J. Appl. Phys. 108, 053511 (2010); https://doi.org/10.1063/1.3467780 108, 053511 © 2010 American Institute of Physics. Limits for -type doping in and : A theoretical approach by first-principles calculations using hybrid-functional methodology Cite as: J. Appl. Phys. 108, 053511 (2010); https://doi.org/10.1063/1.3467780 Submitted: 01 June 2010 • Accepted: 29 June 2010 • Published Online: 08 September 2010 Péter Ágoston, Christoph Körber, Andreas Klein, et al. ARTICLES YOU MAY BE INTERESTED IN Evaporated Sn-doped In2O3 films: Basic optical properties and applications to energy- efficient windows Journal of Applied Physics 60, R123 (1986); https://doi.org/10.1063/1.337534 First-principles analysis of structural and opto-electronic properties of indium tin oxide Journal of Applied Physics 111, 103110 (2012); https://doi.org/10.1063/1.4719980 A review of Ga2O3 materials, processing, and devices Applied Physics Reviews 5, 011301 (2018); https://doi.org/10.1063/1.5006941 https://images.scitation.org/redirect.spark?MID=176720&plid=1401535&setID=379065&channelID=0&CID=496959&banID=520531443&PID=0&textadID=0&tc=1&type=tclick&mt=1&hc=a8ed6d6accfc4f6e55ce8ba7eb988496e95a35fd&location= https://doi.org/10.1063/1.3467780 https://doi.org/10.1063/1.3467780 https://aip.scitation.org/author/%C3%81goston%2C+P%C3%A9ter https://aip.scitation.org/author/K%C3%B6rber%2C+Christoph https://aip.scitation.org/author/Klein%2C+Andreas https://doi.org/10.1063/1.3467780 https://aip.scitation.org/action/showCitFormats?type=show&doi=10.1063/1.3467780 https://aip.scitation.org/doi/10.1063/1.337534 https://aip.scitation.org/doi/10.1063/1.337534 https://doi.org/10.1063/1.337534 https://aip.scitation.org/doi/10.1063/1.4719980 https://doi.org/10.1063/1.4719980 https://aip.scitation.org/doi/10.1063/1.5006941 https://doi.org/10.1063/1.5006941 Limits for n-type doping in In2O3 and SnO2: A theoretical approach by first-principles calculations using hybrid-functional methodology Péter Ágoston,1,a� Christoph Körber,1 Andreas Klein,1 Martti J. Puska,2 Risto M. Nieminen,2 and Karsten Albe1 1Institut für Materialwissenschaft, TU Darmstadt, Petersenstr. 32, D-64287 Darmstadt, Germany 2Department of Applied Physics, Aalto University School of Science and Technology, P.O. Box 11100, FIN-00076 AALTO, Finland �Received 1 June 2010; accepted 29 June 2010; published online 8 September 2010� The intrinsic n-type doping limits of tin oxide �SnO2� and indium oxide �In2O3� are predicted on the basis of formation energies calculated by the density-functional theory using the hybrid-functional methodology. The results show that SnO2 allows for a higher n-type doping level than In2O3. While n-type doping is intrinsically limited by compensating acceptor defects in In2O3, the experimentally measured lower conductivities in SnO2-related materials are not a result of intrinsic limits. Our results suggest that by using appropriate dopants in SnO2 higher conductivities similar to In2O3 should be attainable. © 2010 American Institute of Physics. �doi:10.1063/1.3467780� I. INTRODUCTION Transparent conducting oxides �TCO� exhibit a unique combination of electrical conductivity and optical transpar- ency in the visual range.1 In2O3 and SnO2 are widely used in optoelectronic devices2 and in gas-sensing applications.3 Un- der reducing conditions these materials exhibit n-type con- ductivity and oxygen deficiency due to the occurrence of oxygen vacancies4–6 and possibly hydrogen.7–9 The conductivity in these TCO materials is usually ob- tained by adding large amounts �2%–10%� of n-type dopants to the host.1 The conductivity is then mainly determined by the free electron concentration in the conduction band. On the other hand, the conductivity is given by the doping effi- ciency, i.e., the degree of ionization of the dopant, which is generally high for frequently-used material combinations such as tin in In2O3 �ITO� or fluorine or antimony in SnO2 �FTO and ATO, respectively�. While ITO shows the highest conductivities of all the TCO materials its high price has stimulated research for find- ing cheaper alternatives.10,11 ATO, on the other hand, is cheap but lower conductivities obtained12 hinder its commer- cial application. Doping on the anion site with fluorine in FTO increases the conductivities but FTO is still signifi- cantly