Defect Processes in Halogen Doped SnO 2

: In the present study, we performed density functional theory calculations (DFT) to investigate structural changes and their impact on the electronic properties in halogen (F, Cl, Br, and I) doped tin oxide (SnO 2 ). We performed calculations for atoms intercalated either at interstitial or substitutional positions and then calculated the electronic structure and the optical properties of the doped SnO 2 . In all cases, a reduction in the bandgap value was evident, while gap states were also formed. Furthermore, when we insert these dopants in interstitial and substitutional positions, they all constitute a single acceptor and donor, respectively. This can also be seen in the density of states through the formation of gap states just above the valence band or below the conduction band, respectively. These gap states may contribute to signiﬁcant changes in the optical and electronic properties of SnO 2 , thus affecting the metal oxide’s suitability for photovoltaics and photocatalytic devices. In particular, we found that iodine (I) doping of SnO 2 induces a high dielectric constant while also reducing the oxide’s bandgap, making it more efﬁcient for light-harvesting applications.


Introduction
SnO 2 is a wide bandgap, n-type semiconductor that adopts a tetragonal crystal structure [1][2][3][4][5][6]. Doping is also used to increase further its electrical conductivity as well as its transparency in the visible region [4][5][6]. SnO 2 is mainly used as an opacifier of glazes [1], polishing powder [2], protective polymer coating [3], as a functional material in the solar cell technology [4], transparent conducting oxide [5,6] and gas sensor [7]. Recently Zhao et al. [8] demonstrated that a NO gas sensor based on Sn 2 O 3 has an improved selectivity to NO, NO 2 , and CO gases [8]. Wang et al. [9] have shown that Sn 3 O 4 in ultrathin SnO 2 nanosheets exhibits great performance for Li-ion storage for battery technology. Furthermore, there are many experiments that examine the effect of halogen doping in SnO 2 thin films with fluorine (F) being the most commonly used dopant because it significantly increases the conductivity and transparency of SnO 2 , hence making it appropriate for use as the transparent electrode in several classes of optoelectronics [10][11][12][13][14]. These include the sol-gel preparation of F:SnO 2 nanostructures [11], studies on the structural characteristics, and the changes through the fluorine doping using X-ray diffraction (XRD) techniques [12] as well as deposition methods, such us spray pyrolysis [13] and chemical vapor deposition [14,15] for producing the F:SnO 2 . Regarding the F doping mechanism, several studies on F-doped SnO 2 nanopowders using X-ray diffraction (XRD) analysis, transmission electron microscopy (TEM), X-ray photoelectron spectroscopy (XPS), and Fourier transformed infrared spectroscopy (FTIR) [16] revealed that at low concentration, F atoms occupy oxygen vacancy sites as substitutional dopants, but for higher concentrations F atoms site in interstitial positions in the host lattice. Moreover, few reports have also demonstrated the effects of chlorine (Cl), bromine (Br), and I doping in SnO 2 . Abass et al. [17][18][19], using several experiments with emphasis on optical and electrical properties, found pronounced improvements in these properties by halogen doping. Agashe et al. [20] also studied the electrical properties of sprayed deposited SnO 2 films and showed that when replacing F dopants with Br, conductivity was reduced.
Except for experimental studies, there are also many theoretical research efforts using DFT that examine the role of defects such as F, Sb, and Cl in substitutional positions in SnO 2 [21][22][23][24][25][26][27]. They revealed that such doping contributes to the formation of single donor states; however, the effect of interstitially doped SnO 2 has not been studied yet. Additionally, the influence of other halogen dopants (besides F, Cl) in SnO 2 and the corresponding changes in the oxide's band structure and optical properties have not been systematically investigated yet. In most previously published DFT studies, the bandgap is significantly underestimated within the range 1 eV-2 eV [27][28][29]. This is a common problem when DFT calculations on wide bandgap semiconductors are conducted [30,31]. As a result, a number of methods have been developed in order to calculate more accurately the bandgap of these materials, with the Hubbard + U correction method and the computationally demanding but more accurate hybrid pseudopotentials being the most commonly used. Many researchers have applied the Hubbard + U method for the d orbitals of Sn, but still, the band gap was substantially underestimated (2.5 eV). In the case of hybrid pseudopotentials, although the band gap reaches the correct experimental value of 3.7 eV [32], the computational cost is very high, and this is why the majority of these researchers use a small number of atoms in their unit cells [33].
In the present study, we investigate the halogen doping of the bulk SnO 2 using DFT in order to examine changes in the electronic structure as well as improvements in the photocatalytic properties of SnO 2 . To achieve such an endeavor, we apply hybrid DFT calculations. With this method, the bandgap reaches the correct value of 3.35 eV and it is in good agreement with similar DFT works [34]. We examined all the possible defect sites for the halogen dopants and we also calculated the minimum energies for these dopants being at interstitial positions and the changes in the electrical properties. Using the total density of states (DOS) and the projected density of states (pDOS), we analyzed the minimum energy sites of the defects and their effect on the bandgap. Furthermore, we predicted the optical properties of all the doping cases and we compared our results with the available experimental data.

