World Journal of Nano Science and Engineering, 2012, 2, 53-57
http://dx.doi.org/10.4236/wjnse.2012.22009 Published Online June 2012 (http://www.SciRP.org/journal/wjnse)
Electrical Conductivity of Collapsed Multilayer
Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Coyoacán, México
Received January 27, 2012; revised February 18, 2012; accepted March 25, 2012
Synthesis of multilayer graphene on copper wires by a chemical vapor deposition method is reported. After copper
etching, the multilayer tube collapses forming stripes of graphitic films, their electrical conductance as a function of
temperature indicate a semiconductor-like behavior. Using the multilayer graphene stripes, a cross junction is built and
owing to its electrical behavior we propose that a tunneling process exists in the device.
Keywords: Multilayer Graphene; Electrical Conductivity; Klein Tunneling; Chemical Vapor Deposition
Graphene and related systems are of great interest due to
their physical properties and also by their possible appli-
cations. Although graphene is a zero band gap semimetal,
chemical and geometrical modifications of this material
allow different electronic and optical properties. For exam-
ple, in hydrogenated  and fluorinated  graphene a
band gap is opened, besides graphene nanoribbons can
also have a gap and other novel electronic properties .
Nanoholes in periodic arrangements can induce magnetic
behavior  or band gap opening . Change of the local
electrical conductivity by moving the Fermi level, using
an external bias for example, following predetermined
geometrical patterns has been proposed as a mean of con-
trolling the propagation of electromagnetic modes. That
is, graphene has been proposed as a metamaterial with
cloaking properties  or more complex functionalities
based on transformation optics .
On the other hand, under radial deformation carbon
nanotube eventually collapses and for radius greater than
a crossover value, the collapsed state is more stable than
the tubular geometry . In some cases collapse induces
metallic carbon nanotubes to become semiconducting,
and vice versa . In this work, we explore the synthesis
and the study of some electrical properties of similar
collapsed tubes, but at the macroscopic scale, depositing
multilayer graphene on copper wires by a chemical vapor
deposition (CVD) method.
CVD method is a promising technique to grow gra-
phene in large area using copper foil as a catalyst and
hydrocarbon vapors as the carbon source . Due to the
low carbon solubility in copper, the reaction of hydro-
carbon species is limited to a region near to the copper
surface, allowing the synthesis of graphene in almost
any arbitrary form of the copper surface. Here we ex-
ploit this advantage to synthesize few-layer graphene
 on cylindrical copper surface by CVD at atmos-
2. Experimental Details
Multilayer graphene were grown on copper wire by a
chemical vapor deposition method at ambient pressure.
The wires were heated in an hydrogen ambient with 25
sccm flux up to 1000˚C and maintained at this tempera-
ture by 15 min to anneal the copper wire. After this
process hydrogen flux were adjusted to 90 sccm and
methane was added with 25 sccm flux during 15 minutes,
at the end of the process, methane flux was cut off and
the furnace was turned off and the sample was cooled in
the hydrogen atmosphere to room temperature. Copper
was etched in a ferric nitrate aqueous solution, washed
with deionized water and the carbonaceous film was
transferred to copper grids for transmission electron mi-
croscopy (TEM) observation, and to glass substrates for
optical observation and electrical characterization. Care
should be taken because in this process the films may be
damaged by tearing or be folded in some regions. The
electrical characterization was carried out in a chamber
equipped with a heater and a cold stage for cooling be-
low room temperature using liquid nitrogen. Silver strips
obtained by thermal evaporation 1 mm apart were used
as electrical contacts, at a fixed bias voltage the electrical
current through the sample was measured under vacuum
conditions (~10–4 Torr).
opyright © 2012 SciRes. WJNSE
3. Results and Discussion
3.1. Collapsed Multilayer Graphene Tubes
Two kinds of wires with different diameters were used,
the diameter being measured after the synthesis process
using an optical microscope such as is observed in Fig-
ure 1(a). The average diameter of the thinner one is 63
μm and 163 μm for the thicker wire (at this level, the
thickness of the multilayer graphene is negligible). In
Figure 1(b) the collapsed multilayer graphene tube on
glass substrate as observed by an optical microscope in
the transmission mode is shown.
The mean width (W) of the collapsed tubes is 92 μm
and 203 μm for the thinner and thicker copper wires,
respectively. It should be noted that similar structures
have been reported by other authors but using nickel
nanowires as the template .
