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Hyperfine Interactions ISSN 0304-3843 Hyperfine InteractDOI 10.1007/s10751-013-0946-y

The magnetic and hyperfine properties ofiron in silicon carbide

M. Elzain, S. H. Al-Harthi,A. Gismelseed, A. Al-Rawas, A. Yousif,H. Widatallah & M. Al-Barwani

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Hyperfine InteractDOI 10.1007/s10751-013-0946-y

The magnetic and hyperfine properties of iron in siliconcarbide

M. Elzain · S. H. Al-Harthi · A. Gismelseed ·A. Al-Rawas · A. Yousif · H. Widatallah · M. Al-Barwani

© Springer Science+Business Media Dordrecht 2013

Abstract The magnetic and hyperfine properties of iron impurities in 3C- and 6H- silicon-carbide are calculated using the abinitio method of full-potential linear-augmented-plane-waves. The iron atoms are introduced at substitutional carbon, FeC , and silicon, FeSi , sites aswell as at the tetrahedral interstitial sites with four nearest neighbours carbon atoms, FeI (C),and four nearest neighbours silicon atoms, FeI (Si). The effect of introducing vacancies atthe neighbours of these sites is also studied. Fe atoms with complete neighbors substitutedat Si or C sites are found to be nonmagnetic, while Fe atoms at interstitial sites are magnetic.Introduction of a vacancy at a neighboring site reverse the picture.

Keywords Isomer shift · Magnetic moment · Hyperfine field · Vacancies

1 Introduction

The combinations of interesting fundamental science and potential applications are reflectedin the intense research in dilute magnetic semiconductors (DMS) [1–3]. Among the candi-dates of potential DMS materials, Mn doped GaAs system is the most studied. However, themaximum Curie temperature TC reached in Mn doped GaAs is about 190 K [4, 5], whichis far below room temperature. Using carrier mediated exchange interaction Dietl et al. [6,7] predicted large TC for wide band gap semiconductors. This prediction prompted searchfor higher TC in wide band gap semiconductors and among these are the SiC polytypes [8].The validity of this quest was questioned mainly due to the fact that in wide band gap semi-conductors the top occupied states arising from the transition metal dopants fall deeper inthe band gap and hence are more localized [9].

Proceedings of the 32nd International Conference on the Applications of the Mossbauer Effect(ICAME 2013) held in Opatija, Croatia, 1-6 September 2013

M. Elzain (�) · S. H. Al-Harthi · A. Gismelseed · A. Al-Rawas · A. Yousif · H. WidatallahDepartment of Physics, Sultan Qaboos University, Box 36, Al Khod 123, Muscat, Omane-mail: elzain@squ.edu.om

M. Al-BarwaniNYU Abu Dhabi, Box 129188, Abu Dhabi, United Arab Emirates

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M. Elzain et al.

Silicon-carbide semiconductor materials are suitable for electronic devices operatingunder high frequency and high temperature conditions. Consequently, searching for DMScharacteristics of the transition metal doped SiC is a well warranted endeavor. In particular,we consider here the Fe doped hexagonal 6H-SiC and cubic 3C-SiC systems. The solubilityof Fe in SiC is rather low and hence most Fe doped SiC systems are attained through ionimplantation. As expected, ion implantation is accompanied by creation of diverse defectsin the crystalline systems [10, 11]. The measured magnetic and hyperfine properties aredependent on the nature of the existing defects. Theodoropoulou et al. [12] found that 5atom% Fe implanted p-type 6H-SiC is ferromagnetic up to temperatures of approximately250 K. No secondary iron-silicon phases were detected in their samples. Similar conclusionswere reached by Pearton et al. [13]. On the other hand, the detected ferromagnetism in ionimplanted samples is attributed to the formation of iron-silicon secondary phases by otherauthors [14–16]. For sample synthesized through solid-state reaction Song et al. [17] foundtwo Curie temperatures ascribing the lower to DMS properties of the Fe doped 6H-SiC andthe higher to iron-silicon secondary phases.

