Computational Screening of Useful HoleâElectron Dopants in SnO2

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Computational screening of useful hole-electron dopants in SnO Migl# Graužinyt#, Stefan Goedecker, and José A. Flores-Livas

Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.7b03862 • Publication Date (Web): 13 Nov 2017 Downloaded from http://pubs.acs.org on November 14, 2017

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Chemistry of Materials

Computational screening of useful hole-electron dopants in SnO2 Migl˙e Graužinyt˙e,∗ Stefan Goedecker, and José A. Flores-Livas∗ Department of Physics, Universität Basel, Klingelbergstr. 82, 4056 Basel, Switzerland E-mail: [email protected]; [email protected]

Abstract

earth abundance (and hence lower production cost than indium) has spurred a large experimental and computational effort into understanding and enhancing the properties of Znand Sn-oxides. 9–20 In order to bring SnO2 on a level playing field with indium based TCO’s a thorough understanding of useful dopants is needed. Unfortunately, the use of different codes (i.e. basis sets), exchange-correlation functionals, and approaches used to overcome deficiencies inherent to the level of theory has resulted in a large scatter of results that are hardly, if at all, comparable with each other. Even the cause for unintentional n-type doping is still an open debate in the scientific community. 13,21–23 With contradicting predictions reported for oxygen vacancies and cation interstitials –that have been blamed for decades for the unintentional n-type TCO conductivity. This has even lead to the proposal of hydrogen interstitials and hydrogen trapped in oxygen vacancy sites as an alternative explanation for the unintentional n-type doping in conductive oxides. 22 Needless to say, examination of external dopants suffers from similar issues. It is well known that Kohn-Sham densityfunctional theory (KS-DFT) band structures systematically underestimate the band gap for semiconductor materials. The band gap problem of standard density functionals is particularly troublesome in the case of TCOs. 13,24 For instance, the calculated generalized gradient approximation (GGA-PBE) band gap of SnO2 is 0.6 eV, while experimental results indicate a direct gap of 3.6 eV. 25 Different approaches have

Doped tin-dioxide (SnO2 ) is an important semiconductor that is already used in diverse applications. However, in order to uncover the entire potential of this material in more advanced applications of optoelectronics further improvements in electrical properties are necessary. In this work we perform an extensive search for useful substitutional dopants of SnO2 . We use a well-converged protocol to scan the entire periodic table for dopants finding excellent agreement between our predictions and those substitutional dopants that have been experimentally examined to date. The results of this large-scale dopant study allows us to better understand the doping trends in this important TCO material.

Introduction The combination of optical transparency and high electrical conductivity enables transparent conductive oxide (TCO) materials to be used for a wide range of applications - from simple smart window coatings to OLEDs and futuristic see-through displays. 1–4 The niche of these futuristic materials is heavily dominated by electron (n−) doped SnO2 , In2 O3 and ZnO. Currently, many optoelectronic applications are primarily based on indium oxide, 5,6 this material is taking the lead with its superior conductivity, while tin and zinc oxides are close runnerups, having promising yet not quite sufficient properties for widespread use as electronic materials. 7,8 In spite of that, the advantage of

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Table 1: Lattice parameters, bulk modulus and electronic gap of rutile SnO2 calculated with different functionals.

correction and a potential alignment term. For the final PBE0 calculations we further include a band-filling correction term. 33 Thermodynamic transition levels ǫ(q1 /q2 ) between two charged states q1 and q2 of a substitutional defect were calculated using Equation 2.

Exp. PBE HSE06 PBE0 a (Å) 4.73 a 4.82 4.75 4.75 3.24 3.19 3.19 c (Å) 3.18 a a 0.306 0.306 0.306 x 0.307 F b E (eV) -6.0 -4.9 -5.2 -5.2 a B0 (GPa) 205 165 203 204 7.4 a 5 5 5 B′0 c 3.6 0.63 2.8 3.6 EG (eV) a 31 b 32 c Reference Reference Reference 25

