Formation and Physical Properties of h-BN Atomic Layers : A First-Principles Density-Functional Study

Hexagonal boron nitride (h-BN) atomic layers have attracted much attention as a potential device material for future nanoelectronics, optoelectronics, and spintronics applications. This review aims to describe the recent works of the first-principles densityfunctional study on h-BN layers. We show physical properties induced by introduction of various kinds of defects in h-BN layers. We further discuss the relationship among the defect size, the strain, and the magnetic as well as the electronic properties.


Introduction
Since the discovery of a single atomic layer of graphite, that is, graphene, other atomic layers have received much attention [1][2][3][4][5][6][7][8].Hexagonal boron nitride (h-BN) atomic layers, in which alternating boron and nitrogen atoms are arranged on the honeycomb lattices, have also gained a lot of interest because of the similar structural and mechanical properties to graphene [9][10][11].On the other hand, electronic properties of h-BN layers are considerably different from those of graphene; graphene is a gapless material with metallic conduction [12], and the h-BN atomic layers possess a wide band gap [13][14][15].Such wide band gap nature of h-BN layers is expected to give rise to new physical properties as well as relevant electronic/optoelectronic applications in nanotechnology.
The purpose of this review is to provide the recent progress of the first-principles density-functional calculations that clarify various physical properties of h-BN atomic layers with lattice defects including atomic vacancies and carbon defects.In Section 2, the magnetic properties of atomic vacancies in h-BN layer are discussed.Section 3 is devoted to discussions on the electronic properties of carbon-doped h-BN layers.In Section 4, the behaviors of the magnetic properties and the energy band gaps are shown with the variation of the graphene-like defect size.Finally, Section 5 summarizes this paper together with outlook. 2 defect as a function of imposed magnetic moment.Reproduced with permission from [24]; copyright 2012, the American Institute of Physics.

Atomic Vacancy
Atomic vacancies in h-BN layers can be created by electron beam irradiation [10,[25][26][27].Triangular-shaped vacancies are observed experimentally by using high-resolution transmission electron microscopy and these vacancies in h-BN layers are arranged with various sizes and peculiar orientation [10].It is therefore surmised that the B atoms are removed more easily than the N atoms from h-BN monolayers by electron beam irradiation [10].
The introductions of the atomic vacancies into the h-BN monolayers are reported to give rise to the magnetic moment [24,47].In Figure 1(a), the schematic view of the triangular atomic vacancies in the ℎ-BN monolayer is shown, where the multivacancies   are defined with  = √ B +  N and  B and  N are the numbers of removed B and N atoms, respectively.The total magnetic moments of  N 1 ,  N 2 , and  N  3 are calculated to be 1, 0, and 3  , respectively.Unlike graphene [48], the behavior of vacancies  N  in the magnetic properties does not follow Lieb's theorem because of the structural reconstructions with the N-N bond formation [49].When the N-N bond formation is broken, the total magnetic moment increases.The total magnetic moment of the  N 2 defect increases as the N-N distance around the vacancy increases, though the ground state of  N 2 exhibits zero magnetic moment (see Figure 1(b)).

Carbon Impurity
Substitutional carbon doping to h-BN layers and BN nanotubes has been performed using the electron beam irradiation technique [32,33] and substitutionally doped C atoms in the h-BN monolayers have been observed via a transmission electron microscopy method [31].It was found that the substitution with C atoms decomposed from hydrocarbon molecules takes place mostly at B atom sites, and it was surmised that the substitutional doping proceeds by repairing the B atom vacancies with C atoms broken by the knock-on electron beam [32,34].
Recent first-principles calculations showed that the substitution of B atoms with C atoms needs less energy costs than that of N atoms under N-rich conditions.Moreover, it was shown that positive charging favors the substitution of B atom with C atom (C B ), whereas negative charging favors the substitution of N atom with C atom (C N ).In addition, it was shown that the substitution of B atom with C atoms may predominately take place even under B-rich conditions [34,35].
It was reported that the electronic transport properties of h-BN layers can transform from insulating to conductive properties when C atom is doped [32].The donor-like impurity states appear below the conduction-band minimum (CBM) when C atom is doped at B atom site, whereas the substitution of N atom with C atom gives rise to the acceptor-like impurity states above the valence-band maximum (VBM) [35,41].It was shown that ionization energies for acceptorlike as well as donor-like states can be controlled by applying strains (see Figure 2(a)) [41].The strains can often produce not only the new structural properties but also the novel electronic properties [19,50,51].Interestingly, in the case of the ℎ-BN monolayers, the exotic transport channel will behave as an active state under more than ∼1% compressive strains (Figure 2(b)).In addition, the band gaps are also tunable under strains [52][53][54].
Scanning tunneling microscopy (STM) measurements are one of the effective tools to observe the surface electronic structures at atomic level [55][56][57][58][59][60][61].The B atoms and N atoms in graphene can be clearly identified experimentally and theoretically [62][63][64][65][66].The STM image of the h-BN monolayer has a large bright triangular shape around the C defect surrounded by six bright spots above each N atom, since the C defect state consists of the triangular-shaped spatial distributions of local density of states (LDOS), and in addition to this defect state, the  states in the valence bands contribute the STM image (Figure 3(a)).On the other hand, for the C substitution of the B atom, the STM image has a small dark spot above the C defect which is surrounded by six bright spots above each B atom (Figure 3(b)) [41].The C defects in the h-BN monolayers might be identified by using STM methods.