The hyperfine properties of low Fe doped SiC have also been measured. Gunnlaugssonet al. [18] measured the isomer shift (δ) and the quadruple splitting (�) of Fe in 6H-SiCand identified the Fe probes at interstitial and substitutional sites. Their results indicate thata fraction of Fe goes into carbon substitutional site with isomer shift of about −0.16 mm/s,whereas Fe at interstitial sites with neighboring carbon has isomer shift of +0.35 mm/sand that at interstitial sites with neighboring silicon has isomer shift of +0.81 mm/s. Thesame trends were reported by Bharuth-Ram [19] for low Fe doped 3C-SiC. Declemy et al.[20] using CEMS reported average δ values of 0.12 mm/s for as-implanted samples and0.14 mm/s for thermally annealed samples.

The dilute magnetic semiconducting property is ascribed to the ferromagnetic couplingbetween magnetic transition metals distributed randomly in the parent semiconductor lat-tice. Thus to have a DMS, the transition metal impurities must possess local magneticmoments which are ferromagnetically coupled. The nature of this coupling is still controver-sial [2, 5, 21–23]. However, the local magnetic properties of the transition metal impuritiesin semiconductors are in general concordance. Miao and Lambrecht [24] using the lin-earized muffin-tin orbitals studied the magnetic properties of transitional metals in 3C-SiC.They found that substitutional Fe impurities on C or Si sites are both nonmagnetic andthat the substitutional Fe favors the Si site. Shaposhnikov and Sobolev [25] using the full-potential linearized-augmented-plane-wave method found that substitutional Fe impuritiesin 3C-SiC are nonmagnetic, while Fe at Si site in 6H-SiC is fully magnetic. Los and Los [26]computed a small difference in energy between the magnetic and nonmagnetic solutions ofFe in 3C-SiC and concluded that at higher temperatures Fe may coexist in both states. Therole of transition metal interstitials and substitutional-interstitial dimers in 3C-SiC was stud-ied by Zhou et al. [27]. They found the substitutional site to be favored for Fe under C-richenvironment, while the dimers to be favored under Si-rich environment. Furthermore, theFe dimers were found to be ferromagnetic.

No calculation of the hyperfine properties of Fe in SiC were reported. Also the effectof defects on the magnetism of transition metals in SiC were not considered apart fromthat reported for Mn in 3C-SiC by Bouziane et al. [28]. In this article we present resultsof hyperfine properties and local magnetic moments for Fe in 3C-SiC and 6H-SiC. Weconsider Fe at substitutional and interstitial sites and the effect of the associated neighboringvacancies.

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The magnetic and hyperfine properties of iron in silicon carbide

2 Computational method

Silicon-Carbide crystallizes in many different structural polytypes. We consider only thecubic zinc-blende structured 3C-SiC and the hexagonal 6H-SiC. The polytypes differ inthe stacking sequences of the silicon– carbon bilayers. The cubic 3C-SiC polytype has3 bilayers in the unit cell with cubic stacking (k). The hexagonal 6H-SiC polytype has12 bilayers in the unit cell stacked in cubic and hexagonal (h) sequences as hk1k2hk1k2.The tetrahedral configurations and the number of nearest neighbors are maintained withinall stackings, however further neighbors may differ. The experimental lattice constantof 3C-SiC is a = 4.36 A and the lattice parameters of 6H-SiC are a = 3.08 A andc = 15.12 A.

To study the Fe impurities in SiC we have used supercells composed of 2 × 2 × 2conventional cells for 3C-SiC and 2 × 2 × 1 conventional cells for 6H-SiC. We have usedthe experimental lattice constants in the calculation; however, relaxation in atomic positionsis allowed for.

The full-potential linear-augmented-plane –wave (FP-LAPW) method as employed inthe WIEN2k package [29] is used to calculate the electronic and magnetic properties of Fedoped SiC polytypes.

