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Cite this: Phys. Chem. Chem. Phys., 2014, 16, 23214
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Realizing semiconductor–half-metal transition in zigzag graphene nanoribbons supported on hybrid fluorographene–graphane nanoribbons† Shaobin Tang*a and Xinrui Caob Hydrogenation and fluorination provide promising applications for tuning the properties of graphenebased nanomaterials. Using first-principles calculations, we investigate the electronic and magnetic properties of zigzag graphene nanoribbons (ZGNRs) supported on hydrogenated and fluorinated ZGNRs. Our results indicate that the support of zigzag graphane nanoribbon with its full width has less impact on the electronic and magnetic properties of ZGNRs, whereas the ZGNRs supported on fluorographene nanoribbons can be tuned to metal with almost degenerated ferro- and anti-ferromagnetic states due to the intrinsic polarization of substrate. The ZGNRs supported on zigzag hybrid fluorographene–graphane nanoribbons are spin-polarized half-semiconductors with distinct band gaps for spin-up and spin-down channels. Interestingly, in the absence of an external electric field, the spin-polarized band gaps of supported ZGNRs can be well modulated in the opposite direction by changing the ratio of fluorination
Received 24th July 2014, Accepted 9th September 2014 DOI: 10.1039/c4cp03291h
to hydrogenation concentration in hybrid substrates. Furthermore, the ZGNRs supported on hybrid nanoribbons exhibit the half-semiconducting to half-metallic behavior transition as the interlayer spacing is gradually reduced, which is realized more easily for the hybrid support with a relatively wide fluorographene moiety compared to its narrow counterpart. Present results provide a novel way for designing substrate-
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supported graphene spintronic devices.
1. Introduction Graphene nanoribbons (GNRs) have attracted a large amount of attention for future nanoscale electronics due to their outstanding physical properties.1–5 In particular, it is predicted1,6,7 that the zigzag-edged GNRs (ZGNRs) exhibit a promising magnetic property that are arising from two localized edge states, which are ferromagnetically coupled within each edge, but antiferromagnetically between the two edges. Interestingly, the ZGNRs become half-metallic when an external transverse electric field is applied.8–10 In contrast to the widely-used gate voltage in the current nanotechnology, a very high critical electric field is required to obtain the half-metallicity with the increase in ribbon width, suggesting the difficulty for realizing these properties. a
Key Laboratory of Organo-Pharmaceutical Chemistry of Jiangxi Province, Gannan Normal University, Ganzhou 341000, China. E-mail: [email protected]; Fax: +86-797-8393536 b Department of Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, S-106 91 Stockholm, Sweden † Electronic supplementary information (ESI) available: Geometric structures, band structures, and partial charge densities by LSDA for other hybrid structures and geometric structures and band structures for selected systems by PBE + D. See DOI: 10.1039/c4cp03291h
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Chemical modification may provide a promising way for tuning the electronic and magnetic properties of low-dimensional nanomaterials. Theoretically, The two edge-modified ZGNRs with CH3 and NO2 groups,11 boron nitride (BN) sheet-embedded ZGNRs,12 and carbon chain-doped zigzag boron nitride nanoribbons (ZBNNRs)13 are predicted to be half-metal. Similar to the chemically functionalized graphene by H (called graphane) and F atoms (fluorographene),14–16 the full hydrogenation17,18 and fluorination19 of GNRs can effectively modulate the band gap of perfect nanoribbons. More importantly, our recent studies19 indicate that the partial fluorination of ZGNRs induces the interesting electronic property of half-semiconductors, which are considerably different from the hybrid graphane–graphene nanoribbons.18 However, the structural and chemical modification on carbon nanostructures may result in the destruction of the honeycomb structure, and even destroy the intrinsic properties of materials. The graphene–substrate interactions play an important role in tuning the properties of graphene-based nanomaterials, without degrading its intrinsic electronic properties. Many experiments and theoretical calculations20–26 reveal that the hexagonal boron nitride (h-BN) could be chosen to be the best matching substrate for graphene for realizing its high carrier mobility. It was found that the h-BN substrate opens a finite
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band gap in graphene, which preserves the Dirac cone of graphene. Interestingly, the interactions of graphene with fully or partially patterned hydrogenated and fluorinated graphene27–29 and h-BN30 can lead to n- or p-type doping of graphene, and it can also create a finite band gap in graphene due to the CH–p or CF–p interaction. The similar SiH–p interactions also exist between silicene and hydrogenated silicene.29 More importantly, the systematic density functional theory (DFT) computations by Chen et al.31 revealed the existence of considerable C–H F–C bonding in graphane–fluorographene bilayers, which can reduce the band gap of the corresponding individual monolayer. The recent comprehensive reviews report many methods for tuning the properties of graphene-related nanomaterials.32 Similarly, the weak interaction induced by substrates or molecules is extensively used to modify the properties of GNRs in both experimental33 and theoretical works.34–36 Recently, using the theoretical calculations, Wong et al.34 and Chen et al.35 demonstrated that many dipolar molecules, such as the mechanochromic polymers and ladder-structure polydiacetylene derivatives that are noncovalently deposited on GNRs, can alter the electrostatic environment of the nanoribbons and cause a large change in band gap. In addition, they can even induce the spin gapless semiconductor–half-metal–metal transition in ZGNRs through the dipole–dipole interactions. Such weak interaction also tunes the band structure of the C4F bilayer rather than the individual C4F monolayer.36 Very recently, Guo et al.37 reported that the half-metallicity in ZGNRs sandwiched between two ZBNNRs can be realized by a bias voltage or a moderate compressive strain. In addition, the h-BN (0001) substrates induce a band gap and cause insignificant splitting of the bands in 8-ZGNR.38 Despite these important contributions, developing an effective route to realize the half metallicity of GNRs, especially in the absence of an external electric field, is still a challenge. Because of the wide band-gap in semiconductors such as graphane and fluorographene and their high stabilities, as well as due to the large difference in electronegativity among H, C, and F atoms, these functionalized carbon nanomaterials when used as a support of ZGNRs may induce promising electronic and magnetic properties. In this work, we reveal that ZGNRs supported on zigzag fluorographene nanoribbons can be tuned into metal by extensive first-principles calculations. In the absence of an applied electric field, the ZGNRs supported on hybrid fluorographene–graphane ribbons exhibit half-semiconducting to half-metallic behavior transitions via gradually reducing the interlayer spacing.
2. Computational details All calculations were performed within the framework of the plane-wave pseudopotential density-functional theory (DFT) implemented in CASTEP.39 The local spin density approximation (LSDA) proposed by Ceperley and Alder40 was used to deal with the exchange and correlation terms. The ultrasoft pseudopotentials41 for the ion–electron interactions and a kinetic energy cutoff of 350 eV in the plane-wave expansion were used.
