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Jul 8, 2013 - ... Lopez-Bezanilla*, Jingsong Huang, Paul R. C. Kent, and Bobby G. ... zigzag silicon carbide nanoribbons (zSiC-NRs) with bare edges as...
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Tuning from Half-Metallic to Semiconducting Behavior in SiC Nanoribbons Alejandro Lopez-Bezanilla,*,† Jingsong Huang, Paul R. C. Kent, and Bobby G. Sumpter Center for Nanophase Materials Science and Computer Science & Mathematics Division, Oak Ridge National Laboratory, One Bethel Valley Road, Oak Ridge, Tennessee 37831-6493, United States S Supporting Information *

ABSTRACT: Half-metallic nanoscale conductors, highly sought after for spintronic applications, are usually realized through metal elements, chemical doping, or external electric fields. By means of local and hybrid density functional theory calculations, we identify pristine zigzag silicon carbide nanoribbons (zSiC-NRs) with bare edges as a metal-free monolayered material that exhibits intrinsic half-metallic behavior without chemical doping or an external electric field. Ab initio molecular dynamics simulations indicate that the half-metallicity is robust at room temperature. We also demonstrate that edge termination with O and S atoms transforms the zSiC-NRs into a full metal or a semiconducting material, respectively, due to the presence of O dimerization only on the Si edge and of S trimerization on both Si and C edges, the latter being driven by an unusual Peierls-like distortion along the functionalizing S atoms. The rich electronic properties displayed by zSiC-NRs may open new perspectives for spintronic applications using layered, metal-free, and light atom material.

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INTRODUCTION Electronics that utilize spin-dependent phenomena, namely spintronics, offer the potential for new functionality over conventional charge-based devices, with increased speeds, lower electric power consumption, and increased integration densities.1 Half-metallic materials are required to realize the spin-polarized currents, where one of the material’s spin channels exhibits metallic behavior, enabling conduction, whereas the other has an electronic gap, displaying an insulating behavior. Thus, new half-metallic materials are highly desirable for spintronic applications. Although bulk materials such as the ferromagnetic perovskite oxides and Heussler alloys exhibit many of the desired properties, in the vast majority of cases the materials involve heavy metals or rare-earth elements. These are not ideal due to cost and availability reasons. Preferred materials are (i) synthesizable from earth-abundant elements, (ii) simple in structure for facile synthesis, and (iii) readily integratable with current or near-term electronic materials. Recent candidate materials include the following: C-doped graphitic C3N42 and carbon nanoribbons, such as the zigzag graphene nanoribbons (zGNRs) that can be made half-metallic by using an external electric field3 or by edge functionalization.4 Here we use first-principles methods to study the intrinsic half-metallic properties of one-atom-thick zigzag silicon carbide nanoribbons (zSiC-NRs) that can be achieved with no intervention of external applied fields, metallic elements, doping, or chemical functional groups. Silicon carbide (SiC) in its bulk form has many applications due to high thermal © 2013 American Chemical Society

conductivity and strength, along with an excellent chemical stability. Efficient hydrogen evolution during electrolysis at electrodes made of a 3C−SiC nanocrystal associated with the high surface activity suggests potential applications of SiC nanoparticles for the hydrogen evolution catalysts.5,6 Since the 1990s, numerous techniques for obtaining SiC nanostructures with distinct properties have been suggested, such as carbothermal reduction of silica from carbon nanotubes,7 or by using a technique of extreme hole injection.8 Crystalline SiC nanoribbons of tens of nanometers in thickness and hundreds of micrometers in length have been synthesized via catalyst-free growth methods.9 SiC nanotubes have also been synthesized,10 and a pathway was proposed to obtain SiC cages.11 The recent development of techniques to unzip carbon12 and BN13 nanotubes to produce nanoribbons might be applicable to the preparation of SiC nanoribbons from their nanotubes. This variety of synthesis methods allows us to envision the synthesis of one-atom-thick SiC nanoribbons. In this work, we present encouraging results based on theoretical investigations of the electronic and magnetic properties of zigzag SiC nanoribbons, both pristine and with O and S atom functionalization of the ribbon edges. Different electronic structures are obtained, ranging from half-metallic to metallic or insulating, suggesting a rich functionality and potential applicability for spintronics applications. We provide Received: July 2, 2013 Published: July 8, 2013 15447

