Abstract

A modification of the Lorentz oscillator model for optical constants is proposed in an effort to achieve better agreement with experimental data while keeping the calculation simple. Improvement in agreement between theoretical and experimental data obtained with a variable line shape (frequency-dependent damping constant) over a wide spectral range is demonstrated through modeling the index of refraction of Si3N4 (1–24 eV), SiO (0.15–25 eV) and amorphous and crystalline SiO2 (0.15–25 eV). Model parameters are estimated by acceptance-probability-controlled simulated annealing. Excellent agreement between the modified model and the experimental data is obtained for both real and imaginary parts of the index of refraction.

© 1998 Optical Society of America

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  1. A. D. Rakić, “Algorithm for the determination of intrinsic optical constants of metal films: application to aluminum,” Appl. Opt. 34, 4755–4767 (1995).
    [CrossRef] [PubMed]
  2. C. J. Powell, “Analysis of optical- and inelastic-electron-scattering data. II. Application to Al,” J. Opt. Soc. Am. 60, 78–93 (1970).
    [CrossRef]
  3. M. Erman, J. B. Theeten, P. Chambon, S. M. Kelso, D. E. Aspnes, “Optical properties and damage analysis of GaAs single crystals partly amorphized by ion implantation,” J. Appl. Phys. 56, 2664–2671 (1984).
    [CrossRef]
  4. F. L. Terry, “A modified harmonic oscillator approximation scheme for the dielectric constants of AlxGa1-xAs,” J. Appl. Phys. 70, 409–417 (1991).
    [CrossRef]
  5. G. N. Maracas, C. H. Kuo, S. Anand, R. Droopad, “Temperature-dependent pseudodielectric functions of GaAs determined by spectroscopic ellipsometry,” J. Appl. Phys. 77, 1701–1704 (1995).
    [CrossRef]
  6. C. M. Herzinger, H. Yao, P. G. Snyder, F. G. Celii, Y.-C. Kao, B. Johs, J. A. Woollam, “Determination of AlAs optical constants by variable angle spectroscopic ellipsometry,” J. Appl. Phys. 77, 4677–4687 (1995).
    [CrossRef]
  7. M. Schubert, V. Gottschak, C. M. Herzinger, H. Yao, P. G. Snyder, J. A. Woollam, “Optical constants of GaxIn1-xP lattice matched to GaAs,” J. Appl. Phys. 77, 3416–3419 (1995).
    [CrossRef]
  8. C. M. Herzinger, P. G. Snyder, F. G. Celii, Y.-C. Kao, D. Chow, B. Johs, J. A. Woollam, “Studies of thin strained InAs, AlAs, and AlSb layers by spectroscopic ellipsometry,” J. Appl. Phys. 79, 2663–2674 (1996).
    [CrossRef]
  9. S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
    [CrossRef] [PubMed]
  10. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1989).
  11. A. D. Rakić, J. M. Elazar, A. B. Djurišić.“Acceptance-probability-controlled simulated annealing: a method for modeling the optical constants of solids,” Phys. Rev. E 52, 6862–6867 (1995).
    [CrossRef]
  12. A. B. Djurišić, A. D. Rakić, J. M. Elazar, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with an adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
    [CrossRef]
  13. A. B. Djurišić, J. M. Elazar, A. D. Rakić, “Modeling the optical constants of solids using genetic algorithms with parameter space size adjustment,” Opt. Commun. 134, 407–414.
  14. O. Stenzel, R. Petrich, W. Scharff, A. Tikhonravov, V. Hopfe, “A hybrid method for determination of optical thin film constants,” Thin Solid Films 207, 324–329 (1992).
    [CrossRef]
  15. A. Franke, A. Stendal, O. Stenzel, C. von Borczyskowski, “Gaussian quadrature approach to the calculation of the optical constants in the vicinity of inhomogenously broadened absorption lines,” Pure Appl. Opt. 5, 845–853 (1996).
    [CrossRef]
  16. C. C. Kim, J. W. Garland, H. Abad, P. M. Raccah, “Modeling the optical dielectric function of semiconductors: extension of critical-point parabolic-band approximation,” Phys. Rev. B 45, 11749–11767 (1992).
    [CrossRef]
  17. A. D. Rakić, M. L. Majewski, “Modeling the optical dielectric function of GaAs and AlAs: extension of Adachi’s model,” J. Appl. Phys. 80, 5509–5915 (1996).
  18. S. Ozaki, S. Adachi, “Spectroscopic ellipsometry and thermoreflectance of GaAs,” J. Appl. Phys. 78, 3380–3386 (1995).
    [CrossRef]
  19. A. K. Harman, S. Ninomiya, S. Adachi, “Optical constants of sapphire (α-Al2O3) single crystals,” J. Appl. Phys. 76, 8032–8036 (1994).
    [CrossRef]
  20. H. R. Philipp, “Silicon nitride (Si3N4) (noncrystalline),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 771–774.
  21. J. B. Theeten, D. E. Aspnes, F. Simondet, M. Erman, P. C. Mürau, “Nondestructive analysis of Si3N4/SiO2/Si structures using spectroscopic ellipsometry,” J. Appl. Phys. 52, 6788–6797 (1981).
    [CrossRef]
  22. H. R. Philipp, “Silicon monoxide (SiO) (noncrystalline),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 765–770.
  23. H. R. Philipp, “Silicon dioxide (SiO2) (glass),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 749–764.
  24. H. R. Philipp, “Silicon dioxide (SiO2) type α (crystalline),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 719–748.

