Abstract

A diode array rapid scan spectrometer is used for measuring the intensity of polychromatic light in the 300–420-nm range reflected from a diamondlike carbon film as a function of wavelength. With a fixed grating setting, the wavelength range of 120 nm can be covered in 23 ms. From the reflected intensity, a new two-step regression procedure is utilized to determine refractive index, bandgap, slope of the absorption edge, and film thickness. The calculated parameters are independent of the starting set and the sequence of parameter estimation. The accuracy of the regression procedure is verified by comparison to the envelope method. It is shown using simulated data that, for strongly absorbing films, the new regression procedure is more accurate than the envelope method. The new regression method can handle very noisy reflectance spectra also.

© 1991 Optical Society of America

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References

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  1. F. Rodriguez, P. D. Krasicky, R. J. Groele, “Dissolution Rate Measurements,” Solid State Technol. 5, 125 (1985).
  2. B. Vidal, A. Fornier, E. Pelletier, “Optical Monitoring of Nonquarterwave Multilayer Filters,” Appl. Opt. 18, 3851–3856 (1979).
    [PubMed]
  3. F. J. Van Milligen et al., “Development of an Automated Scanning Monochromator for Monitoring of Thin Films,” Appl. Opt. 24, 1799–1802 (1985).
    [CrossRef] [PubMed]
  4. L. Li, Y. Yen, “Wideband Monitoring and Measuring System for Optical Coatings,” Appl. Opt. 28, 2889–2894 (1989).
    [CrossRef] [PubMed]
  5. B. Bovard, F. J. Van Milligen, M. J. Messerly, S. G. Saxe, H. A. Macleod, “Optical Constants Derivation for an Inhomogeneous Thin Film from in situ Transmission Measurements,” Appl. Opt. 24, 1803–1807 (1985).
    [CrossRef] [PubMed]
  6. D. A. Minkov, “Method for Determining the Optical Constants of a Thin Film on a Transparent Substrate,” J. Phys. D 22, 199 (1989).
    [CrossRef]
  7. I. Ohlidahl, K. Navratil, “Simple Method of Spectroscopic Reflectometry for the Complete Optical Analysis of Weakly Absorbing Thin Films: Application to Silicon Films,” Thin Solid Films 156, 182 (1988).
  8. J. P. Borgogno, B. Lazarides, E. Pelletier, “Automatic Determination of the Optical Constants, of Inhomogeneous Thin Films,” Appl. Opt. 21, 4020–4029 (1982).
    [CrossRef] [PubMed]
  9. L. S. Miller, A. J. Walder, P. Linsell, A. Blundell, “Reflectometry Measurement of Optical Parameters of Au/SiO2/Si Films,” Thin Solid Films 165, 11 (1988).
    [CrossRef]
  10. J. C. Manifacier, J. Gasiot, J. P. Fillard, “A Simple Method for the Determination of the Optical Constants n1, k and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. E 9, 1002 (1976).
    [CrossRef]
  11. E. Pelletier, P. Roche, B. Vidal, “Determination Automatique des Constantes Optiques et de Epaisseur des Couches Minces: Application aux Couches Dielectriques,” Nouv. Rev. Opt. 7, 353 (1976).
    [CrossRef]
  12. O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).
  13. N. F. Mott, E. A. Davis, Electronic Processes in Non-Crystalline Materials (Clarendon, Oxford, 1979).
  14. K. Levenberg, “A Method for the Solution of Certain Problems in Least Squares,” Q. Appl. Math. 2, 164 (1944).
  15. D. Marquardt, “An Algorithm for Least-Squares Estimation of Non-Linear Parameters,” SIAM J. Appl. Math. 11, 431 (1963).
    [CrossRef]
  16. M. David, S. V. Babu, B. Flint, “Optical Characterization of DLC, AlN and SiC Thin Films,” Appl. Phys. Lett. 57, 1093–1095 (1990).
    [CrossRef]
  17. R. C. Weast, Ed., Handbook of Chemistry and Physics (CRC Press, Boca Raton, FL, 1986).
  18. H. H. Madden, “Comments on the Savitzky-Golay Convolution Method for Least-Squares Fit Smoothing and Differentiation of Digital Data,” Anal. Chem. 50, 1383 (1978).
    [CrossRef]
  19. V. Natarajan, J. D. Lamb, J. A. Wollam, D. C. Lin, D. A. Gulino, “Diamondlike Carbon Films: Optical Absorption, Dielectric Properties, and Hardness Dependence on Deposition Parameters,” J. Vac. Sci. Technol. A 3, No. 3, 681 (1985).
    [CrossRef]
  20. M. Hirose, Plasma Deposited Thin Films, J. Mort, F. Jansen, Eds. (CRC Press, Boca Raton, FL, 1986).
  21. F. Hasegawa, T. Takahashi, K. Kubo, Y. Nannichi, “Plasma CVD of Amorphous AlN from Metalorganic Al Source and Properties of the Deposited Films,” Jpn. J. Appl. Phys. 26, 1555 (1987).
    [CrossRef]

