Contrast in the Electronic and Magnetic Properties of Doped Carbon

In recent years, boron nitride nanotubes (BN-NTs) and carbon nanotubes ... hard to use them in device applications. ...... Ordejon, P.; Sanchez-Portal...
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3464

J. Phys. Chem. C 2008, 112, 3464-3472

ARTICLES Contrast in the Electronic and Magnetic Properties of Doped Carbon and Boron Nitride Nanotubes: A First-Principles Study Mousumi Upadhyay Kahaly and Umesh V. Waghmare* Theoretical Sciences Unit, Jawaharlal Nehru Centre for AdVanced Scientific Research, Jakkur PO, Bangalore 560 064, India ReceiVed: March 24, 2007; In Final Form: December 2, 2007

We determine atomic and electronic structures of boron- and/or nitrogen-doped carbon nanotubes (CNTs) and carbon-doped boron nitride nanotubes (BN-NTs) of armchair and zigzag types using first-principles pseudopotential-based density functional theory calculations. For comparison, we also determine the atomic and electronic structures of two-dimensional honeycomb lattices of carbon (graphene) and boron nitride. Although carbon doping at either the B or N site in BN-NTs results in anti-ferromagnetically ordered semiconducting state, B or N doping in CNTs gives a simple shift in the Fermi energy and a nonmagnetic state.

I. Introduction In recent years, boron nitride nanotubes (BN-NTs) and carbon nanotubes (CNTs) have attracted a good deal of attention in the scientific community because of their unique electrical and mechanical properties, high thermal conductivity, and potential for use industrial applications. BN-NTs are inorganic analogues of CNTs. A single-wall nanotube can be constructed by rolling a two-dimensional graphene sheet (for CNT) or graphitic boron nitride sheet (for BN-NT). Single-wall carbon nanotubes exhibit either metallic or semiconducting behavior depending on their chirality and diameter.1,2 In contrast, electronic properties of BN-NTs of large diameter are relatively uniform and not dependent on their chirality.3,4 The remarkable electronic properties of CNTs and their ability to display fundamentally distinct electronic structure without changing the local bonding make them potential candidates for novel applications. However, because of the lack of synthesis techniques available to control the chiral angles and diameters of CNTs, BN-NTs are considered to be better suited for some electronics applications in which uniformity in electronic properties is desirable.5 Introduction of donor/acceptor levels through substitutional doping in a material is an attractive alternative for controlling the electronic properties and conductivities of nanotubes.6,7 Most BN-NTs are insulating because of the ionic nature of B and N, and doping with a suitable atom is desirable to obtain semiconducting tubes that can be useful in charge transport applications. Moreover, it has already been noted that although there is no spin polarization in the neutral BN-NTs spin polarization could occur when electrons or holes were injected.8 Ferromagnetic interaction of 3d transition metals with CNTs9,10 can lead to half-metallic systems, which are of interest for spintronic devices. Implantation of N or other defects in nanodiamond is known to introduce magnetism.11 It is fundamentally interesting * Corresponding author. E-mail: [email protected].

to explore if similar substitutional doping of CNTs with nitrogen or boron, or of BN-NTs with carbon, can lead to magnetic moments. If so, then it would open up a new set of applications of these nanotubes. The electronic structure of nano-objects is known to be rather sensitive to correlations as well as defects. For example, in strictly one-dimensional systems, even a small degree of disorder can lead to a localized state and insulating behavior. Although nanotubes are thought to be one-dimensional nanostructures, with their diameter on the scale of a nanometer, defects can yield interesting effects on their electronic structure. Although doped CNTs and BN-NTs have been realized experimentally,12,13 it is very hard to determine the ordering and distribution of dopant atoms over the atomic sites of a nanotube. A few ordering configurations were used in density functional theory based calculations to estimate the band gaps6 and quadrupole coupling constants of doped BN-NTs.14 Determining how the electronic structure would depend on this ordering would help in interpreting experimental observations. Polydispersity in size and chirality of carbon nanotubes lead to a mixture of metallic and semiconducting nanotubes, making it hard to use them in device applications. Although BN-NTs are always insulating irrespective of their size and chirality, the large effecitive mass (flat bands arising from the ionic nature of B and N) of electrons in their valence and conduction states limits their applications. It is fundamentally interesting and of importance to technology how the electronic structure of BNNTs and CNTs can be altered through suitable doping. In addition, the study of boron or nitrogen doping in carbon nanotubes would lead to understanding of their contrasting electronic properties in comparison with carbon-doped boron nitride nanotubes. Here we determine the stability and electronic structures of CNTs and BN-NTs for various distributions and various concentrations of dopant atoms.

