Analytical description of the electron microscope diffraction contrast of lattice defects in the two-beam case

Abstract

Abstract Simple analytical equations are derived for the bright- and dark-field intensities in the two-beam case which describe, for a large variety of lattice defects, the dependence of the contrast on the defect depth position z 0, the specimen thickness t, the excitation error w and the anomalous absorption parameter τ. These dependences may be characterized by the modulus q of the interband scattering at the lattice defect, which is responsible for the variation with z 0 and t, and a thickness parameter t w, which describes the combined influence of w and τ. For zero beam divergence the z 0 and t dependence of the contrast can be neglected only for lattice defects with large q. Lattice defects with small q are invisible for certain values of z 0 and t. For finite beam divergence, the z 0 dependence of weak-beam images is suppressed for lattice defects located near the centre of the specimen (distance from the surfaces larger than 0·7 extinction distances). A simple method is proposed for calculating t...