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The one-dimensional (1D) periodic boundary conditions were applied along the growth directions of nanoribbons. Vacuum spacings of 10 Å for layers and 15 Å for edges between the adjacent cells were considered for calculations. Monkhorst– Pack mesh42 of k-points 1 1 13 were used for sampling the 1D Brillouin zones during geometry optimization. All atomic positions were optimized by the conjugate gradient method with a converging tolerance of 0.02 eV Å1 for the forces on all the atoms. The convergence criterion of energy for self-consistent field computations was set to 106 eV. The electronic structure calculations were performed by using 21 k-points along the periodic orientation. For comparison, we also applied the Perdew–Burke–Ernzerhof (PBE)43 functional including van der Waals (vdW) correction proposed by Grimme44 (referred as PBE + D, where D stands for dispersion) to calculate binding energies and other properties for all the systems. Usually, both the LSDA and the generalized-gradient approximation (GGA) underestimate the band gap, while the HSE06 hybrid functional typically predicts more accurate band gaps close to experimental data; however, it is still not the ultimate solution.45,46
3. Results and discussions 3.1 ZGNRs supported on graphane and fluorographene nanoribbons Similar to ZGNRs, the fully hydrogenated and fluorinated zigzag graphene nanoribbons, namely as graphane and fluorographene nanoribbons, can be obtained by cutting them from graphane and fluorographene in chair configurations, respectively. The geometrical structure calculations show that all the carbon atoms in zigzag graphane and fluorographene nanoribbons have the same sp3 hybridization as the corresponding sheet in which the slightly site-dependent C–H and C–F bond lengths are 1.11 Å and 1.37 Å, which is consistent with the previous results.17–19 The mismatch between the lattice constants of ZGNRs and those functionalized ribbons is less than 5%. Following the previous convention, the pristine zigzag graphene and graphane or fluorographene nanoribbons are labeled by the number of parallel zigzag chains m and n, which can be defined as m-ZGNR and nH-G or nF-G, respectively. Accordingly, ZGNRs supported on zigzag graphane or fluorographene nanoribbons are denoted as m-ZGNR/nH-G or nF-G. Fig. 1a and b present the schematic illustration of the model geometry of 7-ZGNR/9H-G and 9F-G. The edge atoms of pristine ZGNRs are terminated with hydrogen atoms. Two stacking patterns for hybrid ZGNRs-support structures, called AA and AB stacking, are considered. In the case of AA stacking, the carbon atoms of one sublattice of ZGNRs are placed on top of H or F atoms, whereas the carbon atoms from the other sublattice almost point to carbon atoms attached to H or F atoms that are away from ZGNRs. For AB stacking, the carbon atoms of one sublattice are similar with those of AA stacking, but those carbon atoms from the other sublattice point to the hexagonal ring center of supports. Fig. 1 and Fig. S1a and b in ESI† present the optimized structures of 7-ZGNR/9H-G and 9F-G in an AA stacking pattern, whereas those of 6-ZGNR/9H-G
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Fig. 1 Top and side views of geometric structures of ZGNRs supported on fully (a) hydrogenated and (b) fluorinated ZGNRs with AA stacking pattern. The widths of ZGNRs and substrates are denoted by the number of zigzag chains m and n, respectively. The black dashed lines in (a) show the unit cells for hybrid ZGNRs-support systems. The interlayer distances are shown in Å.
and 9F-G in an AB stacking pattern. The AA stacked hybrids are more favorable in terms of energy than that of AB stacking by 38 meV per unit cell for 6-ZGNR/9H-G and 26 meV for 6-ZGNR/ 9F-G. Further electronic structure analyses (see Fig. S1c and d, ESI†) show that the stacking patterns have less impact on the electronic and magnetic properties of supported ZGNRs. Therefore, we mainly focus on the interaction of ZGNR with substrates in AA stacking pattern. As shown in Fig. 1, the substrate-supported ZGNRs well maintain the similar planar structure with freestanding nanoribbons, although very slight distortion near the left carbon edge of ZGNR in 7-ZGNR/9F-G is found. The equilibrium interlayer spacing between 7-ZGNR and 9H-G and 9F-G are evaluated to be 2.73 and 2.91 Å, respectively, which are comparable to 3.2–3.5 Å (ref. 25) for graphene supported on h-BN and 2.54–2.89 Å (ref. 30) for graphene on hydrogenated and fluorinated h-BN. To evaluate the interaction of ZGNRs with the support, the binding energies (Eb) are calculated by the equation Eb = EG + EX-G EG/X-G, where EG, EX-G, and EG/X-G are the total energies of perfect ZGNR, functionalized ZGNR with X atom, and ZGNR-support hybrid, respectively, and the X represents H and (or) F atoms. The binding energy of 7-ZGNR/9H-G is 23 meV per carbon atom of ZGNR, which is larger than that of 7-ZGNR/9F-G with 18 meV, suggesting a stronger interaction of ZGNR with graphane nanoribbons than that with fluorographene. Our computational results reveal that the vdW correction has a significant effect on the equilibrium interaction spacing and binding energy for the hybrid ZGNR-support structures. Comparing with the results obtained by LSDA functional, the interlayer distances of 7-ZGNR 9H-G, 7-ZGNR 9F-G, and 6-ZGNR 9H-G are expanded to 2.82, 3.06, and 2.8 Å (see Fig. S2, ESI†), and the corresponding binding energies are increased to 45, 36, and 42 meV per carbon atom by PBE functional with the vdW correction, respectively. Note that the predicted relative energy stabilities of ZGNRs/nH and nF-G hybrids for the AA and AB stacking patterns are less affected by the vdW correction. The spin-polarized and spin-unpolarized calculations were performed to determine the ground state of ZGNR-support hybrids. It was found that ZGNRs supported on graphane nanoribbons still have the similar antiferromagnetic (AFM) ground state with
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freestanding ZGNRs1 because the AFM state of 7-ZGNR/9H-G is energetically more favorable than the ferromagnetic (FM) state and the spin-unpolarized state by 8 and 45 meV per unit cell, respectively, and the magnetic moments in the AFM state are mainly localized at two carbon atoms of ZGNRs at the edge with antiparallel spin orientation, as shown in Fig. 2a. However, qualitatively different from the fully hydrogenated substrate, the AFM and FM states in 7-ZGNR/9F-G are nearly degenerated with only energy difference of 2 meV per unit cell. The small energy difference between AFM and FM states is found to be less dependent on the width of ZGNRs. This relative stability among various magnetic states distinctly differs from perfect ZGNRs1 and partially hydrogenated ZGNRs.18,47 The spin density distribution of 7-ZGNR/9F-G in the AFM state is plotted in Fig. 2c. Fig. 2b and e display the band structures and spin-polarized total density of states (TDOS) of 7-ZGNR/9H-G in the AFM state. The band gaps of perfect ZGNR are less changed by the CH–p interaction between ZGNR and graphane nanoribbon. The spin-up and spin-down channels in 7-ZGNR/9H-G are almost degenerated with band gaps of 0.25 and 0.27 eV (see Fig. 2b and e), respectively, which are comparable to that of the freestanding 7-ZGNR (0.27 eV). Further spin-polarized projected density of states (PDOS) (right panel in Fig. 2e) and partial charge densities within energy range |E Ef| r 0.2 eV (Fig. S3a, ESI†) also reveal that the support of zigzag graphane nanoribbon has less influence on the electronic and magnetic properties of ZGNRs. The support of graphane nanoribbons with other widths n also presents similar effect on the electric and magnetic properties of ZGNR, comparable with that of 9H-G. In contrast to fully hydrogenated substrate, the interaction of zigzag fluorographene remarkably reduces the band gap of supported ZGNRs, and even induces the semiconducting to metallic behavior transitions. Compared with the band structures of 7-ZGNR/9H-G (Fig. 2b), as shown in Fig. 2d, the a bands near the G point for both spin channels in 7-ZGNR/9F-G are notably shifted downwards and cross the Fermi level, leading to the formation of metallic ZGNR. The TDOS (left panel in Fig. 2f) also confirms that the 7-ZGNR becomes a metal when this nanoribbon is supported on 9F-GNR. The predicted metallic
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Fig. 2 Spin densities (a), spin-polarized band structures (b), and spin-polarized TDOS and PDOS (e) of 7-ZGNR/9H-G in the AFM state. The (c), (d), and (f) for 7-ZGNR/9F-G are similar to (a), (b), and (e) for 7-ZGNR/9H-G, respectively. The Fermi level is set to 0, and the isosurface in (a) and (c) is 0.01 e Å3 with blue for spin up and yellow for spin down. The a and b bands in (b) and (d) are shown in red, and the inset in (d) shows bands near the Fermi level. Electrostatic potentials of (g) 7-ZGNR/9H-G and (h) 7-ZGNR/9F-G are along the xz plane direction.