Methodology
For the DFT calculations, we used the Cambridge Serial Total Energy Package (CASTEP) [35,36]. DFT calculations were performed using the Local Density Approximation (LDA) exchange-correlation Functional [37] with ultrasoft pseudopotentials [38]. The cutoff energy that met the convergence criteria was chosen at 800 eV and also for the geometry optimization of a 48 atom supercell, a 2 × 2 × 3 Monkhorst-Pack (MP) k-points set [39] was selected with the Broyden-Fletcher-Goldfard-Shanno (BFGS) method. As it was previously described, to consider the effects of the localized electrons, we used the hybrid functional PBE0 [39], which overcomes the LDA band gap error. Lastly, the DOS calculations were performed using a 3 × 3 × 3 k points mesh and the pDOS were performed using a k point mesh of 7 × 7 × 7. The convergence criteria for our analyses were chosen as 0.05 eV/Å for the Max force tolerance, 0.001 Å for the Max displacement tolerance, 0.1 GPa for the Max stress tolerance, and 2.0 × 10 −5 eV/atom for the SCF tolerance.

Structural Properties
SnO 2 has a rutile structure and it belongs to the space group of P4 2 /mmm (space group no 136) of the tetragonal system. The calculated lattice parameters of the unit cell are a = b = 4.717 Å and c = 3.189 Å (α = β = γ = 90 • ), in good agreement with the experimental results (a = b = 4.737 Å and c = 3.186 Å) [40]. In Figure 1a-h, the geometry of doped SnO 2 structures is presented for the examined dopants (F, Cl, Br, and I) in substitutional and interstitial positions, where in each case the local distortion of the lattice is shown. The respective lattice parameters are presented in Table 1. An increase of cell dimensions due to the halogen incorporation in the SnO 2 lattice is observed, as the substitution of oxygen with a larger atom (all halogens have a larger atomic radius than oxygen) will distort the lattice, increasing total volume, more so in the case of interstitial doping. It is interesting to note that in the case of iodine at an interstitial position, I i , the cell increases in volume as both a and b increase, but the c parameter decreases. The anisotropic changes in the lattice parameters upon the introduction of the I atom is due to the reduction in the c-direction of the Sn-Ii bond length (3.31 Å) as compared to the Sn-I bond before our optimization (3.40 Å).

