Effects of edge hydrogenation in zigzag silicon carbide nanoribbons: stability, electronic and magnetic properties, as well as spin transport property

Abstract

Based on density functional theory and nonequilibrium Green's function method, we systematically investigated the hydrogenated effects on the stability, electronic and magnetic properties, as well as electronic spin transport property of an N chains zigzag silicon carbide nanoribbon (N-ZSiC NR). Our calculated results indicate that by controlling the hydrogen content of the environment, one can get three types of stable edge hydrogenated ZSiC NRs. They are: (a) each edge Si and C atom bonded with one hydrogen atom (N-ZSiC-1H1H), (b) each edge Si atom bonded with two H atoms and each edge C bonded with one H atom (N-ZSiC-2H1H), and (c) each edge Si and C atom bonded with two H atoms (N-ZSiC-2H2H). It was unexpectedly found that N-ZSiC-1H1H NR, which has been studied theoretically to a large extent, is stable only at extremely low ultravacuum pressures. Under more standard conditions, the most stable edge hydrogenated structure is N-SiC-2H2H NR. More interestingly, when N ≤ 4, the N-ZSiC-2H2H NR is a nonmagnetic semiconductor, while when 5 ≤ N ≤ 7, it is a ferrimagnetic ferromagnetic semiconductor. When N ≥ 8, the N-SiC-2H2H NR turns into a ferrimagnetic half-metallic. As regards the N-ZSiC-2H1H NR, when N ≤ 12, it is a ferromagnetic semiconductor, while when N ≥ 13, it becomes a ferromagnetic half-metallic. These results manifest that by controlling the hydrogen content of the environment and the temperature, as well as the ribbon width N, one can precisely modulate the electronic and magnetic properties of N-ZSiC NRs, which endows ZSiC NRs with many potential applications in spintronics and nanodevices.

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1 Introduction

The silicon carbide (SiC) crystal is a binary compound of group IV elements, which may crystallize in many different close-packing sequences with cubic, hexagonal, or rhombohedral Bravais lattices. The six most commonly used stacking configurations are: 3C-SiC (cubic unit cell, zinc-blende); 2H-SiC; 4H-SiC; 6H-SiC (hexagonal unit cell, wurtzite); 15R-SiC; 21R-SiC (rhombohedral unit cell).¹ It is well known that bulk SiC possesses a wide band-gap, high saturated electron mobility, large critical breakdown strength, high thermal conductivity, high resistance to radiation, etc., and is widely used in high temperature, high pressure, high frequency, high-power fields.^1–3 Moreover, various lower dimensional SiC structures, such as zero-dimensional nanoparticles and nanospheres, and one-dimensional SiC nanotubes (SiCNTs) and nanowires (SiCNWs), have also already been synthesized,^4–9 which has stimulated many studies.^10–19 For example, it was found that single wall SiC nanotubes are semiconductors independent of helicity, unlike the case of carbon nanotubes.^10–12 The bulk SiC polytypes are indirect semiconductors, while the zig-zag SiC single wall nanotubes are direct semiconductors.¹⁰

In recent years, the SiC graphene-like structure, which is a two-dimensional (2D) monolayer of SiC in a honeycomb structure and may be the new lower dimensional SiC structure material, have been studied theoretically. In contrast to graphene,²⁰ which is essentially a zerogap semiconductor, the 2D monolayer SiC is a wide-band-gap semiconductor due to the ionicity of SiC.^24–28 The SiC nanoribbons (SiC NRs) are made by cutting the SiC graphene-like sheets, just like in producing graphene nanoribbons.²⁰ The edge carbon atoms of graphene NR are passivated by a hydrogen atom.^21–23 Each edge atom of SiC NR is usually passivated by one hydrogen atom, as shown in Fig. 1a, which is referred to as the H-passivated SiC NR. The electronic and magnetic properties of the H-passivated SiC NRs have been studied theoretically to a large extent by using spin-polarized first-principles. It is found that the H-passivated zigzag SiC NRs (ZSiC-1H1H NRs) are magnetic metals,²⁴ while the H-passivated armchair SiC NRs (ASiC-1H1H NRs) are nonmagnetic semiconductors.^24,25 In detail, the ZSiC-1H1H NRs narrower than 0.6 nm have only a nonmagnetic semiconducting state with a direct band gap of 0.74 eV at the X point. The ZSiC-1H1H NRs wider than 0.6 nm and narrower than 1.7 nm are ferrimagnetic semiconductors with two different direct band gaps for the spin-up and the spin-down channels.²⁹ Moreover, the ZSiC-1H1H NRs can be utilized for manipulating the magnetization by applying an electric field,³⁰ as well as by carrier (hole and electron) doping.^31,32 Recently, Zheng et al.³³ studied the band-gap modulations of SiC-1H1H NRs by transverse electric fields. Lou studied the edge reconstruction effect in pristine and H-passivated ZSiC NRs,³⁴ as well as boron and nitrogen substitutional impurities inducing magnetic and half-metallic behavior in ZSiC-1H1H NRs.³⁵ Guan et al. found that the fully hydrogenated ASiC and ZSiC NRs are all nonmagnetic semiconductors, independent of the ribbon widths. They also proposed for the first time the concept of successive hydrogenation starting from the edge(s) as an effective approach to realize the fine-tuning of the electronic and magnetic behaviors of SiC NRs.³⁶

