Abstract

The electronic and optical properties of TiO2 atomic structures representing simulated thin films have been investigated using density functional theory. Suitable model parameters and system sizes have been identified in advance by validation of the results with experimental data. Dependencies of the electronic band gap and the refractive index have been calculated as a function of film density. The results of the performed calculations have been compared to characterized optical properties of titania single layers deposited using different coating techniques. The modeled dependencies are consistent with experimental observations, and absolute magnitudes of simulated values are in agreement with measured optical data.

© 2013 Optical Society of America

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  1. A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, G. DeBell, V. Pervak, A. K. Sytchkova, M. L. Grilli, and D. Ristau, “Optical parameters of oxide films typically used in optical coating production,” Appl. Opt. 50, C75–C85 (2011).
    [CrossRef]
  2. O. Stenzel, S. Wilbrandt, N. Kaiser, C. Schmitz, M. Turowski, D. Ristau, P. Awakowicz, R. P. Brinkmann, T. Musch, I. Rolfes, H. Steffen, R. Foest, A. Ohl, T. Köhler, G. Dolgonos, and T. Frauenheim, “Plasma and optical thin film technologies,” Proc. SPIE 8168, 81680L (2011).
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    [CrossRef]
  6. B. Zhao, J. Zhou, and L. Rong, “Microstructure and optical properties of TiO2 thin films deposited at different oxygen flow rates,” Trans. Nonferrous Met. Soc. China 20, 1429–1433 (2010).
    [CrossRef]
  7. T. Köhler, M. Turowski, H. Ehlers, M. Landmann, D. Ristau, and T. Frauenheim, “Computational approach for structure design and prediction of optical properties in amorphous TiO2 thin-film coatings,” J. Phys. D 46, 325302 (2013).
    [CrossRef]
  8. V. Georgieva, I. T. Todorov, and A. Bogaerts, “Molecular dynamics simulation of oxide thin film growth: Importance of the inter-atomic interaction potential,” Chem. Phys. Lett. 485, 315–319 (2010).
    [CrossRef]
  9. M. Saraiva, V. Georgieva, S. Mahieu, K. Van Aeken, A. Bogaerts, and D. Depla, “Compositional effects on the growth of Mg(M)O films,” J. Appl. Phys. 107, 034902 (2010).
    [CrossRef]
  10. V. Georgieva, M. Saraiva, N. Jehanathan, O. I. Lebelev, D. Depla, and A. Bogaerts, “Sputter-deposited Mg–Al–O thin films: linking molecular dynamics simulations to experiments,” J. Phys. D 42, 065107 (2009).
    [CrossRef]
  11. M. Turowski, H. Ehlers, K. Heinrich, and D. Ristau, “Modeling of Al2O3 thin film growth in modern ion coating processes,” Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2013), paper MA.8.
  12. M. Landmann, T. Köhler, S. Köppen, E. Rauls, T. Frauenheim, and W. G. Schmidt, “Fingerprints of order and disorder in the electronic and optical properties of crystalline and amorphous TiO2,” Phys. Rev. B 86, 064201 (2012).
    [CrossRef]
  13. G. Kresse and J. Furthmüller, “Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set,” Comput. Mater. Sci. 6, 15 (1996).
    [CrossRef]
  14. P. Hohenberg, “Inhomogeneous Electron Gas,” Phys. Rev. 136, B864–B871 (1964).
    [CrossRef]
  15. W. Kohn and L. J. Sham, “Self-consistent equations including exchange and correlation effects,” Phys. Rev. 140, A1133–A1138 (1965).
    [CrossRef]
  16. P. E. Blöchl, “Projector augmented-wave method,” Phys. Rev. B 50, 17953–17979 (1994).
    [CrossRef]
  17. J. Heyd, G. E. Scuseria, and M. Ernzerhof, “Hybrid functionals based on a screened Coulomb potential,” J. Chem. Phys. 118, 8207–8216 (2003).
    [CrossRef]
  18. J. Heyd, G. E. Scuseria, and M. Ernzerhof, “Erratum: “Hybrid functionals based on a screened Coulomb potential” [J. Chem. Phys. 118, 8207 (2003)],” J. Chem. Phys. 124, 219906 (2006).
    [CrossRef]
  19. J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865–3868 (1996).
    [CrossRef]
  20. M. Landmann, E. Rauls, and W. G. Schmidt, “The electronic structure and optical response of rutile, anatase and brookite TiO2,” J. Phys. Condens. Matter 24, 195503 (2012).
    [CrossRef]
  21. B. Prasai, B. Cai, M. K. Underwood, J. P. Lewis, and D. A. Drabold, “Properties of amorphous and crystalline titanium dioxide from first principles,” J. Mater. Sci. 47, 7515–7521 (2012).
    [CrossRef]
  22. H. Hellmann, “A new approximation method in the problem of many electrons,” J. Chem. Phys. 3, 61 (1935).
    [CrossRef]
  23. J. Pack and H. Monkhorst, “Special points for Brillouin-zone integrations,” Phys. Rev. B 16, 1748–1749 (1977).
    [CrossRef]
  24. H. Ehrenreich and M. Cohen, “Self-consistent field approach to the many-electron problem,” Phys. Rev. 115, 786–790 (1959).
    [CrossRef]
  25. M. Gajdoš, K. Hummer, G. Kresse, J. Furthmüller, and F. Bechstedt, “Linear optical properties in the projector-augmented wave methodology,” Phys. Rev. B 73, 045112 (2006).
    [CrossRef]
  26. T. Amotchkina, M. Trubetskov, A. Tikhonravov, I. Angelov, and V. Pervak, “Reliable characterization of e-beam evaporated TiO2 films,” Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2013), paper FA.6.
  27. M. Vergöhl, O. Werner, and S. Bruns, “New developments in magnetron sputter processes for precision optics,” Proc. SPIE 7101, 71010B (2008).
    [CrossRef]
  28. M. Jupé, L. Jensen, A. Melninkaitis, V. Sirutkaitis, and D. Ristau, “Calculations and experimental demonstration of multi-photon absorption governing fs laser-induced damage in titania,” Opt. Express 17, 12269–12278 (2009).
    [CrossRef]
  29. J. Tauc, R. Grigorovici, and A. Vancu, “Optical properties and electronic structure of amorphous germanium,” Phys. Status Solidi 15, 627–637 (1966).
    [CrossRef]