properties of supported ZGNRs are obviously different from the bilayer ZGNRs48 and nanoribbons supported on h-BN,37 in which the semiconducting properties with a finite band gap are maintained. The PDOS (right panel in Fig. 2f) and partial charge densities within energy range |E Ef| r 0.2 eV (Fig. S3b, ESI†) show that the electronic states around the Fermi level of 7-ZGNR/9F-G are mainly contributed by the ZGNR, suggesting that the transport behaviors of this hybrid structure are still controlled by ZGNR. The predicted electronic properties of 7-ZGNR/9H(F)-G by PBE + D (see Fig. S2c and d, ESI†) exhibit similar trend with that of LSDA, although the small band gap of 37 meV in 7-ZGNR/9F-G is found by the vdW correction. The remarkable modification of electronic properties of ZGNRs by fluorographene support may be attributed to larger change in electrostatic potentials due to the intrinsic polarization induced by the substrate (see Fig. 2h), compared to that of graphane support (Fig. 2g). To further understand the interaction mechanism between ZGNRs and support, the charge density difference, Dr = rG/X-G rX-G rG, is calculated,
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where rG/X-G, rX-G, and rG represent the total charge densities of hybrid ZGNRs-support systems, zigzag graphane or fluorographene support, and pristine ZGNR, respectively. The calculated results (see Fig. S4a and b, ESI†) show that the charge densities of the hybrid are redistributed with the electron depletion that are mainly located at the edge atoms of ZGNR and electron accumulation at support. Comparing with the graphane support (Fig. S4a, ESI†), the interlayer interaction between ZGNR and fluorographene via CF–p lead to more prominent charge transfers (Fig. S4b, ESI†). The electronic structures of ZGNRs/nF-G may depend on the width n of fluorographene support. Fig. 3a and b; Fig. S5a and b (ESI†) show the geometric structures of 6-ZGNR/nF-G by LSDA. The calculations on 6-ZGNR/nF-G by PBE functional with the vdW correction were also performed as shown in Fig. S6 (ESI†). The predicted binding energy change of 6-ZGNR/nF-G with n by LSDA efficiently agrees with the results by PBE + vdW; however, the binding strength is improved by the latter. The substrate width n-dependent band gaps of 6-ZGNR/nF-G for spin-up and
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the valence band maximum (VBM) of 6-ZGNR with respect to the Fermi level induced by the wider fluorographene substrate, compared to the narrow one. In addition, our calculated results suggest that the electronic properties of m-ZGNRs supported on fluorographene substrate, with the fixed width, is slightly dependent on the ribbon width m. Although the supported m-ZGNRs with width m less than 6 exhibit the semiconducting properties, the band gaps are reduced to very small values with 63, 44, and 41 meV for m = 3, 4, and 5 (see Fig. S5c–e, ESI†), respectively, compared to the corresponding pristine ZGNRs. 3.2
Fig. 3 Side view of geometric structures of (a) 6-ZGNR/5F-G and (b) 6-ZGNR/9F-G. (c) The support width n-dependent band gaps of 6-ZGNR/ nF-G for spin-up and spin-down channels.
spin-down channels are shown in Fig. 3c. The 6-ZGNR supported on nF-G with width n less than 9 in the AFM state presents the semiconducting property, and their band gaps for spin up and spin down channels monotonically decrease with increasing the substrate width n, ranging from 224 and 281 meV for n = 3 to 27 meV for n = 8, respectively. When the fluorographene support width is further increased to 10, the metallicity of 6-ZGNR is realized. The band structures (Fig. S5a and b, ESI†) show the larger shift of conduction band minimum (CBM) and
Hybrid graphane–fluorographene nanoribbons
As discussed above, the electronic and magnetic properties of ZGNRs are less affected by the graphane nanoribbon substrates, whereas ZGNRs supported on fluorographene ribbons can realize the semiconducting to metallic behavior transition, which are attributed to the different electrostatic potentials induced by graphane and fluorographene supports. Therefore, both hydrogenation and fluorination on ZGNRs used as support, referred as hybrid graphane–fluorographene ribbons, could be expected to induce the intriguing electronic and magnetic properties, and even realize the half-metal property of ZGNRs. We first discuss the stabilities and electronic structures of zigzag hybrid graphane–fluorographene nanoribbons. As shown in Fig. 3a, the zigzag hybrid nanoribbons, which include fluorographene side with width n and graphane side with width m, were denoted as mH–nF-G. We mainly focus on the hybrid nanoribbons mH–nF-G with widths m + n = 9 because the ribbons with other widths give the similar results. Fig. S7 (ESI†) presents the optimized structure of (9 n)H–nF-G with different width n.
Fig. 4 (a) Schematic representation of mH–nF-G with m + n = 9 and top and side views of geometric structure of 6H–3F-G. (b) Formation energies and (e) band gaps of (9 n)H–nF-G as a function of the number of fluorinated zigzag chains n. (c) Band structures of 6H–3F-G with the Fermi level being set to 0. (d) Partial charge densities of VBM (top panel) and CBM (bottom panel) states at G point in (c). The isosurface is 0.03 e Å3.
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In order to evaluate the thermodynamic stability of hydrogenation and fluorination of ZGNRs, the formation energies are nH nF calculated by Ef ¼ EHF-G EG EH2 EF2 , where EH–F-G, 2 2 EG, EH2, and EF2 are the total energies of hybrid graphane– fluorographene nanoribbons, pristine graphene nanoribbons, and free hydrogen and fluorine molecules, respectively, whereas nH and nF represent the number of hydrogen and fluorine atoms on hybrid ribbons, respectively. Note that the negative formation energy Ef indicates the hybrid graphane– fluorographene nanoribbons with higher stability than its constituents. As shown in Fig. 4b, the calculated formation energies of hybrid nanoribbons (9 n)H–nF-G monotonically decrease with increasing the fluorographene domain width n, ranging from 0.46 eV for n = 0 to 1.68 eV per adsorbed atom for n = 9, suggesting that the hybrid ribbons with wider fluorographene moieties are more likely accessible than the narrow one. However, the observation of favorable formation energies do not mean that the hybrid graphane–fluorographene nanoribbons can be prepared by directly exposing GNRs to H2 and F2 because it is difficult to dissociate these molecules on GNRs.17 Cutting the experimentally available graphane and fluorographene layers in the same way for obtaining GNRs may provide the potential method for the transformation of GNRs to hybrid ribbons. The electronic structures show that the hybrid nanoribbons (9 n)H–nF-G are still semiconductors in comparison to pristine graphane and fluorographene nanoribbons, but the band gaps are well tuned by changing the ratio of fluorination to hydrogenation. Fig. 4c and e present the band structures of 6H–3F-G and width n dependence of band gaps of (9 n)H–nF-G, respectively. It is surprising that a nonmonotonic behavior of the energy gap as a function of width n is found. The partial charge densities of 6H–3F-G (Fig. 4d) show that the contribution to the VBM and CBM stems from different domain, which may be responsible for the nonmonotonic variety of the band gaps of hybrid ribbons with the width n.
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3.3
ZGNRs supported on zigzag hybrid nanoribbons
We now discuss the structural and electronic properties of ZGNRs supported on hybrid fluorographene–graphane nanoribbons (ZGNR/(9 n)H–nF-G). Fig. 5a and b present the geometric structures of 7-ZGNR/6H–3F-G and 3H–6F-G, respectively. Because of the hybrid support interaction, the ribbon domain of 7-ZGNR above fluorographene side is slightly pulled out-ofplane with respect to other domain above the graphane side, leading to a significant interlayer spacing difference between these two domains and support. The calculated binding energies show (Fig. 5c) that the interaction of ZGNRs with the hybrid support with all ratios of F to H is thermodynamically favorable, although the binding strength of 7-ZGNR with (9 n)H–nF-G decreases with the increasing fluorographene width n, as observed the corresponding binding energies range from 27 to 13 meV per carbon atom for n = 1 to 7, respectively. The PBE functional with vdW correction predicts the similar change of binding energies compared with LSDA (red in Fig. 5c), but improves the binding strength between 7-ZGNR and the hybrid substrate. Based on the spin-polarized and spin-unpolarized calculations, ZGNRs supported on hybrid fluorographene–graphane ribbons maintain the AFM ground state, and the energy difference between the AFM and FM states decreases as the ratio of fluorination to hydrogenation in substrate increases. The electronic structure calculations show that the hybrid nanoribbon supported ZGNRs in the AFM state are spinpolarized half-semiconductors with distinct band gaps for both spin channels, which is considerably different from the freestanding ZGNRs. Fig. 6a and b display the band structures and spin densities of 7-ZGNR/6H–3F-G and 3H–6F-G in the AFM state, respectively. It is obviously found that the spin degeneracies of a and b bands near the Fermi level from ZGNR are completely broken due to its interaction with the substrate (red in Fig. 6a and b). The spin-up band gaps of 7-ZGNR supported on 6H–3F-G and 3H–6F-G are reduced to 0.161 and 0.092 eV, while their
Fig. 5 Top and side views of geometric structures of (a) 7-ZGNR/3H–6F-G (b) 7-ZGNR/6H–3F-G. The interlayer spacing shown in (a) and (b) is in Å. The binding energies (c) and the up-spin and down-spin band gaps (d) of 7-ZGNR/(9 n)H–nF-G as a function of the number of fluorinated zigzag chains n by LSDA and PBE + D.