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Figure 1. (a) Fully relaxed unit cell geometry of the bare-edged -[SiC]7-(2) ribbon for one of the two energetically degenerate magnetic ground states, noted as (↑↑-↑↑), that has a total magnetic moment of 4.0 μB. Green and gray spheres represent Si and C atoms, respectively. Si atoms are denoted by Si-1 and Si-2 to show the inequivalency on the Si edge. The relative lateral displacement of the Si atoms by 0.2 Å at the zigzag edge has implications for both the electronic structure and the magnetic edge states. C atoms are equivalent along the opposite C edge. (b) Spin density distribution of this ground state at an isosurface of 10−3 e/Å3. The blue and red isosurfaces correspond to net spin-up and spin-down electron densities, respectively. (c) Spin-resolved band diagram for the spin-up and spin-down channels, showing intrinsic half-metallic properties. For this ribbon, the projected density of states (PDoS) of Si-1 and Si-2 edge atoms are plotted in (d) and (e), respectively. (f) PDoS is shown for one of the two equivalent C atoms at the opposite ribbon edge. The total density of states (TDoS) of the -[SiC]7-(2) ribbon is plotted in (g). Horizontal dashes indicate the Fermi energy level.

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THEORETICAL METHODS The geometry optimizations and electronic structure calculations were primarily performed by means of the SIESTA DFT-based code.16 We used a double-ζ basis set with additional polarization orbitals within the spin-dependent local density approximation (LSDA) approach for the exchange-correlation functional. The Troullier−Martins scheme was used for the norm-conserving pseudopotentials. SiC-NRs were modeled within a supercell with at least 10 Å of vacuum to avoid interactions between neighboring cells. Atomic positions were relaxed with a force tolerance of 5 meV/Å, and unit cell vectors were relaxed with the maximum stress component being smaller than 0.02 GPa. The integration over the Brillouin zone was performed using a Monkhorst sampling of 1 × 1 × 60 k-points for ribbons with one row of atoms. The number of k-points along the ribbon direction was decreased proportionally as the number of rows increased in the unit cell. The solutions of the Kohn−Sham equations were expanded as a linear combination of the localized orbitals, which allowed us to determine the contribution of each orbital to total density of state of the material. Radial extension of

accurate descriptions based on spin-polarized density functional theory (DFT) calculations of the geometry and magnetic ground states of pristine zSiC-NRs, showing that this is a robust example of a metal-free monolayered material that exhibits halfmetallicity without requiring chemical modification or application of external fields. In contrast to previous studies that used a single SiC-dimer row,14,15 we find that at least two SiC-dimer rows are needed as a unit cell to account for a sufficiently converged description of the electronic states and lateral edge distortion of the bare ribbons. In addition, we explored new features of zSiC-NRs by terminating the edges with O and S atoms. The half-metallic and magnetic characteristics of the bare-edged ribbons are altered with O terminations, yielding an overall metallic character. Interestingly, the opposite is found with S atom edge termination. A Peierls-like distortion occurs uniquely along the S atom edges, causing the ribbons to become semiconducting through a band gap opening. 15448

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orbitals had a finite range with a kinetic energy cutoff of 100 meV. The numerical integrals were computed on a real space grid with an equivalent cutoff of 400 Ry. For each ribbon structure, we tested multiple initial magnetic configurations, particularly along the nanoribbon edges, to determine the ground and nearby electronic states. Except where stated, our results were obtained from the LSDA-based simulations. However, because the largest source of uncertainty in our calculations is the choice and accuracy of the functional, we also performed hybrid density functional calculations as provided by the HSE06 functional,17 using the VASP code18 and the plane wave projector augmented wave pseudopotential method as an additional check on the LSDA predictions. In this case, a plane wave cutoff of 400 eV and Brillouin zone sampling identical to the SIESTA calculations was used. For the largest (24 atom) cells considered, this resulted in 16 k-points within the irreducible Brillouin zone (iBZ) and 30 in the full zone. Electronic states were occupied using either the Methfessel− Paxton method or Gaussian smearing of up to 0.25 eV. Selected LSDA results from SIESTA were also validated with the plane wave results.

