Spatially-Resolved Band Gap and Dielectric Function in 2D Materials from Electron Energy Loss Spectroscopy

The electronic properties of two-dimensional (2D) materials depend sensitively on the underlying atomic arrangement down to the monolayer level. Here we present a novel strategy for the determination of the band gap and complex dielectric function in 2D materials achieving a spatial resolution down to a few nanometers. This approach is based on machine learning techniques developed in particle physics and makes possible the automated processing and interpretation of spectral images from electron energy-loss spectroscopy (EELS). Individual spectra are classified as a function of the thickness with $K$-means clustering and then used to train a deep-learning model of the zero-loss peak background. As a proof-of-concept we assess the band gap and dielectric function of InSe flakes and polytypic WS$_2$ nanoflowers, and correlate these electrical properties with the local thickness. Our flexible approach is generalizable to other nanostructured materials and to higher-dimensional spectroscopies, and is made available as a new release of the open-source EELSfitter framework.