1997 (1)

A. B. Djurišić, A. D. Rakić, J. M. Elazar, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with an adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
[CrossRef]

1996 (3)

C. M. Herzinger, P. G. Snyder, F. G. Celii, Y.-C. Kao, D. Chow, B. Johs, J. A. Woollam, “Studies of thin strained InAs, AlAs, and AlSb layers by spectroscopic ellipsometry,” J. Appl. Phys. 79, 2663–2674 (1996).
[CrossRef]

A. D. Rakić, M. L. Majewski, “Modeling the optical dielectric function of GaAs and AlAs: extension of Adachi’s model,” J. Appl. Phys. 80, 5509–5915 (1996).

A. Franke, A. Stendal, O. Stenzel, C. von Borczyskowski, “Gaussian quadrature approach to the calculation of the optical constants in the vicinity of inhomogenously broadened absorption lines,” Pure Appl. Opt. 5, 845–853 (1996).
[CrossRef]

1995 (6)

A. D. Rakić, “Algorithm for the determination of intrinsic optical constants of metal films: application to aluminum,” Appl. Opt. 34, 4755–4767 (1995).
[CrossRef] [PubMed]

S. Ozaki, S. Adachi, “Spectroscopic ellipsometry and thermoreflectance of GaAs,” J. Appl. Phys. 78, 3380–3386 (1995).
[CrossRef]

G. N. Maracas, C. H. Kuo, S. Anand, R. Droopad, “Temperature-dependent pseudodielectric functions of GaAs determined by spectroscopic ellipsometry,” J. Appl. Phys. 77, 1701–1704 (1995).
[CrossRef]

C. M. Herzinger, H. Yao, P. G. Snyder, F. G. Celii, Y.-C. Kao, B. Johs, J. A. Woollam, “Determination of AlAs optical constants by variable angle spectroscopic ellipsometry,” J. Appl. Phys. 77, 4677–4687 (1995).
[CrossRef]

M. Schubert, V. Gottschak, C. M. Herzinger, H. Yao, P. G. Snyder, J. A. Woollam, “Optical constants of GaxIn1-xP lattice matched to GaAs,” J. Appl. Phys. 77, 3416–3419 (1995).
[CrossRef]

A. D. Rakić, J. M. Elazar, A. B. Djurišić.“Acceptance-probability-controlled simulated annealing: a method for modeling the optical constants of solids,” Phys. Rev. E 52, 6862–6867 (1995).
[CrossRef]

1994 (1)

A. K. Harman, S. Ninomiya, S. Adachi, “Optical constants of sapphire (α-Al2O3) single crystals,” J. Appl. Phys. 76, 8032–8036 (1994).
[CrossRef]

1992 (2)

C. C. Kim, J. W. Garland, H. Abad, P. M. Raccah, “Modeling the optical dielectric function of semiconductors: extension of critical-point parabolic-band approximation,” Phys. Rev. B 45, 11749–11767 (1992).
[CrossRef]