Table 1. Comparison of Total Energies and Magnetic Moments of the -[SiC]7-(2) Ribbon with Different Spin Configurations on the Edgesa -[SiC]7-(1 or 2) spin configuration

ΔE/cellb (meV)

total magnetic moment (μB)

↑-↑c ↑↑-↑↑ ↑↑-↓↓ ↑↓-↑↑ ↑↑-↑↓ ↑↓-↑↓

8d 0 0 6 98 105

2.0 4.0 −1.3 3.3 2.0 1.2

a

The magnetic configuration for the -[SiC]7-(1) ribbon is also provided for comparison. A combination of arrows is used to label the spin orientations on the edge atoms. The arrows before and after the dash are for Si and C atoms, respectively. bEnergy difference of each particular spin configuration with respect to the ground state (↑↑-↑↑). c Equivalent to (↑↑-↑↑) but without lateral displacement on the edge Si atoms. dThe energy of 2 × E (↑-↑) relative to that of E (↑↑-↑↑).

exhibits ferromagnetic spin coupling along the ribbon edges and the same spin orientation across the ribbon width, with a total magnetic moment of 4.0 μB for the unit cell (Table 1). Mulliken population analysis gives 0.7 and 0.3 μB on Si-1 and Si-2 edge atoms, respectively. In contrast, C atoms at the opposite ribbon edge remain aligned, and the local magnetic moments of 1.1 μB are equivalent for the two edge C atoms in the unit cell. The rationale for the symmetry breaking of spin densities on the Si edge atoms can be further analyzed with the assistance of the spin-resolved electronic band diagram shown in Figure 1c. Due to the presence of 14 dimers in the unit cell, the valence electronic band structure close to the Fermi level is characterized by 14 bands of π-symmetry for both the spin-up and spin-down channels, which are associated with the pxorbitals perpendicular to the ribbon plane. In addition, each spin channel has four more bands associated with the dangling bonds on the four edge atoms, which are rather localized pyorbitals. The projected densities of states (PDoS) shown in Figure 1d−f allow us to assign these four bands to the dangling bonds on the edge atoms without ambiguity. In the spin-up channel, two rather dispersionless bands around −1.5 eV can be attributed to the edge C atoms, as can be seen from Figure 1f. Two more flat bands just below the Fermi level are due to Si-1 and Si-2, as can be seen from Figure 1d,e. Note that due to the lateral displacement of the Si edge, the two bands associated with the Si dangling bonds split at the zone edge (Z-point). In comparison, the two bands associated with the C dangling bonds remain degenerate at the zone edge. All of these four bands are singly occupied. In the spin-down channel, the four bands due to the dangling bonds of the four edge atoms are close to the Fermi level. Likewise, the two bands associated with the Si dangling bonds split at the zone edge, whereas the other two associated with C dangling bonds remain degenerate. These bands are empty except for the partially occupied band that is mainly associated with the py-orbital of Si-2. The partially occupying electrons are transferred from the px-orbital on the edge C atoms (Figure 1f). Because this electron transfer took place only within the spin-down channel, it does not alter the number of spin-down electrons, and the spin-up channel has four more electrons than the spin-down channel, leading to a total magnetic moment of 4.0 μB for this ground state (Figure 1g). However, a direct consequence of the partial py-orbital occupancy on Si-2 is that it partially cancels the spin-up

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RESULTS AND DISCUSSION The unit cell structures of the bare-edged and O or S edgeterminated SiC-NRs are depicted in Figures 1−3. Ribbons extend along the z-axis, and the surface vector points in the xaxis. Bare-edged SiC-NRs are represented by -[SiC]m-(n), where [SiC]m stands for m SiC-dimers across each ribbon row, and n indicates the number of rows in the unit cell along the ribbon axis. Edge-functionalized nanoribbons are denoted as X[SiC]m-X(n), where X represents O or S atoms attached to both zigzag edges. Electronic and Magnetic Properties of Bare SiC Zigzag Nanoribbons. The fully relaxed geometric structure of the -[SiC]7-(2) ribbon for one of its two energetically degenerate magnetic grounds states is shown in Figure 1a. This solution is denoted as (↑↑-↑↑) to show that all the magnetic edge states on the Si atoms (↑↑ before the dash) and on the C atoms (↑↑ after the dash) have the same spin orientation. The second solution with the magnetic edge states on the C edge flipped to the opposite spin orientation (↑↑-↓↓) is shown in Figure S1 (Supporting Information). The ribbon is completely flat with a Si−C dimer bond length of 1.78 Å in the central part of the ribbon, the same as that in a 2D SiC sheet. The most striking feature is the 0.20 Å relative lateral displacement of the two Si atoms at the Si edge, which gives rise to two inequivalent Si atoms. Following the notation of Figure 1a, Si-1 is displaced inward and its corresponding Si−C distance projected on the yaxis is shortened by 0.07 Å with respect to the nondistorted structure. Si-2 in the next row is displaced outward, and its corresponding projected Si−C distance is elongated by 0.13 Å. The asymmetrical amount of displacement can be attributed to the typical asymmetrical potential energy surface of diatomic species19 where the bond compressing costs more energy than bond stretching. The Si−C σ bond should behave similarly, and thus it is easier to stretch it than to compress it. The distorted structure is lower in energy by 8 meV than the nondistorted structure (Table 1). An outcome of this lateral displacement is the nonequivalent spin densities on the two Si atoms. Figure 1b shows a real-space representation of the net spin density (i.e., the difference at each point in space between the spin-up and the spin-down charge density distribution) of this ground state solution. It 15449

