Abstract

We introduce single angle-of-incidence (SAI) ellipsometry [U.S. patent application 20070024850 (14 July 2006)] as a technique to completely identify, i.e., totally characterize, film–substrate systems. We show that only one measurement of the ellipsometric function ρ at one angle of incidence and one wavelength is totally sufficient to determine the optical constant of the film N1, its thickness d, and the substrate’s optical constant N2. Obviously, it is also sufficient for characterizing only the film, determining N1 and d, and for characterizing only the substrate, determining N2 and d, as well as for characterizing only bare substrates. An inverse genetic algorithm (IGA) for complete identification is presented that is based on a physical condition of the transparent-film–absorbing-substrate system . This IGA is used to identify the film–substrate system in four separate cases. We show that removing the film thickness from the fitness function of the genetic algorithm and using the defined optimum population size to characterize the film reduces the computational effort from 20,000 to 69 fitness-function calculations; the number of calculations to characterize an absorbing layer is reduced from 80,000 to 180. This is a very significant reduction and is very welcome in real-time applications. An error analysis is presented that shows that the IGA is resilient to, not affected by, random experimental errors and that it gives very good results in the presence of both random and systematic errors of the ellipsometer system. Experimental results are given that also prove the robustness, stability, and high accuracy of the method. We present data only for the SiO2–Si film–substrate system, but the IGA works for any film–substrate system, physical or not.

© 2008 Optical Society of America

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  1. D. Goldstein, Polarized Light (Marcel Dekker, 2003).
  2. S. C. Warnick and M. A. Dahleh, “Ellipsometry as a sensor technology for the control of deposition processes,” in Proceedings of the 37th IEEE Conference on Decision and Control (IEEE, 1998). Vol. 3, pp. 3162-3167.
  3. P. Drude, “Uber Oberflaechenschichten. I. Theil,” Ann. Phys. 272, 532-560 (1889).
    [CrossRef]
  4. M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 2002).
  5. A. R. M. Zaghloul, “Ellipsometric function of a film-substrate system: applications to the design of reflection-type optical devices and to ellipsometry,” Ph.D. dissertation (University of Nebraska-Lincoln, 1975).
  6. M. M. Ibrahim and N. M. Bashara, “Parameter-correlation and computational considerations in multiple-angle ellipsometry,” J. Opt. Soc. Am. 61, 1622-1629 (1971).
  7. G. H. Bu-Abbud, N. M. Bashara, and John A. Woollam, “Variable wavelength, variable angle ellipsometry including a sensitivities correlation test,” Thin Solid Films 138, 27-41 (1986).
    [CrossRef]
  8. T. E. Jenkins, “Multiple-angle-of-incidence ellipsometry,” J. Phys. D 32, R45-R56 (1999).
  9. K. Vedam, “Spectroscopic ellipsometry: a historical overview,” Thin Solid Films 313-314, 1-9 (1998).
    [CrossRef]
  10. G. E. Jellison, Jr., “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313-314, 33-39 (1998).
  11. A. Laskarakis, S. Logothetidis, E. Pavlopoulou, and M. Gioti, “Muller matrix spectroscopic ellipsometry: formulation and application,” Thin Solid Films 455-456, 43-49 (2004).
    [CrossRef]
  12. A. R. M. Zaghloul and Y. A. Zaghloul, “Complete system identification of film-substrate systems using single-angle-of-incidence ellipsometry: a fast genetic algorithm,” U.S. patent application 20070024850 (14 July 2006).
  13. P. C. Yip, Y.-H. Pao, S. R. LeClair, and K. G. Eyink, “A real-time evolutionary algorithm for the in-situ ellipsometer data analysis,” in Proceedings of the International Conference on Neural Information Processing (Springer, 1996), Vol. 2, pp. 827-831.
  14. Z. Meng, Q. Yang, P. C. Yip, K. G. Eyink, W. T. Taferner, and B. Igelnik, “Combined use of computational intelligence and materials data for on-line monitoring and control of MBE experiments,” Eng. Applic. Artif. Intell. 11, 587-595 (1998).
  15. G. Cormier and R. Boudreau, “Genetic algorithm for ellipsometric data inversion of absorbing layers,” J. Opt. Soc. Am. A 17, 129-134 (2000).
    [CrossRef]
  16. P. Zilong, L. Zuoyi, H. Yu, T. Liguo, and Y. Xiaofei, “Thickness and refractivity computation in ellipsometry measurement by genetic algorithm,” Proc. SPIE 4077 , 492-495 (2000).
  17. J. Leng, J. J. Sidorowich, and J. L. Opsal, “Multi-domain genetic algorithm (MDGA) and its applications to thin film metrology,” Proc. SPIE 4779, 132-138 (2002).
  18. A. Kudla, “Application of the genetic algorithms in spectroscopic ellipsometry,” Thin Solid Films 455-456, 804-808(2004).
    [CrossRef]
  19. R. M. A. Azzam, A. R. M. Zaghloul, N. M. Bashara, “Ellipsometric function of a film-substrate system: applications to the design of reflection-type optical devices and to ellipsometry,” J. Opt. Soc. Am. 65, 252-260 (1975).
  20. A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “An angle-of-incidence tunable SiOs-Si (film-substrate) reflection retarder for the UV mercury line ?=2537Å,” Opt. Commun. 14, 260-262 (1975).
  21. A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “Design of film-substrate single-reflection retarders,” J. Opt. Soc. Am. 65, 1043-1049 (1975).
  22. A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “SiO2-Si film-substrate single-reflection retarders for different mercury spectral lines,” Opt. Eng. 17, 180-184 (1978).
  23. A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “Inversion of the nonlinear equations of reflection ellipsometry on film-substrate systems,” Surf. Sci. 56, 87-96 (1976).
    [CrossRef]
  24. A. R. M. Zaghloul and R. M. A. Azzam, “Single-element rotating-polarizer ellipsometer for film-substrate systems,” J. Opt. Soc. Am. 67, 1286-1287 (1977); see also .
  25. A. R. M. Zaghloul, “Modified O'Bryan ellipsometer (MOE) for film-substrate systems,” Opt. Commun. 27, 1-3 (1978).
  26. A. R. M. Zaghloul and R. M. A. Azzam, “Single-element rotating-polarizer ellipsometer for film-substrate systems: psi-meter,” Surf. Sci. 96, 168-173 (1980).
    [CrossRef]
  27. A. R. M. Zaghloul, M. M. El-Bahy, and M. S. Abou-Seada, “Single-element rotating-polarizer (SERP) ellipsometer: film thickness determination,” Opt. Commun. 61, 363-368(1987).
  28. R. M. A. Azzam, A. R. M. Zaghloul, and N. M. Bashara, “Polarizer-surface-analyzer null ellipsometry for film-substrate systems,” J. Opt. Soc. Am. 65, 1464-1471 (1975).
  29. R. M. A. Azzam and A. R. M. Zaghloul, “Determination of the refractive index and film thickness of a transparent film on a transparent substrate from the angles of incidence of zero reflection-induced ellipticity,” Opt. Commun. 24, 351-354(1978).
  30. R. M. A. Azzam and A. R. M. Zaghloul, “Polarization-independent reflectance matching (PIRM)--a technique for the determination of the refractive index and thickness of transparent films,” J. Opt. (Paris) 8, 201-205 (1977).
    [CrossRef]
  31. J. L. Ord and B. L. Wills, “Computer-operated following ellipsometer,” App. Opt. 6, 1673-1677 (1967).
  32. R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, (North-Holland, 1977).
  33. D. E. Aspnes and A. A. Studna, “High precision scanning ellipsometer,” App. Opt. 14, 220-228 (1975).
  34. R. W. Collins, “Automatic rotating element ellipsometers: calibration, operation, and real-time applications,” Rev. Sci. Instrum. 61, 2029-2062 (1990).
    [CrossRef]
  35. R. F. Cohn, J. W. Wagner, and J. Kruger, “Dynamic imaging microellipsometry: theory, system design, and feasibility demonstration,” App. Opt. 27, 4664-4671 (1988).
  36. D. E. Aspnes, “Analysis of semiconductor materials and structures by spectroellipsometry,” Proc. SPIE 946, 84-97(1988).
  37. A. Roseler, “Spectroscopic ellipsometry in the infrared,” Infrared Phys. 21, 349-355 (1981).
    [CrossRef]
  38. J. H. Holland, “Genetic algorithms and the optimal allocation of trials,” SIAM J. Comput. 2, 88-105 (1973).
  39. These values are chosen so that the results could be compared with those of .

