Composition dependent intrinsic defect structures in ASnO₃ (A = Ca, Sr, Ba)

1. Introduction

Perovskite oxides with general formula ABO₃ are attracting great attentions owing to their excellent optical-electric and magnetic properties, such as pyroelectricity, piezoelectricity, ferroelectricity, antiferroelectricity and ferromagnetic etc [[1], [2], [3], [4]]. Therefore, perovskite oxides are regarded as suitable materials for widely engineering applications, for instance, insulating layers in dynamic random-access memories [5], ferroelectric thin-film structures [6], high-T_c superconductor substrates [7], and gate oxides [8]. Meanwhile, as a result of the ability of accommodating defects and low thermal conductivities, perovskite oxides also manifest the potential as the nuclear material and thermal barrier coating candidates [[9], [10], [11], [12]]. Especially, the alkaline earth metal stannates (ASnO₃), owing to their wide band gap (∼3.0 eV), high visible light transmittance and proper conductivity, have been proposed to be applied as transparent conductive oxides (TCOs) [13,14].

Recently, scientists have revealed that perovskite stannates (ASnO₃, A = Ca, Sr, Ba) with designed extrinsic defects by doping different elements will acquire excellent optoelectronic properties [[15], [16], [17], [18], [19]]. Lee et al. reported that La doped BaSnO₃ has the high electron mobility (85-100 cm² V^-1 S^-1) at room temperature, which guarantees its excellent electrical conductivity [20]. Liu et al. further found that the transmittance of the Ba_1-xLa_xSnO₃ film exceeds 90 % in the visible light range when the doping ratio is in the range of 0-20 % and its metal-semiconductor transition depends on the dopant concentration [21]. Similar phenomena have also been observed in cases of Sb-doped SrSnO₃ and Sb-doped BaSnO₃ etc [15,16,18,19].

Meanwhile, the first principles calculations were performed on the TCO materials to uncover the underlying mechanisms of the point defects modified optical and electrical properties [15,16,[18], [19], [20], [21], [22], [23]]. Both intrinsic and extrinsic point defects have significant influences on the electrical and optical properties of TCO materials as they would bring extra energy levels in band gaps and enhance the concentration of free carriers in these materials [15,16]. King et al. found that the conductive electron concentration of CdO increases and then saturates accompanying with introducing intrinsic defects through He-ion irradiation [22]. The theoretical investigations on TCOs such as SnO₂, In₂O₃, and Ga₂O₃ showed that their oxygen vacancies all present negative-U characteristics and are stable in the two plus and neutral charge states [[23], [24], [25], [26], [27], [28], [29], [30]]. In the case of perovskite stannates, Wang et al. revealed that the metal dopants of La, Sn and Nb obviously adjust their conductivity and optical properties [31]. The point defects play a predominate role on the acquired properties of the perovskites and have been a focus of semiconductor relevant investigations. However, the complexity of the concentration and diversity on their intrinsic defects still remains unsystematic, which, as the basis of the defect interaction, has invisible but nonnegligible influence on the defect behaviors.

The influence of intrinsic defects on the properties of these materials is also uncovered by available reports. Xi et al. studied the formation energy dependent site preferences for oxygen vacancies and their migration pathways, which are supportive for their behaviors under irradiations [32,33]. Nunn et al. found that the dielectric constant of the BaSnO₃ film with nonstoichiometric Ba to Sn ratio is larger than that of the stoichiometric one, of which the origin is attributed to the cation vacancies by first principle calculations [34]. The CaSnO₃ containing a plenty of oxygen vacancies was prepared by Li et al., in order to improve its photocatalytic performance and accelerate the production of superoxide radicals [35]. Using first principles calculations, Hines et al. found that oxygen vacancies are more stable than holes in stannates [36]. Furthermore, in the cases of SrSnO₃ and BaSnO₃, defect electrons are found to be less stable comparing to cationic vacancies [36]. Considering different chemical potential environments, Liu et al. systematically studied the intrinsic point defect complexes of SrTiO₃ using the first principles calculations, and they proposed that the properties of SrTiO₃ can be optimized by controlling the non-stoichiometric composition of SrO and TiO₂ [37]. Similarly, the intrinsic defects of yttrium silicates [38] and LiNbO₃ [39] are also clarified to be linked to different chemical conditions. Until now, the types and concentrations of possible native defect complexes for stannates in stoichiometric and non-stoichiometric compounds are not clear yet.

