Oxygen vacancy dipoles in strained epitaxial BaTiO 3 ﬁlms

The existence of out-of-plane-oriented oxygen vacancy dipoles was experimentally established in (001) perovskite epitaxial ﬁlms of ferroelectric barium titanate by analyses of the crystal and electronic structure as well as the ferroelectric and optical properties. The formation of the defects was shown to occur in the presence of in-plane compressive strain and oxygen-deﬁcient deposition conditions. The in-plane compressive strain was suggested to favor the formation of oxygen vacancies V O in the Ba-O planes and thus stabilize the out-of-plane orientation of the dipolar (V + 2O -Ti 3 + ) + defects.


I. INTRODUCTION
Barium titanate (BaTiO 3 , BTO) is one of the beststudied perovskite oxide ferroelectrics, which are known for their large switchable spontaneous polarization and excellent piezoelectric, pyroelectric, photovoltaic, electrocaloric, and other properties, as well as devices based thereon [1][2][3][4]. The polarization and charge-transport properties, important for applications, depend on the presence of unintentional or intentional point defects in ferroelectrics. It is worth mentioning that oxygen vacancies are the most common point defects in perovskite oxides. In titanate ferroelectrics such as BTO and SrTiO 3 (STO), oxygen vacancies V O may exist as neutral (V 0 O ), singly positive (V + O ), and/or doubly positive (V +2 O ) ones [5][6][7][8][9][10]. The vacancy V +2 O can trap one to two electrons in the form of small polarons. In such polarons, the electrons are localized on Ti atoms near the vacancy, which changes Ti 4+ to Ti 3+ [5,6]. The lowest formation energy is found for the doubly charged vacancies V +2 O and the complexes of V +2 O and one polaron, or (V +2 O -Ti 3+ ) + [5,6]. In practice, the oxygen vacancies form to compensate the charge imbalance induced by heterovalent doping and/or in the result of oxygen-deficient processing such as synthesis or annealing in a reducing atmosphere [11][12][13], or during thinfilm deposition at sufficiently low oxygen pressures [14][15][16]. In epitaxial films, the influence of lattice strain on the formation of oxygen vacancies was also recently recognized [17][18][19][20].
Here we demonstrate the formation of oxygen vacancy dipoles occurring under a combined action of low-pressure deposition and in-plane compressive strain in epitaxial BTO films. By analyzing the crystal and electronic structures, ferroelectric behavior, and optical properties of the films, we establish the presence and out-of-plane orientation of (V +2 O -Ti 3+ ) + defects. We discuss the strain-driven formation of these defects.

II. EXPERIMENT
Thin films of BTO (∼150 nm) were deposited with SrRuO 3 (∼15-20 nm, SRO) bottom electrode layers and also without such layers on epitaxially polished single-crystal (001) SrTiO 3 (STO) substrates (MTI Corp.). The BTO and SRO films were grown by pulsed laser deposition (PLD) using a KrF excimer laser (wavelength 248 nm, energy density ∼2 J/cm 2 , pulse repetition rate 2 Hz) at a substrate temperature of 973 K. The ambient oxygen pressure during SRO deposition was 20 Pa. The BTO films were deposited using different pressures of 0.1, 2, 5, 10, and 20 Pa. In addition to the 150-nm-thick BTO films, BTO films of different thicknesses (∼35 and ∼70 nm) were deposited at a pressure of 5 Pa. Postdeposition cooling was conducted at a rate of 5 K/min and the BTO deposition pressure. Capacitor stacks were formed using a bottom SRO electrode layer and circular top Pt contact pads (area 0.2 mm 2 ), which were created by a room-temperature vacuum PLD of Pt through a shadow mask.
The crystal structure of the films was studied by highresolution x-ray diffraction (XRD) with a D8 DISCOVER diffractometer (Bruker corporation) using Cu Kα radiation.
