Anisotropic electron inelastic scattering and Monte Carlo simulation of electron emission from graphite

We developed a dielectric-functional formulation of anisotropic electron inelastic scattering and an anisotropic Monte Carlo (MC) model for electron transport in uniaxial materials. Within a tensorial dielectric-response framework, the inelastic scattering probability is expressed as a triple differential cross section in a crystal-fixed coordinate system. For a uniaxial crystal with parallel and perpendicular dielectric-function components, an explicit analytical expression is derived without invoking the small-angle approximation. The corresponding double differential cross section, single differential energy-loss distribution, and inelastic mean free path (IMFP) are obtained by numerical integration, all of which depend on the electron-velocity orientation relative to the crystal axis. The anisotropic differential inverse IMFP is implemented in MC simulations down to the low-energy cascade-secondary-electron region, which enables the calculation of electron emission yields for graphite. No statistically meaningful difference is found in the secondary electron yield or backscattering coefficient for normal incidence on graphite basal- and edge-plane surfaces. This supports the hypothesis that multiple scattering, especially large-angle elastic scattering, smoothens the weak directional dependence of anisotropic inelastic scattering.