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Fig. 6 Band structures and spin densities of (a) 7-ZGNR/6H–3F-G and (b) 7-ZGNR/3H–6F-G. The Fermi level is set to 0, and the isosurface is 0.01 e Å3 with blue for spin up and yellow for spin down. The bands near the Fermi level coming from 7-ZGNR are shown in red. (c, d) The spin-polarized TDOS (left panel) and PDOS (right panel) and (e, f) electrostatic potential of hybrid ZGNR-support nanocomplex along the xz-plane direction: (c) and (e) 7-ZGNR/ 6H–3F-G, and (d) and (f) 7-ZGNR/3H–6F-G.
spin-down band gaps are increased to 0.422 and 0.317 eV compared with freestanding 7-ZGNR with 0.27 eV. The TDOS calculations (left panel in Fig. 6c and d) also reveal the halfsemiconductor property of ZGNR induced by the support interaction. Further PDOS analyses (right panel in Fig. 6c and d) show that the spin-polarized electronic states near the Fermi level of ZGNR/support are controlled by ZGNR. Interestingly, in the absence of an applied electric field, the spin-up and spin-down band gaps of supported ZGNRs can be well tuned in the opposite direction by changing the ratio of fluorographene to graphane width in hybrid support. Fig. 5d show the up-spin and down-spin band gaps of 7-ZGNR/(9 n)H–nF-G as a function of the fluorographene width n. With increasing the width n, the band gaps of 7-ZGNR/support for spin-up channel steadily decrease from 0.278 to 0.068 eV for n = 1 to 8, while the down-spin band gaps first increase from 0.296 eV for n = 1 to the maximum value of 0.422 eV for n = 4, and then decrease to 0.317, 0.146, and 0.092 eV for n = 6, 7, and 8 respectively. The notable difference in electrostatic potential (Fig. 6e and f)
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and charge density difference (Fig. S4c and d, ESI†) between 7-ZGNR/6H–3F-G and 3H–6F-G explains the effect of different hybrid support on electronic properties of ZGNRs. Similar to the graphene–graphane hybrid structures,29 both the CH–p and CF–p interactions between GNRs and hybrid graphane– fluorographene ribbons also play an important role for tuning the spin-polarized band gaps of ZGNRs. For comparison, we also performed the calculations on the electronic and magnetic properties of 7-ZGNR/(9 n)H–nF-G by the PBE functional with vdW correction (red and black triangles in Fig. 5d and Fig. S8, ESI†). It is clearly observed that the vdW correction has less influence on the predicted tendency for the width n-dependent band gaps of ZGNR, although the band gaps by PBE + D are larger than those by LSDA. The band gaps tuned by hybrid support notably differ from the previous studies for ZGNRs sandwiched between h-BN nanoribbons or sheets,37 in which the tunable band gaps for both spin channels are realized under a bias voltage that is normal to the ribbon plane. Thus, tuning the ratio of fluorination to hydrogenation in a
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hybrid fluorographene–graphane support may provide an efficient path for spin-resolved band engineering of the ZGNRs. The modified spin-polarized band gaps of ZGNRs in the opposite direction have important applications for the fabrication of graphene-based spin filtering devices. The previous studies show that the electronic and magnetic properties of graphene supported on substrate30,37 are very sensitive to the interlayer spacing. Similar behavior can be expected in our ZGNR/(9 n)H–nF-G hybrid systems here. The calculated results show that the half-semiconducting ZGNR can be tuned into half-metal via reducing the interlayer spacing between the ZGNR and substrate. Fig. 7a presents the interlayer spacing dependence of band gaps of 7-ZGNR/6H–3F-G and 3H–6F-G for spin-up and spin-down channels. Note that we only select the distance between the center of ZGNR and the support to represent the interlayer spacing in Fig. 7a because of the local structural distortion of planar ribbons. In the case of 6H–3F-G support (circle in Fig. 7a), with reducing the interlayer distance, the spin-up band gaps of 7-ZGNR steadily decrease until the spacing is reduced to 1.82 Å, whereas the band gap of 0.42 eV for the spin down is not considerably changed. When the interlayer spacing is further reduced to 1.65 and 1.53 Å, the spin-down band gap disappears, while the spin-up band gap is still about 0.35 and 0.28 eV, respectively, leading to the half-semiconducting to half-metallic behavior transition. For example, the band structures (see Fig. S9a, ESI† and Fig. 7b) show that as the interlayer spacing is reduced to 1.65 and 1.53 Å, the b band of the spin-up channel shifts upward and crosses the Fermi level, resulting in the metallic behavior of 7-ZGNR, whereas the spin-down channel has a significant band gap. The transition from half-semiconductor
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to half-metal can be explained by the enhanced charge density redistribution (Fig. 7c and d). Comparing the charge density differences of 7-ZGNR/3H–6F-G with interlayer spacing of 2.75 and 2.02 Å, it can be seen that the charge transfers and orbital interaction between 7-ZGNR and the support dramatically increase as the interlayer distance is reduced. When 7-ZGNR is supported on 3H–6F-G with a wider fluorographene domain, the band gaps for both spin channels decrease with increasing the interlayer distance (triangles in Fig. 7a), but the gap for spin up drops to zero before that for spin down, resulting in a half-metallic state. Fig. S9b (ESI†) displays the band structures of 7-ZGNR/3H–6F-G with interlayer spacing of 2.21 Å. Interestingly, we find that the critical interlayer spacing realizing the transition from half-semiconductor to half-metal in 7-ZGNR/3H–6F-G is increased to 2.21 Å, which is larger than that of 6H–3F-G substrate with 1.65 Å. A compressive strain along the direction perpendicular to the ribbon plane may be used to realize the interlayer distance change.37 Fig. S10 (ESI†) presents the interaction energy between 7-ZGNR and 3H–6F-G and 6H–3F-G as a function of the interlayer spacing. Note that the negative binding energy indicates the thermodynamically favorable interaction. It is clear from Fig. S9 (ESI†) that when the interlayer spacing is reduced to the critical value, the interaction of 7-ZGNR with 3H–6F-G is more favorable in energy than with 6H–3F-G because the binding energy of the former is significantly less than that of the latter, although the two layers will be repulsive with reducing the interlayer distance. These results indicate that a less compressive strain between ZGNR and a substrate with a wider fluorographene domain is needed to reach the critical interlayer spacing, compared to this complex with a narrow one.
Fig. 7 (a) Interlayer spacing-dependent band gaps of 7-ZGNR/6H–3F-G and 3H–6F-G for spin-up and spin-down channels. (b) Band structures of 7-ZGNR/3H–6F-G at the interlayer spacing of 1.53 Å. The Fermi level is set to 0, and the inset in (b) show bands around the Fermi level. Charge density differences of 7-ZGNR/3H–6F-G with the interlayer spacing of (c) 2.75 and (d) 2.02 Å. The blue and yellow areas in (c) and (d) denote electron accumulation and depletion, respectively, and isosurfaces are 0.002 e Å3.
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Therefore, ZGNRs supported hybrid fluorographene–graphane ribbons open an alternative avenue toward the realization of graphene-based spintronics applications.
4. Conclusion In conclusion, by using DFT calculations, we have systematically investigated the electronic and magnetic properties of ZGNRs supported on selectively hydrogenated and fluorinated ZGNRs. The supports of graphane and nanoribbons present different impacts on the electronic and magnetic properties of ZGNRs. The ZGNRs supported on the zigzag hybrid fluorographene– graphane nanoribbons are spin-polarized half-semiconductors with distinct band gaps for both spin channels. More importantly, in the absence of an electric field, the spin-up and spindown band gaps of supported ZGNRs can be well tuned in the opposite direction by changing the ratio of fluorographene to graphane domain in hybrid substrates, which is attributed to the enhanced potential difference between these two domains of ZGNRs above the fluorographene and graphane side of the substrate. Interestingly, with the reduction in interlayer spacing, the ZGNRs supported on hybrid nanoribbons exhibit the half-semiconducting to half-metallic behavior transitions. The half-metallicity in ZGNRs/hybrid support with a wider fluorographene domain can be realized more easily than that with a narrow one because the intrinsic polarization of the former substrate is enhanced.
Acknowledgements This work was supported by the National Science Foundation of China (21103026 and 21133007). We acknowledge simulating discussions with Z. Cao and thank the computational resources and assistance provided by the State Key Laboratory of Physical Chemistry of Solid Surfaces (Xiamen University).
