Structural and electronic properties of SnO2 doped with non-metal elements

Crystal structure and electronic properties of SnO2 doped with non-metal elements (F, S, C, B, and N) were studied using first-principles calculations. The theoretical results show that doping of non-metal elements cannot change the structure of SnO2 but result in a slight expansion of the lattice volume. The most obvious finding from the analysis is that F-doped SnO2 has the lowest defect binding energy. The doping with B and S introduced additional defect energy levels within the forbidden bandgap, which improved the crystal conductivity. The Fermi level shifts up due to the doping with B, F, and S, while the Fermi level of SnO2 doped with C or N has crossed the impurity level. The Fermi level of F-doped SnO2 is inside the conduction band, and the doped crystal possesses metallicity. The optical properties of SnO2 crystals doped with non-metal elements were analyzed and calculated. The SnO2 crystal doped with F had the highest reflectivity in the infrared region, and the reflectance of the crystals doped with N, C, S, and B decreased sequentially. Based on this theoretical calculations, F-doped SnO2 is found to be the best photoelectric material for preparing low-emissivity coatings.


Structural and electronic properties of SnO 2 doped with non-metal elements
Introduction Thin film solar cells are devices that convert solar energy into electrical energy. Transparent conductive films (TCFs) are a thin film material with both conductive capabilities and high transmittance in the visible light range (300-800 nm) [1][2][3]. TCFs serve as the front electrode of thin film solar cells. Up to now, the solar energy conversion efficiency is about 23.3% [4], and it is important to increase the photovoltaic power generation efficiency, as well as the performance of the front electrode.
The intrinsic semiconductor SnO 2 is not conductive due to the absence of free carriers. However, the bandgap of 3.6 eV of SnO 2 makes it a potentially ideal material for transparent electrode films. It had been proved that the doping of heteroatoms to replace Sn or O can lead to more carriers or holes. Therefore, extensive research works has been done examining different doping elements. Doped tin oxide thin film have been widely used in the fields of thin film solar cell electrodes, electronic display devices, and gas sensors. Also doped SnO 2 been used for energy-saving low-emissivity glass coatings due to low resistivity, high transmittance of visible light, good thermal stability, acid-base corrosion resistance, high material hardness, and easiness of preparation processes [5]. Non-metal atoms, such as fluorine (F) and nitrogen (N), were proved to be proper elements for doping. After doping with heteroatoms, the preferred orientation, optical properties, and electrical properties of SnO 2 film are improved.
Analysis of the electrical properties of SnO 2 films doped with different non-metal elements showed that the resistance of SnO 2 films doped with N was higher [6][7][8] than that of SnO 2 doped with other elements. Nguyen successfully prepared p-type N-doped SnO 2 films using magnetron sputtering [9]. The results show that the SnO 2 films were n-type semiconductors, and the concentration of free carriers in the film increased as the temperature for sedimentation increased. Also, p-type semiconductors were successfully prepared from N-doped SnO 2 films. Through Al/N co-doping, a p-type SnO 2 semiconductor thin film with excellent electrical properties was prepared. The resistivity, hole concentration and hole mobility were 7.1 × 10 −3 Ω·cm, 6.24 × 10 19 cm −3 and 14.1 cm 2 ·V −1 ·s −1 , respectively [8]. Doping SnO 2 with F (substituting O) can effectively increase the carrier concentration and improve the conductivity. Majumder successfully prepared SnO 2 :F thin films using spray pyrolysis with SnF 2 as the precursor. By adjusting the concentration of the precursor solution, doped SnO 2 films with different properties were obtained. When the concentration of the precursor solution was adjusted to 0.15 M and the substrate temperature was 773 K, a film with a resistivity of 1.2 × 10 −4 Ω·cm was obtained [10]. Theoretical calculations, based on first principles, show that the doping of N into the SnO 2 crystal structure can introduce oxygen vacancies, and thus, increase the charge density of the Sn sites. The replacement of O with N can simultaneously decrease the release of CO 2 .
While there are reports on experiments regarding the doping of SnO 2 with non-metal elements, the mechanism of the effect of non-metal element doping on the performance of SnO 2 is not yet clear. In recent years, many researchers used first-principles calculations to scrutinize the doping of SnO 2 with non-metal elements such as F [11,12] and S [13]. The results show that the optical and electrical properties of SnO 2 thin films can be changed by doping with different elements. However, the calculation conditions used in these works are uniform, so it is difficult to compare the effects of different doping elements. Also, some results are even inconsistent. We selected several nonmetal atoms (N, C, B, F, and S) with an atomic radius similar to that of O to dope SnO 2 . The calculations were carried out with the CASTEP software. In this paper, density functional theory (DFT) is used to analyze electronic structure and optical properties of SnO 2 doped with non-metal elements.

