Electron resonance reflections from perfect crystal surfaces and surfaces with steps

Dynamical calculations are carried out to investigate the creation processes of reflection waves under the (660) specular reflection case of GaAs (110) in the geometry of reflection high energy electron diffraction (RHEED). It is shown that the resonance waves are localized at the top two to three atomic surface layers. The monolayer resonance characteristic happens only at some specified low angle incidence cases but not in general. Most of the reflection intensity in the RHEED pattern is created while the electrons are propagating along the surface. The probability of immediate reflections of electrons from a surface is small. This is the reason that the resonance excitation of a surface can greatly enhance the total reflectance of a surface. The propagation of a electron beam at a crystal surface can be characterized by a mean travelling distance, which is 500 to 700 Å for GaAs (110). It is pointed out that a column approximation may not be a good treatment for RHEED calculations. Dynamical calculations for surfaces with steps show that the one-atom-high down-step can critically interrupt the resonance propagation of the resonance wave along the surface. The interrupted wave goes out of the surface and forms some "extra" spots in the RHEED pattern, which are observed in RHEED experiments in a scanning transmission electron microscope. This confirms the existence of surface resonance waves and their oscillating propagations along crystal surfaces.