Unsupervised Deep Learning for Limited-Angle STEM-EDX Tomography -- Application to 3D Chemical Analysis of Phase-Change Memory Devices

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 $100^\circ$ 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 $-40^\circ$ to $+40^\circ$ with $5^\circ$ steps and a dose of $2.0\times10^5$ $e^-/Ang^2$. 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.

Low-Dose 3D Bonding Mapping Through "Soft" Core-Loss EELS Tomography and Unsupervised Deep Learning

Resolving the 3D chemical configuration of beam-sensitive nanomaterials at high spatial resolution remains a persistent frontier in scanning transmission electron microscopy (STEM). The main limitation lies in the trade-off between high electron dose required for analytical signals and the large number of projections needed for tomographic reconstruction. Here, we achieve dose-efficient 3D bonding mapping of FeO/Fe$_3$O$_4$ core-shell nanocubes with high resolution via electron energy loss spectroscopy (EELS). Our approach relies on two developments. First, a standardless "soft" core-loss EELS methodology exploiting Fe-M$_{2,3}$ edges provides ${\sim}50\times$ higher dose efficiency than conventional Fe-L$_{2,3}$ edges, using the latter only as a source of FeO and Fe$_3$O$_4$ standards. Second, we introduce multi-channel deep image prior with total variation regularization (DIPm-TV), an unsupervised method for spectroscopic tomography that jointly reconstructs multiple channels by exploiting spatial correlations under sparse-view and low-dose conditions. Using simulated datasets, high-quality reconstructions are obtained from as few as nine projections over $-70^\circ$ to $+70^\circ$, without HAADF-STEM signal or symmetry constraints. Applied to FeO/Fe$_3$O$_4$ nanocubes, Fe-M$_{2,3}$ EELS maps show improved SNR and spatial resolution, revealing a thin outer FeO shell surrounding the magnetite shell. DIPm-TV yields ${\sim}1$ nm isotropic resolution oxidation-state volumes preserving cubic morphology, recovering the outer FeO shell, and revealing a small internal void, features not accessible with conventional reconstruction methods. This work establishes a pathway for low-dose 2D and 3D analytical mapping of beam-sensitive materials using shallow core-loss edges, enabling orders-of-magnitude dose reduction while maintaining spectral fidelity and reliable 3D information.

Unsupervised Deep Image Prior for Sparse-View and Limited-Angle Electron Tomography

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.