# Ferroelectricity in Single-Crystalline BaTiO3 Nanodisks on Silicon

Ibukun Olaniyan, Jürgen Albert, Beatriz Canabarro, Haidong Lu, Sven Wiesner, Nikolay Cherkashin, Alexei Gruverman, Sylvie Schamm-Chardon, Dong-jik Kim, Catherine Dubourdieu

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Ibukun Olaniyan, Jürgen Albert, Beatriz Canabarro, Haidong Lu, Sven Wiesner, et al. Ferroelectricity in Single-Crystalline BaTiO3 Nanodisks on Silicon. Advanced Functional Materials, 2025, 10.1002/adfm.202507905. hal-05202953

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# Ferroelectricity in Single-Crystalline BaTiO₃ Nanodisks on Silicon

Ibukun Olaniyan,* Jürgen Albert, Beatriz Canabarro, Haidong Lu, Sven Wiesner, Nikolay Cherkashin, Alexei Gruverman, Sylvie Schamm-Chardon, Dong-Jik Kim, and Catherine Dubourdieu*

The miniaturization of ferroelectrics with lateral size reduction is crucial for technological advancement but requires an understanding of the fundamental behavior of ferroelectrics at the nanoscale. While much attention has been focused on vertical scaling of perovskite ferroelectrics with thickness reduction, lateral scaling remains less explored. In this study, ferroelectricity is investigated in 20 nm thick single-crystalline BaTiO₃ nanodisks with a diameter ranging from ≈ 400 down to 100 nm. They are fabricated by Ne ion milling of a 20 nm BaTiO₃ film epitaxially grown on SrTiO₃-buffered silicon. The nanodisks are ferroelectric with a Curie temperature in the range 230–270 °C as determined by temperature-dependent piezoresponse force microscopy. In 100 nm-diameter nanodisks, the vertical polarization component adopts three distinct patterns in the pristine state, aligning with theoretical predictions. The most prevalent pattern features a uniformly up-oriented vertical component. The rotational invariance of these domain patterns in the plane suggests a combination of center-type and flux-closure domains. Additionally, the up polarization can be switched progressively to down polarization upon application of a pulsed bias of increasing time width. The control of the polarization in nanostructures and of their progressive switching is of particular interest for memory applications.

## 1. Introduction

The switchable polarization of ferroelectric perovskite oxides makes them attractive for designing devices such as capacitors, tunnel junctions, or field-effect transistors for nonvolatile memory and logic applications.[1,2] Their diverse functional properties are also of interest, such as piezoelectricity for micro/nanoactuators,[3] pyroelectricity for energy harvesting,[4] and bulk photovoltaicity for photonic applications.[5] The monolithic integration of perovskite oxides on silicon gives the possibility to harness these various functionalities on the ubiquitous complementary metal-oxide-semiconductor (CMOS) technology platform.[6–10] Integration into nanoelectronics (such as ferroelectric capacitors, tunnel junctions or field-effect transistors for neuromorphic computing) requires miniaturizing the perovskite materials on silicon, while still retaining their switchable polarization and understanding/controlling the domain pattern.[9,10]

The effect of thickness reduction on the ferroelectricity of perovskite thin films has been extensively studied both theoretically and experimentally.[11–18] The stabilization of an out-of-plane polarization in ultrathin films (despite the depolarization field) and its switchability depend on the electrical, mechanical, and chemical boundary conditions, which determine the ability to screen the bound charges at the interfaces with the ferroelectric.[14,19] Experimentally, room temperature ferroelectricity has been observed in ultrathin films epitaxially grown on SrTiO₃ substrates, including 2 nm-thick BiFeO₃,[15] 1.5 unit-cell-thick PZT,[16] 2.6 nm-thick PbTiO₃.[18] For BaTiO₃, ferroelectricity was reported in thin films of 2.4 nm-thick[17] and down to 1 nm-thick films[20] in ferroelectric tunnel junctions. On silicon, ferroelectricity in BaTiO₃ films (with a switchable polarization) has been observed down to 4 unit cells (1.6 nm), with ferroionicity playing a major role.[21] For such ultrathin films, the asymmetry in top and bottom interfaces leads to a clear preferred polarization orientation, which can nevertheless be switched under an applied electric field.[21]

What happens when dimensions are reduced in three dimensions? Ferroelectric nanoparticles/nanocrystals, either free standing[22–25] or attached to a conducting substrate,[26] are model

I. Olaniyan, J. Albert, S. Wiesner, D.-J. Kim, C. Dubourdieu
Institute Functional Oxides for Energy Efficient Information Technology
Helmholtz-Zentrum Berlin für Materialien und Energie GmbH
Hahn-Meitner-Platz 1, 14109 Berlin, Germany
E-mail: olaniyan@helmholtz-berlin.de;
catherine.dubourdieu@helmholtz-berlin.de

I. Olaniyan, C. Dubourdieu
Physical and Theoretical Chemistry
Freie Universität Berlin
Arnimallee 22, 14195 Berlin, Germany
B. Canabarro, N. Cherkashin, S. Schamm-Chardon
CEMES-CNRS and Université de Toulouse
29 rue Jeanne Marvig, Toulouse 31055, France
H. Lu, A. Gruverman
Department of Physics and Astronomy
University of Nebraska
Lincoln, NE 68588, USA

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The ORCID identification number(s) for the author(s) of this article can be found under https://doi.org/10.1002/adfm.202507905

© 2025 The Author(s). Advanced Functional Materials published by Wiley-VCH GmbH. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

