Scanning tunneling microscope investigation of carbon nanotubes produced by catalytic decomposition of acetylene

Article abstract of DOI:10.1103/PhysRevB.56.12490

A detailed scanning tunneling microscopy (STM) study of carbon nanotubes prepared by catalytic decomposition of acetylene over a supported transition metal catalyst is reported. Nanotubes with diameters in the 10-nm range and others with diameters as small as 1 nm were found. The mechanism of STM image formation and image deconvolution with respect to the tip shape are discussed, as well as the corrections which have to be applied when measuring by STM nanotube diameters in the ranges of 10 nm and of 1 nm, respectively. The behavior of a nanotube crossing steps on the graphite surface is analyzed. Modified height values measured on a single-wall nanotube in regions where it was subjected to strong mechanical stresses indicate changes in the electrical conductivity by several orders of magnitude. Carbon nanotubes are found to be good candidates to be used for STM tip shape characterization in the nm range.

Full text of DOI:10.1103/PhysRevB.56.12490

PHYSICAL REVIEW B
VOLUME 56, NUMBER 19
15 NOVEMBER 1997-I
Scanning tunneling microscope investigation of carbon nanotubes produced
by catalytic decomposition of acetylene
´
L. P. Biro
KFKI, Research Institute for Materials Science, H-1525 Budapest, P.O. Box 49, Hungary
S. Lazarescu, Ph. Lambin, P. A. Thiry, A. Fonseca, J. B. Nagy, and A. A. Lucas
´
ISIS, Facultes Universitaires Notre-Dame de la Paix, 61 Rue de Bruxelles, B 5000 Namur, Belgium
͑Received 23 December 1996͒
A detailed scanning tunneling microscopy ͑STM͒ study of carbon nanotubes prepared by catalytic decom-
position of acetylene over a supported transition metal catalyst is reported. Nanotubes with diameters in the
10-nm range and others with diameters as small as 1 nm were found. The mechanism of STM image formation
and image deconvolution with respect to the tip shape are discussed, as well as the corrections which have to
be applied when measuring by STM nanotube diameters in the ranges of 10 nm and of 1 nm, respectively. The
behavior of a nanotube crossing steps on the graphite surface is analyzed. Modified height values measured on
a single-wall nanotube in regions where it was subjected to strong mechanical stresses indicate changes in the
electrical conductivity by several orders of magnitude. Carbon nanotubes are found to be good candidates to be
used for STM tip shape characterization in the nm range. ͓S0163-1829͑97͒02543-5͔
I. INTRODUCTION
II. EXPERIMENT
A. Sample preparation and experimental conditions
Since the first observation of carbon nanotubes1 and the
subsequent report of the conditions for synthesizing large
quantities of nanotubes,2 different methods have been devel-
oped to produce and purify macroscopic quantities of this
material. A modification of the arc method uses transition
metal as a catalyst to enhance the production of single-wall
carbon nanotubes.3 A method based on the catalytic decom-
position of carbon containing gas on a transition metal cata-
lyst and subsequent chemical purification resulted in carbon
nanotubes with a yield of 23% of C weight.4,5 More recently,
a modification of the vapor growth method6 using transition
metal catalyst has been reported giving a yield of over 70%
of single-wall nanotubes ͑SWNT͒.7
The carbon nanotubes were produced by catalytic decom-
position of acetylene at 700 °C on a supported Co catalyst, as
described earlier.4,5 Samples were prepared by ultrasonica-
tion in toluene of the material resulting from the chemical
removal of the catalyst ͑A type sample͒; and by ultrasonica-
tion in toluene of the material obtained after the chemical
oxidation of the A type material in an aqueous solution of
KMnO4 /H2SO4 ͑B type sample͒. Both A and B type suspen-
sions were placed on freshly cleaved HOPG and the toluene
was evaporated at room temperature.
B. STM results
In the past decade, scanning tunneling microscopy8
͑STM͒ and atomic force microscopy9 ͑AFM͒ became basic
tools in the rapidly developing field of nanoscience. An over-
view of their applications to the investigation of fullerenes
and carbon nanotubes has been published recently.10 The
carbon nanotubes which have been investigated by STM can
be grouped in two families: The 1-nm diameter range11–14
and the 10-nm diameter range.15–18 A number of groups have
The samples were examined by STM under ambient con-
ditions, using mechanically prepared Pt tips. Tunneling volt-
ages in the range of 100–400 mV and tunneling currents in
the range of 0.2–1 nA were used. The horizontal and vertical
calibration of the STM was checked against the HOPG sub-
strate of the samples.