10.1021/jp072340d CCC: $40.75 © 2008 American Chemical Society Published on Web 02/15/2008

Contrast in Electronic and Magnetic Properties In this work, first-principles calculations are performed to determine the atomic structures and electronic properties of boron- and nitrogen-doped CNTs and carbon-doped BN-NTs of armchair and zigzag types. We try to understand the origin of the nonmagnetic metallic properties of B/N-doped CNTs in comparison to magnetic, semiconducting C-doped BN-NTs, for dopant substitution at different possible sites. In Section II, we describe details of the density functional theory (DFT) based methods used in this work, benchmarking the atomic structures of the parent materials, that is, graphite and bulk honeycomb boron nitride (h-BN) and electronic properties of their respective single layers. We discuss the effect of B/N doping on electronic structures of CNTs and the effect of carbon doping on electronic structures of BN-NTs in Section III. We particularly focus our discussions on the magnetic properties of the doped nanotubes and summarize our work in Section IV. II. Methods A. Technical Details. Our calculations are based on firstprinciples pseudopotentials within density functional theory as implemented in SIESTA,15,16 which employs a localized orbital basis in the representation of wave functions. We use soft normconserving pseudopotentials and Ceperley-Alder exchange correlation energy within a local density approximation (LDA) and include dependence on spin density (local spin density approximation (LSDA)) whenever necessary, particularly in the case of carbon-doped BN-NTs or B/N-doped CNTs. We have used this methodology earlier in simulations of carbon nanotubes.17 Real space meshes used for representation of charge density have a resolution corresponding to a plane-wave energy cutoff of 200 Rydberg. A linear combination of numerical atomic orbitals with double-ζ polarizations (DZP) is used in the basis set to describe the valence electrons. The generation of the basis set is based on finite-range slightly excited pseudo-atomic orbitals.18 The radial part of the basis function is described using zeta function. With twice as many basis functions as in a minimum basis being used, this is called a “double-ζ” basis set. The confining radii r are different for the two different zeta functions for the representation of two split valence orbitals. Furthermore, the basis sets are made more flexible in by adding higher-angular momentum basis functions, that is, allowing the polarization, if any. For example, the highest angular momentum orbital for carbon is a p orbital; hence, the “polarization” of the atom is described by adding a set of d functions. Polarization orbitals are constructed using perturbation theory, and they are defined in a way so that they have the minimum angular momentum l such that there are not occupied orbitals with the same l in the valence shell of the ground-state atomic configuration. They polarize the corresponding (l - 1) shell. The basis set superposition error while computing the cohesive energies is eliminated by replacing the conventional Hamiltonian with one designed to prevent basis-set mixing a priori, by removing all of the projector-containing terms that would allow basis-set extension. Periodic boundary conditions are used with a unit cell that has the periodicity of the nanotube along the z axis and hexagonal symmetry in the xy plane. To simulate an isolated nanotube, the size of the unit cell in the xy plane is chosen to be much larger than the diameter of the nanotube. Structural optimization was carried out until all of the forces acting on all of the atoms decreased below 0.03 eV/Å-1. Integrations over Brillouin zones (BZ) were sampled with Monkhorst-Pack meshes.19 The BZ of the periodic lattice in

J. Phys. Chem. C, Vol. 112, No. 10, 2008 3465 TABLE 1: Structural Parameters of Graphite and Boron Nitride (Honeycomb): a is the Lattice Constant in the xy Plane, c is the Lattice Constant along the z Axis, r0 (Å) is the Minimum Interatomic Separation, and Eg (eV) is the Band Gap system

methods

a(Å)

c(Å)

r0 (Å)

Eg (eV)