2013 (1)

T. Köhler, M. Turowski, H. Ehlers, M. Landmann, D. Ristau, and T. Frauenheim, “Computational approach for structure design and prediction of optical properties in amorphous TiO2 thin-film coatings,” J. Phys. D 46, 325302 (2013).
[CrossRef]

2012 (3)

M. Landmann, T. Köhler, S. Köppen, E. Rauls, T. Frauenheim, and W. G. Schmidt, “Fingerprints of order and disorder in the electronic and optical properties of crystalline and amorphous TiO2,” Phys. Rev. B 86, 064201 (2012).
[CrossRef]

M. Landmann, E. Rauls, and W. G. Schmidt, “The electronic structure and optical response of rutile, anatase and brookite TiO2,” J. Phys. Condens. Matter 24, 195503 (2012).
[CrossRef]

B. Prasai, B. Cai, M. K. Underwood, J. P. Lewis, and D. A. Drabold, “Properties of amorphous and crystalline titanium dioxide from first principles,” J. Mater. Sci. 47, 7515–7521 (2012).
[CrossRef]

2011 (2)

O. Stenzel, S. Wilbrandt, N. Kaiser, C. Schmitz, M. Turowski, D. Ristau, P. Awakowicz, R. P. Brinkmann, T. Musch, I. Rolfes, H. Steffen, R. Foest, A. Ohl, T. Köhler, G. Dolgonos, and T. Frauenheim, “Plasma and optical thin film technologies,” Proc. SPIE 8168, 81680L (2011).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, G. DeBell, V. Pervak, A. K. Sytchkova, M. L. Grilli, and D. Ristau, “Optical parameters of oxide films typically used in optical coating production,” Appl. Opt. 50, C75–C85 (2011).
[CrossRef]

2010 (3)

B. Zhao, J. Zhou, and L. Rong, “Microstructure and optical properties of TiO2 thin films deposited at different oxygen flow rates,” Trans. Nonferrous Met. Soc. China 20, 1429–1433 (2010).
[CrossRef]

V. Georgieva, I. T. Todorov, and A. Bogaerts, “Molecular dynamics simulation of oxide thin film growth: Importance of the inter-atomic interaction potential,” Chem. Phys. Lett. 485, 315–319 (2010).
[CrossRef]

M. Saraiva, V. Georgieva, S. Mahieu, K. Van Aeken, A. Bogaerts, and D. Depla, “Compositional effects on the growth of Mg(M)O films,” J. Appl. Phys. 107, 034902 (2010).
[CrossRef]

2009 (2)

V. Georgieva, M. Saraiva, N. Jehanathan, O. I. Lebelev, D. Depla, and A. Bogaerts, “Sputter-deposited Mg–Al–O thin films: linking molecular dynamics simulations to experiments,” J. Phys. D 42, 065107 (2009).
[CrossRef]

M. Jupé, L. Jensen, A. Melninkaitis, V. Sirutkaitis, and D. Ristau, “Calculations and experimental demonstration of multi-photon absorption governing fs laser-induced damage in titania,” Opt. Express 17, 12269–12278 (2009).
[CrossRef]

2008 (1)

M. Vergöhl, O. Werner, and S. Bruns, “New developments in magnetron sputter processes for precision optics,” Proc. SPIE 7101, 71010B (2008).
[CrossRef]

2006 (2)

M. Gajdoš, K. Hummer, G. Kresse, J. Furthmüller, and F. Bechstedt, “Linear optical properties in the projector-augmented wave methodology,” Phys. Rev. B 73, 045112 (2006).
[CrossRef]

J. Heyd, G. E. Scuseria, and M. Ernzerhof, “Erratum: “Hybrid functionals based on a screened Coulomb potential” [J. Chem. Phys. 118, 8207 (2003)],” J. Chem. Phys. 124, 219906 (2006).
[CrossRef]

2003 (1)

J. Heyd, G. E. Scuseria, and M. Ernzerhof, “Hybrid functionals based on a screened Coulomb potential,” J. Chem. Phys. 118, 8207–8216 (2003).
[CrossRef]

2000 (1)

D. Mergel, D. Buschendorf, S. Eggert, R. Grammes, and B. Samset, “Density and refractive index of TiO2 films prepared by reactive evaporation,” Thin Solid Films 371, 218–224 (2000).
[CrossRef]

1996 (2)

G. Kresse and J. Furthmüller, “Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set,” Comput. Mater. Sci. 6, 15 (1996).
[CrossRef]

J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865–3868 (1996).
[CrossRef]

1994 (1)

P. E. Blöchl, “Projector augmented-wave method,” Phys. Rev. B 50, 17953–17979 (1994).
[CrossRef]

1992 (1)

1977 (1)

J. Pack and H. Monkhorst, “Special points for Brillouin-zone integrations,” Phys. Rev. B 16, 1748–1749 (1977).
[CrossRef]

1966 (1)

J. Tauc, R. Grigorovici, and A. Vancu, “Optical properties and electronic structure of amorphous germanium,” Phys. Status Solidi 15, 627–637 (1966).
[CrossRef]

1965 (1)

W. Kohn and L. J. Sham, “Self-consistent equations including exchange and correlation effects,” Phys. Rev. 140, A1133–A1138 (1965).
[CrossRef]

1964 (1)

P. Hohenberg, “Inhomogeneous Electron Gas,” Phys. Rev. 136, B864–B871 (1964).
[CrossRef]

1959 (1)

H. Ehrenreich and M. Cohen, “Self-consistent field approach to the many-electron problem,” Phys. Rev. 115, 786–790 (1959).
[CrossRef]

1935 (1)

H. Hellmann, “A new approximation method in the problem of many electrons,” J. Chem. Phys. 3, 61 (1935).
[CrossRef]

Amotchkina, T.