Fig. 1 Top view (left) and side view (right) of the geometric structure for the N-ZSiC-nHmH NR with N zigzag chains across the ribbon width, here N = 8, and with n hydrogen atoms passivating each edge Si atom as well as with m hydrogen atoms passivating each edge C atom. (a) 8-ZSiC-1H1H, (b) 8-ZSiC-1H2H, (c) 8-ZSiC-2H1H, and (d) 8-ZSiC-2H2H. The red dashed lines show the unit cell with periodicity along the x axis, while the width is along the y axis. The large, middle, and small spheres denote Si, C, and H atoms, respectively, and the structures were drawn by the XCrySDen program.⁴⁸

On the other hand, understanding of the structure and stability of the possible edges is a crucial issue to control the experimental conditions of the formation of ZSiC NRs of desired properties, just like in graphene nanoribbons.^37–40 It is known that in the ordinary experimental conditions there exist finite temperature and pressure. However, so far the study of edge structure stability of ZSiC NRs is performed only in vacuum at absolute zero temperature (0 K). How the experimental conditions, such as the hydrogen content of the environment and the finite temperature, would influence the edge structure stability, the electronic and magnetic properties of ZSiC NRs is still not clear. Moreover, the large number of theoretical works that appeared in the literature on ZSiC NRs (ref. 20, 24 and 29–35) has almost exclusively focused on single-hydrogen saturation of each edge atom. To fully understand the effect of the edge hydrogenation on the electronic and magnetic properties of the ZSiC NR, a systemic study is required. Motivated by these issues, we systematically investigated the effect of the hydrogen content of the environment on the edge structure, the electronic and magnetic properties, as well as electronic spin transport property of the ZSiC NRs, by using the spin polarized first principles density functional theory (DFT) calculations and the first-principles nonequilibrium Green's function method.

The remainder of this paper is organized as follows. In Section 2, we briefly describe computational method and models details. In Section 3, we discuss the results calculated for the effect of the hydrogen content of the environment, first the issue of the zero-temperature edge formation-energy per unit length of the edge, then the Gibbs free energy of the edge hydrogenated, and lastly the electronic and magnetic properties of the system, as well as the spin transport property. We conclude the paper in Section 4.

2 Computational method and models

Our calculations were carried out with the OPENMX computer code.⁴¹ DFT within the generalized gradient approximation (GGA)⁴² for the exchange-correlation energy was adopted. Norm-conserving Kleinman–Bylander pseudopotentials⁴³ were employed, and the wave functions were expanded by a linear combination of multiple pseudo atomic orbitals (LCPAO)^44,45 with a kinetic energy cutoff of 300 Ry. The basis functions used were: C5.5-s²p²d¹, Si5.5-s²p²d¹, and H4.5-s¹p¹. The first symbol designates the chemical name, followed by the cutoff radius (in Bohr radius) in the confinement scheme and the last set of symbols defines the primitive orbitals applied.

