A first-principles investigation on the effect of the divacancy defect on the band structures of boron nitride (BN) nanoribbons

Author’s Accepted Manuscript A first-principles Investigation on the effect of the divacancy defect on the band Structures of boron nitride (BN) nanoribbons Hui Zhang, Guangtao Yu, Wei Chen, Jia Guan, Xuri Huang www.elsevier.com/locate/physe

PII: DOI: Reference:

S1386-9477(15)00025-9 http://dx.doi.org/10.1016/j.physe.2015.01.024 PHYSE11848

To appear in: Physica E: Low-dimensional Systems and Nanostructures Received date: 21 November 2014 Revised date: 9 January 2015 Accepted date: 13 January 2015 Cite this article as: Hui Zhang, Guangtao Yu, Wei Chen, Jia Guan and Xuri Huang, A first-principles Investigation on the effect of the divacancy defect on the band Structures of boron nitride (BN) nanoribbons, Physica E: Lowdimensional Systems and Nanostructures, http://dx.doi.org/10.1016/j.physe.2015.01.024 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

A First-Principles Investigation on the Effect of the Divacancy Defect on the Band Structures of Boron Nitride (BN) Nanoribbons

Hui Zhang, Guangtao Yu,* Wei Chen,* Jia Guan, Xuri Huang

The State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun 130023, People’s Republic of China

E-mail: [email protected] (G.Y.), [email protected] (W.C.)

Abstract On the basis of the comprehensive first-principles computations, we investigated the geometries, electronic and magnetic properties of zigzag and armchair boron nitride nanoribbons (BNNRs) with the divacancy defect of 5-8-5 ring fusions formed by removing B-N pair, where the defect orientation and position are considered. Our computed results reveal that all of the defective BNNRs systems can uniformly exhibit nonmagnetic semiconducting behavior, and the formation of the divacancy 5-8-5 defect can significantly impact the band structures of BNNRs with not only the zigzag but also armchair edges, where their wide band gaps are reduced and the defect orientation and position play an important role. Clearly, introducing divacancy defect can be a promising and effective approach to engineer the band structures of BNNRs, and the present computed results can provide some valuable insights for promoting the practical applications of excellent BN-based nanomaterials in the nanodevices.

Keywords: boron nitride nanoribbons; first-principles computation; band structure; divacancy defect (5-8-5) 1

1. Introduction Graphene and graphene nanoribbons (GNRs) have been fabricated successfully [1-3], and their realization has evoked a new revolution to materials science. The unique structure, a single-atom-thick sp2-hybridized carbon network, can make them exhibit the extraordinary mechanical, chemical and electronic properties [4-7], endowing them with many potential applications, especially in nanoelectronics [1,5,7,8]. The extensive investigations of carbon-based low-dimensional nanosystems [9-13] have stimulated the research progress of inorganic counterparts [14-23]. Particularly, as the structural analogues of graphene and GNRs, the two-dimensional (2D) hexagonal inorganic BN nanosheet and one-dimensional (1D) BN nanoribbons (BNNRs) can exhibit the high thermal and chemical stabilities, and have received considerable attention in experiment and theory [24-31]. Currently, the single/multi-layer h-BN sheets [24-27] and BNNRs [28-30] have been realized in experiment, and some applications are foreseen. For example, it is revealed that the polymeric composites containing BN nanosheets can exhibit the enhanced mechanical property [24]. However, different from the graphene/GNRs with the zero/small band gap, the low dimensional BN nanosheet and BNNRs exhibit intrinsic semiconducting characteristic with a large band gap (ca. 4~6 eV), which somewhat inhibits the application of BNNRs in nano-electronic devices. To address this important issue, various strategies have been proposed to effectively engineer the band structures of low-dimensional BN nanosystems [32-36]. Among them, it is found that the wide band gap of BNNRs can be effectively engineered, such as, by applying an external transverse electric field [32], edge-modification through chemical groups [33,36], and (non)covalent surface-modification [19,35], where semiconducting, half-metallic and metallic behaviors can be observed. Currently, great efforts have been focused on the effect of various defects on electronic and magnetic properties of BNNRs [20-22,31,37-46], in view of the case that the formation of defect is inevitable in the process of the growth or manipulation 2

