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Effect of hydrogenation on the band gap of graphene nano-flakes
Thin Solid Films 554 (2014) 199–203
Contents lists available at ScienceDirect
Thin Solid Films journal homepage: www.elsevier.com/locate/tsf
Effect of hydrogenation on the band gap of graphene nano-flakes Hiroto Tachikawa ⁎, Tetsuji Iyama, Hiroshi Kawabata Division of Materials Chemistry, Graduated School of Engineering, Hokkaido University, Sapporo 060-8628, Japan
a r t i c l e
i n f o
Available online 7 September 2013 Keywords: Graphene Hydrogen atom Band gap DFT Broken symmetry
a b s t r a c t The effects of hydrogenation on the band gap of graphene have been investigated by means of density functional theory method. It is generally considered that the band gap increases with increasing coverage of hydrogen atom on the graphene. However, the present study shows that the band gap decreases first with increasing hydrogen coverage and reaches the lowest value at finite coverage (γ = 0.3). Next, the band gap increases to that of insulator with coverage from 0.3 to 1.0. This specific feature of the band gap is reasonably explained by broken symmetry model and the decrease of pi-conjugation. The electronic states of hydrogenated graphene are discussed. © 2013 Elsevier B.V. All rights reserved.
1. Introduction During the last decade, the graphene-based molecular devices were widely used as energy-related material, sensor, field-effect transistor, and biomedical application, due to their excellent electrical, mechanical, and thermal properties [1,2]. As well as pure graphene, functionalized graphenes were synthesized and characterized by several groups [3–6]. The tuning of graphene-based molecular devices to obtain the higher performance molecular devices is now an important field. Recently, Elias et al. have investigated hydrogenated graphene by exposing to hydrogen plasma [7]. They found that a highly conductive graphene is converted from semimetal to insulator after the hydrogenation. Raman spectroscopy revealed that the hydrogenation breaks the π-bonding system of graphene surface after the formation of sp3 carbon–hydrogen bonds. Transmission electron microscopy study indicates that the original hexagonal bonding arrangement is retained, whereas the lattice constant is significantly reduced. The hydrogenation is reversible through annealing, thereby restoring the conductivity and structure of graphene. This reversibility also creates the possibility of using such materials for hydrogen storage. Thus, the addition of hydrogen atom can be used to tune the electronic properties of graphene-based molecular devices [8]. From a theoretical point of view, density functional theory (DFT) calculations of hydrogenated graphene have been carried out by several groups [9–14]. Sofo et al. proposed that full hydrogenation of graphene forms a stable two dimensional (2D) hydrocarbon named graphane [10]. By means of the DFT computations, they also predicted that graphane has a wide band gap. Gao et al. calculated the band gap as a
⁎ Corresponding author. Fax: +81 11 706 7897. E-mail address: [email protected] (H. Tachikawa). 0040-6090/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.tsf.2013.08.108
function of coverage in the range of 66–100% [11]. They found that the band gap increases gradually up to 8 eV. Casolo et al. investigated the adsorption of hydrogen atom to a 5 × 5 surface unit cell of graphene using DFT method [14]. The binding energy per hydrogen atom was calculated to be 0.8–1.9 eV. It suggested that the change of hybrid orbital from sp2 to sp3 is important due to the hydrogen atom adsorption to graphene. Thus, the binding energy of hydrogen atom on the surface of graphene is quite well understood. However, the coverage dependence of band gap was only investigated in the range of 0.7– 1.0 coverage (i.e., higher coverage regions). Therefore, the relation between the band gap and coverage in a wider coverage range remains unclear. In the present study, the DFT method was applied to the hydrogen atom interacting with a graphene flake. The dependence of band gap on hydrogen coverage was investigated in detail in order to elucidate the effects of hydrogen addition on the electronic structures of graphene nano-flakes. In a previous paper [15], we conducted a preliminary investigation on the effects of hydrogen addition on the electronic states of graphene surface. We found that hydrogen addition causes a lowering of band gap of graphene flake in case of low coverage regions. However, the calculation was carried out at the semi-empirical PM3 molecular orbital level. In the present study, accurate DFT calculation was performed for the hydrogen added graphene to elucidate the origin of specific band gap property. The paper is organized as follows: in Section 2, we present the method of calculations. In Section 3, the structures and electronic states of hydrogenated graphene with 19 benzene rings are reported. Subsequently, we give the results of larger graphene with 37 benzene rings to elucidate the size-dependence of the band gap. In Section 4, we discuss the specific band gap properties of hydrogenations.
