INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER
J. Phys.: Condens. Matter 16 (2004) R901–R960 PII: S0953-8984(04)77483-4
TOPICAL REVIEW
Functionalized carbon nanotubes and device
applications
SCiraci
1
,SDag
1
,TYildirim
2
,OG
¨
ulseren
1
and R T Senger
1,3
1
Department of Physics, Bilkent University, 06800 Ankara, Turkey
2
NIST Center for Neutron Research, NationalInstitute of Standards and Technology,
Gaithersburg, MD 20899, USA
3
T
¨
UB
˙
ITAK-UEKAE, P.K. 74, 41470 Gebze, Kocaeli, Turkey
E-mail: ciraci@fen.bilkent.edu.tr
Received 8 March 2004
Published 9 July 2004
Online at stacks.iop.org/JPhysCM/16/R901
doi:10.1088/0953-8984/16/29/R01
Abstract
Carbon nanotubes, in which the two-dimensional hexagonal lattice of graphene
is transformed into a quasi-one-dimensional lattice by conserving the local
bond arrangement, provide several structural parameters for engineering novel
physical properties suitable for ultimateminiaturization. Recent interest in
nanoscience and nanotechnology has driven a tremendous research activity in
carbon nanotubes, which has dealt with a variety of problems and produced
a number of new results. Most of the effort has gone into revealing various
physical properties of nanotubes and functionalizing them in different ways.
This paper covers a narrow region in this enormous research field and reviews
only a limited number of recent studies which fit within its scope. First,
we examine selected physical properties of bare carbon nanotubes, and then
study how the mechanical and electronic properties of different tubes can be
modified by radial strain, structural defects and adsorption of foreign atoms and
molecules. Magnetization of carbon nanotubes by foreign atom adsorption has
been of particular interest. Finally, we discuss specific device models as well
as fabricated devices which exploit various properties of carbon nanotubes.
(Some figures in this article are in colour only in the electronic version)
Contents
1. Introduction 902
2. Atomic and electronic structure 904
2.1. Geometric structure and energetics of bare SWNTs 904
2.2. Energy band structure 906
3. Hydrogenation of carbon nanotubes 908
0953-8984/04/290901+60$30.00 © 2004 IOP Publishing Ltd Printed in the UK R901
R902 Topical Review
4. Oxygenation of carbon nanotubes 912
4.1. Physisorption of O
2
molecules 913
4.2. Chemisorption of oxygen atoms 916
5. Adsorption of individual atoms on SWNTs 917
5.1. Binding geometry and binding energies 919
5.2. Electronic structure 923
5.3. Transition element covered or filled SWNTs 926
6. Radial deformation of carbon nanotubes 927
6.1. Elasticity 928
6.2. Effect on the electronic structure 930
6.3. Effect on the chemical reactivity 932
6.4. Effect of pressure on nanoropes 934
7. Devices based on carbon nanotubes 936
7.1. Ab initio methods in transport calculations 936
7.2. Device models 942
8. Devices fabricated using carbon nanotubes 952
8.1. Transistors based on carbon nanotubes 952
8.2. Chemical sensors 955
9. Conclusions 955
Acknowledgments 956
References 956
1. Introduction
Research on carbon nanotubes is ever intensifying indiversefieldsofscience and engineering
in spite of the twelve years that have passed since its first discovery by Iijima [1]. There are
several reasons that so much interest has been focused on these materials. First of all, carbon
nanotubes have been a natural curb for several research programmes, which were tuned to
C
60
butall of a sudden came to an end without any great technological applications having
been found. Secondly, researchers, who can touch and relocate individual atoms have been
challenged to discover the novel properties of these strange materials in order to transform
them into new devices or use them in other technological applications. As a result of the rapid
rise in the speed, as well as the rapid reduction in the size of electronic devices, new paradigms
will be needed to overcome the barriers set by the traditional technologies to produce ever
smaller and faster devices. Extensive research dealingwith the modification of electronic
structure for desired device operations has indicated that carbon nanotubes can be considered
as a new frontier in the search for the ultimate miniaturization of electronic circuits with
ultrahigh density components and new functionalities. Several devices fabricated so far with
different functionalities appear to meet the great expectations for carbon nanotubes.