2004

A. Laskarakis, S. Logothetidis, E. Pavlopoulou, and M. Gioti, “Muller matrix spectroscopic ellipsometry: formulation and application,” Thin Solid Films 455-456, 43-49 (2004).
[CrossRef]

A. Kudla, “Application of the genetic algorithms in spectroscopic ellipsometry,” Thin Solid Films 455-456, 804-808(2004).
[CrossRef]

2003

D. Goldstein, Polarized Light (Marcel Dekker, 2003).

2002

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 2002).

J. Leng, J. J. Sidorowich, and J. L. Opsal, “Multi-domain genetic algorithm (MDGA) and its applications to thin film metrology,” Proc. SPIE 4779, 132-138 (2002).

2000

G. Cormier and R. Boudreau, “Genetic algorithm for ellipsometric data inversion of absorbing layers,” J. Opt. Soc. Am. A 17, 129-134 (2000).
[CrossRef]

P. Zilong, L. Zuoyi, H. Yu, T. Liguo, and Y. Xiaofei, “Thickness and refractivity computation in ellipsometry measurement by genetic algorithm,” Proc. SPIE 4077 , 492-495 (2000).

1999

T. E. Jenkins, “Multiple-angle-of-incidence ellipsometry,” J. Phys. D 32, R45-R56 (1999).

1998

K. Vedam, “Spectroscopic ellipsometry: a historical overview,” Thin Solid Films 313-314, 1-9 (1998).
[CrossRef]

G. E. Jellison, Jr., “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313-314, 33-39 (1998).

S. C. Warnick and M. A. Dahleh, “Ellipsometry as a sensor technology for the control of deposition processes,” in Proceedings of the 37th IEEE Conference on Decision and Control (IEEE, 1998). Vol. 3, pp. 3162-3167.