T. Amotchkina, M. Trubetskov, A. Tikhonravov, I. Angelov, and V. Pervak, “Reliable characterization of e-beam evaporated TiO2 films,” Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2013), paper FA.6.

Amotchkina, T. V.

Angelov, I.

T. Amotchkina, M. Trubetskov, A. Tikhonravov, I. Angelov, and V. Pervak, “Reliable characterization of e-beam evaporated TiO2 films,” Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2013), paper FA.6.

Awakowicz, P.

O. Stenzel, S. Wilbrandt, N. Kaiser, C. Schmitz, M. Turowski, D. Ristau, P. Awakowicz, R. P. Brinkmann, T. Musch, I. Rolfes, H. Steffen, R. Foest, A. Ohl, T. Köhler, G. Dolgonos, and T. Frauenheim, “Plasma and optical thin film technologies,” Proc. SPIE 8168, 81680L (2011).
[CrossRef]

Bechstedt, F.

M. Gajdoš, K. Hummer, G. Kresse, J. Furthmüller, and F. Bechstedt, “Linear optical properties in the projector-augmented wave methodology,” Phys. Rev. B 73, 045112 (2006).
[CrossRef]

Blöchl, P. E.

P. E. Blöchl, “Projector augmented-wave method,” Phys. Rev. B 50, 17953–17979 (1994).
[CrossRef]

Bogaerts, A.

M. Saraiva, V. Georgieva, S. Mahieu, K. Van Aeken, A. Bogaerts, and D. Depla, “Compositional effects on the growth of Mg(M)O films,” J. Appl. Phys. 107, 034902 (2010).
[CrossRef]

V. Georgieva, I. T. Todorov, and A. Bogaerts, “Molecular dynamics simulation of oxide thin film growth: Importance of the inter-atomic interaction potential,” Chem. Phys. Lett. 485, 315–319 (2010).
[CrossRef]

V. Georgieva, M. Saraiva, N. Jehanathan, O. I. Lebelev, D. Depla, and A. Bogaerts, “Sputter-deposited Mg–Al–O thin films: linking molecular dynamics simulations to experiments,” J. Phys. D 42, 065107 (2009).
[CrossRef]

Brinkmann, R. P.

O. Stenzel, S. Wilbrandt, N. Kaiser, C. Schmitz, M. Turowski, D. Ristau, P. Awakowicz, R. P. Brinkmann, T. Musch, I. Rolfes, H. Steffen, R. Foest, A. Ohl, T. Köhler, G. Dolgonos, and T. Frauenheim, “Plasma and optical thin film technologies,” Proc. SPIE 8168, 81680L (2011).
[CrossRef]

Bruns, S.

M. Vergöhl, O. Werner, and S. Bruns, “New developments in magnetron sputter processes for precision optics,” Proc. SPIE 7101, 71010B (2008).
[CrossRef]

Burke, K.

J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865–3868 (1996).
[CrossRef]

Buschendorf, D.

D. Mergel, D. Buschendorf, S. Eggert, R. Grammes, and B. Samset, “Density and refractive index of TiO2 films prepared by reactive evaporation,” Thin Solid Films 371, 218–224 (2000).
[CrossRef]

Cai, B.

B. Prasai, B. Cai, M. K. Underwood, J. P. Lewis, and D. A. Drabold, “Properties of amorphous and crystalline titanium dioxide from first principles,” J. Mater. Sci. 47, 7515–7521 (2012).
[CrossRef]

Cohen, M.

H. Ehrenreich and M. Cohen, “Self-consistent field approach to the many-electron problem,” Phys. Rev. 115, 786–790 (1959).
[CrossRef]

DeBell, G.

Depla, D.

M. Saraiva, V. Georgieva, S. Mahieu, K. Van Aeken, A. Bogaerts, and D. Depla, “Compositional effects on the growth of Mg(M)O films,” J. Appl. Phys. 107, 034902 (2010).
[CrossRef]

V. Georgieva, M. Saraiva, N. Jehanathan, O. I. Lebelev, D. Depla, and A. Bogaerts, “Sputter-deposited Mg–Al–O thin films: linking molecular dynamics simulations to experiments,” J. Phys. D 42, 065107 (2009).
[CrossRef]

Dobrowolski, J. A.

Dolgonos, G.

O. Stenzel, S. Wilbrandt, N. Kaiser, C. Schmitz, M. Turowski, D. Ristau, P. Awakowicz, R. P. Brinkmann, T. Musch, I. Rolfes, H. Steffen, R. Foest, A. Ohl, T. Köhler, G. Dolgonos, and T. Frauenheim, “Plasma and optical thin film technologies,” Proc. SPIE 8168, 81680L (2011).
[CrossRef]

Drabold, D. A.

B. Prasai, B. Cai, M. K. Underwood, J. P. Lewis, and D. A. Drabold, “Properties of amorphous and crystalline titanium dioxide from first principles,” J. Mater. Sci. 47, 7515–7521 (2012).
[CrossRef]

Eggert, S.

D. Mergel, D. Buschendorf, S. Eggert, R. Grammes, and B. Samset, “Density and refractive index of TiO2 films prepared by reactive evaporation,” Thin Solid Films 371, 218–224 (2000).
[CrossRef]

Ehlers, H.

T. Köhler, M. Turowski, H. Ehlers, M. Landmann, D. Ristau, and T. Frauenheim, “Computational approach for structure design and prediction of optical properties in amorphous TiO2 thin-film coatings,” J. Phys. D 46, 325302 (2013).
[CrossRef]

M. Turowski, H. Ehlers, K. Heinrich, and D. Ristau, “Modeling of Al2O3 thin film growth in modern ion coating processes,” Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2013), paper MA.8.

Ehrenreich, H.

H. Ehrenreich and M. Cohen, “Self-consistent field approach to the many-electron problem,” Phys. Rev. 115, 786–790 (1959).
[CrossRef]

Ernzerhof, M.

