Exploring the Electronic Properties of Relaxed Bilayer Nitrogen-Graphene Alloy Using Density

Functional Theory Md Tanvir Arafin1,* and Saiful Islam1◊

1Department of Electrical and Electronic Engineering, Bangladesh University of Engineering and Technology Dhaka-1000, Bangladesh

*tanvirarafin@buet.ac.bd, ◊sislamk@yahoo.com

Abstract— In this work, a novel bilayer material based on nitrogen-graphene alloy (C3N) has been proposed. The structural and electronic properties of this bilayer system have been studied using first principle calculations. The crystal structure of this material is first calculated using the Hellmann-Feynman theorem with a Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton optimization algorithm. Next, using plane-wave self-consistent field (PWscf) codes, the band structure and the density-of-states (DOS) of the alloy have been computed. From these density functional calculations, it has been found that, the electronic and structural properties of this system are substantially different from the monolayer C3N-alloy. Interestingly, a relaxed bilayer C3N structure behaves as a metal whereas its monolayer counterpart acts as a semi-conductor.

Index Terms—Graphene, Graphene-Nitrogen Alloy, Density Functional Study.

I. INTRODUCTION Graphene is a one-atom-thick monolayer of sp2-bonded

carbon atoms packed in a two-dimensional honeycomb lattice structure [1][2]. Graphene has some unique physical and chemical properties, such as - very high carrier mobility, linear band dispersion at the Dirac point of the Brillouin zone, small spin-orbit interaction and anomalous Quantum Hall effect etc. [1][2][3][4]. These properties have created a plethora of opportunities for developing nano-electronic devices based on this material. However, one of the major concerns regarding graphene nano-electronics is that, it is very hard to control the electronic properties of graphene. The bandgap of graphene is zero and therefore, it is very difficult to use this material in the conventional semiconductor electronics. A general way of exploiting novel electronic properties in graphene is chemical functionalization. Chemical functionalization and doping of graphene renders several new graphene derivatives [11][12] and doped structures such as graphane, fluorinated graphene etc. [11][12]. These graphene derivatives have demonstrated some exciting new properties such as bandgap tunability, distinct charge and spin transport properties and others [11][12]. Other approaches for controlling the electronic properties of graphene includes substrate induced band-gap opening [6][7], application of external gate bias [8][9], creating graphene nano-ribbons [10] etc.

Various research groups [13]-[16], have very recently showed that introducing nitrogen in a graphene structure can render a multitude of stable nitrogen-doped graphene systems and nitrogen-graphene alloys. These materials can behave as semiconductors, metals and half-metals. Hence, doping of nitrogen into graphene can provide additional approaches for

tuning the electronic properties of graphene and graphene derivatives. Panchakarla et al. [17] has demonstrated that boron and nitrogen doped graphene bilayer systems are stable and can exhibit interesting electronic properties. Later, different research groups have proposed several application of such nitrogen-doped graphene in bio-sensing, electrochemical applications and fuel cells [13]-[18]. The spin gapless semiconductor-metal-half metal properties of N-doped zigzag graphene nano-ribbons are considered to have promising applications in future nano-electronic devices [15]. Recently, Xiang et al. [18] have theoretically revealed two stable ordered nitrogen-graphene alloys - C3N and C12N. Using density functional calculations with Local Density approximation (LDA), they have predicted some interesting electrical properties of such system.

In continuation of the above mentioned works, in this work, a novel bilayer system of ordered nitrogen-graphene alloy is proposed. Density functional calculations have been performed using LDA approximation to study the structural and electronic properties of this novel material system. Using Hellmann-Feynman theorem with a Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton optimization algorithm, optimized crystal structure for bilayer C3N alloy is computed. Then, the band structure and the density-of-states (DOS) of this ordered bilayer alloy is computed. To understand and compare the properties of this bilayer material, a complete relaxation and DFT study on monolayer C3N is also performed. The electronic properties of both these system are studied and compared for understanding the behavior of nitrogen-graphene alloys. A detailed discussion on the computational details and the results obtained are given in the following sections.