of nanomaterials, for example, the triangular vacancy defects [37] and line defects with 5/7- or 4/8-membered rings [38-41] have been experimentally observed in the BN nanostructures. The theoretical studies showed that the formation of the defect can significantly impact the band structures of BN nanostructures [20-22,42-45], and introducing the proper defect can be also regarded as an effective strategy to modulate the electronic and magnetic behaviors of the BN-based nanosystems. For instance, it is revealed that the formation of triangular vacancy defects can endow the zigzag and even armchair BNNRs with the half-metallicity and spin gapless semiconductor [42]. Additionally, the existence of a 5-8-5 or antisite line defect [21,22], as well as a 5/7 line defect [43,44] can uniformly impact the band structures of BNNRs, where the half-metallic, semiconducting and metallic behaviors can be observed. Besides, forming the Stone-Wales defect can effectively decrease the band gap of BNNRs independent of the defect orientation, although the nonmagnetic semiconducting behavior is still maintained [20]. Moreover, doping C atom [31] or carbon-chain [46] can also modulate the electronic and magnetic behaviors of zBNNR, especially increasing the carbon segment can even cause a transition of semiconductor – half-metal – metal [46]. In this work, we intend to investigate how introducing the divacancy defect created by removing one B-N pair (usually reconstructed to a single 5-8-5 defect, different from the 5-8-5 line defect mentioned above) will affect the electronic and magnetic properties of BNNRs with zigzag and armchair edges, where the some crucial factors involving the defect orientation and position are considered. It is worth mentioning that the divacancy defect with the 5-8-5 fusion rings has been experimentally observed in the C- and BN-based low-dimensional nanomaterials etc., e.g. graphene [47], carbon nanotube [48] and BN nanotube [49]. Great efforts have been made on the effect of forming the divacancy 5-8-5 defect on the electronic and magnetic properties of C and BN nanosystems [49-53]. For example, it is revealed that the formation of divacancy defect can effectively reduce the band gap of armchair GNR, eventually leading to a transition from the semiconductor to the metal-like [50], while contrarily it can open a band gap in armchair carbon nanotube, namely, causing 3

a transition from the metal to the semiconductor [51]. Moreover, the presence of the divacancy 5-8-5 defect can effectively narrow the wide band gap of not only the BN nanotube [49,52] but also the BN layer [53], where the original band gap can be considerably decreased by 1.0~2.0 eV. Clearly, the formation of the 5-8-5 defect can significantly impact the band structures of C- and BN-based low-dimensional nanomaterials. However, to the best of our knowledge, the related study on the 1D BN nanoribbons with the divacancy 5-8-5 defect is rather scarce, in spite of the great importance. Here, we have carried out systematic first-principles computations to investigate the structures, electronic and magnetic properties of zigzag and armchair BNNRs with the divacancy 5-8-5 defect. The following specific issues are mainly addressed: (1) How will the formation of divacancy 5-8-5 defect impact the band structures of zigzag and armchair BNNRs? (2) Have the defect orientation any effect on the electronic and magnetic properties of BNNRs? (3) How will changing the defect position from the center to the edge (even leading to the edge-reconstruction) impact the electronic and magnetic behaviors of BNNRs? Our computed results reveal that all of these defective BNNRs systems can uniformly exhibit nonmagnetic semiconducting behavior, and forming the divacancy 5-8-5 defect can significantly affect the band structures of not only the zigzag but also the armchair BNNRs, where their band gaps are reduced and the defect orientation and position play an important role. 2. Computational Methods The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof exchange-correlation functional was employed for all the density-functional theory (DFT) computations, as implemented in the Vienna ab initio simulation package (VASP) [54-57],

where

the

projector

augmented

wave

(PAW)

[58,59]

pseudo-potentials were used to model the electron-ion interactions with a 400 eV cutoff for the plane-wave basis set. In this work, the edges of the studied BNNRs systems are terminated by hydrogen atoms to remove dangling bonds. The used 4

supercell models for the perfect zBNNR and aBNNR possess eight zigzag BN chains (Figure 1a) and eleven BN dimer lines (Figure 1d), respectively, in which 144 and 130 atoms have been involved accordingly. Then, the corresponding defective structures of zBNNR and aBNNR were constructed by removing the B-N pairs, as shown in Figures 1b, 1c, 1e and 1f. For all the computations, the distance larger than 10 Å between two defects along the periodic direction and the vacuum regions wider than 10 Å along the nonperiodic directions were adopted to avoid interactions between the adjacent

defects/images

in

the repeated

supercells.

