Dopant-Induced Surface Magnetism in β-SiC Controlled by Dopant

Oct 10, 2014 - ... of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, P. R. China ... reach the third and seventh layers, the dopant-induced magnetism...
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Dopant-Induced Surface Magnetism in β‑SiC Controlled by Dopant Depth L. Z. Liu,† X. L. Wu,*,† X. X. Liu,† S. J. Xiong,† and Paul K. Chu‡ †

National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, P. R. China Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, P. R. China

‡

S Supporting Information *

ABSTRACT: First-principles calculation discloses local magnetism on the β-SiC (110) and (001) surfaces due to nonmetallic dopants. The spontaneously polarized β-SiC (111) surface without dopants also exhibits strong magnetism which can be reduced significantly by dopant incorporation. The magnetic values depend on the arrangement of superfluous p electrons and location of dopants. If the dopants reach the third and seventh layers, the dopant-induced magnetism on the (001) and (110) surfaces disappears and the nonmagnetic bulk behavior is reverted. Our results suggest that surface magnetism can be tailored by facet engineering and dopant incorporation.

1. INTRODUCTION Diluted magnetic semiconductors (DMS) have attracted much attention because of their potential applications to spintronics devices.1 The original idea of DMS is to incorporate magnetic transition metals such as Fe, Co, and Mn into a semiconductor host to produce a magnetic semiconductor at room temperature.2−7 The local magnetic moments usually stem from the transition metals containing partially filled 3d or 4f subshells where the electron arrangement obeys Hund’s rule. However, dopants at a high concentration precipitate in second phases, thus thwarting attempts to enhance the Curie temperatures, and so new approaches have been proposed.5,7 Recently, unexpected high temperature magnetism has been observed from a series of materials such as ZnO, GaN, and SiC which do not contain transition metals.8−14 Theoretical studies disclose that the local magnetic moments stem from sp state spin polarization induced by the cationic defect and extended tails of the spin wave functions mediated by long-range magnetic coupling.15−18 This is accompanied by some experimental investigations which show the possibility of tuning magnetization of DMS by defect engineering.9 However, some inconsistent results have also been reported. For example, in GaN and BN crystals, the defect state associated with an isolated neutral Ga (or B) vacancy splits into a singlet and triplet.14 The singlet state is fully occupied whereas the remaining three electrons occupy the triplet state, consequently resulting in a net local magnetic moment of 3 μB. Accordingly, it can be inferred that if one N atom is replaced by O atom and cation vacancy does not exist, a local magnetic moment (∼1 μB) may be present due to the superfluous p state electron. However, no local moment has been observed from this system. Magnetism in many nonmagnetic nanostructures such © 2014 American Chemical Society

as nanowires and nanocrystals can be induced by superficial cation vacancies or capping different types and concentrations of surfactants.19,20 For nanoscale ZnO, the local magnetic moment can be observed from various nanostructured compounds that are not magnetic in the bulk state.21,22 Hence, the origin of magnetism is still unknown, and the new physical factor associated with DMS must be identified and explored in addition to better understanding of the magnetic elements and cationic defect. As important DMS materials, SiC is widely used in electronic devices requiring high power, high temperature, and high frequency operation.16 Owing to the wide band gap and high Curie temperatures, its magnetic properties and origin have aroused much interest.12 In this work, β-SiC is selected as a representative system to investigate the relationship between the dopant and magnetic behavior in an attempt to elucidate the magnetic origin in DMS. A surface structure without magnetic elements and cationic defects is adopted to investigate the magnetism induced by nonmetallic dopants. First-principles calculation confirms that incorporation of nonmetals into the clean (110) and (001) surfaces gives rise to magnetism, which disappears gradually with depth. Our results also reveal that the clean (111) surface displays strong magnetism which can be reduced by doping. The surface structure plays an important role in the magnetism, but if β-SiC is bulk-doped, no magnetism can be observed. Hence, the magnetic behavior induced by the surface structure has a different mechanism compared to that of the bulk materials, suggesting the Received: July 19, 2014 Revised: August 30, 2014 Published: October 10, 2014 25429

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3. RESULTS AND DISCUSSION In the absence of spin polarization, the calculated band structure and total density of state (DOS) of the 15-layer (110) surface with N doping in the first layer are displayed in Figure 2. Detailed orbital analysis shows that the unoccupied band (up

possibility of tailoring the magnetic properties of DMS by facet and dopant engineering.