Here, we implement comprehensive investigations focusing on the intrinsic defect structures of perovskite stannates ASnO₃ (A = Ca, Sr, Ba). Firstly, the defect formation energies of isolated defects are calculated. Then, the types and concentrations of the predominant defect complexes under stoichiometric and non-stoichiometric ASnO₃ are quantitatively predicted. This study aims to provide a comprehensive understanding of the mechanism of charged point defect complexes in stannate perovskites and to guide future experimental materials design by controlling their intrinsic point defects.

2. Computational details

2.1. DFT calculation details

The present density functional theory (DFT) [40,41] calculations were performed using Vienna Ab Initio Simulation Package (VASP) code [42]. The generalized gradient approximation (GGA) [43] of Perdew-Burke-Ernzerh for solids (PBESOL) [44] was selected as the exchange-correlation function. The plane wave cutoff was set to 400 eV. The computations were calculated with 3 × 3 × 3 supercell for BaSnO₃ (135 atoms) and 3 × 3 × 1 supercell for SrSnO₃ and CaSnO₃ (180 atoms). The k-point mesh for BaSnO₃, SrSnO₃ and CaSnO₃ were 2 × 2 × 2, 2 × 2 × 4, and 2 × 2 × 4, respectively. Spin polarization was considered in all calculations. The crystal structures were optimized until the force on each atom was smaller than 5 × 10^-3 eV/Å.

2.2. Point defect formation energy

The defect formation energies, Ef, were evaluated as [45]:

$ E_{f}= E_{d}-E_{p}+\sum\ n_{i}μ_{i}+q(ΔE_{F}+E_{VBM}) $ (1)

where E_d and E_p correspond to the energies of the supercell with and without point defects, respectively; n_i is the number of atoms being removed or added and μ_i is the corresponding chemical potential; q is the charge state of the defect. EVBM and ΔE_F are the energy levels corresponding to the valance band maximum (VBM) and the Fermi energy measured from the VBM, respectively. ΔE_F is the position of Fermi energy in the band gap, E_g, E_g = E_p (-1) + E_p (+1) - 2 E_p (0), where -1, +1 and 0 are the charge states. As the well-known deviation in the DFT calculation of the band gap, the calculated band gap for BaSnO₃, SrSnO₃ and CaSnO₃ are 0.64 eV, 1.68 eV and 2.00 eV, respectively, being smaller than their corresponding experimental values of 3.10 eV, 4.10 eV and 3.87 eV [[46], [47], [48]]. In order to eliminate the influence of the deviation on the point defect formation energies, a constant energy shift, ΔE_g, (in this case, BaSnO₃, SrSnO₃ and CaSnO₃ are 2.46 eV, 2.42 eV and 1.87 eV, respectively) is added to the conduction states so as to match the experimental values [49,50]. For an isolated defect, the acceptor-like and deep donor-like defects follow VBM and their energy levels do not change, but the shallow donor-like defect energy levels are moved up to the same amount as the band gap since they follow the conduction-band minimum (CBM) change [49,50].

The thermodynamic transition level of a defect between charge states q and q',εq/q',corresponds to the Fermi energy at which the formation energies for charge states q and q, are equal. When measured from the VBM, the thermodynamic transition level is given by:

$ε(q/q')=\frac{E^{q}_{f,VBM}-E^{q'}_{f,VBM}}{q'-q}$ (2)

where $E^{q}_{f,VBM}$ represents the defect formation energy for charge state q. The position of the thermodynamic transition level given in Eq. (2) corresponds to the ionization energy of a defect, i.e., the acceptor or donor energy [37].

2.3. Formalism for chemical potential in ternary oxides

The chemical potential μ_i of each element is always restrained by the various conditions relating to the thermodynamic stability of ternary ASnO₃. The chemical potential limitation of stoichiometric ASnO₃ (A = Ca, Sr, Ba) is expressed as: [51]

$μ_{A}+μ_{Sn}+3μ_{O}=μ_{AsnO_{3}}$ (3)

In addition, the chemical potential of each element in its simple reference substances presents the upper limit of its chemical potential in the perovskite stannate. The reference substances are A (A = Ca, Sr, Ba) and Sn solids, together with the molecular oxygen (O₂). These restrictions are formulated as:

$μ_{A}≤μ^{bulk}_{A}$ (4.1)

$μ_{Sn}≤μ^{bulk}_{Sn}$ (4.2)

$μ_{O}≤μ^{O_{2}}_{O}$ (4.3)

Meanwhile, neither AO (A = Ca, Sr, Ba) nor SnO₂ separates form bulk ASnO₃, which is expressed by:

$μ_{A}+μ_{O}≤μ_{AO}$ (5.1)

$μ_{Sn}+2μ_{O}≤μ_{SnO_{2}}$ (5.2)

Using above equations, the chemical potential areas of the single phase ASnO₃ are defined and the chemical potential dependent defect formation energies can be investigated.

