[Paper Review] Charting the low-loss region in Electron Energy Loss Spectroscopy with machine learning

Laurien I. Roest, Sabrya E. van Heijst+3 more|arXiv (Cornell University)|Sep 10, 2020

2D Materials and Applications73 references20 citations

TL;DR

This paper presents a machine learning-based, model-independent method for accurately extracting the zero-loss peak (ZLP) in electron energy-loss spectroscopy (EELS) with reliable uncertainty quantification. Using neural networks and Monte Carlo replica sampling trained on vacuum spectra, the method enables precise subtraction of the ZLP from polytypic WS2 nanoflowers, revealing a clear indirect bandgap of $E_{\rm BG}=1.6_{-0.2}^{+0.3}$ eV and resolving excitonic transitions down to 1.5 eV with statistical significance.

ABSTRACT

Exploiting the information provided by electron energy-loss spectroscopy (EELS) requires reliable access to the low-loss region where the zero-loss peak (ZLP) often overwhelms the contributions associated to inelastic scatterings off the specimen. Here we deploy machine learning techniques developed in particle physics to realise a model-independent, multidimensional determination of the ZLP with a faithful uncertainty estimate. This novel method is then applied to subtract the ZLP for EEL spectra acquired in flower-like WS$_2$ nanostructures characterised by a 2H/3R mixed polytypism. From the resulting subtracted spectra we determine the nature and value of the bandgap of polytypic WS$_2$, finding $E_{\ m BG} = 1.6_{-0.2}^{+0.3}\\,{\ m eV}$ with a clear preference for an indirect bandgap. Further, we demonstrate how this method enables us to robustly identify excitonic transitions down to very small energy losses. Our approach has been implemented and made available in an open source Python package dubbed EELSfitter.

Motivation & Objective

• To overcome the limitations of model-dependent ZLP subtraction methods in EELS that introduce bias and lack uncertainty estimates.
• To develop a model-independent, multidimensional ZLP parametrization using machine learning techniques from high-energy physics.
• To enable robust identification of low-loss features such as excitons and bandgaps in complex 2D materials like polytypic WS2.
• To provide a generalizable, open-source tool for high-precision EELS data analysis across varying microscope conditions.

Proposed method

• Employing artificial neural networks as unbiased interpolators to parametrize the ZLP in the low-loss region of EELS spectra.
• Using the Monte Carlo replica method to construct a probability distribution over ZLP shapes, enabling faithful uncertainty propagation.
• Training the model on vacuum EELS spectra collected at different beam energies and exposure times to capture instrumental and operational dependencies.
• Applying the trained ZLP model to subtract contributions from real specimen spectra, enabling analysis of intrinsic low-loss features.
• Validating the method by comparing predictions with actual measurements of FWHM across beam energy and exposure time variations.
• Implementing the full workflow in an open-source Python package named EELSfitter for community use.

Experimental results

Research questions

• RQ1 Can a model-independent machine learning approach accurately extract the ZLP in EELS while providing reliable uncertainty estimates?
• RQ2 How does the ZLP shape vary with beam energy and exposure time in a monochromated TEM?
• RQ3 What is the nature and value of the bandgap in polytypic 2H/3R WS2 nanostructures as revealed by ZLP-subtracted spectra?
• RQ4 Can ultra-low-loss excitonic transitions be robustly identified and quantified using this method?
• RQ5 To what extent can the ZLP model trained on one microscope be generalized to other operating conditions or instruments?

Key findings

• The bandgap of polytypic 2H/3R WS2 was determined to be $E_{\rm BG}=1.6_{-0.2}^{+0.3}$ eV, with a clear preference for an indirect bandgap.
• Two dominant excitonic transitions were identified at 1.5 eV and 2.0 eV, with a weaker feature at 1.7 eV, consistently observed across spatially separated regions of the sample.
• The method enabled robust statistical significance assessment of low-loss features, including excitonic peaks, through uncertainty propagation.
• The ZLP parametrization was successfully extrapolated to predict FWHM variations with beam energy and exposure time, showing good agreement with measured data.
• The open-source EELSfitter package enables automated, high-throughput analysis of spectral images with minimal human intervention.
• The approach outperforms traditional model-based ZLP subtraction by eliminating methodological bias and providing quantifiable uncertainties.