Z. Meng, Q. Yang, P. C. Yip, K. G. Eyink, W. T. Taferner, and B. Igelnik, “Combined use of computational intelligence and materials data for on-line monitoring and control of MBE experiments,” Eng. Applic. Artif. Intell. 11, 587-595 (1998).

1996

P. C. Yip, Y.-H. Pao, S. R. LeClair, and K. G. Eyink, “A real-time evolutionary algorithm for the in-situ ellipsometer data analysis,” in Proceedings of the International Conference on Neural Information Processing (Springer, 1996), Vol. 2, pp. 827-831.

1990

R. W. Collins, “Automatic rotating element ellipsometers: calibration, operation, and real-time applications,” Rev. Sci. Instrum. 61, 2029-2062 (1990).
[CrossRef]

1988

R. F. Cohn, J. W. Wagner, and J. Kruger, “Dynamic imaging microellipsometry: theory, system design, and feasibility demonstration,” App. Opt. 27, 4664-4671 (1988).

D. E. Aspnes, “Analysis of semiconductor materials and structures by spectroellipsometry,” Proc. SPIE 946, 84-97(1988).

1987

A. R. M. Zaghloul, M. M. El-Bahy, and M. S. Abou-Seada, “Single-element rotating-polarizer (SERP) ellipsometer: film thickness determination,” Opt. Commun. 61, 363-368(1987).

1986

G. H. Bu-Abbud, N. M. Bashara, and John A. Woollam, “Variable wavelength, variable angle ellipsometry including a sensitivities correlation test,” Thin Solid Films 138, 27-41 (1986).
[CrossRef]

1981

A. Roseler, “Spectroscopic ellipsometry in the infrared,” Infrared Phys. 21, 349-355 (1981).
[CrossRef]

1980

A. R. M. Zaghloul and R. M. A. Azzam, “Single-element rotating-polarizer ellipsometer for film-substrate systems: psi-meter,” Surf. Sci. 96, 168-173 (1980).
[CrossRef]

1978

A. R. M. Zaghloul, “Modified O'Bryan ellipsometer (MOE) for film-substrate systems,” Opt. Commun. 27, 1-3 (1978).

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “SiO2-Si film-substrate single-reflection retarders for different mercury spectral lines,” Opt. Eng. 17, 180-184 (1978).

R. M. A. Azzam and A. R. M. Zaghloul, “Determination of the refractive index and film thickness of a transparent film on a transparent substrate from the angles of incidence of zero reflection-induced ellipticity,” Opt. Commun. 24, 351-354(1978).

1977

R. M. A. Azzam and A. R. M. Zaghloul, “Polarization-independent reflectance matching (PIRM)--a technique for the determination of the refractive index and thickness of transparent films,” J. Opt. (Paris) 8, 201-205 (1977).
[CrossRef]

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, (North-Holland, 1977).

A. R. M. Zaghloul and R. M. A. Azzam, “Single-element rotating-polarizer ellipsometer for film-substrate systems,” J. Opt. Soc. Am. 67, 1286-1287 (1977); see also .

1976

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “Inversion of the nonlinear equations of reflection ellipsometry on film-substrate systems,” Surf. Sci. 56, 87-96 (1976).
[CrossRef]

1975

R. M. A. Azzam, A. R. M. Zaghloul, and N. M. Bashara, “Polarizer-surface-analyzer null ellipsometry for film-substrate systems,” J. Opt. Soc. Am. 65, 1464-1471 (1975).

D. E. Aspnes and A. A. Studna, “High precision scanning ellipsometer,” App. Opt. 14, 220-228 (1975).

R. M. A. Azzam, A. R. M. Zaghloul, N. M. Bashara, “Ellipsometric function of a film-substrate system: applications to the design of reflection-type optical devices and to ellipsometry,” J. Opt. Soc. Am. 65, 252-260 (1975).

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “An angle-of-incidence tunable SiOs-Si (film-substrate) reflection retarder for the UV mercury line ?=2537Å,” Opt. Commun. 14, 260-262 (1975).

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “Design of film-substrate single-reflection retarders,” J. Opt. Soc. Am. 65, 1043-1049 (1975).

A. R. M. Zaghloul, “Ellipsometric function of a film-substrate system: applications to the design of reflection-type optical devices and to ellipsometry,” Ph.D. dissertation (University of Nebraska-Lincoln, 1975).

1973

J. H. Holland, “Genetic algorithms and the optimal allocation of trials,” SIAM J. Comput. 2, 88-105 (1973).

1971

1967

J. L. Ord and B. L. Wills, “Computer-operated following ellipsometer,” App. Opt. 6, 1673-1677 (1967).

1889

P. Drude, “Uber Oberflaechenschichten. I. Theil,” Ann. Phys. 272, 532-560 (1889).
[CrossRef]

Abou-Seada, M. S.

A. R. M. Zaghloul, M. M. El-Bahy, and M. S. Abou-Seada, “Single-element rotating-polarizer (SERP) ellipsometer: film thickness determination,” Opt. Commun. 61, 363-368(1987).

Aspnes, D. E.

D. E. Aspnes, “Analysis of semiconductor materials and structures by spectroellipsometry,” Proc. SPIE 946, 84-97(1988).

D. E. Aspnes and A. A. Studna, “High precision scanning ellipsometer,” App. Opt. 14, 220-228 (1975).

Azzam, R. M. A.

