# Sol-gel derived barium strontium titanate thin films using a highly diluted precursor solution

Claudette Mansour, Mohammed Benwadih, Christine Revenant

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Claudette Mansour, Mohammed Benwadih, Christine Revenant. Sol-gel derived barium strontium titanate thin films using a highly diluted precursor solution. AIP Advances, 2021, 11 (8), pp.085302. 10.1063/5.0055584. hal-03323032

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# Sol-gel derived barium strontium titanate thin films using a highly diluted precursor solution

Claudette Mansour; Mohammed Benwadih; Christine Revenant

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AIP Advances 11, 085302 (2021)

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# Sol-gel derived barium strontium titanate thin films using a highly diluted precursor solution

Cite as: AIP Advances 11, 085302 (2021); doi: 10.1063/5.0055584

Submitted: 7 May 2021 • Accepted: 13 July 2021 •

Published Online: 2 August 2021

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Claudette Mansour,<fnref n="1" /> Mohammed Benwadih,<fnref n="1" /> and Christine Revenant<fnref n="2" />,ª

## AFFILIATIONS

## ABSTRACT

Among lead-free ferroelectric materials, Barium Strontium Titanate (BST) has interesting ferroelectric, pyroelectric, piezoelectric, and energy-harvesting properties. This material can be advantageously solution-deposited. There is a need for homogeneous and dense films with optimized electrical properties. BST thin films are elaborated with a highly diluted precursor solution of less than 0.05 M. The electric properties are correlated with the morphology and structure of the films as a function of precursor solution dilution. The film growth is columnar with a tetragonal perovskite structure. As the dilution increases, the roughness of the top surface and of the columns decreases, facilitating grain coalescence. In addition, the permittivity of the grains and of the grain boundaries decreases. The highest dielectric strength (400 kV/cm) is obtained for the sample elaborated with the most diluted precursor solution of 0.008 M. For a given polarization, the necessary poling electric field decreases by a factor 2.3 as dilution increases by a factor 4. Finally, hysteresis loops are obtained with increasing saturation and remnant polarizations as the dilution increases. The saturation polarization is approximately doubled as the solution dilution is multiplied by four. To conclude, BST films elaborated with highly diluted solutions have enhanced ferroelectric properties.

© 2021 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0055584

## I. INTRODUCTION

Nowadays, there is tremendous research on lead-free ferroelectric materials. Among the materials that can be deposited by sol-gel, Barium Strontium Titanate (BST) has interesting ferroelectric,<fnref n="1" /> pyroelectric, piezoelectric,<fnref n="2" /> and energy-harvesting³ properties.

BST has a perovskite type structure. The formula of a perovskite is ABX₃, where A and B are cations and X is an anion, which, in most cases, is oxygen O. A cations are on the unit cell corners, while B cations are at the center, and anions occupy the face-center sites of the cube. In the case of BST, Ba and Sr occupy the A sites, Ti occupies the B sites, and O occupies the face-center of the unit cell. The cubic structure has B cations in a six-fold coordination surrounded by an octahedron of anions (BO₆), and the A cations sit in a 12-fold coordinate site.⁴ Frenkel *et al*. found that in quasi-amorphous BaTiO₃, the TiO₆ octahedron is distorted and the Ti-off center displacement occurs in the [111] direction of the TiO₆ octahedron.⁵

The ferroelectric to paraelectric transition temperature, called Curie temperature $T_C$, can be tailored by varying the Sr

concentration.⁶⁻⁹ Changes in the dielectric behavior and lattice parameters of BaₓSr₁₋ₓTiO₃ films have been reported as a function of x values.¹⁰ Compositions in the paraelectric phase (x < 0.5) exhibit high dielectric tunability and low dielectric losses at microwave frequencies.¹¹⁻¹⁵ The composition Ba₀.₇Sr₀.₃TiO₃ with the $T_C$ at room temperature (RT) is ferroelectric and exhibits high technological interest due to its high permittivity at RT. This composition has applications in high permittivity capacitors.¹⁶,¹⁷

