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Anomalous Stabilization in Nitrogen-doped Graphene Tsuguto Umeki, Akira Akaishi, Akihide Ichikawa, and Jun Nakamura J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp511938r • Publication Date (Web): 03 Mar 2015 Downloaded from http://pubs.acs.org on March 10, 2015

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The Journal of Physical Chemistry

Anomalous Stabilization in Nitrogen-doped Graphene Tsuguto Umeki,†,‡ Akira Akaishi,∗,†,‡ Akihide Ichikawa,†,‡ and Jun Nakamura∗,†,‡ Department of Engineering Science, The University of Electro-Communications (UEC-Tokyo), 1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan, and CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan E-mail: [email protected]; [email protected] Phone: +81 (0)42 4435156. Fax: +81 (0)42 4435156

∗

To whom correspondence should be addressed The University of Electro-Communications ‡ CREST, Japan Science and Technology Agency †

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Abstract Structural stability and electronic structure of homogeneously-arranged nitrogendoped graphene have been investigated using first-principles calculations within the density functional theory. The structures of the homogeneously-doped graphene are uniquely specified by the chiral index (n, m) inherent in each model and by the doping configurations. While the formation energy increases in proportional to the nitrogen density, there are specific arrangements for which the formation energies become lower compared to the proportional trend. Such an anomalous stabilization has been found in the honeycomb-type configuration with the chiral index (n, m) which satisfies the relation n − m = 3ℓ + 2(ℓ = 0, 1, · · · ). This stabilization is originated from the lowering of the one-electron energy with the band gap formation, which is attributed to the decoupling of the degenerate states.

Keywords First-principles calculations, Structural stability, Formation energy, Electronic properties

Introduction Graphene, a two dimensional material form of carbon with atoms arranged in a honeycomb lattice, has attracted immense attention because of its exceptional electronic 1,2 and thermal 3–5 properties, and thus has established itself as one of the promising candidates for future nanoelectronic materials. To realize graphene-based electronics, modulation techniques of its electronic properties are important. The most fundamental approach to tailor the electronic properties of graphene is the doping of hetero-atoms. 6,7 For example, it has been theoretically shown that hydrogenated boron- or nitrogen-doped graphene becomes an electron-phonon superconductor with a critical temperature above the boiling point of liquid nitrogen. 8 It has been experimentally reported that the nitrogen-doped graphene film shows


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superb performance for oxygen reduction reaction associated with alkaline fuel cells. 9–11 Furthermore, the properties for doped graphene nanoribbons, which are one-dimensional carbon material, have also been studied theoretically. 12–14 The ground state for graphene nanoribbons with different zigzag edges becomes ferrimagnetic. 15,16 For thermoelectric properties, moreover, graphene/h-BN superlattices which consist of zigzag graphene nanoribbons and zigzag h-BN nanoribbons marks up to 20 times larger in the Seebeck coefficient than graphene. 17 The doped graphene can be synthesized using various experimental techniques. Nitrogen atoms can be doped into graphene using chemical vapor deposition (CVD) method, 10,18–21 NH3 annealing after ion irradiation, 22 or NH3 plasma exposure. 23 Boron-doped graphene can be also obtained using CVD method 24 or reaction with the ion atmosphere of trimethylboron decomposed by microwave plasma. 25 As for the boron-doped graphene, a homogeneouslyarranged composite has been successfully fabricated: the BC3 sheets can be grown in an epitaxial way on the NbB2 (0001) substrate. 26,27 Recent studies have been devoted to the interaction between dopants in atomic scale. It has been theoretically shown that the interaction energies between two substitutional nitrogen atoms in graphene decrease generally with increasing distance between dopants, and two doped nitrogen atoms at third or seventh nearest neighbors have very small interaction energies. 28,29 It has also been reported that carbon atoms near defects prefer to be substituted by nitrogen atoms. 28 Recently, it has been suggested that the doped boron atoms are distributed randomly in both of two distinct sublattices of graphene, 24 while the nitrogen-doped graphene shows a strong tendency for the dopants to cluster locally on the same sublattice. 20 With regard to electronic properties, it has been suggested experimentally that the nitrogen-doped graphene exhibits an n-type behavior, 10,22,23 while the boron-doped graphene has a p-type character. 24,25 A single nitrogen dopant at divacancy acts as an acceptor rather than a donor. 30 It has been claimed that two arrangements in nitrogen-doped graphene, the substitution of carbon



