δ-Doping of oxygen vacancies dictated by thermodynamics in epitaxial SrTiO₃ films

Transition metal oxide interfaces have exhibited a variety of novel phenomena, including the high-mobility two-dimensional electron gas,^1–5 superconductivity⁶ and unusual magnetism.⁷ While these phenomena are inherently related to the artificially designed architecture, oxygen vacancies (V_Os) are recognized to be particularly important in determining the exotic behaviors of the oxides systems.^8,9 As electron donors in oxides, V_Os were observed to be one of the major factors for the high carrier density at the LaAlO₃/SrTiO₃ interface.¹⁰ V_Os induce ferromagnetism in the epitaxial LaCoO₃ films via the ordering of excess electrons in Co 3d orbit.¹¹ It was also suggested that the existence of V_Os plays an important role in the formation of undesirable insulating phase in ultrathin films of many metallic oxide materials,^12,13 referred to as the “dead layer” behavior. How V_Os are involved in such complex phenomena is still unclear.

One essential issue toward the design of emergent properties of oxide films is how to characterize and control V_Os at the atomic scale. Recently, quantitative measurements of V_O concentration have been realized with high spatial resolution benefited by the development of the state-of-the-art aberration-corrected scanning transmission microscope (STEM) and related spectroscopy techniques.^14–16 However, tuning the V_O density precisely by growth control is still extremely challenging. Different oxidants, i.e., molecular O₂, O₃ and atomic O, have been used with different feeding pressure during the growth.^10,17–19 This approach is limited by thermodynamics of the material since the pressure of oxidant has to coordinate with temperature and other parameters in order to ensure the formation of the desired phase.^10,19 In many cases the optimal condition for oxygen stoichiometry cannot be reached, and residual V_Os are inevitably formed. It has been reported that V_Os even form inhomogeneous clusters in SrTiO₃ (STO) films.²⁰ Post annealing is another thermodynamic approach and seems to be effective to reduce the V_O density. However, it does not allow the precise control of V_Os distribution at the atomic scale either.

In the current work, to study the control of V_Os at the atomic scale, we grow SrTiO₃ homoepitaxial films along the polar [110] direction. Atomically well-defined (4 × 1) reconstruction is maintained on the surface all through the growth [see Fig. 1 (a) and (b)], which compensates the polarity.²¹ More importantly, the energy configuration associated with the surface reconstruction results in the spatial confinement of V_Os within only few subsurface layers of the film, while their concentration remains extremely low on the topmost surface and in the bulk of STO substrate. We show that such a quasi-two-dimensional (2D) V_O-doped layer, mimicking the δ-doping case in conventional semiconductors, can be precisely controlled.

The films were grown on Nb-doped (0.7 wt. %) SrTiO₃(110) substrates in a molecular beam epitaxy (MBE) system, following the recipe reported previously²² as described in the supplementary material. The high angle annular dark field (HAADF) and annular bright field (ABF) micrograph STEM images as well as the electron energy loss spectroscopy (EELS) were obtained by the aberration-corrected JEOL JEM-ARM200CF equipped with a cold field-emission electron source. The STEM sample was prepared by mechanical polishing and ion milling at liquid nitrogen temperature. The density functional theory (DFT) calculations were performed with the projector augmented-wave method²³ and Perdew-Burke-Ernzerhof functional²⁴ with the slab model and implemented in the “Vienna ab initio simulation package” (VASP) code.²⁵ 

To grow the SrTiO₃(110) film in UHV, the recently developed shuttered MBE technique²² is used, in which the growth can be precisely controlled by switching the shutter status of the metal (Sr or Ti) evaporation source with the reflection high-energy electron diffraction (RHEED) intensity (I_R) as the feedback signal [illustrated in Fig. 1 (c)].²⁶ The film surface maintains the (4 × 1) reconstruction as on the substrate all through the growth. Further characterized by cross-sectional STEM, the SrTiO₃ film keeps the perovskite lattice structure without any other phase formed. The interface between film and substrate is not distinguishable, indicating the high quality of the homoepitaxial film (Fig. 2). And the uniform image intensity of Sr/Ti manifests the cation stoichiometry.²² 

Shimoyama et al. grew homoepitaxial SrTiO₃(001) films by MBE in UHV without introducing any gaseous oxidant.^27–29 The continuous oxygen feeding from the oxide substrate to the surface was attained by the fast diffusion of V_Os deep into the bulk substrate.^28,29 Similarly, in the current work for SrTiO₃(110) where the residual oxygen in the growth chamber (⁠$P O 2 <2×1 0 − 10$ mbar) can only supply $<$ 1 % required by the epitaxy with the growth rate of 0.3 ML/min, the substrate has to act as an oxygen source. The key is to keep the growing surface (4 × 1) reconstructed, whose atomistic structure has been resolved,^30,31 as shown in Fig. 1 (a) and (b). The surface energy of SrTiO₃(110) is effectively reduced by the formation of TiO₄ tetrahedra. And the formation of V_Os on the reconstructed surface layer will cost energy (⁠$∼1.2eV$ for each V_O relative to the one in bulk (supplementary material)). Therefore, oxygen in the substrate would be driven to diffuse toward the surface to make Ti four-coordinated, as demonstrated by the extremely low V_Os density on (4 × 1) surface [see Ref. 31 and Fig. 1 (b)]. The chemical potential of such an oxygen source in solid state is equivalent to that of a gaseous oxidant with the area density of $∼2×1 0 15$ /cm², unachievable in any normal film growth conditions. Therefore the V_O density is effectively reduced in the film.

