Atomic structureand electronic properties of single-walled carbon nanotubes

Atomic structure
and electronic properties
of single-walled
carbon nanotubes

Teri Wang Odom*, Jin-Lin Huang*, Philip Kim†
& Charles M. Lieber*†
* Department of Chemistry and Chemical Biology, and † Division of Engineering
and Applied Sciences, HarvardUniversity, Cambridge,Massachusetts 02138, USA
 

Carbon nanotubes1 are predicted to be metallic or semiconducting
depending on their diameter and the helicity of the arrangement
of graphitic rings in their walls2–5. Scanning tunnelling
microscopy (STM) offers the potential to probe this prediction,
as it can resolve simultaneously both atomic structure and the
electronic density of states. Previous STM studies of multi-walled
nanotubes6–9 and single-walled nanotubes (SWNTs)10 have provided
indications of differing structures and diameter-dependent
electronic properties, but have not revealed any explicit relationship
between structure and electronic properties. Here we report
STM measurements of the atomic structure and electronic properties
of SWNTs. We are able to resolve the hexagonal-ring
structure of the walls, and show that the electronic properties
do indeed depend on diameter and helicity. We find that the
SWNT samples exhibit many different structures, with no one
species dominating.
The diameter and helicity of a defect-free SWNT are uniquely
characterized by the vector ch ¼ na1 þ ma2 [ ðn;mÞ that connects
crystallographically equivalent sites on a two-dimensional graphene
sheet, where a1 and a2 are the graphene lattice vectors and n and m
are integers (Fig. 1). Electronic band structure calculations2–5
predict that the (n,m) indices determine the metallic or semiconducting
behaviour of SWNTs. Zigzag (n,0) SWNTs should have two
distinct types of behaviour: the tubes will be metals when n/3 is an
integer, and otherwise semiconductors3–5. As ch rotates away from

(n,0), chiral (n,m) SWNTs are possible with electronic properties
similar to the zigzag tubes; that is, when ð2n þ mÞ=3 is an integer the
tubes are metallic, and otherwise semiconducting. The gaps of the
semiconducting (n,0) and (n,m) tubes should depend inversely on
diameter. Finally, when ch rotates 308 relative to (n,0), n ¼ m. The
(n,n) or armchair tubes are expected to be truly metallic with band
crossings at k ¼ 6 2=3 of the one-dimensional Brilluoin zone. It
has been suggested that SWNT samples produced by laser
vaporization11 and arc12 methods consist predominantly of (10,10)
metallic armchair tubes.
We have carried out STM measurements in ultra-high vacuum at
77 K on purified SWNT samples produced by laser vaporization11.
Typical atomically resolved images of a SWNT on the surface of a
rope, which consists of parallel tubes11, and isolated SWNTs on a
Au(111) substrate are shown in Fig. 2a and b, respectively. Figure 2a
shows the expected honeycombe lattice for a SWNT with a C–C
spacing of 0:14 6 0:02 nm. The chiral angle is readily determined by
identifying the zigzag tube axis direction (the line connecting sites
separated by 0.426 nm) relative to the sample tube axis. This shows
quite clearly that the tube is chiral with an axis orientated at an angle
of 28:0 6 0:58 relative to that for a zigzag nanotube. As the tube
axis is perpendicular to ch, this corresponds to the angle between ch
and (n,0) in Fig. 1. From this angle and the measured diameter of
1:0 6 0:05 nm, we can assign (n,m) indices of either (11,2) or (12,2);
the angle/diameter for (11,2) and (12,2) are -8.28/0.95nm and
-7.68/1.03 nm, respectively. We note that an (11,2) tube is expected
to be metallic, whereas a (12,2) tube should be semiconducting. The
helicity of the lower isolated SWNT in Fig. 2b was determined in a
similar manner, yielding a chiral angle of 211:0 6 0:58; the
diameter of this tube is 1:08 6 0:05 nm. These parameters match
closely the values expected for a (12,3) tube, 610.98/1.08 nm, and
reasonably exclude other choices of indices.
Central to the work reported here is our ability to characterize the
electronic properties of the atomically resolved nanotubes by
tunnelling spectroscopy. Specifically, current (I) versus voltage
(V) was measured at specific sites along the tubes and differentiated
to yield the normalized conductance, (V/I)dI/dV, which has been
shown13 to provide a good measure of the main features in the local
density of electronic states (LDOS) for metals and semiconductors.
The gradual increase in current in the I–V data (Fig. 2c, d) recorded
on the SWNTs imaged in Fig. 2a, b shows qualitatively that both
tubes are metallic. The LDOS determined from data sets recorded at
different locations along the tubes are very similar, demonstrating
the reproducibility of the measurements; furthermore, the LDOS
for both tubes are roughly constant between -600 and þ600mVas
expected for a metal. Small variations in the LDOS with energy are
not significant and arise from noise in the data. These spectroscopy
results are similar to those obtained on the Au(111) substrate except
that the surface state 450 meV below the Fermi level14 is also
observed on the latter.

