Charge distributions in BN nanocones: electric field and tip termination effects

Chemical Physics Letters 392 (2004) 428–432 www.elsevier.com/locate/cplett

Charge distributions in BN nanocones: electric field and tip termination effects M. Machado, P. Piquini *, R. Mota Departamento de Fısica, Universidade Federal de Santa Maria, Cidade Universitaria, Santa Maria, RS 97105-900, Brazil Received 15 March 2004; in final form 24 May 2004 Available online 17 June 2004

Abstract The electronic charge distributions in boron–nitride nanocones with 240° disclination are investigated through first-principles calculations based on the density-functional theory. The charge distributions in BN cones are analyzed and compared with a planar BN sheet and BN nanotubes. The cones are submitted to different external electric fields applied along the axis, ranging from 0 up to  and the charge rearrangements are studied. The tip charge concentrations and the electronic behaviors of these cones show 1.7 V/A, different characteristics depending on the terminating atoms. The cone’s particular structure and the response to the electric field make the BN cones promising candidates to be used as probes in electronic microscopy as well as electron field emitters. Ó 2004 Elsevier B.V. All rights reserved.

1. Introduction Nanocones were observed by the first time in 1992 as caps at the ends of nanotubes [1], just after the discovery of carbon nanotubes, and as free standing structures two years latter [2,3]. More recently, nanocones have started to be the focus of increasing scientific and technological interests due to their special electronic and mechanical features. In fact, today, BN structures are believed to lead to incredibly durable materials that could have even better electronic qualities than C counterparts. Cones can be built departing in specific ways from a flat hexagonal network, resulting in different topological defects at their apexes. For carbon, the most common of such defects is known to be pentagonal ring. Similar structures with B and N atoms, instead of C atoms, have been proposed [4] and also, more recently, experimentally observed [5,6]. An analogy between C and BN nanocones needs to be done very carefully because any pentagonal ring with B and N atoms must contain at

*

Corresponding author. Fax: +55-55-2208032. E-mail address: [email protected] (P. Piquini).

0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.05.088

least one homonuclear bond. Then, for BN cones, the situation concerning the apex defects is not well established, as it is for C cones [7], and the possible terminations for BN structures are still open questions, demanding much more study and experimental characterization. We have proposed one particular configuration for BN nanocones with 240° disclination presenting as characteristic four pentagons at the apex and termination in two atoms [8–10]. Depending on the terminating atoms (BN, BB or NN), different densities of states (DOS) are observed and particular sharp resonant states are found in the regions close to the Fermi energy. A previous study of the electronic properties of such proposed structure, under electric fields, demonstrated that the DOS show different patterns depending on the terminating two atoms and the electric field strength [11]. A decreasing of the gap is observed with increasing field strength and the electric field is shown to contribute to enhance the electron field emission, as expected. A possible application of BN nanocones is their use as cold electron sources in field emission displays in a similar way that was showed for their C counterparts [12,13]. Also, they can be thought as appropriate probes for electronic microscopy devices.

M. Machado et al. / Chemical Physics Letters 392 (2004) 428–432

2. Calculational procedure The proposed nanocone with 240° disclination, showed in Fig. 1, is simulated by a cluster containing 62 (B + N) atoms with the dangling bonds at the open edge saturated by 12 H atoms. This cone presents an apex formed by four pentagons sharing two three-coordinated atoms (BN, BB or NN). Here, one must pay attention that there is an energy cost resulting from the unavoidable homonuclear bonds, two for the BN terminated cone, and three for the BB and NN ones. These homonuclear bonds are, in general, weaker than regular B–N bonds. As a solution for the BN cone apexes, the even membered rings, like squares for example, have been thought since they do not necessitate the inclusion of homonuclear bonds [14]. However, the structural stress involved in going from pentagonal to square defect rings carries with it an energy penalty, making these propositions competitive energetically [8–10] with others, like the one here proposed with four pentagons at the apex and termination in two atoms. To make our analysis easier, our system is divided in several layers of atoms, perpendicular to the cone axis, ordered from the tip apex to the H-saturated edge, as shown in Fig. 1a. These layers are constituted by: (1) two atoms; (2) ten atoms; (3) fourteen atoms; (4) eighteen atoms. The fifth layer is not considered in our analysis due to its proximity with the H-atoms, being consequently much affected by their presences. In order to compare the charge distributions in BN systems with different geometric constraints, we performed supercell calculations for a BN planar sheet and (5,5) armchair and (9,0) zigzag BN nanotubes. We choose these par-

Fig. 1. (a) Two lateral views of the cone structure, rotated by 90° from each other. The layers of atoms are schematically shown. The apexes are constituted by four pentagons with termination in two three-coordinated atoms: (b) BN, (c) BB, and (d) NN.

