Fluorographene

Article pubs.acs.org/JPCC

Electronic and Magnetic Properties of Graphene/Fluorographene Superlattices Hongliang Shi,† Hui Pan,† Yong-Wei Zhang,*,† and Boris I. Yakobson*,‡ †

Institute of High Performance Computing, A*STAR, Singapore 138632 Department of Mechanical Engineering and Materials Science, and Department of Chemistry, Rice University, Houston, Texas 77005, United States

Downloaded via KAOHSIUNG MEDICAL UNIV on July 21, 2018 at 06:29:46 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

‡

ABSTRACT: On the basis of density functional theory calculations, the electronic and magnetic properties of graphene/fluorographene superlattices (GFSLs) are systematically investigated. Our calculations show that the electronic properties are both interface-orientation- and graphene-widthdependent. All armchair GFSLs (AGFSLs) are semiconducting with a band gap being graphene-width-dependent and exhibiting three distinct families of characteristics similar to that of armchair graphene nanoribbons. The zigzag GFSLs (ZGFSLs) with an extremely small graphene width are nonmagnetic and semiconducting. As the width of graphene increases, however, ZGFSLs become magnetic with the antiferromagnetic (AFM) state being their ground state. Our results also reveal that, if the graphene width is kept constant, the total energy differences between the non-spin-polarized (NSP) state and the AFM state and between the ferromagnetic (FM) state and the AFM are independent of the superlattice period. When the graphene width is large, the AFM and FM states are nearly degenerated as their total energy difference is less than 10 meV. In addition, our results also show that the strain can be practically used to tune the band gap of flat AGFSLs while the strain effect can be effectively shielded by the accordion structure of ZGFSLs. surface, for example, the Ru(0001) substrate.10 It was shown that a single-layer graphene forms a corrugated sp2-hybridized network and displays a π band gap at the K̅ point of its 1 × 1 Brillouin zone. Up to now, chemical functionalization of graphene appears to be the most promising method to tailor its electronic properties due to the versatile bonding hybridizations of sp, sp2, and sp3 of carbon atoms. Currently, there are several chemically functionalized graphene derivatives, namely, graphene oxide,11 graphane,12,13 and fluorographene,14−16 with the latter two being obtained by hydrogenation and fluorination of graphene, respectively. These chemical derivatives change carbon hybridization from sp2 to sp3 and yet preserve the two-dimensional structure. Since the pz electrons participate in the covalent π bonding between C and H or F atoms, a large band gap similar to that of diamond is created.14−19 Robinson et al.14 systematically studied properties of fluorinated graphene films with different fluorine coverages. Their results demonstrated that fluorination of graphene significantly changes the optical, structural, and transport properties of the material. It is noted that there is an energy barrier in the hydrogenation of graphene, but there is not one in the fluorination of graphene. Because of the strong C−H and C−F bonds, both graphane and fluorographene are very stable at

1. INTRODUCTION Graphene, a two-dimensional allotrope of carbon, has attracted extensive attention since it was experimentally separated in 2004.1 In graphene, carbon atoms are arranged in a composite lattice with two physically equivalent sublattices staggered together. This leads to both inversion and time reversal symmetries, which, in turn, give rise to many fascinating properties and novel applications.2 However, many applications of graphene in electronic devices require the presence of a tunable gap between the conduction and the valence bands.3 Therefore, how to open and tune the band gap of graphene is a challenging issue. So far, different methods have been proposed to introduce a band gap in graphene. One of them is by cutting graphene along two parallel lines to form graphene nanoribbons.4−7 Firstprinciples calculations predict that graphene nanoribbons are semiconducting, and their band gaps can be tuned by varying their width and orientation. However, there are several challenges defying the wide use of graphene nanoribbons for electronic applications. First, it is still a challenge to control their width and orientation. Second, it is still difficult to produce them in high quality and high volume.8 Third, it is also difficult to integrate graphene nanoribbons to form nanodevices. Last, but not least, a recent experiment also indicates that the edges of graphene nanoribbons are metastable and may undergo edge reconstruction to lower their edge energy.9 Another method to introduce a band gap in single-layer graphene is through its epitaxial interaction with a metal © 2012 American Chemical Society

