Unsupervised Deep Learning for Limited-Angle STEM-EDX Tomography -- Application to 3D Chemical Analysis of Phase-Change Memory Devices
Authors: Daniel del Pozo Bueno, Serge Brosset, Theo Monniez, Gabriele Navarro, Philippe Ciuciu, Zineb Saghi
Abstract
Energy Dispersive X-ray (EDX) tomography in Scanning Transmission Electron Microscopy (STEM) enables 3D compositional and elemental mapping at the nanoscale, but its use is limited by restricted tilt ranges and low-dose conditions required to avoid beam damage. Limited-angle acquisition introduces missing-wedge artefacts such as elongation and anisotropic resolution, while noisy low-dose data further degrade reconstruction quality and quantitative reliability. Here, we introduce an unsupervised deep learning framework based on Deep Image Prior with total variation regularization (DIP-TV) for limited-angle STEM-EDX tomography. We extend it to a multi-channel formulation (DIPm-TV) that jointly reconstructs multiple elemental maps by exploiting spatial correlations. Using a synthetic 3-channel phantom, we show that the method compensates for severe missing-wedge artefacts corresponding to approximately 100∘ of missing angular range under moderate noise, outperforming simultaneous iterative reconstruction technique and compressed sensing approaches. We apply the method to 3D chemical analysis of Ge-Sb-Te (GST) memory devices in virgin (as-fabricated) and SET (crystalline) operational states. Samples were prepared as cross-sectional focused ion beam lamellae and acquired under a limited-angle tilt range from −40∘ to +40∘ with 5∘ steps and a dose of 2.0×105e−/Ang2. The multi-channel approach enables voxel-by-voxel elemental reconstruction using only EDX signals without external structural priors such as high-angle annular dark-field imaging. The reconstructed volumes show near-isotropic spatial resolution and reveal compositional heterogeneities associated with device operation. This approach enables 3D chemical characterization in experimentally accessible sample geometries where conventional methods fail due to severe angular limitations.
Electron tomography (ET) plays an important role in the three-dimensional (3D) characterization of nanomaterials. However, under limited-angle and sparse-view conditions, conventional algorithms produce degraded reconstructions, which compromise the quality and interpretability of resulting 3D data. In this paper, we present deep image prior (DIP), an unsupervised deep learning (DL) approach, for highly degraded tomography acquisitions and demonstrate, using simulated data, that its performance is comparable to that of supervised approaches requiring training datasets, even for tilt ranges as limited as 60° and tilt increments of 10°. We then apply it to experimental data and show that it enables reliable 3D quantification under both sparse-view and limited-angle conditions, highlighting its potential for a wide range of materials and acquisition modalities.
Serge Brosset, Daniel del Pozo Bueno, Thomas David +3
Precise 3D characterization of nanomaterials is essential for unlocking structure-property relationships. However, standard electron tomography is fundamentally limited by the missing wedge problem. Consequently, conventional algorithms suffer from severe geometric distortions, a challenge further complicated by pervasive noise interference. Current learning-based methods either rely on physics-blind post-processing or employ end-to-end architectures constrained by local receptive fields, failing to capture complex 3D topologies. We propose NanoMorph-3D, a unified end-to-end framework grounded in a comprehensive Nanomorphological Taxonomy. Powered by a large-scale synthetic dataset explicitly modeling non-linear electron attenuation, we design a Physics-Driven Unrolled Network mapping proximal gradient descent into a learnable architecture. To capture complex internal topologies, we formulate a hierarchical attention mechanism with Physics-Normalization for long-range 3D dependencies and scale invariance. Crucially, our Dual-Domain strategy leverages Sinusoidal Attention to explicitly model physical projection trajectories, enforcing strict sinogram consistency to mitigate missing wedge artifacts. Finally, an unsupervised dual-stream mechanism bridges the simulation-to-reality gap. Experiments demonstrate NanoMorph-3D reconstructs diverse topologies with superior fidelity and speed.
A central premise of autonomous scientific imaging is that smarter navigation, whether Bayesian, RL-based, or otherwise adaptive, is the principal lever for sample-efficient acquisition. We present evidence to the contrary in scanning transmission electron microscopy (STEM), an atomic-resolution imaging modality whose every measurement deposits damaging electron dose. We introduce STEMGym, an open-source Gymnasium benchmark of 15 physics-simulated STEM worlds spanning five materials, three difficulty levels, and four characterisation tasks, scored by the Dose-Efficiency Curve area (DEC-AUC), a single scalar capturing the information-vs-dose Pareto frontier. Across 33 agent configurations under realistic dose budgets, the dominant determinant of dose efficiency is the analyst (perception) pipeline, not the navigator: pairing a trained CNN analyst with naïve raster scanning raises DEC-AUC by 5.5x over a CNN-free raster baseline (0.287 vs.\ 0.052), while substituting Bayesian or adaptive finite-state-machine navigation for raster yields no statistically significant further gain. Production-tier vision-language models further underperform task-specific CNNs by {\sim}13x on crystallographic defect analysis. By decoupling perception, navigation, and planning under a unified dose budget, STEMGym reframes where ML effort should be invested in autonomous electron microscopy and provides the measurement infrastructure to test it.