Quantum theory of high-energy electron transport in the surface region

A quantum Boltzmann's equation is derived to describe the transport of high-energy electrons in spatially inhomogeneous media. In the lowest approximation this equation reduces to a local Boltzmann's equation where the scattering function is expressed in terms of a generalized dielectric function of the media. The inelastic scattering of high-energy electrons near the surface of the solid is investigated by use of the local Boltzmann's equation. For a solid with an abrupt surface and a nondispersive dielectric function the inelastic-scattering function shows an oscillatory behavior in the surface region that can be explained as a resonant interaction of the electron with its image. Numerical calculations of the scattering function for several previously introduced models for a solid with a dispersive dielectric Function are also presented. The calculated results indicate that the oscillatory behavior near the surface is a general phenomenon. Moreover, it is found that the inelastic-scattering function depends significantly on the surface model. A proper choice of model is therefore a prerequisite for a comet interpretation of experimental energy-loss spectra.