429

ticular nanotubes due to the similarity between the di for the (5,5) tube, 7.1 A  ameters, which are around 6.8 A  for the (9,0) tube and around 6.8 A for the cone near the H-saturated edge. The adopted scheme for survey of the geometric structure optimizations and electronic properties of the studied systems is the density-functional theory, as implemented in the SIESTA code [15,16]. It performs fully self-consistent calculations solving the Kohn–Sham equations. The Kohn–Sham orbitals are expanded using a linear combination of pseudo-atomic orbitals proposed by Sankey and Niklewski [17]. In all calculations we have used a double-zeta basis set with polarization functions [18]. The standard norm-conserving Troullier– Martins pseudopotentials are utilized [19]. For the exchange and correlation term, we use the local-density approximation [20], with the parameterization proposed by Perdew–Zunger [21]. A supercell with dimensions large enough to exclude interactions between cones in adjacent cells and to avoid the presence of electric charges near the cell boundaries is employed in all cone’s calculations. As the effect of the electric field is local, the effect of the field discontinuity at the cell boundaries in the cone charge, due to the translational symmetry, can be neglected.

3. Results and discussion To analyze the relationship between geometry and charge distributions in BN cones, a comparison with BN planar sheets and nanotubes would be useful. Planar sheets present translational symmetry along two directions. When forming nanotubes from planar sheets, the translational symmetry along one direction is lost, resulting in quasi one-dimensional structures. For nanocones, on the other hand, the translational symmetry is completely lost, with the cones being semi-infinite along the cone axis. In a BN system, the B–N bonds are heteropolar, being the polarity of a particular bond dependent on the arrangement of the surrounding atoms. In a planar sheet a sp2 hybridization of the atomic orbitals occurs and there is an overlap of the valence electrons orbitals. As a result, the valence electrons tend to screen the B and N ionic potentials leading to B–N bonds with a relatively low polarity. The calculated Mulliken charges of the B and N atoms at the planar BN sheet are 3.80 and 4.20, respectively. For a nanotube, its cylindrical geometry induces an intermediate sp2þa hybridization on the atomic orbitals, except for the ones along the axis direction, which remain with the same original hybridization. As smaller the radius of the nanotube, greater will be the value of a [22]. This reduces the overlap between the valence orbitals that, by its turn, reduces the screening of the B and N ionic potentials and, consequently,

430

M. Machado et al. / Chemical Physics Letters 392 (2004) 428–432

increases the polarity of the B–N bond. This leads to more localized charge distributions as compared to planar sheets (which can be seen as nanotubes with infinite radius). The calculated charges on B and N atoms for the (5,5) and (9,0) nanotubes are similar, being around 3.77 (B atoms) and 4.23 (N atoms). The peculiar geometry of the nanocone leads to different structural environments for atoms at different distances from the cone tip. Thus, the charge distribution analysis is performed considering the nanocones as the stacking of BN layers of atoms with increasing diameters, as seen in Fig. 1a. The average values for the charges on the B and N atoms at the different cone layers are shown in Table 1 for the three studied cone terminations (BN, BB and NN). The calculated atomic Mulliken charges are shown in Table 1. For the cone terminating in BN atoms, the B–N bonds present a higher polarity when closer to the tip. The polar character can be estimated by the difference between the average electronic charges on B and N neighboring atoms at different layers in the cone Table 1 Average electronic charge values for the B (QB ), N (QN ), and BN pair (QB + QN ) atoms for the BN, BB and NN terminated cones. (QN )QB )/ 2 is the electronic charge difference per atom Termination

Layer

QB

QN

(QN )QB )/2

(QB + QN )

BN

1 2 3 4

3.41 3.55 3.63 3.64

4.64 4.45 4.37 4.35

0.61 0.45 0.37 0.35

8.05 8.00 8.00 7.99

BB

1 2 3 4

3.23 3.51 3.63 3.64

– 4.41 4.37 4.35

– 0.45 0.37 0.35

6.46 7.92 7.99 7.99

NN

1 2 3 4

– 3.60 3.63 3.64

4.86 4.47 4.37 4.35

– 0.44 0.37 0.35

9.71 8.07 8.00 7.99

((QN )QB )/2), which varies from 0.35 at the fourth layer to 0.61 at the tip. These values should be compared with the same values for the BN planar sheet and corresponding BN nanotubes, which are 0.20 and 0.23, respectively. The higher the confinement of the valence electrons, lesser will be the capability of these electrons to screen the ionic potentials and, consequently, higher the average charge differences between B and N atoms. Furthermore, for the case of the BN terminated cone, it is noticeable that basically all the charge rearrangements occur within the atoms belonging to the same layers, with practically no charge transfer between layers. For the BB and NN terminated cones, on the other hand, charge transfers between the first and the second layers are observed. The B (N) atoms at the BB (NN) tip take (give) charge from (to) both B and N atoms in the second layer, as seen in Table 1. Even in these cases, the charge transfers between layers are smaller than those within the corresponding layers. As a general result, we note that the charge distributions in the third and fourth layers are basically not affected by the tip termination and, as a trend, stabilization can be assumed occurring at the fourth layer. Further, a comparison between the average charge distributions at the fourth layer of the cones and at the nanotubes shows relatively small differences, with variations equal to 0.12 for the armchair (5,5) and 0.08 for the zigzag (9,0) tubes.  applied The effects of electric fields up to 1.7 V/A, along the cones axis, on the charge distributions are illustrated in Fig. 2. It is remarkable that for the BN terminated system (Fig. 2a) the B atoms around the tip apex (layers 1 and 2) are much more sensitive to the external electric fields than the N atoms. It is also noticeable that, for the layers 3 and 4, the atoms (B and N) are much less affected by the electric fields. Similarly to the BN terminated cone, for the case of the NN terminated one, the valence shells of the N atoms at the tip are practically saturated, presenting a

Fig. 2. Variation of the average charge concentrations for the B and N atoms at different layers for the (a) BN, (b) BB, and (c) NN terminated cones  under electric field ranging from 0 to 1.7 V/A.

M. Machado et al. / Chemical Physics Letters 392 (2004) 428–432 Table 2 Total variation of the average charge concentrations on the B and N atoms at different layers of atoms, for the BN, BB and NN terminated  compared cones, due to the application of an electric field of 1.7 V/A with no field Termination

Layer

DQB

DQN

DQB þ N

BN

1 2 3 4

0.46 0.15 0.05 0.00

0.07 0.02 0.00 0.00

0.53 0.17 0.05 0.00

BB

1 2 3 4

0.49 0.12 0.04 0.01

– 0.05 0.02 0.01

0.49 0.17 0.06 0.02

NN

1 2 3 4

– 0.15 0.05 0.01

0.18 0.06 0.02 0.01

0.18 0.21 0.07 0.02

 As value of 5.04 for the electric field strength of 1.7 V/A. shown in Table 2, it represents an increase of 0.18 in the electronic charge on the N atoms as compared to the case under no electric field, and it is around 2.5 times smaller than the amount of additional charge in BN and BB terminated cones, under the influence of the same electric field. This charge enhancement for the N atoms at the tip of the NN terminated cone is of the same magnitude as that observed for the B atoms at the second layer, in the same cone. This reinforces the greater sensibility of B atoms, compared with N atoms, to the external applied fields. Our results clearly show a charge accumulation on the B atoms at the cone tip with increasing electric field. The great polarity of the BN bond at the tip leads to an increased atomic-like character of the charge at this region. This additional charge on the B atoms at the tip, due to the external electric field, will reduce the energy necessary to extract an electron from the cone tip, which implies in a reduction of the work function of the system. These results could be related with recent reports on the electron field emission enhancement for capped B-doped carbon nanotubes [23], composed BCN nanotubes [24], and open tubes terminated with B atoms [25]. Also, Dorozhkin et al. [26] showed that the reduction of the threshold voltage is directly related to the decrease in the radius of the apex of a BCN nanotube rope in a field emission experiment. For the BN nanocones, both the natural occurrence of B atoms in the structure and the particular sharp tips contribute to enhance the field emission properties.

