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Tuning electronic and magnetic properties of partially hydrogenated graphene by biaxial tensile strain: a computational study
Nanoscale Research Lettersvolume 9, Article number: 491 (2014)
Using density functional theory calculations, we have investigated the effects of biaxial tensile strain on the electronic and magnetic properties of partially hydrogenated graphene (PHG) structures. Our study demonstrates that PHG configuration with hexagon vacancies is more energetically favorable than several other types of PHG configurations. In addition, an appropriate biaxial tensile strain can effectively tune the band gap and magnetism of the hydrogenated graphene. The band gap and magnetism of such configurations can be continuously increased when the magnitude of the biaxial tensile strain is increased. This fact that both the band gap and magnetism of partially hydrogenated graphene can be tuned by applying biaxial tensile strain provides a new pathway for the applications of graphene to electronics and photonics.
Graphene has recently attracted considerable attention owing to its remarkable electronic and structural properties in many emerging application areas such as electronic devices [1–3]. However, graphene exhibits a zero band gap and nonmagnetic behavior, which limits its application in electronics and photonics . Earlier investigations, both theoretically [5–33] and experimentally [34–43], have been made to adjust electronic and magnetic properties of graphene. There are two basic mechanisms cataloged among these schemes, either to disturb the band crossing at Dirac points via breaking the equivalence of the two sublattices of graphene or to transform the carbon hybridization from sp2 into sp3 via chemical functionalization.
The first mechanism can be achieved by substrate-graphene interaction [5, 6, 35], applying external electric field [36, 37], uniaxial strain [7, 8], cutting graphene into nanoribbons [9–11, 38] and adsorption of molecules on graphene surface [12–14]. However, the efforts of the abovementioned approaches are limited and can only open a tiny band gap because of the robust π bands of graphene. Another mechanism can be realized via chemical functionalization of graphene, such as H, F, OH, COOH, and O chemisorbed on either one side or both sides of graphene [15–23]. At present, this approach can induce a large band gap opening of graphene: for example, fully hydrogenated graphene has been shown to be a wide band gap semiconductor , whereas half-hydrogenated graphene results in an indirect gap and ferromagnetism .
Motivated by the above results, we have carried out a systematic investigation to explore the stability and electronic and magnetic properties of partially hydrogenated graphene (PHG) by applying biaxial tensile strain using density functional theory. The calculated results indicate that the configuration with removing H-hexagon is the most energetically favorable in several types of HG configurations, while the appropriate biaxial tensile strain can effectively tune the band gap and magnetism of the partially hydrogenated graphene.
All calculations in this study were performed using the spin-polarized first-principle method as implemented in the DMol3 code . The generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional was used , in combination with the double numerical plus polarization (DNP). The empirically corrected density functional theory (DFT + D) method within the Grimme scheme was employed in all the calculations to consider the van der Waals forces . All-electron core treatment was adopted, and the real space global cutoff radius was set to be 4.6 Å to achieve high accuracy. We used the smearing techniques with a smearing value of 0.005 Ha.
A hexagonal graphane supercell (7 × 7 graphane unit cell) was established with a lattice parameter of 2.54 Å. The modulus supercell vector in the z direction was set to 15 Å, which led to negligible interactions between the system and their mirror images. For geometric optimization, the Brillouin zone integration was performed with 10 × 10 × 1 k-point sampling, which brings out the convergence tolerance of energy in 1.0 × 10−5 hartree, and that of maximum force in 0.002 hartree. The stability of hydrogenated graphene was determined from the formation energy Ef by the following:
where Etotal(n) is the cohesive energy of the system, n was the number of H atoms removed from a graphane sheet, and μH (μgraphane) is the chemical potential of the constituent H (graphane) at a given state. Here, we chose the binding energy per atom of H2 molecule as μH. And μgraphane was taken as the cohesive energy of a single graphane sheet.
Results and discussion
According to the previous reports [16, 47], two favorable structures of fully hydrogenated graphene (graphene), chair and boat conformations, exist. In the chair configuration, every two adjacent C atoms are hydrogenated from the opposite sides of the graphene sheet. The induced strains compensate each other and thereby the energy of graphane is low. While in the boat conformation, H atoms are alternately bonded to C atoms on both sides in pairs. Due to the repulsion of two neighboring H on the same side, the boat configuration is less stable than the chair one. Therefore, we only consider the chair configuration. For the case of graphane, the obtained lattice parameter, C-C bond length, and C-H bond length of graphane are 2.54, 1.54, and 1.11 Å, respectively, which are in good agreement with previous reported data .
