Unravelling the Impact of Surface Roughness and Cationic Ni2+ Vacancies to Ni3+ Ions Ratio on Optical Properties of Niox Thin Film: Insights Fractal and Multi-Fractal Dimension

This study explores the impact of roughness-fractal parameters on the optical properties of NiOx thin films, including reflection, band gap, Urbach energy, and refractive index. The films were grown on silicon (Si) substrates using magnetron sputtering. By analyzing atomic force microscopy (AFM) images, we calculated several surface parameters, including fractal dimension, roughness exponent, lateral correlation length, local surface slope, and steepness factor. We also independently determined the roughness exponent, growth exponent, and dynamic exponents (α = 0.99–0.66, β = 1.01, and z = 2.5). Furthermore, we introduced the local surface slope (m ≈ w/ξ) as a measure of surface irregularities, noting that an increase in the w/ξ ratio corresponded to greater surface roughness. Minkowski functionals, including volume, boundary, and connectivity, were also calculated for each thin film. The analysis revealed that the NiOx thin films exhibit multifractal behavior, with parameters such as the generalized fractal dimensions function (Dq) and the singularity strength spectrum (f(α)) providing valuable insights into their nanoscale properties. A wider spectrum in f(α) indicated higher surface roughness. X-ray photoelectron spectroscopy (XPS) studies revealed the presence of nickel (III) oxidation states in the NiOx thin films, confirming their non-stoichiometric structure. Additionally, the ratio of cationic Ni2+ vacancies to Ni3+ ions, expressed as Ni3+/ Ni2+ was estimated, indicating that defect density increases with film thickness. Using UV–Vis spectroscopy, we explored the relationship between optical parameters and fractal characteristics, finding that optical absorption increased with higher fractal dimensions. Furthermore, the band gap decreased as the fractal dimension and w/ξ ratio increased. These results suggest that such films could be used effectively as active layers in advanced optoelectronic devices. © 2025 Elsevier Ltd and Techna Group S.r.l.