The metallic behaviour of our (12,3) tube is in agreementwith the

prediction that ð2n þ mÞ=3 is an integer, and additionally suggests

that the indices for the tube in Fig. 2a are (11,2) rather than (12,2).

We have also characterized a metallic, achiral zigzag SWNT with a

diameter of 0:95 6 0:05 nm. This diameter is very close to the

expected 0.94nm diameter of a (12,0) tube, although possibly

indistinguishable from the 1.02nm diameter expected for a (13,0)

tube. There are two other important points that these data address.

First, curvature in the graphene sheet of a SWNT should cause

the p/j bonding and p*/j* antibonding orbitals on carbon to

mix and create a small gap at the Fermi level in these metallic

tubes3,5. We have not observed evidence for this small gap,

although it is possible that the thermal energy at 77 K, 7 meV,

smears the gap structure predicted to be of the order of 8 meV

for a (12,0) tube3. Second, the LDOS recorded on metallic

SWNTs in a rope and isolated on the substrate are similar, thus

suggesting that inter-tube interactions do not perturb the

electronic structure on an energy scale of 77 K.

We have also characterized a number of semiconducting SWNTs

in our studies. Indeed, more than half of the SWNTs observed either

as isolated tubes or in ropes were found to be moderate gap

semiconductors. A typical example of the atomically resolved

structural and tunnelling spectroscopy data obtained from isolated

SWNTs is shown in Fig. 3. Analysis of the image (Fig. 3a) shows that

the upper tube has a chiral angle of 11:2 6 0:58 (that is, opposite

helicity to the tubes in Fig. 2) and a diameter of 0:95 6 0:05 nm.

These angle/diameter constraints agree best with the 11.78/1.0nm

for a (14,-3) tube, although the 10.98/1.08nm angle/diameter of the

next closest (15,-3) indices are close to our uncertainty. The I–V

data recorded with this atomic-resolution image (Fig. 3b inset)

shows distinctly different behaviour from the metallic tubes and is

consistent with a semiconductor; that is, the current is very small for

2300 < V < þ400mVbut increases sharply when jVj is increased

further. The calculated (V/I)dI/dV shows sharp increases at -325

and þ425mV that correspond to the conduction and valence band

edges in the LDOS, and thus we assign a bandgap of 750 meV.

The observed semiconducting behaviour is consistent with the

expectation that a (14,-3) tube should be a moderate gap semiconductor

(that is, ð2n þ mÞ=3 is not an integer). In addition, we

have observed similar semiconducting behaviour for other chiral

and zigzag tubes characterized with atomic resolution. A summary

of the energy gaps (Eg) obtained from these measurements for tubes

with diameters between 0.6 and 1.1nm is shown in Fig. 3c. These

results show the expected1 1/diameter (d) dependence, and can be

fitted to Eg ¼ 2g0aC–C=d, where g0 ¼ 2:45 eV is the nearest-neighbour

overlap integral and aC–C is the C–C distance. Significantly, this

value of g0 is in good agreement with the value (2.5 eV) determined

from calculations1, and provides an additional consistency check in

this work.

Our observation of semiconducting and metallic SWNTs with

subtle changes in structure clearly confirm the remarkable electronic

behaviour of the nanotubes that may be exploited in future

Agustin Egui

EES

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