Abstract

Titanium nitride is a CMOS-compatible alternative material to conventional metals for plasmonics and metamaterials applications. We demonstrate complete tunability at visible and near-infrared frequencies of the optical dispersion of titanium nitride nanolayers deposited on Si (100) substrates from metallic to dielectric behavior by alteration of reactive magnetron sputtering growth conditions and, via co-deposition, the addition of Si and/or O2 elemental components. The dielectric function and region of metallic character is found to be further modified by post-deposition vacuum annealing. We categorize this dispersion behavior as anomalous due to a distinctive line shape that allows for double-plasmon resonances, which we investigate analytically using Mie scattering theory.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4(6), 795–808 (2010).
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  3. W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
    [Crossref] [PubMed]
  4. S. Shrestha, Y. Wang, A. C. Overvig, M. Lu, A. Stein, L. Dal Negro, and N. Yu, “Indium Tin Oxide Broadband Metasurface Absorber,” ACS Photonics 5(9), 3526–3533 (2018).
    [Crossref]
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    [Crossref]
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    [Crossref]
  8. G. V. Naik, J. L. Schroeder, X. Ni, A. V. Kildishev, T. D. Sands, and A. Boltasseva, “Titanium nitride as a plasmonic material for visible and near-infrared wavelengths,” Opt. Mater. Express 2(4), 478–489 (2012).
    [Crossref]
  9. P. Patsalas and S. Logothetidis, “Optical, electronic, and transport properties of nanocrystalline titanium nitride thin films,” J. Appl. Phys. 90(9), 4725–4734 (2001).
    [Crossref]
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    [Crossref] [PubMed]
  12. C. M. Zgrabik and E. L. Hu, “Optimization of sputtered titanium nitride as a tunable metal for plasmonic applications,” Opt. Mater. Express 5(12), 2786–2797 (2015).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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  26. A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Multipole light scattering by nonspherical nanoparticles in the discrete dipole approximation,” Phys. Rev. B Condens. Matter 84(23), 235429 (2011).
    [Crossref]
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    [Crossref] [PubMed]

2018 (1)

S. Shrestha, Y. Wang, A. C. Overvig, M. Lu, A. Stein, L. Dal Negro, and N. Yu, “Indium Tin Oxide Broadband Metasurface Absorber,” ACS Photonics 5(9), 3526–3533 (2018).
[Crossref]

2017 (2)

L. Braic, N. Vasilantonakis, A. Mihai, I. J. Villar Garcia, S. Fearn, B. Zou, N. M. Alford, B. Doiron, R. F. Oulton, S. A. Maier, A. V. Zayats, and P. K. Petrov, “Titanium Oxynitride Thin Films with Tunable Double Epsilon-Near-Zero Behavior for Nanophotonic Applications,” ACS Appl. Mater. Interfaces 9(35), 29857–29862 (2017).
[Crossref] [PubMed]

D. Shah, H. Reddy, N. Kinsey, V. M. Shalaev, and A. Boltasseva, “Optical properties of plasmonic ultrathin TiN films,” Adv. Opt. Mater. 5(13), 1700065 (2017).
[Crossref]

2016 (1)

N. A. Butakov and J. A. Schuller, “Designing multipolar resonances in dielectric metamaterials,” Sci. Rep. 6(1), 38487 (2016).
[Crossref] [PubMed]

2015 (2)

2014 (2)

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[Crossref] [PubMed]

R. Pandian, G. Natarajan, S. Rajagopalan, M. Kamruddin, and A. K. Tyagi, “On the phase formation of titanium oxide thin films deposited by reactive DC magnetron sputtering: influence of oxygen partial pressure and nitrogen doping,” Appl. Phys., A Mater. Sci. Process. 116(4), 1905–1913 (2014).
[Crossref]

2013 (1)

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref] [PubMed]

2012 (2)

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(19), 195503 (2012).
[Crossref] [PubMed]

G. V. Naik, J. L. Schroeder, X. Ni, A. V. Kildishev, T. D. Sands, and A. Boltasseva, “Titanium nitride as a plasmonic material for visible and near-infrared wavelengths,” Opt. Mater. Express 2(4), 478–489 (2012).
[Crossref]

2011 (1)

A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Multipole light scattering by nonspherical nanoparticles in the discrete dipole approximation,” Phys. Rev. B Condens. Matter 84(23), 235429 (2011).
[Crossref]

2010 (1)

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4(6), 795–808 (2010).
[Crossref]

2007 (1)

J. Chappé, N. Martin, J. Lintymer, F. Sthal, G. Terwagne, and J. Takadoum, “Titanium oxynitride thin films sputter deposited by the reactive gas pulsing process,” Appl. Surf. Sci. 253(12), 5312–5316 (2007).
[Crossref]

2003 (1)

S. Zerkout, S. Achour, A. Mosser, and N. Tabet, “On the existence of superstructure in TiNx thin films,” Thin Solid Films 441(1–2), 135–139 (2003).
[Crossref]

2001 (1)

P. Patsalas and S. Logothetidis, “Optical, electronic, and transport properties of nanocrystalline titanium nitride thin films,” J. Appl. Phys. 90(9), 4725–4734 (2001).
[Crossref]

2000 (1)

L. Rebouta, C. J. Tavares, R. Aimo, Z. Wang, K. Pischow, E. Alves, T. C. Rojas, and J. A. Odriozola, “Hard nanocomposite Ti–Si–N coatings prepared by DC reactive magnetron sputtering,” Surf. Coat. Tech. 133-134, 234–239 (2000).
[Crossref]