DOI: 10.1002/adfm.202507905
systems for the study of ferroelectricity at the nanoscale. Quadrants of 90° stripe domains were reported in free standing meso- and nanoscale BaTiO₃ dots fabricated by Ga-focused ion beam, milled from BaTiO₃ single crystals.[24] The stripe domains were interpreted as some hierarchical twin boundaries oriented in a self-confined way.[24] A center-converging domain pattern was observed by PFM in ≈160 nm cubic-shaped BaTiO₃ nanocrystals.[26] In a 160 nm nanoparticle from a powder, the 3D structure of a vortex pattern was imaged by Bragg coherent diffraction imaging.[22] Recently, BaTiO₃ nanoparticles of ≈ 8–10 nm analysed by atomic electron tomography using scanning transmission electron microscopy revealed a 3D polar topological ordering, along with size-dependent transitions from a single vortex state to multiple vortices.[23] Free standing nanoparticles are, however, not practical for nanoelectronic applications. They are mainly studied by TEM techniques[23,24,27–29] or have to be embedded in a matrix for PFM studies.[22] Nanostructures fabricated on a substrate, such as nanodisks, nanoislands, or nanodots, are much better suited for integration into nanoelectronics devices and are suitable systems to study the effect of lateral size reduction by techniques such as piezoresponse force microscopy (PFM) and spectroscopy. Initial experimental studies in the late 1990's and early 2000's have focused on polycrystalline nanostructures,[30–34] but their inherent structural inhomogeneity leads to randomness in the ferroelectric properties and does not allow for the design of controlled polarization domain patterns. Therefore, epitaxial ferroelectric nanostructures are of greater interest for potential nanoelectronic applications, particularly those based on topological polar states. The theoretical predictions of the possible emergence of complex polar textures in these systems have triggered a renewed interest in epitaxial nanostructures on oxide substrates.[35–41]

Most experimental studies on ferroelectric epitaxial nanostructures have focused on Pb- or Bi-based compounds on SrTiO₃ substrates.[42–51] For nanoelectronic applications, BaTiO₃ may be more suitable as it is Pb free (Ph is a toxic element) and Bi free (Bi is a volatile element that is not welcome in an industrial clean room environment). The Curie temperature (T_c) of bulk BaTiO₃ (120-130 °C[52]) is (too) close to the typical 85 °C that microelectronic devices need to sustain. However, strained BaTiO₃ thin films exhibit larger Curie temperatures[53–55] and therefore there is the potential that nanostructures also exhibit a larger T_c than the bulk.

There are very few experimental works on reduced lateral dimensions in single crystalline BaTiO₃ nanostructures on an oxide substrate[56] and on silicon.[57] In pyramidal BaTiO₃ nanostructures on Nb:SrTiO₃ substrates, a strong imprint, both horizontally and vertically, was evidenced with highly slanted hysteresis loops (piezoresponse close to zero under positive bias); no information was reported on the domain pattern in these pyramids.[56] Recent work demonstrated topological polar chiral domains in trapezoidal 30–60 nm wide epitaxial BaTiO₃ nanoislands grown on silicon.[57] This severe lack of experimental realizations is probably due to the difficulty in shaping single crystalline BaTiO₃ nanostructures, whether by bottom-up or top-down approaches.

In this study, we investigate ferroelectricity and polarization patterns of BaTiO₃ single crystalline nanodisks on silicon, with a 20 nm height and a sub-500 nm diameter. The disks are com-

posed of a single crystalline core surrounded by an amorphized shell. The single crystalline region is ferroelectric for all investigated diameters (≈ 400 down to 100 nm) with in-plane and out-of-plane polarization components. The proportion of upward versus downward polarization increases with decreasing diameter. In 100 nm-diameter nanodisks, the vertical polarization component in the pristine state exhibits three distinct patterns, consistent with theoretical predictions. The in-plane rotational symmetry of these patterns suggests a coexistence of center-type and flux-closure domains. The most prevalent pattern has a uniformly up-oriented vertical component, which can be reversibly switched under a DC field. Moreover, the polarization switching can be progressively performed by applying pulses of varying time width. The intermediate states are stable for several hours. The ability to shape nanostructures with control of the out-of-plane polarization direction and on its progressive reversal is of much interest for future analog memory design.

## 2. Results

### 2.1. Fabrication of Single Crystalline BaTiO₃ Nanodisks on Silicon

BaTiO₃ nanodisks were fabricated by Ne ion milling starting from an epitaxial 20 nm BaTiO₃ film on a 4 nm SrTiO₃-templated Si substrate (Figure 1a). The X-ray diffraction (XRD) patterns of the epitaxial film are shown in Figure 1b,c, and Figure S1 (Supporting Information). The BaTiO₃ and SrTiO₃ cells are rotated by 45 degrees in-plane relative to the Si one. The epitaxial relationship is [110] BaTiO₃// [110] SrTiO₃ // [100] Si and (001) BaTiO₃ // (001) SrTiO₃ // (001) Si. The average out-of-plane and in-plane lattice parameters are 4.068 and 3.996 Å, respectively, indicating that the c-axis of the tetragonal cell is oriented mainly out-of-plane (c-domains). The expanded out-of-plane lattice parameter compared to the bulk one (4.038 Å[58]) and related enhanced average tetragonality of 1.018 (the bulk value is 1.01) are typical for epitaxial 10–20 nm BaTiO₃ on Si.[9,10] The presence of a-domains (the c-axis of the unit cell is oriented in-plane) is evidenced by Raman spectroscopy (Figure 1d) with the occurrence of the A₁(TO₃) mode at 521 cm⁻¹.[59,60] The modes at 476 and at 723 cm⁻¹, the E(LO₃)/A(LO₂) and E(LO₄)/A(LO₃) respectively, are indicative of c-domains.[59,60] The a-domains appear as a result of the competition between compressive stress from epitaxy and tensile stress occurring during cooling the sample from the growth temperature down to room temperature. High-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) images of the stack are shown in Figure 1e,f. The SiOₓ layer at the interface between SrTiO₃ and Si results from the oxygen diffusion down to Si during the BaTiO₃ deposition.[9,61] The interface between the BaTiO₃ and SrTiO₃ films is atomically sharp as shown in Figure 1f.

