PL and ESR study for defect centers in 4H-SiC induced by oxygen ion implantation

PL and ESR study for defect centers in 4 H -SiC induced by oxygen ion implantation 1 2 first-author 1 2 corresp Corresponding author.E-mail address: yanlong@sinap.ac.cn Corresponding author.E-mail address: yanlong@sinap.ac.cn yanlong@sinap.ac.cn 2 Key Laboratory of Polar Materials and Devices, Ministry of Education of China, East China Normal University, Shanghai 200241, China Key Laboratory of Polar Materials and Devices, Ministry of Education of China, East China Normal University, Shanghai 200241, China Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China Radiation damage in 4 H -SiC samples implanted by 70 keV oxygen ion beams was studied using photoluminescence and electron spin resonance techniques. ESR peak of g =2.0053 and two zero-phonon lines (ZPL) were observed with the implanted samples. Combined with theoretical calculations, we found that the main defect in the implanted 4 H -SiC samples was oxygen-vacancy complex. The calculated defect formation energies showed that the oxygen-vacancy centers were stable in n -type 4 H -SiC. Moreover, the <math id="M1"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>C</mtext><mtext>0</mtext></msubsup></mrow></math> and <math id="M2"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>C</mtext><mrow><mtext>-1</mtext></mrow></msubsup></mrow></math> centers were optically addressable. The results suggest promising spin coherence properties for quantum information science. Ion implantation Electron spin resonance Photoluminescence First-principles calculations 1 Introduction 1 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 1 ] . A negatively charged nitrogen-vacancy (NV −1 ) center in diamond as a solid-state qubit was once studied intensively [ 2 2 ] . Recently, several defects in silicon carbide (SiC) were predicted to be promising candidates of spin qubit [ 3 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 sp 3 dangling-bond orbitals. The spin coherence times of the defects in 4 H -SiC were found to be suitable for qubit application [ 4 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 ( <math id="M3"><mrow><msubsup><mtext>V</mtext><mrow><mtext>Si</mtext></mrow><mrow><mtext>-1</mtext></mrow></msubsup></mrow></math> ) [ 5 5 ] , divacancies (V Si V C ) [ 3 3 ] , carbon antisite- vacancy pairs (V C C Si ) [ 6 6 ] , and <math id="M4"><mrow><msubsup><mtext>V</mtext><mrow><mtext>Si</mtext></mrow><mrow><mtext>-1</mtext></mrow></msubsup><mo> </mo></mrow></math> with one neighboring carbon atom substituted by a nitrogen atom (N C <math id="M5"><mrow><msubsup><mtext>V</mtext><mrow><mtext>Si</mtext></mrow><mrow><mtext>-1</mtext></mrow></msubsup></mrow></math> ) [ 7 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 8 , 9 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 4 H -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 Si O C ) centers, which consist of a substitutional oxygen atom at the carbon site and an adjacent silicon vacancy in 4 H -SiC. The spin coherence time of the V Si O C centers in 4 H -SiC is calculated using a mean- field-based scheme model. It is demonstrated that V Si O C centers is suitable for qubit controlling. 2 Experimental procedure and Computation method 1 The n -type 4 H -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 1×10 14 ions/cm 2 . 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 10 ] , which were was treated within the generalized gradient approximation (GGA) presented by Perdew-Burke-Ernzerhof (PBE) [ 11 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 12 ] . The spin-conserved optical transitions were calculated using the Heyd-Scuseria-Ernzerhof (HSE06) hybrid function [ 13 13 ] , which had well reproduced the ZPL experimental values [ 14 14 ] . 3 Results and discussion 1 Figure 1 Figure 1 shows the X -band ESR spectra of the pristine and oxygen ion-implanted 4 H -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 4 H -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 4 H -SiC reported in Refs.