Structural and electronic properties study on B-N co-doped (4,3) carbon nanotubes through first-principles calculations

Abstracts

We carry out theoretical studies for both the pristine and boron-nitrogen co-doped (4,3) single-walled carbon nanotubes (SWCNTs). We first acquire the optimized geometries using a pure functional. We then obtain the electronic structures with a relatively accurate hybrid functional. We systematically study four different patterns for doping along different chain directions. Our calculated results reveal that the energy band splits, and many new states appear in the gap after doping. The band gap gradually decreases with the increasing number of dopants, while it begins to expand when the doping concentration is larger. Through projected density of states analyses, we find that the individual atoms make different contribution to the valence states, gap region states, and conduction states. These findings are expected to provide some reliable theoretical supports with the following research on the modification of carbon nanotubes.

Introduction

Carbon nanotubes, especially the single-walled carbon nanotubes (SWCNTs), have attracted considerable attention in the past few years since its discovery in 1991 by lijima [1], both experimentally and theoretically, because they have unique structural and electronic performances and promising applications in nanoelectronic devices [2], [3], [4], [5]. Recent research interests have been greatly focused on the studies of band structures and band gaps of SWCNTs, due to the importance to the electrical and optical performances. Mintmire et al. first studied the electronic properties of carbon nanotubes with the first-principles calculations based on the local density approximations (LDA). They found that the infinitely long tubules with D_5h helical symmetry would appear to have the advantages of a carrier density similar to metals, with a concomitant relatively high conductivity [6]. Blase et al. calculated the band gap of small tubes by using detailed plane-wave ab initio pseudopotential local density approximation calculations [7]. The band structure calculated by LDA substantially differs from that obtained by tight binding approximation, due to the strong σ–π rehybridization [8]. Kane et al. found out the curvature-induced narrowing gap in the research of metallic helical and zigzag carbon nanotubes experimentally. They concluded that the band gap is inversely proportional to the square of tube diameter [9]. Using the low-temperature atomically resolved scanning tunneling microscopy (STM), Ouyang et al. also investigated the energy gaps of zigzag and armchair nanotubes [10]. Their results suggested that metallic zigzag nanotubes have energy gaps depending inversely on the square of the tube radius, while the armchair nanotubes packed in bundles have pseudogaps exhibiting an inverse dependence on tube radius. Cao et al. calculated the electronic band structures for single-walled carbon nanotubes (n,0)(n=6,7,8,9) through a simple sp³s^∗ tight-binding model [11], they obtained different results from the findings of previous work that (6,0) and (9,0) tubes are narrow-gap semiconductors rather than metallic ones. Miyake et al. studied the electronic structure theoretically with first-principles techniques [12], finding that the (5,0) tube is metallic even at the GW level, being different from the tight-binding result. The carbon nanotubes would present different characteristics of metallicity and semiconductor due to the influence of different tube diameters and chiralities [7], [13], [14], [15], [16].

Generally, the presence of defects and impurities has an important effect on the structural and electronic properties of SWCNTs, in particular causing some superior modifications [17], [18], [19], thus receiving significant attention from the science community. Boron and nitrogen atoms have been regarded as the ideal dopants incorporated into carbon nanotubes, due to their similar atomic radius to carbon atoms. Many researchers have successfully prepared B-N doped carbon nanotubes [20], [21], [22]. With the ab initio molecular dynamics method, Yi et al. reported that the substitution of B and N has a great influence on the electronic properties of carbon nanotubes [23]. Nevidomskyy et al. calculated the nitrogen impurity substitution in semiconducting zigzag and metallic armchair SWCNTs through density functional theory [24]. They reported the formation of an inter-tube covalent bond when two neighboring tubes make their impurities face each other, which will lead to the huge potential applications in tunnel junctions of SWCNTs. Using ab initio density functional theory, Yu et al. studied the single-walled zigzag (n,0) carbon nanotubes containing substitutional nitrogen impurities and B/N impurities, respectively [25], [26]. Their calculated results suggested that the formation energies of these doped nanotubes depend on the tube diameter and the electronic properties. Saikia et al. investigated BN co-doped (5,5) and (8,0) SWCNTs within the framework of DFT using generalized gradient approximation [27]. They found the BN impurities tend to form the segregated BN domains in SWCNTs. The formation and cohesive energies increase with the number of BN domains. Jana et al. reported the density functional calculations for the electronic, optical and electrochemical properties along with electronic behaviors of B and N substituted SWCNTs [28]. They observed significant changes in the electronic as well as optical behaviors in different systems (radius <1 nm) with different polarizations. To investigate the effect of B on the structure and electronic properties, Saloni et al. calculated the boron-doped (4,0) and (9,0) carbon nanotubes [29], using the B3LYP functional. The B doped carbon nanotubes presented local structural distortions due to the elongation of bonds. Peralta et al. suggested that the stronger electrostatic potentials are associated with the regions of higher curvature by the computation on electrostatic potentials for the open and closed (5,5) and the open (6,1), (7,1) and (8,1) carbon nanotubes at the Hartree-Fock STO-5G//STO-3G level [30].

Nevertheless, most of these works acquire the electronic properties using pure DFT calculations. This would doubtlessly underestimate the bandgap and possibly gap states. On the other hand, even the B3LYP hybrid functional would sometimes overestimate bandgap. The HSE06 has a reputation of reproducing experimentally acquired bandgap and optical transitions. We would also like to study the contribution to the DOS of the doped systems from individual atoms. We focus on the top states of the valence band, the gap region states, and the bottom states of the conduction band. In this work, we first optimize the structure of the substitutional BN pairs co-doped (4,3) single-walled carbon nanotubes using pure functional. Then, we calculate the electronic properties using the HSE06 functional. We adopt four different chain doping patterns with BN atoms in pairs, compared with previous work doping with BN rings [27]. The results indicate that the electronic properties of doped systems depend on the doping patterns as well as the doping concentrations. The PDOS plots reveal that these new states in the gap mainly consist of C 2p orbitals, while the B 2p and N 2p orbitals from dopants are very low states in the gap. We also find that when doped with one pair, both the N and B atoms contribute slightly bigger to the gap region states than the C atom, although collectively, their contribution are buried under the C atoms. When a C atom has high valence state, its conduction state is low. The wavefunction plots display the distribution of HOMO within pure (4,3) SWCNT and BN co-doped systems. Although the HOMO presents different distribution features because of different doping concentrations, it is always localized around the carbon and boron atoms in different doped systems, especially carbon atoms.