Nanosdisks were fabricated by Ne ion milling in a helium ion microscope (see Experimental Section). The focused ion beam was used to mechanically etch out the BaTiO₃/SrTiO₃ bilayer and part of the Si substrate (Figure 2a). We recently reported a detailed investigation on the fabrication of nanopillars starting from a BaTiO₃ single crystal.[62] We explored the different parameters of the milling (beam energy, dose, patterning style) to control the shape of the nanopillars and minimize the damage inherent to ion irradiation.[62] We showed that the backscattering
<figure><img src="image_4.png" /><figcaption>**Figure 1.** a) Schematic of the BaTiO₃/SrTiO₃/Si heterostructure. θ-2θ XRD patterns of the heterostructure in b) the out-of-plane configuration and c) the in-plane configuration. d) Raman spectrum of the heterostructure. The Gaussian fitting was carried out between 430 and 850 cm⁻¹, and the fitted modes are shown in colors. e) Low resolution and f) high resolution cross-sectional (110)Si high-angle annular dark-field STEM images of the heterostructure.</figcaption></figure>

of Ne ions leads to the amorphization of the side and top of the nanostructures. Here, to avoid amorphization of the top of the thin BaTiO₃ layer, we added a top Au/W hardmask, which was subsequently removed after fabrication using a KI solution. Regarding the amorphized shell around the nanodisks, we see it as an advantage to achieve small dimensions for the crystalline core and to provide reproducible boundary conditions no matter the atmosphere and humidity conditions.

Representative scanning electron microscopy (SEM) images of nanodisks are shown in Figure 2b. The targeted diameters were 200, 300, 400, and 500 nm, and the resultant ones were 180, 270, 380, and 480 nm, respectively. The pores observed in the trenches of the milled area (Figure 2b) are the result of Ne ion interstitial aggregation below the silicon surface, forming bubbles which eventually lead to the fracture of the material as the pressure increases.[63] This phenomenon is analogous to the formation of pores in many materials, e.g. GaAs, Si, Cu, by Ga or He ion milling.[64–66]

The energy dispersive X-ray spectrometry (EDX) analyses (Figure 2c) confirm the presence of BaTiO₃ and the complete removal of the hardmaks (W/Au) used for the fabrication.

The low-resolution HAADF STEM image (Figure 2d) shows the amorphized sides surrounding the crystalline region both in the silicon substrate and in the BaTiO₃/SrTiO₃ heterostructure.

High-resolution HAADF STEM images prove that the crystalline regions are well-ordered with no notable damage except in the regions near the amorphous sides (Figure 2e; Figure S2, Supporting Information). The amorphized regions at the sidewall of the nanodisks are caused by backscattered ions from the trench being milled.

## 2.2. Size Effect on Ferroelectricity and Domain Patterns

In the following, the dimension given for the nanodisks is the diameter of the crystalline part, which is smaller than the disk diameter due to the amorphous shell (see Figure 2d). These dimensions have been determined from STEM images and from the PFM images since the amorphous shell has only a negligible piezoresponse (as shown in Figure S3, Supporting Information). The crystalline nanodisks under study have diameters of ≈ 410, 310, 210, and 100 nm. Note that the amorphized shell created by Ne ion milling is conducting, as shown by conductive atomic force microscopy (Figure S4, Supporting Information), which is attributed to the creation of oxygen vacancies during the ion bombardment.

**Figure 3a–j** shows the off-field switching spectroscopy PFM (SSPFM) amplitude, phase, and resulting hysteresis loops
<figure><img src="image_5.png" /><figcaption>**Figure 2.** a) The fabrication process of the nanodisks. b) SEM images of nanodisks of different lateral sizes. c) EDX maps of a 180 nm nanodisk. d) Low resolution HAADF STEM image of a nanodisk. e) High resolution HAADF STEM image of the part highlighted in red in (d).</figcaption></figure>

acquired on the BaTiO₃ thin film and at the center of the nanodisks. All loops were measured in the same session and with the same tip.

It is well known that ferroelectric-like hysteresis loops can be obtained in non-ferroelectric materials due to electrostatic interaction between the tip and the sample, charge injection, surface charging, and/or ionic motions.[67-69] Hence, SSPFM temperature-dependent measurements were performed on the film, and on the 410 and 100 nm nanodisks. They are shown in **Figure 4**. The hysteresis loops disappear above a certain temperature (250 °C < T_c < 270 °C for the film and 410 nm nanodisk, and 230 °C < T_c < 250 °C for the 100 nm nanodisk), which is a strong indication of a ferroelectric to paraelectric phase transition. The phenomenon is fully reversible. In Figure S5a (Supporting Information), we show the PFM images of the nanodisks with their surroundings. The silicon substrate around the nanodisks has approximately zero PFM amplitude. The SSPFM measurements performed on the milled substrate also show no sign of ferroelectricity (Figure S5b,c, Supporting Information). In Figure S6 (Supporting Information) we show PFM images for different temperatures recorded before the hysteresis loop measurements shown in Figure 4 (due to a severe drift of the atomic force microscope scanner, it was extremely difficult to get reli-

able PFM images of the nanodisks at elevated temperatures). The PFM amplitudes from the nanodisk and its surrounding substrate become comparable at 270 °C (Figure S6, Supporting Information). Temperature-dependent Raman spectroscopy measurements performed on the thin film and on a (001) BaTiO₃ single crystal (as reference) support that the T_c of the BaTiO₃ thin film is larger than 227 °C (Figure S7, Supporting Information). Hence, we conclude that the responses measured in SSPFM and in PFM originate from the ferroelectricity in the BaTiO₃ heterostructure and in the nanodisks.