Carbon nanotubes are unique materials, which offer a variety of structural parameters for
engineering their physical and chemical properties [2, 3]. They can be synthesized as single-
wall (SWNT) or multiple-wall (MWNT) nanotubes; they can form ropes or even crystals.
Even an ultimate one-dimensional carbon chain at the centre of a MWNT (and stabilized by
theinnermost nanotube) has been discovered in cathode deposits [4]. SWNTs are basically
rolled graphite sheets, which are characterized by two integers (n, m) defining the rolling (or
chiral vector) C = na
1
+ ma
2
,interms of the two-dimensional (2D) hexagonal Bravais lattice
vectors of graphene, a
1
and a
2
.Thenthe radius of the tube is given in terms of (n, m) by the
relation R = a
0
(n
2
+ m
2
+ nm )
1/2
/2π,wherea
0
=|a
1
|=|a
2
|.SWNTsexhibit different
electronic structures depending on n and m (i.e. on their chirality and radius).
Topical Review R903
The mechanical properties of carbon nanotubes are striking. They are flexible and can
sustain large elastic deformations radially; at the same time they are very strong axially with
high yield strength [5, 6]. Their strength far exceeds that of any other fibre. Even more
striking is the response of the electronic structure to the radial deformation leading to dramatic
changes. As has been predicted theoretically and confirmed experimentally, a semiconducting
zigzag tube becomes metallic with finite state density at the Fermi level as a result of radial
deformation transforming the circular cross section into an ellipse. At the same time the
chemical activity of the surface of the tube undergoes a change; the interaction of adatoms
with theSWNToccurs differently at high and low curvature sites. The metal–semiconductor
transition induced by elastic deformation has important implications.
Physical and chemical properties of a SWNT can also be modified by the adsorption
of foreign atoms or molecules. This process is usually named functionalization, and
carries great potential in tailoring new nanostructures for engineering them according to a
desired application. For example, depending on the pattern of hydrogen atom coverage,
while a metallic armchair SWNT can be transformed to a wide band gap semiconductor, a
semiconducting zigzag tube may become a metal with very high state density. A free SWNT,
whichisnormally nonmagnetic, becomes magnetic with unpaired spins upon the adsorption
of oxygen molecules or specific transition metal atoms. A recent study demonstrates that a
semiconducting zigzag tube becomes both a magnetic and a high conductancewireas a resultof
Ti coating [7]. A selectable functionalization of the (5,5) SWNT resulting from CH
n
(n = 1–3)
adsorption and decoration gives rise to a substantial change in the density of states [8].
Suitably doped carbon nanotubes can be functionalized by selectively forming chemical
bonds with ligands at the chemically active impurity site [9]. Apparently, functionalization
of carbon nanotubes, in particular biological and chemical functionalization, is an extensive
field incorporating several recentstudies in diverse fields. This review is confined rather to the
functionalized SWNTs which have their electronic and magnetic properties modified.
Clearly, carbon nanotubes offer many parameters to deal with and many options for
generating properties suitable for a desired functionality. One of the great challenges of
research on carbon nanotubes has been the realization of nanometre-sized optoelectronic
devicesand nanomagnets. In anefforttodiscover newfeatures of technologicalinterest,several
theoretical and experimental studies activelyexplored SWNTs, MWNTs, ropes and their
functionalized forms, which resulted in many papers. However, due to its focus compounded
with the space limitations, the scope of this review article has been kept necessarily limited.
The subject matter that we have left out is in no way less significant than what we have included.
We followed a logical order that starts from fundamental aspects and ends with
technological applications. We first established a background concerning the atomic and
electronic structure of various SWNTs. We then examined various methods which are used
to modify the properties of SWNTs to generate new nanostructures. Finally, we discussed
how these properties have been used to model devices. The organization of the article is as
follows. In section 2, we have presented a discussionof electronic structureobtainedfrom first-
principles calculations together with a comparison made to empirical studies. Hydrogenation
and oxygenation of SWNTs have been dealt separately in sections 3 and 4, respectively, owing
to the several recent papers in this area, as well as due to the relevance to hydrogen storage.