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Realizing semiconductor–half-metal transition in zigzag graphene nanoribbons supported on hybrid fluorographene–graphane nanoribbons† Shaobin Tang*a and Xinrui Caob Hydrogenation and fluorination provide promising applications for tuning the properties of graphenebased nanomaterials. Using first-principles calculations, we investigate the electronic and magnetic properties of zigzag graphene nanoribbons (ZGNRs) supported on hydrogenated and fluorinated ZGNRs. Our results indicate that the support of zigzag graphane nanoribbon with its full width has less impact on the electronic and magnetic properties of ZGNRs, whereas the ZGNRs supported on fluorographene nanoribbons can be tuned to metal with almost degenerated ferro- and anti-ferromagnetic states due to the intrinsic polarization of substrate. The ZGNRs supported on zigzag hybrid fluorographene–graphane nanoribbons are spin-polarized half-semiconductors with distinct band gaps for spin-up and spin-down channels. Interestingly, in the absence of an external electric field, the spin-polarized band gaps of supported ZGNRs can be well modulated in the opposite direction by changing the ratio of fluorination
Received 24th July 2014, Accepted 9th September 2014 DOI: 10.1039/c4cp03291h
to hydrogenation concentration in hybrid substrates. Furthermore, the ZGNRs supported on hybrid nanoribbons exhibit the half-semiconducting to half-metallic behavior transition as the interlayer spacing is gradually reduced, which is realized more easily for the hybrid support with a relatively wide fluorographene moiety compared to its narrow counterpart. Present results provide a novel way for designing substrate-
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supported graphene spintronic devices.
1. Introduction Graphene nanoribbons (GNRs) have attracted a large amount of attention for future nanoscale electronics due to their outstanding physical properties.1–5 In particular, it is predicted1,6,7 that the zigzag-edged GNRs (ZGNRs) exhibit a promising magnetic property that are arising from two localized edge states, which are ferromagnetically coupled within each edge, but antiferromagnetically between the two edges. Interestingly, the ZGNRs become half-metallic when an external transverse electric field is applied.8–10 In contrast to the widely-used gate voltage in the current nanotechnology, a very high critical electric field is required to obtain the half-metallicity with the increase in ribbon width, suggesting the difficulty for realizing these properties. a
Key Laboratory of Organo-Pharmaceutical Chemistry of Jiangxi Province, Gannan Normal University, Ganzhou 341000, China. E-mail: [email protected]; Fax: +86-797-8393536 b Department of Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, S-106 91 Stockholm, Sweden † Electronic supplementary information (ESI) available: Geometric structures, band structures, and partial charge densities by LSDA for other hybrid structures and geometric structures and band structures for selected systems by PBE + D. See DOI: 10.1039/c4cp03291h
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Chemical modification may provide a promising way for tuning the electronic and magnetic properties of low-dimensional nanomaterials. Theoretically, The two edge-modified ZGNRs with CH3 and NO2 groups,11 boron nitride (BN) sheet-embedded ZGNRs,12 and carbon chain-doped zigzag boron nitride nanoribbons (ZBNNRs)13 are predicted to be half-metal. Similar to the chemically functionalized graphene by H (called graphane) and F atoms (fluorographene),14–16 the full hydrogenation17,18 and fluorination19 of GNRs can effectively modulate the band gap of perfect nanoribbons. More importantly, our recent studies19 indicate that the partial fluorination of ZGNRs induces the interesting electronic property of half-semiconductors, which are considerably different from the hybrid graphane–graphene nanoribbons.18 However, the structural and chemical modification on carbon nanostructures may result in the destruction of the honeycomb structure, and even destroy the intrinsic properties of materials. The graphene–substrate interactions play an important role in tuning the properties of graphene-based nanomaterials, without degrading its intrinsic electronic properties. Many experiments and theoretical calculations20–26 reveal that the hexagonal boron nitride (h-BN) could be chosen to be the best matching substrate for graphene for realizing its high carrier mobility. It was found that the h-BN substrate opens a finite
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band gap in graphene, which preserves the Dirac cone of graphene. Interestingly, the interactions of graphene with fully or partially patterned hydrogenated and fluorinated graphene27–29 and h-BN30 can lead to n- or p-type doping of graphene, and it can also create a finite band gap in graphene due to the CH–p or CF–p interaction. The similar SiH–p interactions also exist between silicene and hydrogenated silicene.29 More importantly, the systematic density functional theory (DFT) computations by Chen et al.31 revealed the existence of considerable C–H F–C bonding in graphane–fluorographene bilayers, which can reduce the band gap of the corresponding individual monolayer. The recent comprehensive reviews report many methods for tuning the properties of graphene-related nanomaterials.32 Similarly, the weak interaction induced by substrates or molecules is extensively used to modify the properties of GNRs in both experimental33 and theoretical works.34–36 Recently, using the theoretical calculations, Wong et al.34 and Chen et al.35 demonstrated that many dipolar molecules, such as the mechanochromic polymers and ladder-structure polydiacetylene derivatives that are noncovalently deposited on GNRs, can alter the electrostatic environment of the nanoribbons and cause a large change in band gap. In addition, they can even induce the spin gapless semiconductor–half-metal–metal transition in ZGNRs through the dipole–dipole interactions. Such weak interaction also tunes the band structure of the C4F bilayer rather than the individual C4F monolayer.36 Very recently, Guo et al.37 reported that the half-metallicity in ZGNRs sandwiched between two ZBNNRs can be realized by a bias voltage or a moderate compressive strain. In addition, the h-BN (0001) substrates induce a band gap and cause insignificant splitting of the bands in 8-ZGNR.38 Despite these important contributions, developing an effective route to realize the half metallicity of GNRs, especially in the absence of an external electric field, is still a challenge. Because of the wide band-gap in semiconductors such as graphane and fluorographene and their high stabilities, as well as due to the large difference in electronegativity among H, C, and F atoms, these functionalized carbon nanomaterials when used as a support of ZGNRs may induce promising electronic and magnetic properties. In this work, we reveal that ZGNRs supported on zigzag fluorographene nanoribbons can be tuned into metal by extensive first-principles calculations. In the absence of an applied electric field, the ZGNRs supported on hybrid fluorographene–graphane ribbons exhibit half-semiconducting to half-metallic behavior transitions via gradually reducing the interlayer spacing.
2. Computational details All calculations were performed within the framework of the plane-wave pseudopotential density-functional theory (DFT) implemented in CASTEP.39 The local spin density approximation (LSDA) proposed by Ceperley and Alder40 was used to deal with the exchange and correlation terms. The ultrasoft pseudopotentials41 for the ion–electron interactions and a kinetic energy cutoff of 350 eV in the plane-wave expansion were used.