1990 (1)

M. David, S. V. Babu, B. Flint, “Optical Characterization of DLC, AlN and SiC Thin Films,” Appl. Phys. Lett. 57, 1093–1095 (1990).
[CrossRef]

1989 (2)

D. A. Minkov, “Method for Determining the Optical Constants of a Thin Film on a Transparent Substrate,” J. Phys. D 22, 199 (1989).
[CrossRef]

L. Li, Y. Yen, “Wideband Monitoring and Measuring System for Optical Coatings,” Appl. Opt. 28, 2889–2894 (1989).
[CrossRef] [PubMed]

1988 (2)

L. S. Miller, A. J. Walder, P. Linsell, A. Blundell, “Reflectometry Measurement of Optical Parameters of Au/SiO2/Si Films,” Thin Solid Films 165, 11 (1988).
[CrossRef]

I. Ohlidahl, K. Navratil, “Simple Method of Spectroscopic Reflectometry for the Complete Optical Analysis of Weakly Absorbing Thin Films: Application to Silicon Films,” Thin Solid Films 156, 182 (1988).

1987 (1)

F. Hasegawa, T. Takahashi, K. Kubo, Y. Nannichi, “Plasma CVD of Amorphous AlN from Metalorganic Al Source and Properties of the Deposited Films,” Jpn. J. Appl. Phys. 26, 1555 (1987).
[CrossRef]

1985 (4)

V. Natarajan, J. D. Lamb, J. A. Wollam, D. C. Lin, D. A. Gulino, “Diamondlike Carbon Films: Optical Absorption, Dielectric Properties, and Hardness Dependence on Deposition Parameters,” J. Vac. Sci. Technol. A 3, No. 3, 681 (1985).
[CrossRef]

F. J. Van Milligen et al., “Development of an Automated Scanning Monochromator for Monitoring of Thin Films,” Appl. Opt. 24, 1799–1802 (1985).
[CrossRef] [PubMed]

B. Bovard, F. J. Van Milligen, M. J. Messerly, S. G. Saxe, H. A. Macleod, “Optical Constants Derivation for an Inhomogeneous Thin Film from in situ Transmission Measurements,” Appl. Opt. 24, 1803–1807 (1985).
[CrossRef] [PubMed]

F. Rodriguez, P. D. Krasicky, R. J. Groele, “Dissolution Rate Measurements,” Solid State Technol. 5, 125 (1985).

1982 (1)

1979 (1)

1978 (1)

H. H. Madden, “Comments on the Savitzky-Golay Convolution Method for Least-Squares Fit Smoothing and Differentiation of Digital Data,” Anal. Chem. 50, 1383 (1978).
[CrossRef]

1976 (2)

