Comparative Theoretical Analysis of BN Nanotubes Doped with Al, P, Ga, As, In, and Sb

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1 pubs.acs.org/jpcc Comparative Theoretical Analysis of BN Nanotubes Doped with Al, P, Ga, As, In, and Sb Yuri F. Zhukovskii, Sergei Piskunov,*, Jurijs Kazerovskis, Dmitry V. Makaev, and Pavel N. D yachkov Institute for Solid State Physics, University of Latvia, 8 Kengaraga Str., Riga LV-1063, Latvia Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences, Leninskii pr. 31, Moscow , Russia ABSTRACT: The electronic structure of a (5,5) boron nitride nanotube (BN NT) doped with periodically distributed Al, P, Ga, As, In, or Sb atoms is calculated using two methods: linear combination of atomic orbitals (LCAO) realized via atomic centered Gaussian-type functions as a basis set (BS) and linearized augmented cylindrical wave (LACW) method accompanied with the local density functional and muffin-tin approximations for the electronic potential. Both methods predict with a qualitative agreement the formation of relatively stable point defects associated with the atom substitutions in the BN NT wall. Substantial atomic relaxation of defective NTs leads to the increase of covalency in the defect B(N) bond along with extra charge redistribution between the defect and the nanotube. The calculated density of states shows narrowing of the band gap, due to formation of midgap states induced by defects. INTRODUCTION Boron nitride nanostructures, such as BN nanotubes (NTs) and individual nanosheets, 1 have the same atomic structure as their carbon counterparts, but alternating B and N atoms substitute for C atoms in graphene-like planes with almost no change in atomic spacing. The interest in BN nanotubes and related structures is constantly growing, because the BN tubular structures are always insulators with a band gaps ranging from 4 to 5.5 ev., irrespective of tube chirality and morphology, in contrast to carbon nanotubes, which can be metallic or semiconducting. The large band gap makes the BN NTs promising materials for a number of potential applications in polymeric composites, sensors, catalysts, molecule-based logic gates, as well as nano- and opto-electronic devices. The electronic, optical, and other properties such as conductivity and transverse dielectric properties of BN nanotubes in the external fields have been intensively studied in recent years. If the electronic properties of BN nanotubes, for example, their band gaps could be controlled through a regular mechanism, their ranges of application would be greatly extended, particularly in sensors and nanoelectronics. Various methods attempted to tune the electronic structure of BN nanotubes, including physical methods (such as applying electric field) and strain or chemical methods (such as doping), introduce defects and modify NT walls. The physical methods change directly the band gap while the chemical methods tune the band gap by introducing a localized energy level inside the gap. 2 In fact, the tailoring of the BN NT electronic properties can be achieved by doping the nanotube as predicted in recent calculations and found in experimental studies. 3 For example, carbon doping transforms the insulating BN NTs into an n-type or a p-type semiconductor in the cases of carbon located in boron (C B ) and nitrogen (C N ) positions, respectively. 4,5 The carbon substitutional defects have small deformation energies, which are suggested to explain the experimentally obtained formation of boron carbonitride nanotubes. 6 After incorporation of an O atom in the BN NT, the deformation energies are larger; however, deformation around O N is considerably smaller compared with O B, making the former more probable and confirming relative stability of BN x O 1 x nanotubes. 7 It was also found from the band structure calculations that the system O B /BN NT behaves as an impurity-doped wide gap semiconductor or as a metal for O N substitution. 3 In this study, we have continued theoretical simulations performed recently on perfect and defective BN NTs and nanoarches Using two different methods, we have carried out large-scale density functional theory (DFT) calculations on the single-walled BN nanotubes of uniform diameter with armchair chirality (5,5) containing a number of substitutes for B and N atoms. For this purpose, we have performed hybrid (DFT + HF) calculations using the CO-LCAO formalism (crystalline orbitals as linear combinations of atomic orbitals) as implemented in CRYSTAL code, 14 as well as DFT calculations using the linearized augmented cylindrical wave (LACW) method accompanied with the local density functional and muffin-tin approximation for the electron potential. 15,16 So far, the information about theoretical simulations on these kinds of impurities found in the literature is rather scarce: (i) Received: December 13, 2012 Revised: May 1, 2013 Published: June 5, American Chemical Society 14235