outperformed by ITO.10 Additionally, it is difficult to use fluorine in conjunction with sputtering techniques. For these materials degenerate carrier densities can easily be ob- tained, reflected in a Fermi level position within the conduc- tion band. High Fermi energies, however, can only be achieved, if no compensating intrinsic defects such as cation vacancies and oxygen interstitials are limiting the range of accessible Fermi level positions. Therefore a detailed under- standing of the properties of intrinsic acceptor-type compen- sating defects is necessary for estimating n-type doping lim- its in these materials. Frank and Köstlin13 proposed the well-established view that the doping limit in ITO should be exclusively ruled by the occurrence of interstitial oxygen, which at the same time binds to the tin dopants. To the best of our knowledge a similar model for ATO or FTO has not yet been established. Experimentally, no significant influence of the oxygen partial pressure on the conductivity was found for ATO samples,12 which suggests that the presence of intrinsic acceptors is of minor importance in this material. In the case of FTO, a decrease in conductivity, however, has been reported for high fluorine contents, which was assumed to be due to the occur- rence of fluorine interstitial acceptors.14,15 On the other hand, anomalies in electrical conductivity measurements of pure and slightly acceptor-doped SnO2 samples as a function of oxygen partial pressure and dilatation measurements16 hint to the presence of cation vacancies at elevated temperatures. Density-functional theory �DFT� calculations within the generalized gradient approximation �GGA� have confirmed that oxygen interstitials in In2O3 are more stable than indium vacancies,5 which is in line with the defect model of Frank and Köstlin. Of intrinsic acceptor in SnO2, tin vacancies have lower formation energies than oxygen interstitials.6 In both studies, however, the formation energies are severely underestimated leading to pinning values of the Fermi energy well below those experimentally accessible.17 This would imply, that in contrast to experimental findings, n-type dop- ing is hardly possible especially under more oxygen-rich conditions and that the Fermi level cannot enter into conduc- tion band significantly. If one considers the large formation entropies of acceptor-type defects18 the situation becomes even worse. The main reason for this deficiency is the short- comings of local approximations to DFT which are espe- cially significant in the case n-type TCOs.4 In this study, we revisit the problem of the thermody- namic stability of acceptor-type point defects in In2O3 and SnO2 using hybrid-functional DFT in conjunction with finite-size corrections based on the local density approxima- tion �LDA� and large supercells.a�Electronic mail: agoston@mm.tu-darmstadt.de. JOURNAL OF APPLIED PHYSICS 108, 053511 �2010� 0021-8979/2010/108�5�/053511/6/$30.00 © 2010 American Institute of Physics108, 053511-1 http://dx.doi.org/10.1063/1.3467780 http://dx.doi.org/10.1063/1.3467780 http://dx.doi.org/10.1063/1.3467780 II. METHODOLOGY A. Computational approach Total energy calculations were carried out using the VI- ENNA AB INITIO SIMULATION PACKAGE.19,20 For the representa- tion of exchange and correlation we use the hybrid- functionals HSE06 and PBE0 for In2O3 and SnO2, respectively.21–24 The two functionals are closely related and only differ by the value of the range-separation parameter which we have adjusted in order to reproduce the band gaps. Within this approach the band-gap problem is resolved and no correction schemes need to be applied. The potentials due to the nuclei and the core electrons were represented by the projector augmented wave scheme.25,26 The plane wave-cut- off energy was set to 500 eV to assure well converged results �better than 0.01 eV/atom�. Except for the nonlocal-exchange part of PBE0/HSE06 calculations, the Brillouin-zones were sampled with 2�2�2 Monkhorst–Pack k-point grids.27 Ionic relaxations were carried out until the forces on the unclamped ions decayed to less than 0.01 eV/Å. Within the hybrid-functionals scheme, structural as well as thermodynamic parameters are reproduced well and the band gaps agree closely with the experimental values.28–30 In