Reflection High Energy Electron Diffraction (RHEED)
The RHEED method in a spectacular way utilises wave nature of electrons. A collimated monoenergetic electron beam with energy of tens keV impinges surface at a small angle of order 1deg, and is scattered by surface atoms. The scattered waves interfere and produce a diffraction pattern of bright spots on a luminescence screen. The pattern shape, symmetry and details carry information on crystallographic structure of the crystal surface, its morphology and electron interaction with atoms.
In a simple, kinematic theory of RHEED diffraction it is assumed that electron wave scatters on atom only once and then interferes with waves scattered on other atoms. This model is acceptable for small angles of incidence, less than 1 deg, when the electron beam does not penetrate the crystal volume. In the kinematic model of diffraction the geometric Ewald construction is used for reciprocal lattice determination and intensity of mirror reflected electron beam is considered as an effect of surface roughness.
More advanced theories of RHEED diffraction take into consideration multiple electron wave scattering and require quantum-mechanical formalism. In that model a plane electron wave is scattered by atomic potential of the crystal lattice. The theory, known as dynamical theory of diffraction, may include temperature effects (lattice vibration) and well models angular distribution and intensities of diffracted electron beams.
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