The BaTiO₃/SrTiO₃/SiOₓ/Si heterostructure exhibits a hysteresis loop (Figure 3a,f) similar to the ones reported previously for the same system.[10,61] It shows a positive shift along the applied bias axis (horizontal imprint) and a negative shift along the d<sub>zz</sub> piezoresponse axis (vertical imprint) indicating asymmetries in the polarization switching.

The largest nanodisks (diameter of 410, 310, and 210 nm) show similar hysteresis loops as the BaTiO₃ continuous film, with slightly increased imprints both horizontally and vertically. The piezoresponse for the 100 nm disks (with two minima of the d<sub>zz</sub> amplitude response measured for positive biases) is attributed to back-switching of the polarization due to a strong built-in internal field. Hysteresis loops measured at other
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Local PFM spectroscopy amplitude and phase responses as well as hysteresis loops of a,f) thin film, b,g) 410 nm nanodisk, c,h) 310 nm nanodisk, d,i) 210 nm nanodisk, and e,j) 100 nm nanodisk. Size dependence of k) the horizontal imprint and l) the vertical imprint.</figcaption></figure>

locations of this nanodisk (not at the center) show the presence of a down-oriented polarization but much smaller compared to the larger nanodisks (see Figure S8, Supporting Information). Imaging the 100 nm nanodisks after writing a domain of downward polarization shows back-switching at many locations (see Figure S9, Supporting Information). It is also observed in the film, as shown in Figure S10 (Supporting Information), but is more prominent in the 100 nm nanodisks. Note that similar strongly shifted hysteresis loops along the x-axis have been observed in La<sub>0.7</sub>Sr<sub>0.3</sub>MnO<sub>3</sub>/3 nm BaTiO<sub>3</sub>/Au ferroelectric tunnel junctions by SSPFM[70] and in SrRuO<sub>3</sub>/100 nm BaTiO<sub>3</sub>/SrRuO<sub>3</sub> microscale capacitors by standard polarization-voltage measurements.[71] Lee et al. have also reported that one of the polarization states was hardly detectable in SrRuO<sub>3</sub>/12
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Temperature dependent SSPFM of a) 20 nm epitaxial BaTiO₃ thin film on 4 nm SrTiO₃-buffered Si, b) 410 nm nanodisk, and c) 100 nm nanodisk.</figcaption></figure>

u.c. (4.8 nm) BaTiO₃/Au because the retention time was too low.[72]

In Figure 5, we show the PFM amplitude and phase images of the nanodisks in the vertical and lateral modes as well as the topography images associated with the PFM measurements. The nanodisks have a smooth surface (Figure S11, Supporting Information), with a root-mean-square roughness of less than 0.90 nm, allowing us to rule out crosstalk between the observed PFM signals and the topography. In the vertical phase (V-phase) image, the dark and bright contrast corresponds to the upward ($P_{up}$) and downward ($P_{down}$) projections of the polarization, respectively. In the lateral phase (L-phase) image, due to the ambiguity in determining the actual polarization direction, we assigned bright and dark contrast to represent the right-pointing ($P_{right}$) and left-pointing ($P_{left}$) lateral polarization, respectively.

There is a clear preferred $P_{up}$ polarization in the pristine state of the largest nanodisks (410 nm) and a systematic increase in the domain fraction of $P_{up}$ at the expense of $P_{down}$ with the decrease of the nanodisk diameter.

The 100 nm disks exhibit a full upward polarization in the pristine state (see V-phase in Figure 5d). Overall, three distinct domain patterns in the 100 nm nanodisks were observed and are presented in Figure 6. The domain pattern in Figure 6a is

observed in 6 out of 8 nanodisks, which likely corresponds to the ground state (Figure S12, Supporting Information). There is a uniform vertical $P_{up}$ component. Regarding the lateral component, there is a mixture of left and right components with no particular pattern, as shown for five other nanodisks in Figure S12 (Supporting Information). Another occurring domain pattern (Figure 6b) exhibits half dark/half bright domains in V-phase, corresponding to $P_{up}$ and $P_{down}$ orientations respectively, and a stripe-like pattern laterally, alternating $P_{left}$ and $P_{right}$. The third type of pattern, shown in Figure 6c, has a core $P_{down}$ domain embedded in a $P_{up}$ matrix and a roughly half-$P_{right}$/half-$P_{left}$ lateral orientation.

We found that the domains in 100 nm nanodisks have a symmetry with azimuthal rotation, as shown in Figures 7 and S13 (Supporting Information). Given that the lateral PFM detects only the projection of the polarization perpendicular to the cantilever axis, the lateral domain image depends on the azimuthal angle between the sample and the cantilever axis. While the vertical domain pattern does not depend on the azimuthal angle as expected, the lateral domain shapes are rotated by 90° following exactly the 90° rotation of the sample. Such a rotation of a domain pattern occurs for flux-closure rotational patterns and for center-type patterns, as illustrated in Figure S14 (Supporting
<figure><img src="image_8.png" /><figcaption>**Figure 5.** Topography and PFM images of the pristine nanodisks of diameter a) 410 nm, b) 310 nm and c) 210 nm, and d) 100 nm. The vertical piezoresponse amplitude and phase are labelled as V-amp and V-phase, respectively, while the lateral piezoresponse amplitude and phase are labelled as L-amp and L-phase, respectively. The nanodisks' orientation relative to the cantilever (in grey) is shown in the bottom-right corner. The white arrow indicates the fast scan direction.</figcaption></figure>

Information). In the flux-closure pattern, the lateral domain wall should be perpendicular to the cantilever axis, whereas in the center-type pattern, the lateral domain wall should be parallel to the cantilever axis. Given that the observed lateral domain wall does not exactly align parallel or perpendicular to the cantilever axis, we infer that the polar textures in Figure 6a,b might be a mixture of center-type and flux-closure patterns.

