Dynamical scattering in super-resolution electron microscopy

This thesis is concerned with the discussion of the limitations and the opportunities of super-resolution imaging in the scanning transmission electron microscope (STEM) as these are determined by the dynamical interaction of the electron wave with the potential distribution in the local environment of atoms. Throughout most of the thesis, the assumption of a perfect crystal structure is made, in which case super-resolution imaging is a straightforward extension to a technique called 'ptychography', which was introduced by Walter Hoppe in the sixties as a means of directly measuring phases of diffraction orders. The dynamical theory of high-energy electron scattering and its computation are reviewed with an emphasis on the specific scattering geometry of ptychography. The interpretation of ptychographical reconstructions and the validity range of two simple reconstruction methods are discussed, using calculations on silicon aligned along . The investigation is continued for the case of sphalerite structures (again along ), which are asymmetric and thus more complicated. Experiments on gallium phosphide are presented in which the length scale of resolved detail is reduced by a factor of three in the particular microscope used and the reconstructed images show the locations of individual atomic columns. A new technique to measure the polarity of semiconductor nanocrystals based on the direct measurement of the quasi-kinematical phases of the diffraction discs is introduced and demonstrated experimentally. The imaging theory is extended to the case of aperiodic structures, and it is argued that a reconstruction technique referred to as aberration-free projection imaging is particularly suited for the examination of amorphous structures. Finally, a brief analysis of the inversion problem and its relevance for super-resolution imaging is carried out