Effect of the vacancy on the electrical transport properties of boron nitride nanosheets


 Vacancies occur naturally in all crystalline materials. A vacancy is a point defect in a crystal in which an atom is removed at one of the lattice sites. The defect could be imported during the synthesis of the material or be added by defect engineering. In this paper by employing the density functional theory as well as the non-equilibrium Green’s function approach, the structure and electronic properties of the perfect and defected BN nanosheet would be obtained and compared. Besides, the influence of the vacancy defect position is evaluated. For this purpose, the defect is considered at the center, left, and right hand sides of the nanosheet. It is seen that the electric current changes by changing the position of the vacancy defect, which is related to the electronic structures of BN nanosheets. In addition, the transmission and conductance for BN nanosheets with vacancy continuously change by changing the bias voltage. The obtained results can benefit the design and implementation of BN nanosheets in nanoelectronic systems and devices.


Introduction
In recent years, molecular devices have been suggested as applicable components to be used in the future electronic circuits. To form such devices, one molecule or a group of molecules are considered in a layer arrangement which is connected to two or more electrodes. It has been shown that the transport characteristics of such molecular devices are affected by different factors including their electronic structures as well as physical and chemical properties of their constitutive molecules. In the structure of the molecular devices, molecules are considered as quantum dots. The discrete energy levels of these quantum dots are at least one order of magnitude smaller than the semiconductor quantum dots [1][2][3]. As a weak contact is created between the molecules and the electrodes, caused by the potential barriers, electronic isolation would be occur between the metallic electrodes and molecular quantum dots. Furthermore, if the molecular quantum dots are utilized for the conduction purposes, they could be thermally activated and vibrated at the finite temperatures. This behavior is not seen in the semiconductor quantum dots. Based on the interactions between the electrons and phonons, by Walczak and Zhou developed the Green's function approach to study the transport of the electron in the DNA molecules [4][5].
If the electrons are passed through some energetically accessible molecular states (i.e. conduction channels) , the energy could be exchanged between the electrons and nuclear degrees of freedom. Hence, an inelastic component would be appeared in the current [6].
Recently, different approaches used for controlling this process have been applied. The molecular electronics is a developing research area whose purpose is to improve the efficiency of these devices.
Caused by the attractive chemical and physical properties of the fullerene, a spherical allotrope of carbon, several research groups have investigated the properties of fullerene-like structures which are made from other atoms, including the members of the groups III, IV and V of the periodic table [7]. Furthermore, some applications have been found for these fullerene-like structures .Similarly, 2D graphene-like nanostructures have also been considered for investigation on their physical and chemical properties. Boron nitride has the same structural properties as 2D carbon materials.As a sample, boron nitride (BN) nanosheets, also called "white graphene", may be a good candidate to alternate graphene in some applications. Having desirable physical properties, including mechanical properties, impermeability, and thermal conductivity boron nitride (BN) nanosheets would not cause galvanic corrosion. Moreover, due to wider bandgap than graphene, more transparency to visible light is observed in the BN nanosheets than the graphene. Besides, BN nanosheets are more chemically and thermally stable than the graphene [8].
It has been shown that the BN nanosheets possess thermal and chemical stabilities larger than graphene. Moreover, a significant charge transfer is observed from B to N atoms. Hence, B-N bonds which are partially ionic sp 2 -hybridized leads to notably different optics and electronics properties in BN nanosheets from graphene. For example, the color of BN is white with a large bandgap of 5.5 eV. While the color of graphene is black and it is conductive [9]. Due to these unusual structures and characteristics, BN nanosheets have found diverse functionalities. They are intrinsic insulators which make them as a valuable choice for dielectric applications for example to be used as a dielectric gate layer and ultraviolet luminescent agent [10].
One of the most important properties of the BN nanosheets is that they are electrically insulating and do not increase the galvanic corrosion of the underlying metal. The chemical vapour deposition (CVD) approach can be used to synthesize the BN nanosheets with relatively large sizes [11]. In many practical applications, the anti-oxidation protection of the metals at low temperatures for a considerably long time is of great importance. Similar to the graphene, BN nanosheets can be employed as an anti-corrosion coating on the metal substrates or some arbitrary other substrates. It has been reported that the copper surface can be protected from oxidation at 500 °C for 0.5h by adding a BN nanosheet layer with the thickness of 0.5 nm [12]. In recent years, the construction of electronic structures of boron nitride through point defect design has become widespread. The point defects during synthesis can alter the nanostructured properties of BN [13].
The investigation of the nanostructures having different types of defeats is of great importance. The considered defects in the literature are as vacancy, substitution, and interstitial defects.
In this paper, the transport properties of perfect and defective BN nanosheets are investigated.
For this purpose, the single vacancy defect is considered at different positions on the structure of the nanosheet. The transport, conductance and electronic properties of the BN nanosheets with and without single vacancy defect are evaluated. For this purpose, the density functional theory (DFT) is used.