graphite

LDA-ours GGA-Marzari23 experimental21 LDA-ours GGA-Liu24 experimental22

2.47 2.46 2.46 2.49 2.49 2.50

6.62 6.90 5.44 6.48 6.49 6.66

1.43 1.43 1.43 1.44 1.44 1.45

0.0

h-BN

0.0 4.90 4.03 4.50

case of an isolated nanotube has a very small dimension in the xy plane and hence is sampled with a 1 × 1 × 25 mesh corresponding to 13 k-points, obtained using time-reversal symmetry (which is present in all of these systems), in the Brillouin zone (BZ). We used 7 × 7 × 5 k-point meshes for calculations of graphite and h-BN. We used a very dense k-point mesh of 105 × 105 × 1 (5565 k-points in the BZ) for single graphene sheet calculations in order to capture its special features in the electronic band structures and 33 × 33 × 1 (561 k-points in the BZ) for calculations of a single layer of h-BN. In the case of doped nanotubes, we use a supercell consisting of three unit cells stacked along the z axis. Thus, the unit cell for each of the doped nanotubes is constructed by stacking three unit cells of the undoped pristine nanotube and then substituting one or two atoms in the nanotube by the dopant. For example, a (5,5) pristine BN-NT has 20 atoms per unit cell. A (5,5) BNNT with C doped at the N site has total of (20 × 3), that is, 60 atoms: 30 B atoms, 29 N atoms, and 1 C atom. Similarly, in an (8,0) CNT, there are 32 atoms per pristine nanotube unit cell. Thus, the single B-doped (8,0) CNT in our calculation contains (32 × 3), that is, 96 atoms per unit cell: 95 C atoms and 1 B atom. Resulting BZs are even smaller along the z axis and are sampled with k-point meshes 1 × 1 × 15 (8 k-points in BZ) and 1 × 1 × 10 (6 k-points in BZ) for doped armchair and zigzag nanotubes, respectively. Our calculations correspond to carbon concentrations of about 1-2 atomic % in BN-NTs and B/N concentrations of 2-4 atomic % in CNTs. The size of a unit cell of isolated nanotubes in the xy plane is chosen to ensure a wall-to-wall distance (vacuum) of about 16; this ensures negligible interaction between the periodic images of the nanotubes. We note that this is particularly important in the case of BN-NTs (unlike in CNTs) because of the long-range ionic interactions. B. Structures of Graphite, Boron Nitride, and their SingleLayer Forms. Structures of graphite and hexagonal boron nitride (h-BN), the parent materials for carbon nanotubes and boron nitride nanotubes, are quite similar. Both of them are layered materials composed of atomic layers of honeycomb lattices; graphite has carbon atoms at all lattice points, whereas h-BN is composed of alternating atoms of boron and nitrogen. The lattice constants and bond lengths of graphite and h-BN (see Table 1) are in very good agreement with the experimental results21,22 and earlier theoretical works.23,24 The interlayer distances for graphite and h-BN are 3.31 and 3.24 Å, respectively. A slightly underestimated c value, for both systems, is obtained because (i) interlayer interactions dominated by van der Waals forces are not taken into account properly in DFT presently and (ii) energy surfaces of graphite and h-BN as a function of c/a ratio are very flat. Though the interlayer distances are similar in both cases, one important difference between these two materials is in the stacking of their layers. In h-BN, layers are arranged so that boron atoms in one layer are located directly on top of nitrogen atoms in neighboring layers and vice versa;

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Kahaly and Waghmare substituted preferably at the nearest-neighbor B and N sites forming a C-C bond. A. Energetics of Doped CNTs and Doped BN-NTs. To assess the stability of doped nanotubes, we determine an average cohesive energy per atom (Ecoh)

Ecoh ) (Σi Ei - Etot)/N

Figure 1. Electronic band structure of (a) graphene sheet and (b) single layer of h-BN. The Fermi level is at zero of the y axis, shown by a black dashed line.

the hexagons lie on top of each other. In graphite, the stacking is slightly different; hexagons are offset and do not lie on top of each other. Because of the different electronegativities of the two atoms in a basis in h-BN and graphite, and interlayer stacking arrangement, electronic properties of graphite and h-BN are radically different from each other. The band structures of a single layer of graphite and a single layer of h-BN along the high symmetry points (see Figure 1) reveal that graphene is a semi-metal and a single layer of h-BN is an insulator with an indirect band gap (K - M) of about 4.9 eV. The semi-metallicity of graphene originates from the crossing of two bands (of the π bonding orbital below the Fermi level and the π* antibonding orbital above the Fermi level) at the high symmetry K wave vector (2/3, 1/3, 0) (Figure 1a). The general features in the band structures of graphene and single-layer h-BN are quite similar except at the K-point; the symmetry condition for gap-closing at this point needs the two basis sites to be equivalent, which is satisfied in graphene but broken in the case of single-layer h-BN. The large, indirect band gap of a single layer of h-BN arises from its ionicity. Experimentally, the band gap of h-BN is measured to be about 5.8 eV.26 III. Doped CNT and BN-NT Nanotubes are obtained by rolling graphene sheets (CNTs) or graphene-like sheets of h-BN (BN-NTs). In order to understand the effect of impurities or doping in a CNT, we simulated B or N doping in a CNT in three different modes: (a) a single B atom doped at a C site, (b) an N atom doped at a C site, and (c) two B and N atoms co-doped at two C sites, each mode of doping in the three unit supercell of nanotube. We have examined these doping possibilities in (5,5) armchair and (5,0) and (8,0) zigzag CNTs in the isolated form. In the case of a single B or N atom substituted at a C site in a CNT, there is only one possible distinct configuration because all C sites in the unit cell are equivalent. When one boron and one nitrogen atom are co-doped in a CNT, there can be many configurations corresponding to different distances between the substituted atoms. We find that the energetics favors substitution of B and N atoms preferably at the nearest-neighbor C sites, forming a B-N bond. Similarly, in the case of carbon doping in a BN-NT, simulations were carried out in three different modes: (a) C atom doped at a B site, (b) C atom doped at an N site, and (c) two C atoms co-doped at B and N sites. We discuss here results for these modes of carbon doping in (5,5) armchair and (5,0) zigzag BN-NTs. Like in the doped CNTs, we find from the energetics that the two carbon atoms get

