 eV
2.41 eV
2.33 eV

2.41 eV
2.33 eVR elative inten sity to c-Si (a rb. u nits)

From the transmission electron microscope (TEM)
observation and A1g breathing mode frequencies in Raman spectra,[12] it was found that diameters of SWNTs were distributed from1.24 to 1.58 nm for NiY catalyst, from 1.06 to 1.45 nm for NiCo
and Ni, and from 0.68 to 1.00 nm for RhPd. Most of the catalysts,
except for the RhPd, show very similar diameter distribution forboth the laser vaporization and the electric arc methods at acondition giving the highest yield. In the case of RhPd catalyst,
however, none of SWNTs are synthesized by arc discharge incontrast with a high yield by laser vaporization method.
Solid curve in Fig. 1 shows optical absorption spectrum of
SWNTs synthesized by the electric arc method using NiY catalyst.
Three large absorption peaks at 0.68, 1.2 and 1.7 eV are
superposed on the broad absorption due to π plasmon. To confirm
that these peak structures are characteristics of SWNTs, it needs
to be checked that the peaks are due to neither the absorption of
metal catalysts remaining in the sample nor the light scattering
losses by the soot. In the beginning, to remove the soot andcatalyst, purification was performed as mentioned above and thedecrease of nanosphere and catalysts was confirmed by TEM
images and X-ray diffraction. Broken curve in Fig. 1 shows theabsorption spectrum of the purified sample. Almost the sameabsorption structure with pristine sample indicates that theabsorption structure is originated from SWNTs. As a second
approach, optical absorption spectrum was measured by PDS,
which is not affected by the light scattering. PDS signal is plottedin Fig. 1 with a dotted curve. Since carbon black powder wasused as a reference, PDS signal reflects the difference inelectronic states between amorphous carbon and SWNTs. Sharp
absorption peaks are apparently observed almost the same
position to the optical density, which indicates that these peaks
are not due to the light scattering losses. Since it was recognizedthat the remaining nanosphere and metal particles do not affectthe optical absorption spectrum, optical absorption spectra ofpristine samples were adopted as those of the SWNTs.
Figure 2 shows the optical absorption spectra of SWNTs withdifferent diameter distributions. For a convenience, large
background due to π plasmon was subtracted. Inset shows the low
frequency Raman spectra of the SWNTs. Diameter distributions
can be estimated from the peak frequencies with a rule, ω ∝ 1 / D,where D is a diameter of SWNT. [4] Thus, higher lying Raman
peak indicates existence of smaller diameter of SWNT.
For all the samples, very similar absorption structures are seen.
In the case of NiY catalyst, a sharp absorption band at 0.68 eV,slightly broad band at 1.2 eV and rather broad band at 1.7 eV are
observed. This structure is kept in the case of NiCo and Ni
catalysts but peak positions are considerably different. For
example, in NiCo case, the first peak lies at 0.72 eV and in caseof Ni catalyst, lies at 0.8 eV. In the thinnest case of RhPd, thefirst peak is observed around 1 eV and has shoulder. Further, thethird absorption band is not observed clearly.
To explain these absorption spectra, band structure of SWNT
was calculated using zone-folding method. [4] Tight-binding πband structure of two-dimensional graphite sheet is expressed by

2.17 eV
2.10 eV
2.00 eV
1.80 eV

2.17 eV

1.72 eV
2.10 eV

2.00 eV
1.68 eV
1.59 eV
1.50 eV
200

240

280

320
-1

Ram an shift [cm ]1.80 eV
1.72 eV
1.68 eV
1400

1500

1600

1700
-1

Ram an shift [cm ]Fig. 4. Resonance Raman spectra of SWNTs. (a) SWNTs
synthesized using NiY catalyst and (b) SWNTs using RhPd. For
the discussion, SWNTs displayed in (a) have been chosen tohave thinner diameter distribution than that in Fig. 2.
Here, γ is the overlap integral and a is a lattice constant. Using eq.
(1), one-dimensional energy band of SWNT could be calculated
applying a periodic boundary condition for any chiral vectors.
Wave vector conserving optical transition would occur between
mirror image spikes of density of states due to the
one-dimensional van Hove singularities. Gap energies between
the mirror spikes are indicated in Fig. 3. When the chiral index isexpressed in (n1, n2), the condition to be metallic is 2n1 + n2 = 3l,where l is an integer. [4] Thus, one third of all the indexes show
metallic character, which is indicated by circles on zero line andthe other indexes are semiconducting , finite value of energy gaps.
In Fig.3, it is clear that the first and second lowest energy gaps
between spikes come from the semiconducting tubes and the third