1998 (1)

F. Vaz, L. Rebouta, S. Ramos, M. F. Da Silva, and J. C. Soares, “Physical, structural and mechanical characterization of Ti1-xSixNy films,” Surf. Coat. Tech. 108-109, 236–240 (1998).
[Crossref]

1997 (1)

V. Srikant and D. R. Clarke, “Optical absorption edge of ZnO thin films: the effect of substrate,” J. Appl. Phys. 81(9), 6357–6364 (1997).
[Crossref]

1995 (1)

S. Vepřek, S. Reiprich, and L. Shizhi, “Superhard nanocrystalline composite materials: the TiN/Si3N4 system,” Appl. Phys. Lett. 66(20), 2640–2642 (1995).
[Crossref]

1989 (1)

L. Hultman, J. E. Sundgren, L. C. Markert, and J. E. Greene, “Ar and excess N incorporation in epitaxial TiN films grown by reactive bias sputtering in mixed Ar/N2 and pure N2 discharges,” J. Vac. Sci. Technol. A 7(3), 1187–1193 (1989).
[Crossref]

1983 (1)

B. Karlsson, R. P. Shimshock, B. O. Seraphin, and J. C. Haygarth, “Optical properties of CVD-coated TiN, ZrN and HfN,” Sol. Energy Mater. 7(4), 401–411 (1983).
[Crossref]

1972 (1)

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

1965 (1)

V. Ern and A. C. Switendick, “Electronic band structure of TiC, TiN, and TiO,” Phys. Rev. 137(6A), A1927–A1936 (1965).
[Crossref]

Achour, S.

S. Zerkout, S. Achour, A. Mosser, and N. Tabet, “On the existence of superstructure in TiNx thin films,” Thin Solid Films 441(1–2), 135–139 (2003).
[Crossref]

Aimo, R.

L. Rebouta, C. J. Tavares, R. Aimo, Z. Wang, K. Pischow, E. Alves, T. C. Rojas, and J. A. Odriozola, “Hard nanocomposite Ti–Si–N coatings prepared by DC reactive magnetron sputtering,” Surf. Coat. Tech. 133-134, 234–239 (2000).
[Crossref]

Alford, N. M.

L. Braic, N. Vasilantonakis, A. Mihai, I. J. Villar Garcia, S. Fearn, B. Zou, N. M. Alford, B. Doiron, R. F. Oulton, S. A. Maier, A. V. Zayats, and P. K. Petrov, “Titanium Oxynitride Thin Films with Tunable Double Epsilon-Near-Zero Behavior for Nanophotonic Applications,” ACS Appl. Mater. Interfaces 9(35), 29857–29862 (2017).
[Crossref] [PubMed]

Alves, E.

L. Rebouta, C. J. Tavares, R. Aimo, Z. Wang, K. Pischow, E. Alves, T. C. Rojas, and J. A. Odriozola, “Hard nanocomposite Ti–Si–N coatings prepared by DC reactive magnetron sputtering,” Surf. Coat. Tech. 133-134, 234–239 (2000).
[Crossref]

Boltasseva, A.

D. Shah, H. Reddy, N. Kinsey, V. M. Shalaev, and A. Boltasseva, “Optical properties of plasmonic ultrathin TiN films,” Adv. Opt. Mater. 5(13), 1700065 (2017).
[Crossref]

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[Crossref] [PubMed]

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref] [PubMed]

G. V. Naik, J. L. Schroeder, X. Ni, A. V. Kildishev, T. D. Sands, and A. Boltasseva, “Titanium nitride as a plasmonic material for visible and near-infrared wavelengths,” Opt. Mater. Express 2(4), 478–489 (2012).
[Crossref]

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4(6), 795–808 (2010).
[Crossref]

Braic, L.

L. Braic, N. Vasilantonakis, A. Mihai, I. J. Villar Garcia, S. Fearn, B. Zou, N. M. Alford, B. Doiron, R. F. Oulton, S. A. Maier, A. V. Zayats, and P. K. Petrov, “Titanium Oxynitride Thin Films with Tunable Double Epsilon-Near-Zero Behavior for Nanophotonic Applications,” ACS Appl. Mater. Interfaces 9(35), 29857–29862 (2017).
[Crossref] [PubMed]

Butakov, N. A.

N. A. Butakov and J. A. Schuller, “Designing multipolar resonances in dielectric metamaterials,” Sci. Rep. 6(1), 38487 (2016).
[Crossref] [PubMed]

Capretti, A.

Chappé, J.

J. Chappé, N. Martin, J. Lintymer, F. Sthal, G. Terwagne, and J. Takadoum, “Titanium oxynitride thin films sputter deposited by the reactive gas pulsing process,” Appl. Surf. Sci. 253(12), 5312–5316 (2007).
[Crossref]

Chichkov, B. N.

A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Multipole light scattering by nonspherical nanoparticles in the discrete dipole approximation,” Phys. Rev. B Condens. Matter 84(23), 235429 (2011).
[Crossref]

Christy, R.

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Clarke, D. R.

V. Srikant and D. R. Clarke, “Optical absorption edge of ZnO thin films: the effect of substrate,” J. Appl. Phys. 81(9), 6357–6364 (1997).
[Crossref]

Da Silva, M. F.

F. Vaz, L. Rebouta, S. Ramos, M. F. Da Silva, and J. C. Soares, “Physical, structural and mechanical characterization of Ti1-xSixNy films,” Surf. Coat. Tech. 108-109, 236–240 (1998).
[Crossref]

Dal Negro, L.

