Bloch wave HREM

Abstract

An analysis of the effects of beam convergence is carried out for high resolution electron microscope imaging, including the changes in diffraction across the illumination aperture by a Bloch wave approach. It is shown that the effect of a small tilt u is to introduce a perturbation u ·▿ ϱ into the projected 2D Schrödinger equation for the Bloch waves. By using perturbation theory (essentially a k · p analysis), it is shown that the dominant effect is a modification of the non-linear convergence envelope term between different Bloch waves. The effects should be larger for defects than for single crystals, and important for thicknesses of more than ∼ 50 nm, thicknesses similar to those at which non-linear effects are important. The general trends with structure, elemental composition and incident electron voltage are briefly described.