Morphology-Embedded Signatures of Lattice Strain in Ferroelectric BaTiO₃ Thin Films Revealed by Machine Learning

Lattice strain is a key parameter governing the ferroelectric functionality of BaTiO₃ (BTO) thin films; however its precise evaluation typically requires extensive structural and electrical characterizations. Here, we introduce a machine-learning framework that extracts strain information embedded in the surface morphology of epitaxial BTO thin films. By systematically correlating atomic force microscopy-based surface morphology images with strain-dependent structural and ferroelectric properties, including lattice parameters, crystalline coherence, and ferroelectric imprint, across thickness-controlled BTO films, we construct a data-driven model that infers lattice strain directly from surface morphology. The resulting framework accurately identifies strain states and classifies strain-engineered functional regimes without relying on conventional diffraction-based characterization. Notably, a model trained exclusively on BTO films on SrTiO₃(001) substrates successfully generalizes to BTO films grown on LaAlO₃(001), despite the distinct lattice mismatch and epitaxial environment. This result demonstrates that morphology-encoded strain signatures persist beyond a specific epitaxy platform. Therefore, our approach establishes surface morphology as a powerful, non-destructive descriptor for probing lattice strain and provides a scalable, data-driven pathway for exploring strain-engineered ferroelectric and emergent quantum functionalities in complex oxide thin films.