Ellipsometric function of a film–substrate system: characterization and detailed study

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Abstract

To permit clear understanding and study of the ellipsometric function of a film–substrate system, an intermediate plane is introduced. This plane provides a tool for simplifying the treatment and analysis of the ellipsometric function. Accordingly, the film–substrate systems are divided into three categories; negative, zero, and positive systems. Each category is identified clearly and characterized. Simple expressions are given for each category. The behavior of each category is studied extensively. Families of curves representing each group are given. For a negative film–substrate system, the closed contours describing the behavior of the ellipsometric function in the complex ρ plane are divided into two groups in two separate domains filling the whole complex plane, with no intersection between any of the contours. The closed contours in the zero film–substrate system are also divided into two groups. One of the groups has one element (null contour ρ = −1), and the other group fills the interior of a unit circle in the ρ plane with a common point +1 for all the elements. For the positive film–substrate system, the closed contours that describe the behavior of ρ are not divided, and the intersection property between any two adherent contours exists. This is proved through a rigorous mathematical development. The mathematical development is carried out for the general case of a transparent film on an absorbing substrate system. The behavior of the ellipsometric function is analyzed in detail for the case of a transparent film on a transparent substrate system. The effect of the substrate absorption is indicated. The introduction of the intermediate plane also proves to be useful for obtaining the film thickness and the optical properties of the system in closed forms, tasks that, in addition to the design of reflection-type optical devices, will be discussed in subsequent papers.

© 1989 Optical Society of America

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