O. Stenzel, R. Petrich, W. Scharff, A. Tikhonravov, V. Hopfe, “A hybrid method for determination of optical thin film constants,” Thin Solid Films 207, 324–329 (1992).
[CrossRef]

1991 (1)

F. L. Terry, “A modified harmonic oscillator approximation scheme for the dielectric constants of AlxGa1-xAs,” J. Appl. Phys. 70, 409–417 (1991).
[CrossRef]

1984 (1)

M. Erman, J. B. Theeten, P. Chambon, S. M. Kelso, D. E. Aspnes, “Optical properties and damage analysis of GaAs single crystals partly amorphized by ion implantation,” J. Appl. Phys. 56, 2664–2671 (1984).
[CrossRef]

1983 (1)

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

1981 (1)

J. B. Theeten, D. E. Aspnes, F. Simondet, M. Erman, P. C. Mürau, “Nondestructive analysis of Si3N4/SiO2/Si structures using spectroscopic ellipsometry,” J. Appl. Phys. 52, 6788–6797 (1981).
[CrossRef]

1970 (1)

Abad, H.

C. C. Kim, J. W. Garland, H. Abad, P. M. Raccah, “Modeling the optical dielectric function of semiconductors: extension of critical-point parabolic-band approximation,” Phys. Rev. B 45, 11749–11767 (1992).
[CrossRef]

Adachi, S.

S. Ozaki, S. Adachi, “Spectroscopic ellipsometry and thermoreflectance of GaAs,” J. Appl. Phys. 78, 3380–3386 (1995).
[CrossRef]

A. K. Harman, S. Ninomiya, S. Adachi, “Optical constants of sapphire (α-Al2O3) single crystals,” J. Appl. Phys. 76, 8032–8036 (1994).
[CrossRef]

Anand, S.

G. N. Maracas, C. H. Kuo, S. Anand, R. Droopad, “Temperature-dependent pseudodielectric functions of GaAs determined by spectroscopic ellipsometry,” J. Appl. Phys. 77, 1701–1704 (1995).
[CrossRef]

Aspnes, D. E.

M. Erman, J. B. Theeten, P. Chambon, S. M. Kelso, D. E. Aspnes, “Optical properties and damage analysis of GaAs single crystals partly amorphized by ion implantation,” J. Appl. Phys. 56, 2664–2671 (1984).
[CrossRef]

J. B. Theeten, D. E. Aspnes, F. Simondet, M. Erman, P. C. Mürau, “Nondestructive analysis of Si3N4/SiO2/Si structures using spectroscopic ellipsometry,” J. Appl. Phys. 52, 6788–6797 (1981).
[CrossRef]

Celii, F. G.

C. M. Herzinger, P. G. Snyder, F. G. Celii, Y.-C. Kao, D. Chow, B. Johs, J. A. Woollam, “Studies of thin strained InAs, AlAs, and AlSb layers by spectroscopic ellipsometry,” J. Appl. Phys. 79, 2663–2674 (1996).
[CrossRef]

C. M. Herzinger, H. Yao, P. G. Snyder, F. G. Celii, Y.-C. Kao, B. Johs, J. A. Woollam, “Determination of AlAs optical constants by variable angle spectroscopic ellipsometry,” J. Appl. Phys. 77, 4677–4687 (1995).
[CrossRef]

Chambon, P.

M. Erman, J. B. Theeten, P. Chambon, S. M. Kelso, D. E. Aspnes, “Optical properties and damage analysis of GaAs single crystals partly amorphized by ion implantation,” J. Appl. Phys. 56, 2664–2671 (1984).
[CrossRef]

Chow, D.

C. M. Herzinger, P. G. Snyder, F. G. Celii, Y.-C. Kao, D. Chow, B. Johs, J. A. Woollam, “Studies of thin strained InAs, AlAs, and AlSb layers by spectroscopic ellipsometry,” J. Appl. Phys. 79, 2663–2674 (1996).
[CrossRef]

Djurišic, A. B.

A. B. Djurišić, A. D. Rakić, J. M. Elazar, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with an adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
[CrossRef]

A. B. Djurišić, J. M. Elazar, A. D. Rakić, “Modeling the optical constants of solids using genetic algorithms with parameter space size adjustment,” Opt. Commun. 134, 407–414.

Djurišic., A. B.