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atoms by nitrogen and the vacancy with pyridinic nitrogen, have opposite effects on the band structure. For the pyridinic nitrogen-doped graphene, the π band is shifted to lower binding energies, while the π band for substitutional nitrogen-doped graphene is shifted towards higher binding energies. 31 Such an opposing effect has been confirmed also for nitrogendoped graphite. The distinct localized π states appear in occupied and unoccupied regions near the Fermi level around pyridinic-nitrogen and graphitic-nitrogen species, respectively. 32 Although structural stability and electronic properties for the isolated nitrogen doping have been studied, systematic studies with respect to the nitrogen density are needed to reveal the effect of nitrogen-doping and the relation between the stabilization and electronic properties. In this work, we have systematically investigated, by changing the doping density, the structural stability and the electronic properties of nitrogen-doped graphene using firstprinciples calculations within the density functional theory. In particular, we pay attention to the interaction between nitrogen atoms in graphene.

Calculation models and method First, we have investigated the distance dependence of the interaction energy between two substitutional nitrogen atoms in graphene, in the wake of past findings. 28,29 A (4 × 4) supercell for graphene is employed, where two carbon atoms are replaced at an arbitrarily chosen site and those at its close neighbor sites by nitrogen atoms. As shown in Fig.1, the chosen site is labeled as 0 and its neighbor sites, up to the 8th neighbor, are labeled as 1 to 8, respectively. A (3 × 3 × 1) k-point grid is used to sample the Brillouin zone of the (4 × 4) supercell. The interaction energy is defined as

Ei = (ENN + E0 ) − 2EN ,

(1)

where E0 , EN , and ENN are the total energies for graphene with zero, one, and two substitutional nitrogen atoms, respectively. 4 ACS Paragon Plus Environment

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Figure 1: (4 × 4) graphene supercell. The brown balls indicate carbon atoms. Doping sites are labeled by the numbers. Next, we have prepared the homogeneously-arranged nitrogen-doped graphene in order to clarify the density dependence on the structural stability. The configurations of the homogeneously-doped graphene are uniquely identified by the chiral index (n, m) of the fundamental lattice vector of the supercell (see Fig.2) and configuration of doped atoms. Two types of doping configurations are the triangular one and the honeycomb one, namely (0,0)

(1,0)

(2,0)

(1,1)

(3,0)

(2,1)

(4,0)

(3,1)

(2,2)

(5,0)

(4,1)

(3,2)

(5,1)

(4,2)

(3,3)

(6,0)

(5,2)

(4,3) (4,3)

Figure 2: Chiral index for graphene. The red circles indicate the chiral indices which satisfy the equation (3). the configurations for which doped atoms are arranged at the triangular lattice and the honeycomb one, respectively. For instance, the (2,0)-Triangular, the (2,0)-Honeycomb, and (3,1)-Honeycomb configurations are shown in Fig.3. A (12 × 12 × 1) k-point grid is employed to sample the Brillouin zone of the (1 × 1) unit cell for graphene 1 . We choose k-points grid, for each structure, as it fits to (12 × 12)

1

The formation energy has no qualitative change by using a larger k-point grid, (24 × 24) for the primitive

cell.



