Fourier optics of image formation in aberration-corrected LEEM.

We present the extended Fourier Optics (FO) approach for modeling image formation in aberration-corrected low energy electron microscopy (ac-LEEM). The FO formalism is also generalized for image simulations of one or two-dimensional objects in ac and uncorrected (nac) LEEM. A comparison is made of the extended FO approach presented here and the extended contrast transfer function (CTF) approach for ac-LEEM that was developed earlier. The mathematically rigorous extended FO approach gains an advantage under conditions, particularly defocus, that partial coherence of the illumination may compromise the validity of the approximate CTF intensity calculation. The drawback of the FO approach compared to the CTF approach, which is its slow computational speed, is mitigated partly here by the implementation of a multi-core, multi-threading programming architecture. This work broadens our capabilities to understand the origins of LEEM image contrast and to perform quantitative evaluation of contrast observed in an image focal series.

High throughput scanning µLEED imaging of surface structural heterogeneity: Defective graphene on Cu(111).

Micro-low energy electron diffraction (µLEED) is frequently used in conjunction with low energy electron microscopy (LEEM) to learn about local surface structural features in small selected areas. Scanning µLEED measurements performed with a very small electron beam (250 nm) can provide precise quantitative information about structural variations with high spatial resolution. We have developed the Source Extraction and Photometry (SEP) - Spot Profile Analysis (SPA) tool for evaluating scanning µLEED data with high throughput. The capability to automate diffraction peak identification with SEP-SPA opens up the possibility to investigate systems with complex diffraction patterns in which diffraction peak positions vary rapidly for small lateral displacements on the surface. The application of this tool to evaluate scanning µLEED data obtained for defective graphene on Cu(111) demonstrates its capabilities. A rich rotational domain structure is observed in which a majority of the graphene is co-aligned with the Cu(111) substrate and the significant remainder comprises domains with large rotations and small sizes that are comparable to the small beam size.