1 Introduction
The relentless push for higher bandwidth and minimal energy dissipation in next-generation optical interconnects has exposed the intrinsic limitations of current photonic platforms [
1-
3]. Despite its dominance of large-scale integration, silicon is a centrosymmetric crystal structurally devoid of a linear electro-optic (Pockels) response. Consequently, high-speed light modulation in silicon relies primarily on carrier-dispersion effects, which inevitably suffer from issues such as free-carrier absorption and signal distortion [
4-
6]. While thin-film lithium niobate (LN) offers excellent linear modulation, its Pockels coefficient of approximately 30 pm·V
−1 imposes a lower bound on device miniaturization and driving voltage reduction [
7-
9]. To overcome these bottlenecks, epitaxial barium titanate (BTO) has emerged as a compelling electro-optic material platform for silicon photonics [
10-
12]. Owing to its intrinsically large Pockels coefficient, which can exceed that of LN by more than one order of magnitude, BTO offers strong potential for low-voltage and energy-efficient electro-optic modulation. Beyond this intrinsic advantage, recent advances in ferroelectric oxides have shown that electro-optic responses can be further enhanced by tailoring domain and phase configurations [
13,
14], highlighting an additional degree of freedom for optimizing BTO-based photonic materials. Therefore, epitaxially integrating BTO on Si is of particular significance, as it combines a high-performance and engineerable ferroelectric electro-optic material with a technologically mature photonic platform, providing a viable route toward compact, ultralow-voltage photonic integrated circuits (PICs) [
15-
17].
However, the epitaxial growth of high-quality BTO on Si presents specific technical challenges. Even when exploiting a 45° in-plane lattice rotation, the oxidizing environment required for perovskite synthesis typically forms an amorphous SiO
2 layer, disrupting the essential crystalline registry [
18-
20]. To address this, oxide molecular beam epitaxy (MBE) utilizes a sub-monolayer Sr reconstruction to passivate the Si surface, subsequently growing a SrTiO
3 (STO) buffer layer to serve as a compatible epitaxial template [
21-
23]. Nevertheless, continuing the BTO growth via conventional oxide MBE introduces practical limitations for scalable manufacturing. The low oxygen pressure characteristic of standard MBE processes generally leads to elevated oxygen vacancy concentrations. Furthermore, Ti metal sources exhibit low and unstable evaporation fluxes from a solid effusion cell, which restricts the standard MBE process to slow growth rates [
24].
To address these scalability limitations, hybrid MBE (hMBE) using titanium tetraisopropoxide (TTIP) as the Ti source offers a distinct mechanistic pathway [
25,
26]. TTIP’s specific decomposition kinetics create a self-regulated, adsorption-controlled growth window that eliminates the strict flux-matching constraints of conventional MBE, thereby enabling higher growth rates [
27,
28]. Furthermore, upon thermal decomposition at the heated substrate, TTIP acts as both the titanium source and a local oxygen supplier [
29]. This intrinsic oxygen supply fulfills the lattice requirement while maintaining a sufficiently mild oxidizing environment to preserve the STO/Si interface [
30]. By reducing the reliance on an external oxygen flux, the hMBE approach affords substantial process robustness for high-quality oxide epitaxy on silicon.
While this TTIP-driven approach provides a flexible framework for oxide epitaxy, the continuous synthesis of both STO buffer layers and BTO films entirely via hMBE on large-scale silicon wafers has yet to be demonstrated [
31-
35]. In this work, we realize this fully hMBE-based integration of BTO films on STO-buffered 4-inch Si (001) wafers. By utilizing TTIP as the Ti precursor, we achieved a BTO growth rate of ~75 nm·h
−1 while strictly maintaining an adsorption-controlled, layer-by-layer growth mode. Structural characterizations confirm the pristine monocrystalline nature, atomically sharp interfaces, and well-defined atomic terraces of these hMBE-grown heterostructures. We additionally deposited BTO films on these virtual substrates using pulsed laser deposition (PLD) and radio-frequency (RF) magnetron sputtering. This comparative approach validates the structural robustness of the underlying hMBE-grown STO templates while simultaneously benchmarking the domain states and electro-optic (EO) properties of the BTO films grown by these different techniques.