(1)

where Etot is the total energy of the doped nanotube, Ei’s are energies of the individual atoms, and N is the total number of atoms. Cohesive energies per atom (see Table 2) of a pristine CNT and its three doped forms considered here show that an N atom doped at a C site (n-type doping) of the pristine CNT is the most preferred substitution followed by BN pair substitution at neighboring C-C sites and B substituted at a C site (p-type doping). Similarly, the stability of the three doped forms of a BN-NT, as understood from the respective cohesive energies per atom (see Table 2) is (i) a C atom doped at a B site (n-type doping), (ii) C-C pair substitution at neighboring B-N sites, and (iii) C substituted at an N site (p-type doping). Thus, we understand that n-type doping tends to make a nanotube more stable over p-type doping for both CNTs and BN-NTs. Comparing Ecoh of doped forms of (5,0) and (8,0) (Table 2), we understand that as the concentration of doping decreases the difference of cohesive energies between these three doped forms of nanotubes reduces. A selection of characteristic C-C, C-N, C-B, and B-N bond lengths for different doped nanotubes (see Table 2) show that (i) for doped CNTs, lattice constant c along the axis of the tube is always larger in the case of a B-doped CNT than that in the case of an N-doped CNT, (ii) for doped BN-NTs, c is larger when the C atom is doped at an N site than when the C atom is doped at a B site, (iii) with B-N (or C-C) pair doping at CNT (or BN-NT), the value of c is intermediate between single B and N (or C at B and C at N site) doped nanotubes. We note that donor-acceptor bond length associated with n-doping is always smaller than that for p-doping (see lB values from Table 2). For example, (i) the C-N bond length in N-doped (5,5) CNT (equivalent to n-doping) is about 1.4, whereas C-B bond length in B-doped (5,5) CNT (equivalent to p-doping) is about 1.5; (ii) C-B bond length in C doped at a B site of (5,5) BNNT (equivalent to n-doping) is about 1.4, whereas the C-N bond length in C doped at an N site of (5,5) BN-NT (equivalent to p-doping) is about 1.5. Although our estimates of C-B and B-N bond lengths in doped BN-NTs agree well with (within 0.5%) earlier work,6 our estimated bond lengths of C-C and C-N bonds deviate by up to 4-5%. This is understandable in terms of the difference in the exchange-correlation functionals used here and in the work of Zhao et al.6 We note that out estimate of C-C bond length in both CNTs and doped BNNTs is very close the C-C bond lengths estimated for CNTs, in an sp2 hybridized network using DFT calculations.27 Furthermore, lattice constant c (for three unit cells stacked, as described for) along the axis of the nanotube is smaller in the n-doped nanotubes than that in the p-doped nanotubes. This results in stronger bonds in the n-doped nanotubes than that in p-doped nanotubes, consistent with the observations (last paragraph) that the Ecoh values of n-doped tubes are larger than the Ecoh values of p-doped tubes, for both CNTs and BN-NTs. B. Effect of Doping on the Electronic Properties of CNT and BN-NT. Upon substitution of single B or N atom at a carbon site (per supercell) in either armchair or zigzag CNTs, new bands and changes in the existing bands arise near the Fermi level and thus the electronic band structure is modified. The

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J. Phys. Chem. C, Vol. 112, No. 10, 2008 3467

Figure 2. Electronic densities of states (DOS) of pristine and doped forms of (5,5) and (8,0) CNTs obtained from spin-polarized calculations: (a and e) for pristine CNT; (b and f) for a B atom doped at a C site; (c and g) for N doped at a C site, (d and h) for a BN pair doped at two neighboring carbon sites. The dotted lines with positive DOS represent the density of spin-up states, and solid lines with negative DOS represent the density of minority states. The Fermi level is at zero, as shown by the vertical dot-dashed line.

TABLE 2: Cohesive Energy Ecoh (eV) per Atom and Lattice Constant c (Å) along the Axis of the Nanotube, and Bond Lengths of C-C, C-B, C-N, and B-N Bonds (lB(C-C), lB(C-B), lB(C-N), and lB(B-N) Respectively) of Different Nanotubes system

CNT

BN-NT

(5,5) clean (5,5): B doped in C site (5,5): N doped in C site (5,5): BN pair in C-C sites (5,0) clean (5,0): B doped in C site (5,0): N doped in C site (5,0): BN pair in C-C sites (8,0) clean (8,0): B doped in C site (8,0): N doped in C site (8,0): BN pair in C-C sites (5,5) clean (5,5): C doped in B site (5,5): C doped in N site (5,5): C pair in BN sites (5,0) clean (5,0): C doped in B site (5,0): C doped in N site (5,0): C pair in BN sites

Ecoh (eV) 10.64 7.38 13.83 10.60 10.32 7.07 13.53 10.29 10.61 8.57 12.61 10.59 10.35 13.53 7.07 10.32 10.11 13.31 6.84 10.09

c (Å)

lB (C-C) (Å)

7.425 7.412 7.379 7.396 12.807 12.832 12.725 12.771 12.858 12.824 12.771 12.794 7.476 7.464 7.500 7.482 12.825 12.818 12.878 12.825

1.435-1.437 1.416-1.432 1.418-1.432 1.439-1.434 1.415-1.458 1.404-1.462 1.401-1.435 1.410-1.425 1.424-1.436 1.410-1.442 1.405-1.438 1.408-1.434

