Effect of elastic strain and Sc dopant concentration-dependent cell volume on the electrical properties of Epitaxial (Ba,Sr)TiO$_{3}$ thin films

We present the results of a systematic study of the correlation between dopant concentration-dependent elastic strain and dielectric properties in (Ba,Sr)TiO$_{3 }$films. For this work, undoped and Sc-doped (Ba,Sr)TiO$_{3}$ thin film capacitors epitaxially grown on SrTiO$_{3}$ substrate were prepared by a sputtering deposition method. Sc-doped BST capacitors exhibit significantly higher permittivity and lower leakage current density, but little effect on the loss tangent, as compared to nominally undoped BST capacitors. The Ti/(Ba+Sr) ratio of the films and Sc dopant concentration-dependent unit cell volume, as determined by x-ray sin$^{2}\psi $ analysis, are consistent with the preferential B-site occupancy of the Sc dopant. Furthermore, this work suggests that dopant concentration-dependent elastic strain as well as the 2D clamping effect of thin films on a thick substrate$^{1}$ must be considered to fully understand the dielectric behavior of perovskite titanate thin films. 1. N. A. Pertsev, A. G. Zembilgotov, and A. K. Tagantsev, Phys. Rev. Lett. 80, 1988 (1998)