# Epitaxial cerium oxide films deposited on r-plane sapphire substrates: A comprehensive study of growth mechanisms

Edgar Chaslin, Quentin Simon, Alexandro Borroto, S. Bruyere, Sylvie Migot, Mohamed Himdi, Xavier Castel

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Edgar Chaslin, Quentin Simon, Alexandro Borroto, S. Bruyere, Sylvie Migot, et al., Epitaxial cerium oxide films deposited on r-plane sapphire substrates: A comprehensive study of growth mechanisms. Applied Surface Science, 2025, 696, pp.162917. 10.1016/j.apsusc.2025.162917. hal-05105449

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Full Length Article

# Epitaxial cerium oxide films deposited on r-plane sapphire substrates: A comprehensive study of growth mechanisms

E. Chaslin<sup>a,∗</sup>, Q. Simon<sup>a,∗</sup>, A. Borroto<sup>a,†</sup>, S. Bruyère<sup>b,†</sup>, S. Migot<sup>b</sup>, M. Himdi<sup>a,†</sup>,
X. Castel<sup>a,∗,‡</sup>

ARTICLE INFO

Keywords:

Cerium oxide
r-plane sapphire
rf-sputtering
Thin films
Epitaxy
Dislocations

A B S T R A C T

Epitaxial growth of CeO₂ thin films onto sapphire single crystals is of great interest for high-quality hetero-
structures. Here, the growth mechanisms and crystallographic characteristics of CeO₂ films, from 5 to 40 nm-
thick deposited by rf-sputtering on r-plane sapphire substrates, were explored by X-ray diffraction, atomic-force
microscopy and high-resolution transmission electron microscopy. A growth competition between (1 1 1)/(0 0 2)
orientations was identified during the early stages of growth. While both orientations coexist within the first
nanometers, the (0 0 2)-orientation progressively dominates due to its higher growth rate, while (1 1 1)-oriented
domains remain contained close to the substrate surface. Post-annealing was achieved to enhance the crystalline
quality of the films, removing (1 1 1)-oriented domains and providing (0 0 2)-single-oriented CeO₂ epitaxial
layers. Misorientation was linked to strain relaxation induced by periodic dislocations, as revealed by TEM
analysis. Additionally, in-plane dislocations are present within the entire film thickness. Both contribute
significantly to the local misorientation. This study provides detailed pictures of defects and quantifies their
effect on the film crystallographic quality. It offers insights into both fundamental growth mechanisms and
practical strategies to facilitate the epitaxial growth of complex oxides onto the surface of CeO₂ thin films,
thereby paving the way for innovative applications in catalysis, electronics and/or energy applications.

1. Introduction

Cerium oxide (CeO₂) thin films have garnered significant attention
due to their wide interest in various technological applications, such as
buffer layers for functional oxides growth on different substrates [1–11],
oxidation-resistant coatings [12,13], optoelectronic devices [12–14],
catalysis [14–16] and energy conversion [17–19]. Epitaxial growth of
CeO₂ films on sapphire (Al₂O₃) substrates is of particular interest due to
the unique optical, (di-)electrical, and mechanical properties of the
resulting heterostructures. Indeed sapphire, a versatile substrate, offers
multiple crystallographic orientations – such as (1 0 ¯1 0) m-plane,
(1 ¯1 0 2) r-plane, (0 0 0 1) c-plane, and (1 1 ¯2 0) a-plane – each
enabling the growth of different materials by varying the crystallo-
graphic alignments. Among these, r-plane orientation is especially well-
suited for the growth of cubic or pseudo-cubic structures, making it an
ideal choice for CeO₂ growth endowed with cubic fluorite structure
[1,20–31]. Despite a large lattice mismatch between the r-plane

sapphire and CeO₂ material, epitaxial layers are obtained, which is
crucial for ensuring the performance of such films for advanced
applications.

The growth of epitaxial CeO₂ on r-plane sapphire is influenced by
several parameters, including deposition technique, substrate tempera-
ture, deposition atmosphere composition, substrate surface oxidation
state and annealing processes. Understanding the mechanisms that
govern the orientation and crystallinity of the films is essential for
optimizing their performance in practical applications. Many studies
have observed a dual orientation, namely (1 1 1) and (0 0 1) orientations
in CeO₂ films deposited by radio-frequency sputtering [20,23,29,31].
These studies indicate competition between these crystallographic ori-
entations which are influenced by tuning the aforementioned parame-
ters. On the one hand, increasing substrate deposition temperature,
ensuring a fully oxygenated substrate surface and carrying out post-
annealing processes tend to favor the [0 0 1] growth direction. On the
other hand, the simultaneous emerging of both crystallographic

<footnote><sup>a</sup> Univ Rennes, CNRS, IETR-UMR 6164, F-35000 Rennes, France</footnote>

<footnote><sup>b</sup> Université de Lorraine, CNRS, IJL, F-54000 Nancy, France</footnote>

<footnote>* Corresponding authors.</footnote>

<footnote>E-mail addresses: quentin.simon@univ-rennes.fr (Q. Simon), xavier.castel@univ-rennes.fr (X. Castel).</footnote>
orientations is not fully understood. Sunder *et al.* [29] suggest that (0 0 1)-oriented epitaxial growth occurs when surface adatoms have sufficient mobility and time to locate optimal nucleation sites. Otherwise, if adatom mobility is limited, (1 1 1)-oriented epitaxial growth is favored due to the lower surface energy of (1 1 1) CeO₂ nuclei. Based on these observations, they propose a low deposition rate, combined with the formation of terraces on the substrate surface through a pre-annealing at 1430 °C to promote the growth of (0 0 1)-oriented films. Nevertheless, Bick *et al.* [30] report the formation at low deposition rates of high-quality single-oriented (1 1 1) CeO₂ thin films on pre-annealed substrates. The open literature presents a variety of deposition parameters to achieve single-oriented (0 0 1) epitaxial CeO₂ layers and some studies are quite different from one another. In addition, they report a misorientation in the [0 0 1] growth direction, evidenced by a dual contribution (a broad and a narrow peak) in ω-scans provided by X-ray diffraction [21–26,29]. Although this misorientation seems inherent to the formation of epitaxial CeO₂ layers on sapphire substrates, its origin remains not well understood.

To be effectively used as a buffer layer for the growth of complex oxide heterostructures, it is essential to understand the CeO₂ growth mechanisms to both prevent the formation of the (1 1 1)-oriented grains and reduce misorientation in the [0 0 1] growth direction. Therefore, achieving high-quality (0 0 1)-oriented epitaxial CeO₂ layers is crucial for advancing the broader application of CeO₂ films in emerging technologies. By varying the thickness of CeO₂ films, the present study aims to provide a comprehensive understanding of the competition between the (1 1 1) and (0 0 1) orientations, and the development of misorientation into the epitaxial layers. The use of a post-annealing process further enhances the understanding in the internal evolvement occurring into the CeO₂ films, leading to high-quality (0 0 1)-oriented epitaxial layers. The use of various and complementarity characterization techniques, including X-ray diffraction (XRD), atomic-force microscopy (AFM), and transmission electron microscopy (TEM), will provide detailed analyses of the CeO₂ films growth mechanisms and will offer insights into strategies for high-quality heterostructures growth.

