No Access Submitted: 30 July 2019 Accepted: 24 September 2019 Published Online: 11 October 2019
Journal of Vacuum Science & Technology B 37, 062909 (2019);
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  • Jiří Vohánka
  • David Nečas
  • Daniel Franta
The broadening of a sharp (unbroadened) dielectric function is a fruitful approach to the construction of models of dielectric response of materials. It naturally includes structural disorder or finite state lifetime and allows parameterization of such effects. The unbroadened function is often taken as a piecewise polynomial. Broadening it with the Lorentzian then leads to relatively simple analytical formulae. The Gaussian broadening, however, requires evaluation of several special functions, including the antiderivative of the Dawson function which is not generally available in mathematical libraries. Recently, the authors described the simple recurrent formulae for the construction of a Gaussian-broadened piecewise polynomial model of a complex dielectric function using three special functions, the error function, the Dawson function, and its antiderivative. In this paper, for the Dawson function and its antiderivative an efficient evaluation method is developed enabling the utilization of this model in optical spectra fitting. The effectiveness of this approach is illustrated using elementary and real-world examples of complex dielectric function models.
This research was supported by Project Nos. LO1411 (NPU I) and LQ1601 (NPU II) funded by the Ministry of Education, Youth and Sports of Czech Republic.
  1. 1. S. Adachi, Phys. Rev. B 35, 7454 (1987)., Google ScholarCrossref, ISI
  2. 2. S. Adachi, Phys. Rev. B 38, 12966 (1988)., Google ScholarCrossref
  3. 3. C. C. Kim, J. W. Garland, H. Abad, and P. M. Raccah, Phys. Rev. B 45, 11749 (1992)., Google ScholarCrossref, ISI
  4. 4. C. Tanguy, Solid State Commun. 98, 65 (1996)., Google ScholarCrossref
  5. 5. B. D. Johs, C. M. Herzinger, J. H. Dinan, A. Cornfeld, and J. D. Benson, Thin Solid Films 313–314, 137 (1998)., Google ScholarCrossref, ISI
  6. 6. A. B. Djurišić and E. H. Li, Phys. Status Solidi B 216, 199 (1999).<199::AID-PSSB199>3.0.CO;2-X, Google ScholarCrossref
  7. 7. Y. S. Ihn, T. J. Kim, T. H. Ghong, Y. Kim, D. E. Aspnes, and J. Kossut, Thin Solid Films 455–456, 222 (2004)., Google ScholarCrossref
  8. 8. D. Franta, D. Nečas, L. Zajíčková, and I. Ohlídal, Thin Solid Films 571, 496 (2014)., Google ScholarCrossref
  9. 9. D. Franta, J. Vohánka, and M. Čermák, Universal dispersion model for characterization of thin films over wide spectral range, in Optical Characterization of Thin Solid Films, Springer Series in Surface Sciences Vol. 64, edited by O. Stenzel and M. Ohlídal (Springer, Berlin, 2018), pp. 31–82. Google Scholar
  10. 10. B. Johs and J. S. Hale, Phys. Status Solidi A 205, 715 (2008)., Google ScholarCrossref
  11. 11. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, edited by M. Abramowitz and I. A. Stegun (National Bureau of Standards, Gaithersburg, MD, 1964). Google Scholar
  12. 12. M. E. Thomas, S. K. Andersson, R. M. Sova, and R. I. Joseph, Infrared Phys. Technol. 39, 235 (1998)., Google ScholarCrossref
  13. 13. D. De Sousa Meneses, M. Malki, and P. Echegut, J. Non-Cryst. Solids 352, 769 (2006)., Google ScholarCrossref, ISI
  14. 14. J. Humlíček, J. Quant. Spectrosc. Radiat. Transfer 27, 437 (1982)., Google ScholarCrossref
  15. 15. R. Brendel and D. Bormann, J. Appl. Phys. 71, 1 (1992)., Google ScholarCrossref, ISI
  16. 16. D. De Sousa Meneses, G. Gruener, M. Malki, and P. Echegut, J. Non-Cryst. Solids 351, 124 (2005)., Google ScholarCrossref
  17. 17. S. M. Abrarov and B. M. Quine, Appl. Math. Comput. 218, 1894 (2011)., Google ScholarCrossref
  18. 18. J. Kischkat et al., Appl. Opt. 71, 6789 (2012)., Google ScholarCrossref
  19. 19. “GNU Scientific Library,” see Google Scholar
  20. 20. “libcerf,” see Google Scholar
  21. 21. W. J. Cody, K. A. Paciorek, and H. C. Thacher, Math. Comput. 24, 171 (1970)., Google ScholarCrossref
  22. 22. E. Y. Remez, General Computational Methods of Chebyshev Approximation: The Problems with Linear Real Parameters (U.S. Atomic Energy Commission, Oak Ridge, TN, 1962). Google Scholar
  23. 23. D. Franta et al., “Software for optical characterization newAD2,” see Google Scholar
  24. 24. D. Franta, A. Dubroka, C. Wang, A. Giglia, J. Vohánka, P. Franta, and I. Ohlídal, Appl. Surf. Sci. 421, 405 (2017)., Google ScholarCrossref
  25. 25. D. Franta, D. Nečas, L. Zajíčková, and I. Ohlídal, Opt. Mater. Express 4, 1641 (2014)., Google ScholarCrossref
  26. 26. W. Romberg, Det Kongelige Norske Videnskabers Selskab Forhandlinger, Trondheim 28, 30 (1955). Google Scholar
  27. 27. See supplementary material at for C implementation of the functions D(x) and Di(x). Google Scholar
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