Electronic Properties of Boron and Nitrogen Doped Graphene

Graphene is the thinnest 2-D material which can be regarded as a single layer of graphite. The unique electrical, mechanical and optical properties of graphene can be used in many technological applications. 2-D nanomaterials with semiconducting properties are of great interest since they can be applied in electronics industry. Pure graphene is a zerogap semiconductor or semimetal, since the electron states just cross the Fermi energy. However, the electronic properties of graphene can be tuned by doping boron or nitrogen atoms. Understanding the electronic properties in terms of density of states and band structure of doped graphene is of great relevance today. In our work, we have analyzed the electronic properties of boron and nitrogen doped graphene using Density Functional Theory (DFT). The stability and charge analysis of doped structures have been studied. The Local Density Approximation (LDA) calculations have been used to find the total energies of the structures. In addition to the electronics industry, doped graphene also has great potential to adsorb gas molecules. Therefore, we have analyzed the H2 molecule adsorption in pure, B-doped and N-doped graphene.


Introduction
Graphene is the thinnest material which can be considered as single layer of graphite. Graphene is the base material for some of the carbon based nanostructures such as carbon nanotubes (CNTs), bucky ball, and nanocones. CNTs are the graphene sheets rolled in to a seamless cylinder. The carbon atoms in these nanostructures are bonded by sp 2 hybridization. The carbon based nanomaterials have attracted the scientific community since their unique structural, electronic, magnetic, mechanical, optical and chemical properties [1]. Carbon nanotubes (CNTs) and graphene are proposed to have potential applications in electronics industry, hydrogen storage, biotechnology etc. Even though CNTs and graphene have remarkable properties, they are functionalized or doped to enhance or tune their properties. Doping is an efficient way to enhance the unique properties of carbon nanostructures and use them in potential applications [2][3][4][5][6][7][8][9].
As far as substitutional doping is considered, boron and nitrogen doping in CNTs and graphene is studied. The electronic properties and the hydrogen adsorption on these structures are reported in literatures [8][9][10][11][12][13][14][15][16][17][18][19][20]. These studies mainly focus on the local changes in the geometry, electron distribution and the doped structure's H 2 adsorption behaviour. We have computed the density of states and band structure of boron and nitrogen doped graphene, using DFT. The boron concentration has been increased from 1 to 9 and the changes in the electronic structures have been analyzed. The suitability of these doped structures based on the adsorption distance and binding energy has been studied. The graphene was optimized and the density of states and band structures were calculated using DFT. Even though DFT underestimates the band gap of semi-conducting materials, this study can give some insight on the understanding of graphene based semiconductors. The HOMO-LUMO analysis have been carried our on doped structues. In addition to the structural and electronic state changes, hydrogen adsorption has also been studied in boron and nitrogen doped graphene supercell.

Methodological Approach and Computational Details
The calculations have been done using DMol 3 package as implemented in the Materials Studio [21].
The Density Functional Theory (DFT) based study was performed using Local Density Approximation (LDA) with Perdew-Wang Functional (PWC) [22]. Geometry optimization and total energy calculations were performed using spin unrestricted, periodic boundary conditions. The structures were optimized so that force on each atom is less than 0.004 Ha/Å. The convergence threshold for maximum energy change was set to 2x10 -5 Ha. An orbital cut off quality of 0.1 eV/ atom was used which corresponds to a real space cut off of 6.5 Å. The electronic wave functions were expanded in a double numerical polarization (DNP) basis set. All electrons were included for the calculation. The SCF tolerance was set to 10 -5 and a smearing value of 0.005 Ha was used for the calculations. The binding energy of H 2 adsorption was calculated using the formula- where E TOT (host-H 2 ), E TOT (host), E TOT (H 2 ) are the total energies of optimized structures of H 2 adsorbed host materials, pure host materials and pure H 2 molecule respectively.

Results and Discussion
Geometry and Electronic Structure of B-doped Graphene. The periodic structure of graphene was obtained from graphite. Supercell with 2 units along a and b axis was considered for the study.  Table 1. The density of states and band structures are given in Fig. 2 (a-d) and Fig. 3 (a,b) respectively. The Fermi energy of pure graphene is -0.1690 Ha.
Addition of nitrogen dopants drastically changes the DOS near Fermi energy. The band structure also reflects this change (Fig. 6). When 1 nitrogen atom is doped, allowed states observed just above the Fermi energy. In contrast, on doping with 2 nitrogen atoms, energy gap is introduced above Fermi energy. On doping with 4 and 9 nitrogen atoms in graphene, the band gap increases and the system becomes n-type semiconductor.
In order to understand the chemical stability of the doped graphene, we have analysed the Highest Occupied Molecular Orbital (HOMO) and Lowest Unoccupied Molecular Orbital (LUMO). The HOMO-LUMO gap will provide some insight on the chemical stability. The HOMO and LUMO of the pure and doped graphene is shown in Fig. 7 and the HOMO-LUMO gaps are listed in Table 3.
The variation of HOMO-LUMO gap in the doped structres is plotted in Fig. 8 and 9 which show drastic changes .   Based on the HOMO-LUMO gap, it is observed that the doped structures are highly stable than the pure graphene and boron sheets, as seen in Fig. 8 and 9. The graphene, doped with 2B and 4B is less stable compared to 1B and 9B-doped graphene with low HOMO-LUMO gap. In the case of nitrogen doped graphene, 9N-doped system is highly stable with large HOMO-LUMO gap of 0.4787 eV.
The stability of pure graphene and 4N-doped graphene is almost similar comparted to other structures.   The H 2 adsorption in nitrogen atom doped graphene also has been studied and the adsorption distances listed in Table 3. There is no much change in the binding energy of adsorption and adsorption distance when the number of nitrogen atoms is increased to 2 and 4.

Conclusion
The structural changes in the geometry of graphene sheet have been examined using DFT based