Y Mendez-González

A Ferri

E C Lima

A Hamieh

D Remiens

A Peláiz-Barranco

A C Silva

J D S Guerra

Structural and microstructural features of lead-free BNT-BT thin films -Nanoscale electromechanical response analysis

Keywords: lead-free thin films, BNT-BT, piezoelectrics, ferroelectrics, PFM

The structural, microstructural and electromechanical properties have been investigated at the nanoscale, as a function of the lanthanum concentration, in Bi0.506Na0.46Ba0.08-3x/2LaxTiO3 (x = 0, 2 and 3 at%) (BNLBT-x) lead-free thin films. The structural characterization, investigated from X-ray diffraction and Raman spectroscopy, confirmed the formation of the perovskite structure and suggest the coexistence of both antiferroelectric (tetragonal) and ferroelectric (rhombohedral) phases. The surface morphology, characterized by atomic force microscopy, has shown a dense and crack-free nanostructured surface for all the studied compositions, noting that the increase in the lanthanum content promoted a decrease of both the grain-size and surface roughness. PFM imaging analyses have evidenced the ferroelectric domain structure over the surface, as well as the presence of non-piezoelectric regions attributed to the antiferroelectric phase. PFM spectroscopy measurements revealed a reliable switching behavior for locally probed ferroelectric domains, yielding a noticeable local piezo-activity, which indeed shows to increase with the increase of the doping content. The static domain-wall was also analyzed in terms of the nanoscale domains structure and the obtained dimensionality indicated a local electric field induced structural disorder. The clear local piezo/ferroelectric nature highlighted on the studied materials underlines the potential for applications of the BNLBT-x films for their integration into advanced electronic nanodevices.

INTRODUCTION

It is known that lead-based ferroelectric compounds, such as Pb(Zr,Ti)O3 and PbTiO3, and others based on them, have attracted most of the attention of the scientific community for several decades due to their excellent piezo-, pyro-and ferro-electric properties. [START_REF] Uchino | Ferroelectric devices[END_REF][START_REF] Rabe | Physics of ferroelectrics[END_REF][START_REF] Saito | Lead-free piezoceramics[END_REF][START_REF] Zhang | High performance ferroelectric relaxor-PbTiO3 single crystals: Status and perspective[END_REF] However, the lead toxicity and the negative implications to the environment and human health, have conducted to the researchers to re-evaluate their efforts in order to develop environmentallyfriendly lead-free materials as an alternative to substitute lead-based systems. An important number of results have been reported in the specialized literature concerning the study and the development of a wide range of lead-free materials, such as: (i) perovskite compounds based on BaTiO3 (BT), Ba1-xSrxTiO3 (BST), KNbO3 (KN), LiNbO3 (LN), NaBiO3 (NB) and Ba (1-x)CaxTi(1-y)ZryO3 (BCTZ), [START_REF] Yoon | Fabrication and characterization of ferroelectric oxide thin films: in Handbook of thin films[END_REF][START_REF] Choi | Enhancement of ferroelectricity in strained BaTiO3 thin films[END_REF][START_REF] Schwarzkopf | Epitaxial growth of ferroelectric oxide films[END_REF][START_REF] Du | The microstructure and ferroelectric properties of (K0.5Na0.5)NbO3-LiNbO3 lead-free piezoelectric ceramics[END_REF][START_REF] Liu | Large piezoelectric effect in Pb-free ceramics[END_REF] (ii) A2B2O7 layered perovskite structures including Sr2Nb2O7 (SNO) [START_REF] Nanamatsu | Ferroelectric properties of Sr2Nb2O7 single crystal[END_REF] and Nd2Ti2O7 (NTO), [START_REF] Kimura | Ferroelectric, electrooptic and piezoelectric properties of Nd2Ti2O7 single crystal[END_REF][START_REF] Bayart | Microstructural investigations and nanoscale ferroelectric properties in lead-free Nd2Ti2O7 thin films grown on SrTiO3 substrates by pulsed laser deposition[END_REF] (iii) bismuth layer-structured ferroelectrics based on SrBi2Nb2O9 (SBiN) [START_REF] Kato | Sol-gel route to ferroelectric layer-structured perovskite SrBi2Ta2O9 and SrBi2Nb2O9 thin films[END_REF] and Bi4Ti3O12 (BIT), [START_REF] Cummins | Electrical and optical properties of ferroelectric Bi4Ti3O12 single crystals[END_REF] and (iv) tungsten bronze oxides such as Sr1-xBaxNb2O6 (SBN) and Ba2NaNb5O15 (BNN), [START_REF] Glass | Investigation of the electrical properties of Sr1-xBaxNb2O6 with special reference to pyroelectric detection[END_REF][START_REF] Singh | Role of hydrogen in polarization reversal of ferroelectric Ba2NaNb5O15[END_REF] or more recently those containing A2MO6type compounds such as La2WO6 (LWO) [START_REF] Carlier | Lead-free α-La2WO6 ferroelectric thin films[END_REF] and Nd2WO6 (NdWO). [START_REF] Carlier | Ferroelectric state in a α-Nd2WO6 polymorph stabilized in thin film[END_REF] Among this non-exhaustive amount of lead-free compounds, the potassium sodium niobate (K0.5Na0.5)NbO3 (KNN), the bismuth potassium titanate (Bi0.5K0.5)TiO3 (BKT) and the bismuth sodium titanate (Bi0.5Na0.5)TiO3 (BNT) based systems, are examples of materials showing remarkable piezoelectric properties. [START_REF] Zhang | Lead-free piezoceramics with giant strain in the system Bi0.5Na0.5TiO3-BaTiO3-K0.5Na0.5NbO3. I. Structure and room temperature properties[END_REF][START_REF] Cordero | Phase transitions and phase diagram of the ferroelectric perovskite (Na0.5Bi0.5)1-xBaxTiO3 by anelastic and dielectric measurements[END_REF][START_REF] Coondoo | Lead-free piezoelectrics: Current status and perspectives[END_REF] In particular, the (1-x)Bi0.5Na0.5TiO3-xBaTiO3 (BNT-BT) compound has been considered as one of the promising lead-free piezoelectric materials. 22- 24 For this system, similarly to the Pb(Zr,Ti)O3, it has been stated a morphotropic phase boundary (MPB) delimiting the presence of the rhombohedral (R3c) and tetragonal (P4mm) phases, where the dielectric and piezoelectric properties are enhanced. [START_REF] Takenaka | Bi1/2Na1/2)TiO3-BaTiO3 system for lead-free piezoelectric ceramics[END_REF][START_REF] Shrout | Lead-free piezoelectric ceramics: Alternatives for PZT?[END_REF] It has also been reported that the MPB holds an antiferroelectric (P4bm) phase, separating the tetragonal (P4mm, BT-rich) and rhombohedral (R3c, BNT-rich) ferroelectric phases. [START_REF] Ma | Domain structure-dielectric property relationship in leadfree (1-x)Bi1/2Na1/2TiO3-xBaTiO3 ceramics[END_REF] From the technological point of view, the need for the integration of lead-free piezoelectric materials in microelectronic devices makes the fabrication of thin-films a priority assignment for the construction of non-volatile memory devices, as well as for high-speed and low-power electronic applications. [START_REF] Kundu | Integration of lead-free ferroelectric on HfO2/Si (100) for high performance non-volatile memory applications[END_REF] The high compositional control required to obtain films with composition close to the MPB in these complex oxides makes chemical solution deposition (CSD) processes one of the most appropriate techniques to fabricate BNT(1-x)-BTx thinfilms. [START_REF] Schwartz | Chemical solution deposition of electronic oxide films[END_REF][START_REF] Christensen | Fabrication of lead-free Bi0.5Na0.5TiO3 thin films by aqueous chemical solution deposition[END_REF] Other advantages of this method include the low cost, effective to fabricate highquality ferroelectric films with good stoichiometry control as well as a chemical homogeneity and uniform film over a large area. [START_REF] Schwartz | Chemical solution deposition of electronic oxide films[END_REF] In this context, several investigations have been conducted on BNT1-x-BTx thin-films particularly for those compositions close to the MPB. [START_REF] Zheng | Thermo-electrical energy conversions in Bi0.5Na0.5TiO3-BaTiO3 thin-films prepared by sol-gel method[END_REF][START_REF] Cernea | Piezoelectric BNT-BT0.11 thinfilms processed by sol-gel technique[END_REF][START_REF] Cernea | Structural and piezoelectric characteristics of BNT-BT0.05 thin films processed by sol-gel technique[END_REF][START_REF] Cernea | Structural, optical, and electric properties of BNT-BT0.08 thin-films processed by sol-gel technique[END_REF][START_REF] Acharya | Ferroelectric and piezoelectric properties of lead-free BaTiO3 doped Bi0.5Na0.5TiO3 thin-films from metalorganic solution deposition[END_REF] For instance, structural properties studied on (1-x)Bi0.5Na0.5TiO3-xBaTiO3 films (with x = 0, 0.1, 0.9 and 1.0) revealed a rhombohedral symmetry for the pure BNT and BNT-0.1BT compositions, as well as a tetragonal symmetry for the BNT-0.9BT compositions. [START_REF] Zheng | Thermo-electrical energy conversions in Bi0.5Na0.5TiO3-BaTiO3 thin-films prepared by sol-gel method[END_REF][START_REF] Cernea | Piezoelectric BNT-BT0.11 thinfilms processed by sol-gel technique[END_REF] On the other hand, Cernea et al. reported studies for the 0.89(Na0.5Bi0.5)TiO3-0.11BaTiO3, (BNT-BT0.11) [START_REF] Cernea | Piezoelectric BNT-BT0.11 thinfilms processed by sol-gel technique[END_REF] as well as (Bi0.5Na0.5)0.95Ba0.05TiO3 (BNT-NT0.05) [START_REF] Cernea | Structural and piezoelectric characteristics of BNT-BT0.05 thin films processed by sol-gel technique[END_REF] thin films, both fabricated via a sol-gel process and spin-coating technique. These researches revealed the formation of the cubic structure for the BNT-BT0.11 thin film, [START_REF] Cernea | Piezoelectric BNT-BT0.11 thinfilms processed by sol-gel technique[END_REF] as well as the crystallization of the rhombohedral structure for BNT-BT0.05 composition. [START_REF] Cernea | Structural and piezoelectric characteristics of BNT-BT0.05 thin films processed by sol-gel technique[END_REF] Moreover, other structural properties have also been previously investigated for the (1-x)Bi0.5Na0.5TiO3-xBi0.5K0.5TiO3 [BNT-BKT-100x] thin films, [START_REF] Yu | The synthesis of lead-free ferroelectric Bi0.5Na0.5TiO3-Bi0.5K0.5TiO3 thin films by sol-gel method[END_REF][START_REF] Wu | Effect of Na/K excess on the electrical properties of Na0.5Bi0.5TiO3-K0.5Bi0.5TiO3 thin films prepared by sol-gel processing[END_REF] where the presence of the perovskite phase without specifying the symmetry-type has been reported. However, despite the extensive reports on the physical properties related to the BNT-BT system, most of them carried out in ceramics, no clear understanding of the phase diagram has been offered to date.

