Precision of Silicon Oxynitride Refractive-Index Profile Retrieval Using Optical Characterization

Layers with a 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 that has usually been solved with a simplified model of mixed materials. Although such an 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 SiOxNy 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 the refractive index. The expected profile used in our fit was based on the characterization of SiOxNy layers with a varying stoichiometry. By altering the profile, we discussed the sensitivity of alternation on the fit quality and we studied the ambiguity of the 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 the model for a broad range of gradient shapes. Our calculation shows that the refractive-index value on the major part of the profile can differ as much as 0.02 from the mean value.