# Phase stability, electronic structure, and optical properties of indium oxide... S. Zh. Karazhanov, P. Ravindran, P. Vajeeston,

PHYSICAL REVIEW B 76, 075129 共2007兲 Phase stability, electronic structure, and optical properties of indium oxide polytypes S. Zh. Karazhanov,1,2 P. Ravindran,1 P. Vajeeston,1 A. Ulyashin,3 T. G. Finstad,4 and H. Fjellvåg1 1Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway Institute, 2B Mavlyanov Street, Tashkent 700084, Uzbekistan 3 Institute for Energy Technology, P.O. Box 40, NO-2027 Kjeller, Norway 4Department of Physics, University of Oslo, P.O. Box 1048 Blindern, N-0316 Oslo, Norway 共Received 17 January 2007; revised manuscript received 13 July 2007; published 29 August 2007兲 2Physical-Technical Structural phase stability, electronic structure, optical properties, and high-pressure behavior of polytypes of In2O3 in three space group symmetries I213, Ia3̄, and R3̄ are studied by first-principles density-functional calculations. From structural optimization based on total energy calculations, lattice and positional parameters have been established, which are found to be in good agreement with the corresponding experimental data except for I213, where the symmetry analysis for optimized structure indicates that it arrived at the Ia3̄ phase. In2O3 of space group symmetry Ia3̄ is found to undergo a pressure-induced phase transition to the R3̄ phase at pressures around 3.8 GPa. From the analysis of band structure coming out from the calculations within the local density and generalized gradient approximations, it is found that In2O3 of space group symmetry I213 and R3̄ are indirect band gap semiconductors, while the other phase of space group Ia3̄ is having direct band gap. The calculated carrier effective masses for all these three phases are compared with available experimental and theoretical values. From charge-density and electron localization function analysis, it is found that these phases have dominant ionic bonding with noticeable covalent interaction between indium and oxygen. The magnitudes of the absorption and reflection coefficients for In2O3 with space groups Ia3̄ and R3̄ are small in the energy range 0 – 5 eV, indicating that these phases can be regarded and classified as transparent. DOI: 10.1103/PhysRevB.76.075129 PACS number共s兲: 71.15.⫺m, 71.22.⫹i I. INTRODUCTION Transparent conducting oxides 共TCOs兲 have increased scientific interest because of their many useful features such as transparency in the visible spectrum of incident light and high electrical conductivity. The main interest for the investigation of TCO is their extensive applications such as window layers in solar cells, sensors, front electrodes in flat panel displays, low emissive windows, electrochromic materials in rare-view mirrors of automobiles, smart windows, etc. Investigations on TCO have lead to the formation of a new field in optoelectronic device technology called transparent electronics or invisible electronics.1–7 Here, a combination of n- and p-type homo-p-n-junction based on TCO could lead to a functional window, which transmits visible portion of solar radiation and, at the same time, generates electricity by the absorption of the ultraviolet part of sunlight.6 One of the materials widely used as TCO is Sn doped In2O3 共commonly referred to as ITO兲. In2O3 can exist in three different phases characterized by space group symmetries I213, Ia3̄, and R3̄, which we refer to throughout the paper as phases In2O3-I, -II, and -III, respectively. Among them, the In2O3-I is rarely studied. Only a few papers8 are available on crystal structure studies of this phase. In2O3-II with band gap of Eg = 3.7 eV 共Ref. 9兲 is widely studied both theoretically and experimentally. Until recently, In2O3-III was also rarely studied because it is a high-pressure phase and therefore not easily available. However, recent works have changed this situation. Nanoparticles of In2O3 in rhombohedral structure have been synthesized by hydrothermal method, followed by postannealing at moderate temperatures and pressures.10 Phase selective growth of this phase was also demonstrated11 by means of metal organic 1098-0121/2007/76共7兲/075129共13兲 chemical vapor deposition method at high substrate temperatures 共⬎550 ° C兲 and low 共⬎4 mol/ min兲 trimethylindium flow rates. Furthermore, it is found12 that this phase can be formed upon annealing in air at ⬎550 ° C from the amorphous indium zinc oxide. The electronic structures of ideal and defective In2O3 with oxygen vacancies have been studied by the discrete variational X␣ method, and it was found9 that vacancy levels appear in the band gap. From comparative analysis of electronic structure of In2O3, ZnO, and SnO2, it was shown that they possess a unique feature that the holes are heavier than conduction band 共CB兲 electrons.13 Ab initio studies of In2X3 共X = O , S , Se, Te兲 using the tight-binding linear muffin-tin orbital 共LMTO兲 method show that compression of the lattice increases the band gap.14 Further, this method has been applied to analyze the x-ray photoelectron, bremsstrahlung isochromat, and optical spectra of In2O3 and ITO. Based on band-structure calculations for In2O3 and ITO15,16 using the density-functional full-potential 共FP兲 LMTO and fullpotential linearized augmented plane wave method, criteria for transparent conducting behavior have been formulated, and it is found that position, dispersion, and character of the lowest conduction band are responsible for electro-optical properties. By a systematic study17 using the densityfunctional theory 共DFT兲 within the local density 共LDA兲 and generalized gradient approximations 共GGA兲 with the multiorbital mean-field Hubbard potential 共LDA+ U and GGA+ U兲, it is found that the band gap of In2O3-II calculated within pure LDA and GGA is direct, while that calculated within LDA+ U and GGA+ U with and without the spin-orbit coupling is indirect. The latter approximation is found to correct also energy location of the In 4d electrons. From firstprinciples molecular orbital calculations, native donors such as the oxygen vacancy 共VO兲, indium interstitial 共Ini兲 and the 075129-1 ©2007 The American Physical Society PHYSICAL REVIEW B 76, 075129 共2007兲 KARAZHANOV et al. (a) VO-Ini complex were studied18 in undoped In2O3, and it is found that Ini generates a shallow donor level, VO-Ini creates even shallower level, while VO forms a very deep donor level and facilitates emergence of Ini. Schematic energy band model for ITO was constructed19 based on x-ray photoelectron spectroscopy 共XPS兲 studies. A systematic study of the electronic structure as well as optical and transport properties for cubic ITO was performed20–22 using the ab initio software CRYSTAL. Dependence of carrier mobility and film resistance with carrier concentration in the range 1018 – 1022 cm−3 共Ref. 21兲, optical spectra in the energy range 0.0– 3.1 eV 共Ref. 22兲, and carrier concentrations of 1018 – 1022 cm−3 共Ref. 20兲 were analyzed, and good agreement with experimental data was achieved. The electronic band structure and the cohesive energies of In4Sn3O12 and In5SnSbO12 were calculated by DFT within GGA, and it is found23 that incorporation of Sb into the In4Sn3O12 matrix broadens the conduction band. There still exist some points which should be clarified: 共i兲 Among the In2O3-I, -II, and -III polymorphs, only In2O3-II is widely studied; 共ii兲 charge density, Bader and Voronoi charges, as well as electron localization function analysis were not performed; 共iii兲 structural properties of In2O3-I, -II, and -III and possibility of phase transition between these phases were not studied; 共iv兲 optical spectra are available only for films, and In2O3-II and -III in a narrow energy range 0 – 6 eV; and 共v兲 there are no experimentally measured effective masses for In2O3-I and -III. The aim of this paper is to study the structural, electronic, and optical properties of In2O3-I, -II, and -III by ab initio calculations. (b) (c) In1 In2 In3 O II. STRUCTURAL ASPECTS AND COMPUTATIONAL DETAILS A. Crystal structures Crystal structures 共Fig. 1兲 and lattice parameters 共Table I兲 for In2O3-I, -II, and -III taken from Ref. 24 are used as input for the structural optimization. In all the three polymorphs, the coordination is sixfold for In atoms and fourfold for O atoms. In2O3-I crystallizes in a cubic bixbyite-type structure 共space group No. 199兲 with 8 f.u. per unit cell, with those containing three types of In and two types of O atoms occupying 8a, 12b, 12b, 24c, and 24c Wyckoff positions, respectively. In Fig. 1, the three types of In atoms are indicated by different colors and all are surrounded by oxygen in trigonal biprism coordination. The In2O3-II phase also crystallizes in a cubic bixbyite-type structure with space group No. 206 and 8 f.u. per unit cell. Distinct from In2O3-I, it has different atomic arrangements and bond lengths, and consists of two types of In 共they are surrounded by oxygen in the octahedral and trigonal prismatic coordinations alternatively, as shown in Fig. 1兲 and one type of O atoms located at Wyckoff positions 8b, 24d, and 48e, respectively. It may be noted that the polyhedra surrounding the two types of In atoms differ from those of In2O3-I. In2O3-III is of corundum structure with 2 f.u. per unit cell 共space group No. 167兲. It consists of one type of In 共surrounded by oxygen in trigonal biprism coordination兲 and one type of O atoms occupying 12c and 18e FIG. 1. 共Color online兲 Crystal structures of 共a兲 In2O3-I 共experimental structural parameters兲, 共b兲 In2O3-II, and 共c兲 In2O3-III. Different types of In atoms are marked by different colors. Wyckoff positions, respectively. This is a high-pressure phase10 and, consequently, has been rarely produced, but it has been claimed10,11 that the stability and conductivity of this phase should be favorable to that of cubic phase. B. Computational details The band-structure calculations have been performed using the VASP projector-augmented wave 共PAW兲 package,27 which calculates the Kohn-Sham eigenvalues in the framework of DFT within LDA. For the exchange-correlation potential and energy, we have used the Perdew-Zunger 075129-2 PHYSICAL REVIEW B 76, 075129 共2007兲 PHASE STABILITY, ELECTRONIC STRUCTURE, AND… TABLE I. Equilibrium lattice parameters 共a, b, and c兲 and volumes 共V兲, positional parameters, bulk modulus 共B0兲, and its pressure derivative 共B⬘0兲 for different phases of In2O3 derived from the total energies obtained from present DFT calculations. Values given in parentheses refer to experimental data 共Ref. 24兲. Compound space group Unit cell 共Å兲 Atom Site x y B0⬘ 共0.2500兲 共0.2500兲 共0.2500兲 共0.3950兲 共0.3730兲 172.44 4.79 172.87 4.75 183.61 4.62 In2O3-I I213 a = 10.080 共10.120兲a b = 10.080 共10.120兲a c = 10.080 共10.120兲a V = 1024.26 共1036.43兲a Å3 In1 In2 In3 O1 O2 8a 12b 12b 24c 24c 0.2500 0.0335 0.5338 0.1182 0.1543 In2O3-II a = 10.077 共10.117兲b b = 10.077 共10.117兲b In1 In2 8b 24d 0.2500 共0.2500兲 0.4665 共0.4668兲 0.2500 共0.2500兲 0.0000 共0.0000兲 0.2500 共0.2500兲 0.2500 共0.2500兲 c = 10.077 共10.117兲b V = 1023.28 共1035.51兲b Å3 O 48e 0.3900 共0.3905兲 0.1544 共0.1529兲 0.3820 共0.3832兲 a = 5.4928 共5.4870兲c b = 5.4928 共5.4870兲c In O 12c 18e 0.0000 共0.0000兲 0.2961 共0.2980兲 0.0000 共0.0000兲 0.0000 共0.0000兲 0.3576 共0.3573兲 0.2500 共0.25000兲 Ia3̄ In2O3-III R3̄c 共0.2500兲 共0.0210兲 共0.5420兲 共0.1250兲 共0.1000兲 B0 共GPa兲 z 0.2500 0.0000 0.0000 0.1099 0.3821 共0.2500兲 共0.0000兲 共0.0000兲 共0.1350兲 共0.3580兲 0.2500 0.2500 0.2500 0.3456 0.3901 c = 14.4242 共14.5100兲c V = 376.89 共378.33兲c Å3 a Experimental values from Ref. 8. values from Ref. 25. c Experimental values from Refs. 10 and 26. bExperimental interpolation28 of the many-body calculations of Ceperley and Alder.29 To clarify whether In2O3-II possesses direct or indirect band gap, we have performed additional calculations using generalized gradient approximations 共GGA兲 where Perdew-Burke-Ernzerhof exchange-correlation functional30 has been used. The interaction between electrons and atomic cores was described by means of non-norm-conserving pseudopotentials implemented in the VASP package. The pseudopotentials are generated in accordance with the PAW method.31,32 The use of the PAW pseudopotentials addresses the problem of the inadequate description of the wave functions in the core region—a problem common to all pseudopotential approaches.33 The application of the pseudopotentials allow us to construct orthonormalized all-electron-like wave functions for the In 4d and 5s, and O 2s and 2p valence electrons. Except spin-orbit coupling, all the other relativistic effects are included in the present calculations. The diagonal elements of the effective mass tensor for the conduction band 共CB兲 electrons are calculated by 1 2E共k兲 1 = 2 mc共k兲 ប k2 共1兲 in different directions in the k space from the ⌫ point toward the other high-symmetry points in the Brillouin zone of In2O3-I, -II, and -III. We use this to give an indication of the conduction, since the CB minimum of the band dispersions of all the compounds considered 关see Sec. III B兴 are located at the ⌫ point of the Brillouin zone. The band edge energies E共k兲 have been extracted from DFT calculations, and ninth order polynomial fitting has been performed. From the fitted polynomial, second order derivative was calculated, which was used in the effective mass calculations in Eq. 