1.394-1.432

1.512, 1.528 1.546-1.550

1.371

1.514-1.532 1.547

Fermi level (as seen in the electronic densities of states (DOS)) is pushed down during B-doping at a carbon site (equivalent to p-type doping) and pushed up during N-doping at a carbon site (equivalent to n-type doping) as shown for (5,5) and (8,0) CNTs in Figure 2c, c, f, and g, in comparison to their respective pristine DOS. Semiconducting carbon nanotubes with B or N doping thus become metallic (as evident from the case of (8,0) CNT shown in Figure 2) through a shifting of the Fermi level. These effects are not so prominently observed for nanotubes with smaller diameters, for example in the case of a doped (5,0) CNT. Because of the rather small diameter (hence large curvature effect) of the (5,0) CNT, the densities of electronic states (DOS) are very asymmetric and result in nonzero DOS in the pristine nanotube (contrary to the expectation from the tight-binding approximation). The tight binding approximation is a model calculation where structure is not relaxed; the effect of curvature

lB (C-B) (Å)

lB (C-N) (Å)

lB (B-N) (Å)

1.395, 1.403 1.397

1.455

1.546-1.550

1.364-1.431 1.421-1.432

1.425

1.498-1.516 1.519

1.378-1.411 1.396-1.399

1.497, 1.516 1.489 1.516, 1.533

1.410, 1.412 1.421-1.432 1.362-1.387 1.412-1.415

1.436 1.442-1.444 1.425 1.436, 1.454 1.425 1.431-1.463 1.449-1.491 1.424-1.464 1.429-1.457

is thus not fully captured in tight binding calculations. In contrast, the unrestricted first-principle calculations allows all of the bond lengths and bond angles of the system to be relaxed fully. The smaller the nanotube, the stronger the effect of curvature. This affects the electronic eigen energies specially around the Fermi level. That is why we get asymmetric DOS for the pristine carbon nanotube in contrary to the expectation from tight binding results. Comparing the amount of the Fermi level shifting (see Figure 2b, c, f, and g) in the doped (5,5) CNT (1 B or N atom per supercell that consists of 60 C atoms) and (8,0) CNTs (1 B or N atom per supercell that consists of 96 C atoms), we understand that the amount of shift of the Fermi level decreases with decrease in concentration of doping. When two B and N atoms are substituted at neighboring C-C sites, one hetero-polar π-bond is formed between the dopant atoms and thus the DOS becomes similar to that of the

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Kahaly and Waghmare

Figure 3. Isosurfaces of HOMO and LUMO wave functions at Γ point for doped (5,5) CNT: (a) HOMO (isovalue ) 0.19 e/bohr3) and (b) LUMO (isovalue ) 0.13 e/bohr3) of B-doped CNT; (c) HOMO (isovalue ) 0.125 e/bohr3) and (d) LUMO (isovalue ) 0.23 e/bohr3) of N-doped CNT. Ash-colored balls represent C atoms, magenta balls represent B atoms, and green balls represent N atoms. Red and blue regions mean the isosurfaces at positive and negative isovalues. Orientation of coordinate axes in all figures are not same for the purpose of better visualization.

corresponding pristine CNT (Figure 2 d and h). For semiconducting nanotubes (e.g., (8,0) CNT), a band gap comparable to that of the corresponding pristine CNT opens up. Deviations in the local charge density with respect to the pristine CNT is less for a B- and N-pair-doped CNT than for single B or N substitution at a C site. These findings are consistent with our results for the energetics (Ecoh) of B- and N-pair substitution in two neighboring C sites that a CNT with this kind of doping is very close in energy to its pristine form. The DOS of the up and down spin states of a doped CNT are identical (Figure 2), indicating their 2-fold degeneracy and vanishing magnetic moment. We visualize the total charge densities F, wave function of the highest occupied molecular orbital (HOMO), and wave function of the lowest unoccupied molecular orbital (LUMO) at the Γ (k ) (0, 0, 0)) point in order to determine the nature of the states near the Fermi level in doped nanotubes. Only one of the HOMO or LUMO wave functions is observed to be modified significantly by the p-states of the dopant. We discuss here the figures for HOMO and LUMO for only a (5,5) doped CNT in Figure 3; pictures for other CNTs are similar. In either of the systems studied, the major contribution to F comes from the most electronegative atom(s). For example, the N atom being more electronegative than the C or B atoms, F has major contribution from N atoms in N-doped CNTs or BN-pair doped CNTs (not shown). The HOMO for single B doping has partial contribution from boron p-states along with the major contribution from carbon p-states (see Figure 3a); this state is relatively

localized. The LUMO, however, does not exhibit any contribution from boron states (Figure 3b) and is delocalized. Alternatively, for single N doping, though the HOMO does not show any contribution from dopant states, the LUMO is a localized state with mainly nitrogen p character (see Figure 3c and d). For a CNT with B-N pair doping, both the HOMO and LUMO have major a contribution from carbon p-states (not shown). In contrast to the properties of the three forms of doped CNTs (with zero spontaneous polarization), the substitution of a single C atom at a B or N site in either zigzag or armchair BN-NTs results in the magnetic moment from localized carbon p-states appearing at the pristine band gap. The defects create narrow bands (shown and discussed later) corresponding to the localized spins at the dopant C sites, thereby driving the polarization of the otherwise unpolarized (closed shell) electronic structures. The energy gain associated with the unrestricted electronic structure calculations in comparison to the closed-shell (nonmagnetic) calculations, ∆E ) Etot(LDA) - Etot(LSDA), are listed for some of the doped BN-NTs in Table 3. Greater stability of the polarized doped BN-NTs explains the necessity of LSDA calculations for such systems and shows that magnetic coupling is preferred in such systems. Furthermore, to check whether the ferromagnetic or the antiferromagnetically coupled state will be more stable, we doubled the unit cell of the doped BN-NTs and performed calculations for two different orderings of spins: (i) ferromagnetic, with spins on the two C atoms parallel, and (ii) antiferromagnetic, with spins on the two C atoms antiparallel.