It is noted that the two side edges of the pristine ZSiC NRs are either terminated by Si or C atoms and are called the Si-edge and the C-edge, respectively. When the pristine ZSiC NRs are exposed to H₂ gas, its edge hydrogenation will take place. The edge Si and C atoms are allowed to terminate with either one (sp² hybridization) or two (sp³ hybridization) hydrogen atoms. It is noted that in a recent paper³⁴ we have studied the edge reconstruction effect in pristine ZSiC NRs and ZSiC-1H1H NRs, and reported that in the un-passivated systems, the C-edge reconstructed (Crc) could effectively lower the edge energy of the system, while the Si-edge reconstructed (Sirc) could raise the edge energy of the system. Thus, the Crc edge is the best edge for edge reconstruction of the system, while the both edge reconstructed (brc) system is metastable. However, in the systems with single-hydrogen saturation of each edge atom, the unreconstructed zigzag edge (ZSiC-1H1H) is the best edge. The Crc-H system is the metastable. The Sirc-H system has only slightly higher energy than the Crc-H system, whereas the brc-H system of the pristine SiC NR has the highest edge energy, i.e., the H passivation would prevent the occurrence of edge reconstruction. Therefore, here we do not consider the edge reconstruction effect and only consider four possible hydrogen terminations that are displayed in Fig. 1. They are: (a) each edge Si and C atom is passivated with one H atom (N-ZSiC-1H1H), which has been studied in the literature,^{20,24,29–35} (b) each edge Si atom is passivated with one H atom and each edge C atom is passivated with two H atoms (N-ZSiC-1H2H), (c) each edge Si atom is passivated with two H atoms and each edge C atom is passivated with one H atom (N-ZSiC-2H1H), and (d) each edge Si and C atom is passivated with two H atoms (N-ZSiC-2H2H). They are referred to as N-ZSiC-nHmH NRs, where the prefix ‘N’ represents the number of zigzag chains across the ribbon width.

We adopted a supercell geometry where the length of a vacuum region along the non-periodic direction (y- and z-directions) was 20 Å, and the lattice constant (a) along the periodic direction (x-direction) was 3.116 Å. Previously, it was suggested that a sufficient number of k-point sampling in the Brillouin zone integration should be performed for reliable results.^24,29 Thus, we used 121 × 1 × 1 k-point sampling points in the Brillouin zone integration. As for the geometry optimization, the positions of all the atoms including the passivated hydrogen atoms in the supercell were not constrained and could be fully relaxed under the condition that the supercell parameters were fixed, which was performed using the conjugate gradient scheme until the force acting on every atom is less than 10⁻⁴ Hartree per bohr. The transport properties were calculated using the nonequilibrium Green's function formalism⁴⁶ as implemented in version 3.5 of the OPENMX code.⁴⁷ We have also increased the size of the supercell to make sure that it does not produce any discernible difference in the results.

3 Results and discussion

First, we have carried out optimization of different width N-ZSiC-nHmH NRs with a number of chosen spin states. Upon optimization, the systems stabilize in the ground states. The zero-temperature edge formation-energy per unit length of the edge (E_edge+nHmH) of N-ZSiC-nHmH NR, simply called the edge energy, is given as^37,38where E_T (ZSiC + nHmH NR) is the total energy of N-ZSiC-nHmH NR, L is the length of an edge (the length of the unit cell), E_SiC is the energy of a pair of SiC atoms in the infinite, flat SiC sheet with the lattice parameter that minimizes the energy, and n_ZSiC is the number of SiC pairs in the ZSiC NR. The factor of 2 in eqn (1) accounts for the fact that a ZSiC NR has two edges. n_H and m_H are the total number of H atoms at Si edge and C edge, respectively. E_H2 is the energy of the isolated hydrogen molecule (H₂) and the factor of 2 in the last term accounts for the fact that each H₂ molecule contributes two H atoms. It is this edge energy that is usually used to determine the stability of different edge structures.^34,37–40

Fig. 2 shows the edge energy of N-SZiC-nHmH NRs as a function of ribbon width N from 2 to 15. We find that the edge energies saturate quickly with the increase in the width, indicating that the addition of extra C and Si atoms in the middle of the nanoribbon has a diminishing effect on the edge stability. Notably, the 8-ZSiC-2H1H and 8-ZSiC-2H2H NRs are spontaneously formed at T = 0 K since their formation energies are negative. In detail, the edge energy of the N-ZSiC-2H2H NR is minimum. The N-ZSiC-2H1H NR is the metastable. The N-ZSiC-1H2H has only slightly higher edge energy than the N-ZSiC-2H1H NR, whereas the N-ZSiC-1H1H NR has the highest edge energy. It is notable that at T = 0 K, the most stable edge hydrogenated structure is the N-ZSiC-2H2H NR instead of the N-ZSiC-1H1H NR that has been studied theoretically to a large extent.^{20,24,29–35} In addition, the calculation result that the N-ZSiC-2H1H has a lower edge energy than the N-ZSiC-1H2H NR indicates that the hydrogen atom prefers to occupy the Si edge, which generates local sp³ coordination at the edge Si atoms, before full coverage is reached. This can be understood by the fact that in the carbon family a sp² hybridization is the most stable phase. In the contrary, silicon prefers a sp³ hybridization.