共1兲. We have studied the effective masses along the crystallographic directions 关001兴, 关011兴, and 关111兴 corresponding to the directions ⌫ → H, ⌫ → N, and ⌫ → P, respectively, for In2O3-I and -II and ⌫ → L, ⌫ → F, and ⌫ → Z for In2O3-III. The equilibrium lattice parameters and bulk modulus for In2O3-I, -II, and -III are determined from the total energies obtained as a function of volume calculated including cell shape as well as atom position relaxations into the computation using the universal equation of state fitting.34 The calculations have been performed on a ⌫ centered 10⫻ 10⫻ 10 k grid in the entire Brillouin zone. The imaginary part of the optical dielectric function ⑀2共兲 has been derived from DFT results by summing interband transitions from occupied to unoccupied states for energies much higher than those of phonons. The real part of the dielectric function ⑀1共兲 is calculated using the KramersKronig transformation. The knowledge of both the real and imaginary parts of the dielectric tensor allows one to calculate other important optical parameters. In this paper, we present and analyze the reflectivity R共兲, the absorption coefficient ␣共兲, the refractive index n共兲, and the extinction coefficient k共兲. More details about the optical calculations were discussed in Refs. 35 and 36. For simplification of analysis of the optical spectra, the labels E0, E1, E2, d1, and d2 have been used. Here, the subscript 0 in E refers to transitions occurring at ⌫, 1 for transitions at points in the 关111兴 direction, and 2 for transitions in the 关100兴 direction of the k space.37 These notations are used based on those of Ref. 37 to describe the reflectivity spectra of semiconductors of wurtzite and zinc blende structures. 075129-3 PHYSICAL REVIEW B 76, 075129 共2007兲 Total energy (eV/f.u.) KARAZHANOV et al. In2O3-I In2O3-II In2O3-III -30.8 -31.2 -31.6 55 60 65 3 Volume (Å /f.u.) FIG. 2. Dependence of total energy Etot with cell volume V per formula unit cell for In2O3-I, In2O3-II, and In2O3-III. III. RESULTS AND DISCUSSION A. Ground-state properties Using the experimentally determined crystal structure information as input, structural optimization has been performed for In2O3-I, -II, and -III. Positional and lattice parameters derived from the DFT calculations for the equilibrium lattices are given in Table I together with the experimentally determined values. Analysis of the Table I shows that deviation of the calculated equilibrium volumes are ⬍1.2% of the experimentally determined values, which indicates that the theoretical calculations are reliable in predicting structural parameters for such complex systems. Furthermore, symmetry of the thus optimized lattices is checked for In2O3-I, -II, and -III, and it is found that it is the same as that of the corresponding experimentally determined one. Although for the In2O3 phases studied in this paper the calculated and experimentally determined lattice parameters do not deviate much from each other, such a structural study is still needed because the optimized atomic positions deviate from experiment for In2O3-I. min for In2O3-III is larger Analysis of Fig. 2 shows that Etot than that of In2O3-I and -II. Total energies, volumes, and crystal structures for In2O3-I and -II are nearly the same and the difference is within the accuracy of the calculations. So, In2O3-I can be regarded as distorted In2O3-II, and small variation of temperature or pressure can cause structural transformation of In2O3-I into In2O3-II. The transition is well demonstrated in Table II about atomic distances of the relaxed and unrelaxed lattices of In2O3-I, -II, and -III. It is seen that after optimization, positional parameters for In2 and In3 atoms of In2O3 become almost the same when we use LDA and exactly the same for GGA. Furthermore, the positional parameters obtained from calculations within GGA are closer to experimental data than the LDA derived values. This result is in agreement with the general opinion that structural optimization using GGA is more preferable than that using LDA. However, as we noted above, underestimation of the equilibrium volume even within LDA is ⬍1.2%, which indicates that the relaxation within LDA, in this particular case, shall not lead to large deviations of electronic structure and optical spectra from experimental values except for In2O3-I. Due to the difference in the optimized and experimental positional parameters for In2O3-I, there is large difference in the electronic structure and optical properties between experimental and theoretically optimized structures for this phase. From Fig. 2, it is seen that equilibrium volume for In2O3-III is smaller, but the total energy is higher than that for In2O3-II, which indicates that In2O3-III is less stable than In2O3-II. Furthermore, at lower volumes, and, respectively, higher pressures, the dependence Etot共V兲 for In2O3-III crosses that for In2O3-II. It indicates that, upon compression, In2O3-II can be transformed into In2O3-III. In order to estimate the pressure value for the transitions from In2O3-II to -III, we have plotted the dependence of Gibbs free energy 共defined as G = U + PV, where U is the total energy for the particular pressure P at volume V兲 difference 共⌬G兲 as a function of the applied pressure 共Fig. 3兲. The pressure value at which ⌬G = 0 is the transition pressure at the structural phase transition point. According to our findings in Fig. 3, the pressure-induced phase transitions from In2O3-II to -III occurs at P = 3.83 GPa. TABLE II. Interatomic distances 共multiplicity in parentheses兲 for relaxed and unrelaxed lattices of In2O3-I, -II, and -III calculated by DFT within the LDA and GGA. The interatomic distances of the experimentally determined crystal structures correspond to unrelaxed lattices. Phase In2O3-I 共expt.兲 In1-O1 In1-O1 In2-O1 In2-O2 In2-O2 In3-O1 In3-O1 In3-O2 2.247 2.260 2.232 2.268 2.273 2.264 2.285 2.261 共3 ⫻ 兲 共3 ⫻ 兲 共2 ⫻ 兲 共2 ⫻ 兲 共2 ⫻ 兲 共2 ⫻ 兲 共2 ⫻ 兲 共2 ⫻ 兲 In2O3-I 共LDA兲 In2O3-I 共GGA兲 2.166 共3 ⫻ 兲 2.167 共3 ⫻ 兲 2.121 共2 ⫻ 兲 2.186 共2 ⫻ 兲 2.212 共2 ⫻ 兲 2.120 共2 ⫻ 兲 2.186 共2 ⫻ 兲 2.211 共2 ⫻ 兲 2.213 2.213 2.165 2.235 2.255 2.165 2.235 2.255 共3 ⫻ 兲 共3 ⫻ 兲 共2 ⫻ 兲 共2 ⫻ 兲 共2 ⫻ 兲 共2 ⫻ 兲 共2 ⫻ 兲 共2 ⫻ 兲 In2O3-II 共expt.兲 In2O3-II 共LDA兲 In2O3-III 共expt.