1 Introduction

Quantum information and quantum calculation have attracted intensive attention, but a key problem hampering the progress in this area is to find suitable materials for implementing the spin-qubit ^[1]. A negatively charged nitrogen-vacancy (NV⁻¹) center in diamond as a solid-state qubit was once studied intensively^[2]. Recently, several defects in silicon carbide (SiC) were predicted to be promising candidates of spin qubit^[3]. Comparing with NV⁻¹ centers in diamond, the defects in SiC have much lower transition frequencies and sharp zero-phonon line (ZPL), owing to the larger lattice constant and the small overlap among the sp³ dangling-bond orbitals. The spin coherence times of the defects in 4H-SiC were found to be suitable for qubit application^[4]. All these encourage researches for applying the defects in SiC to the area of quantum information.

Techniques to produce defects in SiC materials include irradiation, annealing and ion implantation. Till now, several defects and complexes in SiC, such as negatively charged silicon vacancies (${\text{V}}_{\text{Si}}^{\text{-1}}$)^[5], divacancies (V_SiV_C)^[3], carbon antisite- vacancy pairs (V_CC_Si)^[6], and ${\text{V}}_{\text{Si}}^{\text{-1}}$ with one neighboring carbon atom substituted by a nitrogen atom (N_C${\text{V}}_{\text{Si}}^{\text{-1}}$) ^[7], have been produced and identified. Studies on vacancy-type defects induced by oxygen ion-implantation in SiC and annealing showed evidences that new defect complex combined the vacancy-type defects with oxygen might be formed^{[8, 9]}. However, this shall be further studied for detailed information about the defect stability, especially the spin electronic structure and optical properties. In this paper, oxygen ion-implanted 4H-SiC samples are implanted with 70 keV oxygen ion beams. Electron spin resonance (ESR) and photoluminescence (PL) analyses, and first-principles calculations, show that the mainly defect produced by oxygen ion implantation is (V_SiO_C) centers, which consist of a substitutional oxygen atom at the carbon site and an adjacent silicon vacancy in 4H-SiC. The spin coherence time of the V_SiO_C centers in 4H-SiC is calculated using a mean- field-based scheme model. It is demonstrated that V_SiO_C centers is suitable for qubit controlling.

2 Experimental procedure and Computation method

The n-type 4H-SiC crystals were supplied by Shanghai Institute of optics and fine mechanics, the Chinese academy of sciences. The samples were implanted at room temperature by 70 keV oxygen ions to 1×10¹⁴ ions/cm². According to SRIM calculation, the implantation-induced vacancies and implanted oxygen atoms were distributed in depths of 60–160 nm. The ESR measurements were performed on a JEOL-FA200 spectrometers at 9.098-GHz (X-band) under standard conditions at 100–160 K. The excitation laser wavelength was 785 nm, with a laser spot of 2 µm in diameter. The PL signal were recorded by using a Bruker Raman system with 100×objective.

The linear combinations of pseudo atomic orbitals (LCPAOs) method based on the density functional theory (DFT) was adopted in our first-principles calculations. The norm-conserving pseudopotentials were used in electron-ion interactions^[10], which were was treated within the generalized gradient approximation (GGA) presented by Perdew-Burke-Ernzerhof (PBE) ^[11]. A supercell containing 127 atoms and a silicon monovacancy were employed. A 4×4×4 Monkhorst-Pack special k grid was used to the Brillouin zone integration. The atomic positions were optimized until the Hellmann-Feynman forces were less than 0.001 Hartree/a.u. The characteristic g-value shifts of vacancy defects were calculated by the Quantum-Espresso package^[12]. The spin-conserved optical transitions were calculated using the Heyd-Scuseria-Ernzerhof (HSE06) hybrid function^[13], which had well reproduced the ZPL experimental values ^[14].

