Computational study on the impact of Nb doping on electronic structure, magnetic and optical properties of hexagonal bilayer BN

We investigate the impact of Niobium (Nb) doping on the electronic structure, and magnetic and optical properties of the bilayer hexagonal boron nitride (BL hBN) using spin-polarized density functional theory (DFT). The calculated values of formation energy reveal the structural stability of Nb-doped BL hBN. The structural parameter analysis indicates the bond length and lattices constant of BL hBN increase due to Nb doping. In addition, it is found that the energy band gap of BL hBN is reduced from 5.1 eV to 3.9 eV due to 5.5% of Nb doping. Moreover, the obtained magnetic moment of 2 μ B and 4 μ B for Nb concentrations of 5.55% and 11.11% respectively, indicate the turning of the paramagnetic behavior of pure BL hBN to ferromagnetic. Besides, we have also found that the first and second nearest neighboring (NN) magnetic interaction between two dopants (Nb atoms) is ferromagnetic. Whereas, the third nearest neighbor interaction is antiferromagnetic. More interestingly, using mean field theory together with spin-polarized DFT ferromagnetic transition temperature (T c ) of 367 K is obtained for 11.11% of Nb-doped BL hBN. Furthermore, a significant enhancement of the absorption coefficient due to Nb doping in both the visible and mid-to-far-infrared regions was observed. Based on those results, we suggest that Nb-doped BL hBN is a good candidate material for nanoelectronics, spintronics, and optoelectronics applications.


Introduction
Graphene is one of the thinnest and hardest two-dimensional (2D) materials to be exploited from its bulk form or graphite [1]. Over the last few decades, significant progress in graphene-based materials has resulted in the emergence of a new class of functional heterostructure 2D materials such as transition metal dichalcogenides (TMDs) with chemical formula MX 2 , where M stands for transition metals and X stands for chalcogenides, layered boron nitride (BN) [2], and transition metal oxides [3]. Among those, BN becomes interesting candidate material due to its promising material properties for optoelectronic [4] and spintronics [5]. Especially, low dimensional structures of BN such as nanotubes have attracted much attention due to their unique optical and electronic properties which depend on tube diameter and chirality [6].
BN compounds can exist in various crystal structures such as sphalerite, wurtzite, and hexagonal(h) structures [7]. Particularly, hexagonal BN has received a great deal of interest from researchers due to its structural similarity with graphene [8]. However, unlike zero-band gap metallic graphene [9] BN is an insulator with a wide band gap. It has been reported that BN materials are an ideal substrate for graphene and a key building block in the van der Waals heterostructure [10]. One of the intriguing aspects of layered BN material is the magnitude and nature of the band gap vary based on the number of layers. Thus, the direct-gap semiconductor with a band-gap around 6eV in monolayer (ML) [10] and 4.56 eV in bilayer (BL) limit [11]. Moreover, the band gaps in the BL hBN depend on the nature of the layers stacked together, the interlayer distance between them, and strain [12]. Experimental observation has confirmed the presence of five possible stacking sequences in BL hBN compounds, namely: AA, AA', AB, AB 1 and AB 2 [13]. Among those configurations, AA and AA' stacking is the more common and stable forms of BL hBN stacking sequences [14]. More recently, it has been reported that the most stable form of BL BN stacking is AA stacking in which boron is on the top of nitrogen and nitrogen on the top of boron [11,15,16].
Commonly, in their pure state ML and BL hBN exhibit nonmagnetic and insulator features, but flexibility in controlling their band gap by application of external electric field, strain, doping, and creating defects make those materials promising for spintronics, nano-electronics, and optoelectronics applications [17][18][19]. There have been recent studies that reveal the possibility of introducing ferromagnetism in ML hBN by doping magnetic elements like; Covalent(Co) and Nickel(Ni) [20], Titanium (Ti) and Iron (Fe) [21], Vanadium(V) [22]. More recently, using first principles DFT Chettri et al [11] studied the electronic and optical properties of bilayer AA' stacked hBN with B and N vacancy defects. They have reported that B and N vacancies have a significant impact on the optical and magnetic properties of pristine BL hBN. Furthermore, Singh R. S has shown that oxygen impurity has a significant effect on the electronic properties of carbon and boron nitride nanotubes [23].
A recent experimental study has shown that among various transition metals, Nb doping plays a significant role in affecting the physical and chemical properties of graphene-like 2D material MoS 2 [24]. Based on those literature surveys, we found that there have been a few studies done on the electronic structure, magnetic and optical properties of hBN, and its low dimensional structure. However, the fundamental problems such as how the magnetic impurities in doped in hBN interact with each other and stabilize their magnetic ground state, the ferromagnetic transition temperature (T c ) of doped BL hBN material, and the optical properties of a transition metal like Nb-doped BL hBN have not yet studied.
In this paper, we have studied the effect of Nb substitution doping on the electrical structure, magnetic, and optical properties of BL hBN using spin-polarized DFT. Our results indicate that Nb doping results in significant improvement of electronic, magnetic, and optical properties of pure BL hBN. Moreover, for the first time, we have found T c of 367 K for 11.11% of Nb-doped BL hBN. This study opens a significant step forward to enhance the application of Nb-doped BL hBN for nanoelectronics, spintronics, and optoelectronics.