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Figure 3: Calculation models for the homogeneously-arranged nitrogen-doped graphene. (a) (2,0)-Triangular model. (b) (2,0)-Honeycomb model. (c) (3,1)-Honeycomb model. The brown and white balls indicate carbon and nitrogen atoms, respectively. The dotted lines indicate the boundary of the unit cell and the thick broken lines indicate the nitrogen arrangement for the triangular and the honeycomb models. The local arrangement of two nitrogen atoms for the (2,0)-Triangular model corresponds to the 0-6 type(see Fig. 1). For the (2,0)-Honeycomb (the (3,1)-Honeycomb), the local arrangement corresponds the 0-3 type (the 0-7 type), respectively. grid of the primitive cell. Here, we define the formation energy Ef as

Ef =

(ENtotal + nN µC ) − (E total + nN µN ) , nN

(2)

where ENtotal and E total are the total energies for the nitrogen-doped graphene and the pristine graphene, and nN is the number of doped nitrogen atoms. µC and µN are the chemical potentials for carbon and nitrogen. We have adopted, in this work, the energy per an atom for pristine graphene or a nitrogen molecule as the chemical potential for carbon or nitrogen, respectively. We employed the first-principles calculations within the density functional theory. 33 The results were obtained through the use of program code, ABINIT. 34,35 We used the localdensity approximation parameterized by Perdew and Wang 36 for exchange correlation functional. The norm-conserving pseudopotentials generated by the Troullier-Martins strategy 37 were adopted. The plane wave basis set with the cutoff energy of 50 Hartree was used to expand wave functions. For all models, the structural optimization with respect to both ionic positions and the unit cell was performed until each component of the interatomic force became less than 5.0 × 10−5 Hartree/a.u. During the structural optimization, all atoms


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were kept in the initial two-dimensional plane and no buckled structures were observed.

Results and discussion Interaction energy between two substitutional nitrogen atoms Figure 4 shows the interaction energy between two doped-nitrogen atoms as a function of their distance. The interaction energies decrease with increasing distance and their value are 1.4 Interaction energy Ei (eV)

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0−1

1.2 1 0.8 0.6

0−2

0.4

0−4 0−5 0−6 0−3

0.2 0

0

1

2

3 4 Distance (Å)

0−7 5

0−8 6

Figure 4: Interaction energy between two substitutional nitrogen atoms as a function of the distance between doped atoms. The arrows indicate the third and seventh neighbor doping sites. basically positive (i.e. repulsive). However, it should be noted that nitrogen atoms prefer to locate at third or seventh nearest neighbors. Such an anomalous stabilization for the nitrogen-doped graphene has also been pointed out in the recent studies. 28,29 It has been explained that the anomalous stabilization are ascribed to the low Coulomb repulsion owing to the anisotropic redistribution of electronic charge density, which is led by the nitrogen substitution. 28 The other explanation for the stabilization has been shown that two nitrogen atoms form a strong bond through impurity resonance states appeared just above the Fermi level. 29 Let us here mention that the 0-2 arrangement has been experimentally observed, 21 although the 0-3 arrangement is locally stable structure for free-standing nitrogen-doped 7 ACS Paragon Plus Environment


graphene. 29 This inconsistency is possibly considered to be caused by an effect of the presence of substrates. It is important to discuss the effect of substrate during the CVD synthesis on the stability of local arrangement of doped nitrogen atoms. However, the discussions about the substrate effects are beyond our scope of study and remain unsettled.

Structural stability of the homogeneously-arranged nitrogen-doped graphene Figure 5 shows the formation energy of the homogeneously-arranged nitrogen-doped graphene as a function of the density of nitrogen atoms in graphene. The formation energy for the 1 Formation energy Ef (eV)

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Triangular Honeycomb

0.8 0.6 0.4 0.2 0 0

10

20 30 Density (%)

40

50

Figure 5: Formation energies of the homogeneously-arranged nitrogen-doped graphene as a functions of the density of nitrogen atoms. The arrows indicate data at the density 25.0%, 7.69%, and 4.0%, respectively. The dashed line indicates the fitting line for the data except the densities indicated by arrows. nitrogen-doped graphene increases with increasing dopant density. What has to be noticed is that for specific densities the formation energies become lower compared to the proportional trend: exceptional densities are confirmed at 25.0%, 7.69%, and 4.0% where the configurations are (2,0)-Honeycomb, (3,1)-Honeycomb, and (5,0)-Honeycomb, respectively. Such an anomaly occurs only for the honeycomb-type configurations. It should be noted that the local arrangements of nitrogen atoms in (2,0)-Honeycomb and (3,1)-Honeycomb configurations correspond to the 3rd and 7th nearest neighbors (the 0-3 and 0-7 arrangements) that 8 ACS Paragon Plus Environment

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are found to be locally stable as discussed in the previous section.

