X F Cai, P Zhang, S H Wei, Revisit of the band gaps of rutile SnO2 and TiO2: a first-principles study[J]. J. Semicond., 2019, 40(9): 092101. doi: 10.1088/1674-4926/40/9/092101.
Abstract: From the recent experimentally observed conduction band offset and previously reported band gaps, one may deduce that the valence band offset between rutile SnO2 and TiO2 is around 1 eV, with TiO2 having a higher valence band maximum. This implication sharply contradicts the fact that the two compounds have the same rutile structure and the Γ3+ VBM state is mostly an oxygen p state with a small amount of cation d character, thus one would expect that SnO2 and TiO2 should have small valence band offset. If the valence band offset between SnO2 and TiO2 is indeed small, one may question the correctness of the previously reported band gaps of SnO2 and TiO2. In this paper, using first-principles calculations with different levels of computational methods and functionals within the density functional theory, we reinvestigate the long-standing band gap problem for SnO2. Our analysis suggests that the fundamental band gap of SnO2 should be similar to that of TiO2, i.e., around 3.0 eV. This value is significantly smaller than the previously reported value of about 3.6 eV, which can be attributed as the optical band gap of this material. Similar to what has been found in In2O3, the discrepancy between the fundamental and optical gaps of SnO2 can be ascribed to the inversion symmetry of its crystal structure and the resultant dipole-forbidden transitions between its band edges. Our results are consistent with most of the optical and electrical measurements of the band gaps and band offset between SnO2 and TiO2, thus provide new understanding of the band structure and optical properties of SnO2. Experimental tests of our predictions are called for.
Key words: SnO2, TiO2, band gap, band offset, dipole-forbidden transition
Abstract: From the recent experimentally observed conduction band offset and previously reported band gaps, one may deduce that the valence band offset between rutile SnO2 and TiO2 is around 1 eV, with TiO2 having a higher valence band maximum. This implication sharply contradicts the fact that the two compounds have the same rutile structure and the Γ3+ VBM state is mostly an oxygen p state with a small amount of cation d character, thus one would expect that SnO2 and TiO2 should have small valence band offset. If the valence band offset between SnO2 and TiO2 is indeed small, one may question the correctness of the previously reported band gaps of SnO2 and TiO2. In this paper, using first-principles calculations with different levels of computational methods and functionals within the density functional theory, we reinvestigate the long-standing band gap problem for SnO2. Our analysis suggests that the fundamental band gap of SnO2 should be similar to that of TiO2, i.e., around 3.0 eV. This value is significantly smaller than the previously reported value of about 3.6 eV, which can be attributed as the optical band gap of this material. Similar to what has been found in In2O3, the discrepancy between the fundamental and optical gaps of SnO2 can be ascribed to the inversion symmetry of its crystal structure and the resultant dipole-forbidden transitions between its band edges. Our results are consistent with most of the optical and electrical measurements of the band gaps and band offset between SnO2 and TiO2, thus provide new understanding of the band structure and optical properties of SnO2. Experimental tests of our predictions are called for.