J. Heyd, G. E. Scuseria, and M. Ernzerhof, “Erratum: “Hybrid functionals based on a screened Coulomb potential” [J. Chem. Phys. 118, 8207 (2003)],” J. Chem. Phys. 124, 219906 (2006).
[CrossRef]

J. Heyd, G. E. Scuseria, and M. Ernzerhof, “Hybrid functionals based on a screened Coulomb potential,” J. Chem. Phys. 118, 8207–8216 (2003).
[CrossRef]

J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865–3868 (1996).
[CrossRef]

Foest, R.

O. Stenzel, S. Wilbrandt, N. Kaiser, C. Schmitz, M. Turowski, D. Ristau, P. Awakowicz, R. P. Brinkmann, T. Musch, I. Rolfes, H. Steffen, R. Foest, A. Ohl, T. Köhler, G. Dolgonos, and T. Frauenheim, “Plasma and optical thin film technologies,” Proc. SPIE 8168, 81680L (2011).
[CrossRef]

Frauenheim, T.

T. Köhler, M. Turowski, H. Ehlers, M. Landmann, D. Ristau, and T. Frauenheim, “Computational approach for structure design and prediction of optical properties in amorphous TiO2 thin-film coatings,” J. Phys. D 46, 325302 (2013).
[CrossRef]

M. Landmann, T. Köhler, S. Köppen, E. Rauls, T. Frauenheim, and W. G. Schmidt, “Fingerprints of order and disorder in the electronic and optical properties of crystalline and amorphous TiO2,” Phys. Rev. B 86, 064201 (2012).
[CrossRef]

O. Stenzel, S. Wilbrandt, N. Kaiser, C. Schmitz, M. Turowski, D. Ristau, P. Awakowicz, R. P. Brinkmann, T. Musch, I. Rolfes, H. Steffen, R. Foest, A. Ohl, T. Köhler, G. Dolgonos, and T. Frauenheim, “Plasma and optical thin film technologies,” Proc. SPIE 8168, 81680L (2011).
[CrossRef]

Furthmüller, J.

M. Gajdoš, K. Hummer, G. Kresse, J. Furthmüller, and F. Bechstedt, “Linear optical properties in the projector-augmented wave methodology,” Phys. Rev. B 73, 045112 (2006).
[CrossRef]

G. Kresse and J. Furthmüller, “Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set,” Comput. Mater. Sci. 6, 15 (1996).
[CrossRef]

Gajdoš, M.

M. Gajdoš, K. Hummer, G. Kresse, J. Furthmüller, and F. Bechstedt, “Linear optical properties in the projector-augmented wave methodology,” Phys. Rev. B 73, 045112 (2006).
[CrossRef]

Georgieva, V.

V. Georgieva, I. T. Todorov, and A. Bogaerts, “Molecular dynamics simulation of oxide thin film growth: Importance of the inter-atomic interaction potential,” Chem. Phys. Lett. 485, 315–319 (2010).
[CrossRef]

M. Saraiva, V. Georgieva, S. Mahieu, K. Van Aeken, A. Bogaerts, and D. Depla, “Compositional effects on the growth of Mg(M)O films,” J. Appl. Phys. 107, 034902 (2010).
[CrossRef]

V. Georgieva, M. Saraiva, N. Jehanathan, O. I. Lebelev, D. Depla, and A. Bogaerts, “Sputter-deposited Mg–Al–O thin films: linking molecular dynamics simulations to experiments,” J. Phys. D 42, 065107 (2009).
[CrossRef]

Grammes, R.

D. Mergel, D. Buschendorf, S. Eggert, R. Grammes, and B. Samset, “Density and refractive index of TiO2 films prepared by reactive evaporation,” Thin Solid Films 371, 218–224 (2000).
[CrossRef]

Grigorovici, R.

J. Tauc, R. Grigorovici, and A. Vancu, “Optical properties and electronic structure of amorphous germanium,” Phys. Status Solidi 15, 627–637 (1966).
[CrossRef]

Grilli, M. L.

Heinrich, K.

M. Turowski, H. Ehlers, K. Heinrich, and D. Ristau, “Modeling of Al2O3 thin film growth in modern ion coating processes,” Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2013), paper MA.8.

Hellmann, H.

H. Hellmann, “A new approximation method in the problem of many electrons,” J. Chem. Phys. 3, 61 (1935).
[CrossRef]

Heyd, J.

J. Heyd, G. E. Scuseria, and M. Ernzerhof, “Erratum: “Hybrid functionals based on a screened Coulomb potential” [J. Chem. Phys. 118, 8207 (2003)],” J. Chem. Phys. 124, 219906 (2006).
[CrossRef]

J. Heyd, G. E. Scuseria, and M. Ernzerhof, “Hybrid functionals based on a screened Coulomb potential,” J. Chem. Phys. 118, 8207–8216 (2003).
[CrossRef]

Hohenberg, P.

P. Hohenberg, “Inhomogeneous Electron Gas,” Phys. Rev. 136, B864–B871 (1964).
[CrossRef]

Hummer, K.

M. Gajdoš, K. Hummer, G. Kresse, J. Furthmüller, and F. Bechstedt, “Linear optical properties in the projector-augmented wave methodology,” Phys. Rev. B 73, 045112 (2006).
[CrossRef]

Jehanathan, N.

V. Georgieva, M. Saraiva, N. Jehanathan, O. I. Lebelev, D. Depla, and A. Bogaerts, “Sputter-deposited Mg–Al–O thin films: linking molecular dynamics simulations to experiments,” J. Phys. D 42, 065107 (2009).
[CrossRef]

Jensen, L.

Jupé, M.

Kaiser, N.

O. Stenzel, S. Wilbrandt, N. Kaiser, C. Schmitz, M. Turowski, D. Ristau, P. Awakowicz, R. P. Brinkmann, T. Musch, I. Rolfes, H. Steffen, R. Foest, A. Ohl, T. Köhler, G. Dolgonos, and T. Frauenheim, “Plasma and optical thin film technologies,” Proc. SPIE 8168, 81680L (2011).
[CrossRef]

Köhler, T.

