GUAN Xiao-Min ZHANG Hong-Yu

ZHANG Meng LUO You-Hua②

(Department of Physics, East China University of Science and Technology, Shanghai 200237, China)

1 INTRODUCTION

Graphene, a monolayer of graphite, has gained much attention since its first experimental synthesis in 2004[1]. Due to its highly stable sp2hybrid structure and considerably high charge carrier mobility, graphene is expected to become one of the most promising materials for electronic devices[2].However, graphene behaves as a semi-metal with zero band gap at the Dirac point, which restricts its applications in semiconductor materials. As everyone knows, graphene with an opened band gap is the new front-runner in field effect transistors (FETs). In recent years, a huge number of attempts have been made to open a sizable band gap both experimentally and theoretically. The generally available methods involve: surface modification with atoms or polar molecules[3-7], chemical doping[8-15], applying electric fields[16-17], deposition on substrates[18-20],generating graphene ribbons[21-23]and symmetry breaking. The formation of new chemical bonds has great influence on the stability of graphene. Doping heteroatom can cause deviation from sp2framework,break the π bond, and then open the band gap around the Fermi energy.

The excellent doped system should be in need of large band gap, high binding energy and small deformation. For boron/nitrogen codoped graphene with lithium atom adsorbed, the maximum gap can reach 0.49 eV[12], while single B or N atom doping graphene opens only a band gap of 0.14 eV[24],which is not large enough. Phosphorus or sulfur doped monolayer graphene has a 0.67 or 0.57 eV gap[6], but the distortion of it is extremely obvious.

In order to widely apply graphene to the field of electronics by opening band gap, single atom chemically doped graphene has been investigated by density functional theory in the present work.Platinum, cobalt, and indium single atoms have been successfully doped in graphene experimentally[14],which can strongly support this article. The two largest band gaps, 0.62 and 0.60 eV, were induced by doping As and Sn, yet their binding energies were not high enough. Owing to the strong electronnegativity of O atom and similar atomic radius to that of carbon atom, O atom doped graphene (O-graphene)has a band gap of 0.52 eV with little distortion and high stability. And doping Fe atom opens a band gap of 0.54 eV with high binding energy and slight distortion for strong hybridization between 3d orbital of Fe and graphene. They are excellent candidates for electronic materials.

2 METHOD

All calculations performed in this paper are based on spin-unrestricted density functional theory (DFT).Core treatment has chosen DFT semi-core pseudopots (DSPPs), which introduce some degree of relativistic correction into the core. 4 × 4 graphene unit cell containing 32 atoms is adopted to model the doped system where a heteroatom substitutes one carbon atom. To avoid interlayer interaction, the distance along the z-axis is set to 15 ?. During the geometry optimization, the conver- gence thresholds for the maximum energy change and maximum force are specified of 1 × 10-5Ha and 0.002 Ha/?.All parameter accuracy of the calcula- tion is selected to be fine, and the Brillouin-zone is sampled by 3 × 3 × 2 k-points within Mon- khorst-Pack grid,which is one of the most popular schemes for hexagonal systems. Band structure is calculated along the path of Γ–Κ–Μ–Γ.

In order to ensure the reliability of results, three different functions PBE[25], PW91[26]and BLYP[27-28]within generalized gradient approximation (GGA)are used as the exchange-correlation functional respectively by DMol3 5.0[29], then their outcomes show tiny discrepancies. 0.65 and 0.57 eV band gaps and metallicity induced by phosphorus, sulfur and aluminum doping graphene have a good agreement with Denis[6]. B- and N-graphene display a bit difference from Rani[24]. As we all know, band gap always goes to be underestimated by the GGA analysis, yet the values under these three methods are stable enough, so this is worth for further discussion.

Binding energy between the doped heteroatom and the graphene with single vacancy is defined as

wheretE refers to the total energy of the system;are the energies of a single doped atom and optimized graphene with single vacancy, respectively. The following analysis is based on the PBE.

3 RESULTS AND DISCUSSION

The binding energy (Eb)and band gap (Eg)of some heteroatom doped graphenes have been calculated by DFT method, and the results are shown in Table 1.

Table 1. Binding Energy Eb (eV)and Band Gap Eg (eV)of As etc. Single Atom Doped Graphene by Using Three Different Functionals. “ / ” Indicates Metallicity

?

It was found that the system has 0.62 eV / 0.60 eV band gap by embedding single As/Sn atom into pure graphene by Figs. 1 and 2, and the second larger 0.54 eV by Se, as shown in Fig. 3. The new As-graphene belongs to p-type semiconductor on account that 0.47 e electrons have been transferred from C atoms to As, and the Fermi level has been dropped below the Dirac point by Fig. 3a, which means hole doping. Similar features also come up in Sn- and Se-graphene systems.