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TABLE 3: Energy Gain ∆E (eV) Associated with the Unrestricted SCF Calculations as Compared to the Closed-Shell Calculations for Doped BN-NTs: ∆E ) Etot(LDA) - Etot(LSDA) system

energy gain ∆E (eV)

(5,5) BN-NT pristine (5,5) BN-NT with C at B site (5,5) BN-NT with C at N site (5,5) BN-NT with C-C at B-N site

0.006 0.216 0.102 0.001

(5,0) BN-NT pristine (5,0) BN-NT with C at B site (5,0) BN-NT with C at N site (5,0) BN-NT with C-C at B-N site

0.005 0.002 0.175 0.002

TABLE 4: Difference in Energies (EFM-AFM) between Ferromagnetic and Antiferromagnetic Coupling in Doped BN-NTs: EFM-AFM ) EFM - EAFM, Where FM and AFM Stand for Ferromagnetic and Antiferromagnetic Phases doped BN-NTs (each 60 atoms/unit cell)

type of doping

EFM-AFM (eV)

(5,5) with C at B site (5,5) with C at N site (5,0) with C at N site (9,0) with C at B site (9,0) with C at N site

n doping p doping p doping n doping p doping

-0.0016 0.0179 0.0139 0.0173 0.0014

The results for some of the doped BN-NTs are shown in Table 4. We find that the optimized state with antiferromagnetic ordering has the lowest energy, followed by ferromagnetically ordered and nonmagnetic states of increasing energy. The difference in energy of the ferro- and antiferromagnetic phases is given by EFM-AFM ) EFM - EAFM (see Table 4), where FM and AFM stand for ferromagnetic and antiferromagnetically coupled states. For doped (5,5) BN-NTs with C in a B site, we find that EFM-AFM is (1.6 meV) smaller than the computational errors (of about 5 meV), and we cannot resolve the relative stability of FM and AFM states. All other doped BN-NTs exhibit AFM ground energy state, with EFM-AFM e 18 meV. This implies that at room temperature (equivalent to 25 meV energy) there is the possibility of a jump from the antiferromagnetic to ferromagnetic state. We used a plane-wave-based density functional theory code (PWSCF28 code) to benchmark our results through a calculation of EFM-AFM for a (5,5) BN-NT with C at an N site with an estimate of 14.8 meV, which compares reasonably well with the SIESTA15,16 (local orbitals based) estimate of 17.9 meV. The difference of 3.1 meV in energy in the results from the two codes can be attributed to (i) different vacuum used and (ii) different choices of pseudopotentials. Energy differences less than 5 meV are smaller than the computational accuracy of our calculations and should not be taken seriously. However, we point out that the estimation of magnetic properties depends sensitively on the k-point sampling of the Brillouin zone and the efficient local orbital codes such as SIESTA (used here) allow us to use a very fine mesh (1 × 1 × 25 mesh used in our calculations!) as opposed to the plane wave codes where the computation intensity often forces one to use coarser k-point meshes. This is an advantage of the SIESTA method used here. Electronic states in the single C-doped BN-NT in either a B or N site produce flat and almost dispersionless bands in the gap in all BN-NTs (see Figure 4 for doped (5,5) BN-NT results), in agreement with recent DFT results.29 These flat bands have a character of predominantly carbon π-states and are mostly responsible for the induced magnetic moment. For example, in the calculated band structure of a (5,5) BN-NT with C doped at a B site (Figure 4a), we notice a flat band each of spin up states located 0.44 eV below (black line) and of spin down states

Figure 4. Comparison of electronic band structure from spin-up electrons (black solid lines) and spin-down electrons (red dot-dashed lines) for an armchair (5,5) BN-NT with (a) carbon doped at a B site and (b) carbon doped at an N site. The horizontal black dashed line shows the Fermi level in both cases.