S. Shrestha, Y. Wang, A. C. Overvig, M. Lu, A. Stein, L. Dal Negro, and N. Yu, “Indium Tin Oxide Broadband Metasurface Absorber,” ACS Photonics 5(9), 3526–3533 (2018).
[Crossref]

Y. Wang, A. Capretti, and L. Dal Negro, “Wide tuning of the optical and structural properties of alternative plasmonic materials,” Opt. Mater. Express 5(11), 2415–2430 (2015).
[Crossref]

Doiron, B.

L. Braic, N. Vasilantonakis, A. Mihai, I. J. Villar Garcia, S. Fearn, B. Zou, N. M. Alford, B. Doiron, R. F. Oulton, S. A. Maier, A. V. Zayats, and P. K. Petrov, “Titanium Oxynitride Thin Films with Tunable Double Epsilon-Near-Zero Behavior for Nanophotonic Applications,” ACS Appl. Mater. Interfaces 9(35), 29857–29862 (2017).
[Crossref] [PubMed]

Emani, N. K.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4(6), 795–808 (2010).
[Crossref]

Ern, V.

V. Ern and A. C. Switendick, “Electronic band structure of TiC, TiN, and TiO,” Phys. Rev. 137(6A), A1927–A1936 (1965).
[Crossref]

Evlyukhin, A. B.

A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Multipole light scattering by nonspherical nanoparticles in the discrete dipole approximation,” Phys. Rev. B Condens. Matter 84(23), 235429 (2011).
[Crossref]

Fearn, S.

L. Braic, N. Vasilantonakis, A. Mihai, I. J. Villar Garcia, S. Fearn, B. Zou, N. M. Alford, B. Doiron, R. F. Oulton, S. A. Maier, A. V. Zayats, and P. K. Petrov, “Titanium Oxynitride Thin Films with Tunable Double Epsilon-Near-Zero Behavior for Nanophotonic Applications,” ACS Appl. Mater. Interfaces 9(35), 29857–29862 (2017).
[Crossref] [PubMed]

Greene, J. E.

L. Hultman, J. E. Sundgren, L. C. Markert, and J. E. Greene, “Ar and excess N incorporation in epitaxial TiN films grown by reactive bias sputtering in mixed Ar/N2 and pure N2 discharges,” J. Vac. Sci. Technol. A 7(3), 1187–1193 (1989).
[Crossref]

Guan, J.

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[Crossref] [PubMed]

Guler, U.

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[Crossref] [PubMed]

Haygarth, J. C.

B. Karlsson, R. P. Shimshock, B. O. Seraphin, and J. C. Haygarth, “Optical properties of CVD-coated TiN, ZrN and HfN,” Sol. Energy Mater. 7(4), 401–411 (1983).
[Crossref]

Hu, E. L.

Hultman, L.

L. Hultman, J. E. Sundgren, L. C. Markert, and J. E. Greene, “Ar and excess N incorporation in epitaxial TiN films grown by reactive bias sputtering in mixed Ar/N2 and pure N2 discharges,” J. Vac. Sci. Technol. A 7(3), 1187–1193 (1989).
[Crossref]

Ishii, S.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4(6), 795–808 (2010).
[Crossref]

Johnson, P.

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Kamruddin, M.

R. Pandian, G. Natarajan, S. Rajagopalan, M. Kamruddin, and A. K. Tyagi, “On the phase formation of titanium oxide thin films deposited by reactive DC magnetron sputtering: influence of oxygen partial pressure and nitrogen doping,” Appl. Phys., A Mater. Sci. Process. 116(4), 1905–1913 (2014).
[Crossref]

Karlsson, B.

B. Karlsson, R. P. Shimshock, B. O. Seraphin, and J. C. Haygarth, “Optical properties of CVD-coated TiN, ZrN and HfN,” Sol. Energy Mater. 7(4), 401–411 (1983).
[Crossref]

Kildishev, A. V.

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[Crossref] [PubMed]

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref] [PubMed]

G. V. Naik, J. L. Schroeder, X. Ni, A. V. Kildishev, T. D. Sands, and A. Boltasseva, “Titanium nitride as a plasmonic material for visible and near-infrared wavelengths,” Opt. Mater. Express 2(4), 478–489 (2012).
[Crossref]

Kinsey, N.

D. Shah, H. Reddy, N. Kinsey, V. M. Shalaev, and A. Boltasseva, “Optical properties of plasmonic ultrathin TiN films,” Adv. Opt. Mater. 5(13), 1700065 (2017).
[Crossref]

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[Crossref] [PubMed]

Landmann, M.

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(19), 195503 (2012).
[Crossref] [PubMed]

Li, W.

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[Crossref] [PubMed]

Lintymer, J.

J. Chappé, N. Martin, J. Lintymer, F. Sthal, G. Terwagne, and J. Takadoum, “Titanium oxynitride thin films sputter deposited by the reactive gas pulsing process,” Appl. Surf. Sci. 253(12), 5312–5316 (2007).
[Crossref]

Logothetidis, S.

P. Patsalas and S. Logothetidis, “Optical, electronic, and transport properties of nanocrystalline titanium nitride thin films,” J. Appl. Phys. 90(9), 4725–4734 (2001).
[Crossref]

Lu, M.

