Oxygen deficiency in TiO2: Similarities and differences between the Ti self-interstitial and the O vacancy in bulk rutile and anatase

Physical Review B - Condensed Matter and Materials Physics

Volumn 92, Issue 4, 2015, Pages

  Deák, Peter ^a   Aradi, Bálint ^a   Frauenheim, Thomas ^a  

^a UNIVERSITY OF BREMEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84937899433     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.92.045204     Document Type: Article

References (79)

1. In ionic crystals with strong electron-phonon coupling (such as many II-VI semiconductors, alkali halides, oxides, etc.), a charge carrier is dressed in a cloud of virtual phonons and can be considered as a new composite particle, called a polaron. If the phonon cloud corresponds to a strong local relaxation of the lattice, the carrier is essentially trapped in a so-called "small polaron" state and transport can proceed only through thermally activated hopping.
2. N.B.: we use, e.g., (Equation presented) as notation for the oxidation state, while (Equation presented) denotes an interstitial Ti atom in the triply negative charged state.
3. P. Deák, B. Aradi, and T. Frauenheim, Phys. Rev. B 83, 155207 (2011). 10.1103/PhysRevB.83.155207
4. M. Setvin, C. Franchini, X. Hao, M. Schmid, A. Janotti, M. Kaltak, C. G. Van de Walle, G. Kresse, and U. Diebold, Phys. Rev. Lett. 113, 086402 (2014). 10.1103/PhysRevLett.113.086402
5. T. Sarkar, K. Gopinadhan, Zh. Jun, S. Saha, J. M. D. Coey, Y. P. Feng, A. Ariando, and T. Venkatesan (unpublished).
6. P. Deák, J. Kullgren, and T. Frauenheim, Phys. Status Solidi RRL 8, 583 (2014). 10.1002/pssr.201409139
7. S. K. Wallace and K.P. McKenna, J. Phys. Chem. C 119, 1913 (2015). 10.1021/jp511529u
8. S. Wendt, P. T. Sprunger, E. Lira, G. K. H. Madsen, Z. S. Li, J. O. Hansen, J. Matthiesen, A. Blekinge-Rasmussen, E. Laegsgaard, B. Hammer, and F. Besenbacher, Science 320, 1755 (2008). 10.1126/science.1159846
9. C. M. Yim, C. L. Pang, and G. Thornton, Phys. Rev. Lett. 104, 036806 (2010). 10.1103/PhysRevLett.104.036806
10. M. Aono and R. R. Hasiguti, Phys. Rev. B 48, 12406 (1993). 10.1103/PhysRevB.48.12406
11. C. L. Pang, R. Lindsay, and G. Thornton, Chem. Soc. Rev. 37, 2328 (2008). 10.1039/b719085a
12. P. Deák, B. Aradi, and T. Frauenheim, Phys. Rev. B 86, 195206 (2012). 10.1103/PhysRevB.86.195206
13. S. Lany and A. Zunger, Phys. Rev. B 80, 085202 (2009). 10.1103/PhysRevB.80.085202
14. P. Deák, B. Aradi, T. Frauenheim, E.Janzén, and A. Gali, Phys. Rev. B 81, 153203 (2010). 10.1103/PhysRevB.81.153203
15. HF exchange gives a total energy, which is a concave, while local/semi-local DFT is a convex function of the fractional occupation numbers. Proper mixing may lead to linear behavior, with the correlation- and the self-interaction error cancelling each other.
16. X. Zheng, A. J. Cohen, P. Mori-Sanchez, X. Hu, and W. Yang, Phys. Rev. Lett. 107, 026403 (2011). 10.1103/PhysRevLett.107.026403
17. S. J. Clark and J. Robertson, Phys. Rev. B 82, 085208 (2010); 10.1103/PhysRevB.82.085208
18. K. Xiong, J. Robertson, M. C. Gibson, and S. J. Clark, Appl. Phys. Lett. 87, 183505 (2005). 10.1063/1.2119425
19. J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003). 10.1063/1.1564060
20. J. A. V. Krukau, O. A. Vydrov, A. F. Izmaylov, and G. E. Scuseria, J. Chem. Phys. 125, 224106 (2006). 10.1063/1.2404663
21. M. Marsman, J. Paier, A. Stroppa and G. Kresse, J. Phys. Condens. Matter 20, 064201 (2008). 10.1088/0953-8984/20/6/064201
22. J. P. Perdew, M. Ernzerhof, and K. Burke, J. Chem. Phys. 105, 9982 (1996). 10.1063/1.472933
