Optoelectronic and elastic response of fluorinated hexagonal boron nitride monolayer

The inherited insulating behavior of hexagonal boron nitride (h-BN) monolayer restricts its application in several optoelectronic devices, so finding a technique to reduce the bandgap allows it to possess the semiconducting functionality. Here, an experimentally feasible fluorinated hexagonal boron nitride (FBNF), a structurally, dynamically, and mechanically stable monolayer is reported by using density functional theory calculations. The significant geometrical transformation from planer h-BN to buckled FBNF softens the structure by retaining the mechanical isotropy and structural symmetry. Remarkably, the induced direct bandgap semiconducting behavior after fluorination enhances the optical absorbance and reflectivity, reduces energy loss, creates strong optical anisotropy, and makes FBNF monolayer a proper material in the optoelectronic and nanomechanical applications.

Unfortunately, the electronic bandgap of the h-BN is too large (natural insulator) that lacks the semiconducting functionality. Therefore, most of the h-BN materials are used as insulating materials [20] [21] and restricts its application in several optoelectronic devices. Various approaches such as doping, vacancy defects, absorption, strain, external electric field, and chemical passivation in the pristine 2D structure [22] [23][23] [24]have been implemented to settle this problem. However, applying an external electric field or strain would considerably make the device configuration complicated [25]. Meanwhile, several experimental and theoretical works show that chemical passivation is one of the best approaches to tune the * Corresponding author shambhubhandari789@gmail.com (S.B. Sharma) ORCID(s): structural, electronic, and optical properties of the compound. For instance, the first-principles calculations demonstrate that fluorination is a practical route to induce halfmetallicity in zigzag boron nitride nanoribbon [26]. Similarly, the passivation of hydrogen and fluorine on the h-BN monolayer changes the electronic and magnetic properties drastically [27]. The structural and electronic properties of graphene supported on FBNF monolayer substrate modifies the electronic properties of graphene supporting the fabrication of high-performance graphene-based nanodevices [28]. Additionally, the controlled adsorption of fluorine atoms on both sides of a pristine h-BN sheet induces flatness distortion and an out-of-plane dipole moment in a chair conformer [29]. The fluorination of electrically insulating the h-BN subsequently modifies the electronic band structure to a wide bandgap magnetic semiconductor via the introduction of defect levels. The electrophilic nature of fluorine causes changes in the charge distribution around neighboring nitrogen atoms in the h-BN, leading to room temperature weak ferromagnetism [30]. Very recently, an experimental study shows that exfoliation of the h-BN sheets from bulk material and surface treatment by fluorination makes structural improvements that lead to enhancement in electrical and optical properties [31].
Multiple theoretical and experimental investigations have been conducted to study various features of pure and passivated the h-BN monolayer, what is lacking here is a meticulous study on the structural, mechanical, and optoelectronic response of fluorinated h-BN. Intrigued by the prior findings, the first-principles calculations are performed with the density functional theory to investigate and unravel the underlined properties of fluorinated hexagonal boron nitride monolayer.

Computational Details
The density functional theory (DFT) implemented in the Spanish initiative for electronic simulations with thousands of atoms (SIESTA) [32,33] with norm-conserving pseudopotentials in the semilocal form [34] is used for the calculations. The employed generalized gradient approximation (GGA) functional with Perdew-Burke-Ernzerhof (PBE) [35] treats underlying exchange and correlation within the double zeta plus polarization (DZP) basis sets. The K points 20×20×1 of Monkhrost pack scheme [36] is used to perform Brillouin zone integration. The reciprocal space is expanded by using an energy cutoff of 350 Rydberg. The atomic relaxation is achieved when the force reached the value of 0.02 eV/Å using the standard conjugate-gradient (CG) technique. The convergence criteria for the energy of the self-consistent field is set to 1.0 × 10 −6 eV. The vacuum gap of 25 Å is used along the z-direction to prevent unnecessary interactions between the adjacent unit cells. The chemical stability is achieved by calculating and analyzing the formation ( ) and cohesive ( ℎ ) [29] energies. tion band states, respectively. ( , ) ( ) and ( , ), are the corresponding energy and eigenfunction of these states. ⃗ and̂ are the momentum operator and polarization vector, respectively. The equation (4) displays the connection between optical and electronic properties. Further, real part of dielectric fuction 1 ( ) is obtained by Kramer-Kronig transformation (KK) of 2 ( ) and is expressed as: where denotes the principle part of 1 ( ) [38]. Further, the complex refractive index ( ) is expressed as = √ ( ) = ( ) + ( ), where ( ) and ( ) are the refractive index and extinction coefficient, respectively. These parameters are expressed as: Further, the reflectivity, R( ) and absorption coefficient, ( ) are expressed as [39]: Additionally, the electron energy loss function, L( ) is given by the relation ( ) = Im − 1 ( ) and also in terms of 1 ( ) and 2 ( ), All these optical parameters are calculated in the interval between 0 to 25 eV for in-plane (E‖x), and out-of-plane polarization (E‖z) of electric field.