H. Kataura et al. / Synthetic Metals 103 (1999) 2555 − 2558

2558

while electronic scattering backgrounds are very small in both thespectra compared with the alkali metal doped systems. [13]Now we return to the resonance Raman spectra in Fig. 4(a).
At the “metallic window” region, from 1.66 to 1.81 eV, lowfrequency spectra show very simple feature. Only four large andrather broad peaks arise in this energy region. From theirfrequencies and resonance energies, these peaks are assigned as(16,4) for 154 cm-1, (10,10) for 163 cm-1, (18,0) for 157 cm-1 and(12,6) for 178 cm-1. Since these SWNTs with even-evennumbered indexes have small unit cells, they would show thestrong Raman intensities. [12]SW N T (N iY / thick)Intensity (arb. units)

1.77 e V

1/q = − 0.2 2, ω =1 556 cm
Γ = 2 5 cm

-1

-1

0

SW N T (R hPd)
2.41 eV
1/q = − 0.2 5, ω =1 530 cm
Γ = 4 5 cm

0

400

-1

8 00

4. Conclusion

-1

0

1 200

1 6 00-1

R am an shift (cm )Fig. 5. Raman spectra of metallic SWNTs. Dotted curves show
Breit-Wigner-Fano line shapes.
one comes from the metallic tubes with almost the same diameter.
If the sample contain both type of SWNTs with indicateddiameter distribution, SWNTs by NiY catalyst will show opticalabsorption peaks at 0.55, 1.1 and 1.7 eV and higher lying peak
will have larger half width. On the other hand, in the case of
RhPd, absorption peaks around 0.9 and 1.8 eV are expected but
the third group by metallic tubes is extended too widely to beobserved as an absorption band. These theoretical predictions
show very good correspondences with experimental results shownin Fig. 2. Each absorption peak consists of a lot of narrowabsorption peaks of constituent SWNTs. Indeed, observed eachabsorption peak in Fig. 2 has fine structures. From these analyses,
we have concluded that the first and second absorption peaks are
due to the semiconducting SWNTs and third one is due to themetallic SWNTs. If this is true, only metallic SWNTs will beresonated in Raman spectrum when the laser excitation is tuned at“metallic window” shown in Fig. 3.
Figure 4 (a) and 4(b) show the wide range resonance Raman
spectra of SWNTs using NiY and RhPd catalysts, respectively.
Relative Raman intensity of low frequency region is roughly
proportional to the magnitude of optical absorption of SWNTs.
At the high frequency region, broad and asymmetric Raman peak
was observed around 1.8 eV for NiY case and around 2.4 eV for
RhPd case, which correspond to the “metallic window”. Thisasymmetric Breit-Wigner-Fano (BWF) line shape was alreadyreported by Rao et al. in K and Rb doped SWNTs. [13] The BWF
line shape is given by
I (ω) = I0 {1 + (ω − ω0) / qΓ}2 / {1 + ((ω − ω0) / Γ)2},(2)

where I0, ω0, Γ and q are intensity, renormalized frequency,
broadening parameter and the lineshape parameter, respectively.
Because of the broad resonance feature of high frequency Raman
mode [14], there remain the sharp peaks from semiconducting
SWNTs. Nevertheless, main part of Raman spectra in Fig.5 could
be fitted with eq. (2) successfully. Fitting parameters are indicatedin Fig. 5. This means that SWNTs on resonance are metallic,

Optical absorption spectra of SWNTs were measured andthree large absorption peaks were observed. One-dimensionalband calculation and resonance Raman scattering indicate that thefirst and second lowest peaks are due to optical transition between
mirror image spikes in density of states of semiconducting tubes
and the third one is due to metallic tubes. Since the peak positionis very sensitive to the diameter like a breathing mode in the
Raman spectrum, diameter distribution of the SWNTs can also be
estimated from the absorption spectrum. Furthermore, the mixture
ratio between the metallic and semiconducting tubes may roughly
be estimated from the intensity ratio between absorption peaks
due to metallic and semiconducting phases.
Ando [15] has shown that the considerable amount of the
optical intensity is transferred to exciton bound states because ofquasi one-dimensional nature of SWNTs. Indeed, the firstabsorption peak position is slightly higher than the calculated
energy gap and corresponds to the exciton states under the
Coulomb interaction.

Acknowledgements
The authors thank Prof. R. Saito for fruitful discussion about
phonon mode in SWNT. The authors thank Mr. Misaki for TEM
observations. This work was partially supported by Japan Society
for the Promotion of Science Research for the Future Program
and was partially supported by Grant-Aid for Scientific Researchfrom Ministry of Education, Science and Culture.

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