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one another, leading to two energetically degenerate magnetic ground states (i.e., (↑↑-↑↑) and (↑↑-↓↓)). The first magnetic ground state, involving the same spin orientation of the edges states, shows a similar half-metallic electronic structure to the one described above. The second magnetic ground state can be obtained by flipping one of the magnetic edge states to the opposite spin orientation, yielding a metallic system with a total magnetic moment of 1.3 μB. The absolute value of the local magnetic moments on the edge atoms remains independent of the ribbon width for wider ribbons, evidencing the strong localization of the spin density at the edges. For wide bareedged zSiC-NRs, this degeneracy may be removed by applying a magnetic field perpendicular to the ribbon plane or by choosing an appropriate substrate that would favor a single spin orientation. However, both spin configurations present interesting potential applications for spintronic devices because they combine in a single object two polarized electric currents which flow independent of each other along each ribbon edge. To verify that the half-metallicity is robust at room temperature, we performed spin-polarized DFT-based molecular dynamic (MD) simulations with a Nosé thermostat at 300 K on a 4× longer supercell, that is, -[SiC]7-(8). It was observed that the original hexagonal SiC network is conserved throughout a 5 ps MD simulation, although it adopts an undulating shape whose amplitude is more pronounced at the C edge than at the Si edge. Interestingly, the magnetic moment is very robust as the ribbon shape evolves over time and maintains a value of 4 μB per primitive unit cell with the largest variation of 0.2 μB over the 5 ps run. The absence of large fluctuations on the total magnetic moment is due to both the highly localized character of the spins on the ribbon edges and the fact that no atomic or orbital rearrangement occurs with ribbon motion, which could lead to a possible quenching of magnetic moments. The absence of any structural rearrangements and the thermal stability of the magnetic moment are essential for applications. Recently, spin-polarized edge states in graphitic Si nanowires at room temperature have been spectroscopicly measured.20 Electronic and Magnetic Properties of O and S EdgeTerminated SiC Zigzag Nanoribbons. The unique distribution of spin density on the bare-edged zSiC-NRs offers potential applications in spintronics; however, the enhanced reactivity of the unsaturated edges mandates that the bareedged ribbons must be isolated from other chemical reagents. We have, therefore, investigated how different chemical terminations of the bare edges may affect the electronic structure. zGNRs with S-terminated zigzag edges were recently synthesized within a carbon nanotube. Microscopy images showed that the S terminations form dithiolium pentagonal rings in oxidized (positively charged) GNRs that involve S−S bonds along the edges.21 Thus, we studied the electronic and magnetic properties that arise in zSiC-NRs when both of their edges are terminated with O as well as S atoms. Each edge termination yields very different electronic features that fundamentally depend on the ability of these atoms to tilt and to bond to each other forming dimers or trimers along the ribbon edges, illustrating the high tunability of the electronic structure of zSiC-NRs. A complete description of the functionalization requires several SiC-dimer rows in order to account for the O−O and S−S bonds along the ribbon edges. It was observed that both types of edge terminations remove the edge distortion of bare ribbons and align the Si atoms parallel to the ribbon axis.

electron density on and only on Si-2, leading to a symmetry breaking of the spin densities on the two Si edge atoms (Figure 1b). Also due to the electron transfer, the dispersive px-band of C crosses the Fermi level, leading to a half-metallic property for this bare-edged ribbon along the C edge. Although the pyderived band for Si-2 also crosses the Fermi level and contributes to the half-metallic property, the electronic state is rather localized, as can be observed from its negligible band dispersion. Therefore, it can be concluded that the halfmetallicity mainly comes from the px-derived π-bands on the C edge. The half-metallicity of -[SiC]n-(2) found by LSDA is fully confirmed by hybrid DFT calculations with the HSE06 functional. In the left panel of Figure 2, a clear gap is visible

Figure 2. Half-metallic electronic band structures of the (↑↑-↑↑) state (left panel) and metallic band structure of the (↑↑-↓↓) state (right panel) of a -[SiC]n-(2) calculated with the HSE06 hybrid functional.