3 Results and discussion

Figure 1 shows the X-band ESR spectra of the pristine and oxygen ion-implanted 4H-SiC measured at 100–160 K. The magnetic field is parallel to the c axis of the crystal (B||c) in the measurements. No signal was detected with the pristine 4H-SiC measured at 100 K. After oxygen ion implantation, a very strong signal was detected with the g factor equals to 2.0053. This is different from the vacancy defect centers in 4H-SiC reported in Refs.[7.15.16](V_Si at g=2.0034, V_C at g=2.0038, V_SiV_C at g=2.0023, V_SiN_C at g=2.0029 and C_SiV_C at g=2.0032), but is consistent with that of oxygen-vacancy complex in silicon (V_SiO_Si at g=2.0057)^[17]. Fig. 1a lso shows that ESR signals of the implanted samples decreased with increasing temperatures (disappeared at 160 K), and the peak position shifted with temperature due to the electron-phonon interaction^[18].

Fig.1.Full-screen View

(Color online) X-band ESR spectra measured at 100–160 K for pure and oxygen ion-implanted 4H-SiC. The magnetic field is parallel to the c axis (B||c)

Figure 2 shows the PL spectra of 4H-SiC samples measured at 100–180 K before and after ion implantation. The pristine 4H-SiC has just two Raman peaks, corresponding to the two inequivalence Si-C bonding configurations, while the implanted samples exhibit two sharp of ZPL peaks at 1.43 eV (866 nm) and 1.37 eV (907 nm), in addition to the two Raman peaks. The ZPL peaks decrease in height with increasing temperature (disappears at 180 K). It is well know that the ZPL peaks of the neutral V_SiV_C center, the negatively charged state V_SiN_C, and the neutral C_SiV_C are at 1.1±0.05, 0.98±0.01, and 1.0±0.05 eV, respectively^{[3, 6, 19]}, and the ZPL peaks of the negatively charged state V_Si center are at 1.44 eV (860 nm) and 1.35 eV (917 nm) with two inequivalent sites^[5].. The ZPL peaks of the oxygen ion-implanted 4H-SiC differ from those vacancy defect centers and the V_Si center in 4H-SiC. These indicate that the oxygen ion implanted in 4H-SiC introduce new defect centers.

Fig.2.Full-screen View

(Color online) Photoluminescence spectra of oxygen ion-implanted 4H-SiC measured at 100–180 K

Generally, implantation mainly produce vacancy-type defects^{[16, 20]}. To study these defects in 4H-SiC produced by oxygen ion implantation, the calculation of formation energies for all types of vacancy defects are necessary. The defect formation energy (E^f) depends on the defect charge states (q) and Fermi level (ε_F). For V_SiO_C in 4H-SiC, the E^f can be extracted from the total energies via first-principle calculations^[21]:

$E^{\text{f}}\left(V_{\text{Si}}{O}_C^q\right)=E_{\text{tot}}\left(V_{\text{Si}}{O}_C^q\right)-E_{\text{tot}}\left(SiC\right)-{\mu }_{\text{O}}+{\mu }_{\text{SiC}}+q\left({\epsilon }_{\text{F}}+{\epsilon }_v+\Delta V\right)$

where, $E_{\text{tot}}\left(SiC\right)$ and $E_{\text{tot}}\left(V_{\text{Si}}{O}_C^q\right)$ are the total energies of the perfect 4H-SiC supercell and defective supercell containing the V_SiO_C center in charge state q, respectively; μ_O is the chemical potential of O atom in an O₂ molecule (because the oxygen ion implantation into 4H-SiC is a non-equilibrium process, the V_SiO_C center is formed with oxygen atoms, hence the adoption of chemical potential of oxygen atom, which is more reasonable to our experiment); μ_SiC is the energy per SiC pairs which is calculated from a perfect 4H-SiC crystal; ε_F is the Fermi level, which is the band gap of the bulk 4H-SiC crystal; ε_v is the Fermi level reference to the valence band maximum of the bulk 4H-SiC and ΔV is the potential alignment calculated from the difference of average potentials of supercell without and with the defect. The formation energies of vacancy defects centers in 4H-SiC with different charge states are plotted in Fig. 3. Comparing the defect formation energies of different vacancy defect centers, the V_SiO_C center is the most stable in n-type 4H-SiC.

