Surface roughness effects on energy losses of fast electrons crossing metallic samples

The unevenness of the surface of a metallic sample affects the surface plasmon spectrum and thence the energy losses of fast charged particles crossing the sample. A theory of this effect is presented in which the metal is characterized by a simple local dielectric constant and the interaction with the probe particle is treated semi-classically. By a classical Green's function method, a closed expression is obtained for the loss spectral profile as a function of the momentum transfer, without assumption on the roughness shape. The geometry of a rough surface is then considered in detail. The loss spectral profile is calculated for some examples of weak periodic corrugations. For a general weak roughness, the width and the mean shift of the loss profile are given in terms of the roughness correlation function. Finally, the case of strong roughnesses is examined for small and large values of the momentum transfer.