in one spin channel for the (↑↑-↑↑) configuration, whereas two bands cross the Fermi energy in the energetically degenerate (↑ ↑-↓↓) configuration. The system becomes metallic when the orientation of the majority spins on C atoms flips and the corresponding electronic states switch to the opposite spinpanel. The total moment of the former configuration is 4.0 μB, whereas for the latter it is 1.3 μB. Although the band structure around the gap differs between the two functionals, the origin of the metallic bands is the same in both cases. The hybrid functional shifts other nearby bands away from the Fermi energy. These results give confidence that the chemical descripton of the origin of the metallicity described above is correct. The outermost Si−C bond lengths on either side of the ribbon differ by only 0.02 Å between HSE06 and LSDA predictions, indicating that the hybrid functional causes little additional change in the geometry. Other -[SiC]n-(2) ribbons with different widths were also studied, all showing the lateral displacement of Si atoms on the Si edge, independent of the ribbon width, pointing out that the lateral displacement of Si atoms is a local effect of the zigzag edge. For narrower ribbons with n < 7, the most energetically favorable magnetic configuration corresponds to a ferromagnetic coupling across the ribbon width (i.e., (↑↑-↑↑)). This is contrary to the trend found in H-terminated zGNRs where the antiferromagnetic coupling between edges is always preferred, which is a consequence of the contribution of the whole graphitic network to the connection between both states. For wider zSiC-NRs with n ≥ 7, the edge states do not interact with 15450

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Figure 3. (a) Fully relaxed unit cell geometry of the O-[SiC]7-O(1) ribbon. Green, gray, and red spheres represent Si, C, and O atoms, respectively. (b) Fully relaxed unit cell geometry of the O-[SiC]7-O(2) ribbon showing a dimerization of the edge-terminating O atoms on the Si edge (O@Si). In contrast, the O atoms on the opposite C edge (O@C) remain equidistant. (c) Spin density distribution of the magnetic ground state at an isosurface of 10−3 e/Å3. The blue and red isosurfaces correspond to net spin-up and spin-down electron densities, respectively. (d, e) Spin-resolved electronic band diagrams corresponding to the structures in (a,b), respectively. Labels 1−4 (and 1′−4′) in (d) refer to the p-derived bands of O as explained in the text. (f) and (g) Projected density of states (PDoS) of O@Si and O@C for the electronic structure shown in (e). (h) Total density of states (TDoS) of the weakly dimerized O-[SiC]7 -O(2) ribbon. Horizontal dashed lines indicate the Fermi energy level.

O atoms on the C edge remain equidistant. This dimerization lowers the total energy by 74 meV per unit cell. Interestingly, the dimerization does not quench but instead strengthens the magnetism on the O@Si edge, as indicated by the slightly enhanced local magnetic moments of 0.5 μB on O atoms and a total magnetic moment of 1.1 μB. Meanwhile, the O@C edge remains nonmagnetic (Figure 3c). Due to this dimerization, the pz-derived bands of O@Si (4 and 4′) split into four bands, two for each spin channel (Figure 3e). As can be seen from the PDoS for O@Si (Figure 3f), the split bands are 1 and 1.5 eV apart for the spin-up and spin-down components, respectively. In addition, the dimerization also removed the degeneracy for the px-derived bands of O@Si (3 and 3′) at Z-point. In comparison, due to the absence of a dimerization, the px- and pz-derived bands of O@C are simply back folded in the irreducible Brillouin zone (iBZ). The spin-up and the spindown components of these bands are degenerate in the whole iBZ, as shown in Figure 3g. These bands cross the Fermi level and are responsible for the fully metallic character on the C edge. Interestingly, the magnetic properties reside on the O@Si edge, whereas the metallic properties reside on the opposite O@C edge. This differs from the previously studied O-[BN]8-