F F ED (q1 , ∆ǫF = 0) − ED (q2 , ∆ǫF = 0) q2 − q1 (2) Thermodynamic transition levels indicate the value of ∆ǫF at which the substitutional defect changes its stable charge state. Strong structural relaxations between different charge states can, nevertheless, create kinetic barriers that stabilize an excited charge state above its thermodynamic transition level. 34 It is clear that accessing all this information for all the elements in the periodic table using hybrid functional calculations is computationally prohibitive. In order to circumvent this issue the computational work-flow illustrated in Fig. 1 was used. All the dopants were first calculated with GGA-PBE level of theory within DFT and if both the above conditions –desired stable charge state and defect-free band gap– were fulfilled, a subsequent hybrid functional calculation cycle was performed to verify the result. The choice of PBE for pre-screening is justified by the following considerations. In the SnO2 host hybrid-functional calculations shift the valence band and conduction band edge states predicted by PBE, resulting in a simple opening of the band gap. In this context, the PBE calculations are qualitatively similar to hybrid PBE0 for any emergent defect states that are rigidly shifted together with the relevant band edge. This should indeed always be the case for a perturbative host state - the ideal doping scenario. In contrast, for a localized defect state this is not a guaranteed condition. Nevertheless, the reduced band-gap of PBE will tend to stabilize a donating charge state, when compared to PBE0. While the opposite behavior - a charge neutral PBE state becoming a donor on PBE0 level of theory - is extremely unlikely, as this would require the defect state

ǫ(q1 /q2 ) =

given Fermi energy, ǫF . For n-type conductors ǫF should lie close to the conduction band and the substitutional dopant should be positively ionized (donated one or more electrons into the conduction band), while for p-type conductors ǫF should lie close to the valence band and the substitutional dopant should be negatively ionized (donated one or more holes into the valence band). Defect formation energies of a given charge state were calculated using Equation 1. q F − ESnO2 − ED = ED

X

ni [µi + ∆µi ]

i

+ q[ǫVBM + ∆ǫF ] + Ecor

(1)

q is the energy of a supercell containWhere ED ing a defect atom D in a charge state q; ESnO2 is the energy of the same size supercell of pure SnO2 ; ni is the number of atoms of species i that was added (ni > 0) or subtracted (ni < 0) to create the defect; µi is the chemical potential of species i in its pure phase; ∆µi define the boundaries imposed on the total chemical potentials of species i due to secondary phase formation (further information on the reference phases can be found in the Supplemental Material); ǫVBM is the position of the valence band maximum of the pure SnO2 ; ∆ǫF is the position of the Fermi level w.r.t the ǫVBM . In this work we regard ∆ǫF as a free parameter, though it is, in principle, constrained by all the defects/defect-complexes contained in the system. Finally, Ecor contains all additional correction terms. This includes a charge interaction


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that warrant further investigation, marked by a dashed outline in Fig. 2; c) transition d-metals resulting in defect states lying inside the band gap due to metal-d and O-2p orbital interactions (plots of DOS can be found in the Supplemental Material). Clear trends across the periodic table can be identified, with electron-donor regions seen within the transition metals and the elements of group V and VII. Two intriguing outliers to the general trend can also be spotted: i) Te the only element of those in group VI acting as a double donor in a +2 charge state; ii) Au offering up an electron, despite its typical +3 oxidation state. This (as will be shown in more detail later) is in fact an artifact of PBE preferentially stabilizing electron donating states. Due to the small band gap the induced defectstates for the two elements are predicted to be energetically close to the CBM, artificially increasing the total energy of the charge neutral state, when compared to hybrid-functional results. With the use of hybrid-functionals calculations the outliers are seen to disappear acquiring the same charge state as the rest of the elements in the group - Te is found to be charge neutral, while Au is stable in the negative charge state. PBE formation energies under Sn-poor conditions, when DSn formation is favourable, are shown in Fig. 3 as a function of ∆ǫF for all 19 n-type dopants. Panels a), b) and c) correspond to the three categories outlined above. The points at which a change in slope is seen for Os and Tc indicate the thermodynamic transition levels. Both elements undergo a q = +2 to q = +1 transition as the Fermi level passes the mid-gap region. However, as mentioned previously the localized defect states seen inside the band-gap for elements of panel c) are likely to negatively impact both the optical and electronic properties of SnO2 . These elements were, thus, excluded from more detailed investigations. We did not perform an extensive search for DO substitutionals in this work. And we stress here that there are certainly elements such as fluorine (F), a well established dopant 36,37 for SnO2 , that could act as an n-type donor on a

