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Electronic structures and ferromagnetism in (Fe, Cr)-codoped 4H–SiC from first-principles investigations
Vacuum 167 (2019) 59–63
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Electronic structures and ferromagnetism in (Fe, Cr)-codoped 4H–SiC from first-principles investigations
T
Bing Zhanga, Linghao Zhub, Long Linb,c,∗, Weiyang Yud, Hualong Taoe, Yonghao Xud, FeiPeng Guod, Lixin Lib, Jingtao Huangb a
Yellow River Conservancy Technical Institute, Kaifeng, Henan, 475004, China Cultivating Base for Key Laboratory of Environment-Friendly Inorganic Materials in Henan Province, School of Materials Science and Engineering, Henan Polytechnic University, Jiaozuo, 454000, China c School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo, 454000, China d School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo, 454000, China e School of Materials Science and Engineering, Dalian Jiaotong University, Dalian, 116028, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: First-principles Dilute magnetic semiconductors Electronic structure Magnetic properties 4H–SiC
Electronic structures and magnetic properties for double impurities (Fe and Cr) doped 4H silicon carbide (SiC) are studied by first principles calculations within the generalized gradient approximation (GGA) +U scheme. For single Fe-doped 4H–SiC, the local magnetic moments of Fe atom is about 3.76 μB and the system exhibits halfmetallic character. For single Cr atom doped 4H–SiC, the local magnetic moments of Cr atom is about 3.15 μB. The introduction of Cr impurities does not destroy the semiconducting nature of Cr-doped 4H–SiC system. For (Fe, Cr)-codoped 4H–SiC, the magnetic coupling between the moments induced by Fe and Cr dopants is ferromagnetic and the origin of strong ferromagnetic coupling can be attributed to p-d hybridization interaction. We discuss the effect of silicon vacancy on the magnetism as well. Our calculations results show that (Fe, Cr)codoped 4H–SiC exhibit half-metallic behavior, which is suitable for spintronic devices applications.
1. Introduction Diluted magnetic semiconductors (DMSs) were extensively research because of their potential applications for spintronic devices [1]. Silicon carbide (SiC) is an important candidate material for spin electronic applications. SiC has more than 200 polytypes in the crystal structure with different stacking sequences. 4H–SiC [2,3] and 3C–SiC [4,5] are relatively important in the SiC series. SiC-based DMSs has excellent physical features such as thermal stability, chemical inertness, high thermal conductivity, and others [6]. Magnetic 3d transition-metal (TM) doped SiC-based DMSs have attracted a great interest because of their spintronic devices applications [7]. Recently TM-doped SiC on magnetic properties have been reported by first-principle computation [8–12]. Theoretically, Pan et al. studied N-TM (TM = Cr, Mn, Fe, and Co)-codoped SiC by emplying density functional theory based calculations. The calculation results demonstrate that N-TM codoped SiC was ferromagnetic, and the ferromagnetism originates from the strong carrier-mediated interaction between the spin-polarized TM-d and N-p electrons [13].
The magnetic properties of SiC doped by transition metals Mn and Cr have been investigated by using first principles density functional calculations. The result of calculation verify that the Curie temperature (TC) of 3C–Si1-xTMxC and 3C–Si1-x-yMnxCryC increases with increasing transition metal concentration [8]. Lin et al. researched the electronic structures and magnetic properties for (Al, Fe)-codoped 4H–SiC. They found that (Al, Fe)-codoped 4H–SiC show the ferromagnetic characteristics [10]. Several reports were published documenting experimental studies of magnetic properties of SiC with transition metal impurities. Zhang et al. prepared the specimens of (Al, Co)-codoped 4H–SiC and the structural and magnetic properties have been researched. They suggested that the samples show increased ferromagnetism with increasing of Co concentration [14]. Jin et al. fabricated Cr-doped SiC thin films on Al2O3 and Si substrates by using dual ion beam sputtering deposition at room temperature. The magnetic measurements results reveal that the Cr-doped α-SiC thin films are ferromagnetic with Curie temperature (Tc) above room temperature [15]. Sun et al. fabricated (Mn, Co)-codoped SiC films on Si (100) substrates by RF-magnetic sputtering. They
∗ Corresponding author. Cultivating Base for Key Laboratory of Environment-Friendly Inorganic Materials in Henan Province, School of Materials Science and Engineering, Henan Polytechnic University, Jiaozuo, 454000, China. E-mail address: [email protected] (L. Lin).
https://doi.org/10.1016/j.vacuum.2019.05.039 Received 18 March 2019; Received in revised form 26 May 2019; Accepted 28 May 2019 Available online 29 May 2019 0042-207X/ © 2019 Elsevier Ltd. All rights reserved.
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studied the structure and luminescence properties of the films in details [16]. Jin et al. investigated Cr-doped SiC films by the RF magnetic sputtering technique. The results show that the SiC crystal is formed and that majority of Cr doped in the SiC resulted in the formation of the C clusters [17]. The magnetic properties of TM doped SiC-based DMSs have been extensively investigated both computationally and experimentally. While, whether magnetic clusters or secondary ferromagnetic plays a more important role in the ferromagnetism origin. Meanwhile, many computational results suggest that the generalized gradient approximation (GGA) +U scheme play a crucial role in the ferromagnetism in TM doped SnO2 [18–23]. SnO2-based and SiC-based DMSs have similar physical properties. However, to the best of our knowledge in the literature, so far few results are realized in electronic structures and magnetic properties for (Fe, Cr)-codoped 4H–SiC by first principles calculations within the GGA + U scheme. In the present study, we carried out the first principles calculations by means of the GGA + U scheme for (Fe, Cr)-codoped 4H–SiC without and with Si vacancies. We investigate the effect of Fe and Cr dopants and silicon vacancies on the electronic structures and magnetic properties of (Fe, Cr)-codoped 4H–SiC.
Fig. 2. (Color online) Density of states for intrinsic 4H–SiC and partial density of states for C and Si, respectively. And (a) is the total density of states (TDOS) for intrinsic doped 4H–SiC, (b)–(c) are the partial density of states (PDOS) of C and Si. The Fermi level is set to 0 eV.
during the integral calculation in the Brillouin zone. We applied plane wave basis cutoff energy of 450 eV. The convergence threshold for selfconsistent field energy was set at 10−6 eV, and the internal coordinates are fully relax until the forces on the ions are below 0.05 eV/Å.