II. COMPUTATIONAL DETAILS Ab initio calculations for this work are performed using

density-functional theory (DFT) [19] with a plane-wave basis set. To introduce the electronic exchange and correlational effects local density approximation (LDA) of Perdew-Zunger (PZ) [20] is employed. The electron–ion interaction is incorporated by using the projector-augmented-wave pseudopotentials for carbon and nitrogen atoms. The plane wave basis cut off is kept at 40 Ry for wave functions and 240 Ry for charge density. For calculating self-consistent solutions of the Kohn–Sham equations [21], a 12 × 12 × 1 k-points Monkhorst–Pack grid [22] is applied. . For relaxation calculation of the unit cell, the convergence threshold for energy and force is taken as 10-4 Ry and 10-3 Ry/au

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2012 7th International Conference on Electrical and Computer Engineering20-22 December, 2012, Dhaka, Bangladesh

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respectively. During band structure calculation, all atoms are kept in the relaxed positions which are obtained through geometric optimization. The band structure is plotted on the lines joining the high-symmetry points M, Γ, K, and M. All calculations are performed using the PWscf code of QUANTUM ESPRESSO [23] and the figures are generated using XCrySDen [24] and Gnuplot [25].

III. STRUCTURAL PROPERTIES OF BILAYER C3N For calculating the crystal structure of bilayer C3N, first a

complete relaxation of the unit cell geometry and the atomic positions for monolayer C3N are carried out using the total-energy and force minimization methods. Then, using two of this optimized monolayer, a bilayer system is developed. Total-energy and force minimization methods are used again to compute the atomic positions and crystal structure for this bilayer material. For these relaxation calculations, Hellmann-Feynman theorem with a Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton optimization algorithm is applied.

The unit cell of monolayer C3N has six carbon atoms and two nitrogen atoms. During unit cell optimization, one nitrogen atom is kept fixed at the origin and the other atoms are relaxed. To avoid interaction between different layers, the vacuum thickness of the cell is kept as 25Ǻ. As seen from the figure, the lattice structure is similar to that of graphene. However, the lattice constant is somewhat reduced in C3N. For relaxation using LDA with PZ functional, the C-C bond length is found to be around 1.392 Ǻ as reported by Xiang et al. [18]. The optimized geometry of the structure using LDA with PZ exchange correlation functional is shown in the figure 1. This figure is generated with the help of XCrySDen using the PWSCF results obtained through the relaxation calculations.

Figure 1. Relaxed crystal structure of monolayer C3N (The brown rhombus marks the unit cell). The carbon atoms are shown in blue and the nitrogen

atoms are shown in golden.

The unit cell of the bilayer C3N contains sixteen atoms. During the relaxation calculation the first monolayer is kept fixed at x-y plane. The optimization starts from an initial point where two C3N monolayers are placed 1 Ǻ apart. The vacuum thickness over the unit cell is taken as 20Ǻ. The optimized geometry of the bilayer structure using LDA with PZ exchange correlation functional is shown in the figure 2. This figure is also generated with the help of XCrySDen using the PWSCF results obtained through the relaxation calculations.

After the complete optimization, it is found that, the interlayer distance between C atoms is about 3.383 Ǻ and the interlayer distance between N atoms is about 3.071 Ǻ. Therefore, it can be said that the planer structure of the monolayer system is no longer present in the bilayer C3N. From the total energy calculations, it is found that the total

energy of the optimize system is -321.23 Ry which is about twice of the total energy of a monolayer system (-161.7 Ry). Therefore, it is seen that the energy/atom values for both the systems remain nearly the same. Using cluster expansion method, the stability of the monolayer system has been explored in detail in [18]. After comparing the total energy per atom of the system of the proposed bilayer C3N with the same of [18] it is observed that the figure is -20.07 Ry for the bilayer in contrast to -20.21Ry of [18]. Therefore, from the binding energy viewpoint, the bilayer system with the similar energy/atom value may be regarded as a stable one. The crystalline parameters obtained through relaxation computations for the bilayer structure are presented in table 1.