兲 In2O3-III 共LDA兲 2.191 共6 ⫻ 兲 2.166 共6 ⫻ 兲 2.116 共3 ⫻ 兲 2.258 共3 ⫻ 兲 2.120 共3 ⫻ 兲 2.248 共3 ⫻ 兲 2.120 共2 ⫻ 兲 2.192 共2 ⫻ 兲 2.210 共2 ⫻ 兲 2.118 共2 ⫻ 兲 2.187 共2 ⫻ 兲 2.211 共2 ⫻ 兲 075129-4 PHYSICAL REVIEW B 76, 075129 共2007兲 PHASE STABILITY, ELECTRONIC STRUCTURE, AND… In2O3-II to -III ∆G (kJ/mol) 0.10 3.83 0.05 0.00 -0.05 3.0 4.0 3.5 4.5 Pressure (GPa) 5.0 FIG. 3. Gibbs free-energy difference for In2O3-III relative to In2O3-II 共open circles兲 as a function of the applied pressure. Structural phase transition point is marked with an arrow and the corresponding pressure value 共in GPa兲 is also stated. The pressure-induced structural transition is well demonstrated in the total energy variation with volume curves 共see Fig. 2兲, and from that, the dependence of the cell volume on applied pressure is derived 共Fig. 4兲. It is seen that the volume shrinkage at the transition pressure is 1.72 Å3. The phase transition In2O3-II-to-III is accompanied by breaking and transformations of chemical bonds between atoms and reconstruction of anion and cation sublattices. 3 cell volume (Å /f.u.) 65 In2O3-II In2O3-III 64 63 62 3.83 61 60 59 0 1 2 3 4 5 Pressure (GPa) 6 7 FIG. 4. Calculated cell volume as a function of pressure for In2O3-II and -III. The pressure-induced phase transition point is marked with an arrow and the corresponding pressure value at the transition point 共in GPa兲 is also stated. Phase transition from In2O3-II to -III was studied experimentally in the literature before. However, the reported transition pressure value from different experimental studies differs noticeably. In Ref. 38, such a transition has been demonstrated experimentally at 6.5 GPa and 1250 ° C. However, at pressures up to 6 GPa and temperatures 550, 1000, and 1450 ° C, In2O3 has been retained39 in phase -II. According to experiments of Ref. 26, the mixture of In2O3 and Co possesses the same structure as In2O3-III. The experimental results from Ref. 26 for pure In2O3 show that the formation of In2O3-III was possible at 800 ° C provided that the sample is initially preheated at 1250 ° C. Without the preheating, formation of In2O3-III occurred at 1000 ° C only. In contrast to the experimental report from Refs. 26, 38, and 39, the pressure-induced phase transition obtained in the present work is small and, however, it corresponds to 0 K. It may be noted that the phase selective growth of In2O3-III in the experiments of Ref. 11 always occurred at very low pressures 共20 kPa兲. Bulk modulus is the parameter characterizing the compressibility of a solid. The bulk modulus of In2O3-III is larger than those of In2O3-I and -II. Consequently, the phases -I and -II are more easily compressible than In2O3-III. No experimental data on bulk modulus values for pure In2O3-I, -II, and -III have been reported so far. So, the calculated bulk modulus values are compared to 99± 32 GPa of ITO films.40 It is seen that our calculated bulk moduli for In2O3 phases 共Table I兲 are much larger than that for the ITO films and, consequently, the pure In2O3 phases are hardly compressible than the Sn doped In2O3 films. B. Band structure For a better understanding of the electronic and optical properties and chemical bonding of the polytypes of indium oxide, the analysis of band structures can be quite helpful. Band structures for In2O3-I, -II, and -III calculated in this work are presented in Fig. 5. Although we noted above that In2O3-I is distorted In2O3-II, we still plotted band structure for both In2O3-I and -II to demonstrate how lattice distortion can drastically change the band structure. For example, a well distinct band region is seen in the bottom of the CB of In2O3-I 关Fig. 5共a兲兴 compared with other two polymorphs. This distinct band region is split from the rest of the CB, and it is located in the energy range 0.009– 2.391 eV above the topmost valence band 共VB兲. This band region can be called as intermediate band 共IB兲. Since IB is well dispersive, recombination of electrons and holes through this band is not expected to be very high. As this band region is completely empty, it can be useful for photoemission of electrons from VB to the IB. The small difference in total energy of In2O3-I and -II and large difference in the band features at the CB minimum in these two modifications indicate that one can drastically change the optical properties by different preparatory conditions by stabilization of different proportions of these two phases. Despite the large difference in crystal structures, In2O3-I, -II, and -III have some similar features. Particularly, the bottommost CB of In2O3-I, -II, and -III is dispersive and is 075129-5 PHYSICAL REVIEW B 76, 075129 共2007兲 KARAZHANOV et al. 4 3 2 1 (a) 0 Energy (eV) Γ 4 (b) 3 2 1 0 Γ H P Γ N 2.86 eV 1.10 eV H 4 3 2 (c) 1 0 F N N P Γ N L Γ 3.12 eV 1.25 eV Γ Z F FIG. 5. Band structure for 共a兲 unrelaxed In2O3-I, 共b兲 In2O3-II, and 共c兲 In2O3-III near the VB maximum and CB minimum. The Fermi level is set to zero. located at the ⌫ point, while the topmost VB is flat, which are the important properties inherent to TCO materials. The VB consists of three regions in all the three phases. The lowest one is located below −15 eV from the topmost VB. The bands at the intermediate energy region is located between −14 and −10 eV. Both these band energy regions are very narrow, while the topmost VB region is quite broad. The VB maximum is located at ⌫ point for In2O3-I and -II and at L point for In2O3-III. Consequently, one can conclude that the In2O3-III is an indirect band gap material, while In2O3-I and -II are direct band gap materials. The direct band gaps 共Edir g 兲 coming out from the LDA calculations are presented in Table III along with the experimentally determined values. Analysis of Table III shows that the calculated Edir g for In2O3-I, -II, and -III are underestimated due to the well-known problem of the DFT. Experimental data for the band gap of In2O3-I are not yet available. Our calculated Edir g for In2O3-II is in good agreement with 0.9 eV,13 1.0 eV,15 and ⬍1.0 eV,14 reported from DFT calculations. The second band gap 共Esg兲, which is the energy difference between the two lowest CBs, has been calculated. We found that Esg of In2O3-III is larger than that of In2O3-I and -II. So, one can expect transparency in a wider energy range of the solar spectra from In2O3-III than from In2O3-I and -II. The character 共direct or indirect兲 and value of the band gap are important factors for the characterization of TCO materials. Until recently, band-structure results obtained from different theoretical studies of In2O3-II have been controversial. From the band-structure calculations using the LMTO method within the atomic sphere approximation 共ASA兲 based on the LDA, it is found14 that the band gap of In2O3-II is indirect with CB minimum at the ⌫ point and VB maximum at H point. However, DFT calculations of Refs. 13, 15, and 42 show that the band gap of In2O3-II is direct with CB minimum and VB maximum located at the ⌫ point. The band