3. Results and discussion

The calculated lattice constants of the relaxed structures are: (1) a = 4.19 Å (The experimental one is 4.12 Å) for BaSnO₃; (2) a = 5.77 Å (5.71 Å), b = 5.86 Å (5.70 Å) and c = 8.18 Å (8.07 Å) for SrSnO₃; (3) a = 5.57 Å (5.51 Å), b = 5.78 Å (5.66 Å) and c = 8.00 Å (7.88 Å) for CaSnO₃, being consistent with experimental values [46,47,52]. After comprehensively considering all chemical potential constraints mentioned above, the ternary phase diagrams of ASnO₃ are shown in Fig. 1. These chemical potential diagrams depict the regions of the stable ASnO₃ single phases, defined by the quadrangle ABCD and restricted by the Sn, O₂, AO and SnO₂ precipitation lines. The points A, B, C and D, correspond to Sn- & SnO₂-rich, O- & SnO₂- rich, O- & AO-rich, and Sn- & AO-rich precipitate phase boundaries, respectively. The values of chemical potentials at corner points for A, Sn and O are given in Table 1.

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Fig. 1.   Chemical potential diagram of (a) BaSnO₃, (b) SrSnO₃, (c) CaSnO₃, where in the quadrangle ABCD is stable area of ASnO₃.

3.1. Isolated point defects

Crystalized in Pm$\bar{3}$m symmetry, the structural configurations of vacancies (V_O, V_Sn and V_Ba) and cation antisite defects (Ba_Sn and Sn_Ba) in BaSnO₃ are unique and readily identified. For SrSnO₃ and CaSnO₃ with Pbnm space group, the structures of atomic vacancies (V_Sn and V_Ba) and cation antisite defects (Ba_Sn and Sn_Ba) are also exclusive. As there are two kinds of oxygen atoms in the SrSnO₃ and CaSnO₃, the VO types with the lower formation energy ((0.4287, 0.5715, 0.5390) for SrSnO₃ and (0.4343, 0.5670, 0.5567) for CaSnO₃) are adopted. The structures of interstitial configurations (A_i, Sn_i and O_i, where i refers to interstitial) of ASnO₃ are more complex. By calculating the defect formation energies in all possible interstitial positions as described in Refs. [28,38], the final interstitial positions with the lowest value in each species are determined. For BaSnO₃ (Fig. 2(a-c)), both Ba and O favor the split-interstitial configuration along the <100> direction, with two atoms sharing a single lattice site. However, the Sn interstitial occupies a bridge site between two Ba atoms along a channel and in-plane with four nearest neighboring Sn and/or O atoms. SrSnO₃ and CaSnO₃ share the same interstitial configurations as shown in Fig. 2(d and e). The oxygen forms a split-interstitial configuration along <001> direction, while the Sr(Ca) forms a split-interstitial configuration along the <110> direction. The Sn interstitial occupies a bridge site between two Ca atoms along a channel and in-plane with four nearest neighboring Sn atoms.

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Fig. 2.   Interstitial configurations of cubic perovskite BaSnO₃ with (a) Ba_i (orange ball), (b) Sn_i (blue ball) and (c) O_i (brown ball), orthorhombic perovskite SrSnO₃ and CaSnO₃ with (d) Sri or Ca_i (black ball), (e) Sn_i (blue ball) and (f) O_i (brown ball).