A. R. M. Zaghloul and R. M. A. Azzam, “Single-element rotating-polarizer ellipsometer for film-substrate systems: psi-meter,” Surf. Sci. 96, 168-173 (1980).
[CrossRef]

R. M. A. Azzam and A. R. M. Zaghloul, “Determination of the refractive index and film thickness of a transparent film on a transparent substrate from the angles of incidence of zero reflection-induced ellipticity,” Opt. Commun. 24, 351-354(1978).

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “SiO2-Si film-substrate single-reflection retarders for different mercury spectral lines,” Opt. Eng. 17, 180-184 (1978).

R. M. A. Azzam and A. R. M. Zaghloul, “Polarization-independent reflectance matching (PIRM)--a technique for the determination of the refractive index and thickness of transparent films,” J. Opt. (Paris) 8, 201-205 (1977).
[CrossRef]

A. R. M. Zaghloul and R. M. A. Azzam, “Single-element rotating-polarizer ellipsometer for film-substrate systems,” J. Opt. Soc. Am. 67, 1286-1287 (1977); see also .

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, (North-Holland, 1977).

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “Inversion of the nonlinear equations of reflection ellipsometry on film-substrate systems,” Surf. Sci. 56, 87-96 (1976).
[CrossRef]

R. M. A. Azzam, A. R. M. Zaghloul, and N. M. Bashara, “Polarizer-surface-analyzer null ellipsometry for film-substrate systems,” J. Opt. Soc. Am. 65, 1464-1471 (1975).

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “Design of film-substrate single-reflection retarders,” J. Opt. Soc. Am. 65, 1043-1049 (1975).

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “An angle-of-incidence tunable SiOs-Si (film-substrate) reflection retarder for the UV mercury line ?=2537Å,” Opt. Commun. 14, 260-262 (1975).

R. M. A. Azzam, A. R. M. Zaghloul, N. M. Bashara, “Ellipsometric function of a film-substrate system: applications to the design of reflection-type optical devices and to ellipsometry,” J. Opt. Soc. Am. 65, 252-260 (1975).

Bashara, N. M.

G. H. Bu-Abbud, N. M. Bashara, and John A. Woollam, “Variable wavelength, variable angle ellipsometry including a sensitivities correlation test,” Thin Solid Films 138, 27-41 (1986).
[CrossRef]

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “SiO2-Si film-substrate single-reflection retarders for different mercury spectral lines,” Opt. Eng. 17, 180-184 (1978).

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, (North-Holland, 1977).

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “Inversion of the nonlinear equations of reflection ellipsometry on film-substrate systems,” Surf. Sci. 56, 87-96 (1976).
[CrossRef]

R. M. A. Azzam, A. R. M. Zaghloul, and N. M. Bashara, “Polarizer-surface-analyzer null ellipsometry for film-substrate systems,” J. Opt. Soc. Am. 65, 1464-1471 (1975).

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “Design of film-substrate single-reflection retarders,” J. Opt. Soc. Am. 65, 1043-1049 (1975).

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “An angle-of-incidence tunable SiOs-Si (film-substrate) reflection retarder for the UV mercury line ?=2537Å,” Opt. Commun. 14, 260-262 (1975).

R. M. A. Azzam, A. R. M. Zaghloul, N. M. Bashara, “Ellipsometric function of a film-substrate system: applications to the design of reflection-type optical devices and to ellipsometry,” J. Opt. Soc. Am. 65, 252-260 (1975).

M. M. Ibrahim and N. M. Bashara, “Parameter-correlation and computational considerations in multiple-angle ellipsometry,” J. Opt. Soc. Am. 61, 1622-1629 (1971).

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 2002).

Boudreau, R.

Bu-Abbud, G. H.

G. H. Bu-Abbud, N. M. Bashara, and John A. Woollam, “Variable wavelength, variable angle ellipsometry including a sensitivities correlation test,” Thin Solid Films 138, 27-41 (1986).
[CrossRef]

Cohn, R. F.

R. F. Cohn, J. W. Wagner, and J. Kruger, “Dynamic imaging microellipsometry: theory, system design, and feasibility demonstration,” App. Opt. 27, 4664-4671 (1988).

Collins, R. W.

R. W. Collins, “Automatic rotating element ellipsometers: calibration, operation, and real-time applications,” Rev. Sci. Instrum. 61, 2029-2062 (1990).
[CrossRef]

Cormier, G.

Dahleh, M. A.

S. C. Warnick and M. A. Dahleh, “Ellipsometry as a sensor technology for the control of deposition processes,” in Proceedings of the 37th IEEE Conference on Decision and Control (IEEE, 1998). Vol. 3, pp. 3162-3167.

Drude, P.

P. Drude, “Uber Oberflaechenschichten. I. Theil,” Ann. Phys. 272, 532-560 (1889).
[CrossRef]

El-Bahy, M. M.

A. R. M. Zaghloul, M. M. El-Bahy, and M. S. Abou-Seada, “Single-element rotating-polarizer (SERP) ellipsometer: film thickness determination,” Opt. Commun. 61, 363-368(1987).

Eyink, K. G.

