Dynamical Diffraction Effect on HOLZ-Pattern Geometry for Semiconductor Alloys of Sil-xGex and Gal-xInxAs

Abstract

A network of dark lines for higher order Laue zone (HOLZ) reflections often appears in the bright-field disc of convergent beam electron diffraction under zone axis incidence. As geometry of the network (HOLZ pattern) depends sensitively on the crystal lattice parameters, the observation of HOLZ pattern has been applied to measure local change in the lattice parameters in various materials. The kinematical diffraction approximation has been usually employed in the analysis of observed HOLZ patterns, where the lattice parameters and the accelerating voltage exist as independent variables. However the positions of HOLZ lines depend also on the crystal potential for electrons, because the lines arise from intersections of dispersion spheres for the HOLZ reflections with the zeroth-order dispersion surface. In the kinematical analysis, an effective accelerating voltage Ee should be used in place of the actual one Ea, in order to compensate for line shift due to the dispersion effect.