Recently, special attention was paid to the (Bi0.50Na0.50)0.92Ba0.08-3x/2LaxTiO3 ceramic system. [START_REF] Mendez-González | Effect of the lanthanum concentration on the physical properties of the (Bi0.5Na0.5)0.92Ba0.08-3x/2LaxTiO3 ceramic system[END_REF][START_REF] Mendez-González | Raman spectroscopy study of the La-modified (Bi0.5Na0.5)0.92Ba0.08TiO3 lead-free ceramic system[END_REF] Indeed, detailed research regarding the structural, ferroelectric and dielectric behavior has then been reported by Mendez-Gonzáles et al. [START_REF] Mendez-González | Effect of the lanthanum concentration on the physical properties of the (Bi0.5Na0.5)0.92Ba0.08-3x/2LaxTiO3 ceramic system[END_REF][START_REF] Mendez-González | Raman spectroscopy study of the La-modified (Bi0.5Na0.5)0.92Ba0.08TiO3 lead-free ceramic system[END_REF] For such ceramics, the structural analysis has revealed the coexistence of both ferroelectric (P4mm) and antiferroelectric (P4bm) tetragonal phases for the lanthanum-free composition. However, for the lanthanum modified compositions, both antiferroelectric tetragonal (P4bm) and ferroelectric rhombohedral (R3c) phases have been shown that coexist. On the other hand, the Polarization -Electric field (P-E) hysteresis loops have suggested a higher stability of the ferroelectric phase for x = 0, 2 and 3 at% La at room temperature. The antiferroelectric phase has been shown to be more stable at room temperature for x = 1 at%. [START_REF] Mendez-González | Effect of the lanthanum concentration on the physical properties of the (Bi0.5Na0.5)0.92Ba0.08-3x/2LaxTiO3 ceramic system[END_REF] Interesting results have also been shown concerning the electrocaloric effect on these ceramic materials. [START_REF] Mendez-González | Improved electrocaloric properties in La doped (Bi0.5Na0.5)0.92Ba0.08TiO3 lead-free ceramics[END_REF][START_REF] Li | Electrocaloric effect in La-doped BNT-6BT relaxor ferroelectric ceramics[END_REF] Nevertheless, to the best of our knowledge, there are no previous systematic studies carried out in the (Bi,Na,La)(Ba,Ti)O3 system when grown in thin films. In addition, nanoscale physical properties of the matter required to be probed since they can govern the global performance of the devices at the macroscopic scale. For this, atomic force microscopy (AFM) technique is known as a powerful non-destructive tool for high-resolution characterization of matter on the nanoscale. In particular, the piezoresponse mode (PFM) of the AFM offers the opportunity for imaging and characterizing ferroelectric thin films by assessing domain structure, switching behavior and electromechanical activity. [START_REF] Gruverman | Piezoresponse force microscopy and recent advances in nanoscale studies of ferroelectrics[END_REF][START_REF] Gruverman | Piezoresponse force microscopy and nanoferroic phenomena[END_REF] In this framework, the PFM seems to be very suitable for probing local electrical properties of such (Bi,Na,La)(Ba,Ti)O3 thin films.

The present work aims the investigation of the structural, microstructural and local electrical properties of Bi0.506Na0.46Ba0.08-3x/2LaxTiO3 (x = 0, 2 and 3 at%) lead-free thin films.

In particular, a comprehensive study on the structural characteristics, which indeed have not been previously reported, is presented. The room temperature piezoelectric and ferroelectric performances of the films were particularly investigated on the nanoscale by using imaging and spectroscopic PFM approaches. Specific emphasis is devoted on the opportunities of these thin films for further development of advanced electronic devices.

EXPERIMENTAL PROCEDURE

Bi0.506Na0.46Ba0.08-3x/2LaxTiO3 lead-free thin films, considering x = 0, 2 and 3 at %, were synthesized via a sol-gel process by the spin-coating technique. Bismuth (III) acetate ((CH3COO)3Bi, > 99.99 %, Aldrich), sodium acetate (CH3COONa, > 98 %, Synth) and barium acetate ((CH3COO)2Ba, > 99 %, Synth) were separately dissolved in acetic acid (99 %, Synth) producing transparent stock solutions. Then, titanium (IV) isopropoxide, 97 % solution in 2propanol (Ti{OCH(CH3)2}4, Aldrich), was added drop by drop under magnetic stirring at 80 °C for 240 min. A chemical stabilizer was included during solutions synthesis in order to increase the stability of titanium isopropoxide. After this process, yellowish colored stable gels were obtained. N, N-dimethylformamide (99.8 %, Neon) was used to minimize the formation of cracks during the drying and the annealing steps. The precursor-solutions were obtained considering 10 mol % excess bismuth, in order to compensate its high volatility, and deposited on Pt(111)/TiO2/SiO2/Si substrates with a spinning speed of 7000 rpm for 40 sec. The films were preheated at 150 o C for 30 min in order to evaporate the solvent, and then the pyrolysis process was carried out at 450 o C for 30 min in order to remove other organic compounds. This step was repeated until the desired thickness was obtained. The coated films were finally annealed at 700 o C for 60 min to complete crystallization. The samples were hereafter labeled as BNLBT-x, where BNLBT-0, BNLBT-2 and BNLBT-3 correspond to x = 0, 2 and 3 at% La, respectively.

