Electron energy-loss spectroscopy of inhomogeneous systems

After beginning with a brief review of the theory of electron energy loss by an unbounded random system of spherical inclusions characterized by a local dielectric function, we examine several extensions of this theory. We first treat an inhomogeneous system of spherical particles confined to a half-space. A surface response function, which can be used to calculate the energy-loss spectrum for charged particles moving outside the system, is defined, and this response function is written in a spectral representation. We discuss different approaches to this problem: the semiclassical infinite barrier model, an exact formal theory, and a continuous effective medium theory. Finally, we develop a theory of electron energy loss for a mixture of two components with arbitrary geometry, unbounded in three dimensions.