Z. Meng, Q. Yang, P. C. Yip, K. G. Eyink, W. T. Taferner, and B. Igelnik, “Combined use of computational intelligence and materials data for on-line monitoring and control of MBE experiments,” Eng. Applic. Artif. Intell. 11, 587-595 (1998).

P. C. Yip, Y.-H. Pao, S. R. LeClair, and K. G. Eyink, “A real-time evolutionary algorithm for the in-situ ellipsometer data analysis,” in Proceedings of the International Conference on Neural Information Processing (Springer, 1996), Vol. 2, pp. 827-831.

Gioti, M.

A. Laskarakis, S. Logothetidis, E. Pavlopoulou, and M. Gioti, “Muller matrix spectroscopic ellipsometry: formulation and application,” Thin Solid Films 455-456, 43-49 (2004).
[CrossRef]

Goldstein, D.

D. Goldstein, Polarized Light (Marcel Dekker, 2003).

Holland, J. H.

J. H. Holland, “Genetic algorithms and the optimal allocation of trials,” SIAM J. Comput. 2, 88-105 (1973).

Ibrahim, M. M.

Igelnik, B.

Z. Meng, Q. Yang, P. C. Yip, K. G. Eyink, W. T. Taferner, and B. Igelnik, “Combined use of computational intelligence and materials data for on-line monitoring and control of MBE experiments,” Eng. Applic. Artif. Intell. 11, 587-595 (1998).

Jellison, G. E.

G. E. Jellison, Jr., “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313-314, 33-39 (1998).

Jenkins, T. E.

T. E. Jenkins, “Multiple-angle-of-incidence ellipsometry,” J. Phys. D 32, R45-R56 (1999).

Kruger, J.

R. F. Cohn, J. W. Wagner, and J. Kruger, “Dynamic imaging microellipsometry: theory, system design, and feasibility demonstration,” App. Opt. 27, 4664-4671 (1988).

Kudla, A.

A. Kudla, “Application of the genetic algorithms in spectroscopic ellipsometry,” Thin Solid Films 455-456, 804-808(2004).
[CrossRef]

Laskarakis, A.

A. Laskarakis, S. Logothetidis, E. Pavlopoulou, and M. Gioti, “Muller matrix spectroscopic ellipsometry: formulation and application,” Thin Solid Films 455-456, 43-49 (2004).
[CrossRef]

LeClair, S. R.

P. C. Yip, Y.-H. Pao, S. R. LeClair, and K. G. Eyink, “A real-time evolutionary algorithm for the in-situ ellipsometer data analysis,” in Proceedings of the International Conference on Neural Information Processing (Springer, 1996), Vol. 2, pp. 827-831.

Leng, J.

J. Leng, J. J. Sidorowich, and J. L. Opsal, “Multi-domain genetic algorithm (MDGA) and its applications to thin film metrology,” Proc. SPIE 4779, 132-138 (2002).

Liguo, T.

P. Zilong, L. Zuoyi, H. Yu, T. Liguo, and Y. Xiaofei, “Thickness and refractivity computation in ellipsometry measurement by genetic algorithm,” Proc. SPIE 4077 , 492-495 (2000).

Logothetidis, S.

A. Laskarakis, S. Logothetidis, E. Pavlopoulou, and M. Gioti, “Muller matrix spectroscopic ellipsometry: formulation and application,” Thin Solid Films 455-456, 43-49 (2004).
[CrossRef]

Meng, Z.

Z. Meng, Q. Yang, P. C. Yip, K. G. Eyink, W. T. Taferner, and B. Igelnik, “Combined use of computational intelligence and materials data for on-line monitoring and control of MBE experiments,” Eng. Applic. Artif. Intell. 11, 587-595 (1998).

Opsal, J. L.

J. Leng, J. J. Sidorowich, and J. L. Opsal, “Multi-domain genetic algorithm (MDGA) and its applications to thin film metrology,” Proc. SPIE 4779, 132-138 (2002).

Ord, J. L.

J. L. Ord and B. L. Wills, “Computer-operated following ellipsometer,” App. Opt. 6, 1673-1677 (1967).

Pao, Y.-H.

P. C. Yip, Y.-H. Pao, S. R. LeClair, and K. G. Eyink, “A real-time evolutionary algorithm for the in-situ ellipsometer data analysis,” in Proceedings of the International Conference on Neural Information Processing (Springer, 1996), Vol. 2, pp. 827-831.

Pavlopoulou, E.

A. Laskarakis, S. Logothetidis, E. Pavlopoulou, and M. Gioti, “Muller matrix spectroscopic ellipsometry: formulation and application,” Thin Solid Films 455-456, 43-49 (2004).
[CrossRef]

Roseler, A.

A. Roseler, “Spectroscopic ellipsometry in the infrared,” Infrared Phys. 21, 349-355 (1981).
[CrossRef]

Sidorowich, J. J.

J. Leng, J. J. Sidorowich, and J. L. Opsal, “Multi-domain genetic algorithm (MDGA) and its applications to thin film metrology,” Proc. SPIE 4779, 132-138 (2002).

Studna, A. A.

D. E. Aspnes and A. A. Studna, “High precision scanning ellipsometer,” App. Opt. 14, 220-228 (1975).

Taferner, W. T.

