Lattice Relaxation and Domain Structure Engineering in BaTiO₃ Thin Films Epitaxially Grown on Silicon

Silicon photonics has emerged as a critical technology for high-performance communication and computing, with electro–optic modulators serving as essential components. Barium titanate (BaTiO₃, BTO) exhibits exceptional promise due to its outstanding electro–optic coefficient (r₄₂ ≈ 923 pm/V) and compatibility with silicon-based fabrication processes. However, achieving high-performance BTO devices requires overcoming key materials integration challenges. The primary obstacles include the formation of amorphous SiO₂ interfacial layer during high-temperature, oxygen-rich BTO growth, which prevents effective epitaxy, and the substantial lattice mismatch between BTO (a = b = 3.992 Å, c = 4.036 Å) and Si (5.431 Å), resulting in approximately 4.0% mismatch even with 45° rotational epitaxy. This mismatch induces high-density dislocations and strain relaxation, compromising film quality. Strontium titanate (SrTiO₃, STO) buffer layers (3.905 Å) can reduce lattice mismatch to 1.7%, providing stress relief and serving as an epitaxial template. The electro-optic effect in BTO strongly depends on ferroelectric domain structure and crystallographic orientation, with in-plane polarization achieving maximum coefficients. While domain structures can be controlled through strain engineering and growth conditions, current analyses rely on post-growth characterization, lacking real-time monitoring of domain evolution processes and critical transition mechanisms.

Oxide molecular beam epitaxy (MBE) combined with in situ reflection high-energy electron diffraction (RHEED) for real-time monitoring was employed to achieve controlled growth of high-quality BTO films at 2 in wafer scale. The systematic investigation focused on lattice relaxation behavior during the growth of STO buffer layers and BTO layers with varying thicknesses. Silicon substrates underwent hydrofluoric acid (HF, 10% mass fraction) treatment to remove surface SiO₂ amorphous layers, followed by rapid transfer to ultra-high vacuum chambers (background pressure ≤ 5×10^–8 Pa). STO epitaxial growth employed a two-stage process: first, 2.5 monolayers (ML) of Sr and Ti metals were deposited at a substrate temperature of 200 ℃ under ultra-high vacuum (＜5×10^–7 Pa) with precisely controlled oxygen partial pressure (＜5×10^–6 Pa). The second stage involved in situ annealing at 500 ℃ for 8 minutes under ultra-high vacuum conditions (＜1×10^–6 Pa). After three such cycles, additional STO layers were epitaxially grown using co-deposition at a thermocouple temperature of 600 ℃ under an oxygen partial pressure of 6×10^–5 Pa. BTO layers were continuously co-deposited at 700 ℃ thermocouple temperature under 6×10^–5 Pa oxygen partial pressure, ultimately obtaining 310 nm BTO/5 nm STO/Si heterostructures. Comprehensive characterization employed high-resolution four-circle X-ray diffraction (XRD) for 2θ–ω scanning and rocking curve analysis, spectroscopic ellipsometry for determining optical constants and thickness, atomic force microscopy (AFM) for surface morphology assessment, and piezoresponse force microscopy (PFM) for ferroelectric domain characterization.

Systematic RHEED diffraction pattern analysis during film growth enable quantitative analysis of lattice relaxation processes in both STO and BTO epitaxial films. STO buffer layers completed relaxation after 12.5 ML, reducing the lattice mismatch between BTO and Si from 4.0% to 2.2%. BTO films underwent progressive relaxation from the interface to a depth of 30 nm, with in-plane lattice constants evolving from 3.905 Å (STO-templated) to 4.013 Å at 30 nm, then stabilizing. During cooling from 700 ℃ to room temperature, thermal constraints from Si substrate significantly modified BTO behavior. The effective thermal expansion coefficient was ~1.5×10^–6 K^–1, much lower than that of bulk BTO (~14.6×10^–6 K^–1) but comparable to Si (2.6×10^–6 K-1), indicating strong substrate constraint effects. The resulting 300 nm BTO films exhibited excellent quality: a rocking curve full width at half maximum (FWHM) of 0.45°, surface roughness＜0.2 nm, and critical lattice parameters a = 4.010 Å, c = 3.990 Å (c/a = 0.994＜1). This represents a 0.45% in-plane expansion and 1.2% out-of-plane contraction compared to bulk BTO, indicating a tetragonal phase reorientation with the long-axis in-plane. This anisotropic distortion creates residual tensile stress in-plane and compression stress out-of-plane, driving polarization reorientation from out-of-plane to in-plane throughout the entire film. PFM characterization confirmed this structure: lateral PFM (LPFM) signals significantly exceeded vertical PFM (VPFM) signals, demonstrating dominant in-plane polarization components. Optical characterization at 1550 nm revealed ideal performance with a refractive index n = 2.28 and an extinction coefficient k ~10^–6, indicating extremely low optical loss suitable for high-performance electro-optic modulators.

High-quality BTO epitaxial growth on 2-inch silicon wafers was achieved via molecular beam epitaxy. In situ RHEED monitoring enabled real-time observation of lattice relaxation processes during STO buffer layer and BTO film growth, revealing that STO lattice relaxation occurs within the first 12.5 ML from the interface, while BTO lattice relaxation occurs within the first 30 nm from the interface. Based on this relaxation behavior, the STO intermediate layer provides BTO with a low-mismatch template, while BTO lattice relaxation is critical for ultimately achieving in-plane polarized films. In situ RHEED data analysis demonstrated that constraints from low thermal expansion coefficient Si substrate enable BTO films to maintain larger in-plane lattice constants during cooling to room temperature, thereby stabilizing domain structures with predominantly in-plane polarization. This in situ monitoring technique provides crucial information for precise analysis of BTO film lattice relaxation processes and domain engineering, offering significant implications for developing silicon-based BTO electro–optic modulators, high-speed communication devices, and optical quantum computing chips.