The phase compositions of the near-surface layers were examined at room temperature by grazing incidence X-ray diffraction analysis (GIXRD) using an XRD6000 (Shimadzu) diffractometer with Cu-Kα (0.15406 nm) radiation. In order to study the structure of the films in depth profile, X-ray diffraction (XRD) measurements were collected at a fixed angle of 8° and a scanning angle from 20° to 80°. This GIXRD method has been carried out in order to reduce the contribution of the substrate (Pt) to the XRD pattern. Structural refinement was performed through the Rietveld method, using the GSAS software suite and EXPGUI interface. [START_REF] Larson | General Structure Analysis System (GSAS)[END_REF][START_REF] Toby | EXPGUI, a graphical user interface for GSAS[END_REF] The unit-cell parameters, atomic positions, scale factor, background and lineshape parameters were refined during the fitting processes. The peak profiles were fitted using the Thompson-Cox-Hastings pseudoVoigt function, [START_REF] Thompson | Rietveld refinement of Debye-Scherrer synchrotron X-ray data from Al2O3[END_REF] while a sixth-order polynomial was used to fit the background. Raman data were collected, at room temperature, by using a micro-Raman Horiba Jobin Yvon (LabRam HR Evolution) spectrometer with a 532 nm laser. Local electromechanical experiments were performed using AFM (MFP-3D, Asylum Research/Oxford Instruments) under ambient conditions. The surface morphology and roughness were characterized in Tapping mode. Piezoelectric and ferroelectric behaviors were investigated with the PFM tool using Pt/Ir coated probes (PPP-EFM, NanoSensors) and stiff cantilevers (k ~3.8 N/m). Dual AC resonance tracking (DART) [START_REF] Rodriguez | Dual-frequency resonance-tracking atomic force microscopy[END_REF] mode was employed for PFM analysis in order to enhance the piezoelectric signal, under a driving voltage VAC of 2 V at the probe tip and by grounding the conductive substrate. PFM in spectroscopic mode was used to evaluate piezoelectric deformation and switching behavior of the domains located beneath the AFM tip by recording piezoresponse loops.

RESULTS AND DISCUSSION

Structural analyses

Figure 1 shows the room temperature XRD patterns for the as-prepared BNLBT-x thin films. For the sake of comparison, the XRD patterns of the standard BNT system, with tetragonal (P4bm) [START_REF] Jones | The tetragonal phase of Na0.5Bi0.5TiO3 -a new variant of the perovskite structure[END_REF] and rhombohedral (R3c) [START_REF] Jones | Investigation of the structure and phase transitions in the novel Asite substituted distorted perovskite compound Na0.5Bi0.5TiO3[END_REF] symmetries, and the platinum (Pt) from the electrode contribution, with cubic (Fm-3m) symmetry, [START_REF] Davey | Precision measurements of the lattice constants of twelve common metals[END_REF] are also shown in the Figure 1. A minor Bi2Ti2O7 pyrochlore secondary phase is marked with an asterisk. The crystalline structures of the BNLBT-x films analyzed based on their XRD patterns correspond well with the BNT-based perovskite structure, with a well-developed crystallinity, for all the studied compositions.

Results indicate that the above-mentioned synthesis method is effective in preparing perovskite BNLBT-x thin-film structures with a wide range of composition x. The crystal structures of the films are also found to be in agreement with the reported results by Zheng et al. [START_REF] Zheng | Thermo-electrical energy conversions in Bi0.5Na0.5TiO3-BaTiO3 thin-films prepared by sol-gel method[END_REF] and are similar to those previously reported for BNLBT-x ceramics. [START_REF] Mendez-González | Effect of the lanthanum concentration on the physical properties of the (Bi0.5Na0.5)0.92Ba0.08-3x/2LaxTiO3 ceramic system[END_REF] For complementary information, crosssectional SEM images, collected by using a JEOL JSM-840 Microscope (Germany), have been obtained in order to estimate the thickness of the studied films. The inset of Figure 1 displays the result for the BNLBT-2 film as a representative, with no apparent difference for the other compositions, indicating to be dealing with films showing a thickness of about 400 nm. Recent studies have reported a coexistence between two tetragonal phases (P4bm and P4mm space groups) for BNT-BT ceramics, where the (111) and (200) pseudocubic reflections, observed for 2θ values around 40.0° and 46.5°, respectively, appear as singlet and doublet, respectively. [START_REF] Mendez-González | Effect of the lanthanum concentration on the physical properties of the (Bi0.5Na0.5)0.92Ba0.08-3x/2LaxTiO3 ceramic system[END_REF] Considering lanthanum-modified compositions, however, it was assumed the coexistence between the rhombohedral ferroelectric (R3c space group) and tetragonal antiferroelectric (P4bm space group) phases, as the lanthanum content increases. As a result, different to the pure system, a splitting in the (111) reflection is observed, together with the splitting in the (200) reflections, thus revealing the doublet character for both pseudocubic reflections. Nevertheless, different to the results reported for ceramics, the X-ray diffraction patterns for the thin films studied in the present work have shown relative broader profile peaks, with not very well resolved reflections, the result of which can be attributed to the overlapping of different diffraction reflections as well as the intrinsic microstructural properties such as small grain-size distribution and additional stresses driven by the interface effects, typical in thin films. [START_REF] Pertsev | Effect of mechanical boundary conditions on phase diagrams of epitaxial ferroelectric thin films[END_REF][START_REF] Guerra | Investigation of nonlinear dielectric properties in relaxor ferroelectric thin films[END_REF] The existence of an induced strain (or mechanical tensile) at the film-substrate interface, caused by the different thermal expansion coefficients between the film and the substrate, significantly reflect in the physical properties of the thin films.

In this context, a detailed investigation on the structural characteristics of these thin films was carried out by a refinement analysis of the above XRD patterns, the results of which are shown in Figures 2(a)-(c). The experimental (observed) and theoretical (calculated profiles) data are represented by symbols and solid lines (in red), respectively. The vertical marks, below the patterns, correspond to the calculated Bragg's reflections. The differences between the experimental and theoretical data are identified by bottom blue lines. Four different initial structural models were considered for the calculation of the diffraction patterns: (i) tetragonal (T), with P4bm space group (ICSD-280381), [START_REF] Jones | The tetragonal phase of Na0.5Bi0.5TiO3 -a new variant of the perovskite structure[END_REF] (ii) rhombohedral (R), with R3c space group (ICSD-280983), [START_REF] Jones | Investigation of the structure and phase transitions in the novel Asite substituted distorted perovskite compound Na0.5Bi0.5TiO3[END_REF] (iii) cubic phase (C1), with Fm-3m space group (ICSD-64923), [START_REF] Davey | Precision measurements of the lattice constants of twelve common metals[END_REF] in order to reproduce the contribution of the substrate (Pt) and (iv) cubic-phase pyrochlore (C2), with Fd-3m space group (ICSD-99437), for the simulation of the secondary phase percentage. [START_REF] Hector | Synthesis and structural study of stoichiometric Bi2Ti2O7 pyrochlore[END_REF] The starting structural data for refinement were taken from the "Inorganic Crystal Structure Database" (ICSD). [START_REF]Inorganic Crystal Structure Database (ICSD-2014)[END_REF] It is worth noting that, while most of the reflections demonstrate the same relative peak intensities for all the lanthanum concentrations, a noticeable increase in the intensity can be observed for the (111)C1 plane around 2  39.83° as the lanthanum content increases. Although the used GIXRD method reduces the contribution of the substrate to the XRD pattern, it is important to point out that the penetration depth profile inside the film strongly depends on the incidence angle and the attenuation coefficient of the material. [START_REF] Birkholz | Thin film analysis by X-ray scattering[END_REF] In fact, the increase in the intensity of the (111)C1 reflection is a clear indicative for the increase of the substrate contribution. In addition, it can be observed a change in the DRX profile for the patterns around 46.5°, as can be confirmed in the insets of Figures 2(a)-(c). The refined profiles for this region suggest a tendency of splitting for the BNLBT-0 composition, with a trend for the formation of a single reflection with the increase of the lanthanum concentration, as observed for the BNLBT-3 thin film. This tendency provides an important qualitative information about the structure of the BNLBT-x films and indirectly infer about the phases' coexistence with the increase of the La content. Similar results have been reported in the literature for La-doped BNT-BT ceramics with the same compositions, showing the coexistence of both tetragonal (P4bm) and rhombohedral (R3c) phases by transmission electron microscopy (TEM). [START_REF] Liu | Evolution of structure and electrical properties with lanthanum content in [(Bi1/2Na1/2)0.95Ba0.05]1-xLaxTiO3 ceramics[END_REF] Figure 2.