A. D. Rakić, J. M. Elazar, A. B. Djurišić.“Acceptance-probability-controlled simulated annealing: a method for modeling the optical constants of solids,” Phys. Rev. E 52, 6862–6867 (1995).
[CrossRef]

Droopad, R.

G. N. Maracas, C. H. Kuo, S. Anand, R. Droopad, “Temperature-dependent pseudodielectric functions of GaAs determined by spectroscopic ellipsometry,” J. Appl. Phys. 77, 1701–1704 (1995).
[CrossRef]

Elazar, J. M.

A. B. Djurišić, A. D. Rakić, J. M. Elazar, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with an adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
[CrossRef]

A. D. Rakić, J. M. Elazar, A. B. Djurišić.“Acceptance-probability-controlled simulated annealing: a method for modeling the optical constants of solids,” Phys. Rev. E 52, 6862–6867 (1995).
[CrossRef]

A. B. Djurišić, J. M. Elazar, A. D. Rakić, “Modeling the optical constants of solids using genetic algorithms with parameter space size adjustment,” Opt. Commun. 134, 407–414.

Erman, M.

M. Erman, J. B. Theeten, P. Chambon, S. M. Kelso, D. E. Aspnes, “Optical properties and damage analysis of GaAs single crystals partly amorphized by ion implantation,” J. Appl. Phys. 56, 2664–2671 (1984).
[CrossRef]

J. B. Theeten, D. E. Aspnes, F. Simondet, M. Erman, P. C. Mürau, “Nondestructive analysis of Si3N4/SiO2/Si structures using spectroscopic ellipsometry,” J. Appl. Phys. 52, 6788–6797 (1981).
[CrossRef]

Franke, A.

A. Franke, A. Stendal, O. Stenzel, C. von Borczyskowski, “Gaussian quadrature approach to the calculation of the optical constants in the vicinity of inhomogenously broadened absorption lines,” Pure Appl. Opt. 5, 845–853 (1996).
[CrossRef]

Garland, J. W.

C. C. Kim, J. W. Garland, H. Abad, P. M. Raccah, “Modeling the optical dielectric function of semiconductors: extension of critical-point parabolic-band approximation,” Phys. Rev. B 45, 11749–11767 (1992).
[CrossRef]

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

Gottschak, V.

M. Schubert, V. Gottschak, C. M. Herzinger, H. Yao, P. G. Snyder, J. A. Woollam, “Optical constants of GaxIn1-xP lattice matched to GaAs,” J. Appl. Phys. 77, 3416–3419 (1995).
[CrossRef]

Harman, A. K.

A. K. Harman, S. Ninomiya, S. Adachi, “Optical constants of sapphire (α-Al2O3) single crystals,” J. Appl. Phys. 76, 8032–8036 (1994).
[CrossRef]

Herzinger, C. M.

C. M. Herzinger, P. G. Snyder, F. G. Celii, Y.-C. Kao, D. Chow, B. Johs, J. A. Woollam, “Studies of thin strained InAs, AlAs, and AlSb layers by spectroscopic ellipsometry,” J. Appl. Phys. 79, 2663–2674 (1996).
[CrossRef]

M. Schubert, V. Gottschak, C. M. Herzinger, H. Yao, P. G. Snyder, J. A. Woollam, “Optical constants of GaxIn1-xP lattice matched to GaAs,” J. Appl. Phys. 77, 3416–3419 (1995).
[CrossRef]

C. M. Herzinger, H. Yao, P. G. Snyder, F. G. Celii, Y.-C. Kao, B. Johs, J. A. Woollam, “Determination of AlAs optical constants by variable angle spectroscopic ellipsometry,” J. Appl. Phys. 77, 4677–4687 (1995).
[CrossRef]

Hopfe, V.

O. Stenzel, R. Petrich, W. Scharff, A. Tikhonravov, V. Hopfe, “A hybrid method for determination of optical thin film constants,” Thin Solid Films 207, 324–329 (1992).
[CrossRef]

Johs, B.

C. M. Herzinger, P. G. Snyder, F. G. Celii, Y.-C. Kao, D. Chow, B. Johs, J. A. Woollam, “Studies of thin strained InAs, AlAs, and AlSb layers by spectroscopic ellipsometry,” J. Appl. Phys. 79, 2663–2674 (1996).
[CrossRef]

C. M. Herzinger, H. Yao, P. G. Snyder, F. G. Celii, Y.-C. Kao, B. Johs, J. A. Woollam, “Determination of AlAs optical constants by variable angle spectroscopic ellipsometry,” J. Appl. Phys. 77, 4677–4687 (1995).
[CrossRef]

Kao, Y.-C.