Structural Properties
SnO2 has a rutile structure and it belongs to the space group of P42/mmm (space group no 136) of the tetragonal system. The calculated lattice parameters of the unit cell are a = b = 4.717 Å and c = 3.189 Å (α = β = γ = 90°), in good agreement with the experimental results (a = b = 4.737 Å and c = 3.186 Å) [40]. In Figure 1a-h, the geometry of doped SnO2 structures is presented for the examined dopants (F, Cl, Br, and I) in substitutional and interstitial positions, where in each case the local distortion of the lattice is shown. The respective lattice parameters are presented in Table 1. An increase of cell dimensions due to the halogen incorporation in the SnO2 lattice is observed, as the substitution of oxygen with a larger atom (all halogens have a larger atomic radius than oxygen) will distort the lattice, increasing total volume, more so in the case of interstitial doping. It is interesting to note that in the case of iodine at an interstitial position, Ii, the cell increases in volume as both a and b increase, but the c parameter decreases. The anisotropic changes in the lattice parameters upon the introduction of the I atom is due to the reduction in the c-direction of the Sn-Ii bond length (3.31 Å) as compared to the Sn-I bond before our optimization (3.40 Å).

Electrical Properties
We examine the effect of halogen doping on the electronic properties and band gap of SnO2 by calculating the Density of States (DOS) of perfect and doped SnO2.
The bandgap of the undoped SnO2 is calculated using the PBE0 functional, at 3.35 eV ( Figure 2a) close (but still underestimated) to the experimental value of 3.7 eV [32], in agreement with other theoretical studies [41][42][43]. As it is observed from Figure 2b, the F interstitial in SnO2 gives rise to energy states inside the band gap, near the band edges with a small reduction of 0.2 eV of the bandgap width, calculated at 3.12 eV (Figure 2b). When F is situated in an O-substitutional position, the bandgap is notably reduced to 2.90 eV without the presence of gap states ( Figure 2c).

Electrical Properties
We examine the effect of halogen doping on the electronic properties and band gap of SnO 2 by calculating the Density of States (DOS) of perfect and doped SnO 2 .
The bandgap of the undoped SnO 2 is calculated using the PBE0 functional, at 3.35 eV (Figure 2a) close (but still underestimated) to the experimental value of 3.7 eV [32], in agreement with other theoretical studies [41][42][43]. As it is observed from Figure 2b, the F interstitial in SnO 2 gives rise to energy states inside the band gap, near the band edges with a small reduction of 0.2 eV of the bandgap width, calculated at 3.12 eV (Figure 2b). When F is situated in an O-substitutional position, the bandgap is notably reduced to 2.90 eV without the presence of gap states (Figure 2c).

