Be₃N₂ monolayer: A graphene-like two-dimensional material and its derivative nanoribbons

The discovery of graphene has ignited universal interest in two-dimensional nano materials. Graphene is overwhelming because it possesses extraordinary physical properties and meets the strong demands of nano electronics. However, graphene is not the single member in the family of 2D nanomaterials. Other graphene-like nanomaterials, such as silicene,¹ germanene,² metal dichalcogenides,³ borophene^4,5 and Black Phosphorus⁶ etc, also joined the 2D family. As research on graphene has increased, methods for finding materials of similar nature and structure to graphene have been created. Recently, 2D metal-nitride sheets received great attention due to their novel versatile electronic, superconducting, optical, plasmonic photocatalytic properties, as well as many potential applications, such as semiconductor devices, high-performance catalyst for energy conversion and storage, Li-ion batteries, and ultracapacitors.^7–11 The painstaking research has uncovered a large number of nitride single-layer structures with special properties, for example the BeN₂ monolayer¹² which has a direct band gap and a high carrier mobility.

In this paper, we report a first principles prediction of a new 2D inorganic material, namely, the Be₃N₂ monolayer. Using material prediction software, the lowest-energy structure can be found by providing a given stoichiometry of Be atoms and N atoms. Applying the same method, a novel binary layer of beryllium nitride with similar graphene structure is predicted. We examined various properties and structures of the Be₃N₂ monolayer in the same manner as graphene was studied. Based on the calculated band structure, Be₃N₂ was found to be a direct wide bandgap semiconductor which has its potential application in light-emitting devices such as light-emitting diodes (LEDs) and semiconductor lasers as well as RF signal processing devices.

We used the Vienna ab initio simulation package (VASP¹³) to performed the DFT computations, and used the projector-augmented plane ware (PAW¹⁴)approach to represent the ion-electron interaction. The electron exchange-correlation functional was treated using generalized gradient approximation (GGA¹⁵) in the form proposed by Perdew, Burke and Ernzerhof (PBE). The 500 eV energy cutoff was adopted and Brillouin zone was with a 4x4x2 Γ-centered Monkhorst-Pack k-points grid for geometry optimization and self-consistent calculation. The energy precision was set to 10^-6eV and atomic position was fully relaxed until the maximum force on each atom was less than 10^-4eV/Å.¹⁶ 

The band gaps was underestimated by the standard GGA, but we prefer to use the Heyd-Scuseria-Ernzerhof (HSE06^17,18) hybrid function, which was proven to be a reliable method for the calculation of calculating the band structure of Be3N2 monolayers. The band structure of Be3N2 was computed along the special lines of Γ(0, 0, 0)→M(1/2, 0, 0)→K (-1/3, 2/3, 0)→Γ(0, 0, 0) in the k-space.

To determine the stability of this Be₃N₂ monolayer, we measured its phonon spectra and molecular dynamics data. Among them, phonon dispersion¹⁹ analysis was performed using the Phonopy code interfaced with the density functional perturbation theory (DFPT) as implemented in VASP. Ab initio Molecular Dynamics²⁰ (AIMD) simulations were performed using the PAW method and the PBE function to assess all the thermal predictions of the Be₃N₂ monolayer. The vibrational and thermodynamic properties are all obtained with PBE. And in the MD simulations, the initial configuration of Be₃N₂ monolayers with 4×4 supercell (48 Be atoms and 32 N atoms) was annealed at different temperatures, each MD simulation in NVT ensemble lasted for 10 ps with a time step of 2.0 fs, and the temperature was controlled by using the Nose-Hoover method.

The lowest-energy structure of Be₃N₂ with a flat hexagonal structure predicted by CALYPSO²¹ code is shown in Fig. 1a, The Be3N2 monolayer is placed in the x-y plane with the z-direction perpendicular to the layer plane and a vacuum space of 19.8075Å in the z-direction is used to avoid the interaction between adjacent layers. The optimized Be₃N₂ flake crystallizes in the hexagonal space group P6/mmm (No.191) with a lattice constant of a = b = 5.24212 Å. There is a unique Be atom (site symmetry 3g) and An independent N atom (site symmetry 3g). Be atoms at the Wyckoff²² 3g site act as a “bridge”, forming a strong band with N atoms, each of which is a triangular coordination without any distortion characteristics. The length of the sp2-hybridized, Be-N band is 1.51327Å with an angle of 120 °as shown in Fig. 1b. Structural evolution can be seen as the process of inserting a “bridge” into the network by expanding the pore size in flat nitrogen.

