Formation, stabilities, and electronic properties of nitrogen defects in graphene

We investigate nitrogen-doping effects in a graphene sheet using a first-principles electronic-structure study in the framework of density-functional theory. As possible configurations of nitrogen impurities in graphene, substitutional nitrogen and pyridine-type defects around a monovacancy and around a divacancy are considered, and their energetics and electronic structures are discussed. The formation-energy calculations suggest that substitutional doping of the nitrogen atom into a graphene sheet is energetically the most favorable among the possible nitrogen-doping configurations. Furthermore, by comparison of the total energy of the pyridine-type defects with that of the substitutional nitrogen defect in graphene, it is revealed that formation of the pyridine-type defects becomes energetically favorable compared with formation of the substitutional nitrogen defect in the presence of a vacancy. From the results of electronic-band-structure calculations, it is found that the nitrogen-impurity states appear around the Fermi level as either acceptorlike or donorlike states, depending on the atomic geometries of the nitrogen impurities in graphene. We also calculate the scanning tunneling microscopy (STM) images associated with impurity-induced electronic states for future experimental identification of nitrogen impurities. The simulated STM images of the three N-doping configurations considered here are found to be strongly dependent on the local density of states around the nitrogen impurity, and therefore the doping configurations should be distinguishable from one another. The similarities and differences of the electronic structures and STM corrugations between N-doped and undoped graphenes are also discussed.

Figure 1

Atomic configurations of the N-doped graphenes and undoped but defective graphenes considered: (a) substitutional nitrogen defect (C${}_{31}$N), (b) trimerized pyridine-type defect (C${}_{28}$N${}_3$), (c) monomeric pyridine-type defect (C${}_{30}$N), (d) dimerized pyridine-type defect (C${}_{29}$N${}_2$), (e) tetramerized pyridine-type defect (C${}_{26}$N${}_4$), (f) a monovacancy (C${}_{31}$), and (g) a divacancy (C${}_{30}$). In each case, the geometry is fully optimized in the framework of density-functional theory (see text). The dashed lines show the supercell.

Figure 2

(a) Energy band and (b) isosurface of electron density of substitutional nitrogen defect in graphene (see text). The isosurface value of the electron density is set to 0.03 electron/Å${}^3$. The Fermi energy is set to zero. The dashed lines show the supercell.

Figure 3

(a) Energy band and (b)–(d) isosurfaces of electron densities of the three states associated with trimerized pyridine-type defects in graphene (see text). The isosurface value of the electron density is set to 0.03 electron/Å${}^3$. The Fermi energy is set to zero. The dashed lines show the supercell.

Figure 4

(a) Energy band and (b) isosurface of electron density of tetramerized pyridine-type defects in graphene (see text). The isosurface value of the electron density is set to 0.03 electron/Å${}^3$. The Fermi energy is set to zero. The dashed lines show the supercell.

Figure 5

Simulated STM images of N-doped graphenes with (a) substitutional nitrogen and (b) trimerized and (c) tetramerized pyridine-type defects. The STM images are generated at applied bias voltages of (a) $+0.5$, (b) $-0.5$, and (c) $-0.5$ eV. The maximal height of corrugations in the STM images is set to be approximately 5 Å above the graphene sheet. The dashed lines show the supercell.