Electrical Properties
We examine the effect of halogen doping on the electronic properties and band gap of SnO2 by calculating the Density of States (DOS) of perfect and doped SnO2.
The bandgap of the undoped SnO2 is calculated using the PBE0 functional, at 3.35 eV (Figure 2a) close (but still underestimated) to the experimental value of 3.7 eV [32], in agreement with other theoretical studies [41][42][43]. As it is observed from Figure 2b, the F interstitial in SnO2 gives rise to energy states inside the band gap, near the band edges with a small reduction of 0.2 eV of the bandgap width, calculated at 3.12 eV (Figure 2b). When F is situated in an O-substitutional position, the bandgap is notably reduced to 2.90 eV without the presence of gap states (Figure 2c).  Regarding the Cl doping, in the case of interstitial doping, Cli: SnO2, the bandgap is further reduced to 2.85 eV with gap states present near the valence band. When Cl is at an O-substitutional position, Clo, a more significant bandgap reduction occurs, to 2.70 eV (Figure 2d,e). In a previous DFT research on F and Cl doped TiO2 [44], we also observed a significant bandgap reduction when a Cl atom was inserted in an interstitial position.
Regarding the effect of a Br interstitial intercalation (Figure 2f), the calculated bandgap is reduced to 2.90 eV with gap states near the valence band edge (minimum) are created. In comparison, in the case of substitutional Bro, the bandgap reaches a value of Regarding the Cl doping, in the case of interstitial doping, Cl i : SnO 2 , the bandgap is further reduced to 2.85 eV with gap states present near the valence band. When Cl is at an O-substitutional position, Cl o , a more significant bandgap reduction occurs, to 2.70 eV (Figure 2d,e). In a previous DFT research on F and Cl doped TiO 2 [44], we also observed a significant bandgap reduction when a Cl atom was inserted in an interstitial position.
Regarding the effect of a Br interstitial intercalation (Figure 2f), the calculated bandgap is reduced to 2.90 eV with gap states near the valence band edge (minimum) are created. In comparison, in the case of substitutional Br o , the bandgap reaches a value of 2.71 eV ( Figure 2g). It is evident that regarding the electronic structure, Br doping has the same effect as Cl doping in terms of bandgap reduction.
Lastly, I interstitial and substitutional doping is examined. We calculated that the bandgap is reduced to a value of 2.62 eV for the interstitial and 2.61 eV for the substitutional case, respectively, while states near the valence band are again presented. In this case, the substitutional doping has a smaller bandgap value than the interstitial case. This can be attributed to the states that are created to the valence band edge, which is due to the hybridization of the 2p orbitals of the nearest oxygen atom with the iodine 5p orbitals. As iodine is larger than the other halogens, even in the substitutional position, its orbitals are mixing with the nearest oxygen atom, giving rise to the states near the valence band. These results indicate that halogen interstitial dopants serve as single acceptors when they are intercalated within the SnO 2 host lattice. Such gap states near the oxide's valence band maximum and those near the conduction band position may act as shallow and deep acceptors, respectively, hence contributing to performance enhancements of devices based on doped SnO 2 . However, the gap states may also act as traps for the photogenerated carriers in specific photovoltaic devices such as organic and halide perovskite photovoltaics, thus decreasing the device photocurrent and overall performance.
However, the incorporation of substitutional halogen atoms in oxygen position does not introduce any gap states. This is in stark contrast with the intercalation of interstitial halogens that create some localized perturbations upon the upper valence band and the conduction band of the material. That implies free electrons' presence contributing to the n-type conductivity, in accordance with experimental observations [45][46][47][48]. The halogen substitutional doping is seen to induce states inside or near the valence band. We believe that this can be explained because in the substitutional doping, the halogen orbitals are not mixing with the nearest Sn-5p or O-2p orbitals. As a result, no hybridized mid-gap states arise.
In Table 2 we have summarized our results. According to these calculations, the minimum value of the calculated bandgap is 2.61 eV for the case of I o doping. It is therefore suggested as the most effective of the halogen SnO 2 dopants for photocatalytic applications. Therefore, it is suggested that this type of doping can be used to develop better photocatalysts.
In Figures 3 and 4, the pDOS for the doped SnO 2 are shown. From the pDOS, we can gain important information about the gap states and the contribution of each element's orbitals to the valence and conduction band. As seen in Figure 3a, which shows the pDOS of the plain SnO 2 , the valence band is mainly consisting of O-2p and Sn-5p orbitals, whereas the conduction band is created from the Sn-5s, Sn-5p, O-2s, and O-2p. This is in good agreement with previous theoretical studies [41,42]. Referring to Figure 3b, we see that F doped SnO 2 has a similar valence and conduction band structure with the undoped SnO 2 with a small deviation coming from the contribution of fluorine in the doped oxide. Focusing on the gap states formed near the valence band in the F-doped material, calculations show that it is created due to the hybridization of O-2p with F-2p orbitals (refer to Figure 4a). This is the same phenomenon that we predicted to occur in the case of TiO 2 [43] upon doping with interstitial F atoms. Appl. Sci. 2021, 11, x FOR PEER REVIEW 7 of 14   Similarly, in Figure 4b-d the rise of gap states is mainly created by the O-2p and Cl-2p and O-2p and Br -4p and I-5p. This probably indicates that the formation of mid-gap states in halogen doped n-type metal oxides such as SnO2 and TiO2 may have a universal origin. In any case, further investigation is needed, which is beyond the scope of the present manuscript.

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 SnO2 is presented. The real part of the dielectric function of the undoped SnO2 is descended as we increase the energy,   Similarly, in Figure 4b-d the rise of gap states is mainly created by the O-2p and Cl-2p and O-2p and Br -4p and I-5p. This probably indicates that the formation of mid-gap states in halogen doped n-type metal oxides such as SnO2 and TiO2 may have a universal origin. In any case, further investigation is needed, which is beyond the scope of the present manuscript.

