Document Type
Article
Publication Date
3-1975
Abstract
The ratio ρ = Rp/Rs of the complex amplitude-reflection coefficients Rp and Rs for light polarized parallel (p) and perpendicular (s) to the plane of incidence, reflected from an optically isotropic film-substrate system, is investigated as a function of the angle of incidence ϕ and the film thickness d. Both constant-angle-of-incidence contours (CAIC) and constant-thickness contours (CTC) of the ellipsometric function ρ(ϕ,d) in the complex ρ plane are examined. For transparent films, ρ(ϕ,d) is a periodic function of d with period Dϕ that is a function of ϕ. For a given angle of incidence ϕ and film thickness d (0 ≤ ϕ ≤ 90, 0 ≤ d ≤ Dϕ), the equispaced linear array of points (ϕ,d + mDϕ) (m = 0, 1, 2,…) in the real (ϕ,d) plane is mapped by the periodic function ρ(ϕ,d) into one distinct point in the complex ρ plane. Conversely, for a given film-substrate system, any value of the ellipsometric function ρ can be realized at one particular angle of incidence ϕ and an associated infinite series of film thicknesses d, d + Dϕ, d + 2Dϕ,.... This analysis leads to (1) a unified scheme for the design of all reflection-type optical devices, such as polarizers and retarders, (2) a novel null ellipsometer without a compensator, for the measurement of films whose thicknesses are within certain permissible ranges, and (3) an inversion procedure for the nonlinear equations of reflection ellipsometry that separates the determination of the optical constants (refractive indices and extinction coefficients) of the film and substrate from the film thickness. Extension of the work to absorbing films is discussed.
Journal Name
Journal of the Optical Society of America (1917-1983)
Recommended Citation
R. M. A. Azzam, A.-R. M. Zaghloul, and N. M. Bashara, "Ellipsometric function of a film-substrate system: Applications to the design of reflection-type optical devices and to ellipsometry," J. Opt. Soc. Am. 65, 252-260 (1975)
Comments
This paper was published in Journal of the Optical Society of America (1917-1983)and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-65-3-252. Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.