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The one-dimensional (1D) periodic boundary conditions were applied along the growth directions of nanoribbons. Vacuum spacings of 10 Å for layers and 15 Å for edges between the adjacent cells were considered for calculations. Monkhorst– Pack mesh42 of k-points 1 1 13 were used for sampling the 1D Brillouin zones during geometry optimization. All atomic positions were optimized by the conjugate gradient method with a converging tolerance of 0.02 eV Å1 for the forces on all the atoms. The convergence criterion of energy for self-consistent field computations was set to 106 eV. The electronic structure calculations were performed by using 21 k-points along the periodic orientation. For comparison, we also applied the Perdew–Burke–Ernzerhof (PBE)43 functional including van der Waals (vdW) correction proposed by Grimme44 (referred as PBE + D, where D stands for dispersion) to calculate binding energies and other properties for all the systems. Usually, both the LSDA and the generalized-gradient approximation (GGA) underestimate the band gap, while the HSE06 hybrid functional typically predicts more accurate band gaps close to experimental data; however, it is still not the ultimate solution.45,46
3. Results and discussions 3.1 ZGNRs supported on graphane and fluorographene nanoribbons Similar to ZGNRs, the fully hydrogenated and fluorinated zigzag graphene nanoribbons, namely as graphane and fluorographene nanoribbons, can be obtained by cutting them from graphane and fluorographene in chair configurations, respectively. The geometrical structure calculations show that all the carbon atoms in zigzag graphane and fluorographene nanoribbons have the same sp3 hybridization as the corresponding sheet in which the slightly site-dependent C–H and C–F bond lengths are 1.11 Å and 1.37 Å, which is consistent with the previous results.17–19 The mismatch between the lattice constants of ZGNRs and those functionalized ribbons is less than 5%. Following the previous convention, the pristine zigzag graphene and graphane or fluorographene nanoribbons are labeled by the number of parallel zigzag chains m and n, which can be defined as m-ZGNR and nH-G or nF-G, respectively. Accordingly, ZGNRs supported on zigzag graphane or fluorographene nanoribbons are denoted as m-ZGNR/nH-G or nF-G. Fig. 1a and b present the schematic illustration of the model geometry of 7-ZGNR/9H-G and 9F-G. The edge atoms of pristine ZGNRs are terminated with hydrogen atoms. Two stacking patterns for hybrid ZGNRs-support structures, called AA and AB stacking, are considered. In the case of AA stacking, the carbon atoms of one sublattice of ZGNRs are placed on top of H or F atoms, whereas the carbon atoms from the other sublattice almost point to carbon atoms attached to H or F atoms that are away from ZGNRs. For AB stacking, the carbon atoms of one sublattice are similar with those of AA stacking, but those carbon atoms from the other sublattice point to the hexagonal ring center of supports. Fig. 1 and Fig. S1a and b in ESI† present the optimized structures of 7-ZGNR/9H-G and 9F-G in an AA stacking pattern, whereas those of 6-ZGNR/9H-G
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Fig. 1 Top and side views of geometric structures of ZGNRs supported on fully (a) hydrogenated and (b) fluorinated ZGNRs with AA stacking pattern. The widths of ZGNRs and substrates are denoted by the number of zigzag chains m and n, respectively. The black dashed lines in (a) show the unit cells for hybrid ZGNRs-support systems. The interlayer distances are shown in Å.
and 9F-G in an AB stacking pattern. The AA stacked hybrids are more favorable in terms of energy than that of AB stacking by 38 meV per unit cell for 6-ZGNR/9H-G and 26 meV for 6-ZGNR/ 9F-G. Further electronic structure analyses (see Fig. S1c and d, ESI†) show that the stacking patterns have less impact on the electronic and magnetic properties of supported ZGNRs. Therefore, we mainly focus on the interaction of ZGNR with substrates in AA stacking pattern. As shown in Fig. 1, the substrate-supported ZGNRs well maintain the similar planar structure with freestanding nanoribbons, although very slight distortion near the left carbon edge of ZGNR in 7-ZGNR/9F-G is found. The equilibrium interlayer spacing between 7-ZGNR and 9H-G and 9F-G are evaluated to be 2.73 and 2.91 Å, respectively, which are comparable to 3.2–3.5 Å (ref. 25) for graphene supported on h-BN and 2.54–2.89 Å (ref. 30) for graphene on hydrogenated and fluorinated h-BN. To evaluate the interaction of ZGNRs with the support, the binding energies (Eb) are calculated by the equation Eb = EG + EX-G EG/X-G, where EG, EX-G, and EG/X-G are the total energies of perfect ZGNR, functionalized ZGNR with X atom, and ZGNR-support hybrid, respectively, and the X represents H and (or) F atoms. The binding energy of 7-ZGNR/9H-G is 23 meV per carbon atom of ZGNR, which is larger than that of 7-ZGNR/9F-G with 18 meV, suggesting a stronger interaction of ZGNR with graphane nanoribbons than that with fluorographene. Our computational results reveal that the vdW correction has a significant effect on the equilibrium interaction spacing and binding energy for the hybrid ZGNR-support structures. Comparing with the results obtained by LSDA functional, the interlayer distances of 7-ZGNR 9H-G, 7-ZGNR 9F-G, and 6-ZGNR 9H-G are expanded to 2.82, 3.06, and 2.8 Å (see Fig. S2, ESI†), and the corresponding binding energies are increased to 45, 36, and 42 meV per carbon atom by PBE functional with the vdW correction, respectively. Note that the predicted relative energy stabilities of ZGNRs/nH and nF-G hybrids for the AA and AB stacking patterns are less affected by the vdW correction. The spin-polarized and spin-unpolarized calculations were performed to determine the ground state of ZGNR-support hybrids. It was found that ZGNRs supported on graphane nanoribbons still have the similar antiferromagnetic (AFM) ground state with
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freestanding ZGNRs1 because the AFM state of 7-ZGNR/9H-G is energetically more favorable than the ferromagnetic (FM) state and the spin-unpolarized state by 8 and 45 meV per unit cell, respectively, and the magnetic moments in the AFM state are mainly localized at two carbon atoms of ZGNRs at the edge with antiparallel spin orientation, as shown in Fig. 2a. However, qualitatively different from the fully hydrogenated substrate, the AFM and FM states in 7-ZGNR/9F-G are nearly degenerated with only energy difference of 2 meV per unit cell. The small energy difference between AFM and FM states is found to be less dependent on the width of ZGNRs. This relative stability among various magnetic states distinctly differs from perfect ZGNRs1 and partially hydrogenated ZGNRs.18,47 The spin density distribution of 7-ZGNR/9F-G in the AFM state is plotted in Fig. 2c. Fig. 2b and e display the band structures and spin-polarized total density of states (TDOS) of 7-ZGNR/9H-G in the AFM state. The band gaps of perfect ZGNR are less changed by the CH–p interaction between ZGNR and graphane nanoribbon. The spin-up and spin-down channels in 7-ZGNR/9H-G are almost degenerated with band gaps of 0.25 and 0.27 eV (see Fig. 2b and e), respectively, which are comparable to that of the freestanding 7-ZGNR (0.27 eV). Further spin-polarized projected density of states (PDOS) (right panel in Fig. 2e) and partial charge densities within energy range |E Ef| r 0.2 eV (Fig. S3a, ESI†) also reveal that the support of zigzag graphane nanoribbon has less influence on the electronic and magnetic properties of ZGNRs. The support of graphane nanoribbons with other widths n also presents similar effect on the electric and magnetic properties of ZGNR, comparable with that of 9H-G. In contrast to fully hydrogenated substrate, the interaction of zigzag fluorographene remarkably reduces the band gap of supported ZGNRs, and even induces the semiconducting to metallic behavior transitions. Compared with the band structures of 7-ZGNR/9H-G (Fig. 2b), as shown in Fig. 2d, the a bands near the G point for both spin channels in 7-ZGNR/9F-G are notably shifted downwards and cross the Fermi level, leading to the formation of metallic ZGNR. The TDOS (left panel in Fig. 2f) also confirms that the 7-ZGNR becomes a metal when this nanoribbon is supported on 9F-GNR. The predicted metallic
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Fig. 2 Spin densities (a), spin-polarized band structures (b), and spin-polarized TDOS and PDOS (e) of 7-ZGNR/9H-G in the AFM state. The (c), (d), and (f) for 7-ZGNR/9F-G are similar to (a), (b), and (e) for 7-ZGNR/9H-G, respectively. The Fermi level is set to 0, and the isosurface in (a) and (c) is 0.01 e Å3 with blue for spin up and yellow for spin down. The a and b bands in (b) and (d) are shown in red, and the inset in (d) shows bands near the Fermi level. Electrostatic potentials of (g) 7-ZGNR/9H-G and (h) 7-ZGNR/9F-G are along the xz plane direction.