S. Shrestha, Y. Wang, A. C. Overvig, M. Lu, A. Stein, L. Dal Negro, and N. Yu, “Indium Tin Oxide Broadband Metasurface Absorber,” ACS Photonics 5(9), 3526–3533 (2018).
[Crossref]

Maier, S. A.

L. Braic, N. Vasilantonakis, A. Mihai, I. J. Villar Garcia, S. Fearn, B. Zou, N. M. Alford, B. Doiron, R. F. Oulton, S. A. Maier, A. V. Zayats, and P. K. Petrov, “Titanium Oxynitride Thin Films with Tunable Double Epsilon-Near-Zero Behavior for Nanophotonic Applications,” ACS Appl. Mater. Interfaces 9(35), 29857–29862 (2017).
[Crossref] [PubMed]

Markert, L. C.

L. Hultman, J. E. Sundgren, L. C. Markert, and J. E. Greene, “Ar and excess N incorporation in epitaxial TiN films grown by reactive bias sputtering in mixed Ar/N2 and pure N2 discharges,” J. Vac. Sci. Technol. A 7(3), 1187–1193 (1989).
[Crossref]

Martin, N.

J. Chappé, N. Martin, J. Lintymer, F. Sthal, G. Terwagne, and J. Takadoum, “Titanium oxynitride thin films sputter deposited by the reactive gas pulsing process,” Appl. Surf. Sci. 253(12), 5312–5316 (2007).
[Crossref]

Mihai, A.

L. Braic, N. Vasilantonakis, A. Mihai, I. J. Villar Garcia, S. Fearn, B. Zou, N. M. Alford, B. Doiron, R. F. Oulton, S. A. Maier, A. V. Zayats, and P. K. Petrov, “Titanium Oxynitride Thin Films with Tunable Double Epsilon-Near-Zero Behavior for Nanophotonic Applications,” ACS Appl. Mater. Interfaces 9(35), 29857–29862 (2017).
[Crossref] [PubMed]

Mosser, A.

S. Zerkout, S. Achour, A. Mosser, and N. Tabet, “On the existence of superstructure in TiNx thin films,” Thin Solid Films 441(1–2), 135–139 (2003).
[Crossref]

Naik, G. V.

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[Crossref] [PubMed]

G. V. Naik, J. L. Schroeder, X. Ni, A. V. Kildishev, T. D. Sands, and A. Boltasseva, “Titanium nitride as a plasmonic material for visible and near-infrared wavelengths,” Opt. Mater. Express 2(4), 478–489 (2012).
[Crossref]

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4(6), 795–808 (2010).
[Crossref]

Natarajan, G.

R. Pandian, G. Natarajan, S. Rajagopalan, M. Kamruddin, and A. K. Tyagi, “On the phase formation of titanium oxide thin films deposited by reactive DC magnetron sputtering: influence of oxygen partial pressure and nitrogen doping,” Appl. Phys., A Mater. Sci. Process. 116(4), 1905–1913 (2014).
[Crossref]

Ni, X.

Odriozola, J. A.

L. Rebouta, C. J. Tavares, R. Aimo, Z. Wang, K. Pischow, E. Alves, T. C. Rojas, and J. A. Odriozola, “Hard nanocomposite Ti–Si–N coatings prepared by DC reactive magnetron sputtering,” Surf. Coat. Tech. 133-134, 234–239 (2000).
[Crossref]

Oulton, R. F.

L. Braic, N. Vasilantonakis, A. Mihai, I. J. Villar Garcia, S. Fearn, B. Zou, N. M. Alford, B. Doiron, R. F. Oulton, S. A. Maier, A. V. Zayats, and P. K. Petrov, “Titanium Oxynitride Thin Films with Tunable Double Epsilon-Near-Zero Behavior for Nanophotonic Applications,” ACS Appl. Mater. Interfaces 9(35), 29857–29862 (2017).
[Crossref] [PubMed]

Overvig, A. C.

S. Shrestha, Y. Wang, A. C. Overvig, M. Lu, A. Stein, L. Dal Negro, and N. Yu, “Indium Tin Oxide Broadband Metasurface Absorber,” ACS Photonics 5(9), 3526–3533 (2018).
[Crossref]

Pandian, R.

R. Pandian, G. Natarajan, S. Rajagopalan, M. Kamruddin, and A. K. Tyagi, “On the phase formation of titanium oxide thin films deposited by reactive DC magnetron sputtering: influence of oxygen partial pressure and nitrogen doping,” Appl. Phys., A Mater. Sci. Process. 116(4), 1905–1913 (2014).
[Crossref]

Patsalas, P.

P. Patsalas and S. Logothetidis, “Optical, electronic, and transport properties of nanocrystalline titanium nitride thin films,” J. Appl. Phys. 90(9), 4725–4734 (2001).
[Crossref]

Petrov, P. K.

L. Braic, N. Vasilantonakis, A. Mihai, I. J. Villar Garcia, S. Fearn, B. Zou, N. M. Alford, B. Doiron, R. F. Oulton, S. A. Maier, A. V. Zayats, and P. K. Petrov, “Titanium Oxynitride Thin Films with Tunable Double Epsilon-Near-Zero Behavior for Nanophotonic Applications,” ACS Appl. Mater. Interfaces 9(35), 29857–29862 (2017).
[Crossref] [PubMed]

Pischow, K.

L. Rebouta, C. J. Tavares, R. Aimo, Z. Wang, K. Pischow, E. Alves, T. C. Rojas, and J. A. Odriozola, “Hard nanocomposite Ti–Si–N coatings prepared by DC reactive magnetron sputtering,” Surf. Coat. Tech. 133-134, 234–239 (2000).
[Crossref]

Rajagopalan, S.