We calculated the charge density of the Be₃N₂ monolayer to further understand the bond formation between the Be and N atoms (see Fig. 2). It can be seen from the figure that the electron cloud around the Be atom is relatively sparse, the electrons are all surrounded by N atoms, and the N atom is electronegative. Two electrons in the outermost 2s orbit of the Be atom are transferred to the N atom and participate in the N atom 2s and 2p orbital hybrids go in. The N-Be-N connected rings form a graphene-like benzene six-membered ring structure.²³ 

We further calculated the charge density difference and electron localization function (ELF) of the Be₃N₂ monolayer to understand its unique structure and chemical bond formation mechanism. Charge density difference is a useful tool for determining the bond. The negative position which is usually shown in blue is the electron divergence area, where the electron is lost, while the positive position is the electron convergence area which is shown in yellow, where the electron is gained. The covalent bond electrons converge toward the middle of the two atoms, and the ionic bonds converge the electrons that are biased toward one side of them. As fig. 3(a) shows, electrons converge between Be and N atoms to form a Be-N covalent bond. The blue area on both sides of the Be atom and the yellow area in the middle of the six-ring indicate that the Be atom contributes to the construction of N-Be-N six-ring frameworks. Electron localization function (ELF) can effectively describe the chemical bonding of molecules and solids in the form of a contour pot in real space with values ranging from 0 to 1. In areas surrounded by isosurfaces with high numerical values, the electrons are more strongly localized in their regions. And in areas with low ELF values, the electronic localization is weak. we plotted the the ELF map of Be₃N₂ monolayer with the iso-value of 0.5 au. shown in fig. 3(b). As a whole, the Be and N atoms are surrounded by a red region, connected into a six-ring. Moreover, the ELF value of yellow color between the adjacent Be atoms is lower than the red between Be and N atoms, Showing that the possibility of forming a covalent bond between Be and N atoms is higher than that between Be atoms. Accordingly, this electron distribution analysis suggests that Be₃N₂ monolayer is a honeycomb structure consisting of a six-ring structure consisting of N-Be-N covalent bonds.

By calculating the energy band structure of the Be₃N₂ monolayer, We studied its electrical properties. Fig. 4 shows the band structure and PDOS of Be and N. The PBE calculations give a band gap of 2.773 eV, while HSE06 brings a band gap of 3.831 eV (Fig. 4). Obviously, the Be₃N₂ sheet is a direct band gap semiconductor with the valence band maximum (VBM) and conduction band minimum (CBM) at the same point Γ. Considering the bulk structure of Be₃N₂, the beryllium nitride alpha phase has the same direct band gap in the central Brillouin zone Γ point of 4.43 eV. The α-Be₃N₂ is a cubic bcc structure like bixbyte, in which the metal ion has four tetrahedral neighbors and N has two types of distorted octahedral coordination groups.²⁴ And the phase β-Be₃N₂, converted from α-Be₃N₂ crystals to 1400 degrees Celsius, is a wide band gap semiconductor with an indirect gap of 12.50 eV.²⁵ The structure and properties of the two body structures of Be3N2 are very different from those of Be3N2 monolayer.

It can be seen from the energy band structure diagram of Be₃N₂ monolayer that the band closest to the Fermi surface is the valence band. And, the N atom contributes most to the valence band according to the density of states. Of course, the electrons on the orbit of the Be atom are also involved in the formation of the electron orbits near the Fermi surface. Based on the PDOS of Be₃N₂ nanosheet (shown in Fig. 5), the Be atoms and N atoms have the similar shape in the valence band near the Fermi surface. The electrons of the Be atom s orbital and the N atom p orbital participate in the formation of electron orbitals. In order to further understand the bonding situation between Be₃N₂ monolayer atoms, we calculated the electronic charge distribution near the Fermi energy (see Fig. 6). It can be seen that some of the electrons surround the N atom participate in the electron orbital formation of the conduction band near the Fermi surface, and the other part forms the electron orbit of the valence band near the Fermi surface. Seen from the electron cloud profile, the VB is mainly filled with the electrons of the N-atom π orbital, and the CB is mainly filled with the electrons of the σ orbit of the N atom.