Carbon Flake
The h-BN monolayers embedded with triangular graphene flakes can modify the electronic properties as well as the magnetic properties [34,37].The magnetic moments of the graphene-like flake embedded h-BN monolayer can be controlled depending on the number of the substituted C atoms in the h-BN monolayers (Figure 4), where  and  are the numbers of the B atoms and the N atoms replaced with the C atoms and positive and negative ( − ) values are used for the T1-C  C  and T2-C  C  structures, respectively.T1-C  C  and T2-C  C  structures give rise to | − | B magnetic moments per unit cell.By tuning the sizes of the triangle graphene flakes, the magnetic moments of T1-and T2-graphene-embedded BN sheet are controllable.The energy band gap values of h-BN monolayers are shown to be tunable [37][38][39].By replacing B and N atoms with graphene quantum dots (QD), the energy band gaps of h-BN monolayers decrease.As the size  of the graphene QD increases, it was shown that the band gaps diminish from ∼3.6 eV to ∼1.6 eV (Figure 5).Reproduced with permission from [38]; copyright 2011, the American Institute of Physics.

Concluding Remarks
We have reviewed the recent works of the first-principles density-functional study of h-BN atomic layers.The atomic vacancies can be created in the h-BN layers by electron beam irradiation techniques.The triangular-shaped atomic vacancies in h-BN layers can give rise to the magnetic moment depending on the vacancy sizes, and moreover the magnetic moment is shown to be tunable under strain.The C atom can be doped to the h-BN layers by using electron beam irradiation combined with introducing the hydrocarbon molecules, and it is deduced that C atoms are doped more easily at B atom sites than at N atom sites.The first-principles density-functional calculations have revealed that the substitution of B atoms with C atoms becomes more favorable in energy than that of N atoms under Nrich conditions.The substitutions of the B atom and the N atom with the C atom induce the donor-like state below the CBM and the acceptor-like state above the VBM, respectively.The ionization energies are controllable for the donor and the acceptor states by applying strain, and furthermore the exotic electronic state can be opened as an active conduction channel under strain.
The graphene-like flake in the h-BN layers can modify the magnetic and the electronic properties.By substituting B atoms and N atoms at the two different sublattices with C atoms, the magnetic moment of the h-BN layers can be tuned.In addition, the variation of the size of the QD can tune the energy band gaps.
By tuning not only the sizes of the atomic vacancies and the C atoms flake but also strains, new magnetic and electronic properties of the h-BN layers would emerge, which might provide the novel nanoelectronics, optoelectronics, and spintronics devices.

Figure 1 :
Figure 1: (a) Schematic view of h-BN monolayers for atomic vacancies.(b) Total energy and N-N distance near  N2 defect as a function of imposed magnetic moment.Reproduced with permission from[24]; copyright 2012, the American Institute of Physics.

Figure 2 :Figure 3 :
Figure 2: (a) Relative ionization energy (ΔIE) for acceptor and donor states in C-doped h-BN monolayers as a function of applied strain.(b) Contour plot of electron density of C-doped ℎ-BN monolayer at the Γ point of the CBM, where B atom is replaced by C atom.Reproduced with permission from[41]; copyright 2016, the American Physical Society.

Figure 4 :
Figure 4: Variation of magnetic moments of T1-C  C  and T2-C  C  with (−).Reproduced with permission from[37]; copyright 2011, the American Physical Society.

Figure 5 :
Figure5: Energy band gap value   as a function of QD diameter .Reproduced with permission from[38]; copyright 2011, the American Institute of Physics.