[7.15.16](V Si at g =2.0034, V C at g =2.0038, V Si V C at g =2.0023, V Si N C at g =2.0029 and C Si V C at g =2.0032), but is consistent with that of oxygen-vacancy complex in silicon (V Si O Si at g =2.0057) [ 17 17 ] . Fig. 1a 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 18 ] . Figure 2 Figure 2 shows the PL spectra of 4 H -SiC samples measured at 100–180 K before and after ion implantation. The pristine 4 H -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 Si V C center, the negatively charged state V Si N C , and the neutral C Si V C are at 1.1±0.05, 0.98±0.01, and 1.0±0.05 eV, respectively [ 3 3 , 6 6 , 19 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 5 ] .. The ZPL peaks of the oxygen ion-implanted 4 H -SiC differ from those vacancy defect centers and the V Si center in 4 H -SiC. These indicate that the oxygen ion implanted in 4 H -SiC introduce new defect centers. Generally, implantation mainly produce vacancy-type defects [ 16 16 , 20 20 ] . To study these defects in 4 H -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 Si O C in 4 H -SiC, the E f can be extracted from the total energies via first-principle calculations [ 21 21 ] : <math id="M6"><mrow><msup><mi>E</mi><mtext>f</mtext></msup><mrow><mo>(</mo><mrow><msub><mi>V</mi><mrow><mtext>Si</mtext></mrow></msub><msubsup><mi>O</mi><mi>C</mi><mi>q</mi></msubsup></mrow><mo>)</mo></mrow><mo>=</mo><msub><mi>E</mi><mrow><mtext>tot</mtext></mrow></msub><mrow><mo>(</mo><mrow><msub><mi>V</mi><mrow><mtext>Si</mtext></mrow></msub><msubsup><mi>O</mi><mi>C</mi><mi>q</mi></msubsup></mrow><mo>)</mo></mrow><mo>−</mo><msub><mi>E</mi><mrow><mtext>tot</mtext></mrow></msub><mrow><mo>(</mo><mrow><mi>S</mi><mi>i</mi><mi>C</mi></mrow><mo>)</mo></mrow><mo>−</mo><msub><mi>μ</mi><mtext>O</mtext></msub><mo>+</mo><msub><mi>μ</mi><mrow><mtext>SiC</mtext></mrow></msub><mo>+</mo><mi>q</mi><mrow><mo>(</mo><mrow><msub><mi>ε</mi><mtext>F</mtext></msub><mo>+</mo><msub><mi>ε</mi><mi>v</mi></msub><mo>+</mo><mi>Δ</mi><mi>V</mi></mrow><mo>)</mo></mrow></mrow></math> where, <math id="M7"><mrow><msub><mi>E</mi><mrow><mtext>tot</mtext></mrow></msub><mrow><mo>(</mo><mrow><mi>S</mi><mi>i</mi><mi>C</mi></mrow><mo>)</mo></mrow></mrow></math> and <math id="M8"><mrow><msub><mi>E</mi><mrow><mtext>tot</mtext></mrow></msub><mrow><mo>(</mo><mrow><msub><mi>V</mi><mrow><mtext>Si</mtext></mrow></msub><msubsup><mi>O</mi><mi>C</mi><mi>q</mi></msubsup></mrow><mo>)</mo></mrow></mrow></math> are the total energies of the perfect 4 H -SiC supercell and defective supercell containing the V Si O C center in charge state q, respectively; μ O is the chemical potential of O atom in an O 2 molecule (because the oxygen ion implantation into 4 H -SiC is a non-equilibrium process, the V Si O 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 4 H -SiC crystal; ε F is the Fermi level, which is the band gap of the bulk 4 H -SiC crystal; ε v is the Fermi level reference to the valence band maximum of the bulk 4 H -SiC and Δ V 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 4 H -SiC with different charge states are plotted in Fig. 3 Fig. 3 . Comparing the defect formation energies of different vacancy defect centers, the V Si O C center is the most stable in n -type 4 H -SiC. To understand the nature of V Si O C centers in 4 H -SiC, the density of state (DOS), optical and spin properties of the defect centers were calculated. The optimized V Si O C centers with the charge state of q =+2, 0, −1 and −2 exhibit a perfect <math id="M9"><mrow><msub><mi>C</mi><mrow><mn>3</mn><mi>v</mi></mrow></msub></mrow></math> symmetry. Fig. 4 Fig. 4 shows the calculated DOS of the V Si O C centers for the four charge states. According to the molecular orbitals (MOs) theory, the C 3 v point group formed by four sp 3 dangling bonds (DB) surrounding the Si vacancy. The