In order to have reliable BST capacitors, the dielectric properties should be well controlled. As a matter of fact, the dielectric constant may be inhomogeneous due to an amorphous layer at the interface between the Pt electrode and the film.¹⁸ The dielectric permittivity may also decrease due to a tensile residual stress due to the thermal expansion mismatch between the film and the substrate.¹⁹ Among the possible conduction mechanisms,²⁰ the Space-Charge Limited Conduction (SCLC) may occur. In addition, some works have evidence of the important role played by oxygen vacancies, which provide n-type carriers, giving rise to electronic conduction in BST.²¹ Regarding the deposition technique, the chemical solution

<footnote n="1">¹ University Grenoble Alpes, CEA, LITEN, 38000 Grenoble, France</footnote>

<footnote n="2">² University Grenoble Alpes, CEA, IRIG-MEM, 38000 Grenoble, France</footnote>

<footnote>ª Author to whom correspondence should be addressed: christine.revenant@cea.fr</footnote>
deposition (CSD) such as sol-gel is particularly interesting as it is an easy and low-cost route that can be used on large surfaces. The microstructure of BST thin films can be tailored by adjusting the parameters of CSD such as the precursor solution chemistry, heat treatment, and solution concentration.²² The physics of solution-processed thin films allow tailoring the morphology of sol-gel thin films and, ultimately, the properties.²³ With the sol-gel deposition method, growth can be granular or columnar according to the annealing efficiency in removing organic species depending on the dilution/thickness of the deposited layers.²⁴ When the solution dilution is increased, the film morphology changed from a granular structure to a columnar one.²⁵ Moreover, the microstructure has a strong influence on the thin film properties. Hoffmann et al. studied the dielectric permittivity for different morphologies of CSD processed BST using different concentrations of the precursor solution.²⁶,²⁷ Interestingly, the dielectric values increased as the morphology evolved from a granular structure to a columnar one. In addition, Ba₀.₈Sr₀.₂TiO₃ thin films were elaborated with several precursor solution concentrations (0.4, 0.1, and 0.05 M).²⁸ BST films with the most diluted solution have the best ferroelectric characteristics. More precisely, large grains with a size of 100–200 nm are obtained from highly dilute solutions. Polarization-electric field and dielectric constant-temperature measurements reveal that the ferroelectricity improves as the grain size increases. Moreover, the ferroelectric and pyroelectric properties of highly diluted Ba₀.₈Sr₀.₂TiO₃ thin films (0.05 M) were extensively studied.²⁹ These highly diluted BST films display pronounced ferroelectric hysteresis loops. A work by another group confirmed that the growth is columnar for diluted solutions and sufficiently annealing.³⁰ More recently, the dependence of ferroelectric properties was theoretically studied as a function of grain height and width in columnar-grained BaTiO₃ thin films.³¹ For a grain size smaller than 200–300 nm, most of the grains consist of single domains and do not have domain walls.³² As the grain size decreases, the polarization also decreases due to the depolarization field associated with the charges at the material surfaces.

Although a large number of studies have been carried out on BST thin films, the use of a highly diluted precursor solution of less than 0.05 M has not been considered so far as a way to get more homogeneous and denser films that will lead to enhanced ferroelectric properties.

Against that background, the objective of this paper is to study solution-based Ba₀.₇Sr₀.₃TiO₃ thin films elaborated with a highly diluted precursor solution of less than 0.05 M. The morphological, structural, and (ferro)electric properties of the films are studied as a function of precursor solution dilution. In addition, the poling process is detailed. The influence of poling on the ferroelectric properties is discussed, and the impact of the grain size on the poling voltage is presented.

## II. EXPERIMENTAL SECTION

Ba₀.₇Sr₀.₃TiO₃ sol-gel commercial solution from Mitsubishi Chemical Corporation was used to elaborate the films.²⁴ Let us denote the three film samples with 0.032, 0.016, and 0.008 M precursor concentrations as BST32, BST16, and BST8, respectively. The solutions were deposited onto a platinized silicon substrate Pt (100 nm)/TiO₂ (10 nm)/SiO₂ (500 nm)/Si (725 µm) by spin coating

the solutions at 4000 rpm for 30 s. The substrate was cleaned in acetone in an ultrasonic cleaner for 3 min prior to solution deposition. The as-deposited films were annealed at 450 °C for 5 min on a hot plate in air for solvent evaporation and organic decomposition and then annealed at 700 °C for 1 min in air using a furnace for film crystallization. The annealing cycle was repeated after deposition of each layer to achieve the desired film thickness.