T. Köhler, M. Turowski, H. Ehlers, M. Landmann, D. Ristau, and T. Frauenheim, “Computational approach for structure design and prediction of optical properties in amorphous TiO2 thin-film coatings,” J. Phys. D 46, 325302 (2013).
[CrossRef]

M. Landmann, T. Köhler, S. Köppen, E. Rauls, T. Frauenheim, and W. G. Schmidt, “Fingerprints of order and disorder in the electronic and optical properties of crystalline and amorphous TiO2,” Phys. Rev. B 86, 064201 (2012).
[CrossRef]

O. Stenzel, S. Wilbrandt, N. Kaiser, C. Schmitz, M. Turowski, D. Ristau, P. Awakowicz, R. P. Brinkmann, T. Musch, I. Rolfes, H. Steffen, R. Foest, A. Ohl, T. Köhler, G. Dolgonos, and T. Frauenheim, “Plasma and optical thin film technologies,” Proc. SPIE 8168, 81680L (2011).
[CrossRef]

Kohn, W.

W. Kohn and L. J. Sham, “Self-consistent equations including exchange and correlation effects,” Phys. Rev. 140, A1133–A1138 (1965).
[CrossRef]

Köppen, S.

M. Landmann, T. Köhler, S. Köppen, E. Rauls, T. Frauenheim, and W. G. Schmidt, “Fingerprints of order and disorder in the electronic and optical properties of crystalline and amorphous TiO2,” Phys. Rev. B 86, 064201 (2012).
[CrossRef]

Kresse, G.

M. Gajdoš, K. Hummer, G. Kresse, J. Furthmüller, and F. Bechstedt, “Linear optical properties in the projector-augmented wave methodology,” Phys. Rev. B 73, 045112 (2006).
[CrossRef]

G. Kresse and J. Furthmüller, “Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set,” Comput. Mater. Sci. 6, 15 (1996).
[CrossRef]

Landmann, M.

T. Köhler, M. Turowski, H. Ehlers, M. Landmann, D. Ristau, and T. Frauenheim, “Computational approach for structure design and prediction of optical properties in amorphous TiO2 thin-film coatings,” J. Phys. D 46, 325302 (2013).
[CrossRef]

M. Landmann, E. Rauls, and W. G. Schmidt, “The electronic structure and optical response of rutile, anatase and brookite TiO2,” J. Phys. Condens. Matter 24, 195503 (2012).
[CrossRef]

M. Landmann, T. Köhler, S. Köppen, E. Rauls, T. Frauenheim, and W. G. Schmidt, “Fingerprints of order and disorder in the electronic and optical properties of crystalline and amorphous TiO2,” Phys. Rev. B 86, 064201 (2012).
[CrossRef]

Lebelev, O. I.

V. Georgieva, M. Saraiva, N. Jehanathan, O. I. Lebelev, D. Depla, and A. Bogaerts, “Sputter-deposited Mg–Al–O thin films: linking molecular dynamics simulations to experiments,” J. Phys. D 42, 065107 (2009).
[CrossRef]

Lewis, J. P.

B. Prasai, B. Cai, M. K. Underwood, J. P. Lewis, and D. A. Drabold, “Properties of amorphous and crystalline titanium dioxide from first principles,” J. Mater. Sci. 47, 7515–7521 (2012).
[CrossRef]

Mahieu, S.

M. Saraiva, V. Georgieva, S. Mahieu, K. Van Aeken, A. Bogaerts, and D. Depla, “Compositional effects on the growth of Mg(M)O films,” J. Appl. Phys. 107, 034902 (2010).
[CrossRef]

Melninkaitis, A.

Mergel, D.

D. Mergel, D. Buschendorf, S. Eggert, R. Grammes, and B. Samset, “Density and refractive index of TiO2 films prepared by reactive evaporation,” Thin Solid Films 371, 218–224 (2000).
[CrossRef]

Monkhorst, H.

J. Pack and H. Monkhorst, “Special points for Brillouin-zone integrations,” Phys. Rev. B 16, 1748–1749 (1977).
[CrossRef]

Musch, T.

O. Stenzel, S. Wilbrandt, N. Kaiser, C. Schmitz, M. Turowski, D. Ristau, P. Awakowicz, R. P. Brinkmann, T. Musch, I. Rolfes, H. Steffen, R. Foest, A. Ohl, T. Köhler, G. Dolgonos, and T. Frauenheim, “Plasma and optical thin film technologies,” Proc. SPIE 8168, 81680L (2011).
[CrossRef]

Ohl, A.

O. Stenzel, S. Wilbrandt, N. Kaiser, C. Schmitz, M. Turowski, D. Ristau, P. Awakowicz, R. P. Brinkmann, T. Musch, I. Rolfes, H. Steffen, R. Foest, A. Ohl, T. Köhler, G. Dolgonos, and T. Frauenheim, “Plasma and optical thin film technologies,” Proc. SPIE 8168, 81680L (2011).
[CrossRef]

Pack, J.

J. Pack and H. Monkhorst, “Special points for Brillouin-zone integrations,” Phys. Rev. B 16, 1748–1749 (1977).
[CrossRef]

Perdew, J. P.

J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865–3868 (1996).
[CrossRef]

Pervak, V.

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, G. DeBell, V. Pervak, A. K. Sytchkova, M. L. Grilli, and D. Ristau, “Optical parameters of oxide films typically used in optical coating production,” Appl. Opt. 50, C75–C85 (2011).
[CrossRef]

T. Amotchkina, M. Trubetskov, A. Tikhonravov, I. Angelov, and V. Pervak, “Reliable characterization of e-beam evaporated TiO2 films,” Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2013), paper FA.6.

Prasai, B.

B. Prasai, B. Cai, M. K. Underwood, J. P. Lewis, and D. A. Drabold, “Properties of amorphous and crystalline titanium dioxide from first principles,” J. Mater. Sci. 47, 7515–7521 (2012).
[CrossRef]

Rauls, E.