Band structures In order to explore the reason why the nitrogen-doped graphene are anomalously stabilized at the specific density, we have investigated the band structures for the homogeneouslyarranged nitrogen-doped graphene. Figure 6 shows the band structures for the pristine (2 × 2) graphene, (2,0)-Triangular, and (2,0)-Honeycomb. The Fermi level for the perfect (a) (2 × 2) Graphene

(b)

(2,0) Triangular

(c)

10

10

10

5

5

5

(2,0) Honeycomb

M(1), M(2) M(LUCB) Energy (eV)

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0

0

0 M(HOVB)

-5

-5

-10

-5

-10 Γ

M

K

Γ

-10 Γ

M

K

Γ

Γ

M

K

Γ

Figure 6: Band structures for (a) (2 × 2) pristine graphene, (b) (2,0)-Triangular nitrogendoped graphene (12.5%), (c) (2,0)-Honeycomb nitrogen-doped graphene (25.0%). The red circle for (a) indicates the doubly-degenerated LUCB states at the M point (denoted as M(1) and M(2)). For (2,0)-Honeycomb, this state is decoupled into M(HOVB) and M(LUCB), as marked by the red circles in (c). graphene is just located at the so-called Dirac point. For the nitrogen-doped graphene, the Fermi level is shifted up into the conduction band, which is due to the electron donation from the doped-nitrogen atom to the anti-bonding π ∗ band. 38 While the nitrogendoped graphene with the (2,0)-Triangular configuration exhibits a metallic nature, that with the (2,0)-Honeycomb one shows a semiconducting band structure with an indirect band gap of 0.27 eV between the M point of highest occupied valence band (HOVB) and the Γ point of lowest unoccupied conduction band (LUCB). It has been confirmed that the other anomalously-stabilized systems, i.e. (3,1)-Honeycomb and (5,0)-Honeycomb, also have finite



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bandgaps. Such a band gap formation leads to the lowering of the one-electron energy for HOVB. This is the origin of the anomalous stabilization for the specific density of dopants.

Probability density We explain the mechanism of the band gap formation from the viewpoint of the orbital symmetry. Figures 7(a) and 7(b) show the probability densities of the pristine graphene for the doubly-degenerate LUCB at the M point. The two identical states are denoted as

Figure 7: Probability densities for (a) and (b) the doubly-degenerate LUCB of the pristine graphene at the M point and (c) the HOVB and (d)the LUCB for (2,0)-Honeycomb at the M point. The brown and white balls indicate carbon and nitrogen atoms, respectively. The light-yellow shadowed area indicates the isosurface of the probability density projected into the graphene plane. M(1) and M(2) (see Fig.6(a)). Figures 7(c) and 7(d) show the probability densities of the (2,0)-Honeycomb configuration for M(HOVB) and M(LUCB) (see Fig.6(c)). As clearly seen in Fig. 7(d), the probability density of M(LUCB) for (2,0)-Honeycomb has a similar spatial distribution to that of M(2) for graphene and is localized only around carbon atoms. On the other hand, the probability density of M(HOVB) for (2,0)-Honeycomb is localized not only on carbon atoms but also on nitrogen atoms as shown in Fig.7(c). This state corresponds


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to the M(1) state for pristine graphene. Since the one-electron energy of the M(HOVB) for (2,0)-Honeycomb becomes lower than that of M(2) state for graphene, which is derived from the symmetry breaking with doping, the band gap is formed. The schematic energy diagram for the local bondings between C-C and C-N is shown in Fig.8. The one-electron energy for C N

C

C

C-2pz

C-2pz

N 2pz C N

C

C

Figure 8: Schematic energy diagram for the local bondings between C-C and C-N. N-2p is lower than that for C-2p, so that the anti-bonding π ∗ orbital for N-C has a lower energy than that for C-C.