Section 5 has been be devoted to the individual adsorption of 24 different atoms (ranging from
alkali and simple metal atoms to group IV atoms and most transition metal atoms), where their
binding structures and binding energies, and the effect of their adsorption on the electronic
structure, have been investigated. Since the ground state for most of the transition metal atoms
adsorbed on the surface of SWNTs is magnetic, and hence has net spin, this section is important
for the magnetic properties of functionalized nanotubes. In section 6, we have investigated the
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effects of radial deformation, and have examinedhowtheelectronic and chemical properties
are modified. Here, the atomic structure, elasticity and electronic structure and binding of
adatoms under radial deformation have been discussed. In section 7, we have reviewed recent
developments in transport theory and have presented some device models developed using
thefeatures and physical properties discussed in previous sections. Section 8 reviews briefly
the recent progress made in the fabrication of electronic devices basedoncarbon nanotubes
and has described a few such devices produced. The paper is concluded with outlooks and
prospective developments.
2. Atomic and electronic structure
The electronic band structure of SWNTs can be deduced by mapping the band structure of
graphene in a 2D hexagonal lattice onto a cylinder [3, 10–14]. In this respect, the SWNT
presents an interesting example, in which dimensionality is reduced from two to one. The
analysis based on the band folding indicates that the (n, n) armchair nanotubes are always
metalwith π
∗
conduction, and π valence bands crossing at the Fermi level, and exhibit 1D
quantum conduction [14, 15]. The (n, 0) zigzag SWNTs are generally semiconductor and
are only metal if n is an integer multiple of 3. Although the overall electronic structure of
SWNTs has been described by this simple picture, recent studies [16, 18] have shown much
more complicated structural dependence. For example, the (9, 0) tube is, in fact, a small band
gap semiconductor. The semiconducting behaviour of SWNTs has been of particular interest,
since the electronic properties can be controlledby doping or implementing defects in nanotube
based optoelectronic devices [19–26].
Band calculations of SWNTs were initially performed by using a one-band π orbital
tight binding model [11]. Subsequently, experimental data [27–30] on the band gaps were
extrapolated to confirm the inverse proportionality with the radius of the nanotube [13].
Later, first-principles calculation [31] within the local density approximation (LDA) showed
that the σ
∗
–π
∗
hybridization becomes significant at small R (or at high curvature). Recent
analytical studies [32–34] showed the importance of curvature effects in carbon nanotubes.
Nonetheless, band calculations performed by using different methods have been at variance
on the values of the band gap. Extensive theoretical analysis of the band structure of SWNTs
together with the curvature effects on geometric and electronic structure has been carried out
recently [18] by using first-principles pseudopotential plane wave method [35] calculations
within the generalized gradient approximation (GGA) [36].
2.1. Geometric structure and energetics of bare SWNTs
Because of cylindrical symmetry, the structuralparameters of SWNTs deviate from those of
graphene. The inset to figure 1 shows a schematic side view of a zigzag SWNT which indicates
twotypes of C–C bonds (d
1
and d
2
)and C–C–C bond angles (
1
and
2
). The variations of
the normalized bond lengths (i.e. d
1
/d
0
and d
2
/d
0
where d
0
is the optimized C–C bond length
in graphene) and the bond angles with tube radius R (or n)areshowninfigures 1(a) and (b),
respectively. Both the bond lengths and the bond angles display a monotonic variation and
approach the graphene values as the radius increases. As pointed out earlier for the armchair
SWNTs [37], the curvature effects, however, become significant at small radii. The zigzag
bond angle (θ
1
)decreases with decreasing radius. It is about 12
◦
less than 120
◦
for the (4, 0)
SWNT,while the length of the corresponding zigzag bonds (d
2
)increases with decreasing R
and the length of the parallel bond (d
1
)decreases to a lesser extent with decreasing R.The
angle involving this latter bond (θ
2
)isalmostconstant.
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Figure 1. Inset: a schematic side view of a zigzag SWNT, indicating two types of C–C bonds and
C–C–C bond angles. These are labelled as d
1
, d
2
, θ
1
and θ
2
.(a) Normalized bond lengths (d
1
/d
0
and d
2
/d
0
)versusthetube radius R (d
0
= 1.41 Å). (b) The bond angles (θ
1
and θ
2
)versusR.