-2 scans in the range of 2 = (10−130) deg and reciprocal space maps (RSM) in the vicinity of the perovskite (002) and (103) diffractions were acquired. The in-plane (parallel to substrate surface) and out-of-plane (normal to substrate surface) lattice parameters were estimated from the positions of the diffraction maxima using STO as a reference.
The local crystal structure was inspected by transmission electron microscopy (TEM) and high-resolution transmission electron microscopy (HRTEM) using a JEOL JEM-2200FS microscope operated at 200 kV. Cross-sectional samples were prepared for analysis by focused ion beam (FIB) milling using a Dual-Beam scanning electron microscope FEI Helios Nanolab 600 equipped with a Ga+ FIB. The bright-field TEM (BF-TEM), scanning TEM (STEM), selected area electron diffraction (SAED), nanobeam electron diffraction (nBED), and HRTEM imaging combined with fast Fourier transforms (FFT) and Fourier filtering were employed to investigate the crystal structure of BTO. Energy dispersive x-ray spectroscopy (EDS) and electron energy loss spectroscopy (EELS) were utilized to define the elemental composition. The EDS and EELS spectra were acquired and quantified using GATAN software.
A special algorithm was applied to accurately quantify the spatial distribution of the lattice parameters in the in-plane and out-of-plane directions inside the BTO film deposited at 5 Pa. The algorithm was as follows. The HRTEM images with a field of view ∼(50 nm×50 nm) were acquired along the out-of-plane [100] axis and in-plane [001] axis of BTO. The images overlapped and covered the whole BTO film in the outof-plane direction and a region with a width of ∼150 nm in the in-plane direction. The (010) and (001) interplanar distances, corresponding to the in-plane and out-of-plane lattice parameters of BTO, were extracted from fast Fourier transforms of the images using a sliding-window technique and CRYSTBOX DIFFRACT GUI software [21,22]. The lattice parameters were estimated as a function of the position in the film using averaging and binning of the data extracted from each of the windows. Compared to the widely applied geometrical phase analysis (GPA), this approach ensures better accuracy in our films [21,22]. The lattice parameters were determined with an accuracy of ±0.005 Å.
The impedance of the capacitors was measured by a NOVOCONTROL Alpha-AN High Performance Frequency Analyzer. The ferroelectric polarization was inspected by using a TF 2000E Analyzer (aixACCT Systems GmbH). In all measurements, the electric field was applied and the response was measured along the out-of-plane direction for the SRO/BTO/Pt capacitors.
The local piezoresponse was investigated by piezoresponse force microscopy (PFM) using Multimode 8 atomic force microscope (Bruker) and Pt-coated silicon tips (HQ:NSC18/Pt, MikroMasch). The out-of-plane PFM signal was acquired at a probing ac voltage of 2 V and as a function of superposed dc voltage, which was swept in the range of −8 to 8 V.
The optical constants (index of refraction, extinction coefficient, and absorption coefficient) of the BTO films were studied using variable angle spectroscopic ellipsometry. The measurements were carried out on a J. A. Woollam ellipsometer (wavelengths of 146-1600 nm) at room temperature in an atmosphere of dry nitrogen. The ellipsometric spectra were taken at incident angles of 65 and 70 deg. The dielectric functions and optical constants of the films were extracted from the ellipsometric spectra using a commercial WVASE32 software package. More details for the ellipsometric procedures can be found elsewhere [23][24][25].

A. Crystal structure
XRD and TEM studies evidenced a cube-on-cube-type epitaxy for all the BTO and SRO films on STO. The BTO films are perovskite-type and oriented with the (00l ) planes parallel to the (001) plane of STO ( Fig. S1 in Supplemental Material [26]). Other phases were not detected. Inspections of the elemental composition by EDS and EELS did not reveal stoichiometric deviations either. The SRO layers grow pseudomorphically on STO (Supplemental Material in Figs. S2 and S3 [26]): the in-plane lattice parameters of the perovskite SRO cell are equal to those of the underlying STO.