gap value of 1.0 eV was found for experimental lattice constant and 1.5 eV for theoretically determined lattice constants.15 Recent systematic study of Ref. 17 by DFT calculations within LDA+ U and GGA+ U has shed light on the problem. It is found that the band gap of In2O3-II calculated within pure LDA and GGA is direct, while that calculated within LDA+ U and GGA+ U for U − J = 7 eV is indirect. Our results given in Table III are in agreement with these findings. We have calculated the band structure of In2O3-II using the theoretically and experimentally determined lattice constants within LDA and GGA. It shows that the CB minimum and VB maximum are located at the ⌫ point. Hence, we conclude that the band gap of In2O3-II calculated within pure LDA and GGA is direct. Our experience shows that the indirect band gap predicted by LMTO method is associated with the use of ASA in the calculation. From room temperature fundamental absorption edge studies, it was found43 that direct and indirect band gaps of single crystal In2O3-II are 3.750 and 2.619 eV, respectively. Similar band gap values have been found44 from absorption measurements for In2O3 films, which decreased with increasing film thickness from 2.65 eV for 100 nm to 2.40 eV for 400 nm. The band gap also decreased with increasing deposition temperature from 2.50 eV at 20 K to 2.30 eV at 270 K. Band gap reduction from 2.46 to 2.30 eV was reported to be caused also by increase of the annealing temperature from 200 to 500 K. From these reports, it appears that structural defects play an important role in defining the band gap of In2O3 and hence optical properties. C. Density of states Insight into the bonding interaction between constituents can be obtained from the site and orbital projected partial density of states 共DOS兲 analysis. Moreover, analysis of the projected density of states 共PDOS兲 gives detailed information about the origin of CB and VB electronic energy levels. Such analysis has been performed for all the phases of In2O3 considered in the present work 共Fig. 6兲. The main feature in Fig. 6 is that the DOS distribution of In and O are energeti- 075129-6 PHYSICAL REVIEW B 76, 075129 共2007兲 PHASE STABILITY, ELECTRONIC STRUCTURE, AND… TABLE III. Second band gap 共in parentheses兲 and fundamental band gap 共in eV兲 for In2O3-I, -II, and -III calculated from DFT within LDA 共ELDA 兲 and GGA 共EGGA 兲 using the lattice parameters determined theoretig g cally 共a0兲 and experimentally 共ae兲 along with experimentally measured values 共Eexpt. g 兲. ELDA g Phase In2O3-I In2O3-I In2O3-II EGGA g a0 ae 1.16 共2.93兲 1.17 共2.86兲 0.009 1.100 共2.860兲 In2O3-III 1.250 共3.120兲 a0 ae Eexpt g 1.33 共2.80兲 1.29 共2.84兲 3.70a 3.60b 3.70c 3.80d 3.00c a Reference 9. Reference 41. c Reference 11. dReference 26. b -1 -1 PDOS (States eV atom ) cally not separated, indicating that the nature of chemical bonding between In and O is not pure ionic and it contains some covalency, consistent with our charge-density analysis given below. Since the basic feature of In2O3-I has already been discussed in the previous section, below we concentrate our attention on the analysis of In2O3-II and -III. The VB of In2O3-II and -III can be divided into three regions. It is seen in Fig. 6 that the bands at the lowest 0.4 0.2 In1 0.4 0.2 In2 0.4 0.2 O EF s p d (a) In2O3-II 0.4 0.2 In 0.4 0.2 O EF 0 -15 -10 -5 (b) In2O3-III Energy (eV) 5 FIG. 6. 共Color online兲 The orbital and site-projected DOS for 共a兲 In2O3-II and 共b兲 -III. The Fermi level is set to zero. energy region 共below −15 eV from the topmost VB, we call it VB1兲 are mainly contributed by O 2s electrons with noticeable In 4d electrons. The bands at the intermediate energy region 共located between −14 and −10 eV, we call it VB2兲 are basically from In 4d electrons with small contribution from O 2s and 2p states due to hybridization interaction. Both these band energy regions are very narrow, while the topmost VB region is quite broad. The states around −5 eV in the VB 共we call VB3兲 are equally contributed by both In 5s and O 2p electrons. The main contribution to the topmost valence band of In2O3-III is from O 2p electrons, which has noticeable hybridization interaction with In 4d / 5p electrons. The results from the PDOS analysis are in good agreement with those of previous ab initio calculations9,14,15 and recent soft x-ray emission 共SXE兲 and soft x-ray absorption 共SXA兲 spectra measurements45 for In2O3-II. The character of the topmost VB is similar to that of ZnO, which is also a transparent conducting oxide 共see, e.g., Ref. 46兲. The position, dispersion, and character of the lowest CB carry the key features responsible for electro-optic properties of TCO materials.15 The bottommost CBs of In2O3-II and -III are mainly originating from In 5s electrons with finite O 2p contribution. Orbital and site decomposed DOS analysis is used for the detailed characterization of the contributions of electrons from s, px, py, pz, dxy, dxz, dyz, dx2−y2, and dz2 orbitals into the bands of particular interest. From such analysis, it is found that the topmost VB of In2O3-II and -III is contributed by electrons from O 2px, 2py, 2pz orbitals, which slightly hybridized with electrons from In 4dxy, 4dxz, 4dyz orbitals. The origin for the CB minimum of In2O3-II and -III is more or less the same, and it basically originates from electrons of In 5s orbitals with small O 2s, 2px, 2py, and 2pz character. Based on this analysis and the basic formulations suggested in Ref. 15 regarding highly dispersed and single character s-type band at the bottommost CB, the features that favor TCO behavior, one can conclude that In2O3 possesses the feature of s-electron based TCO. 075129-7 PHYSICAL REVIEW B 76, 075129 共2007兲 Intensity (arb. units) -1 -1 TDOS (States eV f.u. ) KARAZHANOV et al. 8 (a) 6 4 2 In2O3-II EF 8 (b) VB1 6 4 2 (c) VB3 VB2 BIS (×10) XPS (×10) XPS (×20) -15 In2O3-III -10 0 -5 Energy (eV) - - SXE SXA 5 FIG. 7. Calculated total DOS for 共a兲 In2O3-II and 共b兲 -III as compared with 共c兲 experimental data obtained from different techniques: BIS 共open triangles兲 共Ref. 47兲, XPS 共closed triangles, Ref. 47兲, XPS 共thick solid lines, Ref. 48兲, SXE 共Ref. 45兲, and SXA 共Ref. 45兲. The Fermi level is set to zero. The total DOSs for In2O3-II and -III are displayed in Fig. 7 along with XPS, bremsstrahlung isochromat spectroscopy 共BIS兲, SXE, and SXA measurements. The DOSs exhibit sharper peaks than the experimental spectra, since we have not included the lifetime broadening and instrumental resolution. As noted in the Introduction, there are no experimental XPS studies available on In2O3-I. So, comparative analysis with experimental data