2 The Journal of Physical Chemistry C Figure 1. Schematic representation of substitutional defect-containing BN NT (Ah/BN NT) unit cells as calculated using the PBE0-LCAO method with the al geometry optimization: (a) AlB/BN NT; (b) GaB/BN NT; (c) InB/BN NT; (d) PN/BN NT; (e) AsN/BN NT; (f) SbN/BN NT. Nitrogens are shown as blue balls, while borons are shown as pink ones. Host atoms nearest to the defect neighbor (h n) are shown in lighter colors. The defect defect interaction in such a supercell has been estimated and found to be negligible with practically no dispersion of defect level inside the band gap. The defective nanostructures have been modeled using the host B or N atom substitution by the isoelectronic impurity atom, Ah, that is, AlB, GaB, InB, PN, AsN, or SbN (Figure 1). The coordinates of all atoms of each nanostructure containing a substitutional point defect have been optimized using PBE0-LCAO method as implemented in the al energy computer code CRYSTAL.14 Calculations by Means of LCAO Method. We have performed the first principles calculations on doped BN NTs using the formalism of the localized Gaussian-type functions (GTFs). The crystalline orbitals φki(r) of the N-electron system (per unit cell), according to the LCAO approach, are expanded as linear combinations of a set of m Bloch functions built from the local, atom-centered GTFs (χgj(r Rj)): recent DFT LCAO calculations on antisites, vacancies (both B and N), and carbon substitutes of B and N atoms for zigzag-nt present a fairly complete account of their atomic and electronic properties;4,5 (ii) both OB and ON substitutes have been calculated using DFT method for both armchair- and zigzagnt.3,8 Meanwhile, the presence of ON point defect in zigzagbn NT leads to appearance of a new band in the gap, which crosses the Fermi level; that is, such a nanotube shows a metallic behavior. The outline of the paper is as follows. The Theoretical Background section describes the computational details of our calculations. The main part of the paper is formed by the Results and Discussion section. Our conclusions are summarized in Summary and Concluding Remarks. THEORETICAL BACKGROUND Structural Models of Defective BN Nanotubes. The main task of this paper is to compare properties of doped BN NTs calculated using both DFT-LCAO and DFT-LACW methods. To perform their detailed analysis, we have chosen the particular case of energetically stable armchair-type (5,5) nanotube.10,12 A method that allows formation of BN nanotube from hexagonal BN bulk and (0001) monolayer, which are similar to the hexagonal structure of graphite bulk and graphene nanosheet, respectively, can be applied in accordance with a model of structural transformation 3D 2D 1D as described elsewhere.10 Using this approach, we have constructed the monoperiodic unit cell for ideal (5,5) BN NT. To achieve a dilute limit of single substitutional point defect, we have built a supercell having an interdefect distance as large as 7.5 Å with 60 atoms in the periodically repeated cell. m φki(r) = N aij(k)( χgj (r) exp(i k g)) j=1 g (1) ng χgj (r R j) = cμg(αμ; r R j g) μ (2) where k is the wave vector of the irreducible representation of the group of crystal translations {g}; Rj denotes the coordinates of nuclei in the zero cell in which the atomic orbital χgj(r) is centered; G, cμ, and αμ are the normalized GTFs, their coefficients, and exponents, respectively. Earlier, this LCAO formalism was successfully applied by us for simulations on single- and double-walled BN nanotubes and nanoarcs

3 Our calculations on DW NTs have been performed using the hybrid Hartree Fock/Kohn Sham (HF/KS) exchange-correlation functional PBE0 by Perdew Becke Erzerhof 17,18 combining exact HF nonlocal exchange and KS exchange operator within the generalized gradient approximation (GGA) as implemented in CRYSTAL code. 14 The advantage of the hybrid PBE0-LCAO calculations is that they make results of the band structure calculations more plausible. An all-valence basis set (BS) in the form of 6s 21sp 1d and 6s 31p 1d Gaussiantype functions have been used for B and N atoms, 10 respectively. For substitutional impurity atoms Al, Ga, In, P, As, and Sb, the 21sp 1d BSs with effective core pseudopotential (ECP) from Durand have been adopted. To provide the balanced summation over the direct and reciprocal lattices, the reciprocal space integration has been performed by sampling the Brillouin zone (BZ) with the Pack Monkhorst k-mesh 22 that results in six eventually distributed k-points at the segment of irreducible BZ. The