IOP PUBLISHING
NANOTECHNOLOGY
Nanotechnology 18 (2007) 165702 (7pp)
doi:10.1088/0957-4484/18/16/165702
Effects of doping nitrogen atoms on the
structure and electronic properties of
zigzag single-walled carbon nanotubes
through first-principles calculations
S S Yu1 , Q B Wen1 , W T Zheng1,2 and Q Jiang1,2
1
Department of Materials Science, Jilin University, Qianjing Road 2699, Changchun 130012,
People’s Republic of China
2
Key Laboratory of Automobile Materials of MOE, Qianjing Road 2699, Changchun 130012,
People’s Republic of China
E-mail: [email protected]
Received 19 November 2006, in final form 13 February 2007
Published 23 March 2007
Online at stacks.iop.org/Nano/18/165702
Abstract
Calculations have been made for single-walled zigzag (n, 0) carbon
nanotubes containing substitutional nitrogen impurity atoms using ab initio
density functional theory. It is found that the formation energies of these
nanotubes depend on the tube diameter, as do the electronic properties, and
that they show periodic features which result from their different π bonding
structures compared to those of perfect zigzag carbon nanotubes. When two
nitrogen atoms are doped in the same hexagon per five tube units, the
semiconducting tubes exhibit some special electronic structures, in which the
impurity level is occupied fully by two excess electrons from doped nitrogen
atoms. The electronic structures for the tubes depend on the sites that two
nitrogen atoms occupy in the hexagon, by which the impurity states can be
near the bottom of the conduction band or can be far apart from the bottom of
the conduction band.
that the CNx tubes are metallic [15–17], and N-doping is
also beneficial for the release of atomic hydrogen adsorbed
in SWCNTs [18], as predicted by theoretical models. When
the tubes are defective with the impurity, their bonding
structures will be destroyed at the sites of the defects and
reconstructed [19]. Through introducing impurity states
between the band gap by the defects [20, 21], the conductivity
for semiconducting tubes can be improved [15–17].
According to their electronic structures, zigzag (n, 0)
SWCNTs have been divided into categories of semiconductor
and metal depending on the index n . It is reported in
some papers that the curves of the formation energy versus
diameter for these tubes are of sawtooth-like shapes due
to adsorption [22] and interstitial [19] atoms. We have
investigated that carbon nanotubes doped with B/N also show
similar periodic features, which results from the different π
bonding structures of the perfect zigzag carbon tubes with
different diameters, rather than the defects (substitutional
1. Introduction
Since 1991 [1], carbon nanotubes, in particular singlewalled carbon nanotubes (SWCNTs), have attracted a
lot of attention from the science community because of
their interesting quasi-one-dimensional character and wide
potential applications such as molecular-scale machines and
nanoelectronic devices [2–5]. The presence of defects and
impurities that are electronically or chemically active can
significantly change the properties of SWCTNs. For instance,
N doping of carbon nanotubes can give rise to nanotube
functionalization [6] and other changes in the structure, e.g.,
transformations from the atomic network to bamboo-like
structures [7, 8], which can enhance field emission [9] from
the nanotubes. Hence N-doped carbon nanotubes as well as
nanotubes made of noncarbon elements such as boron nitride
(BN) have received significant attention [10–14]. Several
groups have studied nanotubes containing nitrogen, and found
0957-4484/07/165702+07$30.00
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© 2007 IOP Publishing Ltd Printed in the UK
Nanotechnology 18 (2007) 165702
S S Yu et al
impurity atom B/N) in the zigzag tubes [23]. However,
a clear picture that explains these features is not given in
previous work. It is well known that there is a donor
state near the bottom of the conduction band when a
nitrogen atom substitutes a carbon atom in the semiconducting
tubes. Consequently, they can be converted into n-type
semiconductors upon N doping.
