Solution of the Inverse Spectroscopic Ellipsometry Problem for an Absorbing Substrate with a Dielectric Layer

Abstract

An analytical solution of the inverse spectroscopic ellipsometry problem for a transparent layer on an absorbing substrate is obtained based on the envelope function approximation. It is used to determine the spectral dependences of the refractive index n(λ) and absorption k(λ) for model and real silicon substrates with silicon dioxide layers. It was possible to determine analytically the effective optical characteristics of the silicon substrate in the approximation of a layer-substrate model with ideal interface boundaries. This result, together with the relative positions of the spectral curves for the ellipsometric angles tan ψ(λ) and cos Δ(λ) measured for a silicon substrate with a natural surface layer and for a silicon dioxide layer–silicon substrate structure, can be explained by the fact that the silicon dioxide layer is surrounded by transition and surface layers.