Behavior of oxygen vacancies in single-crystal SrTiO3: Equilibrium distribution and diffusion kinetics

Abstract

${}^{18}$O/${}^{16}$O exchange and subsequent time-of-flight secondary ion mass spectrometry (ToF-SIMS) analysis was employed to investigate the transport of oxygen, and thus the behavior of oxygen vacancies, in [nominally undoped, (100) oriented] single-crystal SrTiO${}_{3}$ substrates. Isotope exchange anneals were performed as a function of temperature, 948 $l$ $T$/K $l$ 1123, at an oxygen activity $a$O${}_{2}$ $=$ 0.50 and as a function of oxygen activity, 0.01 $l$ $a$O${}_{2}$ $l$ 0.70, at $T$ $=$ 1073 K. All isotope profiles show the same characteristic form: an initial drop over tens of nanometers close to the surface, which is attributed to an equilibrium space-charge layer depleted of oxygen vacancies, followed by a profile extending several microns into the solid, which is attributed to diffusion in a homogeneous bulk phase. The entire isotope profile can be described quantitatively by a numerical solution to the diffusion equation with a position-dependent diffusion coefficient; the description yields the tracer diffusion coefficient in the bulk ${D}^{*}$(\ensuremath{\infty}), the surface exchange coefficient ${k}_{\mathrm{s}}^{*}$, and the space-charge potential ${\ensuremath{\Phi}}_{0}$. All ${D}^{*}$(\ensuremath{\infty}) data are consistent with nominally undoped SrTiO${}_{3}$ substrates being weakly acceptor doped; the activation enthalpy for the migration of oxygen vacancies in bulk SrTiO${}_{3}$ is found to be $\ensuremath{\Delta}{H}_{\mathrm{mig},\mathrm{V}}$ \ensuremath{\approx} 0.6 eV. The surface termination of the SrTiO${}_{3}$ substrates was seen to affect significantly the surface exchange coefficient ${k}_{\mathrm{s}}^{*}$. Values of ${\ensuremath{\Phi}}_{0}$ obtained as a function of $T$ and $a$O${}_{2}$ are approximately 0.5 V, indicating strong depletion of oxygen vacancies within the equilibrium surface space-charge layers. Thermodynamic modeling indicates that space-charge formation at the TiO${}_{2}$-terminated (100) surface is driven by the Gibbs formation energy of oxygen vacancies at the interface being lower than in the bulk.