The BST thin films were studied by SEM, and the final film thickness Δ*F* was estimated from the cross section SEM images. Atomic force microscopy (AFM) was used to investigate the grain size and the roughness of the thin films. The measurement was performed in tapping mode on the surface of the thin films in the range of 1 µm using an atomic force microscope from Innova-Bruker. The lateral grain size and the root mean squared roughness of the films were obtained using the NanoScope Analysis software. X-ray diffraction (XRD) measurements were conducted to investigate the crystallinity of the thin films. The measurement setup consisted of a Panalytical Empyrean diffractometer with a cobalt x-ray source with a wavelength λKα = 1.789 Å. The incident optics elements were a fixed 1/4° divergence slit, a Soller slit, and a 4 mm mask. The diffracted optics elements were a parallel plate collimator and a proportional one-dimensional detector.

A metal-ferroelectric film-metal (MFM) structure was achieved by depositing 100 nm of Pt thin films using ion beam evaporation at room temperature (RT), through a shadow mask with a circular diameter of 1 mm. The dielectric measurements of the thin film capacitors were conducted in the range of 100 Hz – 1 MHz using the Agilent E4980A Precision LCR Meter. In addition, the dc current of the films was measured at RT up to a voltage of 5 V with the voltage-step technique with a step voltage of 50 mV. Moreover, the polarization-electric field (P–E) hysteresis loop measurements were performed using a Precision 10 kV Single Channel High Voltage Interface (HVI-SC) from Radiant Technologies at 1 kHz.

## III. RESULTS AND DISCUSSION

### A. Morphology of the diluted thin films

The cross section SEM views in Fig. 1 show the columnar morphology through the entire film thickness for the BST thin films. There is no amorphous layer along the electrode. By taking into account the number of deposited layers *N*, the average layer thickness Δ was then calculated (Table I).

For BST32 [Fig. 1(a)], several columns may succeed from the film bottom to the free surface, and the columns may be slightly curved, leaving pores between them. Moreover, individual oblong grains can be observed in the columns. For BST16 [Fig. 1(b)], the columns are straighter and taller than those in BST32. Some pores are also visible between irregular columns. For BST8 [Fig. 1(c)], the columns can barely be distinguished, and there are no large voids anymore. As the solution dilution increases, the thin film becomes more homogeneous, and the surface roughness decreases. Moreover, plane-view images show the BST film surface. For BST32 [Fig. 1(d)], the grains may have curved shapes and are separated by numerous pores. Intergranular cracks are visible and are probably due to tensile stress. For BST16 [Fig. 1(e)], the grains are larger, more regular, and rounded. For BST8 [Fig. 1(f)], the particles widen globally, and pores are scarce and extremely small. The intergranular cracks are thinner
<figure><img src="image_13.png" /><figcaption>FIG. 1. SEM images of the BST thin films with different precursor concentrations: (a)–(c) the cross section view and (d)–(f) the surface view of BST32, BST16, and BST8 from left to right.</figcaption></figure>

than those of previous samples. As dilution increases, the size of the pores and of the cracks decreases, and the film becomes denser. The dilution has a strong impact on the morphology of the grains and of the film.

Figure 2 displays the film surface observed by AFM as a function of the solution dilution. For BST32 [Fig. 2(a)], the surface is not homogeneous, and the dots are extremely small. For BST16 [Fig. 2(b)] and BST8 [Fig. 2(c)], the surface becomes more homogeneous, and the particles seem to be larger.

The grain width *W* and roughness *R* rms of the films are reported in Table I. From BST32 to BST8, the average grain width increases by a factor of ~2, and the roughness decreases by a factor of 2.6. As the precursor solution dilution increases, the average grain width increases, and the surface roughness decreases. These observations are coherent with those made by SEM.

## B. Structure of the diluted thin films

Figure 3 displays the θ-2θ XRD patterns for the thin films. The most intense peak belongs to the Pt(111) present on the silicon substrate. The other peaks (100), (110), (111), (200), (210), and (211) indicate that the films crystallized in a polycrystalline perovskite phase of BST.