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 SnO2 is presented. The real part of the dielectric function of the undoped SnO2 is descended as we increase the energy, Similarly, in Figure 4b-d the rise of gap states is mainly created by the O-2p and Cl-2p and O-2p and Br-4p and I-5p. This probably indicates that the formation of mid-gap states in halogen doped n-type metal oxides such as SnO 2 and TiO 2 may have a universal origin. In any case, further investigation is needed, which is beyond the scope of the present manuscript.

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 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 i : SnO 2 , which shows an improvement, and it reaches a value of 2.7. For the substitutional doping cases, in the case of I o : SnO 2 , we calculate that the maximum value of the dielectric constant is achieved, which is 2.4.
Appl. Sci. 2021, 11, x FOR PEER REVIEW 9 of 14 reaching a maximum at 8.5 eV. The negative value in the energy range from 16-17 eV indicates that SnO2 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 Ii: SnO2, which shows an improvement, and it reaches a value of 2.7. For the substitutional doping cases, in the case of Io: SnO2, we calculate that the maximum value of the dielectric constant is achieved, which is 2.4.  The calculated refractive index (refer to Figure 6) for the undoped SnO2 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 Fi shows an increase at the refractive index and reaches a value of 1.8. Afify et al. [52] experimentally predicted that the refractive index of F: SnO2 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: SnO2. The increase of the refractive index for Fi and Io boosts the antireflectivity (AR) of SnO2 and might be beneficial for application in energy harvesting devices. 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 i shows an increase at the refractive index and reaches a value of 1.8. Afify 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. The calculated refractive index (refer to Figure 6) for the undoped SnO2 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 Fi shows an increase at the refractive index and reaches a value of 1.8. Afify et al. [52] experimentally predicted that the refractive index of F: SnO2 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: SnO2. The increase of the refractive index for Fi and Io boosts the antireflectivity (AR) of SnO2 and might be beneficial for application in energy harvesting devices.  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 SnO2 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- 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.
3.12 eV), I doped SnO2 has the highest absorption both for the interstitial and the substitutional positions.

Conclusions
DFT calculations were performed for halogen doped SnO2 and the effects of the exact kind of doping on the bandgap value and electronic properties were discussed. In this research, interstitial and substitutional halogen defects were examined. In all cases, it was observed that gap states were created from hybridization of O-2p with halogen 1s orbitals. Such energy states are beneficial for the oxide's photocatalytic activity as they significantly reduce the optical band gap concerning that of undoped SnO2. They can also serve as charge transport paths in a certain type of optoelectronic device, whereas this might be detrimental for the application of halogen-doped oxide as electron transport material in other classes of photovoltaic devices. Iodine doped SnO2 has the lowest bandgap value of 2.60 eV and it is one of the lowest values reported for SnO2. Interestingly, when iodine resides in an oxygen site, it has a better refractive index and absorbance than the other halogen dopants. This makes it a suitable dopant candidate for SnO2-based energy harvesting devices.

Conclusions
DFT calculations were performed for halogen doped SnO 2 and the effects of the exact kind of doping on the bandgap value and electronic properties were discussed. In this research, interstitial and substitutional halogen defects were examined. In all cases, it was observed that gap states were created from hybridization of O-2p with halogen 1s orbitals. Such energy states are beneficial for the oxide's photocatalytic activity as they significantly reduce the optical band gap concerning that of undoped SnO 2 . They can also serve as charge transport paths in a certain type of optoelectronic device, whereas this might be detrimental for the application of halogen-doped oxide as electron transport material in other classes of photovoltaic devices. Iodine doped SnO 2 has the lowest bandgap value of 2.60 eV and it is one of the lowest values reported for SnO 2 . Interestingly, when iodine resides in an oxygen site, it has a better refractive index and absorbance than the other halogen dopants. This makes it a suitable dopant candidate for SnO 2 -based energy harvesting devices.