In the L/APW + lo method the Kohn-Sham orbitals are expanded in terms of atomicorbitals inside the atomic muffin-tin (MT) sphere of radius RMT and in terms of planewaves in the interstitial regions. The Kohn-Sham equations were solved using Perdew-Burke-Ernerhof GGA approximation. Core and valence states were separated by an atomicenergy of −7.1 Ry. For the valence electrons the potential and charge density are expandedin spherical harmonics up to L = 4, while the wavefunctions are expanded inside the MTsphere up to � = 10 partial waves. Mixed basis are used depending on the partial wave �

with APW + lo being used for s, p and d valence orbitals. LAPW is used for the remaining� values. For the plane wave expansion in the interstitial region we have used wavenumbercut off Kmax such that RMT Kmax = 7.0 and the potential and charge density are Fourierexpanded with Gmax = 14.0. The mesh size and the number of points in the Brillouin zonewere tested for the conventional unit cell using the convergence of the values of the electricfield gradient and the total energy as indicators. A k -sampling with a 6 × 6 × 6 Monkhost-Pack mesh is used for cubic supercell and a sampling of 8 × 8 × 2 is used for the hexagonalsupercell.

In the following chapter we present and discuss the results of our calculation of themagnetic and hyperfine properties of Fe in SiC systems. Among the reported results, thequadruple splitting is the least accurate because it is sensitive to the number of k-points andother parameters. A short conclusion is presented in the last section.

3 Results and discussion

We determined the lattice parameters of the cubic and hexagonal SiC by optimizing the vol-ume dependence of energy using the corresponding primitive unit cells. The values obtainedare comparable to the experimental results, where we computed the parameters a = 4.38 Afor the cubic system and a = 3.09 A and c = 15.2 A for the hexagonal system.

Supercells were used for the calculation of the electronic properties of Fe in SiC systems.Implantation of Fe in SiC is expected to lead to various associated defects like vacanciesand interstitials. We report here the results for Fe at substitutional and interstitial sites withand without neighboring vacancies.

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Table 1 The local magnetic moment, m, in Bohr Magnetrons, the Fermi contact hyperfine field, Bhf inTeslas, the isomer shift, δ (relative to α-Fe) in mm/s and the quadruple splitting � in mm/s at Fe sites withoutneighboring vacancy at the substitutional sites FeC and FeSi and the interstitial sites FeI(C) and FeI(Si) for6H-SiC

FeC FeSi FeI(C) FeI(Si)

m(μB) 0.0 0.0 1.27 1.29

Bhf(T) 0.0 0.0 −9.6 −9.8

δ (mm/s) −0.55 −0.24 0.27 0.49

� (mm/s) 0.50 0.04 0.17 −0.01

Table 1 shows the magnetic moment inside the muffin-tin sphere, the Fermi contactmagnetic hyperfine field, the isomer shift and the quadruple splitting at Fe substitutionaland interstitials sites without neighboring vacancies for 6H-SiC. We note that Fe atoms atthe substitutional sites are nonmagnetic, while those at the interstitials sites are magnetic.We have calculated the properties for substitutional Fe at sub-layers of stacking h, k1, k2

and found no significant difference between the results of the different sites.The nonmagnetic nature of Fe atoms at the substitutional sites can be ascribed to the

low density of states at the Fermi level in the corresponding paramagnetic phase. Figure 1shows the 3d density of states for paramagnetic Fe at C and Si sites. In comparison to thecorresponding results for Mn, the density of states at the Fermi level at Fe sites is very low.In the case of Fe at C site the density of states is almost zero, while it is finite for Fe at Sisite but not as large as that of Mn at Si site. The low density of states at the Fermi levelfor substitutional Fe in SiC is expected to lead to nonmagnetic states according to Stonercriterion.

Since the substitutional Fe at Si site is more favorable [24], we compare its propertiesto the experimental results. We note that the calculated isomer shift is negative and close tothe values reported in refs 18 and 19. No quadruple splitting is reported for substitutionalFe sites in SiC.

We found that the Fe interstitials at tetrahedral sites surrounded by C, FeI (C), are ener-getically more favorable than Fe interstitials at sites surrounded by Si, FeI (Si). However, Featoms at both sites are magnetic, exhibiting both sizeable magnetic moments and hyperfinefields. The Fe interstitials differ in their values of isomer shifts and quadruple splittings. Nohyperfine field was detected for Fe at interstitial sites in SiC [18, 19]. Hence, the tetrahe-drally coordinated Fe interstitial sites with complete neighboring Si or C atoms cannot beidentified with the interstitial sites observed experimentally.