<table><caption>TABLE I. Structural characteristics of the samples. The parameter *N* is the number of deposited layers, Δ*F* is the final film thickness, Δ is the average layer thickness, *W* is the grain width, *R* is the roughness rms, and *a* and *c* are the experimental lattice parameters. The tetragonality ratio *a/c* and the lattice volume *V*<sub>L</sub> are also indicated.</caption><thead><tr><th>Sample</th><th><i>N</i></th><th>Δ<sub>F</sub><br>(nm)</th><th>Δ<br>(nm)</th><th><i>W</i><br>(nm)</th><th><i>R</i><br>(nm)</th><th><i>a</i> (Å)</th><th><i>c</i> (Å)</th><th><i>a</i>/<i>c</i></th><th><i>V</i><sub>L</sub><br>(Å<sup>3</sup>)</th></tr></thead><tbody><tr><td>BST32</td><td>8</td><td>443</td><td>55.4</td><td>58</td><td>12.9</td><td>3.977</td><td>3.963</td><td>1.004</td><td>62.5</td></tr><tr><td>BST16</td><td>15</td><td>390</td><td>26</td><td>119</td><td>9.5</td><td>3.975</td><td>3.972</td><td>1.001</td><td>62.7</td></tr><tr><td>BST8</td><td>20</td><td>250</td><td>12.5</td><td>121</td><td>5.0</td><td>3.974</td><td>3.988</td><td>0.996</td><td>63.2</td></tr></tbody></table>

From the JCPDS card (04-019-7881 of the ICDD PDF-4 database), tetragonal symmetry was found for all the films. Table I displays the calculated lattice parameters from the XRD data. The lattice parameter *a* (respectively, *c*) slightly decreases (respectively, increases) as dilution increases. The lattice parameter *a* of the three films is slightly higher than the bulk value of BST (3.974 Å).³³ As most of the particles have the lattice vector *c* aligned parallel to the surface, the tetragonality ratio of the films is calculated as *a/c*. It slightly decreases with the increase in dilution. The tetragonal structure evolves from a slightly elongated to a slightly flattened one. Indeed, the thermal expansion coefficient of BST (α<sub>BST</sub> = 10.5 × 10<sup>-6</sup> °C<sup>-1</sup>) is larger than that of Pt (α<sub>Pt</sub> = 9 × 10<sup>-6</sup> °C<sup>-1</sup>). Hence, the substrate limits the layer contraction during cooling after thermal annealing. The resulting tensile stress of the film can be relaxed by the pores or by the lattice. As dilution increases, porosity decreases, and the stress relaxation by the pores decreases. As a consequence, the tensile stress on the lattice increases. As a consequence, the lattice volume *V*<sub>L</sub> slightly increases with dilution (Table I).

As the intensity of the (111) peak decreases from BST8 to BST32 for which there is only a shoulder at the low angle side of the Pt(111) peak, BST is more crystallized with (111)-oriented lattices in the BST8 sample than in others. In addition, the (211) peak is more intense for the BST8 sample than in the BST32 one, and it is similar to the BST16 one. Let us calculate the crystallite height from Scherrer's equation,

$$H = k\lambda/\beta \cos(\theta), \quad (1)$$

where *k* is the Scherrer constant, taken to be 0.9, and *β* is the full width at half maximum (FWHM) of the XRD peaks. As dilution increases, the FWHM of the (110) BST peak decreases, indicating a larger particle height (Table II). More precisely, from BST32 to BST8, the (110) particle height increases from 42 to 51 nm. The ratio *H*/*Δ* increases with dilution. As dilution increases, the (110)
<figure><img src="image_14.png" /><figcaption>FIG. 2. AFM images of (a) BST32, (b) BST16, and (c) BST8.</figcaption></figure>

grain height corresponds approximately to one to four individual deposited layers. The roughness decrease makes coalescence possible. Thus, particles higher than one deposited layer are obtained. For BST (211), the grain height varies from 29 to 36 nm as dilution increases, corresponding approximately from half to three individual deposited layers.