Figure 2. Relaxed crystal structure of a bilayer C3N shown at the bottom of the figure with an inter layer distance D. The carbon atoms are shown in blue

and the nitrogen atoms are shown in golden. At the top of the diagram the bottom layer of another bilayer C3N is shown because the calculations are

performed on a periodic supercell of bilayer C3N with a vacuum distance of 20 Ǻ.

TABLE I. CRYSTALLINE PARAMETERS FOR BILAYER C3N CALCULATED USING LDA-PZ.

C-C average bond length (in Ǻ) 1.392 C-N average bond length (in Ǻ) 1.393 C-C interlayer distance 3.383 N-N interlayer distance 3.071 Lattice constant (in Ǻ) 2.411

IV. BAND-STRUCTURE AND DENSITY OF STATES IN BILAYER C3N

The band-structure and density of states for both monolayer and bilayer C3N is calculated to investigate the electronic properties of these alloys. The band structure plotted on the lines joining the high-symmetry points M, Γ, K, and M. The band-structure for monolayer C3N is given in figure 4. From LDA calculation, it is found that monolayer C3N is a semiconductor with indirect bandgap. The bandgap calculated using LDA is found to be 0.36 eV. The conduction band minimum (CBM) is found in the Γ-point and the valance band maximum (VBM) is found on the M-point of the Brillouin zone. The calculated band-structure for bilayer C3N is given in figure 4. A comparison on the density of states for monolayer and bilayer C3N is given in figure 5.

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Figure 3. Band structure of a relaxed monolayer C3N calculated using LDA. The dashed line at 0 eV indicates the valence band maximum.

Figure 4. Band structure of a relaxed bilayer C3N calculated using LDA. The solid line at 0 eV indicates the valence band maximum.

From LDA calculation, it is found that bilayer C3N behaves as metal. A close examination of the band structure and DOS of monolayer and bilayer C3N reveals that the band that defines the valance band maximum is originated from pz orbitals on nitrogen atoms and it plays the most significant part in determining the band gap. The lowest band at the conduction band comes from the pz orbitals on carbon atoms. Comparing with the band structure of graphene, the effect of introducing nitrogen atoms in a graphene crystal can be clearly recognized. The pz orbitals on nitrogen atoms create the lowering of degeneracy at K-point and introduce a bandgap at M-point in monolayer C3N. However, at bilayer C3N this bandgap is reduced due to pz orbitals of the nitrogen atoms of the second layer. As a result, the bilayer system is predicted to exhibit metallic properties. This observation also supports the earlier prediction by Panchakarla et al [17].

However, it may be mentioned here that LDA generally underestimates the bandgap and therefore, in practical experiments, an increase in the distance between VBM and CBM can be expected. Also, from the DOS plot, it is evident that, there are very few states available at E=0. As the indirect overlap between the CBM at Γ-point and VBM at M-point is very small, in practice, a relaxed bilayer C3N alloy may also behave as a semi-metal. Moreover, as the monolayer C3N is predicted to behave as a semiconductor, increase in the bilayer distance by external means can make this bilayer system semiconducting. Therefore, from this study, it can be reasoned that this metallic bilayer alloy is a potential applicant for bandgap tuneable material in future nano electronic devices.

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Density of states (in arb. units)

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Figure 5. Density of states for monolayer and bilayer C3N calculated using LDA.

V. CONCLUSIONS In this work, the electronic nature of a bilayer nitrogen-

graphene alloy has been explored using density functional theory. Along with the complete band-structure and DOS plots, the optimized crystal structure of this bilayer alloy has been presented. From the study of its electronic properties, it has been found that, this novel bilayer material should behave as a metal or a semimetal. This behaviour is quite different from semiconducting monolayer C3N. The indirect location of CBM and VBM of this material together with the metal/semimetal behaviour appears to be interesting and may find some useful application in the near future. Furthermore, there is a possibility of creating a bandgap in this bilayer system by varying the interlayer distance. Hence, further research should be focused on this bilayer system to harness these exciting properties of this novel material.

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