J. Phys. Chem. C 2009, 113, 15043–15045
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Structural and Electronic Properties of Graphane Nanoribbons Yafei Li,† Zhen Zhou,*,† Panwen Shen,† and Zhongfang Chen*,‡ Institute of New Energy Material Chemistry, College of Chemistry, Institute of Scientific Computing, Nankai UniVersity, Tianjin 300071, P. R. China, and Department of Chemistry, Institute for Functional Nanomaterials, UniVersity of Puerto Rico, Rio Piedras Campus, San Juan, PR 00931 ReceiVed: June 7, 2009
The structural and electronic properties of graphane nanoribbons, i.e., completely hydrogenated graphene nanoribbons, were investigated by means of density functional theory computations. Because all the carbon atoms are sp3-hybridized and saturated with hydrogen atoms, graphane nanoribbons present completely different electronic properties compared with graphene nanoribbons. Independent of the chirality, graphane nanoribbons are always wide-band-gap semiconductors. Graphane nanoribbons have favorable formation energies, and can be realized by hydrogenating graphene nanoribbons or cutting experimentally available graphanes. These one-dimensional hydrocarbons will find their potential applications to nanotechnology after further band structure tuning. 1. Introduction Graphene, a single layer of carbon atoms tightly packed in a honeycomb sublattice, is the building block of graphite, fullerenes, and carbon nanotubes.1 Once graphene was thought physically impossible; however, the successful isolation of this two-dimensional (2D) crystal in 2004 by Geim and co-workers2 wholly refreshed our minds and is bringing us a new revolution to materials science3-5 due to its outstanding mechanical,6 electronic,7,8 and magnetic properties.9 The achievements in large-scale preparation of graphenes10-13 make us more confident in the wide application of these novel materials in the very near future. Very recently, Elias et al.14 experimentally realized the hydrogenated graphene, as named graphane, by exposing graphene to hydrogen plasma discharge. Ryu et al.15 demonstrated that hydrogenation of graphenes can also be realized by dissociating hydrogen silsesquioxane on graphene. The electronic properties of materials are closely associated with their dimensionality. When 2D graphene is cut into onedimensional (1D) graphene nanoribbons (GNRs), a nonzero band gap is opened in all GNRs.16 Especially, the GNRs with zigzag edges are characterized with special localized edge states, which are ferromagnetically ordered at each edge but with opposite spin directions between two edges.15-20 Moreover, further studies show that an external transverse electronic field21 or chemically selective modifications22 can realize half-metallicity in zigzag GNRs, which opens possibilities for GNR-based spintronic devices. Stimulated by the intensive studies on GNRs, researchers have also extended the direction to inorganic nanoribbons, such as BN,23 B,24 BC3,25 B2C,26 SiC,27 ZnO,28 and MoS229 nanoribbons, and revealed intriguing electronic and magnetic properties associated with low dimensionality and edge states in these nanoribbons. Experimentally, graphane nanoribbons can be obtained by cutting the graphane layer, or hydrogenating GNRs. Since the properties of GNRs are different from those of graphene, it is attractive to explore 1D graphane nanoribbons. Sofo et al.30 have performed a detailed theoretical * To whom correspondence should be addressed. E-mail: zhouzhen@ nankai.edu.cn (Z.Z.);
[email protected] (Z.C.). † Nankai University. ‡ University of Puerto Rico.
