Mathematical model depicting the deposition kinetics process into rf-magnetron co-sputtering of strontium barium titanate thin films

Thin films deposition kinetics of Ba_XSr_1-XTiO₃ (BST)/nichrome is modeled by the stoichiometric rate of a perovskite-type material such as ABO₃, where cations A, B, and the anion oxygen should ideally have a 1:1:3 rate, respectively. The experimental stoichiometry data measured by EDS on films of 240 nm, and the Ba/Sr, (Ba+Sr)/Ti rates considered in percentages starting from arithmetic and the sigmoidal relationship between Ba and Sr. They show relationships in sigmoidal, exponential, and parabolic mathematical functions that together describe the BST thin films deposition kinetics by means of RF-Magnetron Co-Sputtering (RFMCS). The proposed mathematical model is fundamental to optimize, explain and use the deposition process working conditions, such as the working pressure, the Ar/O₂ rate in percentage, and sccm. The controlled applied power on each BaTiO₃ (BTO) and SrTiO₃ (STO) targets achieve more accurate stoichiometry in thin films deposition for solid solutions on quaternary materials.