Fig.3.Full-screen View

(Color online) The calculated formation energies (E^f) as a function of Fermi level for single vacancies (V_C and V_Si), divancancy (V_SiV_C) and vacancy-impurity complex (V_SiO_C, V_CC_Si) in the oxygen ion-implanted 4H-SiC

To understand the nature of V_SiO_C centers in 4H-SiC, the density of state (DOS), optical and spin properties of the defect centers were calculated. The optimized V_SiO_C centers with the charge state of q=+2, 0, −1 and −2 exhibit a perfect $C_{3v}$ symmetry. Fig. 4 shows the calculated DOS of the V_SiO_C centers for the four charge states. According to the molecular orbitals (MOs) theory, the C_3v point group formed by four sp³ dangling bonds (DB) surrounding the Si vacancy. The V_SiO_C center have two nondegenerate (u and v) and two-fold degenerated ($e_x\text{ and }{e}_y$) MOs following the symmetries of the A₁ and E irreducible representations of C_3v point group^{[22, 23]}. For the vacancy-related defect complex, these defect electronic states align in the order of $E_u<E_v<E_{e_x,e_y}$ and they can totally hold four spin-up (↑) and four spin-down (↓) DB electrons. For example, the ${\text{V}}_{\text{Si}}{\text{O}}_{\text{C}}^{\text{0}}$ center has six DB electrons so that two spin-polarized levels remain unoccupied. As shown the calculated DOS in Fig. 4(b), all four majority-spin (↑) defect levels are occupied (one beneath the VBM and three in the band gap), while only two minority-spin (↓) defect levels are occupied. According to the DOS results, the Kohn-Sham eigenvalue associated with the ${\text{V}}_{\text{Si}}{\text{O}}_{\text{C}}^{\text{0}}$ center can be plotted (Fig. 5b). Similarly, the defect centers energy levels for the other charge states can be plotted, too (Fig. 5). The occupations of the defect levels shown in Figs. 4 and 5 determine the spin angular momenta (S) of different defect charge states. The net spin of the ${\text{V}}_{\text{Si}}{\text{O}}_{\text{c}}^{\text{q}}$ center is obtained as S=0, 1, 1/2 and 0 for the charge state q=+2, 0, −1 and −2 (q=+1 is not stable in SiC), respectively. It is clear that the ${\text{V}}_{\text{Si}}{\text{O}}_{\text{c}}^{\text{0}}$ and ${\text{V}}_{\text{Si}}{\text{O}}_{\text{c}}^{\text{-1}}$ centers possess nonzero net spin, which can be reflected in ESR measurement.

Fig.4.Full-screen View

(Color online) Calculated DOS for ${\text{V}}_{\text{Si}}{\text{O}}_{\text{C}}^{\text{q}}$ centers at different charge states in 4H-SiC. The energies are relative to the calculated chemical potentials (E=0 eV) denoted by thin vertical lines

Fig.5.Full-screen View

(Color online) Schematic diagrams of defect energy levels of ${\text{V}}_{\text{Si}}{\text{O}}_{\text{C}}^{\text{q}}$ centers at different charge states in 4H-SiC, (a) q=+2 and S=0, (b) q=0 and S=1, (c) q=-1 and S=1/2, and (d) q=-2 and S=0. Majority (minority) spins are denoted by upward (downward) arrows