Figure 5. Electronic density of states (DOS) of a carbon-doped BNNT obtained from spin-polarized calculations: (a) (5,5) BN-NT with a single C atom doped at a B site, (b) (a 5,0) BN-NT with a single C atom doped at an N site. The dotted line with positive DOS represents the density of majority states, and solid lines with negative DOS represent the density of minority states. The Fermi level is at zero, as shown by the vertical dot-dashed line.

located 0.45 eV above (red dot-dashed line) the Fermi level; they are absent in the pristine (5,5) electronic band structure. Two similar bands with carbon p character appear in the band structure of the (5,5) BN-NT with C doped at an N site (Figure 4b), from spin up band at 0.23 eV below the Fermi level (black line) and from spin down band at 0.21 eV above the Fermi level. The magnetic properties of C-doped BN-NTs can be better understood through analysis of the density of majority (spin up) and minority (spin down) states at the Fermi energy in the three different modes of C-doping in BN-NTs. The density of up and down spin states of any pristine BN-NT are identical, indicating vanishing magnetic moment. Substitution of a C atom at a B site (n-type doping) pushes the Fermi energy up just below the conduction band (see Figure 5a for the DOS of the (5,5) BN-NT with C doped at a B site). Substitution of a C atom at an N site (p-type doping) pushes the Fermi level down just above the valence band (example, Figure 5b for the DOS of the (5,0) BN-NT with C doped at an N site). Spin-dependent

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Figure 6. Isosurfaces of a doped (5,5) BN-NT: (a) Electronic charge density (isovalue ) 1.47 e/bohr3) and (b) HOMO (isovalue ) 0.45 e/bohr3) of a BN-NT with C doped at a B site; (c) HOMO (isovalue ) 0.38 e/bohr3) of a BN-NT with C doped at an N site and (d) HOMO (isovalue ) 0.38 e/bohr3) of a BN-NT with a C-C pair doped at neighboring B and N sites. HOMO wave functions are shown at Γ point obtained from spin-polarized calculations. Maximum charge density occurs at N atoms. HOMO for single C substitution correspond to carbon p majority states. With the carbon pair doped at the neighboring B and N sites, the HOMO corresponds to C-C covalent π-bonding states. Light-green balls represent B atoms, sky-pink balls represent N atoms, and magenta balls represent C atoms. Orientation of coordinate axes in these figures are not same for the purpose of better visualization. Red and blue regions mean the isosurfaces at positive and negative isovalues.

splitting of the p-states of a C atom in single C doping in either a B or N site results in two bands: spin up states are occupied contributing to the valence band ,and spin down states are left unoccupied giving rise to the conduction band. This splitting gives rise to a spontaneous magnetic moment of about 1.0 µB per C atom. Apart from these bands of carbon states near the Fermi energy, other bands are fully occupied and degenerate for both types of spin. With substitution of a pair of carbon atoms at the neighboring B and N sites (DOS not shown), a C-C covalent bond is formed from the overlap between the p-states of the dopant atoms. It results in the opening up of a large band gap comparable to that of the corresponding pristine BN-NT. Visualization of the F, HOMO, and LUMO at the Γ point (k ) (0, 0, 0)) confirms our understanding of the origin of the spontaneous magnetization in the cases of carbon atom substitution at a B or N site. F in all of these doped BN-NT nanotubes has a major contribution from nitrogen, which is more electronegative than the C or B atoms (see Figure 6a for the (5,5) BN-NT with C doped at a B site). For BN-NTs with carbon doped at either the B or N site, the HOMO originates predominantly from carbon p up-spin states (Figure 6b and c) whereas the LUMO originates from carbon p down-spin states (not shown). For the BN-NT with carbon pair doping, F and especially the HOMO (Figure 6d) have strong character of the C-C covalent bond formed.

IV. Discussion and Summary On the basis of our results, we understand that a single boron or nitrogen atom doped in the three unit supercell of carbon nanotube does not give rise to magnetization, whereas a single carbon atom doped at a boron or nitrogen site in a boron nitride nanotube (in a three unit supercell) results in a spontaneous magnetic moment of about 1.0 µB per C atom. Similar to the edge states appearing in the electronic structure of finite ribbons of graphene,30 doping in nanotubes is found to result in almost flat bands near the Fermi level. Similar to the edge states, these states are also localized near the dopant atom. The three electrons in the outermost orbit of a dopant B atom with sp2 hybridization and 3-fold coordination lead to zero lone pair electrons. Alternatively, five electrons in the outermost orbit of the dopant N atom results in a single lone pair. Because of the even (zero or two) number of electrons belonging to the lone pair, the associated magnetic moment is zero. Thus, we suggest that an even number of lone pair electrons of the dopant atom in a doped CNT is responsible for its nonmagnetic state. Alternatively, in a single carbon-doped BNNT (in three unit supercell) the dopant carbon atom has only one lone pair electron, resulting in the associated magnetic moment and nonzero magnetization. Second, the bonding electron of the dopant atom hybridizes strongly with the electronic states of carbon in CNTs, whereas in BN-NTs,

Contrast in Electronic and Magnetic Properties

J. Phys. Chem. C, Vol. 112, No. 10, 2008 3471

TABLE 5: Spin Magnetization S (µB) of Doped (5,0) BN-NT, for Different Concentration and Position of Dopant C Atoms (Total Number of Atoms ) 60 per Unit Cell)a doping type 2 C in 2 B sites 2 C in 2 N sites 3 C in 2 B and 1 N sites (one B and the N atoms are neighbors) 3 C in 1 B and 2 N sites (B and one of the N atoms are neighbors)

a

dopant positions

C-C distance (Å)

S (µB)

2 C in B1 and B3 positions 2 C in B1 and B7 positions 2 C in B3 and B11 positions 2 C in N2 and N4 positions 2 C in N2 and N8 positions 2 C in N2 and N12 positions 3 C in B1, B3, N2 positions

2.387 3.730 3.802 2.387 4.154 4.928

0 0 0 0 0 0 0

3 C in B1, B5, N2 positions 3 C in B1, B7, N2 positions 3 C in B1, N2, N4 positions

0 0 1

3 C in B1, N2, N6 positions 3 C in B1, N2, N8 positions

1 1

An atom M at ith site is marked by Mi. Different Mi’s are shown in Figure 7.