Received: June 3, 2012 Revised: August 9, 2012 Published: August 10, 2012 18278

dx.doi.org/10.1021/jp305441b | J. Phys. Chem. C 2012, 116, 18278−18283

The Journal of Physical Chemistry C

Article

ambient conditions. Recent experiments showed that the formation of graphane can be controllable and reversible,17 which might be useful for hydrogen storage.18 Recently, composite nanostructures based on graphene and its chemical derivatives, such as graphane and fluorographene, have attracted a great deal of interest. For example, graphene nanoroads,20 embedded in a graphane sheet, were predicted using first-principles calculations. It was shown that its electronic structures depend sensitively on the orientation and width of the nanoroads. It was also shown that semiconducting as well as metallic graphene nanoroads were able to be patterned on the same graphene sheet, forming hybrid graphene/graphane superlattices.21−23 Experimentally, Lee et al.16 fabricated graphene nanoribbons surrounded by wide-band-gap fluorographene on a graphene sheet using polymer nanowire masks. Sun et al.24 also patterned graphane/ graphene superlattices within a single sheet of graphene. Through controlling both the spatial distribution and the density of the functional group, multifunctional electronic circuits and chemical sensors might be realized using a single graphene sheet, facilitating the development of graphene-based devices. It is noted that graphene/fluorographene superlattices (GFSLs) are more stable and robust than graphene/graphane superlattices. Since GFSLs may have many potential applications in nanoelectronic devices, it is, therefore, both interesting and necessary to understand the electronic and magnetic properties of graphene/fluorographene superlattices. In this work, we employ first-principles methods to systematically study the electronic structures and magnetic properties of GFSLs, focusing on the effects of interfacial orientation, superlattice period, graphene width, and strain. The obtained calculation results and revealed physical insights provide important guidelines for using GFSLs in nanoelectronic applications.

Figure 1. Relaxed structure of armchair (a, b) and zigzag (c, d) GFSLs from top and side views, respectively. The width of graphene is measured by the number (n) of pristine sp2 carbon dimer lines or zigzag chains for armchair or zigzag GFSLs, respectively.

calculations. Convergence in the total energies for magnetic states were checked carefully. It is known that graphene and fluorographene are both structurally stable. Hence, the structural stability of graphene/ fluorographene superlattices is dictated by their interfaces. To have a well-defined superlattice, the sharpness of the inferfaces between fluorinated and pristine graphene is necessary; we choose the (4,6) AGFSL and (3,6) ZGFSL to examine the stability of these interfaces. By moving one fluorine atom from the interface to its nearest carbon in the graphene region, we calculate the energy cost by energy minimization. We find that the energy cost is 2.20 and 1.72 eV, respectively, for the two cases. Clearly, the energy cost is too high, and fluorine is unable to diffuse into the graphene region at room temperature. This is consistent with the result that the fluorine migration process can only occur at higher temperatures.29 Therefore, we conclude that the interfaces are structurally stable and so are the graphene/fluorographene superlattices. Similarly, the phonon dispersions or frequency analysis can also decide the stability of structures. In our current case, the structural stability of superlattices is dictated by that of their interfaces; therefore, phonon dispersions or frequency analysis is not performed here.