threshold parameters of CRYSTAL code (ITOLn) for evaluation of different types of bielectronic integrals (overlap and penetration tolerances for Coulomb integrals, ITOL1 and ITOL2, overlap tolerance for exchange integrals ITOL3, and pseudo-overlap tolerances for exchange integral series, ITOL4 and ITOL5) 14 have been set to 8, 8, 8, 8, and 16, respectively. (If the overlap between the two atomic orbitals is smaller than 10 ITOLn, the corresponding integral is truncated.) Further increasing of k-mesh and threshold parameters results in much more expensive calculations yielding only a negligible gain in the al energy ( 10 7 au). Calculations are considered as converged when the al energy obtained in the self-consistent field procedure differs by less than 10 7 au in the two successive cycles. Effective charges on atoms as well as net bond populations have been calculated according to the Mulliken population analysis Calculated equilibrium lattice constants for the hexagonal BN bulk structures have been found to be qualitatively close to their experimental values (cf., a 0 of 2.51 vs 2.50 Å obtained in experiment and c 0 of 7.0 vs 6.7 Å), 27 thus indicating reliable optimization of BN BSs. For these calibrating calculations, 3D periodicity has been employed, while for all the calculations on nanotubular structures, 1D periodicity has been applied within the rotohelical formalism as implemented in the CRYSTAL code. 14 On the other hand, unlike the optical band gap energy (E g ) measured experimentally (5.96 ev for hexagonal BN bulk 28 ) the value of E g, calculated by us, has been found to be slightly overestimated (6.94 ev), which is rather a result of the PBE0 hybrid functional application for BN calculations (since PWGGA exchange-correlation functional gives a better agreement of these values 9 ). Nevertheless, due to its ability to predict reliable atomic and electronic structures of wide-gap nanotubular semiconductors, 10,11,29 as well as to be consistent with our previous studies on BN nanomaterials, we have chosen PBE0 hybrid exchange-correlation functional for LCAO calculations on BN NTs with substitutional defects. Also, the alternative hybrid method for description of the band structure (HSE03) 30,31 is not yet implemented in the CRYSTAL code. Calculations by Means of LACW Method. Additionally, we have calculated the electron densities of states in the terms of alternative approach, namely, the linear augmented cylindrical wave (LACW) method. The LACW method is an extension of a linear augmented plane wave (LAPW) technique well-known in the theory of band structure of the bulk materials to the specific case of one-dimensional polyatomic systems having the cylindrical rolled up structure. 15,16 Recently, this method has been successfully employed in reliable electronic structure calculations on carbon and boron nitride nanotubes independently of their chirality indexes. 12,13,32 37 In the LACW method, a cylindrical muffin-tin (MT) approximation is used for the electronic potential; that is considered to be spherically symmetric in the region of atoms versus constant in the interatomic space between the two impenetrable cylindrical barriers, inner and outer, surrounding the atoms of the nanotube. As different from the LCAO method, the basis functions of the LACW technique contain the localized atomic orbital type contributions and the delocalized cylindrical wave type components. The electronic structure of the system is determined by the free motion of electrons in the interatomic space between cylindrical barriers and by electron scattering from atomic centers. Similar to the LAPW approach, the LACW method typically underestimates the optical gaps of the wide-gap materials. 15,16 The results of calculations depend on one parameter only: the cylindrical layer thickness δ. 32,33 In this case, the value δ = 2.4 Å is obtained from the condition that the LACW width of the band gap E g of ideal BN NT to be as large as possible (E g = 3.4 ev). Due to large difference with the value of the corresponding band gap calculated using the LCAO method (6.9 ev), the arrangement of defect levels within the gap is different in both cases. For instance, the midgap states, which are well observed in the density of states (DOS) calculated using LCAO approach, are shifted to the bottom of conduction band in the DOSs calculated using LACW approach. This can result in different interpretations of optical transitions in both cases, from this point of view, the corresponding LCAO values are much more reliable (see Results and Discussion). Energy of Defect Formation. The formation energies of a single substitutional impurity defect A h in BN NTs have been estimated as follows: form Ah A h/bnnt B(N) Ah BNNT (3) E = E + E E E