# Tailoring the composition and deposition kinetics of RF-sputtered BaTiO3 thin films through working pressure and target-substrate distance adjustments

Edgar Chaslin, Jade Clément, Quentin Simon, Alejandro Borroto, Mohamed

Himi, Xavier Castel

► To cite this version:

Edgar Chaslin, Jade Clément, Quentin Simon, Alejandro Borroto, Mohamed Himdi, et al. Tailoring the composition and deposition kinetics of RF-sputtered BaTiO3 thin films through working pressure and target-substrate distance adjustments. Thin Solid Films, 2026, 833, pp.140836. 10.1016/j.tsf.2025.140836. hal-05449105

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Submitted on 13 Jan 2026

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# Tailoring the composition and deposition kinetics of RF-sputtered BaTiO₃ thin films through working pressure and target-substrate distance adjustments

Edgar Chaslin ID, Jade Clément ID, Quentin Simon * ID, Alejandro Borroto ID, Mohamed Himdi, Xavier Castel * ID

Univ Rennes, CNRS, IETR-UMR 6164 F-35000 Rennes, France

## ARTICLE INFO

**Keywords:**

Perovskite

Barium titanate

BaTiO₃

Ba/Ti ratio

Radiofrequency sputtering

Combinatorial

## ABSTRACT

Optimizing the growth of BaTiO₃ thin films is essential for operating their ferroelectric and dielectric properties for embedded microelectronic applications. The present study investigates in a combinatorial-like approach the deposition of BaTiO₃ thin films by radiofrequency magnetron sputtering on SiO₂/Si substrates under various working pressures (1 to 6 Pa) and target-substrate distances (7.5 to 9.2 cm). X-ray diffraction (XRD), Atomic Force Microscopy (AFM) and Rutherford Backscattering Spectroscopy (RBS) characterizations were used to establish the relationships between the sputtering deposition parameters and the resulting deposition rates, crystalline quality, surface roughness, and stoichiometry of the BaTiO₃ thin films. Low pressures and short distances lead to high kinetic growth of amorphous Ba-deficient films. Increasing working pressure × target-substrate distance values above 0.30 Pa.m enables to attain the stoichiometric Ba/Ti ratio. This result is related to both Ba and Ti species thermalization into the plasma leading to improve the chemical composition of the films. Furthermore, crystalline quality of the BaTiO₃ films is improved by reducing the deposition rate through working pressure and target-substrate distance adjustment. These results can provide valuable roadmaps to set BaTiO₃ sputtering parameters for high-quality thin films deposition based on the stoichiometry balance and deposition kinetics, that can be further extended to other perovskite compounds.

## 1. Introduction

ABO₃ complex oxides with a perovskite structure are of considerable interest for numerous applications in data or energy conversion/storage due to their extensive range of composition-dependent functional properties. Among them, barium titanate (BaTiO₃) and the related compounds, such as (Ba,Sr)TiO₃, stand out as lead-free ferroelectric alternatives characterized by high dielectric permittivity values [1–4] together with high piezoelectric and electro-optical coefficients. Many applications require their implementation as thin films for advanced electronic devices, such as capacitors, sensors and/or actuators [5–7].

The crystallization of BaTiO₃ thin films was subject of in-depth investigations, particularly across various deposition techniques including chemical routes, e. g. sol-gel related processes [8–10] and chemical vapor deposition (CVD) techniques [11–13], as well as physical routes, e. g. evaporation [14–17], pulsed laser deposition (PLD) [18–20], molecular beam epitaxy (MBE) [21–23], and/or radiofrequency (RF)

magnetron sputtering [4,24–32]. RF magnetron sputtering technique gains prevalence due to its high reproducibility and up-scaling ability, making it particularly attractive for industrial development and production. Nevertheless, elaboration of high-quality complex oxides by sputtering technique with homogeneous properties over large substrate area still remains tricky regarding the control of the stoichiometry, especially the A/B ratio for the ABO₃ compounds.

Numerous studies carried out on BaTiO₃ and (Ba,Sr)TiO₃ film raised that deficiencies in alkaline-earth elements lead to the deleterious formation of TiOₓ phases [33]. Regarding the RF sputtering deposition technique, formation of Ti-rich phases in thin films was related to the tendencies of Ba (and Sr) to be preferentially i) re-evaporated because of their higher vapor pressure, and ii) re-sputtered by energetic negative ions (usually O⁻) ejected from the target because of their higher sputtering yield [34,35].