Worth noting is that,
when semiconducting tubes are doped with more nitrogen
atoms, especially if the nitrogen atoms occupy sites in
the same hexagon, their excess electrons would interact,
and their electronic structures would present some special
characteristics, which has not been reported so far. In this
work, we will theoretically investigate the formation energies
and the electronic structures for large periodic hosts of zigzag
(10, 0) SWCNTs doped with two nitrogen atoms in the same
hexagon per five tube units, using density-functional theory.
Figure 1. Formation energies of (n, 0) SWCNTs per three tube units
containing one substitutional nitrogen atom as a function of nanotube
diameter.
2. Methods
During calculation of the formation energies for SWCNTs
doped with nitrogen atoms, (n, 0) tubes with n = 8–19
were chosen. Because the diameter of tube was so large,
three tube units and a sampling point in the Brillouin zone
were used for cohesive energy calculations per atom. As
for the calculations of electronic structures, we adopted a
(10, 0) tube doped with two nitrogen atoms and 1 × 1 ×
6 k -points for the Brillouin zone integration along the tube
axis. Nitrogen atoms could be incorporated into the hexagonal
network of SWCNTs through substituting carbon atoms. As
the excess electrons of nitrogen atoms were highly dispersive
to about 3 nm [6], we should expect an interaction of excess
electrons from nitrogen atoms with those in neighbouring cells.
Considering the exponential decaying density of the excess of
electrons of nitrogen atoms [6] and our computational power,
our calculations were done on the (10, 0) supercell which
consists of 200 atoms (5 tube units).
We used the code DMOL3 [24, 25] based on density-functional
theory (DFT), available from Accelrys Inc. In this code each
electronic wavefunction was expanded into a localized atomcentred basis set with each basis function defined numerically
on a dense radial grid. We adopted a double numeric basis with
polarization (DNP) set and all electrons for core treatment. For
the exchange and correlation term, the generalized gradient
approximation (GGA) was used as proposed by Perdew, Burke
and Ernzerhof (PBE) [26]. The orbital cutoff was 0.37 nm.
Self-consistent field (SCF) tolerance was 1.0 × 10−6 Ha.
A one-dimensional periodic boundary condition was
applied along the tube axis, in which periodically repeating
tetragonal supercells with lattice constants a , b, and c were
used, and both a and b were chosen to ensure negligible
interaction between the tubes and their periodic images (a =
b = diameter + 1.0 nm). A C–C bond length of 0.142 nm
was chosen before geometry optimization. The positions of all
the atoms including the doping nitrogen atoms in the supercell
were not constrained and could be fully relaxed under the
condition that the cell parameters were fixed on the values
optimized for the original tubes. In order to test our method,
we calculated the density of states (DOS) for perfect (10, 0)
and (9, 0) zigzag SWCNTs. Our energy differences between
the first two van Hove singularities (VHSs) were 0.82 eV for
the (10, 0) tube and 2.50 eV for the (9, 0) tube, respectively.
The results were in good agreement with [27].
The formation energy for an SWCNT doped with one
nitrogen atom ( E f ) and the cohesive energies per atom for
SWCNT doped nitrogen atoms ( E c1 ) and a perfect SWCNT
( E c2 ) are defined as
E f = (E t1 + E 2 ) − (E t2 + E 1 )
(1)
E c1 = (E t1 − E 1 − (m − 1)E 2 )/m
(2)
E c2 = (E t2 − m E 2 )/m
(3)
3. Results and discussion
When the (n, 0) tubes contain one substitutional nitrogen atom
(one nitrogen atom per three tube units), the formation energies
curve exhibits the feature of periodicity, and such periodicity is
characterized by the lower formation energies of defected tubes
with n as a multiple of 3 as compared to their neighbouring
tubes, as shown in figure 1. This periodic feature results from
the different π bonding structures of the perfect zigzag carbon
tubes with different diameters, rather than the defects in the
tubes [23]. However, a clear picture that explains this periodic
feature is not given in previous work [23].
