## 3 Results and Discussion
### Single Neutral Silicon Vacancy in the H-, O-, or N-Terminated C (001) Surfaces
#### 3.3.2 Binding Energies  
Table 2 represents the binding energies of SiV\({}^{0}\) under H, O, or N termination in diamond (001) surfaces. Under H termination, we can see that the composition of _configuration 1_, with its original Si placed in the fourth C layer and its V in the fifth C layer, possessed the largest binding energy of 5.61 eV, yet it did not have the lowest formation energy. The configuration with the lowest formation energy was in the third to fourth layers, _configuration 2_, the binding energy of which was the second largest at 5.31 eV when its original V was in the third C layer, with Si in the fourth C layer, and smaller at 3.32 eV the other way around. From this phenomenon, we concluded that despite having the same formation energy, it is more stable for this composition to form with its Si in the fourth C layer and its V in the third C layer. To achieve this, the practical production process can dope the Si impurity first in the fourth C layer, prior to the introduction of a vacancy to its upper layer. For O-terminated surfaces, the configuration in the second to third layers, which also possessed the lowest formation energy, indicated the largest binding energy of 6.55 eV when its original Si was in the second C layer and V was in the third. When its original V was placed in the second and Si in the third layer, it had a smaller binding energy of 4.83 eV. This indicated that to gain a more stable SiV \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**H-terminated**} & \multicolumn{4}{c}{**O-terminated**} & \multicolumn{4}{c}{**N-terminated**} \\ \cline{2-10}  & \multicolumn{2}{c}{**1**} & \multicolumn{2}{c}{**2**} & \multicolumn{4}{c}{**1**} & \multicolumn{2}{c}{**2**} \\ \cline{2-10}  & **Si** & **V** & **Si** & **V** & **Si** & **V** & **Si** & **V** & **Si** & **V** \\ \hline
**2-3** & 1.95 & 4.30 & 3.79 & 2.68 & 6.55 & 4.83 & 7.80 & 3.81 & 3.63 & 5.26 \\
**3-4** & 4.92 & 4.52 & 3.32 & 5.31 & 5.13 & 5.47 & 6.27 & 5.84 & 3.75 & 4.58 \\
**4-5** & 5.61 & 5.03 & 3.74 & 4.22 & 5.59 & 5.27 & 5.29 & 5.01 & & \\
**5-6** & 4.88 & 4.99 & & & 5.08 & 5.20 & 5.06 & 4.79 & 5.42 & 5.62 \\
**6-7** & 4.70 & 4.53 & 5.13 & 5.12 & 5.27 & 5.22 & 4.94 & 5.15 & 5.31 & 5.24 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Binding energies (eV) of different SiV\({}^{0}\) configurations under completely H-, O-, or N-terminated diamond (001) surfaces. Numbers \(1\) and \(2\) in the second row refer to the configurations depicted in Figure 2. Si (V) in the third row represents SiV\({}^{0}\) in a specific position, created with its original Si (V) in the upper layer and its V (Si) in the lower layer. configuration, we can introduce Si in the second C layer before forming a single vacancy in the lower layer of Si. Regarding N termination, the configuration with the lowest formation energy, which was observed in the second to third layers, _configuration 2_, did not have the largest binding energy. When its original V was placed in the second C layer and Si in the third, its binding energy was larger at 5.26 eV, and the other way around led to a smaller binding energy of 3.63 eV. Therefore, V should be introduced in the second C layer after doping Si in the third C layer. The configuration with the largest binding energy of 7.80 eV was situated in the second to third layers, _configuration 1_, when its Si was originally located in the second C layer and V in the third. According to formation energies, we can see that Si generally indicated a lower formation energy than SiV near H-, O-, or N-terminated diamond (001) surfaces. As a result, during the fabrication of SiV near diamond surfaces, whether using in situ doping during the CVD process, ion implantation or laser ablation, more substitutional Si impurities will arise than SiV centers.