Conductance quantization in multiwalled carbon nanotubes

Abstract

We present results of carbon nanotube conductance measurements. The experiments were performed using an scanning probe microscope (SPM) system where a carbon nanotube fiber is connected to the SPM tip and then lowered into a liquid mercury contact. Experiments were also performed using a modified transmission electron microscope (TEM) specimen holder supplied with piezo and micrometer positioning system. Thus the contacting process of the nanotubes with the mercury could be monitored while simultaneously recording the conductance. These measurements and observations confirm previously reported conductance quantization (Frank et al.: Science 280, 1744 (1998)) of the nanotubes while providing additional details concerning the mercury nanotube contacts. We also report conductance versus voltage characteristics of carbon nanotubes.

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Eur. Phys. J. D 9, 77–79 (1999)
THE EUROPEAN
PHYSICAL JOURNAL D
EDP Sciences
? c Societ` a Italiana di Fisica
Springer-Verlag 1999
Conductance quantization in multiwalled carbon nanotubes
Ph. Poncharal1, St. Frank1, Z.L. Wang2, and W.A. de Heer1
1School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA
2School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
Received: 2 September 1998 / Received in final form: 8 February 1999
Abstract. We present results of carbon nanotube conductance measurements. The experiments were per-
formed using an scanning probe microscope (SPM) system where a carbon nanotube fiber is connected
to the SPM tip and then lowered into a liquid mercury contact. Experiments were also performed using
a modified transmission electron microscope (TEM) specimen holder supplied with piezo and micrometer
positioning system. Thus the contacting process of the nanotubes with the mercury could be monitored
while simultaneously recording the conductance. These measurements and observations confirm previously
reported conductance quantization (Frank et al.: Science 280, 1744 (1998)) of the nanotubes while provid-
ing additional details concerning the mercury nanotube contacts. We also report conductance versus voltage
characteristics of carbon nanotubes.
PACS. 85.40.-e Microelectronics: LSI, VLSI, ULSI: integrated circuit fabrication technology – 61.46.+w
Clusters, nanoparticles, and nanocrystalline materials
1 Introduction
Transport in multiwalled carbon nantotubes has been in-
vestigated using from the simplest to the most complex of
experimental approaches[1]. In the simplest cases, the con-
ductance ofthe nanotube is deduced frommeasurementsof
bulk samples or films made of nanotubes [2]. In the more
complex cases, the contacts are lithographically patterned
on a substrate and a single nanotube is then connected
to them. In this manner, two, three and four probe meas-
urements of carbon nanotubes have been made [3–5]. The
electrical conductivity has also been measured using scan-
ning probe methods, where a nanotube is anchored at one
end to a conducting lead and the conducting tip of a scan-
ning force microscope is slid along the tube facilitating
conductance versus length measurements [6].
The measurements gave very diverse results with resis-
tances and resistivities spanning several orders of magni-
tude [3–5]. In fact in one case it appeared as if the cur-
rent was flowing in a tortuous manner through the tube
in a four probe measurement, since the voltage measured
at the inner conductors was in the opposite direction com-
pared to the voltage applied to the outer conductors [3].
In contrast, transport theory predicts entirely differ-
ent behavior: the conductance of single wall nanotubes
should be quantized [7,8] and either 0 or 2G0, where
G0= 2e2/h = 1/(12.9kΩ) [9–12]. This logically should
be a lower conductance bound for multiwalled nano-
tubes. In fact the measured conductances are usually much
smaller than G0(i.e. typically on the order of 1/(100kΩ) ≈
G0/10).Hence the contactsbetween the nanotubes andthe
leads were suspect. In principle, four probe measurements
should be immune to contact resistances, however in these
cases it may be that the gold/nanotube contacts are not
well reproducible and hence compensation is imperfect.
Another problem lies with the processing of the carbon
nanotubes. In principle, the nanotubes are quite robust,
due the extreme durability of the graphitic bond. However,
ultrasonification and other processes typically used to sep-
arate and manipulate the nanotubes can be destructive,
which may affect their transport properties [13,14].
2 Experiment
A better method to contact the nanotubes in pristine con-
dition is therefore to be sought. To this end we used the
nanotube fibers which were recovered from the nanotube
deposits of arc produced carbon nanotubes [15]. These
fibers consist mainly of densely packed multiwalled nano-
tubes and are about 1mm long and 0.1mm wide. The
fibers are attached to a gold wire (using silver colloid) and
attached to the piezo of a SPM (Park Instruments Auto-
probe). The assembly is lowered towards a liquid mercury
filled copper cup so that the conductance can be measured.
As we have previously demonstrated [1] the conductance
abruptly jumps from 0 to values close to 1G0. This value
might be sligtly less in some cases (up to 14kΩ), which
is what expected if the nanotube is not in perfect contact
with the fiber. When the fiber is submerged even further
the conductance increased stepwise (typically in units of
1G0, Fig. 1), until ultimately contact was made with the
stock, where the residual conductance is about 1000G0,

