Investigations of Vacancy Structures Related to Their Growth in h-BN Sheet
© The Author(s). 2017
Received: 28 March 2017
Accepted: 11 June 2017
Published: 6 July 2017
The atomic, electronic, and magnetic properties of vacancy structures with triangular shape related to their growth in single hexagonal boron nitride (h-BN) sheet are investigated using density functional theory calculations. We find that the optimized structures of triangular vacancies depend on the vacancy sizes with N-terminated zigzag edge. Then, vacancy structures obtained during the vacancy evolution in h-BN sheet are considered by removing a boron-nitrogen pair (BN pair) from edges of triangular vacancies. The magnetic properties of those vacancy structures are investigated by local density of states and spin densities. It is found that the stability of the optimized structures with a BN missing pair depends on the BN-pair missing position: the most stable structure is a BN-pair missing structure at the edge face region with the smallest magnetic moment.
Hexagonal boron nitride (h-BN) sheet is a single-layered material similar to graphene, consisting of equal numbers of boron and nitrogen atoms and it has attractive physical properties in relation to the application of nanodevices. During its synthesis, single-layer h-BN sheet has various defects such as vacancies and grain boundaries [1, 2]. These defects can change atomic and electronic structure of single-layer h-BN sheet and thus affect performance of h-BN-based devices.
Because h-BN sheet consists of two types of atoms, in contrast to graphene sheet, the edge structures of its clusters, nanoribbons, or nanoholes divide into two types: N-terminated and B-terminated. The most stable structure of the edge of cluster has N-terminated edge with zigzag structure [3, 4]. In previous theoretical studies, the atomic and electronic structures of vacancy structures in single-layer h-BN sheet depend on the type of termination atoms and their vacancy size [3–11]. That is, the calculated stability of triangle vacancy structures and the magnetic properties were found to depend on the type of terminated atoms and vacancy sizes of triangle vacancy due to lone electrons at edge atoms. The triangular vacancy structures were found in experiments for using a free-standing h-BN sheet [12–15]. Electron beam irradiation results in increasing size of vacancy structures that maintain triangular shape [12, 13] regardless of the vacancy size.
Recently, we reported the study for growth of triangular vacancy of single-layer h-BN sheet . It was observed in the experiment that atoms in h-BN sheet are ejected in the form of the bundles, not each atom, at the edge of vacancy structures. Furthermore, we briefly mentioned theoretical results to explain the growth of vacancy in h-BN sheet with triangular shape.
In this paper, we address the detailed study of the atomic structures of triangular vacancy of single-layer h-BN sheet. The locally stable structures of triangular vacancies are found to depend on the vacancy sizes with N-terminated zigzag edge. Then, by increasing the vacancy size, we investigate the stability of the optimized structures with a BN missing pair and their magnetic properties.
We have performed the density functional theory calculations using the Vienna ab initio simulation package (VASP) [16, 17]. The plane-wave basis set with the energy cutoff of 400 eV is employed to describe electronic wave functions. The ions are represented by projector-augmented wave potentials [18, 19] and generalized gradient approximation is employed to describe the exchange-correlation functional [20, 21]. To take the weak van der Waals (vdW) interactions, we adopt Grimme’s DFT-D2 vdW correction  based on a semi-empirical GGA-type theory.
The atomic positions of all structures are relaxed with residual forces smaller than 0.01 eV/Å. For the Brillouin-zone integration, we use only gamma point in the Monkhorst-Pack special k-points scheme. The lattice constant of our model is calculated to be 2.56 Å, which is in agreement with experimental value . To study the difference in the reconstructed structures after BN-pair missing, we consider (9 × 9) and (15 × 15) supercell in our calculations.