DO site, but is found to be non-donating on a DSn position. Only elements with an ionic radius similar to that of oxygen are likely to incorporate on an O-site without causing strong distortions in the lattice and hence being energetically expensive. Small ionic-radii, however, would also lead to a smaller cost of interstitial incorporation. This is both a disadvantage for experimental realization of the material and problematic from the theory-modeling point of view, as all potential competing sites should be included in the calculations before any realistic conclusions could be drawn. In contrast, dopants preferentially incorporating on a DSn are generally expected to be larger in size and, hence, significantly more expensive to incorporate on other (potentially electrically inactive) sites. To verify this assertion, formation energies for doping on an O-site, DO , were calculated for all elements in panel a) and b) of Fig. 3 and were included in the plot as solid black lines. For all but two elements – Br and Cl – the oxygen-site formation energies are so much higher they lie above the 5 eV range shown in the plot. For these elements DO substitutions are extremely unlikely in the oxygenrich growth conditions considered throughout this work. Chlorine is seen (Fig. 3 b)) as the only element of those found to be suitable Sn-site dopants to have a lower formation energy of DO , than DSn . Nevertheless, all DO substitutions were also found to be exclusively stable in a positive charge state for the elements considered. We thus conclude, that even if the dopant atoms were to incorporate at a more energetically expensive (except for Cl) O-site location, they would still act as free carrier donors. On the other hand, in many of the cases –as with unoccupied oxygen vacancies– oxygen site substitution results in localized defect states inside the band gap and would as such be less favorable. Additionally, we found that a 72-atom supercell is too small for the short-range electrostatic potential to reach a plateau even far away from the defect site (see Supplemental Material) when oxygen site substitutions are considered. This inhibits the proper evaluation of the potential alignment term and indicates that


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we see that the features of the electronic structure are well captured with PBE and PBE0 represents an effective rigid shift of the band gap. Similar behavior is seen for all other defects in panel a) of Fig 4 identified as suitable dopants. Two notable exceptions - BrSn and ISn - are seen to introduce a localized occupied defect state close to the valence band maximum. The defect-states are seen to be shifted deeper into the band gap using PBE0 level of theory, however, remain shallow enough to not be significantly detrimental to the optical transparency given the large optical band gap expected for n-doped SnO2 . Furthermore, occupied defectstates could only act as scattering centers, but should not be expected to act as electron traps.

Electronic structure The electronic structure arising from doping by substitution was closely investigated for every element considered throughout this work. We separated all n-type dopants into three categories based on their DOS as described in the previous section and condensed in Fig. 3. Left panel on Figure 6 compares the electronic structure of tantalum doped SnO2 with the undoped case by showing the band structure around the high-curvature directions of the conduction band minimum. The highly-dispersive CBM of SnO2 is responsible for the high mobility of electron carriers in this material, thus changes to the CBM will have a large impact on the conductivity, especially when no other defect states arise. The bandUP 53,54 code was used to unfold the Ta-doped (supercell) electronic structure (green) for direct comparison with the undoped case (orange). Here PBE results are shown. Our calculations indicate that tantalum doping preserves the features of SnO2 and close inspection of the electronic structure reveals most prominent effects of Ta, indicated by arrows in Fig. 6. Breaking of degeneracy at high symmetry points is seen, for example the in-plane dispersion from M → Γ at -6 eV below the VBM and at 4 eV above the CBM. Additionally, the appearance of states, like those at 2.2 eV in Γ-points can be identified. The band splittings at 2.6 eV and at 4 eV above the CBM are clearly linked to Ta-d states, shown in the central panel of Fig. 6. A slight opening of the band gap upon Ta doping is also observed, with a calculated ∼ 140 meV change (with both PBE and PBE0). The renormalization of the gap is nevertheless not significant enough to be detrimental for conductivity or to significantly affect the optical properties, affirming the conclusion that Ta is a suitable dopant for n-type SnO2 . In agreement with out results an experimental band gap of 3.78 eV upon 10% Ta doping has also been reported 55 for thin-films of larger thickness, where bulk like properties are expected to dominate. The two right-side panels on Fig. 6 compare the DOS of PBE and PBE0 functionals. Overall

Conclusions We conducted a thorough investigation of Snsite substitutional dopants in rutile SnO2 . Only 6 elements –P, I, Ta, As, Nb and Sb– are predicted to dope SnO2 n-type while preserving its good optoelectronic properties. Tungsten is also predicted to act as a free-carrier donor, yet likely at the cost of conductivity. In contrast, we show that there exists no single element in the entire periodic table (excluding lanthanides and noble gases, not examined in this study) that can dope SnO2 p-type via Snsite substitution. We compared our results with the relevant literature on SnO2 and found that many of the suitable dopants identified in the study have been previously synthesized experimentally. We find our predictions to be in good agreement with the experiments, providing consistent explanation for the observations seen. We, therefore, conclude that iodine doping could also significantly improve the free carrier concentration of SnO2 if grown under suitable experimental conditions (such that Sn-site substitution is favored). In this work we use a simple approach to efficiently, yet consistently, scan for suitable dopants in large band-gap materials, that call for a higher level of theory than the generalized gradient approximation. Such a workable method, could be easily adopted for sim-