## 2. Experimental

Cerium oxide (CeO₂) thin films were deposited by confocal magnetron radio-frequency sputtering technique with deposition parameters listed in Table 1. The deposition time was varied to control the film thickness. 10 × 10 × 0.5 mm³ r-plane sapphire substrates (Crystal GmbH) were annealed at 1430 °C for 10 h prior each deposition stage to achieve atomically flat surfaces with steps [29]. Post-annealing of the CeO₂ films was conducted in air at 1000 °C for 30 min (Nabertherm GmbH furnace).

The CeO₂ film crystallographic structure and thickness were investigated by X-ray diffraction (XRD) and X-ray reflectometry (XRR) on a Rigaku SmartLab 9 kW equipment with a monochromatic parallel beam configuration (CuKα₁ radiation with λ = 1.54056 Å) and a scintillator point detector. Measurement were performed in ω-2θ configuration with an angular resolution of 0.02° and in ω-scan configuration with an angular resolution of 0.005°. Pole figure and ϕ-scan measurements were

<table><caption>**Table 1**
Sputtering deposition parameters of CeO₂ thin films.</caption><thead><tr><td>Target</td><td>CeO<sub>2</sub> (Kurt Lesker supplier)</td></tr></thead><tbody><tr><td>Target diameter</td><td>50.8 mm</td></tr><tr><td>Target-substrate distance</td><td>80 mm</td></tr><tr><td>Substrate-holder rotation speed</td><td>5 rpm</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>2 × 10<sup>-5</sup> Pa</td></tr><tr><td>Working pressure</td><td>7 Pa</td></tr><tr><td>Sputtering gas</td><td>Ar/O<sub>2</sub> (48/2 sccm)</td></tr><tr><td>Substrate temperature</td><td>800 °C</td></tr><tr><td>Deposition rate</td><td>0.25 nm/min</td></tr></tbody></table>

performed through the in-plane configuration with an angular resolution of 0.05°. All measurements were analyzed by using the SmartLab Studio II software. Surface topology was analyzed by atomic-force microscopy (AFM) in tapping mode using a ParkSystem NX10. Images were performed with Olympus OMCL-AC160TS tips on a surface of 2 × 0.8 µm² with a resolution of 1500px × 600px. Transmission electron microscopy (TEM) analyses were conducted using a JEOL-ARM 200F microscope equipped with spherical aberration (Cs) correctors, achieving a point resolution of 0.12 nm in TEM mode and 0.078 nm in STEM mode. Cross-sectional TEM samples of 10 nm and 30 nm thick CeO₂ films were prepared using a focused ion beam (FIB) scanning electron microscope dual-beam system (FEI Helios NanoLab 600i).

## 3. Results and discussion

### 3.1. Structural characterization and thickness dependence of CeO₂ thin films

X-ray diffraction (XRD) analysis in ω-2θ configuration of as-deposited cerium oxide thin films shows dual orientation growth in the [1 1 1] and [0 0 1] directions regardless of the thickness, in accordance with previous studies [20,23,29,31] (Fig. 1a). Integrated intensity of the (1 1 1) peak remains nearly constant with increasing thickness, whereas integrated intensity of the (0 0 2) peak increases proportionally with the expected thickness (Fig. 1b). Volume fraction of the [1 1 1]-oriented crystallites is therefore independent of the film thickness, while that of the [0 0 1]-oriented crystallites increases with the film thickness. This first observation suggests a fundamental mechanism in the growth process: a competition between the (1 1 1) and (0 0 2) orientations. It appears that the (1 1 1) orientation grows primarily within the first 5 to 10 nm, while the (0 0 2) orientation continues to develop throughout the entire film thickness. This is corroborated by the crystallite size calculations based on the Scherrer law (Fig. 1c), showing a crystalline coherence length stabilization around 5 to 8 nm for the (1 1 1) crystallites whereas it corresponds closely to the total film thickness for the (0 0 2) crystallites.

Clearly visible Laue oscillations around the (0 0 2) diffraction peak for each thickness denote a good layer quality with sharp interfaces between the substrate and CeO₂ thin films, and the CeO₂ thin films with air. High crystalline quality is also confirmed by the ω-scans of the (1 1 1) and (0 0 2) diffraction peaks (Fig. 1d-e). For the (1 1 1) orientation, a narrow peak with a full-width at half maximum (FWHM) close to 0.06° indicates weak angular dispersion and is consistent with the values reported in the literature for thin films deposited by rf-sputtering [21,23,25,26,29], molecular beam epitaxy [30] and pulsed laser deposition [22,24]. For the (0 0 2) orientation, films thinner than 10 nm exhibit also a narrow peak with FWHM = 0.06°, indicating also weak dispersion. However, for films with thicknesses ranging from 10 to 40 nm, the ω-scans show a dual contribution: a broad peak topped with a narrow peak. This suggests the onset of a misorientation at ~10 nm, which increases with film thickness, evidenced by the increasing intensity of the broad peak relative to the narrow one.

After *ex situ* post-annealing process in air at 1000 °C for 30 min, ω-2θ scans show a complete disappearance of the (1 1 1) orientation regardless of CeO₂ film thickness (Fig. 2a). This vanishing is accompanied by an improved intensity of the (0 0 2) orientation peak with well-defined Laue oscillations indicating an increasing interface quality. Symmetric reciprocal-space mapping (RSM) of the (0 0 2) Bragg reflection points out two contributions, in accordance with the previously observed ω-scans of the as-deposited CeO₂ thin films: a narrow peak superimposed on a broad one (Fig. 2b). Following the post-annealing step, the broad contribution becomes more pronounced, with an increased relative intensity compared with that of the as-deposited films. Symmetric RSM displays a thinning of both contributions along the Qz axis as the thickness increases: the crystallite size grows, thereby narrowing the contributions in accordance with the
<figure><img src="image_2.png" /><figcaption>**Fig. 1.** Structural analysis of the as-deposited CeO₂ thin films. (a) ω-2θ scans of the 5–40 nm thick CeO₂ films deposited on Al₂O₃ r-plane sapphire substrates (log. scale). The (1 ¯10 2) r-plane peak is observed at 25.58° (*), along with the (111) and (002) reflections of CeO₂ exhibiting Laue oscillations. (b) Integrated intensity of the (111) and (002) planes of CeO₂ as a function of the expected film thickness. (c) Crystallite size computation based on the Scherrer law for (111) and (002)-oriented crystallites as a function of CeO₂ film thickness. (d, e) ω-scans of the (111) and (002) CeO₂ planes showing a dual contribution (broad peak topped with a narrow peak), (linear scale).</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Structural analysis of the post-annealed CeO₂ thin films. (a) ω-2θ scans of the 5–40 nm thick CeO₂ films deposited on Al₂O₃ r-plane sapphire substrates (log. scale). The (1 ¯10 2) r-plane peak is observed at 25.58° (*), along with the CeO₂ (002) reflection, exhibiting Laue oscillations. (b) Symmetrical reciprocal space mapping (RSM) along the [001] direction of the CeO₂ layers. (c) Integrated intensity extracted from RSM at the maximum and along the Qₓ axis for the narrow and broad peak contributions.</figcaption></figure>
Scherrer law. Integrated intensities from each contribution along the Qx axis show that while the broad contribution increases, the narrow contribution remains constant, regardless of the CeO₂ thickness (Fig. 2c). The integrated intensity of the narrow peak reaches its maximum for 5 nm-thick, suggesting that the well-oriented (0 0 2) planes are located close to the substrate surface. Thus, the post- annealing process promotes a single-oriented CeO₂ thin film in [0 0 1] direction but accentuates the misorientation in the layer.