2. Computational details Perfect 4H–SiC has a hexagonal structure, which belongs to P63mc space group at normal temperature and pressure [24,25]. The optimized lattice constants, a = b = 3.095 Å, c = 10.135 Å, are in good agreement with the experimental values (a = b = 3.081 Å, c = 10.096 Å) [33], which indicates the calculation model and parameters are reasonable. We considered a reference undoped 3✕3✕1 supercell containing 72 atoms, as shown in Fig. 1. 4H–SiC consists of an equal number of cubic and hexagonal bonds with a stacking sequences of ABCB. Our calculations were performed using the CASTEP code based on plane-wave basis sets. The ultrasoft pseudopotential was used for electron-ion interactions. The electron-electron exchange and correlation effects were described by the generalized gradient approximation (GGA) functional using the Perdew-Burke-Ernzerhof (PBE) method [26] and the strong correlation effects are introduced by means of GGA + U scheme, and GGA + U and PBE were used to optimize the lattice parameters. The value of parameter U for Fe:3d states and Cr:3d states are taken to be 5.1 eV [27–29] and 3.8 eV [30–32], respectively. Following the Monkhorst-Park method, a 2 × 2 × 2 k-mesh is adoped
3. Results and discussions The structural optimization is first performed for pristine 4H–SiC. We began with a study of the pristine 4H–SiC without Cr and Fe incorporation. The electronic properties of the pure 4H–SiC were calculated. We found that pristine 4H–SiC is obviously shown to be an indirect band gap semiconductor. The band-gap width is about 2.25 eV and the total magnetic moments is zero. To understand the spin state of pristine 4H–SiC. We studied the density of states (DOS) for pristine 4H–SiC which are plotted in Fig. 2. From Fig. 2, the majority-spin density of states and minority-spin density of states are identical. The conduction band is mainly contributed by Si-3p orbitals and the valence band is mainly contributed by C-2p and Si-3p orbitals. The calculations results show that pure 4H–SiC material is nonmagnetic ground state. Moreover, we study the electronic structures and magnetic properties in TM (TM = Fe, Cr) doped 4H–SiC system, we first consider an isolated TM doped 4H–SiC by replacing one Si atom with one TM atom, and the doping positions of Cr and Fe atoms are both at site 5, corresponding to a doping concentration of 2.28 at.%. Next, in order to simulate the Fe and Cr codoping and study the magnetic couping interaction between Fe atom and Cr atom dopants. The ten configurations are obtained by introducing one Fe atom and one Cr atom to the Si sites which corresponds to the concentration of 2.28 at.% Fe and 2.28 at.% Cr and 4.56 at.% (Fe, Cr) co-doped 4H–SiC, respectively. For convenience of discussion, we use (i, j) to denote a Fe–Cr pair in which two Si sites are replaced by Fe atoms at i sites and Cr atoms at j sites. Here, the substituted Si atoms are marked with numbers 1–10 in Fig. 1. For each of these configurations, ΔEFM corresponds to the energy difference (ΔEFM = EFM−EAFM) was estimated from the total energies for the two spin configurations, namely, parallel [ferromagnetic (FM)] and antiparallel [antiferromagnetic (AFM)] orientations of the localized magnetic moments on the doped Fe atom and Cr atom. Firstly, we study the electronic structures and magnetic properties of single Fe atom doping. Our results of calculation show that the local magnetic moments of Fe is 3.76 μB for single Fe atom doped 4H–SiC. To further make out the origin of magnetic moments, the total density of states (TDOS) and partial density of states (PDOS) are calculated and are plotted in Fig. 3. From the TDOS in Fig. 3, it can be seen that doped with a single Fe atom has spin polarization for GGA + U calculation, the Fermi level passes through the majority-spin states at the top of the
Fig. 1. 72-Atom 3✕3✕1 supercell model of (Fe, Cr)-codoped 4H–SiC, Colored spheres are Si (yellow), C (gray), atom. The Si atoms labeled by 1–10 are the sites to be replaced by Fe and Cr atoms, V1, V2, and V3 represent silicon vacancies in different layers. 60
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Table 1 Calculation results for ten configurations of (Fe, Cr)-doped 4H–SiC. Fe, Cr distance after relaxation in nonspin-polarized (NSP), ΔE, ΔEFM and the FM magnetic moments of Fe and Cr atoms, respectively. Structure (i, j)
(5, 6) (1, 4) (8, 7) (3, 1) (6, 10) (4, 7) (2, 8) (9, 2) (9, 3) (10, 9)
DFe-Cr (Å) NSP
FM
3.082 3.085 4.360 6.163 6.892 8.153 8.158 5.344 6.169 8.153
3.037 3.063 4.352 6.243 6.931 8.212 8.196 5.362 6.209 8.192
ΔE (eV)
−5.8795 −5.8987 −5.6453 −5.9453 −5.7095 −5.9624 −5.8629 −5.6477 −5.8222 −5.9505
ΔEFM (meV)
−316.0 −558.9 −388.5 −225.4 −142.3 −157.3 −323.6 −181.6 −348.8 −345.0
Local Magnetic Moments Fe (μB)
Cr (μB)
3.69 3.70 3.77 3.69 3.76 3.69 3.73 3.77 3.73 3.70
3.25 3.25 3.17 3.22 3.16 3.28 3.22 3.14 3.22 3.22
components present a band gap, indicating that the introduction of Cr impurity does not destroy the semiconductor properties of the 4H–SiC system doped with Cr atom for GGA + U approximation. The PDOS of Cr-3d, Cr-3p and C-2p indicate that Cr-3d, Cr-3p and C-2p orbitals are hybridize with each other near the Fermi level. The magnetic moments mainly comes from the Cr-3d and C-2p orbitals in the spin channel. After understanding the local magnetic moments formation of Fe and Cr doped 4H–SiC, we will address another important issue of coupling between magnetic moments. Consider that two Si atoms are replaced by one Fe atom and one Cr atom, as shown in Fig. 1. We calculated the total energy differences between the FM states and the AFM states of the 10 configurations for (Fe, Cr)-codoped 4H–SiC. All configurations of Fe–Cr distance, difference energy of FM-nonspin polarized(NSP) (ΔE), FM-AFM (ΔEFM) and FM magnetic moments of Fe and Cr atoms are shown in Table 1. Table 1 also list the local magnetic moments of each doped atom. As we can see from Table 1, the energy difference between FM and NSP are all negative, which show that FM is the most stable state. Table 1 shows that the local structure of (Fe, Cr) co-doped 4H–SiC, which is slightly distorted. Here, we take the FM state of the ground state configuration (1, 4) as an example. Local magnetic moments of Si double substituent in all configurations increased. The local magnetic moments of Fe atom and Cr atom are around 3.70 μB and 3.25 μB, which is obviously larger than the magnetic moments induced by the isolated cases. For comparison, the magnetism of 4H–SiC systems doped with 2Cr and 2Fe are calculated, respectively, and the doping concentration are all 4.56 at.%. The total magnetic moment of 2Cr and 2Fe doped 4H–SiC systems are 4.03 and 6.05 μB. The total magnetic moment of (Fe, Cr) co-doped 4H–SiC system is 6.06 μB. The results show that the codoping system give higher magnetic moments than single doping at the same concentration. This magnetic enhancement may be due to the long-distance FM coupling between the Fe and Cr atoms through the intermediate C atoms. It is found that calculations from GGA + U that △EFM for each configuration are negative, which indicates that the FM order is more positive than the positive for all (Fe, Cr)-codoped 4H–SiC configurations relative to the AFM order. The calculations results also show that the (1, 4) configuration is the most stable configuration, which the distance is 3.085 Å between the dopants and the largest negative △EFM (−558.9 meV) in all configurations. We also calculated the energy difference between the ferromagnetic and antiferromagnetic states of (4,1), (6,5), (7,8) configurations to consider the effect of atomic inerchange for magnetic state, and found that ΔEFM of (4, 1), (6, 5), and (7, 8) configurations are −146, −491, and −549 meV, respectively. The doping system presents a stable ferromagnetic state, which is consistent with our calculation results of (1, 4), (5, 6) and (8, 7) configurations. Therefore, (1, 4) configuration can be considered as FM ground state. This states that it is possible to (Fe, Cr)codoped 4H–SiC with ferromagnetism at room temperature. Therefore, (Fe, Cr)-codoped 4H–SiC can be commercialized.