Table 1 illustrates the unit-cell (a, b and c), volume (V) and goodness-of-fit (Rwp, Rp and χ 2 ) parameters, as well as the phases fractional weight (w), calculated from the refinement process. The final atomic parameters of the lattice sites (x, y, z) were also calculated from the simulation with a very low standard deviation for the four involved phases, the result of which are not shown in Table 1 because of the large amount of data. The obtained values for Rwp, Rp and χ 2 are indicative of a high-quality data refinement, evidencing a good agreement between the experimental (observed) and theoretical (calculated) results. [START_REF] Toby | EXPGUI, a graphical user interface for GSAS[END_REF] Table 1.

For a better analysis of the structural properties from refinement results, the behaviors of the lattice parameters (a and c) for both tetragonal (T) and rhombohedral (R) phases, as well as the phases fractional weight reported in Table 1, as a function of the La content (x), are shown in Figures 3(a) and 3(b), respectively. The calculated lattice parameters reveal no significant variation with the increase of the lanthanum concentration, the values of which fall in the range of those reported in the literature for bulk materials. [START_REF] Mendez-González | Effect of the lanthanum concentration on the physical properties of the (Bi0.5Na0.5)0.92Ba0.08-3x/2LaxTiO3 ceramic system[END_REF] This result could be due to the considerable achieved films thickness (around 400 nm). As observed from Figure 3(b), different to the obtained results for their ceramic counterparts, the refinements for the thin films confirmed the coexistence of the tetragonal antiferroelectric (AFE) and rhombohedral ferroelectric (FE) phases for the studied BNLBT-x films, revealing the major contribution of the AFE phase for the BNLBT-0 and BNLBT-2 compositions. The phases fraction also revealed an increase in the C1 phase, from 2.5 % up to 15.1 %, with the increase of the lanthanum content from 0 to 3 %, respectively. This result, which can be better observed in Figure 3(c), confirms the increase of the substrate contribution, as previously suggested from the analysis of the intensity for the (111)C1 reflection around 39.83°. It can be seen, however, that the fractional weight of the tetragonal AFE phase decreases, whereas the contribution of the rhombohedral FE one increases, with the increase of the lanthanum concentration. In this way, it is worth noting that for the BNLBT-3 composition, an inversion in the phases fraction has been observed, showing the major contribution for the FE phase (44.5 %), while the fractional weight for the AFE, cubic-C1 (Pt) and cubic-C2 (pyrochlore) phases were found to be around 39.4 %, 15.1 % and 1.0 %, respectively. Furthermore, as can be seen, a very low fractional weight (< 3 %) for the C2 pyrochlore phase (Bi2Ti2O7) was also confirmed for all the compositions. Thus, the splitting observed in the inset of Figure 2(a) for the reflection around 46.5°, which revealed to be more evident for the BNLBT-0 and BNLBT-2 compositions, clearly agrees with the refinement results (phase fractional weight), showing the major contribution of the AFE phase (with tetragonal symmetry) for these compositions. Raman spectroscopy was also used to analyze the structural properties and phase evolution of the studied BNLBT-x thin films. The Raman data are shown in Figure 4 for the studied compositions, in which the spectral signature for BNT-type perovskites is confirmed, represented by three typical regions identified as I, II and III in the Raman spectra. [START_REF] Kreisel | An X-ray diffraction and Raman spectroscopy investigation on A-site substituted perovskite compounds: the (Na1-xKx)0.5Bi0.5TiO3 (0<x<1) solid solution[END_REF][START_REF] Pal | Investigation of MPB region in lead free BLNT-BCT system through XRD and Raman spectroscopy[END_REF][START_REF] Shi | Large electrostrictive strain in (Bi0.5Na0.5)TiO3-BaTiO3-(Sr0.7Bi0.2)TiO3 solid solutions[END_REF] Figure 4.

In order to better explore the Raman results, the experimental data have been fitted by considering a theoretical mathematical model based on the location of the curvature maxima in concave-down (CMCD) spectral regions, reported by Buixaderas et al. [START_REF] Buixaderas | Compositional behavior of Raman-active phonons in Pb(Zr1-xTix)O3 ceramics[END_REF] . Results are shown in The peak's position for each Raman active mode (natural wavenumber, cm -1 ), obtained at room temperature after the fitting procedure, as well as their symmetry modes are presented in Table 2 for the compositions. Results reveal that seven active modes are located for the BNLBT-0 sample, whereas eight modes were observed for the BNLBT-2 and BNLBT-3 compositions in the whole analyzed wavenumber range. The additional modes detected for the modified samples, and observed below 200 cm -1 , could be related to the overlapping of the modes associated with the La-O vibration in this spectral region. In addition, a noticeable dependence of the wavenumber for several vibrational modes on the lanthanum concentration can be observed, which have been identified as M2, M4, M5 and M6 in Table 2.

Table 2.

The vibrational modes for both tetragonal and rhombohedral contributions have been identified (scripted by T and R, respectively, in both Figure 4 and Table 2) and the peaks were indexed accordingly. In the region I, below 200 cm -1 , the vibrational modes are associated with the A-O stretching vibrations, [START_REF] Kreisel | An X-ray diffraction and Raman spectroscopy investigation on A-site substituted perovskite compounds: the (Na1-xKx)0.5Bi0.5TiO3 (0<x<1) solid solution[END_REF] involving in that case the Bi, Na, Ba cations for the BNLBT-0 sample and also La cations for the BNLBT-2 and BNLBT-3 compositions. The Raman bands between 200 and 400 cm -1 (region II) are related to the Ti-O stretching vibrations, [START_REF] Pal | Investigation of MPB region in lead free BLNT-BCT system through XRD and Raman spectroscopy[END_REF] and the stretching modes related to the TiO6 oxygen octahedral are assigned to the higher wavenumbers of the spectra (region III, above 400 cm -1 ). [START_REF] Shi | Large electrostrictive strain in (Bi0.5Na0.5)TiO3-BaTiO3-(Sr0.7Bi0.2)TiO3 solid solutions[END_REF] Previous report, regarding bulk ceramic BNLBTx compositions, revealed the coexistence of tetragonal and rhombohedral phases. [START_REF] Mendez-González | Raman spectroscopy study of the La-modified (Bi0.5Na0.5)0.92Ba0.08TiO3 lead-free ceramic system[END_REF] For the undoped sample (x = 0), the vibration modes have been associated with both P4mm and P4bm tetragonal phases, while for lanthanum-doping bulk ceramics the Raman spectra have shown the coexistence of both R3c rhombohedral and P4bm tetragonal phases. As observed, the obtained results on the structural properties from XRD and Raman spectroscopy are in agreement with the results reported for their bulk ceramics counterparts, which could confirm a possible phase coexistence for the studied thin films. However, in order to better clarify this issue, additional quantitative analyses are needed, which include the temperature dependence of both Raman spectroscopy (considering not only the behavior of the peak positions, but also for the full-width at half-maximum and intensity of the Raman modes) and higher resolution XRD measurements, as a function of the lanthanum concentration. Such investigations are in progress and the results will be presented in further works.

