Exploring the Charge Localization and Band Gap Opening of Borophene: A First-Principles Study

Recently synthesized two-dimensional (2D) boron, borophene, exhibits a novel metallic behavior rooted in the s-p orbital hybridization, distinctively different from other 2D materials such as sulfides/selenides and semi-metallic graphene. This unique feature of borophene implies new routes for charge delocalization and band gap opening. Herein, using first-principles calculations, we explore the routes to localize the carriers and open the band gap of borophene via chemical functionalization, ribbon construction, and defect engineering. The metallicity of borophene is found to be remarkably robust against H- and F-functionalization and the presence of vacancies. Interestingly, a strong odd-even oscillation of the electronic structure with width is revealed for H-functionalized borophene nanoribbons, while an ultra-high work function (~ 7.83 eV) is found for the F-functionalized borophene due to its strong charge transfer to the atomic adsorbates.


Introduction
Recent success in synthesizing atomically thin two-dimensional (2D) borophene on Ag (111) substrates 1,2 has stimulated great interest in exploring the growth, structure and properties of this elemental 2D material. 3-7 As a magic element with coexistence of covalent and ionic characters, boron can show a versatile electronic structure, including semiconducting, semi-metallic, and metallic phases. [8][9][10] Previous studies showed that free-standing borophene exhibits a highly anisotropic electronic structure. 11,12 With its high carrier concentration at the Fermi level, which is absent in graphene with a zero carrier density at the Dirac cone, the atomically thin borophene serves as an ideal platform for investigating the distribution and response of electron gas confined in an ultrathin layer with external perturbations.
So far, various atomic models for boron clusters and 2D models have been theoretically proposed. [13][14][15] Concerning the structure of borophene, recent experiments reported two dramatically different atomic structures on the Ag substrate: the closely packed structure 1 and the hole-containing structure. 2 While experiments claimed the stability of a borophene sheet supported by the Ag substrate, the stability of a free-standing borophene is still elusive. First-principles phononic calculations showed that the long-wavelength imaginary modes always exist in isolated triangular sheets and other polymorphs like β12 sheets (refer to phonon dispersion in the supplementary information in Ref. 14). Physically or chemically bound species were found to promote the stability of borophene. 16,17 Recent theoretical studies proposed a viable approach of using substrates 18,19 or chemical functionalization 20 to tune the adsorption and energetics of borophene. In principle, a proper truncation of the borophene sheet by breaking the lattice periodicity can eliminate these long-wavelength softening phonons, thus stabilizing structures without the need of chemical functionalization.
As the boron atom has three valence electrons, it needs to pair with five additional electrons to satisfy the octet rule. However, in borophene, each boron atom forms bonds with six neighbors, thus favoring the metallic phase according to the band theory. For electronic applications of borophene, an intriguing issue is the localization of its itinerant electrons and ultimately its band gap opening. Approaches for the band gap opening in 2D materials can be categorized into two groups: i) quantum confinement induced by the construction of finite-sized structures, like ribbons, edges and dots, [21][22][23] and ii) chemical functionalization. 24,25 However, the effectiveness of both approaches on the borophene band gap opening remains unclear. The formation of ionic bonds in a high-pressure boron phase 26 suggests a different charge distribution in boron materials in comparison with other 2D materials, especially graphene. The failure of the octet rule in pure borophene implies a new mechanism of the charge localization/delocalization, which is yet to be understood.
In this work, we explore the routes for the charge localization and the band gap opening of borophene via chemical functionalization, defect engineering, and ribbon construction by using first-principles calculations. We show that the metallicity of borophene is remarkably robust against H-and F-functionalization and the presence of vacancies. Interestingly, a strong odd-even oscillation of the electronic structure with the ribbon width is revealed for H-functionalized borophene nanoribbons, and band gap opening occurs only for a specific type of ribbons. Owing to the high density of states (DOS) near the Fermi level, a record-high work function is found for the F-functionalized borophene. These unique features of chemically functionalized borophene sheets and ribbons may indicate many interesting applications.

