*2.3. Optical Properties*

Optical properties of the coatings, such as index of refraction (n) and extinction coe fficient (k), as well as their thickness, were determined using a J.A. Woollam variable angle spectroscopic ellipsometer (VASE) and the related software. All the measurements were performed in the spectral range of 260–1000 nm for three di fferent angles of incidence (65◦, 70◦, 75◦), with the measurement step equal 5 nm. The measurements were made in the reflectance mode and optical properties of one component coatings, either SiOC or SiNC, were modelled with a Cauchy model layer with Urbach absorption represented by the following mathematical expression:

$$m(\lambda) = A + \frac{B}{\lambda^2} + \frac{C}{\lambda^4} \tag{1}$$

where *A*, *B* and *C* are parameters describing the dispersion of the refractive index *n*(λ). The extinction coe fficient *k*(λ) was modelled by an exponential absorption tail. Fitting the procedure of *A*, *B*, and *C* parameters gave a mean square error of an order of magnitude of MSE = 20 (mean square error) for all the films examined. For each sample, average values of thickness and refractive index were computed from (at least) three ellipsometric measurements performed at di fferent sites of the sample. Mean thickness values varied within the range of 260–1000 nm.

Gradient optical thin films, i.e., films with refractive index changing along their thickness, were analyzed using a graded layers algorithm supplied with the WVASE32 software by the ellipsometer manufacturer. In the gradient model, the real layer is divided into homogeneous sub-layers whose refractive indices *n*i change slightly for a particular layer (characteristic jumps of the value of *n*). The refractive index n profiles were determined taking into account the thickness of the film and the number of sublayers determined for the best fit of the model to the experimental data.

Transmittance of the coatings within the range of 190–1000 nm was studied with the help of ThermoScientific™ Evolution 220 UV-Vis systems. Absorbance spectra, on the other hand, were used to determine the magnitude of optical gap using the Tauc model and the following equation:

$$
abla \nu = B(h\nu - E\_{\mathcal{K}})^m \tag{2}$$

where:

> α—denotes the absorption coefficient,

*h*—denotes the Planck constant,

a

υ—denotes photon frequency, *Eg*—denotes optical energy band gap,*B*—denotesconstant

 Thevalueofmcoefficientamountedto1/2

 .