The assessment of strain relaxation is performed through Williamson-Hall plots (Fig. 3a) on the post-annealed CeO₂ thin films with various thicknesses using the FWHM and ω-2θ scan peak positions of the (0 0 2), (0 0 4), and (0 0 6) reflections to separate microstrain and crystallite size contributions in peak broadening. The data points are fitted with a linear trend. The slope is related to microstrain and the intercept provides crystallite size into the layer. The decreasing slope versus the increasing thickness denotes a clear microstrain reduction into CeO₂ layers, consistent with previous results. This reduction occurs due to the formation of dislocations beyond a critical thickness, which would contribute to the film misorientation. Additionally, the decreasing slope with thickness is supported by a decrease in the intercept, indicating an increase of the crystallite size. In fact, the calculated crystallite size corresponds to the total film thickness for each sample. Comparison of the measured versus the expected thicknesses (Fig. 3b) is presented using three different methods, namely the Williamson-Hall method, the Laue oscillations one and the XRR analysis (results detailed hereafter). The excellent convergence of the results highlights the strong matching between measured and expected

thicknesses, and also the accuracy and reliability of these methods. Furthermore, it highlights that the broadening of the ω-2θ peaks is primarily attributed to the crystallite size effect, resulting in minimal measured strain in the films, regardless of their thickness. Deviations observed for the thickest films can be attributed to deposition parameters, such as higher deposition time at high temperature, resulting in better densification of the films, or minor errors in the initial calculation of the deposition rate, leading to slight deviations.

The log-log plot of microstrain versus expected thicknesses (Fig. 3c) exhibits a clear inverse relationship between microstrain and film thickness, as discussed previously. The microstrain values, extracted from the slopes of the Williamson-Hall plots, are fitted with a thickness-dependent strain decay model (Eq. (1)) as follows:

$$ \epsilon = A \times h^{-m} \qquad (1) $$

where ε is the microstrain, A is a constant factor, h is the thickness, and m is a constant equal to 1 for the ideal Matthews-Blakeslee theory [32]. The fit shows a high degree of correlation (R² = 0.998) with parameters A = 3.19 ± 0.41 and m = 1.532 ± 0.065. The continuous decrease in strain with increasing thicknesses suggests that CeO₂ films do not appear to be fully constrained, even at very low thickness (~5 nm). This observation further indicates that relaxation, driven by dislocations, occurs from the very beginning of the deposition stage.

In addition to an oriented out-of-plane layer, CeO₂ thin films also exhibit an in-plane orientation. This is evident by the in-plane pole figure of the as-deposited 20 nm-thick layer, which shows four spots located at φ = 45°, 135°, 225°, and 315° for χ = 54.50°, close to the χ =

<figure><img src="image_4.png" /><figcaption>Fig. 3. Microstrain and thickness dependency of the post-annealed CeO₂ thin films. (a) Williamson-Hall plots for CeO₂ films depending on the thickness using (0 0 2), (0 0 4) and (0 0 6) diffraction peaks. (b) Comparison of the measured thickness versus the expected thickness of CeO₂ films by X-ray reflectivity (XRR), Laue oscillations, and Williamson-Hall analysis. (c) Log-log plot of microstrain depending on the CeO₂ expected film thickness (microstrain values retrieved from Williamson-Hall plot slopes and fitted with a thickness-dependent strain decay model).</figcaption></figure>
54.74° theoretical angle between the (0 0 2) and (1 1 1) planes (Fig. 4a). A lower intensity central spot, associated with the minor out-of-plane (1 1 1) orientation seen in the ω-2θ scans (Fig. 1a), is also noticed. After annealing, the central spot disappears and the intensity of the four spots at χ = 54.50° increases, confirming the complete (0 0 2) orientation of the CeO₂ layer (Fig. 4b).

In-plane φ-scans of the (0 0 6) planes of the r-plane sapphire sub-
strate define the in-plane growth relationship with the CeO₂ layer
(Fig. 4c). The figure shows four peaks, related to the (1 1 1) CeO₂ planes,
spaced by 90° due to the four-fold symmetry of the CeO₂ cubic fluorite
structure around [0 0 1] axis and shifted by 45° relative to the substrate
peaks, indicating alignment between a-axis of the substrate and a-axis of
the CeO₂ layer. The results provide the following crystallographic re-
lationships: (0 0 2)film // (0 1 2)sub; [1 0 0]film // [1 0 0]sub and [0 1 0]film
// [1 ¯2 1] sub (Fig. 4e).

The FWHM calculated from the in-plane φ-scans decreases with increasing thickness before annealing (Fig. 4d). Lattice mismatch between the substrate and the layer (5.4 % and 13.7 % in the [1 ¯2 1] and [1 0 0] substrate directions, respectively) causes an in-plane misorientation in the early stages of growth, confirmed by the higher FWHM values of the 5 and 10 nm-thick layers (4.9° and 4.6°, respectively). Thicker films show more homogeneous and stabilized growth, leading to lower in-plane misorientation and a decrease in FWHM values (less than 4.0°). Finally, post-annealing stage reduces the in-plane misorientation by relaxing strain, resulting in a constant FWHM value close to 2.5° regardless of the CeO₂ layer thickness.

The microstructural features of CeO₂ layers were further investigated using XRR and AFM. As previously mentioned, XRR measurements provide differences between the expected thickness (calculated by adjusting the deposition time based on a reference sample) and the measured thickness by the periodicity of Kiessig fringes (Fig. 5a). In accordance with the best quality of Laue oscillations, post-annealing

results in well-defined Kiessig fringes demonstrate an improved in-
terfaces quality between the substrate surface, CeO₂ layer and air. These
very smooth surfaces are noticeable in the three-dimensional AFM im-
ages, especially with the post-annealed thicker samples (Fig. 5b). Even
at thicknesses exceeding 20 nm or 40 nm, the layer continues to repli-
cate the atomic terraces of the annealed substrates. The smooth surface
of the 20 nm and 40 nm-thick layers is also evident in the extracted
height profile, where the variation in height is lower than for thinner
CeO₂ films (Fig. 5c). At lower thicknesses, island formation is observed
due to the predominance of surface tension effects at the interface be-
tween the substrate surface and the CeO₂ layer. This phenomenon is
particularly pronounced for the 10 nm-thick sample, where the height
value of the atoms clusters is close to the total thickness of the film,
resulting in a discontinuous film. For the 5 nm-thick sample, atoms
clusters are more numerous but smaller, resulting in a low variation of
the height profile, although the film remains discontinuous.