Fig. 1. (color online)Optimized supercell structure from top of the As/Sn/Se doped graphene

Fig. 2. (color online)Optimized supercell structure from side of the As/Sn/Se doped graphene

Fig. 3. Band structure of the As/Sn/Se doped graphene

However, remarkable deformation in Fig. 2 and not enough high binding energy make these doped graphenes defective, thus influencing the stability of the system. The shortest bond lengths between heteroatom and the carbon atom are As?C 1.875 ?,Sn?C 2.136 ? and Se?C 1.869 ?, much longer than C?C. Yet on the positive side, such distortion broke the sp2hybridization to make the system more active,which can open up new application fields of graphene.

Among all the results, it is lucky to find that O-and Fe-doped graphene (Fe-graphene)have larger binding energy than As-graphene and big band gap(Table 1). Fig. 5a shows that the distortion of graphene system induced by O atom doping Fig. 4a is so slight, which is attributed to the similar atomic radius of O atom to that of C atom. But for the other heteroatoms, they are too large to preserve the hexagonal structure. As a result, those other atoms protrude from graphene surface obviously, followed by the nearest surrounded carbon atoms, and then the second-nearest carbon atoms.

Fig. 4. (color online)Optimized supercell structure from top of the O/Fe/Ga doped grapheme

Fig. 5. (color online)Optimized supercell structure from side of the O/Fe/Ga doped graphene

The system doped of O atom shows C?O bond length of 1.490 ?, little longer than that of C?C by 1.420 ?, and the nearest three C atoms protrude slightly from the surface by 0.024 ?. Focusing on the band structure of O-graphene in Fig. 6a, substituted for C atom, the O atom combines with three dangling bonds, and then the spare valence electrons cause Fermi level to shift up the Dirac point. We can see that O atom doping equals to electron doping,for the Fermi level has been shifted up the Dirac point, thus O-graphene is a n-type doped semiconductor. During the interaction process, charge transfer between the surrounded C atoms is intense,which may be caused by the strong electronnegativity of the O atom. The excellent sp2hybridization has been broken by electron redistribution, resulting in the separation of conduction band and the valence band.

Fe atom is the only metal atom that can open a large band gap with small structural distortion Fig. 4b.Moreover, Fe-graphene has comparatively large binding energy to keep the stability, and the band gap is opened by 0.54 eV in Fig. 6b. In Fe doped graphene, the bond length of Fe?C is 1.754 ?, and the nearest C atom protrudes from the surface by 0.275 ?, followed by the second one by 0.06 ?.Small deformation is shown in Fig. 5b. The interaction between Fe atom and graphene is strong due to the intense charge transfer. Fe-graphene should be p-type doped semiconductor due to the slight downward shift of Fermi level. While embedding a Fe atom, a doping state is brought about, which is the curve approaching 0.5 eV, as displayed in Fig. 6b.Then we can find that the lowest point of conduction band is 0.54 eV at the Γ point and the highest point of valence band is 0.00 eV at the K point, which means that this gap belongs to an indirect band gap.Near the Fermi level, the 3d orbital strongly hybridizes with graphene to open a band gap.Nevertheless, this hybridization shortens the Fe?C bond length and stabilizes the Fe-graphene configuration with high binding energy.

Fig. 6. Band structure of the O/Fe/Ga doped graphene

In point of doping In, Sb, Te, Ge and Pb heteratoms, the systems are not stable enough with small binding energy, in despite of opening sizable gaps.The considerably obvious corrugations created by heteroatom are fallen with atoms of long radius. The weak interaction between doped atom and graphene can not open a large band gap. Nevertheless, the nearest carbons to heteroatom restricted by sp2hybridization of pure graphene protrude from the system surface and become more active when doping these heteroatoms. Maybe we can suppose that doping heteroatom can increase the graphene reactivity, and then the new system can be applied to sensor or catalyst areas preferably. However, to open a large band gap, doping O and Fe single atoms meet the conditions for chemical doping.

It is also worth to point out that doping Ga single atom into graphene Fig. 4c can bring up the Fermi level by 0.73 eV, and then the π band crosses the Fermi level obviously. With stable inner electron structure, Ga atom has three valence electrons,working with three dangling bonds of single vacancy graphene. Increasing the Fermi level makes doped graphene display metallic, which may dig out another application of grapheme.

4 CONCLUSION

For the sake of more extensive application areas of graphene, this paper employed the first principles to analyze heteroatom doped graphene in order to get a large band gap. Three different functionals have been adopted to ensure the reliability of the results. As-, Sn- and Se-graphene are lack of stability in spite of their large gaps. In O-graphene, electron redistribution breaks the excellent sp2hybridization, and thus opens a band gap of 0.52 eV with slight structural distortion and stabilized construction. Affected by strong hybridization, Fe-graphene has a 0.54 eV band gap with high binding energy and little deformation. Ga-grahene is the only system that shows metallicity among results. We can believe that broad application of graphene will make electronic products develop rapidly.

(1)Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Electric field effect in atomically thin carbon films. Science 2004, 306, 666?669.

(2)Hu, Y. J.; Jin, J.; Zhang, H.; Wu, P.; Cai, C. X. Graphene synthesis, functionalization and applications in chemistry. Acta Phys. Chim. Sin. 2010, 26, 2073?2086.