Key words:
SnO2, TiO2, band gap, band offset, dipole-forbidden transition
References:
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Nomura K, Ohta H, Ueda K, et al. Thin-film transistor fabricated in single-crystalline transparent oxide semiconductor. Science, 2003, 300, 1269 |
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Wager J F. Transparent electronics. Science, 2003, 300, 1245 |
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Nomura K, Ohta H, Takagi A, et al. Room-temperature fabrication of transparent flexible thin-film transistors using amorphous oxide semiconductors. Nature, 2004, 432, 488 |
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Minami T. Transparent conducting oxide semiconductors for transparent electrodes. Semicond Sci Technol, 2005, 20, S35 |
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Granqvist C G. Transparent conductors as solar energy materials: a panoramic review. Sol Energy Mater Sol Cells, 2007, 91, 1529 |
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Zhang K H, Xi K, Blamire M G, et al. P-type transparent conducting oxides. J Phys Condens Matter, 2016, 28, 383002 |
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Weiher R, Ley R. Optical properties of indium oxide. J Appl Phys, 1966, 37, 299 |
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Erhart P, Klein A, Egdell R G, et al. Band structure of indium oxide: Indirect versus direct band gap. Phys Rev B, 2007, 75, 153205 |
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Karazhanov S Z, Ravindran P, Vajeeston P, et al. Phase stability, electronic structure, and optical properties of indium oxide polytypes. Phys Rev B, 2007, 76, 075129 |
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Walsh A, Da Silva J L, Wei S H, et al. Nature of the band gap of In2O3 revealed by first-principles calculations and X-ray spectroscopy. Phys Rev Lett, 2008, 100, 167402 |
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Reimann K, Steube M. Experimental determination of the electronic band structure of SnO2. Solid State Commun, 1998, 105, 649 |
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Fröhlich D, Kenklies R, Helbig R. Band-gap assignment in SnO2 by two-photon spectroscopy. Phys Rev Lett, 1978, 41, 1750 |
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Nagasawa M, Shionoya S. Temperature dependence of the fundamental optical absorption edge in stannic oxide. J Phys Soc Jpn, 1971, 30, 1118 |
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Schleife A, Varley J, Fuchs F, et al. Tin dioxide from first principles: Quasiparticle electronic states and optical properties. Phys Rev B, 2011, 83, 035116 |
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Berger J, Reining L, Sottile F. Efficient GW calculations for SnO2, ZnO, and rubrene: The effective-energy technique. Phys Rev B, 2012, 85, 085126 |
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Sabino F P, Oliveira L N, Wei S H, et al. Optical and fundamental band gaps disparity in transparent conducting oxides: new findings for the In2O3 and SnO2 systems. J Phys: Condens Matter, 2017, 29, 085501 |
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Snaith H J, Ducati C. SnO2-based dye-sensitized hybrid solar cells exhibiting near unity absorbed photon-to-electron conversion efficiency. Nano Lett, 2010, 10, 1259 |
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Jiang Q, Zhang L, Wang H, et al. Enhanced electron extraction using SnO2 for high-efficiency planar-structure HC(NH2)2PbI3-based perovskite solar cells. Nat Energy, 2017, 2, 16177 |
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Scanlon D O, Dunnill C W, Buckeridge J, et al. Band alignment of rutile and anatase TiO2. Nat Mater, 2013, 12, 798 |
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Harrison W A. Elementary theory of heterojunctions. J Vac Sci Technol, 1977, 14, 1016 |
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Wei S H, Zunger A. Role ofdorbitals in valence-band offsets of common-anion semiconductors. Phys Rev Lett, 1987, 59, 144 |