has been performed only for In2O3-II and -III. As noted in the previous section, there are three distinct regions in the VB of the In2O3 phases considered in the present work. According to the band dispersion and total DOS analysis, the widths of the band regions corresponding to VB1, VB2, and VB3 are 2.22, 1.52, and 6.38 eV for In2O3-I, 1.5, 1.77, and 5.46 for In2O3-II, and 0.81, 1.74, and 5.5 eV for In2O3-III, respectively. These results are in fair agreement with that of Ref. 13, where 2.33 eV for the VB2 and 5.70 eV for the topmost valence band are reported. This small discrepancy may be related to different approximations and methods used in the calculations. It should also be noted that the locations of the In 4d bands in In2O3-II and -III coming out from the DFT calculations are shifted toward higher energies and their intensity is also higher compared to experimental data 关Fig. 7共d兲兴. Analysis of Fig. 7 shows that the widths of VB3 of In2O3-II and -III more or less agree with SXE measurements, which show a well-defined intensive peak closer to the topmost VB. Such a peak is smeared out in other experimental spectra shown in Fig. 7. However, the experimental spectroscopic measurements show only one peak centered around −15 eV, whereas the DFT calculation show two 共VB1 and VB2兲 around this energy range. As mentioned in the PDOS analysis, the VB1 is mainly originating from O 2s electrons the photoionization cross section of which is much smaller than that of In 4d electrons; hence, VB1 band feature is not observed experimentally. So, the peak centered around −15 eV in the spectroscopic measurements can be concluded as the band features arising from In 4d electrons. However, the calculated 4d band 共VB2兲 position is shifted around 2.5 eV toward the valence band maximum. It may be noted that there is discrepancy in the XPS results of different groups. For example, the binding energy of the In 4d band is found to be at 14 eV in Ref. 47 and 18 eV in Ref. 48. This discrepancy may be associated with the use of different reference points in estimating the peak positions.45 The width of the calculated VB1 band agrees with experimental data of Refs. 45, 47, and 48. Furthermore, in our calculations, these two peaks are much more intense than the topmost valence band, which disagrees with experimental data but agrees with theoretical calculations of Refs. 9 and 14. The reason for the discrepancy can be that the photoionization cross section is important in accounting for the intensity. So, only locations of the calculated total DOS have been compared with the experimental measurements. It is important to note that the pseudocore d bands are not placed correctly in systems such as ZnO 共Ref. 49兲 and CdTe 共Ref. 50兲 by the present type of calculations. So, one should go beyond the LDA/GGA calculations by taking into account the Coulomb correlation effects from the In 4d electrons through methods such as LDA+ U, LDA+ SIC, etc. Recent study17 of band structure of In2O3 showed that within LDA + U and GGA+ U calculations for U − J = 7 eV, the In 4d levels have been shifted toward lower energies and split the O 2s band into two parts. D. Conduction band effective masses Effective masses characterize band dispersion and are one of the important parameters linking electronic structure with transport properties of solids. As noted above, the lowest CBs of In2O3-II and -III are more dispersive than the topmost VB, which means that the CB electrons are lighter than holes. Almost flat topmost VB indicates that valence electrons are tightly bound to the atoms. Consequently, the dominant intrinsic charge carriers in In2O3 are expected to be electrons and not holes, consistent with experimental observations. Hence, we focus on the CB electron effective masses, and the calculated results are presented in Table IV. Analysis shows that the calculated masses for In2O3-II and -III are almost isotropic. The observed small anisotropy can be related to the effect of p and d orbitals hybridizing with s orbitals. The deviation in the calculated effective masses from the experimentally measured values are in the range 23%–33%. This deviation can be related to the deficiency of DFT in the calculation of the eigenvalue of electrons. So, not only the band gap but also the band dispersion comes out incorrectly, and this effect is generally well pronounced in 075129-8 PHYSICAL REVIEW B 76, 075129 共2007兲 PHASE STABILITY, ELECTRONIC STRUCTURE, AND… TABLE IV. Calculated effective masses of CB electrons 共in units of the free-electron mass m0 and in the directions indicated兲 for In2O3-II and -III are compared with available experimental and calculated values. In2O3-II 0.23 0.20 0.23 0.42 0.30 0.36 0.30 0.36 0.41 0.30 共⌫-H兲 共⌫-N兲 共⌫-P兲 共⌫-H兲c 共⌫-N兲c 共⌫-P兲c 共⌫-H兲f 共⌫-N兲f 共⌫-P兲f 共⌫-P兲g In2O3-III ZnO 0.16 共⌫-F兲 0.14 共⌫-L兲 0.15 共⌫-Z兲 0.23 共E 储 c兲a 0.21 共E ⬜ c兲a 0.24b 0.28 共E 储 c兲d 0.32 共E ⬜ c兲d 0.14 共E 储 c兲e 0.13 共E ⬜ c兲e FIG. 8. 共Color online兲 共a兲 Charge density 共in e / Å3兲 and 共b兲 ELF for In2O3-II in the 共011兲 plane. aFP LMTO, Ref. 51. Ref. 56 c LMTO ASA, Ref. 14. dLCAO, Ref. 57. eVASP-PAW, Ref. 49. f DMOL3, Ref. 58 gExperiment, Refs. 41 and 59. bExperiment, transition metal oxides 共see, e.g., Refs. 51–55兲. Experimental data for CB electron effective masses are available for In2O3-II only. The calculated effective masses from the present study are compared with available experimental and other theoretical values available for In2O3-II and ZnO 共other well-known TCO兲 in Table IV. Overall, the presently calculated CB effective masses for In2O3-II are smaller than those from experimental and other theoretical values. In particular, the masses calculated by the LMTO ASA 共Ref. 14兲 method agree fairly with experimental data and are more anisotropic than our results. Analysis shows that the calculated effective masses for In2O3-II are considerably larger than those for In2O3-III. Hence, carrier mobility in In2O3-III is expected to be larger than that in In2O3-II. The calculated effective masses for In2O3-II are much closer to experimental data than that for ZnO. This difference in accuracy of the calculated masses comes from Coulomb correlation effects, which are strong in ZnO.49 In DFT calculations within LDA, the Zn 3d bands are located inappropriately close to the topmost VB, falsifying the band dispersion and, consequently, effective masses. As noted in the analysis of the band dispersion 共Fig. 5兲, In 4d band is located much below the topmost VB than the 3d band in ZnO. So, Coulomb correlation effects in In2O3-II and -III are not as strong as that in ZnO to falsify the band masses significantly. distribution