Crystal Structure Model and Calculation Method
The SnO 2 crystal has a tetragonal structure with space group P4 2 /mnm. There are six O 2− ions as nearest neighbors of each Sn 4+ site, and three Sn 4+ ions as nearest neighbors of each O 2− ion. Hence, the coordination numbers for Sn and O are six and three, respectively. The CASTEP package was used to construct a 3 × 2 × 1 SnO 2 supercell. To study the effect of non-metal element doping on the structure of SnO 2 , N, C, B, F, or S was used to replace one O atom in the supercell. The model diagram of doped SnO 2 is shown in Figure 1. The crystal structure optimization and electronic structure of the doped SnO 2 cell were obtained through the CASTEP program based on DFT. The Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) was selected as the exchange-correlation functional. The interaction between inner  The valence electronic configuration in the system are Sn 5s 2 5p 2 , O 2s 2 2p 4 , N 2s 2 2p 3 , C 2s 2 2p 2 , B 2s 2 2p 1 , and F 2s 2 2p 6 , S 3s 2 3p 4 . The calculation parameters of the doping system were as follows: The plane waves cut-off energy is 571.4 eV, the Brillouin zone k-space was divided by 2 × 3 × 8, the convergence accuracy of each atom was 10 −5 eV/atom, the internal stress between atoms was less than 0.05 GPa, and the atom displacement was less than 0.0001 nm.

Results and Discussion
Structural optimization Table 1 shows the results of geometric optimization of the crystal structure of SnO 2 doped with non-metal elements. After replacing one O atom in SnO 2 , the crystal structure is distorted and the volume expands. The atomic radius of S is much larger than that of the other doping atoms resulting in a volume expansion of 8.315%. The lattice expansion rate also decreases in the sequence B > C > N. However, the F-doped SnO 2 has a larger volume expansion. Therefore, it is necessary to analyze the bond formation before and after F atom doping, as shown in Table 2. The population value is usually used to present the bonding characteristics of crystals. In general, a strong covalent bond shows a high population value, while a strong ionic bond is characterized by a low value. The results in Table 2 reveal that after doping with heteroatoms, the population value of the Sn-O bond decreased, indicating that it to be more ionic. The population value of the Sn-F chemical bond is the lowest with only 0.125, showing strong iconicity, obvious electron localization, and a high electron affinity. The chemical bonds of other elements (C, B, N) and Sn elements exhibit the characteristics of covalent bonds. Therefore, SnO 2 doped with F element exhibits an abnormal lattice expansion rate.
Therefore, there are surplus electrons in F-doped SnO 2 crystals. The average net charge of SnO 2 before and after doping is also presented in Table 2 (1) are the chemical potentials of the atoms, and n is the total number of atoms in the unit cell structure. The total energy and binding energy of the doped structure are shown in Table 3.
The defect binding energy values of the doped systems (Table 3) are all negative, illustrating that all the doped crystal structures are stable structures. The defect binding energy decreases in the order of B, S, C, N, and F. The SnO 2 doped with F has the lowest binding energy, which makes it the most stable structure.

