Oxygen vacancies in strained SrTiO$_{3}$ thin films: formation enthalpy and manipulation

TL;DR

This study investigates how epitaxial strain affects oxygen vacancy formation in SrTiO₃ thin films, revealing that strain reduces formation energy and enables manipulation of vacancies and local properties via electric fields.

Contribution

It provides new insights into the effects of strain on oxygen vacancy formation enthalpy and demonstrates electric field control of vacancy distribution and associated mechanical responses.

Findings

Both compressive and tensile strain decrease vacancy formation enthalpy.

Electric fields can modulate oxygen vacancy concentration locally.

Vacancies influence TiO₆ octahedral rotation patterns.

Abstract

We report the enthalpy of oxygen vacancy formation in thin films of electron-doped SrTiO$_{3}$, under different degrees of epitaxial stress. We demonstrate that both compressive and tensile strain decrease this energy at a very similar rate, and promote the formation of stable doubly ionized oxygen vacancies. Moreover, we also show that unintentional cationic vacancies introduced under typical growth conditions, produce a characteristic rotation pattern of TiO$_6$ octahedra. The local concentration of oxygen vacancies can be modulated by an electric field with an AFM tip, changing not only the local electrical potential, but also producing a non-volatile mechanical response whose sign (up/down) can be reversed by the electric field.

Tables

Table 1. Table 1 : List of substrates used in this work for deposition of Nb-doped SrTiO 3 films under different degrees of epitaxial strain. Where 3.905 (Å) and a s refer to the lattice parameter of bulk STO and to the pseudocubic lattice parameter of the substrate, respectively.

	Pseudocubic lattice parameter (Å)	Strain (%=$\frac{a_s-3.905}{3.905}$$\times$100)
(100) LaAlO3 (LAO)	3.791	-2.91
(100) (NdAlO3)0.39-(SrAl0.5Ta0.5O3)0.61(NSAT)	3.840	-1.66
(100) (LaAlO3)0.29-(SrAl0.5Ta0.5O3)0.71(LSAT)	3.868	-0.95
(110) LaGaO3 (LGO)	3.885	-0.51
(100) SrTiO3 (STO)	3.905	0
(110) DyScO3 (DSO)	3.950	+1.15
(110) GdScO3 (GSO)	3.970	+1.66

Equations

$$SrTi{O}_3(s)\rightleftharpoons SrTi{O}_{3-x}(s)+\frac{x}{2}{O}_2(g)\uparrow$$

$$O^{2-}\rightleftharpoons \frac{1}{2}{O}_2+V_O+2e$$

$$K=\left[V_O\right]n_e^2{P}_{O_2}^{1/2}$$

$$log{n}_e\propto -\frac{1}{6}\log P_{O_2}$$

$$K=K_0{e}^{-\Delta H/k_{B}T}$$

$$\log n=K_0^{\prime }-\frac{1}{9}\log P_{O_2}-\frac{\Delta H}{3\kappa T}$$

$$\log n=K_0^{\prime \prime }-\frac{\Delta H}{3\kappa T}$$

Full text

thin films,oxygen vacancies, epitaxial strain

I Introduction

The flexibility of oxoperovskites for accepting a large number of cationic dopants is extremely useful for the systematic study of the correlations between crystalline structure, electronic structure, and functionality. Their high chemical stability also makes them well suited materials for growth in single-crystalline and thin film form. Combining these characteristics with the mixed valence states of 3$d$ transition metal ions, results in some of the most remarkable properties and functionalities found in solids.Goodenough (1963); Tsuda et al. (1991) A good example of this richness is the case of SrTiO3 (STO), a diamagnetic quantum paraelectric insulator Rowley et al. (2014), in which cationic vacancies induce polar regions of nanometer size stabilized by stress. Jang et al. (2011, 2010) Oxygen vacancies, (VO), are also readily formed in this material; due to their donor-character and the very large electron mobilities characteristic of delta-doped STO, even the slightest concentration of vacancies produces a measurable electrical conductivity.Son et al. (2010); Santander-Syro et al. (2010); Meevasana et al. (2011); Reagor and Butko (2005) Actually, reduced STO was the first oxide reported to show superconductivity, with a maximum TC$\approx$0.3 K for electron densities of n$$\approx1020 cm*-3*.Schooley et al. (1964, 1965)

