Angular distribution of electrons elastically backscattered from non-crystalline solid surfaces

In the energy range 100 eV-2 keV, we applied the Monte Carlo method to analyse the elastic reflection coefficient and the angular distribution of electrons elastically backscattered from the solid surface of an isotropic and homogeneous medium. Results indicated that elastically backscattered electrons arose substantially from only a few scatterings with a single scattering event contributing to approximately half of these electrons. Thus, neither the multiple scattering model nor the single scattering model is sufficient to describe the angular distribution. To improve these models, we evaluated the contribution from one, two and three scatterings exactly and higher scatterings by the Pi-approximation, an approximate method to solve the Boltzmann transport equation assuming multiple elastic scattering of electrons in the solid. This approach allowed us to derive analytical formulations for the elastic reflection coefficient and the angular distribution of elastically backscattered electrons. Results calculated based on these formulations were in good agreement with those using Monte Carlo simulations and experimental data.