We present {\it ab initio} and self-consistent tight-binding calculations on
the band structure of single wall semiconducting carbon nanotubes with high
degrees (up to 25 %) of boron substitution. Besides a lowering of the Fermi
energy into the valence band, a regular, periodic distribution of the p-dopants
leads to the formation of a dispersive ``acceptor''-like band in the band gap
of the undoped tube. This comes from the superposition of acceptor levels at
the boron atoms with the delocalized carbon $\pi$-orbitals. Irregular (random)
boron-doping leads to a high concentration of hybrids of acceptor and
unoccupied carbon states above the Fermi edge.Comment: 4 pages, 2 figure

Rubio, Angel

Wirtz, Ludger

English

arXiv

Ludger Wirtz

Crossref

Band structure of boron doped carbon nanotubes

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Band structure of boron doped carbon nanotubes
Ludger Wirtz∗ and Angel Rubio∗
∗Department of Material Physics, University of the Basque Country, Centro Mixto CSIC-UPV, and
Donostia International Physics Center, Po. Manuel de Lardizabal 4,
20018 Donostia-San Sebastián, Spain
Abstract. We presentab initio and self-consistent tight-binding calculations on the band structure
of single wall semiconducting carbon nanotubes with high degre s (up to 25 %) of boron substitu-
tion. Besides a lowering of the Fermi energy into the valenceband, a regular, periodic distribution
of the p-dopants leads to the formation of a dispersive “acceptor”-like band in the band gap of the
undoped tube. This comes from the superposition of acceptorlevels at the boron atoms with the
delocalized carbonπ-orbitals. Irregular (random) boron-doping leads to a highconcentration of
hybrids of acceptor and unoccupied carbon states above the Fermi edge.
INTRODUCTION
The electronic properties of single wall carbon nanotubes dpend sensitively on the
diameter and the chirality of the tubes. Therefore, in orderto use tubes as elements
in nano-electronical devices, a controlled way to produce and separate a large quantity
of tubes of specific radius and chirality has to be found. Alternatively, doping of tubes
by boron and nitrogen [1] may lead to electronic properties that are more controlled
by the chemistry (i.e., the amount of doping) than the specific geometry of the tubes.
Indeed, theoretical investigations of BCN nanotube heterojunctions have predicted that
the characteristics of these junctions are largely independent of geometrical parameters
[2]. It has been predicted that even stochastic doping may led to useful electronic
elements such as chains of random quantum dots and nanoscalediodes in series [3].
The realization of p-type doping of pure carbon nanotubes bya substitution reaction
with boron atoms [4, 5, 6] offered the possibility to transform semiconducting tubes
into metallic tubes by lowering the Fermi level into the valenc band. Indeed, transport
measurements [7, 8, 9] have shown a clearly enhanced conductivity of B-doped tubes.
The metallic behavior of B-doped multiwall carbon nanotubes was also confirmed by
scanning tunneling spectroscopy [10].
In bulk semiconductors, typical doping concentrations of impurity atoms are around
10−3 %. At such low concentration, the presence of group III atoms(e.g., B) in a group
IV semiconductor leads to the formation of an acceptor state(non-dispersive band) in the
band gap at low energy above the valence band edge [11]. For B dping in a C(8,0) tube,
Yi and Bernholc [12] have calculated (using a B/C ratio of 1/80) that this acceptor state
is located at 0.16 eV above the Fermi energy. However no discussion has been made up-
to-date on the evolution of this acceptor-like level with the degree of B-doping. Since in
recent experiments [6], Boron substitution up to 15 % has been r ported, we investigate
in this paper the band structure of strongly B-doped single wall carbon nanotubes.
Γ X
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band structure DOS
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band structure DOS
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b)
d)
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c)
FIGURE 1. Band structure and DOS of a C(16,0) tube with a) 0%, b) 6.25%, c) 12.5%, and d) 25%
boron doping. Zero energy denotes the Fermi edge. Filled states are indicated by grey shadowing. Insets
display the corresponding unit cells (C atoms black, B atomswhite).
COMPUTATIONAL METHOD
In order to demonstrate the effect of B doping on a semiconducting tube, we have
chosen a (16,0) tube with a diameter of 12.5 Å which is close tothe average radius of
commonly produced SWNT samples. Since the distribution of borons in B-doped tubes
is still unknown, we have performed two sets of calculations. 1.) For regular periodic
distributions that are commensurate with the unit-cell of the undoped tubes, we perform
ab initiocalculations [13] of electronic band structure and densityof states (DOS). 2.) In
order to test the effect of disordered B doping, we employ a supercell comprising 6 unit-
cells (384 atoms) and distribute the boron atoms “randomly”with the only constraint
that they cannot occupy nearest neighbor positions on the hexagonal carbon grid. For
this large system, we use a self-consistent tight-binding (SCTB) method [3, 15].
RESULTS
Fig. 1 shows the band structure and DOS of a C(16,0) tube without d ping and with
various concentrations of B-doping in a periodic manner (see insets). For the undoped
tube it can be noted, that the DOS is symmetric around the bandg p for the 1st and 2nd
Van-Hove singularities (VHSs). However, beyond this smallenergy regime around the
band gap, asymmetries arise due to the mixing of p and s orbitals. Doping of the tubes
DOS (arb. units)
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DOS (arb. units) DOS (arb. units)
a) b) c)
b)
a)
FIGURE 2. DOS of a C(16,0) tube with 12.5% B doping: a) regular doping (as in Fig. 1), b) regular
doping (alternative geometry, c) random doping.
leads to a lowering of the Fermi level into the valence band ofthe undoped tube. Clearly,
the stronger the doping, the stronger is also the shift of theFermi level. Above the highest
occupied bands of the undoped tube new bands are formed. These bands correspond to
the formation of an acceptor level in semiconductors with very low dopant concentration.
Due to the strong concentration in the present case, the boron levels hybridize with the
carbon levels and form strongly dispersive “acceptor-likebands”. The band structure of
the valence band is strongly distorted upon doping, becausethe levels of carbon atoms
that are substituted by boron move upwards in energy. In addition, the lowering of the
symmetry by doping leads to many clear avoided crossings between states that perform
a real crossing in the case of the undoped tube where they posses a different symmetry.
Clearly, in all cases displayed in Fig. 1, the doping with B leads to a metallic character
of the tube. However, the density of states at the Fermi levelstrongly depends on the
geometry of the structure and varies non-monotonously withthe doping concentration.
In fact, in BC3 tubes with a different geometry than in Fig. 1 d), a gap between π-
type orbitals andσ type orbitals opens up at the Fermi level and renders the tubes
semiconducting in this particular case [17].
Fig. 2 compares the DOS of a C(16,0) tube with 12.5% boron substit tion in three
different geometries. The two regular structures both display a pattern with the familiar
pronounced Van Hove singularities of a 1-dim. band structure. However, the different
ordering of the boron atoms gives rise to a different hybridization of the bands and
thereby to a pronounced difference in the peak structure of the DOS. The DOS at
the Fermi level strongly depends on the ordering of the B atoms. In the DOS of the
randomly doped tube, the pattern of the VHSs is mostly smeared out [18]. Due to the
missing translational geometry, the 1-dim. band structureof the regularly doped tubes
is transformed into the DOS of a 0-dimensional structure, i.e. of a large molecule or
cluster without periodicity. The states between the Fermi level and the original valence
band edge of the undoped tubes are hybrids of acceptor levelsand unoccupied carbon
levels. The electronic excitations into these levels should explain the optical absorption
spectra of B-doped carbon tubes [6]: In addition to the pronounced absorption peaks that
are commonly affiliated with the transitionsEii (i = 1,2) from the first/second occupied
VHS to the first/second unoccupied VHS of the pure semiconducting arbon tubes, the
spectra of B-doped tubes display additional absorption at eergies lower thanE11.
CONCLUSION
The calculations on the band structure of boron doped carbonnanotubes clearly confirm
the expectation (and experimental observation) that thesetub s are metallic with low
resistance. For regularly doped structures, we have observed the formation of a disper-
sive “acceptor” band while the Fermi level is shifted downwards into the valence band
of the undoped tubes. Electronic excitations into these hybrids of acceptor states and
unoccupied carbon levels are expected to play an important role in optical absorption
spectra. Randomly doped tubes display the same downshift ofthe Fermi edge but cease
to display strongly dispersive bands. We hope that in the near future, spatially resolved
TEM/EELS will help to elucidate the exact geometry of the boron dopants and scanning
tunneling spectroscopy will probe the exact density of state .
Work supported by COMELCAN (contract number HPRN-CT-2000-00128). We ac-
knowledge stimulating discussion with T. Pichler, J. Fink ad G. G. Fuentes.
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k-points. Since the tubes have large diameter, we have neglect d the effect of local atomic distortion
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displayed in Fig. 1 that the SCTB yields results in very closeagreement with theab initio calculations.
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some of the dispersive band structure, including Van-Hove singularities, is still visible.


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Band structure of boron doped carbon nanotubes

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