Calculated quadratic roughness (Rq) confirms these results (Fig. 5d-
e). Before annealing, roughness increases with thickness, reaching a
maximum for layers thicker than 20 nm. Though the trends are the same
between XRR and AFM measurements, a shift is observed due to dif-
ferences in roughness calculation: AFM considers only the surface of the
layer (interface layer/air) while XRR considers both interfaces (sub-
strate surface/layer and layer/air), resulting in higher calculated values
for XRR measurements. After annealing, roughness is higher for the 10
nm-thick sample, as seen in the 3D AFM images, even more than before
post-annealing stage, due to the island formation. The 5 nm-thick layer,
although having a discontinuous surface, presents very low roughness
due to smaller atoms clusters and smaller overall thickness. Finally, the
20 nm-thick film presents the lowest roughness with Rq = 0.3 nm, while
the 40 nm-thick film starts to show some protrusions, contributing to a
slight increase in roughness.

From XRR measurements, the film density can also be calculated and

<figure><img src="image_5.png" /><figcaption>**Fig. 4.** Epitaxial relationships in the CeO₂/Al₂O₃ heterostructure. In-plane pole figures of (1 1 1) planes of (a) as-deposited and (b) post-annealed 20 nm-thick CeO₂ films. (c) φ-scans of Al₂O₃ (006) planes and CeO₂ (1 1 1) planes from 20 nm-thick films and (d) calculated full-width at half maximum from φ-scans before and after annealing step. (e) Scheme showing epitaxial relationship between r-plane sapphire substrate and (0 0 2)-oriented CeO₂ film. The reference corresponds to Al₂O₃ crystallographic axis.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Fig. 5.** Surface and density analysis of the CeO₂ thin films. (a) XRR measurements before and after post-annealing stage versus thickness value of post-annealing CeO₂ films. (b) 3D AFM images of CeO₂ film surface with substrate steps (when noticeable) and (c) height profiles extracted from previous images. Quadratic roughness extracted from XRR and AFM measurements for (d) as-deposited and (e) post-annealed CeO₂ films. (f) density of CeO₂ layers retrieved from XRR measurements before and after annealing stage.</figcaption></figure>

compared with the 7.22 g/cm³ theoretical value (Fig. 5f). As-deposited CeO₂ films exhibit lower density than expected for the 5 and 10 nm-thick samples, while the 20 nm and 40 nm-thick samples present a fully dense cerium oxide layer. This can be attributed to the higher roughness

measured on thinner samples, thus impacting their density. In addition, the longer deposition time promotes the densification of the films. Post-annealing process further helps densification of the CeO₂ films by enhancing atom mobility, particularly for the 10 nm-thick sample,

<figure><img src="image_7.png" /><figcaption>**Fig. 6.** Growth mechanism of the CeO₂ thin films. (a) HRTEM image of the 10 nm-thick CeO₂ film showing evidence of (1 1 1) orientation surrounded by (0 0 2) orientation. (b) Fast Fourier Transform (FFT) patterns of two identified areas corresponding to (0 0 2) and (1 1 1) orientations. (c) Schematic representation of the competition between (1 1 1) and (0 0 2) orientations during CeO₂ film growth.</figcaption></figure>
where atoms clusters achieve full density. In a different way, the 5 nm-thick sample cannot achieve a fully dense layer due to its lack of continuity.

In view of these results, the 20 nm-thick CeO₂ films present the best compromise in terms of crystalline quality with sharp interfaces, no formation of atoms clusters, a continuous layer with the lowest

roughness and a fully dense value.

## 3.2. Identification of the growth mechanisms of the CeO₂ thin films

To bring details on the growth mechanism of the as-deposited CeO₂ films, local observations by high-resolution TEM analysis were

<figure><img src="image_8.png" /><figcaption>**Fig. 7.** Cross-sectional TEM images and Fast Fourier Transform (FFT) patterns of the CeO₂ films. Cross-sectional low magnification TEM images of (a) as-deposited and (b) post-annealed 30 nm-thick CeO₂ films. Black dashed boxes represent enlarged area where HRTEM images were performed for (c) as-deposited and (d) post-annealed films. Yellow boxes correspond to filtered HRTEM images. Red box labelled from 1 to 4 correspond to (e) FFT patterns of post-annealed films exhibiting (0 0 2) orientation growth. Violet box corresponding to (f) (0 0 6) reflection in FFT patterns showing a slight angular spread in the diffraction spots (1.6° ± 0.7°).</figcaption></figure>
performed at the interface of the 10 nm-thick CeO₂ film and the Al₂O₃ surface substrate (Fig. 6a). At the early stage of the growth, the film exhibits mixed crystallographic orientations, predominantly (1 1 1) and (0 0 2) ones, as confirmed by FFT patterns performed along the CeO₂/Al₂O₃ interface (Fig. 6b). We can observe that during the film growth, the [0 0 1]-oriented domains (with the (0 0 2) crystallographic planes parallel to the substrate surface) overgrow gradually the [1 1 1]-oriented domains (with (1 1 1) crystallographic planes parallel to the substrate surface). In the fluorite structure, [0 0 1] is the geometrically fastest growing direction [33]. Consequently, this direction will progressively overgrow the [1 1 1] one until the film becomes fully [0 0 1]-oriented. It is worth noting that it is the fastest geometrical growth direction that prevails rather than the energetically favorable direction, i.e. the one with the lowest surface energy ([1 1 1]-direction in the case of fluorite). This is due to the limited adatom mobility during the film growth under our experimental deposition parameters, a necessary requirement for limiting the energetically favorable [1 1 1] direction growth. The resulting microstructure corresponds to a typical film structure identified by J. A. Thornton as 'zone II' [34,35]. In this zone, a preferential orientation is developed along the fastest growth direction, accompanied by V-shaped faceted columns whose structure evolves with the increasing film thickness [33]. In addition, TEM results presented herein corroborate the previous XRD observations of the as-deposited films (Fig. 1). Indeed, the overgrowth of the [1 1 1]-oriented domains by the [0 0 1]-oriented ones limits the size of the former and favors the growth of the latter. This explains the stabilization of both integrated intensity and crystallite size of the (1 1 1) Bragg reflection, as well as the continuous increase of these two data in the case of the (0 0 2) reflection (Fig. 1b-c). A schematic CeO₂ film growth process is presented in Fig. 6c.