V Si O C center have two nondegenerate ( u and v ) and two-fold degenerated ( <math id="M10"><mrow><msub><mi>e</mi><mi>x</mi></msub><mtext> and </mtext><msub><mi>e</mi><mi>y</mi></msub></mrow></math> ) MOs following the symmetries of the A 1 and E irreducible representations of C 3 v point group [ 22 22 , 23 23 ] . For the vacancy-related defect complex, these defect electronic states align in the order of <math id="M11"><mrow><msub><mi>E</mi><mi>u</mi></msub><mo><</mo><msub><mi>E</mi><mi>v</mi></msub><mo><</mo><msub><mi>E</mi><mrow><msub><mi>e</mi><mi>x</mi></msub><mo>,</mo><msub><mi>e</mi><mi>y</mi></msub></mrow></msub></mrow></math> and they can totally hold four spin-up (↑) and four spin-down (↓) DB electrons. For example, the <math id="M12"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>C</mtext><mtext>0</mtext></msubsup></mrow></math> center has six DB electrons so that two spin-polarized levels remain unoccupied. As shown the calculated DOS in Fig. 4(b) 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 <math id="M13"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>C</mtext><mtext>0</mtext></msubsup></mrow></math> center can be plotted ( Fig. 5b Fig. 5b ). Similarly, the defect centers energy levels for the other charge states can be plotted, too ( Fig. 5 Fig. 5 ). The occupations of the defect levels shown in Figs. 4 Figs. 4 and 5 5 determine the spin angular momenta (S) of different defect charge states. The net spin of the <math id="M14"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>c</mtext><mtext>q</mtext></msubsup></mrow></math> 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 <math id="M15"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>c</mtext><mtext>0</mtext></msubsup></mrow></math> and <math id="M16"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>c</mtext><mrow><mtext>-1</mtext></mrow></msubsup></mrow></math> centers possess nonzero net spin, which can be reflected in ESR measurement. In order to compare the ESR measurements, the g tensors of defect centers were calculated. Table 1 Table 1 presents the calculated results of g tensors for vacancy defect centers in 4 H -SiC. In 4 H -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 Si V C ( kh ), and V C C 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 Si O 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 Si O C centers in 4 H -SiC. Fig. 6 Fig. 6 shows the minority-spin v and e x states. From the minority-spin e x state of <math id="M19"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>C</mtext><mtext>0</mtext></msubsup></mrow></math> and <math id="M20"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>c</mtext><mrow><mtext>-1</mtext></mrow></msubsup></mrow></math> centers ( Fig. 6a and Fig. 6c 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 <math id="M21"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>C</mtext><mtext>0</mtext></msubsup></mrow></math> and <math id="M22"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>c</mtext><mrow><mtext>-1</mtext></mrow></msubsup></mrow></math> centers in 4 H -SiC might be surprising. However, as can be seen in Fig. 6 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 <math id="M23"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>C</mtext><mtext>0</mtext></msubsup></mrow></math> and <math id="M24"><mrow><mo> </mo><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>c</mtext><mrow><mtext>-1</mtext></mrow></msubsup><mo> </mo></mrow></math> centers are similar. Thus, the similar g values of <math id="M25"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>C</mtext><mtext>0</mtext></msubsup></mrow></math> and <math id="M26"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>c</mtext><mrow><mtext>-1</mtext></mrow></msubsup><mo> </mo></mrow></math> centers are reasonable. From the g tensors calculation, ESR signals of the oxygen ion implantation 4 H -SiC may be attributed to the V Si O C centers. 