For the pattern shown in Figure 6c, both a bubble domain and a cylindrical domain can give rise to such a V-phase image. A bubble domain possesses a complex 3D pattern with both vertical and lateral polarization components[73] and does not extend vertically to the bottom of the sample. A cylindrical domain has only a vertical polarization that is opposite to the surrounding medium. A bubble domain typically exhibits a fuzzy domain wall, whereas the cylindrical domain displays a sharp 180° domain wall in the vertical polarization component.[74] The presence of lateral polarization components in Figure 6c indicates that the polarization pattern is not that of a simple cylindrical configuration.

## 2.3. Electric Field Tuning and Switching of the Polarization Pattern

The vertical component of the polarization in the 100 nm disks can be switched from $P_{up}$ to $P_{down}$ by applying a DC electrical field, and the uniform $P_{down}$ state can be electrically reversed back to a uniform $P_{up}$ state as shown in Figure S15 (Supporting Information). Moreover, the fraction of $P_{up}$ and $P_{down}$ can be electrically tuned by applying pulses of varying duration. Figure 8

shows the sequence of polarization states achieved by applying different pulse widths of 8 V to the tip located at the center of a 100 nm nanodisk. The pristine domain image exhibits uniform $P_{up}$ with a dominant $P_{right}$ lateral component. Through sequential electrical pulses, the $P_{up}$ is progressively switched to $P_{down}$. The nucleation of the $P_{down}$ occurs under the tip, and with subsequent pulses, the $P_{down}$ core domain grows laterally until the nanodisk is fully switched. The lateral polarization component also switches, forming stripes of opposite directions (alternating dark and bright stripes contrast in L-phase images of Figure 8c) and eventually forming two domains (half bright/half dark) of opposite direction when the nanodisk is fully switched (Figure 8d). The rotation of the fully switched nanodisk by 90 degrees shows that the lateral domain pattern also rotates by 90 degrees (Figure S16, Supporting Information). This half/half pattern in L-phase indicates that this configuration corresponds to a center-type domain pattern,[57,75] which is clearly different from the pristine state and results from writing a $P_{down}$ domain in a progressive way.

We considered the possibility that the localized high electric field of the PFM tip during pulsing could lead to effects that resemble a polarization switching-like response.[67–69] The topography of the nanodisk remained unchanged throughout the sequential poling, indicating no crosstalk between the PFM signal and the surface topography. Moreover, the zero PFM amplitude response at the domain walls between the switched and unswitched regions, along with the clear in-plane polarization switching, indicates that the PFM images in Figure 8 arise from polarization switching and not from tip-induced artifacts.
<figure><img src="image_9.png" /><figcaption>**Figure 6.** PFM images showing V-amp, V-phase, L-amplitude, and L-phase maps obtained from three different 100 nm nanodisks. The domain patterns show a) P<sub>up</sub> and mixture of P<sub>left</sub>/P<sub>right</sub>, b) half-P<sub>up</sub>/half-P<sub>down</sub> and stripe-like pattern of P<sub>left</sub>/P<sub>right</sub>, c) P<sub>down</sub> embedded in P<sub>up</sub> matrix and half-P<sub>right</sub>/half-P<sub>left</sub>. The nanodisks' orientation relative to the cantilever (in grey) is shown in the bottom-right corner. The white arrow indicates the fast scan direction.</figcaption></figure>

Notably, the written domains remain stable for at least 10 h after switching, as shown in Figure S17 (Supporting Information).

### 3. Discussion

In this work, we investigate the ferroelectricity of 20 nm-thick BaTiO₃ epitaxial nanodisks on silicon, with diameter ranging from 410 down to 100 nm. The ferroelectricity is ascertained by the temperature-dependent PFM experiments, which show a transition from a ferroelectric to a non-ferroelectric phase. The Curie temperature T_c of the epitaxial BaTiO₃ heterostructure is comprised between 250 and 270 °C. Note that there is so far, to the best of our knowledge, no report of T_c values for epitaxial BaTiO₃ thin films on silicon. The Curie temperature of epitaxial BaTiO₃ depends largely on the film thickness and strain imparted by the substrate. Much larger T_c values than the bulk one (120–130 °C/393–403 K) have been reported experimentally for coherently strained films on oxide substrates: ≈ 654 °C (≈ 927 K) for a 10 nm film on SrTiO₃,[55] 400 °C (673 K) and 540 °C (813 K) for 200 nm films with a SrRuO₃ bottom electrode on GdScO₃ and DyScO₃, respectively.[53] These values are in good agreement with those calculated by phase field modelling.[76] However, defects can also impact T_c. Fully strained 130–170 nm films on