Fig. 3. (Color online) Density of states for Fe doped 4H–SiC and partial density of states for Fe, C and Si, respectively. And (a) is the total density of states (TDOS) for Fe doped 4H–SiC, (b)–(d) are the partial density of states (PDOS) of Fe, C and Si. The Fermi level is set to 0 eV valence band, which reflects the system exhibits half-metallic properties and allows electrons to transfer. From the PDOS of Fe doped 4H–SiC, it reveals that Fe-3d, C-2p and Si-3p orbitals are hybridized with each other at the Fermi level. The magnetic moments mainly come from the Fe-3d, C-2p and Si-3p orbitals in the majority spin channel.
TDOS. Secondly, we study a single Cr substitution, which Cr-doped 4H–SiC with CrSi was modeled by replacing one Si atom with one Cr atom. The total magnetic moments of Cr doped 4H–SiC is 1.96 μB. The local magnetic moments on Cr and C atom are 3.15 μB and 0.29 μB, respectively. The results of calculation indicate that the magnetic moments of the Cr-doped 4H–SiC system mainly come from the Cr atom. So spinpolarization occurs mainly from the Cr atom. Fig. 4(a)–(d) present the calculated total density of states (DOS) and the partial DOS of the Cr dopant, the nearest-neighboring C atoms and the second-nearestneighboring Si atoms. As shown in Fig. 4 (a), most spins and a few spin
Fig. 4. (Color online) Density of states for Cr, doped 4H–SiC and partial density of states for Cr C and Si, respectively. And (a) is the total density of states (TDOS) for Cr doped 4H–SiC, (b)–(d) are the partial density of states (PDOS) of Cr, C and Si. The Fermi level is set to 0 eV. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 61
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Fig. 5. (Color online) Density of states for (Fe, Cr)-codoped 4H–SiC and partial density of states for Fe, Cr, C and Si, respectively. And (a) is the total density of states (TDOS) for (Fe, Cr) codoped 4H–SiC, (b)–(e) are the partial density of states (PDOS) of Fe, Cr, C and Si. The Fermi level is set to 0 eV. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Fig. 6. (Color online) Spin density distribution for (Fe, Cr)-codoped 4H–SiC in (1, 4) configuration in FM coupling. The isovalue is set to 0.085 e/Å3. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) Table 2 Calculation results for five configurations of (Fe, Cr, V2)-codoped 4H–SiC. Fe, Cr distance after relaxation in nonspin-polarized (NSP), ΔEFM and the FM magnetic moments of Fe and Cr atoms, respectively.
In order to study the origin of magnetism, we calculated the TDOS and PDOS of (Fe, Cr)-codoped 4H–SiC system, as shown in Fig. 5. It can be seen from Fig. 5 (a) that spin polarized TDOS in the (Fe, Cr) codoped 4H–SiC system has a significant spin splitting near the Fermi level, which means that after Si replaced by Fe and Cr, magnetism can be generated in the (Fe, Cr)-codoped 4H–SiC system. Similar to the situation of single doped Fe, we can also see that (Fe, Cr)-codoped 4H–SiC system has half-metallic properties. Obviously, C atom, Fe atom and Cr atom induced the magnetism of (Fe, Cr)-codoped 4H–SiC. The 3d orbitals of Fe and Cr are spin-polarized and strongly hybridized with 2p orbitals of C. The Fermi energy is mainly dominated by the Fe-3d orbitals, Cr-3d orbitals and C-2p orbitals, indicating that magnetism is mainly induced by Fe and Cr 3d orbitals and located in Fe atom, Cr atom and C atom. To further clarify the mechanism for magnetic moments change in (Fe, Cr)-codoped 4H–SiC, the spin density isovalue of (1, 4) configurationin as shown in Fig. 6. As seen in Fig. 6, the spin density distribution of Fe and Cr atoms in (1,4) configurations FM coupling of GGA + U was calculated, respectively. As shown in Fig. 6, the polarization components are mainly distributed on Fe atoms and Cr atoms, and the spin directions are parallel. Due to the strong hybridization of Fe and Cr dopants with adjacent C atom, the adjacent C atom spin polarized and ferromagnetic coupling occurred with Fe and Cr atoms. So, the hybridized Fe: 3d-C: 2p-Cr: 3d chain formed through p-d coupling is responsible for the long-range FM coupling. It is possible to introduce room-temperature ferromagnetism in the presence of inherent defects [34]. silicon vacancies plays an important role in ferromagnetic tuning in SiC based DMSs [35,36]. Consequently, it is essential to contemplate Si vacancy effect. Therefore, this section studies the magnetic coupling of (Fe, Cr)-codoped 4H–SiC with silicon vacancy to understand the ferromagnetism of (Fe, Cr)-codoped 4H–SiC. We investigated the effect of silicon vacancy on the electronic structures and magnetic properties (Fe, Cr)-codoped 4H–SiC. In the calculation and analysis of this part, we only consider the substitution defect. We first calculated the (Fe, Cr)-codoped 4H–SiC systems, in which a V2 generated by removing a neutral Si atom in the supercell. The relative position of the V2 is shown in Fig. 1. The Fe–Cr distance, FM-AFM energy difference and FM local magnetic moment of Fe and Cr atoms in the super lattice under silicon vacancy configuration are given in Table 2. As seen in Table 2, all ΔEFM
Structure (i, j)
(5, 6) (1, 4) (8, 7) (6,10) (4, 7) (2, 8)
ΔEFM(meV)
DFe-Cr (Å) NSP
FM
3.082 3.026 4.360 6.892 8.153 8.158