R. Pandian, G. Natarajan, S. Rajagopalan, M. Kamruddin, and A. K. Tyagi, “On the phase formation of titanium oxide thin films deposited by reactive DC magnetron sputtering: influence of oxygen partial pressure and nitrogen doping,” Appl. Phys., A Mater. Sci. Process. 116(4), 1905–1913 (2014).
[Crossref]

Ramos, S.

F. Vaz, L. Rebouta, S. Ramos, M. F. Da Silva, and J. C. Soares, “Physical, structural and mechanical characterization of Ti1-xSixNy films,” Surf. Coat. Tech. 108-109, 236–240 (1998).
[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(19), 195503 (2012).
[Crossref] [PubMed]

Rebouta, L.

L. Rebouta, C. J. Tavares, R. Aimo, Z. Wang, K. Pischow, E. Alves, T. C. Rojas, and J. A. Odriozola, “Hard nanocomposite Ti–Si–N coatings prepared by DC reactive magnetron sputtering,” Surf. Coat. Tech. 133-134, 234–239 (2000).
[Crossref]

F. Vaz, L. Rebouta, S. Ramos, M. F. Da Silva, and J. C. Soares, “Physical, structural and mechanical characterization of Ti1-xSixNy films,” Surf. Coat. Tech. 108-109, 236–240 (1998).
[Crossref]

Reddy, H.

D. Shah, H. Reddy, N. Kinsey, V. M. Shalaev, and A. Boltasseva, “Optical properties of plasmonic ultrathin TiN films,” Adv. Opt. Mater. 5(13), 1700065 (2017).
[Crossref]

Reinhardt, C.

A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Multipole light scattering by nonspherical nanoparticles in the discrete dipole approximation,” Phys. Rev. B Condens. Matter 84(23), 235429 (2011).
[Crossref]

Reiprich, S.

S. Vepřek, S. Reiprich, and L. Shizhi, “Superhard nanocrystalline composite materials: the TiN/Si3N4 system,” Appl. Phys. Lett. 66(20), 2640–2642 (1995).
[Crossref]

Rojas, T. C.

L. Rebouta, C. J. Tavares, R. Aimo, Z. Wang, K. Pischow, E. Alves, T. C. Rojas, and J. A. Odriozola, “Hard nanocomposite Ti–Si–N coatings prepared by DC reactive magnetron sputtering,” Surf. Coat. Tech. 133-134, 234–239 (2000).
[Crossref]

Sands, T. D.

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(19), 195503 (2012).
[Crossref] [PubMed]

Schroeder, J. L.

Schuller, J. A.

N. A. Butakov and J. A. Schuller, “Designing multipolar resonances in dielectric metamaterials,” Sci. Rep. 6(1), 38487 (2016).
[Crossref] [PubMed]

Seraphin, B. O.

B. Karlsson, R. P. Shimshock, B. O. Seraphin, and J. C. Haygarth, “Optical properties of CVD-coated TiN, ZrN and HfN,” Sol. Energy Mater. 7(4), 401–411 (1983).
[Crossref]

Shah, D.

D. Shah, H. Reddy, N. Kinsey, V. M. Shalaev, and A. Boltasseva, “Optical properties of plasmonic ultrathin TiN films,” Adv. Opt. Mater. 5(13), 1700065 (2017).
[Crossref]

Shalaev, V. M.

D. Shah, H. Reddy, N. Kinsey, V. M. Shalaev, and A. Boltasseva, “Optical properties of plasmonic ultrathin TiN films,” Adv. Opt. Mater. 5(13), 1700065 (2017).
[Crossref]

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[Crossref] [PubMed]

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref] [PubMed]

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4(6), 795–808 (2010).
[Crossref]

Shimshock, R. P.

B. Karlsson, R. P. Shimshock, B. O. Seraphin, and J. C. Haygarth, “Optical properties of CVD-coated TiN, ZrN and HfN,” Sol. Energy Mater. 7(4), 401–411 (1983).
[Crossref]

Shizhi, L.

S. Vepřek, S. Reiprich, and L. Shizhi, “Superhard nanocrystalline composite materials: the TiN/Si3N4 system,” Appl. Phys. Lett. 66(20), 2640–2642 (1995).
[Crossref]

Shrestha, S.

S. Shrestha, Y. Wang, A. C. Overvig, M. Lu, A. Stein, L. Dal Negro, and N. Yu, “Indium Tin Oxide Broadband Metasurface Absorber,” ACS Photonics 5(9), 3526–3533 (2018).
[Crossref]

Soares, J. C.

F. Vaz, L. Rebouta, S. Ramos, M. F. Da Silva, and J. C. Soares, “Physical, structural and mechanical characterization of Ti1-xSixNy films,” Surf. Coat. Tech. 108-109, 236–240 (1998).
[Crossref]

Srikant, V.

V. Srikant and D. R. Clarke, “Optical absorption edge of ZnO thin films: the effect of substrate,” J. Appl. Phys. 81(9), 6357–6364 (1997).
[Crossref]

Stein, A.

S. Shrestha, Y. Wang, A. C. Overvig, M. Lu, A. Stein, L. Dal Negro, and N. Yu, “Indium Tin Oxide Broadband Metasurface Absorber,” ACS Photonics 5(9), 3526–3533 (2018).
[Crossref]

Sthal, F.