M. Landmann, E. Rauls, and W. G. Schmidt, “The electronic structure and optical response of rutile, anatase and brookite TiO2,” J. Phys. Condens. Matter 24, 195503 (2012).
[CrossRef]

M. Landmann, T. Köhler, S. Köppen, E. Rauls, T. Frauenheim, and W. G. Schmidt, “Fingerprints of order and disorder in the electronic and optical properties of crystalline and amorphous TiO2,” Phys. Rev. B 86, 064201 (2012).
[CrossRef]

Ristau, D.

T. Köhler, M. Turowski, H. Ehlers, M. Landmann, D. Ristau, and T. Frauenheim, “Computational approach for structure design and prediction of optical properties in amorphous TiO2 thin-film coatings,” J. Phys. D 46, 325302 (2013).
[CrossRef]

A. V. Tikhonravov, M. K. Trubetskov, T. V. Amotchkina, G. DeBell, V. Pervak, A. K. Sytchkova, M. L. Grilli, and D. Ristau, “Optical parameters of oxide films typically used in optical coating production,” Appl. Opt. 50, C75–C85 (2011).
[CrossRef]

O. Stenzel, S. Wilbrandt, N. Kaiser, C. Schmitz, M. Turowski, D. Ristau, P. Awakowicz, R. P. Brinkmann, T. Musch, I. Rolfes, H. Steffen, R. Foest, A. Ohl, T. Köhler, G. Dolgonos, and T. Frauenheim, “Plasma and optical thin film technologies,” Proc. SPIE 8168, 81680L (2011).
[CrossRef]

M. Jupé, L. Jensen, A. Melninkaitis, V. Sirutkaitis, and D. Ristau, “Calculations and experimental demonstration of multi-photon absorption governing fs laser-induced damage in titania,” Opt. Express 17, 12269–12278 (2009).
[CrossRef]

M. Turowski, H. Ehlers, K. Heinrich, and D. Ristau, “Modeling of Al2O3 thin film growth in modern ion coating processes,” Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2013), paper MA.8.

Rolfes, I.

O. Stenzel, S. Wilbrandt, N. Kaiser, C. Schmitz, M. Turowski, D. Ristau, P. Awakowicz, R. P. Brinkmann, T. Musch, I. Rolfes, H. Steffen, R. Foest, A. Ohl, T. Köhler, G. Dolgonos, and T. Frauenheim, “Plasma and optical thin film technologies,” Proc. SPIE 8168, 81680L (2011).
[CrossRef]

Rong, L.

B. Zhao, J. Zhou, and L. Rong, “Microstructure and optical properties of TiO2 thin films deposited at different oxygen flow rates,” Trans. Nonferrous Met. Soc. China 20, 1429–1433 (2010).
[CrossRef]

Samset, B.

D. Mergel, D. Buschendorf, S. Eggert, R. Grammes, and B. Samset, “Density and refractive index of TiO2 films prepared by reactive evaporation,” Thin Solid Films 371, 218–224 (2000).
[CrossRef]

Saraiva, M.

M. Saraiva, V. Georgieva, S. Mahieu, K. Van Aeken, A. Bogaerts, and D. Depla, “Compositional effects on the growth of Mg(M)O films,” J. Appl. Phys. 107, 034902 (2010).
[CrossRef]

V. Georgieva, M. Saraiva, N. Jehanathan, O. I. Lebelev, D. Depla, and A. Bogaerts, “Sputter-deposited Mg–Al–O thin films: linking molecular dynamics simulations to experiments,” J. Phys. D 42, 065107 (2009).
[CrossRef]

Schmidt, W. G.

M. Landmann, E. Rauls, and W. G. Schmidt, “The electronic structure and optical response of rutile, anatase and brookite TiO2,” J. Phys. Condens. Matter 24, 195503 (2012).
[CrossRef]

M. Landmann, T. Köhler, S. Köppen, E. Rauls, T. Frauenheim, and W. G. Schmidt, “Fingerprints of order and disorder in the electronic and optical properties of crystalline and amorphous TiO2,” Phys. Rev. B 86, 064201 (2012).
[CrossRef]

Schmitz, C.

O. Stenzel, S. Wilbrandt, N. Kaiser, C. Schmitz, M. Turowski, D. Ristau, P. Awakowicz, R. P. Brinkmann, T. Musch, I. Rolfes, H. Steffen, R. Foest, A. Ohl, T. Köhler, G. Dolgonos, and T. Frauenheim, “Plasma and optical thin film technologies,” Proc. SPIE 8168, 81680L (2011).
[CrossRef]

Scuseria, G. E.

J. Heyd, G. E. Scuseria, and M. Ernzerhof, “Erratum: “Hybrid functionals based on a screened Coulomb potential” [J. Chem. Phys. 118, 8207 (2003)],” J. Chem. Phys. 124, 219906 (2006).
[CrossRef]

J. Heyd, G. E. Scuseria, and M. Ernzerhof, “Hybrid functionals based on a screened Coulomb potential,” J. Chem. Phys. 118, 8207–8216 (2003).
[CrossRef]

Sham, L. J.

W. Kohn and L. J. Sham, “Self-consistent equations including exchange and correlation effects,” Phys. Rev. 140, A1133–A1138 (1965).
[CrossRef]

Sirutkaitis, V.

Steffen, H.

O. Stenzel, S. Wilbrandt, N. Kaiser, C. Schmitz, M. Turowski, D. Ristau, P. Awakowicz, R. P. Brinkmann, T. Musch, I. Rolfes, H. Steffen, R. Foest, A. Ohl, T. Köhler, G. Dolgonos, and T. Frauenheim, “Plasma and optical thin film technologies,” Proc. SPIE 8168, 81680L (2011).
[CrossRef]

Stenzel, O.

O. Stenzel, S. Wilbrandt, N. Kaiser, C. Schmitz, M. Turowski, D. Ristau, P. Awakowicz, R. P. Brinkmann, T. Musch, I. Rolfes, H. Steffen, R. Foest, A. Ohl, T. Köhler, G. Dolgonos, and T. Frauenheim, “Plasma and optical thin film technologies,” Proc. SPIE 8168, 81680L (2011).
[CrossRef]

Sullivan, B. T.

