Theory of electron backscattering from crystals

The contrast in electron channeling patterns is quantitatively treated using a theory in which electrons in Bloch states excited by the incident electron are scattered through large angles by the fluctuation part of the potential (thermal diffuse scattering). The subsequent multiple elastic and inelastic scattering is described by an inhomogeneous transport equation. Formally this is shown to be identical to the solution of the kinetic equation for the one-particle spectral density matrix. Employing the supermatrix algorithm proposed by Fathers and Rez, we develop a computational technique which makes it possible to perform full-scale multiple scattering simulations of electron backscattering from crystals and to provide a consistent quantitative explanation of a number of experimental observations, including the dependence of the contrast on the detector position and on the energy of the backscattered electrons, the origin of which has not previously been fully accounted for. Our computational results show a substantial increase in the channeling contrast and in the signal-to-noise ratio for the conditions of oblique incidence and low takeoff angle of backscattering, which agrees with recent experimental studies. We show that under the conditions of multiple scattering there exists a perturbation expansion which considerably simplifies the problem of evaluation of the contrast and which can be employed for interpretation of channeling images of defects.