For O-functionalized zSiC-NRs, we start by analyzing the one-row O edge-terminated ribbon O-[SiC]7-O(1) (Figure 3a). The magnetic ground state of O-[SiC]7-O(1) features a ferromagnetic coupling along the O@Si edge with a local magnetic moment of 0.4 μB on each O atom and a total magnetic moment of 0.5 μB. The magnetic moment of the O@ C edge is completely quenched. As can be seen from its spinresolved electronic structure, shown in Figure 3d, its valence electronic band structure is mainly characterized by four bands near the Fermi level. These bands originate from the mutually perpendicular px- and pz-orbitals located on the functional O atoms. Dictated by the orbital orientations, the px-derived bands of O@C (1 and 1′) ascend monotonically from Γ to Z, crossing the Fermi level, and the px-derived bands of O@Si (3 and 3′) run up initially from the Γ-point and then descend near the zone edge; in comparison, all of the pz-derived bands of O@C (2 and 2′) and of O@Si (4 and 4′) descend monotonically from Γ to Z, crossing the Fermi level except for the spin-up component of O@Si (4). For the two-row ribbon O-[SiC]7-O(2) (Figure 3b), the neighboring O atoms on the Si edge dimerize weakly, giving an O−O distance of 2.31 Å, longer than those found in typical peroxide compounds. The 15451

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Figure 4. (a) Fully relaxed unit cell geometry of S-[SiC]7-S(1). Green, gray, and gold spheres represent Si, C, and S atoms, respectively. The unit cell length is a = 3.05 Å. (b) Fully relaxed unit cell geometry of S-[SiC]7-S(3) that undergoes an unusual Peierls-like distortion manifested as a trimerization of the functional S atoms. The distortion leads to a S−S−S bond length of 2.51 Å on both Si and C edges. (c) Electronic band structure of the nonmagnetic system represented in (a). The green and red dots are located at 1/3 and 2/3 of the irreducible Brillouin zone. (d) Band structure obtained by simply back folding the bands in (c) three times, which represents the band structure of S-[SiC]7-S(3) without distortion. (e) Electronic band structure of the fully relaxed S-[SiC]7-S(3), exhibiting a direct band gap of 0.17 eV at the Γ-point. (f,g) The projected density of states on the edge-terminating S atoms at the Si (S@Si) and C (S@C) edges, respectively. (h) Total density of states of the ground state of the S[SiC]7-S(3) ribbon. Horizontal dashed lines indicate the Fermi energy level.

O(2) ribbon where both magnetism and metallicity coincide on the same O@N edge.22 The edge oxidation of the -[SiC]7-(2) represents a stabilization of 14.75 eV relative to the bare ribbon and two triplet O2 molecules. This type of edge functionalization converts the half-metallic bare zSiC-NRs into a fully metallic system with enhanced stability due to the passivation of the reactive dangling bonds of the ribbon edges. Functionalization with S atoms on both edges of a zSiC-NR results in a more intriguing behavior that involves an unusual Peierls-like distortion consisting of a trimerization of the edgeterminating S atoms. This distortion results in semiconducting properties. We begin by considering the electronic band structure of the S-[SiC]7-S(1) ribbon (Figure 4a), and then we analyze what kind of S-wire distortions can provide additional stability. The attachment of a S atom at each edge of a bare -[SiC]7-(1) lowers the formation energy by 4.77 eV with respect to that ribbon plus a quarter of the corresponding energy of a singlet S8 ring, revealing that this is an exothermic reaction. Figure 4c shows the energy band diagram of this ribbon, which unlike the O counterpart does not exhibit spin polarization. However, the band structure of the S-[SiC]7-S(1) ribbon still bears some degree of similarity to the O edge termination. The S atom is iso-valence-electronic to the O

atom, and its s and p-orbitals also undergo an sp-hybridization on attaching to the ribbon edges so that one electron participates in the σ bond and two electrons populate the other sp-hybridized lone pair orbital that points outward. The remaining 3 out of 6 sulfur valence electrons are accommodated in the mutually perpendicular px- and pz-orbitals. A notable similarity is observed between the electronic band structure of O and S edge-terminated ribbons in terms of the four dispersive bands around the Fermi level, which are derived from the px- and pz-orbitals of S. The px-derived band of S@C runs up monotonically from Γ to Z-point and crosses the Fermi level, while the px-derived band of S@Si runs up initially but then descends at about 2/3 of the iBZ. The former is partially occupied, while the latter is fully occupied. The two pz-derived bands from the S atoms on both edges run down nearly in parallel from Γ to Z, crossing the Fermi level, as well. The three partially occupied bands should accommodate a total of 4 electrons which, along with the two of the fully occupied pxderived bands of S@Si, account for the six electrons of the two S atoms. These band dispersions are greatly enhanced with respect to the O bands as a result of the more diffusive valence orbitals of S atoms than those of O atoms. The pz-derived bands exhibit a delocalized character with ∼3 eV dispersion and 15452