2. DETAILS OF CALCULATION Since the superlattice in our calculation model is in an A/B/A/ B configuration, according to the atomic arrangement at the interfaces, we define two types of superlattices: ZGFSLs and AGFSLs. Furthermore, we adopt two parameters to define the periodical unit cell structure, i.e., (n,N), where n is the number of dimer lines or zigzag chains of graphene within the unit cell and N is the number of dimer lines or zigzag chains of both graphene and fluorographene within the unit cell, following the conventional definition in ref 7. Figure 1 shows the relaxed structures for AGFSLs and ZGFSLs. In fluorographene, the fluorine atoms are bonded from both sides of graphene, and this conformation was shown to be the most stable structure.25 Our first-principles calculations were performed using the density functional theory (DFT) in the generalized gradient approximation (GGA) of the PBE functional26 for the exchange-correlation potential and the projector augmented wave (PAW)27 method as implemented in the Vienna Ab-initio Simulation Package.28 The electron wave function was expanded in a plane-wave basis set with an energy cutoff of 600 eV. The structures of the system studied were fully relaxed until the quantum mechanical forces acting on the atoms were less than 0.005 eV/Å. A period of more than 12 Å was adopted in the direction normal to the superlattice plane. For the (n,18) AGFSLs and (n,12) ZGFSLs, 14 and 20 irreducible k-points were used for the structural relaxation calculations, respectively; 91 and 105 irreducible k-points were used for static total energy

3. RESULTS AND DISCUSSION 3.1. Electronic Structures of AGFSLs. First, we studied the AGFSLs. The relaxed AGFSLs, as shown in Figure 1b, are completely flat. The alternate C atoms bonded to fluorine atoms displace out of the plane in opposite directions, keeping the AGFSLs flat. The length of C−F bonds at the two interfaces, next to the interfaces, and far from the interfaces are 1.42, 1.39, and 1.38 Å, respectively. Note that the last one is the same as the C−F bond in the pure fluorographene sheet, consistent with both experimental (1.41 Å)30,31 and theoretical (1.37 Å) values.32 In the graphene region, the C−C bonds at the interfaces are about 1.51 Å, while in the fluorographene 18279

dx.doi.org/10.1021/jp305441b | J. Phys. Chem. C 2012, 116, 18278−18283

The Journal of Physical Chemistry C

Article

function of ribbon width also exhibits three distinct families of characteristic behaviors and the gap hierarchy follows Δ3p+1 > Δ3p > Δ3p+2.7 Hence, the AGFSLs and graphene nanoribbons share the similar band gap characteristics. All the (n,18) AGFSLs are of the Γ−Γ or Y−Y direct band gap, except n = 1 (Γ-X), and the energies of their highest occupied bands at Γ and Y points are nearly degenerated since their energy differences are less than 4 meV. 3.2. Electronic Structures and Magnetism of ZGFSLs. For ZGFSLs, an accordion structure with misorientation at the two interfaces after relaxation, as shown in Figure 1d, is formed. As for the electronic structure, we also start with small (n,6) ZGFSLs. Our results show that the (1,6) and (2,6) ZGFSLs are nonmagnetic, while the (3,6) ZGFSL is antiferromagnetic (AFM). Our calculated band structures are collected in Figure 4. For the (1,6) ZGFSL, it can be viewed as a semiconducting fluorographene sheet with ordered F vacancies, resulting in the creation of holes in the valence band. Thus, it is like a p-type doped semiconductor, as revealed by Figure 4a. The (2,6) ZGFSL is semiconducting with a band gap of 2.68 eV, as shown in Figure 4b. The (3,6) ZGFSL is semiconducting in the AFM ground state (Figure 4c), and its band structures for the spin-up and spin-down channels are degenerated and equally occupied. However, its metastable FM state is metallic for both majority (Figure 4d) and minority (Figure 4e) spins. We also plot the spin density (ρ↑ − ρ↓) for both (3,6) and (4,6) ZGFSLs, as shown in Figure 5. It is obvious that the spin density is mainly localized at the C atoms in the graphene region, especially near the two interfaces. The partially paired pz orbitals of the C atoms in the two interfaces contribute to the spin density, while the C atoms in the fluorographene region are of sp3 hybridization, and no unpaired π electrons are left. For the AFM state (Figure 5a,c), there is a ferromagnetic coupling between C atoms at each zigzag interface and the spin orientations between C atoms at the two interfaces are opposite, whereas for the FM state (Figure 5b), the C atoms at both interfaces have the same spin direction. To gain an in-depth understanding of magnetic properties of ZGFSLs, we select the (n,12) and (3,N) ZGFSLs as prototypes to study how the stability of magnetism and magnetic interaction vary with the width of graphene n and the width of the superlattice N. Our results show that the (1,12) and (2,12) ZGFSLs are nonmagnetic, similar to the (1,6) and (2,6) ZGFSLs. From n = 3 onward, the ZGFSLs become magnetic. For the (3,N) ZGFSLs, the total energy differences between FM and AFM vary from 20 to 23 meV, insensitive to N, as shown in Figure 6a. It can also be seen from Figure 6a that the total energy differences between NSP and AFM are 37 meV, again insensitive to N. Our results demonstrate that, for the (3,N) ZGFSLs with a fixed n, their magnetic interaction between two interfaces is independent of the width of the fluorographene region due to the lack of unpaired π electrons. For the (n,12) ZGFSLs, with increasing n, the total energy differences ΔE between NSP and AFM first increases from 41 meV (n = 3) to 60 meV (n = 6), and then decreases to 46 meV (n = 10), as shown in Figure 6b. The total energy difference ΔE between FM and AFM, however, decreases monotonically from 23 meV (n = 3) to 6 meV (n = 10). It is known that roomtemperature magnetic order can be achieved if the ΔE between FM and AFM is larger than 23 meV. Therefore, it is possible to realize room-temperature magnetic order for large-period ZGFSLs with a small width of graphene.