Figure 1. (a) Copper wire with average diameter of 63 μm
with bilayer graphene on its surface; (b) Collapsed tube of
multilayer graphene after copper etching with an average
width of 92 μm transferred to a glass substrate, the darker
fringe on the middle of this image is a folded region of the
Using a digital image obtained through the optical mi-
croscope to measure the transmittance of the film ,
we found a value of ~91%, and using the generalized rule
of 2.3% of absorbance per graphene layer , then our
films approximately have 4 layers of graphene. But the
film is formed by the collapsed tube, therefore this means
that under our experimental conditions of synthesis, mainly
a bilayer graphene is formed on the surface of the copper
As complementary information, in Figure 2 TEM image
(a) and the diffraction pattern (b) of the freely supported
collapsed tube are shown. Note from Figure 2(a) that the
films are somehow inhomogeneous, and the diffraction
pattern shows that the sample is polycrystalline.
Figure 2. (a) TEM image of freely supported multilayer film,
scale bar is 50 nm; (b) Diffraction pattern of the same film.
Copyright © 2012 SciRes. WJNSE
D. MENDOZA 55
3.2. Electrical Characterization of Collapsed
In Figure 3 electrical conductance as a function of tem-
perature for the two kinds of samples is presented. A
linear behavior for both samples appears to be a good
description of the electrical conductivity, as is observed
by the straight line fit to the upper curve in Figure 3(b).
Using the results presented in Figure 3(b) at T = 300 K,
and the following geometrical data: L = 10–3 m, W = 9.2
× 10–5 m and W = 2.03 × 10–4 m for the narrow and
broad samples, respectively, and for the thickness t we
suppose 4 layers (see Section 3.1) with 0.34 nm thick per
layer, that is, t = 1.36 × 10–9 m; which yield values for
the electrical conductivity of 1.04 × 106/Ωm and 9.05 ×
105/Ωm for the narrow and broad samples, respectively.
These values are close to the reported 1.1 × 106/Ωm ob-
tained by fitting the results for a variety of multilayer
graphene films synthesized by CVD .
Regarding the linear temperature dependence of the
conductivity, theoretically this dependence has been pre-
dicted for a monolayer in the ballistic regime  and for
bilayer graphene for diffusive transport mediated by
100 150 200 250 300 350
C o n d u c t a n c e (m S)
Stra ig h t lin e fit
Figure 3. (a) Schematic of the geometry of the multilayer
graphene stripe along with electrical contacts. (b) Measured
electrical conductance as a function of temperature for the
two kinds of films. The corresponding sheet resistance at
room temperature is: ~707 Ω/sq for W = 92 μm and ~812
Ω/sq for W = 203 μm.
disorder , in both cases at high temperatures. But it
should be noted that even in the early theoretical work on
graphite, a linear dependence of the electrical conductiveity
along the graphene layers was also predicted . Alth-
ough bilayer graphene was grown on the copper wire in
our case, in the collapsed situation and owing to ts lateral
dimension, the film can be considered as a four layer
graphene. But some care should be taken since the lateral
edges along the dimension L (see schematic in Figure
3(a)) may contribute to the electrical conduction because
ideally the edges are curved and closed borders.
3.3. A Cross-Stripe Junction Device
On the other hand, taking advantage of the shape of the
obtained multilayer graphene films, we built devices in
the typical cross-stripe junction used in tunneling spec-
troscopy . Firstly, two copper wires (~5 mm long, 63
μm diameter) covered with multilayer graphene were
crossed and fixed on a glass slide substrate using an epoxy
glue in their extremities, then copper was etched and the
sample washed with deionized water. Current (I) against
voltage (V) characterization was made by injecting cur-
rent into two adjacent arms and measuring voltage across
the opposite arms of the device . In Figure 4(a)
conductance near zero bias as a function of temperature
of the junction is shown, and in Figure 4(b) I(V) curves
at three different temperatures in a log-log scale are pre-
sented. Due to the geometrical configuration of the device
one should expect that the primary contribution to the
electrical transport across the junction is perpendicular to
the graphene layers, at least in the layers in close contact
between the two stripes. An estimation of the electrical
conductivity of the junction can be done as follows. The
area corresponds to the intersection of the two stripes (92
μm × 92 μm in this case), for the length the graphite in-
terlayer distance is taken as a first approximation, the
conductance at room temperature is (see Figure 4(b)) 15
× 10–3/Ω; all these finally yield to a value of ~6 × 10–4/Ωm
for the conductivity. If this value is taken as the conduc-
tivity perpendicular to the layers, and a value of ~1 × 106/
Ωm (see Section 3.2) for the conductivity along the gra-
phene layers; then an anisotropy factor of the parallel to
the perpendicular conductivity of ~1.7 × 109 is obtained.
