Behavior of cation vacancies in single-crystal and in thin-film <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">SrTiO</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>: The importance of strontium vacancies and their defect associates
Ute N. Gries, Markus Kessel, Felix V. E. Hensling, Regina Dittmann, Manfred Martin, Roger A. De Souza
Abstract
Solid-state diffusion experiments were used to probe the behavior of cation vacancies in the perovskite oxide ${\mathrm{SrTiO}}_{3}$. Two types of nominally undoped (effectively acceptor-doped) ${\mathrm{SrTiO}}_{3}$ systems were studied: (1) single crystals and (2) epitaxial thin films with different Sr/Ti stoichiometries produced by pulsed laser deposition. As diffusion sources, thin films of the perovskite oxide ${\mathrm{BaZrO}}_{3}$ were employed, and diffusion anneals were carried out in air at $1323\ensuremath{\le}T/\mathrm{K}\ensuremath{\le}1523$ for single crystals and at $1073\ensuremath{\le}T/\mathrm{K}\ensuremath{\le}1223$ for thin films. Sample analysis by means of time-of flight secondary ion mass spectrometry (ToF-SIMS) yielded diffusion coefficients of Ba and Zr in ${\mathrm{SrTiO}}_{3}\phantom{\rule{4pt}{0ex}}({D}_{\mathrm{Ba}}$ and ${D}_{\mathrm{Zr}})$. Diffusion profiles in single-crystal samples showed the expected error-function form and yielded ${D}_{\mathrm{Ba}}\ensuremath{\approx}{D}_{\mathrm{Zr}}$ at each temperature, and hence, activation enthalpies of diffusion that are approximately the same, at $(3.0\ifmmode\pm\else\textpm\fi{}0.4)$ eV and $(2.8\ifmmode\pm\else\textpm\fi{}0.4)$ eV. Diffusion profiles in the thin-film samples were unexpectedly complex, showing multiple error-function features. They also yielded ${D}_{\mathrm{Ba}}\ensuremath{\approx}{D}_{\mathrm{Zr}}$ at each temperature, however, but no clear trend was found as a function of Sr/Ti ratio. Comparing results for the two systems, we conclude that the concentration of cation vacancies is orders of magnitude higher in our thin-film samples than in the single crystals. Our results also provide experimental evidence that oxygen vacancies, ${\mathrm{v}}_{\mathrm{O}}^{\ifmmode\bullet\else\textbullet\fi{}\ifmmode\bullet\else\textbullet\fi{}}$, can decrease the activation enthalpy of strontium-vacancy migration by forming ${({\mathrm{v}}_{\mathrm{O}}{\mathrm{v}}_{\mathrm{Sr}})}^{\ifmmode\times\else\texttimes\fi{}}$ defect associates, and we derive an analytical model for the cation diffusivity as a function of temperature and defect concentrations.