Abstract

The complex refractive index components, n and k, have been studied for thin films of several common dielectric materials with a low to medium refractive index as functions of wavelength and stoichiometry for mid-infrared (MIR) wavelengths within the range 1.54–14.29 μm (7006500cm1). The materials silicon oxide, silicon nitride, aluminum oxide, aluminum nitride, and titanium oxide are prepared using room temperature reactive sputter deposition and are characterized using MIR variable angle spectroscopic ellipsometry. The investigation shows how sensitive the refractive index functions are to the O2 and N2 flow rates, and for which growth conditions the materials deposit homogeneously. It also allows conclusions to be drawn on the degree of amorphousness and roughness. To facilitate comparison of the materials deposited in this work with others, the index of refraction was also determined and provided for the near-IR and visible ranges of the spectrum. The results presented here should serve as a useful information base for designing optical coatings for the MIR part of the electromagnetic spectrum. The results are parameterized to allow them to be easily used for coating design.

© 2012 Optical Society of America

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References

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  1. F. Tittel, D. Richter, and A. Fried, “Mid-infrared laser applications in spectroscopy,” in Solid-State Mid-Infrared Laser Sources (Springer, 2003), pp. 458–529.
  2. J. D. T. Kruschwitz and W. T. Pawlewicz, “Optical and durability properties of infrared transmitting thin films,” Appl. Opt. 36, 2157–2159 (1997).
    [CrossRef]
  3. K. Marsh and J. Savage, “Infrared optical materials for 8–13 μm—current developments and future prospects,” Infrared Phys. 14, 85–97 (1974).
    [CrossRef]
  4. P. Black and J. Wales, “Materials for use in the fabrication of infrared interference filters,” Infrared Phys. 8, 209–222 (1968).
    [CrossRef]
  5. P. Kelly and R. Arnell, “Magnetron sputtering: A review of recent developments and applications,” Vacuum 56, 159–172 (2000).
    [CrossRef]
  6. S. Berg, T. Larsson, C. Nender, and H.-O. Blom, “Predicting thin-film stoichiometry in reactive sputtering,” J. Appl. Phys. 63, 887–891 (1988).
    [CrossRef]
  7. H. Tompkins and E. Irene, Handbook of Ellipsometry (William Andrew, 2005).
  8. G. Jellison and F. Modine, “Parameterization of the optical functions of amorphous materials in the interband region,” Appl. Phys. Lett. 69, 371–373 (1996).
    [CrossRef]
  9. J. Tauc, R. Grigorovici, and A. Vancu, “Optical properties and electronic structure of amorphous germanium,” Phys. Status Solidi B 15, 627–637 (1966).
    [CrossRef]
  10. H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (Wiley, 2007).
  11. J. Humlíček, “Sensitivity extrema in multiple-angle ellipsometry,” J. Opt. Soc. Am. A 2, 713–722 (1985).
    [CrossRef]
  12. R. P. Howson, “The reactive sputtering of oxides and nitrides,” Pure Appl. Chem. 66, 1311–1318 (1994).
    [CrossRef]
  13. E. Palik and G. Ghosh, Handbook of Optical Constants of Solids (Academic, 1998).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  17. S. Schiller, G. Beister, W. Sieber, G. Schirmer, and E. Hacker, “Influence of deposition parameters on the optical and structural properties of TiO2 films produced by reactive d.c. plasmatron sputtering,” Thin Solid Films 83, 239–245 (1981).
    [CrossRef]
  18. M. Bass, ed., Handbook of Optics (McGraw-Hill, 2001).
  19. K. S. Shamala, L. C. S. Murthy, and K. N. Rao, “Studies on optical and dielectric properties of Al2O3 thin films prepared by electron beam evaporation and spray pyrolysis method,” Mater. Sci. Eng. B 106, 269–274 (2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  22. D. Tyte, “Red (B2Π−A2σ) band system of aluminium monoxide,” Nature 202, 383–384 (1964).
    [CrossRef]
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    [CrossRef]
  24. J. Harper, J. Cuomo, and H. Hentzell, “Synthesis of compound thin films by dual ion beam deposition. I. Experimental approach,” J. Appl. Phys. 58, 550–555 (1985).
    [CrossRef]

