Deep Learning Enabled Nanoscale X-ray Photoemission Electron Microscopy (nanoXPEEM)

TL;DR

The paper addresses the challenge of high-throughput, high-resolution characterization of 2D materials with soft X-ray XPEEM, where aberrations and space-charge degrade image quality. It proposes a two-stage, self-supervised deep-learning approach using a Spatial Transformer Network to correct rigid and non-uniform distortions in XPEEM images, enabling nanometer-scale imaging over a 232 μm field of view at 700–1000 eV. The results achieve a record 48 nm spatial resolution across the field of view, with substantial improvements in contrast and SNR validated by quantitative metrics across multiple core-levels. This work significantly enhances throughput and nanoscale material-structure mapping capabilities, bridging nanoscale and atomic-scale insights for 2D materials and buried interfaces, and it lays groundwork for live instrument tuning and broader applicability to X-ray and electron microscopy.

Abstract

Understanding and manipulating two-dimensional materials for real-world applications remains challenging due to a lack of effective and high-throughput characterization techniques. Soft X-ray time-of-flight photoemission electron microscopy (XPEEM) provides element- and depth-sensitive information of materials and buried interfaces. However, chromatic and spherical aberrations cannot be corrected with electron-lens combinations. These aberrations, combined with astigmatism and space-charge effects, significantly degrade the spatial and energy resolutions. To overcome this limitation, we outline a spatial-attention based deep learning approach to automatically correct for these effects and attain nanometer resolution over the entire field-of-view (FoV). The combination of this corrective algorithm with XPEEM, termed as nanoXPEEM, establishes a new record of 48-nm spatial resolution with a 232-micrometer diameter FoV in the soft x-ray regime (700-1000 eV). nanoXPEEM provides unique spatial mapping of the element-specificity, depth-sensitivity, and local structure on the nanoscale. It can bridge the current gap to achieve angstrom (atomic) scale resolution.

Figures (5)

• Figure 1: Schematic for end-to-end correction of nonlinear effects in x-ray photoemission microscopy (XPEEM) experiments. (a) Starting from the soft-x-ray to sample interaction, where an optical image of 12%-doped Vanadium-WS$_{2}$ is shown. We apply voltages to the electron lens stack to guide the emitted photoelectrons through the lens stack to the detector. A schematic for the lens stack with corresponding electron trajectories is shown with more details explained in Ref MetNM17TkachAX24. At the detector, we collect XPEEM images of W-atoms within a V-WS$_2$ flake at the W$4f$ core-levels. (b) Different types of variation and distortion introduced from the round lenses to the XPEEM images, which serve as the main limiting factors for the resolution. Specifically, time-dependent modulation, magnification difference, translation/rotation, and deformation. Similar outcomes to the XPEEM image may stem from different phenomena, such as chromatic (CA) and spherical (SA) aberrations, astigmatism, electric-field enhancement at sample edges, and space-charge. (c) We train and then apply the pre-trained deep-learning based algorithms to acquired data sets to correct for the exhibited variation and distortion to achieve nanoscale resolution for full field-of-view. (d) The corrected nanoXPEEM image of V-WS$_{2}$ at the W$4f$ core-level (33.6 eV).
• Figure 2: Schematics for deep-learning correction approach, including a) uniform rigid body (translation, rotation, and magnification) and b) non-uniform deformation correction. During training, a set of two random XPEEM images (reference (blue) and moving (pink)) are inputted to the localization network, which learns a parametric mapping to transform the moving image to minimize the mean squared error difference of moving and reference images. During prediction, the XPEEM image at the peak of the XPS acts as the fixed $I_{reference}$, while all remaining XPEEM images along the x-ray photoelectron spectrum ($I_{moving}$) are aligned to this reference. The generator transforms a structured grid using the learned mapping. The sampler uses bilinear interpolation to sample the intensities of a moving image at the transformed pixel locations, which results in a transformation of the moving image.
• Figure 3: (a) Acquired XPEEM image of the full detector for W$4f_{5/2}$ core-level, which sums over the entire stack of images acquired over 33 ns time-of-flight range. We divided it into three regions: Left (green), Center (red), Right (blue), to apply the DL-corrections separately as they experienced different linear and nonlinear effects that cause rotation, translation, magnification variation, and distortions to the XPEEM images. The resulting asymmetry in the photoelectron wavefront result in significant distortion around the center of the detector, particularly the Left and Right areas. (b) Horizontal and (c) vertical (on the detector plane) corrective shift magnitude to the XPEEM images, which are extracted from the Rigid Body Correction for all three regions. (d) The norm ($l_2$) of the deformation field for the XPEEM images in the corresponding regions that represent the non-uniform Deformation Correction magnitude. In panels (b-d), the vertical dotted line (grey) indicates the reference image for the Rigid Body and non-uniform Deformation Corrections as described in Methods. The reference image corresponds to the focal point of the electron lenses, which is also the XPEEM image at the peak intensity of the W$4f_{5/2}$ XPS.
• Figure 4: (a) Schematic of XPEEM setup with multilayered V-WS$_2$ sample and 824 eV x-ray photons.(b) Schematic diagram for electric-field enhancement from the edges of the multilayered system likely resulting from the strong field applied at the sample position (1.3 kV/mm to 3.8 kV/mm) Simoni25TkachU23TkachAX24. Similar enhancement effect was observed in for multilayered TMDs that result in an energy shift of the corresponding photoelectron spectrum (XPS) Li2015LiNano12Fukai93. (c) XPS of W$4f_{5/2}$ core-level as a function of electron time of flight. (e)The XPEEM image at the peak (blue circle) of the spectrum is used as a shape-reference for the correction algorithms. (d, f) An example of moving XPEEM images (pink & red circles) that are corrected based on the reference. The quiver plots show the direction & magnitude of the correction, which indicate that most corrections occur near the mulitlayered islands, where the electric-field enhancement occurs as depicted in panel (b). In (d-f) green lines are guide to eye to show the monolayer of (1L) of V-WS$_2$. Dotted lines are added to show the multilayer islands of three (3L), four (4L), and five (5L) stacked layers. The same guides to the eye for mono- and multilayer stacks are also shown on the corresponding deformation map, which confirm that most deformation corrections take place at the edges of the multilayer islands to compensate for field-enhancement and accompanied space-charge effects.
• Figure 5: Comparison of raw (XPEEM) and corrected (nanoXPEEM) images: (a) Raw, Rigid Body, and Non-uniform Deformation corrected images of V-WS$_2$ flake for the Left (green), Center (red), Right (blue) regions at the W$4f_{5/2}$ core-level. A set of zoom-in images of a single flake in the center region, acquired at the (b) V$3p$ (37.2 eV) and (c) W$4f_{5/2}$ (33.6 eV) core-levels. (d) Line-outs with fits applied to the XPEEM and nanoXPEEM images, where the yellow line in panel (c) indicates the location of the line-outs. The instrument resolution is 250-nm, which improves by 5x with the Rigid Body and Non-uniform Deformation corrections to achieve a record 48-nm resolution.