Only tubes with diameters in the 10-nm range have been
found in B type samples, with a few exceptions. In A type
samples, by contrast, individual tubes and bundles of tubes
with 1 nm diameter have been found in addition to the 10-nm
diameters. In a single occasion two nanotubes with an esti-
mated diameter in the 1 nm range were found in a B type
sample. These nanotubes were partly embedded in amor-
phous carbon, which made it difficult to determine their ex-
act diameter. The fact that these nanotubes were embedded
in amorphous material suggests that they were partially un-
covered by the ultrasonication of the sample in toluene, and
the amorphous coating may be the reason why they survived
the oxidation treatment.
reported atomic resolution on the outer wall of
a
nanotube.12,15,16 It was found that the periodicity of tunneling
current maxima is coincident with the value for highly ori-
ented pyrolytic graphite ͑HOPG͒, this being an indication
that the measured tubes were at least double-wall tubes.
To our knowledge, no detailed STM work has been re-
ported on carbon nanotubes produced by the catalytic de-
composition of a gaseous hydrocarbon. In the present paper
we report STM investigation of nanotubes produced by cata-
lytic decomposition and we discuss the influence that the tip
shape has on the apparent morphology of carbon nanotubes
in the STM images, a problem which has received less atten-
tion up to now.
A typical example of tubes of 10-nm diameter, from a B
type sample, is shown in Fig. 1. Several nanotubes emerge
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© 1997 The American Physical Society

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SCANNING TUNNELING MICROSCOPE INVESTIGATION . . .
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FIG. 2. Constant current plane view image of a single nanotube
from an A type sample, crossing a plateau with two unequal steps
on both sides. The apparent tube width is in the 160-Å range, while
the apparent height of the tube is in the 8–9 Å range. See dimen-
sions in Fig. 4 and Table I.
density of states ͑LDOS͒ in the vicinity of the Fermi level,
corresponding to the point of the sample surface over which
the tip is found. If the nanotubes were lying on a surface
made of a different material, such as gold, or had a different
electronic structure, the variations of the tunneling current
could not be translated into topography in a straightforward
way.
The images of nanotubes with diameter in the 1-nm range
prepared by the catalytic procedure have been compared with
STM images of SWNT ropes prepared by laser ablation as
reported in Ref. 7 and used here as size standards. It was
found that the nanotubes look similar in the two different
samples. This confirms the validity of our estimation of the
measured diameter, since the nanotubes prepared by laser
ablation are known to have diameter in the 1-nm range.
FIG. 1. Constant-current STM image of carbon nanotubes of a
10-nm diameter in a B type sample. ͑a͒ Plane view image; note the
light object ͑marked with a cross in the center͒ from which emerge
three nanotubes. ͑b͒ Line cut along the black line shown in part a;
the protruding ‘‘hill’’ of 460 Å corresponds to the tip shape; note
the plateau in the line cut on the right-hand side of the ‘‘hill’’ which
corresponds to the height of the nanotube.
from the light object near the lower right corner of the im-
age. The height of the tube along which the line cut is run-
ning, is in the 10–12 nm range over a distance of 0.5 ␮m.
We prefer to use the height of the tube for estimating its
diameter, for reasons that will be discussed in detail later.
In Fig. 2, a plane view image of a long nanotube is shown
from an A type sample. The estimated diameter of the tube is
in the 1-nm range. The tube crosses several steps; particu-
larly interesting is the plateau which runs from the lower
edge of the image towards the upper right-hand corner. As
can be seen from the gray shades, the step height is different
on the left- and right-hand sides of the plateau. One can
notice from the gray scale given at the right-hand side of the
image and from the horizontal image scale, that there is a
mismatch between the apparent height and apparent width of
the tube. This matter will be discussed in detail later.
Figure 3͑a͒ shows a large scale image of a ‘‘raft’’ of
parallel nanotubes of 10–20 Å diameters. Figures 3͑b͒ and
3͑c͒ show details taken over the raft. The profile along the
line cut marked in Fig. 3͑c͒ is shown in Fig. 3͑d͒. Having a
raft of nanotubes with similar diameters is an ideal situation
for deconvoluting the tip shape and the tube shape, as will be
discussed in more detail later on. In this case one of the
parameters which is difficult to determine, namely, the dif-
ference in the widths of the tunneling gaps over the support
͑HOPG in our case͒ and over the nanotubes, can be dis-
carded. According to the model proposed by Tersoff and
Hamann,19 the tunneling current is dependent on the local
C. Image analysis and deconvolution
Two diameter ranges of nanotubes ͑10 and 1 nm͒ have
been observed experimentally. Different aspects of the image
formation are to be considered in these two ranges. For in-
stance, in the case of a tube with a diameter of 10 nm one
can neglect the effects arising from the different values of
LDOS over HOPG and over the tube. It is justified to do so,
because the rule of thumb is that a modification by a factor
of 10 of the tunneling current induces a variation of the tun-
neling gap of 1 Å. So, the error produced by the difference in
the LDOS is not significant as compared with the total diam-
eter of 100 Å. However the nanostructure of the tip cannot be
neglected in this case. It is extremely unlikely to have nan-
otips with a very high aspect ratio having a length exceeding
say 15 nm. This means that the shape of the tip on the last 10
nm will have a significant effect on the apparent topography
of the nanotube.
