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Applied Optics

Applied Optics


  • Vol. 30, Iss. 19 — Jul. 1, 1991
  • pp: 2801–2806

Transmission ellipsometry on transparent unbacked or embedded thin films with application to soap films in air

R. M. A. Azzam  »View Author Affiliations

Applied Optics, Vol. 30, Issue 19, pp. 2801-2806 (1991)

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The ratio ρt = Tp/Ts of the complex amplitude transmission coefficients for the p and s polarizations of a transparent unbacked or embedded thin film is examined as a function of the film thickness-to-wavelength ratio d/λ and the angle of incidence ϕ for a given film refractive index N. The maximum value of the differential transmission phase shift (or retardance), Δt = argρt, is determined, for given N and ϕ, by a simple geometrical construction that involves the iso–ϕ circle locus of ρt in the complex plane. The upper bound on this maximum equals arctan{[N − (1/N)]/2} and is attained in the limit of grazing incidence. An analytical noniterative method is developed for determining N and d of the film from ρt measured by transmission ellipsometry (TELL) at ϕ = 45°. An explicit expression for Δt of an ultrathin film, d/λ ≪ 1, is derived in product form that shows the dependence of Δt on N, ϕ, and d/λ separately. The angular dependence is given by an obliquity factor, fo(ϕ) = 21/2 sinϕ tanϕ, which is verified experimentally by TELL measurements on a stable planar soap film in air at λ = 633 nm. The singularity of fo at ϕ = 90° is resolved; Δt is shown to have a maximum just short of grazing incidence and drops to 0 at ϕ = 90°. Because N and d/λ are inseparable for an ultrathin film, N is determined by a Brewster angle measurement and d/λ is subsequently obtained from Δt. Finally, the ellipsometric function in reflection ρr is related to that in transmission ρt.

© 1991 Optical Society of America

Original Manuscript: July 13, 1990
Published: July 1, 1991

R. M. A. Azzam, "Transmission ellipsometry on transparent unbacked or embedded thin films with application to soap films in air," Appl. Opt. 30, 2801-2806 (1991)

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  1. R. M. A. Azzam, “Simple and Direct Determination of Complex Refractive Index and Thickness of Unsupported or Embedded Thin Films by Combined Reflection and Transmission Ellipsometry at 45° Angle of Incidence,” J. Opt. Soc. Am 73, 1080–1082 (1983); “Ellipsometry of Unsupported or Embedded Thin Films,” J. Phys. (Paris) Colloq. 44, C10-67–C10-70 (1983). [CrossRef]
  2. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1987).
  3. See, for example, W. R. LePage, Complex Variables and the Laplace Transform for Engineers (Dover, New York, 1961), Sec. 3.10.
  4. R. M. A. Azzam, “Polar Curves for Transmission Ellipsometry,” Opt. Commun. 14, 145–147 (1975). [CrossRef]
  5. See, for example, A. E. Taylor, Calculus with Analytic Geometry (Prentice Hall, Englewood Cliffs, NJ, 1959), Ch. 7.
  6. D. A. Holmes, “Wave Optics Theory of Rotary Compensators,” J. Opt. Soc. Am. 54, 1340–1347 (1964). [CrossRef]
  7. R. M. A. Azzam, A.-R. M. Zaghloul, “Determination of the Refractive Index and Thickness of a Transparent Film on a Transparent Substrate from the Angles of Incidence of Zero Reflection-Induced Ellipticity,” Opt. Commun. 24, 351–354 (1978). [CrossRef]
  8. A. R. Reinberg, “Ellipsometer Data Analysis with a Small Programmable Desk Calculator,” Appl. Opt. 11, 1273–1274 (1972). [CrossRef] [PubMed]
  9. F. Abelès, “Un Théoreme relatif à la réflexion metallique,” C. R. Acad. Sci. 220, 1942–1943 (1950).
  10. Wonder Bubbles, Chemtoy Corp., Chicago, IL 60624. At normal room temperature and pressure, the stable film can stay intact, without rupture, for 15 min or longer.
  11. R. H. Muller, “Definitions and Conventions in Ellipsometry,” Surf. Sci. 16, 14–33 (1969). [CrossRef]
  12. This is not the case for a partially transmitting thin film with k ≠ 0. Even with a numerically small k value (e.g., 0.01), the difference Δr − Δt assumes anomalously large values in the immediate neighborhood of the pseudo-Brewster angle.

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