(3)Zhou, J.; Wu, M. M.; Zhou, X.; Sun, Q. Tuning electronic and magnetic properties of graphene by surface modification. Appl. Phys. Lett. 2009, 95,103108?103108(3).

(4)Tian, X.; Xu, J.; Wang, X. Band gap opening of bilayer graphene by F4-TCNQ molecular doping and externally applied electric field. J. Phys. Chem.2010, 114, 11377?11381.

(5)Balog, R. Band gap opening in graphene induced by patterned hydrogen adsorption. Nature Mat. 2010, 9, 315?319.

(6)Denis, P. A. Band gap opening of monolayer and bilayer graphene doped with aluminium, silicon, phosphorus, and sulfur. Chem. Phys. Lett. 2010,492, 251?257.

(7)Akturk, E.; Ataca, C.; Ciraci, S. Effects of silicon and germanium adsorbed on graphene. Appl. Phys. Lett. 2010, 96, 123112?123112(3).

(8)Denis, P. A.; Faccio, R.; Mombru, A. W. Is it possible to dope single-walled carbon nanotubes and graphene with sulfur. ChemPhysChem. 2009, 10, 715?722.(9)Dai, J.; Yuan, J.; Giannozzi, P. Gas adsorption on graphene doped with B, N, Al, and S: a theoretical study. Appl. Phys. Lett. 2009, 95,232105?232105(3).

(10)Zanella, I.; Guerini, S.; Fagan, S. B.; Mendes Filho, J.; Souza Filhol, A. G. Chemical doping-induced gap opening and spin polarization in graphene.Phys. Rev. B 2008, 77, 073404?073404(4).

(11)Prashant, P. S; Vijay, K. Direct band gap opening in graphene by BN doping: ab initio calculations. Phys. Rev. B 2011, 84, 125401?125401(6).

(12)Deng, X. H.; Wu, Y. Q.; Dai, J. Y.; Kang, D. D.; Zhang, D. Y. Electronic structure tuning and band gap opening of graphene by hole/electron codoping. Phys. Let. A 2011, 375, 3890?3894.

(13)Mary, C. S. E.; Tien, Q. N.; Hideaki, K. Analysis of band gap formation in graphene by Si impurities: local bonding interaction rules. Chem. Phys.Let. 2011, 515, 85?90.

(14)Wang, H. T.; Wang, Q. X.; Cheng, Y. C. Doping monolayer graphene with single atom substitutions. Nano. Lett. 2012, 12, 141?144.

(15)Cruz-Silva, E.; Barnett, Z. M.; Sumpter, B. G.; Meunier1, V. Structural, magnetic, and transport properties of substitutionally doped graphene nanoribbons from first principles. Phys. Rev. B 2011, 83, 155445?155445(9).

(16)Avetisyan, A. A.; Partoens, B.; Peeters, F. M. Electric field tuning of the band gap in graphene multilayers. Phys. Rev. B 2009, 79,035421?035421(7).

(17)Mak, K. F.; Lui, C. H.; Shan, J.; Heinz, T. F. Observation of an electric-field-induced band gap in bilayer graphene by infrared spectroscopy. Phys.Rev. Lett. 2009, 102, 256405?256405(4).

(18)Shemella, P.; Nayak, S. K. Electronic structure and band-gap modulation of graphene via substrate surface chemistry. Appl. Phys. Lett. 2009, 94,032101?032101(3).

(19)Peng, X.; Ahuja, R. Symmetry breaking induced band gap in epitaxial graphene layers on SiC. Nano. Lett. 2008, 8, 4464?4468.

(20)Lu, Y. H.; He, P. M.; Feng, Y. P. Asymmetric spin gap opening of graphene on cubic boron nitride (111)substrate. J. Phys. Chem. C 2008, 112,12683?12686.

(21)Nilsson, J.; Castro Neto, A. H.; Guinea, F.; Peres, N. M. R. Transmission through a biased graphene bilayer barrier. Phys. Rev. B 2007, 76,165416?165416(10).

(22)Son, Y. W.; Cohen, M. L.; Louie, S. G. Energy gaps in graphene nanoribbons. Phys. Rev. Lett. 2006, 97, 216803?216803(4).

(23)Xu, N.; Zhang, C.; Kong, F. J.; Shi, Y. J. Transport properties of corrugated graphene nanoribbons. Acta Phys. Chim. Sin. 2011, 27, 2107?2110.

(24)Rani, P. J. Designing band gap of graphene by B and N dopant atoms. VK 2012 arXiv:1209.5228 [cond-mat.mes-hall].

(25)Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865?3868.

(26)Perdew, J. P.; Wang, Y. Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Rev. B 1992, 45, 13244?13249.

(27)Becke, A. D. A multicenter numerical integration scheme for polyatomic molecules. J. Chem. Phys. 1988, 88, 2547?2547(7).

(28)Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 1988, 37, 786?789.

(29)Delley, B. DMol3 DFT studies: from molecules and molecular environments to surfaces and solids. Comput. Mater. Sci. 2000, 17, 122?126.