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2. Method of calculation Graphene nano-flakes composed of 19 and 37 benzene rings (n = 19 and 37) were used as models (denoted by GR(19) and GR(37), respectively). The edge carbon of graphene was terminated by a hydrogen atom. In case of hydrogenation of GR(19), even hydrogen atoms (from m = 2 to 54) were bonded to the surface carbon atoms, where m means the number of hydrogen atoms added to the surface. This addition causes a change of coverage from zero to 1.0. The hydrogen atoms were first added to the carbon atoms at central region of GR(19), and then the additions were expanded to the edge region. Two hydrogen atoms were added to carbon atoms on the surface and reverse side. In case of GR(37), a similar hydrogenation was performed up to the maximum hydrogen atoms (m = 96). The structures and electronic states of normal and hydrogenated graphenes were calculated by means of DFT method at the B3LYP/ 6-31G(d) level using Gaussian 03 program package [16]. The excitation energy and band gap were calculated by means of time dependent (TD) DFT method. The electronic states of all molecules were obtained by natural population analysis (NPA) and natural bond orbital (NBO) methods at the B3LYP/6-31G(d) level. The levels of theory calculated for GR(19) and GR(37) were B3LYP/6-31G(d) and 3-21G(d), respectively. These levels give a reasonable electronic state of the graphene as shown in previous calculations [17–20]. 3. Results A. Structures of hydrogenated graphene flakes The structure of GR(19) optimized at the B3LYP/6-31G(d) level is
Fig. 1. Optimized structure of pure graphene GR(19)(m = 0), and hydrogen added graphene flakes (m = 2 and 6) obtained at the B3LYP/6-31G(d) level. Hydrogen atom is bound to central carbon atoms. Notation of m means number of hydrogen atoms added to the graphene. The structures were fully optimized at the B3LYP/6-31G(d) level.
illustrated in Fig. 1 (m = 0). The optimized structure of GR(19) (m = 0) showed a purely planar form. The C–C bond distance was calculated to be 1.420 Å around the center of graphene. Next, two hydrogen atoms were added to the carbon atoms around the central region of GR(19), and then the structure was fully optimized. The optimized structure is illustrated in Fig. 1 (m = 2). The C1–H bond distance between added hydrogen atom and carbon was calculated to be r(C1–H) = 1.111 Å, where C1 means the carbon atom added by a hydrogen atom. The structure around the C1–H bond has a pyramidal form, and the carbon atom was 0.39 Å higher than the graphene plane. The C–C bond length was 1.522 Å around the C1–H bond, which is 0.10 Å longer than that of m = 0. The electronic states of carbon atoms at the binding site (denoted by C1 and C2) were changed by the addition of hydrogen atoms. To elucidate the change of electronic state of the carbon atoms, the NBO analysis was carried out for m = 0 and 2. The NBO of the C1–C2 bond of free graphene (m = 0) is expressed by 1:99 σ C¼C ¼ 0:707 sp
C1
1:99 þ 0:707 sp
C2
ð1Þ
where, C1 and C2 mean carbon atoms in the binding and neighbor sites, respectively. After the addition of the hydrogen atoms, the NBO for m = 2 was expressed by 2:80 σ C−C ¼ 0:707 sp
C1
2:80 þ 0:707 sp
C2
ð2Þ
The coefficient of sp orbital for m = 0 (1.99) was close to 2.00, indicating that the orbitals of the carbon atoms are close to a sp2 orbital before the addition. After the addition of hydrogen atoms, the coefficient is changed from 1.99 to 2.80. The result indicates that the binding nature is changed from sp2 to sp3-like orbitals after the addition of hydrogen atoms. This feature is the same as reported in previous works [7,21]. The structure for m = 6 is also given in Fig. 1 (lower). The C–H bond length was 1.016 Å, and the structure of the six-membered ring added by hydrogen atoms takes an armchair form, which is close to the structure of cyclohexane molecule. The C–C bond length was 1.526 Å around the binding site, which is slightly elongated from that of m = 2. The structures of middle and high coverage graphenes (m = 24 and 54) are illustrated in Fig. 2. In case of m = 24, all carbon atoms in bulk surface are covered with the hydrogen atoms. However, the π orbitals in the edge region still remain. In m = 54, there is no
Fig. 2. Optimized structure of hydrogen added graphene flakes GR(19)(m = 24 and 54) with higher coverage. The structures were fully optimized at the B3LYP/6-31G(d) level.