Methods
Our theoretical calculations are performed by using the Vienna ab initio simulation package (VASP) 27 within the framework of the density functional theory (DFT). The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional is selected together with an energy cutoff of 450 eV. The effects of spin polarization are considered in our calculations. For various chemically modified 2D borophene, a 20×15×1 Monkhorst-Pack grid is used for the k-point sampling in the first Brillouin zone. For the line (zigzag)-edge borophene nanoribbons (BNRs), a 20×1×1 (1× 8×1) k-point sampling is used. To avoid the spurious interaction between periodical images, a vacuum space of 15 Å along the out-of-plane direction is created. All the structures are relaxed until the forces become smaller than 0.01 eV/Å. To more accurately describe the self-interaction and screening of carriers, the hybrid functional Heyd-Scuseria-Ernzerhof (HSE06) 28 is adopted for the work function calculations.

Results and discussion
We first explore the modification of the electronic properties via functionalization of borophene surface by H, F, and O atoms. We notice that several atomic models, showing long-wavelength negative phonon modes, have been proposed for monolayer borophene to match the experimental images of the samples grown under different conditions. 14 In this work, the closely-packed atomic model, as revealed in a recent experiment, 1 is chosen (see Figure 1a) since other atomic models are its direct derivatives. The considered closely-packed model, which consists of equilateral triangles as the basic unit, has a Pmmn space group with a rectangular unit cell. It can be regarded as a staggered honeycomb lattice with additional atoms located at the hexagon centers. Each rectangular unit cell contains two symmetrically inequivalent boron atoms occupying the two 1a The above-mentioned robust metallicity in these surface functionalized borophene sheets is absent in graphene and transition metal dichalcogenides (TMDs). The finite density of these free carriers at the Fermi level suggests that borophene and its functionalized derivatives are promising for applications as interconnecting and field-emitting materials. Since the work function, which quantifies the ability of electrons to move from the surface of a material to vacuum, is critically important for field emission and rectification of conducting barriers, 32,33 in the following, we examine the change in the work functions of these functionalized borophene sheets. Figure 1d shows the energetic diagram of the work functions for various functionalized borophene sheets in comparison with other common bulk metals and graphene. From the diagram, the following important features can be identified. Firstly, the work function of a pristine borophene sheet is 5.31 eV (obtained via HSE calculation), which is larger than that of most listed metals, except Pt. Moreover, the work function of pristine borophene is also higher than that of graphene (~ 4.5 eV). 34 This is surprising since a carbon atom has a larger electronegativity than a boron atom. The higher work function of borophene could be attributed to the nature of atomic states around the Fermi level. Borophene mainly consists of in-plane s-p hybridized (σ) states, which are lying lower than those of the out-of-plane pz (π) states in the graphene case. Thus, an electron in borophene is harder to knock out than that in graphene. Secondly, the work function of borophene increases slightly to 5.88 eV for the H-functionalized and dramatically to 7.83 eV for the F-functionalized borophene. The underlying origin may arise from the strong dipole layer pointing inward towards the central borophene layer due to its transfer of electrons to the functionalizing atoms (see Figure 1d). In other 2D materials, like graphene and TMDs, the density of electrons is negligible at the Fermi level, which means that the magnitude of the dipole layer is modest upon the chemical functionalization due to the limited charge transfer. In contrast, a borophene layer has a considerably high density of carriers at the Fermi level because of its intrinsic metallicity, giving rise to a pronounced charge flow and a built-in dipole layer. This great tunability in the work function suggests that the chemically functionalized borophene sheets can be used as a buffer layer for reducing the contacting resistance and Schottky barrier at the interface. In addition, the high work function in the F-functionalized borophene sheet is particularly useful for electron collection and hole injection.