Fig. 2 The zero-temperature edge formation-energy per unit length of the edge (E_edge+nHmH) of N-ZSiC-nHmH NRs as a function of ribbon width N.

Note that the above DFT-calculated edge energies are performed in vacuum at T = 0 K. However, in real experimental conditions, parameters such as the hydrogen content of the environment and the finite temperature naturally affect the edge hydrogenation of N-ZSiC NRs. In order to take the hydrogen content of the environment and the finite temperature effects into account, we can use an ab initio thermodynamics approach^37,49 to compute the relative stability of the different hydrogenated edges as a function of the chemical potential of the hydrogen. The corresponding Gibbs free energy of the edge hydrogenation, in presence of molecular H₂ gas, at a given chemical potential μ_H2, is calculated by the following formula:³⁷

withIn the above equations, G_nHmH is the Gibbs free energy calculated from the zero-temperature edge energy E_edge+nHmH shown before whereas μ_H2 is the chemical potential of H₂ at an absolute temperature T and pressure P calculated from eqn (3). H° (S°) is the enthalpy (entropy) at the pressure P° = 1 bar obtained from ref. 50. k_B is the Boltzmann constant. ρ_nHmH is the edge hydrogen density expressed as (n_H + m_H)/2L. For a given value of μ_H2, the most stable structure has the lowest value of G_nHmH. Note that by increasing μ_H2 (going to an environment richer in hydrogen), the favorable structures will be those with higher hydrogen-density ρ_nHmH.

The Gibbs free energies (G_nHmH) at T = 300 K versus chemical potential μ_H2 for the most stable 8-SZiC-1H1H, 8-ZSiC-2H1H and 8-ZSiC-2H2H NRs are shown in Fig. 3. The inset of Fig. 3 distinguishes the stability regions that are marked by the vertical lines. At T = 0 K, we have considered four possible edge hydrogenated N-ZSiC NRs: 8-ZSiC-1H1H, 8-ZSiC-1H2H, 8-ZSiC-2H1H, and 8-ZSiC-2H2H. Only three of these, however, have regions of stability at 300 K (see the inset of Fig. 3). In detail, when the chemical potential is lower than the left vertical line (μ_H2 < −0.91 eV), the 8-ZSiC-1H1H type is most stable, while when the chemical potential is located between the two vertical lines (−0.91 eV < μ_H2 < −0.97 eV), 8-ZSiC-2H1H type is most stable, and when the chemical potential is higher than the right vertical line (−0.97 eV < μ_H2), the 8-ZSiC-2H2H type is most stable. These results indicate that we can get the 8-ZSiC-1H1H, 8-ZSiC-2H1H and 8-ZSiC-2H2H NRs by controlling chemical environments, such as H₂ gas pressure. More surprisingly, N-ZSiC-1H1H NR, which has been studied theoretically to a large extent, is stable only at extremely low ultravacuum pressures. Under more standard conditions, the most stable edge hydrogenated structure is N-SiC-2H2H NR. On the other hand, compared to 8-ZSiC-1H1H, 8-ZSiC-2H1H and 8-ZSiC-2H2H NRs, 8-ZSiC-1H2H NR is unstable, and hence is not shown in Fig. 3. It should be pointed out, however, that the stability diagrams presented in Fig. 3 are, of course, idealistic and do not take into account thermal kinetics, but they could serve as rough guidelines to the experimental conditions required to achieve different types of edge hydrogenated N-ZSiC NRs. In addition, one notes that the region of chemical potential μ_H2 where 2H1H is stable, may be too narrow. However, from eqn (3) one can find that at 300 K for −0.91 eV < μ_H2 < −0.97 eV, its corresponding H₂ gas pressure (P) region is 7.62 × 10⁻¹² Pa < P < 7.76 × 10⁻¹¹ Pa, which is in the region that the current experimental technique can control. Of course such hydrogenation pressure control is also not simple.