As shown in Figure 1a,b,c, we first investigate the relative stability of unpaired (Figure 1a,b) and paired H (Figure 1c) vacancies by calculating the formation energies of the vacancies: H vacancy is isolated in the unpaired vacancy, while two neighboring H vacancies are interconnected in the paired vacancy. Ef of the H vacancies on graphane can be calculated from the difference between the total energy of graphane and the sum of the total energy of dehydrogenated graphane and those of detached single H atoms. In Equation (1), positive Ef represents endothermic process of dehydrogenation. The calculations show that Ef of paired vacancies is always smaller than that of two unpaired vacancies (Figure 1a,b,c). In other words, paired vacancies are more easily formed than unpaired vacancies in graphane. This can be explained by the fact that a single H vacancy creates a dangling bond and raises the total energy due to a local strain . In the condition of paired dehydrogenation, both unsaturated C atoms are turned to sp2 hybridized state and form a C = C double bond, through which the two π electrons pair together and the vacancy-induced local strain can be partially released. The removal of radicals by C = C double bond has significant effect on the electronic structures of the dehydrogenated graphane. As shown in Figure 1d,e,f,g,h,i, three adjacent paired vacancies formed a hexagon vacancy and graphane with a hexagon vacancy is more energetically favorable than five separated paired vacancies.
We further investigated the electronic structures of the partially dehydrogenated graphane with different H vacancies. Previous research works predict that the band gap of perfectly hydrogenated graphene is 3.5 ~ 5.4 eV [16, 17, 23]. From our calculations, the band gap (Eg) of the perfect graphane is about 4.41 eV. The Eg opening in graphene can be attributed to the changes of functionalized C atoms from sp2 to sp3 hybridization. However, after partially dehydrogenation of graphane, the Eg and the corresponding electronic structures can be changed. According to the unified geometric rule reported by previous works [48, 49], the spin state at all zigzag edges with angles of either 0° or 120° between the edges should be ferromagnetic (FM), whereas it should be antiferromagnetic (AFM) if the edges are aligned at angles of 60° and 180° with respect to each other. On the basis of this rule, we calculated the band structures of C98H92 (1-hexagon vacancy, Figure 2a), C98H88 (2-hexagon vacancies, Figure 2b), C98H85 (triangle vacancy formed by 3-hexagon vacancies, Figure 2c), C98H72 (2-triangle vacancies, Figure 2d), C98H59 (3-triangle vacancies, Figure 2e), and C98H46 (4-triangle vacancies, Figure 2f) via selective dehydrogenation. As shown in Figure 3, it is found that the values of Eg of partially dehydrogenated graphane decrease as the hexagon vacancies increase. Thus, the insulating graphane with a wide band gap becomes a semiconductor via appropriate dehydrogenation. Eg of PHG which are induced by the quantum confinement effect in PHG with increased vacancies. In other words, the trend of band gap narrowing can be attributed to the number of edge states in the PHG with the hexagon vacancies [22, 49–52]. Taking the structure of C98H85 as an example, the Eg reduces to 0.52 eV and the magnetic moment (m) is about 0.98 μB (Figure 3c). When the triangle vacancies of graphane increase to four, the band structure of C98H46 has an indirect band gap with Eg = 0.33 eV, whereas m increases to 3.90 μB (Figure 3f). Meanwhile, the strong σ-bonds are broken between C and H atoms and removal of the nearest neighbor H atoms leads to C = C double bonds, leaving the electrons in the unpaired C atoms localized and unpaired. In order to study the preferred coupling of these moments, we considered the following three magnetic configurations of C98H46: FM coupling, antiferromagnetic (AF) coupling, and nonmagnetic (NM) state, where the calculation is spin unpolarized. From the calculated results, it is found that the total energy of FM state is lower than that of AF and NM states, respectively. Thus, we can deduce that the ground state is FM state.
