Precision of silicon oxynitride refractive-index profile retrieval using optical characterization

TL;DR

This study evaluates the precision of optical methods in retrieving the gradient refractive index profile of silicon oxynitride layers, revealing that multiple profiles can fit the data well despite differences in index values.

Contribution

It introduces a comprehensive fitting approach combining multiple optical characterization techniques to accurately determine the refractive index profile of gradient layers.

Findings

Multiple index profiles can fit the data with high accuracy.

The index value can differ by up to 0.02 from the mean without affecting fit quality.

Sensitivity analysis shows broad tolerance in profile shape fitting.

Abstract

Layers with gradient refractive-index profile are an attractive alternative to conventional homogeneous stack coatings. However, the optical characterization and monitoring of the graded refractive-index profile is a complex issue, which has been typically solved by using a simplified model of mixed materials. Although this approach provides a solution to the problem, the precision, which can be expected from optical characterization of the refractive index gradient, remains unclear. In this work, we study optical characterization of SiO_xN_y layers deposited via reactive dual ion beam sputtering. To characterize the deposited layers, we use several methods including reflectance, and transmittance spectra at a broad range of incident angles, together with spectral ellipsometry. All the data were simultaneously fitted with a general profile of refractive index. The expected profile used in our fit was based on characterization of SiO_xN_y layers with a varying stoichiometry. By altering of the profile, we discussed sensitivity of such alternation on fit quality and we studied ambiguity of merit-function minimization. We demonstrate that while the scanning of particular parameters of the profile can be seemingly very precise, we obtain a very good agreement between the experimental data and model for a broad range of gradient shapes, where the refractive-index value on major part of the profile can differ as much as 0.02 from the mean value.