The case of a tube with a diameter of 1 nm is totally
different. Here, the variations of the LDOS cannot be ne-
glected. It will be shown that defects in a tube of 1 nm can
have a significant influence on the apparent height of the
tube on account of the extreme sensitivity of the electrical

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12 492
L. P. BIRO et al.
56
FIG. 3. Constant-current STM images of a bundle of single-wall nanotubes from an A type sample. ͑a͒ Large scale plane view image. ͑b͒
Detail of part a ͑image zoomed physically, not by software͒; note the three nanotubes emerging from the lower right hand corner. ͑c͒ Detail
of three nanotubes seen in part b emerging from the lower right-hand corner ͑image zoomed physically, not by software͒; the line cut along
the black line is shown in part d. ͑d͒ The line cut marked in part c. See Fig. 7 and Table II for dimensions averaged over five different line
cuts.
conductivity of carbon nanotubes to defects.20 The effect of
the nanoshape of the tip can be neglected ͑the shape on the
last 10 nm͒ if the image is taken with a sharp nanospike. It is
possible to have high aspect ratio nanospikes with a length of
the order of 15 Å. However, one should not forget that a
mechanically prepared tip can have several nanotips of com-
parable length. This cannot be observed by scanning an
atomically flat surface like HOPG, because in this case only
the longest nanospike is active. During the scanning of a
nanotube however, the cooperative effect of close nanospikes
may lead to an apparent increase of the tube height. If the tip
is not sharp, its shape can be calculated and taken into ac-
count by using the measured profile of steps on HOPG.
1. Nanotubes of 1 nm diameter
In this section the images in Fig. 2, and Fig. 3͑c͒ will be
analyzed. The region of the plateau from Fig. 2 is shown
schematically in Fig. 4 ͑region II͒. The measured apparent
dimensions of the tube, i.e., the half diameter D/2 and the
height h are given in Table I. The numerical values are the
result of averaging 10 values from line cuts taken in different

56
SCANNING TUNNELING MICROSCOPE INVESTIGATION . . .
12 493
FIG. 4. Model structure of the plateau region seen in Fig. 1. The
solid ellipses labeled by numerals show the apparent cross sections
built on the basis of the measured dimension given in Table I.
locations in regions 1, 2, 3, and 4. One notices that, while the
half diameter values fluctuate within the lateral experimental
error, in the vertical direction ͑which is known to have at
least an order of magnitude better resolution than the hori-
zontal direction͒, there is a clear difference in region 3 as
compared with the other regions. The second observation is
that the tube seems to have a height only about 20 times
smaller than its width. An aspect ratio of that sort is highly
unrealistic. In Fig. 4, the cross sections built according to the
measured values are shown as black ellipses. The differences
in the LDOS of HOPG and of the tube cannot account for
this.
One can use the two steps on both sides of the plateau to
get information on the tip shape. The height of the step from
region I to region II is 10 Å. If one compares the ideal
͑geometric͒ step shape with the one measured along a line
cut crossing the step, data about the radius of curvature of the
tip can be extracted. The topographic profile of the step is
extending over 150 Å, which we use as an estimate of the tip
half width at the height of 10 Å. The height of the step from
region II to region III is 39 Å; here a tip half width of 250 Å
is found at 39 Å from the end of the tip. Using these data,
and assuming a spherical tip for simplicity, one can calculate
a radius of curvature of 975 Å for the tip, i.e., an extremely
blunt tip. In Fig. 5͑a͒ a qualitatively similar situation is
sketched of a blunt spherical tip imaging a small nanotube.
The tip may be regarded as a circle of radius Rϩ⌬, the
spherical tip radius plus the width of the tunneling gap, roll-
ing over the circle of radius r representing the nanotube.
Several successive positions of the tip are shown in lighter
gray. One can notice that the apparent diameter D will ex-
ceed several times the real diameter d. The ratio D/d de-
pends on the value of R, r, and ⌬. In the range of tunneling
currents used here, one can assume that ⌬ and r are of simi-
lar magnitude. With this simplification in mind and using
simple geometry, one can estimate r from the formula
FIG. 5. Convolution effects influencing the apparent diameter of
a small nanotube imaged by a blunt tip. ͑a͒ Rolling a sphere of
radius Rϩ⌬ over a tube of radius r, where ⌬ is the tunneling gap
width, considered identical for HOPG and the nanotube; the small
solid dots indicate the point which is considered to be the tunneling
point during the image construction. ͑b͒ More realistic case where
the separation ␦ between the nanotube and the underlying HOPG
and the different tunneling gap widths, ⌬1 for HOPG and ⌬2 for the
nanotube, are considered.
