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Band-Gap Engineering with Hybrid Graphane-Graphene Nanoribbons Y. H. Lu and Y. P. Feng* Department of Physics, National UniVersity of Singapore, 2 Science DriVe 3, Singapore, 117542 ReceiVed: July 16, 2009; ReVised Manuscript ReceiVed: October 27, 2009
The electronic structures of graphane nanoribbons and hybrid graphane-graphene nanoribbons were investigated using the first-principles method. Energy gaps of both zigzag and armchair graphane nanoribbons were found to increase as the nanoribbons become narrower. The hybrid graphane-graphene nanoribbons show structure dependence and tunable electronic properties. The band gap of armchair hybrid nanoribbons is dominated by its graphene section, whereas a spin-split defect level emerges in the band gap of zigzag hybrid nanoribbons, which depends on the hydrogenation of the graphane-graphene interface zigzag carbon chain. These findings provide a basis for achieving band gap engineering and controllable spin filters based only on light elements. Graphene, a one-atom-thick carbon sheet, has been regarded as one of the most promising candidates for the next generation electronic materials due to its unusual electronic properties, such as ultra-high electron mobility and ballistic transport on a submicrometre scale at 300 K.1,2 The perfect graphene, however, is a zero-gap semimetal and for device applications a band gap would be required in order to precisely control the carrier-type and concentration. In this respect, graphene nanoribbons (NRs)3,4 offer a possibility of achieving tunable electronic properties, as confirmed both experimentally5 and theoretically by firstprinciples calculations.6 The size of the energy gap of a graphene nanoribbon was found to depend on the width of the ribbon7,8 and the hydrogen passivation on the edge.9 Furthermore, the zigzag graphene nanoribbon was found to be magnetic10 and can even be made half-metallic by applying an electric field11 or through edge modification with molecules12,13 and defects.14,15 Half-metallicity in zigzag graphene nanoribbon, where only one of the spin channles conducts and the other remains insulating, is promising for spintronic applications. A large number of fascinating graphene-ribbon-based electronic devices have been proposed.16,17 Chemical modification is another approach to lift the degeneracy of π bands at the Fermi level of graphene, an example of which is graphene oxide - a graphene densely covered with hydroxyl or other chemical groups. Unfortunately, graphene oxide is highly disordered and poorly conductive, and it is difficult to control its electronic properties. Recently, Elias et al.18 demonstrated experimentally that electronic structures of graphene can be modified by hydrogenation, which transforms the bond type between carbon atoms in graphene from sp2 into sp3, thus removing the conducting π bands and opening an energy gap. This leads to the creation of a new material, graphane, which was earlier predicted by theory.19 It was further demonstrated that chemical modification of graphene is reversible or controllable and the original properties of graphene can be largely restored by annealing the graphane samples at high temperature. This opens an alternative avenue for tuning the electronic properties of graphene.20 Because the electronic structures of graphane (insulator) are totally different from that of graphene (semimetal),19 a graphane * To whom correspondence should be addressed. E-mail: phyfyp@ nus.edu.sg.
nanoribbon can be expected to have different band structures from its counterpart, graphene nanoribbons. A hybrid system consisting of graphene and graphane nanoribbons would then provide more opportunities for achieving desired electronic properties. Such hybrid systems have not been explored thus far and are the focus of the present work. We carried out firstprinciples electronic structure calculations on graphane nanoribbons and hybrid graphane-graphene nanoribbons and found that the band gaps of graphane nanoribbons are always larger than that of 2D graphane, whereas the hybrid system has abundant electronic properties for band gap engineering and for application as a spin filter without external electric and magnetic fields. In our calculations, we used the DMol321,22 code which is based on the density-functional theory (DFT). All-electron calculations were performed with a double numeric plus polarization basis (DNP) set. The generalized gradient approximation (GGA) proposed by Perdew-Burke-Ernzerhof (PBE)23 was used for the exchange and correlation function. It is noted that the DFT result may be functionally dependent.24,25 A finite basis cutoff of 3.9 Å was adopted and more than 4.0 Å basis cutoff is also tested without any significant change. To model an isolated nanoribbon, we adopted 3D repeating supercells in which individual ribbons are separated by a vacuum region, which is least 20 Å, for both edge-edge and layer-layer distances. The electronic structures of graphene-NRs have been investigated previously.6,26 The band gap (∆N) of an armchair graphene-NR (a-graphene-NR) was found inversely proportional to its width and the variation of its band gap with width can be separated into three different families with a hierarchy of gap size given by ∆3p+1 > ∆3p > ∆3p+2, where p is a positive integer. The ground state of a zigzig graphene-NRs (z-graphene-NRs) is magnetic insulating with ferromagnetic ordering at each zigzag edge and antiparallel spin orientation between the two edges. The slab of bulk graphane is flat, similar to the plane of graphene except that it is distorted due to adsorption of hydrogen atoms on alternating rows of carbon atoms on both sides of the plane. In the following, we focus first on the electronic structures of graphane-NRs. Similar to graphene-NRs,6 a graphane-NR with the armchair-shaped edge on both sides is classified by the number of dimer lines (N) across the ribbon width, as shown
10.1021/jp9067284 2009 American Chemical Society Published on Web 11/16/2009
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Figure 1. (Color online) Schematic of an a-graphene-NR (a) and z-graphene-NR (b). The white balls denote hydrogen atoms passivating the edge carbon atoms, and the black balls represent carbon atoms. The dimer lines or zigzag chains are indicated by N.