2. THEORETICAL METHODS The derivation is based on the density function theory (DFT) using the generalized gradient approximation in the form of Perdew−Burke−Ernzerhof function in Vienna ab inito simulation package (VASP) code with projector augmented wave pseudopotentials.23,24 The plane-wave energy cutoff is set at 450 eV to ensure convergence. The relaxed β-SiC (110), (001), and (111) surfaces without dopants are modeled as (2 × 2), (3 × 2), and (2√3 × 2√3) supercells consisting of a 15layer slab11,25−28 and a 15 Å vacuum thickness, as illustrated in Figure 1a−c and Figure S1 in the Supporting Information. The

Figure 2. Calculated band structure and total DOS for a 15-layer slab of β-SiC (110) surface with N-doping at the first layer. The surfacestate band structure is apparent at the bulk band (marked by red lines), and the N-doped band is present at around Fermi energy (marked by blue line).

red line) originates from surface Si atoms, the occupied band (down red line) arises from C dangling bonds, and the middle band (blue line) at Fermi energy Ef is related to N dopants. It is noted that introducing N atoms into this system produces an obvious DOS peak at the Fermi level which may result in magnetism (arrow). In the band-picture model, spontaneous magnetism occurs when the “Stoner criterion” is satisfied: D(Ef)J(R) > 1, where D(Ef) is the DOS at the Fermi energy and J(R) denotes the strength of exchange interaction.30,31 The joint contribution of D(Ef) and J(R) is responsible for magnetism. The bands caused by superficial dopants may appear at Fermi energy level, which will effectively lead to D(Ef) accretion and spin splitting between the spin-up and spin-down states. The strength of the exchange interaction J(R) is related to the spatial separation distance (R) between two dopants (or vacancies), which can be calculated by the nearestneighbor Heisenberg model. Based on this model, it can be inferred that D(Ef) induced by dopants will cause local magnetism in the surface region. For confirmation, the local magnetic moments in the superficial region of (110), (001), and (111) surfaces with one Si vacancy (VSi) as functions of defect depth are calculated and shown in Figure 3a, where the defect depth is defined as the distance from the first layer of undoped surface (0-layer). A local magnetic moment of 2 μB is induced by one VSi on the (110) and (001) surfaces, and this value remains constant in agreement with the behavior of VSi in bulk materials.16 On the undoped (001) and (110) surfaces, the surface-state band induced by surface atoms may be apparent at the Fermi energy (Figures S2 and S3, Supporting Information), but no obvious D(Ef) is present, thus hindering magnetic emergence. Reconstruction of the Si-terminated (111) surface will undergo a Mott−Hubbard metal−insulator transition, and the metallic behavior occurs. Hence, a larger D(Ef) appears (Figure S4, Supporting Information),28 causing spin splitting between the

Figure 1. Calculated isosurfaces of spin densities, ρ = ρ↑ − ρ↓, for undoping and N-doping at the first, third, and sixth layers of (001) (a, d, g, l), (110) (b, e, h, m) and (111) (c, f, k, n) surfaces. Blue and brown balls stand for Si and C atoms, respectively.

two layers on the bottom are fixed to mimic bulk, and the surface reconstructions are carried out until all forces on the free ions converge to 0.03 eV/Å. The Monkhorst−Pack k-point meshes (in two-dimensional Brillouin zone) of 3 × 3 × 1, 4 × 2 × 1, and 3 × 3 × 1 are used for the (110), (001), and (111) surfaces,29 which have been tested to converge. The doped structures are created by substituting C (or Si) (from the first to tenth layer) with N, O, F, S, and P (or B). Note that this structure is studied only for obtaining the relationship between magnetism and dopants and shall not be considered to represent a realistic distribution of dopants. 25430