Several strategies were explored to counterbalance the stoichiometry deviation and to promote the stabilization of the perovskite structure

<footnote>* Corresponding authors.</footnote>

<footnote>E-mail addresses: quentin.simon@univ-rennes.fr (Q. Simon), xavier.castel@univ-rennes.fr (X. Castel).</footnote>
including the use of Ba/Sr-enriched target, seed/buffer layers, off-axis geometry sputtering, and/or the fine adjustment of numerous sputtering deposition parameters, e.g. working pressure, target-substrate distance, substrate temperature, RF power supplying the target, oxygen partial pressure [33,36–39]. Among these, two of the key parameters are the working pressure and the target-substrate distance. Their influence was singly studied and disclosed similar trend on stoichiometry, deposition rate and crystalline quality. Indeed, to keep the ideal stoichiometric balance, the increase of the working pressure or of the target-substrate distance above specific values was required, as reported by Im et al. [36] and Schafranek et al. [33], respectively.

In the present study, combined effects of variations of the working pressure with the target-substrate distance were studied for the deposition of BaTiO₃ thin films in a combinatorial-like approach. To this aim, depositions were performed at six different working pressures (from 1 to 6 Pa). Each deposition was carried out on three substrates according to three different target-substrate distances (from 7.5 to 9.2 cm), the target being positioned in a tilted-configuration. The 18 resulting samples were systematically characterized to study the interplays between the sputtering deposition parameters and the crystalline quality, surface roughness, and stoichiometry of the BaTiO₃ films. In the first part of the article, variation of the film properties as a function of the working pressure and target-substrate distance were summarized in heatmaps to provide a global overview of the experimental results. Note that all the experimental data are summarized in Table A1 in appendix. In the second part, results were discussed in relation with those of literature to propose general trends to optimize the sputtering conditions for the deposition of BaTiO₃ thin film, that could be further extended to other ABO₃ systems.

## 2. Methods

BaTiO₃ thin films were deposited using a tilted-configuration radiofrequency (RF) magnetron sputtering technique as shown in Fig. 1 and according to the sputtering deposition parameters given in Table 1. Films were grown on (111)-oriented silicon (Si) substrates covered by a SiO₂ layer. Prior each deposition step, substrates were cleaned in hot RBS 25 MD solution (15 min at 60 °C), thoroughly rinsed with deionized water and then dried under pure N₂ gas flow. For each deposition step, three (111) Si substrates (substrate dimensions: 1.5 cm × 1.5 cm × 0.4 mm) were placed on a fixed sample-holder (Fig. 1a) leading to three target-substrate distances $d_{t-s}$ equal to 7.5, 8.3 and 9.2 cm corresponding to angles of 0°, 10° and 18° with respect to the normal of the target surface, respectively. The angular distribution of the sputtered particles

<table><caption>**Table 1**
Sputtering deposition parameters of BaTiO₃ thin films.</caption><tr><td>Target</td><td>BaTiO<sub>3</sub> (Codex supplier)</td></tr><tr><td>Target diameter</td><td>5.08 cm</td></tr><tr><td>Target-substrate distance $d_{t-s}$</td><td>7.5 – 8.3 – 9.2 cm</td></tr><tr><td>RF power</td><td>50 W (2.5 W/cm<sup>2</sup>)</td></tr><tr><td>Base pressure</td><td>5 × 10<sup>-5</sup> Pa</td></tr><tr><td>Working pressure P</td><td>1 to 6 Pa (step: 1 Pa)</td></tr><tr><td>Sputtering gas: Ar / O<sub>2</sub> flux (ratio)</td><td>48 / 2 sccm (96 % / 4 %)</td></tr><tr><td>Substrate temperature / potential</td><td>750 °C / floating potential</td></tr></table>

is commonly assumed to follow a cosine distribution, which results in the present study in a maximal deviation of 5 % (cos18° = 0.95). Although deviations from this assumption may be observed between different sputtered species (i.e. Ba and Ti) or under varying sputtering parameters (i.e. working pressure) [40–44], the following results are presented solely as a function of the target-substrate distance $d_{t-s}$. This hypothesis allows for comparison with literature data on BaTiO₃ and (Ba,Sr)TiO₃ thin films deposited by sputtering technique, either in on- or off-axis configuration at different $d_{t-s}$ values. Depositions were carried out at six different working pressures P equal to 1, 2, 3, 4, 5 and 6 Pa, whereby the working pressure was adjusted at constant gas flows (48 and 2 sccm for Ar and O₂, respectively) by partially closing a valve. Deposition time was adjusted at each working pressure to get comparable thicknesses for similar substrate position.

Crystallographic structure of the BaTiO₃ films were characterized by X-ray diffraction (XRD) using a Rigaku SmartLab 9 kW system with a parallel beam configuration, CuKα₁ radiation (λ = 1.54056 Å), and a scintillator point detector. Lateral anti-scatter slits of 5 mm were used to ensure similar X-Ray footprint on the samples under test. Measurement were performed in ω – 2θ configuration with an angular resolution of 0.02° All XRD measurements were analyzed using the SmartLab Studio II software.

Surface topology was recorded by atomic force microscopy (AFM) in tapping mode with a ParkSystem NX10 equipment. Images were performed with Olympus OMCL-AC160TS tips on a surface of 2 × 2 µm² with a resolution of 600 × 600 pixels. Quadratic roughness (Rq) was retrieved from AFM images using Gwyddion software. Mean grain size were computed from the measurements of at least 20 grains.