Nanoscale microstructural features and electromechanical response

Nanoscale surface and electromechanical properties were then probed. The characteristic AFM surface topography is shown in Figure 6 for the different compositions: (i) BNLBT-0, (ii) BNLBT-2 and (iii) BNLBT-3. The images have been recorded over the 5×5 µm 2 and 2×2 µm [START_REF] Rabe | Physics of ferroelectrics[END_REF] scan regions (a and b, respectively); the grain-size distributions are also shown in Figure 6(c). Regardless the La content, it is observed a dense and crack-free nanostructured surface. However, by looking in more detail, it can be noticed some differences. In the case of the pure BNLBT-0 film (i), as depicted in Figures 6(a)-(c), irregular large grains are observed whose lateral size is ranging from 200 nm up to 900 nm, exhibiting a Gaussian grain-size distribution with an average grain size around 230 nm. For the BNLBT-2 sample (ii), while an onset of coalescence seems to be observed, nanosized rounded grains with diameter ranging between 50 and 130 nm are obtained, resulting in an average grain size around 92 nm. On the other hand, it can be observed that the BNLBT-3 composition (iii) presents randomly-oriented elongated grains with typical widths of about 30 nm and lengths ranging from 50 to 250 nm, with an average grain size around 87 nm. The root mean square roughness, measured over a 10×10 µm² scan area, was found to be around 20.0, 10.6 and 10.4 nm for the BNLBT-0, BNLBT-2 and BNLBT-3 films, respectively. It can be observed, therefore, from these AFM measurements that the introduction of the lanthanum cations promoted a decrease of both the grain size and the surface roughness, allowing for the integration of such films into nano-devices to be considered. Figure 6.

The observed lanthanum concentration dependence of the average grain-size could be associated with an increase of the structural defects (i.e. charged point defects, vacancies, defect-dipole and/or ionic charges) as the doping content increases. Previous evidences, reported for BaTiO3-based ceramics, [START_REF] Ting | Lanthanum-Magnesium and lanthanum-Manganese Donor-Acceptor-Codoped Semiconducting Barium Titanate[END_REF] indicate that the grain growth inhibition is associated with the creation of vacancies, which lead to the space-charge accumulation into the grain boundaries, hence causing a decrease in the grain size. For the studied BNLBT-x thin films, positive vacancies are created due to the substitution of the Na + and/or Ba 2+ ions by the rare-earth cation (with 3+ valence) at the dodecahedral sites of the perovskite structure. It is worth noting that the charge compensation requires that the positive charges excess, resulting from the donor-doping ion, takes place by sodium vacancies (𝑉 Na ′ ), barium vacancies (𝑉 Ba ′′ ) and/or titanium vacancies (𝑉 Ti ′′′′ ). Therefore, the La doping ion could act as a grain growth inhibitor thus promoting a domain-wall pinning effect on the grain boundary with the increase of the lanthanum content. In this context, an increase of the 𝑉 Na ′ , 𝑉 Ba ′′ and/or 𝑉 Ti ′′′′ defects concentration with the increase of the lanthanum content is believed to be a possible cause for the decrease of the average grain-size in the studied thin films. It is worth noting, however, that additional analyses regarding the effect of such positive vacancies, as well as the possible influence of oxygen vacancy defects, will be better explored throughout the investigation of the macroscopic properties (temperature dependence of the dielectric response and macroscopic polarization), and will be in fact the focus of a further work.

Electroactive performances of the films were investigated by measuring the piezoelectric and ferroelectric properties on the nanoscale by PFM measurements. the increase of the lanthanum content has been observed for La-modified BNT-BT ceramic bulk compositions, [START_REF] Mendez-González | Effect of the lanthanum concentration on the physical properties of the (Bi0.5Na0.5)0.92Ba0.08-3x/2LaxTiO3 ceramic system[END_REF] obtained from the solid-state conventional sintering method, where the coercive field (EC) was determined from macroscopic polarization versus electric field (P-E) measurements. The obtained result could be ascribed to the AFE and FE crystalline phases mixing, with the particular feature to be leading here with the major contribution of the AFE component for the pure BNLBT-0 thin film composition. This is particularly true on the nanoscale, where the energy required to efficiently switch the polarization of the probed domain beneath the AFM tip is highly dependent on the crystallite orientation. [START_REF] Desfeux | Correlation between local hysteresis and crystallite orientation in PZT thin films deposited on Si and MgO substrates[END_REF][START_REF] Ferri | Nanoscale investigations of electrical properties in relaxor Pb(Mg1/3Nb2/3)O3-PbTiO3 thin films deposited on platinum and LaNiO3 electrodes by means of local piezoelectric response[END_REF][START_REF] Ferri | Local piezoelectric hysteresis loops for the study of electrical properties of 0.7Pb(Mg1/3Nb2/3)O3-0.3PbTiO3 thin films: bottom electrode dependence and film thickness effects[END_REF] As a consequence, the lower coercivity for the polarizing voltage obtained on the BNLBT-0 film is in good agreement with the minor contribution of the ferroelectric rhombohedral crystallites, compared to the case of the La-doped films where the FE component becomes the dominating phase, as indeed previously confirmed by the structural analyses.

In the case of the amplitude PFM signals, as shown in Figures 8(b), (d) and (f) for the BNLBT-0, BNLBT-2 and BNLBT-3, respectively, well-defined butterfly-like shapes are observed, which confirm the electromechanical behavior related to the converse piezoelectric effect. By considering the PFM loops recorded over the BNLBT-0 surface, for instance, it can be noted a saturation in the local mechanical response at maximum bias voltage leading to an amplitude deformation A of ~5.45 nm. Since this signal is enhanced by the use of the contact resonance through the DART PFM method, this implies taking into account the quality factor Q, which is around 80 for such inorganic compound where the loss is too low. [START_REF] Carlier | Ferroelectric state in a α-Nd2WO6 polymorph stabilized in thin film[END_REF][START_REF] Liu | Rapid nanoimprinting and excellent piezoelectric response of polymer ferroelectric nanostructures[END_REF] Therefore, by considering the detected PFM amplitude proportional to A = d33VACQ it can be estimated the effective piezoelectric constant value to be around d33eff ~ 34 pm/V. This result is in good agreement with the reported value for BNT thin films (d33eff.max ~ 47 pm/V) with similar thickness and deposited on silicon substrates by the sol-gel method. [START_REF] Abou Dargham | Synthesis and electrical properties of lead-free piezoelectric Bi0.5Na0.5TiO3 thin films prepared by Sol-Gel method[END_REF] The PFM amplitude signal also depicts an increase in the A values for the BNLBT-2 and BNLBT-3 compositions, at the same maximum applied DC voltage. Therefore, higher d33eff values are expected for the La-doped samples, since they have not reached their saturated loops condition, thus suggesting an enhanced local piezo-activity with the increase of the lanthanum content. This result also confirms the obtained results from the XRD properties, and reveals the potential of the leadfree BNLBT thin films to replace compounds containing toxic elements such as lead-based materials. Furthermore, each measured amplitude loop exhibits a symmetric shape when considering the maximum deformation under both positive and negative voltages excitation.

This behavior reveals the homogeneous electromechanical properties of the studied films, thus enabling their use in actuators, sensors or energy harvesting devices.

Figure 8.