The unintended presence of oxygen vacancies could be particularly important in thin films of STO: first, typical deposition conditions imply high temperature and low oxygen pressure, which favors the reduction of STO. Second, donation of the extra charge of ionized oxygen vacancies to non-bonding orbitals of the perovskite results in expansion and local TiO6-octahedral rotation.Petrie et al. (2016a); Gazquez et al. (2013) Ab-initio calculations actually support a lowering of the VO formation energy under tensile strain for SrTiO3 Choi et al. (2015) and other perovskite oxides, like CaMnO3,Aschauer et al. (2013); Chandrasena et al. LaAlO3,Johnson-Wilke et al. (2013) or SrCoO3-δ. Petrie et al. (2016a) The same chemical expansion mechanism should in principle disfavor anionic vacancy formation under compressive stress. In this case several calculations have been published in the last few years, but the results are diverse for different oxides: in CaMnO3, the calculated effect of a moderate compressive stress is almost negligible,Aschauer et al. (2013) while it results in a considerable increase of VO formation energy in LaAlO3,Johnson-Wilke et al. (2013) SrCoO3-δ Petrie et al. (2016a) and ferroelectric BaTiO3.Yang et al. (2013) For the case of SrTiO3, however, different authors suggest that both compressive and tensile strain can stabilize VO. Al-Hamadany et al. (2013); Choi et al. (2015); Zhang et al. (2015)

It is vital the inclusion of the precise pattern of TiO6 octahedral rotation and the actual charge of the vacancies in the calculations, to obtain reliable results. Furthermore, the presence of cationic vacancies can have a strong influence and should be taken into account, although rarely are considered jointly with VO in the calculations.Rondinelli and Nicola (2011)

Given the relevance of oxygen vacancy formation in the functional properties (e.g. resistive switching, improved catalytic properties, etc) of STO thin films and other oxides,Petrie et al. (2016b); Tahini et al. (2016) it is very important to experimentally measure the effect of tensile and compressive stress on the formation energy of oxygen vacancies in STO thin films.

Here, we report a thermodynamic study of the process of oxygen vacancy formation in thin films of electron-doped STO under different degrees of epitaxial strain. Our main finding is the experimental demonstration of a significant reduction of the enthalpy of oxygen vacancy formation, for both compressive and tensile stress. This points to a common mechanism irrespective to the sign of epitaxial strain, most probably due to a reduction of the energy gap. Furthermore, we show that even though the actual TiO6-octahedral rotation pattern observed in the film is due to the presence of cationic vacancies, they are cooperative throughout the whole film, and not just around point defects. Finally, we demonstrate that oxygen vacancy manipulation by an electric field can lead to non-volatile changes in the local volume. This offers the possibility of mechanical control of the local electrical properties.

II Experimental Details

Oxygen vacancies are characteristic e-donor defects and therefore their concentration can be determined by Hall effect experiments. In order to detect small concentrations of oxygen vacancies created at relatively high deposition oxygen pressure and high temperature, any source of intrinsic acceptor impurities should be previously neutralized. It is known that nominally undoped SrTiO3 single crystals contain small concentrations of acceptor impurities.De Souza et al. (2012) These occur mainly in the form of ionized Sr vacancies (VSr), which trap part of the electrons donated by the VO to the conduction band of the oxide. The presence of VSr is even more important in thin films, particularly in those deposited by Pulsed Laser Deposition (PLD). Achieving the correct stoichiometry in this case requires a very fine tuning of the laser energy, substrate temperature, and background oxygen pressure during deposition. Furthermore, our acceptor-doped films show an accumulation of oxygen vacancies at the surface and a complex dependence of the conductivity with oxygen pressure.De Souza et al. (2014) Therefore, in order to minimize the effect of extrinsic acceptor impurities over the charge donated by VO, we have chosen Nb-doped SrTiO3 for this study. Around 2% Nb results in a density of free electrons which compensates the presence of intrinsic acceptor impurities, as measured by Hall effect.Sarantopoulos et al. (2015) As a consequence, even small amounts of VO produce measurable changes in the conductivity and Hall effect. On the other hand, we have kept the concentration of Nb small enough for the oxygen vacancies to produce an observable effect at any pressure.

