Deep Learning Analysis of Localized Interlayer Stacking Displacement and Dynamics in Bilayer Phosphorene

The interlayer displacement has recently emerged as a crucial tuning parameter to control diverse physical properties in layered crystals. Transmission electron microscopy (TEM), an exceptionally powerful tool for structural analysis, directly observes the interlayer stacking and strain fields in various crystals. However, conventional analysis methods based on high-resolution phase-contrast TEM images are inadequate for recognizing spatially varying unit-cell patterns and their associated structure factors, hindering precise determination of interlayer displacements. Here, a deep learning-based analysis is introduced for atomic resolution TEM images, enabling unit-cell pattern recognition and precise identification of interlayer stacking displacement in bilayer phosphorene. The deep learning model applied to bilayer phosphorene accurately determines stacking displacement, with an error level of 3.3% displacement within the unit cell and a spatial resolution approaching the individual unit-cell level. Additionally, the model successfully processes a large set of in situ TEM data, capturing spatially varying, time-dependent interlayer displacement dynamics associated with edge reconstruction, demonstrating its potential for processing large-scale microscopy datasets.