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Table 1 Relationship between numbers of hydrogen atom and coverage (γ). GR(19)
Fig. 3. Excitation energies of hydrogen added graphene flakes plotted as a function of number of hydrogen atom number (m). The values are calculated at the B3LYP/631G(d) level. Dashed line indicates the band gap of pure graphene flake GR(19)(m = 0).
conjugation as shown in Fig. 2 (m = 54). The C–C bond lengths for m = 24 and 54 were calculated to be 1.529 and 1.543 Å, respectively. This result indicates that the C–C bond is changed from double to single bonds at higher coverage. B. Band gap In previous section, it was found that the addition of hydrogen atom on GR(19) diminishes the numbers of π-conjugation in graphene. This effect may affect the excitation energy and band gap of the graphene. The excitation energies of GR(19)(m = 0–54) are plotted as a function of m. In m = 0, the low-lying excitation energies were calculated to be 2.24, 2.39, 3.12, 3.12, 3.14, and 3.24 eV, indicating that the band
Fig. 4. Excitation energies of hydrogen added graphene flakes plotted as a function of coverage of hydrogen atom on graphene surface (γ). The values are calculated at the TDDFTB3LYP/6-31G(d) level. The orbital energies of HOMO and LUMO and the energy gap (HOMO–LUMO) are plotted as well.
GR(37)
m
γ
m
γ
0 2 4 6 8 10 14 16 24 54
0.00 0.04 0.07 0.11 0.15 0.19 0.26 0.30 0.44 1.00
0 2 4 6 8 12 24 48 54 78
0.00 0.02 0.04 0.06 0.08 0.13 0.25 0.50 0.56 0.81
gap of GR(19) is Eg(m = 0) = 2.24 eV. This band gap of GR(19) (m = 0) is indicated by a dashed line in Fig. 3. In m = 2, the lowest excitation energy was 2.12 eV, which is 0.12 eV lower than that of m = 0. All excitation energies are plotted in Fig. 3 as a function of m. Although the band gaps of m = 4 and 6 (2.55 and 2.86 eV) were slightly larger than that of m = 0 (2.24 eV), the band gaps of m = 10–24 were lower than that of m = 0. For example, the energies of band gap of m = 16 and 24 were 1.31 and 1.41 eV, respectively. The lowest band gap was appeared at m = 16. On the other hand, fully saturated graphene (m = 54) has a wide band gap (6.95 eV). Band gaps were calculated as a function of coverage of hydrogen atom on graphene surface (γ), together with the highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gap and the orbital energies of HOMO and LUMO. The results are plotted in Fig. 4. Relation between numbers of hydrogen atom and coverage (γ) is given in Table 1. Similar calculations were carried out at the CAM-B3LYP/6-31G(d) level for comparison. All calculations showed that the band gap is minimized at the coverage of 0.3 (i.e., γ = 0.3). C. Orbital energies of hydrogenated graphene In previous section, it was shown that the band gap is minimized at γ = 0.3. In order to elucidate the reason why the band gap is minimized at a finite coverage value (γ = 0.3), the electronic states of partial hydrogenated graphene were analyzed in details. Fig. 5 shows the coverage dependence of the orbital energy. The highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO–LUMO) of graphene without hydrogen atom are doubly
Fig. 5. The orbital splitting of HOMO and LUMO energies and the energy gap (HOMO–LUMO) are plotted as a function of coverage of hydrogen atom on graphene surface (γ). Arrows indicate the excitation energies at γ = 0.04, 0.30, and 1.0.
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Fig. 6. Molecular orbital energy diagrams of hydrogen added graphene flakes GR(19) (γ = 0, 0.04, and 0.30) calculated at the B3LYP/6-31G(d) level. Arrow indicates the first electronic excitation.
degenerated to each other at γ = 0. On the other hand, both HOMO and LUMO split into two single orbitals each other at the finite coverage value (0.0 b γ b 0.45). The orbital energies and spatial distribution of molecular orbitals of γ = 0, 0.04 and 0.30 are given in Fig. 6. In γ = 0, the energy of HOMO is −5.0 eV, and the orbital is doubly degenerated. The LUMO has the same feature as that of HOMO. The HOMO–LUMO gap was calculated to be 2.65 eV. In case of γ = 0.04, HOMO split into two levels (−5.2 and −4.5 eV). Also, LUMO splits into two levels (−2.5 and −1.7 eV) as well. The HOMO–LUMO gap was calculated to be 1.96 eV in γ = 0.04. The energy gap decreased from 2.65 to 1.96 eV with increasing γ from zero to 0.04. In γ = 0.30, the energies of HOMO and LUMO were −4.00 and −2.95 eV, respectively. The HOMO–LUMO gap is 1.05 eV. Thus,
Fig. 7. Excitation energies of hydrogen added graphene flakes plotted as a function of hydrogen atom number (m). The values are calculated at the CAM-B3LYP/6-31G(d) level.