Comprehensive EO characterizations illuminate the distinct physical mechanisms underlying these growth techniques. The PLD-grown BTO films on the hMBE-grown STO templates exhibit a high effective EO coefficient of 220 pm·V
−1, confirming the excellent crystalline quality of the underlying STO buffer. However, this substantial response is primarily driven by uncontrolled, defect-induced strain relaxation, a stochastic process that inherently limits device-to-device reproducibility [
36,
37]. The fully hMBE-grown BTO films not only exhibit superior crystallinity and low leakage (with a high resistivity of 2.2 × 10
4 Ω·cm), but also a larger effective EO coefficient of 248 pm·V
−1. Although both the PLD and hMBE films are predominantly
c-domain oriented, this result indicates that the highly controllable, layer-by-layer growth mode of hMBE can achieve EO performance exceeding that of defect-mediated PLD films. Furthermore, while the TTIP-driven process provides a broad self-regulated growth window, we observe that the macroscopic EO properties remain sensitive to the specific TTIP flux ratio, likely due to subtle variations in defect concentrations as previously reported [
35]. Crucially, the deterministic nature of the hMBE growth mode suggests substantial room for future property enhancement and optimization. For example, by tuning STO buffer thickness that affects strain transfer, successive BTO films can be engineered to favor an in-plane
a-domain orientation, potentially unlocking even higher EO responses. Therefore, this work demonstrates the successful continuous wafer-scale epitaxy of high-quality BTO and STO films on silicon, enabling next-generation, high-performance EO modulators for optical interconnect applications.
2 Experiment
2.1 Thin-film epitaxy
In this work, hybrid MBE was implemented by modifying a commercial 4-inch MBE system (SVT Associates). The growth chamber was evacuated by a turbomolecular pump and a cryopump, together with a liquid-nitrogen-cooled cryopanel, resulting in a base pressure of ~2 × 10−10 torr when the cryopanel was filled. Elemental Sr and Ba beams were supplied from standard effusion cells charged with high-purity source metals. Their beam-equivalent pressures (BEPs), measured using an ion gauge at the growth position, were varied from 1 × 10−8 torr to 1 × 10−7 torr by adjusting the cell temperatures. The Ti-containing metalorganic precursor was introduced by evaporating TTIP through a customized bubbler and injector source. The TTIP flux was controlled using a variable leak valve in combination with a temperature-controlled heating bath for the bubbler, and was typically maintained at 10–50 times the BEPs of Sr and Ba. Atomic oxygen was supplied using a radio frequency (RF) plasma source operated at 300 W with an oxygen flow rate of up to 2 sccm.
High-resistivity Si (001) substrates, either as 10 × 10 mm2 chips or 4-inch wafers, were first rinsed in buffered oxide etch (BOE) solution to remove native SiO2 layers and then quickly loaded into the MBE chamber. The substrates were radiatively heated up to 900 °C using a pyrolytic boron nitride (PBN) heater, with the temperature calibrated by an infrared pyrometer. Film growth was monitored in situ by reflection high-energy electron diffraction (RHEED, Staib). For wafer-scale growth, the 4-inch wafers were continuously rotated at 30 rpm to improve thickness and composition uniformity. Epitaxial STO thin films were first deposited to form STO/Si virtual substrates, followed by BTO film epitaxy either in-line or after air exposure/reloading. The detailed epitaxy growth route on Si is discussed in the Results section.
For comparison, BTO films were also deposited on STO/Si virtual substrates by pulsed laser deposition (PLD) and RF sputtering. For the PLD growth, a BTO ceramic target was ablated using a 248 nm KrF excimer laser with a fluence of 1 J·cm
−2 and a repetition rate of 2 Hz. The substrates were maintained at 680 °C in an oxygen pressure of 5 Pa during deposition. For RF sputtering, a BTO ceramic target was sputtered by Ar plasma at a RF power of 75 W, while the substrates were heated to 700 °C in an Ar/O
2 mixed atmosphere with a ratio of 4:1 and a total pressure of 1.5 Pa. In both cases, the STO/Si virtual substrates used for BTO deposition were cut from the same hybrid MBE-grown wafer to ensure a meaningful comparison among the different growth techniques. Further details of the deposition conditions are provided in our previous reports [
36,
37].