23. P. Deák, B. Aradi, and T. Frauenheim, J. Phys. Chem. C 115, 3443 (2011). 10.1021/jp1115492
24. A. D. J. Becke, J. Chem. Phys. 98, 5648 (1993) 10.1063/1.464913;
25. C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B 37, 785 (1988). 10.1103/PhysRevB.37.785
26. C. Di Valentin and A. Selloni, J. Phys. Chem. Lett. 2, 2223 (2011). 10.1021/jz2009874
27. A. Janotti, J. B. Varley, P. Rinke, N. Umezawa, G. Kresse, and C. G. Van de Walle, Phys. Rev. B 81, 085212 (2010). 10.1103/PhysRevB.81.085212
28. T. Yamamoto and T. Ohno, Phys. Chem. Chem. Phys. 14, 589 (2012). 10.1039/C1CP21547G
29. T. S. Bjørheim, A. Kuwabara, and T. Norby, J. Phys. Chem. C 117, 5919 (2013). 10.1021/jp304146e
30. B. J. Morgan and G. W. Watson, Phys. Rev. B 80, 233102 (2009). 10.1103/PhysRevB.80.233102
31. B. J. Morgan and G. W. Watson, J. Phys. Chem. C 114, 2321 (2010). 10.1021/jp9088047
32. G. Mattioli, P. Alippi, F. Filippone, R. Caminiti, and A. Amore Bonapasta, J. Phys. Chem. C 114, 21694 (2010). 10.1021/jp1041316
33. J. Stausholm-Møller, H. H. Kistoffersen, B. Hinnemann, G. K. H. Madsen, and B. Hammer, J. Chem. Phys. 133, 144708 (2010). 10.1063/1.3492449
34. E. Finazzi, C. Di Valentin, and G. Pacchioni, J. Phys. Chem. C 113, 3382 (2009). 10.1021/jp8111793
35. H.-Y. Lee, S. J. Clark, and J. Robertson, Phys. Rev. B 86, 075209 (2012). 10.1103/PhysRevB.86.075209
36. G. Kresse and J. Hafner, Phys. Rev. B 49, 14251 (1994); 10.1103/PhysRevB.49.14251
37. G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996); 10.1103/PhysRevB.54.11169
38. G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999). 10.1103/PhysRevB.59.1758
39. J. Pascual, J. Camassel, and H. Mathieu, Phys. Rev. B 18, 5606 (1978). 10.1103/PhysRevB.18.5606
40. H. Tang, F. Lévy, H. Berger, and P. E. Schmid, Phys. Rev. B 52, 7771 (1995). 10.1103/PhysRevB.52.7771
41. Y. Tezuka, S. Shin, T. Ishii, T. Ejima, S. Suzuki, and S. Sato, J. Phys. Soc. Jpn. 63, 347 (1994). 10.1143/JPSJ.63.347
42. S. Rangan, S. Katalinic, R. Thorpe, R. A. Bartynski, J. Rochford, and E. Galoppini, J. Phys. Chem. C 114, 1139 (2010). 10.1021/jp909320f
43. W. Kang and M. S. Hybertsen, Phys. Rev. B 82, 085203 (2010). 10.1103/PhysRevB.82.085203
44. L. Chiodo, J. M. García-Lastra, A. Iacomino, S. Ossicini, J. Zhao, H. Petek, and A. Rubio, Phys. Rev. B 82, 045207 (2010). 10.1103/PhysRevB.82.045207
45. M. Landmann, E. Rauls, and W. G. Schmidt, J. Phys.: Condens. Matter 24, 195503 (2012). 10.1088/0953-8984/24/19/195503
46. In the Brillouin-zone of orthogonal lattices, this is the point where a tight binding band of the interacting defects is closest to the level of an isolated defect.
47. H. J. Monkhorst and J. K. Pack, Phys. Rev. B 13, 5188 (1976). 10.1103/PhysRevB.13.5188
48. S. Lany and A. Zunger, Phys. Rev. B 78, 235104 (2008). 10.1103/PhysRevB.78.235104
49. S. Lany and A. Zunger, Phys. Rev. B 81, 113201 (2010). 10.1103/PhysRevB.81.113201
50. H.-P. Komsa, T. T. Rantala, and A. Pasquarello, Phys. Rev. B 86, 045112 (2012). 10.1103/PhysRevB.86.045112
51. P. Deák, Phys. Status Solidi B 217, 9 (2000). 10.1002/(SICI)1521-3951(200001)217:1%3C9::AID-PSSB9%3E3.0.CO;2-6
52. B. Lee, C.-K. Lee, C. S. Hwang, and S. Han, Curr. Appl. Phys. 11, S293 (2011). 10.1016/j.cap.2010.11.104
53. P. Kofstad, Non-Stoichiometry, Diffusion, and Electrical Conductivity in Binary Metal Oxides (Wiley, New York, 1972).
54. T. Bak, J. Nowotny, and M. K. Nowotny, J. Phys. Chem. B 110, 21560 (2006). 10.1021/jp063700k
55. S. Yang, A. T. Brant, N. C. Giles, and L. E. Halliburton, Phys. Rev. B 87, 125201 (2013). 10.1103/PhysRevB.87.125201