1×1×10

Monkhorst-Pack grid k-points were utilized for the geometric optimization, and the convergence threshold was set as 10-4 eV in energy. To further investigate the electronic properties, 21 k-points were used to sample the 1D Brillouin zone on the basis of the fully relaxed structures.

3. Results and Discussion 3.1. Geometrical Structures of the Zigzag and Armchair BNNRs with the Divacancy Defect. Like the analogous GNRs, inorganic BNNRs with two types of edge chiralities (zigzag and armchair), namely, zBNNRs and aBNNRs, have been investigated in this work. As illustrated in Figure 1, their structures are classified by the number of zigzag chains Nz and dimer lines Na across the widths of zBNNRs (Wz) and aBNNRs (Wa), which are denoted as Nz-zBNNRs and Na-aBNNRs, respectively. Figure 1 also displays geometrical structures of the sampled 8-zBNNR and 11-aBNNR, in which both perfect and divacancy-defective cases are considered. It can be found that there are two types of B-N bonds in BNNRs with either the zigzag or armchair edge, that is, one is parallel or vertical to the periodic direction and the other is slanted, which are marked with the bonds “1” and “2”, respectively (Figures 1a and 1d). Thus, two kinds of divacancy defects may occur in each BNNR (denoted as dv-1 (Figures 1b and 1e) and dv-2 (Figures 1c and 1f), respectively) with removing the B-N pair 1 or 2, where the reconstruction by forming new B-B and N-N bonds can be observed at the defective area, leading to the creation of two pentagons and one 5

octagon (5-8-5). Our computed results show that in the 8-zBNNR with the divacancy 5-8-5 defect, the bond lengths of the newly formed B-B bonds are 1.853, 1.849/1.845, 1.799/1.831 Å for the dv-1 and 1.842, 1.793/1.753, 1.798 Å for dv-2 defects in the center, the B/N edge, as well as corresponding to B/N edge reconstruction, respectively (Tables 1~2). We can find that independent of the divacancy orientation, the closer to the ribbon edge, the shorter the new B-B bond length, which can be attributed to the case that the deformation of the edge are usually easier than that of the ribbon interior (Tables 1~2). The similar trend can be also observed in the newly formed N-N bond lengths in the divacancy at the different sites, namely, 1.639, 1.634/1.621, 1.600/1.487 Å for 8-zBNNR systems with the dv-1 defect and 1.619, 1.508/1.528, 1.459 Å for the parallel systems with the dv-2 defect, respectively (Tables 1~2). Moreover, in the armchair 11-aBNNRs with the divacancy, when moving the defect from the center to edge, the newly formed B-B/N-N bond lengths reduce from the corresponding 1.828/1.593 to 1.760/1.499 Å (dv-1) and from 1.826/1.607 to 1.607/1.549 Å (dv-2), respectively (Tables 1~2). This decreasing trend of bond lengths can be also due to the easier edge deformation. Additionally, for all the defective BNNR systems, the B-N bonds at the 5-8-5 ring fusions in divacancy defect are shorter than the corresponding those in the perfect BNNRs, similar to the case of the BNNRs with Stone-Wales (SW) defect reported by Chen et al [20].

3.2. Electronic and Magnetic Properties of zBNNRs and aBNNRs with the Divacancy Defect at the Center. Initially, we take 8-zBNNR and 11-aBNNR as typical examples to explore the effect of forming divacancy defects in the center on the electronic and magnetic properties of BNNRs with the zigzag and armchair edges, respectively. For the simplicity, the corresponding BNNR nanostructures with different defective orientations (dv-1 and dv-2) are denoted as 8-zBNNR-1(c), 8-zBNNR-2(c), as well as 11-aBNNR-1(c), 11-aBNNR-2(c), respectively, where the Arabic numbers “1” and “2” represent the defects dv-1 and dv-2, respectively, and the “c” in parenthesis means the 6

