Jacob's ladder of approximations to paraxial dynamic electron scattering

Abstract

Dynamical scattering theory describes the dominant scattering process of beam electrons at targets in the transmission electron microscope (TEM). Hence, practically every quantitative TEM study has to consider its ramifications, typically by some approximate modeling. Here, we elaborate on a hierarchy within the various approximations focusing on the two principal approaches used in practice, Bloch wave and multislice. We reveal characteristic differences in the capability of these methods to reproduce the correct local propagation of the wave function, while convergent results are obtained over larger propagation distances. We investigate the dependency of local variations of the wave function on the atomic number of the atomic scatterers and discuss their significance for, e.g., inelastic scattering.