Structural properties
The optimized unit cell of pristine h-BN has planer geometry with lattice constant 2.52 Å and sp 2 hybridized B−N bond of length 1.45 Å. By adding F atoms on top of Bsites and bottom of N-sites ( Fig. 1) in the unit cell of h-BN, the FBNF monolayer is designed which is allowed to fully relax until it achieves the favorable stable configuration. The optimized structure is buckled (0.50 Å) with lattice constant 2.66 Å and sp 3 hybridized longer B−N bond of length 1.62 Å. The details of bond lengths in optimized structures are presented in Table 1. The lattice constant of FBNF is 10% more than pristine structure however retains the hexagonal symmetry similar to fluorinated graphene [40] 1 2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18  19  20  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60  61  62  63  and SiC [41]. This increment is attributed to the larger radius of the F atom and inter-atomic repulsion. The structural stability is confirmed by calculating the cohesive energy (Equ. 1) which is -6.91 eV/atom and -4.83 eV/atom for h-BN and FBNF monolayer, respectively. The relatively smaller negative cohesive energy in FBNF is connected to the longer B−N bonding. The formation energy (Equ. bonding. Further, to test the dynamic stability the phonon dispersion calculations are performed ( Fig. 3(a) and (b)) along Γ-K-M-Γ high-symmetry lines. The presence of real frequencies in both monolayers demonstrates good kinetic and dynamical stability. After confirming the structural, and dynamical stability, it's crucial to test the mechanical stability and strength of the material because the strain is unavoidable in material growth and processing [47]

Mechanical properties
The h-BN monolayer, also known as "white graphene", has extremely comparable physical and chemical properties with graphene [18]. Particularly, the 2 hybridized covalent bonds between C atoms in graphene and B−N bonding in h-BN makes both materials mechanically strong and stable. However, the fluorination in h-BN makes the B−N bonding 3 hybridized, which distorts the planar geometry [29], the mechanical response of fluorinated h-BN monolayer, FBNF, is interesting to study.
The computed mechanical parameters are very close to both experimental and theoretical reports ( Table 2). It's worth in mentioning that similar results are computed by previous report in hydrogen passivated hexagonal GeC monolayer [54].