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structure of the S edge-terminated zSiC-NR changes from metallic to semiconducting. Note that the new occupied and unoccupied C atom states related to the pz-orbitals are at lower and higher energy, respectively, than the px-derived states (Figure 4f,g), meaning that the in-plane pz−pz−pz σ bond has a stronger bonding character than the perpendicular px−px−px π bond. The alternation of S−S−S trimers along the ribbon edges illustrates a type of Peierls-like distortion in a quasi-onedimensional system that allows for the stabilization of the occupied bands and the destabilization of the unoccupied ones. It must be emphasized that, in this case, as well as in the O edge-terminated zSiC-NRs, this type of Peierls-like distortion modifies uniquely the positions of the edge-terminating atoms because the lattice parameter of the SiC hexagonal network in the ribbon direction remains unaltered. According to the theory of Peierls distortion, the total energy of the distorted system should be lower than that of the undistorted structure. Indeed, an energy comparison confirms that the tilting of the S atoms lowers the ribbon energy by 0.24 eV/row with respect to the S-[SiC]7-S(1) ribbon. The trimerizations manifest in an intratrimer S−S−S bond length of ∼2.51 Å for both S@C and S@Si. The distance between two consecutive trimers at both edges is 4.15 Å. The S trimers at each edge can be considered as closed-shell species, and therefore, interaction between trimers along an edge might be expected. It is not, however, observed that by doubling the unit cell to S-[SiC]7-S(6) the S trimers adopt opposite tilts above and below the ribbon plane as the distance of 4.15 Å between them is long enough to avoid mutual repulsion and subsequent tilting. The same reasoning that explains the sulfur atom trimerization along the SiC ribbon is valid for other nmerizations, although these are not the ground state structures. Indeed, by increasing the number of SiC-dimer rows in the unit cell up to four, the formation of the S−S−S−S tetramer was observed at the Si edge, whereas two groups of S−S dimers were observed at the opposite C edge of the ribbon (Figure S2, Supporting Information). In terms of band structure analysis, this can be rationalized considering that the pz-derived band of S@Si, which is being filled up to 3/4 (the green dot in Figure 4c would move up along the bands to 1/4 of the iBZ from the Γ-point), and the same band of S@C, which is being emptied down to 1/2 (a second green dot would move down along the bands to 1/2 of the iBZ) at the expense of shifting the pxderived band of S@C up to 3/4 (the red dot would shift up along the band to 3/4 of the iBZ). Thus, the S@Si pz-derived band would accommodate a total of 1.5 electrons, the S@C pzderived band 1 electron, and the px-band 1.5 electrons. This tetramerization and the dimerizations split the pz-band of S@C, although the system remains metallic. The energetic cost of such an interband charge transfer, that is, the energy difference between the two green and red dots in the band diagram, is larger in the four-row case than the three-row case, thus favoring the trimerization. Consequently, the total energy per row to achieve tetramerization is 0.18 eV higher than that for a trimerization. Calculation with n = 2 did not end up with a dimerized structure. In order for dimerization to take place on both edges, the pz-derived band of both S@Si and S@C need to be half-filled, which in turn means that the px-derived band of S@C is fully filled. Thus the energy cost in terms of the interband charge transfer is the highest compared to n = 3 and 4. Comparing with manifold other types of distortion, we conclude that the trimerization is the global minimum, which