In order to compare the ESR measurements, the g tensors of defect centers were calculated. Table 1 presents the calculated results of g tensors for vacancy defect centers in 4H-SiC. In 4H-SiC, there are two inequivalent sites (k stands for quasicubic position and h for quasihexagonal). The calculated g tensors of V_Si(k), V_C(h), V_SiV_C(kh), and V_CC_Si(hk) centers agree well with the measured g values, which all are close to the free-electron value due to the absence impurity atoms. But the calculated g tensors of V_SiO_C(kh) centers are larger than the g tensor of the free-electron due to introducing oxygen atoms. This can be found in the wavefunctions of V_SiO_C centers in 4H-SiC. Fig. 6 shows the minority-spin v and e_x states. From the minority-spin e_x state of ${\text{V}}_{\text{Si}}{\text{O}}_{\text{C}}^{\text{0}}$ and ${\text{V}}_{\text{Si}}{\text{O}}_{\text{c}}^{\text{-1}}$ centers (Fig. 6a and Fig. 6c, respectively), a small part of the density of the unpaired electrons is found at the oxygen atom. The similarity of the g values of the ${\text{V}}_{\text{Si}}{\text{O}}_{\text{C}}^{\text{0}}$ and ${\text{V}}_{\text{Si}}{\text{O}}_{\text{c}}^{\text{-1}}$ centers in 4H-SiC might be surprising. However, as can be seen in Fig. 6, the magnetization density is mainly localized at the carbon dangling bonds of the V_Si component of the defect pair, and the wavefunctions distribution of ${\text{V}}_{\text{Si}}{\text{O}}_{\text{C}}^{\text{0}}$ and ${\text{V}}_{\text{Si}}{\text{O}}_{\text{c}}^{\text{-1}}$ centers are similar. Thus, the similar g values of ${\text{V}}_{\text{Si}}{\text{O}}_{\text{C}}^{\text{0}}$ and ${\text{V}}_{\text{Si}}{\text{O}}_{\text{c}}^{\text{-1}}$ centers are reasonable. From the g tensors calculation, ESR signals of the oxygen ion implantation 4H-SiC may be attributed to the V_SiO_C centers.

Fig.6.Full-screen View

(Color online) Charge density plots of minority-spin e_x (a) and v (b) defect states for ${\text{V}}_{\text{Si}}{\text{O}}_{\text{C}}^0$ center. Charge density plots of minority-spin e_x (c) and v (d) defect states for ${\text{V}}_{\text{Si}}{\text{O}}_{\text{C}}^{-1}$ center. Red, yellow and blue balls denote the oxygen, carbon and silicon atoms, respectively.

Because the ZPL values of the oxygen ion-implanted 4H-SiC are different from those of the present defect types, the spin-conserved optical transitions of V_SiO_C centers in 4H-SiC were calculated. Theoretically, the spin-conserved optical transition of defect states can be approximated by Franck-Condon principle, so the total energy of the two electronic states was calculated using the constrained DFT approach. For example, the neutral V_SiO_C center, there are six electrons to be accommodated in the orbitals. The ground state configuration $a_u^2{a}_v^2{e}_{x,y}^2$ gives rise to the many-electron state ³A₂. Promoting an electron from a singlet to the doublet gives the excited state configuration $a_u^2{a}_v^1{e}_{x,y}^3$ and the many-electron state ³E^{[23, 24]}. The potential energy surfaces (PES) were the difference between the ground and excited states. The lowest PES of excited state and ground state transition was results in the ZPL. The calculated results are plotted in Fig. 7. The spin-conserved optical transition of ${\text{V}}_{\text{Si}}{\text{O}}_{\text{C}}^{\text{0}}\left(kh\right)$ center vertical absorption, vertical emission and ZPL are 1.06, 0.94 and 1.05 eV, respectively. However, the vertical absorption, vertical emission and ZPL of ${\text{V}}_{\text{Si}}{\text{O}}_{\text{c}}^{\text{-1}}\left(kh\right)$ center are 1.55, 1.39 and 1.45 eV, respectively. The ZPLs of defect centers with different inequivalent configurations in 4H-SiC have only small difference (~ 0.1 eV)^{[3, 6, 19]}. The calculated ZPLs of ${\text{V}}_{\text{Si}}{\text{O}}_{\text{c}}^{\text{-1}}\left(kh\right)$ center are close to our experimental PL signatures. Combining the measurement and calculation results, the oxygen ion implantation produces oxygen-vacancy complex in 4H-SiC.