defect locating at the center site (Figure 2 and Table 1). Both spin-polarized and spin-unpolarized DFT computations have been performed to confirm the ground states of these BNNR nanostructures. For the purpose of comparison, the corresponding perfect 8-zBNNR and 11-aBNNR are also considered (Figures 2a and 2d). The computed results reveal that the perfect 8-zBNNR and 11-aBNNR can exhibit the nonmagnetic (NM) semiconductor with the wide band gaps of 4.221eV and 4.508 eV, respectively, which is in good agreement with the earlier reports [31]. Compared with the perfect ones, the similar NM semiconducting characteristic can be still observed in 8-zBNNR and 11-aBNNR with the divacancy defects (dv-1 and dv-2) in the center in view of the 5-8-5 reconstruction effectively eliminating the dangling bonds resulted from removing the B-N pair, yet the formation of divacancies can significantly impact the band structures of BNNRs, where their wide band gaps are decreased to the range of 3.191~3.401 eV (Table 1 and Figure2). Specifically, the band gap of 8-zBNNR is reduced from the original 4.211 eV to 3.191 eV in 8-zBNNR-1(c) and 3.401 eV in 8-zBNNR-2(c), whereas that of 11-aBNNR from the initial 4.508 eV to 3.338 eV in 11-aBNNR-1(c) and 3.295 eV in 11-aBNNR-2(c), respectively. It is worth mentioning that forming divacancy defect to reduce the band gaps of 8-zBNNR and 11-aBNNR (by 1.020/0.810 eV and 1.170/1.213 eV) can be even more evidently than the SW defect previously reported by Chen et al [20]. Moreover, it can be found that the defect orientation brings somewhat different effects on the band gaps of defective zBNNRs and aBNNRs, where the dv-1 defect can be slightly more evident than dv-2 defect for decreasing the band bap in 8-zBNNR, while the opposite trend can be observed in 11-aBNNR, as shown in Table 1. To understand the reason on the decrease of wide band gap of zigzag and armchair BNNRs with divacancy defect, we have plotted the total density of states (TDOS) and local density of states (LDOS) for 8-zBNNRs and 11-aBNNRs with the dv-1/dv-2 defect (Figure 2), as well as the electron density isosurfaces of their corresponding top valence bands (TVBs) and bottom conduction bands (BCBs), as illustrated in Figure 3. Different from the case of perfect systems (Figures 2a and 2d), the computed DOS results revealed that it’s mainly the N atoms in the newly formed N-N bonds at the 7

divacancy defect area that contribute to the new top valence bands (TVBs) of these defective BNNRs, while their new bottom conduction bands (BCBs) originate mostly from the B atoms in the newly obtained B-B bonds at the defect area (Figure 2). This situation can be further reflected well by their respective pictures of electron density isosurfaces, where independent of the ribbon chirality, the electron cloudy mostly distribute at the area of 5-8-5 defect for the defective BNNRs systems, evidently distinct from the corresponding perfect case (Figures 3b1, 3b2, 3c1, 3c2, 3e1, 3e2, 3f1 and 3f2). Obviously, similar to the case of SW-defective BNNRs [20], the formation of divacancy 5-8-5 defect can decrease the wide band gaps of BNNRs regardless of the edge chirality and defect orientation, which can be attributed to the formation of new top valence band and bottom conduction band arising from the N and B atoms in the N-N and B-B bonds at the defect area, instead of the shifting of the intrinsic valence and conduction bands.

3.3. Electronic and Magnetic Properties of zBNNRs and aBNNRs with the Divacancy Defect at the B/N Edge and Divacancy-Inducing the Edge Reconstruction. From the discussions above, we know that regardless of the defect orientation, the formation of divacancy defects (dv-1 and dv-2) in the center can significantly affect the band structures of both zigzag and armchair BNNRs, where the wide band gaps can be reduced. Subsequently, we intend to investigate the effect of defect position on the electronic and magnetic behaviors of zigzag and armchair BNNR nanosystems with the divacancy defect by sampling 8-zBNNR and 11-aBNNR with the defect at the B/N edge as well as even divacancy-inducing the edge-reconstruction, as shown in Figures 4 and 7.