Figure 4 illustrates the particle morphology as a function of dilution. It depicts a summarized scheme of the SEM, AFM, and XRD results for the grain size, shape, and roughness. As shown in Table II, for the (110) BST peak, the particles are higher than those for (211). Surface and grain boundary (GB) roughness decreases as the dilution increases. In addition, Fig. 4 shows the grain elongation parallel to the surface with the increase in dilution.

Moreover, the (101) TiO₂ peak is significant only for the BST32 and BST8 samples (Fig. 3). The n-type semiconductor TiO₂ may act as electron donors and may lead to oxygen vacancies.

<figure><img src="image_15.png" /><figcaption>FIG. 3. XRD curves of the BST thin films.</figcaption></figure>

### C. Analytical roughness model

The observed columnar growth can be explained by a model based on diffusion and convection.²⁴ In case of thermal annealing after each layer deposition, the solvent is fully evaporated. When a liquid film is deposited on an annealed layer, the solution diffusion begins where the solvent fraction is larger (the inorganic fraction is smaller), i.e., above the pores (in between the particles). Then, the convection flow brings inorganic constituents above the existing particles, forming columnar growth. When convection dominates over diffusion, the amplitude *h* of the surface undulations can be expressed as

$$h \sim D_{\text{coop}}\eta/y, \quad (2)$$

where $D_{\text{coop}}$ is the cooperative diffusion coefficient, $\eta$ is the viscosity, and $y$ is the surface tension of the solution.³⁴ When dilution increases, the solution viscosity $\eta$ decreases, and the undulation amplitude $h$, i.e., surface roughness, decreases. This successively happens on the surface of each deposited layer. The film is made of a vertical succession of particles. For concentrated solutions, the surface of the successive deposited layers is rough, yielding pores between the layers. On the contrary, for diluted solutions, the surface of the successive deposited layers is smooth, yielding a homogeneous

<table><caption>TABLE II. Perpendicular characteristics of the BST thin films. The parameter $\beta$ is the FWHM of the corresponding XRD (110), (211) BST, and (101) TiO₂ peaks, and *H* is the grain height.</caption><thead><tr><th>Peak</th><th>Samples</th><th>β (deg)</th><th>H (nm)</th><th>H/Δ</th></tr></thead><tbody><tr><td rowspan="4">(110) BST</td><td>BST32</td><td>0.23</td><td>42.3</td><td>0.8</td></tr><tr><td>BST16</td><td>0.2</td><td>48.6</td><td>1.9</td></tr><tr><td>BST8</td><td>0.19</td><td>51.2</td><td>4.1</td></tr><tr><td>BST32</td><td>0.38</td><td>29.1</td><td>0.5</td></tr><tr><td rowspan="4">(211) BST</td><td>BST16</td><td>0.33</td><td>33.5</td><td>1.3</td></tr><tr><td>BST8</td><td>0.31</td><td>35.7</td><td>2.9</td></tr><tr><td>BST32</td><td>0.23</td><td>43</td><td>0.8</td></tr><tr><td>BST16</td><td>...</td><td>...</td><td>...</td></tr><tr><td>(101) TiO<sub>2</sub></td><td>BST8</td><td>0.15</td><td>68</td><td>5.4</td></tr></tbody></table>
<figure><img src="image_16.png" /><figcaption>FIG. 4. Typical particle morphology evolution in the thin film as a function of dilution: (a) the concentrated case such as BST32 and (b) the diluted case such as BST8. For the sake of simplicity, only two crystallite rows are drawn. The suspension points indicate additional crystallite rows.</figcaption></figure>

particle growth without any pores. In this case, the particles can easily coalesce along the direction perpendicular to the surface.

