Inelastic High-Energy Electron Spectrafrom Plane-Parallel Layer-Nonhomogeneous Surfaces

We consider inelastic backscattering of electrons with initial energy of tens and hundreds of keV by plane-parallel homogeneous and sandwiched targets. Basing on the invariance principle, we find expressions that describe the dynamics of the changes in the energy spectra of electrons reflected into a given solid angle that occur with increase of the thickness of films of different materials on substrates of finite and infinite thickness. We substantiate a procedure of linearizing the equations for the reflection function obtained by the method of invariant imbedding. We obtain an analytical solution of linearized equations in the form of a series in Legendre polynomials. A comparison with experimental data shows that the theory developed gives an adequate description of the process of electron backscattering.