Low-Energy Electron Diffraction Amplitudes for a "Bare-Substrate" Model

A theory of low-energy electron dif fraction (LEED) amplitudes is developed for a model in which the crystal surface is represented by a step-function termination of the bulk crystal potential ("bare-substrate" mode l ) . The crystal is considered to be centro-symmetric and it is assumed that either the crystal has a two-fold axis of rotation normal to the surface or the primay beam is normally incident on the surface. The origin of coordinates is taken to lie at a center of symmetry of the substrate crystal. The dif fraction amplitude is considered as a function of complex electron energy. For a real potential it is shown to have the fo l lowing properties : 1. The imaginary part of the amplitude vanishes at each branch point of the amplitude funct ion ; 2. There are certain segments of the real-energy axis, called " inact ive" segments, throughout which the imaginary part of the amplitude vanishes approximately. The theoretical results are illustrated by a numerical example. It is suggested that the di f fraction amplitude can be represented by a simple expression that has the correct functional form and that satisfies the appropriate dispersion relation. One such expression is proposed and discussed in comparison with exact computational results.