Quantitative chemical analysis was carried out through Rutherford Backscattering Spectrometry (RBS) at the AIFIRA platform [45]. Samples were analyzed using 2.54 MeV H⁺ ions with a charge about 4 µC and a dead time equal to 1 %. The backscattered ions were collected using a collimated Ge-detector at a backscattering angle of 175°. Spectra were

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Schematic representation of the deposition distance distribution. a) Schema of the off-axis cathode showing the measured distance between the target and the three substrates (7.5 – 8.3 – 9.2 cm), and the BaTiO₃ plasma diffusion cone (pink color). Thickness gradient representation along substrates with a color gradient. b) Heatmap of the film deposition rate as a function of the working pressure and of the target-substrate distance.</figcaption></figure>

<figure><img src="image_5.png" /></figure>
fitted using SIMNRA software.

## 3. Results

The deposition rate is affected by both working pressure and target-substrate distance. In the present work, deposition times were extended (from 3 to 7 h) as the working pressure was increased to achieve similar thicknesses for equivalent substrate position. At a given working pressure, a decrease of thickness versus an increase of target-substrate distance was systematically observed. As a whole, whatever the working pressure is, film thicknesses were ranged as follows: 365 ± 15 nm at 7.5 cm, 225 ± 20 nm at 8.3 cm, and 145 ± 30 nm at 9.2 cm.

The corresponding deposition rates for the 18 samples are summarized in a heatmap plotted as a function of the working pressure P and target-substrate distance $d_{t-s}$ (Fig. 1b). It follows a gradual decrease as both P and $d_{t-s}$ increase. The highest deposition rates (1.25 to 2.0 nm/min range) are achieved for the lowest P and $d_{t-s}$ values (red region). Conversely, the lowest deposition rates (0.35 to 0.75 nm/min range) are reached for the highest P and $d_{t-s}$ values (blue region). The region

between these two extrema (white region) corresponds to intermediate deposition rates, from 0.75 to 1.25 nm/min.

$\omega - 2\theta$ XRD patterns of BaTiO$_3$/SiO$_2$/Si heterostructures are shown in Fig. 2a. Note that intensity of each $\omega - 2\theta$ pattern was corrected (i.e. divided) by the thickness of the corresponding sample. Although crystalline quality may be affected by thickness (growth modes, stress relaxation, relative contribution of defects at the substrate interface ...), this approach was applied to counterbalance for variations in diffracting volume for samples with different thicknesses. Raw data (uncorrected for film thickness) are available in Fig. A.1. The diffraction patterns exhibit a characteristic peak at $2\theta = 28.44^{\circ}$, corresponding to the (111) planes of the silicon substrate, along with a broad amorphous hump close to $2\theta = 22^{\circ}$, mainly attributed to the SiO$_2$ passivation layer. Other peaks are attributed to the (100)/(001), (101), (111), and (200)/(002) planes of the BaTiO$_3$ perovskite structure, with various intensities depending on the deposition parameters (JCPDS n° 00-005-0626).

For the two shorter distances ($d_{t-s}$ equal to 7.5 and 8.3 cm), deposition at the lowest working pressure (P = 1 Pa) leads to amorphous films as indicated by the lack of prominent BaTiO$_3$ peaks, while increasing the

<figure><img src="image_6.png" /><figcaption>**Fig. 2.** Impact of the working pressure and target-substrate distance on the BaTiO$_3$ structural characteristics. a) $\omega - 2\theta$ XRD patterns of BaTiO$_3$ thin films deposited on SiO$_2$/Si(111) heterostructure grouped by the target-substrate distance (7.5 – 8.3 – 9.2 cm) from 1 Pa (bottom) to 6 Pa (top). The whole patterns were normalized based on film thickness. XRD patterns exhibit silicon peak (*) at $2\theta = 28.44^{\circ}$ corresponding to the (111) planes together with the (001), (101), (111) and (002) peaks of BaTiO$_3$ films. b) Heatmap of total intensity (sum of (001), (101) and (002) integrated intensities) normalized with respect to the best sample as a function of the working pressure and target-substrate distance. Regions A, B, and C are highlighted to indicate different zones of interest regarding the intensity variation. c) Heatmap of the surface roughness ($R_q$) retrieved from Atomic Force Microscopy (AFM) measurements as a function of the working pressure and target-substrate distance.</figcaption></figure>
working pressure (P ≥ 2 Pa) leads to the formation of BaTiO₃ weak diffraction peaks. At the longest distance (d<sub>t-s</sub> = 9.2 cm), crystallized BaTiO₃ films are obtained over the entire pressure range.

