Spatial distributions of elastically backscattered electrons from copper and silver

We investigated the spatial distributions regarding the pathlength, the pen etration depth, and the lateral displacement of 200-2000 eV electrons elast ically backscattered from copper and silver We calculated these distributio ns by the Monte Carlo method using elastic scattering cross sections and in elastic inverse mean free paths for volume and surface excitations. in our approach, we applied the partial wave expansion method and the finite diffe rence technique to calculate electron elastic cross sections by the Hartree -Fock-Winger-Seitz scattering potential for solid atoms. We employed the ex tended Drude dielectric function to estimate electron inelastic mean free p aths inside the solid and electron surface excitation parameters outside th e solid. Our study was focused on the energy dependence of the pathlength d istribution, the maximum depth distribution and the radial distribution. We found that both the radial displacement and the maximum depth of backscatt ered electrons were on the order of a few angstroms. The maximum depth and the pathlength distributions obeyed the exponential attenuation form. The r atio of the attenuation lengths for the pathlength and the maximum depth di stributions saturated to a value somewhat greater than two. Considering the back and forth trajectories of backscattered electrons, it revealed that m ast electrons were backscattered from the solid through a single elastic sc attering or a few elastic scatterings. As electron energy decreases, this r atio became larger, indicating that the probability for smaller scattering angles increases.