Fig. 3 The Gibbs free energies (G_nHmH) versus chemical potential μ_H2 for the most stable 8-ZSiC-1H1H, 8-ZSiC-2H1H and 8-ZSiC-2H2H NRs after exposure to H₂ gas. The red solid, blue dash and green dash-dotted lines denote the results for 8-ZSiC-2H2H, 8-ZSiC-2H1H, and 8-ZSiC-1H1H NRs, respectively. The inset distinguishes the stability regions that are marked by the vertical lines. The alternative top axis shows the pressure, in bar, of molecular H₂ corresponding to the chemical potentials at T = 300 K.

Note that N-ZSiC-1H1H NRs have been studied before,^{20,24,29–35} and in the following we will focus on the electronic and magnetic properties, as well as electronic spin transport property of N-ZSiC-2H1H and N-ZSiC-2H2H NRs.

The band structures of N-ZSiC-2H1H NRs are shown in Fig. 4, while the corresponding transmission functions and spatial distribution of the spin differences are shown in Fig. 5. One can find that the N-ZSiC-2H1H NR has the ferromagnetic (FM) ground state, independent of the ribbon width N. On the other hand, from Fig. 4 one notes that for 2-ZSiC-2H1H NR (see Fig. 4a), the valence band and conduction band are separated for both up-spin and down-spin bands. However, as the ribbon width N increases, the band gap of the spin-down band remains, but near the Fermi level the valence band and conduction band of the spin-up band approach each other up to N = 12. When N = 13, the valence band and conduction band of the spin-up band touch at the Fermi level, i.e., the band gap of the spin-up band is closed completely, while the band gap of the spin-down band remains, which means that the 13-ZSiC-2H1H NR is half-metallic (see Fig. 5f).^51,52 It is noted that when N = 6, the band gap of the spin-up band is too small and hardly shows in its band structure. However, we can see it by the corresponding transmission function (see Fig. 5c and Table 1). In summary, when N ≤ 12, the N-ZSiC-2H1H NR is a FM semiconductor, while when N ≥ 13, the N-ZSiC-2H1H NR turns into a FM half-metallic. Note that the spin transport polarization η, which is defined as ,⁵² is used to measure the spin filtering behavior. From Fig. 5f one can find that in the range of −0.30–0.25 eV, the transmittance of spin-up channel (T_up) is 2G₀ (G₀ = e²/h⁻¹), while the transmittance of spin-down channel (T_down) is zero. Therefore, the 13-ZSiC-2H1H NR has η = 100% spin transport polarization around the Fermi level (see Table 1) and exhibits good spin filtering behaviors.

Fig. 4 Band structures of the N-ZSiC-2H1H NR. (a) 2-ZSiC-2H1H, (b) 3-ZSiC-2H1H, (c) 5-ZSiC-2H1H, (d) 6-ZSiC-2H1H, (e) 7-ZSiC-2H1H, (f) 8-ZSiC-2H1H, (g) 9-ZSiC-2H1H, (h) 10-ZSiC-2H1H, and (i) 15-ZSiC-2H1H. The red solid and blue dash-dotted lines denote the spin-up (↑) and spin-down bands (↓), respectively. The Fermi level is set to zero.

Fig. 5 Transmission functions and spatial distribution of the spin differences for the N-ZSiC-2H1H NR. (a) 2-ZSiC-2H1H, (b) 5-ZSiC-2H1H, (c) 6-ZSiC-2H1H, (d) 8-ZSiC-2H1H, (e) 12-ZSiC-2H1H, and (f) 13-ZSiC-2H1H. The red and blue surfaces which have been drawn represent the spin-up (↑) and spin-down (↓) spatial distributions. For the corresponding transmission function, where G₀ = e²/h, the red solid and blue dash-dotted lines denote the spin-up (↑) and spin-down (↓) channels, respectively. The Fermi level is set to zero.