Figure 1. (a) Top (upper) and side (lower) view of a 2D graphane layer. Geometric structures of the (b) 7-zigzag and (c) 13-armchair graphane nanoribbons. The ribbons are periodic along the z direction. The ribbon widths are denoted by Wz and Wa, respectively.
study on a 2D graphane layer. Boukhvalov et al.31 systematically studied the hydrogenation of graphenes with defects. Very recently, Singh et al.32 have investigated the electronic and magnetic properties of selectively hydrogenated GNRs, which still preserve some characteristics of GNRs. However, what about the properties of 1D graphane nanoribbons with various edge types and widths? In this work, density functional theory (DFT) computations were performed to investigate the structural and electronic properties of graphane nanoribbons. 2. Computational Method DFT computations were performed by using the plane-wave technique implemented in the Vienna ab initio simulation package (VASP).33 The ion-electron interaction is described with the projector-augmented plane wave (PAW) approach.34,35 The generalized gradient approximation (GGA) expressed by the PW91 functional36 and a 360 eV cutoff for the plane-wave basis set were adopted in all computations. In a typical computation, the 1D periodic boundary condition (PBC) was applied along the growth direction of nanoribbons, and the supercell is large enough to ensure a distance greater than 10 Å between two neighboring ribbons. Five Monkhorst-Pack special k points were used for sampling the 1D Brillouin zone, and the convergence threshold was set as 10-4 eV in energy and 10-3 eV/Å in force. Finally, 21 k points were used to compute the band structures.
10.1021/jp9053499 CCC: $40.75 2009 American Chemical Society Published on Web 07/09/2009
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Figure 2. Band structures (left) and charge densities of VBM (right lower) and CBM (right upper) for (a) 7-zigzag and (b) 13-armchair graphane nanoribbons.
3. Results and Discussion 3.1. 2D Infinite Graphane Single Layer. We began our study with the 2D infinite graphane single layer. The most stable form of the graphane layer favors a chairlike conformation with hydrogen atoms alternating on both sides of the plane.30 Thus, only the chairlike graphane layer and nanoribbons were considered in this work. Figure 1a presents the optimized structure of the graphane layer in a 6 × 6 supercell, which includes 72 carbon atoms and 72 hydrogen atoms. The C-C bond length is 1.52 Å, rather close to those in the sp3-hybridized diamond (1.53 Å), but longer than those in graphene with sp2 hybridization (1.42 Å), in agreement with the expectation that all of the carbon atoms in graphane employ sp3 hybridization. The C-H bond length is uniformly 1.11 Å. According to our DFT computations, the 2D graphane layer is a semiconductor with a direct band gap of 3.43 eV at the Γ point, which achieves good agreement with the previous finding of Sofo et al.,30 but is much lower than the GW calculation value (5.4 eV) reported
Li et al. by Lebegue et al.,37 since DFT usually underestimates band gaps; however, the basic physics should not be changed. 3.2. Geometric Structures of Graphane Nanoribbons. Two types of graphane nanoribons can be obtained by cutting the optimized graphane layer with a zigzag or armchair edge. Figure 1 shows two examples, 7-zigzag (b) and 13-armchair (c) graphane nanoribbons, with respective widths of 20.34 and 22.40 Å. Following the convention of GNRs,15-19 we define the ribbon parameter N as the number of zigzag chains for a zigzag ribbon and the number of dimer lines along the ribbon direction for an armchair ribbon. The edge carbon atoms are all saturated with H atoms to avoid the effects of dangling bonds; therefore, each C atom in the edges is bonded to two H atoms. After full relaxation, the sp3-bonding networks are well kept at the edge regions of both 7-zigzag and 13-armchair graphane nanoribbons. The lengths of edge C-C (1.52 Å) and C-H (1.11 Å) bonds are equal to those inner C-C and C-H bonds. Note that both spin-unpolarized and spin-polarized computations were performed to determine the ground state of graphane nanoribbons, and no energy difference was found. Thus, different from zigzag GNRs with a magnetic ground state,16-19 graphane nanoribbons have a nonmagnetic ground state. Since the magnetism of GNRs is derived form the localized unpaired π state, the disappearance of magnetism in graphane nanoribbons is attributed to the absence of an unpaired π state as a result of sp3 hybridization of all of the carbon atoms. 3.3. Electronic Properties of Graphane Nanoribbons. Figure 2 presents the computed electronic band structures of 7-zigzag and 13-armchair graphane nanoribbons. These two nanoribbons are both semiconducting with a direct band gap of 3.82 and 3.84 eV, respectively. The valence and conduction band edge are both located at the Γ point. The flat bands at the Fermi level associated with the edge states in zigzag GNRs are absent in 7-zigzag graphane nanoribbons. To get further insight, we computed the partial charge densities associated with the valence band maximum (VBM) and the conduction band minimum (CBM) of these two nanoribbons (Figure 2). For both 7-zigzag and 13-armchair graphane nanoribbons, the VBM mainly comes from the 2s2phybridized oribitals localized at the inner carbon atoms, while the CBM consists mainly of 1s electron states of the inner hydrogen atoms. Therefore, the electronic properties of graphane nanoribbons are predominantly determined by the inner carbon and hydrogen atoms. Edge atoms have no contribution to either VBM or CBM, which is quite different from GNRs and other inorganic nanoribbons.15-19,23-29 All of the edge carbon atoms in graphane nanoribbons are completely saturated with H atoms; thus, the edge states are absent in graphane nanoribbons.