3.146 3.067 4.281 6.936 8.131 8.208
−349.2 −267.9 −238.1 −286.1 −345.5 −320.4
Local Magnetic Moments Fe (μB)
Cr (μB)
3.38 3.24 3.43 3.40 3.35 3.42
2.91 3.30 2.90 3.19 2.88 2.89
are negative, which indicates that the ground state of (Fe, Cr, V2)-codoped 4H–SiC are FM coupling between the Fe and Cr atoms. For comparison, we add silicon vacancy in the configuration (1, 4) with the strongest ferromagnetism in Table 1 to indicate the influence of silicon vacancy on the ferromagnetism of the system. As shown in Table 2, we calculate the electronic structures and magnetism of (1, 4) configuration with silicon vacancy. The calculation results show that the (1, 4) configuration is FM states, which the distance is 3.026 Å between the dopants and the negative △EFM (−267.9 meV). The ferromagnetism of the 4H–SiC system is obviously weaker than that without silicon vacancy. Compared with the 4H–SiC system replaced only by Fe and Cr atoms, the magnetic moment of Si atom decreased after the introduction of silicon vacancy. In order to compare the effects of silicon vacancy in different layers on the ferromagnetism of 4H–SiC, we calculated the ferromagnetism of the system under the influence of vacancies in different layers (marked V1, V2, V3), respectively, as shown in Fig. 1. We take the strongest ferromagnetic state (1, 4) configuration as the research object to calculate the effects of different vacancies on the ferromagnetism of 4H–SiC system. The results show that the configuration of V1 is ferromagnetic state with EFM -126.1 meV, V2 is ferromagnetic state with EFM -267.9 meV, and V3 is anti-ferromagnetic state with EFM 74.0 meV. On the whole, the ferromagnetism of all systems decreased or even changed to anti-ferromagnetism after the introduced silicon vacancy. Therefore, silicon vacancy may not be an effective method for obtaining room-temperature ferromagnetism. 62
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4. Conclusions
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In this article, we systematically studied the Fe-, Cr-doped and the (Fe, Cr)-codoped 4H–SiC systems without and with silicon vacancy on the electronic structures and magnetic properties by using the first principles calculations within the GGA + U approximations. The results show that ferromagnetic states is more favorable than anti-ferromagnetic states in (Fe, Cr)- and (Fe, Cr, VSi)-codoped 4H–SiC. In the (Fe, Cr)codoped 4H–SiC system, its ferromagnetism can be attributed to the strong p-d hybridization interaction between Fe and Cr atoms and their closest neighbor C atoms. For (Fe, Cr, VSi)-codoped 4H–SiC systems, the ground state is ferromagnetic coupling between the Fe and Cr atoms. With the presence of silicon vacancy, the ground state stability will decrease. In all configurations, the magnetic moment of Fe and Cr atoms is smaller than that of the atom without silicon vacancy. The results show that (Fe, Cr)-codoped 4H–SiC system may be a promising spin injection ferromagnetic material. Acknowledgements This work was supported by the National Natural Science Foundation of China (21303041), the Innovation Scientists and Technicians Troop Construction Projects of Henan Province (CXTD2017089), the Natural Science Foundation of Henan Province (162300410116, 182300410288), the Science and Technology of Henan Province (182102210305), the Henan Postdoctoral Science Foundation and the Program for Innovative Research Team of Henan Polytechnic University (No. T2016-2). Computational resources have been provided by the Henan Polytechnic University high-performance grid computing platform. References [1] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand, Zener model description of ferromagnetism in zinc-blende magnetic semiconductors, Science 287 (2000) 1019–1022. [2] F.C. Beyer, C.G. Hemmingsson, S. Leone, Y.C. Lin, A. Gällström, A. Henry, E. Janzén, Deep levels in iron doped n- and p-type 4H-SiC, J. Appl. Phys. 110 (2011) 123701 12. [3] F.C. Beyer, C. Hemmingsson, H. Pedersen, A. Henry, E. Janzén, J. Isoya, N. Morishita, T. Ohshima, Annealing behavior of the EB-centers and M-center in low-energy electron irradiatedn-type 4H-SiC, J. Appl. Phys. 109 (2011) 103703 10. [4] F.C. Beyer, C.G. Hemmingsson, A. Gällström, S. Leone, H. Pedersen, A. Henry, E. Janzén, Deep levels in tungsten doped n-type 3C–SiC, Appl. Phys. Lett. 98 (15) (2011) 152104. [5] F.C. Beyer, S. Leone, C. Hemmingsson, A. Henry, E. Janzén, Deep levels in heteroepitaxial as-grown 3C-SiC, AIP Conference Proceedings, 1292 2010, p. 63. [6] D. Zhuang, J.H. Edgar, Wet etching of GaN, AlN, and SiC: a review, Mater. Sci. Eng. R Rep. 48 (2005) 1–46. [7] M.B. Javan, Electronic and magnetic properties of monolayer SiC sheet doped with 3d-transition metals, J. Magn. Magn. Mater. 401 (2016) 656–661. [8] M. Houmad, Z. Zarhri, Y. Ziat, Y. Benhouria, A. Benyoussef, A. El Kenz, Ferromagnetism induced by double impurities Mn and Cr in 3C-SiC, Chin. J. Phys. 56 (2018) 404–410. [9] P. Ma, T. Lei, Y. Zhang, J. Liu, Z. Zhang, First-principle study on magnetic properties of TM-doped 6H-SiC, Adv. Mater. Res. 709 (2013) 197–200. [10] L. Lin, Z. Zhang, H. Tao, M. He, G. Huang, B. Song, Density functional study on ferromagnetism in (Al, Fe)-codoped 4H-SiC, Comput. Mater. Sci. 87 (2014) 72–75.