C. M. Herzinger, P. G. Snyder, F. G. Celii, Y.-C. Kao, D. Chow, B. Johs, J. A. Woollam, “Studies of thin strained InAs, AlAs, and AlSb layers by spectroscopic ellipsometry,” J. Appl. Phys. 79, 2663–2674 (1996).
[CrossRef]

C. M. Herzinger, H. Yao, P. G. Snyder, F. G. Celii, Y.-C. Kao, B. Johs, J. A. Woollam, “Determination of AlAs optical constants by variable angle spectroscopic ellipsometry,” J. Appl. Phys. 77, 4677–4687 (1995).
[CrossRef]

Kelso, S. M.

M. Erman, J. B. Theeten, P. Chambon, S. M. Kelso, D. E. Aspnes, “Optical properties and damage analysis of GaAs single crystals partly amorphized by ion implantation,” J. Appl. Phys. 56, 2664–2671 (1984).
[CrossRef]

Kim, C. C.

C. C. Kim, J. W. Garland, H. Abad, P. M. Raccah, “Modeling the optical dielectric function of semiconductors: extension of critical-point parabolic-band approximation,” Phys. Rev. B 45, 11749–11767 (1992).
[CrossRef]

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Kuo, C. H.

G. N. Maracas, C. H. Kuo, S. Anand, R. Droopad, “Temperature-dependent pseudodielectric functions of GaAs determined by spectroscopic ellipsometry,” J. Appl. Phys. 77, 1701–1704 (1995).
[CrossRef]

Majewski, M. L.

A. D. Rakić, M. L. Majewski, “Modeling the optical dielectric function of GaAs and AlAs: extension of Adachi’s model,” J. Appl. Phys. 80, 5509–5915 (1996).

Maracas, G. N.

G. N. Maracas, C. H. Kuo, S. Anand, R. Droopad, “Temperature-dependent pseudodielectric functions of GaAs determined by spectroscopic ellipsometry,” J. Appl. Phys. 77, 1701–1704 (1995).
[CrossRef]

Mürau, P. C.

J. B. Theeten, D. E. Aspnes, F. Simondet, M. Erman, P. C. Mürau, “Nondestructive analysis of Si3N4/SiO2/Si structures using spectroscopic ellipsometry,” J. Appl. Phys. 52, 6788–6797 (1981).
[CrossRef]

Ninomiya, S.

A. K. Harman, S. Ninomiya, S. Adachi, “Optical constants of sapphire (α-Al2O3) single crystals,” J. Appl. Phys. 76, 8032–8036 (1994).
[CrossRef]

Ozaki, S.

S. Ozaki, S. Adachi, “Spectroscopic ellipsometry and thermoreflectance of GaAs,” J. Appl. Phys. 78, 3380–3386 (1995).
[CrossRef]

Petrich, R.

O. Stenzel, R. Petrich, W. Scharff, A. Tikhonravov, V. Hopfe, “A hybrid method for determination of optical thin film constants,” Thin Solid Films 207, 324–329 (1992).
[CrossRef]

Philipp, H. R.

H. R. Philipp, “Silicon nitride (Si3N4) (noncrystalline),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 771–774.

H. R. Philipp, “Silicon monoxide (SiO) (noncrystalline),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 765–770.

H. R. Philipp, “Silicon dioxide (SiO2) (glass),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 749–764.

H. R. Philipp, “Silicon dioxide (SiO2) type α (crystalline),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 719–748.

Powell, C. J.

Raccah, P. M.

C. C. Kim, J. W. Garland, H. Abad, P. M. Raccah, “Modeling the optical dielectric function of semiconductors: extension of critical-point parabolic-band approximation,” Phys. Rev. B 45, 11749–11767 (1992).
[CrossRef]

Rakic, A. D.

A. B. Djurišić, A. D. Rakić, J. M. Elazar, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with an adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
[CrossRef]

A. D. Rakić, M. L. Majewski, “Modeling the optical dielectric function of GaAs and AlAs: extension of Adachi’s model,” J. Appl. Phys. 80, 5509–5915 (1996).

