Stoichiometry Calculation in Ba_xSr_1−xTiO₃ Solid Solution Thin Films, Prepared by RF Cosputtering, Using X-Ray Diffraction Peak Positions and Boltzmann Sigmoidal Modelling

Abstract

A novel procedure based on the use of the Boltzmann equation to model the parameter, the film deposition rate, and the optical band gap of Ba x Sr 1−x TiO 3 thin films is proposed. The Ba x Sr 1−x TiO 3 films were prepared by RF cosputtering from BaTiO 3 and SrTiO 3 targets changing the power applied to each magnetron to obtain different Ba/Sr contents. The method to calculate consisted of fitting the angular shift of (110), (111), and (211) diffraction peaks observed as the density of substitutional Ba 2+ increases in the solid solution when the applied RF power increases, followed by a scale transformation from applied power to 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.

Temperature–Power Simultaneous Effect on Physical Properties of BaxSr1−x TiO3 Thin Films Deposited by RF–Magnetron Cosputtering for 0 ≤ x ≤1

“…For the temperature of 549 • C, the XRD spectrum (see Figure 5) defines a polycrystalline film with cubic, tetragonal, and orthorhombic phases [13]. These results suggest that the crystalline structure passes through a transition state to achieve stability, and that E g values can decrease with higher deposition temperatures.…”

“…This is due to the substrate effects and plasma geometry into the RFsputtering deposition system, causing a differentiated distribution on substrate [20], such as what happens in thin films deposited by the direct current arc discharge plasma process [21]. The experimental "x" parameter values to build Figure 2 was taken thus: BST/Nichrome 495 °C (BPEDS) [6] is the Boltzmann's profile fit, whose discrete experimental points were obtained by means of EDS measurements, and BST/Quartz 549 °C (BPXRD) [13] is the Boltzmann's profile fit whose discrete experimental points were calculated from XRD reflection patterns of Samples S1-S9 (see Table 1) and T = 549 °C. BPAvT (BST/Quartz) is obtained from the experimental values of the "x" parameter calculated by averaging values of deposition at different temperatures: As-deposited, 375 °C, 435 °C, 495 °C, and 549 °C (see Table 2).…”

“…The experimental "x" parameter values to build Figure 2 was taken thus: BST/Nichrome 495 • C (BP EDS ) [6] is the Boltzmann's profile fit, whose discrete experimental points were obtained by means of EDS measurements, and BST/Quartz 549 • C (BP XRD ) [13] is the Boltzmann's profile fit whose discrete experimental points were calculated from XRD reflection patterns of Samples S1-S9 (see Table 1) and T = 549 • C. BP AvT (BST/Quartz) is obtained from the experimental values of the "x" parameter calculated by averaging values of deposition at different temperatures: As-deposited, 375 • C, 435 • C, 495 • C, and 549 • C (see Table 2). (BPEDS) [6] is the Boltzmann's profile fit, whose discrete experimental points were obtained by means of EDS measurements, and BST/Quartz 549 °C (BPXRD) [13] is the Boltzmann's profile fit whose discrete experimental points were calculated from XRD reflection patterns of Samples S1-S9 (see Table 1) and T = 549 °C. BPAvT (BST/Quartz) is obtained from the experimental values of the "x" parameter calculated by averaging values of deposition at different temperatures: As-deposited, 375 °C, 435 °C, 495 °C, and 549 °C (see Table 2).…”

“…Comparing BP EDS and BP AvT , the substrate effect on the Ba/Sr ratio is evident. Assuming that the interface between the substrate and the film has no decisive influence on the Ba/Sr stoichiometric ratio and that "x" parameter measurements using XRD for the same thin films are more accurate than measurements by means of EDS [13], it is possible to associate each "x" value (obtained from BP XRD ) with each applied power value, that is, x i with a specific value of the applied power p i . In turn, each p i can be associated to particular values of DR, E g , and ρ (we can see in the next figures, respectively).…”

“…The effects of the stoichiometry defined by x and 1 − x parameters into the BST chemical formula have been investigated in some physical properties such as: Resistive switching [5,6], resistivity (ρ) in crystalline and amorphous phases [7][8][9], thickness [10], and band gap energy (E g ) [11][12][13].…”