In order to evaluate the thermodynamic stability, we calculated the cohesive energy $Ecoh=3xEBe+2xEN−EBe3N2/5x$⁠, with E_Be, E_N and E_Be3N2 being the total energies of a single Be atom, N atom and one unit cell of the Be₃N₂ monolayer. The Be₃N₂ monolayer has a cohesive energy²⁶ of 5.82 eV/atom. For comparison, using the same calculation method, the cohesive energies of graphene²⁷ and silicide²⁸ were 7.85, 3.98 eV/atom, respectively. Thus, while the cohesion can be significantly lower than the Be and N 3D bulk phases, this is sufficient when the material is limited to 2D, because of its stability between the graphene and silicence.

We evaluated the kinetic stability of the Be₃N₂ monolayer by calculating the phonon dispersion along the high line of symmetry in the first Brillouin zone, shown in Fig. 7. There is no apparent hypocentric frequency in the phonon spectrum of the Be₃N₂ monolayer, indicating the kinetic stability of the Be₃N₂ monolayer. The highest frequencies of Be₃N₂ sheet were 1265cm-1 (= 37.95THz) higher than the highest frequency of t-TiC sheet (810cm-1),²⁹ Cu₂Si (420cm-1)³⁰ and MoS₂ monolayers (473cm)³¹ These high frequencies in the phonon spectrum also indicate a strong Be-N interaction in the newly predicted Be₃N₂ monolayer.

The stability of the Be₃N₂ sheet can be further tested by AIMD simulations at different temperatures. Simulations were performed using relatively large 4 × 4 supercell at temperatures of 300K, 600K and 900K. The geometry at the end of the 10 ps simulation (Fig. 8) shows that the Be₃N₂ sheet can retain its original structure at 300K and collapse at very high temperatures of 600 and 900K. Its high temperature stability is not very good, but it can be stable at room temperature.

To effectively use the band gap of the Be₃N₂ monolayer, the relevant application might be achieved by changing the size of the band gap by altering the strain. From the Fig. 9, we can find in the process of changing uniaxial strain³² of Be₃N₂ monolayer, The sizes of the band gap decrease linearly with the strain within a certain range without disrupting the cell structure of Be₃N₂.

We further examined the Be₃N₂ nanoribbons³³ by dividing the Be₃N₂ monolayer into armchair and zigzag nanoribbons along the x and y directions, calculating the band along the direction of the nanoribbon repetition (shown in Fig. 10). As examples, the band structures of H-terminated Na-Armchair with Na = 3–9 and Nz-Zigzag with Nz = 3–9 are shown in Fig. 10(a) and (b), respectively. The results obtained show that the bottom of the conduction band and the top of the valance band appeared at Γ point are always separated, representing a direct semiconductor character, indicating that the properties of electron transport are similar in both directions. From Fig. 10(a) and (b) we also find the number of both conduction band and valance band increases with increasing the ribbon width, additionally, as demonstrated in Fig. 11, the size of the band gaps both decrease with the increase of the width of nanoribbon from 0.5nm to 3.5nm while the band gap of armchair one starts to increase when zigzag one converges to 3.5ev.

We performed comprehensive DFT computations to check the possibility to obtain graphene-like materials containing Be atoms and N atoms which process planar hexagonal structure. Be₃N₂ monolayer has sound thermodynamic, kinetic and thermal stabilities and presents a direct band gap semiconductor characteristics which bandgap can be effectively tuned by employing an external strain. Also, the Be₃N₂ nanoribbons are proved to have direct band gaps with various values, depending on the direction of the division and the width of nanoribbons. Those quite rich characteristics might render Be₃N₂ monolayer an outstanding 2D nanomaterial with great promise for applications in novel nanodevices.