2005 (1)

J. M. Khoshman and M. E. Kordesch, “Optical characterization of sputtered amorphous aluminum nitride thin films by spectroscopic ellipsometry,” J. Non-Cryst. Solids 351, 3334–3340 (2005).
[CrossRef]

2004 (1)

K. S. Shamala, L. C. S. Murthy, and K. N. Rao, “Studies on optical and dielectric properties of Al2O3 thin films prepared by electron beam evaporation and spray pyrolysis method,” Mater. Sci. Eng. B 106, 269–274 (2004).
[CrossRef]

2000 (1)

P. Kelly and R. Arnell, “Magnetron sputtering: A review of recent developments and applications,” Vacuum 56, 159–172 (2000).
[CrossRef]

1999 (1)

S. I. Lee, S. G. Rhee, and S. G. Oh, “Spectro-ellipsometric studies of sputtered amorphous titanium dioxide thin films: Simultaneous determination of refractive index, extinction coefficient, and void distribution,” J. Korean Phys. Soc. 34, 319–322 (1999).
[CrossRef]

1997 (1)

1996 (2)

G. Jellison and F. Modine, “Parameterization of the optical functions of amorphous materials in the interband region,” Appl. Phys. Lett. 69, 371–373 (1996).
[CrossRef]

C. Dohmeier, D. Loos, and H. Schnoeckel, “Aluminum (I) and gallium (I) compounds: Syntheses, structures, and reactions,” Angew. Chem. Int. Ed. 35, 129–149 (1996).
[CrossRef]

1995 (1)

1994 (1)

R. P. Howson, “The reactive sputtering of oxides and nitrides,” Pure Appl. Chem. 66, 1311–1318 (1994).
[CrossRef]

1988 (1)

S. Berg, T. Larsson, C. Nender, and H.-O. Blom, “Predicting thin-film stoichiometry in reactive sputtering,” J. Appl. Phys. 63, 887–891 (1988).
[CrossRef]

1985 (2)

J. Humlíček, “Sensitivity extrema in multiple-angle ellipsometry,” J. Opt. Soc. Am. A 2, 713–722 (1985).
[CrossRef]

J. Harper, J. Cuomo, and H. Hentzell, “Synthesis of compound thin films by dual ion beam deposition. I. Experimental approach,” J. Appl. Phys. 58, 550–555 (1985).
[CrossRef]

1982 (1)

1981 (1)

S. Schiller, G. Beister, W. Sieber, G. Schirmer, and E. Hacker, “Influence of deposition parameters on the optical and structural properties of TiO2 films produced by reactive d.c. plasmatron sputtering,” Thin Solid Films 83, 239–245 (1981).
[CrossRef]

1974 (1)

K. Marsh and J. Savage, “Infrared optical materials for 8–13 μm—current developments and future prospects,” Infrared Phys. 14, 85–97 (1974).
[CrossRef]

1968 (1)

P. Black and J. Wales, “Materials for use in the fabrication of infrared interference filters,” Infrared Phys. 8, 209–222 (1968).
[CrossRef]

1966 (1)

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

1965 (1)

1964 (1)

D. Tyte, “Red (B2Π−A2σ) band system of aluminium monoxide,” Nature 202, 383–384 (1964).
[CrossRef]

Arnell, R.

P. Kelly and R. Arnell, “Magnetron sputtering: A review of recent developments and applications,” Vacuum 56, 159–172 (2000).
[CrossRef]

Bååk, T.

Bass, M.

M. Bass, ed., Handbook of Optics (McGraw-Hill, 2001).

Beister, G.

S. Schiller, G. Beister, W. Sieber, G. Schirmer, and E. Hacker, “Influence of deposition parameters on the optical and structural properties of TiO2 films produced by reactive d.c. plasmatron sputtering,” Thin Solid Films 83, 239–245 (1981).
[CrossRef]

Berg, S.

S. Berg, T. Larsson, C. Nender, and H.-O. Blom, “Predicting thin-film stoichiometry in reactive sputtering,” J. Appl. Phys. 63, 887–891 (1988).
[CrossRef]

Black, P.