Figure 2. (Color online) Band gap of N-a-graphane-NRs and N-zgraphane-NRs as a function of width and the number of dimer lines or zigzag chains included in graphane-NRs is denoted. The dashed horizontal line indicates the energy gap of bulk graphane. The insert is the optimized structures of 9-a-graphane-NR and 8-z-graphane-NR. The white balls denote hydrogen atoms, and the black balls represent carbon atoms. The C-C bonds between the dimer lines or zigzag chains are shown in blue.
in part a of Figure 1. Likewise, ribbons with zigzag-shaped edges on both sides are classified by the number of zigzag chains across the ribbon width, as shown in part b of Figure 1. A graphane-NR with N dimer lines is thus referred as a N-agraphane-NR and a graphane-NR with N zigzag chains as Nz-graphane-NR, respectively. Graphane is a wide-gap insulator,19 and the energy gap of graphane-NR is width dependent. As shown in Figure 2, the band gaps of both a-graphane-NRs and z-graphane-NRs decrease as a function of ribbon width and approach the value of bulk graphane (dashed line). The gap opening and variation are not entirely due to electronic structures, as in graphene. The inserts in Figure 2 show the optimized structures of 9-a-graphane-NR and 8-z-graphane-NR, respectively. The distortion of the carbon plane caused by the sp2 - sp3 transformation is similar to that in bulk graphane. All carbon-hydrogen (C-H) bonds of both cases are the same in length, about 1.1 Å. However, the carbon-carbon (C-C) bonds (blue in the inserts of Figure 2) between the dimer lines of a-graphane-NR or zigzag chains of z-graphane-NR are about 2% longer than that of bulk graphane, whereas the length of bonds along the dimer lines or the zigzag chains is almost the same as that in bulk graphane. Therefore, when graphane is cut into ribbons, the graphane-NRs, both armchair and zigzag, expand across the ribbon width. To evaluate the effect of this bond elongation, we increased the corresponding C-C bond length in bulk graphane by 2% and
Lu and Feng
Figure 3. (Color online) (a) M-dependence of band gaps of N/M-ahybrid-NRs with N + M ) 9. The three different families are shown in different colors. The insert is the optimized structure of the 4/5-ahybrid-NR. The white and small balls denote hydrogen atoms, while the black and big balls represent carbon atoms. The interface carbon atoms are shown in blue. (b) Band structure of the 3/6-a-hybrid-NR. The Fermi level is indicated by the dashed line.