GdScO₃ with a SrRuO₃ bottom electrode grown under different pulsed laser deposition conditions exhibit different phase transition temperatures (~500 °C (773 K), ~650 °C (923 K), and ~800 °C (1073 K)).[77] These enhanced values compared to the study of Choi et al.[53] were attributed to an additional enhanced strain state due to epitaxial strain-induced alignment of defect dipoles created during the growth.[77] These T_c values are for relatively thick films (≥ 100nm). The Curie temperature decreases with decreasing film thickness due to the increasing effect of the depolarization field. For 25 nm- and 12.5 nm-thick BaTiO₃ with top and bottom SrRuO₃ electrodes and GdScO₃ substrate, Jiang et al. measured a T_c value of 190 °C (463 K) and 150 °C (423 K), respectively.[71] BaTiO₃ films on silicon are not coherently strained but exhibit significant strain relaxation. BaTiO₃ films (typically 10–20 nm in thickness) show a complex strain pattern, reflecting an inhomogeneous strain distribution both laterally and throughout the thickness.[9] We show in Figure S18 (Supporting Information) typical in-plane and out-of-plane strain maps as well as lattice parameter profiles. The in-plane lattice parameter increases progressively, and the corresponding in-plane strain is in the range of –1.8 to +0.4%. The out-of-plane lattice parameter profile depends very much on the location in the film, while the composition is constant throughout the thickness, as shown by
<figure><img src="image_10.png" /><figcaption>**Figure 7.** a) PFM images of the nanodisk shown in Figure 6a, acquired at azimuthal rotation angles of 0° and 90°. b) PFM images of the nanodisk shown in Figure 6b, acquired at azimuthal rotation angles of 0° and 90°. The nanodisks' orientation relative to the cantilever (in grey) is shown on the right side of the images. The white arrows indicate the fast scan direction.</figcaption></figure>

EELS elemental profile measurements (Figure S19, Supporting Information). Overall, throughout the thickness, there is a mixture of *c*- and *a*-domain orientation. Dislocations are also observed not only at the interface with the SrTiO₃ buffer layer but also in the BaTiO₃ film, adding complexity to the strain pattern. The T_c comprised between 250 and 270 °C is consistent with an overall low strain[76] and is quite high considering the low thickness of 20 nm. The slightly lower T_c for the 100 nm disks (be-

tween 230 and 250 °C) is coherent with a lower strain state expected on the free sides of the nanodisk compared to a thin film.

Let us now discuss the switching behavior and the polarization pattern in the nanodisks. The nanodisks show horizontal and vertical imprints in the SSPFM hysteresis loops, larger than in the reference film. Horizontal imprint has been observed in epitaxial BaTiO₃ thin films on oxide substrates[70–72,77–79] and on Si,[21,61] as well as in single crystalline BaTiO₃ nanowires[80] and
<figure><img src="image_11.png" /><figcaption>**Figure 8.** Topography and PFM images (amplitudes and phases for vertical and lateral modes) of a 100 nm nanodisk showing the domain pattern evolution: a) Pristine state, and after applying 8 V pulses (through the tips) for b) 60 ms, c) 300 ms, and d) 1300 ms. The nanodisk orientation relative to the cantilever (in grey) is shown in the bottom-right corner. The white arrow indicates the fast scan direction.</figcaption></figure>

nanostructures.[56] It is ascribed to internal bias fields (or built-in fields) that can originate from various sources: strain gradient in the film, defect dipoles, trapped charges, interface effects such as band bending at the bottom interfaces and different bound charge screening ability due to the asymmetry of the top and bottom interfaces and asymmetry in domain pinning (related to, e.g., specific defects). Vertical imprint measured in SSPFM loops (larger amplitude of $d_{z2}$ for one of the biases) has been reported in epitaxial BaTiO$_3$ thin films on oxide[72,81] and on Si[10,21] and in BaTiO$_3$ pyramidal nanostructures.[56] It indicates a preferred polarization orientation, possibly due to an asymmetry in the screening ability of the polarization bound charges at the top and bottom interfaces (including an asymmetry in trapped charges at the interfaces) and/or to localized defect dipoles, or strain gradient (same origin as the horizontal imprint). The vertical imprint may also originate from the presence of a non-switching part of the layer (frozen polarization).[82,83] In our systems, the asymmetry in interfaces and their natures (the bottom interface of BaTiO$_3$ is with SrTiO$_3$-$\delta$/SiO$_x$/p-type Si and the top one with air) as well as the strain gradient/relaxation likely play a major role in defining the preferred up-polarization direction. In the smallest nanodisks (100 nm), the imprint is significantly increased, which could be

due to an increased flexoelectricity contribution as the free surface contributions increase.[84]

Three configurations are observed for the vertical component of the polarization in the pristine state (Figure 6): a uniform upward orientation, a half up/half down domain configuration, and a core/shell configuration. These three states are exactly those predicted by Martelli et al. for cylindrical nanodots[40] of a unipolar ferroelectric, and were named monodomain state, two-band state, and concentric cylindrical state, respectively. Note that the nanodots in Martelli et al.,[40] considered to be embedded in a dielectric matrix have much smaller dimensions (radius $r \approx 8$ nm and of thickness $h \approx 1.7$ nm) but a quite similar aspect ratio. A major difference, though, is that our nanodisks also exhibit a lateral polarization component in all stabilized configurations (note that the sidewalls are conducting in our case), while the simulated nanodots do not.

For the domain pattern with a single vertical orientation (Figure 6a), this latter is opposite to the one observed in epitaxial BaTiO$_3$ nanoislands on silicon.[57] One can question the possible role of the shape in defining the polarization orientation. The nanoislands in Ref. [57] have a down-convergent trapezoidal shape, while here the shape is that of a straight
cylinder, or slightly up convergent tapered. The shape may have an influence through flexoelectricity. However, there are many multiple factors that determine the preferred polarization orientation, such as the processing conditions (temperature and oxygen partial pressure), the nature and the termination of the substrate/template and of the top surface, and the defect chemistry.[85] Ultrathin $BaTiO_3$ films on $La_{0.7}Sr_{0.3}MnO_3$ with a top Au electrode exhibit, for example, a down polarization.[72] The exposure of the same film to humidity leads to an upper layer pinned with up polarization.[72] Our nanodisk top surfaces are exposed to air, thus making the role of humidity in defining the preferred up-polarization orientation likely non negligible.