Following this approach, Nb:STO thin films were grown by Pulsed Laser Deposition (KrF, $\lambda$=248 nm) on different substrates (see supporting information for a complete list of the substrates and orientations used in this work), with lattice parameters ranging from pseudocubic as=3.791 $\AA$ of LaAlO3 to as=3.970 $\AA$ of GdScO3, changing the epitaxial stress in the interval s(%)=[-2.91, +1.66] (s(%)=\frac{a_{s}-3.905}{3.905}$$\times100; 3.905 Årefer to the lattice parameter of bulk STO). The deposition conditions were previously optimized in order to minimize the presence of cationic vacancies in the as-deposited films:Sarantopoulos et al. (2015) laser fluence $\approx{}$0.9 J/cm2, repetition rate 4 Hz, 800ºC under oxygen pressure of P(O2)= 100 mTorr. The films were cooled down to room temperature at 5ºC/min under the same atmosphere. The nominal Nb concentration, $\approx$2$\%$, and the thickness $\approx$20$\pm$2 nm, were kept constant for all films studied in this work.

A controlled amount of oxygen vacancies was introduced in the films by post-deposition annealing at different temperature (either 800ºC or 600ºC ) and oxygen pressure, P(O2), according to the following process:

[TABLE]

Samples were left to reach equilibrium with the background oxygen pressure for 2 hours, and then rapidly quenched to room temperature at a cooling rate $\approx$100 ºC/min, to keep the concentration of vacancies unchanged during cooling. The [VO] was quantified immediately after this by Hall effect measurements, using the Van der Pauw configuration.

The local distribution of oxygen vacancies was studied using Electrostatic Force Microscopy (EFM mode), in an NX-10 Atomic Force Microscope (Park Systems).

III Results and Discussion

High-resolution reciprocal space maps (RSM, see supporting information Figure S1) indicate a good epitaxial matching to the substrates for all films, except for these grown on LAO. This is the substrate with the smallest lattice parameter used in this work, and the films are already partially relaxed. As an example of the crystalline quality of the films studied, the Geometrical Phase Analysis (GPA) of High Angle Annular Dark Field-Scanning Transmission Electron Microscopy (HAADF-STEM) images is shown in Figures 1a) to d). The GPA analysis also confirms that the out of plane positive (negative) distortion ($\epsilon{}$zz) in response to the compressive (tensile) in-plane strain ($\epsilon{}$xx) is homogeneous throughout the films, and in complete agreement with the RSM data. For example, for the STO deposited on DSO the c-axis parameter of the film contracts $\approx$1.1% with respect to the substrate (see Figure 1d) and Figures S1 and S2 in the supporting information).

The change of volume with strain was calculated from the X-ray data, and is shown in Figure 1e) for the as-grown Nb:STO films. This is compared to the theoretical volume assuming the Poisson ratio $\nu$ = 0.23 characteristic of bulk SrTiO3.Ledbetter et al. (1990) Introducing oxygen vacancies by post-annealing has a negligible effect in the volume of the lattice (Figure 1f), at least for the amount of vacancies explored in this work.Ohnishi et al. (2008) There is a clear and progressive deviation of the theoretical prediction for tensile stressed samples. From this point of view, it is particularly interesting the elongation of the out of plane lattice parameter by $\approx$1$\%$, for the samples deposited on STO substrates, despite the nule epitaxial stress induced by the substrate in these films. The deviation from the value of $\nu$ = 0.23 points towards slight variations of the stoichiometry, namely VSr.Sarantopoulos et al. (2015)

The effect of cationic vacancies on the structural properties of the films was carefully investigated through the presence of different X-ray half-order reflections. These experiments (see Figure 2) confirmed a complex rotation pattern of the TiO6 octahedra of the films. In the case of samples deposited on STO, the half-order reflections are characteristic of either an a+b+c0 or an a+a+c0 tilt system in the Glazer notation.Glazer (1972) These are consistent with a tetragonal or orthorhombic space group, different from the a0b0c0 of cubic STO. Therefore, given the negligible lattice mismatch between the Nb:STO film and the STO substrate, this result reflects the effect of VSr introduced during growth over the lattice symmetry of the film. Moreover, the clear observation of the X-ray half-order reflection implies that the tilting of the TiO6 octahedra occurs along the whole sample, not just around a local vacancy.