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Supporting Information

code. A plane wave energy cutoff of 700 eV was used in all calculations to obtain energy convergence up to 1 meV/atom. POTCAR files with Sn dshell electrons included as valence were used. All calculations were spin polarized and magnetism was checked for all systems. For PBE 64 primitive cell calculations a k = 4 × 4 × 6 mesh was used, while for PBE0 65,66 a k = 6 × 6 × 8 mesh was required. All supercell relaxations were performed using k = 2 × 2 × 2 MP meshes, while k = 3 × 3 × 4 (PBE) and k = 3 × 3 × 3 (PBE0) Γ-centered meshes were employed for final DOS calculations. All formation energies shown were calculated in the O-rich limit - the most favorable experimental conditions for Sn-site substitution to take place. Under these conditions, when a stable binary-oxide reference phase exists the formation energies are completely independent of the individual metallic references. As the use of the PBE0 functional for metallic reference phase calculations may be inappropriate, we would like to stress here that such deficiencies are circumvented in the work presented. The static dielectric constant of rutile SnO2 was calculated for use in electrostatic corrections of charged defect supercells. Both electronic and ionic contributions of the dielectric constant of SnO2 were evaluated using PBE, obtaining the values ǫk = 4.677(9.054) and ǫ⊥ = 4.907(5.604). For PBE0 we calculated only the electronic contribution including local field effects, obtaining ǫk = 3.627 and ǫ⊥ = 4.013. PBE ratios of electronic and ionic contributions were then used to estimate the ionic contribution for PBE0, recovering ǫk = (7.020) and ǫ⊥ = (4.582) and obtaining a total value of the averaged dielectric constant of 9.96 (comparable to 9.86 value obtained by Varley et al. 16 ). The final corrections are, however, not strongly dependent on the precise value of the dielectric constant - not more than 80 meV changes are seen when the PBE dielectric constants are used instead.

Detailed reference phase information. Comparison of short range electrostatic potentials of dopants on O-site vs Sn-site. Electronic DOS of all dopants shown in Fig. 4 for the stable charge states. This material is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgments M.G. acknowledges funding from the Swiss National Science Foundation under the Disco Project (No. CRSII2_154474). M.G. and J.A.F.-L. acknowledges computational resources under the projects (s707 and s752) from the Swiss National Supercomputing Center (CSCS) in Lugano. This research was partially supported by the NCCR MARVEL.