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A Simple Method for the Determination of the Optical Constants n1, k and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. E 9, 1002 (1976).
[CrossRef]

E. Pelletier, P. Roche, B. Vidal, “Determination Automatique des Constantes Optiques et de Epaisseur des Couches Minces: Application aux Couches Dielectriques,” Nouv. Rev. Opt. 7, 353 (1976).
[CrossRef]

1963 (1)

D. Marquardt, “An Algorithm for Least-Squares Estimation of Non-Linear Parameters,” SIAM J. Appl. Math. 11, 431 (1963).
[CrossRef]

1944 (1)

K. Levenberg, “A Method for the Solution of Certain Problems in Least Squares,” Q. Appl. Math. 2, 164 (1944).

Babu, S. V.

M. David, S. V. Babu, B. Flint, “Optical Characterization of DLC, AlN and SiC Thin Films,” Appl. Phys. Lett. 57, 1093–1095 (1990).
[CrossRef]

Blundell, A.

L. S. Miller, A. J. Walder, P. Linsell, A. Blundell, “Reflectometry Measurement of Optical Parameters of Au/SiO2/Si Films,” Thin Solid Films 165, 11 (1988).
[CrossRef]

Borgogno, J. P.

Bovard, B.

David, M.

M. David, S. V. Babu, B. Flint, “Optical Characterization of DLC, AlN and SiC Thin Films,” Appl. Phys. Lett. 57, 1093–1095 (1990).
[CrossRef]

Davis, E. A.

N. F. Mott, E. A. Davis, Electronic Processes in Non-Crystalline Materials (Clarendon, Oxford, 1979).

Fillard, J. P.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A Simple Method for the Determination of the Optical Constants n1, k and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. E 9, 1002 (1976).
[CrossRef]

Flint, B.

M. David, S. V. Babu, B. Flint, “Optical Characterization of DLC, AlN and SiC Thin Films,” Appl. Phys. Lett. 57, 1093–1095 (1990).
[CrossRef]

Fornier, A.

Gasiot, J.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A Simple Method for the Determination of the Optical Constants n1, k and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. E 9, 1002 (1976).
[CrossRef]

Groele, R. J.

F. Rodriguez, P. D. Krasicky, R. J. Groele, “Dissolution Rate Measurements,” Solid State Technol. 5, 125 (1985).

Gulino, D. A.

V. Natarajan, J. D. Lamb, J. A. Wollam, D. C. Lin, D. A. Gulino, “Diamondlike Carbon Films: Optical Absorption, Dielectric Properties, and Hardness Dependence on Deposition Parameters,” J. Vac. Sci. Technol. A 3, No. 3, 681 (1985).
[CrossRef]

Hasegawa, F.

F. Hasegawa, T. Takahashi, K. Kubo, Y. Nannichi, “Plasma CVD of Amorphous AlN from Metalorganic Al Source and Properties of the Deposited Films,” Jpn. J. Appl. Phys. 26, 1555 (1987).
[CrossRef]

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).

Hirose, M.

M. Hirose, Plasma Deposited Thin Films, J. Mort, F. Jansen, Eds. (CRC Press, Boca Raton, FL, 1986).

Krasicky, P. D.

F. Rodriguez, P. D. Krasicky, R. J. Groele, “Dissolution Rate Measurements,” Solid State Technol. 5, 125 (1985).

Kubo, K.

F. Hasegawa, T. Takahashi, K. Kubo, Y. Nannichi, “Plasma CVD of Amorphous AlN from Metalorganic Al Source and Properties of the Deposited Films,” Jpn. J. Appl. Phys. 26, 1555 (1987).
[CrossRef]

Lamb, J. D.

V. Natarajan, J. D. Lamb, J. A. Wollam, D. C. Lin, D. A. Gulino, “Diamondlike Carbon Films: Optical Absorption, Dielectric Properties, and Hardness Dependence on Deposition Parameters,” J. Vac. Sci. Technol. A 3, No. 3, 681 (1985).
[CrossRef]

Lazarides, B.

