Applied Physics B

, Volume 45, Issue 1, pp 1–5 | Cite as

Regularization in ellipsometry

Near-surface depth profiles of the refractive index
  • J. H. Kaiser
Contributed Papers

Abstract

The continuous variation of the refractive index with the depth in the vicinity of surfaces can be determined by ellipsometry without destroying the object of measurements. The presented method does not impress any given structure to the profile and is applicable to just the range of layer thicknesses interesting to optics (about λ/4 to λ/2). The theoretical approach to interpret the measured data leads to an integral equation that is numerically inverted by regularization to filter out the destabilizing effects of measurement errors. The regularizing operator and regularization parameter responsible for this “filtering” are founded on physical arguments and experiment, respectively. These results can be transferred to other regularization problems based on quantities related to volume (e.g. density, temperature).

PACS

02.60.Nm 07.60.Fs 78.20.−e 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R.M.A. Azzam, N.M. Bashara:Ellipsometry and Polarized Light (North-Holland, Amsterdam 1977)Google Scholar
  2. 2.
    E.D. Palik (ed.):Handbook of Optical Constants of Solids (Academic Press, Orlando 1985)Google Scholar
  3. 3.
    L.D. Landau, E.M. Lifschitz:Lehrbuch der theoretischen Physik, Vol. VIII (Akademie, Berlin 1974) Par. 60Google Scholar
  4. 4.
    R. Jacobsson: In:Progress in Optics, Vol. V., ed. by E. Wolf (North-Holland, Amsterdam 1966)Google Scholar
  5. 5.
    P.M. Morse, H. Feshbach:Methods of Theoretical Physics (McGraw-Hill, New York 1953)Google Scholar
  6. 6.
    J.C. Charmet, P.G. de Gennes: J. Opt. Soc. Am.73, 1777–1784 (1983)Google Scholar
  7. 7.
    U. Frisch: Ann. d'Astrophys.29, 645–682 (1966)Google Scholar
  8. 8.
    S. Twomey:Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements (Elsevier Scientific, Amsterdam 1977)Google Scholar
  9. 9.
    M. Bertero, C. de Mol, G.A. Viano: Opt. Lett.3, 51–53 (1978)Google Scholar
  10. 10.
    M.V. Klein:Optics (Wiley, New York 1970) Chap. 11Google Scholar
  11. 11.
    B. Hofmann:Regularization for Applied Inverse and Ill-Posed Problems (Teubner, Leipzig 1986)Google Scholar
  12. 12.
    V.A. Morozov:Method for Solving Incorrectly Posed Problems (Springer, New York 1984)Google Scholar
  13. 13.
    Bergmann-Schaefer:Lehrbuch der Experimentalphysik, Vol. III (de Gruyter, Berlin 1974) Chap. 1,5Google Scholar
  14. 14.
    A.R. Bayly, P.D. Townsend: J. Phys. D. Appl. Phys.6, 1115–1128 (1973)Google Scholar
  15. 15.
    K. Vedam, M. Malin: Mat. Res. Bull.9, 1503–1510 (1974)Google Scholar
  16. 16.
    A.W. Adamson:Physical Chemistry of Surfaces (Wiley, New York 1976) Chap. V, 7Google Scholar

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • J. H. Kaiser
    • 1
  1. 1.Institut für Angewandte Physik, UniversitätDüsseldorfFed. Rep. Germany

Personalised recommendations