Sytchkova, A. K.

Tauc, J.

J. Tauc, R. Grigorovici, and A. Vancu, “Optical properties and electronic structure of amorphous germanium,” Phys. Status Solidi 15, 627–637 (1966).
[CrossRef]

Tikhonravov, A.

T. Amotchkina, M. Trubetskov, A. Tikhonravov, I. Angelov, and V. Pervak, “Reliable characterization of e-beam evaporated TiO2 films,” Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2013), paper FA.6.

Tikhonravov, A. V.

Todorov, I. T.

V. Georgieva, I. T. Todorov, and A. Bogaerts, “Molecular dynamics simulation of oxide thin film growth: Importance of the inter-atomic interaction potential,” Chem. Phys. Lett. 485, 315–319 (2010).
[CrossRef]

Trubetskov, M.

T. Amotchkina, M. Trubetskov, A. Tikhonravov, I. Angelov, and V. Pervak, “Reliable characterization of e-beam evaporated TiO2 films,” Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2013), paper FA.6.

Trubetskov, M. K.

Turowski, M.

T. Köhler, M. Turowski, H. Ehlers, M. Landmann, D. Ristau, and T. Frauenheim, “Computational approach for structure design and prediction of optical properties in amorphous TiO2 thin-film coatings,” J. Phys. D 46, 325302 (2013).
[CrossRef]

O. Stenzel, S. Wilbrandt, N. Kaiser, C. Schmitz, M. Turowski, D. Ristau, P. Awakowicz, R. P. Brinkmann, T. Musch, I. Rolfes, H. Steffen, R. Foest, A. Ohl, T. Köhler, G. Dolgonos, and T. Frauenheim, “Plasma and optical thin film technologies,” Proc. SPIE 8168, 81680L (2011).
[CrossRef]

M. Turowski, H. Ehlers, K. Heinrich, and D. Ristau, “Modeling of Al2O3 thin film growth in modern ion coating processes,” Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2013), paper MA.8.

Underwood, M. K.

B. Prasai, B. Cai, M. K. Underwood, J. P. Lewis, and D. A. Drabold, “Properties of amorphous and crystalline titanium dioxide from first principles,” J. Mater. Sci. 47, 7515–7521 (2012).
[CrossRef]

Van Aeken, K.

M. Saraiva, V. Georgieva, S. Mahieu, K. Van Aeken, A. Bogaerts, and D. Depla, “Compositional effects on the growth of Mg(M)O films,” J. Appl. Phys. 107, 034902 (2010).
[CrossRef]

Vancu, A.

J. Tauc, R. Grigorovici, and A. Vancu, “Optical properties and electronic structure of amorphous germanium,” Phys. Status Solidi 15, 627–637 (1966).
[CrossRef]

Vergöhl, M.

M. Vergöhl, O. Werner, and S. Bruns, “New developments in magnetron sputter processes for precision optics,” Proc. SPIE 7101, 71010B (2008).
[CrossRef]

Werner, O.

M. Vergöhl, O. Werner, and S. Bruns, “New developments in magnetron sputter processes for precision optics,” Proc. SPIE 7101, 71010B (2008).
[CrossRef]

Wilbrandt, S.

O. Stenzel, S. Wilbrandt, N. Kaiser, C. Schmitz, M. Turowski, D. Ristau, P. Awakowicz, R. P. Brinkmann, T. Musch, I. Rolfes, H. Steffen, R. Foest, A. Ohl, T. Köhler, G. Dolgonos, and T. Frauenheim, “Plasma and optical thin film technologies,” Proc. SPIE 8168, 81680L (2011).
[CrossRef]

Zhao, B.

B. Zhao, J. Zhou, and L. Rong, “Microstructure and optical properties of TiO2 thin films deposited at different oxygen flow rates,” Trans. Nonferrous Met. Soc. China 20, 1429–1433 (2010).
[CrossRef]

Zhou, J.

B. Zhao, J. Zhou, and L. Rong, “Microstructure and optical properties of TiO2 thin films deposited at different oxygen flow rates,” Trans. Nonferrous Met. Soc. China 20, 1429–1433 (2010).
[CrossRef]

Appl. Opt. (2)

Chem. Phys. Lett. (1)

V. Georgieva, I. T. Todorov, and A. Bogaerts, “Molecular dynamics simulation of oxide thin film growth: Importance of the inter-atomic interaction potential,” Chem. Phys. Lett. 485, 315–319 (2010).
[CrossRef]

Comput. Mater. Sci. (1)

G. Kresse and J. Furthmüller, “Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set,” Comput. Mater. Sci. 6, 15 (1996).
[CrossRef]

J. Appl. Phys. (1)

M. Saraiva, V. Georgieva, S. Mahieu, K. Van Aeken, A. Bogaerts, and D. Depla, “Compositional effects on the growth of Mg(M)O films,” J. Appl. Phys. 107, 034902 (2010).
[CrossRef]

J. Chem. Phys. (3)

J. Heyd, G. E. Scuseria, and M. Ernzerhof, “Hybrid functionals based on a screened Coulomb potential,” J. Chem. Phys. 118, 8207–8216 (2003).
[CrossRef]

J. Heyd, G. E. Scuseria, and M. Ernzerhof, “Erratum: “Hybrid functionals based on a screened Coulomb potential” [J. Chem. Phys. 118, 8207 (2003)],” J. Chem. Phys. 124, 219906 (2006).
[CrossRef]

H. Hellmann, “A new approximation method in the problem of many electrons,” J. Chem. Phys. 3, 61 (1935).
[CrossRef]

J. Mater. Sci. (1)

B. Prasai, B. Cai, M. K. Underwood, J. P. Lewis, and D. A. Drabold, “Properties of amorphous and crystalline titanium dioxide from first principles,” J. Mater. Sci. 47, 7515–7521 (2012).
[CrossRef]

J. Phys. Condens. Matter (1)

M. Landmann, E. Rauls, and W. G. Schmidt, “The electronic structure and optical response of rutile, anatase and brookite TiO2,” J. Phys. Condens. Matter 24, 195503 (2012).
[CrossRef]