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Electronic structures and ferromagnetism in (Fe, Cr)-codoped 4H–SiC from first-principles investigations
T
Bing Zhanga, Linghao Zhub, Long Linb,c,∗, Weiyang Yud, Hualong Taoe, Yonghao Xud, FeiPeng Guod, Lixin Lib, Jingtao Huangb a
Yellow River Conservancy Technical Institute, Kaifeng, Henan, 475004, China Cultivating Base for Key Laboratory of Environment-Friendly Inorganic Materials in Henan Province, School of Materials Science and Engineering, Henan Polytechnic University, Jiaozuo, 454000, China c School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo, 454000, China d School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo, 454000, China e School of Materials Science and Engineering, Dalian Jiaotong University, Dalian, 116028, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: First-principles Dilute magnetic semiconductors Electronic structure Magnetic properties 4H–SiC
Electronic structures and magnetic properties for double impurities (Fe and Cr) doped 4H silicon carbide (SiC) are studied by first principles calculations within the generalized gradient approximation (GGA) +U scheme. For single Fe-doped 4H–SiC, the local magnetic moments of Fe atom is about 3.76 μB and the system exhibits halfmetallic character. For single Cr atom doped 4H–SiC, the local magnetic moments of Cr atom is about 3.15 μB. The introduction of Cr impurities does not destroy the semiconducting nature of Cr-doped 4H–SiC system. For (Fe, Cr)-codoped 4H–SiC, the magnetic coupling between the moments induced by Fe and Cr dopants is ferromagnetic and the origin of strong ferromagnetic coupling can be attributed to p-d hybridization interaction. We discuss the effect of silicon vacancy on the magnetism as well. Our calculations results show that (Fe, Cr)codoped 4H–SiC exhibit half-metallic behavior, which is suitable for spintronic devices applications.
1. Introduction Diluted magnetic semiconductors (DMSs) were extensively research because of their potential applications for spintronic devices [1]. Silicon carbide (SiC) is an important candidate material for spin electronic applications. SiC has more than 200 polytypes in the crystal structure with different stacking sequences. 4H–SiC [2,3] and 3C–SiC [4,5] are relatively important in the SiC series. SiC-based DMSs has excellent physical features such as thermal stability, chemical inertness, high thermal conductivity, and others [6]. Magnetic 3d transition-metal (TM) doped SiC-based DMSs have attracted a great interest because of their spintronic devices applications [7]. Recently TM-doped SiC on magnetic properties have been reported by first-principle computation [8–12]. Theoretically, Pan et al. studied N-TM (TM = Cr, Mn, Fe, and Co)-codoped SiC by emplying density functional theory based calculations. The calculation results demonstrate that N-TM codoped SiC was ferromagnetic, and the ferromagnetism originates from the strong carrier-mediated interaction between the spin-polarized TM-d and N-p electrons [13].
The magnetic properties of SiC doped by transition metals Mn and Cr have been investigated by using first principles density functional calculations. The result of calculation verify that the Curie temperature (TC) of 3C–Si1-xTMxC and 3C–Si1-x-yMnxCryC increases with increasing transition metal concentration [8]. Lin et al. researched the electronic structures and magnetic properties for (Al, Fe)-codoped 4H–SiC. They found that (Al, Fe)-codoped 4H–SiC show the ferromagnetic characteristics [10]. Several reports were published documenting experimental studies of magnetic properties of SiC with transition metal impurities. Zhang et al. prepared the specimens of (Al, Co)-codoped 4H–SiC and the structural and magnetic properties have been researched. They suggested that the samples show increased ferromagnetism with increasing of Co concentration [14]. Jin et al. fabricated Cr-doped SiC thin films on Al2O3 and Si substrates by using dual ion beam sputtering deposition at room temperature. The magnetic measurements results reveal that the Cr-doped α-SiC thin films are ferromagnetic with Curie temperature (Tc) above room temperature [15]. Sun et al. fabricated (Mn, Co)-codoped SiC films on Si (100) substrates by RF-magnetic sputtering. They
∗ Corresponding author. Cultivating Base for Key Laboratory of Environment-Friendly Inorganic Materials in Henan Province, School of Materials Science and Engineering, Henan Polytechnic University, Jiaozuo, 454000, China. E-mail address: [email protected] (L. Lin).
https://doi.org/10.1016/j.vacuum.2019.05.039 Received 18 March 2019; Received in revised form 26 May 2019; Accepted 28 May 2019 Available online 29 May 2019 0042-207X/ © 2019 Elsevier Ltd. All rights reserved.
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studied the structure and luminescence properties of the films in details [16]. Jin et al. investigated Cr-doped SiC films by the RF magnetic sputtering technique. The results show that the SiC crystal is formed and that majority of Cr doped in the SiC resulted in the formation of the C clusters [17]. The magnetic properties of TM doped SiC-based DMSs have been extensively investigated both computationally and experimentally. While, whether magnetic clusters or secondary ferromagnetic plays a more important role in the ferromagnetism origin. Meanwhile, many computational results suggest that the generalized gradient approximation (GGA) +U scheme play a crucial role in the ferromagnetism in TM doped SnO2 [18–23]. SnO2-based and SiC-based DMSs have similar physical properties. However, to the best of our knowledge in the literature, so far few results are realized in electronic structures and magnetic properties for (Fe, Cr)-codoped 4H–SiC by first principles calculations within the GGA + U scheme. In the present study, we carried out the first principles calculations by means of the GGA + U scheme for (Fe, Cr)-codoped 4H–SiC without and with Si vacancies. We investigate the effect of Fe and Cr dopants and silicon vacancies on the electronic structures and magnetic properties of (Fe, Cr)-codoped 4H–SiC.
Fig. 2. (Color online) Density of states for intrinsic 4H–SiC and partial density of states for C and Si, respectively. And (a) is the total density of states (TDOS) for intrinsic doped 4H–SiC, (b)–(c) are the partial density of states (PDOS) of C and Si. The Fermi level is set to 0 eV.
during the integral calculation in the Brillouin zone. We applied plane wave basis cutoff energy of 450 eV. The convergence threshold for selfconsistent field energy was set at 10−6 eV, and the internal coordinates are fully relax until the forces on the ions are below 0.05 eV/Å.