the case of hybrid-functional calculations we used su- percells containing 72 and 80 atoms for SnO2 and In2O3, respectively. Due to the high computational cost a systematic finite-size scaling using hybrid functionals is not yet feasible. B. Finite-size effects Because of the existence of highly charged defect states �charge q=−3 for VIn and q=−4 for VSn�, the effects of the finite cell-size have to be considered and corrected. In this case the electrostatic image charge interactions arising from electrostatic monopoles embedded in a jellium counter- charge is the dominating energy contribution. Based on the LDA calculations using cell sizes up to 640 and 576 atoms for In2O3 and SnO2, respectively, we have confirmed the E �V−1/3 long-range scaling behavior in our calculations in- cluding full structural relaxation of the supercells at constant volume. Since we observed the expected long-range interac- tion regime in our calculations we obtained the correction term �E=E80/72 LDA −E� LDA by fitting the two first terms of the Makov–Payne series.31 We have taken the defect formation energies as obtained from the hybrid-functional calculations and added the LDA finite-size correction term to them. For highly charged defects this LDA correction can be seen as a lower boundary of the positive correction values, since the static dielectric constant is overestimated by the LDA. Addi- tional hybrid-functional calculations with cell sizes of 40 and 162 for In2O3 and SnO2, respectively, confirmed this trend. Therefore, also our calculated formation energies mark a lower boundary with respect to the finite-size correction. Us- ing this setup we predicted approximate doping limits arising due to the occurrence of intrinsic acceptor defects in In2O3 and SnO2. III. RESULTS A. Defect energetics The formation energies were obtained as a function of the chemical potentials of the constituents �i and the Fermi energy EF in all relevant charge states q as32 �GD q = Gdef q − Ghost − � i ni�i + q�EVBM + EF� , �1� where the Gibbs free energies of the supercells with �Gdef q � and without �Ghost� the defect are taken at the zero- temperature and zero-pressure limits. The reference for the Fermi energy is the valence band maximum �VBM� of the host material. The allowed stability region is given by the heat of formation of the host compound which we have ob- tained using the hybrid functionals �see Table I�. Figure 1 shows the finite-size corrected formation ener- gies of the acceptor defects in In2O3 and SnO2 for maximally reducing conditions. At this limit the formation energies of all acceptors attain their highest values and are therefore suit- able for the discussion of maximum doping limits. For the two materials the doping limits are approximately given by the lowest-energy intersections of the formation energies with the zero energy line in the left part of the figure. For both materials the intersections are significantly ��2 eV� beyond the conduction band minimum �CBM� rendering the materials truly n-dopable. Moreover, it is very clear that SnO2 is intrinsically compensated only at Fermi energies TABLE I. Comparison of calculated and experimentally measured proper- ties of In2O3 and SnO2 and their constituent phases, i.e., In and Sn metals and the oxygen dimer. Calculations for the compounds and the elements were carried out using the LDA as well as the HSE06 and PBE0 functional for In2O3 / In and SnO2 /Sn, respectively. �Hf, EG, a, c, and r0 denote the compound heat of formation in eV/f.u.’s, band-gap in eV’s, lattice constants in Å, and the dimer bond length in Å respectively. Experiment LDA HSE06 PBE0 Indium oxide �bixbyite, Ia3̄, SG.206� a0 10.117a 10.15 10.23 ¯ EG 2.6–2.9b 1.2 2.6 ¯ �Hf �9.47d �10.6 �10.1 ¯ Tin oxide �rutile, P42 /mnm, SG.136� a 4.738a 4.73 ¯ 4.76 c 3.188a 3.20 ¯ 3.19 EG 3.6 1.2 ¯ 3.6 �Hf �6.01d �6.8 ¯ �6.7 Indium �tetragonal, I4/mmm, SG.139� a 3.332c 3.37 3.35 ¯ c 4.471c 4.35 4.64 ¯ �-tin �tetragonal, I41 /amd, SG.141� a 5.831c 5.72 ¯ 5.80 c 3.181c 3.20 ¯ 3.26 Oxygen �dimer� r0 1.208c 1.22 1.21 1.21 aReference 33. bReferences 28 and 34. cReference 35. dReference 36. 