P. Black and J. Wales, “Materials for use in the fabrication of infrared interference filters,” Infrared Phys. 8, 209–222 (1968).
[CrossRef]

Blom, H.-O.

S. Berg, T. Larsson, C. Nender, and H.-O. Blom, “Predicting thin-film stoichiometry in reactive sputtering,” J. Appl. Phys. 63, 887–891 (1988).
[CrossRef]

Cuomo, J.

J. Harper, J. Cuomo, and H. Hentzell, “Synthesis of compound thin films by dual ion beam deposition. I. Experimental approach,” J. Appl. Phys. 58, 550–555 (1985).
[CrossRef]

Dohmeier, C.

C. Dohmeier, D. Loos, and H. Schnoeckel, “Aluminum (I) and gallium (I) compounds: Syntheses, structures, and reactions,” Angew. Chem. Int. Ed. 35, 129–149 (1996).
[CrossRef]

Fried, A.

F. Tittel, D. Richter, and A. Fried, “Mid-infrared laser applications in spectroscopy,” in Solid-State Mid-Infrared Laser Sources (Springer, 2003), pp. 458–529.

Fujiwara, H.

H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (Wiley, 2007).

Ghosh, G.

E. Palik and G. Ghosh, Handbook of Optical Constants of Solids (Academic, 1998).

Grigorovici, R.

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

Hacker, E.

S. Schiller, G. Beister, W. Sieber, G. Schirmer, and E. Hacker, “Influence of deposition parameters on the optical and structural properties of TiO2 films produced by reactive d.c. plasmatron sputtering,” Thin Solid Films 83, 239–245 (1981).
[CrossRef]

Harper, J.

J. Harper, J. Cuomo, and H. Hentzell, “Synthesis of compound thin films by dual ion beam deposition. I. Experimental approach,” J. Appl. Phys. 58, 550–555 (1985).
[CrossRef]

Hentzell, H.

J. Harper, J. Cuomo, and H. Hentzell, “Synthesis of compound thin films by dual ion beam deposition. I. Experimental approach,” J. Appl. Phys. 58, 550–555 (1985).
[CrossRef]

Howson, R. P.

R. P. Howson, “The reactive sputtering of oxides and nitrides,” Pure Appl. Chem. 66, 1311–1318 (1994).
[CrossRef]

Humlícek, J.

Irene, E.

H. Tompkins and E. Irene, Handbook of Ellipsometry (William Andrew, 2005).

Jellison, G.

G. Jellison and F. Modine, “Parameterization of the optical functions of amorphous materials in the interband region,” Appl. Phys. Lett. 69, 371–373 (1996).
[CrossRef]

Kelly, P.

P. Kelly and R. Arnell, “Magnetron sputtering: A review of recent developments and applications,” Vacuum 56, 159–172 (2000).
[CrossRef]

Khoshman, J. M.

J. M. Khoshman and M. E. Kordesch, “Optical characterization of sputtered amorphous aluminum nitride thin films by spectroscopic ellipsometry,” J. Non-Cryst. Solids 351, 3334–3340 (2005).
[CrossRef]

Kordesch, M. E.

J. M. Khoshman and M. E. Kordesch, “Optical characterization of sputtered amorphous aluminum nitride thin films by spectroscopic ellipsometry,” J. Non-Cryst. Solids 351, 3334–3340 (2005).
[CrossRef]

Kruschwitz, J. D. T.

Larsson, T.

S. Berg, T. Larsson, C. Nender, and H.-O. Blom, “Predicting thin-film stoichiometry in reactive sputtering,” J. Appl. Phys. 63, 887–891 (1988).
[CrossRef]

Lee, S. I.

S. I. Lee, S. G. Rhee, and S. G. Oh, “Spectro-ellipsometric studies of sputtered amorphous titanium dioxide thin films: Simultaneous determination of refractive index, extinction coefficient, and void distribution,” J. Korean Phys. Soc. 34, 319–322 (1999).
[CrossRef]

Loos, D.

C. Dohmeier, D. Loos, and H. Schnoeckel, “Aluminum (I) and gallium (I) compounds: Syntheses, structures, and reactions,” Angew. Chem. Int. Ed. 35, 129–149 (1996).
[CrossRef]

Malitson, I.