1 1 Models 1 1 g xx 1 1 g yy 1 1 g zz 1 1 Measured 1 1 <math id="M27"><mrow><msubsup><mtext>V</mtext><mrow><mtext>Si</mtext></mrow><mrow><mtext>-1</mtext></mrow></msubsup><mtext> </mtext><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></math> 1 1 2.0046 1 1 2.0046 1 1 2.0043 1 1 2.0034 1 1 <math id="M28"><mrow><msubsup><mtext>V</mtext><mtext>C</mtext><mtext>+</mtext></msubsup><mtext> (h)</mtext></mrow></math>   1 1 2.0038 1 1 2.0036 1 1 2.0038 1 1 2.0038 1 1 <math id="M29"><mrow><msubsup><mtext>V</mtext><mtext>C</mtext><mrow><mtext>-1</mtext></mrow></msubsup><mtext> (h)</mtext></mrow></math>   1 1 2.0022 1 1 2.0022 1 1 2.0021 1 1 2.0028 1 1 <math id="M30"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>C</mtext><mrow><mtext>-1</mtext></mrow></msubsup><mtext> (kh)</mtext></mrow></math>   1 1 2.0031 1 1 2.0052 1 1 2.0057 1 1 2.0053 1 1 <math id="M31"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>C</mtext><mtext>0</mtext></msubsup><mtext> (kh)</mtext></mrow></math>   1 1 2.0059 1 1 2.0079 1 1 2.0048 1 1 2.0053 1 1 <math id="M32"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>V</mtext><mtext>C</mtext><mtext>0</mtext></msubsup><mtext> (kh)</mtext></mrow></math>   1 1 2.0022 1 1 2.0022 1 1 2.0022 1 1 2.0023 1 1 <math id="M33"><mrow><msub><mtext>V</mtext><mtext>C</mtext></msub><msubsup><mtext>C</mtext><mrow><mtext>Si</mtext></mrow><mtext>0</mtext></msubsup><mtext> (hk)</mtext></mrow></math>   1 1 2.0021 1 1 2.0021 1 1 2.0021 1 1 2.0032 Because the ZPL values of the oxygen ion-implanted 4 H -SiC are different from those of the present defect types, the spin-conserved optical transitions of V Si O C centers in 4 H -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 Si O C center, there are six electrons to be accommodated in the orbitals. The ground state configuration <math id="M36"><mrow><msubsup><mi>a</mi><mi>u</mi><mn>2</mn></msubsup><msubsup><mi>a</mi><mi>v</mi><mn>2</mn></msubsup><msubsup><mi>e</mi><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mn>2</mn></msubsup></mrow></math> gives rise to the many-electron state 3 A 2 . Promoting an electron from a singlet to the doublet gives the excited state configuration <math id="M37"><mrow><msubsup><mi>a</mi><mi>u</mi><mn>2</mn></msubsup><msubsup><mi>a</mi><mi>v</mi><mn>1</mn></msubsup><msubsup><mi>e</mi><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow><mn>3</mn></msubsup></mrow></math> and the many-electron state 3 E [ 23 23 , 24 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 Fig. 7 . The spin-conserved optical transition of <math id="M38"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>C</mtext><mtext>0</mtext></msubsup><mrow><mo>(</mo><mrow><mi>k</mi><mi>h</mi></mrow><mo>)</mo></mrow></mrow></math> 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 <math id="M39"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>c</mtext><mrow><mtext>-1</mtext></mrow></msubsup><mrow><mo>(</mo><mrow><mi>k</mi><mi>h</mi></mrow><mo>)</mo></mrow></mrow></math> center are 1.55, 1.39 and 1.45 eV, respectively. The ZPLs of defect centers with different inequivalent configurations in 4 H -SiC have only small difference (~ 0.1 eV) [ 3 3 , 6 6 , 19 19 ] . The calculated ZPLs of <math id="M40"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>c</mtext><mrow><mtext>-1</mtext></mrow></msubsup><mrow><mo>(</mo><mrow><mi>k</mi><mi>h</mi></mrow><mo>)</mo></mrow></mrow></math> center are close to our experimental PL signatures. Combining the measurement and calculation results, the oxygen ion implantation produces oxygen-vacancy complex in 4 H -SiC. The calculation of spin-conserved optical transition of <math id="M41"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>C</mtext><mtext>0</mtext></msubsup></mrow></math> and <math id="M42"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>c</mtext><mrow><mtext>-1</mtext></mrow></msubsup></mrow></math> centers in 4 H -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 <math id="M43"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>C</mtext><mtext>0</mtext></msubsup></mrow></math> and <math id="M44"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>c</mtext><mrow><mtext>-1</mtext></mrow></msubsup></mrow></math> centers in 4 H -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 17 , 25 25 ] , <math id="M45"><mrow><mi>Δ</mi><msub><mi>E</mi><mrow><mi>h</mi><mi>y</mi><mi>p</mi></mrow></msub><mo>=</mo><mo> </mo><mstyle displaystyle="true"><mo>∑</mo><mrow><msub><mrow/><mi>n</mi></msub></mrow></mstyle><msub><mi>A</mi><mi>H</mi></msub><mi>Δ</mi><msub><mi>N</mi><mi>n</mi></msub><msub><mi>I</mi><mi>n</mi></msub><mo>·</mo><mi>s</mi><mtext>,</mtext></mrow></math> where, A H is the hyperfine coupling constant, <math id="M46"><mrow><mi>Δ</mi><msub><mi>N</mi><mi>n</mi></msub></mrow></math> is the fraction of the Fermi contact interaction of the defect electron with the n th nucleus, <math id="M47"><mrow><msub><mi>I</mi><mi>n</mi></msub></mrow></math> is the n th nucleus spin in the supercell, and s is the electron spin for defect. The spin operators <math id="M48"><mrow><msub><mi>I</mi><mi>n</mi></msub></mrow></math> and s can be replaced by their average values in the mean-field approximation, i.e., <math id="M49"><mrow><mi>s</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math> and <math id="M50"><mrow><msub><mover accent="true"><mi>I</mi><mo>¯</mo></mover><mi>n</mi></msub><mo>=</mo><munder><mstyle mathsize="140%" displaystyle="true"><mo>∑</mo></mstyle><mi>i</mi></munder><msup><mi>α</mi><mi>i</mi></msup><msubsup><mi>I</mi><mi>n</mi><mi>i</mi></msubsup></mrow></math> , where <math id="M51"><mrow><msubsup><mi>I</mi><mi>n</mi><mi>i</mi></msubsup></mrow></math> and <math id="M52"><mrow><msup><mi>α</mi><mi>i</mi></msup></mrow></math> 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., <math id="M53"><mrow><mi>Δ</mi><mi>τ</mi><mo>=</mo><mi>ℏ</mi><mo>/</mo><mn>2</mn><mi>Δ</mi><msub><mtext>E</mtext><mrow><mtext>hyp</mtext></mrow></msub></mrow></math> , where the <math id="M54"><mi>ℏ</mi></math> = 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 <math id="M55"><mrow><mi>Δ</mi><mi>τ</mi></mrow></math> of the <math id="M56"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>C</mtext><mtext>0</mtext></msubsup></mrow></math> and <math id="M57"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>c</mtext><mrow><mtext>-1</mtext></mrow></msubsup></mrow></math> centers are calculated at 0.6 and 0.51 s, respectively. Such long spin coherence times of <math id="M58"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>C</mtext><mtext>0</mtext></msubsup></mrow></math> and <math id="M59"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>c</mtext><mrow><mtext>-1</mtext></mrow></msubsup></mrow></math> centers make them promising for a spin coherent manipulation and qubit operation in 4 H -SiC. 4 Conclusion 1 In summary, oxygen ion implanted 4 H -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 4 H -SiC. The calculated defects formation energies of vacancy-type defect shown that the V Si O C centers were the most stable vacancy-defect in n -type 4 H -SiC. And then, the calculated g tensors and ZPL values of the V Si O C centers are close to the ESR and PL experiment results. According to the PL experiment and ZPLs calculation, the <math id="M60"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>C</mtext><mtext>0</mtext></msubsup></mrow></math> and <math id="M61"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>c</mtext><mrow><mtext>-1</mtext></mrow></msubsup></mrow></math> centers are optically addressable. Finally, the spin coherence times of the <math id="M62"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>C</mtext><mtext>0</mtext></msubsup></mrow></math> and <math id="M63"><mrow><msub><mtext>V</mtext><mrow><mtext>Si</mtext></mrow></msub><msubsup><mtext>O</mtext><mtext>c</mtext><mrow><mtext>-1</mtext></mrow></msubsup></mrow></math> centers show that oxygen ion implanted 4 H -SiC is a promising system for qubit application. References J.R. Weber , W.F. Koehl , J.B. Varley , et al ., Quantum computing with defects . Proc. Natl. Acad. Sci. U.S.A . 