053511-2 Ágoston et al. J. Appl. Phys. 108, 053511 �2010� considerably higher than In2O3. Namely, in this limit the compensation occurs above �4.7 eV and �5.7 eV for In2O3 and SnO2, respectively. This result is not obtained using the LDA,6 GGA,5 or GGA+U �Ref. 37� functionals. Very generally, the �semi- �local functionals are not able to provide a description of these TCO materials in accordance with experiments,1,10 i.e., the formation energies are significantly overestimated for donors,4,38 whereas they are underestimated for acceptors as we showed in this study. In practice, under experimental deposition/annealing conditions, the oxygen chemical poten- tial is not fully at the reducing limit but may have typically values between �o= �−1.0�– �−2.0� eV �this is true, e.g., for the conditions of T=600 °C and pO2 pO2 ambient�.39 For this reason we have plotted in the right part of Fig. 1 the forma- tion energies of the acceptor defects in their predominant charge states for the Fermi level at the CBM as a function of the oxygen chemical potential. Thus, the n-dopability of both materials can be compared irrespective of the different band gaps. The figure illustrates the fact that unless degenerate doping is achieved, in both materials no acceptor defect can contribute significantly to the defect equilibria. For example, the formation energy of the double negative oxygen intersti- tial in In2O3 is �1 eV in the oxidizing limit and for the Fermi energy at the CBM. Since the oxidizing limit is unre- alistic at elevated temperatures and the Fermi energy is gen- erally below the CBM for undoped and oxidized In2O3 samples,40–42 we can exclude the occurrence of intrinsic ac- ceptor defects under any experimentally accessible condi- tions. As can be seen in the left part of Fig. 1 this effect is even more pronounced for SnO2. For the Fermi energy at the CBM and at most oxidizing conditions the formation ener- gies of both acceptors are larger than 1.8 eV. Note also that the use of the calculated heats of formation for the determi- nation of the stability range underestimates the formation energies in the oxygen-rich limit whereas the values are more reliable in the metal-rich limit.43 In In2O3 oxygen interstitials are the predominant accep- tor defects with the charge state q=−2. However, the indium vacancy is energetically very close to the interstitial at the doping limit, which is easily reached in ITO. In fact, based on the estimated extrapolation error of the finite-size scaling, the remaining uncertainties of the exchange-correlation func- tionals, and the zero-temperature approximation,18 it is not possible to surely predict the energetic order of the acceptor defects at the doping limit. Based on experiment the oxygen interstitial was suggested to compensate the donors.13 Ac- cording to our calculations it is safe to assume that indium vacancies will be present in considerable numbers at high Fermi energy values. This finding is also consistent with the remarkable mobility observed for Sn cation dopants in ITO �Ref. 40� presuming a vacancy-mediated migration mecha- nism. For a further clarification of this point, defect-defect interactions among the donor dopants and acceptors should be still investigated. In SnO2 the energetic order of the defects is unambigu- ous with the vacancies more stable than the oxygen intersti- tials. This is consistent with the previous LDA calculations6 and can be explained by the close packing of the rutile struc- ture which makes the incorporation of large anion intersti- tials energetically expensive. The close packing is also re- flected in a strong structural relaxation of the neighboring atoms around the oxygen interstitial in SnO2 �see Fig. 2�. For FIG. 1. �Color online� On the left: formation energies of acceptor defects in SnO2, and In2O3 in the metal-rich limit �left�. On the right: formation energies of acceptor defects at the conduction band minima as a function of the oxygen chemical potential. The stability limits for the two materials are similar �see Table I�. FIG. 2. �Color online� Comparison of the structural relaxations of oxygen interstitials in SnO2 and In2O3. The outward relaxation of neighboring oxy- gen atoms is especially large in SnO2. Oxygen anions and the metal cations are marked with O and M, respectively. 