It is worthwhile noting that during switching PFM spectroscopy, in some cases no signal was detected. This particular behavior could be related to the absence of piezo-activity shown on the amplitude PFM images in Figures 7(a), (c) and (e) for the BNLBT-0, BNLBT-2 and BNLBT-3 compositions, respectively, attesting that antiferroelectric regions could have been probed by the AFM tip. To the best knowledge of the present authors, only three studies have been reported on the recording of piezo-response loops on antiferroelectric materials, where an incipient double hysteresis loop has been shown. [START_REF] Boldyreva | Microstructure and electrical properties of (120)O-oriented and of (001)O-oriented epitaxial antiferroelectric PbZrO3 thin films on (100) SrTiO3 substrates covered with different oxide bottom electrodes[END_REF][START_REF] Chaudhuri | Epitaxial strain stabilization of a ferroelectric phase in PbZrO3 thin films[END_REF][START_REF] Martin | Ferroelectricity in Si-doped HfO2 revealed: A binary lead-free ferroelectric[END_REF] Therefore, from the obtained PFM analyses, the observed domain pattern, combined with the local switching behavior and electromechanical activity, is a clear evidence of the nanoscale piezo-/ferroelectric nature at room temperature for the studied BNLBT-x thin films. Besides, it is worth noting that the probing of AFE-FE phase transition by PFM has just been recently reported in PbZrO3 capacitors. [START_REF] Lu | Probing Antiferroelectric-Ferroelectric Phase Transitions in PbZrO3 Capacitors by Piezoresponse Force Microscopy[END_REF] As a remark, it is worth pointing out that the hysteresis loops are systematically shifted along the DC bias axis, towards positive voltages. This asymmetry is characteristic of an imprint behavior of the local switching, which commonly arises from the presence of a builtin electric field in the samples. [START_REF] Ferri | Thickness dependence of the nanoscale piezoelectric properties measured by piezoresponse force microscopy on (111)-oriented PLZT 10/40/60 thin films[END_REF][START_REF] Lichtensteiger | Tuning of the depolarization field and nanodomain structure in ferroelectric thin films[END_REF] In order to better evaluate the imprint effect, the voltage offset (Voff) of the hysteresis loops has been obtained by averaging the negative and positive coercive voltages (𝑉 𝐶 -and 𝑉 𝐶 + , respectively) through the following relation: 𝑉 off = (𝑉 𝐶 + + 𝑉 𝐶 -) 2 ⁄ . [START_REF] Okazaki | Effects of grain size and porosity on electrical and optical properties of PLZT ceramics[END_REF][START_REF] Grossmann | The interface screening model as origin of imprint in thin films. I. Dopant, illumination, and bias dependence[END_REF] Results reveal a decrease in the voltage offset value, from about 7 V for the pure sample up to around 5 V for the La-doped compositions, showing a strong influence of the doping cation in the imprint effect.

From the fundamental point of view, although the real nature of this imprint behavior observed in thin films still remains under intense discussions by the scientific community, thus remaining as a non-fully clarified issue up today, several phenomenological models have been proposed to explain the origin of the observed phenomenon. [START_REF] Grossmann | The interface screening model as origin of imprint in thin films. I. Dopant, illumination, and bias dependence[END_REF][START_REF] Carl | Electrical after-effects in Pb(Ti,Zr)O3 ceramic[END_REF][START_REF] Arlt | Internal bias in ferroelectric ceramics: origin and time dependence[END_REF][START_REF] Dimos | Photoinduced hysteresis changes and optical storage in (Pb,La)(Zr,Ti)O3 thin films and ceramics[END_REF][START_REF] Warren | Imprint in ferroelectric capacitors[END_REF] In fact, there has been a

consensus that an internal electric field developed by charged defects is believed to play an important role in the imprint phenomena. In this way, two of the most accepted models in the current literature with a better description of the imprint effect are probably those related to the defect-dipole alignment, proposed firstly by Arlt et al. [START_REF] Arlt | Internal bias in ferroelectric ceramics: origin and time dependence[END_REF] and later modified by Warren et al., [START_REF] Warren | Imprint in ferroelectric capacitors[END_REF] and the interface screening process, proposed by Grossman et al. [START_REF] Grossmann | The interface screening model as origin of imprint in thin films. I. Dopant, illumination, and bias dependence[END_REF] According to the defectdipole alignment model, the asymmetric distribution of trapped charges and the alignment of defect-dipoles near the material-electrode interface have been suggested to be responsible for the voltage shift in ferroelectric thin films. [START_REF] Warren | Imprint in ferroelectric capacitors[END_REF] The defect-dipole alignment produces an internal bias electric field, which induces a voltage shifts thus promoting the imprint effect. On the other hand, the interface screening model considers the presence of a very thin layer at the filmelectrode interface where there is a suppression in the spontaneous polarization. [START_REF] Grossmann | The interface screening model as origin of imprint in thin films. I. Dopant, illumination, and bias dependence[END_REF] This model, which in fact shows to be a modification of the defect dipole alignment model, considers the redistribution of electrons and/or holes as the main cause for the imprint phenomena observed in ferroelectric thin films, being the defect-dipole alignment, a secondary imprint mechanism.

The origin of the voltage offset has been related, in this case, to a large internal electric field originated within the interface layer of the film, with the orientation along the polarization direction. A gradual shifting of the hysteresis loop is thought to be governed, therefore, by the internal field due to the consecutive electronic charges trapping, which are injected from the electrode into the film and have a polarity in the opposite direction to the ferroelectric dipole.

As a consequence, the induced internal field screens the applied external electric field and a higher applied voltage is required to induce the polarization reversal.

As observed from the proposed models, whatever the mechanism that promotes the voltage offset, there have been several strong indications that the defects play the essential role in the polarization degradation phenomena, which result in the asymmetric switching 'imprint'

behavior. The main idea of the defect chemistry models is that the charge electroneutrality could be distorted by the inclusion of doping cations, [START_REF] Grossmann | The interface screening model as origin of imprint in thin films. I. Dopant, illumination, and bias dependence[END_REF][START_REF] Arlt | Internal bias in ferroelectric ceramics: origin and time dependence[END_REF] which possess a different valence than the hosting ions they replace. Therefore, the observed imprint behaviors in this work could be explained considering to the role of the defects, and described according to the following scenario:

It is well known that in ferroelectric perovskites (ABO3) intrinsic defects related with evaporation of some alkali cations, and some other di-and tri-valent elements, during processing and sintering at high temperatures are often present in the material. In order to compensate the charges unbalance promoted by cations volatilization, thus maintaining the charge neutrality, oxygen vacancies are commonly created, which significantly affect the physical properties of the studied system. [START_REF] Eyraud | Influence of simultaneous heterovalent substitutions in both cationic sites on the ferroelectric properties of PZT type ceramics[END_REF] Therefore, oxygen vacancies, which have indeed revealed as the most mobile ionic defects in perovskites, and natural intrinsic oxygen-vacancyrelated defect dipoles, have been shown to be involved in most of the observed anomalous behaviors in the electrical and electromechanical properties of ferroelectrics and related materials. [START_REF] Ang | Oxygen-vacancy-related low-frequency dielectric relaxation and electrical conduction in Bi:SrTiO3[END_REF] Such defects have been suggested, for instance, to play a crucial role in the intrinsic polarization mechanisms and the domain-wall dynamics, thus promoting the voltage offset that leads to the imprint effect. [START_REF] Pike | Voltage offsets in (Pb,La)(Zr,Ti)O3 thin films[END_REF] However, the formation and mobility of defects can be easily controlled by the partial substitution of A-(or B-site) cations, with acceptor and donor species, thus reducing the defect density and improving most of the physical properties. In BNT-based systems, for instance, the evaporation of Na, K and Bi may result in many nonstoichiometric structural defects to form secondary phases during the thermal processes. [START_REF] Yueqiu | Large piezoelectric response of Bi0.5(Na(1-x)Kx)0.5TiO3 thin films near morphotropic phase boundary identified by multipeak fitting[END_REF] As a consequence, a noticeable imprint behavior could be expected, as indeed observed for the pure BNLBT-0 sample. Nevertheless, taking into account that donor doping does mainly introduce immobile defect dipoles, the inclusion of the La 3+ cation, which suppresses the formation of oxygen vacancies, could have led to a decrease of the mobile defect dipole concentration and, therefore, to a reduction of imprint, as observed for the La-doped concentrations (BNLBT-2 and BNLBT-

3). This result is in agreement with those reported in the literature for some perovskite-based structure ferroelectric systems. 72,74

Domain structure nature and fractal dimension analysis

In order to investigate the domain structure in more details, as well as to obtain a quantitative description of the polarization distribution, additional analysis involving the autocorrelation function has been carried out from the PFM results previously discussed (Figure 7). The PFM data have been processed using the Gwyddion image analysis program. [START_REF] Necas | Gwyddion: an open-source software for SPM data analysis[END_REF] To illustrate the domain structure nature of the thin films produced in this work, the autocorrelation function C(r) was applied to quantify the nanodomain structure in terms of the average correlation length (Δ). In this way, important information can be extracted from the OP images obtained for the studied BNLBT-x thin films, by applying the transformation on the piezoresponse images in Figures 7(a),(c) and (e) following the theoretical model recently reported by Shvartsman et al. [START_REF] Shvartsman | Mesoscale domains and nature of the relaxor state by piezoresponse force microscopy[END_REF] According to this model, the short-range correlation length can be obtained from the autocorrelation function, by Equation ( 1), where r is the distance from the central maximum and b is the exponential parameter (0 < 𝑏 < 1).