J. Phys. D (2)

V. Georgieva, M. Saraiva, N. Jehanathan, O. I. Lebelev, D. Depla, and A. Bogaerts, “Sputter-deposited Mg–Al–O thin films: linking molecular dynamics simulations to experiments,” J. Phys. D 42, 065107 (2009).
[CrossRef]

T. Köhler, M. Turowski, H. Ehlers, M. Landmann, D. Ristau, and T. Frauenheim, “Computational approach for structure design and prediction of optical properties in amorphous TiO2 thin-film coatings,” J. Phys. D 46, 325302 (2013).
[CrossRef]

Opt. Express (1)

Phys. Rev. (3)

H. Ehrenreich and M. Cohen, “Self-consistent field approach to the many-electron problem,” Phys. Rev. 115, 786–790 (1959).
[CrossRef]

P. Hohenberg, “Inhomogeneous Electron Gas,” Phys. Rev. 136, B864–B871 (1964).
[CrossRef]

W. Kohn and L. J. Sham, “Self-consistent equations including exchange and correlation effects,” Phys. Rev. 140, A1133–A1138 (1965).
[CrossRef]

Phys. Rev. B (4)

P. E. Blöchl, “Projector augmented-wave method,” Phys. Rev. B 50, 17953–17979 (1994).
[CrossRef]

M. Landmann, T. Köhler, S. Köppen, E. Rauls, T. Frauenheim, and W. G. Schmidt, “Fingerprints of order and disorder in the electronic and optical properties of crystalline and amorphous TiO2,” Phys. Rev. B 86, 064201 (2012).
[CrossRef]

M. Gajdoš, K. Hummer, G. Kresse, J. Furthmüller, and F. Bechstedt, “Linear optical properties in the projector-augmented wave methodology,” Phys. Rev. B 73, 045112 (2006).
[CrossRef]

J. Pack and H. Monkhorst, “Special points for Brillouin-zone integrations,” Phys. Rev. B 16, 1748–1749 (1977).
[CrossRef]

Phys. Rev. Lett. (1)

J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77, 3865–3868 (1996).
[CrossRef]

Phys. Status Solidi (1)

J. Tauc, R. Grigorovici, and A. Vancu, “Optical properties and electronic structure of amorphous germanium,” Phys. Status Solidi 15, 627–637 (1966).
[CrossRef]

Proc. SPIE (2)

M. Vergöhl, O. Werner, and S. Bruns, “New developments in magnetron sputter processes for precision optics,” Proc. SPIE 7101, 71010B (2008).
[CrossRef]

O. Stenzel, S. Wilbrandt, N. Kaiser, C. Schmitz, M. Turowski, D. Ristau, P. Awakowicz, R. P. Brinkmann, T. Musch, I. Rolfes, H. Steffen, R. Foest, A. Ohl, T. Köhler, G. Dolgonos, and T. Frauenheim, “Plasma and optical thin film technologies,” Proc. SPIE 8168, 81680L (2011).
[CrossRef]

Thin Solid Films (1)

D. Mergel, D. Buschendorf, S. Eggert, R. Grammes, and B. Samset, “Density and refractive index of TiO2 films prepared by reactive evaporation,” Thin Solid Films 371, 218–224 (2000).
[CrossRef]

Trans. Nonferrous Met. Soc. China (1)

B. Zhao, J. Zhou, and L. Rong, “Microstructure and optical properties of TiO2 thin films deposited at different oxygen flow rates,” Trans. Nonferrous Met. Soc. China 20, 1429–1433 (2010).
[CrossRef]

Other (3)

N. Kaiser and H. K. Pulker, eds., Optical Interference Coatings, Vol. 88 of Springer Series in Optical Sciences (Springer, 2003).

M. Turowski, H. Ehlers, K. Heinrich, and D. Ristau, “Modeling of Al2O3 thin film growth in modern ion coating processes,” Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2013), paper MA.8.

T. Amotchkina, M. Trubetskov, A. Tikhonravov, I. Angelov, and V. Pervak, “Reliable characterization of e-beam evaporated TiO2 films,” Optical Interference Coatings, OSA Technical Digest (Optical Society of America, 2013), paper FA.6.

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Figures (9)

Fig. 1.
Fig. 1.

Energy relaxation of an atomistic titania ensemble.

Fig. 2.
Fig. 2.

Scheme of the applied simulation chain to calculate optical properties as a function of film density.

Fig. 3.
Fig. 3.

Comparison between the diagonal matrix elements of the refractive index as a function of energy for 12- and 96-atom structure with density 3.93g/cm3.

Fig. 4.
Fig. 4.

Comparison between experimental and calculated index of refraction as a function of wavelength.

Fig. 5.
Fig. 5.

Measured and calculated index of refraction as a function of inverse structure size at 500 and 1000 nm.

Fig. 6.
Fig. 6.

Comparison of refractive indices for different densities. Evaluation of the corresponding values at (a) n=500nm, (b) n=1000nm and (c) n=1500nm. Additionally, the Lorentz–Lorenz dependence for the experimental data is presented in (a) (solid black line).

Fig. 7.
Fig. 7.

Comparison of the DOS calculated for a 30-atom TiO2 structure (3.21g/cm3) with two different functionals: pure DFT and HF.

Fig. 8.
Fig. 8.

Tauc-plot and linear fit for graphically analysis of the Tauc-gap for the 96-atom titania structure with density 3.93g/cm3.

Fig. 9.
Fig. 9.

Comparison of evaluated Tauc-gaps for the calculated and measured optical constants.

Tables (1)

Tables Icon

Table 1. Experimental Samples for Validation

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

Nb12(Na+Ne),
Nb=12(Na+4Ne,O+2Ne,Ti)+1=28.
(nxnxynxznxynynyznxznyznz),(kxkxykxzkxykykyzkxzkyzkz).
nx=ny=nz,nxy=nxz=nyz=0,kx=ky=kz,kxy=kxz=kyz=0.
n21n2+2=Cρ,

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