Using the values of Table I, a radius of 1.9 Å is estimated
for the tube of Fig. 2. This value deviates by a factor of
2–2.5 from the radius values which can be estimated from
the height on the undamaged parts of the tube. The deviation
shows that the differences in the width of tunneling gap for
HOPG and for the nanotube cannot be neglected. If the width
of tunneling gap for the nanotube, ⌬2 , is smaller than the
corresponding value for HOPG, ⌬1 , the sphere representing
TABLE I. Measured half diameter, D/2, and height, h, in re-
gions 1, 2, 3, and 4 ͑see Fig. 4͒ over the nanotube crossing a plateau
shown in Fig. 2.
Region
1
2
3
4
D/2 ͑Å͒
h ͑Å͒
87Ϯ2.88
8.5Ϯ0.17
87Ϯ2.65
9.2Ϯ0.33
84Ϯ1.72
5.5Ϯ0.21
81Ϯ4.64
9.0Ϯ0.35
2
D/2͒
4R
͑
rϭ
.

´
12 494
L. P. BIRO et al.
56
TABLE II. Measured half diameter, D/2, and height, h, for the
three tubes seen in Fig. 3͑c͒.
Tube
1
2
3
Three tubes
D/2 ͑Å͒
h ͑Å͒
11.6Ϯ1.49
8.0Ϯ0.30 10.0Ϯ0.24
8.6Ϯ0.27 13.9Ϯ0.70
8.1Ϯ0.30
29.8Ϯ0.33
to amorphous carbon in region 3. However there is no reason
to expect that the amorphous carbon deposit will conserve
the tube width.
When the tip is sharp enough, one can obtain nearly co-
incident width and height values. However, in this case too,
it is recommended to analyze the images carefully. The de-
convolution of the image and that of the line cut shown in
Fig. 3͑c͒ and Fig. 3͑d͒, respectively, is simplified by the fact
that the three tubes seen in the image lie on top of a bundle
of similar tubes as shown in Fig. 3͑b͒. With the assumption
that the nanotubes of the bundle were formed under similar
conditions ͑they contain similar numbers of defects͒, it is
reasonable to suppose that the width of the tunneling gap is
similar over the tubes of the same bundle. Moreover, the
compression effects due to the tunneling tip, if any, should
be similar as long as the diameter of the nanotubes does not
differ strongly from one tube to the other. With these con-
siderations in mind, one can accept that the measured height
values correspond to the real diameter of the tubes. By aver-
aging over different line cuts taken through the image of Fig.
3͑c͒, the values of Table II have been obtained. The different
quantities measured are shown schematically in Fig. 7. One
can notice from Table II that the sum of the D/2 values of the
three nanotubes is greater than half the D value of the three-
tube unit measured together, which is a geometric impossi-
bility. This result is a consequence of the distorted diameter
resulting from the convolution with the tip shape.
FIG. 6. Three-dimensional detail of the plateau region viewed
from the side of 39-Å high step ͑region III͒. Note the discontinuity
of the tube at the edge of the plateau and the different height values
in region II.
the tip will suffer a ‘‘deformation’’ while rolling over the
nanotube ͓see Fig. 5͑b͔͒ instead of behaving like a rigid body
as in Fig. 5͑a͒. When the tip starts rising in the vicinity of the
nanotube ͑due to the additional tunneling current from the
nanotube͒, the distance between the center of the tip and the
center of the nanotube becomes Rϩ⌬2ϩr, where ⌬2Ͻ⌬1 .
As the tube is not an integral part of the underlying HOPG, it
is reasonable to expect that under identical conditions, the
tunneling current flowing through the tube will be smaller
than the tunneling current over the HOPG. This means that
in constant-current imaging, the width of the tunneling gap
will be reduced over the nanotube as shown in Fig. 5͑b͒. In a
situation like that discussed for Fig. 2, one cannot expect a
better estimation of the tube radius from the measured D
values, unless one finds a reliable way to determine the ad-
sorption distance ␦ and the difference in tunneling distances
⌬1Ϫ⌬2 . As shown in Fig. 5͑b͒, the opposite contributions
of ␦ and ⌬1Ϫ⌬2 to the apparent tube height produce the
least distortion in the tube dimensions when the tip is right
on the top of the nanotube. Therefore, the best value of the
diameter is given by the height of the tube.
Analyzing the data of Table II, and the line cut in Fig.
