Point defect distribution in high-mobility conductive ${\text{SrTiO}}_3$ crystals

We have carried out positron-annihilation spectroscopy to characterize the spatial distribution and the nature of vacancy defects in insulating as-received as well as in reduced ${\text{SrTiO}}_3$ substrates exhibiting high-mobility conduction. The substrates were reduced either by ion etching the substrate surfaces or by doping with vacancies during thin-film deposition at low pressure and high temperature. We show that Ti vacancies are native defects homogeneously distributed in as-received substrates. In contrast, the dominant vacancy defects are the same both in ion etched crystals and substrates reduced during the film growth, and they consist of nonhomogeneous distributions of cation-oxygen vacancy complexes. Their spatial extension is tuned from a few microns in ion-etched samples to the whole substrate in specimens reduced during film deposition. Our results shed light on the transport mechanisms of conductive ${\text{SrTiO}}_3$ crystals and on strategies for defect-engineered oxide quantum wells, wires, and dots.

Figure 1

(Color online) Positron depth profile in STO calculated for indicated positron incident energies according to Ref. 24 with the parameters $A=2.95\mu \text{g}{\text{cm}}^{-2}{\text{keV}}^{-r}$, $m=2$, and $r=1.7$. The inset shows a zoom of the data in the main panel, for positron incident energies between 15 and 25 keV. The dashed line in the inset indicates the mean penetration depth $\overline{z}$ for 18 keV.

Figure 2

(Color online) Positron lifetime spectra of samples IA-LAO and IE1000 before etching. The Gaussian instrumental resolution and the fittings to Eq. (1) are also shown.

Figure 3

(Color online) Normalized low-momentum annihilation fraction $S$ vs incident positron energy $E$ for sample IA-LAO and samples IE10 and IE1000 before and after ${\text{Ar}}^{+}$ etching. Lines are the result of experimental data fitting using VEPFIT (Refs. 25, 26). The fitting parameters are summarized in Table . The derived depth distributions are shown in Fig. 5.

Figure 4

(Color online) Normalized low-momentum annihilation fraction $S$ vs incident positron energy $E$ for the substrates depleted of oxygen during thin-film deposition (LSTO series, frontside, and backside experiments). The IA-LAO data are also shown as the reference of the defect-free STO lattice. Lines represent the fittings using VEPFIT (Refs. 25, 26). The fitting parameters are summarized in Table . The derived depth distributions are shown in Fig. 6.

Figure 5

(Color online) Depth profile of vacancy defects in ion-etched and as-received substrates probed by positrons in STO, extracted from VEPFIT spectra simulation.

Figure 6

(Color online) Depth profile of vacancy defects in substrates reduced during film deposition probed by positrons in STO, extracted from VEPFIT spectra simulation.

Figure 7

(Color online) Normalized low-momentum annihilation fraction $S$ vs incident positron energy $E$ for sample IE10 after etching. Lines are the result of experimental data fitting to the VEPFIT software using one layer and free $L_{+}$ (dashed), and fixed $L_{+}$ with one (dashed dotted), two (dotted), and three (solid) layers. The resulting fitting parameters are summarized in Table .

Figure 8

(Color online) Plot of $\Delta S_{\text{VEPFIT}}$ and vacancy concentration as a function of ion-etching time (upper panel, samples IE10 and IE1000) and of film deposition time (lower panel, substrates depleted of oxygen during film deposition, LSTO series). The carrier density data are indicated by asterisk symbols in both panels.

Figure 9

(Color online) Normalized low annihilation fraction $S$ vs normalized high annihilation fraction $W$ for sample IA-LAO and samples IE1000 and IE10 before and after ${\text{Ar}}^{+}$ etching during, respectively, 1000 s and 10 s. Data of the LSTO series (substrates depleted of oxygen during film deposition) are also plotted. Only $\left(S,W\right)$ points measured between 15 and 25 keV, i.e., where a plateau is observed (see Figs. 3, 4), are represented on this graph. $\left(S,W\right)$ values averaged between 15 and 25 keV are represented in black (same symbols as raw data, bigger size).