the orbital energies were split by the hydrogen addition. The origin of this splitting is caused by a symmetry broken of the orbitals due to the hydrogen addition. D. Exchange-correlation functional dependence of band gap To examine the exchange-correlation functional on the excitation energies, the CAM-B3LYP/6-31G(d) calculation was carried out, and the excitation energy is plotted in Fig. 7. The excitation energy for m = 0 was calculated to be 2.40 eV. The lowest excitation energy was appeared in m = 16 (Eg(m = 16) = 1.0 eV) which is in good agreement with that of B3LYP/6-31G(d). This indicates that the effect of exchange-correlation functional is negligibly small in this system. E. Effects of graphene size on the band gaps In order to check the effects of size of graphene on the band gap property, the excitation energies of the large graphene GR(37) were examined, and the results are given in Fig. 8. The similar feature was obtained in GR(37) as well as GR(19). The lowest excitation energy was appeared at γ = 0.06 (i.e., non-zero) in case
Fig. 8. Excitation energies of hydrogen added graphene flakes plotted as a function of coverage (γ). Insert indicates the graphene used in the calculation of GR(37). The values are calculated at the B3LYP/3-21G(d) level.
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The variation of band gap can be simply explained in terms of the orbital splitting model. The minimum of band gap is caused by splitting of energy levels of HOMO and LUMO (lower panel in Fig. 9). This splitting is caused by a broken symmetry in the hydrogenation to the surface [21]. Namely, the decrease of band gap at low hydrogen coverage is caused by the splitting of energy levels. This is due to the fact that the HOMO level is split to two energy levels. At high hydrogen coverage, the band gap is increased by the decrease of π-conjugation. Acknowledgments This work is partially supported by a Grant-in-Aid for Scientific Research on Innovation Areas “Evolution of Molecules in Space”. H.T also acknowledges a partial support from a Grant-in-Aid for Scientific Research (C) [JSPS KAKENHI Grant Number 2455000102]. References
Fig. 9. Model for coverage dependence of band gap in graphene nano-flake.
of GR(37). This result indicates that the lowering of the excitation energy is caused by addition of hydrogen atom onto the graphene. The γ-dependence of orbital energies of GR(37) was similar to that of GR(19).
4. Discussion In general, it is considered that the band gap increases with increasing coverage of hydrogen atom on the surface of graphene. However, the present calculations showed that the band gap of graphene behaves as a specific feature. On the basis of the present calculations, a model of coverage dependence of band gap in the graphene nano-flakes is proposed. A schematic illustration of the model is given in Fig. 9. Upper figure indicates the relationship between band gap and coverage. The curve of band gap has a minimum at γ = non-zero (γ = 0.3 in case of GR(19)).
[1] C.G. Van de Walle, J. Neugebauer, Annu. Rev. Mater. Res. 36 (2006) 179. [2] A.J. Morris, C.J. Pickard, R.J. Needs, Phys. Rev. B 78 (2008) 184102. [3] X. Wang, Y. Ouyang, X. Li, H. Wang, J. Guo, H. Dai, Phys. Rev. Lett. 100 (2008) 206803. [4] S.S. Datta, D.R. Strachan, S.M. Khamis, A.T.C. Johnson, Nano Lett. 8 (2006) 1912. [5] L. Tapaszto, G. Dobrik, P. Lambin, L.P. Biro, Nat. Nanotechnol. 3 (2006) 397. [6] W.L. Wang, S. Meng, E. Kaxiras, Nano Lett. 8 (2008) 241. [7] D.C. Elias, R.R. Nair, T.M.G. Mohiuddin, S.V. Morozov, P. Blake, M.P. Halsall, A.C. Ferrari, D.W. Boukhvalov, M.I. Katsnelson, A.K. Geim, K.S. Novoselov, Science 323 (2009) 610. [8] D.H. Choe, J. Bang, K.J. Chang, New J. Phys. 12 (2010) 125005. [9] A. Ito, H. Nakamura, A. Takayama, J. Phys. Soc. Jpn. 77 (2008) 114602. [10] J.O. Sofo, A.S. Chaudhari, G.D. Barber, Phys. Rev. B 75 (2007) 153401. [11] H. Gao, L. Wang, J. Zhao, F. Ding, J. Lu, J. Phys. Chem. C 115 (2011) 3236. [12] R.H. Miwa, T.B. Martins, A. Fazzio, Nanotechnology 19 (2008) 155708. [13] P. Zhou, R. Lee, A. Claye, J.E. Fischer, Carbon 36 (1998) 1777. [14] S. Casolo, O.M. Lovvik, R. Martinazzo, G.F. Tantardini, J. Chem. Phys. 130 (2009) 054704. [15] H. Tachikawa, T. Iyama, H. Kawabata, Jpn. J. Appl. Phys. 49 (2010) 01AH06. [16] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, J.A. Montgomery Jr., T. Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S.S. Iyengar, J. Tomasi, V. Barone, B. Mennucci, G. Scalmani MCossi, N. Rega, G.A. Petersson, H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian, J.B. Cross, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J. Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A. Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich, A.D. Daniels, M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, C. Gonzalez, J.A. Pople, Ab-initio calculation program: Gaussian 03, Revision B.04, Gaussian, Inc., Pittsburgh PA, 2003. [17] H. Tachikawa, A. Shimizu, J. Phys. Chem. B 110 (2006) 20445. [18] H. Tachikawa, J. Phys. Chem. C 111 (2007) 13087. [19] H. Tachikawa, J. Phys. Chem. C 112 (2008) 10193. [20] H. Tachikawa, J. Phys. Chem. C 115 (2011) 20406. [21] L.A. Zotti, G. Teobaldi, K. Palotas, W. Ji, H.-J. Gao, W.A. Hofer, J. Comput. Chem. 29 (2008) 1589.
Contents lists available at ScienceDirect
Thin Solid Films journal homepage: www.elsevier.com/locate/tsf
Effect of hydrogenation on the band gap of graphene nano-flakes Hiroto Tachikawa ⁎, Tetsuji Iyama, Hiroshi Kawabata Division of Materials Chemistry, Graduated School of Engineering, Hokkaido University, Sapporo 060-8628, Japan
a r t i c l e
i n f o
Available online 7 September 2013 Keywords: Graphene Hydrogen atom Band gap DFT Broken symmetry
a b s t r a c t The effects of hydrogenation on the band gap of graphene have been investigated by means of density functional theory method. It is generally considered that the band gap increases with increasing coverage of hydrogen atom on the graphene. However, the present study shows that the band gap decreases first with increasing hydrogen coverage and reaches the lowest value at finite coverage (γ = 0.3). Next, the band gap increases to that of insulator with coverage from 0.3 to 1.0. This specific feature of the band gap is reasonably explained by broken symmetry model and the decrease of pi-conjugation. The electronic states of hydrogenated graphene are discussed. © 2013 Elsevier B.V. All rights reserved.
1. Introduction During the last decade, the graphene-based molecular devices were widely used as energy-related material, sensor, field-effect transistor, and biomedical application, due to their excellent electrical, mechanical, and thermal properties [1,2]. As well as pure graphene, functionalized graphenes were synthesized and characterized by several groups [3–6]. The tuning of graphene-based molecular devices to obtain the higher performance molecular devices is now an important field. Recently, Elias et al. have investigated hydrogenated graphene by exposing to hydrogen plasma [7]. They found that a highly conductive graphene is converted from semimetal to insulator after the hydrogenation. Raman spectroscopy revealed that the hydrogenation breaks the π-bonding system of graphene surface after the formation of sp3 carbon–hydrogen bonds. Transmission electron microscopy study indicates that the original hexagonal bonding arrangement is retained, whereas the lattice constant is significantly reduced. The hydrogenation is reversible through annealing, thereby restoring the conductivity and structure of graphene. This reversibility also creates the possibility of using such materials for hydrogen storage. Thus, the addition of hydrogen atom can be used to tune the electronic properties of graphene-based molecular devices [8]. From a theoretical point of view, density functional theory (DFT) calculations of hydrogenated graphene have been carried out by several groups [9–14]. Sofo et al. proposed that full hydrogenation of graphene forms a stable two dimensional (2D) hydrocarbon named graphane [10]. By means of the DFT computations, they also predicted that graphane has a wide band gap. Gao et al. calculated the band gap as a
