Dynamic defect correlations dominate activated electronic transport in SrTiO3

Strontium titanate (SrTiO3, STO) is a critically important material for the study of emergent electronic phases in complex oxides, as well as for the development of applications based on their heterostructures. Despite the large body of knowledge on STO, there are still many uncertainties regarding the role of defects in the properties of STO, including their influence on ferroelectricity in bulk STO and ferromagnetism in STO-based heterostructures. We present a detailed analysis of the decay of persistent photoconductivity in STO single crystals with defect concentrations that are relatively low but significantly affect their electronic properties. The results show that photo-activated electron transport cannot be described by a superposition of the properties due to independent point defects as current models suggest but is, instead, governed by defect complexes that interact through dynamic correlations. These results emphasize the importance of defect correlations for activated electronic transport properties of semiconducting and insulating perovskite oxides.

θ-2θ scan of sample C. Oxygen vacancies as well as cation off-stoichiometry S2 will increase the STO lattice constant above its bulk. Both the out of plane (c) lattice constant of 3.905 Å, i.e. equal to that of relaxed bulk STO, and the absence of shoulders in the (002) reflection show that no defect-induced unit cell volume increases are present within the detection limit of X-ray diffraction, even for this quenched sample C that presumably has the highest defect concentration.

Comparison of experimental relaxation data with results from Density Functional Theory (DFT) calculations.
As discussed in the main text (Table 1), our annealing conditions are expected to create O and Ti vacancies, as well as Sr Ti antisite defects. In an attempt to identify the defects dominating the observed decay in photoconductivity, we compare our experimental data with the results of recent DFT calculations reported in the literature. S2,S3,S4,S5 While we recognize that this comparison is limited by the small number of defect (complexes) that have been studied using state of the art DFT calculations, and potentially suffers from inaccuracies in DFT band gap determinations, DFT data are the only source of a direct relation between a specific defect type and the energy of its defect state within the STO band gap; experimental methods either average spectroscopic data over many different defects, or introduce the very same uncertainties by the need to be aided by theoretical (DFT) calculations to interpret atomically resolved spectroscopic data.

Oxygen vacancies.
Recent DFT calculations predict S2 that oxygen vacancies are most stable when doubly ionized and forming a complex with a small polaron. This produces a localized, singly filled defect state located in the gap about 0.4 to 0.5 eV below the conduction band, and puts one electron in the conduction band. Clearly the energetic position of this level, as well as the conductivity that should arise from the induced conduction band carrier density is not observed in our measurements, and hence we believe a model based on independent oxygen vacancies does not describe our results. Another DFT study predicts S4 that for very high carrier densities ≥10 20 cm -3 , two electrons can be trapped near an oxygen vacancy by two small polarons. Below this critical carrier density, the system contains delocalized charge carriers or delocalized large polarons. As our samples were still visually transparent (except for the quench-cooled sample C) and highly resistive, we conclude that we did not create a defect density larger than this critical density. Our samples should therefore conduct reasonably well due to the polaron delocalization at low carrier densities, but instead they are highly resistive, implying that the defect configuration in our samples has to differ from those considered in Ref. S4 .

Ti vacancies.
While there are not many studies considering Ti vacancies, presumably because of their high formation energy, S2,S5 the formation energy of Ti vacancies should decrease when SrO is present. S3,S5 DFT calculations show that Ti vacancies are most stable as deep acceptors with a -4 charge state. S2,S3 Upon photoexcitation with light just below the bandgap, an electron will be excited from this acceptor state into the conduction band. While recombination of the electron in the conduction band with the hole on the defect state does result in a photon emission peak at 1.2 eV because the state of V Ti -3 is located 1.2 eV below the conduction band, S2 there is no energetic barrier for this capture process, which is necessary to explain the observed long term persistence of the photoconductivity -unless the hole on the Ti vacancy recombines with an electron from the valence band, but this corresponds to a transition energy of 2.1 eV, and leaves an excited electron in the conduction band. The latter recombination would not result in the observed decreasing persistent conductivity. As a result, we conclude that isolated Ti vacancies are not likely candidates to explain the observed persistent photoconductivity.

Sr Ti antisite defects.
Finally, a recent comprehensive study on defect complexes in STO S3 considers the presence of excess SrO, which is comparable to our experimental conditions. It was shown that oxygen vacancies and Sr Ti -2 antisite defects are most prevalent under these conditions, but no energetics for in-gap states were provided. However, the generally lower formation energies of the considered defect complexes as compared to isolated point defects, points to the critical importance of such complexes as compared to individual defects in STO.