Cross-sectional TEM images of thicker CeO₂ samples (~30 nm-thick) provide valuable microstructure insights (Fig. 7). At low magnification (Fig. 7a-b), significant differences are observed between the as-deposited and the post-annealed films. Before annealing, CeO₂ layer exhibits the characteristic columnar growth of 'zone II', as previously discussed and observed in literature [23], with visible grain boundaries, leading to a rougher surface. In contrast, the post-annealing stage reduces the surface roughness sample (consistent with the roughness results shown in Fig. 5d-e), and visible defects. High-resolution TEM (HRTEM) images confirm these first observations (Fig. 7c-d). The as-deposited films exhibit a V-shaped columnar structure, with approximately 10–15 nm wide columns overlying a low-quality region up to ~10 nm-thick (outlined by grey dashed lines). This observation also confirms the previous findings: a competition of orientations creating a low-quality (0 0 2)-oriented region with defects concentrated at the substrate surface-film interface, before evolving into higher-quality columnar growth along the (0 0 2)-orientation (yellow inset in Fig. 7c). Grain boundaries are located on the top of the faceted grains close to the substrate surface, as predicted for a 'zone II' microstructure. This growth mode results in sharped tips, thereby impairing the surface quality for subsequent material deposition. The measured d-spacing in c-direction (~5.54 Å) exceeds the nominal value of 5.41 Å for CeO₂ fluorite, likely due to strain induced by defects and/or oxygen deficiencies which increase the d-spacing value. Additional measurements performed by XRD and the related discussion about lattice parameters (in-plane and out-plane) is available in supplementary information (Fig. S1).

For the post-annealed samples, the crystallographic quality is markedly improved (Fig. 7d), as shown by the low-magnification TEM images. Both substrate surface-film and film-Pt interfaces are flat and well-defined, with roughness confined to ~1-unit cell, in agreement with AFM and XRR results (Rq = 0.3 nm, Fig. 5e). The high-defect region near the substrate surface-film interface observed in the as-deposited films disappears, leading to homogeneous and high-quality CeO₂ epitaxial layer throughout its thickness. The filtered image (yellow inset in Fig. 7d) again reveals a CeO₂ structure with (0 0 2)-orientation along the growth direction, and a d-spacing decrease equal to 5.46 Å, close to

the bulk value. This highlights the benefits of the post-annealing stage which reduces defects and promotes thin film properties in accordance with those of the bulk material. Some residual defects, attributed to the column boundaries as observed in the as-deposited thin film, remain visible (white arrows in Fig. 7d).

Further analyses based on FFT patterns at four distinct spots within the annealed film (labelled 1–4 red rectangle, Fig. 7d) exhibit local misorientations in the out-of-plane direction (Fig. 7e-f). The patterns confirm the (0 0 2)-orientation along the growth direction but show slight angular deviations. A detailed analysis of the (0 0 6) reflection reveals a maximum misorientation of 1.6 ± 0.7° between spots 1 and 3. This value corroborates the ω-scan results (Fig. S2), where FWHM broad contributions range from 1.5° to 2° for 40–20 nm thick samples, respectively.

### 3.3. Origin of the misorientation in the CeO₂ thin films

This part focuses on the relation between misorientations of the films and crystallographic defects, evidenced both by global (XRD, ω-scans and RSM) and local (FFT of HRTEM) characterizations. The presence of dislocations in CeO₂ films is highlighted by using Inverse Fast Fourier Transform (IFFT) images of diffraction spots (Fig. 8). Diffraction spots were selected from the FFT pattern of an HRTEM image at the CeO₂/Al₂O₃ interface (Fig. 8a) corresponding to the [1 0 0] direction of both CeO₂ and Al₂O₃. IFFT images show dislocations concentrated near the interface (indicated by black arrows). These dislocations appear periodically, with an average spacing of 1.9 ± 0.3 nm, which matches closely with the 1.97 nm theoretical spacing value calculated from Eq. (2), as follows:

$$d = \frac{b}{f} \quad \text{where} \quad f = \frac{a_{CeO_2} - a_{Al_2O_3}}{a_{Al_2O_3}} \qquad (2)$$

where d is the spacing between dislocations, b is the Burgers vector, and f is the lattice mismatch. Using a magnitude of Burgers vector b = 1/2 [100] = 1/2 a$_{CeO_2}$ and a mismatch f = 0.137, the critical thickness (h$_{c}$), at which dislocations appear, was computed from the Matthews-Blakeslee model (Eq. (3)), as follows:

$$h_c = \frac{b}{2\pi f} \frac{(1 - \nu \cos^2 \alpha)}{(1 - \nu) \cos \lambda} \left( \ln \frac{h_c}{b} + 1 \right) \qquad (3)$$

where ν is the Poisson ratio, α is the angle between the dislocation line and Burgers vector, and λ is the angle between the slip direction and the one in the film plane which is perpendicular to the intersection line between the slip plane and the interface [36]. Using ν = 0.293 [37] and cosα = cosλ = 0, the critical thickness was computed iteratively (Fig. S3) which gives h$_{c}$ = 5.23 Å, a value lower than that of an unit cell, in accordance with Fig. 8b where dislocations emerge within the first CeO₂ atomic layer. These periodic dislocations facilitate strain relaxation at the onset of deposition, enabling the CeO₂ layer to grow with minimal residual stress. Geometrical phase analysis (GPA) of the lattice parameters (Fig. 8c) confirms relaxation into the CeO₂ layer. Both sides of the interface exhibit almost relaxed lattice parameters: 4.76 ± 0.06 Å for Al₂O₃ (bulk value a$_{Al_2O_3}$ = 4.759 Å, JCPDS card n° 00-042-1468) and 5.44 ± 0.28 Å (bulk value a$_{CeO_2}$ = 5.41 Å, JCPDS card n° 00-034-0394), in agreement with the in-plane XRD scans (a$_{CeO_2}$ ≈ 5.435 Å, Fig. S1) and the direct lattice parameter measurements from filtered HTEM images (a$_{CeO_2}$ = 5.44 Å, Fig. S4) shown in supplementary information.