In the case of the C98H46 model, we apply the external tensile strain to continuously tune the electronic properties of graphene-based materials. Figure 4 shows the influences of tensile strain ϵ on the magnetic and electronic properties of partially hydrogenated graphene (C98H46). It is revealed that the electronic property of C98H46 is rather robust in response to tensile strain. The biaxial strain can be imposed on by changing the lattice parameters of x-y plane and optimized the structures along the z direction. In this work, we considered the tensile strain as it is experimentally more feasible, and the largest tensile strain is chosen to be 9%. Our computations demonstrated that the biaxial strain has a significant impact on the electronic properties of C98H46. With a tensile strain, the Eg of C98H46 increases monotonically as the increase of strain (Figure 4a), even a 1% strain, can result in a 0.02 eV gap increase. This trend is similar to the case of graphene, as Topsakal et al. demonstrated that the Eg of graphane monolayer increases with increasing biaxial tensile strain up to 15% . The Eg of C98H46 system increases to 0.44 eV with tensile strain reaches 9%. Note that when the tensile strain is lower than 9%, C98H46 system is always semiconducting with an indirect band gap. As shown in Figure 4b, we next investigate the influences of tensile ϵ on the magnetic of C98H46 system. Under tensile strain ϵ, C98H46 system always keeps the FM state as in the unstrained case. As ϵ increases to 9%, it is clear that the magnetic moment of C98H46 system slowly increase to 3.94 μ B .
From the above results, we conclude that the electronic and magnetic properties of graphane can be efficiently tuned from insulator to semiconductor (from non-magnetism to ferromagnetism) via selective dehydrogenation, whereas the band gap and magnetism moment of partially hydrogenated graphene can be enhanced by imposing a biaxial tensile strain.
In summary, DFT calculations with biaxial tensile strain are carried out to investigate the effects of biaxial tensile strain on the electronic and magnetic properties of PHG structures. It is found that the configuration with removing H-hexagon is the most energetically favorable in the several types of HG configurations. In addition, the appropriate biaxial tensile strain can effectively increase the band gap and magnetism of PHG. Overall, tuning both band gap and magnetism of hydrogenated graphene by applying biaxial tensile strain provides a new perspective for wide applications of graphene in electronics and photonics.
Geim AK: Graphene: status and prospects. Science 2009, 324: 1530–1534. 10.1126/science.1158877
Novoselov KS, Geim AK, Morozov SV, Jiang D, Zhang Y, Dubonos SV, Grigorieva IV, Firsov AA: Electric field effect in atomically thin carbon films. Science 2004, 306: 666–669. 10.1126/science.1102896
Huang Q, Kim JJ, Ali G, Cho SO: Width-tunable graphene nanoribbons on a SiC substrate with a controlled step height. Adv Mater 2013, 25: 1144–1148. 10.1002/adma.201202746
Novoselov K: Graphene: mind the gap. Nat Mater 2007, 6: 720–721. 10.1038/nmat2006
Giovannetti G, Khomyakov PA, Brocks G, Kelly PJ, van den Brink J: Substrate-induced band gap in graphene on hexagonal boron nitride: Ab initio density functional calculations. Phys Rev B 2007, 76: 073103.
Chen XF, Lian JS, Jiang Q: Band-gap modulation in hydrogenated graphene/boron nitride heterostructures: the role of heterogeneous interface. Phys Rev B 2012, 86: 125437.
Gui G, Li J, Zhong J: Band structure engineering of graphene by strain: first-principles calculations. Phys Rev B 2008, 78: 075435.
Sun L, Li Q, Ren H, Su H, Shi QW, Yang J: Strain effect on electronic structures of graphene nanoribbons: a first-principles study. J Chem Phys 2008, 129: 074704. 10.1063/1.2958285
Dai QQ, Zhu Y, Jiang Q, Dai QQ, Zhu Y, Jiang Q: Electronic and magnetic engineering in zigzag graphene nanoribbons having a topological line defect at different positions with or without strain. J Phys Chem C 2013, 117(9):47914799.
Son Y-W, Cohen ML, Louie SG: Energy gaps in graphene nanoribbons. Phys Rev Lett 2006, 97: 216803.
Dai QQ, Zhu YF, Jiang Q: Electronic and magnetic properties of armchair graphene nanoribbons with 558 grain boundary. Phys Chem Chem Phys 2014, 16: 10607–10613. 10.1039/c4cp00868e
Lu YH, Chen W, Feng YP, He PM: Tuning the electronic structure of graphene by an organic molecule. J Phys Chem B 2008, 113: 2–5.
Zanella I, Guerini S, Fagan SB, Mendes Filho J, Souza Filho AG: Chemical doping-induced gap opening and spin polarization in graphene. Phys Rev B 2008, 77: 073404.