In order to reveal the nature of this periodic feature for the
tubes doped with nitrogen atoms, we deduce equation (4) for
the formation energy for the SWCNTs doped with one N atom
from equations (1)–(3):
E f = m(E c1 −E c2 )
where E t1 and E t2 are the total energy of an SWCNT
containing one substitutional nitrogen atom and a perfect
SWCNT, respectively, m is the total number of atoms, and E 1
and E 2 are the energies of a single free nitrogen and carbon
atom, respectively.
(4)
where m is the total number of atoms, and E c1 and E c2 are the
cohesive energies per atom for a doped tube and a perfect tube,
respectively. The values of E c1 and E c2 , as well as ( E c1 – E c2 )
are plotted as a function of nanotube diameters in figures 2(a)
and (d). It is found that the E c1 – E c2 curve also displays
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Nanotechnology 18 (2007) 165702
S S Yu et al
Figure 2. For (n, 0) tubes doped with one nitrogen atom and perfect zigzag tubes, the diameter-dependent (a) cohesive energies per atom,
(b) cohesive energies per atom (enlarged) for perfect tubes, (c) cohesive energies per atom (enlarged) for doped tubes, (d) difference between
the cohesive energies per atom of doped tubes and perfect tubes and (e) their absolute values of slopes for the cohesive energy curves.
keep monotonically decreasing, as shown in figure 2(e)) as the
tube diameter increases. On the contrary, for (n, 0) tubes with
n = 3k (k is integer), the absolute values of the slope increase
compared to those for corresponding tubes with n = 3k − 1;
that is to say, there exist unusual values for the cohesive
energies of perfect and doped SWCNTs. This means that the
cohesive energies for perfect and doped SWCNTs fluctuate
or are periodic. Because the formation energy is related to
the periodic feature. In order to reveal the characteristics of
the cohesive energy curve, the related mathematical principles
have been utilized. Mathematically, if one curve (only a
monotonically increasing or decreasing function is considered)
is smooth, its slope should keep monotonically decreasing or
increasing. In figure 2(a), the values (negative) of the slope
of the (perfect or doped SWCNTs) cohesive energy curve do
not keep monotonically increasing (the absolute values do not
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S S Yu et al
features. This can be demonstrated in figure 2(e), in which
the gradients at n = 9, 12, 15, 18 in cohesive energy curve
per atom vary abruptly compared to those at other n -values
for the perfect SWCNTs, while for the N-doped SWCNTs this
variation is relatively weak because their bonding structure is
destroyed at the site of the defect and reconstructed. Thus, the
values of cohesive energies per atom for SWCNTs can also be
classified into two types. One is from the (n, 0) tubes with
n = 9, 12, 15, 18 and the other is from those with the other
n -values.
Why does the cohesive energy curve per atom for the
perfect SWCNTs exhibit this periodic feature? It is known that
perfect zigzag (n, 0) tubes are metals when n is a multiple of
3. For the (n, 0) tubes with n = 3k (k is integer), the electrons
that occupy the frontier π orbitals (highest occupied molecular
orbital, HOMO) are more delocalized than other tubes, which,
as shown in figure 3, leads to the energies of HOMOs for the
tubes with n = 9, 12, 15, 18 being higher than those of other
tubes. Consequently, the frontier π orbital bonding structures
of the tubes with n = 9, 12, 15, 18 are less stable than those
of others, i.e. the tubes with n = 9, 12, 15, 18 are more
Figure 3. Energies of the frontier π orbitals for perfect (n, 0)
SWCNTs per three tube units as a function of nanotube diameter.
the cohesive energy through equation (4), the periodic feature
in the formation energy as a function of n for SWCNTs
containing impurity is a consequence of the periodic feature in
the cohesive energy curve per atom for the perfect SWCNTs,
whereas the defects in the zigzag tubes weaken these periodic
Figure 4. Qualitative descriptions of the frontier π orbitals (HOMOs) of a (10, 0) tube with one substitutional nitrogen atom per five tube
units are shown in a lateral view (a) and in a sectional view (b). The substitutional nitrogen atom is denoted by a dark ball. The electronic
density of states of a (10, 0) tube doped with one nitrogen atom per five tube units is plotted in (c), in which the top panel is the total density of
states and the bottom panel is the local density of states for one nitrogen atom and one carbon atom which is far from the nitrogen atom.