A. D. Rakić, J. M. Elazar, A. B. Djurišić.“Acceptance-probability-controlled simulated annealing: a method for modeling the optical constants of solids,” Phys. Rev. E 52, 6862–6867 (1995).
[CrossRef]

A. D. Rakić, “Algorithm for the determination of intrinsic optical constants of metal films: application to aluminum,” Appl. Opt. 34, 4755–4767 (1995).
[CrossRef] [PubMed]

A. B. Djurišić, J. M. Elazar, A. D. Rakić, “Modeling the optical constants of solids using genetic algorithms with parameter space size adjustment,” Opt. Commun. 134, 407–414.

Scharff, W.

O. Stenzel, R. Petrich, W. Scharff, A. Tikhonravov, V. Hopfe, “A hybrid method for determination of optical thin film constants,” Thin Solid Films 207, 324–329 (1992).
[CrossRef]

Schubert, M.

M. Schubert, V. Gottschak, C. M. Herzinger, H. Yao, P. G. Snyder, J. A. Woollam, “Optical constants of GaxIn1-xP lattice matched to GaAs,” J. Appl. Phys. 77, 3416–3419 (1995).
[CrossRef]

Simondet, F.

J. B. Theeten, D. E. Aspnes, F. Simondet, M. Erman, P. C. Mürau, “Nondestructive analysis of Si3N4/SiO2/Si structures using spectroscopic ellipsometry,” J. Appl. Phys. 52, 6788–6797 (1981).
[CrossRef]

Snyder, P. G.

C. M. Herzinger, P. G. Snyder, F. G. Celii, Y.-C. Kao, D. Chow, B. Johs, J. A. Woollam, “Studies of thin strained InAs, AlAs, and AlSb layers by spectroscopic ellipsometry,” J. Appl. Phys. 79, 2663–2674 (1996).
[CrossRef]

C. M. Herzinger, H. Yao, P. G. Snyder, F. G. Celii, Y.-C. Kao, B. Johs, J. A. Woollam, “Determination of AlAs optical constants by variable angle spectroscopic ellipsometry,” J. Appl. Phys. 77, 4677–4687 (1995).
[CrossRef]

M. Schubert, V. Gottschak, C. M. Herzinger, H. Yao, P. G. Snyder, J. A. Woollam, “Optical constants of GaxIn1-xP lattice matched to GaAs,” J. Appl. Phys. 77, 3416–3419 (1995).
[CrossRef]

Stendal, A.

A. Franke, A. Stendal, O. Stenzel, C. von Borczyskowski, “Gaussian quadrature approach to the calculation of the optical constants in the vicinity of inhomogenously broadened absorption lines,” Pure Appl. Opt. 5, 845–853 (1996).
[CrossRef]

Stenzel, O.

A. Franke, A. Stendal, O. Stenzel, C. von Borczyskowski, “Gaussian quadrature approach to the calculation of the optical constants in the vicinity of inhomogenously broadened absorption lines,” Pure Appl. Opt. 5, 845–853 (1996).
[CrossRef]

O. Stenzel, R. Petrich, W. Scharff, A. Tikhonravov, V. Hopfe, “A hybrid method for determination of optical thin film constants,” Thin Solid Films 207, 324–329 (1992).
[CrossRef]

Terry, F. L.

F. L. Terry, “A modified harmonic oscillator approximation scheme for the dielectric constants of AlxGa1-xAs,” J. Appl. Phys. 70, 409–417 (1991).
[CrossRef]

Theeten, J. B.

M. Erman, J. B. Theeten, P. Chambon, S. M. Kelso, D. E. Aspnes, “Optical properties and damage analysis of GaAs single crystals partly amorphized by ion implantation,” J. Appl. Phys. 56, 2664–2671 (1984).
[CrossRef]

J. B. Theeten, D. E. Aspnes, F. Simondet, M. Erman, P. C. Mürau, “Nondestructive analysis of Si3N4/SiO2/Si structures using spectroscopic ellipsometry,” J. Appl. Phys. 52, 6788–6797 (1981).
[CrossRef]

Tikhonravov, A.