3͑d͒, one can conclude that the three tubes lie close to each
The measured height values reported in Table I show that
the tube crossing the plateau in Fig. 2 is a nanotube with a
diameter in the range of 9 Å. This means that it is likely a
single-wall nanotube. Coming to the problem of the height
measured in region 3, detailed three-dimensional images like
that in Fig. 6 reveal that while the tube is continuous from
region I to region II, it has broken from region II to region
III. Furthermore, the line cuts taken on the tube lying on
region II support the idea that the tube has broken in three
parts as indicated by gray shades in Fig. 4. It is reasonable to
assume that before breaking, the nanotube had to support the
highest stresses in region 3 ͑see the stress calculations be-
low͒. Therefore, in this region a lot of defects could have
been produced. As reported recently, the accumulation of
defects can modify the electrical resistivity of a nanotube by
several orders of magnitude.20 So, the apparent height de-
crease of 3 Å may result from a decrease of the conductivity
by three orders of magnitude due to the structural defects
accumulated before breaking. If the tube had collapsed into a
single graphene layer on the HOPG, a step of 3.35 Å would
have been expected together with a simultaneous widening
of the structure. It cannot be ruled out that the tube collapsed
FIG. 7. Schematic representation of the three-tube unit shown in
Fig. 3͑c͒. Solid circles numbered 1, 2, and 3 stand for the three
tubes, light circles labeled by letters represent the effective tip ͑tip
radius plus tunneling gap width͒ modeled by a sphere. Different
positions during the scan are shown. The quantities which are given
as numerical values in Table II are indicated, too. In position A, the
tip starts tunneling to tube 1 and starts lifting; in position B, al-
though the separation between tubes 1 and 2 would allow it, the tip
does not go down to the base line because of tunneling to both
tubes, 1 and 2; in position C, the tip is the tunneling point to the
point with tube 2; in position E, the tip tunnels to tubes 2 and 3; in
position F, the tip separates from tube 3 and starts tunneling to the
base line only.

56
SCANNING TUNNELING MICROSCOPE INVESTIGATION . . .
12 495
other but they do not touch. The sum of rounded height
values ͑considered to be closer to the real diameters͒ is 26 Å,
while the total width of the structure is 59.6Ϯ0.33 Å. Com-
paring the h and D/2 values for the tubes on the left- and
right-hand sides of the group of three tubes, a slightly asym-
metric tip shape can be derived, with an average radius of
curvature of 14.4 Å. This is an effective value, i.e., the cor-
responding ⌬ gap value is included in it. Figure 7 shows the
schematic arrangement. The tip starts moving upwards in
position A due to the proximity of tube 1. In position B,
although the width of the gap between tubes 1 and 2 would
allow it, the tip does not go down to the base line, because
when it enters between tubes 1 and 2, it starts tunneling to
tube 1, to the base line, and to tube 2. So instead of tunneling
to a plane, the tip tunnels to a surface which can be modeled
by half a cylinder concentric to the tip. In position E, the
geometrical width of the gap is smaller than the tip diameter.
Therefore, in this case the apparent half width of tube 2 will
be smaller than in reality. The 1.3-Å difference between the
height and the D/2 value of tube 3 in position F, as com-
pared with position A, shows that the tip has a slightly asym-
metric shape. To make the analysis simpler, it was supposed
that the three nanotubes lie on a flat surface. If one takes into
account that they rest on other tubes of similar diameters, the
vertical diameter should be 1.13 times the measured height.
This yields for the geometrically corrected diameters:
9.0Ϯ0.33 Å, 9.1Ϯ0.33 Å, and 11.3Ϯ0.27 Å, respectively.
One can calculate the expected diameters d of the possible
nanotubes from the formula,10
FIG. 8. Schematic representation of a scan line taken by a flat
tip with a sharp spike shorter than the diameter of the nanotube, the
nanotube is indicated by a solid circle. Several positions of the tip
during the scan are indicated by gray lines. The solid line shows the
scan line; small solid circles indicate the points which would be
used by a hypothetical software for the image construction. Zone A,
correct image of the flat surface; zone B, the right-hand corner of
the flat region of the tip starts tunneling to the nanotube, however,
the points considered for image construction will be those shown by
small solid circles; zone B is a transition region; zone C, the nano-
tube images the flat region of the tip; zone D, transition region;
zone E, correct image of the nanotube taken by the sharp spike;
zone F, correct image of the flat surface.
yields a huge number of nanotips ͑spikes͒. Over an atomi-
cally flat surface, the active tip will be the longest one. The
situation will be drastically different if the scanned object is
a three-dimensional object, since switching from spike to
spike will occur while the tip scans the object. So, if the
object has a diameter of 10 nm, in most of the cases the
resulting image will be a convolution of the sample shape
with the averaged tip shape, as seen in Fig. 1͑b͒ in the por-
tion of the line cut which crosses the light object marked in
its center by a black cross. The radius of curvature of this
object being smaller than the radius of curvature of the tip, it
images the tip. It is difficult to establish the nature of this
object: it could be an upward pointing nanotube grown to-
gether with the three other tubes seen in the image. The
stability of the ensemble may be given by the three nano-
tubes which can be seen in Fig. 1 emerging from the sharp
object.