For the 150-nm-thick BTO films, the measured out-ofplane and in-plane lattice parameters (c and a), tetragonality (c/a − 1), and unit-cell volume V uc = a 2 c are summarized in Fig. 1. The shadowing in Fig. 1(c) qualitatively illustrates an out-of-plane spread of the parameter c as extracted from the full width at half maximum of the (003) -2 diffraction peaks (Supplemental Material in Fig. S1).
The results in Fig. 1 reveal that the BTO lattices apparently differ for different pressures.
The high-pressure 20-Pa film possesses an in-plane elongation and out-of-plane shrinkage compared to bulk BTO: a > a BTO and c < c BTO , where a BTO = 3.992 Å and c BTO = 4.036 Å are the BTO bulk parameters. This behavior implies that the substrate-imposed in-plane compressive misfit strain s a is relaxed (s a = a STO /a 0BTO − 1 ≈ −2.5%, where a STO is the lattice parameter of STO and a 0BTO is the lattice parameter of a cubic cell of BTO a 0BTO = V uc 1/3 ). Because of a mismatch between the thermal expansion coefficients of BTO and STO, a thermal biaxial in-plane tensile strain builds-up during postdeposition cooling [27]. Assuming a complete misfit relaxation during BTO growth at 973 K, the estimated room-temperature thermal strain is s T ≈ 0.3%. The lattice parameters, tetragonality, and unit-cell volume of thermally strained BTO/STO were calculated using the elastic constants of BTO [28]. The measured negative tetragonality agrees well with the calculated value of −0.8%. The measured unitcell volume is also consistent with the calculated volume of ∼64.4 Å 3 . The proper unit-cell volume indicates the absence or a minor density of point defects in the high-pressure film. The film adopts the theoretically predicted a-phase [29,30]. Thus, the complete relaxation of misfit strain and the proper oxygen content are characteristics of our high-pressure BTO films.
With decreasing pressure, the unit-cell volume increases [ Fig. 1(d)]. This lattice expansion is compatible with the previous observations in epitaxial films and commonly ascribed to the formation of oxygen vacancies therein [15,16,[31][32][33][34][35]. However, compared to bulk stoichiometric BTO, the expansion reaches 2-3%, which exceeds that achieved for maximum allowed oxygen deficiency or for oxygen substitution in perovskite phase of BTO [36,37]. Assuming, nevertheless, that the expansion is macroscopically isotropic chemical one, the estimated misfit strain is up to s a ≈ −3.3% in the oxygendeficient films. Such a large strain should have been completely relaxed in the 150-nm-thick films. In contrast to this expectation, the 0.1-5-Pa films exhibit profound out-of-plane elongation [ Fig. 1(a)] and enhanced tetragonality [ Fig. 1(c)]. Moreover, the 5-Pa films are nearly pseudomorphic to STO [ Fig. 1(b)]. These observations imply that ordinary chemical expansion is insufficient for understanding the structural changes in the BTO films.
To elucidate possible role of strain, the peculiar films deposited at 5 Pa are analyzed in more details. The films are practically pseudomorphic to STO (a ≈ a STO < a BTO ) and demonstrate a strong out-of-plane elongation (c c BTO ) with tetragonality up to ∼8%. The lattice parameters, tetragonality, and unit-cell volume of pseudomorphic stoichiometric BTO were calculated assuming that the BTO/STO misfit strain does not relax and overrides the thermal mismatch. The measured tetragonality of ∼8% and unit-cell volume of ∼64.6 Å 3 exceed the calculated ones of ∼5.8% and ∼63 Å 3 , respectively. This discrepancy is in line with the oxygen-vacancy-induced expansion of unstressed film's material and, hence, somewhat larger misfit strain in the oxygen-deficient films compared to that in the stoichiometric films assumed in the calculations. Thus, the pseudomorphic growth and anisotropic lattice expansion of the 5-Pa films suggest that the common relaxation of the substrate-imposed misfit strain can be hindered by the formation of oxygen vacancies.
