Abstract

We calculated the optical constants of the monoclinic phase of a HfO2 film from reflection spectra measured using synchrotron radiation in the spectral region from 143eV to 927eV, which includes the HfN4,5, HfN2,3, and OK absorption edges. The calculations were carried out using the Kramers– Kronig relations. It could be shown that the relation R(E)E4 can be used for extrapolation of the experimental reflection spectrum of HfO2 (and probably of other heavy elements) for energies such that θ/θc>3.7.

© 2010 Optical Society of America

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  1. G. D. Wilk, R. M. Wallace, and J. M. Anthony, “High-K gate dielectrics: current status and materials properties considerations,” J. Appl. Phys. 89, 5243–5275 (2001).
    [CrossRef]
  2. B. H. Lee, L. Kang, R. Nieh, W. J. Qi, and J. C. Lee, “Thermal stability and electrical characteristics of ultrathin hafnium oxide gate dielectric reoxidized with rapid thermal annealing,” Appl. Phys. Lett. 76, 1926–1928 (2000).
    [CrossRef]
  3. A. I. Kingon, J.-P. Maria, and S. K. Streiffer, “Alternative dielectrics to silicon dioxide for memory and logic devices,” Nature 406, 1032–1038 (2000).
    [CrossRef] [PubMed]
  4. V. V. Afanas’ev, A. Stesmans, F. Chen, X. Shi, and S. A. Campbell, “Internal photoemission of electrons and holes from (100)Si into HfO2,” Appl. Phys. Lett. 81, 1053–1055 (2002).
    [CrossRef]
  5. S. Capone, G. Leo, R. Rella, P. Siciliano, L. Vasanelli, M. Alvisi, L. Mirenghi, and A. Rizo, “Physical characterization of hafnium oxide thin films and their application as gas sensing devices,” J. Vac. Sci. Technol. A 16, 3564–3568 (1998).
    [CrossRef]
  6. C. L. Platt, B. Dieny, and A. E. Berkowitz, “Spin-dependent tunneling in HfO2 tunnel junctions,” Appl. Phys. Lett. 69, 2291–2293 (1996).
    [CrossRef]
  7. M. L. Grilli, F. Menchini, A. Piegari, D. Alderighi, G. Toci, and M. Vannini, “Al2O3/SiO2 and HfO2/SiO2 dichroic mirrors for UV solid-state lasers,” Thin Solid Films 517, 1731–1735 (2009).
    [CrossRef]
  8. P. Torchio, A. Gatto, M. Alvisi, G. Albrand, N. Kaiser, and C. Amra, “High-reflectivity HfO2/SiO2 ultraviolet mirrors,” Appl. Opt. 41, 3256–3261 (2002).
    [CrossRef] [PubMed]
  9. B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50–30000 eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
    [CrossRef]
  10. E.D.Palik, ed. Handbook of Optical Constants of Solids(Academic, 1997), Vols.  I, II, and III.
  11. E.D.Palik, ed. Electronic Handbook of Optical Constants of Solids (Academic, 1999).
  12. C. Jaeger, V. B. Il’in, T. Henning, H. Mutschke, D. Fabian, D. A. Semenov, and N. V. Voshchinnikov, “A database of optical constants of cosmic dust analogs,” J. Quant. Spectr. Rad. Trans. 79–80, 765–774 (2003).
    [CrossRef]
  13. E. Filatova, V. Lukyanov, R. Barchewitz, J.-M. Andŕe, M. Idir, and P. Stemmler, “Optical constants of amorphous SiO2 for photons in the range of 60–3000 eV,” J. Phys. Condens. Matter 11, 3355–3370 (1999).
    [CrossRef]
  14. J. S. Toll, “Causality and the dispersion relation: logical foundations,” Phys. Rev. 104, 1760–1770 (1956).
    [CrossRef]
  15. A. V. Vinogradov, N. N. Zorev, I. V. Kozhevnikov, S. I. Sagitov, and A. G. Turyanskii, “X-ray scattering by highly polished surfaces,” Sov. Phys. JETP 67, 1631–1638 (1988).
  16. M. Sheik-Bahae, “Nonlinear optics basics. Kramers–Kronig relations in nonlinear optics,” in Encyclopedia of Modern Optics, R.D.Guenther, ed. (Academic, 2005).
    [CrossRef]
  17. V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer, 2005).
  18. F. W. King, Hilbert Transforms Set (Cambridge U. Press, 2009).
  19. E. O. Filatova, A. A. Sokolov, I. V. Kozhevnikov, E. Yu. Taracheva, O. S. Grunsky, F. Schaefers, and W. Braun, “Investigation of the structure of thin HfO2 films by soft x-ray reflectometry techniques,” J. Phys. Condens. Matter 21, 185012 (2009).
    [CrossRef] [PubMed]
  20. Reflectometer station, see http://www.bessy.de/upload/bitpdfs/reflectometer.pdf.
  21. Optics beamline, see http://www.bessy.de/upload/bitpdfs/D_08_1B2.pdf.
  22. E. O. Filatova, A. I. Stepanov, and V. A. Luk’yanov, “Dispersion of optical constants of amorphous SiO2 in the energy region between 50 and 900 eV,” Opt. Spectrosc. 81, 416–420 (1996).
  23. E. O. Filatova, V. Lukyanov, C. Blessing, and J. Friedrich, “Reflection spectra and optical constants of noncrystalline SiO2 in the soft x-ray region,” J. Electron Spectros. Relat. Phenomena 79, 63–66 (1996).
    [CrossRef]
  24. WebElements: the periodic table on the Web, http://www.webelements.com/.
  25. A. M. James and M. P. Lord, Macmillan’s Chemical and Physical Data (Macmillan, 1992).

2009 (3)

M. L. Grilli, F. Menchini, A. Piegari, D. Alderighi, G. Toci, and M. Vannini, “Al2O3/SiO2 and HfO2/SiO2 dichroic mirrors for UV solid-state lasers,” Thin Solid Films 517, 1731–1735 (2009).
[CrossRef]

F. W. King, Hilbert Transforms Set (Cambridge U. Press, 2009).

E. O. Filatova, A. A. Sokolov, I. V. Kozhevnikov, E. Yu. Taracheva, O. S. Grunsky, F. Schaefers, and W. Braun, “Investigation of the structure of thin HfO2 films by soft x-ray reflectometry techniques,” J. Phys. Condens. Matter 21, 185012 (2009).
[CrossRef] [PubMed]

2005 (2)

M. Sheik-Bahae, “Nonlinear optics basics. Kramers–Kronig relations in nonlinear optics,” in Encyclopedia of Modern Optics, R.D.Guenther, ed. (Academic, 2005).
[CrossRef]

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer, 2005).

2003 (1)

C. Jaeger, V. B. Il’in, T. Henning, H. Mutschke, D. Fabian, D. A. Semenov, and N. V. Voshchinnikov, “A database of optical constants of cosmic dust analogs,” J. Quant. Spectr. Rad. Trans. 79–80, 765–774 (2003).
[CrossRef]

2002 (2)

V. V. Afanas’ev, A. Stesmans, F. Chen, X. Shi, and S. A. Campbell, “Internal photoemission of electrons and holes from (100)Si into HfO2,” Appl. Phys. Lett. 81, 1053–1055 (2002).
[CrossRef]

P. Torchio, A. Gatto, M. Alvisi, G. Albrand, N. Kaiser, and C. Amra, “High-reflectivity HfO2/SiO2 ultraviolet mirrors,” Appl. Opt. 41, 3256–3261 (2002).
[CrossRef] [PubMed]

2001 (1)

G. D. Wilk, R. M. Wallace, and J. M. Anthony, “High-K gate dielectrics: current status and materials properties considerations,” J. Appl. Phys. 89, 5243–5275 (2001).
[CrossRef]

2000 (2)

B. H. Lee, L. Kang, R. Nieh, W. J. Qi, and J. C. Lee, “Thermal stability and electrical characteristics of ultrathin hafnium oxide gate dielectric reoxidized with rapid thermal annealing,” Appl. Phys. Lett. 76, 1926–1928 (2000).
[CrossRef]

A. I. Kingon, J.-P. Maria, and S. K. Streiffer, “Alternative dielectrics to silicon dioxide for memory and logic devices,” Nature 406, 1032–1038 (2000).
[CrossRef] [PubMed]

1999 (2)

E.D.Palik, ed. Electronic Handbook of Optical Constants of Solids (Academic, 1999).

E. Filatova, V. Lukyanov, R. Barchewitz, J.-M. Andŕe, M. Idir, and P. Stemmler, “Optical constants of amorphous SiO2 for photons in the range of 60–3000 eV,” J. Phys. Condens. Matter 11, 3355–3370 (1999).
[CrossRef]

1998 (1)

S. Capone, G. Leo, R. Rella, P. Siciliano, L. Vasanelli, M. Alvisi, L. Mirenghi, and A. Rizo, “Physical characterization of hafnium oxide thin films and their application as gas sensing devices,” J. Vac. Sci. Technol. A 16, 3564–3568 (1998).
[CrossRef]

1997 (1)

E.D.Palik, ed. Handbook of Optical Constants of Solids(Academic, 1997), Vols.  I, II, and III.

1996 (3)

C. L. Platt, B. Dieny, and A. E. Berkowitz, “Spin-dependent tunneling in HfO2 tunnel junctions,” Appl. Phys. Lett. 69, 2291–2293 (1996).
[CrossRef]

E. O. Filatova, A. I. Stepanov, and V. A. Luk’yanov, “Dispersion of optical constants of amorphous SiO2 in the energy region between 50 and 900 eV,” Opt. Spectrosc. 81, 416–420 (1996).

E. O. Filatova, V. Lukyanov, C. Blessing, and J. Friedrich, “Reflection spectra and optical constants of noncrystalline SiO2 in the soft x-ray region,” J. Electron Spectros. Relat. Phenomena 79, 63–66 (1996).
[CrossRef]

1993 (1)

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50–30000 eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[CrossRef]

1992 (1)

A. M. James and M. P. Lord, Macmillan’s Chemical and Physical Data (Macmillan, 1992).

1988 (1)

A. V. Vinogradov, N. N. Zorev, I. V. Kozhevnikov, S. I. Sagitov, and A. G. Turyanskii, “X-ray scattering by highly polished surfaces,” Sov. Phys. JETP 67, 1631–1638 (1988).

1956 (1)

J. S. Toll, “Causality and the dispersion relation: logical foundations,” Phys. Rev. 104, 1760–1770 (1956).
[CrossRef]

Afanas’ev, V. V.

V. V. Afanas’ev, A. Stesmans, F. Chen, X. Shi, and S. A. Campbell, “Internal photoemission of electrons and holes from (100)Si into HfO2,” Appl. Phys. Lett. 81, 1053–1055 (2002).
[CrossRef]

Albrand, G.

Alderighi, D.

M. L. Grilli, F. Menchini, A. Piegari, D. Alderighi, G. Toci, and M. Vannini, “Al2O3/SiO2 and HfO2/SiO2 dichroic mirrors for UV solid-state lasers,” Thin Solid Films 517, 1731–1735 (2009).
[CrossRef]

Alvisi, M.

P. Torchio, A. Gatto, M. Alvisi, G. Albrand, N. Kaiser, and C. Amra, “High-reflectivity HfO2/SiO2 ultraviolet mirrors,” Appl. Opt. 41, 3256–3261 (2002).
[CrossRef] [PubMed]

S. Capone, G. Leo, R. Rella, P. Siciliano, L. Vasanelli, M. Alvisi, L. Mirenghi, and A. Rizo, “Physical characterization of hafnium oxide thin films and their application as gas sensing devices,” J. Vac. Sci. Technol. A 16, 3564–3568 (1998).
[CrossRef]

Amra, C.

Andre, J.-M.

E. Filatova, V. Lukyanov, R. Barchewitz, J.-M. Andŕe, M. Idir, and P. Stemmler, “Optical constants of amorphous SiO2 for photons in the range of 60–3000 eV,” J. Phys. Condens. Matter 11, 3355–3370 (1999).
[CrossRef]

Anthony, J. M.

G. D. Wilk, R. M. Wallace, and J. M. Anthony, “High-K gate dielectrics: current status and materials properties considerations,” J. Appl. Phys. 89, 5243–5275 (2001).
[CrossRef]

Barchewitz, R.

E. Filatova, V. Lukyanov, R. Barchewitz, J.-M. Andŕe, M. Idir, and P. Stemmler, “Optical constants of amorphous SiO2 for photons in the range of 60–3000 eV,” J. Phys. Condens. Matter 11, 3355–3370 (1999).
[CrossRef]

Berkowitz, A. E.

C. L. Platt, B. Dieny, and A. E. Berkowitz, “Spin-dependent tunneling in HfO2 tunnel junctions,” Appl. Phys. Lett. 69, 2291–2293 (1996).
[CrossRef]

Blessing, C.

E. O. Filatova, V. Lukyanov, C. Blessing, and J. Friedrich, “Reflection spectra and optical constants of noncrystalline SiO2 in the soft x-ray region,” J. Electron Spectros. Relat. Phenomena 79, 63–66 (1996).
[CrossRef]

Braun, W.

E. O. Filatova, A. A. Sokolov, I. V. Kozhevnikov, E. Yu. Taracheva, O. S. Grunsky, F. Schaefers, and W. Braun, “Investigation of the structure of thin HfO2 films by soft x-ray reflectometry techniques,” J. Phys. Condens. Matter 21, 185012 (2009).
[CrossRef] [PubMed]

Campbell, S. A.

V. V. Afanas’ev, A. Stesmans, F. Chen, X. Shi, and S. A. Campbell, “Internal photoemission of electrons and holes from (100)Si into HfO2,” Appl. Phys. Lett. 81, 1053–1055 (2002).
[CrossRef]

Capone, S.

S. Capone, G. Leo, R. Rella, P. Siciliano, L. Vasanelli, M. Alvisi, L. Mirenghi, and A. Rizo, “Physical characterization of hafnium oxide thin films and their application as gas sensing devices,” J. Vac. Sci. Technol. A 16, 3564–3568 (1998).
[CrossRef]

Chen, F.

V. V. Afanas’ev, A. Stesmans, F. Chen, X. Shi, and S. A. Campbell, “Internal photoemission of electrons and holes from (100)Si into HfO2,” Appl. Phys. Lett. 81, 1053–1055 (2002).
[CrossRef]

Davis, J. C.

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50–30000 eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[CrossRef]

Dieny, B.

C. L. Platt, B. Dieny, and A. E. Berkowitz, “Spin-dependent tunneling in HfO2 tunnel junctions,” Appl. Phys. Lett. 69, 2291–2293 (1996).
[CrossRef]

Fabian, D.

C. Jaeger, V. B. Il’in, T. Henning, H. Mutschke, D. Fabian, D. A. Semenov, and N. V. Voshchinnikov, “A database of optical constants of cosmic dust analogs,” J. Quant. Spectr. Rad. Trans. 79–80, 765–774 (2003).
[CrossRef]

Filatova, E.

E. Filatova, V. Lukyanov, R. Barchewitz, J.-M. Andŕe, M. Idir, and P. Stemmler, “Optical constants of amorphous SiO2 for photons in the range of 60–3000 eV,” J. Phys. Condens. Matter 11, 3355–3370 (1999).
[CrossRef]

Filatova, E. O.

E. O. Filatova, A. A. Sokolov, I. V. Kozhevnikov, E. Yu. Taracheva, O. S. Grunsky, F. Schaefers, and W. Braun, “Investigation of the structure of thin HfO2 films by soft x-ray reflectometry techniques,” J. Phys. Condens. Matter 21, 185012 (2009).
[CrossRef] [PubMed]

E. O. Filatova, A. I. Stepanov, and V. A. Luk’yanov, “Dispersion of optical constants of amorphous SiO2 in the energy region between 50 and 900 eV,” Opt. Spectrosc. 81, 416–420 (1996).

E. O. Filatova, V. Lukyanov, C. Blessing, and J. Friedrich, “Reflection spectra and optical constants of noncrystalline SiO2 in the soft x-ray region,” J. Electron Spectros. Relat. Phenomena 79, 63–66 (1996).
[CrossRef]

Friedrich, J.

E. O. Filatova, V. Lukyanov, C. Blessing, and J. Friedrich, “Reflection spectra and optical constants of noncrystalline SiO2 in the soft x-ray region,” J. Electron Spectros. Relat. Phenomena 79, 63–66 (1996).
[CrossRef]

Gatto, A.

Grilli, M. L.

M. L. Grilli, F. Menchini, A. Piegari, D. Alderighi, G. Toci, and M. Vannini, “Al2O3/SiO2 and HfO2/SiO2 dichroic mirrors for UV solid-state lasers,” Thin Solid Films 517, 1731–1735 (2009).
[CrossRef]

Grunsky, O. S.

E. O. Filatova, A. A. Sokolov, I. V. Kozhevnikov, E. Yu. Taracheva, O. S. Grunsky, F. Schaefers, and W. Braun, “Investigation of the structure of thin HfO2 films by soft x-ray reflectometry techniques,” J. Phys. Condens. Matter 21, 185012 (2009).
[CrossRef] [PubMed]

Gullikson, E. M.

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50–30000 eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[CrossRef]

Henke, B. L.

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50–30000 eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[CrossRef]

Henning, T.

C. Jaeger, V. B. Il’in, T. Henning, H. Mutschke, D. Fabian, D. A. Semenov, and N. V. Voshchinnikov, “A database of optical constants of cosmic dust analogs,” J. Quant. Spectr. Rad. Trans. 79–80, 765–774 (2003).
[CrossRef]

Idir, M.

E. Filatova, V. Lukyanov, R. Barchewitz, J.-M. Andŕe, M. Idir, and P. Stemmler, “Optical constants of amorphous SiO2 for photons in the range of 60–3000 eV,” J. Phys. Condens. Matter 11, 3355–3370 (1999).
[CrossRef]

Il’in, V. B.

C. Jaeger, V. B. Il’in, T. Henning, H. Mutschke, D. Fabian, D. A. Semenov, and N. V. Voshchinnikov, “A database of optical constants of cosmic dust analogs,” J. Quant. Spectr. Rad. Trans. 79–80, 765–774 (2003).
[CrossRef]

Jaeger, C.

C. Jaeger, V. B. Il’in, T. Henning, H. Mutschke, D. Fabian, D. A. Semenov, and N. V. Voshchinnikov, “A database of optical constants of cosmic dust analogs,” J. Quant. Spectr. Rad. Trans. 79–80, 765–774 (2003).
[CrossRef]

James, A. M.

A. M. James and M. P. Lord, Macmillan’s Chemical and Physical Data (Macmillan, 1992).

Kaiser, N.

Kang, L.

B. H. Lee, L. Kang, R. Nieh, W. J. Qi, and J. C. Lee, “Thermal stability and electrical characteristics of ultrathin hafnium oxide gate dielectric reoxidized with rapid thermal annealing,” Appl. Phys. Lett. 76, 1926–1928 (2000).
[CrossRef]

King, F. W.

F. W. King, Hilbert Transforms Set (Cambridge U. Press, 2009).

Kingon, A. I.