In Fig. 9, two line cuts from consecutive images taken
over the nanotube emerging from the sharp object towards
the right-hand side of the image in Fig. 1 are shown. As
guides for the eyes, the gray ellipses show the cross section
of a nanotube of 120 Å in diameter. One can observe that the
tube is situated close to a step. The imaging conditions for a
flat surface are constant from one image to the other as
shown by the same step height of 26 Å in both line cuts.
However, the apparent tube shape is different. The shape of
the line cut in Fig. 9͑b͒ may be the result of a double tip as
shown in Fig. 10. When the main tip is in position B, the
point marked by a small solid circle is considered as a tun-
neling point for the image construction. In fact, the tunneling
will take place to another point of the main tip and to the
secondary tip, as shown by solid lines. The shape of a line
cut through the nanotube marked as a large solid circle is
also shown. One may conclude that for the case of nanotubes
of 10 nm in diameter, the safest way to measure their diam-
eter is to take a line cut running along the axis of the tube
and comparing it to a nearby flat region of the substrate.
2
ͱm ϩn ϩmn/␲,
2
dtϭ)aCϪC
where aCϪCϭ1.421 Å, m and n being two integers. On that
basis and taking in account the stability criterion given in
Ref. 7, according to which the armchair (m,m) tubes are the
more stable ones, one may tentatively identify the measured
tubes as being ͑7,6͒ or ͑7,7͒, and ͑9,8͒, respectively.
2. Nanotubes of 10-nm diameter
As already mentioned, the problems which have to be
taken in account in the case of nanotubes of 10 nm in diam-
eter are qualitatively different from those encountered in the
case of nanotubes with 1 nm in diameter. The geometry of
the tip on a scale of 10 nm is frequently far from being ideal
in the case of mechanically prepared tips, which have been
widely used for nanotube measurements. A schematic pre-
sentation of the problem that may arise is given in Fig. 8.
The tip has a sharp spike, and it may be regarded as a very
good tip for working on a flat sample. However, if the length
of this spike does not exceed the diameter of the nanotube,
the image will have important contribution from the flat part
of the tip over a significant length of the line cut shown in
the figure: regions B, C, and D. As the radius of curvature
of the nanotube is smaller than that of the flat region of the
tip, over region C, the role of sample and tip will be re-
versed: the nanotube is imaging the tip. Because of mechani-
cal strength of materials, it is unrealistic to suppose that one
can have stable spikes 15-nm long with a diameter of 10 Å,
except if one considers using nanotubes themselves for tips,
as reported recently by Dai and co-workers.21 The second
problem which should be considered is that cutting a Pt wire

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L. P. BIRO et al.
56
nanotubes, very few line cuts were reported and often even
the gray scales were omitted from the images. This omission
makes an STM image very difficult to interpret. STM has a
two orders of magnitude better resolution in the direction
perpendicular to the sample surface as compared with the
in-plane resolution. As a consequence, most commercially
available STM softwares use nonequal axes in image presen-
tation, i.e., the vertical axis is several times extended with
respect to the horizontal ones. Therefore, if no gray scale or
line cut accompanies the image, it is very hard to decide to
what extent the diameter values which are given are accurate.
In most of the cases it is not recommended to take the ap-
parent diameter of the nanotube as geometrical diameter, as
emphasized above.
The presence of nanotubes with both 1-nm and 10-nm
diameters in the material resulting from the catalytic process
suggests that there are two different mechanisms responsible
for the production of nanotubes. The single-wall nanotubes
have been reported most frequently when a transition metal
catalyst was present during the tube synthesis, irrespective of
whether the arc method, laser evaporation, or the catalytic
decomposition of carbon containing gas was used. The ob-
servation of nanotubes with 1 nm in the material produced
by the catalytic method confirms that the factor which en-
hances the production of single-wall nanotubes is the pres-
ence of the transition metal atoms, with less importance
played by the physical or chemical status of the material
which carries the transition metal. This supports the idea that
the transition metal atoms contribute like individual entities
to the production process of the single-wall carbon nano-
tubes. A mechanism which fulfills this criterion is the scooter
mechanism proposed by Thess et al.7 The production mecha-
nism of the nanotubes with diameters in 10-nm range seems
to be correlated with the size of the catalyst particles. The
proposed mechanism is based on the production of C2 units
over the catalyst and their addition to the growing nanotube.