Computational Model
Here, the BN nanosheet with a single-vacancy defect is modeled. The configurations of the optimized BN nanosheet device without and with defect vacancies are depicted in Figs. 1 and 2, respectively. As it can be seen in this figure, the vacancy defect is considered at different positions.
The first principle calculations are performed to optimize the geometry of the considered structures and calculate the electronic properties. For this purpose, the DFT is used along with the technique of non-equilibrium Green's function (NEGF). Semi-Empirical (SE) calculator can be used to model the electronic characteristics of molecules, crystals and devices. For this purpose, self-consistent and non-self-consistent tight-binding models can be employed. Here, tight-binding models are implemented based on Slater-Koster model [13][14][15] .
In Slater-Koster tight-binding model, the density functional based tight binding (DFTB) formalism is closely followed which has been described in. In this model, a numerical function is used to express the distance-dependence of the matrix elements. In the DFTB approach, a second-order expansion of Kohn-Sham expression of the total energy with respect to the fluctuations of the charge density is used [16][17]. The zeroth order method is considered as common standard non-self-consistent (TB) plan. While, in the second order approach, a transparent and parameter-free expression is derived for the elements of the generalized Hamiltonian matrix.
A device of the BN nanosheet is considered here and an electrode with the length of 2.46 Å is located at its left and right sides. Furthermore, the unit cell chiral vector is selected as = 3, = 3 which is repeated along the = 1, = 1 and = 7 axes after optimizing the device.
The Atomistix ToolKit (ATK) is used for all of the calculations. To depict the atom cores, Troullier-Martins normconserving pseudopotentials is employed which is also represent the linear combinations of atomic orbitals which can help to expand the valence states of electrons. The k-point is selected as (1 ,1 , 100) in the Brillouin zone and the electrode temperature is set as = 300 . Furthermore, the cutoff energy for the grid integration is considered as 150 which is mainly used to control the size of the real space in the partitioning of the integral network and solving Poisson's equation [18][19]. Quasi Newton approach is utilized for complete optimizing the atomic structures, including the atomic positions as well as the lattice parameters. Besides, the boundary conditions are considered as periodic. For all of the simulations, initially the geometry is optimized until all of the residual forces are smaller than 0.02 ° .

Results and discussions
According to Figs. 1 and 2, a BN nanosheet device without and with a single vacancy defect is selected. The location of the defect is variable. To calculate the transport property of the BN nanosheets, the DFT is used in combination with Keldysh non-equilibrium Green's functions (NEGF) method. The calculations are performed by the Atomistix ToolKit (ATK) package [20][21][22]. Besides, using the local density approximation is implemented with the Slater-Koster model. As it was previously mentioned, the energy cutoff is used as 150 to for the grid integration of the charge density. The k-point sampling is chosen as 1 × 1 × 100 for calculation the transport properties and total energy. The numerical tolerance of 1 × 10 − was used to control the NEGF-DFT self-consistency. can also be said that the undeformed BN nanosheet is a uniform systems in which no considerable charge transfer is observed.
The step-like appearance of the transmission spectrum is also seen at higher voltages.
However, at sufficiently larger voltages, the step-like behavior would be gradually disappeared.
Moreover, it is observed that the amplitudes of transmission spectra of considered structures are decreased by increasing the voltage.
To further investigate the effect of position defect on the electrical transport of BN nanosheets, the I-V properties of each of the models are calculated and depicted in Fig. 4.
The bias voltage is increased with the steps of 0.1V. Besides, the converged density matrix of each state would be used as the initial guess of the next step. Landauer-Buttiker formula is used to obtain the current through BN nanosheet: According to Fig. 5, the maximum of the conductance peaks of BN nanosheets with single vacancy in center is larger than perfect and other defective nanosheets. By increasing the conductivity, the electric current increases (G=1/R), which can be seen in Fig. 5.
In Fig. 6. the conductance and current, which has been obtained using Eq. On the other hand, the conductivity-energy curves in Fig. 6 show that the electrical conductivity of the nanosheet with a centrally located single vacancy is larger than the nanosheet with the single vacancy located at the left and right hand sides. Similarly, comparison of current curves indicates that the electrical current of nanosheet with a centrally located single vacancy is larger than the nanosheet with the single vacancy located at the left and right hand sides, which is confirmed by Eq. (A).
The transmission coefficient is influenced by two parameters, including electronic and the strength of the electrode/molecule coupling [29]. Hence, Green's function would be changed

Conclusion
In this paper, the transport properties of a perfect and defective BN nanosheet with single vacancy defect were studied and the effect of vacancy defect on the structure and electronic The results also show that as the voltage increases, the electrical conductivity changes so that at voltages above 3V, electrical conductivity of a BN nanosheet with centrally located single vacancy defect would be larger than other considered cases.

CONFLICT OF INTEREST
The authors declare no conflict of interest, financial or otherwise.