Figure 7. Different atomic sites in a (5,0) BN-NT, some of which, marked by Mi (for atom M at ith site) are substituted with C atoms to get (5,0) doped BN-NTs.

because the host tube is insulating, the electronic states of the dopant carbon cannot hybridize strongly with the states of B or N. This results in undisturbed electronic structures of the host BN-NTs but noticeable changes in the bands of CNTs. Thus, in doped BN-NTs dopant states appear as isolated bands (about the Fermi energy) responsible for the magnetic state. We note that the total magnetic moment of a dopant atom in BN-NT is either zero (when a covalent bond is formed between the dopant atoms) or one (results for spin magnetization of doped (5,0) BN-NTs are shown in Table 5), depending on the concentration and position of the dopant C atom. We consider two different concentrations of carbon doping, and for one particular concentration many possible configurations for dopant atoms, as described in Table 5. An atom of type M at site i is described by Mi (for example, B1, N2, etc.) and all sites i is shown in Figure 7. We find that (i) with two C dopant atoms the magnetic moment is zero, (ii) with three C atoms doped in (5,0) BN-NT (two dopant at B sites and one dopant at N site), the magnetic moment is zero, but (iii) with three C atoms doped in (5,0) BN-NT (two dopant in N sites and one dopant in B site, with one B and one N at neighboring sites forming a B-N pair), the magnetic moment is one. Thus, the magnetic moment of the doped system depends on both the concentration and location of dopant atoms. At very high concentration, the total magnetic moment tends to be zero (not shown here) because of the higher probability of formation of a covalent bond between the dopant atoms. At low concentrations, they could be useful in making nanoscale

magnetic memories. Furthermore, the spin-driven magnetism and low energy difference between antiferromagnetic and ferromagnetically coupled magnetic states could be used as sensor. Although the CNTs are not found to support magnetic moments of the dopant atoms, changes in their electronic structure particularly at the Fermi level could be useful in tuning their field emission properties. The defect states in carbon nanotubes and the resultant Fermi-level shifting could be used for band structure engineering in nanostructures. In summary, we have determined the effects of n or p-type doping in carbon nanotubes and boron nitride nanotubes through first-principles density functional theory calculations. Single boron or nitrogen doping in CNTs gives a simple shift in the Fermi energy and a nonmagnetic, metallic state. However, we find that substitution of a single carbon at either a boron or nitrogen site results in much smaller band gaps and a nonzero magnetic moment that arises from the spin-dependent splitting of carbon p-bands occurring in the gap. The magnetic ground state in such systems is antiferromagnetic at 0 K. The difference in energy of ferromagnetic and antiferromagnetic coupling is small enough (less than 18 meV) to be achieved at room temperature. Carbon substitution in BN-NT at neighboring B and N sites results in the formation of C-C covalent bond leading to a large gap and no magnetization. With the introduction of more C-C bonds, this band gap is expected to reduce6 and such nanotubes are expected to have properties intermediate between those of CNTs and BN-NTs. Acknowledgment. We acknowledge use of the Central Computing facility and support from the Centre for Computational Materials Science at JNCASR and DuPont. References and Notes (1) Hamada, N.; Sawada, S.; Oshiyama, A. Phys. ReV. Lett. 1992, 68, 1579. (2) Saito, R.; Fujita, M.; Dresselhaus, G.; Dresselhaus, M. S. Appl. Phys. Lett. 1992, 60, 2204. (3) Rubio, A.; Corkill, J. L.; Cohen, M. L. Phys. ReV. B 1994, 354, 5081. (4) Blase, X.; Rubio, A.; Louie, S. G.; Cohen, M. L. Europhys. Lett. 1994, 28, 335. (5) Radosavljevic, M.; Appenzeller, J.; Derycke, V.; Martel, R.; Avouris, P.; Loiseau, A.; Cochon, J. L.; Pigache, D. Appl. Phys. Lett. 2003, 82, 4131. (6) Zhao, J. X.; Tian, Y.; Dai, B. Q. J. Chin. Chem. Soc. 2005, 52, 395. (7) Sun, G.; Kurti, J.; Kertesz, M.; Baughman, R. H. J. Phys. Chem. B 2003, 107, 6924. (8) Guo, C. S.; Fan, W. J.; Zhang, R. Q. Solid State Commun. 2006, 137, 246.

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