Figure 5. Schematic descriptions of the configurations for (10, 0) tubes containing two substitutional nitrogen atoms per five tube units
denoted by SN1 (a)–SN7 (g), respectively. The substitutional nitrogen atoms are denoted by dark balls.
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S S Yu et al
Figure 6. The density of states (DOS) for a (10, 0) tube doped with two nitrogen atoms per five tube units with the configurations
SN1–SN7 (a)–(g) and for a perfect (10, 0) tube (h). The impurity states are marked by the arrows. The Fermi levels are set at the zero of
energy.
Table 1. The formation energies for zigzag SWCNTs doped with two nitrogen atoms per five tube units with different configurations.
(10, 0)
SN1
SN2
SN3
SN4
SN5
SN6
SN7
Formation energy (eV)
11.15
10.53
9.61
9.92
10.09
10.14
10.05
active chemically than other tubes. Therefore, the energies
of electrons that occupy the frontier π orbitals determine the
periodic feature of the cohesive energies curve per atom for
perfect SWCNTs, as shown in figure 2(b).
It is well known that nitrogen might work as a donor when
incorporated into semiconductors. Thereby, the highest occupied level (highest occupied molecular orbital, HOMO) for
SWCNTs doped with nitrogen atoms are mainly contributed
by the excess electrons of nitrogen atoms, whose distribution
can also be reflected by HOMOs. The HOMOs of a (10, 0)
tube doped with one nitrogen atom are plotted in figure 4.
We can find that most states of the HOMOs are localized
near the nitrogen impurity site. These results are similar to
what has been reported by Nevidomskyy [6], which indicates
that the salient of the semiconducting nanotube demonstrates
rich chemical and electrical aspects of carbon nanotubes upon
doping with one nitrogen atom. However, when semiconducting tubes are doped with more nitrogen atoms, especially if nitrogen atoms occupy sites in the same hexagon for SWCNTs,
their excess electrons would interact, which will lead to some
special characteristics in their electronic structures compared
with tubes doped with one nitrogen atom.
We chose the (10, 0) tube as a typical semiconducting tube
for investigation and suggest that two nitrogen atoms per five
tube units are doped. The two doped nitrogen atoms might be
very near to or far from each other, but which configuration is
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Nanotechnology 18 (2007) 165702
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Figure 7. Qualitative descriptions of the highest occupied levels of a (10, 0) tube with two substitutional nitrogen atoms per five tube units
with different configurations: SN1 (a), SN2 (b), SN3 (c), SN4 (d), SN5 (e), SN6 (f) and SN7 (g). Positive and negative phases of the
wavefunction are denoted by grey and dark nodal structures, whose size represents the magnitude of the phase.
favourable completely depends on its formation energy. For
the former case, there are six configurations in which two
nitrogen atoms are near and lie in the same hexagon, as shown
in figure 5, which are denoted by SN1, SN2, SN3, SN4,
SN5 and SN6, respectively. For the latter case, the typical
configuration that two nitrogen atoms are far apart is chosen,
denoted by SN7, as shown in figure 5(g). The formation
energies of these SWCNTs with two doped nitrogen atoms
per five tube units are listed in table 1. It is clear that the
configurations containing two adjacent substitutional nitrogen
atoms (SN1 and SN2), as shown in figures 5(a) and (b), are
energetically unfavourable, and therefore unlikely appear in
nitrogen-containing SWCNTs [20], which is due to the N–N
bond being weaker than the C–N or C–C bond. The most
stable case for all configurations is SN3, shown in figure 5(c).