calculated its band structure. The band gap of this distorted graphane is about 0.38 eV larger than that of perfect graphane. The elongation of C-C bonds reduces the coupling between carbon atoms at their ends and increases the band gap of the system. Because there are two elongated bonds between dimer lines in each a-graphane-NR unit, whereas only one bond is elongated in each z-graphane-NR unit, the band gaps of a-graphane-NRs are larger than those of z-graphane-NRs of the same width. The bond elongation becomes smaller as the width of a graphane-NR increases and the band gap of the graphaneNR eventually approaches that of bulk graphane when the graphane-NR is sufficiently wide. The large band gap of graphane-NR is very useful for confining charge carriers in highpower applications.27 Next, we discuss the electronic properties of the hybrid graphane-graphene nanoribbons (hybrid-NRs). For simplicity, we consider nanoribbons consisting of side-by-side graphaneNR and graphene-NR connected by a graphane-graphene interface. We specify a hybrid-NR by the number of dimer lines or zigzag chains on the graphane side (N) and graphene side (M), respectively. For example, an armchair hybrid-NR (ahybrid-NR) composed by a 4-a-graphane-NR and a 5-agraphene-NR is denoted by 4/5-a-hybrid-NR, as shown in the insert of part a of Figure 3. Similarly, 4/4-z-hybrid-NR indicates a zigzag hybrid nanoribbon that has 4 zigzag chains on both graphane side and graphene side, as shown in part c of Figure 4. It is noted that, in an a-hybrid-NR, a dimer line either belongs to the graphane side (hydrogenated) or the graphene side (unhydrogenated). But in a z-hybrid-NR, the zigzag chain at the graphane-graphene interface can be fully hydrogenated or half covered by hydrogens, which results in very different electronic properties of the z-hybrid-NRs. In an a-hybrid-NR, although the carbon plane in the graphane side is distorted due to adsorption of hydrogen atoms, the graphene side remains essentially flat. Only the interface atoms (blue atoms in the insert of part a of Figure 3) move out of the plane upon structural relaxation and their heights in the relaxed structure differ by no more than 0.07 Å. Therefore, the band structure near the Fermi level of the a-hybrid-NR is dominated by that of the a-graphene-NR part. For example, the band structure of the 3/6a-hybrid-NR shown in part b of Figure 3 is almost the same as that of the 6-a-graphene-NR. In part a of Figure 3, we show the M dependence of band gap of N/M-a-hybrid-NRs with a fixed width of N + M ) 9. It is clear that the variation is also
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Figure 4. (Color online) The side view (upper row) and top view (bottom row) of the optimized structures of the 4/4-z-hybrid-NR, with half (left panel) and full (right panel) hydrogen coverage of the interface zigzag chain, respectively. The white balls denote hydrogen atoms, whereas the black balls represent carbon atoms. The spin density, defined as the difference between spin-up and spin-down electron densities, Fv - FV, is also shown in the top views. Positive spin densities are in yellow, and negative ones are in blue.
separated into three different families. The hierarchy is such that (9 - M)/M-a-hybrid-NRs with M ) 3p + 1 have larger band gaps than (9 - M)/M-a-hybrid-NRs with M ) 3p, which in turn have larger band gaps than (9 - M)/M-a-hybrid-NRs with M ) 3p + 2, where p is a non-negative integer. We also investigated variation of band gaps of N/M-a-hybrid-NRs with N, the width of the graphane part, and found that the band gaps do not depend on N and are completely determined by M, the width of the graphene part. For example, the energy gap of 4/5a-hybrid-NR is essentially the same as that of 6/5-a-hybridNR. This is understandable because graphane NRs have larger energy gaps than graphene NR and the band structure near the Fermi level of an a-hybrid-NR is thus mainly determined by the graphene section. The properties of z-hybrid-NRs are more interesting than those of a-hybrid-NRs because the ground state of z-hybridNRs is magnetic. Furthermore, either one or both of the two carbon atoms in each unit of the zigzag chain at the graphane-graphene interface can be hydrogenated. It turned out that they lead to very different electronic properties of the z-hyrbid-NR. In the following, we will refer to them as interface zigzag chain half- and fully covered by hydrogens, respectively. If the interface zigzag chain is fully covered by hydrogens, the hydrogenated carbon atoms in the A and B sublattices are balanced (parts c and d of Figure 4) and the band structure of the hybrid NR is similar to that of the corresponding z-grapheneNR (part c of Figure 5). The ground state consists of ferromagnetic ordering along the zigzag chains of the graphene part and antiparallel spin orientation between the graphene edge and graphane-graphene interface (spin density in part d of Figure 4, leading to the openning of a band gap (black line in part a of Figure 5), which is 0.1 eV for the 4/4-z-hybrid-NR. The graphane part also has less influence on the electronic structure of the hybrid NR near the Fermi level due to its large band gap. However, the spin-up and spin-down states are not completely degenerate near the Fermi level because of chemical potential difference between the edge and the interface.12 If the interface zigzag chain is half-covered by hydrogens, the interface carbon atoms on one of the two sublattices are hydrogenated and those on the other sublattice are not, as shown in part a of Figure 4 for the 4/4-z-hybrid-NR. The symmetry between the A and B sublattices is thus broken. This strongly affects the balance between the spin-up and spin-down states on the A and B sublattices of the graphene part of the hybrid NR. Although ferromagnetic ordering remains along the zigzag chains, spin
Figure 5. (Color online) (a) Energy gaps (∆1, ∆2, and ∆3, as defined in b and c) of (8 - M)/M-z-hybrid-NR as a function of M. (b) The spin-polarized band structure of the 4/4-z-hybrid-NR with half hydrogen coverage of the interface zigzag carbon chain. (c) The spin-polarized band structure of the 4/4-z-hybrid-NR with full hydrogenation of interface carbon atoms. The Fermi level (dashed horizontal lines) is set to zero.