properties of supported ZGNRs are obviously different from the bilayer ZGNRs48 and nanoribbons supported on h-BN,37 in which the semiconducting properties with a finite band gap are maintained. The PDOS (right panel in Fig. 2f) and partial charge densities within energy range |E Ef| r 0.2 eV (Fig. S3b, ESI†) show that the electronic states around the Fermi level of 7-ZGNR/9F-G are mainly contributed by the ZGNR, suggesting that the transport behaviors of this hybrid structure are still controlled by ZGNR. The predicted electronic properties of 7-ZGNR/9H(F)-G by PBE + D (see Fig. S2c and d, ESI†) exhibit similar trend with that of LSDA, although the small band gap of 37 meV in 7-ZGNR/9F-G is found by the vdW correction. The remarkable modification of electronic properties of ZGNRs by fluorographene support may be attributed to larger change in electrostatic potentials due to the intrinsic polarization induced by the substrate (see Fig. 2h), compared to that of graphane support (Fig. 2g). To further understand the interaction mechanism between ZGNRs and support, the charge density difference, Dr = rG/X-G rX-G rG, is calculated,
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where rG/X-G, rX-G, and rG represent the total charge densities of hybrid ZGNRs-support systems, zigzag graphane or fluorographene support, and pristine ZGNR, respectively. The calculated results (see Fig. S4a and b, ESI†) show that the charge densities of the hybrid are redistributed with the electron depletion that are mainly located at the edge atoms of ZGNR and electron accumulation at support. Comparing with the graphane support (Fig. S4a, ESI†), the interlayer interaction between ZGNR and fluorographene via CF–p lead to more prominent charge transfers (Fig. S4b, ESI†). The electronic structures of ZGNRs/nF-G may depend on the width n of fluorographene support. Fig. 3a and b; Fig. S5a and b (ESI†) show the geometric structures of 6-ZGNR/nF-G by LSDA. The calculations on 6-ZGNR/nF-G by PBE functional with the vdW correction were also performed as shown in Fig. S6 (ESI†). The predicted binding energy change of 6-ZGNR/nF-G with n by LSDA efficiently agrees with the results by PBE + vdW; however, the binding strength is improved by the latter. The substrate width n-dependent band gaps of 6-ZGNR/nF-G for spin-up and
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the valence band maximum (VBM) of 6-ZGNR with respect to the Fermi level induced by the wider fluorographene substrate, compared to the narrow one. In addition, our calculated results suggest that the electronic properties of m-ZGNRs supported on fluorographene substrate, with the fixed width, is slightly dependent on the ribbon width m. Although the supported m-ZGNRs with width m less than 6 exhibit the semiconducting properties, the band gaps are reduced to very small values with 63, 44, and 41 meV for m = 3, 4, and 5 (see Fig. S5c–e, ESI†), respectively, compared to the corresponding pristine ZGNRs. 3.2
Fig. 3 Side view of geometric structures of (a) 6-ZGNR/5F-G and (b) 6-ZGNR/9F-G. (c) The support width n-dependent band gaps of 6-ZGNR/ nF-G for spin-up and spin-down channels.
spin-down channels are shown in Fig. 3c. The 6-ZGNR supported on nF-G with width n less than 9 in the AFM state presents the semiconducting property, and their band gaps for spin up and spin down channels monotonically decrease with increasing the substrate width n, ranging from 224 and 281 meV for n = 3 to 27 meV for n = 8, respectively. When the fluorographene support width is further increased to 10, the metallicity of 6-ZGNR is realized. The band structures (Fig. S5a and b, ESI†) show the larger shift of conduction band minimum (CBM) and
Hybrid graphane–fluorographene nanoribbons
As discussed above, the electronic and magnetic properties of ZGNRs are less affected by the graphane nanoribbon substrates, whereas ZGNRs supported on fluorographene ribbons can realize the semiconducting to metallic behavior transition, which are attributed to the different electrostatic potentials induced by graphane and fluorographene supports. Therefore, both hydrogenation and fluorination on ZGNRs used as support, referred as hybrid graphane–fluorographene ribbons, could be expected to induce the intriguing electronic and magnetic properties, and even realize the half-metal property of ZGNRs. We first discuss the stabilities and electronic structures of zigzag hybrid graphane–fluorographene nanoribbons. As shown in Fig. 3a, the zigzag hybrid nanoribbons, which include fluorographene side with width n and graphane side with width m, were denoted as mH–nF-G. We mainly focus on the hybrid nanoribbons mH–nF-G with widths m + n = 9 because the ribbons with other widths give the similar results. Fig. S7 (ESI†) presents the optimized structure of (9 n)H–nF-G with different width n.
Fig. 4 (a) Schematic representation of mH–nF-G with m + n = 9 and top and side views of geometric structure of 6H–3F-G. (b) Formation energies and (e) band gaps of (9 n)H–nF-G as a function of the number of fluorinated zigzag chains n. (c) Band structures of 6H–3F-G with the Fermi level being set to 0. (d) Partial charge densities of VBM (top panel) and CBM (bottom panel) states at G point in (c). The isosurface is 0.03 e Å3.
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In order to evaluate the thermodynamic stability of hydrogenation and fluorination of ZGNRs, the formation energies are nH nF calculated by Ef ¼ EHF-G EG EH2 EF2 , where EH–F-G, 2 2 EG, EH2, and EF2 are the total energies of hybrid graphane– fluorographene nanoribbons, pristine graphene nanoribbons, and free hydrogen and fluorine molecules, respectively, whereas nH and nF represent the number of hydrogen and fluorine atoms on hybrid ribbons, respectively. Note that the negative formation energy Ef indicates the hybrid graphane– fluorographene nanoribbons with higher stability than its constituents. As shown in Fig. 4b, the calculated formation energies of hybrid nanoribbons (9 n)H–nF-G monotonically decrease with increasing the fluorographene domain width n, ranging from 0.46 eV for n = 0 to 1.68 eV per adsorbed atom for n = 9, suggesting that the hybrid ribbons with wider fluorographene moieties are more likely accessible than the narrow one. However, the observation of favorable formation energies do not mean that the hybrid graphane–fluorographene nanoribbons can be prepared by directly exposing GNRs to H2 and F2 because it is difficult to dissociate these molecules on GNRs.17 Cutting the experimentally available graphane and fluorographene layers in the same way for obtaining GNRs may provide the potential method for the transformation of GNRs to hybrid ribbons. The electronic structures show that the hybrid nanoribbons (9 n)H–nF-G are still semiconductors in comparison to pristine graphane and fluorographene nanoribbons, but the band gaps are well tuned by changing the ratio of fluorination to hydrogenation. Fig. 4c and e present the band structures of 6H–3F-G and width n dependence of band gaps of (9 n)H–nF-G, respectively. It is surprising that a nonmonotonic behavior of the energy gap as a function of width n is found. The partial charge densities of 6H–3F-G (Fig. 4d) show that the contribution to the VBM and CBM stems from different domain, which may be responsible for the nonmonotonic variety of the band gaps of hybrid ribbons with the width n.
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3.3
ZGNRs supported on zigzag hybrid nanoribbons
We now discuss the structural and electronic properties of ZGNRs supported on hybrid fluorographene–graphane nanoribbons (ZGNR/(9 n)H–nF-G). Fig. 5a and b present the geometric structures of 7-ZGNR/6H–3F-G and 3H–6F-G, respectively. Because of the hybrid support interaction, the ribbon domain of 7-ZGNR above fluorographene side is slightly pulled out-ofplane with respect to other domain above the graphane side, leading to a significant interlayer spacing difference between these two domains and support. The calculated binding energies show (Fig. 5c) that the interaction of ZGNRs with the hybrid support with all ratios of F to H is thermodynamically favorable, although the binding strength of 7-ZGNR with (9 n)H–nF-G decreases with the increasing fluorographene width n, as observed the corresponding binding energies range from 27 to 13 meV per carbon atom for n = 1 to 7, respectively. The PBE functional with vdW correction predicts the similar change of binding energies compared with LSDA (red in Fig. 5c), but improves the binding strength between 7-ZGNR and the hybrid substrate. Based on the spin-polarized and spin-unpolarized calculations, ZGNRs supported on hybrid fluorographene–graphane ribbons maintain the AFM ground state, and the energy difference between the AFM and FM states decreases as the ratio of fluorination to hydrogenation in substrate increases. The electronic structure calculations show that the hybrid nanoribbon supported ZGNRs in the AFM state are spinpolarized half-semiconductors with distinct band gaps for both spin channels, which is considerably different from the freestanding ZGNRs. Fig. 6a and b display the band structures and spin densities of 7-ZGNR/6H–3F-G and 3H–6F-G in the AFM state, respectively. It is obviously found that the spin degeneracies of a and b bands near the Fermi level from ZGNR are completely broken due to its interaction with the substrate (red in Fig. 6a and b). The spin-up band gaps of 7-ZGNR supported on 6H–3F-G and 3H–6F-G are reduced to 0.161 and 0.092 eV, while their
Fig. 5 Top and side views of geometric structures of (a) 7-ZGNR/3H–6F-G (b) 7-ZGNR/6H–3F-G. The interlayer spacing shown in (a) and (b) is in Å. The binding energies (c) and the up-spin and down-spin band gaps (d) of 7-ZGNR/(9 n)H–nF-G as a function of the number of fluorinated zigzag chains n by LSDA and PBE + D.
