Mathematical model of Boltzmann’s sigmoidal equation applicable to the set-up of the RF-magnetron co-sputtering in thin films deposition of Ba$_x$Sr$_{1?x}$TiO$_3$

摘要

In this work, we present the stoichiometric behaviour of Ba$^{2+}$ and Sr$^{2+}$ when they are deposited to make asolid solution of barium strontium titanate. Bax Sr$_{1?x}$ TiO$_3$ (BST) thin films of nanometric order on a quartz substrate were obtained by means of in-situ RF-magnetron co-sputtering at 495$^{circ}$C temperature, applying a total power of 120 W divided into intervals of 15 W that was distributed between two magnetron sputtering cathodes containing targets of BaTiO$_3$ and SrTiO$_3$, as follows: 0–120, 15–105, 30–90, 45–75, 60–60, 75–45, 90–30, 105–15 and 120–0 W. Boltzmann’s sigmoidalmodified equation (Boltzmann’s profile) is proposed to explain the behaviour and the deposition ratio Ba/Sr of the BSTas a function of the RF-magnetron power. The Boltzmann’s profile proposal shows concordance with experimental data ofdeposits of BST on substrates of nichrome under the same experimental conditions, showing differences in the ratio Ba/Srof the BST due to the influence of the substrate.