Levenberg, K.

K. Levenberg, “A Method for the Solution of Certain Problems in Least Squares,” Q. Appl. Math. 2, 164 (1944).

Li, L.

Lin, D. C.

V. Natarajan, J. D. Lamb, J. A. Wollam, D. C. Lin, D. A. Gulino, “Diamondlike Carbon Films: Optical Absorption, Dielectric Properties, and Hardness Dependence on Deposition Parameters,” J. Vac. Sci. Technol. A 3, No. 3, 681 (1985).
[CrossRef]

Linsell, P.

L. S. Miller, A. J. Walder, P. Linsell, A. Blundell, “Reflectometry Measurement of Optical Parameters of Au/SiO2/Si Films,” Thin Solid Films 165, 11 (1988).
[CrossRef]

Macleod, H. A.

Madden, H. H.

H. H. Madden, “Comments on the Savitzky-Golay Convolution Method for Least-Squares Fit Smoothing and Differentiation of Digital Data,” Anal. Chem. 50, 1383 (1978).
[CrossRef]

Manifacier, J. C.

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A Simple Method for the Determination of the Optical Constants n1, k and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. E 9, 1002 (1976).
[CrossRef]

Marquardt, D.

D. Marquardt, “An Algorithm for Least-Squares Estimation of Non-Linear Parameters,” SIAM J. Appl. Math. 11, 431 (1963).
[CrossRef]

Messerly, M. J.

Miller, L. S.

L. S. Miller, A. J. Walder, P. Linsell, A. Blundell, “Reflectometry Measurement of Optical Parameters of Au/SiO2/Si Films,” Thin Solid Films 165, 11 (1988).
[CrossRef]

Minkov, D. A.

D. A. Minkov, “Method for Determining the Optical Constants of a Thin Film on a Transparent Substrate,” J. Phys. D 22, 199 (1989).
[CrossRef]

Mott, N. F.

N. F. Mott, E. A. Davis, Electronic Processes in Non-Crystalline Materials (Clarendon, Oxford, 1979).

Nannichi, Y.

F. Hasegawa, T. Takahashi, K. Kubo, Y. Nannichi, “Plasma CVD of Amorphous AlN from Metalorganic Al Source and Properties of the Deposited Films,” Jpn. J. Appl. Phys. 26, 1555 (1987).
[CrossRef]

Natarajan, V.

V. Natarajan, J. D. Lamb, J. A. Wollam, D. C. Lin, D. A. Gulino, “Diamondlike Carbon Films: Optical Absorption, Dielectric Properties, and Hardness Dependence on Deposition Parameters,” J. Vac. Sci. Technol. A 3, No. 3, 681 (1985).
[CrossRef]

Navratil, K.

I. Ohlidahl, K. Navratil, “Simple Method of Spectroscopic Reflectometry for the Complete Optical Analysis of Weakly Absorbing Thin Films: Application to Silicon Films,” Thin Solid Films 156, 182 (1988).

Ohlidahl, I.

I. Ohlidahl, K. Navratil, “Simple Method of Spectroscopic Reflectometry for the Complete Optical Analysis of Weakly Absorbing Thin Films: Application to Silicon Films,” Thin Solid Films 156, 182 (1988).

Pelletier, E.

Roche, P.

E. Pelletier, P. Roche, B. Vidal, “Determination Automatique des Constantes Optiques et de Epaisseur des Couches Minces: Application aux Couches Dielectriques,” Nouv. Rev. Opt. 7, 353 (1976).
[CrossRef]

Rodriguez, F.

F. Rodriguez, P. D. Krasicky, R. J. Groele, “Dissolution Rate Measurements,” Solid State Technol. 5, 125 (1985).

Saxe, S. G.

Takahashi, T.

F. Hasegawa, T. Takahashi, K. Kubo, Y. Nannichi, “Plasma CVD of Amorphous AlN from Metalorganic Al Source and Properties of the Deposited Films,” Jpn. J. Appl. Phys. 26, 1555 (1987).
[CrossRef]

Van Milligen, F. J.

Vidal, B.

B. Vidal, A. Fornier, E. Pelletier, “Optical Monitoring of Nonquarterwave Multilayer Filters,” Appl. Opt. 18, 3851–3856 (1979).
[PubMed]

E. Pelletier, P. Roche, B. Vidal, “Determination Automatique des Constantes Optiques et de Epaisseur des Couches Minces: Application aux Couches Dielectriques,” Nouv. Rev. Opt. 7, 353 (1976).
[CrossRef]

Walder, A. J.

L. S. Miller, A. J. Walder, P. Linsell, A. Blundell, “Reflectometry Measurement of Optical Parameters of Au/SiO2/Si Films,” Thin Solid Films 165, 11 (1988).
[CrossRef]

Wollam, J. A.

V. Natarajan, J. D. Lamb, J. A. Wollam, D. C. Lin, D. A. Gulino, “Diamondlike Carbon Films: Optical Absorption, Dielectric Properties, and Hardness Dependence on Deposition Parameters,” J. Vac. Sci. Technol. A 3, No. 3, 681 (1985).
[CrossRef]

Yen, Y.

Anal. Chem. (1)

H. H. Madden, “Comments on the Savitzky-Golay Convolution Method for Least-Squares Fit Smoothing and Differentiation of Digital Data,” Anal. Chem. 50, 1383 (1978).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. Lett. (1)

M. David, S. V. Babu, B. Flint, “Optical Characterization of DLC, AlN and SiC Thin Films,” Appl. Phys. Lett. 57, 1093–1095 (1990).
[CrossRef]

J. Phys. D (1)

D. A. Minkov, “Method for Determining the Optical Constants of a Thin Film on a Transparent Substrate,” J. Phys. D 22, 199 (1989).
[CrossRef]

J. Phys. E (1)

J. C. Manifacier, J. Gasiot, J. P. Fillard, “A Simple Method for the Determination of the Optical Constants n1, k and the Thickness of a Weakly Absorbing Thin Film,” J. Phys. E 9, 1002 (1976).
[CrossRef]

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

V. Natarajan, J. D. Lamb, J. A. Wollam, D. C. Lin, D. A. Gulino, “Diamondlike Carbon Films: Optical Absorption, Dielectric Properties, and Hardness Dependence on Deposition Parameters,” J. Vac. Sci. Technol. A 3, No. 3, 681 (1985).
[CrossRef]

Jpn. J. Appl. Phys. (1)

F. Hasegawa, T. Takahashi, K. Kubo, Y. Nannichi, “Plasma CVD of Amorphous AlN from Metalorganic Al Source and Properties of the Deposited Films,” Jpn. J. Appl. Phys. 26, 1555 (1987).
[CrossRef]

Nouv. Rev. Opt. (1)

E. Pelletier, P. Roche, B. Vidal, “Determination Automatique des Constantes Optiques et de Epaisseur des Couches Minces: Application aux Couches Dielectriques,” Nouv. Rev. Opt. 7, 353 (1976).
[CrossRef]

Q. Appl. Math. (1)

K. Levenberg, “A Method for the Solution of Certain Problems in Least Squares,” Q. Appl. Math. 2, 164 (1944).

SIAM J. Appl. Math. (1)

D. Marquardt, “An Algorithm for Least-Squares Estimation of Non-Linear Parameters,” SIAM J. Appl. Math. 11, 431 (1963).
[CrossRef]

Solid State Technol. (1)

F. Rodriguez, P. D. Krasicky, R. J. Groele, “Dissolution Rate Measurements,” Solid State Technol. 5, 125 (1985).

Thin Solid Films (2)

L. S. Miller, A. J. Walder, P. Linsell, A. Blundell, “Reflectometry Measurement of Optical Parameters of Au/SiO2/Si Films,” Thin Solid Films 165, 11 (1988).
[CrossRef]

I. Ohlidahl, K. Navratil, “Simple Method of Spectroscopic Reflectometry for the Complete Optical Analysis of Weakly Absorbing Thin Films: Application to Silicon Films,” Thin Solid Films 156, 182 (1988).

Other (4)

O. S. Heavens, Optical Properties of Thin Solid Films (Dover, New York, 1965).

N. F. Mott, E. A. Davis, Electronic Processes in Non-Crystalline Materials (Clarendon, Oxford, 1979).

M. Hirose, Plasma Deposited Thin Films, J. Mort, F. Jansen, Eds. (CRC Press, Boca Raton, FL, 1986).

R. C. Weast, Ed., Handbook of Chemistry and Physics (CRC Press, Boca Raton, FL, 1986).

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Figures (6)

Fig. 1
Fig. 1

Verification of Eq. (9) for data simulated using different values of n2d and equation set (1)(8). The simulated data points are represented by symbols, while the straight lines are linear fits of the data.

Fig. 2
Fig. 2

Simulated data show the lack of correlation between the sum of squares of error (SSE) and the derivation from the true solution when the extrema are not matched. Here the deviation of curves A and B is measured from C.

Fig. 3
Fig. 3

Schematic of the experimental setup used for measuring reflectance.

Fig. 4
Fig. 4

Comparison of the experimental DLC film reflectance and the two-step regression solution.

Fig. 5
Fig. 5

Linear dependence of 1/λ with the order of extrema indicates negligible dispersion in the refractive index of the DLC film in the scanned wavelength range. Experimental data points are represented by symbols, while the straight line is a linear fit of the data.

Fig. 6
Fig. 6

Example of simulated data used for the two-step regression analysis. The noise level is measured as a percentage of the maximum amplitude of the reflectance oscillation.

Tables (5)

Tables Icon

Table I DLC Film Parameters Estimated by Regression and Published Literature Values19

Tables Icon

Table II Parameters Calculated by the Two-Step Regression Method for Different Values of k2 and Noise Levelsa

Tables Icon

Table III Comparison of the Accuracy of Two-Step Regression and Envelope Methods Using Data Simulated with the Parameters d = 1000 nm, n1 = 1.0, n2 = 2.0, n3 = 3.5, k1 = k3 = 0.0 in the 300–420-nm Wavelength Rangea

Tables Icon

Table IV Comparison of the Accuracy of Two-Step Regression and Envelope Methods Using Data Simulated with the Parameters d = 215 nm, n1 = 1.0, n2 = 4.25, n3 = 1.5, k1 = k3 = 0.0 in the 400–900-nm Wavelength Rangea

Tables Icon

Table V Examples of 1-μm Thick Films for Which αd ≫ 1

Equations (14)

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

R = R R * ,
R = r 1 + r 2 t 1 t 1 exp ( 2 i δ ) 1 + r 1 r 2 exp ( 2 i δ ) ,
r 1 = n 1 n 2 n 1 + n 2 ;
r 1 = n 2 n 3 n 2 + n 3 ;
t 1 = 2 n 1 n 1 + n 2 ;
t 1 = 2 n 2 n 1 + n 2 .
α h ν = m ( h ν E g ) 2 ;
α = 4 π k λ .
λ m = ( m 4 n 2 d ) 1 m = 1 , 2 , ,
1 λ m = m 0 4 n 2 d + m 4 n 2 d .
n 2 = A + B λ 2 + C λ 4 ,
n 2 d = A d + B d λ 2 + C d λ 4 = A + B λ 2 + C λ 4 .
R = ( I m I d I q I d ) × R q
λ = a X + b ,

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