2.2 Structural characterizations
The crystal structures of the films were analyzed by X-ray diffraction (XRD) using a diffractometer (Rigaku Smartlab) equipped with a 9 kW rotating Cu anode X-ray source and a HyPix-3000 high-resolution detector. For wafer-scale mapping, the 4-inch wafer was measured on a grid of 50 points using a motorized xy stage while the diffraction optics remained fixed. The obtained XRD patterns were subsequently fitted to extract the diffraction peak positions and related structural information. Surface morphology and ferroelectric domain structures were examined using an atomic force microscope (AFM, Asylum Research MFP-3D). Piezoresponse force microscopy (PFM) images were collected in both vertical and lateral response channels.
For scanning transmission electron microscopy (STEM) characterization, cross-sectional specimens of the STO/Si and BTO/STO/Si films were prepared along the Si [110] zone axis using focused ion beam (FIB) in a dual-beam microscope (Zeiss Crossbeam). STEM was performed on a double-aberration-corrected transmission electron microscope (Spectra 300, Thermo Fisher Scientific) at an accelerating voltage of 300 kV. High-angle annular dark-field (HAADF) images were collected under a probe convergence angle of 25 mrad and with a detector collection angle of 49–200 mrad. Elemental distributions were analyzed by energy-dispersive X-ray spectroscopy (EDS), with maps collected simultaneously using a Super-X detector.
Time-of-flight secondary ion mass spectrometry (ToF-SIMS) measurements were performed on a reflection-type ToF-SIMS system (M6, IONTOF GmbH) equipped with a 30 keV Bi+ liquid metal ion gun and a Cs ion beam sputter gun.
2.3 Optical property measurements
Second harmonic generation (SHG) measurements were conducted using a custom-built laser-scanning microscopy system [
38-
41]. The fundamental excitation (1
ω) was provided by a Ti:sapphire femtosecond laser (MaiTai, Spectra-Physics) operating at a central wavelength of 800 nm, with a pulse duration of 35 fs and a typical power of 50 mW. The 1
ω beam was directed and focused onto the sample surface using a convex lens (numerical aperture ~0.5). The sample stage was fixed at a 45° tilt angle relative to the incident beam, enabling the specularly reflected SHG (2
ω) signals to be efficiently collected along the detection optical axis. The polarization state of the incident beam was continuously tuned using a zero-order half-wave plate, while the generated 2
ω emission was analyzed by a Glan-Taylor prism polarizer. The resultant SHG signals were subsequently spectrally isolated using proper band-pass filters and recorded by a photomultiplier tube. A customized heater was used to in situ heat the samples to a maximum temperature of ~200 °C.
Spectroscopic ellipsometry measurements were performed on a phase-modulated ellipsometer (Uvisel Plus, HORIBA) over a spectral range of 350–2100 nm with a spot size of 100 μm. The fitting model consisted of a silicon substrate, a 23 nm-thick STO layer (determined by HADDF measurement), an approximately 200–300 nm-thick BTO layer (Drude model), and the fitting spectral range was 400–2000 nm.
For electro-optic measurements, Pt coplanar electrodes were fabricated on the BTO films by standard photolithography, metal deposition, and lift-off, with an electrode gap of ~10 μm. The EO measurements were carried out using a home-designed apparatus employing a single-mode 1550 nm diode laser (Cnilaser TEM-F1550). The polarization state of the incident beam was adjusted using a Glan-Taylor prism together with a motorized half-wave plate, and the beam was then focused by an objective lens into the region between the electrodes. After transmission through the sample, the optical signal was analyzed by a motorized quarter-wave plate and a thin-film polarizer and recorded by an InGaAs detector. Electrical bias was applied through the coplanar electrodes in the form of a combined AC and DC field, and the corresponding phase modulation signal was extracted with a lock-in amplifier. For electro-optic loop measurements, a 5 V peak-to-peak AC modulation at 10 kHz was superimposed on a swept DC offset, and the field-dependent refractive-index change (Δn) was recorded accordingly. To determine the linear electro-optic response, the effective EO coefficient reff was obtained from the slope of Δn as a function of the applied AC electric field under a saturated DC bias. The film thicknesses obtained by spectroscopic ellipsometry were used for calculating the reff.