𝐶(𝑟) ∝ exp[-( 𝑟 ∆ ) 2𝑏 ] (1)
Taking into account the autocorrelation images (not shown here), the autocorrelation function C(r), at small r values, were recorded for all the studied BNLBT-x compositions.

Figure 9(a) depicts the distance (r) dependence of autocorrelation function C(r) over all inplane directions for the BNLBT-0 composition, as an example of the obtained results for all the studied compositions, where the values have been normalized to C(r=0). The average correlation length value obtained from the best fitting of the curve for the BNLBT-0 thin film was found to be around 66.2 ± 0.2 nm.

Figure 9.

The average correlation length (), the fractal dimension of the "polarization interface", and roughness exponent () for the BNLBT-x thin films as a function of the La content (x) are shown in Figure 9(b). The correlation length obtained from the fitting process by using the autocorrelation function, Equation (1), increases from 66 nm up to 529 nm with the increase of the lanthanum contents from 0 % to 3 %. The lower correlation length value, which has been indeed obtained for the BNLBT-0 film, revealed to be close to that reported for classical relaxor systems, such as PMN single crystals (Δ ≈ 70 nm), [START_REF] Shvartsman | Mesoscale domains and nature of the relaxor state by piezoresponse force microscopy[END_REF] suggesting the possible relaxor character for the studied film. It has been also reported that, for PMN-xPT single crystals, such Δ value reveals to be strongly dependent on the PT content, reaching the higher value (~ 650 nm) for the highest titanium content composition. [START_REF] Shvartsman | Mesoscale domains and nature of the relaxor state by piezoresponse force microscopy[END_REF] For other relaxor systems, such as PLZT thin films, intermediate Δ values (close to 350 nm) have also been reported, [START_REF] Melo | Thickness effect on the structure, grain size, and local piezoresponse of self-polarized lead lanthanum zirconate titanate thin films[END_REF] suggesting a strong relationship between the grain size and correlation length. For BNT-BT materials, instead, a lower value for the correlation length have also been recently reported in single crystals, revealing to be around 20 nm. [START_REF] Daniels | Structural origins of relaxor behavior in a 0.96(Bi1/2Na1/2)TiO3-0.04BaTiO3 single crystal under electric field[END_REF] However, different to those previously discussed here, the correlation length obtained for that single crystal composition has been extracted from diffuse X-ray scattering experiments. Results obtained in this work, from Figure 9(b), show that the characteristic length scale of switched domains obtained for the BNLBT-3 thin film (529 nm) is significantly higher than the average grain size (87 nm) for the same composition, which is a clear indicative of the presence of long-range correlations. In fact, the correlation length has been related to the size of the polar nano regions (PNRs) in relaxors materials. [START_REF] Bokov | Recent progress in relaxor ferroelectrics with perovskite structure[END_REF] Therefore, the high correlation length values obtained in the present work suggest the higher size of the PNRs for the BNLBT-3 composition. The observed trend for the correlation length also reveals to be in agreement with the results obtained from the structural properties, showing an increase in the FE phase contribution with the increase of the lanthanum content.

According to the Kolmogorov-Avrami-Ishibashi (KAI) model, domain switching processes can be associated to fractal dimensionality. [START_REF] Ishibashi | Note on ferroelectric domain switching[END_REF] From the fundamental point of view, several theoretical models have been proposed and used in the literature, to account for the microstructural characteristics of electronic materials based on fractal analyses. [START_REF] Mitic | Fractal frontiers in microelectronic ceramic materials[END_REF][START_REF] Mitic | Ceramic materials and energy -Extended Coble's model and fractal nature[END_REF] In this context, intergranular phenomena at the nanoscale dimension could be investigated by considering their fractal nature. [START_REF] Mitic | Ceramic materials and energy -Extended Coble's model and fractal nature[END_REF] Such analyses significantly contribute for researches devoted to microelectronic miniaturization and undoubtedly provide new perspectives for the application of ferroelectric and related materials in electro-electronic devices with very high integration technology. [START_REF] Mitic | The nanoscale modified BaTiO3 morphology influence on electronic properties and ceramics fractal nature frontiers[END_REF] Therefore, in order to better understand the mechanisms responsible for nucleation of nanodomains as well as the change in domain-wall geometry under the action of an external electric field, a fractal analysis has also been performed. The fractal dimension from the OP-PFM images were calculated by using the cube counting method with the abovementioned image data analysis. In the cube counting method, a cubic lattice with lattice constant C is superimposed on the z-expanded surface. The slope of the linear portion of a log(area) vs log(C) plot provides the fractal dimensionality (D). [START_REF] Douketis | Fractal character of cold-deposited silver films determined by low-temperature scanning tunneling microscopy[END_REF] Based on these linear fittings (not shown here), the dimensionalities were found and summarized in Figure 9(b) for all the studied BNLBT-x compositions. Notice that for the BNLBT-0 and BNLBT-2 thin films the fractal dimensionality remains virtually unchangeable at 2.30, whereas the BNLBT-3 sample revealed a higher D value, being around 2.43. Thus, the obtained values for the fractal dimensionality are in good agreement with the experimental values reported for PZT ferroelectric thin films (2.42-2.49), with thicknesses between 50 and 91 nm, [START_REF] Paruch | Domain wall roughness in epitaxial ferroelectric PbZr0.2Ti0.8O3 thin films[END_REF] with an expected theoretical value for D around 2.50. [START_REF] Scott | Absence of true critical exponents in relaxor ferroelectrics: the case for defect dynamics[END_REF] To investigate the boundaries between different contrasted regions upward and downward polarized ferroelectric domains randomly distributed in the layers, the quantitative characterization of domain-wall roughness was now considered. The correlation function B(L)

of relative displacements was used to find the characteristic exponent of roughness (ξ) via the 𝐵(𝐿) ∝ 𝐿 2𝜉 relation. ] relation, where R is the energy barrier and μ is a dynamical exponent, which reflects the nature of the system. [START_REF] Tybell | Domain wall creep in epitaxial ferroelectric Pb(Zr0.2Ti0.8)O3 thin films[END_REF] Indeed, the dynamical exponent is related to the roughness exponent through the relation expressed by the Equation (2).

𝜇 = 𝐷-2+2𝜉 2-𝜉 (2)
Thus, by using the values previously found for D and ξ, it was possible to obtain μ coefficient values around 1.08, 1.06 and 0.77 for the BNLBT-0, BNLBT-2 and BNLBT-3 compositions, respectively. Dynamical exponent values from 1.01 to 1.21 have been reported

for Pb(Zr0.20Ti0.80)O3 thin films with different thicknesses, [START_REF] Tybell | Domain wall creep in epitaxial ferroelectric Pb(Zr0.2Ti0.8)O3 thin films[END_REF] which confirm the agreement between the obtained results in the present work with those reported in the literature. Other studies carried out in thin films have also investigated the influence of the defects purposely generated during crystal growth (or introduced by heavy ion irradiation) and the results revealed a decrease in the creep exponent, with the increase of the defects. [START_REF] Paruch | Nanoscale studies of domain wall motion in epitaxial ferroelectric thin films[END_REF] In this context, according to the results shown in Figure 8, the asymmetric nanoscale loops observed for the studied compositions in the present work, is a clear evidence of the defect dipoles (or defect clusters)

induced by the pinning effect of domain-walls. Under a pinning potential, in the random field scenario, a dynamical exponent (μ) value close to 1.0 is expected. In addition, it has been observed that the μ exponent significantly drops with the increase of the lanthanum concentration for the studied BNLBT-x films. Therefore, the increase in the lanthanum concentration promotes an increase in the structural disorder, probably originated from the local quenched defects, thus confirming the obtained results for the fractal dimension. However, it is important to emphasize that the understanding of the main role of polar nanoregions in the studied material continues to be a challenge up today.

