Developments in the dynamical theory of high energy electron reflection.

High energy electron reflection (HEER) is an important technique in surface science and uses the information carried by high energy electrons reflected from surfaces to study surface structures and surface electronic states. With the development of reflection high energy electron diffraction (RHEED), high energy electron microscopy (REM), and high energy electron energy loss spectroscopy (EEL) in surface science, the usefulness of HEER has been widely recognized and demonstrated. However, a stationary dynamical solution for an arbitrary surface for HEER has not been obtained yet. In this paper, some developments in understanding the dynamical theory of HEER, particularly in recent years, are reviewed: 1. The introduction of the concept of current flow for a semi-infinite crystal model has removed the confusion around the wave points in the "band gap." 2. The consistency between the Bloch wave and multislice in the Bragg case has verified the validity of the argument of current flow and led to the emergence of the BMCR method (Bloch wave + Multislice Combined for Reflection). 3. The failure of the Bloch Wave-Only solution (the BWO solution) on Au (110) surfaces in the Bragg case revealed by the BMCR method implies that previous BWO calculations in the Bragg case might be at fault. 4. The 2-D dependence of the electron wave fields and Picard iteration-like character of multislice calculation in the Bragg case has led to the emergence of an Edge Patching method in Multislice-mode-Only (the EPMO method). The new method yields an infinitely convergent stationary dynamical solution for an arbitrary surface.