3 Results and Discussion
3.1 Epitaxy of SrTiO3 on Si
Figure 1A presents the overall hMBE growth procedure. To prevent oxidation of the Si interface during subsequent growth, the classic Sr passivation strategy was employed. Specifically, 1/2 monolayer (ML) of Sr was deposited and subsequently annealed at 720 °C to enhance Sr surface diffusion. As shown in Figure 1B, compared to the RHEED pattern of the pristine Si substrate, the annealed surface exhibited a characteristic 2 × 1 reconstruction, indicating the successful formation of a Zintl phase template. Following surface passivation, 12 ML of STO was co-deposited with the Sr and TTIP sources at a low temperature of 400 °C. This step resulted in the formation of an amorphous STO layer. The sample was then annealed at 600 °C to drive solid-phase epitaxy. After annealing, the sample exhibited a streaky RHEED pattern, confirming an ideal 2D surface morphology. Furthermore, distinct half-order reflections were observed between the fundamental streaks along the <100> azimuth directions. This feature not only confirms the formation of a highly crystalline, stoichiometric STO film but also indicates the presence of a well-ordered TiO2-terminated surface. Notably, no background oxygen was introduced during this stage, demonstrating that the TTIP precursor alone supplies sufficient lattice oxygen for the epitaxial growth of STO. Following the crystallization of the buffer layer, the substrate temperature was further elevated to 800 °C. Atomic oxygen was then introduced to facilitate the high-temperature epitaxial growth of STO (or BTO) to the targeted thickness. The in-situ RHEED pattern of the STO film after high-temperature growth was exceptionally sharp with a clean background, exhibiting no amorphous scattering. Importantly, it preserved the characteristic TiO2-termination reconstruction streaks, indicating sustained high crystallinity and stoichiometric control throughout the growth process.
Figure 1C presents a cross-sectional schematic of the STO/Si heterostructure. Due to the lattice mismatch between STO (a ≈ 3.905 Å) and Si (a ≈ 5.43 Å), the STO lattice exhibits a 45° in-plane rotation relative to the Si substrate to minimize interfacial strain. Therefore, when viewed along the Si [110] zone axis, the STO lattice is projected along its [100] direction. This crystallographic model provides a reference for the cross-sectional HAADF-STEM image in Figure 1D. An amorphous interfacial layer is present between the Si substrate and the crystalline STO film. This layer forms during the 800 °C growth stage as oxygen diffuses through the STO lattice to the underlying Si surface. Despite the formation of this amorphous interface, the overlying STO film maintains its initial epitaxial orientation. This indicates that the epitaxial registry was established by the Zintl template and the solid-phase crystallized buffer layer prior to the high-temperature oxidation, enabling the continued epitaxial growth of the STO. As shown in Figure 1E, EDS mapping reveals that the amorphous interfacial layer consists primarily of Si, Sr, and O. The absence of Ti in this region indicates its confinement within the perovskite lattice during oxidation, whereas Sr forms a silicate-like layer. Furthermore, the weak Si signal detected throughout the STO film is an artifact arising from the EDS spectral overlap of Si and Sr, rather than actual atomic diffusion.
To evaluate the macroscopic uniformity of the STO film at the wafer scale, Figure 1F presents a photograph of a 4-inch STO/Si wafer with a 23 nm-thick STO film. The surface appears homogeneous, and the absence of interference color fringes indicates a uniform film thickness across the wafer. The crystalline quality and epitaxial orientation were characterized by XRD. A representative θ−2θ scan (10°–80°) collected from the wafer center (Fig. 1H) is plotted on a logarithmic intensity scale. The diffractogram exclusively displays the STO 00l diffraction peaks, including the fundamental 001 and higher-order 002 peaks, alongside the Si 004 substrate peak. No secondary phases or misoriented grain peaks are detected, confirming phase-pure epitaxial growth. An XRD mapping of the STO (001) lattice spacing was performed (Fig. 1G). Referenced to 3.911 Å, the lattice spacing is highly uniform across the entire wafer, with local deviations (Δd/d) strictly bounded within ± 0.2%. Importantly, the XRD spectra from all mapping points consistently match the representative profile in Figure 1H, showing a complete absence of impurity phases or non-epitaxial peaks. This confirms the single-crystal epitaxial nature of the STO film across the entire 4-inch wafer.
