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

O-18/O-16 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 SrTiO3 substrates. Isotope exchange anneals were performed as a function of temperature, 948 < T/K < 1123, at an oxygen activity aO(2) = 0.50 and as a function of oxygen activity, 0.01 < aO(2) < 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*(infinity), the surface exchange coefficient k(s)*, and the space-charge potential Phi(0). All D*(infinity) data are consistent with nominally undoped SrTiO3 substrates being weakly acceptor doped; the activation enthalpy for the migration of oxygen vacancies in bulk SrTiO3 is found to be Delta H-mig, (V) approximate to 0.6 eV. The surface termination of the SrTiO3 substrates was seen to affect significantly the surface exchange coefficient k(s)*. Values of Phi(0) obtained as a function of T and aO(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 TiO2-terminated (100) surface is driven by the Gibbs formation energy of oxygen vacancies at the interface being lower than in the bulk.