3.3.1 zBNNRs with Divacancy Defect at the B/N Edge. Initially, we investigated the electronic and magnetic properties of 8-zBNNR with the divacancy defect at the B/N edge. For the convenience, similar to the center case, 8

these BNNR configurations with different defect positions (B/N edge) and orientations (dv-1 and dv-2) are marked as 8-zBNNR-1(eB), 8-zBNNR-1(eN), 8-zBNNR-2(eB), and 8-zBNNR-2(eN), respectively, where “eB” and “eN” in parenthesis represent the formation of defects at the corresponding B and N edges (Table 2 and Figure 4). The computed results reveal that when moving the divacancy defect from the center to the B edge of ribbon, the NM semiconducting behavior can be sustained in the defective zBNNRs (Table 2, Figures 4b and 4d), yet for systems with the same defect orientation, the corresponding band gaps can be further decreased, that is, the original band gaps (3.191 and 3.401 eV) of zBNNRs with the according dv-1 and dv-2 defects in the center can be decreased to 3.050 and 3.379 eV at the B edge, respectively, where the formation of dv-1 can still decrease the band gap of zBNNR more evidently than the dv-2, as shown in Tables 1~2 and Figure 6a. Compared with the case of B-edge, when the divacancy defect dv-1 occurs at the N edge, the corresponding 8-zBNNR-1(eN) system (3.124 eV) can still exhibit the NM semiconducting characteristic with the slightly smaller band gap than the parallel the 8-zBNNR-1(c) (3.191eV), yet slightly larger than 8-zBNNR-1(eB) with dv-1 at the B edge (3.050 eV) (Tables 1~2 and Figures 2 and 4). Differently, the formation of the divacancy defect dv-2 with another orientation at the N edge can endow the according defective 8-zBNNR-2(eN) (3.424 eV) with slightly larger band gap than the two counterparts of not only 8-zBNNR-2(c) (3.401eV) with dv-2 at the center but also 8-zBNNR-2(eB) (3.379 eV) with dv-2 at the B edge (Tables 1~2 and Figures 2 and 4). Clearly, the defect position can impact the band structures of zBNNRs, and it can be also found that when introducing divacancy defect at the N-edge, the dv-1 defect can still more evidently decrease the band gap of zBNNR than the dv-2 (Figure 6a) Further, we performed the computations of DOSs for all the zBNNRs systems with the divavancy defects (dv-1 and dv-2) at the B/N edge. It is found that their NM semiconducting behaviors can be uniformly dominated by the newly formed TVB and BCB originating from the N and B atoms in the N-N and B-B bonds at the defect area, respectively (Figure 4), similar to the case in the center. Differently, the N atoms in the zigzag BN chains near the N edge have also the somewhat contribution to TVB 9

band of 8-zBNNR-1(eB) (Figure 4b). The similar case can be also observed in their electron density isosurfaces, in which the distribution of electron cloud mainly lies in the defective area (Figure 5). Clearly, in contrast to the corresponding perfect zBNNR (4.211 eV), forming the divacancy defect at the B/N edge can decrease the wide band gap in the range of 3.050~3.424 eV, and except for the case with dv-2 defect at the N edge, the existence of defect at the B/N edge can bring slightly smaller band gap in the defective zBNNRs than in the corresponding center case, indicating that the defect position has an effect on the band gap of zBNNRs. Additionally, the orientation of divacancy defect can also affect the band gap of zBNNR systems, where the formation of the dv-1 defect can more evidently decrease the band gap of zBNNRs than the corresponding dv-2 with another orientation, regardless of the defective site (Figure 6a).

3.3.2 zBNNRs with Divacancy-Inducing the Edge Reconstruction. Subsequently, we have also explored the effect of divacancy-inducing the edge reconstruction by further moving the defect toward the B/N edge, and these defective zBNNR structures are defined as 8-zBNNR-1(eB-rec), 8-zBNNR-1(eN-rec), 8-zBNNR-2(eB-rec) and 8-zBNNR-2(eN-rec) (Table 2 and Figure 7), respectively, in which the “eB-rec” and “eN-rec” in parenthesis represent the formation of the edge-reconstruction at the corresponding B and N edges. The computed results reveal that a similar variation trend of the band gap, corresponding to moving defect from the center to the B/N edge, can be also observed in the zBNNR systems with the edge-reconstruction resulted from further moving the defect towards the edge, and the NM semiconducting behavior is maintained independent of the defect position and orientation (Table 2 and Figure 7). Specifically, when the edge reconstructions related to the dv-1 and dv-2 occur at the B edge, the significant decreasing trend of the band gap can be observed in 8-zBNNR-1(eB-rec) (2.645 eV) and 8-zBNNR-2(eB-rec) (2.904 eV), by making a comparison with the correlative 8-zBNNR-1(eB) (3.050 eV) and 8-zBNNR-2(eB) 10