represent one-dimensional atomic wires as a result of the headover-head overlap of the in-plane sulfur pz-orbitals along the ribbon edges. From the results of S-[SiC]7-S(1), we consider other S edgeterminated zSiC-NRs, with the number of rows increased beyond n = 1 in order to scrutinize possible Peierls-like distortions along the ribbon axis. As the number of S edgeterminated rows increases in the unit cell up to n = 2, 3, 4, and so forth, the px- and pz-derived bands of both S@Si and S@C that contribute to the metallic features of S-[SiC]7-S(1) split into new electronic states except for n = 2, as a result of the bonds created between S atoms along the ribbon edges. The most stable geometric configuration for a zSiC-NR with sulfur atoms on the edges is found to be the S-[SiC]7-S(3) structure (Figure 4b). We now consider the distortion that leads to the appearance of a S−S−S trimer at each side of the ribbon and removes the previous translational symmetry. A precise explanation on the number of rows that yields such a distortion can be deduced from the band filling of the three px- and pzderived bands of S atoms crossing the Fermi level. According to the filling of the electronic bands shown in Figure 4c, each pzderived band of S@Si and S@C is slightly more than 2/3 filled in the iBZ, denoted as 2/3 + δ1 for S@Si and 2/3 + δ2 for S@ C (see the green dot in Figure 4c). Note that these two pzderived bands do not fully overlap each other, and therefore, their occupancies are slightly different, justifying δ1 ≠ δ2. In comparison, the px-derived band of S@C is slightly less than 2/ 3 filled, denoted as 2/3 − δ3 (see the red dot in Figure 4c). An exact fraction of 2/3 for the iBZ implies that the ribbon may undergo a Peierls-like distortion with a periodicity of 3 for the edge S atoms. Including three rows of S-[SiC]7-S(1), one may obtain the band structure shown in Figure 4d, provided that the system is constrained to not vary their atomic positions. It can be interpreted as a triple back folding of the one-row system’s electronic structure shown in Figure 4c, so that the red and green dots coincide with the zone center and the zone edge of the corresponding three-time shorter iBZ (Figure 4d). In order for the Peierls-like distortion to occur, the Fermi level should meet the back-folded points, as indicated by the red and the green dots, so that bands can split at the Γ- and Zpoints. Because the Fermi level is above the green dot and below the red dot, this requires the two pz-derived bands to shift their excess electrons into the px-derived band. An inspection of the distances from the Γ-point to where the bands cross the Fermi level allows us to conclude that δ1 + δ2 = δ3, indicating that the amount of charge that the px-derived band of S@C requires to fill the band occupancy up to the red dot is exactly the same as that the two pz-derived bands of S@Si can release to empty the band occupancy down to the green dot. This supposed interband charge transfer would cause the Fermi level to meet the folding points for all of the three bands, ending up with 4/3 electrons for all three bands crossing the Fermi level (4/3 × 3 gives a total of 4 electrons). If the constraint on the ribbon atoms is released so that the atoms are able to tilt to reach the system ground state, a charge transfer from both of the pz-bands to the px of the S@C band takes place. Then, an efficient in-plane pz-orbital overlap occurs, leading to a distortion that changes the periodic arrangement of S atoms along the ribbon edges. The distortion removes the degeneracy of the px-derived band of S@C at the zone center, giving a 0.17 eV π-band gap opening at the Fermi level (Figure 4e), and the degeneracies of the pz-derived bands of S@Si and S@C at the zone edge (Figure 4e). Thus, the electronic 15453

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can be ascribed to the fact that the interband charge transfer involves the least amount of energy in order to satisfy the requirement for Peierls distortion.

CONCLUSION In summary, three types of electronic structures have been studied in pristine zSiC-NRs and those edge-terminated with O and S atoms. Pristine ribbons are predicted to be a material exhibiting intrinsic half-metallicity in the absence of any chemical doping or applied external field, with a ferromagnetic spin ordering at both Si and C zigzag edges. The Si edge presents an asymmetry of the edge spin states that is due to the lateral distortion of the edged-Si atoms that elongate the unit cell by a factor of 2. This local distortion vanishes with O or S atom edge termination, which in turn introduces new functionalities. The half-metallic behavior of the pristine zSiC-NRs becomes fully metallic as the dangling orbitals at the ribbon edges are passivated with O atoms. This functionalization removes the magnetic states at the C side and modifies those at the Si side due to the formation of an O− O dimer, enhancing the total magnetic moment, while lowering the total energy of the system. S-edge passivation removes the magnetic moment and leads to a Peierls-like distortion in the form of trimerization of the edge-terminating S atoms, which in turn converts the half-metallic bare zSiC-NRs into a small band gap semiconducting material in its ground state. Depending on the arrangement of S atoms at each side of the ribbon, a metallic to semiconductor transition can be induced in the functionalized ribbon. These results show the versatility in the potential application of both pristine and functionalized monolayered SiC for metal-free electronic and spintronic devices without the use of any external field from cheap and environmental friendly chemical elements. ASSOCIATED CONTENT

S Supporting Information *

The second solution of the two energetically degenerate magnetic ground states of the -[SiC]7-(2) ribbon, denoted as (↑ ↑-↓↓) (Figure S1); geometry and electronic structure of a S[BN]7-S(4) nanoribbon (Figure S2). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address †

Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, Illinois 60439, USA. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research used the resources of the National Center for Computational Sciences at Oak Ridge National Laboratory and of the National Energy Research Scientific Computing Center, which are supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC0500OR22750 and Contract No. DE-AC02-05CH11231, respectively. We are also grateful for the support from the Center for Nanophase Materials Sciences (CNMS), sponsored at Oak Ridge National Laboratory by the Division of Scientific User Facilities, U.S. Department of Energy. 15454

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