Optical properties
After making a good understanding of electronic properties, which are inherently connected to the optical behavior of a semiconductor (Equ. 4), it is interesting to discuss the optical behavior of FBNF monolayer. The optical response is calculated by analyzing the amplitude and number of peaks in the optical response curves with the photon energy range of 0 eV to 25 eV. The incident polarized light is considered in in-plane (E‖x), and out-of-plane (E‖z) directions, which are sufficient directions to describe the optical behavior of this 2D system. The spin non-polarized calculations is performed to investigate the important optical parameters such as the real ( 1 ( )) and imaginary ( 2 ( )) parts of dielectric functions, absorption coefficient ( ( )), electron energy loss function (ELF) (L( )), refractive index ( ( )), and reflectivity ( ( )). To make a comparison, these optical parameters are plotted side by side (Fig. 7−12 ) for both directions and also compared with the pristine h-BN.
The real part of the dielectric function ( 1 (w)) is related to the energy stored by the medium when a material is exposed to an electromagnetic spectrum. The optical spectra in 1 ( ) (Fig. 7) for FBNF mainly arise approximately in between 4.6 eV to 15.2 eV with the early sharpest peaks at 8.79 eV and 12.55 eV in E‖x. Meanwhile, such sharpest peaks occur at 7.71 eV and 11.59 eV in E‖z, significantly different from h-BN. The value of 1 ( ) is positive throughout the whole energy range in the in-plane direction but a negative value is detected in between the 11.95 eV to 12.45 eV for out-of-plane direction in FBNF monolayer which is unprecedented in h-BN. The corresponding negative frequency is known as plasma frequency ( ), which is very important to understand many exotic optical phenomena [59]. The static dielectric function ( 1 (0)), the value of 1 ( ) at zero photon energy, is 1.5 (≈ h-BN) for inplane direction but higher (1.65) in out-of-plane direction.
The major optical behavior of a material is linked with the imaginary part of dielectric function ( 2 ( )) (Eqns. (3)(4)(5)(6)(7)(8)). The 2 ( ) describes the inter-band transitions by analyzing the major peaks. All the optical inter-band transitions are essentially due to the orbitals of F, B, and N atoms which can be described by analyzing PDOS (Fig. 6). The major sharper peaks (Fig. 8) arise at 9. 16 and 9.95 ( blue-shifted) in E‖x, and 7.95 , 8.59 and 11.88 (red-shifted) in E‖z displays earlier interband trasitions in FBNF. The higher number and larger intensity in spectra indicates the multiple inter-band transitions and enhanced optical response of FBNF than the pristine counterpart.
The electron energy loss function (ELF) describes the amount of energy loss through the material upon the incidence of photon energy. The multiple energy losses in the energy range 4.25 eV to 25.00 eV (Fig. 9) is detected in FBNF for both directions. The major energy loss peaks arises at 9.29 eV, 10.19 eV, 13.88 eV, 15.23 eV and at 8.83 eV, 12.47 eV, 15.87 eV, 18.0 eV, 19.40 eV for FBNF in in-plane and out-of-plane direction, respectively. The energy loss is significantly lower in FBNF than the pristine counterpart in the in-plane direction. The sharpest resonance peak at 12.47 eV due to plasma frequency ( ) creates significant energy loss. The energy loss is highly anisotropic like other paramters in FBNF as well as h-BN. The absorption coefficient ( ) spectra describe the light-harvesting quality of the material. The absorption edges ( ), the threshold value of energy absorption spectra, are at 6.71 eV (red-shifted) and at 5.49 eV (blue-shifted) for in-plane and out-of-plane direction (Fig. 10), respectively. Null absorption in infrared region (IR) and visible region (VR) for FBNF makes it a perfect material in optical fibers and beam splitters [60]. The highest absorption peak is observed at 12.91 eV (≈ 9.01×10 6 −1 ) and 12.23 eV for in-plane and out-plane direction which is significantly better than pristine h-BN. The exceptional long-range absorbance, from 6.71 eV to 25 eV, and multiple absorption peaks in the ultraviolet region (UV) region make FBNF monolayer an appropriate light-harvesting material. Additionally, the strong optical anisotropy broads its applications in light polarizers and wave guides materials.
Besides, multiple reflection sharp peaks (Fig. 11) within the same range of absorption coefficient peaks are detected in both directions. The maximum reflectivity is 10% (7.95 eV) and 40% (12.29 eV) for in-plane and out-plane direction which is higher than h-BN. The abrupt rise of reflectivity at 12.29 eV in out-of-plane direction is connected to the plasma frequency and the corresponding metallicity. The loss of oscillatory reflectivity curve beyond 20 eV indicates the monolayer's transparency region.
With a careful analysis, it is clear that the induced large bandgap of FBNF tends to create the optical spectra absent in the IR, and in the VR, and only appear around the UV regions from 4.61 eV to 22.10 eV. The multiple oscillatory peaks in the real and imaginary dielectric curve demonstrate the rigorous inter-band transitions. This supports FBNF to possess the highest absorbance (up to 9.01×10 5 −1 ) with small electron energy loss in in-plane direction demonstrating an outstanding optical response. Plus, the strong optical anisotropy enriches its optical quality to make it a proper optoelectronic material. It is worth mentioning that, similar optical behavior is observed in the fluorinated SnC monolayer calculated by using first-principle DFT calculations [63].

Conclusions
In summary, The FBNF is found to be a structurally, mechanically, and dynamically stable monolayer. The sp 3 hybridized B−N in FBNF, is longer than in h-BN is involved in buckling to soften the structure by retaining the structural and elastic isotropy. The F-5 orbital plays a role to create the insulator−semiconductor electronic transition. The visible range PBE-bandgap supports the largest optical absorption, low electron energy loss, and good reflectivity. In addition, the strong optical anisotropy enriches the optical quality and establishes this material as a proper candidate in optoelectronic devices. These outstanding findings are also supported by the experimental evidence [31]. Hence, the FBNF monolayer is a potential candidate for nanomechanical and optoelectronic device applications.