With reducing pressure below 5 Pa, the misfit strain is further enlarged that leads to its partial relaxation. The structural changes as a function of pressure ( Fig. 1) emerge from the combined action of misfit strain and oxygen deficiency. When taken separately, neither strain, nor oxygen vacancies can explain these changes.
To unfold strain-vacancy links, the films' microstructure is scrutinized. The cross-sectional TEM analysis unveils a column-free microstructure in the super-tetragonal 5-Pa BTO film, in contrast to the presence of columns in the other films [Figs. 2(a) to 2(c)]. The columns imply the Stranski-Krastanov growth mode, caused mainly by the relaxation of misfit strain through the formation of dislocations [38]. The absence of columns points to an additional phenomenon, other than the formation of dislocations in the 5-Pa film [ Fig. 2(b)]. The local HRTEM analysis shows a change in the lattice parameters across the thickness, but not along the plane at each thickness [Figs. 2(d) to 2(f)]. The out-of-plane lattice parameter decreases from ∼4.19 Å at the bottom to ∼4.10 Å at the top [ Fig. 2(d)]. The changes agree with the XRD observations in the 5-Pa films of different thicknesses (Supplemental Material in Fig. S1). The bottom-to-top lattice transformation takes place without a massive generation of dislocations and columns. The formation of low-angle boundaries is detected only at a distance of ∼80 nm from the SRO/BTO interface (Supplemental Material in Fig. S4). Such a pseudomorphic growth can be ensured by the presence of point-type defects, which reduce the in-plane compression. The defects are generated under oxygen deficiency and are oxygen vacancies.

B. Ferroelectric behavior
The high-pressure 10-20-Pa films retain the ferroelectric a-phase with the in-plane spontaneous polarization, which is manifested by slim out-of-plane polarization-voltage loops (Supplemental Material in Fig. S5). The 2-Pa and 5-Pa films are ferroelectric with out-of-plane switchable polarization ( Fig. 3 and Supplemental Material in Fig. S5). The large leakage current prevents polarization measurement in the 0.1-Pa films.  The 5-Pa films exhibit the nearly rectangular well-saturated polarization-voltage (P-V) loops [ Fig. 3(a)] and currentvoltage loops [ Fig. 3(b)]. The magnitude of the positive and negative saturation polarization is ∼25 μC/cm 2 and close to the handbook room-temperature spontaneous polarization in bulk unstressed BTO [28]. This polarization similarity shows that neither lattice strain nor strain gradient are responsible for the ferroelectric properties here. Importantly, the ferroelectric loops are shifted along the voltage axis. The coercive voltages are of the same sign (negative here): the film possess an in-built electric field and is self-polarized. With increasing frequency, the coercivity increases, but the saturation polarization does not change [Figs. 3(a) and 3(b)]. This dynamic behavior (under an applied ac electric field) is consistent with the creep and flow motions of back-switched domains in high-quality epitaxial ferroelectric films [39]. The small density leakage current also complies with that found in high-quality epitaxial ferroelectric films [ Fig. 3(c)]. The butterfly type capacitance-voltage loop confirms the ferroelectric switching and voltage offset in the 5-Pa BTO film [ Fig. 3(d)].
The presence of the in-built field and self-polarization in the 5-Pa film without top Pt electrodes is confirmed by piezoresponce force microscopy (Supplemental Material in Fig. S6). The phase of the piezoresponse is around −90 • over the film surface at zero bias. The phase changes by ∼180 • upon biasing and exhibits both the hysteresis and voltage offset, in agreement with the polarization switching measured using the top Pt electrodes.
The ferroelectric properties of the supertetragonal 5-Pa BTO films are akin to those of high-quality epitaxial perovskite ferroelectric films. Peculiarly, these films possess the in-built electric field and self-polarization. The in-built field is also present in the 2-Pa films (Supplemental Material in Fig. S5).