It is essential to clarify whether or not the oxygen diffusion from substrate (equivalently, the V_O diffusion from surface to subsurface layers) is kinetically feasible in this epitaxy process without gaseous oxygen environment. We explore the possible pathways of V_O diffusing from surface to subsurface layers by evaluating the energy barriers with Nudged Elastic Band (NEB) calculations.³² It is found that the two-step diffusion pathway shown in Fig. 3(a) with the barrier of 0.75 eV/0.56 eV is the most favorable one (supplementary material). To diffuse further into the bulk, the barrier that V_Os need to overcome is only about 0.6 eV.^33,34 In the thermal activation scenario, the diffusion rate of V_O, denoted as h, can be estimated by the Arrhenius equation $h=ν⋅exp ( − E b ∕ k B T )$⁠, where E_b is the energy barrier, $ν$ is the attempt frequency (empirically given by 10¹² s⁻¹), and k_B is the Boltzmann constant. Given the film growth rate of ∼ 0.3 ML/min as in the current experiments, 3 oxygen atoms are required to diffuse to surface within 200 seconds. As long as the growth temperature (T) is higher than 90 °C, sufficient oxygen can be supplied (supplementary material). Such an oxygen diffusion is undoubtedly kinetically feasible at the current growth temperature (T = 800 °C).

In MBE growth with the RHEED intensity as feedback control signal, the diffusion of deposited metals needs to be activated to form the long-range order. Considering the cation diffusion barrier in the bulk phase (more than ∼ 3.0 eV³⁵), the required growth temperature is estimated to be ∼800 °C with the current growth rate by the Arrhenius equation. Experimentally the elevated temperature of 800 °C is critical to maintain the surface crystallinity and reconstruction (supplementary material), as shown schematically in Fig. 3 (b).

Oxygen desorption from the surface is another factor that has to be considered during the growth in UHV at such a high temperature. As schematically shown in Fig. 3(c), the desorption energy barrier [variable with the chemical potential of oxygen μ(T, $P O 2$⁠)]³⁶ is estimated to be about 3.0 eV at such a reconstructed surface at T = 800 °C and $P O 2 =1×1 0 − 10$ mbar (supplementary material). Usually increasing the pressure of gaseous oxidant for growth can increase the desorption barrier and suppress the oxygen desorption. But here, the oxygen desorption can be compensated effectively by the bulk oxygen diffusing to the surface due to the low diffusion barrier. Consequently, V_Os are distributed deep in the bulk while their density at the topmost surface remains extremely low.³¹ Further elevating the grow temperature may increase the desorption rate of oxygen, i.e., the total amount of V_Os all through the sample would be increased.

We have further studied the V_O distribution in the epitaxial films with the EELS of STEM. In the simple ionic scenario, each V_O normally donates two electrons that reduce two adjacent Ti⁴⁺ ions to Ti³⁺ in SrTiO₃. Therefore, the V_O density and distribution at the atomic scale can be quantitatively determined by analyzing the layer-dependent Ti valence shown in EELS. Figure 4 (a) presents the layer-resolved EELS spectra of Ti L_2,3 edge from the surface all the way across the interface to substrate. Beneath the 6th layer from the topmost surface, the Ti core level spectra of different layers are uniformly identical to Ti⁴⁺ (supplementary material).³⁷ This implies that V_Os are homogeneously distributed with the density as an undetectable background, and the STEM sample preparation has no significant effect on EELS. The spectra taken at the Ti columns within 6 layers from the topmost surface show clear chemical shift to the lower energy relative to those for the bulk, indicating the existence of Ti³⁺ associated to V_Os. Quantitatively, we fit the spectra with two components of Ti³⁺ and Ti⁴⁺ by the multiple linear least-squares (MLLS) method to determine the V_O density (supplementary material). Figure 4 (b) shows the results of the 15 ML film. Note that the V_Os concentration at topmost layer (extremely low) was determined by the in situ STM and DFT analyses,³¹ rather than from EELS results to avoid possible artifact introduced by the ex situ sample transfer. The V_Os show the highest density (∼ 14%) on the 2nd layer and then quickly diminishes to the background reference level (undetectable by EELS) beneath the 6th layer. The layer dependence of V_O distribution of the sample with 10 ML homoepitaxial film is also resolved and plotted in Fig. 4(b) for comparison. In both cases, the most important finding is that V_Os are mainly confined between the 2nd to 6th layer from the surface with the density maximum at the 2nd layer. The only difference is quantitative-lower V_O density in the thinner film at each respective layers (2nd-5th). This is due to the shorter growth time for the thinner film, which means less oxygen desorption from the surface.

