Theory of electron diffraction from planar ideal crystals

A theory of electron diffraction from a planar ideal crystal of arbitrary thickness is presented. It is based on Schrödinger's equation. Both the relativistic corrections in energy and wavelength and the electron 'absorption' due to the presence of inelastic scattering may be incorporated as usual. This theory is constructed in an exact differential-equation approach known as rigorous coupled-wave analysis. This is an exact method of diffraction analysis that has been extensively tested for its numerical calculation scheme. The exact solution for electron wave amplitudes of all diffraction orders is formally presented in terms of a standard eigenvalue problem and explicitly expressed in matrix form. Numerical calculation can be implemented on digital computers in a straightforward manner. An approximate conservation law is given for the transmittance and reflectance, which are then the relevant dynamical quantities to be measured in a realistic time-dependent diffraction process and to be calculated in this time-independent diffraction theory for comparison. Two derivations of the well known Bragg law are sketched.