3.2 Epitaxy of BaTiO3 on SrTiO3/Si
Building upon the structural stability of the STO/Si template, epitaxial BTO films were subsequently grown at 800 °C. In the hMBE process, the high volatility of the TTIP precursor provides an adsorption-controlled growth window. Within this thermodynamic regime, excess TTIP desorbs from the surface, rendering the growth rate governed by the Ba flux. This self-limiting mechanism allows for sustained epitaxial growth over a broad range of precursor flux ratios. For instance, two representative hMBE samples grown with TTIP/Ba flux ratios of 38:1 (hMBE_1) and 32:1 (hMBE_2) maintained sharp, streaky RHEED patterns throughout the deposition process. Notably, this hMBE process affords a growth rate of 70–100 nm·h−1 (e.g., ~75 nm·h−1 for the 220 nm-thick hMBE_2 film). This rate significantly outpaces conventional oxide MBE processes (typically < 20 nm·h−1).
To demonstrate the universal applicability of the STO/Si pseudo-substrate, BTO films were also deposited using PLD and RF sputtering. Figure 2B presents the RHEED patterns of the STO/Si template before and after the PLD growth of BTO. The preservation of sharp diffraction streaks confirms the layer growth mode of PLD. The crystalline quality and phase purity of the BTO films across all growth methods were evaluated using wide-range XRD θ−2θ scans. As shown in Figure 2A, all four samples exclusively display the fundamental (001) diffraction peaks or their higher-order reflections for BTO, STO, and Si. The absence of impurity phases and non-epitaxial peaks indicates that the STO/Si template supports successful epitaxial integration across different deposition techniques. The inset of Figure 2A presents the BTO (002) peaks plotted on a linear scale. The hMBE_1 film exhibits an out-of-plane lattice parameter closely matching the bulk BTO a-axis. In contrast, the other samples display out-of-plane lattice parameters intermediate between the bulk a- and c-axes. Figure 2D further presents the reciprocal space mapping (RSM) of the hMBE_2 film. The extracted in-plane and out-of-plane lattice parameters are a = 3.993 Å and c = 4.017 Å, respectively, indicating a state closer to the bulk c-domain.
Based on the hMBE_2 process, a 4-inch BTO/STO/Si wafer was continuously grown in-line with a thinner STO buffer layer (~8 nm). Figure 2C presents the XRD mapping of the out-of-plane lattice spacing. Reference to a nominal lattice parameter of 3.996 Å, the map reveals a relatively uniform distribution, with Δ
d/d deviation bounded within ± 0.2%. In comparison with the STO/Si wafer (Fig. 1G), the observed ring-shaped feature suggests a moderate non-smooth flux profile from the Ba effusion cell. Notably, despite using identical growth parameters, this 4-inch BTO film exhibits a reduced out-of-plane lattice parameter (3.996 Å) closer to the bulk a-axis. This structural shift may be related to the strain state imposed by the ultrathin STO/Si template. The ~8 nm STO buffer lies within a thin-buffer regime in which lattice relaxation on Si may remain incomplete, consistent with recent reports showing that relaxation of STO on Si begins within the first ~12.5 monolayers (~5 nm) [
42]. Consequently, residual tensile strain associated with the thermal-expansion mismatch between the oxide stack and Si may be partially transmitted to the overlying BTO layer, thereby favoring a larger fraction of in-plane-polarized
a-domains [
43,
44].