Heatmap of the lattice parameter at the interface further illustrates dislocations as “hot” and “cold” spots. These spots indicate localized compression of the Al₂O₃ lattice to accommodate the CeO₂ lattice expansion caused by the dislocations. Strain ε$_{xx}$ calculations at the CeO₂/Al₂O₃ interface further support this observation (Fig. 8d), strains being calculated by using the lattice deviation from a reference, namely the bulk substrate lattice. As expected, the substrate is nearly stress-free
<figure><img src="image_9.png" /><figcaption>**Fig. 8.** Lattice parameters and strain analysis at the CeO₂/Al₂O₃ interface. (a) Cross-sectional HRTEM image at the post-annealed CeO₂/Al₂O₃ interface of the 30 nm-thick film. The inset shows the FFT pattern, with red ellipses marking areas selected for (b) an inverse FFT (IFFT) image. Black arrows indicate dislocations into the CeO₂ layer, spaced at 1.9 ± 0.3 nm. (c) Lattice parameters along the *a*-direction calculated by geometrical phase analysis (GPA). The color scale highlights lattice parameter variations (orange: lower; violet: higher) based on the theoretical bulk lattice parameters of CeO₂ (5.41 Å) and Al₂O₃ (4.76 Å) in *a*-direction. (d) *ε*<sub>xx</sub> strain distribution at the CeO₂/Al₂O₃ interface calculated from GPA.</figcaption></figure>

($\epsilon_{xx} = 0.00 \pm 0.01$), while CeO₂ layer exhibits significant tensile strain ($\epsilon_{xx} = 0.15 \pm 0.07$), consistent with the mismatch between CeO₂ and Al₂O₃ lattices using as a reference ($f = 0.1366$). Thereby, the strain map confirms the presence of compressive strain into the substrate and tensile strain into the CeO₂ film, both close to the substrate/film interface, in agreement with the local lattice parameter measurements.

The significant lattice mismatch between CeO₂ and Al₂O₃ induces the formation of periodic dislocations at the CeO₂/Al₂O₃ interface. These dislocations facilitate strain relaxation from the onset of deposition, enabling stress-free growth of the CeO₂ layer. However, they also introduce defects and misorientations, promoting the broadening peak as observed in ω-scans (Fig. 1) and potentially affecting the overall quality of the epitaxial layer.

Defects and misorientations into CeO₂ films were further analyzed by

measuring the local deviation of atomic rows in the [100] direction relative to a theoretically horizontal reference line (Fig. 9). Diffraction spots from the FFT pattern of an HRTEM image of the CeO₂/Al₂O₃ interface (Fig. 9a) corresponding to the [001] and [011] directions of CeO₂ and Al₂O₃ respectively, were selected to generate IFFT (Fig. 9b). The resulting IFFT image highlights several defects and dislocations along the atomic rows, the whole contributing to local misorientations. To quantify them, image processing was performed by comparing localized pixel lines (representing atomic rows) to a 0° theoretical horizontal line using a Sobel filter (Fig. 9c). The complete image processing workflow is available as [supplementary information (Fig. S5)](). The substrate region exhibits a uniform deep blue coloration, indicating minimal deviation from 0°, and confirming the nearly perfect alignment in this area. In contrast, the CeO₂ film shows significant misorientation throughout its thickness. These deviations are evident at the interface with the surface substrate, where dislocations are present and propagate into the initial nanometers-thick of the CeO₂ layer. However, misorientations are also observed in the middle and upper regions of the

<figure><img src="image_10.png" /><figcaption>**Fig. 9.** Local misorientation analysis in the CeO₂ thin films. (a) Cross-sectional HRTEM image of the post-annealed 30 nm-thick film. Inset shows the FFT pattern, with red ellipses marking areas selected for (b) IFFT image. (c) Heatmap of out-of-plane local misorientation calculated from IFFT image using a Sobel filter. (d) Zoomed view of the IFFT image around a single dislocation and (e) the corresponding heatmap of local misorientation. (f) Histogram of local misorientation angles calculated from the HRTEM image of the post-annealed 30 nm-thick CeO₂ layer (white boxes with black contours) compared with ω-scans of the 40-nm (red line) and 20-nm (orange line) thick post-annealed films. The inset shows a zoomed view (−1° to 1°) highlighting the maximum difference between broad and narrow contributions (0.13°).</figcaption></figure>
film thickness. Therefore, CeO₂ keeps developing defects and dislocations through its thickness, resulting in a film with a homogeneous defect density.

A zoomed view of an in-plane dislocation (Fig. 9d) provides insight of the local misorientation induced by such defects. Single dislocation generates a misorientation that propagates over several nanometers both above and below the defect in an oblique direction. The maximum misorientation shown on the corresponding heatmap (Fig. 9e) does not occur at the dislocation point itself, but approximately 2 nm above it. Then, the misorientation increases progressively from the dislocation to its maximum. A localized defect or dislocation thus influences a much larger area, propagating misorientations and contributing to the broadening observed in Reciprocal Space Mapping (RSM) (Fig. 2b).

Histogram of measured misorientations derived from the HRTEM image corroborates this phenomenon. The misorientation distribution in the 30 nm-thick sample agrees with the trend observed in normalized ω-scans of the 20 nm and 40 nm-thick CeO₂ layers (Fig. 9f). On the one hand, a narrow peak centered at 0° represents atomic columns perfectly aligned with the (1 ¯1 0 2) substrate planes. On the other hand, an off-centered broad component arises from local misorientations induced by defects and dislocations. Therefore, the narrow peak corresponds to the well-aligned CeO₂ atomic columns, predominantly appearing between dislocations. The high frequency of dislocation formation (spacing of ~1.9 nm) limits the volume of the well-aligned columns. In addition, the spread of local misorientations interrupts the aligned atomic columns continuity and the probability to disrupt the growth of the perfectly aligned columns increases with thickness, explaining the broad peak increase with film thickness in ω-scans.

The off-centering of the broad peak (~0.13°) is attributed to a tilt in the film growth direction. Instead of following the (1 ¯1 0 2) planes of the substrate, CeO₂ film aligns with the vicinal surface, helped by the dislocations energetically more favorable. Annealed Al₂O₃ substrates exhibit atomic terraces due to a miscut with an angle between the (1 ¯1 0 2) planes and the vicinal surface closed to ~0.05° (Fig. S6). The off-centering is higher than the measured miscut, but consistent with the manufacturer who ensures an angle below 0.3° (Crystal GmbH). Thus, variability in miscut angles between substrates may explain the observed differences with off-centering values.

## 4. Conclusion

In this study, the influence of film thickness and post-annealing stage on the growth mechanisms and crystallographic properties of CeO₂ thin films deposited on r-plane sapphire substrates were deeply investigated. A combination of advanced and complementary characterization techniques was used, including X-ray diffraction and reflectivity, atomic-force microscopy, and high-resolution transmission electron microscopy. The results revealed a dual-orientation growth mechanism between highly oriented (1 1 1) and (0 0 2) crystallites during the first nanometers of the as-deposited CeO₂ films. As the film thickness increases, a gradual domination of (0 0 2)-orientation due to higher growth rate is observed, combined with enhanced angular dispersion. The post-annealing film stage significantly improved the interface sharpness and reduced CeO₂ surface roughness while suppressing the whole (1 1 1) orientation, leading to single (0 0 2)-oriented CeO₂ films. These improvements were corroborated by the presence of Laue oscillations and enhanced quality of the epitaxial growth.