CONCLUSIONS

Bi0.506Na0.46Ba0.08-3x/2LaxTiO3 (x = 0, 2 and 3 at%) lead-free thin films were successfully synthesized by a sol-gel method and deposited on Pt(111)/TiO2/SiO2/Si substrate by the spincoating technique. The expected perovskite structure was achieved and the coexistence between the antiferroelectric (tetragonal, P4bm) and ferroelectric (rhombohedral, R3c) phases was confirmed from XRD measurements and Raman spectroscopy, thus revealing the quality of the obtained films. Dense and crack-free nanostructured surface for the studied compositions was evaluated from the AFM surface topography. The increase of the lanthanum concentration has provided a decrease of both the grains size and the surface roughness. The PFM analysis has evidenced the piezo-/ferroelectric nature of the BNLBT-x thin films at the nanoscale, with a homogeneous piezo-activity for each film and a higher electromechanical response detected for the doped BNLBT films. The coercive voltage values VC was also found to be much lower for the undoped film compared to the La 3+ modified samples. The estimated effective piezoelectric constant for the pure sample was d33eff ~ 34 pm/V, also revealing an enhanced local piezo-activity with the increase of the La content, thus suggesting the potential of the leadfree BNLBT thin films to replace lead-based materials. The nanodomain structure nature revealed long-range average correlation lengths for La-doped thin films, whereas the evaluation of the dynamic exponent, which describes the electric field dependence of the domain-wall speed, showed an increase and a decrease in the fractal dimension and exponent of roughness, respectively, with the increase of the doping content. This result confirms an increase in the structural disorder, probably originated from the local quenched defects, promoted by the increase of the lanthanum concentration. The nanoscale analysis of the domain wall revealed an intrinsic dependence of the dynamic coefficient that reflects the nature of the system, with the increase of the lanthanum content, which indeed seems to be the main responsible for the local fields induced structural disorder.

TABLES AND FIGURES CAPTIONS

Table 1. Unit-cell (a, b and c), volume (V) and goodness-of-fit (Rp, Rwp and χ 2 ) parameters obtained after the refinement process for all the compositions. Data for the resulting phases fractional weight (w) are also included. SG refers to the space group.

Table 2. Wavenumber (W) and assigned vibrational modes (VM) for the studied thin films (BNLBT-0, BNLBT-2 and BNLBT-3 compositions).

Figure 1 .

 1 Figure 1.

Figure 3 .

 3 Figure 3.

Figure 5 ,

 5 Figure 5, where Raman scattering spectra (open symbols) as well as the fitting results (solid-

Figure 5 .

 5 Figure 5.

Figure 7

 7 depicts the asgrown out-of-plane (OP) amplitudes (a, c and e) and phase PFM patterns (b, d and f) detected over the surfaces for the BNLBT-0 (a, b), BNLBT-2 (c, d) and BNLBT-3 (e, f) compositions.High electromechanical activity has been detected for all the films as evidenced by the strong contrasts observed on the amplitude PFM images and related to the local deformation of the layer under the AFM tip. This result confirms the enhanced piezo-activity for the studied thin films. Comparing the contrasts of the three samples, higher electromechanical activity is detected for the doped BNLBT films, as seen on the corresponding dark blue-to-yellow contrast scales under similar driving voltage. Phase PFM images (b, d and f) simultaneously recorded also exhibit contrasts associated to the ferroelectric response of the films due to the OP components of the polarization vector in the layer. The various contrasted regions reveal upward and downward polarized ferroelectric domains randomly distributed in the layers, showing a clear domain structure. Besides, both PFM signals are strongly dominated by the surface morphological features. Furthermore, regions with very low deformations are observed on the amplitude PFM images, as highlighted by the white circles on the Figures7(a), (c) and (e). These zones with very limited piezo-activity could be attributed to antiferroelectric phases existing in the fabricated films, which corroborate the aforementioned phase coexistence suggested through the structural characterizations, containing both the tetragonal antiferroelectric (P4bm) and rhombohedral ferroelectric (R3c) phases.

Figure 7 .

 7 Figure 7.

Figure 9 (

 9 c) shows the typical ln-ln plot of the correlation function B(L) and the fitting of the linear part of the curve, yielding the exponent () for the BNLBT-0 composition. Result reveals the ξ value to be around 0.60 ± 0.04. A similar result has also been found for the BNLBT-2 composition, whereas a lower value was observed for the BNLBT-3 sample (0.40 ± 0.02). The expected theoretical value for ξ (~ 3/5) is comparable to the reported values for two-dimensional domain-walls in materials with random local-fields.[START_REF] Paruch | Nanoscale studies of domain wall motion in epitaxial ferroelectric thin films[END_REF] In this scenario, the defects can promote a local asymmetry in the ferroelectric double-well potential and, therefore, a nonlinear creep response. From the presented results, it is possible to find a fundamental parameter for describing the speed of domains-wall motion in ferroelectric materials. Under low electric field levels, below the threshold value (E0) in the creep regime, the electric field dependence of the domain-wall speed can be described by the 𝑣 ∝ 𝑒𝑥𝑝 [-𝑅 𝑘 𝐵 𝑇 ⁄

Figure 1 .

 1 Figure 1. X-ray diffraction patterns of the studied BNLBT-x thin films, collected at room

Figure 2 .

 2 Figure 2. Rietveld refinement of the X-ray diffraction patterns for the BNLBT-0, BNLBT-2

Figure 3 .

 3 Figure 3. (a) Composition (x) dependence of the lattice parameters for the tetragonal (aT and

Figure 4 .

 4 Figure 4. Raman spectra for the studied thin films (BNLBT-0, BNLBT-2 and BNLBT-3

Figure 5 .

 5 Figure 5. Measured Raman scattering spectra (open symbols), together with the fitted spectra (solid-lines) and the decomposed active modes (dashed-lines), for the studied thin films.

Figure 6 .

 6 Figure 6. AFM topographic images of the films recorded over (a) 5×5 µm 2 , (b) 2×2 µm 2 scan

Figure 7 .

 7 Figure 7. As-grown OP amplitude (a, c and e) and phase (b, d and f) PFM patterns detected

Figure 8 .

 8 Figure 8. Remnant phase (a, c and e) and amplitude (b, d and f) PFM loops recorded on the

Figure 9 .Table 2 .

 92 Figure 9. (a) Distance dependence of autocorrelation function for the BNLBT-0 thin film over

Figure 1 .

 1 Figure 1. Mendez-González et al.

Figure 3 .Figure 5 .Figure 6 .Figure 8 .

 3568 Figure 3. Mendez-González et al.

Figure 9 .

 9 Figure 9. Mendez-González et al.

ACKNOWLEDGMENTS

The authors thank the National Council of Scientific and Technological Development (CNPq) grant 303314/2016-8, Minas Gerais Research Foundation (FAPEMIG) grants PPM-00661-16 and APQ-02875-18 and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior -Brasil (CAPES) -Finance Code 001 Brazilian agencies for the financial support. The Abdus Salam International Centre for Theoretical Physics, Trieste-Italy, for financial support of Latin-American Network of Ferroelectric Materials (NT-02) is also acknowledged. Dr. Mendez-González acknowledges the partial financial support by the ICTP-CLAF agreement AF-13. Thanks to the PHC "Carlos J. Finlay" (Project France-Cuba, 2017-2018). Région Hautsde-France and Fonds Européen de Développement Régional (FEDER) are gratefully acknowledged for funding the MFP-3D microscope under Program "Chemistry and Materials for a Sustainable Growth". Chevreul Institute (FR 2638), Ministère de l'Enseignement Supérieur, de la Recherche et de l'Innovation, Hauts-de-France Region, Fonds Européen de Développement Régional (FEDER) and Major Domain of Interest (DIM) "Eco-Energy Efficiency" of Artois University are acknowledged for supporting and funding partially this work.

CONFLICTS OF INTEREST

There are no conflicts of interest to declare. ORCID J. D. S. Guerra https://orcid.org/0000-0002-7906-4343