(3.379 eV), respectively (Table 2, Figures 4 and 7). When forming the edge-reconstruction at the N edge, the dv-1 defect can bring a decrease of band gap from 3.124 eV in 8-zBNNR-1(eN) to 2.762 eV in 8-zBNNR-1(eN-rec), while the dv-2 with another orientation can cause a opposite trend to slightly increase the band gap from 3.424 eV in 8-zBNNR-2(eN) to 3.516 eV in 8-zBNNR-2(eN-rec) (Table 2, Figures 4 and 7). Moreover, it is also revealed that in these zBNNR systems with edge-reconstruction, forming the dv-1 defect is more evidently than the dv-2 defect in reducing the band gap of zBNNR (Table 2 and Figure 6a). The computed DOSs results show that for both the 8-zBNNRs systems with the reconstruction at the B edge, namely, 8-zBNNR-1(eB-rec) and 8-zBNNR-2(eB-rec), their BCBs and TVBs can share a similar DOS origination (Figures 7b and 7d), that is, the BCB originates manly from the B atoms in the B-B bonds at the defective area, and TVB mainly comes from the N atoms in BN chains near the N edge. However, compared with 8-zBNNR-2(eB-rec) without the formation of N-N bond, the N atoms in the N-N bonds have also certain contribution to the TVB of 8-zBNNR-1(eB-rec). All of these can be also presented clearly in their corresponding electron density isosurfaces (Figures 8a1, 8a2, 8c1, 8c2). Comparatively, for the two parallel systems with

reconstruction

at

the

N

edge,

namely,

8-zBNNR-1(eN-rec)

and

8-zBNNR-2(eN-rec), their TVBs can share a similar DOS origination mainly arising from the N atoms in the N-N bonds (Figures 7c, 8b2 and Figures 7e, 8d2), while the BCBs mostly originate from the B atoms in the B-B bonds for the former and the edge B atoms for latter without the formation of B-B bond, respectively (Figures 7c, 8b1 and Figures 7e, 8d1). Obviously, in contrast to the case of the defect at the center/edge, introducing the edge reconstruction can more evidently impact the band structure of pristine zBNNR, where the wide band gap can be further decreased in the range of 2.645~2.904 eV, and the dv-1 defect was also superior to the parallel dv-2 with another orientation (Figure 6a).

11

3.3.3 aBNNRs with the Divacancy Defect at the B/N Edge and Divacancy-Inducing the Edge Reconstruction. Besides the defective zBNNR systems, we also took 11-aBNNR as an example to explore the electronic and magnetic properties of the armchair BNNR systems with the divacancy defect at the edge as well as the corresponding edge-reconstruction. Similarly, these defective aBNNR structures are defined as 11-aBNNR-1(e), 11-aBNNR-2(e), 11-aBNNR-1(e-rec) and 11-aBNNR-2(e-rec) (Table 2 and Figure 9), respectively, where “e” and “e-rec” in parenthesis represent the defect at the edge and the related edge-reconstruction, respectively. When the divacancy defect resides at the edge of 11-aBNNR, the original band gap (4.508 eV) can be reduced to 3.240 eV for 11-aBNNR-1(e) and 3.115 eV for 11-aBNNR-2(e), respectively, slightly smaller than the corresponding 3.338 eV for 11-aBNNR-1(c) and 3.295 eV for 11-aBNNR-2(c). Independent of the defect orientation, both of the studied 11-aBNNR systems with defects (dv-1 and dv-2) at the edge can display NM semiconducting behavior (Tables 1~2, Figures 9b and 9c). Further, the similar NM semiconducting behavior can be also observed in the parallel 11-aBNNR systems with the related edge-reconstruction, yet the occurrence of edge-reconstruction can cause the larger band gaps (4.499 eV for dv-1 and 3.770 eV for dv-2) than the defect at the center and edge, but still smaller than that of pristine 11-aBNNR (4.508 eV) (Tables 1~2, Figures 9d and 9e). Moreover, we can find that similar to the corresponding case in the center, the formation of dv-2 can more evidently decrease the band gap than the parallel dv-1 for these studied defective aBNNR systems with not only the defect at the edge but also the correlative edge-reconstruction (Figure 6b). From the analysis of DOSs, for 11-aBNNR-1(e), 11-aBNNR-2(e) and 11-aBNNR-2(e-rec) systems, the originations of their TVBs are mainly from the N atoms in the N-N bonds (Figures 9b, 9c, 9e), while the BCBs mostly originate from the B atoms in the B-B bonds for both 11-aBNNR-1(e) and 11-aBNNR-2(e) systems with the dv-1/dv-2 defect at the edge, and the B atoms in defective area for 12