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Fig. 6 Band structures and spin densities of (a) 7-ZGNR/6H–3F-G and (b) 7-ZGNR/3H–6F-G. The Fermi level is set to 0, and the isosurface is 0.01 e Å3 with blue for spin up and yellow for spin down. The bands near the Fermi level coming from 7-ZGNR are shown in red. (c, d) The spin-polarized TDOS (left panel) and PDOS (right panel) and (e, f) electrostatic potential of hybrid ZGNR-support nanocomplex along the xz-plane direction: (c) and (e) 7-ZGNR/ 6H–3F-G, and (d) and (f) 7-ZGNR/3H–6F-G.
spin-down band gaps are increased to 0.422 and 0.317 eV compared with freestanding 7-ZGNR with 0.27 eV. The TDOS calculations (left panel in Fig. 6c and d) also reveal the halfsemiconductor property of ZGNR induced by the support interaction. Further PDOS analyses (right panel in Fig. 6c and d) show that the spin-polarized electronic states near the Fermi level of ZGNR/support are controlled by ZGNR. Interestingly, in the absence of an applied electric field, the spin-up and spin-down band gaps of supported ZGNRs can be well tuned in the opposite direction by changing the ratio of fluorographene to graphane width in hybrid support. Fig. 5d show the up-spin and down-spin band gaps of 7-ZGNR/(9 n)H–nF-G as a function of the fluorographene width n. With increasing the width n, the band gaps of 7-ZGNR/support for spin-up channel steadily decrease from 0.278 to 0.068 eV for n = 1 to 8, while the down-spin band gaps first increase from 0.296 eV for n = 1 to the maximum value of 0.422 eV for n = 4, and then decrease to 0.317, 0.146, and 0.092 eV for n = 6, 7, and 8 respectively. The notable difference in electrostatic potential (Fig. 6e and f)
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and charge density difference (Fig. S4c and d, ESI†) between 7-ZGNR/6H–3F-G and 3H–6F-G explains the effect of different hybrid support on electronic properties of ZGNRs. Similar to the graphene–graphane hybrid structures,29 both the CH–p and CF–p interactions between GNRs and hybrid graphane– fluorographene ribbons also play an important role for tuning the spin-polarized band gaps of ZGNRs. For comparison, we also performed the calculations on the electronic and magnetic properties of 7-ZGNR/(9 n)H–nF-G by the PBE functional with vdW correction (red and black triangles in Fig. 5d and Fig. S8, ESI†). It is clearly observed that the vdW correction has less influence on the predicted tendency for the width n-dependent band gaps of ZGNR, although the band gaps by PBE + D are larger than those by LSDA. The band gaps tuned by hybrid support notably differ from the previous studies for ZGNRs sandwiched between h-BN nanoribbons or sheets,37 in which the tunable band gaps for both spin channels are realized under a bias voltage that is normal to the ribbon plane. Thus, tuning the ratio of fluorination to hydrogenation in a
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hybrid fluorographene–graphane support may provide an efficient path for spin-resolved band engineering of the ZGNRs. The modified spin-polarized band gaps of ZGNRs in the opposite direction have important applications for the fabrication of graphene-based spin filtering devices. The previous studies show that the electronic and magnetic properties of graphene supported on substrate30,37 are very sensitive to the interlayer spacing. Similar behavior can be expected in our ZGNR/(9 n)H–nF-G hybrid systems here. The calculated results show that the half-semiconducting ZGNR can be tuned into half-metal via reducing the interlayer spacing between the ZGNR and substrate. Fig. 7a presents the interlayer spacing dependence of band gaps of 7-ZGNR/6H–3F-G and 3H–6F-G for spin-up and spin-down channels. Note that we only select the distance between the center of ZGNR and the support to represent the interlayer spacing in Fig. 7a because of the local structural distortion of planar ribbons. In the case of 6H–3F-G support (circle in Fig. 7a), with reducing the interlayer distance, the spin-up band gaps of 7-ZGNR steadily decrease until the spacing is reduced to 1.82 Å, whereas the band gap of 0.42 eV for the spin down is not considerably changed. When the interlayer spacing is further reduced to 1.65 and 1.53 Å, the spin-down band gap disappears, while the spin-up band gap is still about 0.35 and 0.28 eV, respectively, leading to the half-semiconducting to half-metallic behavior transition. For example, the band structures (see Fig. S9a, ESI† and Fig. 7b) show that as the interlayer spacing is reduced to 1.65 and 1.53 Å, the b band of the spin-up channel shifts upward and crosses the Fermi level, resulting in the metallic behavior of 7-ZGNR, whereas the spin-down channel has a significant band gap. The transition from half-semiconductor
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to half-metal can be explained by the enhanced charge density redistribution (Fig. 7c and d). Comparing the charge density differences of 7-ZGNR/3H–6F-G with interlayer spacing of 2.75 and 2.02 Å, it can be seen that the charge transfers and orbital interaction between 7-ZGNR and the support dramatically increase as the interlayer distance is reduced. When 7-ZGNR is supported on 3H–6F-G with a wider fluorographene domain, the band gaps for both spin channels decrease with increasing the interlayer distance (triangles in Fig. 7a), but the gap for spin up drops to zero before that for spin down, resulting in a half-metallic state. Fig. S9b (ESI†) displays the band structures of 7-ZGNR/3H–6F-G with interlayer spacing of 2.21 Å. Interestingly, we find that the critical interlayer spacing realizing the transition from half-semiconductor to half-metal in 7-ZGNR/3H–6F-G is increased to 2.21 Å, which is larger than that of 6H–3F-G substrate with 1.65 Å. A compressive strain along the direction perpendicular to the ribbon plane may be used to realize the interlayer distance change.37 Fig. S10 (ESI†) presents the interaction energy between 7-ZGNR and 3H–6F-G and 6H–3F-G as a function of the interlayer spacing. Note that the negative binding energy indicates the thermodynamically favorable interaction. It is clear from Fig. S9 (ESI†) that when the interlayer spacing is reduced to the critical value, the interaction of 7-ZGNR with 3H–6F-G is more favorable in energy than with 6H–3F-G because the binding energy of the former is significantly less than that of the latter, although the two layers will be repulsive with reducing the interlayer distance. These results indicate that a less compressive strain between ZGNR and a substrate with a wider fluorographene domain is needed to reach the critical interlayer spacing, compared to this complex with a narrow one.
Fig. 7 (a) Interlayer spacing-dependent band gaps of 7-ZGNR/6H–3F-G and 3H–6F-G for spin-up and spin-down channels. (b) Band structures of 7-ZGNR/3H–6F-G at the interlayer spacing of 1.53 Å. The Fermi level is set to 0, and the inset in (b) show bands around the Fermi level. Charge density differences of 7-ZGNR/3H–6F-G with the interlayer spacing of (c) 2.75 and (d) 2.02 Å. The blue and yellow areas in (c) and (d) denote electron accumulation and depletion, respectively, and isosurfaces are 0.002 e Å3.
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Therefore, ZGNRs supported hybrid fluorographene–graphane ribbons open an alternative avenue toward the realization of graphene-based spintronics applications.
4. Conclusion In conclusion, by using DFT calculations, we have systematically investigated the electronic and magnetic properties of ZGNRs supported on selectively hydrogenated and fluorinated ZGNRs. The supports of graphane and nanoribbons present different impacts on the electronic and magnetic properties of ZGNRs. The ZGNRs supported on the zigzag hybrid fluorographene– graphane nanoribbons are spin-polarized half-semiconductors with distinct band gaps for both spin channels. More importantly, in the absence of an electric field, the spin-up and spindown band gaps of supported ZGNRs can be well tuned in the opposite direction by changing the ratio of fluorographene to graphane domain in hybrid substrates, which is attributed to the enhanced potential difference between these two domains of ZGNRs above the fluorographene and graphane side of the substrate. Interestingly, with the reduction in interlayer spacing, the ZGNRs supported on hybrid nanoribbons exhibit the half-semiconducting to half-metallic behavior transitions. The half-metallicity in ZGNRs/hybrid support with a wider fluorographene domain can be realized more easily than that with a narrow one because the intrinsic polarization of the former substrate is enhanced.
Acknowledgements This work was supported by the National Science Foundation of China (21103026 and 21133007). We acknowledge simulating discussions with Z. Cao and thank the computational resources and assistance provided by the State Key Laboratory of Physical Chemistry of Solid Surfaces (Xiamen University).
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