Moreover, the previous expression of h on the top surface can be generalized at the particle side. The undulation amplitude around the particle boundaries varies as η. Hence, roughness at the top surface and at the column surface decreases as dilution increases. Moreover, the nanofluidic model allows obtaining the convective roll size e as

$$e \approx \frac{kT}{|y'|\xi} \frac{\eta}{\eta_s(\psi_d - \psi_u)}, \quad (3)$$

where k is the Boltzmann constant, T is the temperature, ψ is the volume fraction of the solvent, y' = dy/dψ, and ξ is the typical size in the solution.²⁴ The subscript d (resp. u) stands for down (resp. up), and the subscript s refers to solvent. When dilution increases, η decreases, and the roll size e decreases. This is in agreement with the decrease in the grain size observed in the SEM plane-view images as dilution increases. In addition, when dilution increases, the column surface is smooth, the flow process can continue up to near the contact between parallel columnar particles, and lateral coalescence can occur between adjacent grains. Finally, the average grain size increases due to possible coalescence. In this case, the film becomes densified without voids. On the contrary, when the column surface is rough, the flow process stops when no path is available anymore, leaving pores.

## D. Permittivity of the diluted thin films

Capacitance was measured as a function of frequency from 10² to 10⁵ Hz. The relative permittivity of the thin films was calculated from the capacitance using the following equation for a parallel plate capacitor:

$$C = \frac{\varepsilon_0 \varepsilon_r A}{\Delta_F}, \quad (4)$$

where εr is the relative permittivity, ε0 is the vacuum permittivity (8.85 × 10⁻¹² F/m), A is the capacitor area (7.85 × 10⁻⁷ m²), and ΔF is the thin film thickness. According to Fig. 5, the relative permittivity decreases as the frequency f increases. According to the Curie-von Schweidler relaxation, depending on the crystallinity and the strain of the dielectric thin film, the relative permittivity varies as fⁿ⁻¹ with 0 ≤ n ≤ 1.³⁵ The relative permittivity of BST8 is smaller than that of

BST16 and BST32. These more concentrated samples have relative permittivity between 600 and 700 at 10 kHz. For comparison, the relative permittivity of polycrystalline Ba0.7Sr0.3TiO3 thin films in a Pt/BST/Pt structure was ~670 at the same frequency.²⁶ Hence, our results are in agreement with previously published results.

In our case, the very first deposited layer was thermally annealed for all the samples to get crystallized, and no amorphous layer was observed by SEM. Frey et al. proposed a model with ferroelectric grains having high permittivity εg surrounded by a GB having lower permittivity εgb.³⁶ The effective permittivity is

$$\frac{1}{\varepsilon_r} = \frac{v_g}{\varepsilon_g} + g \frac{v_{gb}}{\varepsilon_{gb}}, \quad (5)$$

where g is a factor describing the grain shape (g = 0.8) and v_g and vgb are the volume fraction of the core and of the boundary, respectively. For BST32, the SEM view shows that there are amorphous zones between grains in the out-of-plane direction. From the SEM observations and from the ratio H/Δ for the high (110) BST peaks in Table II, vgb is estimated to be 20%. Similarly, for BST16, vgb is estimated to be 5%. For BST8, no GBs are visible under/above the

<figure><img src="image_17.png" /><figcaption>FIG. 5. Relative permittivity vs frequency for the BST thin films.</figcaption></figure>
grains, but some GBs of a few nanometers wide are slightly visible on the lateral side of the grains. The GB width is estimated to be ~2 nm on each side and yields $v_{gb}$ of ~3%. The relative permittivity of GBs is fixed to 35% that of the grains, i.e., $\epsilon_{gb} = 35\% \epsilon_g$, such as in the work by Zhang and Su.³⁷ The permittivity $\epsilon_g$ is fitted for every sample in order to get the experimental $\epsilon_r$ values at 100 Hz. One obtains $\epsilon_g = 900, 760, \text{ and } 630 (\pm 10)$ for BST32, BST16, and BST8, respectively.

The permittivity of the grains and of the GBs decreases as dilution increases. This may be explained by two main reasons. First, the crystallographic data show that the lattice volume increases with dilution. For a given sum of electric dipole moments, the polarization decreases if the lattice volume $V_L$ increases. Thus, the dielectric susceptibility and the dielectric permittivity decrease. Second, the tetragonality decreases as dilution increases. This out-of-plane reduction in the lattice shrinks the distance between the center of charges in dipoles, decreasing the dipole moment and, consequently, the polarization. Hence, the slight decrease in the tetragonality ratio is another factor explaining the decrease in the permittivity.