Let us consider the polarization patterns for the continuous film and the nanodisks. It is interesting to note that the film does not show a preferred vertical polarization orientation in the pristine state but rather an almost half/half distribution of up and down components (see Figure S10a, Supporting Information). Once a bias has been applied, the preferred-up polarization emerges. There are also lateral components of polarization as expected from the mixed *c*- and *a*-domain orientation determined by Raman spectroscopy (Figure 1d). The largest nanodisks exhibit a mixture of up and down vertical components with a much-preferred $P_{up}$ component and one preferred orientation for the lateral component (Figure 5). The decrease of the diameter down to 100 nm leads to a unique $P_{up}$ component and to a mixture of left/right lateral components. The pattern of the in-plane polarization is quite diverse and complex (Figure 6; Figure S12, Supporting Information), which may be due to defects (e.g., dislocations and Ne interstitials) freezing different domain configurations. The conduction of the amorphized shell surrounding the nanodisks (Figure S4, Supporting Information) contributes to electrostatic screening of bound charges along the sidewalls, which helps stabilize the in-plane domain configurations.[86] However, an important property is that all 100 nm disks exhibit a rotational symmetry of their in-plane polarization configuration. As the size of ferroelectric nanostructures decreases, electrostatic boundary conditions become predominant in determining the polarization pattern, leading to the emergence of non-trivial polar patterns, including whirling polar arrangements.[87-89] Experimentally, center-type domains were observed in 60 nm epitaxial $BiFeO_3$ nanodots on $SrTiO_3$ substrate,[75] vortex-antivortex domains in ≈80 nm epitaxial $BiFeO_3$ nanodots $SrTiO_3$ substrate,[49] center-type quad domains in 200 and 500 nm $BiFeO_3$ nanoislands on $LaAlO_3$ substrate,[44,50] vortex[43] and bubble domains[51,90] in epitaxial Pb(Zr,Ti)O₃ nanodots on $SrTiO_3$ substrate. These findings highlight the key role of confinement and boundary conditions in shaping domain configurations in different perovskites.

As highlighted, there is a scarcity of realization for epitaxial $BaTiO_3$[56,57] nanostructures on a substrate, and few studies on nanoparticles/nanocrystals, either free standing[22-24] or attached to a conducting substrate.[26] We observe some stripe domains for some of the 100 nm disks. Stripes are also induced while switching progressively the polarization (Figure 8c), eventually leading to a center convergent polarization configuration, similarly to the one observed in $BaTiO_3$ epitaxial trapezoidal nanoislands on silicon.[57] Phase field modelling taking the different boundary conditions into account would allow a better understanding of the polar domains in the nanodisks.

More experimental realizations are needed with $BaTiO_3$ to discriminate the role of the dimensions, shape, and electrostatic boundary conditions (template, top electrode, or air), especially on silicon. It includes further reducing the size of the nanodisks to below 100 nm. It can be performed by Ne ion milling, but the measurement by PFM becomes quite challenging due to the height of the disks since milling extends into the silicon substrate. Reactive ion etching would provide an alternative route to pursue the miniaturization of nanostructures on Si and would be better suited for large scale integration on silicon. Increasing the tapering of the nanostructures could be a promising path to not only induce polar textures but also chirality.[57]

Finally, let's emphasize that the ability to progressively switch the vertical component of the polarization in a controlled manner under varying pulse widths is of particular interest for realizing multilevel bit memories on silicon.

## 4. Conclusion

We demonstrated that ferroelectricity can be preserved in 20 nm thick single-crystalline $BaTiO_3$ nanodisks with lateral dimensions as small as ≈100 nm, epitaxially integrated on $SrTiO_3$-buffered Si substrate. In the 100 nm-diameter nanodisks, three patterns are observed in the pristine state for the vertical polarization component, which are those predicted theoretically. Out of eight nanodisks, six exhibit a uniform up mono-oriented vertical component. The lateral size reduction gives rise to the emergence of complex domain patterns for the lateral polarization component. The in-plane rotational invariance of the domain patterns points to a mixture of center-type and flux-closure domains. The upward vertical polarization component can be tuned by an external pulsed electric field, enabling multilevel stable polarization states. The ferroelectricity and peculiar polar patterns in Pb-free $BaTiO_3$ nanodisks integrated on Si – with a much larger $T_c$ (230 °C < $T_c$ < 250 °C) than the bulk's one, highlight their potential for CMOS-compatible applications, advancing nanoscale ferroelectrics toward practical device integration.

## 5. Experimental Section

**Epitaxial $BaTiO_3/SrTiO_3$ Heterostructure Fabrication on Silicon:** The 20 nm $BaTiO_3$ thin film was grown on a 4 nm $SrTiO_3$-buffered Si substrate by molecular beam epitaxy (DCA R450 MBE). The 2-inch p-type Si substrate was cleaned at 100 °C for 10 min by a UV/Ozone cleaner applying UV irradiation and $O_3$ together, and immediately loaded into the vacuum chamber. The native $SiO_x$ layer was removed at 870 °C thermally by sending a Sr flux, which was monitored by reflection high-energy electron diffraction (RHEED) until a 2 × 1 reconstructed dimer Si surface appeared. The Si bare surface was then passivated by depositing a ½ monolayer of Sr followed by an annealing at 670 °C in ultra-high vacuum. The $SrTiO_3$ buffer layer was grown by Sr and Ti co-deposition at 380 °C substrate temperature with a molecular $O_2$ partial pressure of 5 × 10⁻⁸ Torr in the MBE reactor and annealed at 490 °C for 20 min without $O_2$ to improve the crystallization of $SrTiO_3$. Then Ba and Ti were co-deposited at 650 °C substrate temperature. During the $BaTiO_3$ growth, the $O_2$ pressure was kept at 5 × 10⁻⁷ Torr. Finally, the sample was cooled down slowly (5 K min⁻¹) with an $O_2$ flow of 5 × 10⁻⁶ Torr.