Table 1 Transmittances of spin-up (T_up) and -down (T_down) channels, as well as total channels (T_sum), at the Fermi level and transport polarization (η) for the N-ZSiC-2H1H NRs

N	T up	T down	T sum	η
2	0.00	0.00	0.00	0.00
5	0.00	0.00	0.00	0.00
6	0.00	0.00	0.00	0.00
8	0.00	0.00	0.00	0.00
12	0.00	0.00	0.00	0.00
13	2.00	0.00	2.00	100%

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For N-ZSiC-2H2H NRs, the band structures are shown in Fig. 6, while the corresponding transmission functions and spatial distribution of the spin differences are shown in Fig. 7. One can find that when N ≤ 4, the N-ZSiC-2H2H NR has only a nonmagnetic (NM) state, while when N ≥ 5, the N-ZSiC-2H2H NR has the ferrimagnetic ground state where the ferromagnetic (FM) chains at the two edges have opposite directions of magnetic moments, but have different values, and therefore the net magnetic moment in a unit cell is not zero. Moreover, from Fig. 6 one can find that for 5-ZSiC-2H2H NR (see Fig. 6c), the valence band and conduction band are separated for both up-spin and down-spin bands. However, as the ribbon width N increases, the band gap of the spin-down band increases, while near the Fermi level the valence band and conduction band of the spin-up band approach each other up to N = 7. When N = 8, from Fig. 6f one can find that the valence and conduction bands of the spin-up band touch at the Fermi level, i.e., the band gap of the spin-up band is closed completely, while the band gap of the down-spin band remains, which means that the 8-ZSiC-2H2H NR is half-metallic (see Fig. 7d). It is noted that when N = 7, the band gap of the spin-up band of N-ZSiC-2H2H NR is too small and hardly shows in its band structure. However, we can see it by the corresponding transmission function (see Fig. 7c and Table 2). In summary, when N ≤ 7, the N-ZSiC-2H2H NR is a semiconductor, while when N ≥ 8, the N-ZSiC-2H2H NR turns into a half-metallic. Fig. 7 also shows that for N ≤ 7, the N-ZSiC-2H2H NR is a semiconductor, whereas N ≥ 8, the N-ZSiC-2H2H NR turns into a half-metallic and has η = 100% spin transport polarization (see Table 2). Thus, the N-ZSiC-2H1H NR (N ≥ 8) is a good spin filter nanomaterial.

Fig. 6 Band structures of the N-ZSiC-2H2H NR. (a) 3-ZSiC-2H2H, (b) 4-ZSiC-2H2H, (c) 5-ZSiC-2H2H, (d) 6-ZSiC-2H2H, (e) 7-ZSiC-2H2H, (f) 8-ZSiC-2H2H, (g) 9-ZSiC-2H2H, (h) 10-ZSiC-2H2H, and (i) 15-ZSiC-2H2H. The other marks are the same as in Fig. 4.

Fig. 7 Transmission functions and spatial distribution of the spin differences for the N-ZSiC-2H2H NR. (a) 4-ZSiC-2H2H, (b) 5-ZSiC-2H2H, (c) 7-ZSiC-2H2H, (d) 8-ZSiC-2H2H, (e) 10-ZSiC-2H2H, and (f) 15-ZSiC-2H2H. The other marks are the same as in Fig. 5.

Table 2 Transmittances of spin-up (T_up) and -down (T_down) channels, as well as total channels (T_sum), at the Fermi level and transport polarization (η) for the N-ZSiC-2H2H NRs

N	T up	T down	T sum	η
4	0.00	0.00	0.00	0.00
5	0.00	0.00	0.00	0.00
7	0.00	0.00	0.00	0.00
8	1.50	0.00	1.50	100%
10	2.00	0.00	2.00	100%
15	2.00	0.00	2.00	100%

