Theoretical Study Of Intrinsic Defects And Oxygen-vacancy Distribution In In₂O₃

As a transparent conductive oxide(TCO)material,indium oxide(In2O3)has been widely used in solar cells,liquid crystal displays,gas sensors,and catalysts due to its excellent transparent conductivity and gas sensitivity.Based on the first principles method,we have studied the role of four intrinsic defects in the In2O3 system including oxygen vacancy(VO),indium vacancy(VIn),oxygen interstitial(Oi),indium interstitial(Ini),the distribution of oxygen vacancies in non-stoichiometric crystals,and analyzed the interactions between among vacancies.The results are as follows:1.The electronic structures of In2O3 crystal.We employed the GGA-PBE and DFT-1/2 methods to calculate the partial density of states(PDOS)and band structure of the perfect In2O3 crystal,and compared the similarities and differences of the results between the two methods.The PDOS diagrams obtained by the two methods both show that the energy band near the valence band maximum(VBM)is mainly attributed the contribution of the O-2p orbital and the In-4d orbital,while the energy band near the conduction band minimum(CBM)is mainly contributed by O-2p orbital and the In-5s orbital.There is an obvious sp hybridization in the CBM,which can provide an effective three-position transport path for free carriers.It can be seen from the energy band diagram that both VBM and CBM are located at the Γ point,and the band gap obtained by the PBE method and DFT-1/2 method is 1.06 eV and 3.20 eV,respectively.Obviously,the latter is closer to the experimentally measured band gap value of about 2.90 eV.2.Four intrinsic defects in the In2O3 system.We have chosen an In2O3 supercell with 480 atoms to study the intrinsic defects,in order to reduce the interaction between the defects caused by the periodic boundary conditions of the crystal.The formation energies of different defect states of each defect under oxygen-poor and oxygen-rich conditions were calculated by the first-principles,and the formation energy as a function of Fermi level was plotted.The result show that the(+2/0)transition energy level of VO is close to CBM with a low formation energy under O-poor conditions.We determined that the VO is the main defect in In2O3 and exhibits shallow donor behavior,which is the main origin for the n-type conductivity of In2O3,consistent with the experimental VO concentration of 1%.When the Fermi level is close to VBM,the formation energies of VO and Ini are negative,which means that the donor defects act as compensation centers to limit acceptor doping.This is also the main reason why it is difficult to achievep-type doping in In2O3.3.The formation energies of single oxygen vacancies in supercells of different sizes.Based on the structural recognition,we expanded the In2O3 primitive cell into six supercells of different sizes and calculated the formation energies of single VO in these selected supercells,to investigate the influence of oxygen vacancy concentration on formation energy.The results show that as the volume of the supercell increases,the formation energy of VO decreases,and finally tends to converge,indicating that the interaction between VO in the supercell can be neglected.This result also proves the rationality of choosing 480 atom supercell to investigate the intrinsic defects.In order to illustrate the local structural distortion caused by the introduction of the VO,we have compared the changes of In-O bond length by structural optimization.The In atom which is closer to the VO has a greater change in bond length,indicating that the introduction of VO will have a greater impact on neighboring atoms.4.The distribution of oxygen vacancies pair in In2O3.By the structural recognition,we have searched all the possible structures in the 80 and 160 atom supercells with two VO.We calculated their average formation energies and discussed the influence of the distance between the vacancies on the stability of the structure.The study found that when the distance between the vacancies is less than 4.40 (?),the two oxygen vacancies share the same neighboring In atom,and the formation energy increases approximately with the increasing distance,which indicates an attractive attraction.Besides,when the distance between the vacancies is greater than 4.40 (?),the two oxygen vacancies are not attached to the same neighboring In atom,and the formation energy decreases roughly with the increasing distance,and finally tends to converge,which indicates a repulsive interaction between oxygen vacancies.Among them,the minimum and maximum formation energies appear in structures with distances of 2.97 (?) and 4.17 (?),respectively.In the structure with a distance of less than 4.40 (?),the Fermi level of the system with a smaller formation energy is close to the CBM,which plays a positive role in the n-type conductivity of In2O3.In addition,we also analyzed the local structural distortion of the system caused by the introduction of oxygen vacancy pairs.Here,we mainly focus on the changes in In-O bond length of the In atoms near the vacancy pair.The result shows that in the structure with smaller formation energy,the bond length is shortened and the change is larger,which proves that the introduction of vacancy pair can significantly enhance the structural stabilities.5.Prediction of the distribution of polyoxygen vacancies in In2O3.Based on the relationship between the distance and the formation energies of two oxygen vacancies,we proposed a two-body interaction model,and determined the formation energy of two oxygen vacancies in the 480 atom supercell by fitting the obtained data.Further,we can estimate the average formation energy of three oxygen vacancies,and predict that it is unstable to if there are three oxygen vacancies on the same In atom in 480 atom supercell.