## E. Current density

Figure 6(a) displays the current density as a function of the DC voltage. Breakdown occurs at a voltage $V_b \sim 10, 12, \text{ and } 15 \text{ V}$ for BST 8, 16, and 32, respectively, corresponding to a dielectric strength $E_d \sim 400, 310, \text{ and } 340 \text{ kV/cm}$, respectively. Interestingly, the sample elaborated with the most diluted solution has the highest $E_d$. The $\text{Ln J-Ln V}$ plot [Fig. 6(b)] shows that the current density decreases as the solution dilution increases. This is due to a resistivity increase because of larger grains, i.e., a smaller density of GBs and hence fewer possible electric paths. The current density decreases as the roughness, density of GBs, and voids decrease. At very low voltage, the current $J$ varies linearly with $V$, indicating ohmic conduction. This behavior was already observed, for example, by Silva et al. and mentioned by Chiu.¹⁸,²⁰ This current is due to mobile electrons in the conduction band or holes in the valence band.

The current curve for BST16 is different from that for the other samples. The current for BST16 increases significantly at medium and high voltages in contrast to the other samples. This is characteristic of SCLC.³⁸ After the ohmic conduction, with $J$ proportional to $V$, the current density $J$ is proportional to $V^2$. The plot $\text{Ln}(J)$ vs $\text{Ln}(V)$ displayed in Fig. 6 shows that the slope is ~2 from the transition voltage $V_{tr} \sim 0.63 \text{ V}$ to the trap-filled limit voltage $V_{TFL} \sim 0.97 \text{ V}$. The density of trapped electrons is then²⁰

$$N_t = \frac{2}{e} \epsilon_r \epsilon_0 \frac{V_{TFL}}{\Delta_F^2}, \qquad (6)$$

where $e$ is the electron charge. One finds $N_t \sim 5.2 \times 10^{17} \text{ cm}^{-3}$. This value is in the same range as $N_t$ for polycrystalline $La_2O_3$.³⁸ Once all the traps are filled up, the injected electrons are free to move in the film, and the current increases rapidly. The traps correspond to defects, for example, to oxygen vacancies. For the other samples BST32 and BST8, the $\text{TiO}_2$ grains are larger and may yield more electrons and oxygen vacancies. For these samples, the traps may not be filled yet in the explored voltage range.

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /><figcaption>FIG. 6. Current density as a function of DC voltage for the BST samples: (a) the breakdown voltage is indicated for each BST sample and b) the $\text{Ln J-Ln V}$ plot for the BST thin films.</figcaption></figure>

## F. Poling of the diluted thin films

The optimum poling frequency can be estimated from the dissipation factor curve. For a capacitor, the loss tangent $\tan \delta$ can be calculated from the capacitance measurements using the following equation:

$$\tan \delta = \frac{1}{2\pi f C_p R_p}, \qquad (7)$$

where $C_p$ is the parallel capacitance, $R_p$ is the parallel resistance, and $f$ is the frequency. Figure 7 displays the dissipation factor as a function of frequency for the BST samples.

The adequate poling frequency is estimated from the lowest value of the loss tangent as the capacitor has the least losses at this value. The frequency range with the least dielectric loss is around $10^4 \text{ Hz}$ for the BST thin film capacitors, as shown in Fig. 7. Then, poling of the BST capacitors can be achieved. The key parameters are poling voltage, frequency, and time. To begin with, poling is performed at low voltage. At this stage, low frequency and long time can be applied since there is no risk of breakdown. Then, the voltage is progressively increased, and higher frequencies are applied.
<figure><img src="image_20.png" /><figcaption>FIG. 7. Dissipation curve for the BST diluted samples.</figcaption></figure>

As the dipoles respond more easily at low frequencies, poling is applied first at low frequency and then at progressively increased frequencies. As shown in the tan δ curves displayed in Fig. 7, there is a high leakage at low and high frequencies. Hence, one should avoid working at these frequencies. Once some dipoles are well aligned, more time is needed to align as many dipoles as possible. Table III summarizes the parameters used in the poling process, and Fig. 8 shows the evolution of the hysteresis loop with increasing voltage. The saturation polarization Ps increases with the poling voltage reaching 17.5 µC/cm² after a poling at 15 V.