O. Stenzel, R. Petrich, W. Scharff, A. Tikhonravov, V. Hopfe, “A hybrid method for determination of optical thin film constants,” Thin Solid Films 207, 324–329 (1992).
[CrossRef]

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

von Borczyskowski, C.

A. Franke, A. Stendal, O. Stenzel, C. von Borczyskowski, “Gaussian quadrature approach to the calculation of the optical constants in the vicinity of inhomogenously broadened absorption lines,” Pure Appl. Opt. 5, 845–853 (1996).
[CrossRef]

Woollam, J. A.

C. M. Herzinger, P. G. Snyder, F. G. Celii, Y.-C. Kao, D. Chow, B. Johs, J. A. Woollam, “Studies of thin strained InAs, AlAs, and AlSb layers by spectroscopic ellipsometry,” J. Appl. Phys. 79, 2663–2674 (1996).
[CrossRef]

M. Schubert, V. Gottschak, C. M. Herzinger, H. Yao, P. G. Snyder, J. A. Woollam, “Optical constants of GaxIn1-xP lattice matched to GaAs,” J. Appl. Phys. 77, 3416–3419 (1995).
[CrossRef]

C. M. Herzinger, H. Yao, P. G. Snyder, F. G. Celii, Y.-C. Kao, B. Johs, J. A. Woollam, “Determination of AlAs optical constants by variable angle spectroscopic ellipsometry,” J. Appl. Phys. 77, 4677–4687 (1995).
[CrossRef]

Yao, H.

M. Schubert, V. Gottschak, C. M. Herzinger, H. Yao, P. G. Snyder, J. A. Woollam, “Optical constants of GaxIn1-xP lattice matched to GaAs,” J. Appl. Phys. 77, 3416–3419 (1995).
[CrossRef]

C. M. Herzinger, H. Yao, P. G. Snyder, F. G. Celii, Y.-C. Kao, B. Johs, J. A. Woollam, “Determination of AlAs optical constants by variable angle spectroscopic ellipsometry,” J. Appl. Phys. 77, 4677–4687 (1995).
[CrossRef]

Appl. Opt. (1)

J. Appl. Phys. (10)

J. B. Theeten, D. E. Aspnes, F. Simondet, M. Erman, P. C. Mürau, “Nondestructive analysis of Si3N4/SiO2/Si structures using spectroscopic ellipsometry,” J. Appl. Phys. 52, 6788–6797 (1981).
[CrossRef]

M. Erman, J. B. Theeten, P. Chambon, S. M. Kelso, D. E. Aspnes, “Optical properties and damage analysis of GaAs single crystals partly amorphized by ion implantation,” J. Appl. Phys. 56, 2664–2671 (1984).
[CrossRef]

F. L. Terry, “A modified harmonic oscillator approximation scheme for the dielectric constants of AlxGa1-xAs,” J. Appl. Phys. 70, 409–417 (1991).
[CrossRef]

G. N. Maracas, C. H. Kuo, S. Anand, R. Droopad, “Temperature-dependent pseudodielectric functions of GaAs determined by spectroscopic ellipsometry,” J. Appl. Phys. 77, 1701–1704 (1995).
[CrossRef]

C. M. Herzinger, H. Yao, P. G. Snyder, F. G. Celii, Y.-C. Kao, B. Johs, J. A. Woollam, “Determination of AlAs optical constants by variable angle spectroscopic ellipsometry,” J. Appl. Phys. 77, 4677–4687 (1995).
[CrossRef]

M. Schubert, V. Gottschak, C. M. Herzinger, H. Yao, P. G. Snyder, J. A. Woollam, “Optical constants of GaxIn1-xP lattice matched to GaAs,” J. Appl. Phys. 77, 3416–3419 (1995).
[CrossRef]

C. M. Herzinger, P. G. Snyder, F. G. Celii, Y.-C. Kao, D. Chow, B. Johs, J. A. Woollam, “Studies of thin strained InAs, AlAs, and AlSb layers by spectroscopic ellipsometry,” J. Appl. Phys. 79, 2663–2674 (1996).
[CrossRef]

A. D. Rakić, M. L. Majewski, “Modeling the optical dielectric function of GaAs and AlAs: extension of Adachi’s model,” J. Appl. Phys. 80, 5509–5915 (1996).