To evaluate the depth-dependent chemical composition, ToF-SIMS was performed for the hMBE_2 film (Fig. 2E). The carbon (C) signal exhibits a strong initial peak at the film surface, commonly caused by the physical adsorption of airborne CO2 upon ambient air exposure. Within the BTO film, the C intensity drops drastically, stabilizing at a level only slightly above the baseline recorded in the underlying Si substrate. Since the pristine Si substrate is inherently carbon-free, this low baseline represents the instrumental background limit. This comparison confirms negligible carbon incorporation from the TTIP precursor. Furthermore, apparent intensity spikes are observed for multiple elements at the interfacial region. This is an artifact caused by the matrix effect in SIMS, where the abrupt change in the chemical environment at the oxide/semiconductor boundary alters the secondary ion yield. An anomalous Ba peak appears at the deep STO/Si interface. An anomalous Ba peak is observed at the STO/Si interface. ToF-SIMS isotopic analysis shows that this peak exhibits a natural barium isotopic abundance, arguing against significant molecular-ion or cluster-ion mass interference. However, no corresponding Ba accumulation is detected in the cross-sectional STEM-EDS mapping, which reveals an abrupt STO/Si interface within the spatial resolution and detection limit of the measurement. This contrast rules out substantial Ba interdiffusion and supports assigning the interface signal to a sputter-induced knock-on artifact caused by forward sputtering of heavy Ba atoms from the overlying BTO layer during depth profiling.
To directly visualize the microstructural quality and epitaxial registry, HAADF-STEM was performed for the hMBE_2 film. As shown in the large field-of-view image (Fig. 2F), the BTO film exhibits uniform contrast without any observable threading dislocations, planar defects, or secondary phase inclusions, corroborating the excellent macroscopic crystalline quality. The atomic structure of the BTO/STO interface is further resolved in the high-magnification HAADF-STEM image (Fig. 2G). The interface is atomically sharp and structurally coherent. Notably, no significant interfacial misfit dislocations were observed during extensive cross-sectional examinations across multiple regions. This indicates that the epitaxial lattice registry is well-preserved without obvious plastic strain relaxation, maintaining a highly pristine atomic template. Figure 2H displays the corresponding EDS elemental mapping for Sr, Ba, and Ti. The mappings visually confirm the distinct chemical stratification of the BTO and STO layers. While a faint Ba signal appears to be distributed within the STO layer, this is a well-documented EDS deconvolution artifact caused by the severe spectral overlap between the Ba L-lines (~4.46 keV) and the Ti K-lines (~4.51 keV). As definitively established by the highly sensitive ToF-SIMS depth profiling, the STO buffer layer is essentially Ba-free. Thus, the complementary structural and chemical analyses verify the formation of a structurally coherent and chemically abrupt BTO/STO interface. The selected-area polarization mapping (Fig. 2I) and its corresponding large-area statistical analysis reveal a mixed a/c-domain configuration dominated by out-of-plane c-domains.
3.3 Ferroelectric domain structures
To comprehensively evaluate the surface morphology and the local-to-macroscopic ferroelectric properties of the BTO films, we performed AFM/PFM and SHG measurements. Figure 3 presents a comparative analysis of the three samples: two fully hMBE-grown BTO films (hMBE_1 and hMBE_2) and the PLD-grown BTO film on an hMBE-STO template. As shown in the AFM images (Fig. 3A–C), all three BTO films exhibit exceptionally smooth surfaces. The height variations across the measured areas are strictly confined within ± 400 pm, corresponding to roughly a single unit-cell step height. Consistently, the root-mean-square (RMS) roughness is 255 pm for the hMBE_1 film and 223 pm for the optimized hMBE_2 film. Notably, clear atomic step-terrace structures are distinctly resolved on the surfaces of both hMBE_1 and hMBE_2. These well-defined atomic terraces unambiguously confirm that an ideal, adsorption-controlled layer-by-layer growth mode is maintained throughout the hMBE process. While the PLD-grown film also exhibits sub-nanometer roughness, it lacks these distinct terrace features, highlighting the mechanistic difference between the thermodynamically governed hMBE and the more energetic, nonequilibrium PLD process.