Figure 9 shows the poling voltage and electric field as a function of grain width for a polarization P = ±5 µC/cm². The poling voltage and the electric field decrease with increasing grain width, indicating that the samples with wider grains are easier to pole. The film with the largest grain width (BST8) was poled with the lowest electric field. For grains with a limited effect of GBs, the polarization dynamics are dominated by 0°–180° polar reorientation. On the contrary, for narrower grains with an increased effect of GBs, nucleation sites may lead more easily to polar reorientation in the grain. There is a higher probability of non-180° domain switching. GBs may induce depolarization field.³¹ This may explain why wider grains are easier to pole. Moreover, according to the work by Wu et al.,³⁹ some planes such as (111) are stable during/after poling. The stability comes from the equivalence of the three axes with respect to the poling axis, assuming that the tetragonality is small. On the contrary, other planes are not stable and may switch to other orientations due to the poling effect. In our case, according to the XRD results, the (111) grains are larger as dilution increases, and no

<table><caption>TABLE III. Poling conditions for BST thin films at RT.</caption><thead><tr><td>Voltage (V)</td><td>Frequency (Hz)</td><td>Time (s)</td></tr></thead><tbody><tr><td>2</td><td>7 000</td><td>1800</td></tr><tr><td>4</td><td>7 000</td><td>900</td></tr><tr><td>6</td><td>8 000</td><td>600</td></tr><tr><td>10</td><td>11 000</td><td>300</td></tr><tr><td>15</td><td>11 000</td><td>1800</td></tr></tbody></table>

<figure><img src="image_21.png" /><figcaption>FIG. 8. Hysteresis loop evolution as a function of the poling voltage measured at 1 kHz for the BST8 sample.</figcaption></figure>

poling voltage is needed for polarizing these grains. Hence, the poling voltage was decreased by diluting the precursor solution. From BST32 to BST8, the poling electric field was decreased by a factor of 2.3.

### C. Ferroelectricity of the diluted thin films

Figure 10 displays the characteristic polarization–voltage hysteresis loop for the BST thin films. All samples exhibit a ferroelectric behavior. The saturation polarization Ps is 7.1, 10.4, and 14 µC/cm² for BST32, BST16, and BST8, respectively. In a previous study of Ba₀.₈Sr₀.₂TiO₃ elaborated with a diluted precursor solution, Ps ≈ 11 µC/cm².²⁹ Hence, our results are in the same range. Ps is approximately doubled when the dilution is increased by a factor of 4. The remnant polarization Pr is 0.47, 1.06, and 1.08 µC/cm² for BST32, BST16, and BST8, respectively. Both Ps and Pr increase with the grain size. This in agreement with an experimental study

<figure><img src="image_22.png" /><figcaption>FIG. 9. Poling characteristics as a function of grain width: electric field (blue) and voltage (red) at a polarization P = ±5 µC/cm².</figcaption></figure>
<figure><img src="image_23.png" /><figcaption>FIG. 10. Polarization vs voltage for the diluted BST films at RT at 1 kHz.</figcaption></figure>

on Ba₀.₈Sr₀.₂TiO₃, for which the hysteresis loop improved with dilution, and also with a theoretical study on columnar-grained BaTiO₃ thin films.¹¹,²⁸ The slim hysteresis loop with high saturated polarization and low remnant polarization is typical of a ferroelectric relaxor.⁴⁰

## IV. CONCLUSIONS

A highly diluted precursor solution changes the film morphology by decreasing the roughness and increasing the grain size. As a consequence, the BST thin films become more homogeneous and dense. The permittivity of grains and GBs decreases as dilution increases. This solution dilution engineering allows a significant decrease in the poling voltage, which is a very promising result. This should be a general result for ferroelectric sol–gel derived thin films using a diluted precursor solution. Finally, the BST diluted samples exhibit ferroelectric relaxor behavior with increasing saturation polarization and remnant polarization as the dilution increases. This work could contribute to the development of cheap, large-scale thin films with enhanced ferroelectric properties.

## ACKNOWLEDGMENTS

We would like to express our heartfelt gratitude to Christophe Serbutoviez, Audrey Martinent, and David Alincant for their support.

## DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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