Interpreting In Situ 4D-STEM Data for Accurate Measurement of Ferroelectric Polarization using Machine Learning Technique

Ferroelectric materials, such as barium strontium titanate (Ba_0.5Sr_0.5TiO₃, BST), exhibit tiny amounts of ionic displacement under an electric field, which is challenging for reliable detection by STEM based imaging techniques due to the limited precision (typically ~4 pm). Recent progress in 4D-STEM have made it possible to measure these small polarizations with a high degree of accuracy in the reciprocal space as the diffraction intensity varies very sensitively with ionic displacement. However, the quantitative interpretation of the diffraction intensity in 4D-STEM data is challenging due to the unavoidable dynamical diffraction effects included in most 4D-STEM data. In this study, we present a practical machine learning technique to interpret the in-situ 4D-STEM data obtained from 20 nm-thick BST thin film capacitors under electric fields, which allows accurate measurement of the tiny ionic displacements induced by the applied electric field. Our results demonstrate the effectiveness of this approach in accurately detecting and measuring the field-induced ionic polarization in high-κ oxide thin film devices. This breakthrough opens up new avenues for studying not only ferroelectric materials but also piezoelectric and flexoelectric materials. The methodology presented in this study has the potential to revolutionize the field of ferroelectric materials research, enabling researchers to detect and measure tiny amounts of polarization with greater accuracy and efficiency.