107 , 8513 - 8518 ( 2010 ). doi: 10.1073/pnas.1003052107 http://doi.org/10.1073/pnas.1003052107 Quantum computing with defects P. Neumann , N. Mizuochi , F. Rempp , et al ., Multipartite entanglement among single spins in diamond . Science 320 , 1326 - 1329 ( 2008 ). doi: 10.1126/science.1157233 http://doi.org/10.1126/science.1157233 Multipartite entanglement among single spins in diamond A.L. Falk , B.B. Buckley , G. Calusine , et al ., Polytype control of spin qubits in silicon carbide . Nat. Commun . 4 , 1819 ( 2013 ). doi: 10.1038/ncomms2854 http://doi.org/10.1038/ncomms2854 Polytype control of spin qubits in silicon carbide L.P. Yang , C. Burk , M. Widmann , et al ., Electron spin decoherence in silicon carbide nuclear spin bath . Phys. Rev. B 90 , 241203 ( 2014 ). doi: 10.1103/PhysRevB.90.241203 http://doi.org/10.1103/PhysRevB.90.241203 Electron spin decoherence in silicon carbide nuclear spin bath P.G. Baranov , A.P. Bundakova , A.A. Soltamova , et al ., Silicon vacancy in SiC as a promising quantum system for single-defect and single-photon spectroscopy . Phys. Rev. B 83 , 125203 ( 2011 ). doi: 10.1103/PhysRevB.83.125203 http://doi.org/10.1103/PhysRevB.83.125203 Silicon vacancy in SiC as a promising quantum system for single-defect and single-photon spectroscopy K. Szász , V. Ivády , I.A. Abrikosov , et al ., Spin and photophysics of carbon-antisite vacancy defect in 4H silicon carbide: A potential quantum bit . Phys. Rev. B 91 , 121201 ( 2015 ). doi: 10.1103/PhysRevB.91.121201 http://doi.org/10.1103/PhysRevB.91.121201 Spin and photophysics of carbon-antisite vacancy defect in 4H silicon carbide: A potential quantum bit H.J. von Bardeleben , J.L. Cantin , E. Rauls , et al ., Identification and magneto-optical properties of the NV center in 4H-SiC . Phys. Rev. B 92 , 064104 ( 2015 ). doi: 10.1103/Physrevb.92.064104 http://doi.org/10.1103/Physrevb.92.064104 Identification and magneto-optical properties of the NV center in 4H-SiC M. Ishimaru , R.M. Dickerson , K.E. Sickafus , High-dose oxygen ion implantation into 6H-SiC . Appl. Phys. Lett . 75 , 352 - 354 ( 1999 ). doi: 10.1063/1.124372 http://doi.org/10.1063/1.124372 High-dose oxygen ion implantation into 6H-SiC A. Uedono , S. Tanigawa , T. Ohshima , et al ., Oxygen-related defects in O+-implanted 6H-SiC studied by a monoenergetic positron beam . J. Appl. Phys . 86 , 5392 - 5398 ( 1999 ). doi: 10.1063/1.371536 http://doi.org/10.1063/1.371536 Oxygen-related defects in O+-implanted 6H-SiC studied by a monoenergetic positron beam T. Ozaki , Variationally optimized atomic orbitals for large-scale electronic structures . Phys. Rev. B 67 , 155108 ( 2003 ). doi: 10.1103/Physrevb.67.155108 http://doi.org/10.1103/Physrevb.67.155108 Variationally optimized atomic orbitals for large-scale electronic structures N. Troullier , J.L. Martins , Efficient Pseudopotentials for Plane-Wave Calculations . Phys. Rev. B 43 , 1993 - 2006 ( 1991 ). doi: 10.1103/PhysRevB.43.1993 http://doi.org/10.1103/PhysRevB.43.1993 Efficient Pseudopotentials for Plane-Wave Calculations P. Giannozzi , S. Baroni , N. Bonini , et al ., QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials . J. Phys. Condens. Matter 21 , 395502 ( 2009 ). doi: 10.1088/0953-8984/21/39/395502 http://doi.org/10.1088/0953-8984/21/39/395502 QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials J. Heyd , G.E. Scuseria , M. Ernzerhof , Hybrid functionals based on a screened Coulomb potential . J. Chem. Phys . 118 , 8207 - 8215 ( 2003 ). doi: 10.1063/1.1564060 http://doi.org/10.1063/1.1564060 Hybrid functionals based on a screened Coulomb potential A. Gali , E. Janzen , P. Deak , et al ., Theory of spin-conserving excitation of the NV- center in diamond . Phys. Rev. Lett . 