56. D. C. Cronemeyer, Phys. Rev. 113, 1222 (1959). 10.1103/PhysRev.113.1222
57. W.-T. Kim, C.-D. Kim, and Q. W. Choi, Phys. Rev. B 30, 3625 (1984). 10.1103/PhysRevB.30.3625
58. A. K. Gosh, F. G. Wakim, and R. R. Addiss Jr., Phys. Rev. 184, 979 (1969). 10.1103/PhysRev.184.979
59. S. Yang, L. E. Halliburton, A. Mannivanan, P. H. Bunton, D. B. Baker, M. Klemm, S. Horn, and A. Fujishima, Appl. Phys. Lett. 94, 162114 (2009). 10.1063/1.3124656
60. F. D. Brandão, M. V. B. Pinheiro, G. M. Ribeiro, G. Medeiros-Ribeiro, and K. Krambock, Phys. Rev. B 80, 235204 (2009). 10.1103/PhysRevB.80.235204
61. V. E. Henrich and R. L. Kurtz, Phys. Rev. B 23, 6280 (1981). 10.1103/PhysRevB.23.6280
62. R. Sanjines, H. Tang, H. Berger, F. Gozzo, G. Margaritondo, and F. Levy, J. Appl. Phys. 75, 2945 (1994). 10.1063/1.356190
63. A. G. Thomas, W. R. Flavell, A. K. Mallick, A. R. Kumarasinghe, D. Tsoutsou, N. Khan, C. Chatwin, S. Rayner, G. C. Smith, R. L. Stockbauer, S. Warren, T. K. Johal, S. Patel, D. Holland, A. Taleb, and F. Wiame, Phys. Rev. B 75, 035105 (2007). 10.1103/PhysRevB.75.035105
64. H. Sezen, M. Buchholz, A. Nefedov, C. Natzeck, S. Heissler, C. Di Valentin, and C. Wöll, Sci. Rep. 4, 3808 (2014). 10.1038/srep03808
65. H. Najafov, S. Tokita, S. Osshio, A. Kati, and H. Saitoh, Japn. J. Appl. Phys. 44, 245 (2005). 10.1143/JJAP.44.245
66. H. Sezen, H. Shang, F. Bebensee, C. Yang, M. Buchholz, A. Nefedov, S. Heissler, C. Carbogno, M. Scheffler, P. Rinke, and C. Wöll, Nat. Commun. 6, 6901 (2015). 10.1038/ncomms7901
67. S. Moser, L. Moreschini, J. Jaćimović, O. S. Barišić, L. H. Berger, A. Magrez, Y. J. Chang, K. S. Kim, A. Bostwick, E. Rotenberg, L. Forró, and M. Grioni, Phys. Rev. Lett. 110, 196403 (2013). 10.1103/PhysRevLett.110.196403
68. R. Asahi, T. Morikawa, T. Ohwaki, K. Aoki, and Y. Taga, Science, 293, 269 (2001). 10.1126/science.1061051
69. C. Di Valentin, G. Pacchioni, A. Selloni, S. Livraghy, and E. Giamello, J. Phys. Chem. B 109, 11414 (2005). 10.1021/jp051756t
70. J. B. Varley, A. Janotti, and C. G. Van de Walle, Adv. Mater. 23, 2343 (2011). 10.1002/adma.201003603
71. C. N. Druckworth, A. W. Brinkman, and J. Woods, Phys. Status Solidi A 75, K99 (1983). 10.1002/pssa.2210750163
72. B. Santara, P. K. Giri, K. Imakita, and M. Fujii, J. Phys. Chem. C 117, 23402 (2013). 10.1021/jp408249q
73. L. Forro, O. Chauvet, D. Emin, and L. Zuppiroli, J. Appl. Phys. 75, 633 (1994). 10.1063/1.355801
74. Note that the first and second vertical ionization energies of the EMT states of (Equation presented) are computed to be equal (cf. Table I), and the first adiabatic charge transition in Fig. 5 is (Equation presented). The accuracy of the supercell method is quite limited, in case of shallow EMT states.
75. T. Shibuya, K. Yasuoka, S. Mirbt, and B. Sanyal, J. Phys.: Condens. Matter. 24, 435504 (2012). 10.1088/0953-8984/24/43/435504
76. M. J. Jackman, P. Deák, K. L. Syres, J. Adell, B. Thiagarajan, A. Levy and A. G. Thomas, arXiv:1406.3385 [cond-mat.mtrl-sci]
77. S. Wang, L. Pan, J.-J. Song, W. Mi, J.-J. Zou, L. Wang, and X. Zhang, J. Am. Chem. Soc. 137, 2975 (2015). 10.1021/ja512047k
78. A. Rusydi, S. Dhar, A. Roy Barman, Ariando, D.-C. Qi, M. Motapothula, J. B. Yi, I. Santoso, Y. P. Feng, K. Yang, Y. Dai, N. L. Yakovlev, J. Ding, A. T. S. Wee, G. Neuber, M. B. H. Breese, M. Ruebhausen, H. Hilgenkamp, and T. Venkatesan, Phil. Trans. R. Soc. London, Ser. A 370, 4927 (2012). 10.1098/rsta.2012.0198
79. M. K. Nowotny, T. Bak, and J. Nowotny, J. Phys. Chem. B 110, 16270 (2006). 10.1021/jp0606210