Then, the formation energies of all isolated point defect types with different charge states in ASnO₃ are calculated using Eq. (1), in which the influence of the Fermi level on the formation energies of each defect has been considered. The zero point for Fermi level is set at the VBM. The chemical potential diagrams of BaSnO₃, SrSnO₃ and CaSnO₃ are shown in Fig. 1. At all points in the ABCD quadrangle, the defect formation energy is located between the maximum and minimum values for each defect species at points A, B, C, and D. The electron Fermi energy dependent defect formation energies of ASnO₃ at points A, B, C and D are calculated and shown in Fig. 3. Furthermore, the thermodynamic transition levels for the point defects of ASnO₃ are displayed in Fig. 4. All thermodynamic transition energies are measured based on the VBM. For BaSnO₃, the thermodynamic transition energy for O_i from 0 to 2^- is at 0.66 eV, and that of Ba_i from 1⁺ to 2⁺ is at 3.08 eV. The Sni express two charge transitions, which are (4⁺/3⁺) at 3.05 eV and (3⁺/2⁺) at 3.07 eV. For SrSnO₃, the (2⁺/0) transition of VO occurs at 3.76 eV. In the case of O_i, the (0/1^-) and (1^-/2^-) transitions occur at 1.98 eV and 2.00 eV, respectively. The charge transition energy levels of Sn_i from 4⁺ to 2⁺ and SnSr from 2⁺ to 0 are at 3.20 eV and 1.22 eV, respectively. In the case of CaSnO₃, there are two kinds of point defects with charge transitions, which are the (0/2^-) transition occurring at 1.44 eV for O_i and the (2⁺/0) transition at 2.04 eV for Sn_Ca.

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Fig. 3.   Electron Fermi level dependent defect formation energies for charged isolated point defects under (a) Sn- & SnO₂-rich, (b) O- & SnO₂- rich, (c) O- & AO-rich, and (d) Sn- & AO-rich conditions.

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Fig. 4.   Thermodynamic transition levels of O_i, Ba_i and Sn_i for BaSnO₃, V_O, O_i, Sn_i and Sn_Sr for SrSnO₃, O_i and Sn_Ca for CaSnO₃.

3.2. Native defect complexes

It has been reported that the nominally charged defects are the ground state defect structures [37,39,53]. In experiments, the nominally charged defects always appear in the form of defect complexes because of the charge neutrality limitation. According to the classic model for native point defects, the mechanism of defect complexes is described by Frenkel, Schottky and cation antisite defects in materials. For all compounds, the formation energies of all nominally charged (denoted as C-defect complexes) defect complexes are calculated and all results are listed in Table 2. For BaSnO₃, the sequence of formation energies is Schottky < O Frenkel < Cation Antisite < Sn Frenkel < Ba Frenkel. For SrSnO₃, the sequence is Schottky < Cation Antisite < O Frenkel < Sr Frenkel < Sn Frenkel, while it is Cation Antisite < Schottky < O Frenkel < Sr Frenkel < Sn Frenkel in the case of CaSnO₃. Interestingly, the formation energies of the Schottky defect complexes are always relatively low and therefore must be significant for these compounds. In both SrSnO₃ and CaSnO₃, antisite defects are also the dominant defect structures as their low formation energies. Furthermore, the formation energies of oxygen Frenkel defect complexes are not significantly unreachable, indicating their possible appearance in these materials, especially at high temperatures.

Based on the calculated formation energies (Table 2), the concentration of each native defect complex can be calculated using the Arrhenius formula as follows:

$C_{d}=N_{site}N_{config}exp(-E_{f}/(k_{B}T))$ (6)

where N_site and N_config are the numbers of sites per unit volume and of equivalent configurations for the defect, k_B is the Boltzmann constant and T is the temperature. Fig. 5(a-c) depicts the calculated temperature dependent concentrations of various defect complexes of ASnO₃ (A = Ca, Sr, Ba). The concentrations of all kinds of defect complexes would increase with the temperature enhancement. Obviously, Schottky type is the predominant point defect structure and the O Frenkel pairs also exist in BaSnO₃, while the concentration of others are less than 1 cm^-3 even at 1000 K. In SrSnO₃ and CaSnO₃, the concentrations of Schottky and cation antisite defects are both at a high level, meanwhile the O and Sn/Ca Frenkel pairs may also appear at the same time, especially in the high temperatures over 1000 K. However, the concentration of Sn Frenkel pairs reaches the very low level as a result of their high formation energies. Therefore, it can be concluded that the defect complexes (including Schottky and O Frenkel pairs in BaSnO₃, Schottky and cation antisite defects in SrSnO₃ and CaSnO₃) with relatively low formation energies are more likely to have the dominative proportion in defects and thus have practical implications in experiments. However, other defects presenting higher formation energies would unlikely proliferate under equilibrium experimental conditions.

