## 3 Results and Discussion
### Single Neutral Silicon Vacancy in the H-, O-, or N-Terminated C (001) Surfaces
#### 3.3.4 Density of States  
Density of states (DOS) and partial density of states (pDOS) figures can usually present a visual and quick qualitative picture for us to know about the electronic structures of a material and sometimes they can be compared with experimental spectroscopic results directly. The DOS describes the number of different states at a particular energy level that electrons are allowed to occupy. The pDOS corresponds to the relative contribution of a particular atom or orbital to the total DOS. DOS and pDOS can indicate whether any surface or defect states are introduced into the band gap under H, O, or N termination and which type of atoms they were from. The impurity energy level in the band gap is detrimental to the PL performance of SiV\({}^{0}\) and can cause its bleaching or blinking [57]. In the following section, we will analyze the pDOS of different surface states. Figure 6a-c shows the pDOS of the entire layer of according surface termination species, its Si and the six nearest C atoms around Si (denoted as 6C) and the eighth C layer consisting of 16 C atoms as an approximation of bulk diamond (denoted as L8). Figure 6d shows the pDOS of Si, the six nearest C atoms around it (denoted as 6C) and 16C atoms that are selected far away from Si in a 216-atom bulk diamond containing a single SiV\({}^{0}\) (denoted as Bulk-C), as reference. By comparing Figure 6a with Figure 6d, we can see in Figure 6a that the six C atoms around the Si of the H-terminated diamond (001) surface yielded states above its VBM, and its surface absorbate, H, also introduced severe states deep down in its conduction band minimum (CBM), into the middle of its band gap. All of these are detrimental to the fluorescence of SiV\({}^{0}\) color centers and can cause bleaching and blinking. We can also see that H atoms contributed some low states in the valence band and conduction band. Even worse, the six C atoms around Si and its absorbate layer of O clearly created many states both above its VBM and deep down in its CBM, into the middle of its band gap under O termination, as depicted in Figure 6b. This indicates that a single SiV\({}^{0}\) in the O-terminated diamond (001) surface was not suitable for functioning as a single-photon emitter. In addition, we found that O atoms contributed some low states in the conduction band and some relatively high states in the valence band. Interestingly, Figure 6c showed that both the six C atoms around Si and the surface absorbate layer of N in the N-terminated diamond (001) surface did not change its DOS significantly, as compared with the bulk diamond in Figure 6d, but only introduced a small number of states above its VBM and below its CBM, which were almost negligible. Therefore, the N-terminated diamond (001) surface can possibly function as a suitable container for single SiV\({}^{0}\) for application as a single-photon source. In addition, we can see that the states contributed from N atoms are relatively high, and mainly positioned in the valence band and conduction band. Figure 6: The pDOS of configurations when a single SiV\({}^{0}\) is positioned (**a**) in the third to fourth layers of an H-terminated (_configuration 2_) diamond (001) surface; (**b**) in the second to third layers of an O-terminated diamond (001) surface; (**c**) in the second to third layers of an N-terminated (_configuration 2_) diamond (001) surface; and (**d**) in the bulk diamond, as reference. Figure 6 showed that the Si of SiV\({}^{0}\) in bulk diamond, or near the surface of H-, O-, or N-terminated diamond (001) surfaces, did not introduce many states into their band gap, and thus do not have a negative impact on their own PL performance. To further confirm our conclusions, more experimental investigations are needed. Furthermore, similar to the (001) surface, the (111) surface is also considered promising for the artificial synthesis of diamond.