# Nitrogen-Related Defects in Crystalline Silicon
## 2 Background Information of N-Related Defects in Si  
### Nitrogen Substitutional (N\({}_{s}\)) and Interstitial (N\({}_{i}\)) Defects  
In the substitutional configuration a Si atom is substituted with a N atom. N is a Group V impurity. However, unlike the other elements of this group (phosphorous (P), arsenic (As), antimony (Sb), and bismuth (Bi)), which possess on-site T\({}_{\rm d}\) symmetry, N is trigonally distorted from the regular tetrahedral site preserving C\({}_{3v}\) symmetry along the <111> axis, as determined using EPR measurements. An EPR signal Si-SL5 was associated with a N substitutional defect [9; 36; 38]. EPR studies have determined that the off-center substitutional N is more stable than the on-center substitutional N [36; 58; 59; 60]. Interestingly, an argument for a metastable on-center configuration was put forward in order to explain the hyperfine splitting observed in the EPR spectra with increased temperature, and a symmetry breaking mechanism T\({}_{\rm d}\)\(\rightarrow\) C\({}_{3v}\) was proposed [32; 60]. An infrared band at 653 cm\({}^{-1}\) (at 300 K) was ascribed [61] to the N's substitutional impurity. Additionally, unlike the other members of the group that introduce shallow levels in the forbidden gap, N behaves as a deep-level impurity. Indeed, DLTS measurements have found that a single donor level at E\({}_{\rm c}\)\(-\)0.31 eV and a single acceptor level at E\({}_{\rm c}\)\(-\)0.08 eV should be attributed [62] to the N's substitutional impurity. Furthermore, a single acceptor level at E\({}_{\rm c}\)\(-\)0.64 eV and a double acceptor level at E\({}_{\rm c}\)\(-\)0.34 eV were also associated [33] with the N's substitutional impurity.  
Recent DFT calculations by [PERSON] et al. [54] considered bonding between the N\({}_{\rm s}\) (refer to Figure 1a) and the Si atoms by plotting a charge density map (refer to Figure 1c). The strong N-Si bonds have, as expected, shorter N-Si bond lengths and negative Bader charge on N\({}_{\rm s}\) in the NSi\({}_{4}\) tetrahedral unit (refer to Figure 1b) [54]. At this point, the importance of the significantly higher electronegativity of N (3.04) as compared to Si (1.90) should be stressed. It is the reason why, in the Bader charge analysis, the N\({}_{\rm s}\) atom gains nearly three electrons from the nearest neighbor Si atoms (refer to Figure 1b) [54]. The band-decomposed charge density plot for N\({}_{\rm s}\) (refer to Figure 1d) shows the electron density more clearly [54]. In the DOS plots, the states appearing in the bandgap are primarily due to the s electrons of N\({}_{\rm s}\). Accordingly, the \(p\)-states of N\({}_{\rm s}\) are localized with the lattice as they are in the valence band (refer to Figure 1e,f).  
For the N\({}_{\rm i}\) location within the Si lattice, several sites have been investigated theoretically, for instance, investigating the split-interstitial site, the bond center site, the hexagonal site, and the tetrahedral site (refer to Figure 2) [49; 51; 63]. The more stable configuration for the neutral N\({}_{\rm i}\) interstitial defect is a slightly distorted \(<\)001\(>\) split-interstitial site, where the ideal C\({}_{\rm v}\) symmetry has been lost through a slight displacement of the core Si atom along a \(<\)110\(>\) axis [50]. In this configuration, the N\({}_{\rm i}\) has a similar formation energy as the N\({}_{\rm s}\)[63]. An EPR signal labeled Si-NL26 was tentatively associated [37] with a neutral interstitial N. DFT calculations have reported [50] three LVMs of the N interstitial defect at 550, 773, and 885 cm\({}^{-1}\). Additionally, it was found [63] that the defect possesses a donor level at E\({}_{\rm v}\)\(+\)0.5 eV and an acceptor level at E\({}_{\rm c}\)\(-\)0.2 eV in agreement with other previous studies [51].  
Figure 1: (**a**) The N\({}_{\rm s}\) in the Si lattice; (**b**) tetrahedral units comparing Bader charges, bond distances, and angles; (**c**) charge density; (**d**) band-decomposed charge density plot for N\({}_{\rm s}\); (**e**) total DOS, and (**f**) atomic DOS plot of N [54].