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Wei S H, Zunger A. Calculated natural band offsets of all II–VI and III–V semiconductors: Chemical trends and the role of cation d orbitals. Appl Phys Lett, 1998, 72, 2011 |
| [24] |
Walsh A, Da Silva J L F, Wei S H. Multi-component transparent conducting oxides: Progress in materials modelling. J Phys: Condens Matter, 2011, 23, 334210 |
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Chen W, Pasquarello A. Band-edge positions in GW: effects of starting point and self-consistency. Phys Rev B, 2014, 90, 165133 |
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Kresse G, Joubert D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B, 1999, 59, 1758 |
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Heyd J, Scuseria G E, Ernzerhof M. Hybrid functionals based on a screened Coulomb potential. J Chem Phys, 2003, 118, 8207 |
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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 |
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Haines J, Léger J M. 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 |
| [30] |
Landmann M, Rauls E, Schmidt W G. The electronic structure and optical response of rutile, anatase and brookite TiO2. J Phys: Condens Matter, 2012, 24, 195503 |
| [31] |
Perdew J P, Burke K, Ernzerhof M. Generalized gradient approximation made simple. Phys Rev Lett, 1996, 77, 3865 |
| [32] |
Aryasetiawan F, Gunnarsson O. The GW method. Rep Prog Phys, 1998, 61, 237 |
| [33] |
Wei S H, Zunger A. Valence band splittings and band offsets of AlN, GaN, and InN. Appl Phys Lett, 1996, 69, 2719 |
| [34] |
Kang Y, Kang G, Nahm H H, et al. GW calculations on post-transition-metal oxides. Phys Rev B, 2014, 89 |
| [35] |
Reynolds D C, Look D C, Jogai B, et al. Valence-band ordering in ZnO. Phys Rev B, 1999, 60, 2340 |
| [36] |
Koffyberg F P. Thermoreflectance spectra of CdO: Band gaps and band-population effects. Phys Rev B, 1976, 13, 4470 |
| [37] |
Rebien M, Henrion W, Hong M, et al. Optical properties of gallium oxide thin films. Appl Phys Lett, 2002, 81, 250 |
| [38] |
Trukhin A, Kink M, Maksimov Y, et al. Luminescence of GeO2 glass, rutile-like and α-quartz-like crystals. J Non-Cryst Solids, 2006, 352, 160 |
| [39] |
Borgatti F, Berger J A, Céolin D, et al. Revisiting the origin of satellites in core-level photoemission of transparent conducting oxides: The case of n-doped SnO2. Phys Rev B, 2018, 97, 155102 |
| [1] |
Chopra K, Major S, Pandya D. Transparent conductors-a status review. Thin Solid Films, 1983, 102, 1 |
| [2] |
Nomura K, Ohta H, Ueda K, et al. Thin-film transistor fabricated in single-crystalline transparent oxide semiconductor. Science, 2003, 300, 1269 |
| [3] |
Wager J F. Transparent electronics. Science, 2003, 300, 1245 |
| [4] |
Nomura K, Ohta H, Takagi A, et al. Room-temperature fabrication of transparent flexible thin-film transistors using amorphous oxide semiconductors. Nature, 2004, 432, 488 |
| [5] |
Minami T. Transparent conducting oxide semiconductors for transparent electrodes. Semicond Sci Technol, 2005, 20, S35 |
| [6] |
Granqvist C G. Transparent conductors as solar energy materials: a panoramic review. Sol Energy Mater Sol Cells, 2007, 91, 1529 |
| [7] |
Zhang K H, Xi K, Blamire M G, et al. P-type transparent conducting oxides. J Phys Condens Matter, 2016, 28, 383002 |
| [8] |
Weiher R, Ley R. Optical properties of indium oxide. J Appl Phys, 1966, 37, 299 |
| [9] |
Erhart P, Klein A, Egdell R G, et al. Band structure of indium oxide: Indirect versus direct band gap. Phys Rev B, 2007, 75, 153205 |
| [10] |
Karazhanov S Z, Ravindran P, Vajeeston P, et al. Phase stability, electronic structure, and optical properties of indium oxide polytypes. Phys Rev B, 2007, 76, 075129 |
| [11] |
Walsh A, Da Silva J L, Wei S H, et al. Nature of the band gap of In2O3 revealed by first-principles calculations and X-ray spectroscopy. Phys Rev Lett, 2008, 100, 167402 |
| [12] |
Reimann K, Steube M. Experimental determination of the electronic band structure of SnO2. Solid State Commun, 1998, 105, 649 |
| [13] |
Fröhlich D, Kenklies R, Helbig R. Band-gap assignment in SnO2 by two-photon spectroscopy. Phys Rev Lett, 1978, 41, 1750 |
