OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 11 — May. 26, 2008
  • pp: 7789–7803

Influence of cross-correlation effects on the optical quantities of rough films

Daniel Franta, Ivan Ohlídal, and David Nečas  »View Author Affiliations


Optics Express, Vol. 16, Issue 11, pp. 7789-7803 (2008)
http://dx.doi.org/10.1364/OE.16.007789


View Full Text Article

Enhanced HTML    Acrobat PDF (332 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Within the Rayleigh–Rice theory the influence of layer boundary roughness on coherently reflected light is expressed using very complex formulae. Therefore we deal with the simplification of these formulae by employing an approximation based on neglecting cross-correlation effects between both the rough boundaries. It is shown that if the mean distance of the boundaries (mean thickness) is sufficiently large in comparison with the lateral dimensions of the roughness it is possible to describe the individual boundaries of the layers by matrices corresponding to isolated rough surfaces. This fact enables us to simplify the formulae for the optical quantities in a substantial way, which also simplifies the numerical calculation needed for the inverse problem. This statement is illustrated by means of a numerical analysis simulating ellipsometric and reflectometric data of rough silicon dioxide layers placed onto silicon single crystal substrates.

© 2008 Optical Society of America

OCIS Codes
(240.0310) Optics at surfaces : Thin films
(240.5770) Optics at surfaces : Roughness
(240.2130) Optics at surfaces : Ellipsometry and polarimetry

ToC Category:
Optics at Surfaces

History
Original Manuscript: May 5, 2008
Revised Manuscript: May 12, 2008
Manuscript Accepted: May 13, 2008
Published: May 14, 2008

Citation
Daniel Franta, Ivan Ohlídal, and David Necas, "Influence of cross-correlation effects on the optical quantities of rough films," Opt. Express 16, 7789-7803 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-11-7789


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. S. O. Rice, "Reflection of electromagnetic waves from slightly rough surfaces," Commun. Pure Appl. Math. 4, 351-378 (1951). [CrossRef]
  2. G. R. Valenzuela, "Depolarization of EM Waves by Slightly Rough Surfaces," IEEE Trans. Antennas Propag. AP-15, 552-557 (1967). [CrossRef]
  3. K. Krishen, "Scattering of Electromagnetic Waves from a layer with rough front and plane back (Small Perturbation Method by Rice)," IEEE Trans. Antennas Propag. AP-18, 573-576 (1970). [CrossRef]
  4. R. Schiffer, "Reflectivity of a slightly rough surface," Appl. Opt. 26, 704-712 (1987). [CrossRef] [PubMed]
  5. J. I. Larruquert, J. A. Mendez, and J. A. Aznarez, "Far-ultraviolet reflectance measurements and optical-constants of unoxidized aluminium films," Appl. Opt. 34, 4892-4899 (1995). [CrossRef] [PubMed]
  6. D. Franta and I. Ohl??ýdal, "Ellipsometric Parameters and Reflectances of Thin Films with Slightly Rough Boundaries," J. Mod. Opt. 45, 903-934 (1998). [CrossRef]
  7. D. Franta and I. Ohl??ýdal, "Comparison of Effective Medium Approximation and Rayleigh-Rice Theory Concerning Ellipsometric Characterization of Rough Surfaces," Opt. Commun. 248, 459-467 (2005). [CrossRef]
  8. D. Franta and I. Ohlídal, "Influence of Lateral Dimensions of the Irregularities on the Optical Quantities of Rough Surfaces," J. Opt. A-Pure Appl. Opt. 8, 763-774 (2006). [CrossRef]
  9. I. Ohlídal and D. Franta, "Ellipsometry of Thin Film Systems," in Progress in Optics, E. Wolf, ed., (Elsevier, Amsterdam, 2000), Vol. 41, pp. 181-282.
  10. A. Vasí?ek, Optics of Thin Films (North-Holland, Amsterdam, 1960).
  11. Z. Knittl, Optics of Thin Films (Wiley, London, 1976).
  12. M. Born and E. Wolf, Principles of Optics, 3 ed. (Pergamon Press, Oxford, 1965).
  13. D. E. Aspnes, J. B. Theeten, and F. Hottier, "Investigation of effective-medium models of Microscopic Surface Roughness by Spectroscopic Ellipsometry," Phys. Rev. B 20, 3292-3302 (1979). [CrossRef]
  14. I. Ohlídal and F. Lukes, "Ellipsometric parameters of rough surfaces and of a System Substrate-Thin Film with rough boundaries," Opt. Acta 19, 817-843 (1972). [CrossRef]
  15. I. Ohlídal, F. Vidzd??a, and M. Ohlídal, "Optical Analysis by means of Spectroscopic Reflectometry of single and double layers with correlated randomly rough boundaries," Opt. Eng. 34, 1761-1768 (1995). [CrossRef]
  16. D. Franta, I. Ohlídal, and D. Ne?as, "Optical quantities of rough films calculated by Rayleigh-Rice theory," Phys. Status Solidi C 5, 1395-1398 (2008). [CrossRef]

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