Marsh, K.

K. Marsh and J. Savage, “Infrared optical materials for 8–13 μm—current developments and future prospects,” Infrared Phys. 14, 85–97 (1974).
[CrossRef]

Modine, F.

G. Jellison and F. Modine, “Parameterization of the optical functions of amorphous materials in the interband region,” Appl. Phys. Lett. 69, 371–373 (1996).
[CrossRef]

Murthy, L. C. S.

K. S. Shamala, L. C. S. Murthy, and K. N. Rao, “Studies on optical and dielectric properties of Al2O3 thin films prepared by electron beam evaporation and spray pyrolysis method,” Mater. Sci. Eng. B 106, 269–274 (2004).
[CrossRef]

Nender, C.

S. Berg, T. Larsson, C. Nender, and H.-O. Blom, “Predicting thin-film stoichiometry in reactive sputtering,” J. Appl. Phys. 63, 887–891 (1988).
[CrossRef]

Oh, S. G.

S. I. Lee, S. G. Rhee, and S. G. Oh, “Spectro-ellipsometric studies of sputtered amorphous titanium dioxide thin films: Simultaneous determination of refractive index, extinction coefficient, and void distribution,” J. Korean Phys. Soc. 34, 319–322 (1999).
[CrossRef]

Palik, E.

E. Palik and G. Ghosh, Handbook of Optical Constants of Solids (Academic, 1998).

Pawlewicz, W. T.

Rakic, A. D.

Rao, K. N.

K. S. Shamala, L. C. S. Murthy, and K. N. Rao, “Studies on optical and dielectric properties of Al2O3 thin films prepared by electron beam evaporation and spray pyrolysis method,” Mater. Sci. Eng. B 106, 269–274 (2004).
[CrossRef]

Rhee, S. G.

S. I. Lee, S. G. Rhee, and S. G. Oh, “Spectro-ellipsometric studies of sputtered amorphous titanium dioxide thin films: Simultaneous determination of refractive index, extinction coefficient, and void distribution,” J. Korean Phys. Soc. 34, 319–322 (1999).
[CrossRef]

Richter, D.

F. Tittel, D. Richter, and A. Fried, “Mid-infrared laser applications in spectroscopy,” in Solid-State Mid-Infrared Laser Sources (Springer, 2003), pp. 458–529.

Savage, J.

K. Marsh and J. Savage, “Infrared optical materials for 8–13 μm—current developments and future prospects,” Infrared Phys. 14, 85–97 (1974).
[CrossRef]

Schiller, S.

S. Schiller, G. Beister, W. Sieber, G. Schirmer, and E. Hacker, “Influence of deposition parameters on the optical and structural properties of TiO2 films produced by reactive d.c. plasmatron sputtering,” Thin Solid Films 83, 239–245 (1981).
[CrossRef]

Schirmer, G.

S. Schiller, G. Beister, W. Sieber, G. Schirmer, and E. Hacker, “Influence of deposition parameters on the optical and structural properties of TiO2 films produced by reactive d.c. plasmatron sputtering,” Thin Solid Films 83, 239–245 (1981).
[CrossRef]

Schnoeckel, H.

C. Dohmeier, D. Loos, and H. Schnoeckel, “Aluminum (I) and gallium (I) compounds: Syntheses, structures, and reactions,” Angew. Chem. Int. Ed. 35, 129–149 (1996).
[CrossRef]

Shamala, K. S.

K. S. Shamala, L. C. S. Murthy, and K. N. Rao, “Studies on optical and dielectric properties of Al2O3 thin films prepared by electron beam evaporation and spray pyrolysis method,” Mater. Sci. Eng. B 106, 269–274 (2004).
[CrossRef]

Sieber, W.

S. Schiller, G. Beister, W. Sieber, G. Schirmer, and E. Hacker, “Influence of deposition parameters on the optical and structural properties of TiO2 films produced by reactive d.c. plasmatron sputtering,” Thin Solid Films 83, 239–245 (1981).
[CrossRef]

Tauc, J.

