Multimodal Machine Learning Analysis of GaSe Molecular Beam Epitaxy Growth Conditions

Autonomous synthesis platforms integrating machine learning with in situ diagnostics have the potential to revolutionize thin-film growth by enabling real-time process optimization and reducing the need for manual tuning. However, their application to molecular beam epitaxy (MBE) remains underdeveloped. Here, we present a machine learning-guided framework for MBE growth of GaSe films, leveraging reflection high-energy electron diffraction (RHEED) as an in situ diagnostic alongside <i>ex situ</i> characterization via X-ray diffraction and atomic force microscopy. Unsupervised learning on RHEED patterns reveals a well-defined boundary between high- and low-quality samples, capturing physically meaningful features. Mutual information analysis shows a strong correlation between RHEED embeddings and rocking curve full-width at half-maximum (fwhm), while the correlation with AFM root-mean-square (RMS) roughness is weak. Among key growth conditions, growth rate most strongly influences fwhm, whereas the Se/Ga flux ratio primarily affects RMS roughness and the RHEED embeddings. Supervised learning models trained to predict fwhm and RMS roughness demonstrate moderate accuracy, with significant improvement achieved by incorporating RHEED embeddings. Furthermore, anomaly detection via residual analysis in supervised learning aligns well with unsupervised classification from RHEED, reinforcing the reliability of the predictive models. This study establishes a data-driven framework for machine learning-assisted MBE, paving the way for real-time process control and accelerated optimization of thin-film synthesis.