Cherenkov radiation effects in EELS for nanoporous alumina membranes

Swift electron energy losses have been investigated in nanoporous alumina, taking into account retardation effects. A simple analytical expression is obtained for the energy loss probability. The electron energy loss spectra observed with the Scanning transmission electron microscope are reasonably well reproduced using a simple model consisting of a cylindrical shell of alumina surrounded by an effective porous medium. The Cherenkov radiation is responsible for energy losses below 8 eV. These losses are very sensitive to the shape of the nanostructures, up to distances much larger than the adiabatic length v/ω.