2. Computational details Perfect 4H–SiC has a hexagonal structure, which belongs to P63mc space group at normal temperature and pressure [24,25]. The optimized lattice constants, a = b = 3.095 Å, c = 10.135 Å, are in good agreement with the experimental values (a = b = 3.081 Å, c = 10.096 Å) [33], which indicates the calculation model and parameters are reasonable. We considered a reference undoped 3✕3✕1 supercell containing 72 atoms, as shown in Fig. 1. 4H–SiC consists of an equal number of cubic and hexagonal bonds with a stacking sequences of ABCB. Our calculations were performed using the CASTEP code based on plane-wave basis sets. The ultrasoft pseudopotential was used for electron-ion interactions. The electron-electron exchange and correlation effects were described by the generalized gradient approximation (GGA) functional using the Perdew-Burke-Ernzerhof (PBE) method [26] and the strong correlation effects are introduced by means of GGA + U scheme, and GGA + U and PBE were used to optimize the lattice parameters. The value of parameter U for Fe:3d states and Cr:3d states are taken to be 5.1 eV [27–29] and 3.8 eV [30–32], respectively. Following the Monkhorst-Park method, a 2 × 2 × 2 k-mesh is adoped
3. Results and discussions The structural optimization is first performed for pristine 4H–SiC. We began with a study of the pristine 4H–SiC without Cr and Fe incorporation. The electronic properties of the pure 4H–SiC were calculated. We found that pristine 4H–SiC is obviously shown to be an indirect band gap semiconductor. The band-gap width is about 2.25 eV and the total magnetic moments is zero. To understand the spin state of pristine 4H–SiC. We studied the density of states (DOS) for pristine 4H–SiC which are plotted in Fig. 2. From Fig. 2, the majority-spin density of states and minority-spin density of states are identical. The conduction band is mainly contributed by Si-3p orbitals and the valence band is mainly contributed by C-2p and Si-3p orbitals. The calculations results show that pure 4H–SiC material is nonmagnetic ground state. Moreover, we study the electronic structures and magnetic properties in TM (TM = Fe, Cr) doped 4H–SiC system, we first consider an isolated TM doped 4H–SiC by replacing one Si atom with one TM atom, and the doping positions of Cr and Fe atoms are both at site 5, corresponding to a doping concentration of 2.28 at.%. Next, in order to simulate the Fe and Cr codoping and study the magnetic couping interaction between Fe atom and Cr atom dopants. The ten configurations are obtained by introducing one Fe atom and one Cr atom to the Si sites which corresponds to the concentration of 2.28 at.% Fe and 2.28 at.% Cr and 4.56 at.% (Fe, Cr) co-doped 4H–SiC, respectively. For convenience of discussion, we use (i, j) to denote a Fe–Cr pair in which two Si sites are replaced by Fe atoms at i sites and Cr atoms at j sites. Here, the substituted Si atoms are marked with numbers 1–10 in Fig. 1. For each of these configurations, ΔEFM corresponds to the energy difference (ΔEFM = EFM−EAFM) was estimated from the total energies for the two spin configurations, namely, parallel [ferromagnetic (FM)] and antiparallel [antiferromagnetic (AFM)] orientations of the localized magnetic moments on the doped Fe atom and Cr atom. Firstly, we study the electronic structures and magnetic properties of single Fe atom doping. Our results of calculation show that the local magnetic moments of Fe is 3.76 μB for single Fe atom doped 4H–SiC. To further make out the origin of magnetic moments, the total density of states (TDOS) and partial density of states (PDOS) are calculated and are plotted in Fig. 3. From the TDOS in Fig. 3, it can be seen that doped with a single Fe atom has spin polarization for GGA + U calculation, the Fermi level passes through the majority-spin states at the top of the
Fig. 1. 72-Atom 3✕3✕1 supercell model of (Fe, Cr)-codoped 4H–SiC, Colored spheres are Si (yellow), C (gray), atom. The Si atoms labeled by 1–10 are the sites to be replaced by Fe and Cr atoms, V1, V2, and V3 represent silicon vacancies in different layers. 60
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Table 1 Calculation results for ten configurations of (Fe, Cr)-doped 4H–SiC. Fe, Cr distance after relaxation in nonspin-polarized (NSP), ΔE, ΔEFM and the FM magnetic moments of Fe and Cr atoms, respectively. Structure (i, j)
(5, 6) (1, 4) (8, 7) (3, 1) (6, 10) (4, 7) (2, 8) (9, 2) (9, 3) (10, 9)
DFe-Cr (Å) NSP
FM
3.082 3.085 4.360 6.163 6.892 8.153 8.158 5.344 6.169 8.153
3.037 3.063 4.352 6.243 6.931 8.212 8.196 5.362 6.209 8.192
ΔE (eV)
−5.8795 −5.8987 −5.6453 −5.9453 −5.7095 −5.9624 −5.8629 −5.6477 −5.8222 −5.9505
ΔEFM (meV)
−316.0 −558.9 −388.5 −225.4 −142.3 −157.3 −323.6 −181.6 −348.8 −345.0
Local Magnetic Moments Fe (μB)
Cr (μB)
3.69 3.70 3.77 3.69 3.76 3.69 3.73 3.77 3.73 3.70
3.25 3.25 3.17 3.22 3.16 3.28 3.22 3.14 3.22 3.22
components present a band gap, indicating that the introduction of Cr impurity does not destroy the semiconductor properties of the 4H–SiC system doped with Cr atom for GGA + U approximation. The PDOS of Cr-3d, Cr-3p and C-2p indicate that Cr-3d, Cr-3p and C-2p orbitals are hybridize with each other near the Fermi level. The magnetic moments mainly comes from the Cr-3d and C-2p orbitals in the spin channel. After understanding the local magnetic moments formation of Fe and Cr doped 4H–SiC, we will address another important issue of coupling between magnetic moments. Consider that two Si atoms are replaced by one Fe atom and one Cr atom, as shown in Fig. 1. We calculated the total energy differences between the FM states and the AFM states of the 10 configurations for (Fe, Cr)-codoped 4H–SiC. All configurations of Fe–Cr distance, difference energy of FM-nonspin polarized(NSP) (ΔE), FM-AFM (ΔEFM) and FM magnetic moments of Fe and Cr atoms are shown in Table 1. Table 1 also list the local magnetic moments of each doped atom. As we can see from Table 1, the energy difference between FM and NSP are all negative, which show that FM is the most stable state. Table 1 shows that the local structure of (Fe, Cr) co-doped 4H–SiC, which is slightly distorted. Here, we take the FM state of the ground state configuration (1, 4) as an example. Local magnetic moments of Si double substituent in all configurations increased. The local magnetic moments of Fe atom and Cr atom are around 3.70 μB and 3.25 μB, which is obviously larger than the magnetic moments induced by the isolated cases. For comparison, the magnetism of 4H–SiC systems doped with 2Cr and 2Fe are calculated, respectively, and the doping concentration are all 4.56 at.%. The total magnetic moment of 2Cr and 2Fe doped 4H–SiC systems are 4.03 and 6.05 μB. The total magnetic moment of (Fe, Cr) co-doped 4H–SiC system is 6.06 μB. The results show that the codoping system give higher magnetic moments than single doping at the same concentration. This magnetic enhancement may be due to the long-distance FM coupling between the Fe and Cr atoms through the intermediate C atoms. It is found that calculations from GGA + U that △EFM for each configuration are negative, which indicates that the FM order is more positive than the positive for all (Fe, Cr)-codoped 4H–SiC configurations relative to the AFM order. The calculations results also show that the (1, 4) configuration is the most stable configuration, which the distance is 3.085 Å between the dopants and the largest negative △EFM (−558.9 meV) in all configurations. We also calculated the energy difference between the ferromagnetic and antiferromagnetic states of (4,1), (6,5), (7,8) configurations to consider the effect of atomic inerchange for magnetic state, and found that ΔEFM of (4, 1), (6, 5), and (7, 8) configurations are −146, −491, and −549 meV, respectively. The doping system presents a stable ferromagnetic state, which is consistent with our calculation results of (1, 4), (5, 6) and (8, 7) configurations. Therefore, (1, 4) configuration can be considered as FM ground state. This states that it is possible to (Fe, Cr)codoped 4H–SiC with ferromagnetism at room temperature. Therefore, (Fe, Cr)-codoped 4H–SiC can be commercialized.