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The magnetic properties of N-ZSiC-1H1H NR have been studied theoretically to a large extent, and it is found that a spin-polarized solution gives a lower total energy compared to a spin-degenerate calculation.^{20,24,29–35} In order to conveniently compare and analyze the magnetic property difference of the 8-ZSiC-1H1H, 8-ZSiC-1H2H, 8-ZSiC-2H1H, and 8-ZSiC-2H2H NRs, the magnetic moments of each edge atom and nearest-neighboring atom of the edge atom, as well as at the saturated hydrogen atoms (H_Si indicates a hydrogen passivated edge Si atom and H_C marks a hydrogen saturated edge C atom), are listed in Table 3. One can find that compared with N-ZSiC-1H1H NR, the magnetic properties of N-ZSiC-2H2H NR (N ≥ 5) are quite striking, with the edge Si and C atoms being almost spin-degenerate, but the nearest-neighboring C atom of edge Si atom and the nearest-neighboring Si atom of the edge C atom have a spin-polarized solution, as shown in Fig. 7b–f. In other words, the induced magnetic moments are localized on the interedge C atoms at the Si-edge and the interedge Si atoms at the C-edge, while each edge C atom, as well as each edge Si atom, carry very small magnetic moments. Moreover, the magnetic moments in N-ZSiC-2H2H NR are enhanced in comparison to N-ZSiC-1H1H NR, such as the magnetic moment on edge Si atom of 8-SiC-1H1H NR is 0.24 μ_B, while the magnetic moment on the interedge Si atoms at the C-edge of 8-ZSiC-2H2H NR is 0.44 μ_B. The magnetic moment on edge C atom of 8-ZSiC-1H1H NR is −0.21 μ_B, while the magnetic moment on the interedge C atoms at the Si-edge of 8-SiC-2H2H NR is −0.33 μ_B. For the magnetic moment on the H atoms, a similar phenomenon occurs. For example, the magnetic moment on the H atom at edge Si atom of 8-SiC-1H1H NR is −0.02 μ_B, while the magnetic moment on the H atom at edge Si atom of 8-ZSiC-2H2H NR is −0.05 μ_B. The magnetic moment on the H atom at edge C atom of 8-SiC-1H1H NR is 0.02 μ_B, while the magnetic moment on the H atom at edge C atom of 8-ZSiC-2H2H NR is 0.05 μ_B.

Table 3 The magnetic moments at each edge atom (A_eg) and the nearest-neighboring atom of the edge atom (A_B-eg), as well as at the saturated hydrogen atoms (H_Si and H_C), in the unit of μ_B for 8-ZSiC-nHmH NRs

System	Ceg	Sieg	CSi-eg	SiC-eg	HSi	HC
1H1H	−0.21	0.24	−0.03	0.00	−0.02	0.02
2H2H	0.04	−0.03	−0.33	0.44	−0.05	0.05
2H1H	−0.27	−0.02	−0.36	−0.02	−0.06	0.01
1H2H	0.07	0.30	−0.04	0.53	−0.01	0.06

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The above results can be understood by the calculated Mulliken charge and spin population at each edge atom (A_eg) and the nearest-neighboring atom of the edge atom (A_B-eg), as well as at the saturated hydrogen atoms (H_Si and H_C), for 8-ZSiC-nHmH NRs. The Mulliken analysis results are listed in Table 4. Note that for each atom we only list the charge in spin-up channel and the total charge in both spin-up and -down channels. However, the charge in spin-down channel, as well as the magnetic moment at each atom, can be obtained easily by simple calculation. For example, for the edge C atom (C_eg) in 1H1H, from Table 4 one can find that the total charge in both spin-up and -down channels is 4.31 e, and the charge in spin-up channel is 2.05 e. Thus, the charge in spin-down channel is 2.26 e (4.31–2.05) and the magnetic moment is −0.21 μ_B (2.05–2.26) which is listed in Table 3.

Table 4 The Mulliken charge and spin population at each edge atom (A_eg) and the nearest-neighboring atom of the edge atom (A_B-eg), as well as at the saturated hydrogen atoms (H_Si and H_C), in the unit of e for 8-ZSiC-nHmH NRs

System	Ced		Sied		CSi-eg		SiC-eg		HSi		HC
	Spin-up	Total	Spin-up	Total	Spin-up	Total	Spin-up	Total	Spin-up	Total	Spin-up	Total
1H1H	2.05	4.31	1.83	3.43	2.16	4.35	1.71	3.42	0.67	1.36	0.60	1.18
2H2H	2.02	4.00	1.57	3.17	1.98	4.29	1.98	3.52	0.66	1.37	0.60	1.15
2H1H	2.02	4.31	1.56	3.14	1.95	4.26	1.69	3.40	0.66	1.38	0.59	1.17
1H2H	2.03	3.99	1.87	3.44	2.16	4.36	2.04	3.55	0.67	1.35	0.61	1.16