053511-3 Ágoston et al. J. Appl. Phys. 108, 053511 �2010� the same reason also the charge-state transition �0/�2� is found at high Fermi level positions for SnO2 �left part of Fig. 1�. The formation volume of the interstitial oxygen, i.e., the elastic strain can be decreased by releasing two electrons and forming a neutral oxygen dumbbell configuration on a regu- lar oxygen lattice site. This covalently bonded configuration is, therefore, more stable than the negative charge state for Fermi level positions throughout the whole band-gap. In the negative state the surplus atom is necessarily located in the interstitial region due to the destabilization of the covalent bond upon electron addition. In comparison, the structural relaxation around the interstitial in In2O3 is much weaker due to the presence of the large interstitial sites within the bixby- ite structure �Fig. 2�. Therefore the energetic cost for the accommodation of the negative interstitial is low and the charge transition level �0/�2� is below the CBM. B. Electron concentration According to our hybrid-functional calculations the for- mation energies of acceptor defects generally increase in comparison with the LDA/GGA results. Within our choice of hybrid functionals, which reproduce the experimental band gaps, the increase is clearly larger for SnO2 than in In2O3. This contradicts with the experimental trend indicating dop- ing difficulties for SnO2 but not for In2O3.10 In order to il- lustrate this finding more clearly, we have calculated the electron concentrations self-consistently on the basis of the finite-size corrected formation energies of acceptor defects obtained from hybrid-DFT total energy calculations. The defect concentrations were obtained by the usual Boltzmann type expression, c = c0exp�− �Gf kBT , �2� where c0 is the concentration of available sites for the defect and �Gf the free energy of defect formation. Since we are presently only interested in the defect properties of the in- trinsic acceptors, the n-dopant is assumed to be ideal in this calculation, i.e., it has the ionization probability of unity and it is ideally soluble. For both materials we use temperature- independent parabolic band edges with effective electron and hole masses of 0.3 me and 0.6 mh, respectively.1 Because the Fermi level can enter into the conduction band, we use the Fermi function instead of the Boltzmann approximation in order to integrate the charge carriers densities. Note that by relaxing the above approximations our arguments for the theory-experiment discrepancy in n-type doping are further strengthened. Namely, nonparabolic bands, band-gap renormalization,44 and a temperature dependent band gap45 would result in a slower increase in the Fermi level in the conduction band as a function of the free electron concentra- tion. Therefore our calculated carrier concentrations repre- sent lower bounds. Figure 3 shows the free electron concentration due to heavy n-type doping as a function of the oxygen partial pres- sure in the range from 10−15 to 105 Pa, which is accessible within experiments. The oxygen partial pressure is obtained from the oxygen chemical potential via the ideal gas law and using electrochemical tables for the temperature of 600 °C.39,43 The conductivities are given for three different doping concentrations of 2�1020, 6�1020, and 2 �1021 cm−3, corresponding to the range of �1%–10% of substituted cations. The free electron concentrations are highest at low oxy- gen pressures and mainly determined by the doping concen- trations. For every dopant concentration there is a character- istic pressure at which the electron concentration begins to decay with increasing oxygen pressure. This characteristic transition is also found in experiments for ITO �Ref. 46� and has a temperature dependence such that it shifts to higher oxygen pressures at higher temperatures. Our selected tem- perature of 600 °C corresponds to an average deposition/ annealing temperature12 and results for other temperatures can be obtained by shifting the oxygen pressure scale in the figure. For the dopant concentration of 6�1020 cm−3 the decay of free electron concentration for SnO2 is found at oxygen pressures which are more than eight orders of magnitude higher than those for In2O3. Further, for the lower dopant concentration of 2�1020 cm−3 neither of the materials suf- fers from compensation effects in the whole range of oxygen pressures. In comparison, as shown in Fig. 3 the