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References (1) Reineke, S.; Lindner, F.; Schwartz, G.; Seidler, N.; Walzer, K.; Lüssem, B.; Leo, K. White organic light-emitting diodes with fluorescent tube efficiency. Nature 2009, 459, 234–238. (2) Ohta, H.; Hosono, H. Transparent oxide optoelectronics. Mater. Today 2004, 7, 42–51. (3) Ellmer, K. Past achievements and future challenges in the development of optically transparent electrodes. Nat. Photonics 2012, 6, 809–817. (4) Gordon, R. G. Criteria for choosing transparent conductors. MRS Bull. 2000, 25, 52–57. (5) Shih, Y.-C.; Qiu, C. X.; Shih, I.; Qiu, C. Indium oxide-based thin film transistors and circuits. 2007; US Patent 7,211,825. (6) Dixon, S. C.; Scanlon, D. O.; Carmalt, C. J.; Parkin, I. P. n-Type doped transparent conducting binary oxides: an overview. J. Mater. Chem. C 2016, 4, 6946–6961. (7) Morales-Masis, M.; Dauzou, F.; Jeangros, Q.; Dabirian, A.; Lifka, H.; Gierth, R.; Ruske, M.; Moet, D.; Hessler-Wyser, A.; Ballif, C. An Indium-Free Anode for Large-Area Flexible OLEDs: Defect-Free Transparent Conductive Zinc Tin Oxide. Adv. Funct. Mater. 2016, 26, 384–392. (8) Rucavado, E.; Jeangros, Q.; Urban, D. F.; Holovský, J.; Remes, Z.; Duchamp, M.; Landucci, F.; Dunin-Borkowski, R. E.; Körner, W.; Elsässer, C.; Hessler-Wyser, A.; MoralesMasis, M.; Ballif, C. Enhancing the optoelectronic properties of amorphous zinc tin oxide by subgap defect passivation: A theoretical and experimental demonstration. Phys. Rev. B 2017, 95, 245204. (9) Godinho, K. G.; Walsh, A.; Watson, G. W. Energetic and electronic structure analysis of intrinsic defects in SnO2 . J. Phys. Chem. C 2008, 113, 439–448. (10) Janotti, A.; Van de Walle, C. G. LDA+ U and hybrid functional calculations for defects in ZnO, SnO2 , and TiO2 . Phys. Status Solidi B 2011, 248, 799–804. (11) Avadhut, Y. S.; Weber, J.; Hammarberg, E.; Feldmann, C.; Schellenberg, I.; Pöttgen, R.; Schmedt auf der Günne, J. Study on the defect structure of SnO2 : F nanoparticles by highresolution solid-state NMR. Chem. Mater. 2011, 23, 1526–1538. (12) Dominguez, J.; Fu, L.; Pan, X. Effect of crystal defects on the electrical properties in epitaxial tin dioxide thin films. Appl. Phys. Lett. 2002, 81, 5168–5170. (13) Ágoston, P.; Albe, K.; Nieminen, R. M.; Puska, M. J. Intrinsic n-type behavior in transparent conducting oxides: a comparative hybrid-functional study of In2 O3 , SnO2 , and ZnO. Phys. Rev. Lett. 2009, 103, 245501. (14) Lany, S.; Zunger, A. Comment on "Intrinsic n-type Behavior in Transparent Conducting Oxides: A Comparative Hybrid-Functional Study of In2 O3 , SnO2 , and ZnO". Phys. Rev. Lett. 2011, 106, 069601. (15) Oba, F.; Togo, A.; Tanaka, I.; Paier, J.; Kresse, G. Defect energetics in ZnO: A hybrid HartreeFock density functional study. Phys. Rev. B 2008, 77, 245202. (16) Varley, J.; Janotti, A.; Van de Walle, C. Group-V impurities in SnO2 from first-principles calculations. Phys. Rev. B 2010, 81, 245216. ACS Paragon Plus Environment

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Page 13 of 17

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(17) Cheng, D.; Zhang, M.; Chen, J.; Yang, C.; Zeng, X.; Cao, D. Computer screening of dopants for the development of new SnO2 -based transparent conducting oxides. J. Phys. Chem. C 2014, 118, 2037–2043. (18) Behtash, M.; Joo, P. H.; Nazir, S.; Yang, K. Electronic structures and formation energies of pentavalent-ion-doped SnO2 : First-principles hybrid functional calculations. J. Appl. Phys. 2015, 117, 175101. (19) Scanlon, D. O.; Watson, G. W. On the possibility of p-type SnO2 . J. Mater. Chem. 2012, 22, 25236–25245. (20) Clark, S.; Robertson, J.; Lany, S.; Zunger, A. Intrinsic defects in ZnO calculated by screened exchange and hybrid density functionals. Phys. Rev. B 2010, 81, 115311. (21) Kılıç, Ç.; Zunger, A. Origins of coexistence of conductivity and transparency in SnO2 . Phys. Rev. Lett. 2002, 88, 095501. (22) Singh, A. K.; Janotti, A.; Scheffler, M.; Van de Walle, C. G. Sources of electrical conductivity in SnO2 . Phys. Rev. Lett. 2008, 101, 055502. (23) Lany, S.; Zunger, A. Dopability, intrinsic conductivity, and nonstoichiometry of transparent conducting oxides. Phys. Rev. Lett. 2007, 98, 045501. (24) Vidal, J.; Trani, F.; Bruneval, F.; Marques, M. A. L.; Botti, S. Effects of Electronic and Lattice Polarization on the Band Structure of Delafossite Transparent Conductive Oxides. Phys. Rev. Lett. 2010, 104, 136401. (25) Nagasawa, M.; Shionoya, S. Exciton structure in optical absorption of SnO2 crystals. Phys. Lett. 1966, 22, 409–410. (26) Stashans, A.; Puchaicela, P.; Rivera, R. DFT study of chromium-doped SnO2 materials. J. Mater. Sci. 2014, 49, 2904–2911. (27) Deák, P.; Gali, A.; Aradi, B.; Frauenheim, T. Accurate gap levels and their role in the reliability of other calculated defect properties. Phys. Status Solidi B 2011, 248, 790–798. (28) Varley, J.; Janotti, A.; Singh, A.; Van de Walle, C. Hydrogen interactions with acceptor impurities in SnO2 : First-principles calculations. Phys. Rev. B 2009, 79, 245206. (29) Lany, S.; Zunger, A. Generalized Koopmans density functional calculations reveal the deep acceptor state of NO in ZnO. Phys. Rev. B 2010, 81, 205209. (30) Lany, S.; Zunger, A. Polaronic hole localization and multiple hole binding of acceptors in oxide wide-gap semiconductors. Phys. Rev. B 2009, 80, 085202. (31) Haines, J.; Léger, J. X-ray diffraction study of the phase transitions and structural evolution of tin dioxide at high pressure: Relationships between structure types and implications for other rutile-type dioxides. Phys. Rev. B 1997, 55, 11144. (32) Wagman, D. D.; Evans, W. H.; Parker, V. B.; Schumm, R. H.; Halow, I. The NBS tables of chemical thermodynamic properties. Selected values for inorganic and C1 and C2 organic substances in SI units; 1982.


