Evidence for antipolar displacements in NaNbO₃ thin films Open Access

Research on antiferroelectric (AFE) materials has been intensified in recent years due to a number of promising applications, foremost as dielectric for energy storage.^1–3 Among the materials with this unique property, NaNbO₃ has received much attention as a possible replacement for the lead containing state-of-the-art lead zirconate titanate solid solutions. However, the ground state of NaNbO₃ has been a matter of discussion. Due to a very small energy difference^4,5 between the AFE and ferroelectric (FE) phases, both phases co-exist for bulk materials.^6,7 Thus, NaNbO₃ is a model material to study the transition between AFE and FE phases, as little modification by external means leads to a visible shift in the respective energies. In the literature, two main strategies have been adapted to shift the phase balance: the introduction of various dopants and the application of an external strain. The first strategy has been thoroughly explored resulting in an empirical connection of the phase balance to the tolerance factor of perovskites.^2,4,5 The effect of the strain on the phase balance has been demonstrated several times but lacks a complete understanding due to the complexity of the different stress states.¹ Note that electrical characterization usually shows a ferroelectric behavior in the polarization vs electric field (P–E) curve of NaNbO₃, due to the field induced irreversible transition to a FE state.⁸ 

While the impact of strain has already been heavily researched for FE materials, especially by the introduction of an epitaxial strain in thin films,⁹ only a few publications exist concerning AFE materials. Tan et al. have discovered that, for a complex bulk antiferroelectric material, compressive mechanical stress has the potential to increase the field necessary for the phase transition from AFE to FE and, thus, may stabilize the AFE state.¹⁰ Commonly referred to as strain engineering, this approach is mostly utilized for thin films, due to the possibility of strain application via epitaxy on different substrates.¹¹ All works describing NaNbO₃ thin films report exclusively the FE phase.^12–14 Note that most of these reported results concern films with a thickness of several micrometers.^13,14 Schwarzkopf et al. have studied the growth of 10–15 nm fully strained thin films of NaNbO₃ grown onto different substrates and concluded that a compressive strain leads to a ferroelectric phase while a tensile strain has the potential to stabilize an AFE phase.¹² Although several publications predict the AFE state for NaNbO₃ thin films, no experimental evidence has been found.^15,16 In this work, we investigated the structural and electrical properties of NaNbO₃ thin films with varying thicknesses grown onto SrTiO₃ (100) substrates by the pulsed laser deposition (PLD) technique. A KrF excimer laser with a wavelength of 248 nm was utilized to deposit first isostructural LaNiO₃ as a bottom electrode for a parallel plate capacitor configuration,^17,18 followed by the NaNbO₃ layer, both from stoichiometric targets. The corresponding deposition parameters and information about the cation stoichiometry of NaNbO₃ are given in the supplementary material. The structural analysis was carried out with x-ray diffraction (XRD) (SmartLab, Rigaku) as well as transmission electron microscopy (TEM) (JEM-ARM200F, JEOL). The electrical response was probed with a ferroelectric tester (TF2000, aixACCT Systems GmbH).

To quantify the strain of NaNbO₃ on SrTiO₃ (100), the orthorhombic lattice parameters of NaNbO₃ must be expressed in their pseudocubic notation:¹⁹ $apc=3.881 Å, bpc=cpc=3.915 Å$⁠. Note that these values are based on the AFE ground state of bulk NaNbO₃ (Pbcm),²⁰ with the fourfold lattice parameter corresponding to the direction of $apc$⁠. The difference between the lattice parameters implies that the strain depends on the growth orientation of the NaNbO₃ thin film, being anisotropic, if $apc$ grows in-plane or isotropic if $apc$ grows out-of-plane. Furthermore, even the sign of the strain is orientation dependent: tensile, for $apc$ in-plane, matching $aSrTiO3$ = 3.905 Å, resulting in a strain of $ϵ=$ 0.62%, and compressive for matching $bpc$/$cpc$ with $aSrTiO3$⁠, resulting in ϵ = −0.26%. While the deformation of the unit cell would be larger for an in-plane $apc$-axis as compared to an out-of-plane $apc$-axis, the total magnitude of the strain is smaller due to the different contributions opposing each other.

The $θ−2θ$ XRD patterns of the films with varying thicknesses are shown in Fig. 1(a). The areas around the 2θ positions of the 001 and 004 reflection of the SrTiO₃ substrate are depicted. For very thin NaNbO₃ films, the overlapping of Laue oscillations from LaNiO₃ and NaNbO₃ can be seen around the 001 substrate reflection. These oscillations appear due to multiple scattering and are only visible for very homogeneous films with atomically smooth interfaces, thus indicating a high quality of the thin films. The oscillations from the LaNiO₃ electrode of constant thickness are present for films of all NaNbO₃ thicknesses. From the period of the oscillations, a thickness of 25 nm was determined for the LaNiO₃ thin films. The position of the LaNiO₃ reflection shows a variation of the $2θ$ angle of up to 1°. While this variation is not entirely monotonous, a general trend toward larger $2θ$ angles for thicker NaNbO₃ thin films can be identified, indicating a reduction in the out-of-plane lattice parameter. This could be correlated with the extended time for which the thicker films were exposed to higher oxygen pressures and high temperatures during deposition; however, this point was not investigated further in the scope of this publication, as the out-of-plane lattice parameter of the LaNiO₃ film is not expected to affect the subsequent growth of the NaNbO₃.

As the 001 reflection of NaNbO₃ cannot be clearly distinguished from the substrate 001 reflection due to the similarity of their lattice constants, it is necessary to zoom into the 004 reflection. At larger $2θ$ values, the distinction between the reflections of NaNbO₃ and the substrate becomes apparent, revealing an extraordinary dependence on the film thickness: thin films show only one reflection corresponding to NaNbO₃, while another contribution at larger angles than the substrate reflection at $2θ=104.2°$ appears for increased thicknesses. The corresponding lattice parameters for both contributions were extracted by fitting all four reflexes measured in the $θ−2θ$ scan and extrapolation via the Nelson–Riley method. This reveals that the presence of the different reflections can be connected to different orientations of NaNbO₃, as shown in Fig. 1(b). While for films with a thickness below 60 nm, only the reflection corresponding to an out-of-plane b/c-axis is visible, 60 nm and thicker films also show a clear contribution from an out-of-plane a-axis.

This remarkable orientation change during growth has not been previously reported in the literature for NaNbO₃ films grown on SrTiO₃, likely due to the similarity of lattice parameters making the distinction between film and substrate difficult.¹² Schwarzkopf et al. observed a dependence of the growth orientation of NaNbO₃ on the strain induced by various substrates. The extracted out-of-plane lattice parameters correspond to the b/c-orientation for compressive strain and a-orientation for tensile strain. Hence, it is not surprising to see both orientations appear in this work for NaNbO₃ films grown on SrTiO₃, which has a lattice constant between the theoretical pseudocubic a and b/c lattice constants of NaNbO₃. However, it seems that in the nucleation process of the initial growth a b/c-orientation is energetically favorable, despite the larger strain. The energy balance then changes during growth, resulting in the appearance of the a-orientation once a certain threshold thickness is reached. The driving force behind this transition is the relaxation energy gain due to the overall strain reduction.

As often observed for thin films, an additional reflection appears in combination with a strain relaxation toward a more bulk-like state.⁹ Therefore, the strain state of the 310 nm thick NaNbO₃ film was analyzed via a reciprocal space map (RSM) around the 103 reflection of the SrTiO₃ substrate, shown in Fig. 2. In the RSM, both orientations of the NaNbO₃ can be clearly resolved and the Q_x positions of both match the value for SrTiO₃, indicating a fully strained state throughout the whole film thickness. This is unusual for this material, as it is prone to defect formation.²¹ For growth on gallates or scandates, relaxation processes already begin for thicknesses ranging from 15 to 30 nm.^22,23 Here, the change in orientation serves as a stress relief mechanism, as it is accompanied by a reversal of the type of strain: tensile for growth of b/c-orientation to compressive for growth of the a-orientation out-of-plane. At the same time, the magnitude of the strain is reduced; hence, the total strain in the thin film is minimized by a change in crystal orientation during growth. The coexistence of two orientations of the same material with opposite strain has been observed before²⁴ and serves as a relaxation mechanism enabled by the exclusive combination of two pseudocubic lattice parameters with different values of NaNbO₃ and a substrate lattice parameter in between these two values. As a result, much larger film thicknesses in a coherently strained state are possible.

The unique difference between the bulk AFE and FE phase lies in the presence of a fourfold lattice parameter for the AFE phase, emerging from a combination of antiparallel ion displacements and complex octahedral rotations.²⁵ Thus, for bulk ceramics of NaNbO₃, a common way to identify the ground state is via analysis of electron diffraction patterns for the 1/4-satellite reflection.^8,26 As this quadrupling of the primitive perovskite cell is accompanied by the antiparallel displacement of Nb-ions, XRD measurements can reveal this distinction as well.²⁷ Although the determination of the exact phase of a thin film is difficult due to the limited amount of reflections available by XRD scans, the reciprocal space maps enable an unambiguous discrimination of FE and AFE phases. For this purpose, the areas around the theoretically expected reflections for the case of the quadrupling lying in-plane, $34$ 03, as well as out-of-plane, 10 $134$⁠, were measured (see Fig. 2). Reflections can be detected for both directions, thus confirming the presence of antipolar displacements of the Na and Nb-ions, both in-plane and out-of-plane. As the direction of the fourfold axis is parallel to the orthorhombic c-axis, this indicates the orientation of that axis also changes from in-plane for initial growth to out-of-plane after the orientation change. It should be noted here that the in-plane 1/4 superlattice reflection is also present for $Φ$ = 90°, indicating the presence of twinning during the growth of NaNbO₃ (see the supplementary material).

By calculating the lattice parameters of these reflections, the orientation from which the 1/4 superlattice reflection originates can be identified. The c-lattice parameter of the a-orientation (3.886 Å) coincides with the lattice parameter of the superlattice reflection in the z-direction, 10 $134$ (3.891 Å) and the b/c-orientation (3.914 Å) fits to the lattice parameter of the in-plane superlattice reflection, $34$ 03 (3.916 Å). This matches the expected direction of the fourfold lattice parameter for bulk ceramics, as the a-direction corresponds to the bulk direction with quadrupling. The degree of ion displacement in the film can be approximated by the intensity ratio of the satellite reflection to the corresponding film reflection, assuming that the thin film structure is similar to the bulk structure. This was conducted via extraction of line profiles from the RSM of the 103 reflection and its satellite reflections. The corresponding intensity was obtained by fitting pseudo-Voigt reflection profiles and integration of the corresponding area (see the supplementary material). Note that by this method, a second small contribution at slightly larger values of Q_x was unveiled for the b/c-orientation, which seems to be relaxed toward the bulk value. The resulting intensity ratio between these reflections for the thin film amounted to 6.7% for the in-plane direction, $34$ 03, and 1.7% for the out-of-plane case, 10 $134$⁠. In comparison, the ratio for bulk ceramics, based on single crystal values,²⁸ is about 25% in-plane and 2.8% out-of-plane. Obviously, a clear reduction in the intensity of the superstructure reflection for both directions is apparent. This effect is more pronounced for the in-plane direction, which might be connected to the asymmetry introduced by the strain, as the displacement occurs in the $[011]pc$ direction for the given notation. For the out-of-plane superstructure reflection, both directions are affected by the in-plane strain and, thus, result in the same lattice parameter, due to the cubic nature of the substrate.

High-resolution transmission electron microscopy (HRTEM) studies confirm the previously stated strong indications of an antipolar ground state for the NaNbO₃ thin films. In Fig. 3(a), a HRTEM image is shown, revealing a modulation in the structure, characteristic of the AFE phase. Furthermore, the modulation experiences a change in the orientation, confirming the XRD observations. The feature of modulation is enlarged and processed with false color, as shown in Fig. 3(b), where two types of modulation are revealed. The first one corresponds to the fourfold modulated antipolar phase with a modulation length of 1.532 nm and the other one corresponds to a sixfold modulated planar defect with a modulation length of 2.298 nm. In Fig. 3(c), a fast-Fourier transform (FFT) of the HRTEM image is shown. This unambiguously confirms the appearance of 1/4-superlattice reflections. In the present case, these reflections appear for both directions since the area was selected at the boundary of these two modulated structures. It should be noted that regions without this modulation are also present in the sample. However, whether this is an indication of a FE phase co-existing with the AFE phase or whether the direction of the fourfold lattice parameter is parallel to the zone axis, and, hence, is not visible by FFT and HRTEM, cannot be clearly determined by this method.

The P–E behavior was recorded in a parallel plate capacitor configuration. For this method, circular top gold contacts of about 500 nm thickness were fabricated using photolithography and sputtering, with LaNiO₃ acting as the bottom electrode (see inset in Fig. 4). Two measurements of NaNbO₃ thin films with 50 and 310 nm, representative of the electrical behavior, are shown in Fig. 4. Focusing on the thicker film shows a clear ferroelectric hysteresis, which is very similar to that of the standard bulk behavior.²⁹ The saturation polarization of the 310 nm film reaches 26.5 μC $cm−2$⁠, which is among the highest values reported for NaNbO₃ grown on SrTiO₃ (100).^14,30 Note, however, that these literature reports are based on thick films with thicknesses of several μm. It is concluded that the a-oriented thin films undergo an irreversible phase transition into a ferroelectric phase. Although antipolar regions are still present after cycling, the polarization behavior is dominated by the ferroelectric contribution.⁸ Our thin films of this study, therefore, show an equivalent behavior as a typical NaNbO₃ bulk material. The phase with the $apc$-axis in the out-of-plane direction is compressively strained. For bulk ceramics, Tan et al. observed that compressive strain stabilized the AFE state,¹⁰ which is contrary to the observation for the thin films in this work. One major difference between the strain application, though, is, that thin films can relax in one direction, while the ceramics in the mentioned study were under hydrostatic pressure. The result is, that for the bulk ceramics, only the phase transition is affected, while for thin films, the whole phase balance changes. Another important aspect to the measurement of the thin films in this work is the consideration of the polarization vector in the material. For the bulk AFE structure, it is perpendicular to the $apc$-axis, which means no contribution to the polarization would be expected for the case of the $apc$-axis in the out-of-plane direction. However, due to the compressive strain, there is a possibility that the polarization vector is rotated compared to the unstrained state, which would explain the observed behavior. Note that such a behavior has not been reported before for “true” thin films of the order of a few 100 nm. The measurement of hysteresis curves in such thin films is limited by leakage currents. In this work, fields up to approximately 300 $kV cm−1$ could be applied due to an oxygen annealing step.

It is remarkable that the thin films with pure b/c-orientation are stable against a transition into the FE state. For these films, a pure linear behavior is observed as expected for an AFE state in small fields. As the characteristic antipolar displacements were unambiguously observed, the existence of a simple paraelectric phase can be excluded and similarly the presence of a ferrielectric phase, as this would lead to a polarization response. Thus, it must be assumed that for this particular field direction the AFE phase is stabilized, in agreement with the observations for bulk NaNbO₃.³¹ The strain state in this case is tensile, which has the potential to stabilize the AFE phase according to calculations considering the biaxial strain state of thin films.¹⁶ Moreover, the polarization vector should feature an out-of-plane contribution as the $apc$-axis lies in-plane for this orientation. Unfortunately, due to the limitations imposed by the leakage current in particular, for thin films well below 100 nm, the highest applicable fields were about 300 $kV cm−1$⁠. Therefore, the characteristic double hysteretic loop of AFE materials could not be reached, indicating a considerably increased stability of the antipolar structure. While the structural investigation gives a clear smoking gun proof for the antipolar displacements in pure NaNbO₃ thin films, the electrical assessment of the transition between the AFE and FE phases is still elusive due to the residual point defects, most likely oxygen vacancies.

In summary, the characteristic antipolar structure of the AFE phase was confirmed for NaNbO₃ thin films. The presence of this phase was detected by identification of the superlattice reflections originating from the antiparallel displacement of the Na and Nb-ions. A spontaneous change in the growth direction around 60 nm involving a sign change in strain has been observed. The coexistence of compressively and tensile strained regions is a unique strain relaxation mechanism when the substrate lattice constant falls between two pseudocubic lattice constants of NaNbO₃. The shape of the P–E loop hysteresis for the 310 nm thick film is characteristic of a FE material, which is similar to the behavior for bulk ceramics of NaNbO₃ known to undergo an irreversible field induced phase transition from AFE to FE. The absence of an induced ferroelectric state for the b/c-oriented very thin films indicates a possible anomalous increase in the phase stability of the AFE phase due to compressive strain.

See the supplementary material for the growth parameters of the PLD, a RSM at $ϕ$ = 90° indicating the presence of twinning during growth of NaNbO₃, the extracted line shapes and fitting curves from the RSM, as well as the cross section of the TEM lamellae.

This work was supported by the Hessian State Ministry for Higher Education, Research and the Arts under the LOEWE collaborative project “FLAME” (Fermi level engineering of antiferroelectric materials for energy storage and insulation systems).

J.C. is thankful to the Ingenium, TU Darmstadt for the financial support received through its Postdoctoral Career Bridging Grant.H.D., T.J., and L.M.-L. acknowledge the financial support from the European Research Council (ERC) “Horizon 2020” Program under Grant Nos. 805359-FOXON and 7 957521-STARE. The authors are thankful to W. Donner for valuable discussions.