Nonetheless, the significant lattice mismatch between CeO₂ film and Al₂O₃ substrate induces the formation of periodic dislocations at the CeO₂/Al₂O₃ interface. These dislocations facilitate strain relaxation from the onset of deposition, enabling stress-free growth of the CeO₂ layer but also contribute to local misorientations. Beyond this, in-plane dislocations are also observed throughout the entire thickness of the CeO₂ thin film. These in-plane dislocations further amplify the local misorientations by propagating defects deeper into the film, thereby

intensifying angular dispersion. Finally, these results demonstrated that the 20 nm-thick CeO₂ film represents an optimal compromise, balancing low surface roughness, high density, and excellent crystalline quality.

Looking forward, these results open also new perspectives for optimizing the deposition process of high quality CeO₂ thin films on sapphire substrates. Understanding the mechanisms behind orientation competition enable further control of growth dynamics, potentially reducing local misorientations through the management of defect and dislocation densities. The low surface roughness achieved after annealing stage also presents opportunities for the epitaxial growth of complex oxides onto the CeO₂ films, which could be of significant interest for numerous functional material applications.

## CRediT authorship contribution statement

**E. Chaslin:** Writing – original draft, Visualization, Investigation, Formal analysis, Data curation. **Q. Simon:** Writing – review & editing, Supervision, Funding acquisition, Formal analysis, Conceptualization. **A. Borroto:** Writing – review & editing, Formal analysis. **S. Bruyère:** Writing – review & editing, Investigation. **S. Migot:** Writing – review & editing, Investigation. **M. Himdi:** Writing – review & editing, Supervision, Funding acquisition, Conceptualization. **X. 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.

## Acknowledgments

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.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.apsusc.2025.162917.

## Data availability

Data will be made available on request.

## References

[1] F. Wang, R. Wördenweber, Large-area epitaxial CeO₂ buffer layers on sapphire substrates for the growth of high quality YBa₂Cu₃O₇ films, Thin Solid Films 227 (1993) 200–204, https://doi.org/10.1016/0040-6090(93)90040-ν.

[2] B.-E. Park, I. Sakai, E. Tokumitsu, H. Ishiwara, Hysteresis characteristics of vacuum-evaporated ferroelectric PbZr₀.₄Ti₀.₆O₃, films on Si(111) substrates using CeO₂ buffer layers, Appl. Surf. Sci. 117/118 (1997) 423–428, https://doi.org/10.1016/S0169-4332(97)80118-3.

[3] W. Zhang, X. Wang, I.W. Boyd, Enhanced magnetoresistance behaviour in CeO₂ buffered LaCaMnO films on Si, Appl. Surf. Sci. 138–139 (1999) 563–568, https://doi.org/10.1016/S0169-4332(98)00454-1.

[4] J. Tashiro, A. Sasaki, S. Akiba, S. Satoh, T. Watanabe, H. Funakubo, M. Yoshimoto, Room-temperature epitaxial growth of indium tin oxide thin films on Si substrates with an epitaxial CeO₂ ultrathin buffer, Thin Solid Films 415 (2002) 272–275, https://doi.org/10.1016/S0040-6090(02)00623-5.

[5] T. Muroga, H. Iwai, Y. Yamada, T. Izumi, Y. Shiohara, Y. Iijima, T. Saito, T. Kato, Y. Sugawara, T. Hirayama, Pulsed laser deposition method-CeO₂ buffer layer for YBCO coated conductor, Phys. C Supercond. 392–396 (2003) 796–800, https://doi.org/10.1016/S0921-4534(03)01209-7.
[6] C.M. Wang, S. Azad, V. Shutthanandan, D.E. McCready, C.H.F. Peden, L. Saraf, S. Thevuthasan, Microstructure of ZrO₂-CeO₂ hetero-multi-layer films grown on YSZ substrate, Acta Mater. 53 (2005) 1921–1929, https://doi.org/10.1016/j. actamat.2005.01.003.

[7] V. Mihalache, I. Pasuk, Grain growth, microstructure and surface modification of textured CeO₂ thin films on Ni substrate, Acta Mater. 59 (2011) 4875–4885, https://doi.org/10.1016/j.actamat.2011.04.029.

[8] L.-S. Wang, C.-X. Li, C.-J. Li, G.-J. Yang, Performance of La₀.₈Sr₀.₂Ga₀.₈Mg₀.₂O₃-based SOFCs with atmospheric plasma sprayed La-doped CeO₂ buffer layer, Electrochimica Acta 275 (2018) 208–217, https://doi.org/10.1016/j. electacta.2018.04.101.

[9] M. Ismail, A. Ahmad, K. Mahmood, T. Akbar, A.M. Rana, J. Lee, S. Kim, Room temperature deposited oxygen-deficient CeO₂-layer for multilevel resistive switching memory, Appl. Surf. Sci. 483 (2019) 803–810, https://doi.org/10.1016/ j.apsusc.2019.04.013.

[10] P.B. Mozhaev, J.E. Mozhaeva, I.K. Bdikin, I.M. Kotelyanskii, V.A. Luzanov, J. B. Hansen, C.S. Jacobsen, Graphoepitaxial growth of CeO₂ thin films on tilted-axes NdGaO₃ substrates by pulsed laser deposition, Nanomater. Sci. Eng. 2 (2020) 57–73, https://doi.org/10.34624/nmsc.v2i2.9967.

[11] Q. Wang, M. Boubeche, Y. Xia, R. Zhao, K. Ou, J. Yang, J. Xin, W. Wang, K. Jin, B. Tao, MOCVD deposited double-sided CeO₂ buffer layer for YBCO superconducting film grow on r-plane Al₂O₃ substrate, Phys. C Supercond. Its Appl. 615 (2023) 1354392, https://doi.org/10.1016/j.physc.2023.1354392.

[12] X. Kang, D. Yuan, Z. Yi, C. Yu, X. Yuan, Bismuth single atom supported CeO₂ nanosheets for oxidation resistant photothermal reverse water gas shift reaction, Catal, Sci. Technol. 12 (2022) 5559–5564, https://doi.org/10.1039/d2cy00771a.

[13] K. Zheng, Q. Qi, L. Wang, Y. Zhu, Y. Zhao, Effect of CeO₂@Ni on the oxidation resistance of in situ TiC/Ni composite applied for intermediate temperature solid oxide fuel cell interconnects, Adv. Eng. Mater. 26 (2024) 2400949, https://doi. org/10.1002/adem.202400949.

[14] J. Kašpar, P. Fornasiero, M. Graziani, Use of CeO₂-based oxides in the three-way catalysis, Catal. Today 50 (1999) 285–298, https://doi.org/10.1016/S0920-5861 (98)00510-0.

[15] T. Montini, M. Melchionna, M. Monai, P. Fornasiero, Fundamentals and catalytic applications of CeO₂-based materials, Chem. Rev. 116 (2016) 5987–6041, https:// doi.org/10.1021/acs.chemrev.5b00603.

[16] S.-Y. Ahn, W.-J. Jang, J.-O. Shim, B.-H. Jeon, H.-S. Roh, CeO₂-based oxygen storage capacity materials in environmental and energy catalysis for carbon neutrality: extended application and key catalytic properties, Catal. Rev. 66 (2024) 1316–1399, https://doi.org/10.1080/01614940.2022.2162677.