where E Ah /BNNT is the calculated al energy of the BN NT containing a substitutional impurity defect A h, E B(N) is the al energy of host boron or nitrogen atom removed from the nanotube, E Ah is the al energy calculated for the impurity atom, and E BNNT stands for the al energy calculated for the ideal BN NT. RESULTS AND DISCUSSION Analysis of equilibrium distances between substitutional defect and host atoms listed in the Table 1 clearly demonstrates that the bond length between the substitutional impurity defect, A h, and the closest host atoms of the BN NT, h n, tends to be elongated with respect to B N bond length of a pristine BN NT (1.45 Å). Bond length, l Ah h n increases along with increasing atomic mass of the substitutional defect atom, that is, l AlB N 1 = 1.73 Å vs l InB N 1 = 1.97 Å. We note also the outward relaxation of the host BN NT atoms nearest to the A N substitutional atoms, which is noticeably larger than that in the case of A B substitutional defects: that is, l GaB N 1 = 1.80 Å, while l AsN B 1 = 2.07 Å. Obviously, due to a partial covalency of B N bonds, atoms can be more easily rearranged around a substitutional point defect. In the case of A N substitutional atoms, defects displace outward from the nanotube wall. Such a relaxation is 14237

4 Table 1. Equilibrium A h h n Bond Lengths (l Ah h n in Å), A h h n Bond Populations (P Ah h n in milli-e), and Net Charges (Q Ah /h n in e) as Calculated Using the PBE0-LCAO Method a A h Al B Ga B In B P N As N Sb N l Ah h l Ah h l Ah h P Ah h P Ah h P Ah h Q Ah Q h Q h Q h a h n indicates the closest boron and nitrogen host atoms to A h (Figure 1), that is, h is one of the host borons if the dopant substitutes host nitrogen and vice versa. The calculated B N bond length of pristine BN NT (5,5) is Å; bond population P B N = 708 milli-e, while Mulliken effective charges Q B(N) = ±1.005 e. accompanied by slightly increased covalency (cf. P N and Sb N in Table 1) along with extra charge redistribution. Formation energies of a single substitutional point defect onto relaxed BN NT (Table 2) have been found to increase along with atomic mass of the substitutional defect. Calculated formation energies of Al B and P N can be compared (4.37 and 4.86 ev, respectively), while As N and Sb N appear to be more energetically stable with respect to Ga B and In B. Note that the defect formation energy tends to be somewhat increased with increased diameter of the BN NT, for example, E form AlB for a (4,4) BN NT equals 4.19 ev, while that for a (6,6) BN NT is 4.48 ev. Although the BN NT has been calculated for the interdefect distance of 7.5 Å, the interaction between the adjacent substitutes has been found to be negligible. In the current study, the energy dispersion of the populated defect levels in band structures of defective BN NTs does not exceed 0.02 ev; thus, they look like straight lines. In the case of the undoped BN NT, the top of the valence band (VB) consists of mainly boron 2p orbitals, while the bottom of the conduction band (CB) consists of predominantly nitrogen 2p orbitals. Figure 2 shows the al and projected densities of states (DOS) for all nanostructures under study calculated by means of LCAO method. In the case of Al B /BN NT (Figure 2b), the top of the VB is placed on B(2p) orbitals with the bottom of the CB formed by 3p orbitals of Al impurity atom placed slightly below that of ideal BN NT yielding a band gap of 6.42 ev (Table 2). In the case of Ga B /BN NT (Figure 2c), the Ga(4p) defect level splits out 2 ev below the CB yielding a band gap of 5.02 ev. In the case of In B /BN NT (Figure 2d), the In(5p) defect level splitting is much more pronounced with a band gap of 3.55 ev and a vacant midgap state at 3 ev. For the N substitutional defects, the p states of impurity atoms contribute to the top of the VB inducing defect levels in the vicinity of the CB bottom formed mainly by p orbitals of the nearest host nitrogens. Their influence on the band gap of defective BN NTs is more modest with respect to the B substitutional defects (Table 2). The P N /BN NT center yields Figure 2. Total and projected density of states (PDOS) of ideal and doped BN NT as calculated using the PBE0-LCAO method: (a) ideal BN NT, (b) Al-doped BN NT, (c) Ga-doped BN NT, (d) In-doped BN NT, (e) P-doped BN NT, (f) As-doped BN NT, and (g) Sbdoped BN NT. Zero on the energy scale corresponds to the top of the valence band. Table 2. Defect Formation Energy (E form Ah in ev, eq 3) and band gap (E g in ev) of A h /BN NTs as Calculated Using Both PBE0-LCAO and LACW Methods a form E Ah A h LCAO LCAO LACW Al B Ga B In B P N As N Sb N BN NT hex-bn 6.9 a Band gaps calculated for pristine BN NT and hexagonal BN bulk are shown at the end of the table. the band gap of 6.24 ev (Figure 2e), the As N /BN NT center shows a band gap of 5.94 ev (see Figure 2f), while a band gap of 5.03 ev has been predicted for Sb N /BN NT (Figure 2g). E g 14238

