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Applied Optics

Applied Optics


  • Vol. 30, Iss. 7 — Mar. 1, 1991
  • pp: 839–846

Two-step regression procedure for the optical characterization of thin films

S. V. Babu, Moses David, and Ramesh C. Patel  »View Author Affiliations

Applied Optics, Vol. 30, Issue 7, pp. 839-846 (1991)

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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

Original Manuscript: January 5, 1990
Published: March 1, 1991

S. V. Babu, Moses David, and Ramesh C. Patel, "Two-step regression procedure for the optical characterization of thin films," Appl. Opt. 30, 839-846 (1991)

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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]

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