(c) The curvature energy, E
cur
per carbon atom with respect to graphene as a function of the tube
radius. The solid curves are the fit to the data as α/R
2
.(Reproduced from [18].)
An internal strain isimplemented upontheformation of tubularstructure from the graphene
sheet. The associated strain energy, which is specified as the curvature energy, E
cur
,is
calculated as the difference of total energy per carbon atom between the bare SWNT and
the graphene (i.e. E
cur
= E
T,SWNT
− E
T,graphene
)for4 n 15. The calculated curvature
energies are shown in figure 1(c). As expected, E
cur
is positive and increases with increasing
curvature. The cohesive energies of SWNTs are also curvature dependent, and are calculated
from the expression E
coh
= E
T
[C]− E
T
[SWNT] in terms of the total energy of the free carbon
atom, and the total energy of a SWNT per carbon atom. For a zigzag tube, it is small for small
n and increases with n,andeventually saturates to the cohesive energy of graphene. Similar
trends also exist for the armchair tubes. In classical theory of elasticity the curvature energy
is given by the following expression [38–40]: E
cur
= α/R
2
,whereα = Yt
3
/24. Here Y is
theYoung’s modulus, t is the thickness of the tube, and is the atomic volume. Interestingly,
curvature energies obtained from first-principles calculations yield a perfect fit to the relation
α/R
2
as seen in figure 1(c). In this fit α is found to be 2.14 eV Å
2
/atom [18].
![Table 1. Band gap, Eg, as a function of radius R for (n, 0) zigzag nanotubes. M denotes the metallic state. The first-row values were obtained within the GGA in [18]. The second and third rows from [31] give LDA results, while all the rest are tight binding (TB) results. The two rows from [42] are for two different TB parametrizations.](/figures/table-1-band-gap-eg-as-a-function-of-radius-r-for-n-0-zigzag-1pvrujwf.webp)
![Figure 2. A map of chiral vectors that determine the chirality of SWNTs. Each vector is specified by the (n,m) indices. M, S and C denote metals, semiconductors and curvature induced small gap semiconducting SWNTs, respectively. (Reproduced from [17].)](/figures/figure-2-a-map-of-chiral-vectors-that-determine-the-709ooo7i.webp)
![Figure 5. Average binding energies, Eb, of hydrogen atoms adsorbed on various zigzag and armchair SWNTs versus bare tube radius R. Filled and open symbols are for zigzag and armchair nanotubes, respectively. Circles and diamonds are for exohydrogenation and endo– exohydrogenation at full coverage, respectively. The filled squares show the zigzag nanotubes uniformly exohydrogenated at half coverage. The chain and dimer patterns of adsorbed hydrogen atoms at half coverage are shown by down and up triangles, respectively. Curves are analytical fits explained in the text. Insets show top views of several C4nH2n isomers. (Reproduced from [57].)](/figures/figure-5-average-binding-energies-eb-of-hydrogen-atoms-t417j1ws.webp)
![Figure 29. Energies of the discrete states of the (6, 4)/m(5, 5)/(6, 4) quantum dots as a function of the number of (5, 5) unit cells m. (Reproduced from [20, 173].)](/figures/figure-29-energies-of-the-discrete-states-of-the-6-4-m-5-5-6-xrdv1odi.webp)
![Figure 15. Geometric structures of adsorbed Ti chains on (14, 0) (top) and (8, 8) (bottom) SWNTs. Along the tube axis, each unit cell contains two Ti atoms for the (14, 0) tube and one Ti atom for the (8, 8) tube. Several unit cells are shown for the purpose of visualization. The distances between the two neighbouring Ti atoms in the chains are 2.6 Å for (14, 0) and 2.7 Å for (8, 8) tubes. (Reproduced from [108].)](/figures/figure-15-geometric-structures-of-adsorbed-ti-chains-on-14-0-uhkwoktm.webp)
![Figure 26. Upper panel: geometry of the bent (4, 4) nanotubes with bending angles (a) θ = 0◦ , (b) 3◦, (c) 6◦. Lower panel: the calculated transmission function and LDOS for the corresponding geometries. (Reproduced from [144].)](/figures/figure-26-upper-panel-geometry-of-the-bent-4-4-nanotubes-2leyl3z8.webp)