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(33) Freysoldt, C.; Grabowski, B.; Hickel, T.; Neugebauer, J.; Kresse, G.; Janotti, A.; Van de Walle, C. G. First-principles calculations for point defects in solids. Rev. Mod. Phys. 2014, 86, 253. (34) Lany, S.; Zunger, A. Dopability, intrinsic conductivity, and nonstoichiometry of transparent conducting oxides. Phys. Rev. Lett. 2007, 98, 045501. (35) Birch, F. Finite elastic strain of cubic crystals. Phys. Rev. 1947, 71, 809. (36) Rakhshani, A.; Makdisi, Y.; Ramazaniyan, H. Electronic and optical properties of fluorinedoped tin oxide films. J. Appl. Phys. 1998, 83, 1049–1057. (37) Xu, J.; Huang, S.; Wang, Z. First principle study on the electronic structure of fluorine-doped SnO2 . Solid State Commun. 2009, 149, 527–531. (38) Peng, H.; Perkins, J. D.; Lany, S. Multivalency of group 15 dopants in SnO2 . Chem. Mater. 2014, 26, 4876–4881. (39) For some shallow donors the neutral charge state calculations result in a defect state that has an energy above the CBM of SnO2 . Subsequently, in a DFT calculation the electron drops down into the CBM, instead of occupying the defect state, as this results in a lower total energy. Therefore, the formation energy of such a ’defect state free’ defect is rather a lower bound of the true formation energy and must be interpreted with caution. (40) Goyal, D.; Agashe, C.; Marathe, B.; Takwale, M.; Bhide, V. Effect of dopant incorporation on structural and electrical properties of sprayed SnO2 : Sb films. J. Appl. Phys. 1993, 73, 7520–7523. (41) Huang, X.; Feng, M.; Gao, C. Influence of P doping on transparent conductive property of SnO2 : P thin film. J. Mater. Sci. Mater. Electron. 2017, 28, 7593–7599. (42) Turgut, G.; Keskenler, E. F.; Aydın, S.; Sönmez, E.; Doğan, S.; Düzgün, B.; Ertuğrul, M. Effect of Nb doping on structural, electrical and optical properties of spray deposited SnO2 thin films. Superlattices Microstruct. 2013, 56, 107–116. (43) Huang, Y.; Zhang, Q.; Li, G.; Yang, M. Tungsten-doped tin oxide thin films prepared by pulsed plasma deposition. Mater. Charact. 2009, 60, 415–419. (44) Agashe, C.; Major, S. Effect of F, Cl and Br doping on electrical properties of sprayed SnO2 films. J. Mater. Sci. Lett. 1996, 15, 497–499. (45) Van de Walle, C. G. Universal alignment of hydrogen levels in semiconductors and insulators. Physica B Condens. Matter. 2006, 376, 1–6. (46) Pan, S.; Li, G.; Wang, L.; Shen, Y.; Wang, Y.; Mei, T.; Hu, X. Atomic nitrogen doping and p-type conduction in SnO2 . Appl. Phys. Lett. 2009, 95, 222112. (47) Zhou, B.; Dong, S.; Zhao, H.; Liu, Y.; Wu, P. Ferromagnetic spin-order in p-type N-doped SnO2 films prepared by thermal oxidation of SnN x. J. Magn. Magn. Mater. 2014, 362, 14–19. (48) Pan, S. S.; Wang, S.; Zhang, Y. X.; Luo, Y. Y.; Kong, F. Y.; Xu, S. C.; Xu, J. M.; Li, G. H. p-type conduction in nitrogen-doped SnO2 films grown by thermal processing of tin nitride films. Appl. Phys. A 2012, 109, 267–271. ACS Paragon Plus Environment