[17] Q. Li, L. Song, Z. Liang, M. Sun, T. Wu, B. Huang, F. Luo, Y. Du, C.-H. Yan, A review on CeO₂-based electrocatalyst and photocatalyst in energy conversion, Adv. Energy Sustain. Res. 2 (2021) 2000063, https://doi.org/10.1002/aesr.202000063.

[18] S. Sardana, P. Mahajan, A. Mishra, A.K. Chawla, A. Mahajan, Flexible, multifunctional, and durable MXene/CeO₂/cellulose nanofibers for efficient energy conversion-storage capacity toward self-powered monitoring of ammonia, Adv. Mater. Technol. (2024) 2400829, https://doi.org/10.1002/admt.20240829.

[19] Y. Zhang, Y. Zhou, D. Sun, Y. Nie, D. Wu, L. Ban, B. Tang, S. Yang, H. Li, T. Ma, H. Zhang, CeO₂-based functional materials: advancing photo and electro-driven catalysis for environmental remediation and energy conversion, Coord. Chem. Rev. 527 (2025) 216395, https://doi.org/10.1016/j.ccr.2024.216395.

[20] R.-J. Lin, L.-J. Chen, L.-J. Lin, Y.-C. Yu, C.-W. Wang, E.-K. Lin, Growth and characterization of CeO₂ films on sapphire substrates by sputtering process, Jpn. J. Appl. Phys. 35 (1996) 5805–5810, https://doi.org/10.1143/JJAP.35.5805.

[21] A.G. Zaitsev, G. Ockenfuss, D. Guggi, R. Wördenweber, U. Krüger, Structural perfection of (0 0 1) CeO₂ thin films on (1 1 0 2) sapphire, J. Appl. Phys. 81 (1997) 3069–3072, https://doi.org/10.1063/1.364342.

[22] X. Castel, M. Guilloux-Viry, A. Perrin, J. Lesueur, F. Lalu, High crystalline quality CeO₂ buffer layers epitaxied on (1 1 0 2) sapphire for YBa₂Cu₃O₇-thin films, J. Cryst. Growth 187 (1998) 211–220, https://doi.org/10.1016/S0022-0248(97) 00857-9.

[23] M. Spanková, I. Vávra, Š. Gaži, D. Machajdík, Š. Chromik, K. Fröhlich, L. Hellemans, S. Benacka, Growth and recrystallization of CeO₂ thin films deposited on R-plane sapphire by off-axis RF sputtering, J. Cryst. Growth 218 (2000) 287–293, https://doi.org/10.1016/S0022-0248(00)00585-6.

[24] S.H. Bang, J.H. Cho, H.K. Kim, H.J. Cho, X-ray reflectivity studies of highly crystalline CeO₂ films on (1 1 0 2) Al₂O₃, Appl. Surf. Sci. 174 (2001) 257–260, https://doi.org/10.1016/S0169-4332(01)00174-X.

[25] S. Chromik, M. Cannaerts, Š. Gaži, C. Van Haesendonck, M. Spanková, P. Kús, S. Benáčka, The influence of (1 1 0 2) sapphire substrate on structural perfection of CeO₂ thin films, Phys. C Supercond. 371 (2002) 301–308, https://doi.org/ 10.1016/S0921-4534(01)01098-X.

[26] G. Linker, R. Smithey, J. Geerk, F. Ratzel, R. Schneider, A. Zaitsev, The growth of ultra-thin epitaxial CeO₂ films on r-plane sapphire, Thin Solid Films 471 (2005) 320–327, https://doi.org/10.1016/j.tsf.2004.05.126.

[27] Y. Kimura, O. Michikami, S. Fujiwara, K. Sunagawa, Y. Yaguchi, EuBa₂Cu₃O₇ films grown on vicinal R-Al₂O₃ substrates with CeO₂ buffer layers by magnetron sputtering, Phys. C Supercond. 468 (2008) 1847–1850, https://doi.org/10.1016/j. physc.2008.05.098.

[28] Y. Ota, K. Kikuchi, S. Fujiwara, Y. Unuma, Y. Kimura, O. Michikami, Effect of sputter gas pressure and RF power on surface morphology of CeO₂ buffer layers and superconducting properties of EuBa₂Cu₃O₇-δ thin films by magnetron sputtering, Jpn. J. Appl. Phys. 47 (2008) 1559–1562, https://doi.org/10.1143/ JJAP.47.1559.

[29] M. Sunder, P.D. Moran, How r-plane Al₂O₃ surface modifications impact the growth of epitaxial (0 0 1) CeO₂ thin films, J. Electron. Mater. 38 (2009) 1931–1937, https://doi.org/10.1007/s11664-009-0864-6.

[30] D.S. Bick, S.U. Sharath, I. Hoffman, M. Major, J. Kurian, L. Alff, (001) and (111) single-oriented highly epitaxial CeO₂ thin films on r-cut sapphire substrates, J. Electron. Mater. 44 (2015) 2930–2938, https://doi.org/10.1007/s11664-015- 3728-2.

[31] S. Yamamoto, M. Sugimoto, H. Koshikawa, T. Hakoda, T. Yamaki, Orientational control of CeO₂ films on sapphire substrates grown by magnetron sputtering, J. Cryst. Growth 468 (2017) 262–267, https://doi.org/10.1016/j. jcrysgro.2016.12.038.

[32] P. Prete, D. Calabrisso, E. Burresi, L. Tapfer, N. Lovergine, Lattice strain relaxation and compositional control in As-rich GaAsP/(100)GaAs heterostructures grown by MOVPE, Materials 16 (2023) 4254, https://doi.org/10.3390/ma16124254.

[33] S. Mahieu, P. Ghekiere, D. Depla, R. De Gryse, Biaxial alignment in sputter deposited thin films, Thin Solid Films 515 (2006) 1229–1249, https://doi.org/ 10.1016/j.tsf.2006.06.027.

[34] J.A. Thornton, Influence of apparatus geometry and deposition conditions on the structure and topography of thick sputtered coatings, J. Vac. Sci. Technol. 11 (1974) 666–670, https://doi.org/10.1116/1.1312732.

[35] J.A. Thornton, The microstructure of sputter-deposited coatings, J. Vac. Sci. Technol. Vac. Surf. Films 4 (1986) 3059–3065, https://doi.org/10.1116/1.573628.

[36] J.W. Matthews, A.E. Blakeslee, Defects in epitaxial multilayers: I. Misfit dislocations, J. Cryst. Growth 27 (1974) 118–125, https://doi.org/10.1016/S0022- 0248(74)80055-2.

[37] J.C. Goldsby, Basic elastic properties predictions of cubic cerium oxide using first-principles methods, J. Ceram. 2013 (2013) 1–4, https://doi.org/10.1155/2013/ 323018.