Fig. 3. (Color online) Density of states for Fe doped 4H–SiC and partial density of states for Fe, C and Si, respectively. And (a) is the total density of states (TDOS) for Fe doped 4H–SiC, (b)–(d) are the partial density of states (PDOS) of Fe, C and Si. The Fermi level is set to 0 eV valence band, which reflects the system exhibits half-metallic properties and allows electrons to transfer. From the PDOS of Fe doped 4H–SiC, it reveals that Fe-3d, C-2p and Si-3p orbitals are hybridized with each other at the Fermi level. The magnetic moments mainly come from the Fe-3d, C-2p and Si-3p orbitals in the majority spin channel.
TDOS. Secondly, we study a single Cr substitution, which Cr-doped 4H–SiC with CrSi was modeled by replacing one Si atom with one Cr atom. The total magnetic moments of Cr doped 4H–SiC is 1.96 μB. The local magnetic moments on Cr and C atom are 3.15 μB and 0.29 μB, respectively. The results of calculation indicate that the magnetic moments of the Cr-doped 4H–SiC system mainly come from the Cr atom. So spinpolarization occurs mainly from the Cr atom. Fig. 4(a)–(d) present the calculated total density of states (DOS) and the partial DOS of the Cr dopant, the nearest-neighboring C atoms and the second-nearestneighboring Si atoms. As shown in Fig. 4 (a), most spins and a few spin
Fig. 4. (Color online) Density of states for Cr, doped 4H–SiC and partial density of states for Cr C and Si, respectively. And (a) is the total density of states (TDOS) for Cr doped 4H–SiC, (b)–(d) are the partial density of states (PDOS) of Cr, C and Si. The Fermi level is set to 0 eV. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) 61
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Fig. 5. (Color online) Density of states for (Fe, Cr)-codoped 4H–SiC and partial density of states for Fe, Cr, C and Si, respectively. And (a) is the total density of states (TDOS) for (Fe, Cr) codoped 4H–SiC, (b)–(e) are the partial density of states (PDOS) of Fe, Cr, C and Si. The Fermi level is set to 0 eV. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)
Fig. 6. (Color online) Spin density distribution for (Fe, Cr)-codoped 4H–SiC in (1, 4) configuration in FM coupling. The isovalue is set to 0.085 e/Å3. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) Table 2 Calculation results for five configurations of (Fe, Cr, V2)-codoped 4H–SiC. Fe, Cr distance after relaxation in nonspin-polarized (NSP), ΔEFM and the FM magnetic moments of Fe and Cr atoms, respectively.
In order to study the origin of magnetism, we calculated the TDOS and PDOS of (Fe, Cr)-codoped 4H–SiC system, as shown in Fig. 5. It can be seen from Fig. 5 (a) that spin polarized TDOS in the (Fe, Cr) codoped 4H–SiC system has a significant spin splitting near the Fermi level, which means that after Si replaced by Fe and Cr, magnetism can be generated in the (Fe, Cr)-codoped 4H–SiC system. Similar to the situation of single doped Fe, we can also see that (Fe, Cr)-codoped 4H–SiC system has half-metallic properties. Obviously, C atom, Fe atom and Cr atom induced the magnetism of (Fe, Cr)-codoped 4H–SiC. The 3d orbitals of Fe and Cr are spin-polarized and strongly hybridized with 2p orbitals of C. The Fermi energy is mainly dominated by the Fe-3d orbitals, Cr-3d orbitals and C-2p orbitals, indicating that magnetism is mainly induced by Fe and Cr 3d orbitals and located in Fe atom, Cr atom and C atom. To further clarify the mechanism for magnetic moments change in (Fe, Cr)-codoped 4H–SiC, the spin density isovalue of (1, 4) configurationin as shown in Fig. 6. As seen in Fig. 6, the spin density distribution of Fe and Cr atoms in (1,4) configurations FM coupling of GGA + U was calculated, respectively. As shown in Fig. 6, the polarization components are mainly distributed on Fe atoms and Cr atoms, and the spin directions are parallel. Due to the strong hybridization of Fe and Cr dopants with adjacent C atom, the adjacent C atom spin polarized and ferromagnetic coupling occurred with Fe and Cr atoms. So, the hybridized Fe: 3d-C: 2p-Cr: 3d chain formed through p-d coupling is responsible for the long-range FM coupling. It is possible to introduce room-temperature ferromagnetism in the presence of inherent defects [34]. silicon vacancies plays an important role in ferromagnetic tuning in SiC based DMSs [35,36]. Consequently, it is essential to contemplate Si vacancy effect. Therefore, this section studies the magnetic coupling of (Fe, Cr)-codoped 4H–SiC with silicon vacancy to understand the ferromagnetism of (Fe, Cr)-codoped 4H–SiC. We investigated the effect of silicon vacancy on the electronic structures and magnetic properties (Fe, Cr)-codoped 4H–SiC. In the calculation and analysis of this part, we only consider the substitution defect. We first calculated the (Fe, Cr)-codoped 4H–SiC systems, in which a V2 generated by removing a neutral Si atom in the supercell. The relative position of the V2 is shown in Fig. 1. The Fe–Cr distance, FM-AFM energy difference and FM local magnetic moment of Fe and Cr atoms in the super lattice under silicon vacancy configuration are given in Table 2. As seen in Table 2, all ΔEFM
Structure (i, j)
(5, 6) (1, 4) (8, 7) (6,10) (4, 7) (2, 8)
ΔEFM(meV)
DFe-Cr (Å) NSP
FM
3.082 3.026 4.360 6.892 8.153 8.158
3.146 3.067 4.281 6.936 8.131 8.208
