Quantitative Analysis of Spectroscopic Low Energy Electron Microscopy Data: High-dynamic Range Imaging, Drift Correction and Cluster Analysis

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.