ELECTRON DIFFRACTION AT CRYSTAL SURFACES .I. GENERALIZATION OF DARWINS DYNAMICAL THEORY

The dynamical diffraction theory put forward originally by C.G. Darwin in his treatment of X-ray reflection is developed in a more general form suitable for the treatment of electron diffraction at crystal surfaces. The theory applies to a model crystal consisting of two parts: a selvedge with two-dimensional periodicity but otherwise arbitrary structure and a semi-infinite substrate composed of identical and equally-spaced atom layers. In the treatment of this model, the wave field in a region of locally-constant scattering potential between neighboring layers is expressed as a superposition of all possible diffracted (propagating) waves and an arbitrary number of evanescent waves. The diffraction problem is formulated in terms of transfer" matrices involving the scattering properties of individual atom layers parallel to the crystal surface. It is shown that the diffraction problem and the corresponding band-structure problem for the substrate may be reduced to a matrix eigenvalue problem involving the transfer matrix for a substrate layer. The diffraction amplitudes are expressed in terms of the eigenvectors of this transfer matrix. © 1968."