Computational details
First-principles calculations were performed based on spin-polarized DFT using the Quantum Espresso code [25]. The generalized gradient approximation of the Perdew-Burke-Ernzerh of(PBE-GGA) was used for the electronic exchange-correlation potential [26]. The plane-wave basis set with a cutoff energy of 60 Ry was used after performing the convergence test. Integrations over the Brillouin zone (BZ) were sampled based on a Monkhorst-Pack2D grid [27]. The BL hBN heterostructures were created by placing the single layer of BN above the other layer in the form of (AA' stacking).' Grimmes DFT-D2' dispersion correction was applied to account for the long-range Van-der-Waals interactions between different layers [28]. The equilibrium interlayer distance was obtained by calculating total ground state energy for different values of interlayer distances starting from 2.00Å in steeps of 0.1 for both AA' and AA stacking as shown in figure 1(b). A 3 × 3 × 1 supercell with AA' stacking which contains a total of 32 atoms (16 B and 16 N atoms) as shown in figure 2(c) was considered to investigate Nb doping effects on structural, electronic, magnetic, and optical properties of pristine BL hBN. The effect of doping was considered by incorporating the doping concentration amount varying from 5.55% (one atom of the dopant in 18 host atoms) to 11.55% (two atoms of dopant in 18 host atoms). The optical absorption coefficients were computed for both pure and Nb-doped BL hBN heterostructures using post-processing code 'epsilon.x'.  For AA and AA', the computed equilibrium inter-layer distances are 3.45 and 3.15 Å, respectively. These values are reasonably closer to the recently reported experimental equilibrium inter-layer distances, which are 3.6 and 3.4 Å for AA' and AA stacking, respectively [29]. The calculated ground state energy in table 1 indicates that AA' stacking with an interlayer distance of 3.15Å is more stable than AA. For the detail see table (1) and figure 1(c). Thus our results are consistence with recent DFT calculations and experimental observation [11,15,16]. Based on this information, AA' stacking with an inter-layer spacing of 3.15Å is used for the rest of the calculations.

Defect formation energy and structural stability of Nb-doped BL hBN
Before investigating the structural, electrical, magnetic, and optical properties of doped BL hBN, it is crucial to verify the relative stability of the dopant to form with the host BL hBN. To evaluate the relative stability of Nb doping in the BL hBN, the formation energies were obtained from the relation [30], where E Tot (BN) is the total energy of pure BL hBN supercell, E Tot (Nb, BN) is the total energy of Nb-doped supercell, μ B is the chemical potential of boron, μ N is the chemical potential of nitrogen, and μ Nb is the chemical potential of niobium atom(s), whereas n i is a number of Nb atom(s) substituted in boron or nitrogen sites. Equation (1) was applied to two samples to determine the stable configuration (doping site). In the first sample As shown in table 2, the formation energy (E f ) for four of the configurations of sample 2 is larger than for sample 1. The larger formation energy implies lesser stability of the system. In other words, the positive values of formation energy in table 2 of Sample 2 indicate that the energy should be given to form Nb BL hBN material. Therefore, doping Nb at the B site is energetically preferable than at the N sites. In agreement with our results KoK¨TEN, H and co-worker [31] have reported that doping silicon (Si) in B sites are energetically more favorable than N sites of monolayer hBN. Khan et al [32] also reported from DFT formation energy calculations doping Sn at B sites of hBN requires less energy than N sites.
As can be seen from table 2, the formation energy of a single Nb atom doped at the B site and two Nb atoms doped at the 1st NN of B h-BN under N-rich growth conditions are negative. This implies that Nb atom(s) can exist stably in BL hBN super cell preferentially replacing B atom(s). Moreover, as the Nb-Nb separation distance increases, the formation energy increases, which implies that the relative stability of the dopant to exist with host BL hBN decreases. Furthermore, our result reveals that formation energy under N-rich BL hBN growth conditions is lower energy than in B-rich growth conditions. Therefore, doping Nb atoms on BL hBN under N-rich growth conditions is more stable than under B-rich growth conditions. This result is consistent with our previous DFT study on Si-doped monolayer BN [30].

The effect of Nb doping on structural properties of BL hBN
As shown in table 3, after structural optimization, the lattice constant and bond length of pure BL hBN are 2.52 Å and 1.46 Å respectively. When a single Nb atom is substituted at the B site, the lattice constant and bond length increase to 2.72 Å and 1.95 Å. In a contest to this, the bond angle is reduced from 120 0 to 90 0 as a result of the doped Nb atom pushing upward the original crystal to an out-plane direction as can be seen in figure 2(c). The obtained lattice constant agrees with the recently reported experimental value of the lattice constant of hBN 2.504 Å [33]. On the other hand, the enlargement of the lattice constant and bond length of doped BL hBN is associated with the atomic size of the substituted Nb atom being much larger than the atomic size of the B atom.   As shown in figure 3(b) when a single Nb atom is substituted B sites (5.5% of Nb-doping) the extra impurity states appear in the vicinity of the Fermi level. Moreover, some of the spin-up states are crossing the Fermi levels. Thus, spin-up states are more likely metallic. However, there are no spin-down states which cross the Fermi level. This indicates that the spin-down states are more likely to behave as wide-bandgap semiconductors. Thus, overall TDOS analysis indicates that the doped system is half metallic. Moreover, figure 3(b) clearly shows in the presence of Nb dopants, the symmetry of spin-up and spin-down DOS is broken which confirms the ferromagnetic behavior of doped BL hBN.
As Nb concentration increases from 5.5% to 11.11%, more peaks appear in impurity states as can be seen in figure 3(c). These impurity states and Fermi levels are pushed to the CBM which reveals that in the Nb-doped BL hBN system the carriers are more likely electrons (N-type of conductivity). The isosurface plot of charge states in figures 2(b) and (d) confirm the presence of strong hybridization of the Nb atom with host BL hBN. Thus, in pure BL hBN, the charge distribution is more concentrated around the N atom. However, when the Nb dopant is substituted in the B site, the charge distribution is more concentrated around the dopant region (Nb region).
The PDOS plot in figure 4(a) shows that for pure BL hBN a majority of the contribution of electronic states in the vicinity of the Fermi level is derived from boron p-orbital electrons followed by nitrogen p-orbital. However, for the Nb-doped BL hBN as shown in figure 4(b), the dominant contribution for states near the Fermi level originated from the doped Nb d-orbital electrons followed by Nb s-orbital electrons.
Therefore, overall TDOS and PDOS analysis confirm that Nb is doped in B sites of BL hBN the band gap is reduced due to hybridization between dopant (Nb) atoms with neighboring N and P atoms. A narrowing of the band gap implies improvements in the conductivity of Nb-doped BL hBN in comparison to a pure one. In other words, Nb doping results in enhancements to the application of BL hBN materials to semiconductor technology like transistors, thereby reducing the band gap to moderate and tunable.  substituted B site of BL hBN, the band gap decreased to 3.9 eV. Besides, as shown in figure 5(b) there are additional impurity states that appear above the Fermi levels for both spin-up (red color) and spin-down (blue color). Those results also well agree with our TDOS analysis in section 3.1 that the prescience of N-type of conductivity in Nb-doped BL hBN. On the other hand, the reduction in the energy band gap indicates the filling of higher energy levels of pure states with d-orbitals of doped Nb atoms.
Further, the electronic band structure of pure BL hBN in figure 5(a) shows is exact overlapping in spin-up and spin-down band structure. However, in the Nb-doped BL hBN in figure 5(b), it is clear to identify spin up (red color) and spin down (blue color). In other words, as the Nb atom is doped to BL hBN the spin dereference between states is broken as discussed in TDOS of section 3.1. And hence unlike the paramagnetic behavior of pure, NB-doped BL hBN is ferromagnetic. The detailed magnetic behavior and its origin of ferromagnetism in Nb-doped BL hBN are discussed detailed in section 4.1.
4. The effect of Nb doping on magnetic properties of BL hBN 4.1. The effect of single Nb doping on magnetic properties of BL hBN As shown in table 4, the computed total magnetic moments per 3 × 3 × 1 supercell of pure BL hBN is 0μ B . And hence the pure BL hBN is paramagnetic. Whereas, the total magnetic moments are 2 μ B and 4μ B respectively for 5.55% and 11.11% of Nb-doped in B sites of BL hBN indicating the ferromagnetic behavior of the doped system. As shown in figure 3(a) the TDOS for up and down spin channels are symmetric for pure BL hBN. Thus, symmetric TDOS reveals that these materials are nonmagnetic or paramagnetic semiconductors.
As 5.5% of Nb is substituted in B sites of BL hBN, the symmetry between the spin channels is broken for detail see figure 3(b). In other words, the spin-up DOS is likely to behave as metallic since some of the spin-up states are crossing the Fermi level. However, no spin-down states are crossing the Fermi level. Hence, the spindown states are more likely to behave as semiconductors. Therefore, overall TDOS analysis confirms that Nbdoped BL hBN becomes half metallic and ferromagnetic behavior. Those half-metallic and ferromagnetic materials are highly demanding for today's spintronics technology (using the spin of electrons for electronics). Figure 3(c) shows Nb doping concentration increases from 5.5% to 11.11%, additional pecks appear, and those impurity states are merged with CBM leading to a reduction of the band gap and the total magnetic moments also improved 2 μ B to 4 μ B for the detail see table 4. Those results imply that it is possible to control the magnetic behavior of Nb-doped BL hBN materials by changing dopant concentrations instead of applying an

4.2.Distance-dependent magnetic interaction between dopants
The magnetic energy (ΔE), which is the energy difference between the two dopants in the ferromagnetic (E FM ) configuration and the antiferromagnetic (E AFM ) configuration, was calculated to examine the magnetic ground state (the most stable form of magnetic ordering ) of two dopants fixed at a certain distance.

FM AFM
Three configurations with different dopant-dopant (Nb-Nb) separations were considered. The first nearestneighbor (1stNN) configuration in which the two atoms are in the nearest neighboring position with Nb-Nb distance of 2.52 Å. The second nearest-neighbor (2nd NN) configuration in which the two Nb atoms are in the next nearest-neighboring position with Nb-Nb distance of 4.36 Å. And the third nearest-neighbor (3rd NN) configuration is in which the distance between the two doped Nb atoms is at 6.67 Å.
As indicated in table 4, ΔE is negative for 1stNN and 2nd NN Nb-Nb configurations, which reveals that the more stable ground state magnetic ordering is FM. Whereas, for the 3rd NN Nb-Nb configuration the calculated ΔE is small in magnitude and positive in sign. This implies that as the distance between the dopants increases above 2nd NN the magnetic interaction between dopants is suppressed and the magnetic interaction is turned from FM to AF. This can be explained as the distance between impurities (Nb-Nb distance ) increases the probability of overlapping of wave function between one of the Nb atoms with other Nb atoms decreases.

