Neural RHEED alignment with limited training data during CdTe MBE growth

Technical Summary: Neural RHEED Alignment with Limited Training Data during CdTe MBE Growth

Problem Statement
Molecular Beam Epitaxy (MBE) is a critical technique for producing high-quality semiconductor thin films, such as Cadmium Telluride (CdTe). A fundamental requirement for optimizing growth and ensuring reproducibility is the precise alignment of the substrate to specific crystallographic directions. This alignment is typically monitored in-situ using Reflection High-Energy Electron Diffraction (RHEED). While experienced operators manually inspect RHEED patterns to identify symmetric diffraction patterns corresponding to key crystallographic axes, this process is time-consuming, prone to human error, and difficult to automate due to mechanical drifts that shift the beam-sample orientation over time.

Existing machine learning (ML) approaches for RHEED analysis generally fall into two categories: classifying static images of known directions or analyzing fixed-orientation videos to detect growth mode transitions. However, few methods address the automatic identification of crystallographic directions directly from rotating-substrate RHEED videos. Furthermore, a significant bottleneck exists in the availability of diverse, curated RHEED datasets; typical MBE laboratories possess data from only a limited number of structures (often <20), rendering standard deep learning approaches that require large datasets impractical.

Methodology
The authors propose a data-efficient neural-vision pipeline designed to infer crystallographic directions from RHEED images of rotating CdTe substrates, specifically addressing the constraint of limited training data. The study compares two architectural approaches:

1. 2D ResNet with Physics-Aware Postprocessing:

   • Architecture: A 2D ResNet-50 backbone (pre-trained on ImageNet) is used to regress the angular deviation of a single RHEED frame from a target crystallographic direction.
   • Data Strategy: The model is trained on a dataset derived from only 15 CdTe structures (151 single-rotation videos). The data undergoes rigorous preprocessing, including RGB-to-grayscale conversion, region-of-interest (ROI) cropping, resizing to 96×56 pixels, and z-score standardization. On-the-fly augmentation (affine transformations, brightness/contrast variation, and noise) is applied to simulate operator variability without expanding the dataset size.
   • Postprocessing: A critical component of this approach is a physics-aware postprocessing step applied after neural inference. Since the sample rotates at a constant angular velocity, the sequence of predicted angles should follow a linear trend ($NN(P_k) = k\Delta\alpha + \alpha_0$). The postprocessing module:
     • Determines the correct sign of the rotation slope (direction of rotation).
     • Estimates the intercept ($\alpha_0$) using robust statistical methods (circular mean and kernel density estimation) on modular residuals to handle the $0^\circ/180^\circ$ boundary wrap-around.
     • Filters outliers to refine the final crystallographic direction estimate.

2. 3D ResNet (Benchmark):

   • Architecture: A 3D ResNet processes sequences of four consecutive RHEED frames stacked as a tensor to infer the direction directly from temporal structure.
   • Data Strategy: Trained on a larger subset of the available data (19 structures) to compensate for the higher complexity and data hunger of 3D architectures.
   • Limitations: This approach requires significantly more training time and data but does not utilize the specific physical constraints of the rotation in a post-processing step (unless augmented similarly).

Key Contributions

• Data Efficiency: The study demonstrates that a 2D ResNet, when combined with a physics-aware postprocessing pipeline, can achieve high-accuracy crystallographic alignment using training data from as few as 15 structures.
• Architectural Comparison: The authors critically compare 2D and 3D ResNet configurations, showing that the simpler 2D approach with postprocessing outperforms the complex 3D approach in terms of training efficiency (approx. 20x faster) and requires significantly less training data, while achieving comparable or superior inference accuracy.
• Real-Time Feasibility: The proposed pipeline is validated for real-time deployment, capable of running at 10 frames per second (FPS) on a standard CPU, sufficient for controlling substrate rotation during MBE growth.

Results

• 2D ResNet Performance: When trained on 15 structures (15/5 split), the postprocessed 2D ResNet achieved a mean absolute error (MAE) of approximately $0.217^\circ$ (measured as the intercept error) on the holdout set. This places the prediction within the "target error level" ($\pm 0.5^\circ$) for 96% of cases and within the "error tolerance level" ($\pm 1.0^\circ$) for essentially all cases. This accuracy approaches the experimental resolution of the frame collection ($0.33^\circ$).
• 3D ResNet Performance: The bare 3D ResNet (without postprocessing) achieved a raw MAE of $0.771^\circ$ on the holdout set. While it eliminated the outliers seen in the raw 2D predictions, it failed to reach the target error level without the benefit of the postprocessing pipeline.
• Efficiency Gains: The 2D model required approximately 34 minutes of training time on a single GPU, whereas the 3D model required over 11 hours. The 2D approach also utilized 15 training structures compared to 19 for the 3D benchmark.
• Latency Trade-off: The authors note a distinction in latency: the 3D model provides predictions from the first few frames, whereas the 2D postprocessing approach requires accumulating data over a full $180^\circ$ angular window (approx. 30 seconds at 1 RPM) to generate a reliable intercept estimate.

Significance and Claims
The paper claims that this work represents a practical step toward AI-driven, autonomous MBE growth. By leveraging physics-aware postprocessing, the authors demonstrate that lightweight neural architectures can match the performance of more complex models despite severe data limitations. The resulting system is fully trained and ready for closed-loop deployment in future CdTe growth experiments. The methodology is presented as generalizable to other material systems where diverse RHEED datasets are scarce, highlighting the potential of machine-learning-assisted automation in thin-film synthesis without requiring massive data collection efforts. The study does not claim to solve all aspects of MBE automation but specifically addresses the critical bottleneck of automated crystallographic alignment under data-constrained conditions.