Theory of the "Forbidden" (222) Electron Reflection in the Diamond Structure

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Abstract
The dynamical or wave-mechanical theory of electron diffraction is extended to include several diffracted beams. In the Brillouin zone scheme this is equivalent to terminating the incident crystal wave vector at or near a zone edge or corner. The problem is then one of determining the energy levels and wave functions in the neighborhood of a corner. The solution of the Schrödinger equation near a zone corner is a linear combination of Bloch functions in which the wave vectors are determined by the boundary conditions and the requirement that the total energy be fixed. This leads to a multiplicity of wave vectors for each diffracted beam giving rise to interference phenomena and is an essential feature of the dynamical theory.