Next, we investigate the effect of the atomic vacancies on the electronic properties of borophene (see Figure 2). We consider both monovacancies (MV) and divacancies (DV) with the loss of one and two boron atoms in the 6×5 supercell (56 atoms), respectively. In perfect borophene, each boron atom has a coordination number of six. With the creation of an MV, six peripheral atoms become fivefold coordinated and the defect core has a local symmetry of C2v (see Figure 2b). It is well known that the electronic properties around the vacancy core may change dramatically owing to the breaking of the lattice periodicity. [37][38][39] Figure 2a shows the DOS in the perfect, MV-, and DV-containing borophene sheets. It is seen that the metallicity of these borophene sheets is robust against the presence of vacancies. Interestingly, the Fermi level significantly shifts upwards for the MV and DV cases compared with perfect borophene (see the arrows in Figure 2a  We also investigate the F-functionalized BNRs and find that their electronic properties are insensitive to the ribbon width. Therefore, only one ribbon is selected as a representative for each of LE and ZZ BNRs. Figures 4a and b show the optimized atomic structure and the band structure To examine the stability of the considered structures, we calculate the average binding energy (Eb) of perfect borophene which is defined as Eb = (nBEB − Etot)/n, and the Eb of H-, F,-and Ofunctionalized borophene using Eb = (nBEB + nXEX − Etot)/n, where Etot is the total energy of the functionalized system, EB is the energy of a single boron atom, EX is the energy of a single H or F atoms, nB is the total number of B atoms, nx is the total number of H or F atoms, and n is the total number of atoms in the system. The calculated values for the Eb for perfect, H-, and Ffunctionalized borophene are 5.86, 4.78, and 5.25 eV, respectively. Clearly, all the three considered structures of the functionalized borophene show a better stability than the pristine borophene. To verify the stability of BNRs, Eb is also calculated and shown in Table 1. It is seen that the values of Eb are positive for both LE-BNRs and ZZ-BNRs, indicating that these nanoribbon derivatives are energetically stable, which is in a good agreement with the recent work. 43 To confirm the calculation results of Eb, we also consider the edge energy (Eedge), which is defined as Eedge = (EBNR -nEB)/L, where EBNR is the total energy of the BNR, L is the length of the ribbon along the periodic direction, EB is the total energy per atom in 2D borophene, and n is the total number of atoms. As shown in Table 1, the calculated values of Eedge have the following sequence: 0 < LE BNRs < LE H-BNRs < LE F-BNRs and 0 < ZZ F-BNRs < ZZ H-BNRs, confirming the stability of BNRs.
In addition, we also perform ab initio molecular dynamics (AIMD) calculations at 300 K for 8 ps using the Nose-Hoover method to check the stability of the functionalized and vacancy-containing borophene, as well as the pristine and functionalized BNRs. The snapshots of the simulation results are shown in Figure 5. It is seen that during this long time (in terms of ab initio calculations), all the considered structures are stable. It should be noted that the ZZ H-and F-BNRs (Figures 5g and i) exhibit a lower stability than the LE H-and F-BNRs.
Currently, it is still a challenge to obtain free-standing borophene experimentally, and thus double-side functionalized borophene. Nevertheless, various attempts are being made to tackle this issue. One possible way to address this challenge is to grow a borophene layer on a substrate with a weaker interaction, and then the attachment and the transfer of the borophene layer may be achieved according to the previous theoretical prediction. 18 The other way is via surface decoration of supported borophene by creating new bonding states at the surface and edge boron atoms. In this case, dopant atoms may diffuse from the edges to the interior of the borophenesubstrate interface, allowing for possible exfoliation and double-side functionalization of borophene.
In this work, we identify possible avenues for the band gap opening and the charge localization through creating vacancies, forming edges, and surface functionalization. These methods are found to be effective in the band gap adjustment in other 2D materials. However, according to our present simulation, there is no band gap opening from vacancies and chemical functionalization of the pristine 2D borophene, signifying its robust metallicity. To further confirm the absence of a localized state with the surface functionalization and local vacancies, we calculate the electronic localization functions (ELFs) of various borophene derivatives and the results are shown in Figure 6. The value of the ELF (between 0 and 1) reflects the degree of the charge localization in the real space, where 0 represents a free electronic state while 1 represents a perfect localization. The isosurface value of 0.65 is adopted in Figure 6. For the case of vacancies in borophene (Figures 6a-c) -g), where the ELF is zero at the boron atoms, implying that the electrons around the boron atoms are highly delocalized.

Conclusions
We have investigated the electronic properties of surface functionalized borophene sheets and