Fig.7.Full-screen View

(Color online) Configuration coordinate diagrams for neutral and negatively charged state V_SiO_C centers in 4H-SiC. Absorption, emission, and ZPL transitions are indicated along with their energies

The calculation of spin-conserved optical transition of ${\text{V}}_{\text{Si}}{\text{O}}_{\text{C}}^{\text{0}}$ and ${\text{V}}_{\text{Si}}{\text{O}}_{\text{c}}^{\text{-1}}$ centers in 4H-SiC indicates that they are optically addressable. Therefore, some excellent properties suitable for qubit application are expected. As a spin qubit operation, the spin coherent property of defects is important for spin coherent manipulation. The electron spin coherence times of the ${\text{V}}_{\text{Si}}{\text{O}}_{\text{C}}^{\text{0}}$ and ${\text{V}}_{\text{Si}}{\text{O}}_{\text{c}}^{\text{-1}}$ centers in 4H-SiC can be calculated by the mean-field theory and first-principles calculations. The spin coherence is mainly effected by the interaction electronic spin and nuclear spins, which is expressed as^{[17, 25]},

$\Delta E_{hyp}= {\displaystyle \sum {}_n}{A}_H\Delta N_n{I}_n·s\text{,}$

where, AH is the hyperfine coupling constant, $\Delta N_n$ is the fraction of the Fermi contact interaction of the defect electron with the nth nucleus, $I_n$ is the n^th nucleus spin in the supercell, and s is the electron spin for defect. The spin operators $I_n$ and s can be replaced by their average values in the mean-field approximation, i.e., $s=1/2$ and ${\overline{I}}_n={\displaystyle \sum }_i{\alpha }^i{I}_n^i$, where $I_n^i$ and ${\alpha }^i$ are the i^th isotopes of the n^th nucleus nuclear spin and the corresponding of natural proportion. Knowing the hyperfine interaction energy, the electron spin coherence time can be estimated by the uncertainty principle at T = 0 K, i.e., $\Delta \tau =\hslash /2\Delta {\text{E}}_{\text{hyp}}$, where the $\hslash$ = 6.58 ×10⁻¹⁶ eV s is the Planck’s constant. Combine with the primary atomic orbitals of Si 2s, O 2s and C 2s and corresponding the LCPAO coefficients, the spin coherence times $\Delta \tau$ of the ${\text{V}}_{\text{Si}}{\text{O}}_{\text{C}}^{\text{0}}$ and ${\text{V}}_{\text{Si}}{\text{O}}_{\text{c}}^{\text{-1}}$ centers are calculated at 0.6 and 0.51 s, respectively. Such long spin coherence times of ${\text{V}}_{\text{Si}}{\text{O}}_{\text{C}}^{\text{0}}$ and ${\text{V}}_{\text{Si}}{\text{O}}_{\text{c}}^{\text{-1}}$ centers make them promising for a spin coherent manipulation and qubit operation in 4H-SiC.

4 Conclusion

In summary, oxygen ion implanted 4H-SiC were investigated by ESR, PL and theoretical calculations. Combined the experimental results with first-principles calculations, we suggest that the oxygen-vacancy complex was the main defect in the oxygen ion implantation 4H-SiC. The calculated defects formation energies of vacancy-type defect shown that the V_SiO_C centers were the most stable vacancy-defect in n-type 4H-SiC. And then, the calculated g tensors and ZPL values of the V_SiO_C centers are close to the ESR and PL experiment results. According to the PL experiment and ZPLs calculation, the ${\text{V}}_{\text{Si}}{\text{O}}_{\text{C}}^{\text{0}}$ and ${\text{V}}_{\text{Si}}{\text{O}}_{\text{c}}^{\text{-1}}$ centers are optically addressable. Finally, the spin coherence times of the ${\text{V}}_{\text{Si}}{\text{O}}_{\text{C}}^{\text{0}}$ and ${\text{V}}_{\text{Si}}{\text{O}}_{\text{c}}^{\text{-1}}$ centers show that oxygen ion implanted 4H-SiC is a promising system for qubit application.