Clearly, this value does not represent a physical charac-
teristic of the graphite structure because a value of ~3 ×
103 for the anisotropy factor for crystalline graphite has
been reported . In other words: the conductivity of
the junction between the two stripes is at least of the order
of 105 less than the conductivity of the contact between
two graphene layers in the ideal structure of graphite.
Due to this fact, and that the conductance near zero bias
decreases when temperature decreases (Figure 4(a)) and
also because the differential conductance increases as the
Copyright © 2012 SciRes. WJNSE
Figure 4. Electrical characteristics of the cross-stripe junc-
tion device. (a) Conductance against temperature measured
at a fixed current of 10 μA; (b) Current as a function of voltage
for positive and negative polarities at different tempera-
tures: green triangles (89 K), red circles (296 K) and blue
squares (380 K).
voltage bias increases (Figure 4(b)), it is very likely that
the cross-stripe device is a tunnel junction .
As a last observation, it should be noted that superlin-
ear behavior on the current dependence I~Vα, specifically
with α = 3/2, has been predicted for graphene within the
framework of Schwinger´s pair production and Klein
tunneling [21-24]. Under some specific conditions, a
linear behavior for small voltages is also found [23,24].
As a guide for the eye, in Figure 4(b) the linear and su-
perlinear ~V3/2 behaviors are plotted. Note that the linear
behavior is reasonably well reproduced for low voltages,
being a small vertical shift the difference for the three
temperatures, and a ~V3/2 tendency appears to be a good
option for higher voltages. We believe that our device
has the appropriate geometry to observe tunneling phe-
nomena, possibly Klein tunneling, because particles tun-
nel from one electrode to the other through a barrier, that
in this case could be vacuum. Probably, tunneling takes
place between the two adjacent parallel graphene layers
of the multilayer graphene stripes that form the junction.
As the voltage bias across the junction is changed, there
is a relative shift of the Fermi level on the two sides of
the barrier, and therefore scanning a range of energies
around the Fermi energy  of graphene. In any case, it
would be interesting to built hybrid structures, using
multilayer graphene stripe as one electrode and super-
conducting or magnetic films as the counter electrode in
the cross-stripe geometry. Experiments in this direction
are currently in process in our laboratory.
Bilayer graphene was grown on copper wires by means
of CVD method with methane as the carbon source. Af-
ter etching the copper wire, the bilayer tube collapses
forming stripes of four-layer graphene. A linear depend-
ence of the electrical conductance as a function of tem-
perature is found for this kind of films. Using the mate-
rial obtained by this method, a cross-stripe junction is
built, its electrical conductance behavior as a function of
voltage bias and temperature indicates that the device is a
kind of tunnel junction. It is proposed that this kind of
device might be appropriate to observe Klein tunneling.
I thank Carlos Flores IIM-UNAM for the transmission
electron microscopy observations.
 J. O. Sofo, A. S. Chaudhari and G. D. Barber, “Graphane:
A Two-Dimensional Hydrocarbon,” Physical Review B,
Vol. 75, No. 15, 2007, Article ID: 153401.
 R. R. Nair, W. Ren, R. Jalil, I. Riaz, V. G. Kravets, L.
Britnell, P. Blake, F. Schedin, A. S. Mayorov, S. Yuan, M.
I. Katsnelson, H. M. Cheng, W. Strupinski, L. G. Bu-
lusheva, A. V. Okotrub, I. V. Grigorieva, A. N. Grigorenko,
K. S. Novoselov and A. K. Geim, “Fluorographene: A
Two-Dimensional Counterpart of Teflon,” Small, Vol. 6,
No. 24, 2010, pp. 2877-2884.
 X. Wang, Y. Ouyang, L. Jiao, H. Wang, L. Xie, J. Wu, J.
Guo and H. Dai, “Graphene Nanoribbons with Smooth
Edges Behave as Quantum Wires,” Nature Nanotechnol-
ogy, Vol. 6, No. 9, 2011, pp. 563-567.
 D. Yu, E. M. Lupton, M. Liu, W. Liu and F. Liu, “Collec-
tive Magnetic Behavior of Graphene Nanohole Superlat-
tices,” Nano Research, Vol. 1, No. 1, 2008, pp. 56-62.
 W. Lu, Z. F. Wang, Q. W. Shi, J. Yang and F. Liu,
“Band-Gap Scaling of Graphene Nanohole Superlattices,”
Physical Review B, Vol. 80, No. 23, 2009, Article ID:
 P. Y. Chen and A. Alu, “ Atomically Thin Surface Cloak
Using Graphene Monolayers,” ACS NANO, Vol. 5, No. 7,
Copyright © 2012 SciRes. WJNSE
Copyright © 2012 SciRes. WJNSE
2011, pp. 5855-5863. doi:10.1021/nn201622e
 A. Vakil and N. Engheta, “Transformation Optics Using
Graphene,” Science, Vol. 332, No. 6035, 2011, pp. 1291-
 G. Gao, T. Cagin and W. A. Goddard, “Energetics, Struc-
ture, Mechanical and Vibrational Properties of Single-
Walled Carbon Nanotubes,” Nanotechnology, Vol. 9, No.