103 , 186404 ( 2009 ). doi: 10.1103/Physrevlett.103.186404 http://doi.org/10.1103/Physrevlett.103.186404 Theory of spin-conserving excitation of the NV- center in diamond N.T. Son , P.N. Hai , E. Janzen , Silicon antisite in 4H SiC . Phys. Rev. Lett . 87 , 045502 ( 2001 ). doi: 10.1103/PhysRevLett.87.045502 http://doi.org/10.1103/PhysRevLett.87.045502 Silicon antisite in 4H SiC N.T. Son , X.T. Trinh , L.S. Lovlie , et al ., Negative-U System of Carbon Vacancy in 4H-SiC . Phys. Rev. Lett . 109 , 187603 ( 2012 ). doi: 10.1103/Physrevlett.109.187603 http://doi.org/10.1103/Physrevlett.109.187603 Negative-U System of Carbon Vacancy in 4H-SiC Y.G. Zhang , Z. Tang , X.G. Zhao , et al ., A neutral oxygen-vacancy center in diamond: A plausible qubit candidate and its spintronic and electronic properties . Appl. Phys. Lett . 105 , 052107 ( 2014 ). doi: 10.1063/1.4892654 http://doi.org/10.1063/1.4892654 A neutral oxygen-vacancy center in diamond: A plausible qubit candidate and its spintronic and electronic properties N.T. Son , A. Henry , J. Isoya , et al ., Electron paramagnetic resonance and theoretical studies of shallow phosphorous centers in3C-,4H-, and 6H-SiC . Phys. Rev. B 73 , 075201 ( 2006 ). doi: 10.1103/PhysRevB.73.075201 http://doi.org/10.1103/PhysRevB.73.075201 Electron paramagnetic resonance and theoretical studies of shallow phosphorous centers in3C-,4H-, and 6H-SiC L. Gordon , A. Janotti , C.G. Van de Walle , Defects as qubits in 3C- and 4H-SiC . Phys. Rev. B 92 , 045208 ( 2015 ). doi: 10.1103/Physrevb.92.045208 http://doi.org/10.1103/Physrevb.92.045208 Defects as qubits in 3C- and 4H-SiC S. Arpiainen , K. Saarinen , P. Hautojarvi , et al ., Optical transitions of the silicon vacancy in 6H-SiC studied by positron annihilation spectroscopy . Phys. Rev. B 66 , 075206 ( 2002 ). doi: 10.1103/Physrevb.66.075206 http://doi.org/10.1103/Physrevb.66.075206 Optical transitions of the silicon vacancy in 6H-SiC studied by positron annihilation spectroscopy C.G. Van de Walle , J. Neugebauer , First-principles calculations for defects and impurities: Applications to III-nitrides . J. Appl. Phys . 95 , 3851 - 3879 ( 2004 ). doi: 10.1063/1.1682673 http://doi.org/10.1063/1.1682673 First-principles calculations for defects and impurities: Applications to III-nitrides A. Lenef , S.C. Rand , Electronic structure of the N-V center in diamond: Theory . Phys. Rev. B 53 , 13441 - 13455 ( 1996 ). doi: 10.1103/PhysRevB.53.13441 http://doi.org/10.1103/PhysRevB.53.13441 Electronic structure of the N-V center in diamond: Theory J.A. Larsson , P. Delaney , Electronic structure of the nitrogen-vacancy center in diamond from first-principles theory . Phys. Rev. B 77 , 165201 ( 2008 ). doi: 10.1103/Physrevb.77.165201 http://doi.org/10.1103/Physrevb.77.165201 Electronic structure of the nitrogen-vacancy center in diamond from first-principles theory F.M. Hossain , M.W. Doherty , H.F. Wilson , et al ., Ab Initio Electronic and Optical Properties of the NV-1 Center in Diamond . Phys. Rev. Lett . 101 , 226403 ( 2008 ). doi: 10.1103/Physrevlett.101.226403 http://doi.org/10.1103/Physrevlett.101.226403 Ab Initio Electronic and Optical Properties of the NV-1 Center in Diamond Y. Tu , Z. Tang , X.G. Zhao , et al ., A paramagnetic neutral VAlON center in wurtzite AlN for spin qubit application . Appl. Phys. Lett . 103 , 072103 ( 2013 ). doi: 10.1063/1.4818659 http://doi.org/10.1063/1.4818659 A paramagnetic neutral VAlON center in wurtzite AlN for spin qubit application 10.1007/s41365-017-0263-2 **This work was supported by the National Science Foundation of China (Nos. 61076089, 11505265 and 61227902) and the Ministry of Education of China (SRF for ROCS, SEM). 2017-01-10 2017-02-24 2017-02-27 2017-06-29 2017-08-01 2021-04-11 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2017 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-017-0263-2 http://dx.doi.org/10.1007/s41365-017-0263-2 . 2017 Nuclear Science and Techniques 08 28