Quantitative analysis of spectroscopic low energy electron microscopy data: High-dynamic range imaging, drift correction and cluster analysis

Abstract

For many complex materials systems, low-energy electron microscopy (LEEM) offers detailed insights into morphology and crystallography by naturally combining real-space and reciprocal-space information. Its unique strength, however, is that all measurements can easily be performed energy-dependently. Consequently, one should treat LEEM measurements as multi-dimensional, spectroscopic datasets rather than as images to fully harvest this potential. Here we describe a measurement and data analysis approach to obtain such quantitative spectroscopic LEEM datasets with high lateral resolution. The employed detector correction and adjustment techniques enable measurement of true reflectivity values over four orders of magnitudes of intensity. Moreover, we show a drift correction algorithm, tailored for LEEM datasets with inverting contrast, that yields sub-pixel accuracy without special computational demands. Finally, we apply dimension reduction techniques to summarize the key spectroscopic features of datasets with hundreds of images into two single images that can easily be presented and interpreted intuitively. We use cluster analysis to automatically identify different materials within the field of view and to calculate average spectra per material. We demonstrate these methods by analyzing bright-field and dark-field datasets of few-layer graphene grown on silicon carbide and provide a high-performance Python implementation. this, a wide range of properties can be studied, for example, layer interaction, electron bands [5], layer stacking [2], catalysis [6], plasmons [7], and surface corrugation [8].

Observation of flat bands in twisted bilayer graphene

“…Images were recorded in high-dynamic-range mode and corrected for detector artefacts, as described in ref. 32 . Photoemission electron microscopy imaging was performed using an unfiltered mercury short-arc lamp with its main emission at a photon energy of ~6 eV.…”

Optical Near-Field Electron Microscopy

“…Moreover, using novel algorithms, many images can now be stitched together smoothly. Thus, the effective field of view can be dramatically extended, without loss of resolution [33]. Furthermore, we note that a resolution smaller than 3 nm has been predicted for Photo Electron Emission Microscopy (PEEM) on such state-ofthe-art systems [29].…”

Optical Near-Field Electron Microscopy

“…Moreover, using novel algorithms, many images can now be stitched together smoothly. Thus, the effective field of view can be dramatically extended, without loss of resolution [33]. Furthermore, we note that a resolution smaller than 3 nm has been predicted for photoelectron emission microscopy (PEEM) on such state-of-the-art systems [29].…”