⁎ Corresponding author. Fax: +81 11 706 7897. E-mail address: [email protected] (H. Tachikawa). 0040-6090/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.tsf.2013.08.108
function of coverage in the range of 66–100% [11]. They found that the band gap increases gradually up to 8 eV. Casolo et al. investigated the adsorption of hydrogen atom to a 5 × 5 surface unit cell of graphene using DFT method [14]. The binding energy per hydrogen atom was calculated to be 0.8–1.9 eV. It suggested that the change of hybrid orbital from sp2 to sp3 is important due to the hydrogen atom adsorption to graphene. Thus, the binding energy of hydrogen atom on the surface of graphene is quite well understood. However, the coverage dependence of band gap was only investigated in the range of 0.7– 1.0 coverage (i.e., higher coverage regions). Therefore, the relation between the band gap and coverage in a wider coverage range remains unclear. In the present study, the DFT method was applied to the hydrogen atom interacting with a graphene flake. The dependence of band gap on hydrogen coverage was investigated in detail in order to elucidate the effects of hydrogen addition on the electronic structures of graphene nano-flakes. In a previous paper [15], we conducted a preliminary investigation on the effects of hydrogen addition on the electronic states of graphene surface. We found that hydrogen addition causes a lowering of band gap of graphene flake in case of low coverage regions. However, the calculation was carried out at the semi-empirical PM3 molecular orbital level. In the present study, accurate DFT calculation was performed for the hydrogen added graphene to elucidate the origin of specific band gap property. The paper is organized as follows: in Section 2, we present the method of calculations. In Section 3, the structures and electronic states of hydrogenated graphene with 19 benzene rings are reported. Subsequently, we give the results of larger graphene with 37 benzene rings to elucidate the size-dependence of the band gap. In Section 4, we discuss the specific band gap properties of hydrogenations.
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H. Tachikawa et al. / Thin Solid Films 554 (2014) 199–203
2. Method of calculation Graphene nano-flakes composed of 19 and 37 benzene rings (n = 19 and 37) were used as models (denoted by GR(19) and GR(37), respectively). The edge carbon of graphene was terminated by a hydrogen atom. In case of hydrogenation of GR(19), even hydrogen atoms (from m = 2 to 54) were bonded to the surface carbon atoms, where m means the number of hydrogen atoms added to the surface. This addition causes a change of coverage from zero to 1.0. The hydrogen atoms were first added to the carbon atoms at central region of GR(19), and then the additions were expanded to the edge region. Two hydrogen atoms were added to carbon atoms on the surface and reverse side. In case of GR(37), a similar hydrogenation was performed up to the maximum hydrogen atoms (m = 96). The structures and electronic states of normal and hydrogenated graphenes were calculated by means of DFT method at the B3LYP/ 6-31G(d) level using Gaussian 03 program package [16]. The excitation energy and band gap were calculated by means of time dependent (TD) DFT method. The electronic states of all molecules were obtained by natural population analysis (NPA) and natural bond orbital (NBO) methods at the B3LYP/6-31G(d) level. The levels of theory calculated for GR(19) and GR(37) were B3LYP/6-31G(d) and 3-21G(d), respectively. These levels give a reasonable electronic state of the graphene as shown in previous calculations [17–20]. 3. Results A. Structures of hydrogenated graphene flakes The structure of GR(19) optimized at the B3LYP/6-31G(d) level is
Fig. 1. Optimized structure of pure graphene GR(19)(m = 0), and hydrogen added graphene flakes (m = 2 and 6) obtained at the B3LYP/6-31G(d) level. Hydrogen atom is bound to central carbon atoms. Notation of m means number of hydrogen atoms added to the graphene. The structures were fully optimized at the B3LYP/6-31G(d) level.
