Anisotropic Bruggeman Effective Medium Approaches for Slanted Columnar Thin Films

TL;DR

This paper compares two anisotropic Bruggeman effective medium models for analyzing slanted columnar thin films, validating their accuracy against electron microscopy and discussing their applicability for optical device characterization.

Contribution

It introduces and compares two anisotropic Bruggeman formalisms for modeling slanted columnar thin films and validates their effectiveness against microscopy data.

Findings

Both models accurately estimate structural parameters.

The models' results agree well with electron microscopy.

The approaches are suitable for future optical device analysis.

Abstract

Two different formalisms for the homogenization of composite materials containing ellipsoidal inclusions based on Bruggeman's original formula for spherical inclusions can be found in the literature. Both approximations determine the effective macroscopic permittivity of such an idealized composite assuming randomly distributed dielectric particles of equal shape and differ only in the definition of the depolarization factors. The two approaches are applied to analyze ellipsometric Mueller matrix spectra acquired in the visible and near-infrared spectral region from metal and semiconductor slanted columnar thin films. Furthermore, the effective dielectric function tensor generated by the two Bruggeman formalisms is compared to effective major axes dielectric functions individually determined with a homogeneous biaxial layer approach. Best-match model parameters of all three model approaches are discussed and compared to estimates from scanning electron microscope images. The structural parameters obtained from all three optical modeling approaches agree well with the electron microscopy technique. A comparative discussion is given for the validity and applicability of the three model approaches for analysis of future devices structures that may require optical readout using generalized ellipsometry methods.