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

Tittel, F.

F. Tittel, D. Richter, and A. Fried, “Mid-infrared laser applications in spectroscopy,” in Solid-State Mid-Infrared Laser Sources (Springer, 2003), pp. 458–529.

Tompkins, H.

H. Tompkins and E. Irene, Handbook of Ellipsometry (William Andrew, 2005).

Tyte, D.

D. Tyte, “Red (B2Π−A2σ) band system of aluminium monoxide,” Nature 202, 383–384 (1964).
[CrossRef]

Vancu, A.

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

Wales, J.

P. Black and J. Wales, “Materials for use in the fabrication of infrared interference filters,” Infrared Phys. 8, 209–222 (1968).
[CrossRef]

Angew. Chem. Int. Ed. (1)

C. Dohmeier, D. Loos, and H. Schnoeckel, “Aluminum (I) and gallium (I) compounds: Syntheses, structures, and reactions,” Angew. Chem. Int. Ed. 35, 129–149 (1996).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

G. Jellison and F. Modine, “Parameterization of the optical functions of amorphous materials in the interband region,” Appl. Phys. Lett. 69, 371–373 (1996).
[CrossRef]

Infrared Phys. (2)

K. Marsh and J. Savage, “Infrared optical materials for 8–13 μm—current developments and future prospects,” Infrared Phys. 14, 85–97 (1974).
[CrossRef]

P. Black and J. Wales, “Materials for use in the fabrication of infrared interference filters,” Infrared Phys. 8, 209–222 (1968).
[CrossRef]

J. Appl. Phys. (2)

S. Berg, T. Larsson, C. Nender, and H.-O. Blom, “Predicting thin-film stoichiometry in reactive sputtering,” J. Appl. Phys. 63, 887–891 (1988).
[CrossRef]

J. Harper, J. Cuomo, and H. Hentzell, “Synthesis of compound thin films by dual ion beam deposition. I. Experimental approach,” J. Appl. Phys. 58, 550–555 (1985).
[CrossRef]

J. Korean Phys. Soc. (1)

S. I. Lee, S. G. Rhee, and S. G. Oh, “Spectro-ellipsometric studies of sputtered amorphous titanium dioxide thin films: Simultaneous determination of refractive index, extinction coefficient, and void distribution,” J. Korean Phys. Soc. 34, 319–322 (1999).
[CrossRef]

J. Non-Cryst. Solids (1)

J. M. Khoshman and M. E. Kordesch, “Optical characterization of sputtered amorphous aluminum nitride thin films by spectroscopic ellipsometry,” J. Non-Cryst. Solids 351, 3334–3340 (2005).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Mater. Sci. Eng. B (1)

K. S. Shamala, L. C. S. Murthy, and K. N. Rao, “Studies on optical and dielectric properties of Al2O3 thin films prepared by electron beam evaporation and spray pyrolysis method,” Mater. Sci. Eng. B 106, 269–274 (2004).
[CrossRef]

Nature (1)

D. Tyte, “Red (B2Π−A2σ) band system of aluminium monoxide,” Nature 202, 383–384 (1964).
[CrossRef]

Phys. Status Solidi B (1)

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

Pure Appl. Chem. (1)

R. P. Howson, “The reactive sputtering of oxides and nitrides,” Pure Appl. Chem. 66, 1311–1318 (1994).
[CrossRef]

Thin Solid Films (1)

S. Schiller, G. Beister, W. Sieber, G. Schirmer, and E. Hacker, “Influence of deposition parameters on the optical and structural properties of TiO2 films produced by reactive d.c. plasmatron sputtering,” Thin Solid Films 83, 239–245 (1981).
[CrossRef]

Vacuum (1)

P. Kelly and R. Arnell, “Magnetron sputtering: A review of recent developments and applications,” Vacuum 56, 159–172 (2000).
[CrossRef]

Other (5)

H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (Wiley, 2007).

H. Tompkins and E. Irene, Handbook of Ellipsometry (William Andrew, 2005).

M. Bass, ed., Handbook of Optics (McGraw-Hill, 2001).

E. Palik and G. Ghosh, Handbook of Optical Constants of Solids (Academic, 1998).

F. Tittel, D. Richter, and A. Fried, “Mid-infrared laser applications in spectroscopy,” in Solid-State Mid-Infrared Laser Sources (Springer, 2003), pp. 458–529.