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(49) Bagheri-Mohagheghi, M.-M.; Shokooh-Saremi, M. The influence of Al doping on the electrical, optical and structural properties of SnO2 transparent conducting films deposited by the spray pyrolysis technique. J. Phys. D: Appl. Phys. 2004, 37, 1248. (50) Bagheri-Mohagheghi, M.-M.; Shokooh-Saremi, M. Electrical, optical and structural properties of Li-doped SnO2 transparent conducting films deposited by the spray pyrolysis technique: a carrier-type conversion study. Semicond. Sci. Technol. 2004, 19, 764. (51) Ji, Z.; Zhao, L.; He, Z.; Zhou, Q.; Chen, C. Transparent p-type conducting indium-doped SnO2 thin films deposited by spray pyrolysis. Mater. Lett. 2006, 60, 1387–1389. (52) Lee, P.-M.; Liu, Y.-S.; Villamagua, L.; Stashans, A.; Carini, M.; Liu, C.-Y. Experimental observation and computer simulation of Al/Sn substitution in p-type aluminum nitride-doped tin oxide thin film. J. Mater. Chem. C 2016, 120, 4211–4218. (53) Medeiros, P. V.; Stafström, S.; Björk, J. Effects of extrinsic and intrinsic perturbations on the electronic structure of graphene: Retaining an effective primitive cell band structure by band unfolding. Phys. Rev. B 2014, 89, 041407. (54) Medeiros, P. V.; Tsirkin, S. S.; Stafström, S.; Björk, J. Unfolding spinor wave functions and expectation values of general operators: Introducing the unfolding-density operator. Phys. Rev. B 2015, 91, 041116. (55) Cho, H. J.; Seo, Y. J.; Kim, G. W.; Park, K. Y.; Heo, S. N.; Koo, B. H. Ta Doped SnO2 Transparent Conducting Films Prepared by PLD. Korean J. Mater. Res. 2013, 23, 435–440. (56) Scanlon, D. O.; Dunnill, C. W.; Buckeridge, J.; Shevlin, S. A.; Logsdail, A. J.; Woodley, S. M.; Catlow, C. R. A.; Powell, M. J.; Palgrave, R. G.; Parkin, I. P.; Watson, G. W.; Keal, T. W.; Sherwood, P.; Walsh, A.; Sokol, A. A. Band alignment of rutile and anatase TiO2 . Nat. Mater. 2013, 12, 798–801. (57) Hapiuk, D.; Marques, M. A. L.; Melinon, P.; Flores-Livas, J. A.; Botti, S.; Masenelli, B. p Doping in Expanded Phases of ZnO: An Ab Initio Study. Phys. Rev. Lett. 2012, 108, 115903. (58) Botti, S.; Kammerlander, D.; Marques, M. A. Band structures of Cu2 ZnSnS4 and Cu2 ZnSnSe4 from many-body methods. Appl. Phys. Lett. 2011, 98, 241915. (59) Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 1994, 50, 17953. (60) Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 1999, 59, 1758. (61) Kresse, G.; Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54, 11169. (62) Kresse, G.; Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 1996, 6, 15–50. (63) Freysoldt, C.; Neugebauer, J.; Van de Walle, C. G. Fully ab initio finite-size corrections for charged-defect supercell calculations. Phys. Rev. Lett. 2009, 102, 016402. (64) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865. ACS Paragon Plus Environment

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(65) Adamo, C.; Barone, V. Toward reliable density functional methods without adjustable parameters: The PBE0 model. J. Chem. Phys. 1999, 110, 6158–6170. (66) Paier, J.; Marsman, M.; Hummer, K.; Kresse, G.; Gerber, I. C.; Ángyán, J. G. Screened hybrid density functionals applied to solids. J. Chem. Phys. 2006, 124, 154709.


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