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Fig. 5.   Temperature dependent concentrations of various charged native defect complexes of (a) BaSnO₃, (b) SrSnO₃ and (c) CaSnO₃.

3.3. Defect complexes in nonstoichiometric ASnO₃ (A = Ca, Sr, Ba)

The types of existing point defect complexes are also influenced by the compositions of the ternary compounds [37]. In experiments, the nonstoichiometric compounds may often be obtained as a result of the experimental uncertain and thus the modification of the native point defect complexes is natural. In the case of the experimental synthesis of perovskite stannates ASnO₃ (A = Ca, Sr, Ba), the composition of the two binary reactants, i.e. AO and SnO₂, play a key role. The chemical potentials of elements in the cases of the AO excess and the SnO₂ excess are clarified by the lines of CD and AB in Fig. 1, respectively. Here, taking two possible nonstoichiometric mechanisms into account, i.e. the AO excess and the SnO₂ excess, the defect complexes in nonstoichiometric ASnO₃ are studied. The defect formation reactions are shown in Table 3, together with their respective reaction enthalpies (∆H) that are the energy discrepancy of the compounds/defects between the right and left sides of each reaction. Using these reaction enthalpies, the temperature dependent concentrations of the defects in each reaction are provided in Fig. 6 for a quantitative description.

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Fig. 6.   Temperature dependent concentrations of various defect complexes under AO-rich and SnO₂-rich conditions for (a, b) BaSnO₃, (c, d) SrSnO₃, (e, f) CaSnO₃.

After analyzing all the reaction enthalpies collected in Table 3, the nonstoichiometry induced main defect structures for these three compounds can be reached as:

(1) For BaSnO₃, the values of ΔH are in order of R2 < R3 < R4 < R5 < R1 when the BaO is excess. So, the $V^{2+}_{O}$ and $Ba^{2-}_{Sn}$ corresponding to R2 become the predominant defect species. The ΔH of R3 is the second lowest among all ΔH values and therefore its products, $Ba^{2-}_{Sn}$ and $Ba^{2+}_{i}$, would be the second widespread defects. However, the other reactions R1, R4 and R5 are very unlikely due to their high ΔH. Under the condition of the SnO₂ excess, the values of ΔH are in order of R8 < R9 < R10 < R7 < R6. Therefore, the predominant defects are the R8 related defects of $Sn^{2+}_{Ba}$ and $V^{2-}_{Ba}$-. At the same time, as the ΔH values of R9 and R10 are close and also relative low, their reaction products, $V^{2-}_{Ba}$, $V^{2+}_{O}$ and $Sn^{4+}_{i}$, may also exist in this material. Besides, the reactions R6 and R7 are unlikely because of their very high ΔH (19.60 eV and 5.37 eV, respectively).

(2) For SrSnO₃, in the case of SrO excess, the ΔH values are in order of R2 < R3 < R5 < R4 < R1. So, the predominant defect structures are $V^{2+}_{O}$ and $Sr^{2-}_{Sn}$ (R2), while $Sr^{2-}_{Sn}$ + $Sr^{2+}_{i}$ (R3) and $V^{4+}_{Sn}$ + $Sr^{2+}_{i}$ (R5) may also appear as a result of their relative low ΔH. However, the ΔH values of reactions R1 and R4 are very high, so that these related defects unlikely occur. When SnO₂ is excess, the values of ΔH are in order of R8 < R10 < R7 < R9 < R6. The reaction R8 has the lowest ΔH, so $Sn^{2+}_{Sr}$ and $V^{2-}_{Sr}$ are the predominant defects. Moreover, $Sn^{4+}_{i}$ and $V^{2-}_{Sr}$ will also be significant defects as the second low ΔH of R10. Besides, R7 and R9 may proceed more or less but R6 is unlikely.

(3) For CaSnO₃, when CaO is excess, the values of ΔH are in order of R3 < R2 < R5 < R4 < R1. The reactions R2 and R3 have similarly low ΔH s and therefore $V^{2+}_{O}$ + $Ca^{2-}_{Sn}$ and $Ca^{2-}_{Sn}$ + $Ca^{2+}_{i}$ are the predominant defects. The occurrence possibility of other reactions which have high ΔH values is negligible. In the case of SnO₂ excess, the values of ΔH are in order of R8 < R7 < R10 < R9 < R6. The R8 has the lowest ΔH and therefore the $Sn^{2+}_{Ca}$ and $V^{2-}_{Ca}$ are the predominant defects. The ΔH values of reaction R7 and R10 are also relatively low, indicating the greater possibility of $O^{2-}_{i}$ and $Sn^{4+}_{i}$ appearance. However, the reactions R6 and R9 are unlikely because of their high ΔH values.