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It is clear that compared with 8-ZSiC-1H1H NR, a charge redistribution of 8-ZSiC-2H2H NR occurs. From Table 4 one can find that the charges at the edge C and Si atoms decrease obviously, such as the charge at C_eg decreases from 4.31 e to 4.00 e. The charge at Si_eg decreases from 3.43 e to 3.17 e. On the other hand, one notes that for C_eg the charge in the spin-up channel is almost unchanged. Thus, the charge decrease at C_eg originates from the charge in its spin-down channel decreasing, which leads to the weakening of the magnetic moment on C_eg. For example, the charge in the spin-down channel of C_eg decreases from 2.26 e to 1.98 e (4.00–2.02). As a result, the magnetic moment on C_eg is weakened from −0.21 μ_B to 0.04 μ_B. As for Si_eg, its charge decrease originates from the charge in its spin-up channel decreasing, which leads to the weakening of the magnetic moment on Si_eg. For example, the charge in the spin-up channel of Si_eg decrease from 1.83 e to 1.57 e. As a result, the magnetic moment on Si_eg is weakened from 0.24 μ_B to −0.03 μ_B as shown in Table 3.

Where do these charges go? From Table 4 one can find that the charge at the nearest-neighboring Si atom of the edge C atom (Si_C-eg) increases from 3.42 e to 3.52 e, which indicates that the edge C atom passivated with two H atoms would lead to its charge to be transferred to Si_C-eg. This is proved in 8-ZSiC-1H2H NR, where compared with 8-ZSiC-1H1H NR the charge at Si_C-eg increases from 3.42 e to 3.55 e. Moreover, these charges are transferred to the spin-up channel of Si_C-eg, which leads to the enhancement of the magnetic moment on Si_C-eg in comparison to N-ZSiC-1H1H NR. For example, the charge in the spin-up channel of Si_C-eg increases from 1.71 e to 1.98 e. As a result, the magnetic moment on Si_C-eg is enhanced from 0.00 μ_B to 0.44 μ_B as shown in Table 3. However, as for the charge at the nearest-neighboring C atom of the edge Si atom (C_Si-eg), we note that its charge does not increase, but decreased. Specifically, the charge in the spin-up channel of C_Si-eg decreases from 2.16 e to 1.98 e, which leads to the enhancement of the magnetic moment on C_Si-eg from −0.03 μ_B to −0.33 μ_B. It is noted that compared with the C_ed, Si_ed, C_Si-eg, and Si_C-eg, the charges at the saturated hydrogen atoms (H_Si and H_C) show little change.

Lastly, it is worth mentioning that recently one found a simple method for producing graphene nanoribbons by lengthwise cutting and unravelling of multiwalled carbon nanotube (MWCNT) side walls.^53,54 Moreover, the multiwalled SiCNTs are also already synthesized.^7–9 Naturally, it is a possible path towards a SiC NR to lengthwise cut and unravel multiwalled SiCNT side walls, just like in producing the graphene nanoribbons.^53,54 We hope that the study here can stimulate experimentalists to produce SiC NRs.

4 Conclusions

In summary, we have investigated the hydrogenated effect on N-ZSiC NRs by using first-principles calculations based on DFT and nonequilibrium Green's function method. We have determined the structure and stability of hydrogen-terminated N-ZSiC NRs. For reasonable hydrogen concentrations, the most stable structures are the N-ZZSiC-1H1H, N-ZSiC-2H1H, and N-ZSiC-2H2H. Surprisingly, under standard conditions, the most stable edge hydrogenated structure is N-SiC-2H2H NR instead of the N-ZSiC-1H1H NR that has been studied theoretically to a large extent. We also found that the ground state of N-ZSiC-2H1H NR is a ferromagnetic state. Moreover, when N ≤ 12, the N-ZSiC-2H1H NR is a semiconductor, while when N ≥ 13, the N-ZSiC-2H1H NR turns into a half-metallic. As for N-ZSiC-2H2H NR, for N ≤ 4, it has only a NM state, whereas for N ≥ 5, the N-SiC-2H2H NR has the ferrimagnetic ground state. On the other hand, when N ≤ 7, the N-ZSiC-2H2H NR is a semiconductor, while when N ≥ 8, the N-ZSiC-2H2H NR becomes a half-metallic. The study results here can be used to guide the search for the most stable edges in different chemical environments. Moreover, these results show that the electronic and magnetic properties of the N-ZSiC NR can be fully modulated by controlling the hydrogen content of the environment and the temperature, as well as the ribbon width N, which can be utilized in the new generation of nano/molecular electronics and spintronics.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (grant no. 11174003) and the 211 Project of Anhui University.

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