region, the C−C bonds are about 1.57 Å, similar to the C−C bond length of 1.58 Å in the pure fluorographene sheet.33 We chose small (n,6) AGFSLs to investigate how the electronic structures vary with the width of graphene n, while keeping N = 6. The calculated band structures for the (n,6) AGFSLs are presented in Figure 2, where n stands for 1, 2, 3,

Figure 2. Panels (a)−(d) are band structures for the (n,6) AFGSLs; n stands for 1, 2, 3, and 4, respectively. The Fermi level is set to be zero.

and 4, respectively. The Fermi energy is set to be zero. It is clear that all of them are semiconducting with a band gap being 2.76 (Γ−X), 0.65 (Γ−Γ), 1.61 (Y−Γ), and 2.03 (Y−Y) eV, respectively. The high symmetry k-points in parentheses indicate the location of the valence band maximum and conduction band minimum, respectively. We adopted large (n,18) AGFSLs to investigate how their band gap changes with the graphene width n. Our calculation results are presented in Figure 3. It is seen that all (n,18)

Figure 3. Band-gap variation for the (n,18) AGFSLs as a function of the graphene width n. “p” is a positive integer.

AGFSLs are again semiconducting with a band gap decreasing with increasing the graphene width n. It is evident that the band gap is a function of graphene width n, falling into three different families, 3p − 2, 3p − 1, and 3p (where p is a positive integer), and the band gap hierarchy follows Δ3p−2 > Δ3p > Δ3p−1. For the aforementioned small (n,6) AGFSLs, p = 1. Thus, the bandgap values Δ1 = 2.76 eV > Δ3 = 1.61 eV > Δ2 = 0.65 eV also follow the same hierarchy. The above result serves as a basis for engineering the band gap of AGFSLs. It should be noted that previous first-principles calculations predicted that the band gap of graphene nanoribbons as a 18280

dx.doi.org/10.1021/jp305441b | J. Phys. Chem. C 2012, 116, 18278−18283

The Journal of Physical Chemistry C

Article

Figure 4. (a) The band structure of the (1,6) ZGFSL. (b) The band structure of the (2,6) ZGFSL. (c) The band structure of the (3,6) ZGFSL in the AFM state. (d, e) The band structures of majority (d) and minority (e) spin channels of the (3,6) ZGFSL in the FM state. The Fermi level is set to be zero.

Figure 5. Contour plots of the spin density (ρ↑ − ρ↓) of (a) the (3,6) ZGFSL in the AFM state, (b) the (3,6) ZGFSL in the FM state, and (c) the (4,6) ZGFSL in the AFM state (yellow for positive and cyan for negative). The rectangular zone in each figure is the unit cell adopted in our calculations.

In the following, we briefly discuss the origin of the magnetism in ZGFSLs. It is known that graphene consists of two sublattices. As shown in Figure 5, opposite magnetic moments occupy the two nearest different sublattices around each interface for both AFM and FM. The difference is that, for AFM in Figure 5a, the same spin directions are located at the same sublattices around the two interfaces, whereas for FM in Figure 5b, the same spin directions are located at the different sublattices around the two interfaces. The AFM and FM states can be converted by flipping the spin directions of the C atoms around one interface with respect to the other one. However, this flipping will cost additional energies.22,34,35 Therefore, AFM is energetically more favorable. In addition, the magnetic interaction between two interfaces will become very weak if the distance between them is large. This is because the magnetism is mediated by the delocalized π orbital states, which decay exponentially into the center of the graphene region.34−36 Nakada et al.36 systematically studied the zigzag edge state of graphene ribbons and demonstrated that charge density along the direction perpendicular to the edge or interface is proportional to [2 cos(k/2)]2n, where k is the wave vector along the direction perpendicular to the edge or interface and n is the nth zigzag chain from the edge or interface. Meanwhile, our calculations show that the magnetic moments for the FM state within theunit cell become saturated at about 0.54 μB per unit cell (n > 6), as shown in Figure 7. This is also due to the exponential decay of the spin density contributed by π orbitals.34−36 Hence, our calculated results are consistent with previous theoretical analysis.34−36 It should be noted that graphene-based materials with zigzag edges or interfaces, such as graphene nanoribbons,7 graphene

Figure 6. (a) Energy differences between NSP and AFM and between FM and AFM for the (3,N) ZGFSLs; N stands for 6, 8, 10, and 12, respectively. (b) Energy differences between NSP and AFM and between FM and AFM for the (n,12) ZGFSLs; n stands for 3, 4, 5, 6, 7, 8, 9, and 10, respectively.

18281

dx.doi.org/10.1021/jp305441b | J. Phys. Chem. C 2012, 116, 18278−18283

The Journal of Physical Chemistry C

Article

Next, we choose the (3,12) ZGFSLs to study the effect of uniaxial tensile strain on the electronic property of zigzag superlattices. The variation of band gap with uniaxial tensile strain is plotted in Figure 8. It is clear that the magnitude of the band gap is insensitive to the tensile strain. The reason that the band gap of AGFSLs is sensitive to the change of strain is that the AGFSLs have a flat structure. During straining, the chemical bonds are immediately stretched and distorted, leading to the strain sensitivity. On the other hand, the ZGFSLs have an accordion structure. During straining at the early stage, the accordion structure gradually becomes flattened, and the bond stretching is minimal, leading to the insensitivity. Hence, the accordion structures can be used to shield the strain effect. Figure 7. Magnetic moment per unit cell as a function of graphene width n of the (n,12) ZGFSLs in the FM state.

4. CONCLUSIONS Using first-principles calculations, we have systematically investigated the electronic structures of graphene/fluorographene superlattices. According to the arrangement of carbon atoms at the interfaces, we define two types of superlattices: AGFSLs and ZGFSLs. For AGFSLs, all of them are semiconducting, irrespective of the graphene width or superlattice period, and their band gap decreases as the width of graphene increases. For AGFSLs with a fixed superlattice period, their band gaps as a function of graphene width fall into three different families, 3p − 2, 3p − 1, and 3p (where p is a positive integer), and the gap hierarchy follows Δ3p−2 > Δ3p > Δ3p−1. For the ZGFSLs with an extremely small graphene width, they are nonmagnetic. From n = 3 onward, however, the ZGFSLs become magnetic and their ground state is AFM. Room-temperature magnetic order might be realized for ZGFSLs with a small graphene width as our calculated energy difference between FM and AFM is 23 meV for the (3,12) ZGFSL. The stability of magnetism is independent of the width of the fluorographene region since the magnetism is mediated by the unpaired π electrons existing in the graphene region only. If the width of graphene is large, the AFM and FM states become nearly degenerated as their total energy difference is less than 10 meV. This is due to the fact that, in ZGFSLs, the magnetic interaction is mediated by delocalized π orbital states, which decay exponentially into the center of the graphene region, and the resulting magnetic interaction between the two interfaces will become increasingly weak as the graphene width increases. We have also studied the effect of strain on the electronic structure of GFSLs. Our results show that the strain can be practically used to tune the band gap of AGFSLs, while the accordion structure of ZGFSLs can effectively shield the strain effect.

