Stoichiometry Calculation in Ba_xSr_{1- x}TiO₃ Solid Solution Thin Films, Prepared by RF Cosputtering, Using X-Ray Diffraction Peak Positions and Boltzmann Sigmoidal Modelling

A novel procedure based on the use of the Boltzmann equation to model the x parameter, the film deposition rate, and the optical band gap of Ba_xSr_1-xTiO₃ thin films is proposed. The Ba_xSr_1-xTiO₃ films were prepared by RF cosputtering from BaTiO₃ and SrTiO₃ targets changing the power applied to each magnetron to obtain different Ba/Sr contents. The method to calculate x consisted of fitting the angular shift of (110), (111), and (211) diffraction peaks observed as the density of substitutional Ba²⁺ increases in the solid solution when the applied RF power increases, followed by a scale transformation from applied power to x parameter using the Boltzmann equation. The Ba/Sr ratio was obtained from X-ray energy dispersive spectroscopy; the comparison with the X-ray diffraction derived composition shows a remarkable coincidence while the discrepancies offer a valuable diagnosis on the sputtering flux and phase composition. The proposed method allows a quick setup of the RF cosputtering system to control film composition providing a versatile tool to optimization of the process.