Figure 3. Variation of the band gap (a) and the formation energy (b) of zigzag (6 e Nz e 16) and armchair (10 e Nz e 27) graphane nanoribbons as a function of ribbon width.
Properties of Graphane Nanoribbons Figure 3a presents the variation of band gap as a function of ribbon width for a series of zigzag and armchair graphane nanoribbons. All of the graphane nanoribbons considered are semiconducting, and the band gap decreases monotonically with increasing ribbon width. Regardless of the chirality (zigzag or armchair), the graphane nanoribbons with similar widths have very close band gaps (Figure 3a), which is vigorous evidence for the quantum confinement effect. 3.4. Formation Energies of Graphane Nanoribbons. It is important to discuss the experimental preparation of graphane nanoribbons. Here, we evaluated the formation energy (Ef), which is defined as Ef ) EC - xCµC - xHµH, where EC is the cohensive energy per atom of graphane nanoribbons and xi (i ) C or H) is the molar fraction of the atom in the nanoribbons. µC is taken as the cohesive energy per atom of the graphene single layer, and µH is equal to the half binding energy of H2. This approach has been used to estimate the relative stability of GNRs with different chemical compositions.22,38 The formation energy of both zigzag and armchair graphane nanoribbons increases monotonically with increasing ribbon width (Figure 3b), which implies that narrow ribbons are more likely to form than those wider ones. The negative formation energies of all graphane nanoribbons considered here indicate that graphane nanoribbons are more stable than the experimentally available graphenes. However, favorable formation energies do not mean that we can get graphane nanoribbons by directly exposing GNRs to H2, since it is difficult to dissociate H2 on GNRs. However, we can use hydrogen plasma or other H atom sources to transform GNRs to graphane nanoribbons, similar to the process of the formation of graphane,14 or cut the experimentally available graphane layers in the same way of obtaining graphene ribbons. 4. Conclusion In summary, we have studied the structural and electronic properties of graphane nanoribbons with zigzag or armchair edges by DFT computations. Both zigzag and armchair nanoribbons are semiconductors with wide direct band gaps. Since the band gap of graphane nanoribbons is determined by inner atoms instead of edge atoms, the band gap decreases monotonically with increasing ribbon width due to the quantum confinement effect. Graphane nanoribbons have more favorable formation energies than experimentally available graphenes, and the formation energy increases with increasing ribbon width. Overall, graphane nanoribbons have quite promising applications in optics and opto-electronics due to the wide band gap. It is expected that chemical modifications may tune graphane nanoribbons into p- or n-type semiconductors, which would widen the applications of this novel 1D hydrocarbon. Acknowledgment. Support in China by NSFC (20873067) and NCET and in USA by NSF Grant CHE-0716718, the Institute for Functional Nanomaterials (NSF Grant 0701525), and the US Environmental Protection Agency (EPA Grant No. RD-83385601) is gratefully acknowledged.
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