As discussed in earlier papers,22,23 the multiwall nanotubes
grow around the catalytic particles. High-resolution trans-
mission electron microscopy supports this mechanism, see
Fig. 3͑b͒ in Ref. 23.
FIG. 9. Two consecutive line cuts taken over the same nanotube
shown in Fig. 1, extending to the left hand side of the light object
marked in its center by a cross. The gray ellipses are shown to guide
the eyes, they correspond to nanotubes with a diameter of 120 Å.
Note the constant height difference between the upper side and
lower side of the step which runs parallel to the nanotube. The
temporary alteration of the shape of the nanotube is due to a sec-
ondary tip as shown schematically in Fig. 10͑a͒ without secondary
tip; ͑b͒ with secondary tip.
III. DISCUSSION
The absence of nanotubes with a diameter in the range of
1 nm from most of the B type samples suggests that the
single-wall nanotubes were attacked and destroyed during
the chemical oxidation of the soot. This can happen very
easily if the tube is broken during the previous treatments, or
not terminated by a cap. In this case it will be attacked from
the open end and will be oxidized. In Fig. 3͑b͒, one notices
the same phenomenon as reported by Olk and Heremans11
that the broken end of the nanotubes is associated with a
higher tunneling current. This appears in the image as a
brighter end when compared with the body of the tube. This
may be the result of dangling bonds. Again, this supports the
idea that the single-walled nanotubes with broken ends will
be destroyed during the chemical oxidation.
As pointed out in the previous section dedicated to image
analysis and deconvolution, several effects have to be con-
sidered when using STM to produce images of three-
dimensional objects instead of atomically flat surfaces. Un-
fortunately, frequently in the published papers on carbon
The bending of a nanotube crossing a surface step, as
revealed in Fig. 2, was analyzed theoretically by solving the
beam equation of elasticity,
FIG. 10. Schematic representation of the effect on the scan line
of a secondary tip developed on the main tip. Compare with experi-
mental line cuts in Figs. 9͑a͒ and 9͑b͒. Small solid circles mark the
points considered in image construction, heavy line joining the
nanotube and the tips mark the really active tunneling directions.
d4z Kz
ϭ
,
dx4 EI

56
SCANNING TUNNELING MICROSCOPE INVESTIGATION . . .
12 497
fragile there. The fact that the nanotube in Fig. 2 broke at the
edge of the largest step can therefore be understood on these
grounds. However, the stresses computed for the tube cross-
ing a 30-Å step were found roughly the same as the ones
plotted in Fig. 11 for the 10-Å step. The tube is in some way
floating on the repulsive potential from the substrate and it
just takes more place to bend when the step height increases.
Considering now the energetics of the problem, the excess
of energy ⌬E of the deformed nanotube with respect to a
broken one whose two halves lie flat on both terraces is
composed of two parts: ͑a͒ the strain energy, due to the elas-
tic deformation of the nanotube; and ͑b͒ the reduction of
adsorption energy, which merely concerns that part of the
tube that lies over the normal adsorption distance from the
lower terrace. If ⌬E exceeded the energy of the carbon co-
valent bonds, the breaking of the nanotube could occur. One
can estimate the latter as 4␲Rt␥, where ␥ is the surface
tension of graphite perpendicular to the basal planes. On the
other hand, the excess energy ⌬E/4␲Rt calculated from the
solution of the elastic equation is 0.054 and 0.12 eV/Å2 for a
nanotube crossing a 10- and 30-Å step, respectively. The
latter value still is approximately 2 times smaller than ␥
͑0.26 eV/Å 2͒.26 It is only with a step about 100-Å high that
the energy of a broken nanotube becomes smaller than that
of the deformed tube but, still, the breaking of all the C-C
covalent bonds at the step would represent a large potential
barrier to overcome.
FIG. 11. ͑a͒ Bending of a nanotube crossing a 10-Å step on
graphite substrate computed from linear elasticity. ͑b͒ Longitudinal
͑full curve͒ and transverse ͑dashed curve͒ stresses along the lowest
fiber of the deformed nanotube. The x and z scales in part ͑a͒ differ
from each other and, so, the apparent tube diameter ͑10 Å͒ varies
with the slope of its axis.
where z(x) is the curve taken by the axis of the tube when
loaded by the force per unit length Kz , E is the Young
modulus, and Iϭ␲R3t is the moment of inertia of the beam
cross-sectional area, with radius R and an assumed small
layer thickness t. The loading force is the one that binds the
tube to graphite. It was derived from C-C pair potentials
C
12 /r12ϪC6 /r6 that were integrated over the semi-infinite
From both the stress calculations and the energetics ap-
proach just developed, it can be concluded that the breaking
of the nanotube in Fig. 2 was probably caused by the STM
tip. The region shown in Fig. 2 was indeed scanned from
bottom to top, so that the nanotube was first loaded on the
side of the higher step.
substrate and a unit of length of the tube. For a tube with
small thickness, Kz is found proportional to t, so the ratio
Kz /EI becomes independent of this parameter, and the same
holds true for the elastic curve z(x). The potential param-
eters were taken from Girifalco.24 With these parameters, the
equilibrium distance of a 10-Å diameter nanotube to the con-
tinuum edge modeling the graphitic substrate is 2.72 Å. By
comparison, a flat carbon sheet would be 2.98 Å above the
continuum edge.
