Electrical Transport Properties of Individual multi-wall carbon
nanotube
計畫編號：甲-91-E-FA04-1-4
執行期限：93 年 4 月 1 日至 94 年 3 月 31 日
主持人：
彭宗平
共同主持人： 齊正中
計畫參與人員：杜建明 蔡孟諺
Introduction
With many unique properties, Carbon
nanotubes (CNTs) have attracted so much
attention and have great potential for
fabrication of nanometer-scale molecular
electronic devices. For the understanding of
some of the basic transport mechanisms
involved in the electronic transport through
CNTs, today studies become more and more
oriented toward measurements on individual
CNT. In these years, however, we have
developed the technique and platform for
measuring the electrical properties of CNTs.
We have successfully measured several
MWNTs and found the best fitting models of
the electrical transport. Based on our
experience, we will improve the platform and
technique for further study.
Fig. 1 Four leads on individual MWNT.
1.70
-5
Electrical Transport Properties of MWNTs
Resistivity (10 m)
1.65
The electrical properties of two kinds of
MWNTs synthesized with different method
are shown below.
First, we have discussed the electrical
properties of individual MWNT, provided by
Prof. Tai’s group, synthesized by LPCVD
method. Fig. 1 shows the four leads of
MWNT. I-V characteristics and R-T
behaviors of individual MWNT are studied
over a temperature range of 263-4.2K. The
variation of resistivity ρ with the square root
of temperature (T) is linear and is shown in
Fig.2. Indeed, the range of resistivities is
between 1.46x10-5 .m and 1.68 x10-5 .m.
These values compare well to those reported
for MWNTs made with arc discharge
method1. The resistivities are little lower than
that of SWNT about 10-6 .m2-3.
We have tried many models to fit our
data, such as thermally activated transport;
weak localization and variable range hopping
1.60
1.55
1.50
1.45
0
2
4
6
8
T
1/2
10
12
14
16
18
1/2
(K )
Fig.2. Variation of Resistivity with square root of
temperature.
but none can fit the data well. However,
Altshuler and Aronov model4,5 can fit the
data well in a wide temperature range. This
model predicts that the electron - electron
scattering in the presence of random
impurities leads to a pseudogap in density of
state near Fermi level. According to the
model, we have plotted resistivity (ρ) with
the square root of temperature (T1/2) over the
entire experimental temperature range (4.2 –
263K) Fig.2. This behavior has been reported
for disordered Aluminum films and doped
semiconductors6-7 in a narrower temperature,
typical 2 K~ 10 K.
In present case, the resistivity (ρ) with
approximately the square root of temperature
(T1/2) dependence can be the form
Fig.3 SEM photo of ferrocene catalyzed CNT
Δρ / ρ0 ~ βT1/2
Fig.4 I-V characteristics of ferrocene catalyzed
MWNT.
240
240
200
G (S)
200
G (S)
Where ρ0 is a constant and its value is 1.71
x10-5 .m. Experimental value of β exp
is –8.82x10-6 and β exp< 0. According to
Altshuler and Aronov model, β< 0 means
that the interaction between electrons is
effectively repulsive in this disordered
MWNT. We also use free electron model to
estimate the fitting value of β fit (= –
4.26x10-6). Comparing with βexp, we find
β fit /β exp ~50. The discrepancy may be
caused by the uncertainty of carrier density
of CNT film and effective mass of the
quasi-1 dimension SWNT because formula,
however, is for 3-dimension case.
120
160
0
of
The SEM photo of the ferrocene
catalyzed MWNT, provided by Prof. Perng’s
group, is shown in Fig.3. We also
successfully measure the four-probe I-V
(Fig.4) and R-T characteristics of this
MWNT. The I-V curve is linear over the
temperature range 300-4.2K and may be
attributed to the work functions of Nb
(contact material and work functions for Nb~
4.3 eV) being very close to that of MWNTs,
(work function of MWNTs ~ 4.5-4.8 eV).
500
1000
T
1500
2000
4/3
120
0
Electrical
Transport
Properties
ferrocene catalyzed MWNT
160
40
80
120
160
200
240
280
Temperature (K)
Fig.5 Variation of conductance with temperature. The
inset shows the best fitting of conductance with T 4/3.
The tube resistance is estimated to be
0.470 k at room temperature, which
corresponds to 0.235 k/m of the nanotube
length and the resistance increases to 0.896
k (i.e. 4.48 k/m) at 4.2K. We assume
that carriers pass through the entire
cylindrical cross sectional area of the
nanotube, the resistivity of the nanotube is
1.18x10-6 .m at room temperature to
2.25x10-6 .m at 4.2K.