Due to the high diffusion rate of V_Os at the high growth temperature, the film surface almost reaches the thermodynamic equilibrium immediately after Sr/Ti deposition. The spatial confinement of V_Os can be understood by resolving the energetics associated with their distribution that is determined by the (4 × 1) reconstruction. On the 2nd layer from the topmost surface, each TiO₆ octahedron shares two oxygen atoms with the surface TiO₄ tetrahedra [see Fig. 1 (a)]. Such a bonding configuration is quite different from that in the bulk. Given a V_O in the sample, our DFT calculations verify a significant energy gain of ∼ 0.6 eV when it is in the 2nd layer over any other possible locations (supplementary material). Note a V_O in the topmost surface is the most unfavorable and its energy loss is even larger relative to the 2nd layer (∼ 1.8 eV). We systematically calculate the formation energy of a V_O on the i-th layer (⁠$𝜖 i$⁠) and estimate the according V_O concentration determined by the thermodynamics as $e − 𝜖 i ∕ k B T$⁠. The calculated results in Fig. 4(b) show that almost all V_O would have been confined on the 2nd layer. Experimentally, the observed V_O distribution is broadened due to the repulsive Coulomb interaction between ionized V_Os which is not considered in the calculations. In addition, electrons ionized from V_O may diffuse within a certain range, resulting in further broadening of the reduced Ti³⁺ ions distribution.

Post annealing slightly affects the V_O distribution. At 300 °C, annealing in vacuum for 14 hours broadens the V_O distribution to the 7th layer [Fig. 4(b)], while the maximum still locates at the 2nd layer. The broadening might be due to the repulsive interaction between V_Os and the annealing enhances the diffusion of V_Os. More importantly, the density of electrons (ionized from the confined V_Os) in the 2D system beneath the surface can be modified. For the as-grown 15 ML film, the V_O density on the 2nd layer is 14%, corresponding to the electron density of 4 × 10¹⁴ /cm². Annealing at an intermediate temperature [300 °C, see Fig. 4 (b)] allows the V_O diffusing towards the surface region but suppresses the oxygen desorption. As the result, V_O density on the 2nd layer decreases to 7% and the electron density decreases to 2 × 10¹⁴/cm². And the total amount of V_Os through the 7 layers from the surface is significantly reduced by ∼ 17%. Beneath the 7th layer, V_Os are uniformly distributed V_Os with a low density beyond EELS sensitivity.

During the growth, the oxygen chemical potential provided by the solid-state substrate is related to the deposition of metal atoms on the surface. Although the oxygen desorption is difficult to control at high temperature, it is relatively easy to control the growth of cations. This enables us to achieve the robust spatial confinement of V_Os – we obtain the same V_O distribution in STO film with different thickness and actually even in the single crystalline substrate without epitaxy, as long as the (4 × 1) reconstruction is formed on the surface. To conform this, We have used a undoped SrTiO₃(110) with the the (4 × 1) reconstructed surface and perform ex situ electric transport measurements (supplementary material). We found that the bulk is insulating while the subsurface layers is metallic due to the existence of confined V_Os. The resistance of the V_O layer is much lower than that of the bulk by about 3 orders of magnitude in the measured temperature range. Combining with the evidence that the topmost surface is insulating provided by STM spectroscopy and DFT calculations, we concluded that a 2D metallic layer is flanked (and protected against atmosphere exposure) by the insulating bulk and reconstructed surface, mimicking the δ-doping in conventional semiconductors. Such a buried metallic phase beneath the reconstructed SrTiO₃(110) surface has also observed by photoemission spectroscopy.⁴ The above discussions can also be applied to other (n × 1) surfaces since they have the same TiO₄ building blocks.³⁰ In general, using the reconstructed surface as a confinement boundary, one can tune V_O density in a range comparable or even wider than traditional methods such as the gate voltage in field effect transistors.

In conclusion, we have grown homoepitaxial SrTiO₃(110) films in UHV and studied the controllability of V_Os by precisely tuning the surface cation concentration. By preserving the (4 × 1) surface reconstruction, oxygen in the substrate bulk is driven to diffuse toward the surface to supply oxidant continuously. The film growth is associated with the formation of V_Os, which are confined within a few subsurface layers between the fully oxidized topmost surface and the bulk substrate with a low V_Os concentration as undetectable background, mimicking the δ-doping case in conventional semiconductors. The thermodynamics associated with the surface reconstruction determines such V_Os distribution. It is demonstrated that the density and distribution of V_Os in oxides can be controlled at the atomic scale by tailoring the lattice structure of the surfaces, thus providing an opportunity to construct and manipulate novel quantum phenomena in low-dimensional oxide systems.