J. Chappé, N. Martin, J. Lintymer, F. Sthal, G. Terwagne, and J. Takadoum, “Titanium oxynitride thin films sputter deposited by the reactive gas pulsing process,” Appl. Surf. Sci. 253(12), 5312–5316 (2007).
[Crossref]

Sundgren, J. E.

L. Hultman, J. E. Sundgren, L. C. Markert, and J. E. Greene, “Ar and excess N incorporation in epitaxial TiN films grown by reactive bias sputtering in mixed Ar/N2 and pure N2 discharges,” J. Vac. Sci. Technol. A 7(3), 1187–1193 (1989).
[Crossref]

Switendick, A. C.

V. Ern and A. C. Switendick, “Electronic band structure of TiC, TiN, and TiO,” Phys. Rev. 137(6A), A1927–A1936 (1965).
[Crossref]

Tabet, N.

S. Zerkout, S. Achour, A. Mosser, and N. Tabet, “On the existence of superstructure in TiNx thin films,” Thin Solid Films 441(1–2), 135–139 (2003).
[Crossref]

Takadoum, J.

J. Chappé, N. Martin, J. Lintymer, F. Sthal, G. Terwagne, and J. Takadoum, “Titanium oxynitride thin films sputter deposited by the reactive gas pulsing process,” Appl. Surf. Sci. 253(12), 5312–5316 (2007).
[Crossref]

Tavares, C. J.

L. Rebouta, C. J. Tavares, R. Aimo, Z. Wang, K. Pischow, E. Alves, T. C. Rojas, and J. A. Odriozola, “Hard nanocomposite Ti–Si–N coatings prepared by DC reactive magnetron sputtering,” Surf. Coat. Tech. 133-134, 234–239 (2000).
[Crossref]

Terwagne, G.

J. Chappé, N. Martin, J. Lintymer, F. Sthal, G. Terwagne, and J. Takadoum, “Titanium oxynitride thin films sputter deposited by the reactive gas pulsing process,” Appl. Surf. Sci. 253(12), 5312–5316 (2007).
[Crossref]

Tyagi, A. K.

R. Pandian, G. Natarajan, S. Rajagopalan, M. Kamruddin, and A. K. Tyagi, “On the phase formation of titanium oxide thin films deposited by reactive DC magnetron sputtering: influence of oxygen partial pressure and nitrogen doping,” Appl. Phys., A Mater. Sci. Process. 116(4), 1905–1913 (2014).
[Crossref]

Vasilantonakis, N.

L. Braic, N. Vasilantonakis, A. Mihai, I. J. Villar Garcia, S. Fearn, B. Zou, N. M. Alford, B. Doiron, R. F. Oulton, S. A. Maier, A. V. Zayats, and P. K. Petrov, “Titanium Oxynitride Thin Films with Tunable Double Epsilon-Near-Zero Behavior for Nanophotonic Applications,” ACS Appl. Mater. Interfaces 9(35), 29857–29862 (2017).
[Crossref] [PubMed]

Vaz, F.

F. Vaz, L. Rebouta, S. Ramos, M. F. Da Silva, and J. C. Soares, “Physical, structural and mechanical characterization of Ti1-xSixNy films,” Surf. Coat. Tech. 108-109, 236–240 (1998).
[Crossref]

Veprek, S.

S. Vepřek, S. Reiprich, and L. Shizhi, “Superhard nanocrystalline composite materials: the TiN/Si3N4 system,” Appl. Phys. Lett. 66(20), 2640–2642 (1995).
[Crossref]

Villar Garcia, I. J.

L. Braic, N. Vasilantonakis, A. Mihai, I. J. Villar Garcia, S. Fearn, B. Zou, N. M. Alford, B. Doiron, R. F. Oulton, S. A. Maier, A. V. Zayats, and P. K. Petrov, “Titanium Oxynitride Thin Films with Tunable Double Epsilon-Near-Zero Behavior for Nanophotonic Applications,” ACS Appl. Mater. Interfaces 9(35), 29857–29862 (2017).
[Crossref] [PubMed]

Wang, Y.

S. Shrestha, Y. Wang, A. C. Overvig, M. Lu, A. Stein, L. Dal Negro, and N. Yu, “Indium Tin Oxide Broadband Metasurface Absorber,” ACS Photonics 5(9), 3526–3533 (2018).
[Crossref]

Y. Wang, A. Capretti, and L. Dal Negro, “Wide tuning of the optical and structural properties of alternative plasmonic materials,” Opt. Mater. Express 5(11), 2415–2430 (2015).
[Crossref]

Wang, Z.

L. Rebouta, C. J. Tavares, R. Aimo, Z. Wang, K. Pischow, E. Alves, T. C. Rojas, and J. A. Odriozola, “Hard nanocomposite Ti–Si–N coatings prepared by DC reactive magnetron sputtering,” Surf. Coat. Tech. 133-134, 234–239 (2000).
[Crossref]

West, P. R.

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4(6), 795–808 (2010).
[Crossref]

Yu, N.

S. Shrestha, Y. Wang, A. C. Overvig, M. Lu, A. Stein, L. Dal Negro, and N. Yu, “Indium Tin Oxide Broadband Metasurface Absorber,” ACS Photonics 5(9), 3526–3533 (2018).
[Crossref]

Zayats, A. V.