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disappear (Table 1). With increasing VSi depth, the effect of the anion wave function on superficial spin splitting weakens, and the superficial magnetism is resumed accordingly. The magnetism on the (110), (001), and (111) surfaces with 2p (B, N, O, and F) and 3p (S and P) nonmetal dopants as functions of dopant depth is calculated and shown in Figures 3b and 3c, respectively. As a general feature, the effect of dopants on superficial magnetism is reduced with increasing dopant depth. The maximal penetration radius (R) of the dopant wave function can be calculated (shown in the last column in Table 1) by ∫ R0 4πr2ρ(r) dr = superfluous electron numbers and ρ(r) is the radial charge distribution of the dopants. It is responsible for the superficial magnetism decay rate difference on the (110) surface (larger R corresponds to smaller decay rate due to the more delocalized wave function). Two superfluous electrons induced by O and S atoms on the doped (001) surface are symmetrically arranged (one spin-up, one spin-down), and therefore, no magnetism is observed. The Si-terminated (001) surface can more effectively restrict the spin wave function distribution at the surface Si atom (as shown in Figure 1d,g), and so the dopant contributions to superficial magnetism vanish entirely at the fourth layer. On the metallic (111) surface, the magnetic values are reduced to 0 and 1 μB for O and S and 3 μB for F and other dopants, which strongly depend upon the unpaired p state electrons of the dopants (partially counteracting intrinsic spin splitting to form a lower magnetic state). For comparison, the magnetic values of the surface Si and C atoms are calculated and listed in Table 1. It can be seen that the dopant-induced magnetism depends on surface structure difference. In fact, it is found that the nonmetallic dopants can produce local magnetic moments on the (001) and (110) surfaces, thereby weakening the (111) surface magnetism. With increasing dopant depth, the effect of the dopants on superficial magnetism diminishes gradually, and it can also be explained by the simple “Stoner criterion” model:30,31 D(Ef) ∝ m3/2(|EVBM − Ef|)1/2, where m is the effective mass of dopants. For a larger dopant depth, the Fermi level lies just at the VBM (valence band maximum), and D(Ef) approximates zero, resulting in no magnetism because D(Ef)J < 1. When the dopants approach the surface, the Fermi level moves into or out of the valence band and the DOS at the Fermi level increases, as shown in Figure 2, and then when D(Ef)J > 1, superficial magnetism occurs. In addition, the bulk materials with these dopants are studied, but no magnetism is observed. Because the dopant bands are far away from the Fermi energy, it cannot effectively lead to D(Ef) accretion (Figures S6 and S7, Supporting Information). The results further indicate that the magnetic origin in the surface structure is obviously different from that of the bulk materials. To clearly illustrate D(Ef) change at different dopant depths, the spin-resolved Pz orbital DOSs of N-doped (110) surface are presented in Figure 4. For N doping, the number of the magnetic moment in this system is estimated to be 1.85 × 1014 cm−2 (the corresponding N-doped concentration is about 1.85 × 1014 atoms/cm−2), and the spin-polarization energy is 0.13 eV, suggesting that the spin-polarized state is rather stable at or above room temperature.14 If there are two N atoms in this system, the number of the magnetic moment will increase from 1.85 × 1014 to 3.70 × 1014 cm−2. Compared to the results derived for the undoped (110) surface in Figure 4a, the strong spin polarization (1-layer) (Figure 4b) results in complete separation of the spin-up and spin-down states, giving rise to 1 μB magnetic moment. The spin splitting energy [ΔE = E(t↑2 ) −

Figure 3. (a) Calculated local magnetic moments of (110), (001), and (111) surfaces induced by VSi at different depths. (b−d) Calculated local magnetic moments of (110), (001), and (111) surfaces induced by nonmetal doping at different depths, respectively.