The tolerance factor, $t$, quantifies the mismatch of the equilibrium A-O/B-O bond-lengths in ABO3 perovskites. For cubic STO $t$=1, also being true for 2$\%$-Nb:STO. However, a progressive reduction of the ionic radius at the A-site is expected to induce a cooperative rotation of the BO6 octahedra, which reduces the symmetry to tetragonal ($I4/mcm$, rotation along [001] axis), rhombohedral ($R-3c$, rotation along [111] axis), and orthorhombic ($Pbnm$ or $Pnma$, rotation along [110] axis) as t decreases.Goodenough and Zhou (1998) The presence of VSr introduces a distortion similar to an average reduction of the ionic radius of the A-cation. This decreases the tolerance factor and puts the Sr-O (Ti-O) bonds under tensile (compressive) stress. The amount of compression of the Sr-O bonds is usually larger than the one of the Ti-O bonds, resulting in dt/dP$<$0, and therefore compressive stress goes in the same direction as the reduction of the ionic radius. Consistent with this hypothesis, the same rotation pattern was observed for all the films grown under compressive stress, either on cubic LSAT or orthorhombic LAO, in spite of the trigonal $R-3c$ symmetry (a-a-a-) of the latter (see Figure 2).

On the other hand, tensile stress has the opposite effect. For the films deposited under tensile stress only half-order reflections corresponding to the a-b+c- rotations of the substrate (orthorhombic $Pnma$) were observed. The positive stress dominates over the effect of VSr, imposing on the films the rotation pattern of the crystal underneath.

Moreover, we confirmed experimentally that VO introduced by post-deposition annealing do not affect the rotation pattern of the TiO6 octahedra.Zhang et al. (2015); Johnson-Wilke et al. (2013) Only cationic vacancies determine the octahedral rotation pattern in unstrained and compressed STO films.

These results demonstrate that different octahedral rotation patterns are induced in thin films prepared under similar conditions (identical composition), but subject to different degrees (and sign) of epitaxial stress (i.e. deposited on different substrates). This could play a double role: i) changing the formation enthalpy of a vacancy, given the change in local distances and coordination; and ii) influencing the diffusion coefficient of the oxygen vacancies along the different directions of the perovksite structure.

The formation of oxygen vacancies in SrTiO3 thin films may occur as a Schottky defect to compensate acceptor vacancies Sr2+ formed during deposition at low oxygen pressure. Alternatively, VO can be introduced in stoichiometric films by post-annealing in a reducing atmosphere. We introduced a controlled amount of oxygen vacancies in our films by post annealing at high temperature, either at 800ºC or 600ºC, under different oxygen pressures. Although VO in electron-doped STO are not stoichiometric vacancies (cation+anion), a simple mass action law for (1) is applicable as long as the concentration of vacancies is not too large, so the crystal can be still considered nearly stoichiometric. In this case, we can formulate the following equilibrium equation for the material annealed at low oxygen pressures:

[TABLE]

where O2- represents the oxygen ions at their corresponding STO lattice sites. These can be included in an effective equilibrium constant $K$:

[TABLE]

If the effect of Sr2+-acceptor vacancies is compensated by Nb5+-donors originally present in the sample, then the reduction reaction (2) will produce a change in the carrier density that can be measured by Hall effect experiments. If ne=2[VO], i.e. each O2- vacancy donates two electrons to the conduction band, substituting this result in the equation for the equilibrium constant, we obtain:

[TABLE]

An extrinsic source of oxygen vacancies, for example due to acceptor impurities or an excess of TiO2, will render the concentration of vacancies mostly independent of the oxygen pressure; the reduction reaction (2) will not be the main source determining the concentration of vacancies in this case. According to equation (3) the slope of the $n$ vs PO2 plot (equation 4) will change from 1/6 to 1/4 .

The experimental results are shown in Figure 3a). The carrier density, determined by Hall effect measurements, increases progressively after high temperature-low pressure annealing, up to a saturation value of $n$ $\approx$6-7$\times$1020cm*-3* at $\approx$ 10*-5*Torr of oxygen background atmosphere. The increment of $n$e as oxygen pressure decreases is in good agreement with the expectations for doubly ionized vacancies (equation 4), confirming the validity of the previous hypothesis. On the other hand, while re-annealing the previously deoxygenated samples at higher oxygen pressures and 800ºC completely recovers the initial state, this is not the case when the samples are annealed at 600ºC, or lower temperatures (see Figure 3b). Temperature is a critical factor in the creation/annihilation of oxygen vacancies in Nb:STO, and should be taken into account in the synthesis and post-annealing protocols of fully oxygen-stoichiometric samples.