acceptor defects lead to a strong compensation when the smaller LDA formation energies are used instead of the hybrid-functional ones. Additionally, according to the LDA results In2O3 ap- pears to be more dopable than SnO2, a trend which is in- verted with respect to the hybrid-functional results. This is due to the larger LDA band-gap error for SnO2 than for In2O3. The failure of the LDA to describe the strong n-type behavior of these TCOs is reflected in the fact that using LDA formation energies for the acceptor defects a partial- pressure independent region is not reached for the selected realistic dopant concentrations and environmental conditions �Fig. 3�. As we have pointed out above, our calculated free elec- tron concentrations are likely to represent lower boundaries. The uncertainties, which are still connected to the actual ex- perimental band-gap of In2O3 cannot alter our conclusions. Namely, by using the largest presently-suggested band-gap FIG. 3. �Color online� Free electron concentration in In2O3 and SnO2 as a function of the oxygen partial pressure. The results are shown for the tem- perature of 600 °C and for three different doping levels. For comparison, also the corresponding LDA results are given. 053511-4 Ágoston et al. J. Appl. Phys. 108, 053511 �2010� value for In2O3 �Refs. 34 and 47� for tuning the range- separation parameter of the exchange correlation functional does not lead to increased formation energies for the Fermi level at the CBM. Band-gap-related ambiguities do not arise in the case of SnO2. Our findings are surprising in the light of the experi- ments, since the conductivities reported for ITO are gener- ally higher than in any TCO material related to SnO2. There- fore, according to our hybrid-DFT results the origin of the significantly lower free electron concentrations in SnO2 is not due to intrinsic acceptor defects. The results therefore suggest that the limitations of n-type doping in SnO2 mainly arise due to dopant-specific properties rather than properties intrinsically related to SnO2. A further optimization of n-type doping with respect to the resulting free electron concentra- tions is therefore possible. For FTO the doping limit is conjectured to be caused by interstitial fluorine defects12,15 which is now convincingly supported by our calculations. To the best of our knowledge the reason for the low electron concentrations of ATO is presently not known. Beside the occurrence of Sb3+ instead of Sb5+ �Refs. 48 and 49� which could act as acceptor, the segregation of the Sb-dopant is a possible, often-considered origin for low electron concentrations.50 However, our calcu- lations predict a low abundance of cation vacancies and thereby a good kinetic stability of cation dopants against vacancy-mediated migration in SnO2. The kinetics will therefore be slow even if there is a tendency for segregation. More specifically our calculations explain that segregation cannot be observed for ATO �Ref. 12� but it is possible for ITO �Ref. 40� using a comparable experimental setup. As we have shown above, higher cation vacancy concentrations can be expected for highly-doped In2O3 samples. Since the mo- bility of indium vacancies is not prohibitively large51 a higher mobility of cation dopants and higher segregation ki- netics can be expected in In2O3 than in SnO2. In this study we do not present results on specific donor dopants. A com- prehensive study of the compensation mechanisms with spe- cific dopant/material combinations is to follow. IV. SUMMARY AND CONCLUSION We have reinvestigated the electron compensation in two TCO materials In2O3 and SnO2. We have shown that within the hybrid-functional-DFT description In2O3 and SnO2 are highly-n-type dopable against the formation of intrinsic ac- ceptors. We have obtained for In2O3 a doping limit which is in good agreement with experiments. This reflects the robust- ness of the methodology used. Most importantly, we have obtained for SnO2 a doping limit, which is beyond the experimentally-observed one. We conclude that for SnO2 the lower measured electron concentrations are therefore not a consequence of any intrinsic acceptor of the material. Our general result is that SnO2 is more robust toward high Fermi level values and should allow for a higher maxi- mum doping than