C. Optical properties
To discard the possible influence of electrodes and straininduced single-domain state on the in-built field and selfpolarization, we investigate spectra of optical constants in the films without electrodes. In particular, we compare the index of refraction n measured in the transparency range (at wavelengths λ > 400 nm) in the 5-Pa film and the reference polydomain BTO crystal [ Fig. 4(a)]. The smaller n in the film arises due to fundamental electro-and elasto-optic effects in BTO [40,41]. Considering the out-of-plane in-built field E out and strain s out (due to lattice elongation) in the film, the drop in refraction can be presented as [ (n −2 ) = r BTO E out + p BTO s out ], where r BTO and p BTO are the electro-and elasto-optic coefficients of BTO, respectively. Using the maximum coefficients [41] r BTO ≈ 1300 pm/V and p BTO ≈ 0.05 and strain s out ≈ 0.03, we estimated a minimum field E out from the refraction data. The optically estimated field is E out ≈ 8 MV/m, which discards the electrodes and strain as its possible origin.
The in-built field is corroborated by the higher energies of the main optical transitions in the 5-Pa films compared to the reference crystal (as found here from the positions of the peaks in the refraction spectra) [Figs. 4(b) and 4(c)]. The peak in the film is blueshifted to shorter wavelengths (higher photon energies). The blueshift evidences an uplift of the conduction bands [40,42], which contrasts with a common spectral redshift (band-gap narrowing) under lattice expansion [43,44]. Therefore, the observed blueshift proves the presence of in-built field in the electrodeless 5-Pa film. Moreover, using polarization potentials, the blueshift E can be expressed as E = βP 2 , were P is the polarization and β is the temperature-independent band-edge polarization potential [45]. The detected blueshift E ≈ 0.4 eV [ Fig. 4(c)] corresponds to the polarization of ∼50 μC/cm 2 , which is estimated using β = 1.16 eV · m 4 · C −2 of bulk BTO crystal. Because the value of β in the oxygen-deficient supertetragonal BTO film is not exactly known, the estimation is not accurate. Nevertheless, it supports the presence of significant self-polarization in the 5-Pa film without electrodes.
We emphasize that the index of refraction from the transparency range and the position of the main refraction peak in the 20-Pa films are similar with those in the reference crystal [ Fig. 4]. These optical observations agree with the electrical data and confirm that the in-built field and self-polarization are the properties of the 5-Pa films.
Because optical transitions from/to defect-related in-gap states are the fingerprints of the defects, the presence of point defects can be detected optically. To reveal the in-gap states, we examine the defect-containing 5-Pa film and the reference defect-free 20-Pa film. Compared to the near-gap spectrum of the extinction coefficient k in the 20-Pa film [dashed curve in Fig. 5(a)], an additional hump at approximately 410 nm is observed in the 5-Pa film [solid curve in Fig. 5(a)]. This additional absorption is consistent with the optical excitation (at wavelengths shorter than 500 nm) of the (V +2 O -Ti 3+ ) + defects [46]. The corresponding in-gap states are schematically shown in Fig. 5(b).
In addition to the pre-edge absorption due to the ingap states, the absorption edge is blueshifted to shorter wavelengths (higher photon energies), which evidences a band-gap widening in the 5-Pa film [ Fig. 5(a)]. This nearedge behavior fully agrees with the blueshift in the refraction spectra and substantiates the presence of in-built field. While the pre-edge optical absorption is consistent with the excitation of (V +2 O -Ti 3+ ) + complexes, the in-built field can result from an out-of-plane dipolar ordering of these defect complexes.

D. Electronic structure
The presence of (V +2 O -Ti 3+ ) + complexes is further validated by detecting the Ti valence state from EELS Ti L-edge and O K-edge spectra in the 5-Pa BTO film [ Fig. 6]. The reference spectra acquired from the STO substrate [Figs. 6(a) and 6(c)] agree with the published data [47,48] and attest to the correct measurements.