The behavior of conductance (G) v.s.
temperature (T) and the best fitting of
conductance with T4/3 is shown in Fig.5. We
have tried several models, which are used to
explain the behaviors of semiconductors, but
none can fit the data well. A simple power
law of 4/3, which is usually to explain the
transport in disordered superconductors,
metals and disordered alloys can fit the data
well. This power can be the form
G = Go + mT
( = 1.33)
Where G o is a constant and m and  are the
fit parameters. If  is in the range 3-5, it
shows that the electron-phonon scattering
would dominate the temperature dependence
of resistivity8-10. However, if   2, it means
that
the
electron-electron
scattering
12
dominates the behavior. The similar values
of  were reported by Gurvitch et al. and
Webb et al. in their study of low temperature
resistivity of ordered and disordered A15
compounds11-13. In our case, =1.33 gives the
best fitting and it means that the
electron-electron scattering dominates the
behavior of MWNT at low temperature.
Summary and Future works
Reviewing our study, although we have
successfully explained the electrical transport
properties of the measured MWNTs, the lack
of the further measurement of the individual
MWNTs, such as Hall measurement, limits
our study in intrinsic properties of CNTs. In
the present progress on Hall measurement,
we collaborated with Instrument Technology
Reasearch Center (ITRC), and try to utilize
the focus ion beam (FIB) to fabricate central
leads for Hall measurement as shown in
Fig.6. Unfortunately, there is one very thin
undesirable deposited metal layer around the
metal leads and CNT when we use FIB to
fabricate the leads, as shown in Fig.7. We are
trying to use Ion-milling technique to
overcome this problem.
Fig.7. Undesirable thin metal layer around two open
leads.
The conventional technique of e-beam
lithography was employed to make the fine
leads connected to the individual 1-D
nanostructure. Although the study of the
electrical transport property of individual
carbon nanotube (CNT) has been realized by
using this technique, there are some serious
limitations existing. For example, we can
measure the electrical transport properties of
CNT, but we still cannot identify the
structure of the one that we have measured.
So, we are trying to design a new platform to
suspend the CNTs, even other 1-dimension
nanomaterials, for further TEM or optical
spectrum analysis. Making big holes on Si
substrate and small holes on Si3N4 membrane
such that TEM could be used to identify the
structure of the CNT. The design is shown in
Fig.8.
Fig.6. Four leads and a set of central side-contacted
leads deposited on individual CNT.
Fig.8. New platform for TEM and Optical spectrum
analysis.
If the new platform works successfully,
we can identify the structure of measured
nanostructure. We expect this will provide a
powerful experimental tool for controlled
investigations of CNTs and other intriguing
nanomaterials.
Reference
[1].C. Schonenberger, A. Bachtold, C. Strunk,
J.-P. Salvetat, and L. Farro, Appl. Phys. A
69, 283 (1999).
[2]. L. Farro, C. Schnonenberger, in ; M. S.
Dresselhaus, G. Dresselhaus, Ph. Avouris
(Eds.), Carbon nanotubes, Springer 2001,
pp. 329-391.
[3]. A. Thess, R. Lee, P. Nikolaev, H. Dai, P.
Petit, J. Robert, C. Xu, Y. H. Lee, S. G.
Kim, A. G. Rinzler, D. T. Colbert, G. E.
Scuseria, D. Tomanek, J. E. Fischer, and
R. E. Smalley, Science 273, 483 (1996).
[4].B. L. Altshuler and A. G. Aronov, Solid
State Commun. 30, 115 (1979).
[5].B. L. Altshuler and A. G. Aronov, JETP
Lett, 27, 662 (1978).
[6]. R. C. Dynes and J. P. Garno, Phys. Rev.
Lett. 46, 137 (1981).
[7]. E. L. Wolf, in Principles of Tunneling
Spectroscopy, Oxford University Press,
New York, (1985).
[8].G. T. Meadan, Electrical Resistance of
Metals (Plenum, New York, 1965), pp89;
N. W. Ashcroft and N. D. Mernin, Solid
State Physics (W. B. Saunders, USA,
1976), pp.348.
[9].M. Gurvitch, Phys. Rev. Lett. 56 647
(1986).
[10]. J. F. Zasadzinski, A. Saggese, K. E.
Gray, R. T. Kampwirth, and R. Vaglio,
Phys. Rev. B 38, 5065 1988.
[11] M. Gurvitch, J. P. Rameika, J. M.
Rowell, J. Geerk, and W. P. Lowe, IEEE
Trans. Magn. MAG-21, 509 985.
[12]. M. Gurvitch, A. K. Ghosh, H. Lutz, and
M. Strongin, Phys. Rev. B 22, 128
1980.
[13]. G. W. Webb, Z. Fisk, J. J. Engelhardt,
and S. D. Bader, Phys. Rev. B 15,2624
1977.