The improvement of structural features is further supported by the
comparison of the normalized sum of the integrated intensities of the

peaks corresponding to (100)/(001), (101), and (200)/(002) planes in
the ω − 2θ patterns (named as normalized intensity), illustrated in a
heatmap as a function of P and d<sub>t-s</sub> parameters (Fig. 2b). For the sum
calculation, the peaks corresponding to (h00)/(00l) planes are processed
as a single reflection since they are hardly distinguishable due to several

<figure><img src="image_7.png" /><figcaption>Fig. 3. Topographic images recorded by Atomic Force Microscopy (AFM) showing surface morphologies as a function of the working pressure and of the target-substrate distance. The root-mean-square roughness (Rq) is inserted in each image. The greyscale bars correspond to height scales.</figcaption></figure>
effects leading to a peak broadening and overlapping (grain size dimension, strain/composition gradients...). Elsewhere, peaks relating to (111) planes are not considered because of their very low intensity and signal-to-noise ratio. Normalization was done with respect to the best sample (for which the normalized intensity is equal to 1). Note that heatmaps of the integrated intensities of single peaks corresponding to (001), (101), and (002) planes are provided in Fig. A.2. Normalized intensity variation in the heatmap is described through three regions (Fig. 2b). Region A (brown region) corresponds to amorphous or poor crystallization of the BaTiO₃ films and is observed at short target-substrate distances ($d_{t-s}$ = 7.5 and 8.3 cm) and at low working pressures ($P$ = 1 and 2 Pa). Region B (light green region) corresponds to a moderate but homogeneous crystallization of the BaTiO₃ films and is also observed at short distances but at higher working pressures (P between 3 and 6 Pa). Region C (deep green region) is observed nearby $d_{t-s}$ = 9.2 cm and at moderate to high working pressures (P from 3 to 6 Pa). The related parameter values improve the crystalline quality of the films. In this area, well-defined peaks with different orientations are observed, and the integrated intensity reaches its maximum, promoting highest crystalline quality of the films.

Microstructural features of the films are retrieved from AFM observations of their surface. Topographic images of all the samples are presented in Fig. 3. In accordance with the above XRD results, heatmap of roughness plotted as a function of the working pressure P and target-substrate distance $d_{t-s}$ (Fig. 2c) is also divided into three regions. Region A (brown region) corresponds to BaTiO₃ thin films with smooth surface exhibiting very low roughness ($R_q$ = 0.2 nm), in agreement with their amorphous state. Region B (white region) is related to a roughness increase ($R_q$ ≈ 1.0 nm) with a wide dispersion of distinct grains with diameter ranging from 20 to 100 nm, in full agreement with the observation peaks in XRD patterns. In region C (violet region), the film roughness further increases ($R_q$ = 3.7 nm) and the surface is composed of well-defined grains with uniform sizes (close to 80 nm), signature of a columnar growth [33].

Composition of the BaTiO₃ films is assessed by the Ba/Ti ratio retrieved from RBS measurements. A representative RBS spectrum with its fitted model is outlined in Fig. 4. Ba/Ti ratios resulting from RBS fits are summarized in a heatmap as a function of the working pressure P and target-substrate distance $d_{t-s}$ (Fig. 5a). The lowest Ba/Ti ratios close to 0.4 (violet region) are found at short distances ($d_{t-s}$ = 7.5 and 8.3 cm) and low working pressure ($P$ = 1 and 2 Pa), which corresponds to the region previously identified as poorly crystallized (region A). As both $d_{t-s}$ and P increase, Ba/Ti ratio also rises, approaching a maximum value close to 0.87 with a remarkable homogeneity over the previously identified B and C regions (green region). Although Ba/Ti ratio remains below the stoichiometric value (Ba/Ti = 1), these regions correspond to crystallized BaTiO₃ films. The gap between the measured ratio (Ba/Ti ≈ 0.87) and the expected stoichiometric value could be attributed to Ba diffusion into the SiO₂ passivation layer, as observed in RBS spectra (Fig. 4). Indeed, previous studies highlighted that Ba tends to diffuse into SiO₂ layer, producing a Ba-Ti-Si-O amorphous phase or Fresnoite Ba₂TiSi₂O₈ phase [46–48]. In the present study, such diffusion is promoted because of both high deposition temperature (750 °C) and extended deposition times (ranging from 3 to 7 h), though none of the above-mentioned phases were observed in the $\omega - 2\theta$ XRD patterns.

## 4. Discussion

As already reported for BaTiO₃ and (Ba,Sr)TiO₃ systems, stoichiometry and crystalline quality are affected either by the working pressure or the target-substrate distance. To get a global visualization of the combined effect of these two processing parameters, data from the present work and those from literature are plotted in Fig. 5b as a function of the working pressure × target-substrate distance values ($P \times d_{t-s}$). Ba/Ti ratio variation from the present study fits well with that of previous studies (Im et al. [36] and Schafranek et al. [33]). A strong

<figure><img src="image_8.png" /><figcaption>Fig. 4. Rutherford Backscattering Spectroscopy (RBS) measurement (black line) compared with the simulated result (blue line) calculated from the contribution of oxygen (red line), silicon (green line), titanium (purple line) and barium (pink line). Ba and Ti peaks show tails towards low channels characteristic of their diffusion in the SiO₂/Si substrate.</figcaption></figure>

relationship appears showing a Ba/Ti ratio increase according to an asymptotic exponential trend up to the stoichiometric value as the $P \times d_{t-s}$ value is sufficiently high. For the lowest $P \times d_{t-s}$ values, stoichiometry deviation is observed.

