# Defect Processes in Halogen Doped SnO2
## 3 Results
### Optical Properties  
The complex dielectric function can provide important information concerning the polarization mechanisms of the solid. The dominant dispersion/absorption mechanisms in the visible and ultraviolet range are caused by electronic excitations, i.e., transitions from occupied to empty electron levels. The dielectric function can describe these transitions.  
In Figure 5a, the complex dielectric function of undoped SnO\({}_{2}\) is presented. The real part of the dielectric function of the undoped SnO\({}_{2}\) is descended as we increase the energy, reaching a maximum at 8.5 eV. The negative value in the energy range from 16-17 eV  
Figure 4: (**a**) The gap states of the F\({}_{\rm i}\) doped SnO\({}_{2}\); (**b**) The gap states of the Cl\({}_{\rm i}\) doped SnO\({}_{2}\); (**c**) The gap states of Br\({}_{\rm i}\) doped SnO\({}_{2}\); (**d**) The gap states of I\({}_{\rm i}\) doped SnO\({}_{2}\).  
indicates that SnO\({}_{2}\) has metallic properties [49; 50]. The probability of photon absorption is calculated through the imaginary part of the dielectric function. Specifically, we observe two major peaks at 10 eV and at 12.5 eV, which are assigned to the electronic interband transition from O-2p to Sn 5p. The dielectric constant for the undoped case is calculated to 2, which agrees well with the experimental value of 1.6 [49] and similar DFT works predict a value of 2 [50]. In Figure 5b-i, all the dielectric functions for the doped cases are shown. It is evident that in the case of the interstitial doping with F, there is a notable improvement to the dielectric constant as it reaches the value of 3.2 from the real part of the dielectric function. The existence of a major peak at 1 eV can be attributed to the electronic transition of F-2p and the Sn-5p in the conduction band. As regards the other interstitial cases, it is predicted that the dielectric constant is almost unchanged except the I\({}_{1}\): SnO\({}_{2}\), which shows an improvement, and it reaches a value of 2.7. For the substitutional doping cases, in the case of I\({}_{0}\): SnO\({}_{2}\), we calculate that the maximum value of the dielectric constant is achieved, which is 2.4.  
Figure 5: \(Cont.\)  
The calculated refractive index (refer to Figure 6) for the undoped SnO\({}_{2}\) is 1.40. This result is more underestimated than the experimental value of 1.70 [51], but agrees well with the value of other DFT studies [50]. The extinction coefficient can be described through the imaginary part of the refractive index, k. The major peak at the imaginary part of the undoped case is located at 12.5 eV. For the interstitial cases, we calculated that F\({}_{\text{i}}\) shows an increase at the refractive index and reaches a value of 1.8. [PERSON] et al. [52] experimentally predicted that the refractive index of F: SnO\({}_{2}\) was between 1.85-2.2, which agrees well with the present study. For the substitutional cases, the refractive index has its maximum value of 1.51 in the case of Io: SnO\({}_{2}\). The increase of the refractive index for Fi and Io boosts the antireflectivity (AR) of SnO\({}_{2}\) and might be beneficial for application in energy harvesting devices.  
Figure 6: _Cont._  
Lastly, the absorption co-efficiency is presented in Figure 7. The major peaks range from 5 eV to 22 eV, and it is in good agreement with previous DFT studies [50]. The absorption of pure SnO\({}_{2}\) starts at 380 nm, which is somewhat underestimated than the experimental value, which is around 400 nm [52]. It is seen that in the visible region (1.78-3.12 eV), I doped SnO\({}_{2}\) has the highest absorption both for the interstitial and the substitutional positions.