Z. Meng, Q. Yang, P. C. Yip, K. G. Eyink, W. T. Taferner, and B. Igelnik, “Combined use of computational intelligence and materials data for on-line monitoring and control of MBE experiments,” Eng. Applic. Artif. Intell. 11, 587-595 (1998).

Vedam, K.

K. Vedam, “Spectroscopic ellipsometry: a historical overview,” Thin Solid Films 313-314, 1-9 (1998).
[CrossRef]

Wagner, J. W.

R. F. Cohn, J. W. Wagner, and J. Kruger, “Dynamic imaging microellipsometry: theory, system design, and feasibility demonstration,” App. Opt. 27, 4664-4671 (1988).

Warnick, S. C.

S. C. Warnick and M. A. Dahleh, “Ellipsometry as a sensor technology for the control of deposition processes,” in Proceedings of the 37th IEEE Conference on Decision and Control (IEEE, 1998). Vol. 3, pp. 3162-3167.

Wills, B. L.

J. L. Ord and B. L. Wills, “Computer-operated following ellipsometer,” App. Opt. 6, 1673-1677 (1967).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 2002).

Woollam, John A.

G. H. Bu-Abbud, N. M. Bashara, and John A. Woollam, “Variable wavelength, variable angle ellipsometry including a sensitivities correlation test,” Thin Solid Films 138, 27-41 (1986).
[CrossRef]

Xiaofei, Y.

P. Zilong, L. Zuoyi, H. Yu, T. Liguo, and Y. Xiaofei, “Thickness and refractivity computation in ellipsometry measurement by genetic algorithm,” Proc. SPIE 4077 , 492-495 (2000).

Yang, Q.

Z. Meng, Q. Yang, P. C. Yip, K. G. Eyink, W. T. Taferner, and B. Igelnik, “Combined use of computational intelligence and materials data for on-line monitoring and control of MBE experiments,” Eng. Applic. Artif. Intell. 11, 587-595 (1998).

Yip, P. C.

Z. Meng, Q. Yang, P. C. Yip, K. G. Eyink, W. T. Taferner, and B. Igelnik, “Combined use of computational intelligence and materials data for on-line monitoring and control of MBE experiments,” Eng. Applic. Artif. Intell. 11, 587-595 (1998).

P. C. Yip, Y.-H. Pao, S. R. LeClair, and K. G. Eyink, “A real-time evolutionary algorithm for the in-situ ellipsometer data analysis,” in Proceedings of the International Conference on Neural Information Processing (Springer, 1996), Vol. 2, pp. 827-831.

Yu, H.

P. Zilong, L. Zuoyi, H. Yu, T. Liguo, and Y. Xiaofei, “Thickness and refractivity computation in ellipsometry measurement by genetic algorithm,” Proc. SPIE 4077 , 492-495 (2000).

Zaghloul, A. R. M.

A. R. M. Zaghloul, M. M. El-Bahy, and M. S. Abou-Seada, “Single-element rotating-polarizer (SERP) ellipsometer: film thickness determination,” Opt. Commun. 61, 363-368(1987).

A. R. M. Zaghloul and R. M. A. Azzam, “Single-element rotating-polarizer ellipsometer for film-substrate systems: psi-meter,” Surf. Sci. 96, 168-173 (1980).
[CrossRef]

A. R. M. Zaghloul, “Modified O'Bryan ellipsometer (MOE) for film-substrate systems,” Opt. Commun. 27, 1-3 (1978).

R. M. A. Azzam and A. R. M. Zaghloul, “Determination of the refractive index and film thickness of a transparent film on a transparent substrate from the angles of incidence of zero reflection-induced ellipticity,” Opt. Commun. 24, 351-354(1978).

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “SiO2-Si film-substrate single-reflection retarders for different mercury spectral lines,” Opt. Eng. 17, 180-184 (1978).

R. M. A. Azzam and A. R. M. Zaghloul, “Polarization-independent reflectance matching (PIRM)--a technique for the determination of the refractive index and thickness of transparent films,” J. Opt. (Paris) 8, 201-205 (1977).
[CrossRef]

A. R. M. Zaghloul and R. M. A. Azzam, “Single-element rotating-polarizer ellipsometer for film-substrate systems,” J. Opt. Soc. Am. 67, 1286-1287 (1977); see also .

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “Inversion of the nonlinear equations of reflection ellipsometry on film-substrate systems,” Surf. Sci. 56, 87-96 (1976).
[CrossRef]

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “An angle-of-incidence tunable SiOs-Si (film-substrate) reflection retarder for the UV mercury line ?=2537Å,” Opt. Commun. 14, 260-262 (1975).

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “Design of film-substrate single-reflection retarders,” J. Opt. Soc. Am. 65, 1043-1049 (1975).

R. M. A. Azzam, A. R. M. Zaghloul, N. M. Bashara, “Ellipsometric function of a film-substrate system: applications to the design of reflection-type optical devices and to ellipsometry,” J. Opt. Soc. Am. 65, 252-260 (1975).

R. M. A. Azzam, A. R. M. Zaghloul, and N. M. Bashara, “Polarizer-surface-analyzer null ellipsometry for film-substrate systems,” J. Opt. Soc. Am. 65, 1464-1471 (1975).