shows that the highest charge density is residing in the immediate vicinity of the atomic sites, reflecting the dominant ionic-type bonding. If the bonding interaction between In and O is purely ionic, one could expect negligible charge-density distribution between these ions. From Fig. 8, it is clear that there are finite charges distributed in between In and O in all the polytypes. Also, the charge around In and O atoms is not distributed spherically. These features indicate that apart from dominant ionic bonding, finite covalentlike bonding interaction is present between In and O. The observed hybridization interaction is responsible for the mixed nature of the electronic structure of this material discussed in the previous section. This suggestion is also confirmed by the Born-effective-, Bader-, and Voronoi-charge analyses in the following section. The ELF analysis is one of the ways to measure the probability of distribution of paired electrons in solids.60–62 It is seen from Fig. 8 that the maximum value of ELF is around O and the minimum around In atoms, which confirms the dominant ionic bonding. Between the In and O atoms, the ELF does not show any maximum value, and this indicates that there is no dominant covalent-type bonding interaction present between these atoms. However, nonspherical distri- E. Charge-density and electron localization function analysis For qualitative characterization of the bonding interaction between constituents, charge-density and electron localization function 共ELF兲 analysis have been performed for In2O3-II 共Fig. 8兲 and -III 共Fig. 9兲. Analysis of the charge FIG. 9. 共Color online兲 共a兲 Charge density 共in e / Å3兲 and 共b兲 ELF for In2O3-III in the 共100兲 plane. 075129-9 PHYSICAL REVIEW B 76, 075129 共2007兲 KARAZHANOV et al. TABLE V. Atomic charges 共in units of the electron charge e−兲 around In and O atoms calculated according to Voronoi and Bader topological analyses for In2O3-II and -III. Compound Atom Voronoi Bader In2O3-II In1 In2 O 2.00 2.04 −1.36 1.81 1.84 −1.23 In2O3-III In O 2.09 −1.39 1.81 −1.20 bution of ELF at the O site and small but finite value of ELF in between In and O reflect the presence of non-negligible hybridization interaction between these atoms. Unlike intermetallic phases,60 no isolated spot in the interstitial regions with high ELF is found in any of the In2O3 phases considered here. F. Bader- and Voronoi-charge analyses For quantitative characterization of chemical bonding in solids, Bader- and Voronoi-charge analyses63–65 are widely used. In the Bader-charge analysis, each atom of a compound is surrounded by a surface 共called Bader regions兲 that runs through the minima of the charge density and the total charge of the atom is determined by integration within the Bader region. In the Voronoi-charge analysis, each grid point of charge density is assigned to the nearest atom, but each of these distances is not scaled by the radius of each atom. So, the Voronoi charges in the present paper are used just for a sanity check. Table V presents the charges at each atomic site for In2O3-II and -III calculated according to the Bader and Voronoi schemes. As expected, In atoms donate electrons while O atoms accept them. Based on the amount of the transferred charges, one can conclude that chemical bonding is of dominant ionic type. G. Born effective charges Born effective charges 共BECs兲 are the fundamental parameters characterizing the change in electron polarization upon displacement of atoms. They are related to microscopic electron currents produced in a system by a change of the atomic position. These currents may contribute to the BEC, which is unrelated and additional to the static electron charge carried out by the atoms during the displacement, so that BECs can be much larger than their static counterpart, i.e., higher than formal valence charge. In this case, BECs are referred to as anomalous. BECs are helpful in understanding the ferroelectric and piezoelectric properties of materials. For the present study, BECs were obtained from finite differences of macroscopic polarization induced by small displacements of the atomic sublattices using the Berry phase approach.66,67 The calculated BEC for In2O3-III is given in Table VI. The formal valences for In and O are +3 and −2, respectively. The calculated BECs reflect this formal valence picture that the average diagonal components of the BEC at the In and O sites are 3.27 and −2.17, respectively. These values are slightly larger than the formal valence, indicating that there is small anomalous charge 共also called dynamical charge兲 added to the static charge in the atoms. The diagonal components of the BEC are almost the same, indicating that the bonding interaction is more isotropic reflecting ionic-type bonding. It is seen that for In atoms, the off-diagonal elements of the BEC tensor are negligible, reflecting the ionictype interaction. However, there are non-negligible offdiagonal elements of BEC at the O site, indicating that there is finite covalentlike bonding interaction present between O atoms. This result is in agreement with charge density and ELF analysis 共Fig. 9兲, which demonstrates that there is finite directional bonding between nearest neighbor O atoms. H. Optical properties Optical properties of In2O3-I, -II and -III are studied. The real and imaginary parts of the optical dielectric response function, absorption coefficient, reflectivity, refractive index, and the extinction coefficients have been analyzed. Since the crystal structure of In2O3-I and -II is cubic, the optical spectra are isotropic along the crystallographic a, b, and c axes. So, only one of the components is sufficient for the analysis. We also found that the optical spectra of In2O3-I with optimized lattice and In2O3-II are almost the same. Figure 10 presents the calculated optical spectra for In2O3-II and -III. All the calculated optical spectra of In2O3-II and -III are shifted toward lower energies compared with experimental results owing to the underestimation of the band gap in the DFT calculations. One of the ways to rectify it is to use the scissors operator technique, i.e., rigid shift of all the CB states, so that the optical spectra shall also be shifted accordingly.55,68 The search of literature shows that experimental data are available for In2O3-II in Ref. 41, where reflectivity and transmittance spectra were measured by spectrophotometry at room temperature. The other optical spectra such as absorption coefficient, refractive index, and the extinction coefficient are calculated using the KramersKronig relation. These five optical spectra