Results and Discussion
Triangular Vacancy in h-BN Sheet
First, we have considered several vacancy sizes of single h-BN sheet to study the size effect of vacancy structures. Because N-terminated vacancy structure of h-BN sheet is more stable structure than B-terminated one [3, 4], we mainly focus on N-terminated triangular vacancy structures. To control vacancy sizes of h-BN sheet, we increase the number of ejected atoms in h-BN sheet maintaining the triangular shape. The B-terminated vacancy structures after relaxation result in small distortion in their vertex region with weakly binding between B atoms (not shown here) while the N-terminated structures shows a distinct change at the vertices of their triangular vacancy. Among different vacancy sizes of N-terminated triangular shape, we find two types of optimized (i.e., locally stable) structures. One is a symmetric structure (denoted as N-symm) in which no noticeable change of structure at vertex of triangular vacancy is found when compared with the pristine h-BN sheet, whereas the other is a distortion structure (denoted as NN-bond) that shows N-N bonds at all vertices of triangular hole vacancy in h-BN sheet.
In the cases of B monovacancy (V1B) in h-BN sheet, the optimized structure shows only one configuration that is the N-symm structure. Due to strong repulsive force between N atoms located at the vertex of triangular vacancy, the distance between N atoms increases (2.66 Å) compared to that of pristine h-BN sheet (2.48 Å) and B-N bond lengths at the edge of the triangular vacancy decrease.
The distances d0 (Å) between N atoms (N-terminated vacancy) or B atoms (B-terminated vacancy) at vertices of vacancy structures, calculated total magnetic moments M (μ B ), and the relative energies Er (eV) for triangular vacancy configurations of h-BN sheet
M (μ B )
M (μ B )
The calculated total magnetic moments of vacancy structures vary depending on the vacancy size, terminated atoms, and optimized structures (see Table 1). In the N-symm structures, the value of the magnetic moment in units of μ B is equal to the number of nitrogen atoms located at the edge of triangular vacancy structures because these N atoms have dangling bonds after missing of atoms and breaking of B-N bonds in the h-BN sheet. However, total magnetic moments of N-N bond structures with various vacancy sizes are calculated to be different from those of N-symm structures due to formation of the N-N bonds (homopolar sigma bond) at vertices of triangular vacancy structures. The total magnetic moments for the V3B+1N, V6B+3N, and V10B+6N structures with N-N bonds at vertex of vacancy are 0, 3, and 6 μ B, respectively. Figure 1b, d shows the difference in spin densities for the V6B+3N structures with N-symm (M = 9 μ B ) and N-N bond (M = 3μ B ) structures, respectively.
BN Pair Missing at the Edge Region of Vacancy Hole
Next, we have investigated the BN-pair missing situation in N-terminated vacancy structures in detail because the size of vacancy hole structures was observed to be expanded through missing of B and N atoms at the edge of triangular vacancy structures in the experiment . It was also reported that when the vacancies grow maintaining triangular shape in h-BN sheet, B and N atoms are ejected preferentially with pairs or bundles from the edge face of vacancy structures .
After one BN-pair missing at the edge of triangular vacancy structure, the optimized structure shows reconstructed BN hexagonal open ring near the missing position in which the B-N bond lengths at the distorted BN ring are slightly shorter; this means that the interactions between B and N atoms become stronger and change the arrangement of the electron charge distribution in the B-N bonds. The corner-1 missing structure (missing numbering 1) is almost unchanged except the region of distorted BN open ring as shown in the Fig. 2b.
The relative energies Er (eV) and total magnetic moments M (μ B ) of optimized configurations with a BN-pair missing at specific positions
M (μ B )
We have investigated the structural and electronic properties of the triangular vacancy structures of h-BN sheet using first-principles calculations. The optimized triangular vacancy structures were found to depend on their vacancy size. The most stable configuration of large vacancy structures has the N-N bond at each vertex of triangular vacancy, which determines its magnetic moments. When the missing of a BN pair occurs at the edge of triangular vacancy structure with a large hole size in the h-BN sheet, as observed in the experiment, the most stable structure is found to be a face missing structure with formation of N-N bonds. The magnetic moments and LDOS of the optimized structures depend on the missing positions of BN-pair at the edge of triangular vacancy.
This research was supported by Nano•Material Technology Development Program (2012M3A7B4049888) through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (MSIP), and Priority Research Center Program (2010-0020207) through NRF funded by the Ministry of Education (MOE).
JR and JP completed the DFT calculations. JR and SH contributed to writing the manuscript. All the authors read and approved the final manuscript.
The authors declare that they have no competing interests.
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