has so far been reached in experiment. This conclusion is unlikely to be altered by any approxima- tion used in our calculations. Our findings in turn state that the source for lower conductivities in SnO2 in comparison with In2O3 are related to the dopants presently used �F and Sb�. While the doping limit in In2O3 is given by intrinsic acceptors the conductivities are limited by other processes in SnO2. Likely explanations for the presently observed doping limits are therefore either the low ionization rate of the dop- ants, extrinsic acceptors, low solubility, or defect-defect in- teractions. Further improvements of cheap SnO2 based TCO materials are therefore possible by using other dopants and dopant combinations. ACKNOWLEDGMENTS We acknowledge the financial support through the Sonderforschungsbereich 595 “Fatigue of functional materi- als” of the Deutsche Forschungsgemeinschaft and the Acad- emy of Finland through the center of Excellence Program �2006–2011�. Moreover, this work was made possible by grants for computing time at CSC computing facilities in Espoo, Finland, and FZ-Juelich. We also acknowledge finan- cial support through a bilateral travel program funded by the German foreign exchange server �DAAD�. 1H. L. Hartnagel, A. K. J. Dawar, and C. Jagadish, Semiconducting Trans- parent Thin Films �Institute of Physics, Bristol, 1995�. 2D. S. Ginley and C. Bright, MRS Bull. 25, 15 �2000�. 3J. H. W. Goepel and J. Zemel, Sensors: A Comprehensive Survey, Chemi- cal and Biochemical Sensors �VCH, Weinheim, 1991�, Vol. 2. 4P. Ágoston, K. Albe, R. M. Nieminen, and M. J. Puska, Phys. Rev. Lett. 103, 245501 �2009�. 5S. Lany and A. Zunger, Phys. Rev. Lett. 98, 045501 �2007�. 6C. Kılıç and A. Zunger, Phys. Rev. Lett. 88, 095501 �2002�. 7S. Limpijumnong, P. Reunchan, A. Janotti, and C. G. Van de Walle, Phys. Rev. B 80, 193202 �2009�. 8A. K. Singh, A. Janotti, M. Scheffler, and C. G. V. de Walle, Phys. Rev. Lett. 101, 055502 �2008�. 9P. D. C. King, R. L. Lichti, Y. G. Celebi, J. M. Gil, R. C. Vilão, H. V. Alberto, J. Piroto Duarte, D. J. Payne, R. G. Egdell, I. McKenzie, C. F. McConville, S. F. J. Cox, and T. D. Veal, Phys. Rev. B 80, 081201 �2009�. 10T. Minami, Semicond. Sci. Technol. 20, 35 �2005�. 11K. Ellmer, J. Phys. D 34, 3097 �2001�. 12C. Körber, P. Ágoston, and A. Klein, Sens. Actuators B 139, 665 �2009�. 13G. Frank and G. Köstlin, Appl. Phys. A: Mater. Sci. Process. 27, 197 �1982�. 14C. Agashe and S. S. Major, J. Mater. Sci. 31, 2965 �1996�. 15C. D. Canestraro, M. M. Oliviera, R. Vlasaski, M. V. S. da Silva, D. G. F. David, I. Pepe, A. F. da Silva, L. S. Roman, and C. Persson, Appl. Surf. Sci. 255, 1874 �2008�. 16B. Kamp, R. Merkle, R. Lauck, and J. Maier, J. Solid State Chem. 178, 3027 �2005�. 17A. Klein, A. Körber, C. Wachau, F. Säuberlich, Y. Gassenbauer, S. P. Harvey, and T. O. Mason, Thin Solid Films 518, 1197 �2009�. 18P. Ágoston and K. Albe, Phys. Chem. Chem. Phys. 11, 3226 �2009�. 19G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 �1996�. 20G. Kresse and J. Furthmüller, Comput. Mater. Sci. 6, 15 �1996�. 21J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 118, 8207 �2003�. 22J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 124, 219906 �2006�. 23J. Perdew, M. Ernzerhof, and K. Burke, J. Chem. Phys. 105, 9982 �1996�. 24J. Paier, M. Marsman, K. Hummer, G. Kresse, I. C. Gerber, and J. G. Ángyán, J. Chem. Phys. 124, 154709 �2006�. 25P. E. Blöchl, Phys. Rev. B 50, 17953 �1994�. 26G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 �1999�. 27H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 �1976�. 28A. Bourlange, D. J. Payne, R. G. Egdell, J. S. Foord, P. P. Edwards, M. O. Jones, A. Schertel, P. J. Dobson, and J. L. Hutchison, Appl. Phys. Lett. 92, 092117 �2008�. 29A. Walsh, J. L. F. D. Silva, S.