Spatial distributions of elastically backscattered electrons from copper and silver

We investigated the spatial distributions regarding the pathlength, the penetration depth, and the lateral displacement of 200-2000 eV electrons elastically backscattered from copper and silver. We calculated these distributions by the Monte Carlo method using elastic scattering cross sections and inelastic inverse mean free paths for volume and surface excitations. In our approach, we applied the partial wave expansion method and the finite difference technique to calculate electron elastic cross sections by the Hartree-Fock-Winger-Seitz scattering potential for solid atoms. We employed the extended Drude dielectric function to estimate electron inelastic mean free paths inside the solid and electron surface excitation parameters outside the solid. Our study was focused on the energy dependence of the pathlength distribution, the maximum depth distribution and the radial distribution. We found that both the radial displacement and the maximum depth of backscattered electrons were on the order of a few angstroms. The maximum depth and the pathlength distributions obeyed the exponential attenuation form. The ratio of the attenuation lengths for the pathlength and the maximum depth distributions saturated to a value somewhat greater than two. Considering the back and forth trajectories of backscattered electrons, it revealed that most electrons were backscattered from the solid through a single elastic scattering or a few elastic scatterings. As electron energy decreases, this ratio became larger, indicating that the probability for smaller scattering angles increases.