Inelastic interactions of electrons with cylindrical interfaces

A theory was developed to deal with inelastic interactions for an electron moving parallel to the axis of a cylindrical structure. Formulas for the differential inverse inelastic mean free path (DIIMFP) and the total inverse inelastic mean free path (IIMFP) were derived using dielectric response theory. A sum-rule-constrained extended Drude dielectric function with spatial dispersion was applied to calculate DIIMFPs and IIMFPs for a solid wire and a cavity in solid. The calculated results showed that surface excitations occurred as the electron moved near the boundary either inside or outside the solid, whereas volume excitations arose only for electron moving inside the solid. It was found that the probability for surface excitations increases and that for volume excitations decreases for an electron moving close to the surface. Near the surface, the decrease in volume excitations is compensated by the increase in surface excitations. For a cavity in solid, the IIMFP inside the solid can be approximated by a constant value equal to the IIMFP for the infinite solid, except in the immediate vicinity of the cavity boundary.