-H. Wei, C. Körber, A. Klein, L. F. J. Piper, A. DeMasi, K. E. Smith, G. Panaccione, P. Torelli, D. J. Payne, A. Bour- 053511-5 Ágoston et al. J. Appl. Phys. 108, 053511 �2010� http://dx.doi.org/10.1103/PhysRevLett.103.245501 http://dx.doi.org/10.1103/PhysRevLett.98.045501 http://dx.doi.org/10.1103/PhysRevLett.88.095501 http://dx.doi.org/10.1103/PhysRevB.80.193202 http://dx.doi.org/10.1103/PhysRevB.80.193202 http://dx.doi.org/10.1103/PhysRevLett.101.055502 http://dx.doi.org/10.1103/PhysRevLett.101.055502 http://dx.doi.org/10.1103/PhysRevB.80.081201 http://dx.doi.org/10.1088/0268-1242/20/4/004 http://dx.doi.org/10.1088/0022-3727/34/21/301 http://dx.doi.org/10.1016/j.snb.2009.03.067 http://dx.doi.org/10.1007/BF00619080 http://dx.doi.org/10.1007/BF00356009 http://dx.doi.org/10.1016/j.apsusc.2008.06.113 http://dx.doi.org/10.1016/j.apsusc.2008.06.113 http://dx.doi.org/10.1016/j.jssc.2005.07.019 http://dx.doi.org/10.1016/j.tsf.2009.05.057 http://dx.doi.org/10.1039/b900280d http://dx.doi.org/10.1103/PhysRevB.54.11169 http://dx.doi.org/10.1016/0927-0256(96)00008-0 http://dx.doi.org/10.1063/1.1564060 http://dx.doi.org/10.1063/1.2204597 http://dx.doi.org/10.1063/1.472933 http://dx.doi.org/10.1063/1.2187006 http://dx.doi.org/10.1103/PhysRevB.50.17953 http://dx.doi.org/10.1103/PhysRevB.59.1758 http://dx.doi.org/10.1103/PhysRevB.13.5188 http://dx.doi.org/10.1063/1.2889500 lange, and R. G. Egdell, Phys. Rev. Lett. 100, 167402 �2008�. 30O. Madelung, Semiconductors: Basic Data, 2nd ed. �Springer, Berlin, 1996�. 31G. Makov and M. C. Payne, Phys. Rev. B 51, 4014 �1995�. 32S. B. Zhang and J. E. Northrup, Phys. Rev. Lett. 67, 2339 �1991�. 33M. Marezio, Acta Crystallogr. 20, 723 �1966�. 34P. D. C. King, T. D. Veal, F. Fuchs, C. Y. Wang, D. J. Payne, A. Bourlange, H. Zhang, G. R. Bell, V. Cimalla, O. Ambacher, R. G. Egdell, F. Bechst- edt, and C. F. McConville, Phys. Rev. B 79, 205211 �2009�. 35D. R. Lide, Handbook of Chemistry and Physics �CRC, Boca Raton, 2005�. 36Thermodynamic Properties of Compounds SbO2 to Rh2O3 �ed.�, Springer Materials - The Landolt-Börnstein Database � materials.com;/Border �0 0 1�?�http://www.springer materials.com;/Border �0 0 1�?� materials.com;/Border �0 0 1�?�http://www.springer materials.com�; Thermodynamic Properties of Compounds TiI3 to In2O3 �ed.�, Springer Materials - The Landolt-Börnstein Database �http:// www.springermaterials.com�. 37P. Ágoston, P. Erhart, A. Klein, and K. Albe, J. Phys.: Condens. Matter 21, 455801 �2009�. 38F. Oba, A. Togo, I. Tanaka, J. Paier, and G. Kresse, Phys. Rev. B 77, 245202 �2008�. 39D. R. Stull and H. Prohet, JANAF Thermochemical Tables, 2nd ed. �U.S. National Bureau of Standards, Washington, D.C., 1971�. 40Y. Gassenbauer, R. Schafranek, A. Klein, S. Zafeiratos, M. Hävecker, A. Knop-Gericke, and R. Schlögl, Phys. Rev. B 73, 245312 �2006�. 41S. P. Harvey, T. O. Mason, Y. Gassenbauer, R. Schafranek, and A. Klein, J. Phys. D 39, 3959 �2006�. 42A. Klein, Appl. Phys. Lett. 77, 2009 �2000�. 43K. Reuter and M. Scheffler, Phys. Rev. B 65, 035406 �2001�. 44A. Walsh, J. L. F. Da Silva, and S.-H. Wei, Phys. Rev. B 78, 075211 �2008�. 45E. Kohnke, J. Phys. Chem. Solids 23, 1557 �1962�. 46J. H. Hwang, D. D. Edwards, D. R. Kammler, and T. O. Mason, Solid State Ionics 129, 135 �2000�. 47F. Fuchs and F. Bechstedt, Phys. Rev. B 77, 155107 �2008�. 48C. S. Rastomjee, R. G. Egdell, G. C. Geirguadis, M. J. Lee, and T. J. Tate, J. Mater. Chem. 2, 511 �1992�. 49F. J. Berry and B. J. Laundy, J. Chem. Soc. Dalton Trans. 1981, 1442. 50D. E. Williams and V. Dusastre, J. Phys. Chem. B 102, 6732 �1998�. 51P. Ágoston and K. Albe, Phys. Rev. B 81, 195205 �2010�. 053511-6 Ágoston et al. J. Appl. Phys. 108, 053511 �2010� This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Journal of Applied Physics 108, 053511 (2010) and may be found at https://doi.org/10.1063/1.3467780. Available under only the rights of use according to UrhG. http://dx.doi.org/10.1103/PhysRevLett.100.167402 http://dx.doi.org/10.1103/PhysRevB.51.4014 http://dx.doi.org/10.1103/PhysRevLett.67.2339 http://dx.doi.org/10.1107/S0365110X66001749 http://dx.doi.org/10.1103/PhysRevB.79.205211 http://www.springermaterials.com http://www.springermaterials.com http://dx.doi.org/10.1088/0953-8984/21/45/455801 http://dx.doi.org/10.1103/PhysRevB.77.245202 http://dx.doi.org/10.1103/PhysRevB.73.245312 http://dx.doi.org/10.1088/0022-3727/39/18/006 http://dx.doi.org/10.1063/1.1312199 http://dx.doi.org/10.1103/PhysRevB.65.035406 http://dx.doi.org/10.1103/PhysRevB.78.075211 http://dx.doi.org/10.1016/0022-3697(62)90236-6 http://dx.doi.org/10.1016/S0167-2738(99)00321-5 http://dx.doi.org/10.1016/S0167-2738(99)00321-5 http://dx.doi.org/10.1103/PhysRevB.77.155107 http://dx.doi.org/10.1039/jm9920200511 http://dx.doi.org/10.1039/dt9810001442 http://dx.doi.org/10.1021/jp981391v http://dx.doi.org/10.1103/PhysRevB.81.195205