Figure 3D–F presents the PFM images in four channels: vertical amplitude, lateral amplitude, vertical phase, and lateral phase. The PFM images reveal a distinct evolution of the static domain states across the three samples. For the hMBE_1 film (Fig. 3D), the PFM response is characterized by a horizontal boundary separating the region into two parts: the upper region exhibits prominent lateral amplitude (in-plane polarization), while the lower region is dominated by vertical amplitude (out-of-plane polarization). Accompanied by abrupt phase inversions across this boundary, this configuration represents classic 90° domain walls separating a- and c-domains. In contrast, the hMBE_2 film (Fig. 3E), grown with a reduced TTIP flux ratio, exhibits a relatively uniform vertical amplitude with slight phase fluctuations, while the lateral amplitude displays finer, more localized intensity variations accompanied by 90° phase flips. This fragmentation trend is further amplified in the PLD-grown film (Fig. 3F), where the vertical phase is highly uniform, and the lateral signal clearly resolves fine-grained domain structures with frequent phase flips. Overall, the progression demonstrates a morphological evolution where the ferroelectric domains become increasingly fragmented, and the out-of-plane c-domains gradually establish dominance, in line with the XRD measurement results.
To bridge the local domain configurations with macroscopic optical characteristics, SHG polarimetry was performed by rotating the incident fundamental beam polarization while keeping the output polarization fixed in either the s-out or p-out configuration (Fig. 3G–I). In the s-out configuration, all three samples commonly exhibit a clear four-fold symmetry with maximum intensities at 45°, consistent with the fundamental tetragonal 4 mm symmetry of epitaxial BTO. However, the p-out configurations and overall SHG intensities reveal stark differences that directly map to their specific domain evolutions. The hMBE_1 film exhibits a nearly isotropic p-out response coupled with a very low overall SHG intensity, suggesting a weakly developed polar state with a pseudo-cubic structure. In contrast, both the hMBE_2 and PLD-grown films display a clear two-fold symmetry along 0° in the p-out configuration, confirming their transition into a c-domain dominated tetragonal state. Although both hMBE_2 and the PLD films share a similar c-domain dominant architecture, their SHG responses exhibit a clear progressive enhancement. Driven by the increasing tetragonality and c-domain dominance, the effective nonlinear optical coefficient d33 is observed to gradually increase from hMBE_2 to the PLD-grown film. This systematic evolution perfectly traces the structural transition from an a-domain dominated pseudo-cubic state toward a highly robust, c-domain dominated tetragonal state, in line with the PFM and XRD measurement results.
3.4 Electro-optical properties
Building on the structural and polarization-sensitive characterizations above, we next examine the optical responses of the three BTO films. Figure 4A shows the optical constants extracted from spectroscopic ellipsometry. All three films exhibit similar refractive indices in the C-band telecommunication wavelength range, and these values are consistent with those typically reported for bulk BaTiO3. Meanwhile, the extinction coefficient remains close to zero, indicating low optical absorption loss in the operating wavelength range.
Prior to the EO characterizations, the electrical resistivities of the films were determined to be in the range of 2.0–2.2 × 104 Ω·cm, ensuring low leakage currents under high lateral electric fields. Despite their similarly high quality, the three films exhibit markedly different electro-optic responses. As shown in Figure 4B, the PLD-grown film displays a pronounced bipolar hysteresis loop with a clear constriction and step-like feature near zero field. Such a loop shape can be understood in terms of the competition between electric-field-driven polarization reorientation and elastic restoring forces within the film. The dashed gray envelope in Figure 4B is a schematic reference for an ideal switching behavior in the absence of elastic clamping. In the actual films, part of the field-switched regions remains elastically constrained by the compressive strain associated with the STO buffer, forming a partially stable switched state. Under a strong in-plane electric field, these regions can be driven toward an in-plane configuration, accompanied by the buildup of elastic strain energy. Upon reducing the electric field toward zero, the electrostatic energy provided by the external field becomes insufficient to counterbalance the elastic restoring force, causing part of the switched domains to relax prematurely back toward the original c-oriented state. As a result, part of the ideal switching contribution is lost along the descending branch, leading to the constricted and step-like loop shape near zero field.