L. Braic, N. Vasilantonakis, A. Mihai, I. J. Villar Garcia, S. Fearn, B. Zou, N. M. Alford, B. Doiron, R. F. Oulton, S. A. Maier, A. V. Zayats, and P. K. Petrov, “Titanium Oxynitride Thin Films with Tunable Double Epsilon-Near-Zero Behavior for Nanophotonic Applications,” ACS Appl. Mater. Interfaces 9(35), 29857–29862 (2017).
[Crossref] [PubMed]

Zerkout, S.

S. Zerkout, S. Achour, A. Mosser, and N. Tabet, “On the existence of superstructure in TiNx thin films,” Thin Solid Films 441(1–2), 135–139 (2003).
[Crossref]

Zgrabik, C. M.

Zou, B.

L. Braic, N. Vasilantonakis, A. Mihai, I. J. Villar Garcia, S. Fearn, B. Zou, N. M. Alford, B. Doiron, R. F. Oulton, S. A. Maier, A. V. Zayats, and P. K. Petrov, “Titanium Oxynitride Thin Films with Tunable Double Epsilon-Near-Zero Behavior for Nanophotonic Applications,” ACS Appl. Mater. Interfaces 9(35), 29857–29862 (2017).
[Crossref] [PubMed]

ACS Appl. Mater. Interfaces (1)

L. Braic, N. Vasilantonakis, A. Mihai, I. J. Villar Garcia, S. Fearn, B. Zou, N. M. Alford, B. Doiron, R. F. Oulton, S. A. Maier, A. V. Zayats, and P. K. Petrov, “Titanium Oxynitride Thin Films with Tunable Double Epsilon-Near-Zero Behavior for Nanophotonic Applications,” ACS Appl. Mater. Interfaces 9(35), 29857–29862 (2017).
[Crossref] [PubMed]

ACS Photonics (1)

S. Shrestha, Y. Wang, A. C. Overvig, M. Lu, A. Stein, L. Dal Negro, and N. Yu, “Indium Tin Oxide Broadband Metasurface Absorber,” ACS Photonics 5(9), 3526–3533 (2018).
[Crossref]

Adv. Mater. (1)

W. Li, U. Guler, N. Kinsey, G. V. Naik, A. Boltasseva, J. Guan, V. M. Shalaev, and A. V. Kildishev, “Refractory plasmonics with titanium nitride: broadband metamaterial absorber,” Adv. Mater. 26(47), 7959–7965 (2014).
[Crossref] [PubMed]

Adv. Opt. Mater. (1)

D. Shah, H. Reddy, N. Kinsey, V. M. Shalaev, and A. Boltasseva, “Optical properties of plasmonic ultrathin TiN films,” Adv. Opt. Mater. 5(13), 1700065 (2017).
[Crossref]

Appl. Phys. Lett. (1)

S. Vepřek, S. Reiprich, and L. Shizhi, “Superhard nanocrystalline composite materials: the TiN/Si3N4 system,” Appl. Phys. Lett. 66(20), 2640–2642 (1995).
[Crossref]

Appl. Phys., A Mater. Sci. Process. (1)

R. Pandian, G. Natarajan, S. Rajagopalan, M. Kamruddin, and A. K. Tyagi, “On the phase formation of titanium oxide thin films deposited by reactive DC magnetron sputtering: influence of oxygen partial pressure and nitrogen doping,” Appl. Phys., A Mater. Sci. Process. 116(4), 1905–1913 (2014).
[Crossref]

Appl. Surf. Sci. (1)

J. Chappé, N. Martin, J. Lintymer, F. Sthal, G. Terwagne, and J. Takadoum, “Titanium oxynitride thin films sputter deposited by the reactive gas pulsing process,” Appl. Surf. Sci. 253(12), 5312–5316 (2007).
[Crossref]

J. Appl. Phys. (2)

P. Patsalas and S. Logothetidis, “Optical, electronic, and transport properties of nanocrystalline titanium nitride thin films,” J. Appl. Phys. 90(9), 4725–4734 (2001).
[Crossref]

V. Srikant and D. R. Clarke, “Optical absorption edge of ZnO thin films: the effect of substrate,” J. Appl. Phys. 81(9), 6357–6364 (1997).
[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(19), 195503 (2012).
[Crossref] [PubMed]

J. Vac. Sci. Technol. A (1)

L. Hultman, J. E. Sundgren, L. C. Markert, and J. E. Greene, “Ar and excess N incorporation in epitaxial TiN films grown by reactive bias sputtering in mixed Ar/N2 and pure N2 discharges,” J. Vac. Sci. Technol. A 7(3), 1187–1193 (1989).
[Crossref]

Laser Photonics Rev. (1)

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4(6), 795–808 (2010).
[Crossref]

Opt. Mater. Express (3)

Phys. Rev. (1)

V. Ern and A. C. Switendick, “Electronic band structure of TiC, TiN, and TiO,” Phys. Rev. 137(6A), A1927–A1936 (1965).
[Crossref]

Phys. Rev. B (1)

P. Johnson and R. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[Crossref]

Phys. Rev. B Condens. Matter (1)

A. B. Evlyukhin, C. Reinhardt, and B. N. Chichkov, “Multipole light scattering by nonspherical nanoparticles in the discrete dipole approximation,” Phys. Rev. B Condens. Matter 84(23), 235429 (2011).
[Crossref]

Sci. Rep. (1)

N. A. Butakov and J. A. Schuller, “Designing multipolar resonances in dielectric metamaterials,” Sci. Rep. 6(1), 38487 (2016).
[Crossref] [PubMed]

Science (1)