nanoroads,20 graphene/graphane SLs,22 and graphene/fluorographene SLs investigated here, all exhibit similar magnetic behaviors, and their magnetic moments are mainly localized at the edges or interfaces with AFM being their ground state. Furthermore, if the distance between the two edges or interfaces is large, the AFM and FM become nearly degenerated since their total energy differences are less than 10 meV.7,20,22 To realize the applications of graphene in spinbased electronic devices, the FM ground state is required. Interestingly, first-principles calculations showed that the spin angle between two interfaces in graphene nanoribbons can be continuously changed from 180° to 0° through carrier doping.37 This implies that FM can be the ground state for graphene nanoribbons, suggesting a possible route to manipulate the magnetic phase of ZGFSLs, 3.3. Strain Effect on AGFSLs and ZGFSLs. Mechanical strain has been shown to influence the electronic properties of carbon-based materials.34,35 We first select the (3,18) AGFSLs to study how uniaxial tensile strain applied normal to the interfaces affects the electronic structures of the armchair superlattices. Our calculated variation of band gap for the (3,18) AGFSLs with the uniaxial strain is shown in Figure 8. The strain is applied in the range of 0−10%, and the band gap changes from 2.04 to 1.36 eV, correspondingly. Interestingly, the variation of band gap is almost linear with respect to the tensile strain. Our results clearly indicate that the strain can be effectively used to tune the electronic band gap of AGFSLs.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (Y.-W.Z.), [email protected] (B.I.Y.). Notes

The authors declare no competing financial interest.

■

REFERENCES

(1) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Science 2004, 306, 666−669. (2) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. Nature (London) 2005, 438, 197−200. (3) Novoselov, K. Nat. Mater. 2007, 6, 720−721.

Figure 8. Band-gap variation for (3,18) AGFSLS and (3,12) ZGFSLs as a function of the uniaxial tensile strain applied along the direction perpendicular to the armchair and zigzag interface, respectively. 18282