The behavior of the two hMBE-grown films further highlights the sensitivity of the electro-optic response to specific domain configurations. Although both films remain within the high-quality growth window and show nearly indistinguishable average structural characteristics (Fig. 2), the effect of flux-ratio variation becomes evident in the polar-state-sensitive SHG response (Fig. 3). This difference is further reflected in their distinct EO responses. Consistent with its cubic-like SHG response, the hMBE_1 film displays only a very slim EO loop with a small modulation amplitude and no obvious hysteresis, as shown in Figure 4C. By contrast, the hMBE_2 film shows an SHG response much closer to that of the PLD-grown film, indicating the similar mixed a/c-domain configuration. Accordingly, hMBE_2 also exhibits a much larger bipolar electro-optic loop with a constriction near zero field, as shown in Figure 4D, closely resembling the behavior of the PLD-grown film. Such similarity suggests a common switching scenario involving partial field-induced c-to-a reorientation followed by elastic back-relaxation during field removal.
This difference is further reflected in the effective EO coefficient (
reff) measurements, as shown in Figure 4E. All films exhibit linear dependence on the AC electric field, attesting to Pockels effect responses. The extracted
reff is 32 pm·V
−1 for hMBE1, much lower than the values of 248 pm·V
−1 and 220 pm·V
−1 obtained for hMBE_2 and the PLD-grown film, respectively. Despite their similar structural signatures, the pronounced difference in EO response between the two hMBE-grown films suggests that structural characterization alone is insufficient to fully capture the functional variation of these films. By modulating the TTIP/Ba flux ratio, we enhanced the polar order and increased the effective electro-optic coefficient, consistent with recent advancements in domain engineering for BTO thin films [
45,
46]. Taken together, these results indicate that the broad growth window of hMBE does not ensure equivalent device-relevant properties across different flux-ratio conditions, and that careful optimization of the Ba/Ti flux ratio remains essential for achieving strong electro-optic performance.
To evaluate the thermal stability of the polar state of the BTO films, an important factor for optic interconnect applications, temperature-dependent SHG polarimetry was employed. Figure 4F presents the polar plots measured under the p-out detection configuration for the hMBE_2 and PLD-grown films (the s-out polar plots not shown). Both films exhibit consistent SHG patterns as the overall intensity varies as a function of temperature, indicating that their polar structural symmetries are preserved over the measured temperature range. The SHG intensities of the PLD-grown film decreased rapidly at ~150 °C, slightly above the Curie temperature (~130 °C) of bulk BTO. In contrast, a noticeable decrease in the SHG intensity of the hMBE_2 film occurred only at approximately 200 °C. This suggests an elevated Curie temperature in the hMBE_2 film, likely arising from strain-coupling effects.
4 Conclusions
In summary, we have realized the continuous, wafer-scale epitaxial growth of high-quality BTO/STO heterostructures on 4-inch Si (001) substrates via a fully hMBE process. The utilization of a TTIP precursor effectively circumvents the tight flux-matching and slow-growth limitations associated with conventional oxide MBE, achieving a fast growth rate in excess of ~75 nm·h
−1 while strictly preventing amorphous disruption at the STO/Si interface. Structural, ferroelectric, and optical characterizations confirm that this thermodynamically governed, layer-by-layer process yields highly crystalline BTO films with distinct atomic terraces. Crucially, the fully hMBE-grown BTO films demonstrate an outstanding effective electro-optic coefficient of 248 pm·V
−1. Our findings also highlight that achieving this strong performance requires careful optimization of the TTIP/Ba flux ratio, despite the broad self-regulated growth window afforded by hMBE. Ultimately, the continuous hMBE growth of silicon-epitaxial BTO/STO heterostructures establishes a scalable, deterministic, and versatile materials platform for integrated ferroelectric photonics, enabling compact and high-efficiency electro-optic devices while offering broad prospects for further performance enhancement through strain and interface engineering. More broadly, such engineered ferroelectric templates may also be relevant beyond photonics, for example in emerging areas such as reconfigurable magnonics [
47]. This broader relevance further highlights the potential of wafer-scale hMBE growth for developing multifunctional oxide electronic and photonic platforms.
The Author(s). This article is published by Higher Education Press.
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