−349.2 −267.9 −238.1 −286.1 −345.5 −320.4
Local Magnetic Moments Fe (μB)
Cr (μB)
3.38 3.24 3.43 3.40 3.35 3.42
2.91 3.30 2.90 3.19 2.88 2.89
are negative, which indicates that the ground state of (Fe, Cr, V2)-codoped 4H–SiC are FM coupling between the Fe and Cr atoms. For comparison, we add silicon vacancy in the configuration (1, 4) with the strongest ferromagnetism in Table 1 to indicate the influence of silicon vacancy on the ferromagnetism of the system. As shown in Table 2, we calculate the electronic structures and magnetism of (1, 4) configuration with silicon vacancy. The calculation results show that the (1, 4) configuration is FM states, which the distance is 3.026 Å between the dopants and the negative △EFM (−267.9 meV). The ferromagnetism of the 4H–SiC system is obviously weaker than that without silicon vacancy. Compared with the 4H–SiC system replaced only by Fe and Cr atoms, the magnetic moment of Si atom decreased after the introduction of silicon vacancy. In order to compare the effects of silicon vacancy in different layers on the ferromagnetism of 4H–SiC, we calculated the ferromagnetism of the system under the influence of vacancies in different layers (marked V1, V2, V3), respectively, as shown in Fig. 1. We take the strongest ferromagnetic state (1, 4) configuration as the research object to calculate the effects of different vacancies on the ferromagnetism of 4H–SiC system. The results show that the configuration of V1 is ferromagnetic state with EFM -126.1 meV, V2 is ferromagnetic state with EFM -267.9 meV, and V3 is anti-ferromagnetic state with EFM 74.0 meV. On the whole, the ferromagnetism of all systems decreased or even changed to anti-ferromagnetism after the introduced silicon vacancy. Therefore, silicon vacancy may not be an effective method for obtaining room-temperature ferromagnetism. 62
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4. Conclusions
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In this article, we systematically studied the Fe-, Cr-doped and the (Fe, Cr)-codoped 4H–SiC systems without and with silicon vacancy on the electronic structures and magnetic properties by using the first principles calculations within the GGA + U approximations. The results show that ferromagnetic states is more favorable than anti-ferromagnetic states in (Fe, Cr)- and (Fe, Cr, VSi)-codoped 4H–SiC. In the (Fe, Cr)codoped 4H–SiC system, its ferromagnetism can be attributed to the strong p-d hybridization interaction between Fe and Cr atoms and their closest neighbor C atoms. For (Fe, Cr, VSi)-codoped 4H–SiC systems, the ground state is ferromagnetic coupling between the Fe and Cr atoms. With the presence of silicon vacancy, the ground state stability will decrease. In all configurations, the magnetic moment of Fe and Cr atoms is smaller than that of the atom without silicon vacancy. The results show that (Fe, Cr)-codoped 4H–SiC system may be a promising spin injection ferromagnetic material. Acknowledgements This work was supported by the National Natural Science Foundation of China (21303041), the Innovation Scientists and Technicians Troop Construction Projects of Henan Province (CXTD2017089), the Natural Science Foundation of Henan Province (162300410116, 182300410288), the Science and Technology of Henan Province (182102210305), the Henan Postdoctoral Science Foundation and the Program for Innovative Research Team of Henan Polytechnic University (No. T2016-2). Computational resources have been provided by the Henan Polytechnic University high-performance grid computing platform. References [1] T. Dietl, H. Ohno, F. Matsukura, J. Cibert, D. Ferrand, Zener model description of ferromagnetism in zinc-blende magnetic semiconductors, Science 287 (2000) 1019–1022. [2] F.C. Beyer, C.G. Hemmingsson, S. Leone, Y.C. Lin, A. Gällström, A. Henry, E. Janzén, Deep levels in iron doped n- and p-type 4H-SiC, J. Appl. Phys. 110 (2011) 123701 12. [3] F.C. Beyer, C. Hemmingsson, H. Pedersen, A. Henry, E. Janzén, J. Isoya, N. Morishita, T. Ohshima, Annealing behavior of the EB-centers and M-center in low-energy electron irradiatedn-type 4H-SiC, J. Appl. Phys. 109 (2011) 103703 10. [4] F.C. Beyer, C.G. Hemmingsson, A. Gällström, S. Leone, H. Pedersen, A. Henry, E. Janzén, Deep levels in tungsten doped n-type 3C–SiC, Appl. Phys. Lett. 98 (15) (2011) 152104. [5] F.C. Beyer, S. Leone, C. Hemmingsson, A. Henry, E. Janzén, Deep levels in heteroepitaxial as-grown 3C-SiC, AIP Conference Proceedings, 1292 2010, p. 63. [6] D. Zhuang, J.H. Edgar, Wet etching of GaN, AlN, and SiC: a review, Mater. Sci. Eng. R Rep. 48 (2005) 1–46. [7] M.B. Javan, Electronic and magnetic properties of monolayer SiC sheet doped with 3d-transition metals, J. Magn. Magn. Mater. 401 (2016) 656–661. [8] M. Houmad, Z. Zarhri, Y. Ziat, Y. Benhouria, A. Benyoussef, A. El Kenz, Ferromagnetism induced by double impurities Mn and Cr in 3C-SiC, Chin. J. Phys. 56 (2018) 404–410. [9] P. Ma, T. Lei, Y. Zhang, J. Liu, Z. Zhang, First-principle study on magnetic properties of TM-doped 6H-SiC, Adv. Mater. Res. 709 (2013) 197–200. [10] L. Lin, Z. Zhang, H. Tao, M. He, G. Huang, B. Song, Density functional study on ferromagnetism in (Al, Fe)-codoped 4H-SiC, Comput. Mater. Sci. 87 (2014) 72–75.
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