A. I. Kingon, J.-P. Maria, and S. K. Streiffer, “Alternative dielectrics to silicon dioxide for memory and logic devices,” Nature 406, 1032–1038 (2000).
[CrossRef] [PubMed]

Kozhevnikov, I. V.

E. O. Filatova, A. A. Sokolov, I. V. Kozhevnikov, E. Yu. Taracheva, O. S. Grunsky, F. Schaefers, and W. Braun, “Investigation of the structure of thin HfO2 films by soft x-ray reflectometry techniques,” J. Phys. Condens. Matter 21, 185012 (2009).
[CrossRef] [PubMed]

A. V. Vinogradov, N. N. Zorev, I. V. Kozhevnikov, S. I. Sagitov, and A. G. Turyanskii, “X-ray scattering by highly polished surfaces,” Sov. Phys. JETP 67, 1631–1638 (1988).

Lee, B. H.

B. H. Lee, L. Kang, R. Nieh, W. J. Qi, and J. C. Lee, “Thermal stability and electrical characteristics of ultrathin hafnium oxide gate dielectric reoxidized with rapid thermal annealing,” Appl. Phys. Lett. 76, 1926–1928 (2000).
[CrossRef]

Lee, J. C.

B. H. Lee, L. Kang, R. Nieh, W. J. Qi, and J. C. Lee, “Thermal stability and electrical characteristics of ultrathin hafnium oxide gate dielectric reoxidized with rapid thermal annealing,” Appl. Phys. Lett. 76, 1926–1928 (2000).
[CrossRef]

Leo, G.

S. Capone, G. Leo, R. Rella, P. Siciliano, L. Vasanelli, M. Alvisi, L. Mirenghi, and A. Rizo, “Physical characterization of hafnium oxide thin films and their application as gas sensing devices,” J. Vac. Sci. Technol. A 16, 3564–3568 (1998).
[CrossRef]

Lord, M. P.

A. M. James and M. P. Lord, Macmillan’s Chemical and Physical Data (Macmillan, 1992).

Lucarini, V.

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer, 2005).

Luk’yanov, V. A.

E. O. Filatova, A. I. Stepanov, and V. A. Luk’yanov, “Dispersion of optical constants of amorphous SiO2 in the energy region between 50 and 900 eV,” Opt. Spectrosc. 81, 416–420 (1996).

Lukyanov, V.

E. Filatova, V. Lukyanov, R. Barchewitz, J.-M. Andŕe, M. Idir, and P. Stemmler, “Optical constants of amorphous SiO2 for photons in the range of 60–3000 eV,” J. Phys. Condens. Matter 11, 3355–3370 (1999).
[CrossRef]

E. O. Filatova, V. Lukyanov, C. Blessing, and J. Friedrich, “Reflection spectra and optical constants of noncrystalline SiO2 in the soft x-ray region,” J. Electron Spectros. Relat. Phenomena 79, 63–66 (1996).
[CrossRef]

Maria, J.-P.

A. I. Kingon, J.-P. Maria, and S. K. Streiffer, “Alternative dielectrics to silicon dioxide for memory and logic devices,” Nature 406, 1032–1038 (2000).
[CrossRef] [PubMed]

Menchini, F.

M. L. Grilli, F. Menchini, A. Piegari, D. Alderighi, G. Toci, and M. Vannini, “Al2O3/SiO2 and HfO2/SiO2 dichroic mirrors for UV solid-state lasers,” Thin Solid Films 517, 1731–1735 (2009).
[CrossRef]

Mirenghi, L.

S. Capone, G. Leo, R. Rella, P. Siciliano, L. Vasanelli, M. Alvisi, L. Mirenghi, and A. Rizo, “Physical characterization of hafnium oxide thin films and their application as gas sensing devices,” J. Vac. Sci. Technol. A 16, 3564–3568 (1998).
[CrossRef]

Mutschke, H.

C. Jaeger, V. B. Il’in, T. Henning, H. Mutschke, D. Fabian, D. A. Semenov, and N. V. Voshchinnikov, “A database of optical constants of cosmic dust analogs,” J. Quant. Spectr. Rad. Trans. 79–80, 765–774 (2003).
[CrossRef]

Nieh, R.

B. H. Lee, L. Kang, R. Nieh, W. J. Qi, and J. C. Lee, “Thermal stability and electrical characteristics of ultrathin hafnium oxide gate dielectric reoxidized with rapid thermal annealing,” Appl. Phys. Lett. 76, 1926–1928 (2000).
[CrossRef]

Peiponen, K.-E.

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer, 2005).

Piegari, A.

M. L. Grilli, F. Menchini, A. Piegari, D. Alderighi, G. Toci, and M. Vannini, “Al2O3/SiO2 and HfO2/SiO2 dichroic mirrors for UV solid-state lasers,” Thin Solid Films 517, 1731–1735 (2009).
[CrossRef]

Platt, C. L.

C. L. Platt, B. Dieny, and A. E. Berkowitz, “Spin-dependent tunneling in HfO2 tunnel junctions,” Appl. Phys. Lett. 69, 2291–2293 (1996).
[CrossRef]

Qi, W. J.

B. H. Lee, L. Kang, R. Nieh, W. J. Qi, and J. C. Lee, “Thermal stability and electrical characteristics of ultrathin hafnium oxide gate dielectric reoxidized with rapid thermal annealing,” Appl. Phys. Lett. 76, 1926–1928 (2000).
[CrossRef]

Rella, R.

S. Capone, G. Leo, R. Rella, P. Siciliano, L. Vasanelli, M. Alvisi, L. Mirenghi, and A. Rizo, “Physical characterization of hafnium oxide thin films and their application as gas sensing devices,” J. Vac. Sci. Technol. A 16, 3564–3568 (1998).
[CrossRef]

Rizo, A.

S. Capone, G. Leo, R. Rella, P. Siciliano, L. Vasanelli, M. Alvisi, L. Mirenghi, and A. Rizo, “Physical characterization of hafnium oxide thin films and their application as gas sensing devices,” J. Vac. Sci. Technol. A 16, 3564–3568 (1998).
[CrossRef]

Saarinen, J. J.

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer, 2005).

Sagitov, S. I.

A. V. Vinogradov, N. N. Zorev, I. V. Kozhevnikov, S. I. Sagitov, and A. G. Turyanskii, “X-ray scattering by highly polished surfaces,” Sov. Phys. JETP 67, 1631–1638 (1988).

Schaefers, F.

E. O. Filatova, A. A. Sokolov, I. V. Kozhevnikov, E. Yu. Taracheva, O. S. Grunsky, F. Schaefers, and W. Braun, “Investigation of the structure of thin HfO2 films by soft x-ray reflectometry techniques,” J. Phys. Condens. Matter 21, 185012 (2009).
[CrossRef] [PubMed]

Semenov, D. A.

C. Jaeger, V. B. Il’in, T. Henning, H. Mutschke, D. Fabian, D. A. Semenov, and N. V. Voshchinnikov, “A database of optical constants of cosmic dust analogs,” J. Quant. Spectr. Rad. Trans. 79–80, 765–774 (2003).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, “Nonlinear optics basics. Kramers–Kronig relations in nonlinear optics,” in Encyclopedia of Modern Optics, R.D.Guenther, ed. (Academic, 2005).
[CrossRef]

Shi, X.

V. V. Afanas’ev, A. Stesmans, F. Chen, X. Shi, and S. A. Campbell, “Internal photoemission of electrons and holes from (100)Si into HfO2,” Appl. Phys. Lett. 81, 1053–1055 (2002).
[CrossRef]

Siciliano, P.

S. Capone, G. Leo, R. Rella, P. Siciliano, L. Vasanelli, M. Alvisi, L. Mirenghi, and A. Rizo, “Physical characterization of hafnium oxide thin films and their application as gas sensing devices,” J. Vac. Sci. Technol. A 16, 3564–3568 (1998).
[CrossRef]

Sokolov, A. A.

E. O. Filatova, A. A. Sokolov, I. V. Kozhevnikov, E. Yu. Taracheva, O. S. Grunsky, F. Schaefers, and W. Braun, “Investigation of the structure of thin HfO2 films by soft x-ray reflectometry techniques,” J. Phys. Condens. Matter 21, 185012 (2009).
[CrossRef] [PubMed]

Stemmler, P.

E. Filatova, V. Lukyanov, R. Barchewitz, J.-M. Andŕe, M. Idir, and P. Stemmler, “Optical constants of amorphous SiO2 for photons in the range of 60–3000 eV,” J. Phys. Condens. Matter 11, 3355–3370 (1999).
[CrossRef]

Stepanov, A. I.

E. O. Filatova, A. I. Stepanov, and V. A. Luk’yanov, “Dispersion of optical constants of amorphous SiO2 in the energy region between 50 and 900 eV,” Opt. Spectrosc. 81, 416–420 (1996).

Stesmans, A.

V. V. Afanas’ev, A. Stesmans, F. Chen, X. Shi, and S. A. Campbell, “Internal photoemission of electrons and holes from (100)Si into HfO2,” Appl. Phys. Lett. 81, 1053–1055 (2002).
[CrossRef]

Streiffer, S. K.

A. I. Kingon, J.-P. Maria, and S. K. Streiffer, “Alternative dielectrics to silicon dioxide for memory and logic devices,” Nature 406, 1032–1038 (2000).
[CrossRef] [PubMed]

Taracheva, E. Yu.

E. O. Filatova, A. A. Sokolov, I. V. Kozhevnikov, E. Yu. Taracheva, O. S. Grunsky, F. Schaefers, and W. Braun, “Investigation of the structure of thin HfO2 films by soft x-ray reflectometry techniques,” J. Phys. Condens. Matter 21, 185012 (2009).
[CrossRef] [PubMed]

Toci, G.

M. L. Grilli, F. Menchini, A. Piegari, D. Alderighi, G. Toci, and M. Vannini, “Al2O3/SiO2 and HfO2/SiO2 dichroic mirrors for UV solid-state lasers,” Thin Solid Films 517, 1731–1735 (2009).
[CrossRef]

Toll, J. S.

J. S. Toll, “Causality and the dispersion relation: logical foundations,” Phys. Rev. 104, 1760–1770 (1956).
[CrossRef]

Torchio, P.

Turyanskii, A. G.

A. V. Vinogradov, N. N. Zorev, I. V. Kozhevnikov, S. I. Sagitov, and A. G. Turyanskii, “X-ray scattering by highly polished surfaces,” Sov. Phys. JETP 67, 1631–1638 (1988).

Vannini, M.

M. L. Grilli, F. Menchini, A. Piegari, D. Alderighi, G. Toci, and M. Vannini, “Al2O3/SiO2 and HfO2/SiO2 dichroic mirrors for UV solid-state lasers,” Thin Solid Films 517, 1731–1735 (2009).
[CrossRef]

Vartiainen, E. M.

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer, 2005).

Vasanelli, L.

S. Capone, G. Leo, R. Rella, P. Siciliano, L. Vasanelli, M. Alvisi, L. Mirenghi, and A. Rizo, “Physical characterization of hafnium oxide thin films and their application as gas sensing devices,” J. Vac. Sci. Technol. A 16, 3564–3568 (1998).
[CrossRef]

Vinogradov, A. V.

A. V. Vinogradov, N. N. Zorev, I. V. Kozhevnikov, S. I. Sagitov, and A. G. Turyanskii, “X-ray scattering by highly polished surfaces,” Sov. Phys. JETP 67, 1631–1638 (1988).

Voshchinnikov, N. V.

C. Jaeger, V. B. Il’in, T. Henning, H. Mutschke, D. Fabian, D. A. Semenov, and N. V. Voshchinnikov, “A database of optical constants of cosmic dust analogs,” J. Quant. Spectr. Rad. Trans. 79–80, 765–774 (2003).
[CrossRef]

Wallace, R. M.

G. D. Wilk, R. M. Wallace, and J. M. Anthony, “High-K gate dielectrics: current status and materials properties considerations,” J. Appl. Phys. 89, 5243–5275 (2001).
[CrossRef]

Wilk, G. D.

G. D. Wilk, R. M. Wallace, and J. M. Anthony, “High-K gate dielectrics: current status and materials properties considerations,” J. Appl. Phys. 89, 5243–5275 (2001).
[CrossRef]

Zorev, N. N.

A. V. Vinogradov, N. N. Zorev, I. V. Kozhevnikov, S. I. Sagitov, and A. G. Turyanskii, “X-ray scattering by highly polished surfaces,” Sov. Phys. JETP 67, 1631–1638 (1988).

Appl. Opt. (1)

Appl. Phys. Lett. (3)

C. L. Platt, B. Dieny, and A. E. Berkowitz, “Spin-dependent tunneling in HfO2 tunnel junctions,” Appl. Phys. Lett. 69, 2291–2293 (1996).
[CrossRef]

B. H. Lee, L. Kang, R. Nieh, W. J. Qi, and J. C. Lee, “Thermal stability and electrical characteristics of ultrathin hafnium oxide gate dielectric reoxidized with rapid thermal annealing,” Appl. Phys. Lett. 76, 1926–1928 (2000).
[CrossRef]

V. V. Afanas’ev, A. Stesmans, F. Chen, X. Shi, and S. A. Campbell, “Internal photoemission of electrons and holes from (100)Si into HfO2,” Appl. Phys. Lett. 81, 1053–1055 (2002).
[CrossRef]

At. Data Nucl. Data Tables (1)

B. L. Henke, E. M. Gullikson, and J. C. Davis, “X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50–30000 eV, Z=1–92,” At. Data Nucl. Data Tables 54, 181–342 (1993).
[CrossRef]

J. Appl. Phys. (1)

G. D. Wilk, R. M. Wallace, and J. M. Anthony, “High-K gate dielectrics: current status and materials properties considerations,” J. Appl. Phys. 89, 5243–5275 (2001).
[CrossRef]

J. Electron Spectros. Relat. Phenomena (1)

E. O. Filatova, V. Lukyanov, C. Blessing, and J. Friedrich, “Reflection spectra and optical constants of noncrystalline SiO2 in the soft x-ray region,” J. Electron Spectros. Relat. Phenomena 79, 63–66 (1996).
[CrossRef]

J. Phys. Condens. Matter (2)

E. O. Filatova, A. A. Sokolov, I. V. Kozhevnikov, E. Yu. Taracheva, O. S. Grunsky, F. Schaefers, and W. Braun, “Investigation of the structure of thin HfO2 films by soft x-ray reflectometry techniques,” J. Phys. Condens. Matter 21, 185012 (2009).
[CrossRef] [PubMed]

E. Filatova, V. Lukyanov, R. Barchewitz, J.-M. Andŕe, M. Idir, and P. Stemmler, “Optical constants of amorphous SiO2 for photons in the range of 60–3000 eV,” J. Phys. Condens. Matter 11, 3355–3370 (1999).
[CrossRef]

J. Quant. Spectr. Rad. Trans. (1)

C. Jaeger, V. B. Il’in, T. Henning, H. Mutschke, D. Fabian, D. A. Semenov, and N. V. Voshchinnikov, “A database of optical constants of cosmic dust analogs,” J. Quant. Spectr. Rad. Trans. 79–80, 765–774 (2003).
[CrossRef]

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

S. Capone, G. Leo, R. Rella, P. Siciliano, L. Vasanelli, M. Alvisi, L. Mirenghi, and A. Rizo, “Physical characterization of hafnium oxide thin films and their application as gas sensing devices,” J. Vac. Sci. Technol. A 16, 3564–3568 (1998).
[CrossRef]

Nature (1)

A. I. Kingon, J.-P. Maria, and S. K. Streiffer, “Alternative dielectrics to silicon dioxide for memory and logic devices,” Nature 406, 1032–1038 (2000).
[CrossRef] [PubMed]

Opt. Spectrosc. (1)

E. O. Filatova, A. I. Stepanov, and V. A. Luk’yanov, “Dispersion of optical constants of amorphous SiO2 in the energy region between 50 and 900 eV,” Opt. Spectrosc. 81, 416–420 (1996).

Phys. Rev. (1)

J. S. Toll, “Causality and the dispersion relation: logical foundations,” Phys. Rev. 104, 1760–1770 (1956).
[CrossRef]

Sov. Phys. JETP (1)

A. V. Vinogradov, N. N. Zorev, I. V. Kozhevnikov, S. I. Sagitov, and A. G. Turyanskii, “X-ray scattering by highly polished surfaces,” Sov. Phys. JETP 67, 1631–1638 (1988).

Thin Solid Films (1)

M. L. Grilli, F. Menchini, A. Piegari, D. Alderighi, G. Toci, and M. Vannini, “Al2O3/SiO2 and HfO2/SiO2 dichroic mirrors for UV solid-state lasers,” Thin Solid Films 517, 1731–1735 (2009).
[CrossRef]

Other (9)

M. Sheik-Bahae, “Nonlinear optics basics. Kramers–Kronig relations in nonlinear optics,” in Encyclopedia of Modern Optics, R.D.Guenther, ed. (Academic, 2005).
[CrossRef]

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer, 2005).

F. W. King, Hilbert Transforms Set (Cambridge U. Press, 2009).

Reflectometer station, see http://www.bessy.de/upload/bitpdfs/reflectometer.pdf.

Optics beamline, see http://www.bessy.de/upload/bitpdfs/D_08_1B2.pdf.

E.D.Palik, ed. Handbook of Optical Constants of Solids(Academic, 1997), Vols.  I, II, and III.

E.D.Palik, ed. Electronic Handbook of Optical Constants of Solids (Academic, 1999).

WebElements: the periodic table on the Web, http://www.webelements.com/.

A. M. James and M. P. Lord, Macmillan’s Chemical and Physical Data (Macmillan, 1992).

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Figures (3)

Fig. 1
Fig. 1

Reflection spectra measured at the grazing angles 2 ° and 3 ° in the vicinity of (a) the Hf N 2 , 3 and (b) the OK absorption edges.

Fig. 2
Fig. 2

Calculated angular dependence of the reflection coefficient at fixed energies (3220, 4000, 5000, and 6000 eV ). Circles identify the position of the experimental grazing angle.

Fig. 3
Fig. 3

Spectral dependencies of the optical constants (refraction and absorption coefficients) derived from the reflection spectrum measured at 2 ° in the vicinity of (a) the Hf N 2 , 3 and (b) the OK absorption edges.

Tables (2)

Tables Icon

Table 1 Operating Energy Ranges for the Higher Order Filters

Tables Icon

Table 2 Optical Constants for Hf O 2 on Si(100) n-Type Wafer Synthesized by the Atomic Layer Deposition Method, Using Hafnium Tetrachloride ( Hf Cl 4 ) and Water at 300 ° C Substrate Temperature a

Equations (5)

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

r s = sin θ ε cos 2 θ sin θ + ε cos 2 θ ,
r = R exp ( i ψ ) ,
ψ ( E 0 ) = E 0 π P.V. 0 ln R ( E , θ ) E 2 E 0 2 d E ,
R = R F exp [ ( ( 4 π λ ) 3 2 σ 2 a θ ) 2 ] ,
R ( E ) = R ( E 1 ) + [ 1 R ( E 1 ) ] ( 1 E E 1 ) 1 2 ,

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