Dynamic theory of high-angle annular-dark-field stem lattice images for a Ge/Si interface

Abstract

A dynamical multislice approach for simulating the annular-dark-field (ADF) scanning transmission electron microscopy (STEM) images is presented. The ADF imaging contrast is dominated by thermal diffuse scattering (TDS) if the diffraction contrast from the high-order Laue zones (HOLZ) is excluded. The simulation of ADF images can be greatly simplified if the assumption is made of incoherent imaging theory such as is used in optics, that is, the image intensity is a thickness integration of the convolution of the electron probe intensity distribution at depth z with the localized inelastic generation function | G| 2. This result may also be derived on the basis of coherent elastic scattering theory. The calculation according to the simplified theory can give almost exactly the same contrast as obtained from full dynamical inelastic calculations for thin specimens. The TDS can give atomic resolution lattice images if a small probe, less than the size of the unit cell, is used. A programming flow-chart for simulating ADF images is given. Calculations for Ge/Si(100) interfaces have shown that the ADF imaging contrast of the atoms is not affected by correlations of vibrations of neighboring atoms. It is pointed out that the contribution from elastic large-angle scattering will become important only if the atomic vibration amplitudes are less than about 0.03 Å. The ADF image production may not be considered as incoherent imaging if this is the case.