Ribeiro RM, Peres NMR, Coutinho J, Briddon PR: Inducing energy gaps in monolayer and bilayer graphene: local density approximation calculations. Phys Rev B 2008, 78: 075442.
Boukhvalov DW, Katsnelson MI, Lichtenstein AI: Hydrogen on graphene: electronic structure, total energy, structural distortions and magnetism from first-principles calculations. Phys Rev B 2008, 77: 035427.
Sofo JO, Chaudhari AS, Barber GD: Graphane: a two-dimensional hydrocarbon. Phys Rev B 2007, 75: 153401.
Lebègue S, Klintenberg M, Eriksson O, Katsnelson MI: Accurate electronic band gap of pure and functionalized graphane from GW calculations. Phys Rev B 2009, 79: 245117.
Duplock EJ, Scheffler M, Lindan PJD: Hallmark of perfect graphene. Phys Rev Lett 2004, 92: 225502.
Boukhvalov DW, Katsnelson MI: Tuning the gap in bilayer graphene using chemical functionalization: density functional calculations. Phys Rev B 2008, 78: 085413.
Lu N, Li Z, Yang J: Electronic structure engineering via on-plane chemical functionalization: a comparison study on two-dimensional polysilane and graphane. J Phys Chem C 2009, 113: 16741–16746. 10.1021/jp904208g
Yan J-A, Xian L, Chou MY: Structural and electronic properties of oxidized graphene. Phys Rev Lett 2009, 103: 086802.
Dai QQ, Zhu Y, Jiang Q: Stability, electronic and magnetic properties of embedded triangular graphene nanoflakes. Phys Chem Chem Phys 2012, 14: 1253–1261. 10.1039/c1cp22866h
Gao H, Wang L, Zhao J, Ding F, Lu J: Band gap tuning of hydrogenated graphene: H coverage and configuration dependence. J Phys Chem C 2011, 115: 3236–3242. 10.1021/jp1094454
Li Y, Zhou Z, Shen P, Chen Z: Structural and electronic properties of graphane nanoribbons. J Phys Chem C 2009, 113: 15043–15045. 10.1021/jp9053499
Singh AK, Penev ES, Yakobson BI: Vacancy clusters in graphane as quantum dots. ACS Nano 2010, 4: 3510–3514. 10.1021/nn1006072
Zhou J, Wang Q, Sun Q, Chen XS, Kawazoe Y, Jena P: Ferromagnetism in semihydrogenated graphene sheet. Nano Lett 2009, 9: 3867–3870. 10.1021/nl9020733
Ribas M, Singh A, Sorokin P, Yakobson B: Patterning nanoroads and quantum dots on fluorinated graphene. Nano Res 2011, 4: 143–152. 10.1007/s12274-010-0084-7
Wu M, Wu X, Zeng XC: Exploration of half metallicity in edge-modified graphene nanoribbons. J Phys Chem C 2010, 114: 3937–3944. 10.1021/jp100027w
Wehling TO, Katsnelson MI, Lichtenstein AI: Impurities on graphene: midgap states and migration barriers. Phys Rev B 2009, 80: 085428.
Zhu Y, Lian J, Jiang Q: Role of edge geometry and magnetic interaction in opening bandgap of Low-dimensional graphene. ChemPhysChem 2014, 15: 958–965. 10.1002/cphc.201301127
Zhu Y, Zhao N, Lian J, Jiang Q: Toward tandem photovoltaic devices employing nanoarray graphene-based sheets. J Phys Chem C 2014, 118: 2385–2390.
Zhu YF, Dai QQ, Zheng WT, Jiang Q: Gap openings in graphene regarding interfacial interaction from substrates. Phys Chem Chem Phys 2014, 16: 5600–5604. 10.1039/c3cp55222e
Zhu YF, Dai QQ, Zhao M, Jiang Q: Physicochemical insight into gap openings in graphene. Sci Rep 2013., 3:
Jung I, Dikin DA, Piner RD, Ruoff RS: Tunable electrical conductivity of individual graphene oxide sheets reduced at “low” temperatures. Nano Lett 2008, 8: 4283–4287. 10.1021/nl8019938
Zhou SY, Gweon GH, Fedorov AV, First PN, de Heer WA, Lee DH, Guinea F, Castro Neto AH, Lanzara A: Substrate-induced bandgap opening in epitaxial graphene. Nat Mater 2007, 6: 770–775. 10.1038/nmat2003
Zhang Y, Tang T-T, Girit C, Hao Z, Martin MC, Zettl A, Crommie MF, Shen YR, Wang F: Direct observation of a widely tunable bandgap in bilayer graphene. Nature 2009, 459: 820–823. 10.1038/nature08105
Castro EV, Novoselov KS, Morozov SV, Peres NMR, dos Santos JMBL, Nilsson J, Guinea F, Geim AK, Neto AHC: Biased bilayer graphene: semiconductor with a gap tunable by the electric field effect. Phys Rev Lett 2007, 99: 216802.
Han MY, Özyilmaz B, Zhang Y, Kim P: Energy band-gap engineering of graphene nanoribbons. Phys Rev Lett 2007, 98: 206805.
Wu X, Sprinkle M, Li X, Ming F, Berger C, de Heer WA: Epitaxial-graphene/graphene-oxide junction: an essential step towards epitaxial graphene electronics. Phys Rev Lett 2008, 101: 026801.
Jeong HK, Jin MH, So KP, Lim SC, Lee YH: Tailoring the characteristics of graphite oxides by different oxidation times. J Phys D Appl Phys 2009, 42: 065418. 10.1088/0022-3727/42/6/065418
Luo Z, Vora PM, Mele EJ, Johnson ATC, Kikkawa JM: Photoluminescence and band gap modulation in graphene oxide. Appl Phys Lett 2009, 94: 111909. 10.1063/1.3098358
Balog R, Jorgensen B, Nilsson L, Andersen M, Rienks E, Bianchi M, Fanetti M, Laegsgaard E, Baraldi A, Lizzit S, Sljivancanin Z, Besenbacher F, Hammer B, Pedersen TG, Hofmann P, Hornekaer L: Bandgap opening in graphene induced by patterned hydrogen adsorption. Nat Mater 2010, 9: 315–319. 10.1038/nmat2710
Elias DC, Nair RR, Mohiuddin TMG, Morozov SV, Blake P, Halsall MP, Ferrari AC, Boukhvalov DW, Katsnelson MI, Geim AK, Novoselov KS: Control of Graphene's Properties by Reversible Hydrogenation: Evidence for Graphane. Science 2009, 323: 610–613. 10.1126/science.1167130
Delley B: From molecules to solids with the DMol(3) approach. J Chem Phys 2000, 113: 7756–7764. 10.1063/1.1316015
Perdew JP, Burke K, Ernzerhof M: Generalized gradient approximation made simple. Phys Rev Lett 1996, 77: 3865–3868. 10.1103/PhysRevLett.77.3865
Grimme S: Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J Comput Chem 2006, 27: 1787–1799. 10.1002/jcc.20495
Singh AK, Yakobson BI: Electronics and magnetism of patterned graphene nanoroads. Nano Lett 2009, 9: 1540–1543. 10.1021/nl803622c
Yu D, Lupton E, Gao HJ, Zhang C, Liu F: A unified geometric rule for designing nanomagnetism in graphene. Nano Res 2008, 1: 497–501. 10.1007/s12274-008-8053-0
Yu D, Lupton E, Liu M, Liu W, Liu F: Collective magnetic behavior of graphene nanohole superlattices. Nano Res 2008, 1: 56–62. 10.1007/s12274-008-8007-6
Pedersen TG, Flindt C, Pedersen J, Mortensen NA, Jauho A-P, Pedersen K: Graphene antidot lattices: designed defects and spin qubits. Phys Rev Lett 2008, 100: 136804.
Liu W, Wang ZF, Shi QW, Yang J, Liu F: Band-gap scaling of graphene nanohole superlattices. Phys Rev B 2009, 80: 233405.
Park C-H, Yang L, Son Y-W, Cohen ML, Louie SG: Anisotropic behaviours of massless Dirac fermions in graphene under periodic potentials. Nat Phys 2008, 4: 213–217. 10.1038/nphys890
Topsakal M, Cahangirov S, Ciraci S: The response of mechanical and electronic properties of graphane to the elastic strain. Appl Phys Lett 2010, 96: 091912. 10.1063/1.3353968
This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2012–0009523).
The authors declare that they have no competing interests.
EHS carried out the design of the simulation and drafted the manuscript. GA, SHY, and QJ assisted in the simulation. SOC supervised the whole study. All authors read and approved the final manuscript.