We consider next the effect of neighboring vacancies on the properties of Fe at substitu-tional and interstitial sites. Table 2 shows the corresponding calculated properties for samesubstitutional and interstitial sites with neighboring vacancy due to removal of one of thenearest neighboring atoms.

We note that the presence of vacancies leads to formation of magnetic moments on Feat substitutional sites and its vanishing for Fe at interstitial sites. We found that the sub-stitutional site—vacancy complexes consist of two types depending on the location of thevacancy whether it is in the same Si-C bilayer or on a neighboring bilayer. The magneticmoments and hyperfine fields are larger when the vacancy is at the neighboring bilayer tothe substitutional Fe layer. The complex with Fe and neighboring vacancy at the same hbilayer is more favorable in agreement with the results of Ivady et al. [30]. On comparingto the data of refs 18 and 19 the substitutional sites with a neighboring vacancy cannot be

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The magnetic and hyperfine properties of iron in silicon carbide

Fig. 1 The 3d densities of states for substitutional paramagnetic Fe and Mn atoms at C and Si sites. TheFermi level is at the zero of energy. The peaks closer to the Fermi level result from the 3d states withe-character

Table 2 The local magnetic moment, m, in Bohr Magnetrons, the Fermi contact hyperfine field, Bhf inTeslas, the isomer shift, δ (relative to α-Fe) in mm/s and the quadruple splitting � in mm/s at Fe sites withneighboring vacancy at the substitutional sites FeC and FeSi and the interstitial sites FeI(C) and FeI(Si) for6H-SiC. On relaxation of FeC system, the Fe atom moves from the C site to the Si site transforming thesystem to FeSi

FeC FeSi FeI(C) FeI(Si)

m (μB) 0.97 1.96 0.0 0.0

Bhf(T) 20.1 −7.9 0.0 0.0

δ (mm/s) −0.66 0.14 0.16 0.24

� (mm/s) 1.04 −0.21 0.75 0.22

identified with those in the studied samples. On the other hand, both interstitial sites withnearest neighbor vacancy having zero magnetic hyperfine fields and positive isomer shiftscan be related to those observed in refs 18 and 19. However, we note that both sites pos-sess quadruple splitting in contrast to the experimental results. As we mentioned earlier theelectric field gradient is the least accurate of all calculated properties and hence being atvariance with experimental results should not overshadow the results of the more accuratemagnetic hyperfine field and isomer shift.

The respective appearance and disappearance of magnetic moments at the Fe substitu-tional and interstitial sites with introduction of neighboring vacancies can be understood in

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terms of appearance of dangling Fe bonds in the first case and establishment of bonding withneighboring atoms in the second. The calculated densities of states reflect this behavior.

Other defects likes antisites, self-interstitials and Fe at interstitials sites like the hexag-onal and bond-centered sites were also considered. In general the observed picture of Feproperties at substitutional and tetrahedral interstitial sites are retained for Fe at other sites.

The reported results of ref 18 and 19 were carried out on samples with low Fe fluence,where the resulting material is nonmagnetic. To get more information about the nature ofmagnetism of Fe in SiC, Mossbauer measurement need to be carried out on magnetic sam-ples to probe the environment of the magnetic Fe atoms and have more information on theorigin of Fe doped SiC magnetism.

4 Conclusion

The magnetic and hyperfine properties of Fe at substitutional and interstitial sites in 3C-SiC and 6H-SiC were calculated. We found that, in the case of absence of vacancies at theneighboring sites, Fe atoms substituted at Si or C sites are nonmagnetic, while Fe atoms atinterstitial sites are magnetic. On introducing vacancies at the nearest neighbor sites the pic-ture is reversed; the Fe atoms at the substitutional sites become magnetic, whereas Fe atomsat the interstitial sites turn nonmagnetic. We relate the Fe atoms at Si sites without neigh-boring vacancy and the interstitial Fe atoms with neighboring vacancy to those reportedexperimentally.

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