Angle-of-incidence Derivatives of the Complex Parallel and Perpendicular Reflection Coefficients and Their Ratio for a Film-substrate System

Publisher Website
Google Scholar
Abstract
Angle-of-incidence derivatives of the complex parallel (p) and perpendicular (s) reflection coefficients R p and R s, and their ratio ρ = R p/R s, for an absorbing substrate coated by a transparent film are investigated as functions of the angle of incidence φ and film thickness d. Such derivatives are of importance to AIDER (angle-of-incidence derivative ellipsometry and reflectometry).R′ p/R p,R′ s/R s,and ρ′/ρ (where the prime indicates ∂/∂φ) are shown to be aperiodic spiral functions of d at constant φ, except in the limiting cases of normal and grazing incidence when they become periodic. In the latter case (φ= 90°), the locus of R′ v/R v(v = p or s) is found and proved to be exactly a circle. The complementary family of constant-thickness contours of these derivative functions are also plotted in the complex plane. Finally, graphs representing the real AIDER signals ℜ′p /ℜp, ψ′ and Δ′ (where ℜ= |R|2, tan ψ exp (jΔ) = ρ) versus d at constant φ, and versus φ at constant d, are given.