11-aBNNR-2(e-rec) with the edge reconstruction of dv-2, respectively. All of these cases can be also reflected in their corresponding pictures of the electron density isosurfaces, in which the electron density distribution of their TVBs and BCBs mainly localized at the divacancy defect area (Figures 10a1, 10b1, 10d1, 10a2, 10b2 and 10d2). Therefore, for all these three systems, their reduced band gap can be mainly attributed to the new TVBs and BCBs resulted from the existence of defect. Differentially, for the remaining 11-aBNNR-1(e-rec) system with the edge reconstruction of dv-1, its TVB and BCB come from all the N atoms and all the B atoms, respectively (Figures 9d, 10c1 and 10c2), which is consistent with the case of the corresponding geometrical structure, that is, the ribbon edge involving the divacancy defect of 11-aBNNR-1(e-rec) can possess a mixed form of armchair shape and zigzag shape (at the defective area), and thus this edge can be considered as a perfect one in spite of omitting B/N atoms (Figure 9d). Obviously, the position and orientation of the divacancy defect can have an important effect on the band structures of aBNNRs: compared with the cases for the center and edge-reconstruction, the formation of the defect at the edge can reduce the band gap most evidently, and the dv-2 defect is superior to the parallel dv-1.

Conclusions The geometries, electronic and magnetic properties of zigzag and armchair BNNRs with the divacancy defect of 5-8-5 ring fusions have been investigated on the basis of the detailed first-principles DFT computations, where the effects of defect orientation and position are focused. It is revealed that regardless of the edge chirality, the NM semiconducting behavior is observed for all the defective BNNRs systems, and the formation of divacancy defect can evidently impact the band structures of both zigzag and armchair BNNRs, where the defect orientation and position can play an important role. Specifically, forming the corresponding divacancy defects of dv-1/dv-2 in the center can decrease the wide band gaps of 8-zBNNR and 11-aBNNR by 1.020/0.810 and 1.170/1.213 eV, respectively, which is even more evident than the previously 13

reported Stone-Wales (SW) defect. Such an effect can be further enhanced by moving the divacancy defect to the zigzag/armchair edges of BNNRs, even the resulting edge-reconstruction. In zBNNRs systems, the formation of edge-reconstruction can more significantly decrease the band gap than the divacancy at the ribbon edge, where the defect orientation of dv-1 can be superior to dv-2, as well as introducing the divacancy at the B edge superior to the N edge in the same defect orientation. Different from the zBNNRs, the band gap of aBNNR can be reduced most evidently by forming the divacancy at the edge, where the orientation of dv-2 is superior to the dv-1. Obviously, introducing the divacancy defect can be an effective strategy to modulate the band structures of BNNRs with not only the zigzag but also the armchair edges, and these interesting results are highly anticipated to be advantageous for facilitating the application of BN-based nanomaterials in the nanodevices.

Acknowledgements. This work was supported in China by National Basic Research Program of China (973 Program) (2012CB932800), the Ministry of Education of China (20110061120024 and 20130061110020), and NSFC (21103065, 21373099 and 21173097). We acknowledge the High Performance Computing Center (HPCC) of Jilin University for supercomputer time.

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17

Table 1 The electronic and magnetic properties of the pristine BNNRs and the corresponding systems with the divacancy in the center as well as the bond lengths (newly formed B-B and N-N bonds) in the defective area. Note that the “NM” represents the nonmagnetic state.





System

 Ground State

 Electronic Properties

 Band Gap

 Bond Lengths (Å)

(eV)

B-B

N-N

4.211

-

-

3.191

1.853

1.639

8-zBNNR-2(c)

3.401

1.842

1.619

11-aBNNR

4.508

-

-

3.338

1.828

1.593

3.295

1.826

1.607

8-zBNNR 8-zBNNR-1(c)

11-aBNNR-1(c)

NM

Semiconductor

NM

Semiconductor

11-aBNNR-2(c)

Table 2 The electronic and magnetic properties of divacancy BNNRs with dv-1 or dv-2 defect at the edge as well as the corresponding edge-reconstruction, and the bond lengths (Å) of newly formed B-B and N-N bonds in the defective area. Note that the “NM” represents the nonmagnetic state.

 System

 Ground State



Electronic Properties

 Band Gap

 Bond Lengths (Å)

(eV)

B-B

N-N

3.050

1.849

1.634

3.124

1.845

1.621

2.645

1.799

1.600

8-zBNNR-1(eN-rec)

2.762

1.831

1.487

8-zBNNR-2(eB)

3.379

1.793

1.508

3.424

1.753

1.528

2.904

1.798

-

8-zBNNR-1(eB) 8-zBNNR-1(eN) 8-zBNNR-1(eB-rec)

8-zBNNR-2(eN) 8-zBNNR-2(eB-rec)

NM

NM

Semiconductor

Semiconductor

8-zBNNR-2(eN-rec)

3.516

-

1.459

11-aBNNR-1(e)

3.240

1.760

1.499

4.499

-

 -

3.115

1.607

1.549

3.770

-

1.591

11-aBNNR-1(e-rec) 11-aBNNR-2(e) 11-aBNNR-2(e-rec)

NM

Semiconductor

NM

Semiconductor

18

Captions Figure 1. Top view of the geometric structures of H-terminated zigzag (a) and armchair (d) BNNRs as well as their corresponding structures with dv-1 (b, e) and dv-2 (c, f) defects in the center, respectively. The pink, blue, and white colors denote the B, N, and H atoms, respectively. Figure 2. Fully relaxed geometries, band structures, and according DOSs of zigzag and armchair BNNRs: perfect (a, d), with dv-1 defect (b, e) and dv-2 defect (c, f), respectively. The Fermi-level is set as zero and indicated by the green dash line. Figure 3. Electron density isosurfaces of the top valence band (v) and the bottom conduction band (c) for the perfect zBNNRs/aBNNRs and corresponding systems with the defect in the center. Figure 4. Fully relaxed geometries, band structures, and according DOSs of perfect zBNNR (a) and 8-zBNNR with the defect at the B/N edge: dv-1 (b, c) and dv-2 (d, e), respectively. The Fermi-level is set as zero and indicated by the green dash line. Figure 5. Electron density isosurfaces of the top valence band (v) and the bottom conduction band (c) of the zBNNRs systems with the defect at the edge. Figure 6. Variation of the band gap of divacancy (dv-1 ( ) and dv-2 ( )) BNNRs with the change of defect site: (a) 8-zBNNR and (b) 11-aBNNR, respectively. The blue and red colors present the formation of defect related to the N and B edges, respectively. Figure 7. Fully relaxed geometries, band structures, and according DOSs of perfect zBNNR (a) and divacancy 8-zBNNR with the edge-reconstruction at the B/N edge: dv-1 (b, c) and dv-2 (d, e), respectively. The Fermi-level is set as zero and indicated by the green dash line. Figure 8. Electron density isosurfaces of the top valence band (v) and the bottom conduction band (c) of the zBNNRs systems with the defective edge-reconstruction. Figure 9. Fully relaxed geometries, band structures, and according DOSs of perfect aBNNR (a) and 11-aBNNR with divacancy defects (dv-1, dv-2): at the edge (b, c) and the corresponding edge-reconstruction (d, e), respectively. The Fermi-level is set as zero and indicated by the green dash line. 19

Figure 10. Electron density isosurfaces of the top valence band (v) and the bottom conduction band (c) of the aBNNRs systems with the defect at the edge and the corresponding defective edge-reconstruction.

Highlights (1) All the BNNR systems with the 5-8-5 defect are the nonmagnetic semiconductors. (2) 5-8-5 defect more effectively narrows the wide band gap than the reported SW defect. (3) The defect orientation and position plays a crucial role in decreasing the band gap. (4) The reduced band gap is mainly attributed to the new states from the 5-8-5 defect.

20

Graphical Abstract (for review)

Graphical Abstracts

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10