In addition, the thermodynamic equilibrium constant entering the mass action law is related to the Gibbs free energy of the crystal, and therefore to the enthalpy and entropy of oxygen vacancies formation . Assuming that the change in entropy is only due to the increasing possibilities of configurational arrangements, the equilibrium constant is:

[TABLE]

which, through equation (4) can be related to the temperature dependence of the carrier density through:

[TABLE]

and, at constant pressure yields:

[TABLE]

According to the equation (5), the formation enthalpy of an oxygen vacancy can be obtained from the slope of an isobaric plot of log $n$e versus the inverse of the annealing temperature. This is shown in Figure 4 a) for two films, grown respectively on STO (s(%)=0.0) and DSO (s(%)=+1.15) substrates. The value of $\Delta$H calculated for s(%)=0.0 is $\approx$0.51 eV, and decreases about 23%, down to $\approx$0.39 eV, for a tensile stress of s(%)=+1.15. This behavior is very similar for the films synthesized under compressive strain, as shown in 4 b), with a progressive reduction of $\Delta$H about 33% for every 1% of either positive or negative epitaxial stress. Hence both compressive and tensile epitaxial stress have a very similar effect on the reduction formation enthalpy of oxygen vacancies in electron-doped STO thin films, suggesting a common mechanism for the reduction of $\Delta$H under compressive and tensile strain. This is in agreement with ab-initio calculations by Choi et al.,Choi et al. (2015) which suggested to a decrease of the band-gap energy under epitaxial strain (either positive or negative) as the main reason behind this effect.Berger et al. (2011) Indeed, creating an oxygen vacancy involves a redox process, as explained in equation (2), regardless of whether the stress on the film is positive or negative.

Finally, once the parameters which control the formation of oxygen vacancies under different degrees of strain were established, we have studied the migration of vacancies throughout the film under the influence of an electric field. The change in the local concentration of vacancies was studied by EFM. Applying a positive/negative voltage to the sample is able to repeal or attract the positively charged oxygen vacancies, therefore creating regions of vacancy depletion/accumulation.

The results for a Nb:STO film deposited on DSO are shown in Figure 5. Applying a local voltage of -10 V attracts the positively charged VO, changing the electrostatic potential (see supporting information Figure S3). Although a similar effect over the local surface potential and conductivity was recently reported by Waser et Al., Andra et al. (2015) we observed a clear change in the local volume of the sample, consistent with the local chemical expansion associated to the oxygen vacancies. This is further appreciated through the reversibility of the mechanical effect: application of a negative (positive) voltage produces a local expansion (contraction) of the sample, from its original value. The observed increase of the height in different samples ranges between $\approx$0.15-0.4 nm, roughly the size of a half to one unit cell size. Given the low diffusion coefficient of oxygen vacancies at room temperature in these oxides, they undergo an extremely low relaxation after removing the electric field. Therefore, these effects are stable for hours after removing the electric field.

The observation of this voltage-induced mechanical effect opens new possibilities to control the local concentration of oxygen vacancies (and hence the local conductivity) now by purely mechanical methods, i.e. mechanically assisted resistive switching.Sharma et al. (2015)

Further experiments to determine the kinetics of this effect, as well as the influence of surface termination (effectiveness of the electric field through SrO terminated with respect to TiO2 terminated filmsSitaputra et al. (2015)) are underway.

In summary, we have experimentally demonstrated the reduction of the formation energy of oxygen vacancies in films of SrTiO3 under epitaxial stress. The similar trend observed under tensile and compressive stress calls for a common mechanism, probably a reduction in the band gap. We have also demonstrated that the pattern of TiO6 rotations are mostly determined by the concentration of cationic vacancies unintentionally introduced during growth. This effect must be taken into account for a proper understanding of the changes in the electronic band-structure of this material under strain. Oxygen vacancy accumulation/depletion can be achieved by an applied bias voltage, resulting in non-volatile changes of the local electrical potential and, more importantly, a change in the local volume. The latter opens the possibility of a mechanical control of the local concentration of oxygen vacancies, and associated properties, e.g. conductivity, catalytic properties, etc.

Acknowledgements.

This work was supported the Ministry of Science of Spain (Project No. MAT2016-80762-R), the Conselleria de Cultura, Educacion e Ordenacion Universitaria (ED431F 2016/008, and Centro singular de investigacion de Galicia accreditation 2016-2019, ED431G/09) and the European Regional Development Fund (ERDF).L. I. B. also acknowledges the Ministry of Science of Spain for an FPI grant.

IV Supporting information