The composition of ASnO₃ plays a key role in the types and concentrations of their intrinsic point defects. All the predominant defect structures that are the defect complex types owing the firstly and secondly low formation energies in each composition are as collected in Table 4. For BaSnO₃, the reaction enthalpies of defect complexes are low and very similar in both BaO and SnO₂ excess cases (as shown in Table 3), but different defect structures are generated. Comparing to stoichiometric BaSnO₃, $Ba^{2+}_{i}$ and $Ba^{2-}_{Sn}$ appear under BaO excess but $Sn^{2+}_{Ba}$ and $V^{2-}_{Ba}$ occur under SnO₂ excess. At the same time, $V^{2+}_{O}$ always exists more or less in both stoichiometric and nonstoichiometric BaSnO₃. The existing $V^{2+}_{O}$ is beneficial to the reduction of the thermal conductivity and the enhancement of the electronic conductivity, promoting its application as transparent conducting semiconductors in optoelectronic devices [54,55]. Similarly, the defect types also can be modified by controlling the AO to SnO₂ ratio in the cases of SrSnO₃ and CaSnO₃ as indicated by Table 4. Being differently with BaSnO₃, the reaction enthalpies of defect complexes under SnO₂ excess are much lower than those under SrO and/or CaO excess. It means that these two materials can accommodate larger SnO₂ deviation than SrO/CaO in experiments. In all, the predominant defect complexes change under different conditions, which do provide us the possibility of the defect structure tailoring through modifying the synthetic composition of these materials.

4. Conclusions

The intrinsic point defects in the stoichiometric and nonstoichiometric stannate perovskites (ASnO₃; A = Ca, Sr, Ba) were comprehensively studied employing the first-principles calculation. The chemical potential diagrams are constructed. Then the types and concentrations of favorable defect as well as their interconnected evolutions have been deduced considering the external environments. By calculating the formation energies of different charges with various isolated intrinsic point defects, it can be found that the charge state of Sn_i (4⁺/3⁺/2⁺), Ba_i (2⁺/1⁺) and O_i (0/2^-) in BaSnO₃, O_i (0/1^-/2^-), Sn_i (4⁺/2⁺), VO (2⁺/0) and Sn_Sr (4⁺/2⁺) in SrSnO₃ and O_i (0/2^-) and Sn_Sr (2⁺/0) in CaSnO₃ varies with the change of electron Fermi energy, while other defects prefer their nominal charge states over the entire band gap.

Furthermore, investigations in this work uncover the defect preferences of perovskite stannates (ASnO₃; A = Ca, Sr, Ba)under stoichiometric and nonstoichiometric conditions: The dominant defect complexes in stoichiometric BaSnO₃, SrSnO₃ and CaSnO₃ are Schottky defect ($V^{2-}_{Ba}$ + $V^{4-}_{Sn}$ + $3V^{2+}_{O}$), Schottky defect ($V^{2-}_{Sr}$ + $V^{4-}_{ n}$ + $3V^{2+}_{O}$) and antisite defect ($Sr^{2-}_{Sn}$ + $Sn^{2+}_{Sr}$), and antisite defect ($Ca^{2-}_{Sn}$ + $Sn^{2+}_{Ca}$), respectively. In the nonstoichiometric cases, the AO excess is beneficial to the formation of $V^{2+}_{O}$ and $A^{2-}_{Sn}$ in all ASnO₃ compounds. Meanwhile, there also may be considerable amounts of $A^{2-}_{Sn}$ and $A^{2+}_{i}$ defects in SrSnO₃ and CaSnO₃. Being differently, $Sn^{2+}_{A}$ and $V^{2-}_{A}$ are the predominant defect complexes in the SnO₂ excess environment. The calculation results are supposed to inspire the intrinsic defect controlling for the specific defect corresponding properties, so as to accelerate their commercial applications as optic-electronic semiconductors.

Acknowledgements

This work was supported financially by the National Natural Science Foundation of China (Nos. 51602188 and 51972206), the Program for Professor of Special Appointment (Eastern Scholar) by Shanghai Municipal Education Commission (No. TP2015040) and the Science and Technology Committee of Shanghai (No. 19010500400).