IV. CONCLUSIONS
Figure 11 shows the results obtained for a nanotube of
10-Å diameter crossing a 10-Å step ͑three graphite interlayer
distances͒ that aimed at representing the situation realized in
Fig. 2 on the smaller-step side of the terrace. In these calcu-
lations, the Young modulus of the nanotube had the value
recently measured for nanotubes, 1.8 TPa.25 The graphite
substrate was considered as a nondeformable body. The cal-
culations indicate that the deformation of the nanotube is
taking place from roughly 200 Å before to 100 Å after the
step. These results fit reasonably well the experimental ob-
servations. After the step edge, there is a slight overshoot of
the nanotube, where it rises above its normal distance from
the plateau surface, and reaches its maximum deviation ͑0.17
Å͒ 30 Å away from the step.
The stresses computed along the lowest fiber ͑the genera-
tor closest to the substrate͒ of the nanotube are shown in Fig.
11͑b͒. The transverse stress component ␴xz , which was av-
eraged over the cross sectional area of the nanotube, visual-
izes the interaction with the substrate. The largest interaction
is realized just after the step edge, where the nanotube pen-
etrates deeper in the repulsive core of the substrate. The lon-
gitudinal fiber stress ␴xx , due the curvature of the tube axis,
is much larger and it also reaches its maximum amplitude
close to the step. As a consequence, the nanotube should be
Detailed image analysis and deconvolution has been per-
formed on STM images of carbon nanotubes. This study re-
vealed the existence of 1-nm diameter nanotubes in the
samples produced by the catalytic-cracking method. In addi-
tion, a number of recommendations stem from the image
analysis: ͑i͒ if the nanotubes have a diameter in the range of
10 nm and when one can be sure that the nanotubes are lying
on a flat surface, the more accurate estimate of their diameter
is the measured height value; ͑ii͒ if the nanotubes have di-
ameters in the range of 1 nm, due to the different LDOS over
the support and over the nanotube, the use of support mate-
rials other than graphite may complicate the image formation
beyond a desirable level; ͑iii͒ in the case of nanotubes with a
diameter of 1 nm the most advantageous situation is when
one can choose a flat lying bundle and try to determine the
dimensions of the tubes in the topmost layer; however, even
in this case, the geometry of the system has to be analyzed
carefully; ͑iv͒ even blunt tips may be used to estimate diam-
eters of the order of 1 nm if one can be sure that the nanotube
is lying on a flat surface and other structures, like steps on
the HOPG surface, are used to characterize the tip shape.
The variation of the apparent height of the nanotube
crossing the step in Fig. 2 shows that due to accumulation of
defects when subjected to high levels of mechanical stress,

´
12 498
L. P. BIRO et al.
56
the electrical properties of a carbon nanotube may suffer a
strong modification.
for STM and AFM as the latex or gold spheres have in scan-
ning electron microscopy.
The simultaneous presence of tubes with 1-nm diameter,
and tubes with 10-nm diameter suggests that there are two
different formation mechanisms during the nanotube produc-
tion by catalytic decomposition of a gaseous hydrocarbon
over a transition metal catalyst.
ACKNOWLEDGMENTS
The authors wish to thank to Dr. D. T. Colbert for pro-
viding samples of single-wall nanotubes and to D. Bernaerts
´
for helpful discussions. L. P. Biro gratefully acknowledges
The fact that in the B type sample only nanotubes with the
diameter in the 10-nm range have been found is an indication
that the oxidation treatment destroys the single-wall nano-
tubes.
Due to their cylindric shape, carbon nanotubes are good
candidates for being used to characterize the shape of the
STM tip in the nm range. Nanotubes may play a similar role
the financial support of CGRI of the French Community of
Belgium and of the Facultes Universitaires Notre-Dame de la
´
Paix, Namur, Belgium. This work has been partly funded by
the Interuniversity Research Program on Interfacial Materials
and Mesoscopic Structures initiated by the Belgian Science
Policy Programming ͑PAI-IUAP P3-49͒. The work in Hun-
gary was supported by AKP Grant No. 96/2-637.
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