| [14] |
Nagasawa M, Shionoya S. Temperature dependence of the fundamental optical absorption edge in stannic oxide. J Phys Soc Jpn, 1971, 30, 1118 |
| [15] |
Schleife A, Varley J, Fuchs F, et al. Tin dioxide from first principles: Quasiparticle electronic states and optical properties. Phys Rev B, 2011, 83, 035116 |
| [16] |
Berger J, Reining L, Sottile F. Efficient GW calculations for SnO2, ZnO, and rubrene: The effective-energy technique. Phys Rev B, 2012, 85, 085126 |
| [17] |
Sabino F P, Oliveira L N, Wei S H, et al. Optical and fundamental band gaps disparity in transparent conducting oxides: new findings for the In2O3 and SnO2 systems. J Phys: Condens Matter, 2017, 29, 085501 |
| [18] |
Snaith H J, Ducati C. SnO2-based dye-sensitized hybrid solar cells exhibiting near unity absorbed photon-to-electron conversion efficiency. Nano Lett, 2010, 10, 1259 |
| [19] |
Jiang Q, Zhang L, Wang H, et al. Enhanced electron extraction using SnO2 for high-efficiency planar-structure HC(NH2)2PbI3-based perovskite solar cells. Nat Energy, 2017, 2, 16177 |
| [20] |
Scanlon D O, Dunnill C W, Buckeridge J, et al. Band alignment of rutile and anatase TiO2. Nat Mater, 2013, 12, 798 |
| [21] |
Harrison W A. Elementary theory of heterojunctions. J Vac Sci Technol, 1977, 14, 1016 |
| [22] |
Wei S H, Zunger A. Role ofdorbitals in valence-band offsets of common-anion semiconductors. Phys Rev Lett, 1987, 59, 144 |
| [23] |
Wei S H, Zunger A. Calculated natural band offsets of all II–VI and III–V semiconductors: Chemical trends and the role of cation d orbitals. Appl Phys Lett, 1998, 72, 2011 |
| [24] |
Walsh A, Da Silva J L F, Wei S H. Multi-component transparent conducting oxides: Progress in materials modelling. J Phys: Condens Matter, 2011, 23, 334210 |
| [25] |
Chen W, Pasquarello A. Band-edge positions in GW: effects of starting point and self-consistency. Phys Rev B, 2014, 90, 165133 |
| [26] |
Kresse G, Joubert D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B, 1999, 59, 1758 |
| [27] |
Heyd J, Scuseria G E, Ernzerhof M. Hybrid functionals based on a screened Coulomb potential. J Chem Phys, 2003, 118, 8207 |
| [28] |
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 |
| [29] |
Haines J, Léger J M. 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 |
| [30] |
Landmann M, Rauls E, Schmidt W G. The electronic structure and optical response of rutile, anatase and brookite TiO2. J Phys: Condens Matter, 2012, 24, 195503 |
| [31] |
Perdew J P, Burke K, Ernzerhof M. Generalized gradient approximation made simple. Phys Rev Lett, 1996, 77, 3865 |
| [32] |
Aryasetiawan F, Gunnarsson O. The GW method. Rep Prog Phys, 1998, 61, 237 |
| [33] |
Wei S H, Zunger A. Valence band splittings and band offsets of AlN, GaN, and InN. Appl Phys Lett, 1996, 69, 2719 |
| [34] |
Kang Y, Kang G, Nahm H H, et al. GW calculations on post-transition-metal oxides. Phys Rev B, 2014, 89 |
| [35] |
Reynolds D C, Look D C, Jogai B, et al. Valence-band ordering in ZnO. Phys Rev B, 1999, 60, 2340 |
| [36] |
Koffyberg F P. Thermoreflectance spectra of CdO: Band gaps and band-population effects. Phys Rev B, 1976, 13, 4470 |
| [37] |
Rebien M, Henrion W, Hong M, et al. Optical properties of gallium oxide thin films. Appl Phys Lett, 2002, 81, 250 |
| [38] |
Trukhin A, Kink M, Maksimov Y, et al. Luminescence of GeO2 glass, rutile-like and α-quartz-like crystals. J Non-Cryst Solids, 2006, 352, 160 |
| [39] |
Borgatti F, Berger J A, Céolin D, et al. Revisiting the origin of satellites in core-level photoemission of transparent conducting oxides: The case of n-doped SnO2. Phys Rev B, 2018, 97, 155102 |
X F Cai, P Zhang, S H Wei, Revisit of the band gaps of rutile SnO2 and TiO2: a first-principles study[J]. J. Semicond., 2019, 40(9): 092101. doi: 10.1088/1674-4926/40/9/092101.
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Manuscript received: 30 April 2019 Manuscript revised: 11 June 2019 Online: Accepted Manuscript: 14 August 2019 Uncorrected proof: 21 August 2019 Published: 01 September 2019
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