illustrated in Fig. 1 (m = 0). The optimized structure of GR(19) (m = 0) showed a purely planar form. The C–C bond distance was calculated to be 1.420 Å around the center of graphene. Next, two hydrogen atoms were added to the carbon atoms around the central region of GR(19), and then the structure was fully optimized. The optimized structure is illustrated in Fig. 1 (m = 2). The C1–H bond distance between added hydrogen atom and carbon was calculated to be r(C1–H) = 1.111 Å, where C1 means the carbon atom added by a hydrogen atom. The structure around the C1–H bond has a pyramidal form, and the carbon atom was 0.39 Å higher than the graphene plane. The C–C bond length was 1.522 Å around the C1–H bond, which is 0.10 Å longer than that of m = 0. The electronic states of carbon atoms at the binding site (denoted by C1 and C2) were changed by the addition of hydrogen atoms. To elucidate the change of electronic state of the carbon atoms, the NBO analysis was carried out for m = 0 and 2. The NBO of the C1–C2 bond of free graphene (m = 0) is expressed by 1:99 σ C¼C ¼ 0:707 sp
C1
1:99 þ 0:707 sp
C2
ð1Þ
where, C1 and C2 mean carbon atoms in the binding and neighbor sites, respectively. After the addition of the hydrogen atoms, the NBO for m = 2 was expressed by 2:80 σ C−C ¼ 0:707 sp
C1
2:80 þ 0:707 sp
C2
ð2Þ
The coefficient of sp orbital for m = 0 (1.99) was close to 2.00, indicating that the orbitals of the carbon atoms are close to a sp2 orbital before the addition. After the addition of hydrogen atoms, the coefficient is changed from 1.99 to 2.80. The result indicates that the binding nature is changed from sp2 to sp3-like orbitals after the addition of hydrogen atoms. This feature is the same as reported in previous works [7,21]. The structure for m = 6 is also given in Fig. 1 (lower). The C–H bond length was 1.016 Å, and the structure of the six-membered ring added by hydrogen atoms takes an armchair form, which is close to the structure of cyclohexane molecule. The C–C bond length was 1.526 Å around the binding site, which is slightly elongated from that of m = 2. The structures of middle and high coverage graphenes (m = 24 and 54) are illustrated in Fig. 2. In case of m = 24, all carbon atoms in bulk surface are covered with the hydrogen atoms. However, the π orbitals in the edge region still remain. In m = 54, there is no
Fig. 2. Optimized structure of hydrogen added graphene flakes GR(19)(m = 24 and 54) with higher coverage. The structures were fully optimized at the B3LYP/6-31G(d) level.
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Table 1 Relationship between numbers of hydrogen atom and coverage (γ). GR(19)
Fig. 3. Excitation energies of hydrogen added graphene flakes plotted as a function of number of hydrogen atom number (m). The values are calculated at the B3LYP/631G(d) level. Dashed line indicates the band gap of pure graphene flake GR(19)(m = 0).
conjugation as shown in Fig. 2 (m = 54). The C–C bond lengths for m = 24 and 54 were calculated to be 1.529 and 1.543 Å, respectively. This result indicates that the C–C bond is changed from double to single bonds at higher coverage. B. Band gap In previous section, it was found that the addition of hydrogen atom on GR(19) diminishes the numbers of π-conjugation in graphene. This effect may affect the excitation energy and band gap of the graphene. The excitation energies of GR(19)(m = 0–54) are plotted as a function of m. In m = 0, the low-lying excitation energies were calculated to be 2.24, 2.39, 3.12, 3.12, 3.14, and 3.24 eV, indicating that the band
Fig. 4. Excitation energies of hydrogen added graphene flakes plotted as a function of coverage of hydrogen atom on graphene surface (γ). The values are calculated at the TDDFTB3LYP/6-31G(d) level. The orbital energies of HOMO and LUMO and the energy gap (HOMO–LUMO) are plotted as well.
GR(37)
m
γ
m
γ
0 2 4 6 8 10 14 16 24 54
0.00 0.04 0.07 0.11 0.15 0.19 0.26 0.30 0.44 1.00
0 2 4 6 8 12 24 48 54 78
0.00 0.02 0.04 0.06 0.08 0.13 0.25 0.50 0.56 0.81
gap of GR(19) is Eg(m = 0) = 2.24 eV. This band gap of GR(19) (m = 0) is indicated by a dashed line in Fig. 3. In m = 2, the lowest excitation energy was 2.12 eV, which is 0.12 eV lower than that of m = 0. All excitation energies are plotted in Fig. 3 as a function of m. Although the band gaps of m = 4 and 6 (2.55 and 2.86 eV) were slightly larger than that of m = 0 (2.24 eV), the band gaps of m = 10–24 were lower than that of m = 0. For example, the energies of band gap of m = 16 and 24 were 1.31 and 1.41 eV, respectively. The lowest band gap was appeared at m = 16. On the other hand, fully saturated graphene (m = 54) has a wide band gap (6.95 eV). Band gaps were calculated as a function of coverage of hydrogen atom on graphene surface (γ), together with the highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gap and the orbital energies of HOMO and LUMO. The results are plotted in Fig. 4. Relation between numbers of hydrogen atom and coverage (γ) is given in Table 1. Similar calculations were carried out at the CAM-B3LYP/6-31G(d) level for comparison. All calculations showed that the band gap is minimized at the coverage of 0.3 (i.e., γ = 0.3). C. Orbital energies of hydrogenated graphene In previous section, it was shown that the band gap is minimized at γ = 0.3. In order to elucidate the reason why the band gap is minimized at a finite coverage value (γ = 0.3), the electronic states of partial hydrogenated graphene were analyzed in details. Fig. 5 shows the coverage dependence of the orbital energy. The highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO–LUMO) of graphene without hydrogen atom are doubly
Fig. 5. The orbital splitting of HOMO and LUMO energies and the energy gap (HOMO–LUMO) are plotted as a function of coverage of hydrogen atom on graphene surface (γ). Arrows indicate the excitation energies at γ = 0.04, 0.30, and 1.0.