Ferromagnetic transition temperature in Nb-doped BL hBN
The ferromagnetic transition temperature (Tc) below which the material maintains spontaneous magnetization is the most decisive parameter to characterize magnetic materials. By mapping the Heisenberg Hamiltonian and the mean-field approximation (MFA), we calculated T C for 11.11% Nb-doped BL hBN using relations [34].
here N imp is a number of Nb atoms doped in BL hBN, and K B is the Boltzmann constant. The calculated T c for 11% Nb-doped BL hBN after correction to MFA is 367 K, as shown in table (4). Here it should be noted that the MFA always overestimates the critical temperature [35]. To overcome this, we used correction to the MFA as T c corr = (0.506)T c MFA [36]. Interestingly, the obtained T c corr of 367 K exceeds room temperature. The obtained high T c suggests the potential application of Nb-doped BL hBN in spintronic devices.

The effect of Nb Doping on Optical Properties of BL hBN
To study the optical properties of materials like absorption coefficient, it is convenient to start from the complex dielectric function which represents the linear behavior of materials subjected to electromagnetic radiation. In general, the dielectric function can be expressed in real and imaginary terms as ε(ω) = ε 1 (ω) + jε 2 (ω), where ò 1 describes polarization and ò 2 describes material absorption. In particular, the optical absorption coefficient plays a vital role in determining photocatalytic activity, as the absorption coefficient determines the penetration of the light of a particular wavelength before it is absorbed by the material [37].
Employing first principles DFT calculation together with post-processing code 'epsilon.x' [25], we have calculated the absorption coefficient for pure and Nb-doped BL hBN. As shown in figure 6 of absorption coefficient versus photon energy, there are around five high and low peaks are observed for pure BL hBN. The highest peak is observed for the photon energy of 4.7 eV. Whereas 5.55% of Nb is doped, the energy picks are observed at 0.2 and 0.4 eV (in the viable region). Moreover, in comparison to the pure sample, the peaks are larger.
As the concentration of Nb increases from 5.55% to 11.11% in the photon energy range of 1.2 eV to 4.5 eV large peaks are observed at high dopant concentrations. The large change in absorption coefficient in the visible region is associated with large changes in the electronic structures, which are due to the change in the composition of the energy bands and the doped Nb states. Thus, our results indicate that as Nb is doped the absorption of photons is enhanced. Therefore, Nb-doped BL hBN is a good candidate material for optoelectronic applications if the further experimental investigation is conducted.

Conclusion
In conclusion, We have studied the impact of Nb doping on the electronic structure, magnetic and optical properties of BL hBN using spin-polarized DFT. Formation energy calculations revealed that Nb atoms are stable to substitute B sites of BL hBN. From structural optimization, it is found that Nb doping causes the bond length and lattice parameters to increase compared to pure BL hBN. The electronic band structure calculation indicates the transformation of the band gap of pure BL hBN from 5.1 eV to 3.9 eV due to 5.5% Nb doping. Moreover, the obtained total magnetic moment of 2 μ B and 4 μ B for 5.55% and 11.11% of Nb-doped BL hBN shows the turning of the paramagnetic behavior of pure BL hBN to a ferromagnet. It is also found that the magnetic interaction between dopants (Nb atoms) changes from ferromagnet to antiferromagnet depending on the spatial separation distance between dopants. More importantly, using the mean-field approximation together with spin-polarized DFT the Curie temperature of 367K is predicted for 11.11% Nb-doped BL hBN. Furthermore, significant enhancements of absorption peaks due to Nb doping were obtained. Based on those results, we suggest that Nb-doped BL hBN is a good candidate material for nanoelectronics, spintronics, and optoelectronic applications if further experimental work is done to support those important predictions.
This work can be further extended using the DFT +U approach to take account of the correlation effect of d-orbital electrons in the Nb atom. In addition, the present work is limited in using 3 × 3 × 1 supercell due to resource limitations. However, the extension of the sample to higher supercells is required to manage low concentrations of dopants.