have been compared in Fig. 10共a兲 with those calculated from the present band-structure results. The optical spectra of In2O3-II were measured41 for a narrow energy range 0 – 6 eV, which contains only the E0 peak induced by electronic transitions from TABLE VI. Calculated Born-effective-charge-tensor elements 共Z*兲 for the constituents of In2O3-III. Atom In1 O1 xx yy zz xy yz zx xz zy yx 3.300 −2.260 3.306 −2.136 3.206 −2.130 0.009 0.098 0.002 0.432 0.000 0.186 0.001 0.257 0.000 0.308 0.002 0.432 075129-10 PHYSICAL REVIEW B 76, 075129 共2007兲 PHASE STABILITY, ELECTRONIC STRUCTURE, AND… ε2(ω) ε1(ω) 6 In2O3-II 4 4 2 2 6 6 4 4 2 2 R(ω) In2O3-III E || c E⊥c d1 d 2 E0 0.2 d2 0.2 0.1 E1 0.1 E0 E1 E2 d1 E2 2 3 α(ω) 6 2 Expt. 1 k(ω) n(ω) 1 2 2 Expt. 1 1 1.2 1.2 0.8 0.8 0.4 0.4 5 10 15 5 Energy (eV) 10 15 FIG. 10. Optical spectra of In2O3-II and In2O3-III for directions of the electric field 共E兲 parallel 共E 储 c兲 and perpendicular 共E ⬜ c兲 to the crystallographic c axes. Calculated imaginary parts of the optical dielectric function 关2共兲兴, absorption coefficient 关␣共兲 in cm−1 multiplied by 10−5兴, reflectivity 关R共兲兴, refractive index 关n共兲兴, and extinction coefficients 关k共兲兴 for In2O3-II have been compared with experimental data of Ref. 41. Calculated absorption coefficient for In2O3-III has been compared with experimental results of Ref. 11. the VB maximum to CB minimum occurring at the ⌫ point. So, in the present work, these experimental data were used for rigid shift of the calculated optical spectra toward higher energies by 1.65 eV to fit to location of the E0 peak. Since the location of the E0 peak is clearly seen in the spectra of n共兲, fitting was performed for n共兲. The other spectra have been shifted accordingly. From the comparison of the calculated spectra with experimentally measured spectra, one can see that the calculated n共兲 and k共兲 agree well with experimental data. Calculated reflectivity spectra agree with experimental data only at higher energies well above the band gap. At lower energies, near the band gap, experimental reflectivity is higher than that calculated by DFT, and the experimentally observed low energy peak may be associated with excitonic effect, which is not considered in the present calculations. The calculated absorption spectra agree with the measured spectra at lower energies. However, at energies exceeding the location of the E0 peak, the calculated absorption coefficient is found to be much smaller than the experimentally determined values. The origin for the deviation between experimental and theoretical absorption coefficient spectra is not known. Because of the rhombohedral symmetry, there is optical anisotropy present in In2O3-III. The two components of the dielectric functions are calculated for In2O3-III corresponding to the electric field parallel E 储 c and perpendicular E ⬜ c to the crystallographic c axes. The first experimental data for In2O3-III are already available.11 The absorption coefficient was measured for the energy range 0 – 6 eV, which contains the E0 peak. The calculated absorption spectra were shifted to 1.35 eV toward higher energies to fit the E0 peak in order to match with experimental spectra. The other calculated optical spectra have also been shifted accordingly. The anisotropy is well pronounced at energies from ⬃7 to 9 eV, whereas the optical spectra are more or less isotropic at other energies considered. The locations of all the major peaks of the optical spectra corresponding to both the directions are almost the same except the E2 peak. The magnitude of the E2 peak at around 7.5 eV is higher for E 储 c and its shoulder at 8.3 eV is larger than that for E ⬜ c. Absorption and reflectivity spectra for this compound are low in the energy range 0 – 5 eV, indicating that it will be optically transparent. The intensity of the calculated optical spectra differs from the experimentally measured one for both In2O3-II and -III. The reason of this deviation may be related to the factors such as overestimation of the momentum matrix elements, neglect of the Coulomb interaction between free electrons and holes 共excitons兲, and local-field and finite lifetime effects. Furthermore, in the calculations of the imaginary part of the dielectric response function 关2共兲兴, only the direct optical transitions from occupied to unoccupied states are considered. Also, the lifetime effects and the experimental resolution smear out many fine features. Moreover, the experimental measurements11,41 are made on thin films at room temperatures where one could expect considerable amount of defects which will cause changes in optical properties. However, the theoretical optical spectra are valid only for defect free single crystals at low temperatures. IV. CONCLUSION Structural properties, electronic structure, high-pressure behavior, and optical properties of In2O3 of space group symmetries I213, Ia3̄, and R3̄ are studied by DFT calculations. From the structural optimization using total energy cal- 075129-11 PHYSICAL REVIEW B 76, 075129 共2007兲 KARAZHANOV et al. culations, the equilibrium lattice and positional parameters of all the three polytypes of In2O3 have been found, which are in good agreement with experimental data except for the I213 phase where the positional parameters deviate from experiment. In2O3 in space group of I213 is found to be a distorted one of space group Ia3̄. Upon optimization of the lattice, the former is transformed into the latter structure. The present calculations predicted pressure-induced phase transition from In2O3-II to -III. The calculated transition pressure is compared with available experimental values. Based on the analysis of band structure calculated within LDA and GGA, it is found that In2O3-III has indirect band gap, whereas In2O3-II has direct band gap. Intermediate band is found in In2O3-I located right above the valence band, and it is isolated from the valence and conduction bands. From the orbital decomposition analysis and orbital as well as siteprojected density of states, the characters of the valence and conduction bands have been analyzed. It is shown that the topmost valence band consists of O 2p states hybridized with In 4d states. Further, we found that the conduction band minimum of In2O3-II consists of In 5s orbitals hybridized with O 2s orbitals, whereas that for In2O3-III is mainly In 5s states. From orbital and site decomposed band analysis, it is shown that the topmost valence bands of In2O3-II and -III are 1 H. Kawazoe, M. Yasukawa, H. Hyodo, M. Kurita, H. Yanagi, and H. Hosono, Nature 共London兲 389, 939 共1997兲. 2 G. 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