A. R. M. Zaghloul, “Ellipsometric function of a film-substrate system: applications to the design of reflection-type optical devices and to ellipsometry,” Ph.D. dissertation (University of Nebraska-Lincoln, 1975).

A. R. M. Zaghloul and Y. A. Zaghloul, “Complete system identification of film-substrate systems using single-angle-of-incidence ellipsometry: a fast genetic algorithm,” U.S. patent application 20070024850 (14 July 2006).

Zaghloul, Y. A.

A. R. M. Zaghloul and Y. A. Zaghloul, “Complete system identification of film-substrate systems using single-angle-of-incidence ellipsometry: a fast genetic algorithm,” U.S. patent application 20070024850 (14 July 2006).

Zilong, P.

P. Zilong, L. Zuoyi, H. Yu, T. Liguo, and Y. Xiaofei, “Thickness and refractivity computation in ellipsometry measurement by genetic algorithm,” Proc. SPIE 4077 , 492-495 (2000).

Zuoyi, L.

P. Zilong, L. Zuoyi, H. Yu, T. Liguo, and Y. Xiaofei, “Thickness and refractivity computation in ellipsometry measurement by genetic algorithm,” Proc. SPIE 4077 , 492-495 (2000).

Ann. Phys.

P. Drude, “Uber Oberflaechenschichten. I. Theil,” Ann. Phys. 272, 532-560 (1889).
[CrossRef]

App. Opt.

J. L. Ord and B. L. Wills, “Computer-operated following ellipsometer,” App. Opt. 6, 1673-1677 (1967).

D. E. Aspnes and A. A. Studna, “High precision scanning ellipsometer,” App. Opt. 14, 220-228 (1975).

R. F. Cohn, J. W. Wagner, and J. Kruger, “Dynamic imaging microellipsometry: theory, system design, and feasibility demonstration,” App. Opt. 27, 4664-4671 (1988).

Eng. Applic. Artif. Intell.

Z. Meng, Q. Yang, P. C. Yip, K. G. Eyink, W. T. Taferner, and B. Igelnik, “Combined use of computational intelligence and materials data for on-line monitoring and control of MBE experiments,” Eng. Applic. Artif. Intell. 11, 587-595 (1998).

Infrared Phys.

A. Roseler, “Spectroscopic ellipsometry in the infrared,” Infrared Phys. 21, 349-355 (1981).
[CrossRef]

J. Opt. (Paris)

R. M. A. Azzam and A. R. M. Zaghloul, “Polarization-independent reflectance matching (PIRM)--a technique for the determination of the refractive index and thickness of transparent films,” J. Opt. (Paris) 8, 201-205 (1977).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. D

T. E. Jenkins, “Multiple-angle-of-incidence ellipsometry,” J. Phys. D 32, R45-R56 (1999).

Opt. Commun.

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “An angle-of-incidence tunable SiOs-Si (film-substrate) reflection retarder for the UV mercury line ?=2537Å,” Opt. Commun. 14, 260-262 (1975).

A. R. M. Zaghloul, “Modified O'Bryan ellipsometer (MOE) for film-substrate systems,” Opt. Commun. 27, 1-3 (1978).

R. M. A. Azzam and A. R. M. Zaghloul, “Determination of the refractive index and film thickness of a transparent film on a transparent substrate from the angles of incidence of zero reflection-induced ellipticity,” Opt. Commun. 24, 351-354(1978).

A. R. M. Zaghloul, M. M. El-Bahy, and M. S. Abou-Seada, “Single-element rotating-polarizer (SERP) ellipsometer: film thickness determination,” Opt. Commun. 61, 363-368(1987).

Opt. Eng.

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “SiO2-Si film-substrate single-reflection retarders for different mercury spectral lines,” Opt. Eng. 17, 180-184 (1978).

Proc. SPIE

D. E. Aspnes, “Analysis of semiconductor materials and structures by spectroellipsometry,” Proc. SPIE 946, 84-97(1988).

P. Zilong, L. Zuoyi, H. Yu, T. Liguo, and Y. Xiaofei, “Thickness and refractivity computation in ellipsometry measurement by genetic algorithm,” Proc. SPIE 4077 , 492-495 (2000).

J. Leng, J. J. Sidorowich, and J. L. Opsal, “Multi-domain genetic algorithm (MDGA) and its applications to thin film metrology,” Proc. SPIE 4779, 132-138 (2002).

Rev. Sci. Instrum.

R. W. Collins, “Automatic rotating element ellipsometers: calibration, operation, and real-time applications,” Rev. Sci. Instrum. 61, 2029-2062 (1990).
[CrossRef]

SIAM J. Comput.

J. H. Holland, “Genetic algorithms and the optimal allocation of trials,” SIAM J. Comput. 2, 88-105 (1973).

Surf. Sci.

