Mathematical modeling and cross-salt validation of layer-by-layer deposition of cadmium sulfide thin films: correlating thickness, morphology, and functional relevance from sensor to photocatalytic applications

The paper presents a systematic study of the layer-by-layer chemical deposition of cadmium sulfide thin films. The research aimed to establish relationships among concentration parameters, the number of deposition cycles, morphological characteristics, and functional properties. The objective of the study was to develop a mathematical model to quantitatively describe film growth kinetics and predict film thickness from process parameters. A multifactor regression analysis was employed, with model coefficients determined using the least-squares method in matrix form. The construction of the design matrices enabled the inclusion of primary variables, as well as interaction and quadratic terms that capture the nonlinear nature of film growth. This approach ensured high accuracy in approximating experimental data and yielded a statistically significant model capable of reproducing and predicting deposition trends. The model’s reliability was verified through cross-salt validation, in which analogous deposition conditions were applied with various cadmium sources, including sulfate, chloride, iodide, nitrate, and acetate. The comparative analysis confirmed that the fundamental growth patterns are preserved across different salt-system compositions, demonstrating the model’s universality and transferability across various technological environments. To better understand film-forming patterns, 3D visualization of both experimental and modeled data was performed, enabling the spatial relationships among reagent concentration, the number of deposition cycles, and film thickness to be traced. The visualization confirmed the adequacy of the chosen model. The optical and morphological characteristics of the obtained films were analyzed, revealing that variations in film thickness directly influence the transmittance coefficient and the bandgap ( E g ). Thinner films exhibited high optical transparency, potentially relevant to sensing and optoelectronic applications, whereas thicker films showed enhanced optical absorption.