S. Ozaki, S. Adachi, “Spectroscopic ellipsometry and thermoreflectance of GaAs,” J. Appl. Phys. 78, 3380–3386 (1995).
[CrossRef]

A. K. Harman, S. Ninomiya, S. Adachi, “Optical constants of sapphire (α-Al2O3) single crystals,” J. Appl. Phys. 76, 8032–8036 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

A. B. Djurišić, J. M. Elazar, A. D. Rakić, “Modeling the optical constants of solids using genetic algorithms with parameter space size adjustment,” Opt. Commun. 134, 407–414.

Phys. Rev. B (1)

C. C. Kim, J. W. Garland, H. Abad, P. M. Raccah, “Modeling the optical dielectric function of semiconductors: extension of critical-point parabolic-band approximation,” Phys. Rev. B 45, 11749–11767 (1992).
[CrossRef]

Phys. Rev. E (2)

A. D. Rakić, J. M. Elazar, A. B. Djurišić.“Acceptance-probability-controlled simulated annealing: a method for modeling the optical constants of solids,” Phys. Rev. E 52, 6862–6867 (1995).
[CrossRef]

A. B. Djurišić, A. D. Rakić, J. M. Elazar, “Modeling the optical constants of solids using acceptance-probability-controlled simulated annealing with an adaptive move generation procedure,” Phys. Rev. E 55, 4797–4803 (1997).
[CrossRef]

Pure Appl. Opt. (1)

A. Franke, A. Stendal, O. Stenzel, C. von Borczyskowski, “Gaussian quadrature approach to the calculation of the optical constants in the vicinity of inhomogenously broadened absorption lines,” Pure Appl. Opt. 5, 845–853 (1996).
[CrossRef]

Science (1)

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Thin Solid Films (1)

O. Stenzel, R. Petrich, W. Scharff, A. Tikhonravov, V. Hopfe, “A hybrid method for determination of optical thin film constants,” Thin Solid Films 207, 324–329 (1992).
[CrossRef]

Other (5)

H. R. Philipp, “Silicon nitride (Si3N4) (noncrystalline),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 771–774.

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Mass., 1989).

H. R. Philipp, “Silicon monoxide (SiO) (noncrystalline),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 765–770.

H. R. Philipp, “Silicon dioxide (SiO2) (glass),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 749–764.

H. R. Philipp, “Silicon dioxide (SiO2) type α (crystalline),” in Handbook of Optical Constants of Solids, E. D. Palik, ed. (Academic, Orlando, Fla., 1985), pp. 719–748.

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Figures (5)

Fig. 1
Fig. 1

Illustration of the influence of frequency-dependent damping on optical constants.

Fig. 2
Fig. 2

Refractive index of Si3N4 versus energy; circles, experimental data; solid curves, modified LOM; dashed curves, four-oscillator LOM; dotted curves, six-oscillator LOM. Inset, imaginary part of the index of refraction k(ω) as a function of energy.

Fig. 3
Fig. 3

Refractive index of SiO versus energy; circles, experimental data; solid curves, modified LOM; dashed curves, LOM. Inset, imaginary part of the index of refraction k(ω) as a function of energy.

Fig. 4
Fig. 4

Refractive index of amorphous SiO2 versus energy; circles, experimental data; solid curves, modified LOM; dashed curves, LOM. Inset, imaginary part of the index of refraction k(ω) as a function of energy.

Fig. 5
Fig. 5

Refractive index of crystalline SiO2 versus energy; circles, experimental data; solid curves, modified LOM; dashed curves, LOM. Inset, imaginary part of the index of refraction k(ω) as a function of energy.

Tables (1)

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Table 1 Final Values for Modified LOM parameters, Γ j , ω j (eV), Fj (eV2), α j (dimensionless), j = 1, 6

Equations (6)

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1 ω = + j = 1 k F j ω j 2 - ω 2 ω 2 - ω j 2 2 + ω Γ j 2 ,
2 ω = j = 1 k F j ω Γ j ω 2 - ω j 2 2 + ω Γ j 2 ,
n = 0.5 1 + 1 2 + 2 2 1 / 2 1 / 2 ,
k = 0.5 - 1 + 1 2 + 2 2 1 / 2 1 / 2 .
Γ j = Γ j exp - α j ω - ω j Γ j 2 .
F = i = 1 N n ω i n expt ω i - 1 + k ω i k expt ω i - 1 2 ,

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