OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 41, Iss. 19 — Jul. 1, 2002
  • pp: 3978–3987

General transfer-matrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference

Charalambos C. Katsidis and Dimitrios I. Siapkas  »View Author Affiliations

Applied Optics, Vol. 41, Issue 19, pp. 3978-3987 (2002)

View Full Text Article

Enhanced HTML    Acrobat PDF (207 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The optical response of coherent thin-film multilayers is often represented with Fresnel coefficients in a 2 × 2 matrix configuration. Here the usual transfer matrix was modified to a generic form, with the ability to use the absolute squares of the Fresnel coefficients, so as to include incoherent (thick layers) and partially coherent (rough surface or interfaces) reflection and transmission. The method is integrated by use of models for refractive-index depth profiling. The utility of the method is illustrated with various multilayer structures formed by ion implantation into Si, including buried insulating and conducting layers, and multilayers with a thick incoherent layer in an arbitrary position.

© 2002 Optical Society of America

OCIS Codes
(080.2730) Geometric optics : Matrix methods in paraxial optics
(240.0310) Optics at surfaces : Thin films
(240.5770) Optics at surfaces : Roughness
(300.6340) Spectroscopy : Spectroscopy, infrared
(300.6470) Spectroscopy : Spectroscopy, semiconductors
(310.6860) Thin films : Thin films, optical properties

Original Manuscript: June 27, 2001
Revised Manuscript: January 14, 2002
Published: July 1, 2002