spin-up and spin-down states (Figure S5, Supporting Information) and magnetic formation in the surface Si (0.643 μB) and C (0.245 μB) atoms (Table 1). The magnetism Table 1. Calculated Magnetic Moments on Superficial Si and C Atoms Induced by Neighboring Dopants or VSi at the First Layer of (001), (110), and (111) Surfaces and Penetration Radius of Dopant Wave Function (R) in β-SiC Bulk Material SiC (001) dopant none VSi B N O F S P

ΔQSi 0.275 0.142 0.124 0.000 0.183 0.000 0.196

ΔQC 0.206 0.038 0.027 0.000 0.036 0.000 0.046

SiC (110) ΔQSi 0.013 0.029 0.295 0.612 0.159 0.582 0.169

SiC (111)

ΔQC

ΔQSi

ΔQC

R (Å)

1.114 0.376 0.034 0.136 0.063 0.198 0.033

0.643 0.002 0.601 0.462 0.000 0.244 0.000 0.434

0.245 0.001 0.162 0.213 0.000 0.075 0.000 0.143

4.738 8.291 6.385 3.571 6.521 3.582 6.186

disappears abruptly if one VSi is located in the first layer and then increases slowly to 4 μB (at the fourth layer) with increasing VSi depth. Group theory discloses that β-SiC (Td) has two irreducible representations: a singlet (a1) and triplet (t2). With regard to the (110) and (001) surfaces, the a1 singlet state is fully occupied, and the remaining two electrons partially occupy the t2 triplet state, consequently resulting in a local magnetic moment of 2 μB. With increasing supercell size, the defect concentration decreases, which leads to compression of defect level broadening. In (2 × 2) supercells structure of (110) surface, the spin splitting energy is much greater (1.12 eV) than the broadening of the defect levels (0.34 eV). The superficial Si and C atoms (close to VSi) have magnetic moments of (0.275, 0.206) μB on the (001) surface and (0.013, 1.114) μB on the (110) surface (Table 1). On the (111) surface, four unpaired electrons of the anion will distribute into spin splitting Si and C atoms to form lower energy non-spin-polarized phases, and therefore, the magnetic moments in the superficial region 25431

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To calculate the magnetic coupling strength J(R), the surface slab side by side is doubled so that each supercell contains two VSi or dopants (1-layer). Based on the nearest-neighbor Heisenberg model,14 the energy difference between the ferromagnetic (FM) (two spin-up) and antiferromagnetic (AFM) (one spin-up, one spin-down) phases is calculated to be ΔE = EAFM − EFM = 4J(R)S2 (here the AFM structure is designed just for obtaining the magnetic interaction and it is not related to a realistic AFM ordering), where J(R) is the nearest-neighbor magnetic coupling (Table 2), S is the net spin of the defect or doped states, and the separation desistance of adjacent defects or dopants (R) is 6.19, 8.75, and 6.19 Å for the (001), (110), and (111) surfaces,14 respectively. A negative J(R) means that AFM is energetically favored; otherwise FM is favored. The values of J(R) on the (110) surface are generally smaller than those on the (111) and (001) surfaces because the electronic structure is more delocalized in this structure and the large coupling broadens the spin-up and spin-down band widths. As a result, a charge transfer from the majority to minority spin state takes place, thereby reducing the magnetic localization and increasing the exchange interaction. Concerning the (111) and (001) surface, spontaneous polarization restricts overlapping of the majority to minority spin states and charge transfer between the two spin channels is relatively low, thus weakening the exchange interaction (even R is smaller). Therefore, the energy difference ΔE between the AFM and FM states is enlarged (Table 2). The change in J(R) on the same surface represents the difference in the dopant wave function localization. A larger value implies that electrons are more easily distributed in the vicinity of the dopants and magnetic coupling is reduced.

Figure 4. Calculated Pz orbital spin electron DOSs of (110) surfaces with undoping (a) and N-doping at the first (b), third (c), and sixth (d) layers.

E(t↓2)] is dramatically reduced from 1.1 eV (1-layer) (Figure 4b) to 0.1 eV (3-layer) (Figure 4c) and 0 eV (6-layer) (Figure 4d), and meanwhile, D(Ef) decreases accordingly. The DOS changes further disclose that dopants in the near surface can cause spin splitting and create magnetism. The behavior on the (001) and (111) surfaces are similar to this case and shown in Figures S3 and S5 (Supporting Information). After considering intrasite electron−electron interaction,32 we also employed GW and LDA+U methods to calculate the DOSs and magnetic moments of (111) surface, and the same results were obtained (Figure S8, Supporting Information). To visualize spin polarization in real space, the isosurface (isovalue is 1.4 × 10−3 e/au,3 containing 80% spin charge) of the spin charge density ρ = ρ↑ − ρ↓ for (001), (110), and (111) surfaces with different N depths is shown in Figure 1. It is evident that the spin polarization is localized near the surface (both Si and C atoms), and the contribution of dopants is reduced with increasing depth. With regard to the (001) and (110) surfaces, the spin charge density is induced by N doping in the first layer (Figure 1a,d and Figure 1b,e), weakens in the third layer (Figure 1d,g and Figure 1e,h), and eventually disappears in the sixth layer (Figure 1g,l and Figure 1h,m). The trend is in agreement with the calculated DOS changes in Figure 4. Strong spontaneous polarization occurs on the undoped (111) surface (Figure 1c). It is reduced by N doping in the first layer (Figure 1c,f), increases in the third layer (Figure 1f,k), and finally becomes similar to that without a dopant layer (Figure 1k,n). It can be seen that the spinpolarized wave functions are substantially distributed in the surface region and depend on the dopants in the first layer.

4. CONCLUSIONS In summary, local surface magnetism can be induced in β-SiC (001) and (110) by nonmetal dopants, and it diminishes gradually and finally disappears with depth. This phenomenon is different from the magnetic behavior of bulk materials. Spontaneous spin polarization also induces strong magnetism on the undoped (111) surface, and addition of dopants causes the magnetism to diminish significantly and even disappear. With increasing dopant depth, magnetism is resumed slowly. Our results elucidate the origin of the surface magnetism which can be tailored by facet engineering and dopant incorporation.

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ASSOCIATED CONTENT

S Supporting Information *

Relaxed β-SiC (110), (001), and (111) superficial structures, energy band structures and total DOSs of SiC (001) and (111) surfaces, Pz orbital spin electron DOSs of the (001) and (111)

Table 2. Energy Difference ΔE (meV) between FM and AFM Phases and Nearest-Neighbor Magnetic Coupling J(R) (meV)a SiC (001)

a

SiC (110)

SiC (111)

dopant

ΔE

J(R)

ΔE

J(R)

VSi B N O F S P

−17.76 23.81 −149.15

−4.52 6.39 --66.58

118.08

8.85

109.83

32.94

13.69 4.63 9.05 −10.92 11.49 6.42 13.81

14.16 1.16 2.34 −1.57 2.95 0.83 3.52

ΔE

J(R)

−63.20 −137.07

−5.46 −11.48

20.56

23.12

45.98

3.85

Dopants and VSi are located at the first layers of (001), (110), and (111) surfaces. 25432

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surfaces with different N-doping depths, band structure and total DOS of bulk SiC material, DOSs and magnetic moments calculated with different theoretical methods. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Fax 86-25-83595535; Tel 86-2583686303 (X.L.W.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The calculation was carried out at the High Performance Computing Center of Nanjing University. This work was jointly supported by National Basic Research Programs of China (Nos. 2011CB922102 and 2013CB932901) and Natural Science Foundation of China (No. 11374141 and 11404162). Partial support was also from Natural Science Foundations of Jiangsu Province (No. BK20130549), City University of Hong Kong Applied Research Grant (ARG) No. 9667085, and Guangdong - Hong Kong Technology Cooperation Funding Scheme (TCFS) GHP/015/12SZ.

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