5 Figure 3 shows the LACW bands of the pristine (5,5) BN and doped nanotubes with one intrinsic substitution. The Figure 3. Total density of states (DOS) of ideal and doped BN NTs as calculated using the LACW method: (a) ideal BN NT, (b) Al-doped BN NT, (c) Ga-doped BN NT, (d) In-doped BN NT, (e) P-doped BN NT, (f) As-doped BN NT, and (g) Sb-doped BN NT. Zero on the energy scale corresponds to the top of the valence band. LACW DOS of all nanotubes are qualitatively similar to those calculated using the LCAO approach. The valence band consists of predominantly p states, and its low-energy part overlaps with high-energy states of the sp band. In all cases, since the local density approximation is employed, the optical gaps calculated using the LACW are noticeably underestimated compared with those obtained using the LCAO; however, both methods predict that the isoelectronic n and p type dopants do not close the wide forbidden band gap of the pristine BN nanotubes. The formation of new peaks at the boundaries of the valence and conduction bands is predicted to be the main doping effect on the band gap. Possibly, the Ga B and In B centers are the only exceptions; the LCAO (not LACW) method points to formation of a narrow band in the middle of the forbidden gap of the pristine BN NT. The reason for this could be the underestimated band gap in LACW calculations that shifts the midgap states (at 5 and 3 ev seen in Figure 2c,d, respectively) to the bottom of conduction band and, thus, they practically cannot be identified in Figure 3c,d. On the other hand, the widened valence band in Figure 3e,f does not allow one to identify P and As p states located at 11 ev in Figure 2e,f. SUMMARY AND CONCLUDING REMARKS We have performed large-scale first-principles calculations of the electronic structure of (5,5) boron nitride nanotubes containing the following substitutional impurity atoms: Al, P, Ga, As, In, and Sb. Calculations have been performed using the two methods: (i) linear combination of atomic orbitals (LCAO) with the atomic-centered Gaussian-type functions as a basis set and (ii) linearized augmented cylindrical wave (LACW) accompanied with the local density functional and muffin-tin approximations for the electronic potential. In a relatively good qualitative agreement, both methods predict low formation energies and, thus, relative stability of point defects that are associated with the atom substitutions in the BN NT walls. Along with this, the formation energies of a single substitutional point defect onto relaxed BN NT have been found increased along with increased atomic mass of the substitutional defect. Analysis of equilibrium distances between the substitutional defect and nanotube s host atoms demonstrates that their bond lengths tend to be elongated with respect to B N bond length of pristine BN NT. Such a relaxation is accompanied with slightly increased covalency along with extra charge redistribution between the defect and the nanotube. The calculated density of states shows the formation of midgap states in the band gap of BN NT, thus leading to the narrowing of a gap. On the basis of our quantum-chemical calculations, we, therefore, conclude that the presence of isoelectronic impurities significantly affects the band structure of BN nanotubes, which must be taken into account when constructing nanoelectronic devices based on these nanotubes. We assume that all the mentioned effects can be observed by both optical and photoelectron spectroscopy methods, as well as by measuring the electrochemical properties of BN NTs. AUTHOR INFORMATION Corresponding Author * piskunov@lu.lv. Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS The research leading to these results has received funding from the EC s Seventh Framework Programme under Grant Agreement Nr (CACOMEL). The work of D.V.M. and P.N.D. was also supported by Russian Basic Research Foundation (Grant ). The authors are thankful to S. Bellucci and R.A. Evarestov for stimulating discussions. REFERENCES (1) Golberg, D.; Bando, Y.; Huang, Y.; Terao, T.; Mitome, M.; Tang, C.; Zhi, C. Boron Nitride Nanotubes and Nanosheets. ACS Nano 2010, 4, (2) Zhi, C.; Bando, Y.; Tang, C.; Golberg, D. Boron Nitride Nanotubes. Mater. Sci. Eng., R 2010, 70, (3) Silva, L.; Guerini, S.; Lemos, V.; Filho, J. Electronic and Structural Properties of Oxygen-Doped BN Nanotubes. IEEE Trans. Nanotechnol. 2006, 5, (4) Schmidt, T. M.; Baierle, R. J.; Piquini, P.; Fazzio, A. Theoretical Study of Native Defects in BN Nanotubes. Phys. Rev. B 2003, 67, No

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