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78 The European Physical Journal D
Fig. 1. Conductance of a carbon nanotube fiber bundle which
is pushed into a liquid mercury surface (after completion of
the cleaning procedure) using the SPM method. The applied
voltage is 100 mV. According to our survey of the protrud-
ing nanotubes, the typical diameters are in the range of 15
to 35 nm. The four succesive steps are due to four nanotubes
which protrude from the fiber stalk. The nanotubes have differ-
ent lengths and hence they make contact with the mercury at
different times during the approach. Each nanotube contributes
1G0to the conductance and hence the steps. When the fiber is
pushed even deeper into the mercury, so that the stalk of the
fiber makes contact with the mercury, the conductance is on the
order of 1000G0.
(on the orderof10–20Ω). The measurementsarehighly re-
producible for each sample where the fiber can be lowered
into the mercury and retracted for many cycles where the
pattern of steps repeats.
However this reproducibility only occurs after several
thousand initial cycles when using a freshly constructed
nanotube contact. Initial residual conductances are much
smaller (as low as 0.02G0), and poorly quantized steps
which do not reproduce often appear. Moreover, the initial
curing cycles leave a visible black deposit on the mercury
surface which is evidently composed of fragments from the
fiber. Next, the contact position with the mercury is dis-
placed to a clean area, and the experiment is repeated
after which invariably quantized conductance steps are ob-
served (note that often presteps of 0.5G0 are observed,
see Frank [1]). From these observations we concluded that
the curing procedure had a cleansing effect of the tip of
the bundle wherebypoorlyconnected tubes wereseparated
from the tip leaving only well anchored tubes.
More recent experiments were performed in situ, in the
electron microscope, using a specially designed specimen
holder as shown in Fig. 2. With this device, a nanotube
fiber can be moved towards a mercury droplet which is
suspended at the end of a copper wire. The fiber can be
brought into contact with the mercury droplet either by
micrometer control or with using the piezo actuator. In
these experiments we were able to repeatedly make and
break contact between the tip of the fiber and the mercury,
so that the carbon nanotube which made the contact could
be identified.
This in situ configurationalso allowedus to monitor the
cleaning process described above: the nanotubes on a fresh
tip are covered with small graphitic particles and loose
agglomerations of nanotubes, as well as poorly connected
Fig. 2. TEM sample holder for in situ nanotube experiments
(length is 3.5 cm, width 0.7 cm). The nanotube fiber which is
attached to a gold wire (left) can be manually moved toward
the mercury droplet (right) by means of a micrometer. The
piezo actuator is used for the final approach. The micrometer
shaft can be decoupled from the sample to inhibit vibrations.
Fig. 3. Transmission electron micrograph of a nanotube ap-
proaching the mercury surface using the sample holder de-
scribed in Fig. 2. The long vertical nanotube is 2.2 µm long and
25 nm in diameter. A graphitic particle is attached to one of the
nanotubes. Small graphitic particles which have detached from
the fiber adhere to the mercury surface.
nanotubes, which are pushed away during submerging cy-
cles. What remains is a compact stalk from which straight
nanotubes protrude. At this time the mercury surface is
coveredwith patches ofnanotubes and small graphitic par-
ticles, which have been separated from the nanotube fiber
during the dipping process. In order to continue meas-
urements on clean mercury requires removing the sample
from the microscope and replacing the mercury contact.
We used several pre-cleaned fibers which were clearly dis-
tinguished from the untreated ones in that the nanotubes
tend to stick out perpendicular to the surface, and only
very few graphitic particles are observed on the nanotubes
(Fig. 3).
A difficulty important to overcome was to have the
parallax adjustable so that the contact point could be ob-
served (i.e. so that this point was not obscured from the
electron beam). Another difficulty relates to charge accu-
mulation on the sample holder which caused the images
to be unstable and caused blurring in many of the pho-
tographs.