cone geometry, leads to a reduction of the screening of the ionic potentials for the atoms at the first two cone layers and, consequently, to a higher polarity of the bonds at these layers. For the BN terminated cone, there is practically no charge transfer between different atomic layers with all the electronic rearrangements occurring within atoms of the same layer. For the BB and NN terminated cones, on the other hand, charge transfers between layers are observed, although in a smaller amount than those occurring within layers. These results suggest that the influence of the cone tip (BN, BB or NN) on the charge distributions is restricted mainly to the two first layers. The effects of external applied field,  on the charge distributions in ranging from 0 to 1.7 V/A, the BN nanocones are analyzed. The enhanced polarity of the B–N bonds at the tip leads to a concentration of electrons (holes) in the N (B) atoms. It is shown that the electrons pushed by the applied electric field to the cone tips will preferentially occupy the B orbitals, resulting in a greater variation of the charge on B atoms, in the first two layers. In summary, the effects of the applied electric field, as well as the tip termination, are demonstrated to play a crucial role in the field emission properties, making the BN nanocones promising candidates as probes in electronic microscopy or as electron field emitters.

Acknowledgements Almost all calculations were done at the Centro Nacional de Processamento de Alto Desempenho CENAPAD/Campinas. This work was supported by the Brazilian Agencies FAPERGS, CNPq and CAPES. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]

4. Conclusions Before applying the electric field, it is shown that the increase in the electronic confinement, due only to the

431

[13] [14]

S. Iijima, T. Ichihashi, Y. Ando, Nature (London) 356 (1992) 776. M. Ge, K. Sattler, Appl. Phys. Lett. 64 (1994) 710. M. Ge, K. Sattler, Chem. Phys. Lett. 220 (1994) 192. A. Rubio, J.L. Corkill, M.L. Cohen, Phys. Rev. B 49 (1994) 5081. L. Bourgeois, Y. Bando, W.Q. Han, T. Sato, Phys. Rev. B 61 (2000) 7686. M. Terauchi, M. Tanaka, K. Suzuki, A. Ogino, K. Kimura, Chem. Phys. Lett. 324 (2000) 359. J.C. Charlier, G.M. Rignanese, Phys. Rev. Lett. 86 (2001) 5970. M. Machado, P. Piquini, R. Mota, Mat. Charact. 50 (2003) 179. M.P. Machado, R. Mota, P. Piquini, Eur. Phys. J. D 23 (2003) 91. R. Mota, M. Machado, P. Piquini, Phys. Stat. Solidi C 20 (2003) 799. M. Machado, R. Mota, P. Piquini, Microelect. J. 34 (2003) 545. L.R. Baylor, V.I. Merkulov, E.D. Ellis, M.A. Guillorn, D.H. Lowndes, A.V. Melechko, M.L. Simpson, J.H. Whealton, J. Appl. Phys. 91 (2002) 4602. K.A. Dean, B.R. Chamala, J. Appl. Phys. 85 (1999) 3832. S. Azevedo, M.S.C. Mazzoni, H. Chacham, R.W. Nunes, Appl. Phys. Lett. 82 (2003) 2323.

432

M. Machado et al. / Chemical Physics Letters 392 (2004) 428–432

[15] D. S anchez-Portal, P. Ordej on, E. Artacho, J.M. Soler, Int. J. Quant. Chem. 65 (1997) 453. [16] P. Ordej on, E. Artacho, J.M. Soler, Phys. Rev. B 53 (1996) 10 441. [17] O.F. Sankey, D.J. Niklewski, Phys. Rev. B 40 (1989) 3979. [18] E. Artacho, D. S anchez-Portal, P. Ordej on, A. Garcia, J.M. Soler, Phys. Stat. Solidi B 215 (1999) 809, and references therein. [19] N. Troullier, J.L. Martins, Phys. Rev. B 43 (1991) 1993. [20] D.M. Ceperley, B.J. Alder, Phys. Rev. Lett. 45 (1980) 566. [21] J.P. Perdew, A. Zunger, Phys. Rev. B 23 (1981) 5048.

[22] T.W. Ebbesen, T. Takada, Carbon 33 (1995) 973. [23] G. Zhang, W. Duan, B. Gu, Appl. Phys. Lett. 80 (2002) 2589. [24] V. Meunier, C. Roland, J. Bernholc, M.B. Nardelli, Appl. Phys. Lett. 81 (2002) 46. [25] J.C. Charlier, M. Terrones, M. Baxendale, V. Meunier, T. Zacharia, N.L. Rupesinghe, W. Hsu, N. Grobert, H. Terrones, G. Amaturanga, Nano Lett. 2 (2002) 1191. [26] P. Dorozhkin, D. Goldberg, Y. Bando, Z.-C. Dong, Appl. Phys. Lett. 81 (2002) 1083.