Deficiencies in Ba (and Sr) were commonly attributed to their significant trend to be re-evaporated or re-sputtered compared with Ti element. Indeed, using polynomial equations provided by Alcock et al. [49] at $T = 750$ °C, metallic titanium element exhibits a very low vapor pressure (~3.0 × 10⁻¹² Pa) compared with metallic barium (~11.2 Pa). This clear difference suggests that barium atoms are more prone to evaporation, especially at low oxygen content resulting in low oxide formation. Besides, based on the work of Matsunami et al. [50] and considering $Ar^+$ ions energy close to 500 eV with an incidence angle of 0°, the sputtering yield of a metallic Ti target is equal to 0.54 while that of a metallic Ba one equals 1.25 [39]. Although the above values are computed from metallic atoms, it can be assumed that similar trends are obtained for Ba and Ti in BaTiO₃ compounds, leading to preferential re-evaporation or re-sputtering of Ba species.

Re-sputtering phenomena were highlighted by Vargas et al. using high oxygen content ($P_{O_2}$ = 0.35 Pa) and high RF power (resulting in high target bias voltage) in a tilted-sputtering configuration [39]. Acceleration of the $O^-$ species provides sufficient energy to cause the complete etching of the film, evidenced by the absence of deposition at the closest target-substrate distances. In a different way, Schafranek et al. and Rachut et al. showed that, using lower oxygen content ($P_{O_2}$ = 0.04 to 0.05 Pa), the reduction of target-substrate distance leads to an increase in film thickness along with a decrease in Ba/Sr content in
<figure><img src="image_9.png" /><figcaption>**Fig. 5.** Ba/Ti ratios and final energy as a function of deposition parameters. a) Heatmap of the Ba/Ti ratio as a function of the working pressure *P* and target-substrate distance *d*<sub>t-s</sub>. Regions A, B and C correspond to the previously identified areas of interest. b) Ba/Ti ratio as a function of *P* × *d*<sub>t-s</sub> with regions A, B and C matching the areas of interest from the heatmap compared with literature data [33,36]. Values are fitted with an asymptotic exponential law $y = 1 - e^{-a \times P \times d_{t-}}$ (with *a* = 5.7127 Pa⁻¹.m⁻¹). c) Calculated kinetic energy (*E*<sub>f</sub>) of Ba and Ti species reaching the substrate as a function of *P* × *d*<sub>t-s</sub>. d) Schematic representation of barium and titanium diffusion cones as a function of *P* × *d*<sub>t-s</sub> values. Colors are for guidance only.</figcaption></figure>

relation with the re-evaporation of alkaline elements [27,33]. In the present study covering broad oxygen contents (PO₂ = 0.04 to 0.24 Pa), thicker Ba-deficient films are obtained when the target-substrate distance is reduced.

Interestingly, comparing all these studies, it can be noticed that the *P* × *d*<sub>t-s</sub> product required to stabilize the perovskite structure and reach the desired stoichiometry in this work (*P* × *d*<sub>t-s</sub> ≈ 0.30 Pa.m in Fig. 5b) closely matches with those reported by Im *et al.* (*P* × *d*<sub>t-s</sub> = 0.30 Pa.m) for its optimized sputtering parameters [36], Schafranek *et al.* (*P* × *d*<sub>t-s</sub> =

0.30 Pa.m) [33], Rachut *et al.* (*P* × *d*<sub>t-s</sub> = 0.30 Pa.m) [37], Park *et al.* (*P* × *d*<sub>t-s</sub> = 0.25–0.35 Pa.m range depending upon the on/off-axis sputtering configuration) [38], and Vargas *et al.* (*P* × *d*<sub>t-s</sub> = 0.24 Pa.m) [39]. It suggests that re-evaporation and re-sputtering are not the unique effects to be considered to explain the lowering of Ba/Ti ratio as the *P* × *d*<sub>t-s</sub> value is reduced. Thermodynamic analysis of the deposition process can be addressed to shed light on this widespread observation, specifically by considering the energy variation of neutral species produced from the target. The kinetic energy at which Ba and Ti species arrive on the
surface substrate is calculated from Eq. (1), as follows [51]:

$$E_f = (E_0 - k_B \cdot T_G)^{N \cdot \ln \left( \frac{E_f}{E_i} \right)} + k_B \cdot T_G \quad (1)$$

where $E_0$ is the kinetic energy of the sputtered species as they leave the target, $k_B$ is the Boltzmann constant, $T_G$ is the sputtering plasma temperature, $E_f/E_i$ is the energy ratio after and before a collision respectively, and N is the number of collisions that take place in the plasma. The number of collisions is given by the Eq. (2), as follows:

$$N = \frac{d_{t-s} \cdot P \cdot \sigma}{k_B \cdot T_G} \quad (2)$$

where $d_{t-s}$ is the target-substrate distance, P is the working pressure, and $\sigma$ is the collision cross section assuming hard core interactions. The $E_f/E_i$ ratio is therefore estimated from Eq. (3), as follows:

$$\frac{E_f}{E_i} = 1 - \frac{2(m_s \cdot m_g)}{(m_s + m_g)^2} \quad (3)$$

where $m_s$ is the sputtered atom mass (Ba or Ti) and $m_g$ is the sputtering atom mass (Ar) [52]. Thus, considering that initial kinetic energy $E_0$ of the sputtered species leaving the target is approximately half of their surface binding energy $E_{sb}$ [53], the kinetic energy of Ba and Ti species that reach the surface substrate is estimated as a function of the $P \times d_{t-s}$ value, using Eq. (1), (Fig. 5c). Note that heatmaps of the calculated kinetic energy ($E_f$) for Ba and Ti as a function of P and $d_{t-s}$ are provided in Fig. A.3. Since the surface binding energy of Ba is not well established in the literature, this study assumes that $E_{sb}$ is approximately equal to the cohesive energy $E_{co}$. For metallic Ti, $E_{sb} = 4.85$ eV [54] and $E_{co} = 4.85$ eV [55], supporting this approximation.

The kinetic energy of both species decreases rapidly until it stabilizes close to 0.026 eV, corresponding to atoms thermalization. This stabilization occurs after the species undergo many collisions that dissipate their initial kinetic energy, leaving them the thermal energy supplied by the plasma. Although both Ba and Ti species reach thermalization at high $P \times d_{t-s}$ products, this process occurs at different values due to i) the higher initial kinetic energy $E_0$ of Ti, and ii) the lower number of collisions undergone by Ti in relationship with its lower cross-section. Barium species achieve thermalization at 0.20 Pa.m, against 0.30 Pa.m for titanium ones. Experimental results show that a stable Ba/Ti ratio is achieved when the $P \times d_{t-s}$ value remains higher than 0.30 Pa.m, corresponding to a regime where both species are thermalized. Conversely, significant Ba deficiencies are observed for $P \times d_{t-s} \approx 0.10 - 0.20$ Pa.m, a range in which titanium keeps its ballistic behavior while barium is almost thermalized.

As shown in Fig. 5b, besides the fairly good matching between sputtered thin films deposited in tilted- (this work) and on-axis (literature) configurations, two samples deviate from the expected asymptotic exponential trend. These samples exhibit a Ba/Ti ratio of approximately 0.85 despite $P \times d_{t-s}$ values below 0.3 Pa.m. Positioned at the maximum target-substrate distance ($d_{t-s} = 9.2$ cm), corresponding to a tilt angle of 18° relative to the normal of the target surface and deposited at 1 and 2 Pa, they present $P \times d_{t-s}$ value of 0.092 and 0.184 Pa.m, respectively. These deviations highlight that the influence of $P \times d_{t-s}$ product cannot be considered solely at high tilt angle. It is worth recalling that a cosine angular distribution of the sputtered particles was initially assumed in this study. Nonetheless, the angular distribution of particle emission may vary depending on the species and sputtering parameters. In general, higher Ar⁺ energy and greater sputtering yields of species from targets tend to produce narrower distribution [40–44]. Consequently, low-pressure deposition should lead to higher concentration of Ba along the direction normal to the target surface. Contrary to this expectation, experimental results at low pressures (1 and 2 Pa) show Ba-deficient thin films for substrates closer to the normal of the target (Fig. 5a). This suggests that the initial emission angle of species should play a minor

role compared with the diffusion behavior of species within the plasma. At high pressure, numerous collisions promote maximum diffusion, resulting in a plasma that is homogeneous in both energy and composition. In contrast, at low pressures (from 1 to 2 Pa), Ba and Ti should diffuse differently leading to a narrower diffusion cone for Ti compared with that of Ba. In the tilted-configuration, such effect leads to Ti-rich zone at low $d_{t-s}$ (7.5 cm and 8.3 cm) corresponding to region A (Fig. 5d). As the pressure increases, homogeneous distribution of Ba and Ti species in the plasma results in an increase in Ba/Ti ratio for the whole distance, with an appreciable composition uniformity for regions B and C.

