Incoherent scattering of electrons by a crystal surface

It is shown how the two approximate methods of statistical theory of reflection high-energy electron diffraction (the Kirchhoff approximation and the distorted wave Born approximation) can be systematically derived starting from Green's theorem. Conditions of validity of both approximations are discussed together with the possibility of generalizing the second method to the case of multiple incoherent scattering. Two examples are given where solutions of the problem of multiple incoherent scattering have been found in a closed analytical form. In what follows, a new numerical algorithm for reflection high-energy electron diffraction calculations is proposed which bridges the Bethe method and the R-matrix approach. This algorithm brings considerable simplification to the problem of evaluation of RHEED wave functions which are required to calculate the cross-section of diffuse scattering. (C) 1997 Elsevier Science Ltd.