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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 60, Iss. 4 — Apr. 1, 1970
  • pp: 499–505

Reflectance and Ellipsometry When Submicroscopic Particles Bestrew a Surface

DWIGHT W. BERREMAN  »View Author Affiliations


JOSA, Vol. 60, Issue 4, pp. 499-505 (1970)
http://dx.doi.org/10.1364/JOSA.60.000499


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Abstract

A method is described for computing optical properties of surfaces with a sparse distribution of submicroscopic bumps, pits, or foreign particles on or imbedded in them. The particles are assumed to be approximate figures of revolution about an axis normal to the surface. Surface and particle are assumed to have uniform, isotropic values of refractive index. Such foreign particles or roughness are equivalent in optical properties to a thin flat film of uniaxial material with its optic axis normal to the surface. The thickness of the equivalent film is arbitrarily made equal to the volume per unit area of all particles or bumps or pits. The principal values of refractive index of this equivalent film are determined by the shape of the particles and any surface irregularity associated with them, and by the refractive indices of particles and substrate, but not by particle size if size is small compared to wavelength of incident radiation. A recent experimental observation that silver tarnish in the form of isolated particles on a flat substrate gives about the same ellipsometric perturbation as would be expected from a flat film of the same refractive index and density appears to be only a rough approximation. Even that approximation would fail if the substrate were not metallic or if the tarnish particles were embedded in the surface. Differences of optical constants derived from measurements on thick and very thin films are explained.

Citation
DWIGHT W. BERREMAN, "Reflectance and Ellipsometry When Submicroscopic Particles Bestrew a Surface," J. Opt. Soc. Am. 60, 499-505 (1970)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-60-4-499


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References

  1. C. S. Strachan, Proc. Cambridge Phil. Soc. 29, 116 (1933).
  2. A. Sommerfeld, Ann. Physik 81, 1135 (1926).
  3. P. Drude, Ann. Physik u.d. Chem. 39, 481 (1890).
  4. D. W. Berreman, Phys. Rev. 1, B2, 381 (1970).
  5. H. E. Bennett, D. K. Burge, R. L. Peck, and J. M. Bennett, J. Opt. Soc. Am. 59, 675 (1969).
  6. D. V. Sivukhin, Sov. Phys.—JETP 3, 269 (1956).
  7. R. J. Archer, J. Opt. Soc. Am. 52, 970 (1962). R. J. Archer and G. W. Gobeli, J. Phys. Chem. Solids 26, 343 (1965).
  8. D. W. Berreman, Phys. Rev. 130, 2193 (1963). Some of the physical interpretation used here was presented there in another context. In that paper, we used a different origin to describe the phase of the reflected wave that was unconventional and would be less convenient for discussing ellipsometry.
  9. C. G. Darwin, Phil. Mag. 27, 315 (1914).
  10. D. W. Berreman, Phys. Rev. 163, 855 (1967). Although the polarizability obtained there was correct, errors occurred in computing reflectance, which are described in Ref. 4 for the case of light at normal incidence.
  11. See, for example, W. R. Smythe, Static and Dynamic Electricity, 2nd ed. (McGraw–Hill Book Co., New York, 1950), Sec. 5.05.
  12. Landolt-Börnstein, Zahlenwerte und Funktionen, II Band, 8 Teil: Optische Konstanten (Springer-Verlag, Berlin, 1962).
  13. O. S. Heavens, Optical Properties of Thin Solid Films (Butter-worths, London, 1955). See especially pp. 168 and 181 ff.

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