Charalambos C. Katsidis and Dimitrios I. Siapkas, "General transfer-matrix method for optical multilayer systems with coherent, partially coherent, and incoherent interference," Appl. Opt. 41, 3978-3987 (2002)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Born, E. Wolf, Principles of Optics (MacMillan, New York, 1964), p. 254.
  2. O. S. Heavens, Optical Properties of Thin Films (Dover, New York, 1965), p. 69.
  3. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), p. 102.
  4. Z. Knittl, Optics of Thin Films (Wiley, London, 1976), p. 41.
  5. G. K. Hubler, P. R. Malmberg, C. N. Waddell, W. G. Spitzer, J. E. Fredrickson, in Ion Implantation for Materials Processing, F. A. Smidt, ed. (Noyes Data, Park Ridge, N.J., 1983), p. 195–218.
  6. W. Tennant, J. Cape, “Study of the dielectric function of PbSnTe epitaxial film by far-infrared reflectivity,” Phys. Rev. B 13, 2540–2547 (1976). [CrossRef]
  7. C. C. Katsidis, D. I. Siapkas, W. Skorupa, N. Hatzopoulos, D. Panknin, Proceedings of the 10th International Conference on Ion Implantation Technology (Elsevier, Amsterdam, 1995), p. 959–962.
  8. C. C. Katsidis, D. I. Siapkas, in Proceedings of NATO ASI on Application of Particle and Laser Beams in Materials Technology, P. Misaelides, ed. (Kluwer Academic, Dordrecht, 1995), p. 603–612. [CrossRef]
  9. C. C. Katsidis, D. I. Siapkas, D. Panknin, N. Hatzopoulos, W. Skorupa, “Optical characterization of doped Simox structures using FTIR spectroscopy,” Microelectron. Eng. 28, 439–442 (1995). [CrossRef]
  10. N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, “Oxide growth, refractive index, and composition depth profiles of structures formed by 2 MeV oxygen implantation into silicon,” J. Appl. Phys. 77, 577–586 (1995). [CrossRef]
  11. D. I. Siapkas, N. Hatzopoulos, C. C. Katsidis, T. Zorba, C. L. Mitsas, P. L. F. Hemment, “Structural and compositional characterization of high energy separation by implantation of oxygen structures using infrared spectroscopy,” J. Electrochem. Soc. 143, 3019–3032 (1996). [CrossRef]
  12. N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, W. Skorupa, “Formation and characterization of novel Si/SiO2 multilayer structures by oxygen ion implantation into silicon,” J. Appl. Phys. 80, 4960–4970 (1996). [CrossRef]
  13. N. Hatzopoulos, D. I. Siapkas, P. L. F. Hemment, “Optical investigation of structures formed by 2MeV oxygen implantation into silicon,” Thin Solid Films 289, 90–94 (1996). [CrossRef]
  14. C. L. Mitsas, D. I. Siapkas, “Generalized matrix method for analysis of coherent and incoherent reflectance and transmittance of multiplayer structures with rough surfaces, interfaces, and finite substrates,” Appl. Opt. 34, 1678–1683 (1995). [CrossRef] [PubMed]
  15. G. Lubberts, B. C. Burkey, F. Moser, E. A. Trabka, “Optical properties of phosphorous-doped polycrystalline silicon layers,” J. Appl. Phys. 52, 6870–6878 (1981). [CrossRef]
  16. I. Fillinski, “The effects of sample imperfections on optical spectra,” Phys. Status Solidi 49, 577–588 (1972). [CrossRef]
  17. J. Szczyrbowski, A. Czapla, “Optical absorption in d.c. sputtered InAs films,” Thin Solid Films 46, 127–137 (1977). [CrossRef]
  18. J. Pawlikovski, “Comments on the determination of the absorption coefficient of thin semiconductor films,” Thin Solid Films 127, 29–38 (1985). [CrossRef]
  19. H. E. Bennett, J. O. Porteus, “Relation between surface roughness and specular reflectance at normal incidence,” J. Opt. Soc. Am. 51, 123–129 (1961). [CrossRef]
  20. A. Tikhonravov, M. Trubetskov, B. Sullivan, J. Dobrowolski, “Influence of small inhomogeneities on the spectral characteristics of single thin films,” Appl. Opt. 36, 7188–7198 (1997). [CrossRef]
  21. A. Roos, M. Bergquist, C. Ribbing, “Determination of the SiO2/Si interface roughness by diffuse reflectance measurements,” Appl. Opt. 27, 4660–4663 (1988). [CrossRef] [PubMed]
  22. A. Roos, M. Bergquist, C. Ribbing, “Optical scattering from oxidized metals. 1. Model formulation and properties,” Appl. Opt. 28, 1360–1364 (1989). [CrossRef] [PubMed]
  23. A. M. Dioffo, “Étude théorique des caractéristiques optiques d’un système de lames diélectriques,” Rev. Opt. 47, 49–68 (1968).
  24. C. J. Gabriel, A. Nedoluha, “Transmittance and reflectance of systems of thin and thick layers,” Opt. Acta 18, 415–423 (1971). [CrossRef]
  25. R. Z. Vitlina, G. I. Surdutovich, “A ‘blurred film’ model in polarized light reflectometry for characterization of thick films and surface layers,” J. Phys. D. Appl. Phys. 34, 2593–2598 (2001). [CrossRef]
  26. R. Swanepoel, “Determination of the thickness and optical constants of amorphous silicon,” J. Phys. E 16, 1214–1222 (1983). [CrossRef]
  27. C. C. Katsidis, D. I. Siapkas, A. K. Robinson, P. L. F. Hemment, “Formation of conducting and insulating layered structures in Si by ion implantation: process control using FTIR spectroscopy,” J. Electrochem. Soc. 148, G704–G716 (2001). [CrossRef]
  28. A. K. Robinson, K. J. Reeson, P. L. F. Hemment, “Redistribution and electrical activation of implanted arsenic in silicon on insulator substrates formed by oxygen ion implantation,” J. Appl. Phys. 68, 4340–4342 (1990). [CrossRef]
  29. Z. Wenhua, L. Chenglu, S. Zuoyu, Z. Shichang, P. L. F. Hemment, A. Nejim, “Electrical characterization of thin film Simox structures,” Nucl. Instrum. Meth. B 74, 218–221 (1993). [CrossRef]
  30. J. Stoemenos, A. Carcia, B. Aspar, J. Margail, “Silicon on insulator obtained by high dose oxygen implantation, microstructure, and formation mechanism,” J. Electrochem. Soc. 142, 1248–1259 (1995). [CrossRef]
  31. N. Hatzopoulos, W. Skorupa, D. Siapkas, “Double Simox structures formed by sequential high energy oxygen implantation into silicon,” J. Electrochem. Soc. 147, 354–362 (2000). [CrossRef]
  32. D. I. Siapkas, D. B. Kushev, N. N. Zheleva, J. Siapkas, I. Lelidis, “Optical constants of tin-telluride determined from infrared interference spectra,” Infrared Phys. 31, 425–433 (1991). [CrossRef]
  33. K. Krishnan, P. J. Stout, M. Watanabe, Practical Fourier Transform Infrared Spectroscopy (Academic, New York, 1990), p. 294.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited