Huge impact of compressive strain on phase transition temperatures in epitaxial ferroelectric K_xNa_1−xNbO₃ thin films

In order to enhance functional properties in electrical applications based on ferroelectric thin films, the introduction of monoclinic unit cell symmetries via epitaxial strain was widely investigated and is by now well established.^1–9 These symmetries offer increased electromechanical properties due to enhanced polarization rotation within their monoclinic mirror planes. Besides their well-known pronounced piezoelectric response, high transmission coefficients have recently been reported for surface acoustic wave (SAW) sensors based on K_0.70N_0.30NbO₃ thin films grown on (110) TbScO₃ with selective propagation coinciding with monoclinic shearing directions.^10,11 Furthermore, a strong enhancement of SAW transmission coefficients in the vicinity of phase transition temperatures was observed. However, such transition temperatures might differ from desirable operating regimes for, e.g., biosensors which calls for altering them in a selective manner.

The key to predict and subsequently deliberately tailor phase transition temperatures in epitaxial K_xNa_1−xNbO₃ thin films is to understand the relationship between phase formation, transition temperature, and incorporated lattice strain. However, no experimental investigation addressing this topic has been available for this material, yet. In this paper, we present a study in which the impact of different anisotropic epitaxial strains in K_xNa_1−xNbO₃ films on phase transition temperatures is investigated. In this context, the choice of substrate material allows for a gradual modulation of strain, while the change in the potassium to sodium ratio enables a continuous and precise fine tuning. Via the combination of temperature-dependent piezoresponse force microscopy (PFM), temperature-dependent in situ X-ray diffraction (XRD), and laser interferometry, we show that we can indeed continuously shift the transition from the ferroelectric, monoclinic M_C to the ferroelectric c-phase in the range of −15 °C to 400 °C.

K_xNa_1−xNbO₃ films with a thickness of 30 (±10) nm were grown on (110) DyScO₃, (110) TbScO₃, (110) GdScO₃, and (110) SmScO₃ substrates by means of liquid-delivery metal-organic vapor phase epitaxy (MOVPE). This technique allows for growth conditions close to the thermodynamic equilibrium providing smooth film surfaces and highly regular ferroelectric domain formation. The samples were prepared with a molar potassium content x ranging from 0.54 to 0.77, which was varied by adding different amounts of K and Na precursors to the MOVPE growth process, which was carried out at a growth temperature of 700 °C. The details are described in Ref. 4. The rare-earth scandate (REScO₃) substrates have been grown by the Czochralski technique as explained in Ref. 21.

The ferroelectric domain patterns of K_xNa_1−xNbO₃ films on different substrates have been analyzed using the lateral piezoresponse force microscopy (LPFM) mode of an Asylum MFP3D-instrument with dual AC resonance tracking (DART).¹² In Figs. 1(a)–1(d), representative piezoresponse [PR = amplitude $⋅$ sin(phase)] micrographs recorded at room temperature are displayed. The K_xNa_1−xNbO₃ film shown in Fig. 1(a) grown on (110) DyScO₃ does not exhibit a periodic domain structure at room temperature. In contrast, the films presented in Figs. 1(b)–1(e) reveal periodic stripe domain patterns (indicated by white double arrows) forming up to four superdomain variants. A detailed structural analysis of the domain configuration as described in Ref. 11 proves monoclinic M_C domains with Pm symmetry. This structure contains four types of superdomains, which are denoted as 0°, 90°, 180°, and 270° variants, as sketched in Fig. 1(e). Each of them is formed by lamellar nanodomains whose in-plane polarization components alternate by 90° as indicated by small, red arrows. The resulting in-plane net polarization of the superdomains is schematically given by blue arrows.

In order to determine the induced epitaxial strain in K_xNa_1−xNbO₃ thin films, it is most convenient to describe the film structure in pseudocubic (pc) notation.¹³ The strain state of each specimen is determined as follows: first, the variation of pseudocubic (pc) bulk lattice parameters a_pc, b_pc, and c_pc is calculated by applying Vegard's law¹⁴ for 0.5 < x < 1.0 with the end members given in Table I.^15,16 Second, we analyzed the vertical lattice parameter by X-ray diffraction, proving c_pc-orientation for all tested films, which allows for an evaluation of the chemical composition and thus the experienced in-plane strains $εxx$ and $εyy$⁠. Thereby, a Poisson ratio of $υ$ = 0.38 as reported for K_0.5Na_0.5NbO₃ by Matsubara et al.¹⁷ is applied. This calculation method was found to yield almost identical values to the alternative evaluation based on the elastic compliance. However, both methods produce a systematic uncertainty since the Poisson ratio and the elastic compliance are only available for the orthorhombic phase of K_0.5Na_0.5NbO₃. Nonetheless, they allow for a reliable comparison among the different K_xNa_1−xNbO₃ films investigated in this study. For the (110)-oriented rare-earth scandate (REScO₃) substrates, the average in-plane unit cell parameters are taken (Table I) since the possible in-plane unit cell orientations of the film occur with equal likelihood in an M_C domain structure. The potassium contents and in-plane strain values for the samples shown in Figs. 1(a)–1(d) are as follows: (110) DyScO₃ with x = 0.71, $εxx$ = −0.1%, and $εyy$ = −1.7%, (110) TbScO₃ with x = 0.67, $εxx$ = 0.2%, and $εyy$ = −1.3%, (110) GdScO₃ with x = 0.54, $εxx$ = 0.6%, and $εyy$ = −0.9%, and (110) SmScO₃ with x = 0.74, $εxx$ = 0.8%, and $εyy$ = −0.8%.

In order to depict the characteristics of the phase transition in these films upon heating, its investigation by means of different techniques will be presented in the following on the example of the K_0.66Na_0.34NbO₃ film on (110) TbScO₃ which is presented in Fig. 1(b). In Figs. 2(a)–2(d), LPFM measurements recorded within one particular superdomain of the named film reveal the temperature dependence of the ferroelectric domain pattern between 80 °C and 120 °C. Although the noise in PFM measurements increases when heating the sample, the stripe domains can be identified up to 110 °C before they abruptly vanish at 120 °C. Upon cooling back down to 110 °C, the stripe domain pattern in PFM reappears, Fig. 2(d). Due to thermal drift of the sample stage, it was not viable to perform temperature-dependent PFM measurements at a fixed sample position, e.g., at a superdomain boundary recording different superdomains at once. However, individual investigation of the particular superdomains proved that all variants vanish at the same temperature as expected for an M_C domain structure where all superdomains hold the same overall in-plane strain, which we define as (⁠$εxx$ + $εyy$⁠).

For a more detailed determination of the observed phase transition, we have conducted temperature-dependent X-ray diffraction experiments. High-resolution X-ray diffraction (HRXRD) at elevated temperatures was performed on a diffractometer equipped with an 18-kW rotating-anode generator in Bragg-Brentano geometry and using synchrotron radiation at the PHARAO beamline of BESSY II. Additional measurements at cryogenic temperatures were performed on a Bruker Discover D8 diffractometer equipped with a Bruker MTC-Lowtemp stage. Furthermore, X-ray reciprocal space mappings (RSMs) were collected at the KMC2 beamline of BESSY II applying an Anton Paar DHS 1100 hot stage.

As known from several studies on various ferroelectric oxide materials like K_xNa_1−xNbO₃, BaTiO₃, or PbTiO₃, the thermal expansion coefficients in different crystalline phases of ferroelectrics significantly differ, which allows identifying phase transitions.^18–20 In Fig. 3(a), the evolution of the vertical lattice parameter of the K_0.66Na_0.34NbO₃ film presented in Figs. 1(a) and 2 and of the underlying (110) TbScO₃ substrate are shown as function of the temperature. While the substrate reveals a rather linear thermal expansion with an expansion coefficient of about 7 $×$ 10⁻⁶ K⁻¹ well compatible with literature values,²¹ a distinct change in the slope is observed which corresponds to the phase transition in the K_0.66Na_0.34NbO₃ film. The position of the kink at 115 °C is in good agreement with the phase transition temperature observed by means of LPFM. Below 115 °C, the vertical lattice parameter strongly increases. For T > 115 °C, the curve is clearly flattened which indicates a very small or even negative thermal expansion. This effect is known for ferroelectrics like PbTiO₃²² or BaTiO₃²³ and is attributed to the spontaneous volume ferroelectrostriction.^22,24,25 While this effect is present in both phases, its impact is more pronounced when the polarization vector coincides with the measured unit cell axis. As here the vertical lattice parameter is measured, this indicates a transition into a c-phase where the polarization vector is aligned along the c-axis of the unit cell.

In order to clarify the film structure below and above the phase transition, temperature-dependent X-ray reciprocal space mappings were performed in the vicinity of the asymmetric (⁠$444¯$⁠)_TSO substrate Bragg reflection containing both in-plane and out-of-plane scattering vector components, as shown in Figs. 3(b) and 3(c). At room temperature, the intensity distribution consists of a complex diffraction pattern resulting from the periodic arrangement of the M_C domains. Their monoclinic shearing can be identified from the different vertical positions of the two satellite branches (dashed, white lines), which do not intersect in their center position (red dot).¹¹ At 150 °C well above the transition temperature, this diffraction pattern has vanished confirming the absence of a periodic domain structure in agreement with the LPFM images shown in Fig. 2. Meanwhile, the center position of the X-ray intensity scattered by the film is still at the same in-plane $q001¯$ position as the (⁠$444¯$⁠)_TSO substrate Bragg reflection proving that the film does not undergo any plastic relaxation but perfectly preserves its fully strained relation to the substrate. However, no peak splitting can be identified in the intensity pattern anymore. This implies the absence of a monoclinic distortion, proving an orthorhombic symmetry of the K_xNa_1−xNaNbO₃ unit cells in the high temperature phase. Note that the (110) TbScO₃ surface exhibits an anisotropic unit cell, so no tetragonal symmetry is possible in the clamped layer.

To evaluate the ferroelectric properties below and above the phase transition, macroscopic measurements of the effective, vertical piezoelectric coefficient d_33,f were performed using an aixACCT double beam laser interferometer in combination with a TF Analyzer 2000 and a Linkam HFS temperature stage. Thereby, the so-called small-signal measurements were conducted by superimposing an AC electric field with an amplitude of 0.2 V and a frequency of 1 kHz to a DC field, which was gradually varied in the range of ±0.5 V.²⁶ This technique allows one to identify the material's response mainly caused by the intrinsic reverse piezoelectric effect. The measurements were carried out on a K_0.58Na_0.42NbO₃ film on a previously grown SrRuO₃ bottom electrode layer on (110) TbScO₃ with Pt top electrodes.

In Fig. 4, the evolution of the piezoelectric coefficient d_33,f is displayed in the temperature range between 20 °C and 180 °C. From room temperature up to 50 °C, d_33,f is fairly constant with a value of 18 (±1) pm/V, which is comparable to the values for clamped, lead-free BaTiO₃ thin films.²⁷ Above this temperature until 70 °C, a distinct decrease is observed. For the high temperature c-phase, an effective piezoelectric coefficient of 7 (±2) pm/V is found. This behavior is in good agreement with the expectation to gain the highest piezoelectric response for the monoclinic phase. We further note that the low transition temperature in this particular sample might be attributed to screening charges in the additional metallic intermediate layer, which are known to stabilize tetragonal phases.^28–30 Accordingly, PFM measurements confirm the transition from a periodic stripe pattern to an irregular domain arrangement below 60 °C (insets in Fig. 4).

