Validity of the Bethe IMFP model for 2D materials

Determine whether the modified Bethe equation for the electron inelastic mean free path versus incident energy, which assumes bulk-scattering behavior, accurately applies to two-dimensional materials such as graphene whose interactions are dominated by surface effects rather than bulk effects.

Background

The paper analyzes inelastic mean free path (IMFP) trends versus electron energy, using bulk-derived models such as the modified Bethe equation and the Penn algorithm. While these models are well established for bulk materials, two-dimensional systems like graphene are surface-dominated, which casts doubt on the direct applicability of bulk-based IMFP formulations.

The authors note prior evidence that the Bethe model fails at very low energies for graphene (LEEM regime) and present SEM-based measurements suggesting a 5× scale factor relative to a Penn-based curve adapted from bulk graphite. This motivates a precise determination of whether, and under what conditions, bulk-based IMFP models can be validly extended to truly two-dimensional materials.

References

A priori, it is unclear if this model will work for 2D materials as such specimens are dominated by surface rather than the bulk effects assumed in Bethe model.

— Electron Energy Loss Spectroscopy of 2D Materials in a Scanning Electron Microscope  (2410.09291 - Simonaitis et al., 2024) in Main text, discussion around Fig. 2a; paragraph following Eq. (2) introducing the modified Bethe equation