X-Ray diffraction and Raman spectroscopy studies of superlattices BaTiO$_3$/(Ba$_{0.5}$, Sr$_{0.5}$)TiO$_3$/SrTiO$_3$

The structural characteristics of the BaTiO$_3$/(Ba$_{0.5}$, Sr$_{0.5}$)TiO$_3$/SrTiO$_3$ superlattice on a (001) MgO substrate have been studied using X-ray diffraction. The modulation period and unit cell parameters of layers forming the superlattice have been measured. The sizes of coherent scattering regions and average microstrains in the direction perpendicular to the surface have been estimated. The obtained characteristics are compared to those of the two-layer BaTiO$_3$/(Ba$_{0.5}$, Sr$_{0.5}$)TiO$_3$ superlattice. The Raman spectra demonstrate a substantial shift of the soft $E$(TO) mode in the three-layer superlattice as compared to the position in the two-layer superlattice. The effects observed are associated with a substantial increase in the temperature of the phase transition of the three-layer superlattice to the paraelectric phase.