Summarizing the PFM, HR-XRD, and interferometer results, we conclude a thermally induced phase transition from the ferroelectric, monoclinic M_C phase into a ferroelectric, orthorhombic c-phase in K_xNa_1−xNbO₃ films on (110) TbScO₃. From several experimental and theoretical studies, it is well known that the phase transition temperature in a ferroelectric material can be systematically shifted by the application of strain.^31–33 Therefore, we have grown several K_xNa_1−xNbO₃ thin films with a molar potassium content x ranging from 0.54 to 0.77 on different rare-earth scandate substrates (without an intermediate bottom electrode). In Fig. 5, the phase transition temperatures of K_xNa_1−xNbO₃ films with an overall compressive in-plane strain between −1.8% and 0.0% recorded by means of different techniques are gathered. We remark that all provided strain values were calculated for room temperature. The strain change upon temperature variation due to stronger thermal expansion coefficients of the substrates compared to the layers is less than 0.1% per 100 K. The evolution of the transition temperature with increasing compressive strain unveils a systematic and apparently linear dependence, whereby a shift over a wide temperature range of −15 °C to 400 °C was experimentally realized. The lowest phase transition temperature is found for the K_0.71Na_0.29NbO₃ film on (110) DyScO₃ being significantly below room temperature. In contrast, the highest phase transition temperature, which is observed for the K_0.74Na_0.26NbO₃ film on SmScO₃, is already in the vicinity of the Curie temperature of bulk K_0.5Na_0.5NbO₃ of T_C = 415 °C.³⁴ However, we suppose to observe a ferroelectric-to-ferroelectric phase transition also in this case. Even though this sample is assigned a zero overall in-plane strain, it is fully epitaxially and highly anisotropically strained with $εxx$ = 0.8% and $εyy$ = −0.8%. It is widely accepted that any strain, which draws the unit cell symmetry away from being cubic, leads to an increase in the Curie temperature in perovskitelike ferroelectrics. For this reason, the ferroelectric-to-paraelectric phase transition in the layer is expected to have a significantly higher T_C than the unstrained bulk material. In between the DyScO₃ and SmScO₃ samples, the influence of the varying molar potassium amount can be nicely obtained by comparing the different K_xNa_1−xNbO₃ films on, e.g., (110) GdScO₃. Here, the variation of x between 0.54 and 0.77, which corresponds to a change of the overall in-plane strain from −1.0% to −0.3%, leads to a shift of the phase transition temperature from 105 °C to 300 °C. We further note that the slope of the phase transition temperature vs overall in-plane strain (ca. 200 °C/%) is in quite good agreement with calculations recently published by Zhou et al.³⁵ However, we underline the restricted comparability between both studies since Zhou et al. conducted their theoretical investigation on isotropically strained monodomain K_0.5Na_0.5NbO₃ revealing an M_A to c-phase transition. In contrast, the system of anisotropically strained K_xNa_1−xNbO₃ films with a polydomain configuration as present in our films holds a distinctly higher complexity.

In summary, we have studied a thermally induced phase transition in K_xNa_1−xNbO₃ thin films with 0.54 < x < 0.77 grown by MOVPE. Compressive strains were varied between −1.8% and 0.0% by using different (110)-oriented REScO₃ substrates (with Re = Dy, Tb, Gd, Sm). By applying temperature-dependent PFM, different X-ray diffraction methods, and laser interferometry, we verified a ferroelectric-to-ferroelectric phase transition from monoclinic to orthorhombic symmetry in these films. Thereby, a linear correlation between the phase transition temperature and the applied overall in-plane lattice strain has been revealed. Our results underline the great potential to strain engineer K_xNa_1−xNbO₃ layers for technological application. The detailed knowledge of the relation between lattice strain, phase formation, and phase transition temperature will enable the customization of functional properties like the transmission coefficients to the particular temperature regime in which an SAW sensor is desired to operate.

We thank DFG (project funding reference No. FE 1438|2-1) and EFRE (Project No. 1.8/15) for funding this project. We further thank A. Kwasniewski, D. Többens, Z. Cheng, and T. Demuth for assistance with X-ray measurements and M. Klann for MOVPE sample preparation. We are grateful to BESSY (KMC-2 Project Nos. 17206091-ST, 18106401-ST, and in-house research at PHARAO) for providing beam time. Finally, we acknowledge J. Boschker and R. Wördenweber for fruitful discussion.