dx.doi.org/10.1021/jp305441b | J. Phys. Chem. C 2012, 116, 18278−18283

The Journal of Physical Chemistry C

Article

(4) Chen, Z.; Lin, Y.-M.; Rooks, M.; Avouris, P. Physica E 2007, 40, 228. (5) Han, M.; Oezyilmaz, B.; Zhang, Y.; Kim, P. Phys. Rev. Lett. 2007, 98, 206805. (6) Reich, S.; Maultzsch, J.; Thomsen, C.; Ordejón, P. Phys. Rev. B 2002, 66, 035412. (7) Son, Y.-W.; Cohen, M.; Louie, S. Phys. Rev. Lett. 2006, 97, 216803−216806. (8) Jiao, L.; Wang, X.; Diankov, G.; Wang, H.; Dai, H. Nat. Nanotechnol. 2010, 5, 321−325. (9) Koskinen, P.; Malola, S.; Häkinen, H. Phys. Rev. B 2009, 80, 073401. (10) Zhou, S. Y.; Gweon, G.-H.; Fedorov, A. V.; First, P. N.; de Heer, W. A.; Lee, D.-H.; Guinea, F.; Castro Neto, A. H.; Lanzara, A. Nat. Mater. 2007, 6, 770−775. (11) Robinson, J. T.; Perkins, F. K.; Snow, E. S.; Wei, Z.; Sheehan, P. E. Nano Lett. 2008, 8, 3137−3140. (12) Sluiter, M. H. F.; Kawazoe, Y. Phys. Rev. B 2003, 68, 085410. (13) Sofo, J. O.; Chaudhari, A. S.; Barber, G. D. Phys. Rev. B 2007, 75, 153401. (14) Robinson, J. T.; Burgess, J. S.; Junkermeier, C. E.; Badescu, S. C.; Reinecke, T. L.; Perkins, F. K.; Zalalutdniov, M. K.; Baldwin, J. W.; Culbertson, J. C.; Sheehan, P. E.; et al. Nano Lett. 2010, 10, 3001− 3005. (15) Nair, R. R.; Ren, W. C.; Jalil, R.; Riaz, I.; Kravets, V. G.; Britnell, L.; Blake, P.; Schedin, F.; Mayorov, A. S.; Yuan, S.; et al. Small 2010, 6, 2877−2884. (16) Lee, W.-K.; Robinson, J. T.; Gunlycke, D.; Stine, R. R.; Tamanaha, C. R.; King, W. P.; Sheehan, P. E. Nano Lett. 2011, 11, 5461−5464. (17) Ryu, S.; Han, M.; Maultzsch, J.; Heinz, T.; Kim, P.; Steigerwald, M.; Brus, L. Nano Lett. 2008, 8, 4597−4602. (18) Lin, Y.; Ding, F.; Yakobson, B. Phys. Rev. B 2008, 78, 041402. (19) Munoz, E.; Singh, A. K.; Ribas, M. A.; Penev, E. S.; Yakobson, B. I. Diamond Relat. Mater. 2010, 19, 368. (20) Singh, A.; Yakobson, B. Nano Lett. 2009, 9, 1540−1543. (21) Lu, Y. H.; Feng, Y. P. J. Phys. Chem. C 2009, 113, 20841−20844. (22) Lee, J.-H.; Grossman, J. C. Appl. Phys. Lett. 2010, 97, 133102. (23) Hernández-Nieves, A. D.; Partoens, B.; Peeters, F. M. Phys. Rev. B 2010, 82, 165412. (24) Sun, Z.; Pint, C.; Mmarcano, D.; Zhang, C.; Yao, J.; Ruan, G.; Yan, Z.; Zhu, Y.; Hauge, R.; Tour, J. Nat. Commun. 2011, 2, 559−563. (25) Samarakoon, D. K.; Chen, Z.; Nicolas, C.; Wang, X.-Q. Small 2011, 7, 7965−7969. (26) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. (27) Kresse, G.; Joubert, D. Phys. Rev. B 1999, 59, 1758. (28) Kresse, G.; Furthmuller, J. Phys. Rev. B 1996, 54, 11169. (29) Osuna, S.; Torrent-Sucarrat, M.; Solá, M.; Geerlings, P.; Ewels, C. P.; Van Lier, G. J. Phys. Chem. C 2010, 114, 3340−3345. (30) Touhara, H.; Kadono, K.; Fujii, Y.; Watanabe, N. Z. Anorg. Allg. Chem. 1987, 544, 7−20. (31) Mahajan, V. K.; Badachhape, R. B.; Margrave, J. L. Inorg. Nucl. Chem. Lett. 1974, 10, 1103−1109. (32) Charlier, J. C.; Gonze, X.; Michenaud, J. P. Phys. Rev. B 1993, 47, 16162. (33) Ribas, M. A.; Singh, A. K.; Sorokin, P. B.; Yakobson, B. I. Nano Res. 2011, 4, 143−152. (34) Lee, H.; Son, Y.-W.; Park, N.; Han, S.; Yu, J. Phys. Rev. B 2005, 72, 174431. (35) Pisani, L.; Chan, J. A.; Montanari, B.; Harrison, N. M. Phys. Rev. B 2007, 75, 064418. (36) Nakada, K.; Fujita, M.; Dresselhaus, G.; Dresselhaus, M. S. Phys. Rev. B 1996, 54, 17954. (37) Sawada, K.; Ishii, F.; Saito, M.; Okada, S,; Kawai, T. Nano Lett. 2009, 9, 269−272.

18283

dx.doi.org/10.1021/jp305441b | J. Phys. Chem. C 2012, 116, 18278−18283