A. R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, “Inversion of the nonlinear equations of reflection ellipsometry on film-substrate systems,” Surf. Sci. 56, 87-96 (1976).
[CrossRef]

A. R. M. Zaghloul and R. M. A. Azzam, “Single-element rotating-polarizer ellipsometer for film-substrate systems: psi-meter,” Surf. Sci. 96, 168-173 (1980).
[CrossRef]

Thin Solid Films

A. Kudla, “Application of the genetic algorithms in spectroscopic ellipsometry,” Thin Solid Films 455-456, 804-808(2004).
[CrossRef]

G. H. Bu-Abbud, N. M. Bashara, and John A. Woollam, “Variable wavelength, variable angle ellipsometry including a sensitivities correlation test,” Thin Solid Films 138, 27-41 (1986).
[CrossRef]

K. Vedam, “Spectroscopic ellipsometry: a historical overview,” Thin Solid Films 313-314, 1-9 (1998).
[CrossRef]

G. E. Jellison, Jr., “Spectroscopic ellipsometry data analysis: measured versus calculated quantities,” Thin Solid Films 313-314, 33-39 (1998).

A. Laskarakis, S. Logothetidis, E. Pavlopoulou, and M. Gioti, “Muller matrix spectroscopic ellipsometry: formulation and application,” Thin Solid Films 455-456, 43-49 (2004).
[CrossRef]

Other

A. R. M. Zaghloul and Y. A. Zaghloul, “Complete system identification of film-substrate systems using single-angle-of-incidence ellipsometry: a fast genetic algorithm,” U.S. patent application 20070024850 (14 July 2006).

P. C. Yip, Y.-H. Pao, S. R. LeClair, and K. G. Eyink, “A real-time evolutionary algorithm for the in-situ ellipsometer data analysis,” in Proceedings of the International Conference on Neural Information Processing (Springer, 1996), Vol. 2, pp. 827-831.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 2002).

A. R. M. Zaghloul, “Ellipsometric function of a film-substrate system: applications to the design of reflection-type optical devices and to ellipsometry,” Ph.D. dissertation (University of Nebraska-Lincoln, 1975).

D. Goldstein, Polarized Light (Marcel Dekker, 2003).

S. C. Warnick and M. A. Dahleh, “Ellipsometry as a sensor technology for the control of deposition processes,” in Proceedings of the 37th IEEE Conference on Decision and Control (IEEE, 1998). Vol. 3, pp. 3162-3167.

These values are chosen so that the results could be compared with those of .

R. M. A. Azzam and N. M. Bashara, Ellipsometry and Polarized Light, (North-Holland, 1977).

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Figures (3)

Fig. 1
Fig. 1

Average computational effort for 1000 cases, product of the number of generations times the population size, as changed with population sizes from 2 to 100, for the film-identification case of 100 nm at 30 ° .

Fig. 2
Fig. 2

Histogram representing the number of cases that converge at a specific generation, for a total of 1000 case, for the optimum population size of 13, for the film-identification case at 100 nm at 30 ° .

Fig. 3
Fig. 3

Fitness function as changed with N 2 imag ( k 2 ) (middle curve) at the exact value of N 2 real ( n 2 ) , (lower curve) with a + 0.001 ° error, and (upper curve) with a 0.001 ° error for the substrate identification case.

Equations (21)

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ρ = tan ψ e j Δ ,
( r 01 p , r 01 s ) = ( N 1 cos φ 0 N 0 cos φ 1 N 1 cos φ 0 + N 0 cos φ 1 , N 0 cos φ 0 N 1 cos φ 1 N 0 cos φ 0 + N 1 cos φ 1 ) ,
( r 12 p , r 12 s ) = ( N 2 cos φ 1 N 1 cos φ 2 N 2 cos φ 1 + N 1 cos φ 2 , N 1 cos φ 1 N 2 cos φ 2 N 1 cos φ 1 + N 2 cos φ 2 ) ,
N 0 sin φ 0 = N 1 sin φ 1 = N 2 sin φ 2 .
( R p , R s , β ) = ( r 01 p + r 12 p e j 2 β 1 + r 01 p r 12 p e j 2 β , r 01 s + r 12 s e j 2 β 1 + r 01 s r 12 s e j 2 β , 2 π d λ N 1 cos φ 1 ) ,
ρ = R p R s = r 01 p + r 12 p e j 2 β 1 + r 01 p r 12 p e j 2 β 1 + r 01 s r 12 s e j 2 β r 01 s + r 12 s e j 2 β .
( R p , R s ) = ( a + b X 1 + a b X , c + d X 1 + c d X ) .
ρ = A + B X + C X 2 D + E X + F X 2 ,
( a , b , c , d ) = ( r 01 p , r 12 p , r 01 s , r 12 s ) ,
( A , B , C , D , E , F ) = ( a , b + a c d , b c d , c , d + a b c , a b d ) ,
X = exp ( j 4 π d λ N 1 2 N 0 2 sin 2 φ 0 ) = exp ( j 2 π d D φ 0 ) ,
D φ 0 = λ 2 N 1 2 N 0 2 sin 2 φ 0 ,
d = d r + m D φ 0 , 0 d r < D φ 0 .
fitness = abs ( 1 | X | ) .
fitness = 1 / fitness
percentage_fitness = fitness / total_fitness .
| X | = 1.
F F = 1 | X | .
X = ( B ρ E ) ± ( B ρ E ) 2 4 ( C ρ F ) ( A ρ D ) 2 ( C ρ F ) .
d r = j λ ln X 4 π N 1 2 N 0 2 sin 2 ϕ 0 .
d = d r + m λ 2 N 1 2 N 0 2 sin 2 ϕ 0 ,

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