3, 1998, pp. 184-191. doi:10.1088/0957-4484/9/3/007
 P. E. Lamert, P. Zhang and V. H. Crespi, “Gapping by
Squashing: Metal-Insulator and Insulator-Metal Transi-
tions in Collapsed Carbon Nanotubes,” Physical Review
Letters, Vol. 84, No. 11, 2000, pp. 2453-2456.
 X. Li, W. Cai, J. An, S. Kim, J. Nah, D. Yang, R. Piner,
A. Velamakanni, I. Jung, E. Tutu, S. K. Banerjee, L. Co-
lombo and R. S. Ruoff, “Large-Area Synthesis of High-
Quality and Uniform Graphene Films on Copper Foils,”
Science, Vol. 324, No. 5932, 2009, pp. 1312-1314.
 A. W. Robertson and J. H. Warner, “Hexagonal Single
Crystal Domains of Few-Layer Graphene on Copper Foils,”
Nano Letters, Vol. 11, No. 3, 2011, pp. 1182-1189.
 R. Wang, Y. Hao, Z. Wang, H. Gong and J. T. L. Thong,
“Large-Diameter Graphene Nanotubes Synthesized Using
Ni Nanowire Templates,” Nano Letters, Vol. 10, No. 12,
2010, pp. 4844-4850. doi:10.1021/nl102445x
 C. Bautista and D. Mendoza, “Multilayer Graphene Syn-
thesized by CVD Using Liquid Hexane as the Carbon Pre-
cursor,” World Journal of Condensed Matter Physics, Vol.
1, No. 4, 2011, pp. 157-160.
 R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov,
T. J. Booth, T. Stauber, N. M. R. Peres and A. K. Geim,
“Fine Structure Constant Defines Visual Transparency of
Graphene,” Science, Vol. 320, No. 5881, 2008, p. 1308.
 S. Chen, W. Cai, R. D. Piner, J. W. Suk, Y. Wu, Y. Ren, J.
Kang and R. S. Ruoff, “Synthesis and Characterization of
Large-Area Graphene and Graphite Films on Commercial
Cu-Ni Alloy Foils,” Nano Letters, Vol. 11, No. 9, 2011,
pp. 3519-3525. doi:10.1021/nl201699j
 M. Müller, M. Bräuninger and B. Trauzettel, “Tempera-
ture Dependence of the Conductivity of Ballistic Gra-
phene,” Physical Review Letters, Vol. 103, No. 19, 2009,
Article ID: 196801.
 S. Adam and M. D. Stiles, “Temperature Dependence of
the Diffusive Conductivity of Bilayer Graphene,” Physi-
cal Review B, Vol. 82, No. 7, 2010, Article ID: 075423.
 P. R. Wallace, “The Band Theory of Graphite,” Physical
Review, Vol. 71, No. 9, 1947, pp. 622-634.
 E. L. Wolf, “Principles of Electron Tunneling Spectros-
copy,” Oxford University Press, New York, 1989.
 M. S. Dresselhaus and G. Dresselhaus, “Intercalation
Compounds of Graphite,” Advances in Physics, Vol. 30,
No. 2, 1981, pp. 139-326.
 D. Allor, T. D. Cohen and D. A. McGady, “Schwinger
Mechanism and Graphene,” Physical Review D, Vol. 78,
No. 9, 2008, Article ID: 096009.
 R. Rosenstein, M. Lewkowicz, H. C. Kao and Y. Korni-
yenko, “Ballistic Transport in Graphene Beyond Linear
Response,” Physical Review B, Vol. 81, No. 4, 2010, Ar-
ticle ID: 041416. doi:10.1103/PhysRevB.81.041416
 B. Dóra and R. Moessner, “Nonlinear Electric Transport
in Graphene: Quantum Quench Dynamics and the
Schwinger Mechanism,” Physical Review B, Vol. 81, No.
16, 2010, Article ID: 165431.
 N. Vandecastle, A. Barreiro, M. Lazzeri, A. Bachtold and
F. Mauri, “Current-Voltage Characteristics of Graphene
Devices: Interplay between Zenner-Klein Tunneling and
Defects,” Physical Review B, Vol. 82, No. 4, 2010, Arti-
cle ID: 045416. doi:10.1103/PhysRevB.82.045416