Geometrical condition for the band gap formation The condition the symmetry breaking, discussed in the previous section, can be understood in terms of the symmetry in the Brillouin zone. Figure 9 shows the relationship between the symmetry points for the graphene primitive cell and those for the unit cell of the nitrogendoped graphene with the (2,0) chiral index. The K and K’ points for the primitive cell

K K

K’

K’

K K’

Figure 9: Brillouin zones for the graphene primitive cell and for the unit cell for the nitrogendoped graphene with the (2,0) configuration. coincide with the K’ and K points for the (2,0) configuration, respectively. This relationship with respect to the symmetry points in the reciprocal lattice is satisfied for the other 11 ACS Paragon Plus Environment


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configurations, e.g. the (3,1), (5,0), (4,2) configurations and so on. This condition can be rewritten by the chiral index (n, m) with the following equation,

n − m = 3ℓ + 2 (ℓ = 0, 1, 2, · · · ).

(3)

The equation above itself is indeed the condition for the symmetry points in the reciprocal lattice; if n and m satisfy the relation n − m = 3ℓ (or n − m = 3ℓ + 1), then the K point of the primitive cell coincides the Γ (or K) point of the supercell, respectively. We emphasize that the anomalous stabilization, discussed in the previous sections, takes place only for honeycomb doping configurations with the chiral indices satisfying the equation (3). Indeed, we have confirmed that the semiconductive band structure for the nitrogen-doped graphene with the honeycomb configuration for the chiral indices, (2,0), (3,1), (5,0), (4,2), and (6,1). Under this condition, the homogeneously-arranged nitrogen-doped graphene is preferentially stabilized because of the band gap formation resulting in the lowering of the one-electron energy. Our calculations are totally consistent with the results by Xiang et al.; The model C3 N (C12 N) in their paper is equivalent to the (2,0)-Honeycomb (the (3,1)-Honeycomb) in our models, respectively. Our interpretation of the stabilization mechanism provides a more general explanation about the relationship between the stability and the electronic properties of homogeneously-doped graphene.

Conclusions We have studied the structural stability and the band structures for the homogeneouslyarranged nitrogen-doped graphene by changing the doping density. Two types of doping configurations, the triangular lattice and the honeycomb lattice, are taken account. The formation energy increases generally with increasing density of nitrogen atoms. Apart from this proportional trend, the anomalous stabilization occurs for the honeycomb-lattice doping 12 ACS Paragon Plus Environment

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configuration with the specific doping density. The chiral index of the supercell satisfies the relation n − m = 3ℓ + 2 (ℓ = 0, 1, 2, · · · ). The band structure of the doped graphene for the exceptionally-stable configuration exhibits semiconductive behavior, while for the rest of configurations a metallic band structure is confirmed. At the specific density, the one-electron energy is lowered by the band gap formation. The mechanism of the band gap formation is attributed to the decoupling of the degenerate states. The effect of other doping configuration, such as pyridinic nitrogen vacancy that is found to be relevant to the band gap formation, 39 will be discussed in forthcoming papers.

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Graphical TOC Entry The chiral index (n,m) (0,0)

(1,0)

(2,0)

(1,1) Formation energy Ef (eV)

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

1

(3,0)

(2,1)

Triangular Honeycomb

(4,0)

(3,1)

(2,2)

(5,0)

(4,1)

(3,2)

(6,0)

(5,1)

(4,2)

(5,2)

0.5

(5,0) 0 0

(3,1)

(3,3)

(2,0)

25 Density (%)

(4,3)

50


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Anomalous Stabilization in Nitrogen-Doped Graphene - American

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