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Ph. Poncharal et al.: Conductance quantization in multiwalled carbon nanotubes79
Fig. 4. Typical nanotube conductance versus voltage charac-
teristics. The nanotube conductance is constant and close to
integer values for low applied voltages (typically up to 100 mV,
see inset). At higher voltages, the conductance increases lin-
early. The solid curve, recorded using the SPM in air, exhibits
an increase of 0.25G0/Volt. The circles have been recorded in
the TEM and also show a linear increase (0.5G0/Volt). The
slopes are sample dependent and range from between 0.25 to
1G0/Volt. In the TEM measurement, contact was broken at
3 V (corresponding to a current of 0.6 mA) probably due to the
Lorentz force. The SPM measured nanotube was stable at 4 V
(0.5 mA). In the TEM we have observed nanotubes 1 µm in
length which were stable with currents on the order of 0.5 mA
passing through them.
These TEM experiments allowed us to directly verify
that the initial conductance was indeed made by single
nanotubes protruding out of the fiber. Once in contact, we
observed that by applying a sufficiently high voltage (usu-
ally about 3–5 V), one tube would suddenly jump away
and the conductance would drop to 0. The currents are
then typically 0.5mA which gives extraordinarily large
current densities (the observed nanotubes that survive the
cleaning process have diameters between 15 to 30nm). In
fact, even with this high current density, the nanotube may
not have burnt, since there is evidence that it was simply
pushed awaydue to the largeLorentzforcecausingthe con-
tact to be interrupted (note that the objective lens of the
microscope supplies a field of about 1T perpendicular to
the nanotube).
We also observed that not all nanotubes conduct. In
many cases nanotubes clearly contacted the mercury yet
the resistance was very large (> 10MΩ). This may reflect
the theoretical prediction that only one in three tubes con-
duct due to the helicity effect on the conductivity in single
wall nanotubes.
Quantum conductance is expected to be independent of
the nanotube diameter but should scalewith the number of
layers. In order to explain the observed effects, we assume
that only the outer layer of the nanotube participates in
the electrical transport [1].
Conductance versus applied voltage measurements
were performed both in air and in the microscope. Typ-
ically a V shaped flat bottomed curve is observed (see
Fig. 4), where a flat bottom occurs between −0.1V,
+0.1V. We do not have an adequate explanation for this
effect. However it may be related to the tunneling of elec-
trons from one layer to the next. It should be noted that
the loss of quantization at these very large voltages is not
in contradiction to the theory, since quantization is only
expected for low bias voltages.
3 Conclusion
The new results presented here demonstrate the feasibil-
ity of performing experiments where nanotubes are ma-
nipulted with direct visual control under the TEM. The
experiments confirm previous conclusions: the conduc-
tances of individual nanotubes can be measured in a fiber-
mercury contact experiment. The conductances measured
under TEM are consistant with the 1G0per tube reported
in [1].
The conductance versus voltage measurements demon-
strate that the conductance is constant for low bias volt-
ages (−0.1 to +0.1V) and increases linearly for larger volt-
ages with a slope which is sample dependent. We are not
aware of an explanation of this effect.
This work was supported by the ARO under project DAAG55-
97-1-0133. S.F. thanks the Alexander von Humbolt Founda-
tion for financial support. The authors thank U. Landman,
R.L. Whetten and P. First for helpful discussions.
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