Despite similar composition, films elaborated from regions B and C differ in terms of crystalline quality. Samples from region B (low $d_{t-s}$ and high P values) exhibit poor crystalline quality and more inhomogeneous microstructure compared with those from region C (high $d_{t-s}$ and high P values). This difference suggests that beyond suitable Ba/Ti ratio, additional factors influence the overall crystalline quality. Indeed, Fig. 6a shows the deposition rates of BaTiO₃ thin films as a function of the corresponding $P \times d_{t-s}$ value. A marker gradient color points out integrated intensity retrieved from XRD analysis in Fig. 2b (it corresponds to the sum of the integrated intensities of peaks in XRD patterns, normalized with respect to the best sample). As previously mentioned, increasing $P \times d_{t-s}$ value leads to a decrease in the BaTiO₃ deposition rate. At a constant target-substrate distance, increasing working pressure leads to a linear decrease of the deposition rate with a slope becoming steeper as the distance becomes shorter. Another striking observation concerns the significant variation of the deposition rate for almost identical $P \times d_{t-s}$ value. It thus appears that the target-substrate distance exhibits a more critical impact on deposition rate than the working pressure. As a whole, the deposition rate varies significantly, from 2.0 nm/min at low $P \times d_{t-s}$ values down to 0.35 nm/min at high $P \times d_{t-s}$ values (Fig. 1b). A decrease in the deposition rate results in an increase of the integrated intensity of the BaTiO₃ film. At present, lower deposition rates are observed in region C (~ 0.5 nm/min) compared with that of region B (~ 1.0 nm/min), resulting in higher crystalline quality in region C than in region B.

The relationships between deposition rate, crystalline quality and stoichiometry are shown in Fig. 6b. This figure plots deposition rate as a function of Ba/Ti ratio, with marker gradient color representative of the integrated intensity retrieved from Fig. 2b. As the deposition rate decreases, Ba/Ti ratio increases, stabilizing around the value of 0.87 which corresponds to the moderate-to-high $P \times d_{t-s}$ values. At low Ba/Ti ratios and high deposition rates, BaTiO₃ thin films are nearly or completely amorphous. Crystallized layers begin to grow when Ba/Ti ratio increases. Nevertheless, and even at a ratio close to 0.75, a reduction in the deposition rate is still required. The color gradient shows that fully crystallized BaTiO₃ thin films are achieved when the deposition rate is low, namely in the 0.25 to 0.75 nm/min range. In this area, the optimal crystallization sputtering parameters are meet, highlighted by the highest intensity of the diffraction peaks related to a specific microstructural morphology as observed by AFM, resulting from a columnar growth [33]. These optimal deposition rates are fairly consistent with data from literature on (Ba,Sr)TiO₃ films. Indeed, Im et al. report that deposition rate from ~0.5 to 0.65 nm/min are optimal values conversely to higher deposition rates from ~0.75 to 0.95 nm/min [36]. Schafranek et al. report an optimal deposition rate close to ~0.85 nm/min [33]. Therefore, to promote BaTiO₃ thin film crystallization, two key conditions must be met: i) reach $P \times d_{t-s}$ threshold to ensure an optimal stoichiometric Ba/Ti ratio, and ii) restrict the growth kinetic.

## 5. Conclusion

BaTiO₃ thin films were deposited by radiofrequency (RF) magnetron sputtering in a tilted-configuration on SiO₂/Si substrates. This study focuses on the combined effects of the variation of the working pressure and target-substrate distance on BaTiO₃ thin film features in terms of
<figure><img src="image_10.png" /><figcaption>**Fig. 6.** Influence of the deposition rate on the BaTiO₃ film crystalline quality. a) Deposition rate (nm/min) as a function of P × dᵢ₋s values with normalized intensity retrieved from ω – 2θ patterns (Fig. 2b) shown in a color scale. The three data sets corresponding to the three target-substrate distances (7.5 cm – circle, 8.3 cm – square, 9.2 cm – triangle) are fitted by a linear law. b) Deposition rate (nm/min) as a function of Ba/Ti ratio with normalized intensity retrieved from ω – 2θ patterns (Fig. 2b) shown in a color scale.</figcaption></figure>

deposition rate, crystalline quality, surface roughness, and stoichiometry. To address general trends, data are discussed as a function of the working pressure × target-substrate distance values (P × dᵢ₋s). When P × dᵢ₋s values remain lower than 0.30 Pa.m, high kinetic growth of amorphous Ba-deficient thin films is achieved. Alkaline-earth off-stoichiometry is often attributed in literature to their preferential re-evaporation or re-sputtering under low and high plasma oxygen content, respectively. In the present study, results are interpreted considering kinetic energy of the neutral species sputtered from the target. In the 0.10 to 0.20 Pa.m range, Ba species are almost thermalized while Ti species keep ballistic behavior, which is the source of stoichiometry deviations. As a consequence, increasing P × dᵢ₋s values up to a level where both Ba and Ti species are thermalized provides the intended stoichiometry. Indeed, results show that increasing P × dᵢ₋s values above 0.30 Pa.m leads to a Ba/Ti ratio close to 1. This threshold value fairly matches with the optimal values also reported in other studies [33,36–39]. Furthermore, beyond achieving the right stoichiometry balance, crystalline quality needs to be improved by reducing the deposition rate. As a whole, these results offer general trends to optimize BaTiO₃ thin film deposition parameters, that could be further extended to other ABO₃ systems.