Band structure and density of states
After doping not only the crystal structure is distorted, but also the electronic structure of the SnO 2 crystal is changed. The doping atoms introduce impurity levels in the bandgap of SnO 2 . The SnO 2 crystal shows metallicity when the introduction of non-metal atoms causes the Fermi level to enter the conduction band. The electronic structure including the energy band structure, total density of states and partial wave state density of the doped system are shown in Figure 2.
For SnO 2 , the Fermi energy level is at the top of the valence band, indicating that the conductivity of SnO 2 is low. The conduction band minimum (CBM) and the valence band maximum (VBM) are located at the same G point, which is consistent with the calculation results [14,15] indicating that SnO 2 is a direct bandgap semiconductor. In this work, the calculated bandgap is 1.28 eV, which is consistent with previous calculation results [16][17][18]. However, the bandgap is lower than the experimental value of 3.6 eV [19], which is caused by the underestimation of the cross-correlation energy by the GGA function.
The energy of Sn 5s orbits and the interaction between Sn 5s and O 2p orbitals are overestimated, resulting in a wider valence band and narrower bandgap. The changes of bandgap and energy band cannot affect the electronic structure analysis of SnO 2 crystals. The bandgap value can be modified by the complex variable function method (DFT + U) [20] to obtain a more accurate bandgap value. Although there are still some issues needed to be solved with this method, it is sufficient to mainly discuss the photoelectric properties of doped SnO 2 .
The total density of states of the SnO 2 crystal shown in Figure 2 illustrates the that valence band of the system is divided into two parts, one from −19.1 to −14.9 eV and one between −8.1 and 0 eV. According to the density of partial wave states, the contributions to the deep energy level are from Sn 5s and O 2s, orbitals while the shallow energy level mainly consists of O 2p and Sn 5s orbitals with partial contribution of Sn 5p orbitals. The shallow energy level (from −8.1 to −5.8 eV) is mainly due to Sn 5s orbitals, and the O 2p orbital is responsible for the part between −5.8 and 0 eV. The main contributions to the conduction band are from Sn 5s and Sn 5p orbitals.
It is worth noting that the energy band of SnO 2 changes significantly after doping. B 2p, C 2p, S 3p, and N 2p orbitals appear in the SnO 2 bandgap. B, F and S cause the Fermi level of the doped crystal to move up. B and S introduce impurity levels in the SnO 2 bandgap, which enhances the conductivity of the SnO 2 crystal. The doping with B leads to more impurity levels in the forbidden band of SnO 2 , and the bandgap changes clearly, indicating that doping B atoms can adjust the SnO 2 bandgap value well.
It can be seen from the partial wave state density diagram that the B 2p orbital and the S 3p orbital enter the SnO 2 crystal bandgap. After the introduction of F atoms, the Fermi energy level passes through the conduction band of SnO 2 crystal, and SnO 2 becomes a conductor. The energy band structure of SnO 2 doped with C and N shows that the Fermi level crosses the impurity level and the conductivity of SnO 2 semiconductor is enhanced. To sum up, it can be seen that doping with F can enhance the conductivity of SnO 2 crystals effectively.
In order to obtain information about charge transfer after doping, the secondary differential charge distribution of the elements was calculated and the results are shown in Figure 3. Compared with O, the ability of the doping atoms to accumu-  late charge is reduced. This provides more electrons as free carriers, making the system appear metallic. The analysis result is consistent with the analysis result of the energy band structure.

Optical properties
SnO 2 is widely used as a transparent conductive film material, especially in doors and windows, it is also preferred for coatings of low-emissivity glass. The most important property of low-emissivity is the reflectivity in the infrared region. According to the reflectance spectrum of the material, a good adiabatic behavior of the material requires the plasma frequency to be close to the visible region. Plasma is a system in which the dielectric constant is ε r = 0, the concentration of positive and negative charges is the same, and positive and negative charges are free to move. When the probability of collision of free electrons in a solid is 0, the dielectric function is where ω p is the plasma frequency. ω p is the intrinsic characteristic frequency of the material. The plasma oscillation frequencies vary for different crystal materials. In general, it is proportional to the concentration of free electrons. When the vibration frequency of the incident light is greater than the plasma oscillation frequency, the crystal material is transparent. Otherwise, it is impossible for the light to pass through, showing metallic reflectivity.
The reflectance spectra of SnO 2 crystals doped with non-metal elements are shown in Figure 4. It shows that SnO 2 doped with F had the highest reflectance, followed by doping with N, C, S, and B in this order. When the wavelength of light is greater than 1800 nm, the material shows metallic reflectivity, when the wavelength is below 1800 nm, the material shows transparency. Therefore, F-doped SnO 2 is the most suitable material for lowemissivity glass coatings.

Conclusion
Based on first-principles density functional theory, crystal structure, electronic structure, and optical properties of SnO 2 doped with non-metal elements were theoretically analyzed. The calculation results confirm that the doping caused the crystal lattice to expand. The F-doped SnO 2 lattice has the lowest binding energy and is prone to replacement doping. S-doping forms p-type semiconductors, and F-doping forms n-type semiconductors. The optical analysis results revealed that F-doped SnO 2 possesses the highest reflectivity in the infrared region, and is most suitable as a low-emissivity coating material.