A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics with metasurfaces,” Science 339(6125), 1232009 (2013).
[Crossref] [PubMed]

Sol. Energy Mater. (1)

B. Karlsson, R. P. Shimshock, B. O. Seraphin, and J. C. Haygarth, “Optical properties of CVD-coated TiN, ZrN and HfN,” Sol. Energy Mater. 7(4), 401–411 (1983).
[Crossref]

Surf. Coat. Tech. (2)

L. Rebouta, C. J. Tavares, R. Aimo, Z. Wang, K. Pischow, E. Alves, T. C. Rojas, and J. A. Odriozola, “Hard nanocomposite Ti–Si–N coatings prepared by DC reactive magnetron sputtering,” Surf. Coat. Tech. 133-134, 234–239 (2000).
[Crossref]

F. Vaz, L. Rebouta, S. Ramos, M. F. Da Silva, and J. C. Soares, “Physical, structural and mechanical characterization of Ti1-xSixNy films,” Surf. Coat. Tech. 108-109, 236–240 (1998).
[Crossref]

Thin Solid Films (1)

S. Zerkout, S. Achour, A. Mosser, and N. Tabet, “On the existence of superstructure in TiNx thin films,” Thin Solid Films 441(1–2), 135–139 (2003).
[Crossref]

Other (3)

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1997).

C. F. Bohren, and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH Verlag GmbH & Co. KGaA, 2004).

T. Bauer, Thermophotovoltaics: Basic Principles and Critical Aspects Of System Design (Springer Science & Business Media, 2011).

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Figures (13)

Fig. 1
Fig. 1 Real (a) and imaginary (b) permittivity of titanium nitride nanolayers grown by room temperature MSP at high deposition pressures and with and without post-deposition annealing at 900°C.
Fig. 2
Fig. 2 Real (a) and imaginary (b) permittivity of titanium nitride nanolayers grown by MSP at room temperature and at 300°C at high deposition pressures.
Fig. 3
Fig. 3 Real (a) and imaginary (b) permittivity of titanium silicon oxynitride nanolayers grown by a MSP co-deposition with DC Ti and RF SiO2 targets with a DC:RF power ratio at a 300°C deposition temperature and 1.5 mTorr deposition pressure.
Fig. 4
Fig. 4 Real (a) and imaginary (b) permittivity of 4:1 DC:RF titanium silicon oxynitride nanolayers as a function of increasing post-deposition annealing temperature.
Fig. 5
Fig. 5 Real (a) and imaginary (b) permittivity of 4:2 DC:RF titanium silicon oxynitride nanolayers as a function of increasing post-deposition annealing temperature.
Fig. 6
Fig. 6 (a)-(g) Optical reflectance images of nanolayers on Si substrates deposited by DC Ti and RF SiO2 targets with a DC:RF power ratio 4:1 as deposited (a), annealed at 600°C (b), and annealed at 800°C (c), and 4:2 as deposited (d), annealed at 600°C (e), annealed at 800°C (f), and annealed at 1000°C (g). (h)-(n) Reflectance measurements of nanolayers on Si substrates deposited by DC Ti and RF SiO2 targets with a DC:RF power ratio 4:1 as deposited (h), annealed at 600°C (i), and annealed at 800°C (j), and 4:2 as deposited (k), annealed at 600°C (l), annealed at 800°C (m), and annealed at 1000°C (n).
Fig. 7
Fig. 7 Real (a) and imaginary (b) permittivity of tertiary compound titanium silicon nitride nanolayers grown by a MSP co-deposition with DC Ti and RF Si targets with a DC:RF power ratio at a 300°C deposition temperature and 1.5 mTorr deposition pressure.
Fig. 8
Fig. 8 Representative 2θ-θ X-ray diffraction scan showing peaks corresponding to the TiN cubic rock salt structure.
Fig. 9
Fig. 9 Real (a) and imaginary (b) permittivity as a function of frequency in eV of a phenomenological material system with a single Drude and Lorentz contribution to the optical response. Particular arrangement and strength of these two contributions results in a real component to the optical dispersion with two nearby crossings where ��’ = 0.
Fig. 10
Fig. 10 Real component of dielectric function for (a) Au and (b) TiSiON with red dotted line to indicate ε’ = −2, the plasmonic resonance condition in the quasistatic limit of a sphere of each material. Mie theory is used to find the dipole scattering efficiencies of Au and TiSiON in (c) and (d), respectively, when modeled as a sphere of radius r = 80 nm, 100 nm, 120 nm with ε” = 0 in all cases.
Fig. 11
Fig. 11 (a) Real and imaginary permittivity of Au (JC) [23], TiN (Palik) [24], and TiSiON. (b) Calculated skin depth for Au, TiN, and TiSiON using data from (a) and Eq. (3).
Fig. 12
Fig. 12 Mie theory absorption efficiencies of (a) Au (b) TiN and (c) TiSiON when modeled as a sphere of radius r = 40 nm, 80 nm, 100 nm, 120 nm.
Fig. 13
Fig. 13 Mie theory absorption efficiencies of (a) Au (b) TiN and (c) TiSiON when modeled as a sphere of radius r = 40 nm, 80 nm, 100 nm, 120 nm with ε” = 3 in all cases.

Equations (3)

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ε(ω)=ε'(ω)+iε"(ω)= ε ω p 2 ω 2 i Γ D ω + j=1 n A j ω oj 2 ω oj 2 ω 2 +i γ j ω
P abs =(1/2)ωε'' | E | 2 dV
δ λ 2πk

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