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Figures (15)

Fig. 1.
Fig. 1.

Real (black curves) and imaginary (gray curves) parts of the refractive index for SiO2 in the further IR part of the MIR spectrum at different reactive gas flow rates.

Fig. 2.
Fig. 2.

Real refractive index for SiO2 in the nearer IR part of the MIR spectrum at different reactive gas flow rates.

Fig. 3.
Fig. 3.

Real refractive index for SiO2 in the visible spectrum at different reactive gas flow rates.

Fig. 4.
Fig. 4.

Real (black curves) and imaginary (gray curves) parts of the refractive index for SiNx in the further IR part of the MIR spectrum at different reactive gas flow rates.

Fig. 5.
Fig. 5.

Real refractive index for SiNx in the nearer IR part of the MIR spectrum at different reactive gas flow rates.

Fig. 6.
Fig. 6.

Real (black curves) and imaginary (gray curves) parts of the refractive index for SiNx in the visible spectrum at different reactive gas flow rates. Note the different scales for n and k.

Fig. 7.
Fig. 7.

Real (black curves) and imaginary (gray curves) parts of the refractive index for TiO2 in the further IR part of the MIR spectrum at different reactive gas flow rates and targets.

Fig. 8.
Fig. 8.

Real refractive index for TiO2 in the nearer IR part of the MIR spectrum at different reactive gas flow rates and targets.

Fig. 9.
Fig. 9.

Real (black curves) and imaginary (gray curves) parts of the refractive index for TiO2 in the visible part of the spectrum for different reactive gas flow rates and targets. Note the different scales for n and k.

Fig. 10.
Fig. 10.

Real (black curves) and imaginary (gray curves) parts of the refractive index for aluminum oxide in the further IR part of the MIR spectrum at different reactive gas flow rates.

Fig. 11.
Fig. 11.

Real refractive index for aluminum oxide in the nearer IR part of the MIR spectrum at different reactive gas flow rates.

Fig. 12.
Fig. 12.

Real refractive index for aluminum oxide in the visible part of the spectrum for different reactive gas flow rates.

Fig. 13.
Fig. 13.

Real (black curves) and imaginary (gray curves) parts of the refractive index for aluminum nitride in the further IR part of the MIR spectrum at different reactive gas flow rates.

Fig. 14.
Fig. 14.

Real (black curves) and imaginary (gray curves) parts of the refractive index for aluminum nitride in the nearer IR part of the MIR spectrum at different reactive gas flow rates.

Fig. 15.
Fig. 15.

Real (black curves) and imaginary (gray curves) parts of the refractive index for aluminum nitride in the visible part of the spectrum for different reactive gas flow rates.

Tables (6)

Tables Icon

Table 1. Resultant Partial Pressures of O2 and N2 in Sputter Chamber for Given Influx While Vacuum Pumps Are Running

Tables Icon

Table 2. Brendel Oscillator Parameters for Silicon Dioxide with the Resulting MSE (ν0j, ντj, νpj, σj are in cm1)

Tables Icon

Table 3. Brendel Oscillator Parameters for Silicon Nitride with the Resulting MSE (ν0j, ντj, νpj, σj are in cm1)

Tables Icon

Table 4. Brendel Oscillator Parameters for Titanium Dioxide with the Resulting MSE (ν0j, ντj, νpj, σj are given in cm1)

Tables Icon

Table 5. Brendel Oscillator Parameters for Aluminum Oxide with the Resulting MSE (ν0j, ντj, νpj, σj are in cm1)

Tables Icon

Table 6. Brendel Oscillator Parameters for Aluminum Nitride with the Resulting MSE (ν0j, ντj, νpj, σj are given in cm1)

Equations (3)

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

ϵDL(ν)=ϵ+j=1mXj(ν),
Xj(ν)=νpj2ν0j2ν2iντjν
Xj(ν)=12πσjexp((xν0j)22σj2)νpj2x2ν2iντjνdx,

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