**Structural Characterization of the Thin Film:** The crystalline structure of the film was characterized by X-ray diffraction using a PANalytical X'Pert PRO diffractometer with a 1D detector (PIXcel) and a Ge (220)
monochromator. 2θ-ω scans at chi angles of 0° (out-of-plane scan) and 89.5° (in-plane scan) were performed. Raman spectroscopy measurements were carried out using a Horiba HR-evolution Raman spectrometer equipped with a 325 nm laser wavelength, ×40 objective (laser spot size ≈1 µm, numerical aperture = 0.49), 1800 | mm⁻¹ grating, and an incident laser power of 0.3 mW.

**Fabrication of the Nanodisks and Imaging:** The nanodisks were patterned by Ne focused ion beam milling. A Zeiss Orion Nanofab helium ion microscope (HIM) with neon as a source of gas was used. The software "Nano Patterning and Visualization Engine" (NPVE), coupled with FIB-o-mat,[91] controlled the ion beam and automated the nanofabrication process. The nanodisks were fabricated with an acceleration voltage of 15 keV, a beam current of ~2 pA, and a beam dose of ≈ 6000–8000 neon ions/nm². The optimized procedure had been developed in a previous dedicated study on shaping BaTiO₃ nanopillars in commercial single crystal substrates.[62] This procedure has been adapted to the milling of thin films. To avoid amorphization of the top surface, a W/Au hard mask was used. To avoid ion implantation damage, scanning electron microscopy (SEM, Zeiss Merlin) was used to image the nanodisks instead of HIM after the nanofabrication. A Bruker (XFlash 61100) X-ray energy dispersive (EDX) system, which was coupled to the SEM, was used for elemental analysis.

**Scanning Transmission Electron Microscopy (STEM):** High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) was carried out using a probe-corrected JEOL ARM 200 F microscope operated at 200 kV, equipped with a cold field-emission electron gun and a probe aberration corrector allowing a resolution of 0.8 Å at 200 kV in STEM mode. Focused ion beam (Helios Nanolab 600i) was used to prepare cross-sectional lamellae using a standard lift-out procedure. Lamellae were prepared along the [110] crystallographic direction of the Si substrate. Images were recorded using a HAADF detector, which provides imaging of Ba and Ti atomic columns. Stacks of 10 HAADF images were collected with a 21 mrad probe semi-angle, a detector range of 90–370 mrad, and a pixel dwell time of 3 µs. The Abstrain method[92] was used to determine the strain components with reference to the Bravais lattice of BaTiO₃. The lattice parameter profiles were then determined from the strain maps.

**Piezoresponse Force Microscopy (PFM) and Conductive AFM (c-AFM):** PFM measurements were performed at room temperature with an NX10 microscope (Park Systems) and an external UHFLI lock-in amplifier (Zurich Instruments). Platinum/iridium coated tips (PPP-EFM, Nanosensors) with a force constant of ~2.8 N m⁻¹ were used in the dual frequency resonance tracking (DFRT) mode with 0.6 V AC modulation at ~350 kHz (for vertical PFM) and ~630 kHz (for lateral PFM). DC voltage (Vdc) was applied to the tip, and AC modulation (Vac) was applied to the bottom electrode. The temperature-dependent PFM switching spectroscopy data were measured with a MFP3D (Asylum Research) with conductive Pt-coated tips (HQ:NSC18, Mikromash) in the DFRT mode with 0.6 Vac at ≈ 340 KHz. Both Vdc and Vac were applied to the tip. Note that the top Au/W electrode was removed from the nanodisks to perform the measurements. Indeed, the amorphized sidewalls were conducting, which leads to short-circuits from the bottom to the top electrodes.

Conductive-AFM was performed with the same microscope and tips. The AFM tip was grounded, and a DC bias was applied to the sample bottom electrode.

**Supporting Information**

Supporting Information is available from the Wiley Online Library or from the author.

**Acknowledgements**

HZB and CEMES authors acknowledge funding from the Deutsche Forschungsgemeinschaft and Agence Nationale de la Recherche within the project FEAT (DFG 431399790/ANR-19-CE24-0027-01). C.D. and D.J.K acknowledge funding by the European Union (ERC Advanced Grant, LU-CIOLE, project number 101098216). Views and opinions expressed are,

however, those of the authors only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them. HZB authors acknowledge the cooperation and funding of Park Systems. HZB authors acknowledge support from Holger Kropf and Elyas Khairi at the Center for Correlated Microscopy and Spectroscopy (CCMS) at HZB. The authors thank Teresa Hungria-Hernandez from the Centre de Microcaractérisation Raimond Castaing (UAR 3623), in Toulouse, France, for assistance on the STEM microscope. A.G. and C.D. acknowledge the support of Alexander von Humboldt foundation. A.G. acknowledges support by the UNL Grand Challenges catalyst award "Quantum Approaches Addressing Global Threats".

**Conflict of Interest**

The authors declare no conflict of interest.

**Author Contributions**

C.D. initiated and coordinated the study. D.J.K. grew the heterostructure with the assistance of S.W. I.O. performed the XRD, SEM, and Raman experiments. I.O. fabricated the nanodisks with contributions from J.A. I.O. performed the PFM measurements with the assistance of D.J.K. and H.L. B.C. prepared the lamella and performed the STEM imaging with S.S.C. N.C. and S.S.C. analyzed the STEM images. C.D., D.J.K., I.O., N.C., S.S.C., H.L., and A.G. discussed the results. The manuscript was written by I.O., C.D., and D.J.K. All co-authors edited the manuscript.

**Data Availability Statement**

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

**Keywords**

BaTiO3, domains, ferroelectrics, nanodisks, nanostructures, polar texture, scaling

Received: March 28, 2025

Revised: July 16, 2025

Published online:

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