### CRediT authorship contribution statement

**Edgar Chaslin:** Writing – original draft, Visualization, Investigation, Formal analysis, Data curation. **Jade Clément:** Writing – review &

editing, Investigation. **Quentin Simon:** Writing – review & editing, Supervision, Funding acquisition, Formal analysis, Conceptualization. **Alejandro Borroto:** Writing – review & editing, Formal analysis. **Mohamed Hindi:** Writing – review & editing, Supervision, Funding acquisition, Conceptualization. **Xavier Castel:** Writing – review & editing, Supervision, Funding acquisition, Formal analysis, Conceptualization.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgements

This work was supported in part by the European Union through the European Regional Development Fund, in part by the Ministry of Higher Education and Research, France, in part by the Région Bretagne, France, and in part by the Département des Côtes d'Armor and Saint-Brieuc Armor Agglomération, France, through the CPER Projects 2015–2020 MATECOM and SOPHIE/STIC&Ondes. The AIFIRA facility is financially supported by the CNRS, the University of Bordeaux and the Région Nouvelle Aquitaine, France. We would also like to thank the technical staff members of the AIFIRA facility: P. Alfaut and S. Sorieul.

## Appendix
<figure><img src="image_11.png" /><figcaption>Fig. A.1. ω - 2θ XRD patterns of BaTiO₃ thin films deposited on SiO₂/Si(111) heterostructures organized by target-substrate distance (7.5 – 8.3 – 9.2 cm) with working pressures ranging from 1 Pa (bottom) to 6 Pa (top). Diffraction patterns exhibit silicon peak (*) at 2θ = 28.44° corresponding to the (111) planes together with the (001), (101), (111) and (002) peaks of BaTiO₃ films.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. A.2. Heatmap of the normalized integrated intensity (color gradient) of each BaTiO₃ reflection as a function of the working pressure and of the target-substrate distance.</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Fig. A.3. Heatmap of the calculated kinetic energy (E<sub>f</sub>) of Ba and Ti species reaching the substrate as a function of the working pressure and of the target-substrate distance.</figcaption></figure>
<table><caption>**Table A.1**
Experimental data as a function of the working pressure and of the target-substrate distance.</caption><thead><tr><th>Pressure (Pa)</th><th>Distance (cm)</th><th>Deposition rate (nm/min)</th><th>Normalized intensity (arb. units/nm)</th><th>Rugosity R<sub>q</sub> (nm)</th><th>Ba/Ti ratio</th></tr></thead><tbody><tr><td rowspan="3">1</td><td>7.5</td><td>2.03</td><td>0.00</td><td>0.2</td><td>0.41</td></tr><tr><td>8.3</td><td>1.25</td><td>0.01</td><td>1.4</td><td>0.45</td></tr><tr><td>9.2</td><td>0.81</td><td>0.74</td><td>1.3</td><td>0.83</td></tr><tr><td rowspan="3">2</td><td>7.5</td><td>1.74</td><td>0.43</td><td>2.4</td><td>0.57</td></tr><tr><td>8.3</td><td>1.07</td><td>0.44</td><td>1.9</td><td>0.68</td></tr><tr><td>9.2</td><td>0.69</td><td>0.84</td><td>2.2</td><td>0.87</td></tr><tr><td rowspan="3">3</td><td>7.5</td><td>1.62</td><td>0.80</td><td>1.2</td><td>0.71</td></tr><tr><td>8.3</td><td>1.00</td><td>0.60</td><td>2.2</td><td>0.74</td></tr><tr><td>9.2</td><td>0.64</td><td>0.94</td><td>4.0</td><td>0.84</td></tr><tr><td rowspan="3">4</td><td>7.5</td><td>1.22</td><td>0.76</td><td>2.2</td><td>0.70</td></tr><tr><td>8.3</td><td>0.75</td><td>0.54</td><td>2.9</td><td>0.76</td></tr><tr><td>9.2</td><td>0.48</td><td>0.98</td><td>5.4</td><td>0.74</td></tr><tr><td rowspan="3">5</td><td>7.5</td><td>1.12</td><td>0.62</td><td>2.6</td><td>0.76</td></tr><tr><td>8.3</td><td>0.69</td><td>0.51</td><td>2.6</td><td>0.75</td></tr><tr><td>9.2</td><td>0.45</td><td>0.90</td><td>4.3</td><td>0.75</td></tr><tr><td rowspan="3">6</td><td>7.5</td><td>0.87</td><td>0.47</td><td>3.1</td><td>0.84</td></tr><tr><td>8.3</td><td>0.54</td><td>0.86</td><td>4.6</td><td>0.83</td></tr><tr><td>9.2</td><td>0.35</td><td>1.00</td><td>3.7</td><td>0.79</td></tr></tbody></table>

## Data availability

Data will be made available on request.

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