For cases SN3 and SN4, nitrogen impurity atoms are the third
nearest, while nitrogen impurity atoms are the second nearest
for cases SN5 and SN6. The formation energies for cases SN5
and SN6 are higher than those for SN3 and SN4. In addition,
for case SN3, its configuration is symmetric along the tube
axis, which leads to the SN3 configuration being more stable
than SN4. Hence, the stable configurations for SWCNTs doped
with two nitrogen atoms are sensitive to the symmetry.
Figure 6 depicts the electronic density of states for
SWCNTs doped with two nitrogen atoms. It is found that
they all have striking impurity states, marked by the arrow
near the Fermi level. For case SN7, the DOS (figure 6(g))
is similar to that for the tube containing one nitrogen atom
(figure 4(c)). From figure 6(g), the Fermi level locates
nearly at the peak position for the impurity level, which
means that the impurity level is half-occupied. In contrast,
the peak positions representing the impurity levels for other
configurations (figures 6(a)–(f)) all locate below the Fermi
level, which indicates that these impurity levels are fully
occupied. Because of the interaction between two excess
electrons from two doping nitrogen atoms, the impurity levels
for SN1–SN6 shift towards the valence band, compared to that
for SN7 (for SN7 the interaction between two excess electrons
from two doping nitrogen atoms can be neglected since the
two nitrogen atoms are far from each other). We also find
that, for cases SN2 and SN3, the occupied impurity states are
far from the bottom of the conduction band, which leads to
the conductance for the (10, 0) tube with the configurations
SN2 and SN3 being reduced. That is to say, when the
excess electrons are excited from the impurity level to the
conduction band, they need much more energy than other
cases. However, for cases SN4, SN5 and SN6, the occupied
impurity states are near the bottom of the conduction band
as donor states. In order to explain why there is a difference
between the electronic structures for different configurations,
we have investigated the highest occupied levels for the (10, 0)
tube with different configurations, as shown in figure 7. Being
similar to the distribution of HOMOs for the tube doped with
one nitrogen atom in figure 4, most states of HOMOs for
the (10, 0) tubes doped with two nitrogen atoms localize near
the nitrogen impurity sites. However, the densities of excess
electrons in cases SN2 and SN3 are denser than other cases
around the N atoms and the neighbouring C atoms, which
indicates that the excess electrons in cases SN2 and SN3 are
more tightly bound near the impurity nitrogen atoms than
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Nanotechnology 18 (2007) 165702
S S Yu et al
other cases, which results in the impurity levels for cases
SN2 and SN3 being far from the bottom of the conduction
band. It should be emphasized that tubes with different
configurations have different electronic structures. Therefore,
the electronic structures for the (n, 0) SWCNTs can be tuned
through changing the nitrogen doping configurations.
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4. Conclusions
The formation energies, as well as the electronic properties,
of (n, 0) SWCNTs with substitutional nitrogen atoms depend
on the nanotube diameters, and show a periodic feature. This
periodic feature results from the different π bonding structures
of perfect SWCNTs with different diameters, rather than the
defects (substitutional impurity atom N) in the tubes. When
two nitrogen atoms are doped in the same hexagon per five tube
units, the semiconducting tubes exhibit some special electronic
structures, in which the impurity level is fully occupied by two
excess electrons from nitrogen atoms. The electronic structures
depend on the sites that the two nitrogen atoms occupy in
the hexagon, by which the impurity states can be near the
bottom of the conduction band or can be far from the bottom
of conduction band. This suggests that a way to control the
electronic properties of SWCNTs by adjusting the nitrogen
doping sites can be realized.
Acknowledgments
Support from the National Natural Science Foundation of
China (grant nos 50525204 and 50372024), the National
Key Basic Research and Development Program (grant
no 2004CB619301), Project 985—Automotive Engineering
of Jilin University, and the Teaching and Research Award
Program for the Outstanding Young Teachers in High
Education Institutions (no 2002359) is acknowledged.
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