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Fig. 6. Molecular orbital energy diagrams of hydrogen added graphene flakes GR(19) (γ = 0, 0.04, and 0.30) calculated at the B3LYP/6-31G(d) level. Arrow indicates the first electronic excitation.
degenerated to each other at γ = 0. On the other hand, both HOMO and LUMO split into two single orbitals each other at the finite coverage value (0.0 b γ b 0.45). The orbital energies and spatial distribution of molecular orbitals of γ = 0, 0.04 and 0.30 are given in Fig. 6. In γ = 0, the energy of HOMO is −5.0 eV, and the orbital is doubly degenerated. The LUMO has the same feature as that of HOMO. The HOMO–LUMO gap was calculated to be 2.65 eV. In case of γ = 0.04, HOMO split into two levels (−5.2 and −4.5 eV). Also, LUMO splits into two levels (−2.5 and −1.7 eV) as well. The HOMO–LUMO gap was calculated to be 1.96 eV in γ = 0.04. The energy gap decreased from 2.65 to 1.96 eV with increasing γ from zero to 0.04. In γ = 0.30, the energies of HOMO and LUMO were −4.00 and −2.95 eV, respectively. The HOMO–LUMO gap is 1.05 eV. Thus,
Fig. 7. Excitation energies of hydrogen added graphene flakes plotted as a function of hydrogen atom number (m). The values are calculated at the CAM-B3LYP/6-31G(d) level.
the orbital energies were split by the hydrogen addition. The origin of this splitting is caused by a symmetry broken of the orbitals due to the hydrogen addition. D. Exchange-correlation functional dependence of band gap To examine the exchange-correlation functional on the excitation energies, the CAM-B3LYP/6-31G(d) calculation was carried out, and the excitation energy is plotted in Fig. 7. The excitation energy for m = 0 was calculated to be 2.40 eV. The lowest excitation energy was appeared in m = 16 (Eg(m = 16) = 1.0 eV) which is in good agreement with that of B3LYP/6-31G(d). This indicates that the effect of exchange-correlation functional is negligibly small in this system. E. Effects of graphene size on the band gaps In order to check the effects of size of graphene on the band gap property, the excitation energies of the large graphene GR(37) were examined, and the results are given in Fig. 8. The similar feature was obtained in GR(37) as well as GR(19). The lowest excitation energy was appeared at γ = 0.06 (i.e., non-zero) in case
Fig. 8. Excitation energies of hydrogen added graphene flakes plotted as a function of coverage (γ). Insert indicates the graphene used in the calculation of GR(37). The values are calculated at the B3LYP/3-21G(d) level.
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The variation of band gap can be simply explained in terms of the orbital splitting model. The minimum of band gap is caused by splitting of energy levels of HOMO and LUMO (lower panel in Fig. 9). This splitting is caused by a broken symmetry in the hydrogenation to the surface [21]. Namely, the decrease of band gap at low hydrogen coverage is caused by the splitting of energy levels. This is due to the fact that the HOMO level is split to two energy levels. At high hydrogen coverage, the band gap is increased by the decrease of π-conjugation. Acknowledgments This work is partially supported by a Grant-in-Aid for Scientific Research on Innovation Areas “Evolution of Molecules in Space”. H.T also acknowledges a partial support from a Grant-in-Aid for Scientific Research (C) [JSPS KAKENHI Grant Number 2455000102]. References
Fig. 9. Model for coverage dependence of band gap in graphene nano-flake.
of GR(37). This result indicates that the lowering of the excitation energy is caused by addition of hydrogen atom onto the graphene. The γ-dependence of orbital energies of GR(37) was similar to that of GR(19).
4. Discussion In general, it is considered that the band gap increases with increasing coverage of hydrogen atom on the surface of graphene. However, the present calculations showed that the band gap of graphene behaves as a specific feature. On the basis of the present calculations, a model of coverage dependence of band gap in the graphene nano-flakes is proposed. A schematic illustration of the model is given in Fig. 9. Upper figure indicates the relationship between band gap and coverage. The curve of band gap has a minimum at γ = non-zero (γ = 0.3 in case of GR(19)).
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