The Ti L-edge spectrum measured in the BTO film [ Fig. 6(b)] is compared to that reported for a stoichiometric unstressed BTO crystal [49]. The film is characterized by a relative increase in the spectral weight of the Ti L 2,3 e g peaks, especially in the lower-energy L 3 -edge. Previously, such spectral changes were observed with increasing Ti 3+ content in the nominally Ti 4+ -based perovskite oxides [50,51]. The behavior of the Ti L-edge in the BTO film implies the presence of Ti 3+ cations therein. Additionally, the valleys between the peaks at the O K-edge are lifted up in the film compared to the reference crystal [ Fig. 6(c)]. This behavior also substantiates the presence of Ti 3+ states in the BTO film [51].
We note that compared to the nominal [Ti 4+ O 6 ] octahedron in BTO, the [Ti 3+ O 5 V O ] unit containing oxygen vacancy was shown to be elongated along the V O -Ti axis [52,53]. Here the observed anomalous out-of-plane lattice elongation supports the presence of the out-of-plane oriented (V +2 O -Ti 3+ ) + defects in the 5-Pa BTO films.

IV. DISCUSSION
Thus, the strong out-of-plane elongation, in-built electric field, optical properties, and local electronic structure are all consistent with the presence of the out-of-plane oriented dipolar (V +2 O -Ti 3+ ) + defects in the oxygen-deficient BTO films. The defects emerge at low oxygen pressures and large biaxial in-plane compressive strain. We emphasize that neither supertetragonal structure, nor in-built field are obtained in the absence of such strain (Supplemental Material in Fig. S7).
The links between strain and oxygen vacancies are highlighted by recent first-principles analyses [18][19][20]. Compared to unstressed perovskite oxide ferroelectric, an in-plane compressive strain strongly reduces the formation energy for an out-of-plane oxygen vacancy [20]. That is, in the BTO films on STO, the in-plane compression facilitates the formation of oxygen vacancies in the Ba-O planes parallel to the substrate surface (Supplemental Material in Fig. S8) [54]. Moreover, the compressive strain is likely to intensify the formation of the V +2 O vacancies compared to the V 0 O vacancies [20]. Considering that the out-of-plane V +2 O oxygen vacancies (i.e., V +2 O vacancies in the Ba-O planes) are favored by the in-plane compression and that the formation energy is low for the (V +2 O -Ti 3+ ) + defects in BTO [5,6], the formation of the out-of-plane oriented (V +2 O -Ti 3+ ) + complexes is preferred in the compressively strained oxygen-deficient BTO films.
The anisotropic formation of the oxygen vacancies (in the Ba-O planes) can boost anisotropic lattice expansion and enhance the out-of-plane elongation of the unit cell. Concurrently, our observations indicate that the formation of oxygen vacancies can partially release the substrate-induced misfit, in resemblance with the theoretical scenario [18].
In addition to the strain-controlled formation of oxygen vacancies also the migration of oxygen vacancies is governed by strain. For instance, for the compression-promoted out-ofplane vacancies, migration of vacancies in the out-of-plane direction is impeded [20]. (This restriction can be qualitatively understood from Supplemental Material in Fig. S8.) The oxygen vacancy dipoles can efficiently tune the ferroelectric and optical behavior of BTO. These defects may influence the charge transport and, possibly, exhibit magnetism leading to multiferroic states. Comprehensive theoretical investigations of the formation and structure of oxygenvacancy-related defects in epitaxially strained BTO films are absent and highly desirable.

V. CONCLUSION
Cube-on-cube-type epitaxial perovskite BTO films were grown on (001)STO substrates using different oxygen pressures. The crystal structure, ferroelectric properties, optical behavior, and electronic structure of the films were investigated. It was shown that the out-of-plane oriented dipolar (V +2 O -Ti 3+ ) + defects formed in the presence of in-plane compressive strain and oxygen deficiency. It was suggested that the in-plane compressive strain can reduce the formation energy for the out-of-plane oxygen vacancies, which leads to the out-of-plane orientation of the (V +2 O -Ti 3+ ) + dipoles.