orientations at the graphene edge, and at the graphane-graphene interface are parallel (part b of Figure 4) because the interface carbon atoms and the edge atoms belong to the same sublattice. We want to emphasize that this interesting ferromagnetic state can only be realized with the z-hybrid-NRs because the A and B sublattices are always balanced in z-graphene-NRs. The imbalance between the spin-up and spin-down states results in a net magnetic moment which is 1.0 µB per unit along the ribbon. When the graphene side of z-hybrid-NR is wide enough, the spin densities mainly accumulate on the edge and inferface carbon atoms and decay to the central part of graphene section. This integral magnetic moment comes from the spin-polarized defect level in the band gap. As an example, the spin-polarized band structure of the 4/4-z-hybrid-NR with a half-covered interface zigzag carbon chain is shown in part b of Figure 5. Because of the symmetry breaking, there exists a large gap between the valence band maximum (VBM) and the conduction band minimum (CBM), and a defect level emerges in the gap which is spin-split. The spin-down defect level is fully occupied, whereas the spin-up band is completely empty. It is interesting to note that the energy gap between the spin-up and spin-down defect levels (∆2) can be tuned by M, the width of the graphene section. As shown by the blue line in part a of Figure 5, between M ) 1 and M ) 7, the energy gap changes continuously from 1.5 to 0.15 eV, for the (8-M)/M-z-hybrid-NR. Meanwhile, the gap between the VBM and CBM decreases from 4.5 to 2.1 eV. This provides a basis for band gap engineering in devices based on such hybrid graphane-graphene NRs. Recently, Wang et al.28 proposed that a spin-polarized defect in a semiconductor such as GaNAs can effectively deplete conduction electrons with an opposite spin orientation and can thus turn the nonmagnetic
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semiconductor into an efficient spin filter operating at room temperature and zero magnetic field. Compared to such a conventional semiconductor, the N/M-z-hybrid-NRs with half hydrogenated interface carbons would be more advantageous. The spin-polarized defect level is half-filled and it does not require polarized photoexcitation to achieve spin-polarization. With a tunable gap between the unoccupied spin-polarized defect level and VBM or CBM, it is also easy to control electron transport. Furthermore, if hydrogenation can be controlled, the spin-polarized defect level can be quenched by increasing the hydrogen coverage of the interface carbons from 50% to 100%. We also investigated other types of hybrid NRs such as a graphane NR sandwiched between two graphene NRs and found that their formation energies are higher than the hybrid structure discussed above. We wish to point out that hybrid NRs can be fabricated with advanced experimental techniques, such as that using nanowires as a physical protection mask on one side of graphene-NR in hydrogen plasma.29 Such hybrid-NRs structures can be expected to open a new avenue in future design of graphene electronics such as controllable spin filters based on light elements only. In summary, employing first-principles DFT calculations, we have investigated the electronic structures of graphane-NRs and hybrid graphane-graphene NRs. The gap sizes of both armchair and zigzag graphane NRs are width dependent. With increasing width, the band gap decreases monotonically and eventually approaches that of bulk graphane. The band structures of armchair hybrid NRs are dominated mainly by the graphene part in the vicinity of the Fermi energy and do not show spinpolarization. On the other hand, the band structures of zigzag hybrid NRs show more interesting features. The band gap and the spin-split defect level of zigzag hybrid NRs can be controlled by the width of graphane or graphene section. These findings provide new opportunities in band gap engineering of graphenebased devices. We also provide an approach for realizing efficient and controllable spin-filter devices using hydrocarbon materials without electric and magnetic fields. Acknowledgment. This work is supported by a National Research Foundation (Singapore) Competitive Research Program (Grant No. NRF-G-CRP 2007-05). Part of the work was carried out using the computing facility at the Computer Center of National University of Singapore.
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